id	sid	tid	token	lemma	pos
ejpam-6139	1	1	european	european	PROPN
ejpam-6139	1	2	journal	journal	PROPN
ejpam-6139	1	3	of	of	ADP
ejpam-6139	1	4	pure	pure	ADJ
ejpam-6139	1	5	and	and	CCONJ
ejpam-6139	1	6	applied	applied	ADJ
ejpam-6139	1	7	mathematics	mathematic	NOUN
ejpam-6139	1	8	2025	2025	NUM
ejpam-6139	1	9	,	,	PUNCT
ejpam-6139	1	10	vol	vol	NOUN
ejpam-6139	1	11	.	.	PROPN
ejpam-6139	1	12	18	18	NUM
ejpam-6139	1	13	,	,	PUNCT
ejpam-6139	1	14	issue	issue	NOUN
ejpam-6139	1	15	4	4	NUM
ejpam-6139	1	16	,	,	PUNCT
ejpam-6139	1	17	article	article	NOUN
ejpam-6139	1	18	number	number	NOUN
ejpam-6139	1	19	6139	6139	NUM
ejpam-6139	1	20	issn	issn	PROPN
ejpam-6139	1	21	1307	1307	NUM
ejpam-6139	1	22	-	-	SYM
ejpam-6139	1	23	5543	5543	NUM
ejpam-6139	1	24	–	–	PUNCT
ejpam-6139	1	25	ejpam.com	ejpam.com	X
ejpam-6139	1	26	published	publish	VERB
ejpam-6139	1	27	by	by	ADP
ejpam-6139	1	28	new	new	PROPN
ejpam-6139	1	29	york	york	PROPN
ejpam-6139	1	30	business	business	PROPN
ejpam-6139	1	31	global	global	PROPN
ejpam-6139	1	32	trapezoidal	trapezoidal	NOUN
ejpam-6139	1	33	and	and	CCONJ
ejpam-6139	1	34	midpoint	midpoint	NOUN
ejpam-6139	1	35	-	-	PUNCT
ejpam-6139	1	36	type	type	NOUN
ejpam-6139	1	37	inequalities	inequality	NOUN
ejpam-6139	1	38	based	base	VERB
ejpam-6139	1	39	on	on	ADP
ejpam-6139	1	40	extended	extended	ADJ
ejpam-6139	1	41	conformable	conformable	ADJ
ejpam-6139	1	42	operators	operator	NOUN
ejpam-6139	1	43	muhammad	muhammad	PROPN
ejpam-6139	1	44	samraiz1	samraiz1	PROPN
ejpam-6139	1	45	,	,	PUNCT
ejpam-6139	1	46	muhammad	muhammad	PROPN
ejpam-6139	1	47	qasim1	qasim1	PROPN
ejpam-6139	1	48	,	,	PUNCT
ejpam-6139	1	49	gauhar	gauhar	PROPN
ejpam-6139	1	50	rahman2,∗	rahman2,∗	PROPN
ejpam-6139	1	51	,	,	PUNCT
ejpam-6139	1	52	muhammad	muhammad	PROPN
ejpam-6139	1	53	sarwar3,4	sarwar3,4	PROPN
ejpam-6139	1	54	,	,	PUNCT
ejpam-6139	1	55	nahid	nahid	PROPN
ejpam-6139	1	56	fatima3	fatima3	PROPN
ejpam-6139	1	57	,	,	PUNCT
ejpam-6139	1	58	kamaleldin	kamaleldin	NOUN
ejpam-6139	1	59	abodayeh3	abodayeh3	PROPN
ejpam-6139	1	60	1	1	NUM
ejpam-6139	1	61	department	department	NOUN
ejpam-6139	1	62	of	of	ADP
ejpam-6139	1	63	mathematics	mathematics	PROPN
ejpam-6139	1	64	,	,	PUNCT
ejpam-6139	1	65	university	university	PROPN
ejpam-6139	1	66	of	of	ADP
ejpam-6139	1	67	sargodha	sargodha	PROPN
ejpam-6139	1	68	,	,	PUNCT
ejpam-6139	1	69	p.o	p.o	PROPN
ejpam-6139	1	70	.	.	PROPN
ejpam-6139	1	71	box	box	PROPN
ejpam-6139	1	72	40100	40100	PROPN
ejpam-6139	1	73	,	,	PUNCT
ejpam-6139	1	74	sargodha	sargodha	PROPN
ejpam-6139	1	75	,	,	PUNCT
ejpam-6139	1	76	pakistan	pakistan	PROPN
ejpam-6139	1	77	2	2	NUM
ejpam-6139	1	78	department	department	NOUN
ejpam-6139	1	79	of	of	ADP
ejpam-6139	1	80	mathematics	mathematic	NOUN
ejpam-6139	1	81	and	and	CCONJ
ejpam-6139	1	82	statistics	statistic	NOUN
ejpam-6139	1	83	,	,	PUNCT
ejpam-6139	1	84	hazara	hazara	PROPN
ejpam-6139	1	85	university	university	PROPN
ejpam-6139	1	86	,	,	PUNCT
ejpam-6139	1	87	mansehra	mansehra	PROPN
ejpam-6139	1	88	21300	21300	NUM
ejpam-6139	1	89	,	,	PUNCT
ejpam-6139	1	90	pakistan	pakistan	PROPN
ejpam-6139	1	91	3	3	NUM
ejpam-6139	1	92	department	department	NOUN
ejpam-6139	1	93	of	of	ADP
ejpam-6139	1	94	mathematics	mathematic	NOUN
ejpam-6139	1	95	and	and	CCONJ
ejpam-6139	1	96	sciences	science	NOUN
ejpam-6139	1	97	,	,	PUNCT
ejpam-6139	1	98	prince	prince	PROPN
ejpam-6139	1	99	sultan	sultan	PROPN
ejpam-6139	1	100	university	university	PROPN
ejpam-6139	1	101	,	,	PUNCT
ejpam-6139	1	102	riyadh	riyadh	PROPN
ejpam-6139	1	103	11586	11586	NUM
ejpam-6139	1	104	,	,	PUNCT
ejpam-6139	1	105	saudi	saudi	PROPN
ejpam-6139	1	106	arabia	arabia	PROPN
ejpam-6139	1	107	4	4	NUM
ejpam-6139	1	108	department	department	NOUN
ejpam-6139	1	109	of	of	ADP
ejpam-6139	1	110	mathematics	mathematic	NOUN
ejpam-6139	1	111	,	,	PUNCT
ejpam-6139	1	112	university	university	NOUN
ejpam-6139	1	113	of	of	ADP
ejpam-6139	1	114	malakand	malakand	PROPN
ejpam-6139	1	115	,	,	PUNCT
ejpam-6139	1	116	chakdara	chakdara	NOUN
ejpam-6139	1	117	dir	dir	NOUN
ejpam-6139	1	118	(	(	PUNCT
ejpam-6139	1	119	lower	low	ADJ
ejpam-6139	1	120	)	)	PUNCT
ejpam-6139	1	121	,	,	PUNCT
ejpam-6139	1	122	kpk	kpk	PROPN
ejpam-6139	1	123	,	,	PUNCT
ejpam-6139	1	124	pakistan	pakistan	PROPN
ejpam-6139	1	125	abstract	abstract	NOUN
ejpam-6139	1	126	.	.	PUNCT
ejpam-6139	2	1	in	in	ADP
ejpam-6139	2	2	this	this	DET
ejpam-6139	2	3	paper	paper	NOUN
ejpam-6139	2	4	,	,	PUNCT
ejpam-6139	2	5	we	we	PRON
ejpam-6139	2	6	explore	explore	VERB
ejpam-6139	2	7	some	some	DET
ejpam-6139	2	8	inequalities	inequality	NOUN
ejpam-6139	2	9	derived	derive	VERB
ejpam-6139	2	10	from	from	ADP
ejpam-6139	2	11	twice	twice	ADJ
ejpam-6139	2	12	differentiable	differentiable	ADJ
ejpam-6139	2	13	functions	function	NOUN
ejpam-6139	2	14	together	together	ADV
ejpam-6139	2	15	with	with	ADP
ejpam-6139	2	16	the	the	DET
ejpam-6139	2	17	extended	extend	VERB
ejpam-6139	2	18	conformable	conformable	ADJ
ejpam-6139	2	19	fractional	fractional	ADJ
ejpam-6139	2	20	operators	operator	NOUN
ejpam-6139	2	21	.	.	PUNCT
ejpam-6139	3	1	first	first	ADV
ejpam-6139	3	2	,	,	PUNCT
ejpam-6139	3	3	we	we	PRON
ejpam-6139	3	4	investigate	investigate	VERB
ejpam-6139	3	5	two	two	NUM
ejpam-6139	3	6	lemmas	lemma	NOUN
ejpam-6139	3	7	using	use	VERB
ejpam-6139	3	8	extended	extended	ADJ
ejpam-6139	3	9	conformable	conformable	ADJ
ejpam-6139	3	10	fractional	fractional	ADJ
ejpam-6139	3	11	operators	operator	NOUN
ejpam-6139	3	12	.	.	PUNCT
ejpam-6139	4	1	then	then	ADV
ejpam-6139	4	2	,	,	PUNCT
ejpam-6139	4	3	we	we	PRON
ejpam-6139	4	4	utilize	utilize	VERB
ejpam-6139	4	5	these	these	DET
ejpam-6139	4	6	results	result	NOUN
ejpam-6139	4	7	to	to	PART
ejpam-6139	4	8	explore	explore	VERB
ejpam-6139	4	9	some	some	DET
ejpam-6139	4	10	new	new	ADJ
ejpam-6139	4	11	trapezoidal	trapezoidal	ADJ
ejpam-6139	4	12	and	and	CCONJ
ejpam-6139	4	13	midpoint	midpoint	NOUN
ejpam-6139	4	14	-	-	PUNCT
ejpam-6139	4	15	type	type	NOUN
ejpam-6139	4	16	inequalities	inequality	NOUN
ejpam-6139	4	17	through	through	ADP
ejpam-6139	4	18	the	the	DET
ejpam-6139	4	19	use	use	NOUN
ejpam-6139	4	20	of	of	ADP
ejpam-6139	4	21	the	the	DET
ejpam-6139	4	22	convex	convex	ADJ
ejpam-6139	4	23	property	property	NOUN
ejpam-6139	4	24	of	of	ADP
ejpam-6139	4	25	twice	twice	ADJ
ejpam-6139	4	26	differentiable	differentiable	ADJ
ejpam-6139	4	27	functions	function	NOUN
ejpam-6139	4	28	.	.	PUNCT
ejpam-6139	5	1	moreover	moreover	ADV
ejpam-6139	5	2	,	,	PUNCT
ejpam-6139	5	3	using	use	VERB
ejpam-6139	5	4	the	the	DET
ejpam-6139	5	5	power	power	NOUN
ejpam-6139	5	6	mean	mean	NOUN
ejpam-6139	5	7	inequality	inequality	NOUN
ejpam-6139	5	8	and	and	CCONJ
ejpam-6139	5	9	hölder	hölder	NOUN
ejpam-6139	5	10	’s	’s	PART
ejpam-6139	5	11	inequality	inequality	NOUN
ejpam-6139	5	12	,	,	PUNCT
ejpam-6139	5	13	we	we	PRON
ejpam-6139	5	14	introduce	introduce	VERB
ejpam-6139	5	15	a	a	DET
ejpam-6139	5	16	new	new	ADJ
ejpam-6139	5	17	class	class	NOUN
ejpam-6139	5	18	of	of	ADP
ejpam-6139	5	19	inequalities	inequality	NOUN
ejpam-6139	5	20	.	.	PUNCT
ejpam-6139	6	1	the	the	DET
ejpam-6139	6	2	explored	explore	VERB
ejpam-6139	6	3	results	result	NOUN
ejpam-6139	6	4	are	be	AUX
ejpam-6139	6	5	validated	validate	VERB
ejpam-6139	6	6	through	through	ADP
ejpam-6139	6	7	different	different	ADJ
ejpam-6139	6	8	2d	2d	NOUN
ejpam-6139	6	9	and	and	CCONJ
ejpam-6139	6	10	3d	3d	NUM
ejpam-6139	6	11	graphs	graph	NOUN
ejpam-6139	6	12	.	.	PUNCT
ejpam-6139	7	1	this	this	DET
ejpam-6139	7	2	new	new	ADJ
ejpam-6139	7	3	class	class	NOUN
ejpam-6139	7	4	extends	extend	VERB
ejpam-6139	7	5	the	the	DET
ejpam-6139	7	6	results	result	NOUN
ejpam-6139	7	7	of	of	ADP
ejpam-6139	7	8	previous	previous	ADJ
ejpam-6139	7	9	research	research	NOUN
ejpam-6139	7	10	studies	study	NOUN
ejpam-6139	7	11	.	.	PUNCT
ejpam-6139	8	1	the	the	DET
ejpam-6139	8	2	present	present	ADJ
ejpam-6139	8	3	paper	paper	NOUN
ejpam-6139	8	4	seeks	seek	VERB
ejpam-6139	8	5	to	to	PART
ejpam-6139	8	6	motivate	motivate	VERB
ejpam-6139	8	7	researchers	researcher	NOUN
ejpam-6139	8	8	to	to	PART
ejpam-6139	8	9	apply	apply	VERB
ejpam-6139	8	10	these	these	DET
ejpam-6139	8	11	concepts	concept	NOUN
ejpam-6139	8	12	to	to	ADP
ejpam-6139	8	13	other	other	ADJ
ejpam-6139	8	14	fractional	fractional	ADJ
ejpam-6139	8	15	operators	operator	NOUN
ejpam-6139	8	16	.	.	PUNCT
ejpam-6139	9	1	2020	2020	NUM
ejpam-6139	9	2	mathematics	mathematic	NOUN
ejpam-6139	9	3	subject	subject	NOUN
ejpam-6139	9	4	classifications	classification	NOUN
ejpam-6139	9	5	:	:	PUNCT
ejpam-6139	9	6	26a33	26a33	NUM
ejpam-6139	9	7	,	,	PUNCT
ejpam-6139	9	8	35j05	35j05	NUM
ejpam-6139	9	9	key	key	ADJ
ejpam-6139	9	10	words	word	NOUN
ejpam-6139	9	11	and	and	CCONJ
ejpam-6139	9	12	phrases	phrase	NOUN
ejpam-6139	9	13	:	:	PUNCT
ejpam-6139	9	14	extended	extend	VERB
ejpam-6139	9	15	conformable	conformable	ADJ
ejpam-6139	9	16	fractional	fractional	ADJ
ejpam-6139	9	17	operators	operator	NOUN
ejpam-6139	9	18	,	,	PUNCT
ejpam-6139	9	19	trapezoidal	trapezoidal	ADJ
ejpam-6139	9	20	-	-	PUNCT
ejpam-6139	9	21	type	type	NOUN
ejpam-6139	9	22	inequalities	inequality	NOUN
ejpam-6139	9	23	,	,	PUNCT
ejpam-6139	9	24	midpoint	midpoint	NOUN
ejpam-6139	9	25	-	-	PUNCT
ejpam-6139	9	26	type	type	NOUN
ejpam-6139	9	27	inequalities	inequality	NOUN
ejpam-6139	9	28	,	,	PUNCT
ejpam-6139	9	29	hölder	hölder	PROPN
ejpam-6139	9	30	’s	’s	PART
ejpam-6139	9	31	inequality	inequality	NOUN
ejpam-6139	9	32	,	,	PUNCT
ejpam-6139	9	33	power	power	NOUN
ejpam-6139	9	34	mean	mean	VERB
ejpam-6139	9	35	inequality	inequality	NOUN
ejpam-6139	9	36	1	1	NUM
ejpam-6139	9	37	.	.	PUNCT
ejpam-6139	9	38	introduction	introduction	NOUN
ejpam-6139	9	39	convex	convex	NOUN
ejpam-6139	9	40	functions	function	NOUN
ejpam-6139	9	41	form	form	VERB
ejpam-6139	9	42	an	an	DET
ejpam-6139	9	43	essential	essential	ADJ
ejpam-6139	9	44	branch	branch	NOUN
ejpam-6139	9	45	in	in	ADP
ejpam-6139	9	46	mathematics	mathematic	NOUN
ejpam-6139	9	47	with	with	ADP
ejpam-6139	9	48	considerable	considerable	ADJ
ejpam-6139	9	49	applications	application	NOUN
ejpam-6139	9	50	across	across	ADP
ejpam-6139	9	51	diverse	diverse	ADJ
ejpam-6139	9	52	fields	field	NOUN
ejpam-6139	9	53	.	.	PUNCT
ejpam-6139	10	1	by	by	ADP
ejpam-6139	10	2	definition	definition	NOUN
ejpam-6139	10	3	,	,	PUNCT
ejpam-6139	10	4	a	a	DET
ejpam-6139	10	5	convex	convex	NOUN
ejpam-6139	10	6	function	function	NOUN
ejpam-6139	10	7	lies	lie	VERB
ejpam-6139	10	8	above	above	ADP
ejpam-6139	10	9	the	the	DET
ejpam-6139	10	10	straight	straight	ADJ
ejpam-6139	10	11	line	line	NOUN
ejpam-6139	10	12	connecting	connect	VERB
ejpam-6139	10	13	any	any	DET
ejpam-6139	10	14	two	two	NUM
ejpam-6139	10	15	points	point	NOUN
ejpam-6139	10	16	in	in	ADP
ejpam-6139	10	17	its	its	PRON
ejpam-6139	10	18	domain	domain	NOUN
ejpam-6139	10	19	.	.	PUNCT
ejpam-6139	11	1	the	the	DET
ejpam-6139	11	2	study	study	NOUN
ejpam-6139	11	3	of	of	ADP
ejpam-6139	11	4	convex	convex	NOUN
ejpam-6139	11	5	functions	function	NOUN
ejpam-6139	11	6	has	have	AUX
ejpam-6139	11	7	evolved	evolve	VERB
ejpam-6139	11	8	over	over	ADP
ejpam-6139	11	9	the	the	DET
ejpam-6139	11	10	past	past	ADJ
ejpam-6139	11	11	century	century	NOUN
ejpam-6139	11	12	,	,	PUNCT
ejpam-6139	11	13	with	with	ADP
ejpam-6139	11	14	roots	root	NOUN
ejpam-6139	11	15	deeply	deeply	ADV
ejpam-6139	11	16	embedded	embed	VERB
ejpam-6139	11	17	in	in	ADP
ejpam-6139	11	18	geometry	geometry	NOUN
ejpam-6139	11	19	[	[	X
ejpam-6139	11	20	1	1	NUM
ejpam-6139	11	21	]	]	PUNCT
ejpam-6139	11	22	.	.	PUNCT
ejpam-6139	12	1	their	their	PRON
ejpam-6139	12	2	utility	utility	NOUN
ejpam-6139	12	3	spans	span	VERB
ejpam-6139	12	4	various	various	ADJ
ejpam-6139	12	5	disciplines	discipline	NOUN
ejpam-6139	12	6	,	,	PUNCT
ejpam-6139	12	7	notably	notably	ADV
ejpam-6139	12	8	physics	physics	NOUN
ejpam-6139	13	1	[	[	X
ejpam-6139	13	2	2	2	NUM
ejpam-6139	13	3	]	]	PUNCT
ejpam-6139	13	4	,	,	PUNCT
ejpam-6139	13	5	chemistry	chemistry	NOUN
ejpam-6139	13	6	[	[	X
ejpam-6139	13	7	3	3	NUM
ejpam-6139	13	8	]	]	PUNCT
ejpam-6139	13	9	,	,	PUNCT
ejpam-6139	13	10	medicine	medicine	NOUN
ejpam-6139	13	11	[	[	X
ejpam-6139	13	12	4	4	NUM
ejpam-6139	13	13	]	]	PUNCT
ejpam-6139	13	14	,	,	PUNCT
ejpam-6139	13	15	optimization	optimization	NOUN
ejpam-6139	13	16	,	,	PUNCT
ejpam-6139	13	17	economics	economic	NOUN
ejpam-6139	13	18	,	,	PUNCT
ejpam-6139	13	19	statistics	statistic	NOUN
ejpam-6139	13	20	[	[	X
ejpam-6139	13	21	5	5	NUM
ejpam-6139	13	22	]	]	PUNCT
ejpam-6139	13	23	,	,	PUNCT
ejpam-6139	13	24	and	and	CCONJ
ejpam-6139	13	25	bioengineering	bioengineere	VERB
ejpam-6139	13	26	[	[	X
ejpam-6139	13	27	6	6	NUM
ejpam-6139	13	28	]	]	PUNCT
ejpam-6139	13	29	.	.	PUNCT
ejpam-6139	14	1	additionally	additionally	ADV
ejpam-6139	14	2	,	,	PUNCT
ejpam-6139	14	3	fields	field	NOUN
ejpam-6139	14	4	such	such	ADJ
ejpam-6139	14	5	as	as	ADP
ejpam-6139	14	6	dc	dc	PROPN
ejpam-6139	14	7	programming	programming	NOUN
ejpam-6139	14	8	[	[	X
ejpam-6139	14	9	7	7	NUM
ejpam-6139	14	10	]	]	PUNCT
ejpam-6139	14	11	,	,	PUNCT
ejpam-6139	14	12	∗corresponding	∗corresponde	VERB
ejpam-6139	14	13	author	author	NOUN
ejpam-6139	14	14	.	.	PUNCT
ejpam-6139	15	1	doi	doi	NOUN
ejpam-6139	15	2	:	:	PUNCT
ejpam-6139	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6139	https://doi.org/10.29020/nybg.ejpam.v18i4.6139	ADJ
ejpam-6139	15	4	email	email	NOUN
ejpam-6139	15	5	addresses	address	NOUN
ejpam-6139	15	6	:	:	PUNCT
ejpam-6139	15	7	muhammad.samraiz@uos.edu.pk	muhammad.samraiz@uos.edu.pk	PROPN
ejpam-6139	15	8	(	(	PUNCT
ejpam-6139	15	9	m.	m.	NOUN
ejpam-6139	15	10	samraiz	samraiz	PROPN
ejpam-6139	15	11	)	)	PUNCT
ejpam-6139	15	12	,	,	PUNCT
ejpam-6139	15	13	mqasimsultan191@gmail.com	mqasimsultan191@gmail.com	X
ejpam-6139	15	14	(	(	PUNCT
ejpam-6139	15	15	m.	m.	NOUN
ejpam-6139	15	16	qasim	qasim	PROPN
ejpam-6139	15	17	)	)	PUNCT
ejpam-6139	15	18	,	,	PUNCT
ejpam-6139	15	19	gauhar55uom@gmail.com	gauhar55uom@gmail.com	X
ejpam-6139	15	20	(	(	PUNCT
ejpam-6139	15	21	g.	g.	PROPN
ejpam-6139	15	22	rahman	rahman	PROPN
ejpam-6139	15	23	)	)	PUNCT
ejpam-6139	15	24	,	,	PUNCT
ejpam-6139	15	25	sarwarswati@gmail.com	sarwarswati@gmail.com	X
ejpam-6139	15	26	(	(	PUNCT
ejpam-6139	15	27	m.	m.	NOUN
ejpam-6139	15	28	sarwar	sarwar	PROPN
ejpam-6139	15	29	)	)	PUNCT
ejpam-6139	15	30	,	,	PUNCT
ejpam-6139	15	31	nfatima@psu.edu.sa	nfatima@psu.edu.sa	PROPN
ejpam-6139	15	32	(	(	PUNCT
ejpam-6139	15	33	n.	n.	PROPN
ejpam-6139	15	34	fatima	fatima	PROPN
ejpam-6139	15	35	)	)	PUNCT
ejpam-6139	15	36	,	,	PUNCT
ejpam-6139	15	37	kamal@psu.edu.sa	kamal@psu.edu.sa	PROPN
ejpam-6139	15	38	(	(	PUNCT
ejpam-6139	15	39	k.	k.	PROPN
ejpam-6139	15	40	abodayeh	abodayeh	PROPN
ejpam-6139	15	41	)	)	PUNCT
ejpam-6139	15	42	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6139	15	43	1	1	NUM
ejpam-6139	15	44	copyright	copyright	NOUN
ejpam-6139	15	45	:	:	PUNCT
ejpam-6139	16	1	©	©	PROPN
ejpam-6139	16	2	2025	2025	NUM
ejpam-6139	16	3	the	the	DET
ejpam-6139	16	4	author(s	author(s	NOUN
ejpam-6139	16	5	)	)	PUNCT
ejpam-6139	16	6	.	.	PUNCT
ejpam-6139	17	1	(	(	PUNCT
ejpam-6139	17	2	cc	cc	NOUN
ejpam-6139	17	3	by	by	ADP
ejpam-6139	17	4	-	-	PUNCT
ejpam-6139	17	5	nc	nc	PROPN
ejpam-6139	17	6	4.0	4.0	NUM
ejpam-6139	17	7	)	)	PUNCT
ejpam-6139	17	8	m.	m.	NOUN
ejpam-6139	17	9	samraiz	samraiz	PROPN
ejpam-6139	17	10	et	et	PROPN
ejpam-6139	17	11	al	al	PROPN
ejpam-6139	17	12	.	.	PUNCT
ejpam-6139	17	13	/	/	SYM
ejpam-6139	17	14	eur	eur	PROPN
ejpam-6139	17	15	.	.	PUNCT
ejpam-6139	18	1	j.	j.	PROPN
ejpam-6139	18	2	pure	pure	PROPN
ejpam-6139	18	3	appl	appl	PROPN
ejpam-6139	18	4	.	.	PROPN
ejpam-6139	18	5	math	math	PROPN
ejpam-6139	18	6	,	,	PUNCT
ejpam-6139	18	7	18	18	NUM
ejpam-6139	18	8	(	(	PUNCT
ejpam-6139	18	9	4	4	NUM
ejpam-6139	18	10	)	)	PUNCT
ejpam-6139	18	11	(	(	PUNCT
ejpam-6139	18	12	2025	2025	NUM
ejpam-6139	18	13	)	)	PUNCT
ejpam-6139	18	14	,	,	PUNCT
ejpam-6139	18	15	6139	6139	NUM
ejpam-6139	18	16	2	2	NUM
ejpam-6139	18	17	of	of	ADP
ejpam-6139	18	18	34	34	NUM
ejpam-6139	18	19	convex	convex	NOUN
ejpam-6139	18	20	programming	programming	NOUN
ejpam-6139	18	21	[	[	X
ejpam-6139	18	22	8	8	NUM
ejpam-6139	18	23	]	]	PUNCT
ejpam-6139	18	24	,	,	PUNCT
ejpam-6139	18	25	functional	functional	ADJ
ejpam-6139	18	26	analysis	analysis	NOUN
ejpam-6139	18	27	[	[	X
ejpam-6139	18	28	9	9	NUM
ejpam-6139	18	29	]	]	PUNCT
ejpam-6139	18	30	,	,	PUNCT
ejpam-6139	18	31	monotone	monotone	ADJ
ejpam-6139	18	32	operator	operator	NOUN
ejpam-6139	18	33	theory	theory	NOUN
ejpam-6139	18	34	[	[	X
ejpam-6139	18	35	10	10	NUM
ejpam-6139	18	36	]	]	PUNCT
ejpam-6139	18	37	,	,	PUNCT
ejpam-6139	18	38	object	object	VERB
ejpam-6139	18	39	detection	detection	NOUN
ejpam-6139	18	40	algorithm	algorithm	NOUN
ejpam-6139	19	1	[	[	X
ejpam-6139	19	2	11	11	NUM
ejpam-6139	19	3	]	]	PUNCT
ejpam-6139	19	4	,	,	PUNCT
ejpam-6139	19	5	and	and	CCONJ
ejpam-6139	19	6	complex	complex	ADJ
ejpam-6139	19	7	analysis	analysis	NOUN
ejpam-6139	19	8	[	[	X
ejpam-6139	19	9	12	12	NUM
ejpam-6139	19	10	]	]	PUNCT
ejpam-6139	19	11	further	far	ADV
ejpam-6139	19	12	underscore	underscore	VERB
ejpam-6139	19	13	the	the	DET
ejpam-6139	19	14	importance	importance	NOUN
ejpam-6139	19	15	of	of	ADP
ejpam-6139	19	16	convexity	convexity	NOUN
ejpam-6139	19	17	.	.	PUNCT
ejpam-6139	20	1	this	this	DET
ejpam-6139	20	2	characteristic	characteristic	NOUN
ejpam-6139	20	3	plays	play	VERB
ejpam-6139	20	4	a	a	DET
ejpam-6139	20	5	crucial	crucial	ADJ
ejpam-6139	20	6	role	role	NOUN
ejpam-6139	20	7	in	in	ADP
ejpam-6139	20	8	solving	solve	VERB
ejpam-6139	20	9	many	many	ADJ
ejpam-6139	20	10	real	real	ADJ
ejpam-6139	20	11	-	-	PUNCT
ejpam-6139	20	12	world	world	NOUN
ejpam-6139	20	13	problems	problem	NOUN
ejpam-6139	20	14	related	relate	VERB
ejpam-6139	20	15	to	to	ADP
ejpam-6139	20	16	minimizing	minimize	VERB
ejpam-6139	20	17	or	or	CCONJ
ejpam-6139	20	18	maximizing	maximize	VERB
ejpam-6139	20	19	functions	function	NOUN
ejpam-6139	20	20	subject	subject	ADJ
ejpam-6139	20	21	to	to	ADP
ejpam-6139	20	22	certain	certain	ADJ
ejpam-6139	20	23	-	-	PUNCT
ejpam-6139	20	24	constraints	constraint	NOUN
ejpam-6139	20	25	.	.	PUNCT
ejpam-6139	21	1	the	the	DET
ejpam-6139	21	2	exploration	exploration	NOUN
ejpam-6139	21	3	of	of	ADP
ejpam-6139	21	4	convex	convex	NOUN
ejpam-6139	21	5	functions	function	NOUN
ejpam-6139	21	6	can	can	AUX
ejpam-6139	21	7	be	be	AUX
ejpam-6139	21	8	traced	trace	VERB
ejpam-6139	21	9	back	back	ADV
ejpam-6139	21	10	to	to	ADP
ejpam-6139	21	11	the	the	DET
ejpam-6139	21	12	ancient	ancient	ADJ
ejpam-6139	21	13	greek	greek	ADJ
ejpam-6139	21	14	mathematician	mathematician	ADJ
ejpam-6139	21	15	archimedes	archimede	NOUN
ejpam-6139	21	16	(	(	PUNCT
ejpam-6139	21	17	287	287	NUM
ejpam-6139	21	18	bc-212	bc-212	NOUN
ejpam-6139	21	19	bc	bc	PROPN
ejpam-6139	21	20	)	)	PUNCT
ejpam-6139	21	21	,	,	PUNCT
ejpam-6139	21	22	who	who	PRON
ejpam-6139	21	23	,	,	PUNCT
ejpam-6139	21	24	in	in	ADP
ejpam-6139	21	25	his	his	PRON
ejpam-6139	21	26	work	work	NOUN
ejpam-6139	21	27	on	on	ADP
ejpam-6139	21	28	the	the	DET
ejpam-6139	21	29	sphere	sphere	NOUN
ejpam-6139	21	30	and	and	CCONJ
ejpam-6139	21	31	cylinder	cylinder	NOUN
ejpam-6139	22	1	[	[	X
ejpam-6139	22	2	13	13	NUM
ejpam-6139	22	3	]	]	PUNCT
ejpam-6139	22	4	,	,	PUNCT
ejpam-6139	22	5	described	describe	VERB
ejpam-6139	22	6	a	a	DET
ejpam-6139	22	7	convex	convex	NOUN
ejpam-6139	22	8	arc	arc	NOUN
ejpam-6139	22	9	as	as	ADP
ejpam-6139	22	10	a	a	DET
ejpam-6139	22	11	curved	curved	ADJ
ejpam-6139	22	12	line	line	NOUN
ejpam-6139	22	13	in	in	ADP
ejpam-6139	22	14	a	a	DET
ejpam-6139	22	15	plane	plane	NOUN
ejpam-6139	22	16	that	that	PRON
ejpam-6139	22	17	remains	remain	VERB
ejpam-6139	22	18	entirely	entirely	ADV
ejpam-6139	22	19	on	on	ADP
ejpam-6139	22	20	one	one	NUM
ejpam-6139	22	21	side	side	NOUN
ejpam-6139	22	22	of	of	ADP
ejpam-6139	22	23	the	the	DET
ejpam-6139	22	24	straight	straight	ADJ
ejpam-6139	22	25	line	line	NOUN
ejpam-6139	22	26	connecting	connect	VERB
ejpam-6139	22	27	its	its	PRON
ejpam-6139	22	28	endpoints	endpoint	NOUN
ejpam-6139	22	29	[	[	X
ejpam-6139	22	30	14	14	NUM
ejpam-6139	22	31	]	]	PUNCT
ejpam-6139	22	32	.	.	PUNCT
ejpam-6139	23	1	the	the	DET
ejpam-6139	23	2	study	study	NOUN
ejpam-6139	23	3	of	of	ADP
ejpam-6139	23	4	mathematical	mathematical	ADJ
ejpam-6139	23	5	inequalities	inequality	NOUN
ejpam-6139	23	6	started	start	VERB
ejpam-6139	23	7	in	in	ADP
ejpam-6139	23	8	the	the	DET
ejpam-6139	23	9	18th	18th	ADJ
ejpam-6139	23	10	century	century	NOUN
ejpam-6139	23	11	with	with	ADP
ejpam-6139	23	12	work	work	NOUN
ejpam-6139	23	13	by	by	ADP
ejpam-6139	23	14	carl	carl	PROPN
ejpam-6139	23	15	friedrich	friedrich	PROPN
ejpam-6139	23	16	gauss	gauss	PROPN
ejpam-6139	23	17	.	.	PUNCT
ejpam-6139	24	1	later	later	ADV
ejpam-6139	24	2	,	,	PUNCT
ejpam-6139	24	3	mathematicians	mathematician	NOUN
ejpam-6139	24	4	like	like	ADP
ejpam-6139	24	5	augustin	augustin	PROPN
ejpam-6139	24	6	-	-	PUNCT
ejpam-6139	24	7	louis	louis	PROPN
ejpam-6139	24	8	cauchy	cauchy	NOUN
ejpam-6139	24	9	and	and	CCONJ
ejpam-6139	24	10	pafnuty	pafnuty	PROPN
ejpam-6139	24	11	chebyshev	chebyshev	NOUN
ejpam-6139	24	12	explored	explore	VERB
ejpam-6139	24	13	how	how	SCONJ
ejpam-6139	24	14	inequalities	inequality	NOUN
ejpam-6139	24	15	could	could	AUX
ejpam-6139	24	16	be	be	AUX
ejpam-6139	24	17	used	use	VERB
ejpam-6139	24	18	in	in	ADP
ejpam-6139	24	19	analysis	analysis	NOUN
ejpam-6139	24	20	.	.	PUNCT
ejpam-6139	25	1	a	a	DET
ejpam-6139	25	2	key	key	ADJ
ejpam-6139	25	3	result	result	NOUN
ejpam-6139	25	4	came	come	VERB
ejpam-6139	25	5	from	from	ADP
ejpam-6139	25	6	viktor	viktor	NOUN
ejpam-6139	25	7	bunyakovsky	bunyakovsky	NOUN
ejpam-6139	25	8	,	,	PUNCT
ejpam-6139	25	9	who	who	PRON
ejpam-6139	25	10	proved	prove	VERB
ejpam-6139	25	11	an	an	DET
ejpam-6139	25	12	early	early	ADJ
ejpam-6139	25	13	form	form	NOUN
ejpam-6139	25	14	of	of	ADP
ejpam-6139	25	15	the	the	DET
ejpam-6139	25	16	cauchy	cauchy	PROPN
ejpam-6139	25	17	-	-	PUNCT
ejpam-6139	25	18	schwarz	schwarz	PROPN
ejpam-6139	25	19	inequality	inequality	NOUN
ejpam-6139	25	20	[	[	X
ejpam-6139	25	21	15	15	NUM
ejpam-6139	25	22	]	]	PUNCT
ejpam-6139	25	23	.	.	PUNCT
ejpam-6139	26	1	in	in	ADP
ejpam-6139	26	2	the	the	DET
ejpam-6139	26	3	19th	19th	ADJ
ejpam-6139	26	4	century	century	NOUN
ejpam-6139	26	5	,	,	PUNCT
ejpam-6139	26	6	otto	otto	PROPN
ejpam-6139	26	7	hölder	hölder	PROPN
ejpam-6139	26	8	introduced	introduce	VERB
ejpam-6139	26	9	a	a	DET
ejpam-6139	26	10	version	version	NOUN
ejpam-6139	26	11	of	of	ADP
ejpam-6139	26	12	what	what	PRON
ejpam-6139	26	13	would	would	AUX
ejpam-6139	26	14	later	later	ADV
ejpam-6139	26	15	be	be	AUX
ejpam-6139	26	16	known	know	VERB
ejpam-6139	26	17	as	as	ADP
ejpam-6139	26	18	jensen	jensen	PROPN
ejpam-6139	26	19	’s	’s	PART
ejpam-6139	26	20	inequality	inequality	NOUN
ejpam-6139	26	21	,	,	PUNCT
ejpam-6139	26	22	assuming	assume	VERB
ejpam-6139	26	23	the	the	DET
ejpam-6139	26	24	second	second	ADJ
ejpam-6139	26	25	derivative	derivative	NOUN
ejpam-6139	26	26	of	of	ADP
ejpam-6139	26	27	a	a	DET
ejpam-6139	26	28	function	function	NOUN
ejpam-6139	26	29	is	be	AUX
ejpam-6139	26	30	non	non	ADJ
ejpam-6139	26	31	-	-	ADJ
ejpam-6139	26	32	negative	negative	ADJ
ejpam-6139	26	33	.	.	PUNCT
ejpam-6139	27	1	the	the	DET
ejpam-6139	27	2	study	study	NOUN
ejpam-6139	27	3	of	of	ADP
ejpam-6139	27	4	inequalities	inequality	NOUN
ejpam-6139	27	5	grew	grow	VERB
ejpam-6139	27	6	more	more	ADV
ejpam-6139	27	7	important	important	ADJ
ejpam-6139	27	8	in	in	ADP
ejpam-6139	27	9	the	the	DET
ejpam-6139	27	10	20th	20th	ADJ
ejpam-6139	27	11	century	century	NOUN
ejpam-6139	27	12	,	,	PUNCT
ejpam-6139	27	13	with	with	ADP
ejpam-6139	27	14	major	major	ADJ
ejpam-6139	27	15	contributions	contribution	NOUN
ejpam-6139	27	16	by	by	ADP
ejpam-6139	27	17	mathematicians	mathematician	NOUN
ejpam-6139	27	18	like	like	ADP
ejpam-6139	27	19	leonhard	leonhard	PROPN
ejpam-6139	27	20	euler	euler	PROPN
ejpam-6139	27	21	and	and	CCONJ
ejpam-6139	27	22	adrien	adrien	PROPN
ejpam-6139	27	23	-	-	PUNCT
ejpam-6139	27	24	marie	marie	PROPN
ejpam-6139	27	25	legendre	legendre	PROPN
ejpam-6139	27	26	.	.	PUNCT
ejpam-6139	28	1	in	in	ADP
ejpam-6139	28	2	recent	recent	ADJ
ejpam-6139	28	3	years	year	NOUN
ejpam-6139	28	4	,	,	PUNCT
ejpam-6139	28	5	there	there	PRON
ejpam-6139	28	6	has	have	AUX
ejpam-6139	28	7	been	be	AUX
ejpam-6139	28	8	a	a	DET
ejpam-6139	28	9	growing	grow	VERB
ejpam-6139	28	10	interest	interest	NOUN
ejpam-6139	28	11	in	in	ADP
ejpam-6139	28	12	exploring	explore	VERB
ejpam-6139	28	13	new	new	ADJ
ejpam-6139	28	14	aspects	aspect	NOUN
ejpam-6139	28	15	of	of	ADP
ejpam-6139	28	16	convex	convex	NOUN
ejpam-6139	28	17	functions	function	NOUN
ejpam-6139	28	18	,	,	PUNCT
ejpam-6139	28	19	particularly	particularly	ADV
ejpam-6139	28	20	in	in	ADP
ejpam-6139	28	21	deriving	derive	VERB
ejpam-6139	28	22	novel	novel	ADJ
ejpam-6139	28	23	inequalities	inequality	NOUN
ejpam-6139	28	24	such	such	ADJ
ejpam-6139	28	25	as	as	ADP
ejpam-6139	28	26	jensen	jensen	PROPN
ejpam-6139	28	27	’s	’s	PART
ejpam-6139	28	28	inequality	inequality	NOUN
ejpam-6139	29	1	[	[	X
ejpam-6139	29	2	16	16	NUM
ejpam-6139	29	3	]	]	PUNCT
ejpam-6139	29	4	,	,	PUNCT
ejpam-6139	29	5	the	the	DET
ejpam-6139	29	6	power	power	NOUN
ejpam-6139	29	7	mean	mean	VERB
ejpam-6139	29	8	inequality	inequality	NOUN
ejpam-6139	29	9	[	[	X
ejpam-6139	29	10	17	17	NUM
ejpam-6139	29	11	]	]	PUNCT
ejpam-6139	29	12	,	,	PUNCT
ejpam-6139	29	13	the	the	DET
ejpam-6139	29	14	cauchy	cauchy	PROPN
ejpam-6139	29	15	-	-	PUNCT
ejpam-6139	29	16	schwarz	schwarz	PROPN
ejpam-6139	29	17	inequality	inequality	NOUN
ejpam-6139	29	18	[	[	X
ejpam-6139	29	19	18	18	NUM
ejpam-6139	29	20	]	]	PUNCT
ejpam-6139	29	21	,	,	PUNCT
ejpam-6139	29	22	bell	bell	PROPN
ejpam-6139	29	23	’s	’s	PART
ejpam-6139	29	24	inequality	inequality	NOUN
ejpam-6139	30	1	[	[	X
ejpam-6139	30	2	19	19	NUM
ejpam-6139	30	3	]	]	PUNCT
ejpam-6139	30	4	,	,	PUNCT
ejpam-6139	30	5	boole	boole	PROPN
ejpam-6139	30	6	’s	’s	PART
ejpam-6139	30	7	inequality	inequality	NOUN
ejpam-6139	30	8	[	[	X
ejpam-6139	30	9	20	20	NUM
ejpam-6139	30	10	]	]	PUNCT
ejpam-6139	30	11	,	,	PUNCT
ejpam-6139	30	12	the	the	DET
ejpam-6139	30	13	sobolev	sobolev	NOUN
ejpam-6139	30	14	inequality	inequality	NOUN
ejpam-6139	30	15	[	[	X
ejpam-6139	30	16	21	21	NUM
ejpam-6139	30	17	]	]	PUNCT
ejpam-6139	30	18	,	,	PUNCT
ejpam-6139	30	19	chernoff	chernoff	PROPN
ejpam-6139	30	20	’s	’s	PART
ejpam-6139	30	21	inequality	inequality	NOUN
ejpam-6139	30	22	[	[	X
ejpam-6139	30	23	22	22	NUM
ejpam-6139	30	24	]	]	PUNCT
ejpam-6139	30	25	,	,	PUNCT
ejpam-6139	30	26	the	the	DET
ejpam-6139	30	27	hermite	hermite	PROPN
ejpam-6139	30	28	-	-	PUNCT
ejpam-6139	30	29	hadamard	hadamard	ADJ
ejpam-6139	30	30	(	(	PUNCT
ejpam-6139	30	31	h−h	h−h	NOUN
ejpam-6139	30	32	)	)	PUNCT
ejpam-6139	30	33	inequality	inequality	NOUN
ejpam-6139	30	34	[	[	X
ejpam-6139	30	35	23	23	NUM
ejpam-6139	30	36	]	]	PUNCT
ejpam-6139	30	37	,	,	PUNCT
ejpam-6139	30	38	ostrowski	ostrowski	ADJ
ejpam-6139	30	39	type	type	NOUN
ejpam-6139	30	40	inequalities	inequality	NOUN
ejpam-6139	30	41	[	[	X
ejpam-6139	30	42	24	24	NUM
ejpam-6139	30	43	]	]	PUNCT
ejpam-6139	30	44	,	,	PUNCT
ejpam-6139	30	45	midpoint	midpoint	NOUN
ejpam-6139	30	46	and	and	CCONJ
ejpam-6139	30	47	trapezoidal	trapezoidal	ADJ
ejpam-6139	30	48	-	-	PUNCT
ejpam-6139	30	49	type	type	NOUN
ejpam-6139	30	50	inequalities	inequality	NOUN
ejpam-6139	30	51	[	[	X
ejpam-6139	30	52	25	25	NUM
ejpam-6139	30	53	,	,	PUNCT
ejpam-6139	30	54	26	26	NUM
ejpam-6139	30	55	]	]	PUNCT
ejpam-6139	30	56	.	.	PUNCT
ejpam-6139	31	1	while	while	SCONJ
ejpam-6139	31	2	various	various	ADJ
ejpam-6139	31	3	types	type	NOUN
ejpam-6139	31	4	of	of	ADP
ejpam-6139	31	5	inequalities	inequality	NOUN
ejpam-6139	31	6	exist	exist	VERB
ejpam-6139	31	7	,	,	PUNCT
ejpam-6139	31	8	convex	convex	NOUN
ejpam-6139	31	9	inequalities	inequality	NOUN
ejpam-6139	31	10	play	play	VERB
ejpam-6139	31	11	a	a	DET
ejpam-6139	31	12	vital	vital	ADJ
ejpam-6139	31	13	role	role	NOUN
ejpam-6139	31	14	in	in	ADP
ejpam-6139	31	15	this	this	DET
ejpam-6139	31	16	field	field	NOUN
ejpam-6139	31	17	.	.	PUNCT
ejpam-6139	32	1	as	as	SCONJ
ejpam-6139	32	2	fractional	fractional	ADJ
ejpam-6139	32	3	calculus	calculus	NOUN
ejpam-6139	32	4	is	be	AUX
ejpam-6139	32	5	a	a	DET
ejpam-6139	32	6	branch	branch	NOUN
ejpam-6139	32	7	of	of	ADP
ejpam-6139	32	8	mathematical	mathematical	ADJ
ejpam-6139	32	9	analysis	analysis	NOUN
ejpam-6139	32	10	that	that	PRON
ejpam-6139	32	11	generalizes	generalize	VERB
ejpam-6139	32	12	the	the	DET
ejpam-6139	32	13	concepts	concept	NOUN
ejpam-6139	32	14	of	of	ADP
ejpam-6139	32	15	differentiation	differentiation	NOUN
ejpam-6139	32	16	and	and	CCONJ
ejpam-6139	32	17	integration	integration	NOUN
ejpam-6139	32	18	to	to	ADP
ejpam-6139	32	19	non	non	ADJ
ejpam-6139	32	20	-	-	ADJ
ejpam-6139	32	21	integer	integer	ADJ
ejpam-6139	32	22	order	order	NOUN
ejpam-6139	32	23	.	.	PUNCT
ejpam-6139	33	1	there	there	PRON
ejpam-6139	33	2	are	be	VERB
ejpam-6139	33	3	many	many	ADJ
ejpam-6139	33	4	important	important	ADJ
ejpam-6139	33	5	applications	application	NOUN
ejpam-6139	33	6	of	of	ADP
ejpam-6139	33	7	fractional	fractional	ADJ
ejpam-6139	33	8	calculus	calculus	NOUN
ejpam-6139	33	9	,	,	PUNCT
ejpam-6139	33	10	such	such	ADJ
ejpam-6139	33	11	as	as	ADP
ejpam-6139	33	12	modeling	model	VERB
ejpam-6139	33	13	influenza	influenza	NOUN
ejpam-6139	33	14	[	[	X
ejpam-6139	33	15	27	27	NUM
ejpam-6139	33	16	]	]	PUNCT
ejpam-6139	33	17	and	and	CCONJ
ejpam-6139	33	18	trajectory	trajectory	NOUN
ejpam-6139	33	19	tracking	tracking	NOUN
ejpam-6139	33	20	of	of	ADP
ejpam-6139	33	21	the	the	DET
ejpam-6139	33	22	stanford	stanford	PROPN
ejpam-6139	33	23	robot	robot	NOUN
ejpam-6139	33	24	[	[	X
ejpam-6139	33	25	28	28	NUM
ejpam-6139	33	26	]	]	PUNCT
ejpam-6139	33	27	.	.	PUNCT
ejpam-6139	34	1	mathematicians	mathematician	NOUN
ejpam-6139	34	2	have	have	AUX
ejpam-6139	34	3	derived	derive	VERB
ejpam-6139	34	4	different	different	ADJ
ejpam-6139	34	5	operators	operator	NOUN
ejpam-6139	34	6	in	in	ADP
ejpam-6139	34	7	fractional	fractional	ADJ
ejpam-6139	34	8	calculus	calculus	NOUN
ejpam-6139	34	9	to	to	PART
ejpam-6139	34	10	obtain	obtain	VERB
ejpam-6139	34	11	desired	desire	VERB
ejpam-6139	34	12	results	result	NOUN
ejpam-6139	34	13	,	,	PUNCT
ejpam-6139	34	14	such	such	ADJ
ejpam-6139	34	15	as	as	ADP
ejpam-6139	34	16	the	the	DET
ejpam-6139	34	17	riemann	riemann	PROPN
ejpam-6139	34	18	-	-	PUNCT
ejpam-6139	34	19	liouville	liouville	VERB
ejpam-6139	34	20	fractional	fractional	ADJ
ejpam-6139	34	21	operators	operator	NOUN
ejpam-6139	34	22	[	[	X
ejpam-6139	34	23	29	29	NUM
ejpam-6139	34	24	]	]	PUNCT
ejpam-6139	34	25	,	,	PUNCT
ejpam-6139	34	26	the	the	DET
ejpam-6139	34	27	caputo	caputo	PROPN
ejpam-6139	34	28	-	-	PUNCT
ejpam-6139	34	29	fabrizio	fabrizio	PROPN
ejpam-6139	34	30	fractional	fractional	ADJ
ejpam-6139	34	31	operator	operator	NOUN
ejpam-6139	34	32	[	[	X
ejpam-6139	34	33	30	30	NUM
ejpam-6139	34	34	]	]	PUNCT
ejpam-6139	34	35	,	,	PUNCT
ejpam-6139	34	36	the	the	DET
ejpam-6139	34	37	hilfer	hilfer	NOUN
ejpam-6139	34	38	fractional	fractional	ADJ
ejpam-6139	34	39	derivative	derivative	ADJ
ejpam-6139	34	40	operator	operator	NOUN
ejpam-6139	34	41	[	[	X
ejpam-6139	34	42	31	31	NUM
ejpam-6139	34	43	]	]	PUNCT
ejpam-6139	34	44	,	,	PUNCT
ejpam-6139	34	45	hadamard	hadamard	ADJ
ejpam-6139	34	46	-	-	PUNCT
ejpam-6139	34	47	type	type	NOUN
ejpam-6139	34	48	fractional	fractional	ADJ
ejpam-6139	34	49	operators	operator	NOUN
ejpam-6139	34	50	[	[	X
ejpam-6139	34	51	32	32	NUM
ejpam-6139	34	52	]	]	PUNCT
ejpam-6139	34	53	,	,	PUNCT
ejpam-6139	34	54	and	and	CCONJ
ejpam-6139	34	55	katugampola	katugampola	ADJ
ejpam-6139	34	56	fractional	fractional	ADJ
ejpam-6139	34	57	integrals	integral	NOUN
ejpam-6139	34	58	[	[	X
ejpam-6139	34	59	33	33	NUM
ejpam-6139	34	60	]	]	PUNCT
ejpam-6139	34	61	,	,	PUNCT
ejpam-6139	34	62	according	accord	VERB
ejpam-6139	34	63	to	to	ADP
ejpam-6139	34	64	their	their	PRON
ejpam-6139	34	65	needs	need	NOUN
ejpam-6139	34	66	.	.	PUNCT
ejpam-6139	35	1	one	one	NUM
ejpam-6139	35	2	such	such	ADJ
ejpam-6139	35	3	operator	operator	NOUN
ejpam-6139	35	4	is	be	AUX
ejpam-6139	35	5	the	the	DET
ejpam-6139	35	6	conformable	conformable	ADJ
ejpam-6139	35	7	fractional	fractional	ADJ
ejpam-6139	35	8	operator	operator	NOUN
ejpam-6139	35	9	[	[	X
ejpam-6139	35	10	34	34	NUM
ejpam-6139	35	11	]	]	PUNCT
ejpam-6139	35	12	,	,	PUNCT
ejpam-6139	35	13	and	and	CCONJ
ejpam-6139	35	14	(	(	PUNCT
ejpam-6139	35	15	k	k	X
ejpam-6139	35	16	,	,	PUNCT
ejpam-6139	35	17	ρ)−conformable	ρ)−conformable	ADJ
ejpam-6139	35	18	fractional	fractional	ADJ
ejpam-6139	35	19	integrals	integral	NOUN
ejpam-6139	35	20	[	[	X
ejpam-6139	35	21	35	35	NUM
ejpam-6139	35	22	]	]	PUNCT
ejpam-6139	35	23	.	.	PUNCT
ejpam-6139	36	1	moreover	moreover	ADV
ejpam-6139	36	2	mathematicians	mathematician	NOUN
ejpam-6139	36	3	have	have	AUX
ejpam-6139	36	4	made	make	VERB
ejpam-6139	36	5	significant	significant	ADJ
ejpam-6139	36	6	efforts	effort	NOUN
ejpam-6139	36	7	to	to	PART
ejpam-6139	36	8	analyze	analyze	VERB
ejpam-6139	36	9	the	the	DET
ejpam-6139	36	10	behavior	behavior	NOUN
ejpam-6139	36	11	of	of	ADP
ejpam-6139	36	12	inequalities	inequality	NOUN
ejpam-6139	36	13	particularly	particularly	ADV
ejpam-6139	36	14	fractional	fractional	ADJ
ejpam-6139	36	15	inequalities	inequality	NOUN
ejpam-6139	36	16	through	through	ADP
ejpam-6139	36	17	computational	computational	ADJ
ejpam-6139	36	18	methods	method	NOUN
ejpam-6139	36	19	[	[	X
ejpam-6139	36	20	36	36	NUM
ejpam-6139	36	21	]	]	PUNCT
ejpam-6139	36	22	.	.	PUNCT
ejpam-6139	37	1	this	this	DET
ejpam-6139	37	2	work	work	NOUN
ejpam-6139	37	3	is	be	AUX
ejpam-6139	37	4	based	base	VERB
ejpam-6139	37	5	on	on	ADP
ejpam-6139	37	6	investigating	investigate	VERB
ejpam-6139	37	7	new	new	ADJ
ejpam-6139	37	8	inequalities	inequality	NOUN
ejpam-6139	37	9	of	of	ADP
ejpam-6139	37	10	trapezoidal	trapezoidal	ADJ
ejpam-6139	37	11	and	and	CCONJ
ejpam-6139	37	12	midpoint	midpoint	NOUN
ejpam-6139	37	13	type	type	NOUN
ejpam-6139	37	14	for	for	ADP
ejpam-6139	37	15	convex	convex	NOUN
ejpam-6139	37	16	functions	function	NOUN
ejpam-6139	37	17	.	.	PUNCT
ejpam-6139	38	1	these	these	DET
ejpam-6139	38	2	inequalities	inequality	NOUN
ejpam-6139	38	3	are	be	AUX
ejpam-6139	38	4	obtained	obtain	VERB
ejpam-6139	38	5	with	with	ADP
ejpam-6139	38	6	the	the	DET
ejpam-6139	38	7	aid	aid	NOUN
ejpam-6139	38	8	of	of	ADP
ejpam-6139	38	9	the	the	DET
ejpam-6139	38	10	extended	extended	ADJ
ejpam-6139	38	11	conformable	conformable	ADJ
ejpam-6139	38	12	fractional	fractional	ADJ
ejpam-6139	38	13	operators	operator	NOUN
ejpam-6139	38	14	and	and	CCONJ
ejpam-6139	38	15	twice	twice	ADJ
ejpam-6139	38	16	differentiable	differentiable	ADJ
ejpam-6139	38	17	functions	function	NOUN
ejpam-6139	38	18	.	.	PUNCT
ejpam-6139	39	1	the	the	DET
ejpam-6139	39	2	extended	extend	VERB
ejpam-6139	39	3	conformable	conformable	ADJ
ejpam-6139	39	4	fractional	fractional	ADJ
ejpam-6139	39	5	operators	operator	NOUN
ejpam-6139	39	6	generalize	generalize	VERB
ejpam-6139	39	7	the	the	DET
ejpam-6139	39	8	concept	concept	NOUN
ejpam-6139	39	9	of	of	ADP
ejpam-6139	39	10	fractional	fractional	ADJ
ejpam-6139	39	11	calculus	calculus	NOUN
ejpam-6139	39	12	to	to	ADP
ejpam-6139	39	13	a	a	DET
ejpam-6139	39	14	wide	wide	ADJ
ejpam-6139	39	15	range	range	NOUN
ejpam-6139	39	16	of	of	ADP
ejpam-6139	39	17	functions	function	NOUN
ejpam-6139	39	18	,	,	PUNCT
ejpam-6139	39	19	and	and	CCONJ
ejpam-6139	39	20	as	as	ADP
ejpam-6139	39	21	such	such	ADJ
ejpam-6139	39	22	,	,	PUNCT
ejpam-6139	39	23	it	it	PRON
ejpam-6139	39	24	provides	provide	VERB
ejpam-6139	39	25	a	a	DET
ejpam-6139	39	26	strong	strong	ADJ
ejpam-6139	39	27	tool	tool	NOUN
ejpam-6139	39	28	for	for	ADP
ejpam-6139	39	29	studying	study	VERB
ejpam-6139	39	30	inequalities	inequality	NOUN
ejpam-6139	39	31	with	with	ADP
ejpam-6139	39	32	generalized	generalized	ADJ
ejpam-6139	39	33	functions	function	NOUN
ejpam-6139	39	34	.	.	PUNCT
ejpam-6139	40	1	also	also	ADV
ejpam-6139	40	2	,	,	PUNCT
ejpam-6139	40	3	twice	twice	ADV
ejpam-6139	40	4	differentiable	differentiable	ADJ
ejpam-6139	40	5	functions	function	NOUN
ejpam-6139	40	6	are	be	AUX
ejpam-6139	40	7	fundamental	fundamental	ADJ
ejpam-6139	40	8	in	in	ADP
ejpam-6139	40	9	the	the	DET
ejpam-6139	40	10	construction	construction	NOUN
ejpam-6139	40	11	and	and	CCONJ
ejpam-6139	40	12	proof	proof	NOUN
ejpam-6139	40	13	of	of	ADP
ejpam-6139	40	14	these	these	DET
ejpam-6139	40	15	inequalities	inequality	NOUN
ejpam-6139	40	16	.	.	PUNCT
ejpam-6139	41	1	additionally	additionally	ADV
ejpam-6139	41	2	,	,	PUNCT
ejpam-6139	41	3	the	the	DET
ejpam-6139	41	4	absolute	absolute	ADJ
ejpam-6139	41	5	value	value	NOUN
ejpam-6139	41	6	function	function	NOUN
ejpam-6139	41	7	and	and	CCONJ
ejpam-6139	41	8	convex	convex	NOUN
ejpam-6139	41	9	properties	property	NOUN
ejpam-6139	41	10	of	of	ADP
ejpam-6139	41	11	twice	twice	ADJ
ejpam-6139	41	12	differentiable	differentiable	ADJ
ejpam-6139	41	13	functions	function	NOUN
ejpam-6139	41	14	are	be	AUX
ejpam-6139	41	15	utilized	utilize	VERB
ejpam-6139	41	16	to	to	PART
ejpam-6139	41	17	provide	provide	VERB
ejpam-6139	41	18	connections	connection	NOUN
ejpam-6139	41	19	between	between	ADP
ejpam-6139	41	20	the	the	DET
ejpam-6139	41	21	new	new	ADJ
ejpam-6139	41	22	inequalities	inequality	NOUN
ejpam-6139	41	23	.	.	PUNCT
ejpam-6139	42	1	also	also	ADV
ejpam-6139	42	2	,	,	PUNCT
ejpam-6139	42	3	celebrated	celebrate	VERB
ejpam-6139	42	4	inequalities	inequality	NOUN
ejpam-6139	42	5	like	like	ADP
ejpam-6139	42	6	hölder	hölder	NOUN
ejpam-6139	42	7	inequality	inequality	NOUN
ejpam-6139	42	8	[	[	X
ejpam-6139	42	9	37	37	NUM
ejpam-6139	42	10	]	]	PUNCT
ejpam-6139	42	11	and	and	CCONJ
ejpam-6139	42	12	the	the	DET
ejpam-6139	42	13	power	power	NOUN
ejpam-6139	42	14	mean	mean	VERB
ejpam-6139	42	15	inequality	inequality	NOUN
ejpam-6139	43	1	[	[	X
ejpam-6139	43	2	37	37	NUM
ejpam-6139	43	3	]	]	PUNCT
ejpam-6139	43	4	are	be	AUX
ejpam-6139	43	5	utilized	utilize	VERB
ejpam-6139	43	6	in	in	ADP
ejpam-6139	43	7	deriving	derive	VERB
ejpam-6139	43	8	special	special	ADJ
ejpam-6139	43	9	findings	finding	NOUN
ejpam-6139	43	10	.	.	PUNCT
ejpam-6139	44	1	this	this	DET
ejpam-6139	44	2	paper	paper	NOUN
ejpam-6139	44	3	is	be	AUX
ejpam-6139	44	4	organized	organize	VERB
ejpam-6139	44	5	into	into	ADP
ejpam-6139	44	6	sections	section	NOUN
ejpam-6139	44	7	as	as	SCONJ
ejpam-6139	44	8	follows	follow	VERB
ejpam-6139	44	9	:	:	PUNCT
ejpam-6139	44	10	section	section	NOUN
ejpam-6139	44	11	2	2	NUM
ejpam-6139	44	12	offers	offer	VERB
ejpam-6139	44	13	a	a	DET
ejpam-6139	44	14	detailed	detailed	ADJ
ejpam-6139	44	15	review	review	NOUN
ejpam-6139	44	16	of	of	ADP
ejpam-6139	44	17	m.	m.	NOUN
ejpam-6139	44	18	samraiz	samraiz	PROPN
ejpam-6139	44	19	et	et	PROPN
ejpam-6139	44	20	al	al	PROPN
ejpam-6139	44	21	.	.	PUNCT
ejpam-6139	44	22	/	/	SYM
ejpam-6139	44	23	eur	eur	PROPN
ejpam-6139	44	24	.	.	PUNCT
ejpam-6139	45	1	j.	j.	PROPN
ejpam-6139	45	2	pure	pure	PROPN
ejpam-6139	45	3	appl	appl	PROPN
ejpam-6139	45	4	.	.	PROPN
ejpam-6139	45	5	math	math	PROPN
ejpam-6139	45	6	,	,	PUNCT
ejpam-6139	45	7	18	18	NUM
ejpam-6139	45	8	(	(	PUNCT
ejpam-6139	45	9	4	4	NUM
ejpam-6139	45	10	)	)	PUNCT
ejpam-6139	45	11	(	(	PUNCT
ejpam-6139	45	12	2025	2025	NUM
ejpam-6139	45	13	)	)	PUNCT
ejpam-6139	45	14	,	,	PUNCT
ejpam-6139	45	15	6139	6139	NUM
ejpam-6139	45	16	3	3	NUM
ejpam-6139	45	17	of	of	ADP
ejpam-6139	45	18	34	34	NUM
ejpam-6139	45	19	convex	convex	NOUN
ejpam-6139	45	20	functions	function	NOUN
ejpam-6139	45	21	,	,	PUNCT
ejpam-6139	45	22	including	include	VERB
ejpam-6139	45	23	definitions	definition	NOUN
ejpam-6139	45	24	and	and	CCONJ
ejpam-6139	45	25	some	some	DET
ejpam-6139	45	26	properties	property	NOUN
ejpam-6139	45	27	.	.	PUNCT
ejpam-6139	46	1	section	section	NOUN
ejpam-6139	46	2	3	3	NUM
ejpam-6139	46	3	introduces	introduce	VERB
ejpam-6139	46	4	the	the	DET
ejpam-6139	46	5	new	new	ADJ
ejpam-6139	46	6	inequalities	inequality	NOUN
ejpam-6139	46	7	of	of	ADP
ejpam-6139	46	8	trapezoidal	trapezoidal	ADJ
ejpam-6139	46	9	type	type	NOUN
ejpam-6139	46	10	derived	derive	VERB
ejpam-6139	46	11	by	by	ADP
ejpam-6139	46	12	using	use	VERB
ejpam-6139	46	13	extended	extended	ADJ
ejpam-6139	46	14	conformable	conformable	ADJ
ejpam-6139	46	15	fractional	fractional	ADJ
ejpam-6139	46	16	operators	operator	NOUN
ejpam-6139	46	17	along	along	ADP
ejpam-6139	46	18	with	with	ADP
ejpam-6139	46	19	generalized	generalize	VERB
ejpam-6139	46	20	twice	twice	ADJ
ejpam-6139	46	21	differentiable	differentiable	ADJ
ejpam-6139	46	22	functions	function	NOUN
ejpam-6139	46	23	.	.	PUNCT
ejpam-6139	47	1	section	section	NOUN
ejpam-6139	47	2	4	4	NUM
ejpam-6139	47	3	discusses	discuss	VERB
ejpam-6139	47	4	the	the	DET
ejpam-6139	47	5	midpoint	midpoint	NOUN
ejpam-6139	47	6	type	type	NOUN
ejpam-6139	47	7	inequalities	inequality	NOUN
ejpam-6139	47	8	similar	similar	ADJ
ejpam-6139	47	9	to	to	ADP
ejpam-6139	47	10	previous	previous	ADJ
ejpam-6139	47	11	.	.	PUNCT
ejpam-6139	48	1	finally	finally	ADV
ejpam-6139	48	2	,	,	PUNCT
ejpam-6139	48	3	section	section	NOUN
ejpam-6139	48	4	5	5	NUM
ejpam-6139	48	5	wraps	wrap	NOUN
ejpam-6139	48	6	up	up	ADP
ejpam-6139	48	7	the	the	DET
ejpam-6139	48	8	paper	paper	NOUN
ejpam-6139	48	9	by	by	ADP
ejpam-6139	48	10	summarizing	summarize	VERB
ejpam-6139	48	11	the	the	DET
ejpam-6139	48	12	findings	finding	NOUN
ejpam-6139	48	13	and	and	CCONJ
ejpam-6139	48	14	proposing	propose	VERB
ejpam-6139	48	15	avenues	avenue	NOUN
ejpam-6139	48	16	for	for	ADP
ejpam-6139	48	17	future	future	ADJ
ejpam-6139	48	18	research	research	NOUN
ejpam-6139	48	19	.	.	PUNCT
ejpam-6139	49	1	2	2	X
ejpam-6139	49	2	.	.	X
ejpam-6139	49	3	preliminaries	preliminary	NOUN
ejpam-6139	49	4	in	in	ADP
ejpam-6139	49	5	this	this	DET
ejpam-6139	49	6	section	section	NOUN
ejpam-6139	49	7	,	,	PUNCT
ejpam-6139	49	8	we	we	PRON
ejpam-6139	49	9	discuss	discuss	VERB
ejpam-6139	49	10	fundamental	fundamental	ADJ
ejpam-6139	49	11	results	result	NOUN
ejpam-6139	49	12	that	that	PRON
ejpam-6139	49	13	will	will	AUX
ejpam-6139	49	14	later	later	ADV
ejpam-6139	49	15	prove	prove	VERB
ejpam-6139	49	16	beneficial	beneficial	ADJ
ejpam-6139	49	17	.	.	PUNCT
ejpam-6139	50	1	the	the	DET
ejpam-6139	50	2	first	first	ADJ
ejpam-6139	50	3	integrals	integral	NOUN
ejpam-6139	50	4	to	to	PART
ejpam-6139	50	5	be	be	AUX
ejpam-6139	50	6	described	describe	VERB
ejpam-6139	50	7	are	be	AUX
ejpam-6139	50	8	the	the	DET
ejpam-6139	50	9	riemann	riemann	PROPN
ejpam-6139	50	10	-	-	PUNCT
ejpam-6139	50	11	liouville	liouville	NOUN
ejpam-6139	50	12	integrals	integral	NOUN
ejpam-6139	50	13	[	[	X
ejpam-6139	50	14	38	38	NUM
ejpam-6139	50	15	]	]	PUNCT
ejpam-6139	50	16	.	.	PUNCT
ejpam-6139	51	1	additionally	additionally	ADV
ejpam-6139	51	2	,	,	PUNCT
ejpam-6139	51	3	we	we	PRON
ejpam-6139	51	4	recall	recall	VERB
ejpam-6139	51	5	the	the	DET
ejpam-6139	51	6	extended	extended	ADJ
ejpam-6139	51	7	conformable	conformable	ADJ
ejpam-6139	51	8	operators	operator	NOUN
ejpam-6139	51	9	[	[	X
ejpam-6139	51	10	39	39	NUM
ejpam-6139	51	11	]	]	PUNCT
ejpam-6139	51	12	,	,	PUNCT
ejpam-6139	51	13	which	which	PRON
ejpam-6139	51	14	are	be	AUX
ejpam-6139	51	15	well	well	ADV
ejpam-6139	51	16	documented	document	VERB
ejpam-6139	51	17	in	in	ADP
ejpam-6139	51	18	the	the	DET
ejpam-6139	51	19	literature	literature	NOUN
ejpam-6139	51	20	and	and	CCONJ
ejpam-6139	51	21	serves	serve	VERB
ejpam-6139	51	22	as	as	ADP
ejpam-6139	51	23	a	a	DET
ejpam-6139	51	24	crucial	crucial	ADJ
ejpam-6139	51	25	building	building	NOUN
ejpam-6139	51	26	block	block	NOUN
ejpam-6139	51	27	for	for	ADP
ejpam-6139	51	28	this	this	DET
ejpam-6139	51	29	paper	paper	NOUN
ejpam-6139	51	30	.	.	PUNCT
ejpam-6139	52	1	since	since	SCONJ
ejpam-6139	52	2	the	the	DET
ejpam-6139	52	3	beta	beta	NOUN
ejpam-6139	52	4	and	and	CCONJ
ejpam-6139	52	5	gamma	gamma	NOUN
ejpam-6139	52	6	functions	function	NOUN
ejpam-6139	52	7	[	[	X
ejpam-6139	52	8	40	40	NUM
ejpam-6139	52	9	]	]	PUNCT
ejpam-6139	52	10	are	be	AUX
ejpam-6139	52	11	key	key	ADJ
ejpam-6139	52	12	components	component	NOUN
ejpam-6139	52	13	of	of	ADP
ejpam-6139	52	14	fractional	fractional	ADJ
ejpam-6139	52	15	calculus	calculus	NOUN
ejpam-6139	52	16	,	,	PUNCT
ejpam-6139	52	17	both	both	PRON
ejpam-6139	52	18	are	be	AUX
ejpam-6139	52	19	discussed	discuss	VERB
ejpam-6139	52	20	here	here	ADV
ejpam-6139	52	21	.	.	PUNCT
ejpam-6139	53	1	definition	definition	NOUN
ejpam-6139	53	2	1	1	NUM
ejpam-6139	53	3	.	.	PUNCT
ejpam-6139	54	1	for	for	ADP
ejpam-6139	54	2	positive	positive	ADJ
ejpam-6139	54	3	real	real	ADJ
ejpam-6139	54	4	numbers	number	NOUN
ejpam-6139	54	5	ζ	ζ	NOUN
ejpam-6139	54	6	and	and	CCONJ
ejpam-6139	54	7	η	η	PROPN
ejpam-6139	54	8	,	,	PUNCT
ejpam-6139	54	9	the	the	DET
ejpam-6139	54	10	gamma	gamma	NOUN
ejpam-6139	54	11	function	function	PROPN
ejpam-6139	54	12	γ(ζ	γ(ζ	PROPN
ejpam-6139	54	13	)	)	PUNCT
ejpam-6139	54	14	and	and	CCONJ
ejpam-6139	54	15	incomplete	incomplete	ADJ
ejpam-6139	54	16	beta	beta	NOUN
ejpam-6139	54	17	function	function	NOUN
ejpam-6139	54	18	β(ζ	β(ζ	PROPN
ejpam-6139	54	19	,	,	PUNCT
ejpam-6139	54	20	η	η	NOUN
ejpam-6139	54	21	,	,	PUNCT
ejpam-6139	54	22	r	r	NOUN
ejpam-6139	54	23	)	)	PUNCT
ejpam-6139	54	24	are	be	AUX
ejpam-6139	54	25	defined	define	VERB
ejpam-6139	54	26	as	as	ADP
ejpam-6139	54	27	γ(ζ	γ(ζ	NOUN
ejpam-6139	54	28	)	)	PUNCT
ejpam-6139	54	29	=	=	SYM
ejpam-6139	55	1	∫	∫	PROPN
ejpam-6139	55	2	∞	∞	PROPN
ejpam-6139	55	3	0	0	NUM
ejpam-6139	55	4	φζ−1e−φ	φζ−1e−φ	ADP
ejpam-6139	55	5	dφ	dφ	ADP
ejpam-6139	55	6	and	and	CCONJ
ejpam-6139	55	7	β(ζ	β(ζ	PROPN
ejpam-6139	55	8	,	,	PUNCT
ejpam-6139	55	9	η	η	NOUN
ejpam-6139	55	10	,	,	PUNCT
ejpam-6139	55	11	r	r	NOUN
ejpam-6139	55	12	)	)	PUNCT
ejpam-6139	55	13	=	=	SYM
ejpam-6139	56	1	∫	∫	PROPN
ejpam-6139	56	2	r	r	NOUN
ejpam-6139	56	3	0	0	NUM
ejpam-6139	56	4	φζ−1(1−	φζ−1(1−	ADJ
ejpam-6139	56	5	φ)η−1	φ)η−1	NOUN
ejpam-6139	56	6	dφ	dφ	ADP
ejpam-6139	56	7	,	,	PUNCT
ejpam-6139	56	8	respectively	respectively	ADV
ejpam-6139	56	9	.	.	PUNCT
ejpam-6139	57	1	the	the	DET
ejpam-6139	57	2	riemann	riemann	PROPN
ejpam-6139	57	3	-	-	PUNCT
ejpam-6139	57	4	liouville	liouville	VERB
ejpam-6139	57	5	fractional	fractional	ADJ
ejpam-6139	57	6	integrals	integral	NOUN
ejpam-6139	57	7	[	[	X
ejpam-6139	57	8	38	38	NUM
ejpam-6139	57	9	]	]	PUNCT
ejpam-6139	57	10	are	be	AUX
ejpam-6139	57	11	attributed	attribute	VERB
ejpam-6139	57	12	to	to	ADP
ejpam-6139	57	13	mathematicians	mathematician	NOUN
ejpam-6139	57	14	bernhard	bernhard	PROPN
ejpam-6139	57	15	riemann	riemann	PROPN
ejpam-6139	57	16	and	and	CCONJ
ejpam-6139	57	17	joseph	joseph	PROPN
ejpam-6139	57	18	liouville	liouville	PROPN
ejpam-6139	57	19	while	while	SCONJ
ejpam-6139	57	20	liouville	liouville	PROPN
ejpam-6139	57	21	first	first	ADV
ejpam-6139	57	22	explored	explore	VERB
ejpam-6139	57	23	the	the	DET
ejpam-6139	57	24	concept	concept	NOUN
ejpam-6139	57	25	of	of	ADP
ejpam-6139	57	26	fractional	fractional	ADJ
ejpam-6139	57	27	calculus	calculus	NOUN
ejpam-6139	57	28	,	,	PUNCT
ejpam-6139	57	29	riemann	riemann	PROPN
ejpam-6139	57	30	’s	’s	PART
ejpam-6139	57	31	work	work	NOUN
ejpam-6139	57	32	significantly	significantly	ADV
ejpam-6139	57	33	developed	develop	VERB
ejpam-6139	57	34	the	the	DET
ejpam-6139	57	35	integral	integral	ADJ
ejpam-6139	57	36	operator	operator	NOUN
ejpam-6139	57	37	that	that	PRON
ejpam-6139	57	38	is	be	AUX
ejpam-6139	57	39	widely	widely	ADV
ejpam-6139	57	40	used	use	VERB
ejpam-6139	57	41	today	today	NOUN
ejpam-6139	57	42	as	as	ADP
ejpam-6139	57	43	the	the	DET
ejpam-6139	57	44	standard	standard	ADJ
ejpam-6139	57	45	definition	definition	NOUN
ejpam-6139	57	46	of	of	ADP
ejpam-6139	57	47	a	a	DET
ejpam-6139	57	48	fractional	fractional	ADJ
ejpam-6139	57	49	integral	integral	ADJ
ejpam-6139	57	50	.	.	PUNCT
ejpam-6139	58	1	definition	definition	NOUN
ejpam-6139	58	2	2	2	NUM
ejpam-6139	58	3	.	.	PUNCT
ejpam-6139	59	1	for	for	ADP
ejpam-6139	59	2	h	h	PROPN
ejpam-6139	59	3	∈	∈	PROPN
ejpam-6139	59	4	l1[ν	l1[ν	PROPN
ejpam-6139	59	5	,	,	PUNCT
ejpam-6139	59	6	ω	ω	PROPN
ejpam-6139	59	7	]	]	X
ejpam-6139	59	8	,	,	PUNCT
ejpam-6139	59	9	the	the	DET
ejpam-6139	59	10	riemann	riemann	PROPN
ejpam-6139	59	11	-	-	PUNCT
ejpam-6139	59	12	liouville	liouville	NOUN
ejpam-6139	59	13	integrals	integral	NOUN
ejpam-6139	59	14	jαν+h(ζ	jαν+h(ζ	PROPN
ejpam-6139	59	15	)	)	PUNCT
ejpam-6139	59	16	and	and	CCONJ
ejpam-6139	59	17	jαω−h(ζ	jαω−h(ζ	PROPN
ejpam-6139	59	18	)	)	PUNCT
ejpam-6139	60	1	of	of	ADP
ejpam-6139	60	2	order	order	NOUN
ejpam-6139	60	3	α	α	X
ejpam-6139	60	4	>	>	X
ejpam-6139	60	5	0	0	NUM
ejpam-6139	60	6	are	be	AUX
ejpam-6139	60	7	given	give	VERB
ejpam-6139	60	8	as	as	ADP
ejpam-6139	60	9	jαν+h(ζ	jαν+h(ζ	NOUN
ejpam-6139	60	10	)	)	PUNCT
ejpam-6139	61	1	=	=	SYM
ejpam-6139	61	2	1	1	NUM
ejpam-6139	61	3	γα	γα	ADP
ejpam-6139	61	4	∫	∫	PROPN
ejpam-6139	61	5	ζ	ζ	PROPN
ejpam-6139	61	6	ν	ν	NOUN
ejpam-6139	61	7	(	(	PUNCT
ejpam-6139	61	8	ζ	ζ	PROPN
ejpam-6139	61	9	−	−	PROPN
ejpam-6139	61	10	φ)α−1h(φ)dφ	φ)α−1h(φ)dφ	PROPN
ejpam-6139	61	11	,	,	PUNCT
ejpam-6139	61	12	ζ	ζ	NOUN
ejpam-6139	61	13	>	>	X
ejpam-6139	61	14	ν	ν	NOUN
ejpam-6139	61	15	,	,	PUNCT
ejpam-6139	61	16	(	(	PUNCT
ejpam-6139	61	17	1	1	NUM
ejpam-6139	61	18	)	)	PUNCT
ejpam-6139	61	19	jαω−h(ζ	jαω−h(ζ	PROPN
ejpam-6139	61	20	)	)	PUNCT
ejpam-6139	62	1	=	=	SYM
ejpam-6139	62	2	1	1	NUM
ejpam-6139	62	3	γα	γα	ADP
ejpam-6139	62	4	∫	∫	PROPN
ejpam-6139	62	5	ω	ω	PROPN
ejpam-6139	62	6	ζ	ζ	PROPN
ejpam-6139	62	7	(	(	PUNCT
ejpam-6139	62	8	φ−	φ−	PROPN
ejpam-6139	62	9	ζ)α−1h(φ)dφ	ζ)α−1h(φ)dφ	PROPN
ejpam-6139	62	10	,	,	PUNCT
ejpam-6139	62	11	ζ	ζ	PROPN
ejpam-6139	62	12	<	<	X
ejpam-6139	62	13	ω	ω	PROPN
ejpam-6139	62	14	,	,	PUNCT
ejpam-6139	62	15	(	(	PUNCT
ejpam-6139	62	16	2	2	X
ejpam-6139	62	17	)	)	PUNCT
ejpam-6139	62	18	it	it	PRON
ejpam-6139	62	19	is	be	AUX
ejpam-6139	62	20	evident	evident	ADJ
ejpam-6139	62	21	that	that	SCONJ
ejpam-6139	62	22	setting	set	VERB
ejpam-6139	62	23	α	α	NOUN
ejpam-6139	62	24	=	=	SYM
ejpam-6139	62	25	1	1	NUM
ejpam-6139	62	26	causes	cause	VERB
ejpam-6139	62	27	the	the	DET
ejpam-6139	62	28	riemann	riemann	PROPN
ejpam-6139	62	29	-	-	PUNCT
ejpam-6139	62	30	liouville	liouville	VERB
ejpam-6139	62	31	integrals	integral	NOUN
ejpam-6139	62	32	reduce	reduce	VERB
ejpam-6139	62	33	to	to	ADP
ejpam-6139	62	34	the	the	DET
ejpam-6139	62	35	standard	standard	ADJ
ejpam-6139	62	36	integrals	integral	NOUN
ejpam-6139	62	37	.	.	PUNCT
ejpam-6139	63	1	fractional	fractional	ADJ
ejpam-6139	63	2	conformable	conformable	ADJ
ejpam-6139	63	3	operators	operator	NOUN
ejpam-6139	63	4	[	[	X
ejpam-6139	63	5	41	41	NUM
ejpam-6139	63	6	]	]	PUNCT
ejpam-6139	63	7	were	be	AUX
ejpam-6139	63	8	defined	define	VERB
ejpam-6139	63	9	by	by	ADP
ejpam-6139	63	10	khalil	khalil	PROPN
ejpam-6139	63	11	et	et	PROPN
ejpam-6139	63	12	al	al	PROPN
ejpam-6139	63	13	.	.	PROPN
ejpam-6139	64	1	in	in	ADP
ejpam-6139	64	2	2014	2014	NUM
ejpam-6139	64	3	.	.	PUNCT
ejpam-6139	65	1	later	later	ADV
ejpam-6139	65	2	extended	extend	VERB
ejpam-6139	65	3	conformable	conformable	ADJ
ejpam-6139	65	4	fractional	fractional	ADJ
ejpam-6139	65	5	operators	operator	NOUN
ejpam-6139	65	6	[	[	X
ejpam-6139	65	7	39	39	NUM
ejpam-6139	65	8	]	]	PUNCT
ejpam-6139	65	9	were	be	AUX
ejpam-6139	65	10	defined	define	VERB
ejpam-6139	65	11	which	which	PRON
ejpam-6139	65	12	extend	extend	VERB
ejpam-6139	65	13	some	some	DET
ejpam-6139	65	14	new	new	ADJ
ejpam-6139	65	15	concepts	concept	NOUN
ejpam-6139	65	16	to	to	ADP
ejpam-6139	65	17	fractional	fractional	ADJ
ejpam-6139	65	18	calculus	calculus	NOUN
ejpam-6139	65	19	.	.	PUNCT
ejpam-6139	66	1	m.	m.	NOUN
ejpam-6139	66	2	samraiz	samraiz	PROPN
ejpam-6139	66	3	et	et	PROPN
ejpam-6139	66	4	al	al	PROPN
ejpam-6139	66	5	.	.	PUNCT
ejpam-6139	66	6	/	/	SYM
ejpam-6139	66	7	eur	eur	PROPN
ejpam-6139	66	8	.	.	PUNCT
ejpam-6139	67	1	j.	j.	PROPN
ejpam-6139	67	2	pure	pure	PROPN
ejpam-6139	67	3	appl	appl	PROPN
ejpam-6139	67	4	.	.	PROPN
ejpam-6139	67	5	math	math	PROPN
ejpam-6139	67	6	,	,	PUNCT
ejpam-6139	67	7	18	18	NUM
ejpam-6139	67	8	(	(	PUNCT
ejpam-6139	67	9	4	4	NUM
ejpam-6139	67	10	)	)	PUNCT
ejpam-6139	67	11	(	(	PUNCT
ejpam-6139	67	12	2025	2025	NUM
ejpam-6139	67	13	)	)	PUNCT
ejpam-6139	67	14	,	,	PUNCT
ejpam-6139	67	15	6139	6139	NUM
ejpam-6139	67	16	4	4	NUM
ejpam-6139	67	17	of	of	ADP
ejpam-6139	67	18	34	34	NUM
ejpam-6139	67	19	definition	definition	NOUN
ejpam-6139	67	20	3	3	NUM
ejpam-6139	67	21	.	.	PUNCT
ejpam-6139	68	1	for	for	ADP
ejpam-6139	68	2	h	h	PROPN
ejpam-6139	68	3	∈	∈	PROPN
ejpam-6139	68	4	l1[ν	l1[ν	PROPN
ejpam-6139	68	5	,	,	PUNCT
ejpam-6139	68	6	ω	ω	PROPN
ejpam-6139	68	7	]	]	X
ejpam-6139	68	8	,	,	PUNCT
ejpam-6139	68	9	the	the	DET
ejpam-6139	68	10	extended	extended	ADJ
ejpam-6139	68	11	fractional	fractional	ADJ
ejpam-6139	68	12	conformable	conformable	ADJ
ejpam-6139	68	13	integrals	integral	NOUN
ejpam-6139	68	14	α	α	X
ejpam-6139	68	15	k	k	PROPN
ejpam-6139	68	16	j	j	PROPN
ejpam-6139	68	17	µ	µ	PROPN
ejpam-6139	68	18	ν+h(ζ	ν+h(ζ	NOUN
ejpam-6139	68	19	)	)	PUNCT
ejpam-6139	68	20	and	and	CCONJ
ejpam-6139	68	21	α	α	PRON
ejpam-6139	68	22	k	k	PROPN
ejpam-6139	68	23	j	j	PROPN
ejpam-6139	68	24	µ	µ	PROPN
ejpam-6139	68	25	ω−h(ζ	ω−h(ζ	NOUN
ejpam-6139	68	26	)	)	PUNCT
ejpam-6139	68	27	of	of	ADP
ejpam-6139	68	28	order	order	NOUN
ejpam-6139	68	29	α	α	X
ejpam-6139	68	30	∈	∈	PROPN
ejpam-6139	68	31	c	c	X
ejpam-6139	68	32	,	,	PUNCT
ejpam-6139	68	33	re(α	re(α	PROPN
ejpam-6139	68	34	)	)	PUNCT
ejpam-6139	68	35	>	>	X
ejpam-6139	68	36	0	0	NUM
ejpam-6139	68	37	,	,	PUNCT
ejpam-6139	68	38	k	k	PROPN
ejpam-6139	68	39	>	>	X
ejpam-6139	68	40	0	0	NUM
ejpam-6139	68	41	and	and	CCONJ
ejpam-6139	68	42	µ	µ	PRON
ejpam-6139	68	43	∈	∈	NOUN
ejpam-6139	68	44	(	(	PUNCT
ejpam-6139	68	45	0	0	NUM
ejpam-6139	68	46	,	,	PUNCT
ejpam-6139	68	47	1	1	NUM
ejpam-6139	68	48	]	]	PUNCT
ejpam-6139	68	49	are	be	AUX
ejpam-6139	68	50	given	give	VERB
ejpam-6139	68	51	by	by	ADP
ejpam-6139	68	52	α	α	PROPN
ejpam-6139	68	53	k	k	PROPN
ejpam-6139	68	54	j	j	PROPN
ejpam-6139	68	55	µ	µ	PROPN
ejpam-6139	68	56	ν+h(ζ	ν+h(ζ	NOUN
ejpam-6139	68	57	)	)	PUNCT
ejpam-6139	68	58	=	=	SYM
ejpam-6139	68	59	1	1	NUM
ejpam-6139	68	60	kγk(α	kγk(α	PROPN
ejpam-6139	68	61	)	)	PUNCT
ejpam-6139	68	62	∫	∫	PROPN
ejpam-6139	69	1	ζ	ζ	PROPN
ejpam-6139	69	2	ν	ν	NOUN
ejpam-6139	69	3	(	(	PUNCT
ejpam-6139	69	4	(	(	PUNCT
ejpam-6139	69	5	ζ	ζ	NOUN
ejpam-6139	69	6	−	−	NOUN
ejpam-6139	69	7	ν)µ	ν)µ	ADV
ejpam-6139	69	8	−	−	PROPN
ejpam-6139	69	9	(	(	PUNCT
ejpam-6139	69	10	φ−	φ−	PROPN
ejpam-6139	69	11	ν)µ	ν)µ	X
ejpam-6139	69	12	µ	µ	X
ejpam-6139	69	13	)	)	PUNCT
ejpam-6139	69	14	α	α	PROPN
ejpam-6139	69	15	k	k	NOUN
ejpam-6139	69	16	−1	−1	NOUN
ejpam-6139	69	17	h(φ	h(φ	PROPN
ejpam-6139	69	18	)	)	PUNCT
ejpam-6139	69	19	(	(	PUNCT
ejpam-6139	69	20	φ−	φ−	PROPN
ejpam-6139	69	21	ν)1−µ	ν)1−µ	PROPN
ejpam-6139	69	22	dφ	dφ	ADP
ejpam-6139	69	23	,	,	PUNCT
ejpam-6139	69	24	ζ	ζ	NOUN
ejpam-6139	69	25	>	>	X
ejpam-6139	69	26	ν	ν	X
ejpam-6139	69	27	(	(	PUNCT
ejpam-6139	69	28	3	3	NUM
ejpam-6139	69	29	)	)	PUNCT
ejpam-6139	69	30	and	and	CCONJ
ejpam-6139	69	31	α	α	PRON
ejpam-6139	69	32	k	k	PROPN
ejpam-6139	69	33	j	j	PROPN
ejpam-6139	69	34	µ	µ	PROPN
ejpam-6139	69	35	ω−h(ζ	ω−h(ζ	NOUN
ejpam-6139	69	36	)	)	PUNCT
ejpam-6139	69	37	=	=	PUNCT
ejpam-6139	69	38	1	1	NUM
ejpam-6139	69	39	kγk(α	kγk(α	PROPN
ejpam-6139	69	40	)	)	PUNCT
ejpam-6139	69	41	∫	∫	PROPN
ejpam-6139	70	1	ω	ω	NUM
ejpam-6139	70	2	ζ	ζ	X
ejpam-6139	70	3	(	(	PUNCT
ejpam-6139	70	4	(	(	PUNCT
ejpam-6139	70	5	ω	ω	NOUN
ejpam-6139	70	6	−	−	NOUN
ejpam-6139	70	7	ζ)µ	ζ)µ	NOUN
ejpam-6139	70	8	−	−	PROPN
ejpam-6139	71	1	(	(	PUNCT
ejpam-6139	71	2	ω	ω	NUM
ejpam-6139	71	3	−	−	PROPN
ejpam-6139	71	4	φ)µ	φ)µ	X
ejpam-6139	71	5	µ	µ	X
ejpam-6139	71	6	)	)	PUNCT
ejpam-6139	71	7	α	α	PROPN
ejpam-6139	71	8	k	k	NOUN
ejpam-6139	71	9	−1	−1	NOUN
ejpam-6139	71	10	h(φ	h(φ	PROPN
ejpam-6139	71	11	)	)	PUNCT
ejpam-6139	71	12	(	(	PUNCT
ejpam-6139	71	13	ω	ω	NUM
ejpam-6139	71	14	−	−	NOUN
ejpam-6139	71	15	φ)1−µ	φ)1−µ	NOUN
ejpam-6139	71	16	dφ	dφ	ADP
ejpam-6139	71	17	,	,	PUNCT
ejpam-6139	71	18	ω	ω	PROPN
ejpam-6139	71	19	>	>	X
ejpam-6139	71	20	ζ	ζ	NOUN
ejpam-6139	71	21	,	,	PUNCT
ejpam-6139	71	22	(	(	PUNCT
ejpam-6139	71	23	4	4	NUM
ejpam-6139	71	24	)	)	PUNCT
ejpam-6139	71	25	where	where	SCONJ
ejpam-6139	71	26	γk(α	γk(α	NUM
ejpam-6139	71	27	)	)	PUNCT
ejpam-6139	71	28	=	=	SYM
ejpam-6139	72	1	k	k	NOUN
ejpam-6139	72	2	α	α	X
ejpam-6139	72	3	k	k	PROPN
ejpam-6139	72	4	−1γ(αk	−1γ(αk	PROPN
ejpam-6139	72	5	)	)	PUNCT
ejpam-6139	72	6	.	.	PUNCT
ejpam-6139	73	1	it	it	PRON
ejpam-6139	73	2	can	can	AUX
ejpam-6139	73	3	be	be	AUX
ejpam-6139	73	4	observed	observe	VERB
ejpam-6139	73	5	that	that	SCONJ
ejpam-6139	73	6	if	if	SCONJ
ejpam-6139	73	7	k	k	PROPN
ejpam-6139	73	8	=	=	SYM
ejpam-6139	73	9	1	1	NUM
ejpam-6139	73	10	,	,	PUNCT
ejpam-6139	73	11	equations	equation	NOUN
ejpam-6139	73	12	(	(	PUNCT
ejpam-6139	73	13	3	3	NUM
ejpam-6139	73	14	)	)	PUNCT
ejpam-6139	73	15	and	and	CCONJ
ejpam-6139	73	16	(	(	PUNCT
ejpam-6139	73	17	4	4	X
ejpam-6139	73	18	)	)	PUNCT
ejpam-6139	73	19	yield	yield	VERB
ejpam-6139	73	20	the	the	DET
ejpam-6139	73	21	ordinary	ordinary	ADJ
ejpam-6139	73	22	conformable	conformable	ADJ
ejpam-6139	73	23	operator	operator	NOUN
ejpam-6139	73	24	.	.	PUNCT
ejpam-6139	74	1	additionally	additionally	ADV
ejpam-6139	74	2	,	,	PUNCT
ejpam-6139	74	3	from	from	ADP
ejpam-6139	74	4	usual	usual	ADJ
ejpam-6139	74	5	observations	observation	NOUN
ejpam-6139	74	6	,	,	PUNCT
ejpam-6139	74	7	it	it	PRON
ejpam-6139	74	8	can	can	AUX
ejpam-6139	74	9	be	be	AUX
ejpam-6139	74	10	concluded	conclude	VERB
ejpam-6139	74	11	that	that	SCONJ
ejpam-6139	74	12	when	when	SCONJ
ejpam-6139	74	13	µ	µ	X
ejpam-6139	74	14	=	=	SYM
ejpam-6139	74	15	1	1	NUM
ejpam-6139	74	16	and	and	CCONJ
ejpam-6139	74	17	k	k	NOUN
ejpam-6139	74	18	=	=	SYM
ejpam-6139	74	19	1	1	NUM
ejpam-6139	74	20	,	,	PUNCT
ejpam-6139	74	21	equations	equation	NOUN
ejpam-6139	74	22	(	(	PUNCT
ejpam-6139	74	23	3	3	NUM
ejpam-6139	74	24	)	)	PUNCT
ejpam-6139	74	25	and	and	CCONJ
ejpam-6139	74	26	(	(	PUNCT
ejpam-6139	74	27	4	4	X
ejpam-6139	74	28	)	)	PUNCT
ejpam-6139	74	29	coincide	coincide	NOUN
ejpam-6139	74	30	with	with	ADP
ejpam-6139	74	31	(	(	PUNCT
ejpam-6139	74	32	1	1	NUM
ejpam-6139	74	33	)	)	PUNCT
ejpam-6139	74	34	and	and	CCONJ
ejpam-6139	74	35	(	(	PUNCT
ejpam-6139	74	36	2	2	X
ejpam-6139	74	37	)	)	PUNCT
ejpam-6139	74	38	respectively	respectively	ADV
ejpam-6139	74	39	.	.	PUNCT
ejpam-6139	75	1	now	now	ADV
ejpam-6139	75	2	,	,	PUNCT
ejpam-6139	75	3	we	we	PRON
ejpam-6139	75	4	proceed	proceed	VERB
ejpam-6139	75	5	to	to	PART
ejpam-6139	75	6	define	define	VERB
ejpam-6139	75	7	well	well	ADV
ejpam-6139	75	8	documented	document	VERB
ejpam-6139	75	9	concept	concept	NOUN
ejpam-6139	75	10	of	of	ADP
ejpam-6139	75	11	convex	convex	ADJ
ejpam-6139	75	12	function	function	NOUN
ejpam-6139	75	13	[	[	X
ejpam-6139	75	14	42	42	NUM
ejpam-6139	75	15	]	]	PUNCT
ejpam-6139	75	16	and	and	CCONJ
ejpam-6139	75	17	sconvex	sconvex	ADJ
ejpam-6139	75	18	function	function	NOUN
ejpam-6139	75	19	in	in	ADP
ejpam-6139	75	20	second	second	ADJ
ejpam-6139	75	21	sense	sense	NOUN
ejpam-6139	75	22	[	[	X
ejpam-6139	75	23	43	43	NUM
ejpam-6139	75	24	]	]	PUNCT
ejpam-6139	75	25	as	as	ADP
ejpam-6139	75	26	fellows	fellow	NOUN
ejpam-6139	75	27	.	.	PUNCT
ejpam-6139	76	1	definition	definition	NOUN
ejpam-6139	76	2	4	4	NUM
ejpam-6139	76	3	.	.	PUNCT
ejpam-6139	77	1	a	a	DET
ejpam-6139	77	2	function	function	NOUN
ejpam-6139	77	3	h	h	NOUN
ejpam-6139	77	4	:	:	PUNCT
ejpam-6139	78	1	[	[	X
ejpam-6139	78	2	a	a	X
ejpam-6139	78	3	,	,	PUNCT
ejpam-6139	78	4	b	b	NOUN
ejpam-6139	78	5	]	]	X
ejpam-6139	78	6	→	→	PUNCT
ejpam-6139	78	7	r	r	NOUN
ejpam-6139	78	8	is	be	AUX
ejpam-6139	78	9	called	call	VERB
ejpam-6139	78	10	convex	convex	NOUN
ejpam-6139	78	11	if	if	SCONJ
ejpam-6139	78	12	following	follow	VERB
ejpam-6139	78	13	inequality	inequality	NOUN
ejpam-6139	78	14	holds	hold	VERB
ejpam-6139	78	15	for	for	ADP
ejpam-6139	78	16	all	all	DET
ejpam-6139	78	17	x	x	NOUN
ejpam-6139	78	18	,	,	PUNCT
ejpam-6139	78	19	y	y	PROPN
ejpam-6139	78	20	∈	∈	PROPN
ejpam-6139	79	1	[	[	X
ejpam-6139	79	2	a	a	X
ejpam-6139	79	3	,	,	PUNCT
ejpam-6139	79	4	b	b	NOUN
ejpam-6139	79	5	]	]	PUNCT
ejpam-6139	79	6	and	and	CCONJ
ejpam-6139	79	7	ρ	ρ	NUM
ejpam-6139	79	8	∈	∈	PROPN
ejpam-6139	80	1	[	[	X
ejpam-6139	80	2	0	0	NUM
ejpam-6139	80	3	,	,	PUNCT
ejpam-6139	80	4	1	1	NUM
ejpam-6139	80	5	]	]	X
ejpam-6139	80	6	h(ρx+	h(ρx+	PROPN
ejpam-6139	80	7	(	(	PUNCT
ejpam-6139	80	8	1−	1−	NUM
ejpam-6139	80	9	ρ)y	ρ)y	NOUN
ejpam-6139	80	10	)	)	PUNCT
ejpam-6139	80	11	≤	≤	NOUN
ejpam-6139	80	12	ρh(x	ρh(x	NOUN
ejpam-6139	80	13	)	)	PUNCT
ejpam-6139	81	1	+	+	CCONJ
ejpam-6139	81	2	(	(	PUNCT
ejpam-6139	81	3	1−	1−	NUM
ejpam-6139	81	4	ρ)h(y	ρ)h(y	NOUN
ejpam-6139	81	5	)	)	PUNCT
ejpam-6139	81	6	.	.	PUNCT
ejpam-6139	82	1	definition	definition	NOUN
ejpam-6139	82	2	5	5	NUM
ejpam-6139	82	3	.	.	PUNCT
ejpam-6139	83	1	a	a	DET
ejpam-6139	83	2	function	function	NOUN
ejpam-6139	83	3	h	h	NOUN
ejpam-6139	83	4	:	:	PUNCT
ejpam-6139	84	1	[	[	X
ejpam-6139	84	2	0	0	NUM
ejpam-6139	84	3	,	,	PUNCT
ejpam-6139	84	4	ω	ω	NOUN
ejpam-6139	84	5	]	]	X
ejpam-6139	84	6	→	→	PUNCT
ejpam-6139	84	7	r	r	NOUN
ejpam-6139	84	8	is	be	AUX
ejpam-6139	84	9	said	say	VERB
ejpam-6139	84	10	to	to	PART
ejpam-6139	84	11	be	be	AUX
ejpam-6139	84	12	s	s	NOUN
ejpam-6139	84	13	-	-	NOUN
ejpam-6139	84	14	convex	convex	ADJ
ejpam-6139	84	15	in	in	ADP
ejpam-6139	84	16	the	the	DET
ejpam-6139	84	17	second	second	ADJ
ejpam-6139	84	18	sense	sense	NOUN
ejpam-6139	84	19	if	if	SCONJ
ejpam-6139	84	20	the	the	DET
ejpam-6139	84	21	inequality	inequality	NOUN
ejpam-6139	84	22	h(ρx+	h(ρx+	PROPN
ejpam-6139	84	23	(	(	PUNCT
ejpam-6139	84	24	1−	1−	NUM
ejpam-6139	84	25	ρ)y	ρ)y	NOUN
ejpam-6139	84	26	)	)	PUNCT
ejpam-6139	84	27	≤	≤	NOUN
ejpam-6139	84	28	ρsh(x	ρsh(x	PROPN
ejpam-6139	84	29	)	)	PUNCT
ejpam-6139	85	1	+	+	CCONJ
ejpam-6139	85	2	(	(	PUNCT
ejpam-6139	85	3	1−	1−	NUM
ejpam-6139	85	4	ρ)sh(y	ρ)sh(y	NOUN
ejpam-6139	85	5	)	)	PUNCT
ejpam-6139	86	1	,	,	PUNCT
ejpam-6139	86	2	holds	hold	VERB
ejpam-6139	86	3	for	for	ADP
ejpam-6139	86	4	all	all	DET
ejpam-6139	86	5	x	x	NOUN
ejpam-6139	86	6	,	,	PUNCT
ejpam-6139	86	7	y	y	PROPN
ejpam-6139	86	8	∈	∈	PROPN
ejpam-6139	87	1	[	[	X
ejpam-6139	87	2	0	0	NUM
ejpam-6139	87	3	,	,	PUNCT
ejpam-6139	87	4	ω	ω	NOUN
ejpam-6139	87	5	]	]	PUNCT
ejpam-6139	87	6	and	and	CCONJ
ejpam-6139	87	7	ρ	ρ	PROPN
ejpam-6139	87	8	,	,	PUNCT
ejpam-6139	87	9	s∈	s∈	NOUN
ejpam-6139	88	1	[	[	X
ejpam-6139	88	2	0	0	NUM
ejpam-6139	88	3	,	,	PUNCT
ejpam-6139	88	4	1	1	NUM
ejpam-6139	88	5	]	]	PUNCT
ejpam-6139	88	6	.	.	PUNCT
ejpam-6139	89	1	this	this	DET
ejpam-6139	89	2	class	class	NOUN
ejpam-6139	89	3	is	be	AUX
ejpam-6139	89	4	usually	usually	ADV
ejpam-6139	89	5	denoted	denote	VERB
ejpam-6139	89	6	by	by	ADP
ejpam-6139	89	7	k2	k2	PROPN
ejpam-6139	89	8	s	s	PROPN
ejpam-6139	89	9	.	.	PUNCT
ejpam-6139	90	1	let	let	VERB
ejpam-6139	90	2	us	we	PRON
ejpam-6139	90	3	review	review	VERB
ejpam-6139	90	4	hölder	hölder	PROPN
ejpam-6139	90	5	’s	’s	PART
ejpam-6139	90	6	and	and	CCONJ
ejpam-6139	90	7	power	power	NOUN
ejpam-6139	90	8	mean	mean	NOUN
ejpam-6139	90	9	inequalities	inequality	NOUN
ejpam-6139	90	10	[	[	X
ejpam-6139	90	11	37	37	NUM
ejpam-6139	90	12	]	]	PUNCT
ejpam-6139	90	13	as	as	SCONJ
ejpam-6139	90	14	follows	follow	VERB
ejpam-6139	90	15	:	:	PUNCT
ejpam-6139	90	16	definition	definition	NOUN
ejpam-6139	90	17	6	6	NUM
ejpam-6139	90	18	.	.	PUNCT
ejpam-6139	91	1	let	let	VERB
ejpam-6139	91	2	p	p	PRON
ejpam-6139	91	3	>	>	X
ejpam-6139	91	4	1	1	NUM
ejpam-6139	91	5	and	and	CCONJ
ejpam-6139	91	6	1	1	NUM
ejpam-6139	92	1	p	p	NOUN
ejpam-6139	92	2	+	+	NOUN
ejpam-6139	92	3	1	1	NUM
ejpam-6139	92	4	q	q	NOUN
ejpam-6139	92	5	=	=	NOUN
ejpam-6139	92	6	1	1	X
ejpam-6139	92	7	.	.	PUNCT
ejpam-6139	93	1	if	if	SCONJ
ejpam-6139	93	2	|h|p	|h|p	NOUN
ejpam-6139	93	3	,	,	PUNCT
ejpam-6139	93	4	|ϕ|q	|ϕ|q	PROPN
ejpam-6139	93	5	∈	∈	PROPN
ejpam-6139	93	6	l[ν	l[ν	PROPN
ejpam-6139	93	7	,	,	PUNCT
ejpam-6139	93	8	ω	ω	NOUN
ejpam-6139	93	9	]	]	X
ejpam-6139	93	10	are	be	AUX
ejpam-6139	93	11	real	real	ADJ
ejpam-6139	93	12	functions	function	NOUN
ejpam-6139	93	13	defined	define	VERB
ejpam-6139	93	14	on	on	ADP
ejpam-6139	93	15	[	[	X
ejpam-6139	93	16	ν	ν	NOUN
ejpam-6139	93	17	,	,	PUNCT
ejpam-6139	93	18	ω	ω	NOUN
ejpam-6139	93	19	]	]	X
ejpam-6139	93	20	,	,	PUNCT
ejpam-6139	93	21	then	then	ADV
ejpam-6139	93	22	∫	∫	PROPN
ejpam-6139	93	23	ω	ω	PROPN
ejpam-6139	93	24	ν	ν	PROPN
ejpam-6139	93	25	|h(x)ϕ(x)|dx	|h(x)ϕ(x)|dx	NOUN
ejpam-6139	93	26	≤	≤	NUM
ejpam-6139	93	27	(	(	PUNCT
ejpam-6139	93	28	∫	∫	PROPN
ejpam-6139	93	29	ω	ω	PROPN
ejpam-6139	93	30	ν	ν	NOUN
ejpam-6139	93	31	|h(x)|pdx	|h(x)|pdx	X
ejpam-6139	93	32	)	)	PUNCT
ejpam-6139	93	33	1	1	NUM
ejpam-6139	93	34	p	p	NOUN
ejpam-6139	93	35	(	(	PUNCT
ejpam-6139	93	36	∫	∫	PROPN
ejpam-6139	93	37	ω	ω	PROPN
ejpam-6139	93	38	ν	ν	NOUN
ejpam-6139	93	39	|ϕ(x)|qdx	|ϕ(x)|qdx	X
ejpam-6139	93	40	)	)	PUNCT
ejpam-6139	93	41	1	1	NUM
ejpam-6139	93	42	q	q	NOUN
ejpam-6139	93	43	.	.	PUNCT
ejpam-6139	94	1	definition	definition	NOUN
ejpam-6139	94	2	7	7	NUM
ejpam-6139	94	3	.	.	PUNCT
ejpam-6139	95	1	for	for	ADP
ejpam-6139	95	2	q	q	PROPN
ejpam-6139	95	3	≥	≥	NUM
ejpam-6139	95	4	1	1	NUM
ejpam-6139	95	5	and	and	CCONJ
ejpam-6139	95	6	1	1	NUM
ejpam-6139	95	7	p	p	NOUN
ejpam-6139	96	1	+	+	NOUN
ejpam-6139	96	2	1	1	NUM
ejpam-6139	96	3	q	q	NOUN
ejpam-6139	96	4	=	=	NOUN
ejpam-6139	96	5	1	1	X
ejpam-6139	96	6	.	.	PUNCT
ejpam-6139	97	1	if	if	SCONJ
ejpam-6139	97	2	h(x	h(x	PROPN
ejpam-6139	97	3	)	)	PUNCT
ejpam-6139	97	4	,	,	PUNCT
ejpam-6139	97	5	ϕ(x	ϕ(x	X
ejpam-6139	97	6	)	)	PUNCT
ejpam-6139	97	7	are	be	AUX
ejpam-6139	97	8	real	real	ADJ
ejpam-6139	97	9	functions	function	NOUN
ejpam-6139	97	10	defined	define	VERB
ejpam-6139	97	11	on	on	ADP
ejpam-6139	97	12	[	[	X
ejpam-6139	97	13	ν	ν	X
ejpam-6139	97	14	,	,	PUNCT
ejpam-6139	97	15	ω	ω	NOUN
ejpam-6139	97	16	]	]	X
ejpam-6139	97	17	such	such	ADJ
ejpam-6139	97	18	that	that	SCONJ
ejpam-6139	97	19	|h|p,|ϕ|q	|h|p,|ϕ|q	VERB
ejpam-6139	97	20	∈	∈	PROPN
ejpam-6139	97	21	l[ν	l[ν	NOUN
ejpam-6139	97	22	,	,	PUNCT
ejpam-6139	97	23	ω],then∫	ω],then∫	PROPN
ejpam-6139	97	24	ω	ω	NUM
ejpam-6139	97	25	ν	ν	NOUN
ejpam-6139	97	26	|h(x)ϕ(x)|dx	|h(x)ϕ(x)|dx	NOUN
ejpam-6139	97	27	≤	≤	NUM
ejpam-6139	97	28	(	(	PUNCT
ejpam-6139	97	29	∫	∫	PROPN
ejpam-6139	97	30	ω	ω	PROPN
ejpam-6139	97	31	ν	ν	X
ejpam-6139	97	32	|h(x)|dx	|h(x)|dx	NOUN
ejpam-6139	97	33	)	)	PUNCT
ejpam-6139	97	34	1−	1−	NUM
ejpam-6139	97	35	1	1	NUM
ejpam-6139	97	36	q	q	NOUN
ejpam-6139	97	37	(	(	PUNCT
ejpam-6139	97	38	∫	∫	PROPN
ejpam-6139	97	39	ω	ω	PROPN
ejpam-6139	97	40	ν	ν	X
ejpam-6139	97	41	|h(x)||ϕ(x)|qdx	|h(x)||ϕ(x)|qdx	NUM
ejpam-6139	97	42	)	)	PUNCT
ejpam-6139	97	43	1	1	NUM
ejpam-6139	97	44	q	q	NOUN
ejpam-6139	97	45	.	.	PUNCT
ejpam-6139	98	1	m.	m.	NOUN
ejpam-6139	98	2	samraiz	samraiz	PROPN
ejpam-6139	98	3	et	et	PROPN
ejpam-6139	98	4	al	al	PROPN
ejpam-6139	98	5	.	.	PUNCT
ejpam-6139	98	6	/	/	SYM
ejpam-6139	98	7	eur	eur	PROPN
ejpam-6139	98	8	.	.	PUNCT
ejpam-6139	99	1	j.	j.	PROPN
ejpam-6139	99	2	pure	pure	PROPN
ejpam-6139	99	3	appl	appl	PROPN
ejpam-6139	99	4	.	.	PROPN
ejpam-6139	99	5	math	math	PROPN
ejpam-6139	99	6	,	,	PUNCT
ejpam-6139	99	7	18	18	NUM
ejpam-6139	99	8	(	(	PUNCT
ejpam-6139	99	9	4	4	NUM
ejpam-6139	99	10	)	)	PUNCT
ejpam-6139	99	11	(	(	PUNCT
ejpam-6139	99	12	2025	2025	NUM
ejpam-6139	99	13	)	)	PUNCT
ejpam-6139	99	14	,	,	PUNCT
ejpam-6139	99	15	6139	6139	NUM
ejpam-6139	99	16	5	5	NUM
ejpam-6139	99	17	of	of	ADP
ejpam-6139	99	18	34	34	NUM
ejpam-6139	99	19	3	3	NUM
ejpam-6139	99	20	.	.	PUNCT
ejpam-6139	99	21	trapezoidal	trapezoidal	ADJ
ejpam-6139	99	22	type	type	NOUN
ejpam-6139	99	23	inequalities	inequality	NOUN
ejpam-6139	99	24	based	base	VERB
ejpam-6139	99	25	on	on	ADP
ejpam-6139	99	26	extended	extended	ADJ
ejpam-6139	99	27	conformable	conformable	ADJ
ejpam-6139	99	28	fractional	fractional	ADJ
ejpam-6139	99	29	operators	operator	NOUN
ejpam-6139	99	30	in	in	ADP
ejpam-6139	99	31	this	this	DET
ejpam-6139	99	32	section	section	NOUN
ejpam-6139	100	1	,	,	PUNCT
ejpam-6139	100	2	we	we	PRON
ejpam-6139	100	3	derive	derive	VERB
ejpam-6139	100	4	trapezoidal	trapezoidal	ADJ
ejpam-6139	100	5	-	-	PUNCT
ejpam-6139	100	6	type	type	NOUN
ejpam-6139	100	7	inequalities	inequality	NOUN
ejpam-6139	100	8	for	for	ADP
ejpam-6139	100	9	twice	twice	ADV
ejpam-6139	100	10	-	-	PUNCT
ejpam-6139	100	11	differentiable	differentiable	ADJ
ejpam-6139	100	12	functions	function	NOUN
ejpam-6139	100	13	.	.	PUNCT
ejpam-6139	101	1	by	by	ADP
ejpam-6139	101	2	employing	employ	VERB
ejpam-6139	101	3	extended	extend	VERB
ejpam-6139	101	4	conformable	conformable	ADJ
ejpam-6139	101	5	fractional	fractional	ADJ
ejpam-6139	101	6	operators	operator	NOUN
ejpam-6139	101	7	,	,	PUNCT
ejpam-6139	101	8	we	we	PRON
ejpam-6139	101	9	obtain	obtain	VERB
ejpam-6139	101	10	these	these	DET
ejpam-6139	101	11	inequalities	inequality	NOUN
ejpam-6139	101	12	.	.	PUNCT
ejpam-6139	102	1	these	these	DET
ejpam-6139	102	2	results	result	NOUN
ejpam-6139	102	3	extend	extend	VERB
ejpam-6139	102	4	classical	classical	ADJ
ejpam-6139	102	5	inequalities	inequality	NOUN
ejpam-6139	102	6	by	by	ADP
ejpam-6139	102	7	incorporating	incorporate	VERB
ejpam-6139	102	8	the	the	DET
ejpam-6139	102	9	flexibility	flexibility	NOUN
ejpam-6139	102	10	and	and	CCONJ
ejpam-6139	102	11	generality	generality	NOUN
ejpam-6139	102	12	of	of	ADP
ejpam-6139	102	13	fractional	fractional	ADJ
ejpam-6139	102	14	calculus	calculus	NOUN
ejpam-6139	102	15	.	.	PUNCT
ejpam-6139	103	1	to	to	PART
ejpam-6139	103	2	establish	establish	VERB
ejpam-6139	103	3	the	the	DET
ejpam-6139	103	4	trapezoidal	trapezoidal	ADJ
ejpam-6139	103	5	-	-	PUNCT
ejpam-6139	103	6	type	type	NOUN
ejpam-6139	103	7	inequalities	inequality	NOUN
ejpam-6139	103	8	for	for	ADP
ejpam-6139	103	9	extended	extended	ADJ
ejpam-6139	103	10	conformable	conformable	ADJ
ejpam-6139	103	11	fractional	fractional	ADJ
ejpam-6139	103	12	operators	operator	NOUN
ejpam-6139	103	13	,	,	PUNCT
ejpam-6139	103	14	we	we	PRON
ejpam-6139	103	15	consider	consider	VERB
ejpam-6139	103	16	the	the	DET
ejpam-6139	103	17	following	follow	VERB
ejpam-6139	103	18	lemma	lemma	PROPN
ejpam-6139	103	19	,	,	PUNCT
ejpam-6139	103	20	which	which	PRON
ejpam-6139	103	21	forms	form	VERB
ejpam-6139	103	22	the	the	DET
ejpam-6139	103	23	foundation	foundation	NOUN
ejpam-6139	103	24	for	for	ADP
ejpam-6139	103	25	our	our	PRON
ejpam-6139	103	26	subsequent	subsequent	ADJ
ejpam-6139	103	27	analysis	analysis	NOUN
ejpam-6139	103	28	and	and	CCONJ
ejpam-6139	103	29	results	result	NOUN
ejpam-6139	103	30	.	.	PUNCT
ejpam-6139	104	1	lemma	lemma	PROPN
ejpam-6139	104	2	1	1	X
ejpam-6139	104	3	.	.	PUNCT
ejpam-6139	104	4	consider	consider	VERB
ejpam-6139	104	5	a	a	DET
ejpam-6139	104	6	function	function	NOUN
ejpam-6139	104	7	h	h	NOUN
ejpam-6139	104	8	:	:	PUNCT
ejpam-6139	105	1	[	[	X
ejpam-6139	105	2	ν	ν	X
ejpam-6139	105	3	,	,	PUNCT
ejpam-6139	105	4	ω	ω	NOUN
ejpam-6139	105	5	]	]	X
ejpam-6139	105	6	→	→	PUNCT
ejpam-6139	105	7	r	r	NOUN
ejpam-6139	105	8	that	that	PRON
ejpam-6139	105	9	is	be	AUX
ejpam-6139	105	10	twice	twice	ADV
ejpam-6139	105	11	differentiable	differentiable	ADJ
ejpam-6139	105	12	on	on	ADP
ejpam-6139	105	13	(	(	PUNCT
ejpam-6139	105	14	ν	ν	PROPN
ejpam-6139	105	15	,	,	PUNCT
ejpam-6139	105	16	ω	ω	NUM
ejpam-6139	105	17	)	)	PUNCT
ejpam-6139	105	18	and	and	CCONJ
ejpam-6139	105	19	satisfies	satisfy	VERB
ejpam-6139	105	20	h′′	h′′	PROPN
ejpam-6139	105	21	∈	∈	PROPN
ejpam-6139	105	22	l1([ν	l1([ν	PROPN
ejpam-6139	105	23	,	,	PUNCT
ejpam-6139	105	24	ω	ω	NOUN
ejpam-6139	105	25	]	]	NOUN
ejpam-6139	105	26	)	)	PUNCT
ejpam-6139	105	27	.	.	PUNCT
ejpam-6139	106	1	in	in	ADP
ejpam-6139	106	2	this	this	DET
ejpam-6139	106	3	context	context	NOUN
ejpam-6139	106	4	,	,	PUNCT
ejpam-6139	106	5	the	the	DET
ejpam-6139	106	6	following	follow	VERB
ejpam-6139	106	7	equality	equality	NOUN
ejpam-6139	106	8	is	be	AUX
ejpam-6139	106	9	established	establish	VERB
ejpam-6139	106	10	h(ν	h(ν	NOUN
ejpam-6139	106	11	)	)	PUNCT
ejpam-6139	106	12	+	+	CCONJ
ejpam-6139	106	13	h(ω	h(ω	PROPN
ejpam-6139	106	14	)	)	PUNCT
ejpam-6139	106	15	η	η	PROPN
ejpam-6139	106	16	+	+	PROPN
ejpam-6139	106	17	ϕk(µ	ϕk(µ	NUM
ejpam-6139	106	18	,	,	PUNCT
ejpam-6139	106	19	α)−	α)−	PROPN
ejpam-6139	106	20	η	η	PROPN
ejpam-6139	106	21	µα	µα	ADP
ejpam-6139	106	22	k	k	PROPN
ejpam-6139	106	23	−1	−1	NOUN
ejpam-6139	106	24	(	(	PUNCT
ejpam-6139	106	25	ω	ω	NOUN
ejpam-6139	106	26	−	−	NOUN
ejpam-6139	106	27	ν	ν	NOUN
ejpam-6139	106	28	)	)	PUNCT
ejpam-6139	106	29	µα	µα	ADP
ejpam-6139	106	30	k	k	PROPN
ejpam-6139	106	31	(	(	PUNCT
ejpam-6139	106	32	kµ	kµ	PROPN
ejpam-6139	106	33	)	)	PUNCT
ejpam-6139	106	34	α	α	PROPN
ejpam-6139	106	35	k	k	PROPN
ejpam-6139	106	36	γ	γ	X
ejpam-6139	106	37	(	(	PUNCT
ejpam-6139	106	38	α	α	NOUN
ejpam-6139	106	39	k	k	PROPN
ejpam-6139	107	1	+	+	PROPN
ejpam-6139	107	2	1	1	X
ejpam-6139	107	3	)	)	PUNCT
ejpam-6139	107	4	×	×	NOUN
ejpam-6139	107	5	(	(	PUNCT
ejpam-6139	107	6	α	α	PROPN
ejpam-6139	107	7	kj	kj	PROPN
ejpam-6139	107	8	µ	µ	PROPN
ejpam-6139	107	9	(	(	PUNCT
ejpam-6139	107	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	107	11	η	η	PROPN
ejpam-6139	107	12	−	−	PROPN
ejpam-6139	107	13	h(ν	h(ν	PROPN
ejpam-6139	107	14	)	)	PUNCT
ejpam-6139	108	1	+	+	NOUN
ejpam-6139	108	2	α	α	PROPN
ejpam-6139	108	3	k	k	X
ejpam-6139	108	4	jµ	jµ	PROPN
ejpam-6139	108	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	108	6	η	η	PROPN
ejpam-6139	108	7	+	+	PROPN
ejpam-6139	108	8	h(ω	h(ω	PROPN
ejpam-6139	108	9	)	)	PUNCT
ejpam-6139	108	10	)	)	PUNCT
ejpam-6139	109	1	=	=	PUNCT
ejpam-6139	109	2	(	(	PUNCT
ejpam-6139	109	3	ω	ω	NUM
ejpam-6139	109	4	−	−	X
ejpam-6139	109	5	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	109	6	)	)	PUNCT
ejpam-6139	109	7	α	α	PROPN
ejpam-6139	110	1	k	k	PROPN
ejpam-6139	110	2	η3	η3	PROPN
ejpam-6139	110	3	[	[	PUNCT
ejpam-6139	110	4	∫	∫	PROPN
ejpam-6139	110	5	1	1	NUM
ejpam-6139	110	6	0	0	NUM
ejpam-6139	111	1	[	[	X
ejpam-6139	111	2	∫	∫	X
ejpam-6139	111	3	t	t	PROPN
ejpam-6139	111	4	0	0	NUM
ejpam-6139	111	5	(	(	PUNCT
ejpam-6139	111	6	1	1	NUM
ejpam-6139	111	7	(	(	PUNCT
ejpam-6139	111	8	kµ	kµ	PROPN
ejpam-6139	111	9	)	)	PUNCT
ejpam-6139	111	10	α	α	PROPN
ejpam-6139	111	11	k	k	NOUN
ejpam-6139	112	1	−	−	PROPN
ejpam-6139	112	2	(	(	PUNCT
ejpam-6139	112	3	1−	1−	NUM
ejpam-6139	112	4	(	(	PUNCT
ejpam-6139	112	5	1−	1−	NUM
ejpam-6139	112	6	φ)µ	φ)µ	NOUN
ejpam-6139	112	7	kµ	kµ	NOUN
ejpam-6139	112	8	)	)	PUNCT
ejpam-6139	112	9	α	α	PROPN
ejpam-6139	112	10	k	k	PROPN
ejpam-6139	112	11	)	)	PUNCT
ejpam-6139	113	1	dφ	dφ	ADP
ejpam-6139	113	2	]	]	PUNCT
ejpam-6139	113	3	×	×	PROPN
ejpam-6139	113	4	h′′	h′′	NOUN
ejpam-6139	113	5	(	(	PUNCT
ejpam-6139	113	6	η	η	PROPN
ejpam-6139	113	7	−	−	PROPN
ejpam-6139	113	8	t	t	PROPN
ejpam-6139	113	9	η	η	PROPN
ejpam-6139	113	10	ν	ν	PROPN
ejpam-6139	113	11	+	+	PROPN
ejpam-6139	113	12	t	t	PROPN
ejpam-6139	113	13	η	η	PROPN
ejpam-6139	113	14	ω	ω	PROPN
ejpam-6139	113	15	)	)	PUNCT
ejpam-6139	113	16	dt	dt	PUNCT
ejpam-6139	114	1	+	+	CCONJ
ejpam-6139	114	2	∫	∫	PROPN
ejpam-6139	114	3	1	1	NUM
ejpam-6139	114	4	0	0	NUM
ejpam-6139	115	1	[	[	X
ejpam-6139	115	2	∫	∫	X
ejpam-6139	115	3	t	t	PROPN
ejpam-6139	115	4	0	0	NUM
ejpam-6139	115	5	(	(	PUNCT
ejpam-6139	115	6	1	1	NUM
ejpam-6139	115	7	(	(	PUNCT
ejpam-6139	115	8	kµ	kµ	PROPN
ejpam-6139	115	9	)	)	PUNCT
ejpam-6139	115	10	α	α	PROPN
ejpam-6139	115	11	k	k	NOUN
ejpam-6139	116	1	−	−	PROPN
ejpam-6139	116	2	(	(	PUNCT
ejpam-6139	116	3	1−	1−	NUM
ejpam-6139	116	4	(	(	PUNCT
ejpam-6139	116	5	1−	1−	NUM
ejpam-6139	116	6	φ)µ	φ)µ	NOUN
ejpam-6139	116	7	kµ	kµ	NOUN
ejpam-6139	116	8	)	)	PUNCT
ejpam-6139	116	9	α	α	PROPN
ejpam-6139	116	10	k	k	PROPN
ejpam-6139	116	11	)	)	PUNCT
ejpam-6139	117	1	dφ	dφ	ADP
ejpam-6139	117	2	]	]	PUNCT
ejpam-6139	117	3	h′′	h′′	PROPN
ejpam-6139	117	4	(	(	PUNCT
ejpam-6139	117	5	t	t	PROPN
ejpam-6139	117	6	η	η	PROPN
ejpam-6139	117	7	ν	ν	PROPN
ejpam-6139	117	8	+	+	PROPN
ejpam-6139	117	9	η	η	PROPN
ejpam-6139	117	10	−	−	PROPN
ejpam-6139	117	11	t	t	PROPN
ejpam-6139	117	12	η	η	PROPN
ejpam-6139	117	13	ω	ω	PROPN
ejpam-6139	117	14	)	)	PUNCT
ejpam-6139	117	15	dt	dt	X
ejpam-6139	117	16	]	]	PUNCT
ejpam-6139	117	17	,	,	PUNCT
ejpam-6139	117	18	(	(	PUNCT
ejpam-6139	117	19	5	5	X
ejpam-6139	117	20	)	)	PUNCT
ejpam-6139	118	1	where	where	SCONJ
ejpam-6139	118	2	ϕk(µ	ϕk(µ	NUM
ejpam-6139	118	3	,	,	PUNCT
ejpam-6139	118	4	α	α	X
ejpam-6139	118	5	)	)	PUNCT
ejpam-6139	118	6	=	=	SYM
ejpam-6139	118	7	ω	ω	NUM
ejpam-6139	118	8	−	−	NOUN
ejpam-6139	119	1	ν	ν	NOUN
ejpam-6139	119	2	η2	η2	PROPN
ejpam-6139	119	3	(	(	PUNCT
ejpam-6139	119	4	kµ	kµ	PROPN
ejpam-6139	119	5	)	)	PUNCT
ejpam-6139	119	6	α	α	PROPN
ejpam-6139	119	7	k	k	X
ejpam-6139	120	1	[	[	PUNCT
ejpam-6139	120	2	h′	h′	X
ejpam-6139	120	3	(	(	PUNCT
ejpam-6139	120	4	η	η	PROPN
ejpam-6139	120	5	−	−	PROPN
ejpam-6139	120	6	1	1	NUM
ejpam-6139	120	7	η	η	PROPN
ejpam-6139	120	8	ν	ν	X
ejpam-6139	120	9	+	+	PROPN
ejpam-6139	120	10	1	1	NUM
ejpam-6139	120	11	η	η	PROPN
ejpam-6139	120	12	ω	ω	PROPN
ejpam-6139	120	13	)	)	PUNCT
ejpam-6139	120	14	−	−	PROPN
ejpam-6139	120	15	h′	h′	PROPN
ejpam-6139	120	16	(	(	PUNCT
ejpam-6139	120	17	ν	ν	PROPN
ejpam-6139	120	18	η	η	PROPN
ejpam-6139	120	19	+	+	PROPN
ejpam-6139	120	20	η	η	PROPN
ejpam-6139	120	21	−	−	PROPN
ejpam-6139	120	22	1	1	NUM
ejpam-6139	120	23	η	η	PROPN
ejpam-6139	120	24	ω	ω	PROPN
ejpam-6139	120	25	)	)	PUNCT
ejpam-6139	120	26	]	]	PUNCT
ejpam-6139	121	1	×	×	NOUN
ejpam-6139	121	2	[	[	X
ejpam-6139	121	3	∫	∫	PROPN
ejpam-6139	121	4	1	1	NUM
ejpam-6139	121	5	0	0	NUM
ejpam-6139	121	6	(	(	PUNCT
ejpam-6139	121	7	1	1	NUM
ejpam-6139	121	8	(	(	PUNCT
ejpam-6139	121	9	kµ	kµ	PROPN
ejpam-6139	121	10	)	)	PUNCT
ejpam-6139	121	11	α	α	PROPN
ejpam-6139	121	12	k	k	NOUN
ejpam-6139	122	1	−	−	PROPN
ejpam-6139	122	2	(	(	PUNCT
ejpam-6139	122	3	1−	1−	NUM
ejpam-6139	122	4	(	(	PUNCT
ejpam-6139	122	5	1−	1−	NUM
ejpam-6139	122	6	φ)µ	φ)µ	NOUN
ejpam-6139	122	7	kµ	kµ	NOUN
ejpam-6139	122	8	)	)	PUNCT
ejpam-6139	122	9	α	α	PROPN
ejpam-6139	122	10	k	k	PROPN
ejpam-6139	122	11	)	)	PUNCT
ejpam-6139	122	12	dφ	dφ	ADP
ejpam-6139	122	13	]	]	PUNCT
ejpam-6139	122	14	.	.	PUNCT
ejpam-6139	123	1	proof	proof	NOUN
ejpam-6139	123	2	.	.	PUNCT
ejpam-6139	124	1	by	by	ADP
ejpam-6139	124	2	considering	consider	VERB
ejpam-6139	124	3	the	the	DET
ejpam-6139	124	4	integral	integral	ADJ
ejpam-6139	124	5	i1	i1	PROPN
ejpam-6139	124	6	=	=	PUNCT
ejpam-6139	124	7	∫	∫	PROPN
ejpam-6139	124	8	1	1	NUM
ejpam-6139	124	9	0	0	NUM
ejpam-6139	125	1	[	[	X
ejpam-6139	125	2	∫	∫	X
ejpam-6139	125	3	t	t	PROPN
ejpam-6139	125	4	0	0	NUM
ejpam-6139	125	5	(	(	PUNCT
ejpam-6139	125	6	1	1	NUM
ejpam-6139	125	7	(	(	PUNCT
ejpam-6139	125	8	kµ	kµ	PROPN
ejpam-6139	125	9	)	)	PUNCT
ejpam-6139	125	10	α	α	PROPN
ejpam-6139	125	11	k	k	NOUN
ejpam-6139	126	1	−	−	PROPN
ejpam-6139	126	2	(	(	PUNCT
ejpam-6139	126	3	1−	1−	NUM
ejpam-6139	126	4	(	(	PUNCT
ejpam-6139	126	5	1−	1−	NUM
ejpam-6139	126	6	φ)µ	φ)µ	NOUN
ejpam-6139	126	7	kµ	kµ	NOUN
ejpam-6139	126	8	)	)	PUNCT
ejpam-6139	126	9	α	α	PROPN
ejpam-6139	126	10	k	k	PROPN
ejpam-6139	126	11	)	)	PUNCT
ejpam-6139	126	12	dφ	dφ	ADP
ejpam-6139	126	13	]	]	PUNCT
ejpam-6139	126	14	h′′	h′′	PROPN
ejpam-6139	126	15	(	(	PUNCT
ejpam-6139	126	16	η	η	PROPN
ejpam-6139	126	17	−	−	PROPN
ejpam-6139	126	18	t	t	PROPN
ejpam-6139	126	19	η	η	PROPN
ejpam-6139	126	20	ν	ν	PROPN
ejpam-6139	126	21	+	+	PROPN
ejpam-6139	126	22	t	t	PROPN
ejpam-6139	126	23	η	η	PROPN
ejpam-6139	126	24	ω	ω	PROPN
ejpam-6139	126	25	)	)	PUNCT
ejpam-6139	127	1	dt	dt	X
ejpam-6139	127	2	.	.	PUNCT
ejpam-6139	128	1	using	use	VERB
ejpam-6139	128	2	the	the	DET
ejpam-6139	128	3	technique	technique	NOUN
ejpam-6139	128	4	of	of	ADP
ejpam-6139	128	5	integration	integration	NOUN
ejpam-6139	128	6	by	by	ADP
ejpam-6139	128	7	parts	part	NOUN
ejpam-6139	128	8	,	,	PUNCT
ejpam-6139	128	9	it	it	PRON
ejpam-6139	128	10	yields	yield	VERB
ejpam-6139	128	11	i1	i1	PROPN
ejpam-6139	128	12	=	=	PROPN
ejpam-6139	128	13	η	η	PROPN
ejpam-6139	128	14	ω	ω	PROPN
ejpam-6139	128	15	−	−	PROPN
ejpam-6139	128	16	ν	ν	X
ejpam-6139	128	17	h′	h′	X
ejpam-6139	128	18	(	(	PUNCT
ejpam-6139	128	19	η	η	PROPN
ejpam-6139	128	20	−	−	PROPN
ejpam-6139	128	21	1	1	NUM
ejpam-6139	128	22	η	η	PROPN
ejpam-6139	128	23	ν	ν	X
ejpam-6139	128	24	+	+	PROPN
ejpam-6139	128	25	1	1	NUM
ejpam-6139	128	26	η	η	PROPN
ejpam-6139	128	27	ω	ω	PROPN
ejpam-6139	128	28	)	)	PUNCT
ejpam-6139	128	29	∫	∫	PROPN
ejpam-6139	128	30	1	1	NUM
ejpam-6139	128	31	0	0	NUM
ejpam-6139	128	32	(	(	PUNCT
ejpam-6139	128	33	1	1	NUM
ejpam-6139	128	34	(	(	PUNCT
ejpam-6139	128	35	kµ	kµ	PROPN
ejpam-6139	128	36	)	)	PUNCT
ejpam-6139	128	37	α	α	PROPN
ejpam-6139	129	1	k	k	NOUN
ejpam-6139	130	1	−	−	PROPN
ejpam-6139	130	2	(	(	PUNCT
ejpam-6139	130	3	1−	1−	NUM
ejpam-6139	130	4	(	(	PUNCT
ejpam-6139	130	5	1−	1−	NUM
ejpam-6139	130	6	φ)µ	φ)µ	NOUN
ejpam-6139	130	7	kµ	kµ	NOUN
ejpam-6139	130	8	)	)	PUNCT
ejpam-6139	130	9	α	α	PROPN
ejpam-6139	130	10	k	k	PROPN
ejpam-6139	130	11	)	)	PUNCT
ejpam-6139	131	1	dφ	dφ	ADP
ejpam-6139	131	2	−	−	PROPN
ejpam-6139	131	3	η	η	PROPN
ejpam-6139	131	4	ω	ω	PROPN
ejpam-6139	131	5	−	−	PROPN
ejpam-6139	131	6	ν	ν	X
ejpam-6139	131	7	∫	∫	PROPN
ejpam-6139	131	8	1	1	NUM
ejpam-6139	131	9	0	0	NUM
ejpam-6139	131	10	(	(	PUNCT
ejpam-6139	131	11	1	1	NUM
ejpam-6139	131	12	(	(	PUNCT
ejpam-6139	131	13	kµ	kµ	PROPN
ejpam-6139	131	14	)	)	PUNCT
ejpam-6139	131	15	α	α	PROPN
ejpam-6139	131	16	k	k	NOUN
ejpam-6139	132	1	−	−	PROPN
ejpam-6139	132	2	(	(	PUNCT
ejpam-6139	132	3	1−	1−	NUM
ejpam-6139	132	4	(	(	PUNCT
ejpam-6139	132	5	1−	1−	NUM
ejpam-6139	132	6	t)µ	t)µ	NOUN
ejpam-6139	132	7	kµ	kµ	NOUN
ejpam-6139	132	8	)	)	PUNCT
ejpam-6139	132	9	α	α	PROPN
ejpam-6139	132	10	k	k	PROPN
ejpam-6139	132	11	)	)	PUNCT
ejpam-6139	132	12	h′	h′	PROPN
ejpam-6139	132	13	(	(	PUNCT
ejpam-6139	132	14	η	η	PROPN
ejpam-6139	132	15	−	−	PROPN
ejpam-6139	132	16	t	t	PROPN
ejpam-6139	132	17	η	η	PROPN
ejpam-6139	132	18	ν	ν	PROPN
ejpam-6139	132	19	+	+	PROPN
ejpam-6139	132	20	t	t	PROPN
ejpam-6139	132	21	η	η	PROPN
ejpam-6139	132	22	ω	ω	PROPN
ejpam-6139	132	23	)	)	PUNCT
ejpam-6139	132	24	dt	dt	PROPN
ejpam-6139	132	25	.	.	PUNCT
ejpam-6139	132	26	m.	m.	PROPN
ejpam-6139	132	27	samraiz	samraiz	PROPN
ejpam-6139	132	28	et	et	PROPN
ejpam-6139	132	29	al	al	PROPN
ejpam-6139	132	30	.	.	PUNCT
ejpam-6139	132	31	/	/	SYM
ejpam-6139	132	32	eur	eur	PROPN
ejpam-6139	132	33	.	.	PUNCT
ejpam-6139	133	1	j.	j.	PROPN
ejpam-6139	133	2	pure	pure	PROPN
ejpam-6139	133	3	appl	appl	PROPN
ejpam-6139	133	4	.	.	PROPN
ejpam-6139	133	5	math	math	PROPN
ejpam-6139	133	6	,	,	PUNCT
ejpam-6139	133	7	18	18	NUM
ejpam-6139	133	8	(	(	PUNCT
ejpam-6139	133	9	4	4	NUM
ejpam-6139	133	10	)	)	PUNCT
ejpam-6139	133	11	(	(	PUNCT
ejpam-6139	133	12	2025	2025	NUM
ejpam-6139	133	13	)	)	PUNCT
ejpam-6139	133	14	,	,	PUNCT
ejpam-6139	133	15	6139	6139	NUM
ejpam-6139	133	16	6	6	NUM
ejpam-6139	133	17	of	of	ADP
ejpam-6139	133	18	34	34	NUM
ejpam-6139	133	19	again	again	ADV
ejpam-6139	134	1	,	,	PUNCT
ejpam-6139	134	2	we	we	PRON
ejpam-6139	134	3	apply	apply	VERB
ejpam-6139	134	4	the	the	DET
ejpam-6139	134	5	technique	technique	NOUN
ejpam-6139	134	6	of	of	ADP
ejpam-6139	134	7	integration	integration	NOUN
ejpam-6139	134	8	by	by	ADP
ejpam-6139	134	9	parts	part	NOUN
ejpam-6139	134	10	to	to	ADP
ejpam-6139	134	11	the	the	DET
ejpam-6139	134	12	second	second	ADJ
ejpam-6139	134	13	term	term	NOUN
ejpam-6139	134	14	;	;	PUNCT
ejpam-6139	134	15	therefore	therefore	ADV
ejpam-6139	134	16	,	,	PUNCT
ejpam-6139	134	17	we	we	PRON
ejpam-6139	134	18	obtain	obtain	VERB
ejpam-6139	134	19	the	the	DET
ejpam-6139	134	20	following	follow	VERB
ejpam-6139	134	21	expression	expression	NOUN
ejpam-6139	134	22	i1	i1	PROPN
ejpam-6139	134	23	=	=	PROPN
ejpam-6139	134	24	η	η	PROPN
ejpam-6139	134	25	ω	ω	PROPN
ejpam-6139	134	26	−	−	PROPN
ejpam-6139	134	27	ν	ν	X
ejpam-6139	134	28	h′	h′	X
ejpam-6139	134	29	(	(	PUNCT
ejpam-6139	134	30	η	η	PROPN
ejpam-6139	134	31	−	−	PROPN
ejpam-6139	134	32	1	1	NUM
ejpam-6139	134	33	η	η	PROPN
ejpam-6139	134	34	ν	ν	X
ejpam-6139	134	35	+	+	PROPN
ejpam-6139	134	36	1	1	NUM
ejpam-6139	134	37	η	η	PROPN
ejpam-6139	134	38	ω	ω	PROPN
ejpam-6139	134	39	)	)	PUNCT
ejpam-6139	134	40	∫	∫	PROPN
ejpam-6139	134	41	1	1	NUM
ejpam-6139	134	42	0	0	NUM
ejpam-6139	134	43	(	(	PUNCT
ejpam-6139	134	44	1	1	NUM
ejpam-6139	134	45	(	(	PUNCT
ejpam-6139	134	46	kµ	kµ	PROPN
ejpam-6139	134	47	)	)	PUNCT
ejpam-6139	134	48	α	α	PROPN
ejpam-6139	135	1	k	k	NOUN
ejpam-6139	136	1	−	−	PROPN
ejpam-6139	136	2	(	(	PUNCT
ejpam-6139	136	3	1−	1−	NUM
ejpam-6139	136	4	(	(	PUNCT
ejpam-6139	136	5	1−	1−	NUM
ejpam-6139	136	6	φ)µ	φ)µ	NOUN
ejpam-6139	136	7	kµ	kµ	NOUN
ejpam-6139	136	8	)	)	PUNCT
ejpam-6139	136	9	α	α	PROPN
ejpam-6139	136	10	k	k	PROPN
ejpam-6139	136	11	)	)	PUNCT
ejpam-6139	137	1	dφ	dφ	ADP
ejpam-6139	137	2	+	+	CCONJ
ejpam-6139	137	3	(	(	PUNCT
ejpam-6139	137	4	η	η	PROPN
ejpam-6139	137	5	ω	ω	PROPN
ejpam-6139	137	6	−	−	PROPN
ejpam-6139	137	7	ν	ν	NOUN
ejpam-6139	137	8	)	)	PUNCT
ejpam-6139	137	9	2	2	NUM
ejpam-6139	137	10	h(ν	h(ν	NOUN
ejpam-6139	137	11	)	)	PUNCT
ejpam-6139	137	12	1	1	NUM
ejpam-6139	137	13	(	(	PUNCT
ejpam-6139	137	14	ku	ku	PROPN
ejpam-6139	137	15	)	)	PUNCT
ejpam-6139	137	16	α	α	PROPN
ejpam-6139	137	17	k	k	NOUN
ejpam-6139	138	1	−	−	PROPN
ejpam-6139	138	2	(	(	PUNCT
ejpam-6139	138	3	η	η	PROPN
ejpam-6139	138	4	ω	ω	PROPN
ejpam-6139	138	5	−	−	PROPN
ejpam-6139	138	6	ν	ν	NOUN
ejpam-6139	138	7	)	)	PUNCT
ejpam-6139	138	8	2	2	NUM
ejpam-6139	138	9	1	1	NUM
ejpam-6139	138	10	k	k	NOUN
ejpam-6139	138	11	(	(	PUNCT
ejpam-6139	138	12	α	α	NOUN
ejpam-6139	138	13	k	k	PROPN
ejpam-6139	138	14	)	)	PUNCT
ejpam-6139	138	15	∫	∫	PROPN
ejpam-6139	139	1	1	1	NUM
ejpam-6139	139	2	0	0	NUM
ejpam-6139	139	3	[	[	PUNCT
ejpam-6139	139	4	1−	1−	NUM
ejpam-6139	139	5	(	(	PUNCT
ejpam-6139	139	6	1−	1−	NUM
ejpam-6139	139	7	t)µ	t)µ	NOUN
ejpam-6139	139	8	kµ	kµ	PROPN
ejpam-6139	139	9	]	]	PUNCT
ejpam-6139	139	10	α	α	X
ejpam-6139	139	11	k	k	X
ejpam-6139	139	12	−1	−1	NOUN
ejpam-6139	139	13	(	(	PUNCT
ejpam-6139	139	14	1−	1−	NUM
ejpam-6139	139	15	t)µ−1	t)µ−1	NOUN
ejpam-6139	139	16	×	×	PROPN
ejpam-6139	139	17	h	h	PROPN
ejpam-6139	139	18	(	(	PUNCT
ejpam-6139	139	19	η	η	PROPN
ejpam-6139	139	20	−	−	PROPN
ejpam-6139	139	21	t	t	PROPN
ejpam-6139	139	22	η	η	PROPN
ejpam-6139	139	23	ν	ν	PROPN
ejpam-6139	139	24	+	+	PROPN
ejpam-6139	139	25	t	t	PROPN
ejpam-6139	139	26	η	η	PROPN
ejpam-6139	139	27	ω	ω	PROPN
ejpam-6139	139	28	)	)	PUNCT
ejpam-6139	139	29	dt	dt	PROPN
ejpam-6139	139	30	,	,	PUNCT
ejpam-6139	139	31	(	(	PUNCT
ejpam-6139	139	32	6	6	X
ejpam-6139	139	33	)	)	PUNCT
ejpam-6139	139	34	substituting	substitute	VERB
ejpam-6139	139	35	x	x	PUNCT
ejpam-6139	139	36	=	=	SYM
ejpam-6139	139	37	η−t	η−t	PROPN
ejpam-6139	139	38	η	η	PROPN
ejpam-6139	139	39	ν	ν	PROPN
ejpam-6139	139	40	+	+	PROPN
ejpam-6139	139	41	t	t	PROPN
ejpam-6139	139	42	ηω	ηω	NOUN
ejpam-6139	139	43	,	,	PUNCT
ejpam-6139	139	44	we	we	PRON
ejpam-6139	139	45	can	can	AUX
ejpam-6139	139	46	write	write	VERB
ejpam-6139	139	47	i1	i1	PROPN
ejpam-6139	139	48	=	=	PUNCT
ejpam-6139	139	49	η	η	PROPN
ejpam-6139	139	50	ω	ω	PROPN
ejpam-6139	139	51	−	−	PROPN
ejpam-6139	139	52	ν	ν	X
ejpam-6139	139	53	h′	h′	X
ejpam-6139	139	54	(	(	PUNCT
ejpam-6139	139	55	η	η	PROPN
ejpam-6139	139	56	−	−	PROPN
ejpam-6139	139	57	1	1	NUM
ejpam-6139	139	58	η	η	PROPN
ejpam-6139	139	59	ν	ν	X
ejpam-6139	139	60	+	+	PROPN
ejpam-6139	139	61	1	1	NUM
ejpam-6139	139	62	η	η	PROPN
ejpam-6139	139	63	ω	ω	PROPN
ejpam-6139	139	64	)	)	PUNCT
ejpam-6139	139	65	∫	∫	PROPN
ejpam-6139	139	66	1	1	NUM
ejpam-6139	139	67	0	0	NUM
ejpam-6139	139	68	(	(	PUNCT
ejpam-6139	139	69	1	1	NUM
ejpam-6139	139	70	(	(	PUNCT
ejpam-6139	139	71	kµ	kµ	PROPN
ejpam-6139	139	72	)	)	PUNCT
ejpam-6139	139	73	α	α	PROPN
ejpam-6139	139	74	k	k	NOUN
ejpam-6139	140	1	−	−	PROPN
ejpam-6139	140	2	(	(	PUNCT
ejpam-6139	140	3	1−	1−	NUM
ejpam-6139	140	4	(	(	PUNCT
ejpam-6139	140	5	1−	1−	NUM
ejpam-6139	140	6	φ)µ	φ)µ	NOUN
ejpam-6139	140	7	kµ	kµ	NOUN
ejpam-6139	140	8	)	)	PUNCT
ejpam-6139	140	9	α	α	PROPN
ejpam-6139	140	10	k	k	PROPN
ejpam-6139	140	11	)	)	PUNCT
ejpam-6139	141	1	dφ	dφ	ADP
ejpam-6139	141	2	+	+	CCONJ
ejpam-6139	141	3	(	(	PUNCT
ejpam-6139	141	4	η	η	PROPN
ejpam-6139	141	5	ω	ω	PROPN
ejpam-6139	141	6	−	−	PROPN
ejpam-6139	141	7	ν	ν	NOUN
ejpam-6139	141	8	)	)	PUNCT
ejpam-6139	141	9	2	2	NUM
ejpam-6139	141	10	h(ν	h(ν	NOUN
ejpam-6139	141	11	)	)	PUNCT
ejpam-6139	141	12	1	1	NUM
ejpam-6139	141	13	(	(	PUNCT
ejpam-6139	141	14	ku	ku	PROPN
ejpam-6139	141	15	)	)	PUNCT
ejpam-6139	141	16	α	α	PROPN
ejpam-6139	141	17	k	k	NOUN
ejpam-6139	142	1	−	−	PROPN
ejpam-6139	142	2	(	(	PUNCT
ejpam-6139	142	3	η	η	PROPN
ejpam-6139	142	4	ω	ω	PROPN
ejpam-6139	142	5	−	−	PROPN
ejpam-6139	142	6	ν	ν	NOUN
ejpam-6139	142	7	)	)	PUNCT
ejpam-6139	142	8	µα	µα	ADP
ejpam-6139	142	9	k	k	PROPN
ejpam-6139	142	10	+2	+2	PROPN
ejpam-6139	142	11	(	(	PUNCT
ejpam-6139	142	12	γ	γ	X
ejpam-6139	142	13	(	(	PUNCT
ejpam-6139	142	14	α	α	NOUN
ejpam-6139	142	15	k	k	PROPN
ejpam-6139	143	1	+	+	CCONJ
ejpam-6139	143	2	1	1	X
ejpam-6139	143	3	)	)	PUNCT
ejpam-6139	143	4	k.k	k.k	PROPN
ejpam-6139	143	5	α	α	PROPN
ejpam-6139	143	6	k	k	PROPN
ejpam-6139	143	7	−1γ(αk	−1γ(αk	PROPN
ejpam-6139	143	8	)	)	PUNCT
ejpam-6139	143	9	)	)	PUNCT
ejpam-6139	144	1	×	×	NOUN
ejpam-6139	144	2	∫	∫	INTJ
ejpam-6139	144	3	(	(	PUNCT
ejpam-6139	144	4	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	144	5	η	η	PROPN
ejpam-6139	144	6	ν	ν	ADP
ejpam-6139	144	7			PROPN
ejpam-6139	144	8	(	(	PUNCT
ejpam-6139	144	9	ω−ν	ω−ν	PROPN
ejpam-6139	144	10	η	η	PROPN
ejpam-6139	144	11	)	)	PUNCT
ejpam-6139	144	12	µ	µ	NOUN
ejpam-6139	144	13	−	−	PROPN
ejpam-6139	144	14	(	(	PUNCT
ejpam-6139	144	15	(	(	PUNCT
ejpam-6139	144	16	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	144	17	η	η	PROPN
ejpam-6139	144	18	−	−	PROPN
ejpam-6139	144	19	x	x	SYM
ejpam-6139	144	20	)	)	PUNCT
ejpam-6139	144	21	µ	µ	NOUN
ejpam-6139	144	22	µ	µ	X
ejpam-6139	144	23			NOUN
ejpam-6139	144	24	α	α	NOUN
ejpam-6139	144	25	k	k	NOUN
ejpam-6139	144	26	−1	−1	NOUN
ejpam-6139	144	27	[	[	PUNCT
ejpam-6139	144	28	(	(	PUNCT
ejpam-6139	144	29	η	η	X
ejpam-6139	144	30	−	−	PROPN
ejpam-6139	144	31	1)ν	1)ν	NUM
ejpam-6139	144	32	+	+	PROPN
ejpam-6139	144	33	ω	ω	NUM
ejpam-6139	144	34	η	η	NOUN
ejpam-6139	144	35	−	−	PROPN
ejpam-6139	144	36	x	x	SYM
ejpam-6139	144	37	]	]	X
ejpam-6139	144	38	µ−1	µ−1	PROPN
ejpam-6139	144	39	dx	dx	PROPN
ejpam-6139	144	40	.	.	PUNCT
ejpam-6139	145	1	by	by	ADP
ejpam-6139	145	2	using	use	VERB
ejpam-6139	145	3	the	the	DET
ejpam-6139	145	4	relation	relation	NOUN
ejpam-6139	145	5	γk(α	γk(α	NUM
ejpam-6139	145	6	)	)	PUNCT
ejpam-6139	145	7	=	=	SYM
ejpam-6139	146	1	k	k	NOUN
ejpam-6139	146	2	α	α	X
ejpam-6139	146	3	k	k	PROPN
ejpam-6139	146	4	−1γ(αk	−1γ(αk	PROPN
ejpam-6139	146	5	)	)	PUNCT
ejpam-6139	146	6	,	,	PUNCT
ejpam-6139	146	7	we	we	PRON
ejpam-6139	146	8	can	can	AUX
ejpam-6139	146	9	write	write	VERB
ejpam-6139	146	10	i1	i1	PROPN
ejpam-6139	146	11	=	=	PUNCT
ejpam-6139	146	12	η	η	PROPN
ejpam-6139	146	13	ω	ω	PROPN
ejpam-6139	146	14	−	−	PROPN
ejpam-6139	146	15	ν	ν	X
ejpam-6139	146	16	h′	h′	X
ejpam-6139	146	17	(	(	PUNCT
ejpam-6139	146	18	η	η	PROPN
ejpam-6139	146	19	−	−	PROPN
ejpam-6139	146	20	1	1	NUM
ejpam-6139	146	21	η	η	PROPN
ejpam-6139	146	22	ν	ν	X
ejpam-6139	146	23	+	+	PROPN
ejpam-6139	146	24	1	1	NUM
ejpam-6139	146	25	η	η	PROPN
ejpam-6139	146	26	ω	ω	PROPN
ejpam-6139	146	27	)	)	PUNCT
ejpam-6139	146	28	∫	∫	PROPN
ejpam-6139	146	29	1	1	NUM
ejpam-6139	146	30	0	0	NUM
ejpam-6139	146	31	(	(	PUNCT
ejpam-6139	146	32	1	1	NUM
ejpam-6139	146	33	(	(	PUNCT
ejpam-6139	146	34	kµ	kµ	PROPN
ejpam-6139	146	35	)	)	PUNCT
ejpam-6139	146	36	α	α	PROPN
ejpam-6139	146	37	k	k	NOUN
ejpam-6139	147	1	−	−	PROPN
ejpam-6139	147	2	(	(	PUNCT
ejpam-6139	147	3	1−	1−	NUM
ejpam-6139	147	4	(	(	PUNCT
ejpam-6139	147	5	1−	1−	NUM
ejpam-6139	147	6	φ)µ	φ)µ	NOUN
ejpam-6139	147	7	kµ	kµ	NOUN
ejpam-6139	147	8	)	)	PUNCT
ejpam-6139	147	9	α	α	PROPN
ejpam-6139	147	10	k	k	PROPN
ejpam-6139	147	11	)	)	PUNCT
ejpam-6139	148	1	dφ	dφ	ADP
ejpam-6139	148	2	+	+	CCONJ
ejpam-6139	148	3	(	(	PUNCT
ejpam-6139	148	4	η	η	PROPN
ejpam-6139	148	5	ω	ω	PROPN
ejpam-6139	148	6	−	−	PROPN
ejpam-6139	148	7	ν	ν	NOUN
ejpam-6139	148	8	)	)	PUNCT
ejpam-6139	148	9	2	2	NUM
ejpam-6139	148	10	h(ν	h(ν	NOUN
ejpam-6139	148	11	)	)	PUNCT
ejpam-6139	148	12	1	1	NUM
ejpam-6139	148	13	(	(	PUNCT
ejpam-6139	148	14	ku	ku	PROPN
ejpam-6139	148	15	)	)	PUNCT
ejpam-6139	148	16	α	α	PROPN
ejpam-6139	148	17	k	k	NOUN
ejpam-6139	149	1	−	−	PROPN
ejpam-6139	149	2	(	(	PUNCT
ejpam-6139	149	3	η	η	PROPN
ejpam-6139	149	4	ω	ω	PROPN
ejpam-6139	149	5	−	−	PROPN
ejpam-6139	149	6	ν	ν	NOUN
ejpam-6139	149	7	)	)	PUNCT
ejpam-6139	149	8	µα	µα	ADP
ejpam-6139	149	9	k	k	PROPN
ejpam-6139	149	10	+2	+2	PROPN
ejpam-6139	149	11	γ	γ	X
ejpam-6139	149	12	(	(	PUNCT
ejpam-6139	149	13	α	α	NOUN
ejpam-6139	149	14	k	k	PROPN
ejpam-6139	149	15	+	+	PROPN
ejpam-6139	149	16	1	1	NUM
ejpam-6139	149	17	)	)	PUNCT
ejpam-6139	149	18	.	.	PUNCT
ejpam-6139	150	1	(	(	PUNCT
ejpam-6139	150	2	1	1	NUM
ejpam-6139	150	3	kγkα	kγkα	NOUN
ejpam-6139	150	4	)	)	PUNCT
ejpam-6139	150	5	×	×	NOUN
ejpam-6139	150	6	∫	∫	PROPN
ejpam-6139	150	7	(	(	PUNCT
ejpam-6139	150	8	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	150	9	η	η	PROPN
ejpam-6139	150	10	ν	ν	ADP
ejpam-6139	150	11			PROPN
ejpam-6139	150	12	(	(	PUNCT
ejpam-6139	150	13	(	(	PUNCT
ejpam-6139	150	14	η−1)ν+ω	η−1)ν+ω	NOUN
ejpam-6139	150	15	η	η	NOUN
ejpam-6139	150	16	−	−	PROPN
ejpam-6139	150	17	ν	ν	PROPN
ejpam-6139	150	18	)	)	PUNCT
ejpam-6139	150	19	µ	µ	NOUN
ejpam-6139	150	20	−	−	PROPN
ejpam-6139	151	1	(	(	PUNCT
ejpam-6139	151	2	(	(	PUNCT
ejpam-6139	151	3	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	151	4	η	η	PROPN
ejpam-6139	151	5	−	−	PROPN
ejpam-6139	151	6	x	x	SYM
ejpam-6139	151	7	)	)	PUNCT
ejpam-6139	151	8	µ	µ	NOUN
ejpam-6139	151	9	µ	µ	X
ejpam-6139	151	10			NOUN
ejpam-6139	151	11	α	α	PROPN
ejpam-6139	151	12	k	k	NOUN
ejpam-6139	151	13	−1	−1	NOUN
ejpam-6139	151	14			X
ejpam-6139	151	15	h(x)dx	h(x)dx	VERB
ejpam-6139	151	16	[	[	PUNCT
ejpam-6139	151	17	(	(	PUNCT
ejpam-6139	151	18	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	151	19	η	η	PROPN
ejpam-6139	151	20	−	−	PROPN
ejpam-6139	151	21	x	x	SYM
ejpam-6139	151	22	]	]	X
ejpam-6139	151	23	1−µ	1−µ	X
ejpam-6139	151	24			PROPN
ejpam-6139	151	25	.	.	PUNCT
ejpam-6139	152	1	by	by	ADP
ejpam-6139	152	2	using	use	VERB
ejpam-6139	152	3	the	the	DET
ejpam-6139	152	4	definition	definition	NOUN
ejpam-6139	152	5	of	of	ADP
ejpam-6139	152	6	extended	extended	ADJ
ejpam-6139	152	7	conformable	conformable	ADJ
ejpam-6139	152	8	operator	operator	NOUN
ejpam-6139	152	9	(	(	PUNCT
ejpam-6139	152	10	4	4	NUM
ejpam-6139	152	11	)	)	PUNCT
ejpam-6139	152	12	,	,	PUNCT
ejpam-6139	152	13	we	we	PRON
ejpam-6139	152	14	obtain	obtain	VERB
ejpam-6139	152	15	i1	i1	PROPN
ejpam-6139	152	16	=	=	SYM
ejpam-6139	152	17	η	η	PROPN
ejpam-6139	152	18	ω	ω	PROPN
ejpam-6139	152	19	−	−	PROPN
ejpam-6139	152	20	ν	ν	X
ejpam-6139	152	21	h′	h′	X
ejpam-6139	152	22	(	(	PUNCT
ejpam-6139	152	23	η	η	PROPN
ejpam-6139	152	24	−	−	PROPN
ejpam-6139	152	25	1	1	NUM
ejpam-6139	152	26	η	η	PROPN
ejpam-6139	152	27	ν	ν	X
ejpam-6139	152	28	+	+	PROPN
ejpam-6139	152	29	1	1	NUM
ejpam-6139	152	30	η	η	PROPN
ejpam-6139	152	31	ω	ω	PROPN
ejpam-6139	152	32	)	)	PUNCT
ejpam-6139	152	33	∫	∫	PROPN
ejpam-6139	152	34	1	1	NUM
ejpam-6139	152	35	0	0	NUM
ejpam-6139	152	36	(	(	PUNCT
ejpam-6139	152	37	1	1	NUM
ejpam-6139	152	38	(	(	PUNCT
ejpam-6139	152	39	kµ	kµ	PROPN
ejpam-6139	152	40	)	)	PUNCT
ejpam-6139	152	41	α	α	PROPN
ejpam-6139	152	42	k	k	NOUN
ejpam-6139	153	1	−	−	PROPN
ejpam-6139	153	2	(	(	PUNCT
ejpam-6139	153	3	1−	1−	NUM
ejpam-6139	153	4	(	(	PUNCT
ejpam-6139	153	5	1−	1−	NUM
ejpam-6139	153	6	φ)µ	φ)µ	NOUN
ejpam-6139	153	7	kµ	kµ	NOUN
ejpam-6139	153	8	)	)	PUNCT
ejpam-6139	153	9	α	α	PROPN
ejpam-6139	153	10	k	k	PROPN
ejpam-6139	153	11	)	)	PUNCT
ejpam-6139	154	1	dφ	dφ	ADP
ejpam-6139	154	2	+	+	CCONJ
ejpam-6139	154	3	(	(	PUNCT
ejpam-6139	154	4	η	η	PROPN
ejpam-6139	154	5	ω	ω	PROPN
ejpam-6139	154	6	−	−	PROPN
ejpam-6139	154	7	ν	ν	NOUN
ejpam-6139	154	8	)	)	PUNCT
ejpam-6139	154	9	2	2	NUM
ejpam-6139	154	10	h(ν	h(ν	NOUN
ejpam-6139	154	11	)	)	PUNCT
ejpam-6139	154	12	1	1	NUM
ejpam-6139	154	13	(	(	PUNCT
ejpam-6139	154	14	ku	ku	PROPN
ejpam-6139	154	15	)	)	PUNCT
ejpam-6139	154	16	α	α	PROPN
ejpam-6139	154	17	k	k	NOUN
ejpam-6139	155	1	−	−	PROPN
ejpam-6139	155	2	(	(	PUNCT
ejpam-6139	155	3	η	η	PROPN
ejpam-6139	155	4	ω	ω	PROPN
ejpam-6139	155	5	−	−	PROPN
ejpam-6139	155	6	ν	ν	NOUN
ejpam-6139	155	7	)	)	PUNCT
ejpam-6139	155	8	µα	µα	ADP
ejpam-6139	155	9	k	k	PROPN
ejpam-6139	155	10	+2	+2	PROPN
ejpam-6139	155	11	γ	γ	X
ejpam-6139	155	12	(	(	PUNCT
ejpam-6139	155	13	α	α	NOUN
ejpam-6139	155	14	k	k	PROPN
ejpam-6139	156	1	+	+	CCONJ
ejpam-6139	156	2	1	1	X
ejpam-6139	156	3	)	)	PUNCT
ejpam-6139	156	4	α	α	PROPN
ejpam-6139	156	5	k	k	PROPN
ejpam-6139	156	6	j	j	PROPN
ejpam-6139	156	7	µ	µ	X
ejpam-6139	156	8	(	(	PUNCT
ejpam-6139	156	9	η−1)ν+ω	η−1)ν+ω	NOUN
ejpam-6139	156	10	)	)	PUNCT
ejpam-6139	156	11	η	η	PROPN
ejpam-6139	156	12	−	−	NOUN
ejpam-6139	156	13	h(ν	h(ν	PROPN
ejpam-6139	156	14	)	)	PUNCT
ejpam-6139	156	15	.	.	PUNCT
ejpam-6139	157	1	(	(	PUNCT
ejpam-6139	157	2	7	7	X
ejpam-6139	157	3	)	)	PUNCT
ejpam-6139	157	4	similarly	similarly	ADV
ejpam-6139	157	5	i2	i2	PROPN
ejpam-6139	157	6	=	=	SYM
ejpam-6139	157	7	∫	∫	PROPN
ejpam-6139	157	8	1	1	NUM
ejpam-6139	157	9	0	0	NUM
ejpam-6139	158	1	[	[	X
ejpam-6139	158	2	∫	∫	X
ejpam-6139	158	3	t	t	PROPN
ejpam-6139	158	4	0	0	NUM
ejpam-6139	158	5	(	(	PUNCT
ejpam-6139	158	6	1	1	NUM
ejpam-6139	158	7	(	(	PUNCT
ejpam-6139	158	8	kµ	kµ	PROPN
ejpam-6139	158	9	)	)	PUNCT
ejpam-6139	158	10	α	α	PROPN
ejpam-6139	158	11	k	k	NOUN
ejpam-6139	159	1	−	−	PROPN
ejpam-6139	159	2	(	(	PUNCT
ejpam-6139	159	3	1−	1−	NUM
ejpam-6139	159	4	(	(	PUNCT
ejpam-6139	159	5	1−	1−	NUM
ejpam-6139	159	6	φ)µ	φ)µ	NOUN
ejpam-6139	159	7	kµ	kµ	NOUN
ejpam-6139	159	8	)	)	PUNCT
ejpam-6139	159	9	α	α	PROPN
ejpam-6139	159	10	k	k	PROPN
ejpam-6139	159	11	)	)	PUNCT
ejpam-6139	160	1	dφ	dφ	ADP
ejpam-6139	160	2	]	]	PUNCT
ejpam-6139	160	3	h′′	h′′	PROPN
ejpam-6139	160	4	(	(	PUNCT
ejpam-6139	160	5	t	t	PROPN
ejpam-6139	160	6	η	η	PROPN
ejpam-6139	160	7	ν	ν	PROPN
ejpam-6139	160	8	+	+	PROPN
ejpam-6139	160	9	η	η	PROPN
ejpam-6139	160	10	−	−	PROPN
ejpam-6139	160	11	t	t	PROPN
ejpam-6139	160	12	η	η	PROPN
ejpam-6139	160	13	ω	ω	PROPN
ejpam-6139	160	14	)	)	PUNCT
ejpam-6139	160	15	dt	dt	PROPN
ejpam-6139	160	16	,	,	PUNCT
ejpam-6139	160	17	m.	m.	NOUN
ejpam-6139	160	18	samraiz	samraiz	PROPN
ejpam-6139	160	19	et	et	PROPN
ejpam-6139	160	20	al	al	PROPN
ejpam-6139	160	21	.	.	PUNCT
ejpam-6139	160	22	/	/	SYM
ejpam-6139	160	23	eur	eur	PROPN
ejpam-6139	160	24	.	.	PUNCT
ejpam-6139	161	1	j.	j.	PROPN
ejpam-6139	161	2	pure	pure	PROPN
ejpam-6139	161	3	appl	appl	PROPN
ejpam-6139	161	4	.	.	PROPN
ejpam-6139	161	5	math	math	PROPN
ejpam-6139	161	6	,	,	PUNCT
ejpam-6139	161	7	18	18	NUM
ejpam-6139	161	8	(	(	PUNCT
ejpam-6139	161	9	4	4	NUM
ejpam-6139	161	10	)	)	PUNCT
ejpam-6139	161	11	(	(	PUNCT
ejpam-6139	161	12	2025	2025	NUM
ejpam-6139	161	13	)	)	PUNCT
ejpam-6139	161	14	,	,	PUNCT
ejpam-6139	161	15	6139	6139	NUM
ejpam-6139	161	16	7	7	NUM
ejpam-6139	161	17	of	of	ADP
ejpam-6139	161	18	34	34	NUM
ejpam-6139	161	19	i2	i2	NOUN
ejpam-6139	161	20	=	=	PUNCT
ejpam-6139	161	21	−	−	PROPN
ejpam-6139	161	22	η	η	PROPN
ejpam-6139	161	23	ω	ω	PROPN
ejpam-6139	161	24	−	−	PROPN
ejpam-6139	161	25	ν	ν	X
ejpam-6139	161	26	h′	h′	X
ejpam-6139	161	27	(	(	PUNCT
ejpam-6139	161	28	1	1	NUM
ejpam-6139	161	29	η	η	X
ejpam-6139	161	30	ν	ν	X
ejpam-6139	161	31	+	+	CCONJ
ejpam-6139	161	32	η	η	PROPN
ejpam-6139	161	33	−	−	PROPN
ejpam-6139	161	34	1	1	NUM
ejpam-6139	161	35	η	η	PROPN
ejpam-6139	161	36	ω	ω	PROPN
ejpam-6139	161	37	)	)	PUNCT
ejpam-6139	161	38	∫	∫	PROPN
ejpam-6139	161	39	1	1	NUM
ejpam-6139	161	40	0	0	NUM
ejpam-6139	161	41	(	(	PUNCT
ejpam-6139	161	42	1	1	NUM
ejpam-6139	161	43	(	(	PUNCT
ejpam-6139	161	44	kµ	kµ	PROPN
ejpam-6139	161	45	)	)	PUNCT
ejpam-6139	161	46	α	α	PROPN
ejpam-6139	161	47	k	k	NOUN
ejpam-6139	162	1	−	−	PROPN
ejpam-6139	162	2	(	(	PUNCT
ejpam-6139	162	3	1−	1−	NUM
ejpam-6139	162	4	(	(	PUNCT
ejpam-6139	162	5	1−	1−	NUM
ejpam-6139	162	6	φ)µ	φ)µ	NOUN
ejpam-6139	162	7	kµ	kµ	NOUN
ejpam-6139	162	8	)	)	PUNCT
ejpam-6139	162	9	α	α	PROPN
ejpam-6139	162	10	k	k	PROPN
ejpam-6139	162	11	)	)	PUNCT
ejpam-6139	163	1	dφ	dφ	ADP
ejpam-6139	163	2	+	+	CCONJ
ejpam-6139	163	3	(	(	PUNCT
ejpam-6139	163	4	η	η	PROPN
ejpam-6139	163	5	ω	ω	PROPN
ejpam-6139	163	6	−	−	PROPN
ejpam-6139	163	7	ν	ν	NOUN
ejpam-6139	163	8	)	)	PUNCT
ejpam-6139	163	9	2	2	NUM
ejpam-6139	163	10	h(ω	h(ω	PROPN
ejpam-6139	163	11	)	)	PUNCT
ejpam-6139	163	12	1	1	NUM
ejpam-6139	163	13	(	(	PUNCT
ejpam-6139	163	14	ku	ku	PROPN
ejpam-6139	163	15	)	)	PUNCT
ejpam-6139	163	16	α	α	PROPN
ejpam-6139	164	1	k	k	NOUN
ejpam-6139	165	1	−	−	PROPN
ejpam-6139	165	2	(	(	PUNCT
ejpam-6139	165	3	η	η	PROPN
ejpam-6139	165	4	ω	ω	PROPN
ejpam-6139	165	5	−	−	PROPN
ejpam-6139	165	6	ν	ν	NOUN
ejpam-6139	165	7	)	)	PUNCT
ejpam-6139	165	8	µα	µα	ADP
ejpam-6139	165	9	k	k	PROPN
ejpam-6139	165	10	+2	+2	PROPN
ejpam-6139	165	11	γ	γ	X
ejpam-6139	165	12	(	(	PUNCT
ejpam-6139	165	13	α	α	NOUN
ejpam-6139	165	14	k	k	PROPN
ejpam-6139	166	1	+	+	CCONJ
ejpam-6139	166	2	1	1	X
ejpam-6139	166	3	)	)	PUNCT
ejpam-6139	166	4	α	α	NOUN
ejpam-6139	166	5	k	k	NOUN
ejpam-6139	166	6	jµν+(η−1)ω	jµν+(η−1)ω	X
ejpam-6139	166	7	η	η	PROPN
ejpam-6139	166	8	+	+	PROPN
ejpam-6139	166	9	h(ω	h(ω	PROPN
ejpam-6139	166	10	)	)	PUNCT
ejpam-6139	166	11	.	.	PUNCT
ejpam-6139	167	1	(	(	PUNCT
ejpam-6139	167	2	8)	8)	NUM
ejpam-6139	167	3	adding	add	VERB
ejpam-6139	167	4	equations	equation	NOUN
ejpam-6139	167	5	(	(	PUNCT
ejpam-6139	167	6	7	7	NUM
ejpam-6139	167	7	)	)	PUNCT
ejpam-6139	167	8	and	and	CCONJ
ejpam-6139	167	9	(	(	PUNCT
ejpam-6139	167	10	8)	8)	NUM
ejpam-6139	167	11	,	,	PUNCT
ejpam-6139	167	12	we	we	PRON
ejpam-6139	167	13	get	get	VERB
ejpam-6139	167	14	the	the	DET
ejpam-6139	167	15	required	require	VERB
ejpam-6139	167	16	result	result	NOUN
ejpam-6139	167	17	.	.	PUNCT
ejpam-6139	168	1	remark	remark	NOUN
ejpam-6139	168	2	1	1	NUM
ejpam-6139	168	3	.	.	PUNCT
ejpam-6139	169	1	if	if	SCONJ
ejpam-6139	169	2	we	we	PRON
ejpam-6139	169	3	substitute	substitute	VERB
ejpam-6139	169	4	k=1	k=1	PROPN
ejpam-6139	169	5	and	and	CCONJ
ejpam-6139	169	6	η	η	PROPN
ejpam-6139	169	7	=	=	PROPN
ejpam-6139	169	8	2	2	NUM
ejpam-6139	169	9	in	in	ADP
ejpam-6139	169	10	lemma	lemma	PROPN
ejpam-6139	169	11	5	5	NUM
ejpam-6139	169	12	,	,	PUNCT
ejpam-6139	169	13	then	then	ADV
ejpam-6139	169	14	obtained	obtain	VERB
ejpam-6139	169	15	result	result	NOUN
ejpam-6139	169	16	leads	lead	VERB
ejpam-6139	169	17	to	to	ADP
ejpam-6139	169	18	[	[	X
ejpam-6139	169	19	44	44	NUM
ejpam-6139	169	20	,	,	PUNCT
ejpam-6139	169	21	lemma	lemma	PROPN
ejpam-6139	169	22	3	3	NUM
ejpam-6139	169	23	]	]	PUNCT
ejpam-6139	169	24	.	.	PUNCT
ejpam-6139	170	1	theorem	theorem	NOUN
ejpam-6139	170	2	1	1	X
ejpam-6139	170	3	.	.	X
ejpam-6139	171	1	consider	consider	VERB
ejpam-6139	171	2	h	h	NOUN
ejpam-6139	171	3	:	:	PUNCT
ejpam-6139	172	1	[	[	X
ejpam-6139	172	2	ν	ν	X
ejpam-6139	172	3	,	,	PUNCT
ejpam-6139	172	4	ω	ω	NOUN
ejpam-6139	172	5	]	]	X
ejpam-6139	172	6	→	→	SYM
ejpam-6139	172	7	r	r	NOUN
ejpam-6139	172	8	as	as	ADP
ejpam-6139	172	9	a	a	DET
ejpam-6139	172	10	twice	twice	ADV
ejpam-6139	172	11	differentiable	differentiable	ADJ
ejpam-6139	172	12	mapping	mapping	NOUN
ejpam-6139	172	13	on	on	ADP
ejpam-6139	172	14	(	(	PUNCT
ejpam-6139	172	15	ν	ν	PROPN
ejpam-6139	172	16	,	,	PUNCT
ejpam-6139	172	17	ω	ω	NOUN
ejpam-6139	172	18	)	)	PUNCT
ejpam-6139	172	19	such	such	ADJ
ejpam-6139	172	20	that	that	SCONJ
ejpam-6139	172	21	h′′	h′′	PROPN
ejpam-6139	172	22	∈	∈	PROPN
ejpam-6139	172	23	l([ν	l([ν	PROPN
ejpam-6139	172	24	,	,	PUNCT
ejpam-6139	172	25	ω	ω	NOUN
ejpam-6139	172	26	]	]	NOUN
ejpam-6139	172	27	)	)	PUNCT
ejpam-6139	172	28	.	.	PUNCT
ejpam-6139	173	1	if	if	SCONJ
ejpam-6139	173	2	|h′′|	|h′′|	PROPN
ejpam-6139	173	3	is	be	AUX
ejpam-6139	173	4	s	s	NOUN
ejpam-6139	173	5	-	-	NOUN
ejpam-6139	173	6	convex	convex	ADJ
ejpam-6139	173	7	in	in	ADP
ejpam-6139	173	8	second	second	ADJ
ejpam-6139	173	9	sense	sense	NOUN
ejpam-6139	173	10	on	on	ADP
ejpam-6139	173	11	[	[	X
ejpam-6139	173	12	ν	ν	X
ejpam-6139	173	13	,	,	PUNCT
ejpam-6139	173	14	ω	ω	NOUN
ejpam-6139	173	15	]	]	X
ejpam-6139	173	16	then,∣∣∣∣h(ν	then,∣∣∣∣h(ν	NOUN
ejpam-6139	173	17	)	)	PUNCT
ejpam-6139	174	1	+	+	CCONJ
ejpam-6139	174	2	h(ω	h(ω	PROPN
ejpam-6139	174	3	)	)	PUNCT
ejpam-6139	174	4	η	η	PROPN
ejpam-6139	174	5	+	+	PROPN
ejpam-6139	174	6	ϕk(µ	ϕk(µ	NUM
ejpam-6139	174	7	,	,	PUNCT
ejpam-6139	174	8	α)−	α)−	PROPN
ejpam-6139	174	9	η	η	PROPN
ejpam-6139	174	10	µα	µα	ADP
ejpam-6139	174	11	k	k	PROPN
ejpam-6139	174	12	−1	−1	NOUN
ejpam-6139	174	13	(	(	PUNCT
ejpam-6139	174	14	ω	ω	NOUN
ejpam-6139	174	15	−	−	NOUN
ejpam-6139	174	16	ν	ν	NOUN
ejpam-6139	174	17	)	)	PUNCT
ejpam-6139	174	18	µα	µα	ADP
ejpam-6139	174	19	k	k	PROPN
ejpam-6139	174	20	(	(	PUNCT
ejpam-6139	174	21	kµ	kµ	PROPN
ejpam-6139	174	22	)	)	PUNCT
ejpam-6139	175	1	α	α	PROPN
ejpam-6139	175	2	k	k	PROPN
ejpam-6139	175	3	γ	γ	X
ejpam-6139	175	4	(	(	PUNCT
ejpam-6139	175	5	α	α	NOUN
ejpam-6139	175	6	k	k	PROPN
ejpam-6139	176	1	+	+	PROPN
ejpam-6139	176	2	1	1	X
ejpam-6139	176	3	)	)	PUNCT
ejpam-6139	176	4	×	×	NOUN
ejpam-6139	176	5	(	(	PUNCT
ejpam-6139	176	6	α	α	PROPN
ejpam-6139	176	7	kj	kj	PROPN
ejpam-6139	176	8	µ	µ	PROPN
ejpam-6139	176	9	(	(	PUNCT
ejpam-6139	176	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	176	11	η	η	PROPN
ejpam-6139	176	12	−	−	PROPN
ejpam-6139	176	13	h(ν	h(ν	PROPN
ejpam-6139	176	14	)	)	PUNCT
ejpam-6139	177	1	+	+	NOUN
ejpam-6139	177	2	α	α	PROPN
ejpam-6139	177	3	k	k	X
ejpam-6139	177	4	jµ	jµ	PROPN
ejpam-6139	177	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	177	6	η	η	PROPN
ejpam-6139	177	7	+	+	PROPN
ejpam-6139	177	8	h(ω	h(ω	PROPN
ejpam-6139	177	9	)	)	PUNCT
ejpam-6139	177	10	)	)	PUNCT
ejpam-6139	178	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	178	2	≤	≤	NOUN
ejpam-6139	178	3	(	(	PUNCT
ejpam-6139	178	4	ω	ω	NOUN
ejpam-6139	178	5	−	−	NOUN
ejpam-6139	178	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	178	7	)	)	PUNCT
ejpam-6139	178	8	α	α	PROPN
ejpam-6139	178	9	k	k	PROPN
ejpam-6139	178	10	η3	η3	PROPN
ejpam-6139	178	11	(	(	PUNCT
ejpam-6139	178	12	|h′′(ν)|+	|h′′(ν)|+	X
ejpam-6139	178	13	|h′′(ω)|	|h′′(ω)|	INTJ
ejpam-6139	178	14	ηs	ηs	NOUN
ejpam-6139	178	15	)	)	PUNCT
ejpam-6139	178	16	×	×	NOUN
ejpam-6139	178	17	∫	∫	NOUN
ejpam-6139	178	18	1	1	NUM
ejpam-6139	178	19	0	0	NUM
ejpam-6139	178	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	178	21	∫	∫	PROPN
ejpam-6139	178	22	t	t	PROPN
ejpam-6139	178	23	0	0	NUM
ejpam-6139	179	1	(	(	PUNCT
ejpam-6139	179	2	1	1	NUM
ejpam-6139	179	3	(	(	PUNCT
ejpam-6139	179	4	kµ	kµ	PROPN
ejpam-6139	179	5	)	)	PUNCT
ejpam-6139	179	6	α	α	PROPN
ejpam-6139	179	7	k	k	NOUN
ejpam-6139	180	1	−	−	PROPN
ejpam-6139	180	2	(	(	PUNCT
ejpam-6139	180	3	1−	1−	NUM
ejpam-6139	180	4	(	(	PUNCT
ejpam-6139	180	5	1−	1−	NUM
ejpam-6139	180	6	φ)µ	φ)µ	NOUN
ejpam-6139	180	7	kµ	kµ	NOUN
ejpam-6139	180	8	)	)	PUNCT
ejpam-6139	180	9	α	α	PROPN
ejpam-6139	180	10	k	k	PROPN
ejpam-6139	180	11	)	)	PUNCT
ejpam-6139	180	12	dφ	dφ	ADP
ejpam-6139	180	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	180	14	(	(	PUNCT
ejpam-6139	180	15	ts	ts	ADP
ejpam-6139	180	16	+	+	X
ejpam-6139	180	17	(	(	PUNCT
ejpam-6139	180	18	η	η	PROPN
ejpam-6139	180	19	−	−	PROPN
ejpam-6139	180	20	t)s	t)s	ADV
ejpam-6139	180	21	)	)	PUNCT
ejpam-6139	180	22	dt	dt	X
ejpam-6139	180	23	.	.	PUNCT
ejpam-6139	181	1	(	(	PUNCT
ejpam-6139	181	2	9	9	X
ejpam-6139	181	3	)	)	PUNCT
ejpam-6139	181	4	proof	proof	NOUN
ejpam-6139	181	5	.	.	PUNCT
ejpam-6139	182	1	taking	take	VERB
ejpam-6139	182	2	absolute	absolute	ADJ
ejpam-6139	182	3	value	value	NOUN
ejpam-6139	182	4	of	of	ADP
ejpam-6139	182	5	equation	equation	NOUN
ejpam-6139	182	6	(	(	PUNCT
ejpam-6139	182	7	5	5	NUM
ejpam-6139	182	8	)	)	PUNCT
ejpam-6139	182	9	,	,	PUNCT
ejpam-6139	182	10	we	we	PRON
ejpam-6139	182	11	have∣∣∣∣h(ν	have∣∣∣∣h(ν	VERB
ejpam-6139	182	12	)	)	PUNCT
ejpam-6139	183	1	+	+	CCONJ
ejpam-6139	183	2	h(ω	h(ω	PROPN
ejpam-6139	183	3	)	)	PUNCT
ejpam-6139	183	4	η	η	PROPN
ejpam-6139	183	5	+	+	PROPN
ejpam-6139	183	6	ϕk(µ	ϕk(µ	NUM
ejpam-6139	183	7	,	,	PUNCT
ejpam-6139	183	8	α)−	α)−	PROPN
ejpam-6139	183	9	η	η	PROPN
ejpam-6139	183	10	µα	µα	ADP
ejpam-6139	183	11	k	k	PROPN
ejpam-6139	183	12	−1	−1	NOUN
ejpam-6139	183	13	(	(	PUNCT
ejpam-6139	183	14	ω	ω	NOUN
ejpam-6139	183	15	−	−	NOUN
ejpam-6139	183	16	ν	ν	NOUN
ejpam-6139	183	17	)	)	PUNCT
ejpam-6139	183	18	µα	µα	ADP
ejpam-6139	183	19	k	k	PROPN
ejpam-6139	183	20	(	(	PUNCT
ejpam-6139	183	21	kµ	kµ	PROPN
ejpam-6139	183	22	)	)	PUNCT
ejpam-6139	184	1	α	α	PROPN
ejpam-6139	184	2	k	k	PROPN
ejpam-6139	184	3	γ	γ	X
ejpam-6139	184	4	(	(	PUNCT
ejpam-6139	184	5	α	α	NOUN
ejpam-6139	184	6	k	k	PROPN
ejpam-6139	185	1	+	+	PROPN
ejpam-6139	185	2	1	1	X
ejpam-6139	185	3	)	)	PUNCT
ejpam-6139	185	4	×	×	NOUN
ejpam-6139	185	5	(	(	PUNCT
ejpam-6139	185	6	α	α	PROPN
ejpam-6139	185	7	kj	kj	PROPN
ejpam-6139	185	8	µ	µ	PROPN
ejpam-6139	185	9	(	(	PUNCT
ejpam-6139	185	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	185	11	η	η	PROPN
ejpam-6139	185	12	−	−	PROPN
ejpam-6139	185	13	h(ν	h(ν	PROPN
ejpam-6139	185	14	)	)	PUNCT
ejpam-6139	186	1	+	+	NOUN
ejpam-6139	186	2	α	α	PROPN
ejpam-6139	186	3	k	k	X
ejpam-6139	186	4	jµ	jµ	PROPN
ejpam-6139	186	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	186	6	η	η	PROPN
ejpam-6139	186	7	+	+	PROPN
ejpam-6139	186	8	h(ω	h(ω	PROPN
ejpam-6139	186	9	)	)	PUNCT
ejpam-6139	186	10	)	)	PUNCT
ejpam-6139	187	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	187	2	≤	≤	NOUN
ejpam-6139	187	3	(	(	PUNCT
ejpam-6139	187	4	ω	ω	NOUN
ejpam-6139	187	5	−	−	NOUN
ejpam-6139	187	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	187	7	)	)	PUNCT
ejpam-6139	187	8	α	α	PROPN
ejpam-6139	188	1	k	k	PROPN
ejpam-6139	188	2	η3	η3	PROPN
ejpam-6139	188	3	×	×	NOUN
ejpam-6139	189	1	[	[	X
ejpam-6139	189	2	∫	∫	PROPN
ejpam-6139	189	3	1	1	NUM
ejpam-6139	189	4	0	0	NUM
ejpam-6139	189	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	189	6	∫	∫	PROPN
ejpam-6139	189	7	t	t	PROPN
ejpam-6139	189	8	0	0	NUM
ejpam-6139	189	9	(	(	PUNCT
ejpam-6139	189	10	1	1	NUM
ejpam-6139	189	11	(	(	PUNCT
ejpam-6139	189	12	kµ	kµ	PROPN
ejpam-6139	189	13	)	)	PUNCT
ejpam-6139	189	14	α	α	PROPN
ejpam-6139	189	15	k	k	NOUN
ejpam-6139	190	1	−	−	PROPN
ejpam-6139	190	2	(	(	PUNCT
ejpam-6139	190	3	1−	1−	NUM
ejpam-6139	190	4	(	(	PUNCT
ejpam-6139	190	5	1−	1−	NUM
ejpam-6139	190	6	φ)µ	φ)µ	NOUN
ejpam-6139	190	7	kµ	kµ	NOUN
ejpam-6139	190	8	)	)	PUNCT
ejpam-6139	190	9	α	α	PROPN
ejpam-6139	190	10	k	k	PROPN
ejpam-6139	190	11	)	)	PUNCT
ejpam-6139	191	1	dφ	dφ	ADP
ejpam-6139	191	2	∣∣∣∣∣∣∣∣h′′(η	∣∣∣∣∣∣∣∣h′′(η	NOUN
ejpam-6139	191	3	−	−	PROPN
ejpam-6139	191	4	t	t	PROPN
ejpam-6139	191	5	η	η	PROPN
ejpam-6139	191	6	ν	ν	PROPN
ejpam-6139	191	7	+	+	PROPN
ejpam-6139	191	8	t	t	PROPN
ejpam-6139	191	9	η	η	PROPN
ejpam-6139	191	10	ω	ω	PROPN
ejpam-6139	191	11	)	)	PUNCT
ejpam-6139	191	12	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	191	13	+	+	CCONJ
ejpam-6139	191	14	∫	∫	PROPN
ejpam-6139	191	15	1	1	NUM
ejpam-6139	191	16	0	0	NUM
ejpam-6139	191	17	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	191	18	∫	∫	PROPN
ejpam-6139	191	19	t	t	PROPN
ejpam-6139	191	20	0	0	NUM
ejpam-6139	191	21	(	(	PUNCT
ejpam-6139	191	22	1	1	NUM
ejpam-6139	191	23	(	(	PUNCT
ejpam-6139	191	24	kµ	kµ	PROPN
ejpam-6139	191	25	)	)	PUNCT
ejpam-6139	191	26	α	α	PROPN
ejpam-6139	192	1	k	k	NOUN
ejpam-6139	193	1	−	−	PROPN
ejpam-6139	193	2	(	(	PUNCT
ejpam-6139	193	3	1−	1−	NUM
ejpam-6139	193	4	(	(	PUNCT
ejpam-6139	193	5	1−	1−	NUM
ejpam-6139	193	6	φ)µ	φ)µ	NOUN
ejpam-6139	193	7	kµ	kµ	NOUN
ejpam-6139	193	8	)	)	PUNCT
ejpam-6139	194	1	α	α	PROPN
ejpam-6139	194	2	k	k	PROPN
ejpam-6139	194	3	)	)	PUNCT
ejpam-6139	194	4	dφ	dφ	ADP
ejpam-6139	194	5	∣∣∣∣∣∣∣∣h′′	∣∣∣∣∣∣∣∣h′′	PROPN
ejpam-6139	194	6	(	(	PUNCT
ejpam-6139	194	7	t	t	PROPN
ejpam-6139	194	8	η	η	PROPN
ejpam-6139	194	9	ν	ν	PROPN
ejpam-6139	194	10	+	+	PROPN
ejpam-6139	194	11	η	η	PROPN
ejpam-6139	194	12	−	−	PROPN
ejpam-6139	194	13	t	t	PROPN
ejpam-6139	194	14	η	η	PROPN
ejpam-6139	194	15	ω	ω	PROPN
ejpam-6139	194	16	)	)	PUNCT
ejpam-6139	194	17	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	194	18	]	]	PUNCT
ejpam-6139	194	19	.	.	PUNCT
ejpam-6139	195	1	(	(	PUNCT
ejpam-6139	195	2	10	10	NUM
ejpam-6139	195	3	)	)	PUNCT
ejpam-6139	195	4	by	by	ADP
ejpam-6139	195	5	using	use	VERB
ejpam-6139	195	6	s	s	NOUN
ejpam-6139	195	7	-	-	NOUN
ejpam-6139	195	8	convexity	convexity	NOUN
ejpam-6139	195	9	of	of	ADP
ejpam-6139	195	10	|h′′|	|h′′|	VERB
ejpam-6139	195	11	in	in	ADP
ejpam-6139	195	12	second	second	ADJ
ejpam-6139	195	13	sense	sense	NOUN
ejpam-6139	195	14	,	,	PUNCT
ejpam-6139	195	15	we	we	PRON
ejpam-6139	195	16	get∣∣∣∣h(ν	get∣∣∣∣h(ν	NOUN
ejpam-6139	195	17	)	)	PUNCT
ejpam-6139	196	1	+	+	CCONJ
ejpam-6139	196	2	h(ω	h(ω	PROPN
ejpam-6139	196	3	)	)	PUNCT
ejpam-6139	196	4	η	η	PROPN
ejpam-6139	196	5	+	+	PROPN
ejpam-6139	196	6	ϕk(µ	ϕk(µ	NUM
ejpam-6139	196	7	,	,	PUNCT
ejpam-6139	196	8	α)−	α)−	PROPN
ejpam-6139	196	9	η	η	PROPN
ejpam-6139	196	10	µα	µα	ADP
ejpam-6139	196	11	k	k	PROPN
ejpam-6139	196	12	−1	−1	NOUN
ejpam-6139	196	13	(	(	PUNCT
ejpam-6139	196	14	ω	ω	NOUN
ejpam-6139	196	15	−	−	NOUN
ejpam-6139	196	16	ν	ν	NOUN
ejpam-6139	196	17	)	)	PUNCT
ejpam-6139	196	18	µα	µα	ADP
ejpam-6139	196	19	k	k	PROPN
ejpam-6139	196	20	(	(	PUNCT
ejpam-6139	196	21	kµ	kµ	PROPN
ejpam-6139	196	22	)	)	PUNCT
ejpam-6139	197	1	α	α	PROPN
ejpam-6139	197	2	k	k	PROPN
ejpam-6139	197	3	γ	γ	X
ejpam-6139	197	4	(	(	PUNCT
ejpam-6139	197	5	α	α	NOUN
ejpam-6139	197	6	k	k	PROPN
ejpam-6139	198	1	+	+	PROPN
ejpam-6139	198	2	1	1	X
ejpam-6139	198	3	)	)	PUNCT
ejpam-6139	198	4	×	×	NOUN
ejpam-6139	198	5	(	(	PUNCT
ejpam-6139	198	6	α	α	PROPN
ejpam-6139	198	7	kj	kj	PROPN
ejpam-6139	198	8	µ	µ	PROPN
ejpam-6139	198	9	(	(	PUNCT
ejpam-6139	198	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	198	11	η	η	PROPN
ejpam-6139	198	12	−	−	PROPN
ejpam-6139	198	13	h(ν	h(ν	PROPN
ejpam-6139	198	14	)	)	PUNCT
ejpam-6139	199	1	+	+	NOUN
ejpam-6139	199	2	α	α	PROPN
ejpam-6139	199	3	k	k	X
ejpam-6139	199	4	jµ	jµ	PROPN
ejpam-6139	199	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	199	6	η	η	PROPN
ejpam-6139	199	7	+	+	PROPN
ejpam-6139	199	8	h(ω	h(ω	PROPN
ejpam-6139	199	9	)	)	PUNCT
ejpam-6139	199	10	)	)	PUNCT
ejpam-6139	200	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	200	2	≤	≤	NOUN
ejpam-6139	200	3	(	(	PUNCT
ejpam-6139	200	4	ω	ω	NOUN
ejpam-6139	200	5	−	−	NOUN
ejpam-6139	200	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	200	7	)	)	PUNCT
ejpam-6139	200	8	α	α	PROPN
ejpam-6139	201	1	k	k	PROPN
ejpam-6139	201	2	η3	η3	PROPN
ejpam-6139	201	3	×	×	NOUN
ejpam-6139	202	1	[	[	X
ejpam-6139	202	2	∫	∫	PROPN
ejpam-6139	202	3	1	1	NUM
ejpam-6139	202	4	0	0	NUM
ejpam-6139	202	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	202	6	∫	∫	PROPN
ejpam-6139	202	7	t	t	PROPN
ejpam-6139	202	8	0	0	NUM
ejpam-6139	202	9	(	(	PUNCT
ejpam-6139	202	10	1	1	NUM
ejpam-6139	202	11	(	(	PUNCT
ejpam-6139	202	12	kµ	kµ	PROPN
ejpam-6139	202	13	)	)	PUNCT
ejpam-6139	202	14	α	α	PROPN
ejpam-6139	202	15	k	k	NOUN
ejpam-6139	203	1	−	−	PROPN
ejpam-6139	203	2	(	(	PUNCT
ejpam-6139	203	3	1−	1−	NUM
ejpam-6139	203	4	(	(	PUNCT
ejpam-6139	203	5	1−	1−	NUM
ejpam-6139	203	6	φ)µ	φ)µ	NOUN
ejpam-6139	203	7	kµ	kµ	NOUN
ejpam-6139	203	8	)	)	PUNCT
ejpam-6139	203	9	α	α	PROPN
ejpam-6139	203	10	k	k	PROPN
ejpam-6139	203	11	)	)	PUNCT
ejpam-6139	203	12	dφ	dφ	ADP
ejpam-6139	203	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	203	14	(	(	PUNCT
ejpam-6139	203	15	(	(	PUNCT
ejpam-6139	203	16	t	t	PROPN
ejpam-6139	203	17	η	η	PROPN
ejpam-6139	203	18	)	)	PUNCT
ejpam-6139	203	19	s	s	PART
ejpam-6139	204	1	|h′′(ω)|+	|h′′(ω)|+	PROPN
ejpam-6139	204	2	(	(	PUNCT
ejpam-6139	204	3	η	η	PROPN
ejpam-6139	204	4	−	−	PROPN
ejpam-6139	204	5	t	t	PROPN
ejpam-6139	204	6	η	η	PROPN
ejpam-6139	204	7	)	)	PUNCT
ejpam-6139	204	8	s	s	PART
ejpam-6139	204	9	|h′′(ν)|	|h′′(ν)|	NOUN
ejpam-6139	204	10	)	)	PUNCT
ejpam-6139	204	11	dt	dt	PART
ejpam-6139	204	12	m.	m.	PROPN
ejpam-6139	204	13	samraiz	samraiz	PROPN
ejpam-6139	204	14	et	et	PROPN
ejpam-6139	204	15	al	al	PROPN
ejpam-6139	204	16	.	.	PUNCT
ejpam-6139	204	17	/	/	SYM
ejpam-6139	204	18	eur	eur	PROPN
ejpam-6139	204	19	.	.	PUNCT
ejpam-6139	205	1	j.	j.	PROPN
ejpam-6139	205	2	pure	pure	PROPN
ejpam-6139	205	3	appl	appl	PROPN
ejpam-6139	205	4	.	.	PROPN
ejpam-6139	205	5	math	math	PROPN
ejpam-6139	205	6	,	,	PUNCT
ejpam-6139	205	7	18	18	NUM
ejpam-6139	205	8	(	(	PUNCT
ejpam-6139	205	9	4	4	NUM
ejpam-6139	205	10	)	)	PUNCT
ejpam-6139	205	11	(	(	PUNCT
ejpam-6139	205	12	2025	2025	NUM
ejpam-6139	205	13	)	)	PUNCT
ejpam-6139	205	14	,	,	PUNCT
ejpam-6139	205	15	6139	6139	NUM
ejpam-6139	205	16	8	8	NUM
ejpam-6139	205	17	of	of	ADP
ejpam-6139	205	18	34	34	NUM
ejpam-6139	205	19	+	+	CCONJ
ejpam-6139	205	20	∫	∫	PROPN
ejpam-6139	205	21	1	1	NUM
ejpam-6139	205	22	0	0	NUM
ejpam-6139	205	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	205	24	∫	∫	PROPN
ejpam-6139	205	25	t	t	PROPN
ejpam-6139	205	26	0	0	NUM
ejpam-6139	205	27	(	(	PUNCT
ejpam-6139	205	28	1	1	NUM
ejpam-6139	205	29	(	(	PUNCT
ejpam-6139	205	30	kµ	kµ	PROPN
ejpam-6139	205	31	)	)	PUNCT
ejpam-6139	205	32	α	α	PROPN
ejpam-6139	206	1	k	k	NOUN
ejpam-6139	207	1	−	−	PROPN
ejpam-6139	207	2	(	(	PUNCT
ejpam-6139	207	3	1−	1−	NUM
ejpam-6139	207	4	(	(	PUNCT
ejpam-6139	207	5	1−	1−	NUM
ejpam-6139	207	6	φ)µ	φ)µ	NOUN
ejpam-6139	207	7	kµ	kµ	NOUN
ejpam-6139	207	8	)	)	PUNCT
ejpam-6139	208	1	α	α	PROPN
ejpam-6139	208	2	k	k	PROPN
ejpam-6139	208	3	)	)	PUNCT
ejpam-6139	208	4	dφ	dφ	ADP
ejpam-6139	208	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	208	6	(	(	PUNCT
ejpam-6139	208	7	(	(	PUNCT
ejpam-6139	208	8	t	t	PROPN
ejpam-6139	208	9	η	η	PROPN
ejpam-6139	208	10	)	)	PUNCT
ejpam-6139	208	11	s	s	PART
ejpam-6139	209	1	|h′′(ν)|+	|h′′(ν)|+	PROPN
ejpam-6139	209	2	(	(	PUNCT
ejpam-6139	209	3	η	η	PROPN
ejpam-6139	209	4	−	−	PROPN
ejpam-6139	209	5	t	t	PROPN
ejpam-6139	209	6	η	η	PROPN
ejpam-6139	209	7	)	)	PUNCT
ejpam-6139	209	8	s	s	PART
ejpam-6139	209	9	|h′′(ω)|	|h′′(ω)|	NOUN
ejpam-6139	209	10	)	)	PUNCT
ejpam-6139	209	11	dt	dt	X
ejpam-6139	209	12	]	]	PUNCT
ejpam-6139	209	13	∣∣∣∣h(ν	∣∣∣∣h(ν	PROPN
ejpam-6139	209	14	)	)	PUNCT
ejpam-6139	209	15	+	+	CCONJ
ejpam-6139	209	16	h(ω	h(ω	PROPN
ejpam-6139	209	17	)	)	PUNCT
ejpam-6139	209	18	η	η	PROPN
ejpam-6139	209	19	+	+	PROPN
ejpam-6139	209	20	ϕk(µ	ϕk(µ	NUM
ejpam-6139	209	21	,	,	PUNCT
ejpam-6139	209	22	α)−	α)−	PROPN
ejpam-6139	209	23	η	η	PROPN
ejpam-6139	209	24	µα	µα	ADP
ejpam-6139	209	25	k	k	PROPN
ejpam-6139	209	26	−1	−1	NOUN
ejpam-6139	209	27	(	(	PUNCT
ejpam-6139	209	28	ω	ω	NOUN
ejpam-6139	209	29	−	−	NOUN
ejpam-6139	209	30	ν	ν	NOUN
ejpam-6139	209	31	)	)	PUNCT
ejpam-6139	209	32	µα	µα	ADP
ejpam-6139	209	33	k	k	PROPN
ejpam-6139	209	34	(	(	PUNCT
ejpam-6139	209	35	kµ	kµ	PROPN
ejpam-6139	209	36	)	)	PUNCT
ejpam-6139	210	1	α	α	PROPN
ejpam-6139	211	1	k	k	PROPN
ejpam-6139	211	2	γ	γ	X
ejpam-6139	211	3	(	(	PUNCT
ejpam-6139	211	4	α	α	NOUN
ejpam-6139	211	5	k	k	PROPN
ejpam-6139	212	1	+	+	PROPN
ejpam-6139	212	2	1	1	X
ejpam-6139	212	3	)	)	PUNCT
ejpam-6139	212	4	×	×	NOUN
ejpam-6139	212	5	(	(	PUNCT
ejpam-6139	212	6	α	α	PROPN
ejpam-6139	212	7	kj	kj	PROPN
ejpam-6139	212	8	µ	µ	PROPN
ejpam-6139	212	9	(	(	PUNCT
ejpam-6139	212	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	212	11	η	η	PROPN
ejpam-6139	212	12	−	−	PROPN
ejpam-6139	212	13	h(ν	h(ν	PROPN
ejpam-6139	212	14	)	)	PUNCT
ejpam-6139	213	1	+	+	NOUN
ejpam-6139	213	2	α	α	PROPN
ejpam-6139	213	3	k	k	X
ejpam-6139	213	4	jµ	jµ	PROPN
ejpam-6139	213	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	213	6	η	η	PROPN
ejpam-6139	213	7	+	+	PROPN
ejpam-6139	213	8	h(ω	h(ω	PROPN
ejpam-6139	213	9	)	)	PUNCT
ejpam-6139	213	10	)	)	PUNCT
ejpam-6139	214	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	214	2	≤	≤	NOUN
ejpam-6139	214	3	(	(	PUNCT
ejpam-6139	214	4	ω	ω	NOUN
ejpam-6139	214	5	−	−	NOUN
ejpam-6139	214	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	214	7	)	)	PUNCT
ejpam-6139	214	8	α	α	PROPN
ejpam-6139	215	1	k	k	PROPN
ejpam-6139	215	2	η3	η3	PROPN
ejpam-6139	215	3	×	×	NOUN
ejpam-6139	215	4	(	(	PUNCT
ejpam-6139	215	5	|h′′(ν)|+	|h′′(ν)|+	X
ejpam-6139	215	6	|h′′(ω)|	|h′′(ω)|	INTJ
ejpam-6139	215	7	ηs	ηs	NOUN
ejpam-6139	215	8	)	)	PUNCT
ejpam-6139	215	9	∫	∫	PROPN
ejpam-6139	215	10	1	1	NUM
ejpam-6139	215	11	0	0	NUM
ejpam-6139	215	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	215	13	∫	∫	PROPN
ejpam-6139	215	14	t	t	PROPN
ejpam-6139	215	15	0	0	NUM
ejpam-6139	216	1	(	(	PUNCT
ejpam-6139	216	2	1	1	NUM
ejpam-6139	216	3	(	(	PUNCT
ejpam-6139	216	4	kµ	kµ	PROPN
ejpam-6139	216	5	)	)	PUNCT
ejpam-6139	216	6	α	α	PROPN
ejpam-6139	216	7	k	k	NOUN
ejpam-6139	217	1	−	−	PROPN
ejpam-6139	217	2	(	(	PUNCT
ejpam-6139	217	3	1−	1−	NUM
ejpam-6139	217	4	(	(	PUNCT
ejpam-6139	217	5	1−	1−	NUM
ejpam-6139	217	6	φ)µ	φ)µ	NOUN
ejpam-6139	217	7	kµ	kµ	NOUN
ejpam-6139	217	8	)	)	PUNCT
ejpam-6139	217	9	α	α	PROPN
ejpam-6139	217	10	k	k	PROPN
ejpam-6139	217	11	)	)	PUNCT
ejpam-6139	217	12	dφ	dφ	ADP
ejpam-6139	217	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	217	14	×	×	NOUN
ejpam-6139	217	15	(	(	PUNCT
ejpam-6139	217	16	ts	ts	ADP
ejpam-6139	217	17	+	+	X
ejpam-6139	217	18	(	(	PUNCT
ejpam-6139	217	19	η	η	PROPN
ejpam-6139	217	20	−	−	PROPN
ejpam-6139	217	21	t)s	t)s	ADV
ejpam-6139	217	22	)	)	PUNCT
ejpam-6139	217	23	dt	dt	PROPN
ejpam-6139	217	24	.	.	PUNCT
ejpam-6139	217	25	which	which	PRON
ejpam-6139	217	26	lead	lead	VERB
ejpam-6139	217	27	us	we	PRON
ejpam-6139	217	28	to	to	ADP
ejpam-6139	217	29	our	our	PRON
ejpam-6139	217	30	required	require	VERB
ejpam-6139	217	31	result	result	NOUN
ejpam-6139	217	32	.	.	PUNCT
ejpam-6139	218	1	remark	remark	NOUN
ejpam-6139	218	2	2	2	NUM
ejpam-6139	218	3	.	.	PUNCT
ejpam-6139	219	1	if	if	SCONJ
ejpam-6139	219	2	we	we	PRON
ejpam-6139	219	3	set	set	VERB
ejpam-6139	219	4	η	η	PROPN
ejpam-6139	219	5	=	=	PROPN
ejpam-6139	219	6	2,k=1	2,k=1	PROPN
ejpam-6139	219	7	and	and	CCONJ
ejpam-6139	219	8	s=1	s=1	PROPN
ejpam-6139	219	9	in	in	ADP
ejpam-6139	219	10	(	(	PUNCT
ejpam-6139	219	11	9	9	NUM
ejpam-6139	219	12	)	)	PUNCT
ejpam-6139	219	13	,	,	PUNCT
ejpam-6139	219	14	then	then	ADV
ejpam-6139	219	15	inequality	inequality	NOUN
ejpam-6139	219	16	reduced	reduce	VERB
ejpam-6139	219	17	to∣∣∣∣h(ν	to∣∣∣∣h(ν	NOUN
ejpam-6139	219	18	)	)	PUNCT
ejpam-6139	220	1	+	+	CCONJ
ejpam-6139	220	2	h(ω	h(ω	PROPN
ejpam-6139	220	3	)	)	PUNCT
ejpam-6139	220	4	2	2	NUM
ejpam-6139	220	5	−	−	NOUN
ejpam-6139	220	6	2µα	2µα	NOUN
ejpam-6139	220	7	−	−	NOUN
ejpam-6139	220	8	1	1	NUM
ejpam-6139	220	9	(	(	PUNCT
ejpam-6139	220	10	ω	ω	NOUN
ejpam-6139	220	11	−	−	X
ejpam-6139	221	1	ν)µα	ν)µα	PROPN
ejpam-6139	221	2	(	(	PUNCT
ejpam-6139	221	3	µ)αγ(α+	µ)αγ(α+	NOUN
ejpam-6139	221	4	1	1	NUM
ejpam-6139	221	5	)	)	PUNCT
ejpam-6139	221	6	(	(	PUNCT
ejpam-6139	221	7	αjµ	αjµ	NOUN
ejpam-6139	221	8	ν+ω	ν+ω	NOUN
ejpam-6139	221	9	2	2	NUM
ejpam-6139	221	10	−	−	PRON
ejpam-6139	221	11	h(ν	h(ν	PRON
ejpam-6139	221	12	)	)	PUNCT
ejpam-6139	221	13	+	+	NOUN
ejpam-6139	221	14	α	α	NOUN
ejpam-6139	221	15	jµ	jµ	X
ejpam-6139	221	16	ν+ω	ν+ω	NOUN
ejpam-6139	221	17	2	2	NUM
ejpam-6139	221	18	+	+	CCONJ
ejpam-6139	221	19	h(ω	h(ω	PROPN
ejpam-6139	221	20	)	)	PUNCT
ejpam-6139	221	21	)	)	PUNCT
ejpam-6139	221	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	221	23	≤	≤	NOUN
ejpam-6139	221	24	(	(	PUNCT
ejpam-6139	221	25	ω	ω	NUM
ejpam-6139	221	26	−	−	PROPN
ejpam-6139	221	27	ν)2µα	ν)2µα	NOUN
ejpam-6139	221	28	8	8	NUM
ejpam-6139	221	29	(	(	PUNCT
ejpam-6139	221	30	|h′′(ν)|+	|h′′(ν)|+	X
ejpam-6139	221	31	|h′′(ω)|	|h′′(ω)|	X
ejpam-6139	221	32	)	)	PUNCT
ejpam-6139	221	33	∫	∫	PROPN
ejpam-6139	221	34	1	1	NUM
ejpam-6139	221	35	0	0	NUM
ejpam-6139	221	36	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	221	37	∫	∫	PROPN
ejpam-6139	221	38	t	t	PROPN
ejpam-6139	221	39	0	0	NUM
ejpam-6139	222	1	(	(	PUNCT
ejpam-6139	222	2	1	1	NUM
ejpam-6139	222	3	µα	µα	ADP
ejpam-6139	222	4	−	−	PROPN
ejpam-6139	222	5	(	(	PUNCT
ejpam-6139	222	6	1−	1−	NUM
ejpam-6139	222	7	(	(	PUNCT
ejpam-6139	222	8	1−	1−	NUM
ejpam-6139	222	9	φ)µ	φ)µ	X
ejpam-6139	222	10	µ	µ	X
ejpam-6139	222	11	)	)	PUNCT
ejpam-6139	222	12	α	α	NOUN
ejpam-6139	222	13	)	)	PUNCT
ejpam-6139	222	14	dφ	dφ	ADP
ejpam-6139	222	15	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	222	16	.	.	PUNCT
ejpam-6139	223	1	(	(	PUNCT
ejpam-6139	223	2	11	11	NUM
ejpam-6139	223	3	)	)	PUNCT
ejpam-6139	223	4	remark	remark	NOUN
ejpam-6139	223	5	3	3	NUM
ejpam-6139	223	6	.	.	PUNCT
ejpam-6139	224	1	when	when	SCONJ
ejpam-6139	224	2	we	we	PRON
ejpam-6139	224	3	substitute	substitute	VERB
ejpam-6139	224	4	µ=1	µ=1	PUNCT
ejpam-6139	224	5	in	in	ADP
ejpam-6139	224	6	(	(	PUNCT
ejpam-6139	224	7	11	11	NUM
ejpam-6139	224	8	)	)	PUNCT
ejpam-6139	224	9	,	,	PUNCT
ejpam-6139	224	10	then	then	ADV
ejpam-6139	224	11	theorem	theorem	VERB
ejpam-6139	224	12	1	1	NUM
ejpam-6139	224	13	leads	lead	VERB
ejpam-6139	224	14	to	to	ADP
ejpam-6139	224	15	[	[	X
ejpam-6139	224	16	45	45	NUM
ejpam-6139	224	17	]	]	PUNCT
ejpam-6139	224	18	,	,	PUNCT
ejpam-6139	224	19	corollary	corollary	ADJ
ejpam-6139	224	20	7	7	NUM
ejpam-6139	224	21	.	.	PUNCT
ejpam-6139	224	22	remark	remark	PROPN
ejpam-6139	224	23	4	4	NUM
ejpam-6139	224	24	.	.	PUNCT
ejpam-6139	224	25	by	by	ADP
ejpam-6139	224	26	setting	set	VERB
ejpam-6139	224	27	η	η	PROPN
ejpam-6139	224	28	=	=	PROPN
ejpam-6139	224	29	2	2	NUM
ejpam-6139	224	30	,	,	PUNCT
ejpam-6139	224	31	k	k	NOUN
ejpam-6139	224	32	=	=	SYM
ejpam-6139	224	33	1	1	NUM
ejpam-6139	224	34	,	,	PUNCT
ejpam-6139	224	35	s	s	PART
ejpam-6139	224	36	=	=	SYM
ejpam-6139	224	37	1	1	NUM
ejpam-6139	224	38	,	,	PUNCT
ejpam-6139	224	39	µ	µ	NOUN
ejpam-6139	224	40	=	=	SYM
ejpam-6139	224	41	1	1	NUM
ejpam-6139	224	42	and	and	CCONJ
ejpam-6139	224	43	α	α	NOUN
ejpam-6139	224	44	=	=	NOUN
ejpam-6139	224	45	1	1	NUM
ejpam-6139	224	46	in	in	ADP
ejpam-6139	224	47	theorem	theorem	NOUN
ejpam-6139	224	48	1	1	NUM
ejpam-6139	224	49	then	then	ADV
ejpam-6139	224	50	inequality	inequality	NOUN
ejpam-6139	224	51	reduced	reduce	VERB
ejpam-6139	224	52	to	to	ADP
ejpam-6139	224	53	[	[	X
ejpam-6139	224	54	46	46	NUM
ejpam-6139	224	55	]	]	PUNCT
ejpam-6139	224	56	,	,	PUNCT
ejpam-6139	224	57	proposition	proposition	NOUN
ejpam-6139	224	58	2	2	NUM
ejpam-6139	224	59	.	.	NOUN
ejpam-6139	224	60	example	example	NOUN
ejpam-6139	225	1	1	1	NUM
ejpam-6139	225	2	.	.	PUNCT
ejpam-6139	225	3	this	this	DET
ejpam-6139	225	4	example	example	NOUN
ejpam-6139	225	5	illustrates	illustrate	VERB
ejpam-6139	225	6	the	the	DET
ejpam-6139	225	7	verification	verification	NOUN
ejpam-6139	225	8	of	of	ADP
ejpam-6139	225	9	the	the	DET
ejpam-6139	225	10	inequality	inequality	NOUN
ejpam-6139	225	11	stated	state	VERB
ejpam-6139	225	12	in	in	ADP
ejpam-6139	225	13	theorem	theorem	ADJ
ejpam-6139	225	14	1	1	NUM
ejpam-6139	225	15	using	use	VERB
ejpam-6139	225	16	graphs	graph	NOUN
ejpam-6139	225	17	and	and	CCONJ
ejpam-6139	225	18	a	a	DET
ejpam-6139	225	19	table	table	NOUN
ejpam-6139	225	20	.	.	PUNCT
ejpam-6139	226	1	to	to	PART
ejpam-6139	226	2	achieve	achieve	VERB
ejpam-6139	226	3	this	this	PRON
ejpam-6139	226	4	,	,	PUNCT
ejpam-6139	226	5	consider	consider	VERB
ejpam-6139	226	6	the	the	DET
ejpam-6139	226	7	function	function	NOUN
ejpam-6139	226	8	h(x	h(x	PROPN
ejpam-6139	226	9	)	)	PUNCT
ejpam-6139	227	1	=	=	SYM
ejpam-6139	227	2	x6	x6	PROPN
ejpam-6139	227	3	+	+	SYM
ejpam-6139	227	4	2x4	2x4	NUM
ejpam-6139	227	5	defined	define	VERB
ejpam-6139	227	6	over	over	ADP
ejpam-6139	227	7	the	the	DET
ejpam-6139	227	8	interval	interval	NOUN
ejpam-6139	227	9	h	h	NOUN
ejpam-6139	227	10	:	:	PUNCT
ejpam-6139	228	1	[	[	X
ejpam-6139	228	2	2	2	NUM
ejpam-6139	228	3	,	,	PUNCT
ejpam-6139	228	4	7	7	NUM
ejpam-6139	228	5	]	]	PUNCT
ejpam-6139	228	6	→	→	PUNCT
ejpam-6139	228	7	r.	r.	PROPN
ejpam-6139	228	8	the	the	DET
ejpam-6139	228	9	parameters	parameter	NOUN
ejpam-6139	228	10	are	be	AUX
ejpam-6139	228	11	chosen	choose	VERB
ejpam-6139	228	12	as	as	ADP
ejpam-6139	228	13	k	k	PROPN
ejpam-6139	228	14	=	=	SYM
ejpam-6139	228	15	3	3	NUM
ejpam-6139	228	16	,	,	PUNCT
ejpam-6139	228	17	α	α	NOUN
ejpam-6139	228	18	=	=	SYM
ejpam-6139	228	19	4,s=1	4,s=1	PROPN
ejpam-6139	228	20	,	,	PUNCT
ejpam-6139	228	21	and	and	CCONJ
ejpam-6139	228	22	η	η	PROPN
ejpam-6139	228	23	=	=	PROPN
ejpam-6139	228	24	8	8	PROPN
ejpam-6139	228	25	.	.	PUNCT
ejpam-6139	229	1	explanation	explanation	NOUN
ejpam-6139	229	2	:	:	PUNCT
ejpam-6139	229	3	a	a	DET
ejpam-6139	229	4	2d	2d	NUM
ejpam-6139	229	5	plot	plot	NOUN
ejpam-6139	229	6	is	be	AUX
ejpam-6139	229	7	created	create	VERB
ejpam-6139	229	8	to	to	PART
ejpam-6139	229	9	observe	observe	VERB
ejpam-6139	229	10	the	the	DET
ejpam-6139	229	11	function	function	NOUN
ejpam-6139	229	12	’s	’s	PART
ejpam-6139	229	13	behavior	behavior	NOUN
ejpam-6139	229	14	across	across	ADP
ejpam-6139	229	15	the	the	DET
ejpam-6139	229	16	interval	interval	NOUN
ejpam-6139	229	17	µ	µ	X
ejpam-6139	229	18	∈	∈	PROPN
ejpam-6139	229	19	(	(	PUNCT
ejpam-6139	229	20	0	0	NUM
ejpam-6139	229	21	,	,	PUNCT
ejpam-6139	229	22	1	1	NUM
ejpam-6139	229	23	]	]	PUNCT
ejpam-6139	229	24	shown	show	VERB
ejpam-6139	229	25	in	in	ADP
ejpam-6139	229	26	fig	fig	NOUN
ejpam-6139	229	27	.	.	PUNCT
ejpam-6139	230	1	1	1	NUM
ejpam-6139	230	2	,	,	PUNCT
ejpam-6139	230	3	providing	provide	VERB
ejpam-6139	230	4	a	a	DET
ejpam-6139	230	5	visual	visual	ADJ
ejpam-6139	230	6	way	way	NOUN
ejpam-6139	230	7	to	to	PART
ejpam-6139	230	8	analyze	analyze	VERB
ejpam-6139	230	9	the	the	DET
ejpam-6139	230	10	inequality	inequality	NOUN
ejpam-6139	230	11	(	(	PUNCT
ejpam-6139	230	12	9	9	NUM
ejpam-6139	230	13	)	)	PUNCT
ejpam-6139	230	14	.	.	PUNCT
ejpam-6139	231	1	to	to	PART
ejpam-6139	231	2	check	check	VERB
ejpam-6139	231	3	the	the	DET
ejpam-6139	231	4	validity	validity	NOUN
ejpam-6139	231	5	of	of	ADP
ejpam-6139	231	6	the	the	DET
ejpam-6139	231	7	theorem	theorem	NOUN
ejpam-6139	231	8	,	,	PUNCT
ejpam-6139	231	9	we	we	PRON
ejpam-6139	231	10	proceed	proceed	VERB
ejpam-6139	231	11	to	to	PART
ejpam-6139	231	12	calculate	calculate	VERB
ejpam-6139	231	13	numerical	numerical	ADJ
ejpam-6139	231	14	values	value	NOUN
ejpam-6139	231	15	of	of	ADP
ejpam-6139	231	16	the	the	DET
ejpam-6139	231	17	inequality	inequality	NOUN
ejpam-6139	231	18	for	for	ADP
ejpam-6139	231	19	different	different	ADJ
ejpam-6139	231	20	µ	µ	PROPN
ejpam-6139	231	21	and	and	CCONJ
ejpam-6139	231	22	k	k	PROPN
ejpam-6139	231	23	values	value	NOUN
ejpam-6139	231	24	,	,	PUNCT
ejpam-6139	231	25	which	which	PRON
ejpam-6139	231	26	confirm	confirm	VERB
ejpam-6139	231	27	our	our	PRON
ejpam-6139	231	28	results	result	NOUN
ejpam-6139	231	29	.	.	PUNCT
ejpam-6139	232	1	these	these	DET
ejpam-6139	232	2	results	result	NOUN
ejpam-6139	232	3	are	be	AUX
ejpam-6139	232	4	compiled	compile	VERB
ejpam-6139	232	5	into	into	ADP
ejpam-6139	232	6	a	a	DET
ejpam-6139	232	7	table	table	NOUN
ejpam-6139	232	8	shown	show	VERB
ejpam-6139	232	9	in	in	ADP
ejpam-6139	232	10	tables	table	NOUN
ejpam-6139	232	11	1	1	NUM
ejpam-6139	232	12	and	and	CCONJ
ejpam-6139	232	13	2	2	NUM
ejpam-6139	232	14	highlighting	highlight	VERB
ejpam-6139	232	15	the	the	DET
ejpam-6139	232	16	precision	precision	NOUN
ejpam-6139	232	17	and	and	CCONJ
ejpam-6139	232	18	reliability	reliability	NOUN
ejpam-6139	232	19	of	of	ADP
ejpam-6139	232	20	the	the	DET
ejpam-6139	232	21	inequality	inequality	NOUN
ejpam-6139	232	22	.	.	PUNCT
ejpam-6139	233	1	m.	m.	NOUN
ejpam-6139	233	2	samraiz	samraiz	PROPN
ejpam-6139	233	3	et	et	PROPN
ejpam-6139	233	4	al	al	PROPN
ejpam-6139	233	5	.	.	PUNCT
ejpam-6139	233	6	/	/	SYM
ejpam-6139	233	7	eur	eur	PROPN
ejpam-6139	233	8	.	.	PUNCT
ejpam-6139	234	1	j.	j.	PROPN
ejpam-6139	234	2	pure	pure	PROPN
ejpam-6139	234	3	appl	appl	PROPN
ejpam-6139	234	4	.	.	PROPN
ejpam-6139	234	5	math	math	PROPN
ejpam-6139	234	6	,	,	PUNCT
ejpam-6139	234	7	18	18	NUM
ejpam-6139	234	8	(	(	PUNCT
ejpam-6139	234	9	4	4	NUM
ejpam-6139	234	10	)	)	PUNCT
ejpam-6139	234	11	(	(	PUNCT
ejpam-6139	234	12	2025	2025	NUM
ejpam-6139	234	13	)	)	PUNCT
ejpam-6139	234	14	,	,	PUNCT
ejpam-6139	234	15	6139	6139	NUM
ejpam-6139	234	16	9	9	NUM
ejpam-6139	234	17	of	of	ADP
ejpam-6139	234	18	34	34	NUM
ejpam-6139	234	19	figure	figure	NOUN
ejpam-6139	234	20	1	1	NUM
ejpam-6139	234	21	:	:	PUNCT
ejpam-6139	234	22	this	this	DET
ejpam-6139	234	23	figure	figure	NOUN
ejpam-6139	234	24	illustrates	illustrate	VERB
ejpam-6139	234	25	the	the	DET
ejpam-6139	234	26	graphical	graphical	ADJ
ejpam-6139	234	27	representation	representation	NOUN
ejpam-6139	234	28	of	of	ADP
ejpam-6139	234	29	(	(	PUNCT
ejpam-6139	234	30	9	9	NUM
ejpam-6139	234	31	)	)	PUNCT
ejpam-6139	234	32	,	,	PUNCT
ejpam-6139	234	33	corresponding	correspond	VERB
ejpam-6139	234	34	to	to	ADP
ejpam-6139	234	35	µ	µ	PRON
ejpam-6139	234	36	∈	∈	NOUN
ejpam-6139	234	37	(	(	PUNCT
ejpam-6139	234	38	0	0	NUM
ejpam-6139	234	39	,	,	PUNCT
ejpam-6139	234	40	1	1	NUM
ejpam-6139	234	41	]	]	PUNCT
ejpam-6139	234	42	validating	validate	VERB
ejpam-6139	234	43	our	our	PRON
ejpam-6139	234	44	results	result	NOUN
ejpam-6139	234	45	.	.	PUNCT
ejpam-6139	235	1	table	table	NOUN
ejpam-6139	235	2	1	1	NUM
ejpam-6139	235	3	:	:	PUNCT
ejpam-6139	235	4	in	in	ADP
ejpam-6139	235	5	this	this	DET
ejpam-6139	235	6	figure	figure	NOUN
ejpam-6139	235	7	summary	summary	NOUN
ejpam-6139	235	8	of	of	ADP
ejpam-6139	235	9	values	value	NOUN
ejpam-6139	235	10	confirming	confirm	VERB
ejpam-6139	235	11	(	(	PUNCT
ejpam-6139	235	12	9	9	X
ejpam-6139	235	13	)	)	PUNCT
ejpam-6139	235	14	corresponding	correspond	VERB
ejpam-6139	235	15	to	to	ADP
ejpam-6139	235	16	µ	µ	PRON
ejpam-6139	235	17	∈	∈	NOUN
ejpam-6139	235	18	(	(	PUNCT
ejpam-6139	235	19	0	0	NUM
ejpam-6139	235	20	,	,	PUNCT
ejpam-6139	235	21	1	1	NUM
ejpam-6139	235	22	]	]	PUNCT
ejpam-6139	235	23	.	.	PUNCT
ejpam-6139	236	1	µ	µ	PROPN
ejpam-6139	236	2	0.2	0.2	NUM
ejpam-6139	236	3	0.4	0.4	NUM
ejpam-6139	236	4	0.6	0.6	NUM
ejpam-6139	236	5	0.8	0.8	NUM
ejpam-6139	236	6	1	1	NUM
ejpam-6139	236	7	lhs	lhs	PROPN
ejpam-6139	236	8	1368.99	1368.99	NUM
ejpam-6139	236	9	1289.62	1289.62	NUM
ejpam-6139	236	10	1213.3	1213.3	NUM
ejpam-6139	236	11	1142.93	1142.93	NUM
ejpam-6139	236	12	1078.93	1078.93	NUM
ejpam-6139	236	13	rhs	rhs	PROPN
ejpam-6139	236	14	1715.36	1715.36	NUM
ejpam-6139	236	15	1611.45	1611.45	NUM
ejpam-6139	236	16	1512.02	1512.02	NUM
ejpam-6139	236	17	1420.78	1420.78	NUM
ejpam-6139	236	18	1338.12	1338.12	NUM
ejpam-6139	236	19	table	table	NOUN
ejpam-6139	236	20	2	2	NUM
ejpam-6139	236	21	:	:	PUNCT
ejpam-6139	236	22	summary	summary	NOUN
ejpam-6139	236	23	of	of	ADP
ejpam-6139	236	24	values	value	NOUN
ejpam-6139	236	25	confirming	confirm	VERB
ejpam-6139	236	26	(	(	PUNCT
ejpam-6139	236	27	9	9	NUM
ejpam-6139	236	28	)	)	PUNCT
ejpam-6139	236	29	for	for	ADP
ejpam-6139	236	30	k	k	PROPN
ejpam-6139	236	31	∈	∈	PROPN
ejpam-6139	237	1	[	[	X
ejpam-6139	237	2	1	1	NUM
ejpam-6139	237	3	,	,	PUNCT
ejpam-6139	237	4	5	5	NUM
ejpam-6139	237	5	]	]	PUNCT
ejpam-6139	237	6	,	,	PUNCT
ejpam-6139	237	7	while	while	SCONJ
ejpam-6139	237	8	keeping	keep	VERB
ejpam-6139	237	9	µ	µ	X
ejpam-6139	237	10	=	=	SYM
ejpam-6139	237	11	.5	.5	NUM
ejpam-6139	237	12	fixed	fix	VERB
ejpam-6139	237	13	.	.	PUNCT
ejpam-6139	238	1	k	k	NOUN
ejpam-6139	238	2	1	1	NUM
ejpam-6139	238	3	2	2	NUM
ejpam-6139	238	4	3	3	NUM
ejpam-6139	238	5	4	4	NUM
ejpam-6139	238	6	5	5	NUM
ejpam-6139	238	7	lhs	lhs	PROPN
ejpam-6139	238	8	1457.94	1457.94	NUM
ejpam-6139	238	9	1365.57	1365.57	NUM
ejpam-6139	238	10	1258.87	1258.87	NUM
ejpam-6139	238	11	1157.15	1157.15	NUM
ejpam-6139	238	12	1065.55	1065.55	NUM
ejpam-6139	238	13	rhs	rhs	PROPN
ejpam-6139	238	14	1775.59	1775.59	NUM
ejpam-6139	238	15	1681.23	1681.23	NUM
ejpam-6139	238	16	1560.81	1560.81	NUM
ejpam-6139	238	17	1441.05	1441.05	NUM
ejpam-6139	238	18	1331.05	1331.05	NUM
ejpam-6139	238	19	to	to	PART
ejpam-6139	238	20	extend	extend	VERB
ejpam-6139	238	21	the	the	DET
ejpam-6139	238	22	analysis	analysis	NOUN
ejpam-6139	238	23	,	,	PUNCT
ejpam-6139	238	24	a	a	DET
ejpam-6139	238	25	3d	3d	NUM
ejpam-6139	238	26	plot	plot	NOUN
ejpam-6139	238	27	is	be	AUX
ejpam-6139	238	28	generated	generate	VERB
ejpam-6139	238	29	to	to	PART
ejpam-6139	238	30	evaluate	evaluate	VERB
ejpam-6139	238	31	the	the	DET
ejpam-6139	238	32	inequality	inequality	NOUN
ejpam-6139	238	33	for	for	ADP
ejpam-6139	238	34	parameter	parameter	NOUN
ejpam-6139	238	35	ranges	range	VERB
ejpam-6139	238	36	α	α	PROPN
ejpam-6139	238	37	∈	∈	PROPN
ejpam-6139	239	1	[	[	X
ejpam-6139	239	2	5	5	NUM
ejpam-6139	239	3	,	,	PUNCT
ejpam-6139	239	4	10	10	NUM
ejpam-6139	239	5	]	]	PUNCT
ejpam-6139	239	6	and	and	CCONJ
ejpam-6139	239	7	µ	µ	X
ejpam-6139	239	8	∈	∈	NOUN
ejpam-6139	239	9	(	(	PUNCT
ejpam-6139	239	10	0	0	NUM
ejpam-6139	239	11	,	,	PUNCT
ejpam-6139	239	12	1	1	NUM
ejpam-6139	239	13	]	]	PUNCT
ejpam-6139	239	14	.	.	PUNCT
ejpam-6139	240	1	figure	figure	NOUN
ejpam-6139	240	2	2	2	NUM
ejpam-6139	240	3	displays	display	NOUN
ejpam-6139	240	4	this	this	DET
ejpam-6139	240	5	3d	3d	NUM
ejpam-6139	240	6	visualization	visualization	NOUN
ejpam-6139	240	7	,	,	PUNCT
ejpam-6139	240	8	offering	offer	VERB
ejpam-6139	240	9	further	further	ADJ
ejpam-6139	240	10	support	support	NOUN
ejpam-6139	240	11	for	for	ADP
ejpam-6139	240	12	the	the	DET
ejpam-6139	240	13	theorem	theorem	PROPN
ejpam-6139	240	14	.	.	PROPN
ejpam-6139	240	15	figure	figure	NOUN
ejpam-6139	240	16	2	2	NUM
ejpam-6139	240	17	:	:	PUNCT
ejpam-6139	240	18	in	in	ADP
ejpam-6139	240	19	fig	fig	NOUN
ejpam-6139	240	20	.	.	PUNCT
ejpam-6139	241	1	2	2	NUM
ejpam-6139	241	2	three	three	NUM
ejpam-6139	241	3	dimensional	dimensional	ADJ
ejpam-6139	241	4	visualization	visualization	NOUN
ejpam-6139	241	5	validating	validate	VERB
ejpam-6139	241	6	the	the	DET
ejpam-6139	241	7	inequality	inequality	NOUN
ejpam-6139	241	8	of	of	ADP
ejpam-6139	241	9	theorem	theorem	ADJ
ejpam-6139	241	10	1	1	NUM
ejpam-6139	241	11	corresponding	correspond	VERB
ejpam-6139	241	12	to	to	ADP
ejpam-6139	241	13	µ	µ	PRON
ejpam-6139	241	14	∈	∈	NOUN
ejpam-6139	241	15	(	(	PUNCT
ejpam-6139	241	16	0	0	NUM
ejpam-6139	241	17	,	,	PUNCT
ejpam-6139	241	18	1	1	NUM
ejpam-6139	241	19	]	]	PUNCT
ejpam-6139	241	20	and	and	CCONJ
ejpam-6139	241	21	α	α	PRON
ejpam-6139	241	22	∈	∈	PROPN
ejpam-6139	242	1	[	[	X
ejpam-6139	242	2	5	5	NUM
ejpam-6139	242	3	,	,	PUNCT
ejpam-6139	242	4	10	10	NUM
ejpam-6139	242	5	]	]	PUNCT
ejpam-6139	242	6	.	.	PUNCT
ejpam-6139	243	1	the	the	DET
ejpam-6139	243	2	combination	combination	NOUN
ejpam-6139	243	3	of	of	ADP
ejpam-6139	243	4	these	these	DET
ejpam-6139	243	5	methods	method	NOUN
ejpam-6139	243	6	confirms	confirm	VERB
ejpam-6139	243	7	the	the	DET
ejpam-6139	243	8	robustness	robustness	NOUN
ejpam-6139	243	9	and	and	CCONJ
ejpam-6139	243	10	applicability	applicability	NOUN
ejpam-6139	243	11	of	of	ADP
ejpam-6139	243	12	theorem	theorem	NOUN
ejpam-6139	243	13	1	1	NUM
ejpam-6139	243	14	in	in	ADP
ejpam-6139	243	15	describing	describe	VERB
ejpam-6139	243	16	the	the	DET
ejpam-6139	243	17	behavior	behavior	NOUN
ejpam-6139	243	18	of	of	ADP
ejpam-6139	243	19	h(x	h(x	PROPN
ejpam-6139	243	20	)	)	PUNCT
ejpam-6139	243	21	under	under	ADP
ejpam-6139	243	22	the	the	DET
ejpam-6139	243	23	given	give	VERB
ejpam-6139	243	24	conditions	condition	NOUN
ejpam-6139	243	25	.	.	PUNCT
ejpam-6139	244	1	m.	m.	NOUN
ejpam-6139	244	2	samraiz	samraiz	PROPN
ejpam-6139	244	3	et	et	PROPN
ejpam-6139	244	4	al	al	PROPN
ejpam-6139	244	5	.	.	PUNCT
ejpam-6139	244	6	/	/	SYM
ejpam-6139	244	7	eur	eur	PROPN
ejpam-6139	244	8	.	.	PUNCT
ejpam-6139	245	1	j.	j.	PROPN
ejpam-6139	245	2	pure	pure	PROPN
ejpam-6139	245	3	appl	appl	PROPN
ejpam-6139	245	4	.	.	PROPN
ejpam-6139	245	5	math	math	PROPN
ejpam-6139	245	6	,	,	PUNCT
ejpam-6139	245	7	18	18	NUM
ejpam-6139	245	8	(	(	PUNCT
ejpam-6139	245	9	4	4	NUM
ejpam-6139	245	10	)	)	PUNCT
ejpam-6139	245	11	(	(	PUNCT
ejpam-6139	245	12	2025	2025	NUM
ejpam-6139	245	13	)	)	PUNCT
ejpam-6139	245	14	,	,	PUNCT
ejpam-6139	245	15	6139	6139	NUM
ejpam-6139	245	16	10	10	NUM
ejpam-6139	245	17	of	of	ADP
ejpam-6139	245	18	34	34	NUM
ejpam-6139	245	19	theorem	theorem	NOUN
ejpam-6139	245	20	2	2	NUM
ejpam-6139	245	21	.	.	X
ejpam-6139	245	22	assume	assume	VERB
ejpam-6139	245	23	that	that	SCONJ
ejpam-6139	245	24	h	h	NOUN
ejpam-6139	245	25	:	:	PUNCT
ejpam-6139	246	1	[	[	X
ejpam-6139	246	2	ν	ν	X
ejpam-6139	246	3	,	,	PUNCT
ejpam-6139	246	4	ω	ω	NOUN
ejpam-6139	246	5	]	]	X
ejpam-6139	246	6	→	→	PUNCT
ejpam-6139	246	7	r	r	NOUN
ejpam-6139	246	8	is	be	AUX
ejpam-6139	246	9	a	a	DET
ejpam-6139	246	10	twice	twice	ADV
ejpam-6139	246	11	differentiable	differentiable	ADJ
ejpam-6139	246	12	function	function	NOUN
ejpam-6139	246	13	on	on	ADP
ejpam-6139	246	14	(	(	PUNCT
ejpam-6139	246	15	ν	ν	PROPN
ejpam-6139	246	16	,	,	PUNCT
ejpam-6139	246	17	ω	ω	NOUN
ejpam-6139	246	18	)	)	PUNCT
ejpam-6139	246	19	such	such	ADJ
ejpam-6139	246	20	that	that	SCONJ
ejpam-6139	246	21	h′′	h′′	PROPN
ejpam-6139	246	22	∈	∈	PROPN
ejpam-6139	246	23	lp([ν	lp([ν	PROPN
ejpam-6139	246	24	,	,	PUNCT
ejpam-6139	246	25	ω	ω	NOUN
ejpam-6139	246	26	]	]	PUNCT
ejpam-6139	246	27	)	)	PUNCT
ejpam-6139	246	28	with	with	ADP
ejpam-6139	246	29	ν	ν	X
ejpam-6139	246	30	<	<	X
ejpam-6139	246	31	ω	ω	PROPN
ejpam-6139	246	32	.	.	PUNCT
ejpam-6139	247	1	let	let	VERB
ejpam-6139	247	2	|h′′|q	|h′′|q	NOUN
ejpam-6139	247	3	be	be	AUX
ejpam-6139	247	4	s	s	NOUN
ejpam-6139	247	5	-	-	NOUN
ejpam-6139	247	6	convex	convex	ADJ
ejpam-6139	247	7	in	in	ADP
ejpam-6139	247	8	second	second	ADJ
ejpam-6139	247	9	sense	sense	NOUN
ejpam-6139	247	10	on	on	ADP
ejpam-6139	247	11	[	[	X
ejpam-6139	247	12	ν	ν	X
ejpam-6139	247	13	,	,	PUNCT
ejpam-6139	247	14	ω	ω	NOUN
ejpam-6139	247	15	]	]	PUNCT
ejpam-6139	247	16	with	with	ADP
ejpam-6139	247	17	q	q	PROPN
ejpam-6139	247	18	>	>	X
ejpam-6139	247	19	1	1	NUM
ejpam-6139	247	20	then	then	ADV
ejpam-6139	247	21	inequality	inequality	NOUN
ejpam-6139	247	22	is	be	AUX
ejpam-6139	247	23	given	give	VERB
ejpam-6139	247	24	by,∣∣∣∣h(ν	by,∣∣∣∣h(ν	PROPN
ejpam-6139	247	25	)	)	PUNCT
ejpam-6139	248	1	+	+	CCONJ
ejpam-6139	248	2	h(ω	h(ω	PROPN
ejpam-6139	248	3	)	)	PUNCT
ejpam-6139	248	4	η	η	PROPN
ejpam-6139	248	5	+	+	PROPN
ejpam-6139	248	6	ϕk(µ	ϕk(µ	NUM
ejpam-6139	248	7	,	,	PUNCT
ejpam-6139	248	8	α)−	α)−	PROPN
ejpam-6139	248	9	η	η	PROPN
ejpam-6139	248	10	µα	µα	ADP
ejpam-6139	248	11	k	k	PROPN
ejpam-6139	248	12	−1	−1	NOUN
ejpam-6139	248	13	(	(	PUNCT
ejpam-6139	248	14	ω	ω	NOUN
ejpam-6139	248	15	−	−	NOUN
ejpam-6139	248	16	ν	ν	NOUN
ejpam-6139	248	17	)	)	PUNCT
ejpam-6139	248	18	µα	µα	ADP
ejpam-6139	248	19	k	k	PROPN
ejpam-6139	248	20	(	(	PUNCT
ejpam-6139	248	21	kµ	kµ	PROPN
ejpam-6139	248	22	)	)	PUNCT
ejpam-6139	249	1	α	α	PROPN
ejpam-6139	249	2	k	k	PROPN
ejpam-6139	249	3	γ	γ	X
ejpam-6139	249	4	(	(	PUNCT
ejpam-6139	249	5	α	α	NOUN
ejpam-6139	249	6	k	k	PROPN
ejpam-6139	250	1	+	+	CCONJ
ejpam-6139	250	2	1	1	X
ejpam-6139	250	3	)	)	PUNCT
ejpam-6139	250	4	×	×	NOUN
ejpam-6139	250	5	(	(	PUNCT
ejpam-6139	250	6	α	α	PROPN
ejpam-6139	250	7	kj	kj	PROPN
ejpam-6139	250	8	µ	µ	PROPN
ejpam-6139	250	9	(	(	PUNCT
ejpam-6139	250	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	250	11	η	η	PROPN
ejpam-6139	250	12	−	−	PROPN
ejpam-6139	250	13	h(ν	h(ν	PROPN
ejpam-6139	250	14	)	)	PUNCT
ejpam-6139	251	1	+	+	NOUN
ejpam-6139	251	2	α	α	PROPN
ejpam-6139	251	3	k	k	X
ejpam-6139	251	4	jµ	jµ	PROPN
ejpam-6139	251	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	251	6	η	η	PROPN
ejpam-6139	251	7	+	+	PROPN
ejpam-6139	251	8	h(ω	h(ω	PROPN
ejpam-6139	251	9	)	)	PUNCT
ejpam-6139	251	10	)	)	PUNCT
ejpam-6139	252	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	252	2	≤	≤	NOUN
ejpam-6139	252	3	(	(	PUNCT
ejpam-6139	252	4	ω	ω	NOUN
ejpam-6139	252	5	−	−	NOUN
ejpam-6139	252	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	252	7	)	)	PUNCT
ejpam-6139	252	8	α	α	PROPN
ejpam-6139	253	1	k	k	PROPN
ejpam-6139	253	2	η3	η3	PROPN
ejpam-6139	253	3	×	×	NOUN
ejpam-6139	253	4	(	(	PUNCT
ejpam-6139	253	5	∫	∫	PROPN
ejpam-6139	253	6	1	1	NUM
ejpam-6139	253	7	0	0	NUM
ejpam-6139	253	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	253	9	∫	∫	PROPN
ejpam-6139	253	10	t	t	PROPN
ejpam-6139	253	11	0	0	NUM
ejpam-6139	254	1	(	(	PUNCT
ejpam-6139	254	2	1	1	NUM
ejpam-6139	254	3	(	(	PUNCT
ejpam-6139	254	4	kµ	kµ	PROPN
ejpam-6139	254	5	)	)	PUNCT
ejpam-6139	254	6	α	α	PROPN
ejpam-6139	254	7	k	k	NOUN
ejpam-6139	255	1	−	−	PROPN
ejpam-6139	255	2	(	(	PUNCT
ejpam-6139	255	3	1−	1−	NUM
ejpam-6139	255	4	(	(	PUNCT
ejpam-6139	255	5	1−	1−	NUM
ejpam-6139	255	6	φ)µ	φ)µ	NOUN
ejpam-6139	255	7	kµ	kµ	NOUN
ejpam-6139	255	8	)	)	PUNCT
ejpam-6139	255	9	α	α	PROPN
ejpam-6139	255	10	k	k	PROPN
ejpam-6139	255	11	)	)	PUNCT
ejpam-6139	255	12	dφ	dφ	ADP
ejpam-6139	255	13	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	255	14	)	)	PUNCT
ejpam-6139	255	15	1	1	NUM
ejpam-6139	255	16	p	p	NOUN
ejpam-6139	255	17	×	×	NOUN
ejpam-6139	255	18	(	(	PUNCT
ejpam-6139	255	19	[	[	X
ejpam-6139	255	20	(	(	PUNCT
ejpam-6139	255	21	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	255	22	ηs(s+	ηs(s+	NOUN
ejpam-6139	255	23	1	1	NUM
ejpam-6139	255	24	)	)	PUNCT
ejpam-6139	255	25	−	−	PROPN
ejpam-6139	255	26	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	255	27	ηs(s+	ηs(s+	PROPN
ejpam-6139	255	28	1	1	NUM
ejpam-6139	255	29	)	)	PUNCT
ejpam-6139	255	30	)	)	PUNCT
ejpam-6139	255	31	(	(	PUNCT
ejpam-6139	255	32	(	(	PUNCT
ejpam-6139	255	33	η	η	PROPN
ejpam-6139	255	34	−	−	PROPN
ejpam-6139	255	35	1)s+1	1)s+1	NUM
ejpam-6139	255	36	−	−	PROPN
ejpam-6139	255	37	ηs+1	ηs+1	PROPN
ejpam-6139	255	38	)	)	PUNCT
ejpam-6139	255	39	]	]	PUNCT
ejpam-6139	256	1	1	1	NUM
ejpam-6139	256	2	q	q	NOUN
ejpam-6139	256	3	+	+	X
ejpam-6139	257	1	[	[	X
ejpam-6139	257	2	(	(	PUNCT
ejpam-6139	257	3	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	257	4	ηs(s+	ηs(s+	PROPN
ejpam-6139	257	5	1	1	NUM
ejpam-6139	257	6	)	)	PUNCT
ejpam-6139	257	7	−	−	PROPN
ejpam-6139	257	8	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	257	9	ηs(s+	ηs(s+	NOUN
ejpam-6139	257	10	1	1	NUM
ejpam-6139	257	11	)	)	PUNCT
ejpam-6139	257	12	)	)	PUNCT
ejpam-6139	258	1	(	(	PUNCT
ejpam-6139	258	2	(	(	PUNCT
ejpam-6139	258	3	η	η	PROPN
ejpam-6139	258	4	−	−	PROPN
ejpam-6139	258	5	1)s+1	1)s+1	NUM
ejpam-6139	258	6	−	−	PROPN
ejpam-6139	258	7	ηs+1	ηs+1	PROPN
ejpam-6139	258	8	)	)	PUNCT
ejpam-6139	258	9	]	]	PUNCT
ejpam-6139	259	1	1	1	NUM
ejpam-6139	259	2	q	q	NOUN
ejpam-6139	259	3	)	)	PUNCT
ejpam-6139	259	4	.	.	PUNCT
ejpam-6139	260	1	(	(	PUNCT
ejpam-6139	260	2	12	12	NUM
ejpam-6139	260	3	)	)	PUNCT
ejpam-6139	260	4	proof	proof	NOUN
ejpam-6139	260	5	.	.	PUNCT
ejpam-6139	261	1	by	by	ADP
ejpam-6139	261	2	employing	employ	VERB
ejpam-6139	261	3	hölder	hölder	NOUN
ejpam-6139	261	4	inequality	inequality	NOUN
ejpam-6139	261	5	on	on	ADP
ejpam-6139	261	6	(	(	PUNCT
ejpam-6139	261	7	10	10	NUM
ejpam-6139	261	8	)	)	PUNCT
ejpam-6139	261	9	,	,	PUNCT
ejpam-6139	261	10	we	we	PRON
ejpam-6139	261	11	get∣∣∣∣h(ν	get∣∣∣∣h(ν	NOUN
ejpam-6139	261	12	)	)	PUNCT
ejpam-6139	262	1	+	+	CCONJ
ejpam-6139	262	2	h(ω	h(ω	PROPN
ejpam-6139	262	3	)	)	PUNCT
ejpam-6139	262	4	η	η	PROPN
ejpam-6139	262	5	+	+	PROPN
ejpam-6139	262	6	ϕk(µ	ϕk(µ	NUM
ejpam-6139	262	7	,	,	PUNCT
ejpam-6139	262	8	α)−	α)−	PROPN
ejpam-6139	262	9	η	η	PROPN
ejpam-6139	262	10	µα	µα	ADP
ejpam-6139	262	11	k	k	PROPN
ejpam-6139	262	12	−1	−1	NOUN
ejpam-6139	262	13	(	(	PUNCT
ejpam-6139	262	14	ω	ω	NOUN
ejpam-6139	262	15	−	−	NOUN
ejpam-6139	262	16	ν	ν	NOUN
ejpam-6139	262	17	)	)	PUNCT
ejpam-6139	262	18	µα	µα	ADP
ejpam-6139	262	19	k	k	PROPN
ejpam-6139	262	20	(	(	PUNCT
ejpam-6139	262	21	kµ	kµ	PROPN
ejpam-6139	262	22	)	)	PUNCT
ejpam-6139	263	1	α	α	PROPN
ejpam-6139	263	2	k	k	PROPN
ejpam-6139	263	3	γ	γ	X
ejpam-6139	263	4	(	(	PUNCT
ejpam-6139	263	5	α	α	NOUN
ejpam-6139	263	6	k	k	PROPN
ejpam-6139	264	1	+	+	PROPN
ejpam-6139	264	2	1	1	X
ejpam-6139	264	3	)	)	PUNCT
ejpam-6139	264	4	×	×	NOUN
ejpam-6139	264	5	(	(	PUNCT
ejpam-6139	264	6	α	α	PROPN
ejpam-6139	264	7	kj	kj	PROPN
ejpam-6139	264	8	µ	µ	PROPN
ejpam-6139	264	9	(	(	PUNCT
ejpam-6139	264	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	264	11	η	η	PROPN
ejpam-6139	264	12	−	−	PROPN
ejpam-6139	264	13	h(ν	h(ν	PROPN
ejpam-6139	264	14	)	)	PUNCT
ejpam-6139	265	1	+	+	NOUN
ejpam-6139	265	2	α	α	PROPN
ejpam-6139	265	3	k	k	X
ejpam-6139	265	4	jµ	jµ	PROPN
ejpam-6139	265	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	265	6	η	η	PROPN
ejpam-6139	265	7	+	+	PROPN
ejpam-6139	265	8	h(ω	h(ω	PROPN
ejpam-6139	265	9	)	)	PUNCT
ejpam-6139	265	10	)	)	PUNCT
ejpam-6139	266	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	266	2	≤	≤	NOUN
ejpam-6139	266	3	(	(	PUNCT
ejpam-6139	266	4	ω	ω	NOUN
ejpam-6139	266	5	−	−	NOUN
ejpam-6139	266	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	266	7	)	)	PUNCT
ejpam-6139	266	8	α	α	PROPN
ejpam-6139	267	1	k	k	PROPN
ejpam-6139	267	2	η3	η3	PROPN
ejpam-6139	267	3	×	×	PROPN
ejpam-6139	267	4	[	[	X
ejpam-6139	267	5	(	(	PUNCT
ejpam-6139	267	6	∫	∫	PROPN
ejpam-6139	267	7	1	1	NUM
ejpam-6139	267	8	0	0	NUM
ejpam-6139	267	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	267	10	∫	∫	PROPN
ejpam-6139	267	11	t	t	PROPN
ejpam-6139	267	12	0	0	NUM
ejpam-6139	267	13	(	(	PUNCT
ejpam-6139	267	14	1	1	NUM
ejpam-6139	267	15	(	(	PUNCT
ejpam-6139	267	16	kµ	kµ	PROPN
ejpam-6139	267	17	)	)	PUNCT
ejpam-6139	267	18	α	α	PROPN
ejpam-6139	267	19	k	k	NOUN
ejpam-6139	268	1	−	−	PROPN
ejpam-6139	268	2	(	(	PUNCT
ejpam-6139	268	3	1−	1−	NUM
ejpam-6139	268	4	(	(	PUNCT
ejpam-6139	268	5	1−	1−	NUM
ejpam-6139	268	6	φ)µ	φ)µ	NOUN
ejpam-6139	268	7	kµ	kµ	NOUN
ejpam-6139	268	8	)	)	PUNCT
ejpam-6139	268	9	α	α	PROPN
ejpam-6139	268	10	k	k	PROPN
ejpam-6139	268	11	)	)	PUNCT
ejpam-6139	268	12	dφ	dφ	ADP
ejpam-6139	268	13	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	268	14	)	)	PUNCT
ejpam-6139	268	15	1	1	NUM
ejpam-6139	268	16	p	p	NOUN
ejpam-6139	268	17	×	×	NOUN
ejpam-6139	268	18	(	(	PUNCT
ejpam-6139	268	19	∫	∫	PROPN
ejpam-6139	268	20	1	1	NUM
ejpam-6139	268	21	0	0	NUM
ejpam-6139	268	22	∣∣∣∣h′′((η	∣∣∣∣h′′((η	PROPN
ejpam-6139	268	23	−	−	PROPN
ejpam-6139	268	24	t	t	PROPN
ejpam-6139	268	25	η	η	PROPN
ejpam-6139	268	26	)	)	PUNCT
ejpam-6139	269	1	ν	ν	PROPN
ejpam-6139	269	2	+	+	CCONJ
ejpam-6139	269	3	t	t	PROPN
ejpam-6139	269	4	η	η	PROPN
ejpam-6139	269	5	ω	ω	PROPN
ejpam-6139	269	6	)	)	PUNCT
ejpam-6139	269	7	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	269	8	)	)	PUNCT
ejpam-6139	269	9	1	1	NUM
ejpam-6139	269	10	q	q	NOUN
ejpam-6139	270	1	+	+	CCONJ
ejpam-6139	270	2	(	(	PUNCT
ejpam-6139	270	3	∫	∫	PROPN
ejpam-6139	270	4	1	1	NUM
ejpam-6139	270	5	0	0	NUM
ejpam-6139	270	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	270	7	∫	∫	PROPN
ejpam-6139	270	8	t	t	PROPN
ejpam-6139	270	9	0	0	NUM
ejpam-6139	270	10	(	(	PUNCT
ejpam-6139	270	11	1	1	NUM
ejpam-6139	270	12	(	(	PUNCT
ejpam-6139	270	13	kµ	kµ	PROPN
ejpam-6139	270	14	)	)	PUNCT
ejpam-6139	270	15	α	α	PROPN
ejpam-6139	270	16	k	k	NOUN
ejpam-6139	271	1	−	−	PROPN
ejpam-6139	271	2	(	(	PUNCT
ejpam-6139	271	3	1−	1−	NUM
ejpam-6139	271	4	(	(	PUNCT
ejpam-6139	271	5	1−	1−	NUM
ejpam-6139	271	6	φ)µ	φ)µ	NOUN
ejpam-6139	271	7	kµ	kµ	NOUN
ejpam-6139	271	8	)	)	PUNCT
ejpam-6139	271	9	α	α	PROPN
ejpam-6139	271	10	k	k	PROPN
ejpam-6139	271	11	)	)	PUNCT
ejpam-6139	271	12	dφ	dφ	ADP
ejpam-6139	271	13	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	271	14	)	)	PUNCT
ejpam-6139	271	15	1	1	NUM
ejpam-6139	271	16	p	p	NOUN
ejpam-6139	271	17	×	×	NOUN
ejpam-6139	271	18	(	(	PUNCT
ejpam-6139	271	19	∫	∫	PROPN
ejpam-6139	271	20	1	1	NUM
ejpam-6139	271	21	0	0	NUM
ejpam-6139	271	22	∣∣∣∣h′′	∣∣∣∣h′′	NOUN
ejpam-6139	271	23	(	(	PUNCT
ejpam-6139	271	24	t	t	PROPN
ejpam-6139	271	25	η	η	PROPN
ejpam-6139	271	26	ν	ν	PROPN
ejpam-6139	271	27	+	+	CCONJ
ejpam-6139	271	28	(	(	PUNCT
ejpam-6139	271	29	η	η	PROPN
ejpam-6139	271	30	−	−	PROPN
ejpam-6139	271	31	t	t	PROPN
ejpam-6139	271	32	η	η	PROPN
ejpam-6139	271	33	)	)	PUNCT
ejpam-6139	271	34	ω	ω	PROPN
ejpam-6139	271	35	)	)	PUNCT
ejpam-6139	271	36	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	271	37	)	)	PUNCT
ejpam-6139	271	38	1	1	NUM
ejpam-6139	271	39	q	q	NOUN
ejpam-6139	271	40	.	.	PUNCT
ejpam-6139	272	1	(	(	PUNCT
ejpam-6139	272	2	13	13	NUM
ejpam-6139	272	3	)	)	PUNCT
ejpam-6139	272	4	by	by	ADP
ejpam-6139	272	5	considering	consider	VERB
ejpam-6139	272	6	s	s	NOUN
ejpam-6139	272	7	-	-	NOUN
ejpam-6139	272	8	convexity	convexity	NOUN
ejpam-6139	272	9	in	in	ADP
ejpam-6139	272	10	second	second	ADJ
ejpam-6139	272	11	sense	sense	NOUN
ejpam-6139	272	12	of	of	ADP
ejpam-6139	272	13	|h′′(x)|q	|h′′(x)|q	PROPN
ejpam-6139	272	14	,	,	PUNCT
ejpam-6139	272	15	then∫	then∫	NOUN
ejpam-6139	272	16	1	1	NUM
ejpam-6139	272	17	0	0	NUM
ejpam-6139	272	18	∣∣∣∣h′′((η	∣∣∣∣h′′((η	PROPN
ejpam-6139	272	19	−	−	PROPN
ejpam-6139	272	20	t	t	PROPN
ejpam-6139	272	21	η	η	PROPN
ejpam-6139	272	22	)	)	PUNCT
ejpam-6139	273	1	ν	ν	PROPN
ejpam-6139	273	2	+	+	CCONJ
ejpam-6139	273	3	t	t	PROPN
ejpam-6139	273	4	η	η	PROPN
ejpam-6139	273	5	ω	ω	PROPN
ejpam-6139	273	6	)	)	PUNCT
ejpam-6139	273	7	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	273	8	≤	≤	NUM
ejpam-6139	273	9	∫	∫	NOUN
ejpam-6139	273	10	1	1	NUM
ejpam-6139	273	11	0	0	NUM
ejpam-6139	274	1	[	[	X
ejpam-6139	274	2	(	(	PUNCT
ejpam-6139	274	3	η	η	PROPN
ejpam-6139	274	4	−	−	PROPN
ejpam-6139	274	5	t	t	PROPN
ejpam-6139	274	6	η	η	PROPN
ejpam-6139	274	7	)	)	PUNCT
ejpam-6139	274	8	s	s	PART
ejpam-6139	274	9	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	274	10	+	+	NUM
ejpam-6139	274	11	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	274	12	(	(	PUNCT
ejpam-6139	274	13	t	t	PROPN
ejpam-6139	274	14	η	η	PROPN
ejpam-6139	274	15	)	)	PUNCT
ejpam-6139	274	16	s	s	PART
ejpam-6139	274	17	]	]	X
ejpam-6139	274	18	dt	dt	X
ejpam-6139	274	19	≤	≤	X
ejpam-6139	274	20	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	274	21	ηs(s+	ηs(s+	NOUN
ejpam-6139	274	22	1	1	NUM
ejpam-6139	274	23	)	)	PUNCT
ejpam-6139	274	24	−	−	PROPN
ejpam-6139	275	1	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	275	2	ηs(s+	ηs(s+	PROPN
ejpam-6139	275	3	1	1	NUM
ejpam-6139	275	4	)	)	PUNCT
ejpam-6139	275	5	[	[	PUNCT
ejpam-6139	275	6	(	(	PUNCT
ejpam-6139	275	7	η	η	PROPN
ejpam-6139	275	8	−	−	PROPN
ejpam-6139	275	9	1)s+1	1)s+1	NUM
ejpam-6139	275	10	−	−	PROPN
ejpam-6139	275	11	ηs+1	ηs+1	PROPN
ejpam-6139	275	12	]	]	PUNCT
ejpam-6139	275	13	.	.	PUNCT
ejpam-6139	276	1	(	(	PUNCT
ejpam-6139	276	2	14	14	NUM
ejpam-6139	276	3	)	)	PUNCT
ejpam-6139	276	4	similarly∫	similarly∫	ADJ
ejpam-6139	276	5	1	1	NUM
ejpam-6139	276	6	0	0	NUM
ejpam-6139	276	7	∣∣∣∣h′′	∣∣∣∣h′′	NOUN
ejpam-6139	276	8	(	(	PUNCT
ejpam-6139	276	9	t	t	PROPN
ejpam-6139	276	10	η	η	PROPN
ejpam-6139	276	11	ν	ν	PROPN
ejpam-6139	276	12	+	+	CCONJ
ejpam-6139	276	13	(	(	PUNCT
ejpam-6139	276	14	1−	1−	NUM
ejpam-6139	276	15	t	t	PROPN
ejpam-6139	276	16	η	η	PROPN
ejpam-6139	276	17	)	)	PUNCT
ejpam-6139	276	18	ω	ω	PROPN
ejpam-6139	276	19	)	)	PUNCT
ejpam-6139	277	1	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	277	2	≤	≤	NUM
ejpam-6139	277	3	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	277	4	ηs(s+	ηs(s+	PROPN
ejpam-6139	277	5	1	1	NUM
ejpam-6139	277	6	)	)	PUNCT
ejpam-6139	277	7	−	−	PROPN
ejpam-6139	277	8	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	277	9	ηs(s+	ηs(s+	NOUN
ejpam-6139	277	10	1	1	NUM
ejpam-6139	277	11	)	)	PUNCT
ejpam-6139	277	12	[	[	PUNCT
ejpam-6139	277	13	(	(	PUNCT
ejpam-6139	277	14	η	η	PROPN
ejpam-6139	277	15	−	−	PROPN
ejpam-6139	277	16	1)s+1	1)s+1	NUM
ejpam-6139	277	17	−	−	PROPN
ejpam-6139	277	18	ηs+1	ηs+1	PROPN
ejpam-6139	277	19	]	]	PUNCT
ejpam-6139	277	20	.	.	PUNCT
ejpam-6139	278	1	(	(	PUNCT
ejpam-6139	278	2	15	15	X
ejpam-6139	278	3	)	)	PUNCT
ejpam-6139	278	4	m.	m.	NOUN
ejpam-6139	278	5	samraiz	samraiz	PROPN
ejpam-6139	278	6	et	et	PROPN
ejpam-6139	278	7	al	al	PROPN
ejpam-6139	278	8	.	.	PUNCT
ejpam-6139	278	9	/	/	SYM
ejpam-6139	278	10	eur	eur	PROPN
ejpam-6139	278	11	.	.	PUNCT
ejpam-6139	279	1	j.	j.	PROPN
ejpam-6139	279	2	pure	pure	PROPN
ejpam-6139	279	3	appl	appl	PROPN
ejpam-6139	279	4	.	.	PROPN
ejpam-6139	279	5	math	math	PROPN
ejpam-6139	279	6	,	,	PUNCT
ejpam-6139	279	7	18	18	NUM
ejpam-6139	279	8	(	(	PUNCT
ejpam-6139	279	9	4	4	NUM
ejpam-6139	279	10	)	)	PUNCT
ejpam-6139	279	11	(	(	PUNCT
ejpam-6139	279	12	2025	2025	NUM
ejpam-6139	279	13	)	)	PUNCT
ejpam-6139	279	14	,	,	PUNCT
ejpam-6139	279	15	6139	6139	NUM
ejpam-6139	279	16	11	11	NUM
ejpam-6139	279	17	of	of	ADP
ejpam-6139	279	18	34	34	NUM
ejpam-6139	279	19	substituting	substitute	VERB
ejpam-6139	279	20	both	both	PRON
ejpam-6139	279	21	(	(	PUNCT
ejpam-6139	279	22	14	14	NUM
ejpam-6139	279	23	)	)	PUNCT
ejpam-6139	279	24	and	and	CCONJ
ejpam-6139	279	25	(	(	PUNCT
ejpam-6139	279	26	15	15	NUM
ejpam-6139	279	27	)	)	PUNCT
ejpam-6139	279	28	in	in	ADP
ejpam-6139	279	29	(	(	PUNCT
ejpam-6139	279	30	13	13	NUM
ejpam-6139	279	31	)	)	PUNCT
ejpam-6139	279	32	,	,	PUNCT
ejpam-6139	279	33	we	we	PRON
ejpam-6139	279	34	conclude∣∣∣∣h(ν	conclude∣∣∣∣h(ν	NOUN
ejpam-6139	279	35	)	)	PUNCT
ejpam-6139	280	1	+	+	CCONJ
ejpam-6139	280	2	h(ω	h(ω	PROPN
ejpam-6139	280	3	)	)	PUNCT
ejpam-6139	280	4	η	η	PROPN
ejpam-6139	280	5	+	+	PROPN
ejpam-6139	280	6	ϕk(µ	ϕk(µ	NUM
ejpam-6139	280	7	,	,	PUNCT
ejpam-6139	280	8	α)−	α)−	PROPN
ejpam-6139	280	9	η	η	PROPN
ejpam-6139	280	10	µα	µα	ADP
ejpam-6139	280	11	k	k	PROPN
ejpam-6139	280	12	−1	−1	NOUN
ejpam-6139	280	13	(	(	PUNCT
ejpam-6139	280	14	ω	ω	NOUN
ejpam-6139	280	15	−	−	NOUN
ejpam-6139	280	16	ν	ν	NOUN
ejpam-6139	280	17	)	)	PUNCT
ejpam-6139	280	18	µα	µα	ADP
ejpam-6139	280	19	k	k	PROPN
ejpam-6139	280	20	(	(	PUNCT
ejpam-6139	280	21	kµ	kµ	PROPN
ejpam-6139	280	22	)	)	PUNCT
ejpam-6139	281	1	α	α	PROPN
ejpam-6139	281	2	k	k	PROPN
ejpam-6139	281	3	γ	γ	X
ejpam-6139	281	4	(	(	PUNCT
ejpam-6139	281	5	α	α	NOUN
ejpam-6139	281	6	k	k	PROPN
ejpam-6139	282	1	+	+	CCONJ
ejpam-6139	282	2	1	1	X
ejpam-6139	282	3	)	)	PUNCT
ejpam-6139	282	4	×	×	NOUN
ejpam-6139	282	5	(	(	PUNCT
ejpam-6139	282	6	α	α	PROPN
ejpam-6139	282	7	kj	kj	PROPN
ejpam-6139	282	8	µ	µ	PROPN
ejpam-6139	282	9	(	(	PUNCT
ejpam-6139	282	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	282	11	η	η	PROPN
ejpam-6139	282	12	−	−	PROPN
ejpam-6139	282	13	h(ν	h(ν	PROPN
ejpam-6139	282	14	)	)	PUNCT
ejpam-6139	283	1	+	+	NOUN
ejpam-6139	283	2	α	α	PROPN
ejpam-6139	283	3	k	k	X
ejpam-6139	283	4	jµ	jµ	PROPN
ejpam-6139	283	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	283	6	η	η	PROPN
ejpam-6139	283	7	+	+	PROPN
ejpam-6139	283	8	h(ω	h(ω	PROPN
ejpam-6139	283	9	)	)	PUNCT
ejpam-6139	283	10	)	)	PUNCT
ejpam-6139	284	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	284	2	≤	≤	NOUN
ejpam-6139	284	3	(	(	PUNCT
ejpam-6139	284	4	ω	ω	NOUN
ejpam-6139	284	5	−	−	NOUN
ejpam-6139	284	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	284	7	)	)	PUNCT
ejpam-6139	284	8	α	α	PROPN
ejpam-6139	285	1	k	k	PROPN
ejpam-6139	285	2	η3	η3	PROPN
ejpam-6139	285	3	×	×	NOUN
ejpam-6139	285	4	(	(	PUNCT
ejpam-6139	285	5	∫	∫	PROPN
ejpam-6139	285	6	1	1	NUM
ejpam-6139	285	7	0	0	NUM
ejpam-6139	285	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	285	9	∫	∫	PROPN
ejpam-6139	285	10	t	t	PROPN
ejpam-6139	285	11	0	0	NUM
ejpam-6139	286	1	(	(	PUNCT
ejpam-6139	286	2	1	1	NUM
ejpam-6139	286	3	(	(	PUNCT
ejpam-6139	286	4	kµ	kµ	PROPN
ejpam-6139	286	5	)	)	PUNCT
ejpam-6139	286	6	α	α	PROPN
ejpam-6139	286	7	k	k	NOUN
ejpam-6139	287	1	−	−	PROPN
ejpam-6139	287	2	(	(	PUNCT
ejpam-6139	287	3	1−	1−	NUM
ejpam-6139	287	4	(	(	PUNCT
ejpam-6139	287	5	1−	1−	NUM
ejpam-6139	287	6	φ)µ	φ)µ	NOUN
ejpam-6139	287	7	kµ	kµ	NOUN
ejpam-6139	287	8	)	)	PUNCT
ejpam-6139	287	9	α	α	PROPN
ejpam-6139	287	10	k	k	PROPN
ejpam-6139	287	11	)	)	PUNCT
ejpam-6139	287	12	dφ	dφ	ADP
ejpam-6139	287	13	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	287	14	)	)	PUNCT
ejpam-6139	287	15	1	1	NUM
ejpam-6139	287	16	p	p	NOUN
ejpam-6139	287	17	×	×	NOUN
ejpam-6139	287	18	(	(	PUNCT
ejpam-6139	287	19	[	[	X
ejpam-6139	287	20	(	(	PUNCT
ejpam-6139	287	21	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	287	22	ηs(s+	ηs(s+	NOUN
ejpam-6139	287	23	1	1	NUM
ejpam-6139	287	24	)	)	PUNCT
ejpam-6139	287	25	−	−	PROPN
ejpam-6139	287	26	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	287	27	ηs(s+	ηs(s+	PROPN
ejpam-6139	287	28	1	1	NUM
ejpam-6139	287	29	)	)	PUNCT
ejpam-6139	287	30	)	)	PUNCT
ejpam-6139	287	31	(	(	PUNCT
ejpam-6139	287	32	(	(	PUNCT
ejpam-6139	287	33	η	η	PROPN
ejpam-6139	287	34	−	−	PROPN
ejpam-6139	287	35	1)s+1	1)s+1	NUM
ejpam-6139	287	36	−	−	PROPN
ejpam-6139	287	37	ηs+1	ηs+1	PROPN
ejpam-6139	287	38	)	)	PUNCT
ejpam-6139	287	39	]	]	PUNCT
ejpam-6139	288	1	1	1	NUM
ejpam-6139	288	2	q	q	NOUN
ejpam-6139	288	3	+	+	X
ejpam-6139	289	1	[	[	X
ejpam-6139	289	2	(	(	PUNCT
ejpam-6139	289	3	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	289	4	ηs(s+	ηs(s+	PROPN
ejpam-6139	289	5	1	1	NUM
ejpam-6139	289	6	)	)	PUNCT
ejpam-6139	289	7	−	−	PROPN
ejpam-6139	289	8	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	289	9	ηs(s+	ηs(s+	NOUN
ejpam-6139	289	10	1	1	NUM
ejpam-6139	289	11	)	)	PUNCT
ejpam-6139	289	12	)	)	PUNCT
ejpam-6139	290	1	(	(	PUNCT
ejpam-6139	290	2	(	(	PUNCT
ejpam-6139	290	3	η	η	PROPN
ejpam-6139	290	4	−	−	PROPN
ejpam-6139	290	5	1)s+1	1)s+1	NUM
ejpam-6139	290	6	−	−	PROPN
ejpam-6139	290	7	ηs+1	ηs+1	PROPN
ejpam-6139	290	8	)	)	PUNCT
ejpam-6139	290	9	]	]	PUNCT
ejpam-6139	291	1	1	1	NUM
ejpam-6139	291	2	q	q	NOUN
ejpam-6139	291	3	)	)	PUNCT
ejpam-6139	291	4	.	.	PUNCT
ejpam-6139	292	1	so	so	ADV
ejpam-6139	292	2	inequality	inequality	NOUN
ejpam-6139	292	3	is	be	AUX
ejpam-6139	292	4	proved	prove	VERB
ejpam-6139	292	5	.	.	PUNCT
ejpam-6139	293	1	remark	remark	PROPN
ejpam-6139	293	2	5	5	NUM
ejpam-6139	293	3	.	.	PUNCT
ejpam-6139	294	1	if	if	SCONJ
ejpam-6139	294	2	we	we	PRON
ejpam-6139	294	3	substitute	substitute	VERB
ejpam-6139	294	4	η	η	PROPN
ejpam-6139	294	5	=	=	PROPN
ejpam-6139	294	6	2	2	NUM
ejpam-6139	294	7	,	,	PUNCT
ejpam-6139	294	8	k	k	NOUN
ejpam-6139	294	9	=	=	SYM
ejpam-6139	294	10	1	1	NUM
ejpam-6139	294	11	and	and	CCONJ
ejpam-6139	294	12	s=1	s=1	PROPN
ejpam-6139	294	13	in	in	ADP
ejpam-6139	294	14	equation	equation	NOUN
ejpam-6139	294	15	(	(	PUNCT
ejpam-6139	294	16	12	12	NUM
ejpam-6139	294	17	)	)	PUNCT
ejpam-6139	294	18	,	,	PUNCT
ejpam-6139	294	19	then	then	ADV
ejpam-6139	294	20	following	follow	VERB
ejpam-6139	294	21	result	result	NOUN
ejpam-6139	294	22	is	be	AUX
ejpam-6139	294	23	obtained∣∣∣∣h(ν	obtained∣∣∣∣h(ν	NOUN
ejpam-6139	294	24	)	)	PUNCT
ejpam-6139	295	1	+	+	CCONJ
ejpam-6139	295	2	h(ω	h(ω	PROPN
ejpam-6139	295	3	)	)	PUNCT
ejpam-6139	295	4	2	2	NUM
ejpam-6139	295	5	−	−	PROPN
ejpam-6139	295	6	2µα−1	2µα−1	NUM
ejpam-6139	295	7	(	(	PUNCT
ejpam-6139	295	8	ω	ω	NOUN
ejpam-6139	295	9	−	−	X
ejpam-6139	296	1	ν)µα	ν)µα	PROPN
ejpam-6139	296	2	µαγ(α+	µαγ(α+	NOUN
ejpam-6139	296	3	1	1	NUM
ejpam-6139	296	4	)	)	PUNCT
ejpam-6139	296	5	(	(	PUNCT
ejpam-6139	296	6	αjµ	αjµ	NOUN
ejpam-6139	296	7	ν+ω	ν+ω	NOUN
ejpam-6139	296	8	2	2	NUM
ejpam-6139	296	9	−	−	PRON
ejpam-6139	296	10	h(ν	h(ν	PRON
ejpam-6139	296	11	)	)	PUNCT
ejpam-6139	297	1	+	+	NOUN
ejpam-6139	297	2	α	α	NOUN
ejpam-6139	297	3	jµ	jµ	X
ejpam-6139	297	4	ν+ω	ν+ω	NOUN
ejpam-6139	297	5	2	2	NUM
ejpam-6139	297	6	+	+	CCONJ
ejpam-6139	297	7	h(ω	h(ω	PROPN
ejpam-6139	297	8	)	)	PUNCT
ejpam-6139	297	9	)	)	PUNCT
ejpam-6139	297	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	297	11	≤	≤	NOUN
ejpam-6139	297	12	(	(	PUNCT
ejpam-6139	297	13	ω	ω	NUM
ejpam-6139	297	14	−	−	PROPN
ejpam-6139	297	15	ν)2µα	ν)2µα	NOUN
ejpam-6139	297	16	8	8	NUM
ejpam-6139	297	17	(	(	PUNCT
ejpam-6139	297	18	∫	∫	PROPN
ejpam-6139	297	19	1	1	NUM
ejpam-6139	297	20	0	0	NUM
ejpam-6139	297	21	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	297	22	∫	∫	PROPN
ejpam-6139	297	23	t	t	PROPN
ejpam-6139	297	24	0	0	NUM
ejpam-6139	298	1	(	(	PUNCT
ejpam-6139	298	2	1	1	NUM
ejpam-6139	298	3	(	(	PUNCT
ejpam-6139	298	4	µ)α	µ)α	NOUN
ejpam-6139	298	5	−	−	PROPN
ejpam-6139	298	6	(	(	PUNCT
ejpam-6139	298	7	1−	1−	NUM
ejpam-6139	298	8	(	(	PUNCT
ejpam-6139	298	9	1−	1−	NUM
ejpam-6139	298	10	φ)µ	φ)µ	X
ejpam-6139	298	11	µ	µ	X
ejpam-6139	298	12	)	)	PUNCT
ejpam-6139	298	13	α	α	NOUN
ejpam-6139	298	14	)	)	PUNCT
ejpam-6139	298	15	dφ	dφ	ADP
ejpam-6139	298	16	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	298	17	)	)	PUNCT
ejpam-6139	299	1	1	1	NUM
ejpam-6139	299	2	p	p	NOUN
ejpam-6139	299	3	[	[	X
ejpam-6139	299	4	(	(	PUNCT
ejpam-6139	299	5	3|h′′(ν)|q	3|h′′(ν)|q	PROPN
ejpam-6139	299	6	+	+	NUM
ejpam-6139	299	7	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	299	8	4	4	NUM
ejpam-6139	299	9	)	)	PUNCT
ejpam-6139	299	10	1	1	NUM
ejpam-6139	299	11	q	q	NOUN
ejpam-6139	300	1	+	+	CCONJ
ejpam-6139	300	2	(	(	PUNCT
ejpam-6139	300	3	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	300	4	+	+	CCONJ
ejpam-6139	300	5	3|h′′(ω)|q	3|h′′(ω)|q	NUM
ejpam-6139	300	6	4	4	NUM
ejpam-6139	300	7	)	)	PUNCT
ejpam-6139	300	8	1	1	NUM
ejpam-6139	300	9	q	q	NOUN
ejpam-6139	300	10	]	]	PUNCT
ejpam-6139	300	11	.	.	PUNCT
ejpam-6139	301	1	(	(	PUNCT
ejpam-6139	301	2	16	16	NUM
ejpam-6139	301	3	)	)	PUNCT
ejpam-6139	301	4	corollary	corollary	ADJ
ejpam-6139	301	5	1	1	NUM
ejpam-6139	301	6	.	.	PUNCT
ejpam-6139	302	1	if	if	SCONJ
ejpam-6139	302	2	we	we	PRON
ejpam-6139	302	3	consider	consider	VERB
ejpam-6139	302	4	µ	µ	X
ejpam-6139	302	5	=	=	SYM
ejpam-6139	302	6	α	α	NOUN
ejpam-6139	302	7	=	=	SYM
ejpam-6139	302	8	1	1	NUM
ejpam-6139	302	9	in	in	ADP
ejpam-6139	302	10	(	(	PUNCT
ejpam-6139	302	11	16	16	NUM
ejpam-6139	302	12	)	)	PUNCT
ejpam-6139	302	13	we	we	PRON
ejpam-6139	302	14	arrive	arrive	VERB
ejpam-6139	302	15	at	at	ADP
ejpam-6139	302	16	the	the	DET
ejpam-6139	302	17	conclusion	conclusion	NOUN
ejpam-6139	302	18	that	that	SCONJ
ejpam-6139	302	19	is∣∣∣∣h(ν	is∣∣∣∣h(ν	NOUN
ejpam-6139	302	20	)	)	PUNCT
ejpam-6139	302	21	+	+	CCONJ
ejpam-6139	302	22	h(ω	h(ω	PROPN
ejpam-6139	302	23	)	)	PUNCT
ejpam-6139	302	24	2	2	NUM
ejpam-6139	302	25	−	−	NOUN
ejpam-6139	302	26	1	1	NUM
ejpam-6139	302	27	(	(	PUNCT
ejpam-6139	302	28	ω	ω	NOUN
ejpam-6139	302	29	−	−	NOUN
ejpam-6139	302	30	ν	ν	PROPN
ejpam-6139	302	31	)	)	PUNCT
ejpam-6139	302	32	∫	∫	PROPN
ejpam-6139	302	33	ω	ω	PROPN
ejpam-6139	302	34	ν	ν	PROPN
ejpam-6139	302	35	h(x)dx	h(x)dx	PROPN
ejpam-6139	302	36	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	302	37	≤	≤	NOUN
ejpam-6139	302	38	(	(	PUNCT
ejpam-6139	302	39	ω	ω	NUM
ejpam-6139	302	40	−	−	PROPN
ejpam-6139	302	41	ν)2	ν)2	NOUN
ejpam-6139	302	42	8	8	NUM
ejpam-6139	302	43	(	(	PUNCT
ejpam-6139	302	44	1	1	NUM
ejpam-6139	302	45	p+	p+	NOUN
ejpam-6139	302	46	1	1	NUM
ejpam-6139	302	47	−	−	PROPN
ejpam-6139	302	48	1	1	NUM
ejpam-6139	302	49	2p(2p+	2p(2p+	NUM
ejpam-6139	302	50	1	1	NUM
ejpam-6139	302	51	)	)	PUNCT
ejpam-6139	302	52	)	)	PUNCT
ejpam-6139	302	53	1	1	NUM
ejpam-6139	303	1	p	p	NOUN
ejpam-6139	303	2	[	[	X
ejpam-6139	303	3	(	(	PUNCT
ejpam-6139	303	4	3|h′′(ν)|q	3|h′′(ν)|q	PROPN
ejpam-6139	303	5	+	+	NUM
ejpam-6139	303	6	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	303	7	4	4	NUM
ejpam-6139	303	8	)	)	PUNCT
ejpam-6139	303	9	1	1	NUM
ejpam-6139	303	10	q	q	NOUN
ejpam-6139	303	11	+	+	CCONJ
ejpam-6139	303	12	(	(	PUNCT
ejpam-6139	303	13	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	303	14	+	+	CCONJ
ejpam-6139	303	15	3|h′′(ω)|q	3|h′′(ω)|q	NUM
ejpam-6139	303	16	4	4	NUM
ejpam-6139	303	17	)	)	PUNCT
ejpam-6139	303	18	1	1	NUM
ejpam-6139	303	19	q	q	NOUN
ejpam-6139	303	20	]	]	PUNCT
ejpam-6139	303	21	.	.	PUNCT
ejpam-6139	304	1	proof	proof	NOUN
ejpam-6139	304	2	.	.	PUNCT
ejpam-6139	305	1	substituting	substitute	VERB
ejpam-6139	305	2	value	value	NOUN
ejpam-6139	305	3	µ	µ	X
ejpam-6139	305	4	=	=	SYM
ejpam-6139	305	5	α	α	NOUN
ejpam-6139	305	6	=	=	SYM
ejpam-6139	305	7	1	1	NUM
ejpam-6139	305	8	in	in	ADP
ejpam-6139	305	9	(	(	PUNCT
ejpam-6139	305	10	16),∣∣∣∣h(ν	16),∣∣∣∣h(ν	NUM
ejpam-6139	305	11	)	)	PUNCT
ejpam-6139	305	12	+	+	CCONJ
ejpam-6139	305	13	h(ω	h(ω	PROPN
ejpam-6139	305	14	)	)	PUNCT
ejpam-6139	305	15	2	2	NUM
ejpam-6139	305	16	−	−	NOUN
ejpam-6139	305	17	1	1	NUM
ejpam-6139	305	18	(	(	PUNCT
ejpam-6139	305	19	ω	ω	NOUN
ejpam-6139	305	20	−	−	NOUN
ejpam-6139	305	21	ν	ν	NOUN
ejpam-6139	305	22	)	)	PUNCT
ejpam-6139	305	23	γ(α+	γ(α+	PRON
ejpam-6139	305	24	1	1	NUM
ejpam-6139	305	25	)	)	PUNCT
ejpam-6139	305	26	∫	∫	PROPN
ejpam-6139	306	1	ω	ω	NUM
ejpam-6139	306	2	ν	ν	PROPN
ejpam-6139	306	3	h(x)dx	h(x)dx	PROPN
ejpam-6139	306	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	306	5	≤	≤	NOUN
ejpam-6139	306	6	(	(	PUNCT
ejpam-6139	306	7	ω	ω	NUM
ejpam-6139	306	8	−	−	PROPN
ejpam-6139	306	9	ν)2µα	ν)2µα	NOUN
ejpam-6139	306	10	8	8	NUM
ejpam-6139	306	11	(	(	PUNCT
ejpam-6139	306	12	∫	∫	PROPN
ejpam-6139	306	13	1	1	NUM
ejpam-6139	306	14	0	0	NUM
ejpam-6139	306	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	306	16	∫	∫	PROPN
ejpam-6139	306	17	t	t	PROPN
ejpam-6139	306	18	0	0	NUM
ejpam-6139	306	19	(	(	PUNCT
ejpam-6139	306	20	1−	1−	NUM
ejpam-6139	306	21	φ	φ	NUM
ejpam-6139	306	22	)	)	PUNCT
ejpam-6139	306	23	dφ	dφ	ADP
ejpam-6139	306	24	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	306	25	)	)	PUNCT
ejpam-6139	306	26	1	1	NUM
ejpam-6139	306	27	p	p	NOUN
ejpam-6139	306	28	×	×	NOUN
ejpam-6139	306	29	[	[	X
ejpam-6139	306	30	(	(	PUNCT
ejpam-6139	306	31	3|h′′(ν)|q	3|h′′(ν)|q	PROPN
ejpam-6139	306	32	+	+	NUM
ejpam-6139	306	33	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	306	34	4	4	NUM
ejpam-6139	306	35	)	)	PUNCT
ejpam-6139	306	36	1	1	NUM
ejpam-6139	306	37	q	q	NOUN
ejpam-6139	306	38	+	+	CCONJ
ejpam-6139	306	39	(	(	PUNCT
ejpam-6139	306	40	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	306	41	+	+	CCONJ
ejpam-6139	306	42	3|h′′(ω)|q	3|h′′(ω)|q	NUM
ejpam-6139	306	43	4	4	NUM
ejpam-6139	306	44	)	)	PUNCT
ejpam-6139	306	45	1	1	NUM
ejpam-6139	306	46	q	q	NOUN
ejpam-6139	306	47	]	]	PUNCT
ejpam-6139	306	48	.	.	PUNCT
ejpam-6139	307	1	(	(	PUNCT
ejpam-6139	307	2	17	17	NUM
ejpam-6139	307	3	)	)	PUNCT
ejpam-6139	307	4	consider	consider	VERB
ejpam-6139	307	5	(	(	PUNCT
ejpam-6139	307	6	∫	∫	PROPN
ejpam-6139	307	7	1	1	NUM
ejpam-6139	307	8	0	0	NUM
ejpam-6139	307	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	307	10	∫	∫	PROPN
ejpam-6139	307	11	t	t	PROPN
ejpam-6139	307	12	0	0	NUM
ejpam-6139	308	1	(	(	PUNCT
ejpam-6139	308	2	1−	1−	NUM
ejpam-6139	308	3	φ)dφ	φ)dφ	PROPN
ejpam-6139	308	4	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	308	5	)	)	PUNCT
ejpam-6139	308	6	1	1	NUM
ejpam-6139	308	7	p	p	NOUN
ejpam-6139	308	8	=	=	PUNCT
ejpam-6139	308	9	(	(	PUNCT
ejpam-6139	308	10	∫	∫	PROPN
ejpam-6139	308	11	1	1	NUM
ejpam-6139	308	12	0	0	NUM
ejpam-6139	308	13	∣∣∣∣t−	∣∣∣∣t−	NOUN
ejpam-6139	308	14	t2	t2	NOUN
ejpam-6139	308	15	2	2	NUM
ejpam-6139	308	16	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	308	17	)	)	PUNCT
ejpam-6139	308	18	1	1	NUM
ejpam-6139	308	19	p	p	NOUN
ejpam-6139	308	20	.	.	PUNCT
ejpam-6139	309	1	m.	m.	NOUN
ejpam-6139	309	2	samraiz	samraiz	PROPN
ejpam-6139	309	3	et	et	PROPN
ejpam-6139	309	4	al	al	PROPN
ejpam-6139	309	5	.	.	PUNCT
ejpam-6139	309	6	/	/	SYM
ejpam-6139	309	7	eur	eur	PROPN
ejpam-6139	309	8	.	.	PUNCT
ejpam-6139	310	1	j.	j.	PROPN
ejpam-6139	310	2	pure	pure	PROPN
ejpam-6139	310	3	appl	appl	PROPN
ejpam-6139	310	4	.	.	PROPN
ejpam-6139	310	5	math	math	PROPN
ejpam-6139	310	6	,	,	PUNCT
ejpam-6139	310	7	18	18	NUM
ejpam-6139	310	8	(	(	PUNCT
ejpam-6139	310	9	4	4	NUM
ejpam-6139	310	10	)	)	PUNCT
ejpam-6139	310	11	(	(	PUNCT
ejpam-6139	310	12	2025	2025	NUM
ejpam-6139	310	13	)	)	PUNCT
ejpam-6139	310	14	,	,	PUNCT
ejpam-6139	310	15	6139	6139	NUM
ejpam-6139	310	16	12	12	NUM
ejpam-6139	310	17	of	of	ADP
ejpam-6139	310	18	34	34	NUM
ejpam-6139	310	19	under	under	ADP
ejpam-6139	310	20	condition	condition	NOUN
ejpam-6139	310	21	|a−b|p	|a−b|p	PUNCT
ejpam-6139	310	22	≤	≤	NUM
ejpam-6139	310	23	ap	ap	VERB
ejpam-6139	310	24	−bp	−bp	NOUN
ejpam-6139	310	25	when	when	SCONJ
ejpam-6139	310	26	a	a	DET
ejpam-6139	310	27	>	>	X
ejpam-6139	310	28	b	b	X
ejpam-6139	310	29	>	>	X
ejpam-6139	310	30	0	0	NUM
ejpam-6139	310	31	;	;	PUNCT
ejpam-6139	310	32	and	and	CCONJ
ejpam-6139	310	33	p	p	X
ejpam-6139	310	34	>	>	X
ejpam-6139	310	35	1	1	NUM
ejpam-6139	310	36	so	so	SCONJ
ejpam-6139	310	37	we	we	PRON
ejpam-6139	310	38	can	can	AUX
ejpam-6139	310	39	write(∫	write(∫	VERB
ejpam-6139	310	40	1	1	NUM
ejpam-6139	310	41	0	0	NUM
ejpam-6139	310	42	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	310	43	∫	∫	PROPN
ejpam-6139	310	44	t	t	PROPN
ejpam-6139	310	45	0	0	NUM
ejpam-6139	311	1	(	(	PUNCT
ejpam-6139	311	2	1−	1−	NUM
ejpam-6139	311	3	φ)dφ	φ)dφ	PROPN
ejpam-6139	311	4	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	311	5	)	)	PUNCT
ejpam-6139	311	6	1	1	NUM
ejpam-6139	311	7	p	p	NOUN
ejpam-6139	311	8	≤	≤	NOUN
ejpam-6139	311	9	(	(	PUNCT
ejpam-6139	311	10	∫	∫	PROPN
ejpam-6139	311	11	1	1	NUM
ejpam-6139	311	12	0	0	NUM
ejpam-6139	311	13	tpdt−	tpdt−	NUM
ejpam-6139	311	14	∫	∫	NOUN
ejpam-6139	311	15	1	1	NUM
ejpam-6139	311	16	0	0	NUM
ejpam-6139	311	17	t2p	t2p	NOUN
ejpam-6139	311	18	2p	2p	NUM
ejpam-6139	311	19	dt	dt	NOUN
ejpam-6139	311	20	)	)	PUNCT
ejpam-6139	311	21	1	1	NUM
ejpam-6139	311	22	p	p	NOUN
ejpam-6139	311	23	(	(	PUNCT
ejpam-6139	311	24	∫	∫	PROPN
ejpam-6139	311	25	1	1	NUM
ejpam-6139	311	26	0	0	NUM
ejpam-6139	311	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	311	28	∫	∫	PROPN
ejpam-6139	311	29	t	t	PROPN
ejpam-6139	311	30	0	0	NUM
ejpam-6139	311	31	(	(	PUNCT
ejpam-6139	311	32	1−	1−	NUM
ejpam-6139	311	33	φ)dφ	φ)dφ	PROPN
ejpam-6139	311	34	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	311	35	)	)	PUNCT
ejpam-6139	311	36	1	1	NUM
ejpam-6139	311	37	p	p	NOUN
ejpam-6139	311	38	≤	≤	NOUN
ejpam-6139	311	39	[	[	PUNCT
ejpam-6139	311	40	1	1	NUM
ejpam-6139	311	41	p+	p+	NOUN
ejpam-6139	311	42	1	1	NUM
ejpam-6139	311	43	−	−	PROPN
ejpam-6139	311	44	1	1	NUM
ejpam-6139	311	45	2p(2p+	2p(2p+	NUM
ejpam-6139	311	46	1	1	NUM
ejpam-6139	311	47	)	)	PUNCT
ejpam-6139	311	48	]	]	PUNCT
ejpam-6139	311	49	1	1	NUM
ejpam-6139	311	50	p	p	NOUN
ejpam-6139	311	51	.	.	PUNCT
ejpam-6139	312	1	(	(	PUNCT
ejpam-6139	312	2	18	18	NUM
ejpam-6139	312	3	)	)	PUNCT
ejpam-6139	312	4	substituting	substituting	NOUN
ejpam-6139	312	5	(	(	PUNCT
ejpam-6139	312	6	18	18	NUM
ejpam-6139	312	7	)	)	PUNCT
ejpam-6139	312	8	in	in	ADP
ejpam-6139	312	9	(	(	PUNCT
ejpam-6139	312	10	17	17	NUM
ejpam-6139	312	11	)	)	PUNCT
ejpam-6139	312	12	,	,	PUNCT
ejpam-6139	312	13	we	we	PRON
ejpam-6139	312	14	get	get	VERB
ejpam-6139	312	15	our	our	PRON
ejpam-6139	312	16	desired	desire	VERB
ejpam-6139	312	17	result	result	NOUN
ejpam-6139	312	18	.	.	PUNCT
ejpam-6139	313	1	example	example	NOUN
ejpam-6139	314	1	2	2	NUM
ejpam-6139	314	2	.	.	PUNCT
ejpam-6139	314	3	this	this	DET
ejpam-6139	314	4	example	example	NOUN
ejpam-6139	314	5	illustrates	illustrate	VERB
ejpam-6139	314	6	the	the	DET
ejpam-6139	314	7	applicability	applicability	NOUN
ejpam-6139	314	8	of	of	ADP
ejpam-6139	314	9	theorem	theorem	NOUN
ejpam-6139	314	10	2	2	NUM
ejpam-6139	314	11	through	through	ADP
ejpam-6139	314	12	graphical	graphical	ADJ
ejpam-6139	314	13	and	and	CCONJ
ejpam-6139	314	14	numerical	numerical	ADJ
ejpam-6139	314	15	analyses	analysis	NOUN
ejpam-6139	314	16	.	.	PUNCT
ejpam-6139	315	1	we	we	PRON
ejpam-6139	315	2	consider	consider	VERB
ejpam-6139	315	3	the	the	DET
ejpam-6139	315	4	function	function	NOUN
ejpam-6139	315	5	h(x	h(x	PROPN
ejpam-6139	315	6	)	)	PUNCT
ejpam-6139	315	7	=	=	SYM
ejpam-6139	315	8	x6	x6	PROPN
ejpam-6139	315	9	+	+	CCONJ
ejpam-6139	315	10	2x4	2x4	NUM
ejpam-6139	315	11	,	,	PUNCT
ejpam-6139	315	12	defined	define	VERB
ejpam-6139	315	13	on	on	ADP
ejpam-6139	315	14	the	the	DET
ejpam-6139	315	15	interval	interval	NOUN
ejpam-6139	315	16	[	[	X
ejpam-6139	315	17	2	2	NUM
ejpam-6139	315	18	,	,	PUNCT
ejpam-6139	315	19	7	7	NUM
ejpam-6139	315	20	]	]	PUNCT
ejpam-6139	315	21	,	,	PUNCT
ejpam-6139	315	22	and	and	CCONJ
ejpam-6139	315	23	verify	verify	VERB
ejpam-6139	315	24	the	the	DET
ejpam-6139	315	25	inequality	inequality	NOUN
ejpam-6139	315	26	using	use	VERB
ejpam-6139	315	27	specific	specific	ADJ
ejpam-6139	315	28	parameter	parameter	NOUN
ejpam-6139	315	29	values	value	NOUN
ejpam-6139	315	30	:	:	PUNCT
ejpam-6139	315	31	k	k	X
ejpam-6139	315	32	=	=	SYM
ejpam-6139	315	33	3	3	NUM
ejpam-6139	315	34	,	,	PUNCT
ejpam-6139	315	35	α	α	NOUN
ejpam-6139	315	36	=	=	SYM
ejpam-6139	315	37	4	4	NUM
ejpam-6139	315	38	,	,	PUNCT
ejpam-6139	315	39	s	s	PART
ejpam-6139	315	40	=	=	SYM
ejpam-6139	315	41	1	1	NUM
ejpam-6139	315	42	,	,	PUNCT
ejpam-6139	315	43	1	1	NUM
ejpam-6139	315	44	p	p	NOUN
ejpam-6139	315	45	=	=	SYM
ejpam-6139	315	46	.6	.6	NUM
ejpam-6139	315	47	,	,	PUNCT
ejpam-6139	315	48	1q	1q	NUM
ejpam-6139	315	49	=	=	SYM
ejpam-6139	315	50	.4	.4	NUM
ejpam-6139	315	51	,	,	PUNCT
ejpam-6139	315	52	and	and	CCONJ
ejpam-6139	315	53	η	η	PROPN
ejpam-6139	315	54	=	=	PROPN
ejpam-6139	315	55	8	8	PROPN
ejpam-6139	315	56	.	.	PUNCT
ejpam-6139	316	1	explanation	explanation	NOUN
ejpam-6139	316	2	:	:	PUNCT
ejpam-6139	316	3	figure	figure	VERB
ejpam-6139	316	4	3	3	NUM
ejpam-6139	316	5	presents	present	VERB
ejpam-6139	316	6	a	a	DET
ejpam-6139	316	7	2d	2d	NUM
ejpam-6139	316	8	graph	graph	NOUN
ejpam-6139	316	9	of	of	ADP
ejpam-6139	316	10	the	the	DET
ejpam-6139	316	11	inequality	inequality	NOUN
ejpam-6139	316	12	over	over	ADP
ejpam-6139	316	13	µ	µ	PRON
ejpam-6139	316	14	∈	∈	NOUN
ejpam-6139	316	15	(	(	PUNCT
ejpam-6139	316	16	0	0	NUM
ejpam-6139	316	17	,	,	PUNCT
ejpam-6139	316	18	1	1	NUM
ejpam-6139	316	19	]	]	PUNCT
ejpam-6139	316	20	,	,	PUNCT
ejpam-6139	316	21	showing	show	VERB
ejpam-6139	316	22	the	the	DET
ejpam-6139	316	23	behavior	behavior	NOUN
ejpam-6139	316	24	of	of	ADP
ejpam-6139	316	25	both	both	CCONJ
ejpam-6139	316	26	the	the	DET
ejpam-6139	316	27	left	left	ADJ
ejpam-6139	316	28	-	-	PUNCT
ejpam-6139	316	29	hand	hand	NOUN
ejpam-6139	316	30	side	side	NOUN
ejpam-6139	316	31	and	and	CCONJ
ejpam-6139	316	32	the	the	DET
ejpam-6139	316	33	right	right	ADJ
ejpam-6139	316	34	-	-	PUNCT
ejpam-6139	316	35	hand	hand	NOUN
ejpam-6139	316	36	side	side	NOUN
ejpam-6139	316	37	of	of	ADP
ejpam-6139	316	38	inequality	inequality	NOUN
ejpam-6139	316	39	(	(	PUNCT
ejpam-6139	316	40	12	12	NUM
ejpam-6139	316	41	)	)	PUNCT
ejpam-6139	316	42	.	.	PUNCT
ejpam-6139	317	1	the	the	DET
ejpam-6139	317	2	plot	plot	NOUN
ejpam-6139	317	3	demonstrates	demonstrate	VERB
ejpam-6139	317	4	that	that	SCONJ
ejpam-6139	317	5	the	the	DET
ejpam-6139	317	6	l.h.s	l.h.s	NOUN
ejpam-6139	317	7	remains	remain	VERB
ejpam-6139	317	8	within	within	ADP
ejpam-6139	317	9	the	the	DET
ejpam-6139	317	10	bounds	bound	NOUN
ejpam-6139	317	11	prescribed	prescribe	VERB
ejpam-6139	317	12	by	by	ADP
ejpam-6139	317	13	the	the	DET
ejpam-6139	317	14	r.h.s	r.h.s	NOUN
ejpam-6139	317	15	,	,	PUNCT
ejpam-6139	317	16	visually	visually	ADV
ejpam-6139	317	17	validating	validate	VERB
ejpam-6139	317	18	the	the	DET
ejpam-6139	317	19	theorem	theorem	NOUN
ejpam-6139	317	20	.	.	PUNCT
ejpam-6139	318	1	a	a	DET
ejpam-6139	318	2	numerical	numerical	ADJ
ejpam-6139	318	3	analysis	analysis	NOUN
ejpam-6139	318	4	is	be	AUX
ejpam-6139	318	5	performed	perform	VERB
ejpam-6139	318	6	by	by	ADP
ejpam-6139	318	7	computing	compute	VERB
ejpam-6139	318	8	the	the	DET
ejpam-6139	318	9	l.h.s	l.h.s	NOUN
ejpam-6139	318	10	.	.	PUNCT
ejpam-6139	319	1	and	and	CCONJ
ejpam-6139	319	2	r.h.s	r.h.s	PROPN
ejpam-6139	319	3	.	.	PUNCT
ejpam-6139	319	4	figure	figure	VERB
ejpam-6139	319	5	3	3	NUM
ejpam-6139	319	6	:	:	PUNCT
ejpam-6139	319	7	2d	2d	NUM
ejpam-6139	319	8	plot	plot	NOUN
ejpam-6139	319	9	for	for	ADP
ejpam-6139	319	10	µ	µ	PRON
ejpam-6139	319	11	∈	∈	NOUN
ejpam-6139	319	12	(	(	PUNCT
ejpam-6139	319	13	0	0	NUM
ejpam-6139	319	14	,	,	PUNCT
ejpam-6139	319	15	1	1	NUM
ejpam-6139	319	16	]	]	PUNCT
ejpam-6139	319	17	of	of	ADP
ejpam-6139	319	18	theorem	theorem	ADJ
ejpam-6139	319	19	2	2	NUM
ejpam-6139	319	20	supporting	support	VERB
ejpam-6139	319	21	the	the	DET
ejpam-6139	319	22	validation	validation	NOUN
ejpam-6139	319	23	of	of	ADP
ejpam-6139	319	24	theorem	theorem	PROPN
ejpam-6139	319	25	.	.	PUNCT
ejpam-6139	320	1	values	value	NOUN
ejpam-6139	320	2	for	for	ADP
ejpam-6139	320	3	several	several	ADJ
ejpam-6139	320	4	instances	instance	NOUN
ejpam-6139	320	5	of	of	ADP
ejpam-6139	320	6	µ	µ	NOUN
ejpam-6139	320	7	with	with	ADP
ejpam-6139	320	8	k	k	PROPN
ejpam-6139	320	9	fixed	fix	VERB
ejpam-6139	320	10	,	,	PUNCT
ejpam-6139	320	11	as	as	SCONJ
ejpam-6139	320	12	shown	show	VERB
ejpam-6139	320	13	in	in	ADP
ejpam-6139	320	14	table	table	NOUN
ejpam-6139	320	15	3	3	NUM
ejpam-6139	320	16	.	.	PUNCT
ejpam-6139	320	17	additionally	additionally	ADV
ejpam-6139	320	18	,	,	PUNCT
ejpam-6139	320	19	by	by	ADP
ejpam-6139	320	20	fixing	fix	VERB
ejpam-6139	320	21	µ	µ	X
ejpam-6139	320	22	=	=	SYM
ejpam-6139	320	23	0.5	0.5	NUM
ejpam-6139	320	24	,	,	PUNCT
ejpam-6139	320	25	a	a	DET
ejpam-6139	320	26	table	table	NOUN
ejpam-6139	320	27	is	be	AUX
ejpam-6139	320	28	constructed	construct	VERB
ejpam-6139	320	29	for	for	ADP
ejpam-6139	320	30	different	different	ADJ
ejpam-6139	320	31	values	value	NOUN
ejpam-6139	320	32	of	of	ADP
ejpam-6139	320	33	k	k	NOUN
ejpam-6139	320	34	,	,	PUNCT
ejpam-6139	320	35	as	as	SCONJ
ejpam-6139	320	36	shown	show	VERB
ejpam-6139	320	37	in	in	ADP
ejpam-6139	320	38	table	table	NOUN
ejpam-6139	320	39	4	4	NUM
ejpam-6139	320	40	.	.	PUNCT
ejpam-6139	321	1	this	this	DET
ejpam-6139	321	2	tabular	tabular	PROPN
ejpam-6139	321	3	representation	representation	NOUN
ejpam-6139	321	4	is	be	AUX
ejpam-6139	321	5	highlighting	highlight	VERB
ejpam-6139	321	6	the	the	DET
ejpam-6139	321	7	accuracy	accuracy	NOUN
ejpam-6139	321	8	and	and	CCONJ
ejpam-6139	321	9	consistency	consistency	NOUN
ejpam-6139	321	10	of	of	ADP
ejpam-6139	321	11	the	the	DET
ejpam-6139	321	12	inequality	inequality	NOUN
ejpam-6139	321	13	.	.	PUNCT
ejpam-6139	322	1	table	table	NOUN
ejpam-6139	322	2	3	3	NUM
ejpam-6139	322	3	:	:	PUNCT
ejpam-6139	322	4	summary	summary	NOUN
ejpam-6139	322	5	of	of	ADP
ejpam-6139	322	6	inequality	inequality	NOUN
ejpam-6139	322	7	(	(	PUNCT
ejpam-6139	322	8	12	12	NUM
ejpam-6139	322	9	)	)	PUNCT
ejpam-6139	322	10	confirms	confirm	VERB
ejpam-6139	322	11	its	its	PRON
ejpam-6139	322	12	validity	validity	NOUN
ejpam-6139	322	13	for	for	ADP
ejpam-6139	322	14	µ	µ	PRON
ejpam-6139	322	15	∈	∈	NOUN
ejpam-6139	322	16	(	(	PUNCT
ejpam-6139	322	17	0	0	NUM
ejpam-6139	322	18	,	,	PUNCT
ejpam-6139	322	19	1	1	NUM
ejpam-6139	322	20	]	]	PUNCT
ejpam-6139	322	21	.	.	PUNCT
ejpam-6139	323	1	µ	µ	PROPN
ejpam-6139	323	2	0.2	0.2	NUM
ejpam-6139	323	3	0.4	0.4	NUM
ejpam-6139	323	4	0.6	0.6	NUM
ejpam-6139	323	5	0.8	0.8	NUM
ejpam-6139	323	6	1	1	NUM
ejpam-6139	323	7	lhs	lhs	PROPN
ejpam-6139	323	8	1368.99	1368.99	NUM
ejpam-6139	323	9	1289.62	1289.62	NUM
ejpam-6139	323	10	1213.3	1213.3	NUM
ejpam-6139	323	11	1142.93	1142.93	NUM
ejpam-6139	323	12	1078.93	1078.93	NUM
ejpam-6139	323	13	rhs	rh	NOUN
ejpam-6139	323	14	2448.47	2448.47	NUM
ejpam-6139	323	15	2282.73	2282.73	NUM
ejpam-6139	323	16	2203.15	2203.15	NUM
ejpam-6139	323	17	1986.66	1986.66	NUM
ejpam-6139	323	18	1861.13	1861.13	NUM
ejpam-6139	323	19	m.	m.	NOUN
ejpam-6139	323	20	samraiz	samraiz	PROPN
ejpam-6139	323	21	et	et	PROPN
ejpam-6139	323	22	al	al	PROPN
ejpam-6139	323	23	.	.	PUNCT
ejpam-6139	323	24	/	/	SYM
ejpam-6139	323	25	eur	eur	PROPN
ejpam-6139	323	26	.	.	PUNCT
ejpam-6139	324	1	j.	j.	PROPN
ejpam-6139	324	2	pure	pure	PROPN
ejpam-6139	324	3	appl	appl	PROPN
ejpam-6139	324	4	.	.	PROPN
ejpam-6139	324	5	math	math	PROPN
ejpam-6139	324	6	,	,	PUNCT
ejpam-6139	324	7	18	18	NUM
ejpam-6139	324	8	(	(	PUNCT
ejpam-6139	324	9	4	4	NUM
ejpam-6139	324	10	)	)	PUNCT
ejpam-6139	324	11	(	(	PUNCT
ejpam-6139	324	12	2025	2025	NUM
ejpam-6139	324	13	)	)	PUNCT
ejpam-6139	324	14	,	,	PUNCT
ejpam-6139	324	15	6139	6139	NUM
ejpam-6139	324	16	13	13	NUM
ejpam-6139	324	17	of	of	ADP
ejpam-6139	324	18	34	34	NUM
ejpam-6139	324	19	table	table	NOUN
ejpam-6139	324	20	4	4	NUM
ejpam-6139	324	21	:	:	PUNCT
ejpam-6139	324	22	summary	summary	NOUN
ejpam-6139	324	23	of	of	ADP
ejpam-6139	324	24	inequality	inequality	NOUN
ejpam-6139	324	25	(	(	PUNCT
ejpam-6139	324	26	12	12	NUM
ejpam-6139	324	27	)	)	PUNCT
ejpam-6139	324	28	confirms	confirm	VERB
ejpam-6139	324	29	its	its	PRON
ejpam-6139	324	30	validity	validity	NOUN
ejpam-6139	324	31	for	for	ADP
ejpam-6139	324	32	k	k	PROPN
ejpam-6139	324	33	∈	∈	PROPN
ejpam-6139	325	1	[	[	X
ejpam-6139	325	2	1	1	NUM
ejpam-6139	325	3	,	,	PUNCT
ejpam-6139	325	4	5	5	NUM
ejpam-6139	325	5	]	]	PUNCT
ejpam-6139	325	6	while	while	SCONJ
ejpam-6139	325	7	fixing	fix	VERB
ejpam-6139	325	8	µ	µ	NOUN
ejpam-6139	325	9	=	=	SYM
ejpam-6139	325	10	.5	.5	NUM
ejpam-6139	325	11	.	.	PUNCT
ejpam-6139	326	1	µ	µ	X
ejpam-6139	326	2	1	1	NUM
ejpam-6139	326	3	2	2	NUM
ejpam-6139	326	4	3	3	NUM
ejpam-6139	326	5	4	4	NUM
ejpam-6139	326	6	5	5	NUM
ejpam-6139	326	7	lhs	lhs	PROPN
ejpam-6139	326	8	1415.4	1415.4	NUM
ejpam-6139	326	9	1343.89	1343.89	NUM
ejpam-6139	326	10	1250.8	1250.8	NUM
ejpam-6139	326	11	1157.15	1157.15	NUM
ejpam-6139	326	12	1070.49	1070.49	NUM
ejpam-6139	326	13	rhs	rhs	PROPN
ejpam-6139	326	14	2543.26	2543.26	NUM
ejpam-6139	326	15	2389.52	2389.52	NUM
ejpam-6139	326	16	2203.15	2203.15	NUM
ejpam-6139	326	17	2023.35	2023.35	NUM
ejpam-6139	326	18	1861.33	1861.33	NUM
ejpam-6139	326	19	to	to	PART
ejpam-6139	326	20	extend	extend	VERB
ejpam-6139	326	21	the	the	DET
ejpam-6139	326	22	analysis	analysis	NOUN
ejpam-6139	326	23	,	,	PUNCT
ejpam-6139	326	24	we	we	PRON
ejpam-6139	326	25	explore	explore	VERB
ejpam-6139	326	26	the	the	DET
ejpam-6139	326	27	inequality	inequality	NOUN
ejpam-6139	326	28	in	in	ADP
ejpam-6139	326	29	three	three	NUM
ejpam-6139	326	30	dimensions	dimension	NOUN
ejpam-6139	326	31	by	by	ADP
ejpam-6139	326	32	varying	vary	VERB
ejpam-6139	326	33	the	the	DET
ejpam-6139	326	34	parameters	parameter	NOUN
ejpam-6139	326	35	α	α	X
ejpam-6139	326	36	∈	∈	PROPN
ejpam-6139	327	1	[	[	X
ejpam-6139	327	2	5	5	NUM
ejpam-6139	327	3	,	,	PUNCT
ejpam-6139	327	4	10	10	NUM
ejpam-6139	327	5	]	]	PUNCT
ejpam-6139	327	6	and	and	CCONJ
ejpam-6139	327	7	µ	µ	X
ejpam-6139	327	8	∈	∈	NOUN
ejpam-6139	327	9	(	(	PUNCT
ejpam-6139	327	10	0	0	NUM
ejpam-6139	327	11	,	,	PUNCT
ejpam-6139	327	12	1	1	NUM
ejpam-6139	327	13	]	]	PUNCT
ejpam-6139	327	14	.	.	PUNCT
ejpam-6139	328	1	figure	figure	NOUN
ejpam-6139	328	2	4	4	NUM
ejpam-6139	328	3	illustrates	illustrate	VERB
ejpam-6139	328	4	the	the	DET
ejpam-6139	328	5	resulting	result	VERB
ejpam-6139	328	6	surface	surface	NOUN
ejpam-6139	328	7	,	,	PUNCT
ejpam-6139	328	8	further	far	ADV
ejpam-6139	328	9	confirming	confirm	VERB
ejpam-6139	328	10	the	the	DET
ejpam-6139	328	11	robustness	robustness	NOUN
ejpam-6139	328	12	of	of	ADP
ejpam-6139	328	13	the	the	DET
ejpam-6139	328	14	inequality	inequality	NOUN
ejpam-6139	328	15	across	across	ADP
ejpam-6139	328	16	a	a	DET
ejpam-6139	328	17	range	range	NOUN
ejpam-6139	328	18	of	of	ADP
ejpam-6139	328	19	parameter	parameter	NOUN
ejpam-6139	328	20	values	value	NOUN
ejpam-6139	328	21	.	.	PUNCT
ejpam-6139	329	1	these	these	PRON
ejpam-6139	329	2	figure	figure	VERB
ejpam-6139	329	3	4	4	NUM
ejpam-6139	329	4	:	:	PUNCT
ejpam-6139	329	5	3d	3d	NUM
ejpam-6139	329	6	representation	representation	NOUN
ejpam-6139	329	7	verifying	verify	VERB
ejpam-6139	329	8	the	the	DET
ejpam-6139	329	9	inequality	inequality	NOUN
ejpam-6139	329	10	in	in	ADP
ejpam-6139	329	11	theorem	theorem	NOUN
ejpam-6139	329	12	2	2	NUM
ejpam-6139	329	13	.	.	PUNCT
ejpam-6139	329	14	combined	combine	VERB
ejpam-6139	329	15	analyses	analysis	NOUN
ejpam-6139	329	16	establish	establish	VERB
ejpam-6139	329	17	the	the	DET
ejpam-6139	329	18	reliability	reliability	NOUN
ejpam-6139	329	19	and	and	CCONJ
ejpam-6139	329	20	practical	practical	ADJ
ejpam-6139	329	21	utility	utility	NOUN
ejpam-6139	329	22	of	of	ADP
ejpam-6139	329	23	theorem	theorem	NOUN
ejpam-6139	329	24	2	2	NUM
ejpam-6139	329	25	in	in	ADP
ejpam-6139	329	26	bounding	bound	VERB
ejpam-6139	329	27	the	the	DET
ejpam-6139	329	28	behavior	behavior	NOUN
ejpam-6139	329	29	of	of	ADP
ejpam-6139	329	30	h(x	h(x	PROPN
ejpam-6139	329	31	)	)	PUNCT
ejpam-6139	329	32	under	under	ADP
ejpam-6139	329	33	the	the	DET
ejpam-6139	329	34	given	give	VERB
ejpam-6139	329	35	conditions	condition	NOUN
ejpam-6139	329	36	.	.	PUNCT
ejpam-6139	330	1	theorem	theorem	NOUN
ejpam-6139	330	2	3	3	X
ejpam-6139	330	3	.	.	X
ejpam-6139	330	4	consider	consider	VERB
ejpam-6139	330	5	h:[ν	h:[ν	NOUN
ejpam-6139	330	6	,	,	PUNCT
ejpam-6139	330	7	ω	ω	X
ejpam-6139	330	8	]	]	X
ejpam-6139	330	9	→	→	SYM
ejpam-6139	330	10	r	r	NOUN
ejpam-6139	330	11	as	as	ADP
ejpam-6139	330	12	a	a	DET
ejpam-6139	330	13	twice	twice	ADV
ejpam-6139	330	14	differentiable	differentiable	ADJ
ejpam-6139	330	15	mapping	mapping	NOUN
ejpam-6139	330	16	on	on	ADP
ejpam-6139	330	17	(	(	PUNCT
ejpam-6139	330	18	ν	ν	PROPN
ejpam-6139	330	19	,	,	PUNCT
ejpam-6139	330	20	ω	ω	NOUN
ejpam-6139	330	21	)	)	PUNCT
ejpam-6139	330	22	such	such	ADJ
ejpam-6139	330	23	that	that	SCONJ
ejpam-6139	330	24	h′′	h′′	PROPN
ejpam-6139	330	25	∈	∈	PROPN
ejpam-6139	330	26	lq([ν	lq([ν	PROPN
ejpam-6139	330	27	,	,	PUNCT
ejpam-6139	330	28	ω	ω	NOUN
ejpam-6139	330	29	]	]	NOUN
ejpam-6139	330	30	)	)	PUNCT
ejpam-6139	330	31	.	.	PUNCT
ejpam-6139	331	1	assume	assume	VERB
ejpam-6139	331	2	that	that	SCONJ
ejpam-6139	331	3	|h′′|	|h′′|	PROPN
ejpam-6139	331	4	admits	admit	VERB
ejpam-6139	331	5	the	the	DET
ejpam-6139	331	6	s	s	NOUN
ejpam-6139	331	7	-	-	NOUN
ejpam-6139	331	8	convexity	convexity	NOUN
ejpam-6139	331	9	in	in	ADP
ejpam-6139	331	10	second	second	ADJ
ejpam-6139	331	11	sense	sense	NOUN
ejpam-6139	331	12	on	on	ADP
ejpam-6139	331	13	[	[	X
ejpam-6139	331	14	ν	ν	X
ejpam-6139	331	15	,	,	PUNCT
ejpam-6139	331	16	ω	ω	NOUN
ejpam-6139	331	17	]	]	PUNCT
ejpam-6139	331	18	with	with	ADP
ejpam-6139	331	19	q	q	PROPN
ejpam-6139	331	20	≥	≥	NUM
ejpam-6139	331	21	1	1	NUM
ejpam-6139	331	22	then	then	ADV
ejpam-6139	331	23	,	,	PUNCT
ejpam-6139	331	24	∣∣∣∣h(ν	∣∣∣∣h(ν	PROPN
ejpam-6139	331	25	)	)	PUNCT
ejpam-6139	331	26	+	+	CCONJ
ejpam-6139	331	27	h(ω	h(ω	PROPN
ejpam-6139	331	28	)	)	PUNCT
ejpam-6139	331	29	η	η	PROPN
ejpam-6139	331	30	+	+	PROPN
ejpam-6139	331	31	ϕk(µ	ϕk(µ	NUM
ejpam-6139	331	32	,	,	PUNCT
ejpam-6139	331	33	α)−	α)−	PROPN
ejpam-6139	331	34	η	η	PROPN
ejpam-6139	331	35	µα	µα	ADP
ejpam-6139	331	36	k	k	PROPN
ejpam-6139	331	37	−1	−1	NOUN
ejpam-6139	331	38	(	(	PUNCT
ejpam-6139	331	39	ω	ω	NOUN
ejpam-6139	331	40	−	−	NOUN
ejpam-6139	331	41	ν	ν	NOUN
ejpam-6139	331	42	)	)	PUNCT
ejpam-6139	331	43	µα	µα	ADP
ejpam-6139	331	44	k	k	PROPN
ejpam-6139	331	45	(	(	PUNCT
ejpam-6139	331	46	kµ	kµ	PROPN
ejpam-6139	331	47	)	)	PUNCT
ejpam-6139	331	48	α	α	PROPN
ejpam-6139	331	49	k	k	PROPN
ejpam-6139	331	50	γ	γ	X
ejpam-6139	331	51	(	(	PUNCT
ejpam-6139	331	52	α	α	NOUN
ejpam-6139	331	53	k	k	PROPN
ejpam-6139	332	1	+	+	PROPN
ejpam-6139	332	2	1	1	X
ejpam-6139	332	3	)	)	PUNCT
ejpam-6139	332	4	×	×	NOUN
ejpam-6139	332	5	(	(	PUNCT
ejpam-6139	332	6	α	α	PROPN
ejpam-6139	332	7	kj	kj	PROPN
ejpam-6139	332	8	µ	µ	PROPN
ejpam-6139	332	9	(	(	PUNCT
ejpam-6139	332	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	332	11	η	η	PROPN
ejpam-6139	332	12	−	−	PROPN
ejpam-6139	332	13	h(ν	h(ν	PROPN
ejpam-6139	332	14	)	)	PUNCT
ejpam-6139	333	1	+	+	NOUN
ejpam-6139	333	2	α	α	PROPN
ejpam-6139	333	3	k	k	X
ejpam-6139	333	4	jµ	jµ	PROPN
ejpam-6139	333	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	333	6	η	η	PROPN
ejpam-6139	333	7	+	+	PROPN
ejpam-6139	333	8	h(ω	h(ω	PROPN
ejpam-6139	333	9	)	)	PUNCT
ejpam-6139	333	10	)	)	PUNCT
ejpam-6139	334	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	334	2	≤	≤	NOUN
ejpam-6139	334	3	(	(	PUNCT
ejpam-6139	334	4	ω	ω	NOUN
ejpam-6139	334	5	−	−	NOUN
ejpam-6139	334	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	334	7	)	)	PUNCT
ejpam-6139	334	8	α	α	PROPN
ejpam-6139	335	1	k	k	PROPN
ejpam-6139	335	2	η3	η3	PROPN
ejpam-6139	335	3	×	×	NOUN
ejpam-6139	335	4	(	(	PUNCT
ejpam-6139	335	5	∫	∫	PROPN
ejpam-6139	335	6	1	1	NUM
ejpam-6139	335	7	0	0	NUM
ejpam-6139	335	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	335	9	∫	∫	PROPN
ejpam-6139	335	10	t	t	PROPN
ejpam-6139	335	11	0	0	NUM
ejpam-6139	336	1	(	(	PUNCT
ejpam-6139	336	2	1	1	NUM
ejpam-6139	336	3	(	(	PUNCT
ejpam-6139	336	4	kµ	kµ	PROPN
ejpam-6139	336	5	)	)	PUNCT
ejpam-6139	336	6	α	α	PROPN
ejpam-6139	336	7	k	k	NOUN
ejpam-6139	337	1	−	−	PROPN
ejpam-6139	337	2	(	(	PUNCT
ejpam-6139	337	3	1−	1−	NUM
ejpam-6139	337	4	(	(	PUNCT
ejpam-6139	337	5	1−	1−	NUM
ejpam-6139	337	6	φ)µ	φ)µ	NOUN
ejpam-6139	337	7	kµ	kµ	NOUN
ejpam-6139	337	8	)	)	PUNCT
ejpam-6139	337	9	α	α	PROPN
ejpam-6139	337	10	k	k	PROPN
ejpam-6139	337	11	)	)	PUNCT
ejpam-6139	337	12	dφ	dφ	ADP
ejpam-6139	337	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	337	14	)	)	PUNCT
ejpam-6139	337	15	1−	1−	PROPN
ejpam-6139	337	16	1	1	NUM
ejpam-6139	337	17	q	q	NOUN
ejpam-6139	337	18	(	(	PUNCT
ejpam-6139	337	19	19	19	NUM
ejpam-6139	337	20	)	)	PUNCT
ejpam-6139	337	21	×	×	NOUN
ejpam-6139	337	22	(	(	PUNCT
ejpam-6139	337	23	[	[	PUNCT
ejpam-6139	337	24	|h′′(v)|qψ2(µ	|h′′(v)|qψ2(µ	NOUN
ejpam-6139	337	25	,	,	PUNCT
ejpam-6139	337	26	α	α	NOUN
ejpam-6139	337	27	)	)	PUNCT
ejpam-6139	337	28	+	+	CCONJ
ejpam-6139	337	29	|h′′(w)|qψ1(µ	|h′′(w)|qψ1(µ	ADV
ejpam-6139	337	30	,	,	PUNCT
ejpam-6139	337	31	α	α	NOUN
ejpam-6139	337	32	)	)	PUNCT
ejpam-6139	337	33	ns	ns	NOUN
ejpam-6139	337	34	]	]	PUNCT
ejpam-6139	337	35	1	1	NUM
ejpam-6139	337	36	q	q	NOUN
ejpam-6139	337	37	+	+	X
ejpam-6139	337	38	[	[	PUNCT
ejpam-6139	337	39	|h′′(v)|qψ1(µ	|h′′(v)|qψ1(µ	PROPN
ejpam-6139	337	40	,	,	PUNCT
ejpam-6139	337	41	α	α	NOUN
ejpam-6139	337	42	)	)	PUNCT
ejpam-6139	337	43	+	+	CCONJ
ejpam-6139	337	44	|h′′(w)|qψ2(µ	|h′′(w)|qψ2(µ	PROPN
ejpam-6139	337	45	,	,	PUNCT
ejpam-6139	337	46	α	α	NOUN
ejpam-6139	337	47	)	)	PUNCT
ejpam-6139	337	48	ns	ns	NOUN
ejpam-6139	337	49	]	]	PUNCT
ejpam-6139	337	50	1	1	NUM
ejpam-6139	337	51	q	q	NOUN
ejpam-6139	337	52	)	)	PUNCT
ejpam-6139	337	53	,	,	PUNCT
ejpam-6139	337	54	where	where	SCONJ
ejpam-6139	337	55	m.	m.	NOUN
ejpam-6139	337	56	samraiz	samraiz	PROPN
ejpam-6139	337	57	et	et	PROPN
ejpam-6139	337	58	al	al	PROPN
ejpam-6139	337	59	.	.	PUNCT
ejpam-6139	337	60	/	/	SYM
ejpam-6139	337	61	eur	eur	PROPN
ejpam-6139	337	62	.	.	PUNCT
ejpam-6139	338	1	j.	j.	PROPN
ejpam-6139	338	2	pure	pure	PROPN
ejpam-6139	338	3	appl	appl	PROPN
ejpam-6139	338	4	.	.	PROPN
ejpam-6139	338	5	math	math	PROPN
ejpam-6139	338	6	,	,	PUNCT
ejpam-6139	338	7	18	18	NUM
ejpam-6139	338	8	(	(	PUNCT
ejpam-6139	338	9	4	4	NUM
ejpam-6139	338	10	)	)	PUNCT
ejpam-6139	338	11	(	(	PUNCT
ejpam-6139	338	12	2025	2025	NUM
ejpam-6139	338	13	)	)	PUNCT
ejpam-6139	338	14	,	,	PUNCT
ejpam-6139	338	15	6139	6139	NUM
ejpam-6139	338	16	14	14	NUM
ejpam-6139	338	17	of	of	ADP
ejpam-6139	338	18	34	34	NUM
ejpam-6139	338	19	ψ1(µ	ψ1(µ	NOUN
ejpam-6139	338	20	,	,	PUNCT
ejpam-6139	338	21	α	α	X
ejpam-6139	338	22	)	)	PUNCT
ejpam-6139	338	23	=	=	SYM
ejpam-6139	339	1	∫	∫	PROPN
ejpam-6139	339	2	1	1	NUM
ejpam-6139	339	3	0	0	NUM
ejpam-6139	339	4	ts	ts	ADP
ejpam-6139	339	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	339	6	∫	∫	PROPN
ejpam-6139	339	7	t	t	PROPN
ejpam-6139	339	8	0	0	NUM
ejpam-6139	339	9	(	(	PUNCT
ejpam-6139	339	10	1	1	NUM
ejpam-6139	339	11	(	(	PUNCT
ejpam-6139	339	12	kµ	kµ	PROPN
ejpam-6139	339	13	)	)	PUNCT
ejpam-6139	339	14	α	α	PROPN
ejpam-6139	340	1	k	k	NOUN
ejpam-6139	341	1	−	−	PROPN
ejpam-6139	341	2	(	(	PUNCT
ejpam-6139	341	3	1−	1−	NUM
ejpam-6139	341	4	(	(	PUNCT
ejpam-6139	341	5	1−	1−	NUM
ejpam-6139	341	6	φ)µ	φ)µ	NOUN
ejpam-6139	341	7	kµ	kµ	NOUN
ejpam-6139	341	8	)	)	PUNCT
ejpam-6139	341	9	α	α	PROPN
ejpam-6139	341	10	k	k	PROPN
ejpam-6139	341	11	)	)	PUNCT
ejpam-6139	341	12	dφ	dφ	ADP
ejpam-6139	341	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	341	14	,	,	PUNCT
ejpam-6139	341	15	ψ2(µ	ψ2(µ	NOUN
ejpam-6139	341	16	,	,	PUNCT
ejpam-6139	341	17	α	α	NOUN
ejpam-6139	341	18	)	)	PUNCT
ejpam-6139	341	19	=	=	SYM
ejpam-6139	342	1	∫	∫	PROPN
ejpam-6139	342	2	1	1	NUM
ejpam-6139	342	3	0	0	NUM
ejpam-6139	342	4	(	(	PUNCT
ejpam-6139	342	5	η	η	PROPN
ejpam-6139	342	6	−	−	PROPN
ejpam-6139	342	7	t)s	t)s	ADJ
ejpam-6139	342	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	342	9	∫	∫	PROPN
ejpam-6139	342	10	t	t	PROPN
ejpam-6139	342	11	0	0	NUM
ejpam-6139	343	1	(	(	PUNCT
ejpam-6139	343	2	1	1	NUM
ejpam-6139	343	3	(	(	PUNCT
ejpam-6139	343	4	kµ	kµ	PROPN
ejpam-6139	343	5	)	)	PUNCT
ejpam-6139	343	6	α	α	PROPN
ejpam-6139	343	7	k	k	NOUN
ejpam-6139	344	1	−	−	PROPN
ejpam-6139	344	2	(	(	PUNCT
ejpam-6139	344	3	1−	1−	NUM
ejpam-6139	344	4	(	(	PUNCT
ejpam-6139	344	5	1−	1−	NUM
ejpam-6139	344	6	φ)µ	φ)µ	NOUN
ejpam-6139	344	7	kµ	kµ	NOUN
ejpam-6139	344	8	)	)	PUNCT
ejpam-6139	344	9	α	α	PROPN
ejpam-6139	344	10	k	k	PROPN
ejpam-6139	344	11	)	)	PUNCT
ejpam-6139	344	12	dφ	dφ	ADP
ejpam-6139	344	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	344	14	.	.	PUNCT
ejpam-6139	345	1	proof	proof	NOUN
ejpam-6139	345	2	.	.	PUNCT
ejpam-6139	346	1	by	by	ADP
ejpam-6139	346	2	employing	employ	VERB
ejpam-6139	346	3	power	power	NOUN
ejpam-6139	346	4	mean	mean	VERB
ejpam-6139	346	5	inequality	inequality	NOUN
ejpam-6139	346	6	on	on	ADP
ejpam-6139	346	7	equation	equation	NOUN
ejpam-6139	346	8	(	(	PUNCT
ejpam-6139	346	9	10	10	NUM
ejpam-6139	346	10	)	)	PUNCT
ejpam-6139	346	11	,	,	PUNCT
ejpam-6139	346	12	we	we	PRON
ejpam-6139	346	13	obtain∣∣∣∣h(ν	obtain∣∣∣∣h(ν	VERB
ejpam-6139	346	14	)	)	PUNCT
ejpam-6139	347	1	+	+	CCONJ
ejpam-6139	347	2	h(ω	h(ω	PROPN
ejpam-6139	347	3	)	)	PUNCT
ejpam-6139	347	4	η	η	PROPN
ejpam-6139	347	5	+	+	PROPN
ejpam-6139	347	6	ϕk(µ	ϕk(µ	NUM
ejpam-6139	347	7	,	,	PUNCT
ejpam-6139	347	8	α)−	α)−	PROPN
ejpam-6139	347	9	η	η	PROPN
ejpam-6139	347	10	µα	µα	ADP
ejpam-6139	347	11	k	k	PROPN
ejpam-6139	347	12	−1	−1	NOUN
ejpam-6139	347	13	(	(	PUNCT
ejpam-6139	347	14	ω	ω	NOUN
ejpam-6139	347	15	−	−	NOUN
ejpam-6139	347	16	ν	ν	NOUN
ejpam-6139	347	17	)	)	PUNCT
ejpam-6139	347	18	µα	µα	ADP
ejpam-6139	347	19	k	k	PROPN
ejpam-6139	347	20	(	(	PUNCT
ejpam-6139	347	21	kµ	kµ	PROPN
ejpam-6139	347	22	)	)	PUNCT
ejpam-6139	348	1	α	α	PROPN
ejpam-6139	348	2	k	k	PROPN
ejpam-6139	348	3	γ	γ	X
ejpam-6139	348	4	(	(	PUNCT
ejpam-6139	348	5	α	α	NOUN
ejpam-6139	348	6	k	k	PROPN
ejpam-6139	349	1	+	+	PROPN
ejpam-6139	349	2	1	1	X
ejpam-6139	349	3	)	)	PUNCT
ejpam-6139	349	4	×	×	NOUN
ejpam-6139	349	5	(	(	PUNCT
ejpam-6139	349	6	α	α	PROPN
ejpam-6139	349	7	kj	kj	PROPN
ejpam-6139	349	8	µ	µ	PROPN
ejpam-6139	349	9	(	(	PUNCT
ejpam-6139	349	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	349	11	η	η	PROPN
ejpam-6139	349	12	−	−	PROPN
ejpam-6139	349	13	h(ν	h(ν	PROPN
ejpam-6139	349	14	)	)	PUNCT
ejpam-6139	350	1	+	+	NOUN
ejpam-6139	350	2	α	α	PROPN
ejpam-6139	350	3	k	k	X
ejpam-6139	350	4	jµ	jµ	PROPN
ejpam-6139	350	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	350	6	η	η	PROPN
ejpam-6139	350	7	+	+	PROPN
ejpam-6139	350	8	h(ω	h(ω	PROPN
ejpam-6139	350	9	)	)	PUNCT
ejpam-6139	350	10	)	)	PUNCT
ejpam-6139	351	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	351	2	≤	≤	NOUN
ejpam-6139	351	3	(	(	PUNCT
ejpam-6139	351	4	ω	ω	NOUN
ejpam-6139	351	5	−	−	NOUN
ejpam-6139	351	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	351	7	)	)	PUNCT
ejpam-6139	351	8	α	α	PROPN
ejpam-6139	352	1	k	k	PROPN
ejpam-6139	352	2	η3	η3	PROPN
ejpam-6139	352	3	×	×	PROPN
ejpam-6139	352	4	[	[	X
ejpam-6139	352	5	(	(	PUNCT
ejpam-6139	352	6	∫	∫	PROPN
ejpam-6139	352	7	1	1	NUM
ejpam-6139	352	8	0	0	NUM
ejpam-6139	352	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	352	10	∫	∫	PROPN
ejpam-6139	352	11	t	t	PROPN
ejpam-6139	352	12	0	0	NUM
ejpam-6139	352	13	(	(	PUNCT
ejpam-6139	352	14	1	1	NUM
ejpam-6139	352	15	(	(	PUNCT
ejpam-6139	352	16	kµ	kµ	PROPN
ejpam-6139	352	17	)	)	PUNCT
ejpam-6139	352	18	α	α	PROPN
ejpam-6139	352	19	k	k	NOUN
ejpam-6139	353	1	−	−	PROPN
ejpam-6139	353	2	(	(	PUNCT
ejpam-6139	353	3	1−	1−	NUM
ejpam-6139	353	4	(	(	PUNCT
ejpam-6139	353	5	1−	1−	NUM
ejpam-6139	353	6	φ)µ	φ)µ	NOUN
ejpam-6139	353	7	kµ	kµ	NOUN
ejpam-6139	353	8	)	)	PUNCT
ejpam-6139	353	9	α	α	PROPN
ejpam-6139	353	10	k	k	PROPN
ejpam-6139	353	11	)	)	PUNCT
ejpam-6139	353	12	dφ	dφ	ADP
ejpam-6139	353	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	353	14	)	)	PUNCT
ejpam-6139	353	15	1−	1−	NUM
ejpam-6139	353	16	1	1	NUM
ejpam-6139	353	17	q	q	NOUN
ejpam-6139	353	18	×	×	NOUN
ejpam-6139	353	19	(	(	PUNCT
ejpam-6139	353	20	∫	∫	PROPN
ejpam-6139	353	21	1	1	NUM
ejpam-6139	353	22	0	0	NUM
ejpam-6139	353	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	353	24	∫	∫	PROPN
ejpam-6139	353	25	t	t	PROPN
ejpam-6139	353	26	0	0	NUM
ejpam-6139	354	1	(	(	PUNCT
ejpam-6139	354	2	1	1	NUM
ejpam-6139	354	3	(	(	PUNCT
ejpam-6139	354	4	kµ	kµ	PROPN
ejpam-6139	354	5	)	)	PUNCT
ejpam-6139	354	6	α	α	PROPN
ejpam-6139	354	7	k	k	NOUN
ejpam-6139	355	1	−	−	PROPN
ejpam-6139	355	2	(	(	PUNCT
ejpam-6139	355	3	1−	1−	NUM
ejpam-6139	355	4	(	(	PUNCT
ejpam-6139	355	5	1−	1−	NUM
ejpam-6139	355	6	φ)µ	φ)µ	NOUN
ejpam-6139	355	7	kµ	kµ	NOUN
ejpam-6139	355	8	)	)	PUNCT
ejpam-6139	355	9	α	α	PROPN
ejpam-6139	355	10	k	k	PROPN
ejpam-6139	355	11	)	)	PUNCT
ejpam-6139	356	1	dφ	dφ	ADP
ejpam-6139	356	2	∣∣∣∣∣∣∣∣h′′(η	∣∣∣∣∣∣∣∣h′′(η	NOUN
ejpam-6139	356	3	−	−	PROPN
ejpam-6139	356	4	t	t	PROPN
ejpam-6139	356	5	η	η	PROPN
ejpam-6139	356	6	ν	ν	PROPN
ejpam-6139	356	7	+	+	PROPN
ejpam-6139	356	8	t	t	PROPN
ejpam-6139	356	9	η	η	PROPN
ejpam-6139	356	10	ω	ω	PROPN
ejpam-6139	356	11	)	)	PUNCT
ejpam-6139	356	12	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	356	13	)	)	PUNCT
ejpam-6139	356	14	1	1	NUM
ejpam-6139	356	15	q	q	NOUN
ejpam-6139	356	16	+	+	CCONJ
ejpam-6139	356	17	(	(	PUNCT
ejpam-6139	356	18	∫	∫	PROPN
ejpam-6139	356	19	1	1	NUM
ejpam-6139	356	20	0	0	NUM
ejpam-6139	356	21	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	356	22	∫	∫	PROPN
ejpam-6139	356	23	t	t	PROPN
ejpam-6139	356	24	0	0	NUM
ejpam-6139	356	25	(	(	PUNCT
ejpam-6139	356	26	1	1	NUM
ejpam-6139	356	27	(	(	PUNCT
ejpam-6139	356	28	kµ	kµ	PROPN
ejpam-6139	356	29	)	)	PUNCT
ejpam-6139	356	30	α	α	PROPN
ejpam-6139	356	31	k	k	NOUN
ejpam-6139	357	1	−	−	PROPN
ejpam-6139	357	2	(	(	PUNCT
ejpam-6139	357	3	1−	1−	NUM
ejpam-6139	357	4	(	(	PUNCT
ejpam-6139	357	5	1−	1−	NUM
ejpam-6139	357	6	φ)µ	φ)µ	NOUN
ejpam-6139	357	7	kµ	kµ	NOUN
ejpam-6139	357	8	)	)	PUNCT
ejpam-6139	357	9	α	α	PROPN
ejpam-6139	357	10	k	k	PROPN
ejpam-6139	357	11	)	)	PUNCT
ejpam-6139	357	12	dφ	dφ	ADP
ejpam-6139	357	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	357	14	)	)	PUNCT
ejpam-6139	357	15	1−	1−	NUM
ejpam-6139	357	16	1	1	NUM
ejpam-6139	357	17	q	q	NOUN
ejpam-6139	357	18	×	×	NOUN
ejpam-6139	357	19	(	(	PUNCT
ejpam-6139	357	20	∫	∫	PROPN
ejpam-6139	357	21	1	1	NUM
ejpam-6139	357	22	0	0	NUM
ejpam-6139	357	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	357	24	∫	∫	PROPN
ejpam-6139	357	25	t	t	PROPN
ejpam-6139	357	26	0	0	NUM
ejpam-6139	358	1	(	(	PUNCT
ejpam-6139	358	2	1	1	NUM
ejpam-6139	358	3	(	(	PUNCT
ejpam-6139	358	4	kµ	kµ	PROPN
ejpam-6139	358	5	)	)	PUNCT
ejpam-6139	358	6	α	α	PROPN
ejpam-6139	358	7	k	k	NOUN
ejpam-6139	359	1	−	−	PROPN
ejpam-6139	359	2	(	(	PUNCT
ejpam-6139	359	3	1−	1−	NUM
ejpam-6139	359	4	(	(	PUNCT
ejpam-6139	359	5	1−	1−	NUM
ejpam-6139	359	6	φ)µ	φ)µ	NOUN
ejpam-6139	359	7	kµ	kµ	NOUN
ejpam-6139	359	8	)	)	PUNCT
ejpam-6139	360	1	α	α	PROPN
ejpam-6139	360	2	k	k	PROPN
ejpam-6139	360	3	)	)	PUNCT
ejpam-6139	360	4	dφ	dφ	ADP
ejpam-6139	360	5	∣∣∣∣∣∣∣∣h′′	∣∣∣∣∣∣∣∣h′′	PROPN
ejpam-6139	360	6	(	(	PUNCT
ejpam-6139	360	7	t	t	PROPN
ejpam-6139	360	8	η	η	PROPN
ejpam-6139	360	9	ν	ν	PROPN
ejpam-6139	360	10	+	+	PROPN
ejpam-6139	360	11	η	η	PROPN
ejpam-6139	360	12	−	−	PROPN
ejpam-6139	360	13	t	t	PROPN
ejpam-6139	360	14	η	η	PROPN
ejpam-6139	360	15	ω	ω	PROPN
ejpam-6139	360	16	)	)	PUNCT
ejpam-6139	360	17	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	360	18	)	)	PUNCT
ejpam-6139	360	19	1	1	NUM
ejpam-6139	360	20	q	q	NOUN
ejpam-6139	360	21	]	]	PUNCT
ejpam-6139	360	22	.	.	PUNCT
ejpam-6139	361	1	(	(	PUNCT
ejpam-6139	361	2	20	20	NUM
ejpam-6139	361	3	)	)	PUNCT
ejpam-6139	361	4	by	by	ADP
ejpam-6139	361	5	taking	take	VERB
ejpam-6139	361	6	advantage	advantage	NOUN
ejpam-6139	361	7	of	of	ADP
ejpam-6139	361	8	s	s	NOUN
ejpam-6139	361	9	-	-	NOUN
ejpam-6139	361	10	convexity	convexity	NOUN
ejpam-6139	361	11	of	of	ADP
ejpam-6139	361	12	|h′′|	|h′′|	NUM
ejpam-6139	361	13	on	on	ADP
ejpam-6139	361	14	the	the	DET
ejpam-6139	361	15	following	following	ADJ
ejpam-6139	361	16	terms	term	NOUN
ejpam-6139	361	17	,	,	PUNCT
ejpam-6139	361	18	we	we	PRON
ejpam-6139	361	19	proceed	proceed	VERB
ejpam-6139	361	20	as(∫	as(∫	ADJ
ejpam-6139	361	21	1	1	NUM
ejpam-6139	361	22	0	0	NUM
ejpam-6139	361	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	361	24	∫	∫	PROPN
ejpam-6139	361	25	t	t	PROPN
ejpam-6139	361	26	0	0	NUM
ejpam-6139	362	1	(	(	PUNCT
ejpam-6139	362	2	1	1	NUM
ejpam-6139	362	3	(	(	PUNCT
ejpam-6139	362	4	kµ	kµ	PROPN
ejpam-6139	362	5	)	)	PUNCT
ejpam-6139	362	6	α	α	PROPN
ejpam-6139	362	7	k	k	NOUN
ejpam-6139	363	1	−	−	PROPN
ejpam-6139	363	2	(	(	PUNCT
ejpam-6139	363	3	1−	1−	NUM
ejpam-6139	363	4	(	(	PUNCT
ejpam-6139	363	5	1−	1−	NUM
ejpam-6139	363	6	φ)µ	φ)µ	NOUN
ejpam-6139	363	7	kµ	kµ	NOUN
ejpam-6139	363	8	)	)	PUNCT
ejpam-6139	363	9	α	α	PROPN
ejpam-6139	363	10	k	k	PROPN
ejpam-6139	363	11	)	)	PUNCT
ejpam-6139	364	1	dφ	dφ	ADP
ejpam-6139	364	2	∣∣∣∣∣∣∣∣h′′(η	∣∣∣∣∣∣∣∣h′′(η	NOUN
ejpam-6139	364	3	−	−	PROPN
ejpam-6139	364	4	t	t	PROPN
ejpam-6139	364	5	η	η	PROPN
ejpam-6139	364	6	ν	ν	PROPN
ejpam-6139	364	7	+	+	PROPN
ejpam-6139	364	8	t	t	PROPN
ejpam-6139	364	9	η	η	PROPN
ejpam-6139	364	10	ω	ω	PROPN
ejpam-6139	364	11	)	)	PUNCT
ejpam-6139	364	12	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	364	13	)	)	PUNCT
ejpam-6139	364	14	≤	≤	NUM
ejpam-6139	364	15	∫	∫	PROPN
ejpam-6139	364	16	1	1	NUM
ejpam-6139	364	17	0	0	NUM
ejpam-6139	364	18	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	364	19	∫	∫	PROPN
ejpam-6139	364	20	t	t	PROPN
ejpam-6139	364	21	0	0	NUM
ejpam-6139	364	22	(	(	PUNCT
ejpam-6139	364	23	1	1	NUM
ejpam-6139	364	24	(	(	PUNCT
ejpam-6139	364	25	kµ	kµ	PROPN
ejpam-6139	364	26	)	)	PUNCT
ejpam-6139	364	27	α	α	PROPN
ejpam-6139	365	1	k	k	NOUN
ejpam-6139	366	1	−	−	PROPN
ejpam-6139	366	2	(	(	PUNCT
ejpam-6139	366	3	1−	1−	NUM
ejpam-6139	366	4	(	(	PUNCT
ejpam-6139	366	5	1−	1−	NUM
ejpam-6139	366	6	φ)µ	φ)µ	NOUN
ejpam-6139	366	7	kµ	kµ	NOUN
ejpam-6139	366	8	)	)	PUNCT
ejpam-6139	366	9	α	α	PROPN
ejpam-6139	366	10	k	k	PROPN
ejpam-6139	366	11	)	)	PUNCT
ejpam-6139	366	12	dφ	dφ	ADP
ejpam-6139	366	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	366	14	(	(	PUNCT
ejpam-6139	366	15	(	(	PUNCT
ejpam-6139	366	16	η	η	PROPN
ejpam-6139	366	17	−	−	PROPN
ejpam-6139	366	18	t	t	PROPN
ejpam-6139	366	19	η	η	PROPN
ejpam-6139	366	20	)	)	PUNCT
ejpam-6139	366	21	s	s	PART
ejpam-6139	366	22	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	366	23	+	+	CCONJ
ejpam-6139	366	24	(	(	PUNCT
ejpam-6139	366	25	t	t	PROPN
ejpam-6139	366	26	η	η	PROPN
ejpam-6139	366	27	)	)	PUNCT
ejpam-6139	366	28	s	s	PART
ejpam-6139	366	29	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	366	30	)	)	PUNCT
ejpam-6139	366	31	dt	dt	PUNCT
ejpam-6139	367	1	(	(	PUNCT
ejpam-6139	367	2	∫	∫	PROPN
ejpam-6139	367	3	1	1	NUM
ejpam-6139	367	4	0	0	NUM
ejpam-6139	367	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	367	6	∫	∫	PROPN
ejpam-6139	367	7	t	t	PROPN
ejpam-6139	367	8	0	0	NUM
ejpam-6139	367	9	(	(	PUNCT
ejpam-6139	367	10	1	1	NUM
ejpam-6139	367	11	(	(	PUNCT
ejpam-6139	367	12	kµ	kµ	PROPN
ejpam-6139	367	13	)	)	PUNCT
ejpam-6139	367	14	α	α	PROPN
ejpam-6139	367	15	k	k	NOUN
ejpam-6139	368	1	−	−	PROPN
ejpam-6139	368	2	(	(	PUNCT
ejpam-6139	368	3	1−	1−	NUM
ejpam-6139	368	4	(	(	PUNCT
ejpam-6139	368	5	1−	1−	NUM
ejpam-6139	368	6	φ)µ	φ)µ	NOUN
ejpam-6139	368	7	kµ	kµ	NOUN
ejpam-6139	368	8	)	)	PUNCT
ejpam-6139	368	9	α	α	PROPN
ejpam-6139	368	10	k	k	PROPN
ejpam-6139	368	11	)	)	PUNCT
ejpam-6139	369	1	dφ	dφ	ADP
ejpam-6139	369	2	∣∣∣∣∣∣∣∣h′′(η	∣∣∣∣∣∣∣∣h′′(η	NOUN
ejpam-6139	369	3	−	−	PROPN
ejpam-6139	369	4	t	t	PROPN
ejpam-6139	369	5	η	η	PROPN
ejpam-6139	369	6	ν	ν	PROPN
ejpam-6139	369	7	+	+	PROPN
ejpam-6139	369	8	t	t	PROPN
ejpam-6139	369	9	η	η	PROPN
ejpam-6139	369	10	ω	ω	PROPN
ejpam-6139	369	11	)	)	PUNCT
ejpam-6139	369	12	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	369	13	)	)	PUNCT
ejpam-6139	369	14	≤	≤	NOUN
ejpam-6139	369	15	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	369	16	ηs	ηs	PROPN
ejpam-6139	369	17	(	(	PUNCT
ejpam-6139	369	18	∫	∫	PROPN
ejpam-6139	369	19	1	1	NUM
ejpam-6139	369	20	0	0	NUM
ejpam-6139	369	21	(	(	PUNCT
ejpam-6139	369	22	η	η	PROPN
ejpam-6139	369	23	−	−	PROPN
ejpam-6139	369	24	t)s	t)s	ADJ
ejpam-6139	369	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	369	26	∫	∫	PROPN
ejpam-6139	369	27	t	t	PROPN
ejpam-6139	369	28	0	0	NUM
ejpam-6139	369	29	(	(	PUNCT
ejpam-6139	369	30	1	1	NUM
ejpam-6139	369	31	(	(	PUNCT
ejpam-6139	369	32	kµ	kµ	PROPN
ejpam-6139	369	33	)	)	PUNCT
ejpam-6139	369	34	α	α	PROPN
ejpam-6139	369	35	k	k	NOUN
ejpam-6139	370	1	−	−	PROPN
ejpam-6139	370	2	(	(	PUNCT
ejpam-6139	370	3	1−	1−	NUM
ejpam-6139	370	4	(	(	PUNCT
ejpam-6139	370	5	1−	1−	NUM
ejpam-6139	370	6	φ)µ	φ)µ	NOUN
ejpam-6139	370	7	kµ	kµ	NOUN
ejpam-6139	370	8	)	)	PUNCT
ejpam-6139	370	9	α	α	PROPN
ejpam-6139	370	10	k	k	PROPN
ejpam-6139	370	11	)	)	PUNCT
ejpam-6139	370	12	dφ	dφ	ADP
ejpam-6139	370	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	370	14	)	)	PUNCT
ejpam-6139	370	15	+	+	NUM
ejpam-6139	370	16	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	370	17	ηs	ηs	PROPN
ejpam-6139	370	18	(	(	PUNCT
ejpam-6139	370	19	∫	∫	PROPN
ejpam-6139	370	20	1	1	NUM
ejpam-6139	370	21	0	0	NUM
ejpam-6139	370	22	ts	ts	ADP
ejpam-6139	370	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	370	24	∫	∫	PROPN
ejpam-6139	370	25	t	t	PROPN
ejpam-6139	370	26	0	0	NUM
ejpam-6139	371	1	(	(	PUNCT
ejpam-6139	371	2	1	1	NUM
ejpam-6139	371	3	(	(	PUNCT
ejpam-6139	371	4	kµ	kµ	PROPN
ejpam-6139	371	5	)	)	PUNCT
ejpam-6139	371	6	α	α	PROPN
ejpam-6139	371	7	k	k	NOUN
ejpam-6139	372	1	−	−	PROPN
ejpam-6139	372	2	(	(	PUNCT
ejpam-6139	372	3	1−	1−	NUM
ejpam-6139	372	4	(	(	PUNCT
ejpam-6139	372	5	1−	1−	NUM
ejpam-6139	372	6	φ)µ	φ)µ	NOUN
ejpam-6139	372	7	kµ	kµ	NOUN
ejpam-6139	372	8	)	)	PUNCT
ejpam-6139	372	9	α	α	PROPN
ejpam-6139	372	10	k	k	PROPN
ejpam-6139	372	11	)	)	PUNCT
ejpam-6139	372	12	dφ	dφ	ADP
ejpam-6139	372	13	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	372	14	)	)	PUNCT
ejpam-6139	372	15	.	.	PUNCT
ejpam-6139	373	1	(	(	PUNCT
ejpam-6139	373	2	21	21	NUM
ejpam-6139	373	3	)	)	PUNCT
ejpam-6139	373	4	assuming	assume	VERB
ejpam-6139	373	5	ψ1(µ	ψ1(µ	ADP
ejpam-6139	373	6	,	,	PUNCT
ejpam-6139	373	7	α	α	X
ejpam-6139	373	8	)	)	PUNCT
ejpam-6139	373	9	=	=	SYM
ejpam-6139	374	1	∫	∫	PROPN
ejpam-6139	374	2	1	1	NUM
ejpam-6139	374	3	0	0	NUM
ejpam-6139	374	4	ts	ts	ADP
ejpam-6139	374	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	374	6	∫	∫	PROPN
ejpam-6139	374	7	t	t	PROPN
ejpam-6139	374	8	0	0	NUM
ejpam-6139	374	9	(	(	PUNCT
ejpam-6139	374	10	1	1	NUM
ejpam-6139	374	11	(	(	PUNCT
ejpam-6139	374	12	kµ	kµ	PROPN
ejpam-6139	374	13	)	)	PUNCT
ejpam-6139	374	14	α	α	PROPN
ejpam-6139	375	1	k	k	NOUN
ejpam-6139	376	1	−	−	PROPN
ejpam-6139	376	2	(	(	PUNCT
ejpam-6139	376	3	1−	1−	NUM
ejpam-6139	376	4	(	(	PUNCT
ejpam-6139	376	5	1−	1−	NUM
ejpam-6139	376	6	φ)µ	φ)µ	NOUN
ejpam-6139	376	7	kµ	kµ	NOUN
ejpam-6139	376	8	)	)	PUNCT
ejpam-6139	376	9	α	α	PROPN
ejpam-6139	376	10	k	k	PROPN
ejpam-6139	376	11	)	)	PUNCT
ejpam-6139	376	12	dφ	dφ	ADP
ejpam-6139	376	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	376	14	,	,	PUNCT
ejpam-6139	376	15	(	(	PUNCT
ejpam-6139	376	16	22	22	NUM
ejpam-6139	376	17	)	)	PUNCT
ejpam-6139	376	18	m.	m.	NOUN
ejpam-6139	376	19	samraiz	samraiz	PROPN
ejpam-6139	376	20	et	et	PROPN
ejpam-6139	376	21	al	al	PROPN
ejpam-6139	376	22	.	.	PUNCT
ejpam-6139	376	23	/	/	SYM
ejpam-6139	376	24	eur	eur	PROPN
ejpam-6139	376	25	.	.	PUNCT
ejpam-6139	377	1	j.	j.	PROPN
ejpam-6139	377	2	pure	pure	PROPN
ejpam-6139	377	3	appl	appl	PROPN
ejpam-6139	377	4	.	.	PROPN
ejpam-6139	377	5	math	math	PROPN
ejpam-6139	377	6	,	,	PUNCT
ejpam-6139	377	7	18	18	NUM
ejpam-6139	377	8	(	(	PUNCT
ejpam-6139	377	9	4	4	NUM
ejpam-6139	377	10	)	)	PUNCT
ejpam-6139	377	11	(	(	PUNCT
ejpam-6139	377	12	2025	2025	NUM
ejpam-6139	377	13	)	)	PUNCT
ejpam-6139	377	14	,	,	PUNCT
ejpam-6139	377	15	6139	6139	NUM
ejpam-6139	377	16	15	15	NUM
ejpam-6139	377	17	of	of	ADP
ejpam-6139	377	18	34	34	NUM
ejpam-6139	377	19	ψ2(µ	ψ2(µ	NOUN
ejpam-6139	377	20	,	,	PUNCT
ejpam-6139	377	21	α	α	NOUN
ejpam-6139	377	22	)	)	PUNCT
ejpam-6139	377	23	=	=	SYM
ejpam-6139	378	1	∫	∫	PROPN
ejpam-6139	378	2	1	1	NUM
ejpam-6139	378	3	0	0	NUM
ejpam-6139	378	4	(	(	PUNCT
ejpam-6139	378	5	η	η	PROPN
ejpam-6139	378	6	−	−	PROPN
ejpam-6139	378	7	t)s	t)s	ADJ
ejpam-6139	378	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	378	9	∫	∫	PROPN
ejpam-6139	378	10	t	t	PROPN
ejpam-6139	378	11	0	0	NUM
ejpam-6139	379	1	(	(	PUNCT
ejpam-6139	379	2	1	1	NUM
ejpam-6139	379	3	(	(	PUNCT
ejpam-6139	379	4	kµ	kµ	PROPN
ejpam-6139	379	5	)	)	PUNCT
ejpam-6139	379	6	α	α	PROPN
ejpam-6139	379	7	k	k	NOUN
ejpam-6139	380	1	−	−	PROPN
ejpam-6139	380	2	(	(	PUNCT
ejpam-6139	380	3	1−	1−	NUM
ejpam-6139	380	4	(	(	PUNCT
ejpam-6139	380	5	1−	1−	NUM
ejpam-6139	380	6	φ)µ	φ)µ	NOUN
ejpam-6139	380	7	kµ	kµ	NOUN
ejpam-6139	380	8	)	)	PUNCT
ejpam-6139	380	9	α	α	PROPN
ejpam-6139	380	10	k	k	PROPN
ejpam-6139	380	11	)	)	PUNCT
ejpam-6139	380	12	dφ	dφ	ADP
ejpam-6139	380	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	380	14	.	.	PUNCT
ejpam-6139	381	1	(	(	PUNCT
ejpam-6139	381	2	23	23	NUM
ejpam-6139	381	3	)	)	PUNCT
ejpam-6139	381	4	substituting	substitute	VERB
ejpam-6139	381	5	equations	equation	NOUN
ejpam-6139	381	6	(	(	PUNCT
ejpam-6139	381	7	22	22	NUM
ejpam-6139	381	8	)	)	PUNCT
ejpam-6139	381	9	and	and	CCONJ
ejpam-6139	381	10	(	(	PUNCT
ejpam-6139	381	11	23	23	NUM
ejpam-6139	381	12	)	)	PUNCT
ejpam-6139	381	13	in	in	ADP
ejpam-6139	381	14	(	(	PUNCT
ejpam-6139	381	15	21)(∫	21)(∫	NUM
ejpam-6139	381	16	1	1	NUM
ejpam-6139	381	17	0	0	NUM
ejpam-6139	381	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	381	19	∫	∫	PROPN
ejpam-6139	381	20	t	t	PROPN
ejpam-6139	381	21	0	0	NUM
ejpam-6139	382	1	(	(	PUNCT
ejpam-6139	382	2	1	1	NUM
ejpam-6139	382	3	(	(	PUNCT
ejpam-6139	382	4	kµ	kµ	PROPN
ejpam-6139	382	5	)	)	PUNCT
ejpam-6139	382	6	α	α	PROPN
ejpam-6139	382	7	k	k	NOUN
ejpam-6139	383	1	−	−	PROPN
ejpam-6139	383	2	(	(	PUNCT
ejpam-6139	383	3	1−	1−	NUM
ejpam-6139	383	4	(	(	PUNCT
ejpam-6139	383	5	1−	1−	NUM
ejpam-6139	383	6	φ)µ	φ)µ	NOUN
ejpam-6139	383	7	kµ	kµ	NOUN
ejpam-6139	383	8	)	)	PUNCT
ejpam-6139	383	9	α	α	PROPN
ejpam-6139	383	10	k	k	PROPN
ejpam-6139	383	11	)	)	PUNCT
ejpam-6139	384	1	dφ	dφ	ADP
ejpam-6139	384	2	∣∣∣∣∣∣∣∣h′′(η	∣∣∣∣∣∣∣∣h′′(η	NOUN
ejpam-6139	384	3	−	−	PROPN
ejpam-6139	384	4	t	t	PROPN
ejpam-6139	384	5	η	η	PROPN
ejpam-6139	384	6	ν	ν	PROPN
ejpam-6139	384	7	+	+	PROPN
ejpam-6139	384	8	t	t	PROPN
ejpam-6139	384	9	η	η	PROPN
ejpam-6139	384	10	ω	ω	PROPN
ejpam-6139	384	11	)	)	PUNCT
ejpam-6139	384	12	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	384	13	)	)	PUNCT
ejpam-6139	384	14	≤	≤	NOUN
ejpam-6139	384	15	(	(	PUNCT
ejpam-6139	384	16	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	384	17	ηs	ηs	ADP
ejpam-6139	384	18	ψ2(µ	ψ2(µ	PROPN
ejpam-6139	384	19	,	,	PUNCT
ejpam-6139	384	20	α	α	NOUN
ejpam-6139	384	21	)	)	PUNCT
ejpam-6139	384	22	+	+	NUM
ejpam-6139	384	23	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	384	24	ηs	ηs	ADP
ejpam-6139	384	25	ψ1(µ	ψ1(µ	PROPN
ejpam-6139	384	26	,	,	PUNCT
ejpam-6139	384	27	α	α	NOUN
ejpam-6139	384	28	)	)	PUNCT
ejpam-6139	384	29	)	)	PUNCT
ejpam-6139	384	30	.	.	PUNCT
ejpam-6139	385	1	(	(	PUNCT
ejpam-6139	385	2	24	24	NUM
ejpam-6139	385	3	)	)	PUNCT
ejpam-6139	385	4	similarly	similarly	ADV
ejpam-6139	385	5	(	(	PUNCT
ejpam-6139	385	6	∫	∫	PROPN
ejpam-6139	385	7	1	1	NUM
ejpam-6139	385	8	0	0	NUM
ejpam-6139	385	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	385	10	∫	∫	PROPN
ejpam-6139	385	11	t	t	PROPN
ejpam-6139	385	12	0	0	NUM
ejpam-6139	386	1	(	(	PUNCT
ejpam-6139	386	2	1	1	NUM
ejpam-6139	386	3	(	(	PUNCT
ejpam-6139	386	4	kµ	kµ	PROPN
ejpam-6139	386	5	)	)	PUNCT
ejpam-6139	386	6	α	α	PROPN
ejpam-6139	386	7	k	k	NOUN
ejpam-6139	387	1	−	−	PROPN
ejpam-6139	387	2	(	(	PUNCT
ejpam-6139	387	3	1−	1−	NUM
ejpam-6139	387	4	(	(	PUNCT
ejpam-6139	387	5	1−	1−	NUM
ejpam-6139	387	6	φ)µ	φ)µ	NOUN
ejpam-6139	387	7	kµ	kµ	NOUN
ejpam-6139	387	8	)	)	PUNCT
ejpam-6139	387	9	α	α	PROPN
ejpam-6139	387	10	k	k	PROPN
ejpam-6139	387	11	)	)	PUNCT
ejpam-6139	388	1	dφ	dφ	ADP
ejpam-6139	388	2	∣∣∣∣∣∣∣∣h′′(η	∣∣∣∣∣∣∣∣h′′(η	NOUN
ejpam-6139	388	3	−	−	PROPN
ejpam-6139	388	4	t	t	PROPN
ejpam-6139	388	5	η	η	PROPN
ejpam-6139	388	6	ν	ν	PROPN
ejpam-6139	388	7	+	+	PROPN
ejpam-6139	388	8	t	t	PROPN
ejpam-6139	388	9	η	η	PROPN
ejpam-6139	388	10	ω	ω	PROPN
ejpam-6139	388	11	)	)	PUNCT
ejpam-6139	388	12	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	388	13	)	)	PUNCT
ejpam-6139	388	14	≤	≤	NOUN
ejpam-6139	388	15	(	(	PUNCT
ejpam-6139	388	16	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	388	17	ηs	ηs	ADP
ejpam-6139	388	18	ψ1(µ	ψ1(µ	PROPN
ejpam-6139	388	19	,	,	PUNCT
ejpam-6139	388	20	α	α	NOUN
ejpam-6139	388	21	)	)	PUNCT
ejpam-6139	388	22	+	+	NUM
ejpam-6139	388	23	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	388	24	ηs	ηs	ADP
ejpam-6139	388	25	ψ2(µ	ψ2(µ	PROPN
ejpam-6139	388	26	,	,	PUNCT
ejpam-6139	388	27	α	α	NOUN
ejpam-6139	388	28	)	)	PUNCT
ejpam-6139	388	29	)	)	PUNCT
ejpam-6139	388	30	.	.	PUNCT
ejpam-6139	389	1	(	(	PUNCT
ejpam-6139	389	2	25	25	NUM
ejpam-6139	389	3	)	)	PUNCT
ejpam-6139	389	4	substituting	substituting	NOUN
ejpam-6139	389	5	(	(	PUNCT
ejpam-6139	389	6	24	24	NUM
ejpam-6139	389	7	)	)	PUNCT
ejpam-6139	389	8	and	and	CCONJ
ejpam-6139	389	9	(	(	PUNCT
ejpam-6139	389	10	25	25	NUM
ejpam-6139	389	11	)	)	PUNCT
ejpam-6139	389	12	in	in	ADP
ejpam-6139	389	13	(	(	PUNCT
ejpam-6139	389	14	20)∣∣∣∣h(ν	20)∣∣∣∣h(ν	NUM
ejpam-6139	389	15	)	)	PUNCT
ejpam-6139	389	16	+	+	CCONJ
ejpam-6139	389	17	h(ω	h(ω	PROPN
ejpam-6139	389	18	)	)	PUNCT
ejpam-6139	389	19	η	η	PROPN
ejpam-6139	389	20	+	+	PROPN
ejpam-6139	389	21	ϕk(µ	ϕk(µ	NUM
ejpam-6139	389	22	,	,	PUNCT
ejpam-6139	389	23	α)−	α)−	PROPN
ejpam-6139	389	24	η	η	PROPN
ejpam-6139	389	25	µα	µα	ADP
ejpam-6139	389	26	k	k	PROPN
ejpam-6139	389	27	−1	−1	NOUN
ejpam-6139	389	28	(	(	PUNCT
ejpam-6139	389	29	ω	ω	NOUN
ejpam-6139	389	30	−	−	NOUN
ejpam-6139	389	31	ν	ν	NOUN
ejpam-6139	389	32	)	)	PUNCT
ejpam-6139	389	33	µα	µα	ADP
ejpam-6139	389	34	k	k	PROPN
ejpam-6139	389	35	(	(	PUNCT
ejpam-6139	389	36	kµ	kµ	PROPN
ejpam-6139	389	37	)	)	PUNCT
ejpam-6139	389	38	α	α	PROPN
ejpam-6139	390	1	k	k	PROPN
ejpam-6139	390	2	γ	γ	X
ejpam-6139	390	3	(	(	PUNCT
ejpam-6139	390	4	α	α	NOUN
ejpam-6139	390	5	k	k	PROPN
ejpam-6139	391	1	+	+	PROPN
ejpam-6139	391	2	1	1	X
ejpam-6139	391	3	)	)	PUNCT
ejpam-6139	391	4	×	×	NOUN
ejpam-6139	391	5	(	(	PUNCT
ejpam-6139	391	6	α	α	PROPN
ejpam-6139	391	7	kj	kj	PROPN
ejpam-6139	391	8	µ	µ	PROPN
ejpam-6139	391	9	(	(	PUNCT
ejpam-6139	391	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	391	11	η	η	PROPN
ejpam-6139	391	12	−	−	PROPN
ejpam-6139	391	13	h(ν	h(ν	PROPN
ejpam-6139	391	14	)	)	PUNCT
ejpam-6139	392	1	+	+	NOUN
ejpam-6139	392	2	α	α	PROPN
ejpam-6139	392	3	k	k	X
ejpam-6139	392	4	jµ	jµ	PROPN
ejpam-6139	392	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	392	6	η	η	PROPN
ejpam-6139	392	7	+	+	PROPN
ejpam-6139	392	8	h(ω	h(ω	PROPN
ejpam-6139	392	9	)	)	PUNCT
ejpam-6139	392	10	)	)	PUNCT
ejpam-6139	393	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	393	2	≤	≤	NOUN
ejpam-6139	393	3	(	(	PUNCT
ejpam-6139	393	4	ω	ω	NOUN
ejpam-6139	393	5	−	−	NOUN
ejpam-6139	393	6	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	393	7	)	)	PUNCT
ejpam-6139	393	8	α	α	PROPN
ejpam-6139	394	1	k	k	PROPN
ejpam-6139	394	2	η3	η3	PROPN
ejpam-6139	394	3	×	×	NOUN
ejpam-6139	394	4	(	(	PUNCT
ejpam-6139	394	5	∫	∫	PROPN
ejpam-6139	394	6	1	1	NUM
ejpam-6139	394	7	0	0	NUM
ejpam-6139	394	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	394	9	∫	∫	PROPN
ejpam-6139	394	10	t	t	PROPN
ejpam-6139	394	11	0	0	NUM
ejpam-6139	395	1	(	(	PUNCT
ejpam-6139	395	2	1	1	NUM
ejpam-6139	395	3	(	(	PUNCT
ejpam-6139	395	4	kµ	kµ	PROPN
ejpam-6139	395	5	)	)	PUNCT
ejpam-6139	395	6	α	α	PROPN
ejpam-6139	395	7	k	k	NOUN
ejpam-6139	396	1	−	−	PROPN
ejpam-6139	396	2	(	(	PUNCT
ejpam-6139	396	3	1−	1−	NUM
ejpam-6139	396	4	(	(	PUNCT
ejpam-6139	396	5	1−	1−	NUM
ejpam-6139	396	6	φ)µ	φ)µ	NOUN
ejpam-6139	396	7	kµ	kµ	NOUN
ejpam-6139	396	8	)	)	PUNCT
ejpam-6139	396	9	α	α	PROPN
ejpam-6139	396	10	k	k	PROPN
ejpam-6139	396	11	)	)	PUNCT
ejpam-6139	396	12	dφ	dφ	ADP
ejpam-6139	396	13	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	396	14	)	)	PUNCT
ejpam-6139	396	15	1−	1−	NUM
ejpam-6139	396	16	1	1	NUM
ejpam-6139	396	17	q	q	NOUN
ejpam-6139	396	18	×	×	NOUN
ejpam-6139	396	19	(	(	PUNCT
ejpam-6139	396	20	[	[	PUNCT
ejpam-6139	396	21	|h′′(v)|qψ2(µ	|h′′(v)|qψ2(µ	NOUN
ejpam-6139	396	22	,	,	PUNCT
ejpam-6139	396	23	α	α	NOUN
ejpam-6139	396	24	)	)	PUNCT
ejpam-6139	396	25	+	+	CCONJ
ejpam-6139	396	26	|h′′(w)|qψ1(µ	|h′′(w)|qψ1(µ	ADV
ejpam-6139	396	27	,	,	PUNCT
ejpam-6139	396	28	α	α	NOUN
ejpam-6139	396	29	)	)	PUNCT
ejpam-6139	396	30	ns	ns	NOUN
ejpam-6139	396	31	]	]	PUNCT
ejpam-6139	396	32	1	1	NUM
ejpam-6139	396	33	q	q	NOUN
ejpam-6139	396	34	+	+	X
ejpam-6139	396	35	[	[	PUNCT
ejpam-6139	396	36	|h′′(v)|qψ1(µ	|h′′(v)|qψ1(µ	PROPN
ejpam-6139	396	37	,	,	PUNCT
ejpam-6139	396	38	α	α	NOUN
ejpam-6139	396	39	)	)	PUNCT
ejpam-6139	396	40	+	+	CCONJ
ejpam-6139	396	41	|h′′(w)|qψ2(µ	|h′′(w)|qψ2(µ	PROPN
ejpam-6139	396	42	,	,	PUNCT
ejpam-6139	396	43	α	α	NOUN
ejpam-6139	396	44	)	)	PUNCT
ejpam-6139	396	45	ns	ns	NOUN
ejpam-6139	396	46	]	]	PUNCT
ejpam-6139	396	47	1	1	NUM
ejpam-6139	396	48	q	q	NOUN
ejpam-6139	396	49	)	)	PUNCT
ejpam-6139	396	50	.	.	PUNCT
ejpam-6139	397	1	(	(	PUNCT
ejpam-6139	397	2	26	26	NUM
ejpam-6139	397	3	)	)	PUNCT
ejpam-6139	397	4	consequently	consequently	ADV
ejpam-6139	397	5	,	,	PUNCT
ejpam-6139	397	6	we	we	PRON
ejpam-6139	397	7	obtain	obtain	VERB
ejpam-6139	397	8	the	the	DET
ejpam-6139	397	9	desired	desire	VERB
ejpam-6139	397	10	outcome	outcome	NOUN
ejpam-6139	397	11	.	.	PUNCT
ejpam-6139	398	1	corollary	corollary	ADJ
ejpam-6139	398	2	2	2	NUM
ejpam-6139	398	3	.	.	PUNCT
ejpam-6139	399	1	if	if	SCONJ
ejpam-6139	399	2	we	we	PRON
ejpam-6139	399	3	substitute	substitute	VERB
ejpam-6139	399	4	k	k	PROPN
ejpam-6139	399	5	=	=	SYM
ejpam-6139	399	6	1	1	NUM
ejpam-6139	399	7	,	,	PUNCT
ejpam-6139	399	8	s	s	NOUN
ejpam-6139	399	9	=	=	SYM
ejpam-6139	399	10	1	1	NUM
ejpam-6139	399	11	and	and	CCONJ
ejpam-6139	399	12	µ	µ	X
ejpam-6139	399	13	=	=	SYM
ejpam-6139	399	14	1	1	NUM
ejpam-6139	399	15	in	in	ADP
ejpam-6139	399	16	(	(	PUNCT
ejpam-6139	399	17	26	26	NUM
ejpam-6139	399	18	)	)	PUNCT
ejpam-6139	399	19	,	,	PUNCT
ejpam-6139	399	20	then∣∣∣∣h(ν	then∣∣∣∣h(ν	PROPN
ejpam-6139	399	21	)	)	PUNCT
ejpam-6139	399	22	+	+	CCONJ
ejpam-6139	399	23	h(ω	h(ω	PROPN
ejpam-6139	399	24	)	)	PUNCT
ejpam-6139	399	25	η	η	PROPN
ejpam-6139	399	26	+	+	SYM
ejpam-6139	399	27	ϕ1(1	ϕ1(1	PROPN
ejpam-6139	399	28	,	,	PUNCT
ejpam-6139	399	29	α)−	α)−	PROPN
ejpam-6139	399	30	ηα−1	ηα−1	PROPN
ejpam-6139	399	31	(	(	PUNCT
ejpam-6139	399	32	ω	ω	NOUN
ejpam-6139	399	33	−	−	X
ejpam-6139	400	1	ν)µα	ν)µα	PROPN
ejpam-6139	400	2	γ(α+	γ(α+	DET
ejpam-6139	400	3	1	1	NUM
ejpam-6139	400	4	)	)	PUNCT
ejpam-6139	400	5	(	(	PUNCT
ejpam-6139	400	6	αj	αj	X
ejpam-6139	400	7	(	(	PUNCT
ejpam-6139	400	8	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	400	9	η	η	PROPN
ejpam-6139	400	10	−	−	PROPN
ejpam-6139	400	11	h(ν	h(ν	PROPN
ejpam-6139	400	12	)	)	PUNCT
ejpam-6139	400	13	+	+	PROPN
ejpam-6139	400	14	α	α	PROPN
ejpam-6139	400	15	j	j	PROPN
ejpam-6139	400	16	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	400	17	η	η	PROPN
ejpam-6139	400	18	+	+	PROPN
ejpam-6139	400	19	h(ω	h(ω	PROPN
ejpam-6139	400	20	)	)	PUNCT
ejpam-6139	400	21	)	)	PUNCT
ejpam-6139	400	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	400	23	≤	≤	NOUN
ejpam-6139	400	24	(	(	PUNCT
ejpam-6139	400	25	ω	ω	NUM
ejpam-6139	400	26	−	−	PROPN
ejpam-6139	400	27	ν)2	ν)2	NOUN
ejpam-6139	400	28	η3	η3	NOUN
ejpam-6139	400	29	(	(	PUNCT
ejpam-6139	400	30	1	1	NUM
ejpam-6139	400	31	2	2	NUM
ejpam-6139	400	32	−	−	NUM
ejpam-6139	400	33	1	1	NUM
ejpam-6139	400	34	(	(	PUNCT
ejpam-6139	400	35	α+	α+	NOUN
ejpam-6139	400	36	1)(α+	1)(α+	NUM
ejpam-6139	400	37	3	3	NUM
ejpam-6139	400	38	)	)	PUNCT
ejpam-6139	400	39	)	)	PUNCT
ejpam-6139	401	1	1−	1−	NUM
ejpam-6139	401	2	1	1	NUM
ejpam-6139	401	3	q	q	NOUN
ejpam-6139	401	4	×	×	NOUN
ejpam-6139	401	5	[	[	X
ejpam-6139	401	6	(	(	PUNCT
ejpam-6139	401	7	(	(	PUNCT
ejpam-6139	401	8	η	η	PROPN
ejpam-6139	401	9	(	(	PUNCT
ejpam-6139	401	10	1	1	NUM
ejpam-6139	401	11	2	2	NUM
ejpam-6139	401	12	−	−	NUM
ejpam-6139	401	13	1	1	NUM
ejpam-6139	401	14	(	(	PUNCT
ejpam-6139	401	15	α+	α+	NOUN
ejpam-6139	401	16	1)(α+	1)(α+	NUM
ejpam-6139	401	17	2	2	NUM
ejpam-6139	401	18	)	)	PUNCT
ejpam-6139	401	19	)	)	PUNCT
ejpam-6139	402	1	−	−	PROPN
ejpam-6139	403	1	(	(	PUNCT
ejpam-6139	403	2	1	1	NUM
ejpam-6139	403	3	3	3	NUM
ejpam-6139	403	4	−	−	NOUN
ejpam-6139	403	5	1	1	NUM
ejpam-6139	403	6	(	(	PUNCT
ejpam-6139	403	7	α+	α+	NOUN
ejpam-6139	403	8	1)(α+	1)(α+	NUM
ejpam-6139	403	9	3	3	NUM
ejpam-6139	403	10	)	)	PUNCT
ejpam-6139	403	11	)	)	PUNCT
ejpam-6139	403	12	)	)	PUNCT
ejpam-6139	404	1	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	404	2	η	η	PROPN
ejpam-6139	404	3	+	+	CCONJ
ejpam-6139	404	4	(	(	PUNCT
ejpam-6139	404	5	1	1	NUM
ejpam-6139	404	6	3	3	NUM
ejpam-6139	404	7	−	−	NOUN
ejpam-6139	404	8	1	1	NUM
ejpam-6139	404	9	(	(	PUNCT
ejpam-6139	404	10	α+	α+	NOUN
ejpam-6139	404	11	1)(α+	1)(α+	NUM
ejpam-6139	404	12	3	3	NUM
ejpam-6139	404	13	)	)	PUNCT
ejpam-6139	404	14	)	)	PUNCT
ejpam-6139	404	15	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	404	16	η	η	PROPN
ejpam-6139	404	17	)	)	PUNCT
ejpam-6139	404	18	1	1	NUM
ejpam-6139	404	19	q	q	NOUN
ejpam-6139	404	20	+	+	NUM
ejpam-6139	404	21	(	(	PUNCT
ejpam-6139	404	22	(	(	PUNCT
ejpam-6139	404	23	1	1	NUM
ejpam-6139	404	24	3	3	NUM
ejpam-6139	404	25	−	−	NOUN
ejpam-6139	404	26	1	1	NUM
ejpam-6139	404	27	(	(	PUNCT
ejpam-6139	404	28	α+	α+	NOUN
ejpam-6139	404	29	1)(α+	1)(α+	NUM
ejpam-6139	404	30	3	3	NUM
ejpam-6139	404	31	)	)	PUNCT
ejpam-6139	404	32	)	)	PUNCT
ejpam-6139	405	1	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	405	2	η	η	PROPN
ejpam-6139	405	3	m.	m.	PROPN
ejpam-6139	405	4	samraiz	samraiz	PROPN
ejpam-6139	405	5	et	et	PROPN
ejpam-6139	405	6	al	al	PROPN
ejpam-6139	405	7	.	.	PUNCT
ejpam-6139	405	8	/	/	SYM
ejpam-6139	405	9	eur	eur	PROPN
ejpam-6139	405	10	.	.	PUNCT
ejpam-6139	406	1	j.	j.	PROPN
ejpam-6139	406	2	pure	pure	PROPN
ejpam-6139	406	3	appl	appl	PROPN
ejpam-6139	406	4	.	.	PROPN
ejpam-6139	406	5	math	math	PROPN
ejpam-6139	406	6	,	,	PUNCT
ejpam-6139	406	7	18	18	NUM
ejpam-6139	406	8	(	(	PUNCT
ejpam-6139	406	9	4	4	NUM
ejpam-6139	406	10	)	)	PUNCT
ejpam-6139	406	11	(	(	PUNCT
ejpam-6139	406	12	2025	2025	NUM
ejpam-6139	406	13	)	)	PUNCT
ejpam-6139	406	14	,	,	PUNCT
ejpam-6139	406	15	6139	6139	NUM
ejpam-6139	406	16	16	16	NUM
ejpam-6139	406	17	of	of	ADP
ejpam-6139	406	18	34	34	NUM
ejpam-6139	406	19	+	+	CCONJ
ejpam-6139	406	20	(	(	PUNCT
ejpam-6139	406	21	η	η	PROPN
ejpam-6139	406	22	(	(	PUNCT
ejpam-6139	406	23	1	1	NUM
ejpam-6139	406	24	2	2	NUM
ejpam-6139	406	25	−	−	NUM
ejpam-6139	406	26	1	1	NUM
ejpam-6139	406	27	(	(	PUNCT
ejpam-6139	406	28	α+	α+	NOUN
ejpam-6139	406	29	1)(α+	1)(α+	NUM
ejpam-6139	406	30	2	2	NUM
ejpam-6139	406	31	)	)	PUNCT
ejpam-6139	406	32	)	)	PUNCT
ejpam-6139	407	1	−	−	PROPN
ejpam-6139	407	2	(	(	PUNCT
ejpam-6139	407	3	1	1	NUM
ejpam-6139	407	4	3	3	NUM
ejpam-6139	407	5	−	−	NOUN
ejpam-6139	407	6	1	1	NUM
ejpam-6139	407	7	(	(	PUNCT
ejpam-6139	407	8	α+	α+	NOUN
ejpam-6139	407	9	1)(α+	1)(α+	NUM
ejpam-6139	407	10	3	3	NUM
ejpam-6139	407	11	)	)	PUNCT
ejpam-6139	407	12	)	)	PUNCT
ejpam-6139	407	13	)	)	PUNCT
ejpam-6139	407	14	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	407	15	η	η	PROPN
ejpam-6139	407	16	)	)	PUNCT
ejpam-6139	407	17	1	1	NUM
ejpam-6139	407	18	q	q	NOUN
ejpam-6139	407	19	]	]	PUNCT
ejpam-6139	407	20	.	.	PUNCT
ejpam-6139	408	1	(	(	PUNCT
ejpam-6139	408	2	27	27	NUM
ejpam-6139	408	3	)	)	PUNCT
ejpam-6139	408	4	proof	proof	NOUN
ejpam-6139	408	5	.	.	PUNCT
ejpam-6139	409	1	setting	set	VERB
ejpam-6139	409	2	k	k	PROPN
ejpam-6139	409	3	=	=	PUNCT
ejpam-6139	409	4	µ	µ	X
ejpam-6139	409	5	=	=	SYM
ejpam-6139	409	6	1	1	NUM
ejpam-6139	409	7	in	in	ADP
ejpam-6139	409	8	(	(	PUNCT
ejpam-6139	409	9	22	22	NUM
ejpam-6139	409	10	)	)	PUNCT
ejpam-6139	409	11	,	,	PUNCT
ejpam-6139	409	12	ψ1(1	ψ1(1	PROPN
ejpam-6139	409	13	,	,	PUNCT
ejpam-6139	409	14	α	α	NOUN
ejpam-6139	409	15	)	)	PUNCT
ejpam-6139	409	16	=	=	SYM
ejpam-6139	410	1	∫	∫	PROPN
ejpam-6139	410	2	1	1	NUM
ejpam-6139	410	3	0	0	NUM
ejpam-6139	410	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	410	5	∫	∫	PROPN
ejpam-6139	410	6	t	t	PROPN
ejpam-6139	410	7	0	0	NUM
ejpam-6139	411	1	(	(	PUNCT
ejpam-6139	411	2	1−	1−	NUM
ejpam-6139	411	3	φα	φα	CCONJ
ejpam-6139	411	4	)	)	PUNCT
ejpam-6139	411	5	dφ	dφ	ADP
ejpam-6139	411	6	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	411	7	ψ1(1	ψ1(1	PROPN
ejpam-6139	411	8	,	,	PUNCT
ejpam-6139	411	9	α	α	X
ejpam-6139	411	10	)	)	PUNCT
ejpam-6139	411	11	=	=	SYM
ejpam-6139	411	12	∫	∫	PROPN
ejpam-6139	411	13	1	1	NUM
ejpam-6139	411	14	0	0	NUM
ejpam-6139	411	15	|t−	|t−	PROPN
ejpam-6139	411	16	tα+1	tα+1	NOUN
ejpam-6139	411	17	α+	α+	PUNCT
ejpam-6139	411	18	1	1	NUM
ejpam-6139	411	19	|dt	|dt	NUM
ejpam-6139	411	20	when	when	SCONJ
ejpam-6139	411	21	a	a	DET
ejpam-6139	411	22	>	>	X
ejpam-6139	411	23	b	b	NOUN
ejpam-6139	411	24	then	then	ADV
ejpam-6139	411	25	|a−b|	|a−b|	NUM
ejpam-6139	411	26	=	=	SYM
ejpam-6139	411	27	a−b	a−b	NOUN
ejpam-6139	411	28	ψ1(1	ψ1(1	PROPN
ejpam-6139	411	29	,	,	PUNCT
ejpam-6139	411	30	α	α	NOUN
ejpam-6139	411	31	)	)	PUNCT
ejpam-6139	411	32	=	=	SYM
ejpam-6139	411	33	1	1	NUM
ejpam-6139	411	34	2	2	NUM
ejpam-6139	411	35	−	−	NUM
ejpam-6139	411	36	1	1	NUM
ejpam-6139	411	37	(	(	PUNCT
ejpam-6139	411	38	α+	α+	NOUN
ejpam-6139	411	39	1)(α+	1)(α+	NUM
ejpam-6139	411	40	2	2	NUM
ejpam-6139	411	41	)	)	PUNCT
ejpam-6139	411	42	(	(	PUNCT
ejpam-6139	411	43	28	28	NUM
ejpam-6139	411	44	)	)	PUNCT
ejpam-6139	411	45	similarly	similarly	ADV
ejpam-6139	411	46	ψ2(1	ψ2(1	PROPN
ejpam-6139	411	47	,	,	PUNCT
ejpam-6139	411	48	α	α	NOUN
ejpam-6139	411	49	)	)	PUNCT
ejpam-6139	411	50	=	=	SYM
ejpam-6139	412	1	1	1	NUM
ejpam-6139	412	2	3	3	NUM
ejpam-6139	412	3	−	−	NOUN
ejpam-6139	412	4	1	1	NUM
ejpam-6139	412	5	(	(	PUNCT
ejpam-6139	412	6	α+	α+	NOUN
ejpam-6139	412	7	1)(α+	1)(α+	NUM
ejpam-6139	412	8	3	3	NUM
ejpam-6139	412	9	)	)	PUNCT
ejpam-6139	412	10	(	(	PUNCT
ejpam-6139	412	11	29	29	NUM
ejpam-6139	412	12	)	)	PUNCT
ejpam-6139	412	13	substituting	substituting	NOUN
ejpam-6139	412	14	(	(	PUNCT
ejpam-6139	412	15	28	28	NUM
ejpam-6139	412	16	)	)	PUNCT
ejpam-6139	412	17	and	and	CCONJ
ejpam-6139	412	18	(	(	PUNCT
ejpam-6139	412	19	29	29	NUM
ejpam-6139	412	20	)	)	PUNCT
ejpam-6139	412	21	in	in	ADP
ejpam-6139	412	22	(	(	PUNCT
ejpam-6139	412	23	26),∣∣∣∣h(ν	26),∣∣∣∣h(ν	NUM
ejpam-6139	412	24	)	)	PUNCT
ejpam-6139	412	25	+	+	CCONJ
ejpam-6139	412	26	h(ω	h(ω	PROPN
ejpam-6139	412	27	)	)	PUNCT
ejpam-6139	412	28	η	η	PROPN
ejpam-6139	412	29	+	+	SYM
ejpam-6139	412	30	ϕ1(1	ϕ1(1	PROPN
ejpam-6139	412	31	,	,	PUNCT
ejpam-6139	412	32	α)−	α)−	PROPN
ejpam-6139	412	33	ηα−1	ηα−1	PROPN
ejpam-6139	412	34	(	(	PUNCT
ejpam-6139	412	35	ω	ω	NOUN
ejpam-6139	412	36	−	−	NOUN
ejpam-6139	412	37	ν)α	ν)α	X
ejpam-6139	412	38	γ(α+	γ(α+	X
ejpam-6139	412	39	1	1	NUM
ejpam-6139	412	40	)	)	PUNCT
ejpam-6139	412	41	(	(	PUNCT
ejpam-6139	412	42	αj	αj	X
ejpam-6139	412	43	(	(	PUNCT
ejpam-6139	412	44	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	412	45	η	η	PROPN
ejpam-6139	412	46	−	−	PROPN
ejpam-6139	412	47	h(ν	h(ν	PROPN
ejpam-6139	412	48	)	)	PUNCT
ejpam-6139	412	49	+	+	PROPN
ejpam-6139	412	50	α	α	PROPN
ejpam-6139	412	51	j	j	PROPN
ejpam-6139	412	52	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	412	53	η	η	PROPN
ejpam-6139	412	54	+	+	PROPN
ejpam-6139	412	55	h(ω	h(ω	PROPN
ejpam-6139	412	56	)	)	PUNCT
ejpam-6139	412	57	)	)	PUNCT
ejpam-6139	412	58	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	412	59	≤	≤	NOUN
ejpam-6139	412	60	(	(	PUNCT
ejpam-6139	412	61	ω	ω	NUM
ejpam-6139	412	62	−	−	PROPN
ejpam-6139	412	63	ν)2	ν)2	NOUN
ejpam-6139	412	64	η3	η3	NOUN
ejpam-6139	412	65	(	(	PUNCT
ejpam-6139	412	66	1	1	NUM
ejpam-6139	412	67	2	2	NUM
ejpam-6139	412	68	−	−	NUM
ejpam-6139	412	69	1	1	NUM
ejpam-6139	412	70	(	(	PUNCT
ejpam-6139	412	71	α+	α+	NOUN
ejpam-6139	412	72	1)(α+	1)(α+	NUM
ejpam-6139	412	73	3	3	NUM
ejpam-6139	412	74	)	)	PUNCT
ejpam-6139	412	75	)	)	PUNCT
ejpam-6139	412	76	1−	1−	NUM
ejpam-6139	412	77	1	1	NUM
ejpam-6139	412	78	q	q	NOUN
ejpam-6139	412	79	×	×	NOUN
ejpam-6139	412	80	[	[	X
ejpam-6139	412	81	(	(	PUNCT
ejpam-6139	412	82	(	(	PUNCT
ejpam-6139	412	83	η	η	PROPN
ejpam-6139	412	84	(	(	PUNCT
ejpam-6139	412	85	1	1	NUM
ejpam-6139	412	86	2	2	NUM
ejpam-6139	412	87	−	−	NUM
ejpam-6139	412	88	1	1	NUM
ejpam-6139	412	89	(	(	PUNCT
ejpam-6139	412	90	α+	α+	NOUN
ejpam-6139	412	91	1)(α+	1)(α+	NUM
ejpam-6139	412	92	2	2	NUM
ejpam-6139	412	93	)	)	PUNCT
ejpam-6139	412	94	)	)	PUNCT
ejpam-6139	412	95	−	−	PROPN
ejpam-6139	413	1	(	(	PUNCT
ejpam-6139	413	2	1	1	NUM
ejpam-6139	413	3	3	3	NUM
ejpam-6139	413	4	−	−	NOUN
ejpam-6139	413	5	1	1	NUM
ejpam-6139	413	6	(	(	PUNCT
ejpam-6139	413	7	α+	α+	NOUN
ejpam-6139	413	8	1)(α+	1)(α+	NUM
ejpam-6139	413	9	3	3	NUM
ejpam-6139	413	10	)	)	PUNCT
ejpam-6139	413	11	)	)	PUNCT
ejpam-6139	413	12	)	)	PUNCT
ejpam-6139	414	1	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	414	2	η	η	PROPN
ejpam-6139	414	3	+	+	CCONJ
ejpam-6139	414	4	(	(	PUNCT
ejpam-6139	414	5	1	1	NUM
ejpam-6139	414	6	3	3	NUM
ejpam-6139	414	7	−	−	NOUN
ejpam-6139	414	8	1	1	NUM
ejpam-6139	414	9	(	(	PUNCT
ejpam-6139	414	10	α+	α+	NOUN
ejpam-6139	414	11	1)(α+	1)(α+	NUM
ejpam-6139	414	12	3	3	NUM
ejpam-6139	414	13	)	)	PUNCT
ejpam-6139	414	14	)	)	PUNCT
ejpam-6139	414	15	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	414	16	η	η	PROPN
ejpam-6139	414	17	)	)	PUNCT
ejpam-6139	414	18	1	1	NUM
ejpam-6139	414	19	q	q	NOUN
ejpam-6139	414	20	+	+	NUM
ejpam-6139	414	21	(	(	PUNCT
ejpam-6139	414	22	(	(	PUNCT
ejpam-6139	414	23	1	1	NUM
ejpam-6139	414	24	3	3	NUM
ejpam-6139	414	25	−	−	NOUN
ejpam-6139	414	26	1	1	NUM
ejpam-6139	414	27	(	(	PUNCT
ejpam-6139	414	28	α+	α+	NOUN
ejpam-6139	414	29	1)(α+	1)(α+	NUM
ejpam-6139	414	30	3	3	NUM
ejpam-6139	414	31	)	)	PUNCT
ejpam-6139	414	32	)	)	PUNCT
ejpam-6139	415	1	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	415	2	η	η	PROPN
ejpam-6139	415	3	+	+	PROPN
ejpam-6139	415	4	(	(	PUNCT
ejpam-6139	415	5	η	η	PROPN
ejpam-6139	415	6	(	(	PUNCT
ejpam-6139	415	7	1	1	NUM
ejpam-6139	415	8	2	2	NUM
ejpam-6139	415	9	−	−	NUM
ejpam-6139	415	10	1	1	NUM
ejpam-6139	415	11	(	(	PUNCT
ejpam-6139	415	12	α+	α+	NOUN
ejpam-6139	415	13	1)(α+	1)(α+	NUM
ejpam-6139	415	14	2	2	NUM
ejpam-6139	415	15	)	)	PUNCT
ejpam-6139	415	16	)	)	PUNCT
ejpam-6139	415	17	−	−	PROPN
ejpam-6139	416	1	(	(	PUNCT
ejpam-6139	416	2	1	1	NUM
ejpam-6139	416	3	3	3	NUM
ejpam-6139	416	4	−	−	NOUN
ejpam-6139	416	5	1	1	NUM
ejpam-6139	416	6	(	(	PUNCT
ejpam-6139	416	7	α+	α+	NOUN
ejpam-6139	416	8	1)(α+	1)(α+	NUM
ejpam-6139	416	9	3	3	NUM
ejpam-6139	416	10	)	)	PUNCT
ejpam-6139	416	11	)	)	PUNCT
ejpam-6139	416	12	)	)	PUNCT
ejpam-6139	417	1	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	417	2	η	η	PROPN
ejpam-6139	417	3	)	)	PUNCT
ejpam-6139	417	4	1	1	NUM
ejpam-6139	417	5	q	q	NOUN
ejpam-6139	417	6	]	]	PUNCT
ejpam-6139	417	7	.	.	PUNCT
ejpam-6139	418	1	(	(	PUNCT
ejpam-6139	418	2	30	30	NUM
ejpam-6139	418	3	)	)	PUNCT
ejpam-6139	418	4	ultimately	ultimately	ADV
ejpam-6139	418	5	,	,	PUNCT
ejpam-6139	418	6	the	the	DET
ejpam-6139	418	7	expected	expect	VERB
ejpam-6139	418	8	outcome	outcome	NOUN
ejpam-6139	418	9	has	have	AUX
ejpam-6139	418	10	been	be	AUX
ejpam-6139	418	11	reached	reach	VERB
ejpam-6139	418	12	.	.	PUNCT
ejpam-6139	419	1	remark	remark	NOUN
ejpam-6139	419	2	6	6	NUM
ejpam-6139	419	3	.	.	PUNCT
ejpam-6139	420	1	if	if	SCONJ
ejpam-6139	420	2	we	we	PRON
ejpam-6139	420	3	assign	assign	VERB
ejpam-6139	420	4	η	η	PROPN
ejpam-6139	420	5	=	=	PROPN
ejpam-6139	420	6	2	2	NUM
ejpam-6139	420	7	and	and	CCONJ
ejpam-6139	420	8	α	α	NOUN
ejpam-6139	420	9	=	=	NOUN
ejpam-6139	420	10	1	1	NUM
ejpam-6139	420	11	in	in	ADP
ejpam-6139	420	12	(	(	PUNCT
ejpam-6139	420	13	27	27	NUM
ejpam-6139	420	14	)	)	PUNCT
ejpam-6139	420	15	,	,	PUNCT
ejpam-6139	420	16	our	our	PRON
ejpam-6139	420	17	result	result	NOUN
ejpam-6139	420	18	reduced	reduce	VERB
ejpam-6139	420	19	as	as	ADP
ejpam-6139	420	20	follow∣∣∣∣h(ν	follow∣∣∣∣h(ν	PROPN
ejpam-6139	420	21	)	)	PUNCT
ejpam-6139	421	1	+	+	CCONJ
ejpam-6139	421	2	h(ω	h(ω	PROPN
ejpam-6139	421	3	)	)	PUNCT
ejpam-6139	421	4	2	2	NUM
ejpam-6139	421	5	−	−	PROPN
ejpam-6139	421	6	1	1	NUM
ejpam-6139	421	7	ω	ω	NUM
ejpam-6139	421	8	−	−	NOUN
ejpam-6139	421	9	ν	ν	PROPN
ejpam-6139	421	10	∫	∫	PROPN
ejpam-6139	421	11	ω	ω	PROPN
ejpam-6139	421	12	ν	ν	PROPN
ejpam-6139	421	13	h(x)dx	h(x)dx	PROPN
ejpam-6139	421	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	421	15	≤	≤	NOUN
ejpam-6139	421	16	(	(	PUNCT
ejpam-6139	421	17	ω	ω	NUM
ejpam-6139	421	18	−	−	PROPN
ejpam-6139	421	19	ν)2	ν)2	NOUN
ejpam-6139	422	1	24	24	NUM
ejpam-6139	422	2	[	[	X
ejpam-6139	422	3	(	(	PUNCT
ejpam-6139	422	4	11	11	NUM
ejpam-6139	422	5	16	16	NUM
ejpam-6139	422	6	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	422	7	+	+	CCONJ
ejpam-6139	422	8	5	5	NUM
ejpam-6139	422	9	16	16	NUM
ejpam-6139	422	10	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	422	11	)	)	PUNCT
ejpam-6139	422	12	1	1	NUM
ejpam-6139	422	13	q	q	NOUN
ejpam-6139	422	14	+	+	CCONJ
ejpam-6139	422	15	(	(	PUNCT
ejpam-6139	422	16	5	5	NUM
ejpam-6139	422	17	16	16	NUM
ejpam-6139	422	18	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	422	19	+	+	CCONJ
ejpam-6139	422	20	11	11	NUM
ejpam-6139	422	21	16	16	NUM
ejpam-6139	422	22	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	422	23	)	)	PUNCT
ejpam-6139	422	24	1	1	NUM
ejpam-6139	422	25	q	q	NOUN
ejpam-6139	422	26	]	]	PUNCT
ejpam-6139	422	27	.	.	PUNCT
ejpam-6139	423	1	example	example	NOUN
ejpam-6139	424	1	3	3	X
ejpam-6139	424	2	.	.	PUNCT
ejpam-6139	424	3	this	this	DET
ejpam-6139	424	4	example	example	NOUN
ejpam-6139	424	5	demonstrates	demonstrate	VERB
ejpam-6139	424	6	the	the	DET
ejpam-6139	424	7	application	application	NOUN
ejpam-6139	424	8	of	of	ADP
ejpam-6139	424	9	theorem	theorem	NOUN
ejpam-6139	424	10	3	3	NUM
ejpam-6139	424	11	through	through	ADP
ejpam-6139	424	12	both	both	CCONJ
ejpam-6139	424	13	graphical	graphical	ADJ
ejpam-6139	424	14	and	and	CCONJ
ejpam-6139	424	15	numerical	numerical	ADJ
ejpam-6139	424	16	methods	method	NOUN
ejpam-6139	424	17	.	.	PUNCT
ejpam-6139	425	1	we	we	PRON
ejpam-6139	425	2	analyze	analyze	VERB
ejpam-6139	425	3	the	the	DET
ejpam-6139	425	4	function	function	NOUN
ejpam-6139	425	5	h(x	h(x	PROPN
ejpam-6139	425	6	)	)	PUNCT
ejpam-6139	425	7	=	=	SYM
ejpam-6139	425	8	x6	x6	PROPN
ejpam-6139	425	9	+	+	CCONJ
ejpam-6139	425	10	2x4	2x4	NUM
ejpam-6139	425	11	within	within	ADP
ejpam-6139	425	12	the	the	DET
ejpam-6139	425	13	interval	interval	NOUN
ejpam-6139	425	14	[	[	X
ejpam-6139	425	15	2	2	NUM
ejpam-6139	425	16	,	,	PUNCT
ejpam-6139	425	17	7	7	NUM
ejpam-6139	425	18	]	]	PUNCT
ejpam-6139	425	19	to	to	PART
ejpam-6139	425	20	verify	verify	VERB
ejpam-6139	425	21	the	the	DET
ejpam-6139	425	22	inequality	inequality	NOUN
ejpam-6139	425	23	using	use	VERB
ejpam-6139	425	24	the	the	DET
ejpam-6139	425	25	following	follow	VERB
ejpam-6139	425	26	parameter	parameter	NOUN
ejpam-6139	425	27	values	value	NOUN
ejpam-6139	425	28	:	:	PUNCT
ejpam-6139	425	29	k	k	X
ejpam-6139	425	30	=	=	SYM
ejpam-6139	425	31	3	3	NUM
ejpam-6139	425	32	,	,	PUNCT
ejpam-6139	425	33	α	α	NOUN
ejpam-6139	425	34	=	=	SYM
ejpam-6139	425	35	4	4	NUM
ejpam-6139	425	36	,	,	PUNCT
ejpam-6139	425	37	1	1	NUM
ejpam-6139	425	38	p	p	NOUN
ejpam-6139	425	39	=	=	SYM
ejpam-6139	425	40	0.6	0.6	NUM
ejpam-6139	425	41	,	,	PUNCT
ejpam-6139	425	42	m.	m.	NOUN
ejpam-6139	425	43	samraiz	samraiz	PROPN
ejpam-6139	425	44	et	et	PROPN
ejpam-6139	425	45	al	al	PROPN
ejpam-6139	425	46	.	.	PUNCT
ejpam-6139	425	47	/	/	SYM
ejpam-6139	425	48	eur	eur	PROPN
ejpam-6139	425	49	.	.	PUNCT
ejpam-6139	426	1	j.	j.	PROPN
ejpam-6139	426	2	pure	pure	PROPN
ejpam-6139	426	3	appl	appl	PROPN
ejpam-6139	426	4	.	.	PROPN
ejpam-6139	426	5	math	math	PROPN
ejpam-6139	426	6	,	,	PUNCT
ejpam-6139	426	7	18	18	NUM
ejpam-6139	426	8	(	(	PUNCT
ejpam-6139	426	9	4	4	NUM
ejpam-6139	426	10	)	)	PUNCT
ejpam-6139	426	11	(	(	PUNCT
ejpam-6139	426	12	2025	2025	NUM
ejpam-6139	426	13	)	)	PUNCT
ejpam-6139	426	14	,	,	PUNCT
ejpam-6139	426	15	6139	6139	NUM
ejpam-6139	426	16	17	17	NUM
ejpam-6139	426	17	of	of	ADP
ejpam-6139	426	18	34	34	NUM
ejpam-6139	426	19	1	1	NUM
ejpam-6139	426	20	q	q	NOUN
ejpam-6139	426	21	=	=	NUM
ejpam-6139	426	22	0.4	0.4	NUM
ejpam-6139	426	23	,	,	PUNCT
ejpam-6139	426	24	and	and	CCONJ
ejpam-6139	426	25	η	η	PROPN
ejpam-6139	426	26	=	=	PROPN
ejpam-6139	426	27	8	8	PROPN
ejpam-6139	426	28	.	.	PUNCT
ejpam-6139	427	1	explanation	explanation	NOUN
ejpam-6139	427	2	:	:	PUNCT
ejpam-6139	427	3	figure	figure	NOUN
ejpam-6139	427	4	5	5	NUM
ejpam-6139	427	5	displays	display	VERB
ejpam-6139	427	6	a	a	DET
ejpam-6139	427	7	two	two	NUM
ejpam-6139	427	8	-	-	PUNCT
ejpam-6139	427	9	dimensional	dimensional	ADJ
ejpam-6139	427	10	plot	plot	NOUN
ejpam-6139	427	11	illustrating	illustrate	VERB
ejpam-6139	427	12	the	the	DET
ejpam-6139	427	13	inequality	inequality	NOUN
ejpam-6139	427	14	for	for	ADP
ejpam-6139	427	15	µ	µ	X
ejpam-6139	427	16	∈	∈	NOUN
ejpam-6139	427	17	(	(	PUNCT
ejpam-6139	427	18	0	0	NUM
ejpam-6139	427	19	,	,	PUNCT
ejpam-6139	427	20	1	1	NUM
ejpam-6139	427	21	]	]	PUNCT
ejpam-6139	427	22	.	.	PUNCT
ejpam-6139	428	1	the	the	DET
ejpam-6139	428	2	graph	graph	NOUN
ejpam-6139	428	3	of	of	ADP
ejpam-6139	428	4	inequality	inequality	NOUN
ejpam-6139	428	5	(	(	PUNCT
ejpam-6139	428	6	19	19	NUM
ejpam-6139	428	7	)	)	PUNCT
ejpam-6139	428	8	is	be	AUX
ejpam-6139	428	9	clearly	clearly	ADV
ejpam-6139	428	10	showing	show	VERB
ejpam-6139	428	11	that	that	SCONJ
ejpam-6139	428	12	the	the	DET
ejpam-6139	428	13	lhs	lhs	PROPN
ejpam-6139	428	14	consistently	consistently	ADV
ejpam-6139	428	15	stays	stay	VERB
ejpam-6139	428	16	within	within	ADP
ejpam-6139	428	17	the	the	DET
ejpam-6139	428	18	bounds	bound	NOUN
ejpam-6139	428	19	set	set	VERB
ejpam-6139	428	20	by	by	ADP
ejpam-6139	428	21	the	the	DET
ejpam-6139	428	22	rhs	rhs	PROPN
ejpam-6139	428	23	.	.	PUNCT
ejpam-6139	429	1	numerical	numerical	PROPN
ejpam-6139	429	2	calculations	calculation	NOUN
ejpam-6139	429	3	are	be	AUX
ejpam-6139	429	4	performed	perform	VERB
ejpam-6139	429	5	to	to	PART
ejpam-6139	429	6	compare	compare	VERB
ejpam-6139	429	7	the	the	DET
ejpam-6139	429	8	inequality	inequality	NOUN
ejpam-6139	429	9	at	at	ADP
ejpam-6139	429	10	various	various	ADJ
ejpam-6139	429	11	values	value	NOUN
ejpam-6139	429	12	of	of	ADP
ejpam-6139	429	13	µ.	µ.	NOUN
ejpam-6139	429	14	these	these	DET
ejpam-6139	429	15	results	result	NOUN
ejpam-6139	429	16	are	be	AUX
ejpam-6139	429	17	summarized	summarize	VERB
ejpam-6139	429	18	in	in	ADP
ejpam-6139	429	19	the	the	DET
ejpam-6139	429	20	table	table	NOUN
ejpam-6139	429	21	provided	provide	VERB
ejpam-6139	429	22	in	in	ADP
ejpam-6139	429	23	fig	fig	NOUN
ejpam-6139	429	24	.	.	PUNCT
ejpam-6139	430	1	5	5	NUM
ejpam-6139	430	2	,	,	PUNCT
ejpam-6139	430	3	highlighting	highlight	VERB
ejpam-6139	430	4	the	the	DET
ejpam-6139	430	5	precision	precision	NOUN
ejpam-6139	430	6	and	and	CCONJ
ejpam-6139	430	7	consistency	consistency	NOUN
ejpam-6139	430	8	of	of	ADP
ejpam-6139	430	9	the	the	DET
ejpam-6139	430	10	inequality	inequality	NOUN
ejpam-6139	430	11	.	.	PUNCT
ejpam-6139	431	1	figure	figure	VERB
ejpam-6139	431	2	5	5	NUM
ejpam-6139	431	3	:	:	PUNCT
ejpam-6139	431	4	this	this	DET
ejpam-6139	431	5	figure	figure	NOUN
ejpam-6139	431	6	provides	provide	VERB
ejpam-6139	431	7	a	a	DET
ejpam-6139	431	8	visualization	visualization	NOUN
ejpam-6139	431	9	of	of	ADP
ejpam-6139	431	10	theorem	theorem	NOUN
ejpam-6139	431	11	3	3	NUM
ejpam-6139	431	12	using	use	VERB
ejpam-6139	431	13	a	a	DET
ejpam-6139	431	14	2d	2d	NUM
ejpam-6139	431	15	graph	graph	NOUN
ejpam-6139	431	16	confirming	confirm	VERB
ejpam-6139	431	17	its	its	PRON
ejpam-6139	431	18	validity	validity	NOUN
ejpam-6139	431	19	.	.	PUNCT
ejpam-6139	432	1	table	table	NOUN
ejpam-6139	432	2	5	5	NUM
ejpam-6139	432	3	:	:	PUNCT
ejpam-6139	432	4	table	table	NOUN
ejpam-6139	432	5	shown	show	VERB
ejpam-6139	432	6	the	the	DET
ejpam-6139	432	7	summary	summary	NOUN
ejpam-6139	432	8	of	of	ADP
ejpam-6139	432	9	equation	equation	NOUN
ejpam-6139	432	10	(	(	PUNCT
ejpam-6139	432	11	19	19	NUM
ejpam-6139	432	12	)	)	PUNCT
ejpam-6139	432	13	corresponding	correspond	VERB
ejpam-6139	432	14	to	to	ADP
ejpam-6139	432	15	µ	µ	PRON
ejpam-6139	432	16	∈	∈	NOUN
ejpam-6139	432	17	(	(	PUNCT
ejpam-6139	432	18	0	0	NUM
ejpam-6139	432	19	,	,	PUNCT
ejpam-6139	432	20	1	1	NUM
ejpam-6139	432	21	]	]	PUNCT
ejpam-6139	432	22	as	as	ADP
ejpam-6139	432	23	evidence	evidence	NOUN
ejpam-6139	432	24	of	of	ADP
ejpam-6139	432	25	inequality	inequality	NOUN
ejpam-6139	432	26	.	.	PUNCT
ejpam-6139	433	1	µ	µ	PRON
ejpam-6139	433	2	0.2	0.2	NUM
ejpam-6139	433	3	0.4	0.4	NUM
ejpam-6139	433	4	0.6	0.6	NUM
ejpam-6139	433	5	0.8	0.8	NUM
ejpam-6139	433	6	1	1	NUM
ejpam-6139	433	7	lhs	lhs	PROPN
ejpam-6139	433	8	1368.99	1368.99	NUM
ejpam-6139	433	9	1289.62	1289.62	NUM
ejpam-6139	433	10	1213.3	1213.3	NUM
ejpam-6139	433	11	1142.93	1142.93	NUM
ejpam-6139	433	12	1078.93	1078.93	NUM
ejpam-6139	433	13	rhs	rh	NOUN
ejpam-6139	433	14	2271.79	2271.79	NUM
ejpam-6139	433	15	2132.02	2132.02	NUM
ejpam-6139	433	16	1998.51	1998.51	NUM
ejpam-6139	433	17	1876.17	1876.17	NUM
ejpam-6139	433	18	1765.5	1765.5	NUM
ejpam-6139	433	19	to	to	PART
ejpam-6139	433	20	further	far	ADV
ejpam-6139	433	21	validate	validate	VERB
ejpam-6139	433	22	the	the	DET
ejpam-6139	433	23	results	result	NOUN
ejpam-6139	433	24	,	,	PUNCT
ejpam-6139	433	25	the	the	DET
ejpam-6139	433	26	inequality	inequality	NOUN
ejpam-6139	433	27	is	be	AUX
ejpam-6139	433	28	analyzed	analyze	VERB
ejpam-6139	433	29	in	in	ADP
ejpam-6139	433	30	three	three	NUM
ejpam-6139	433	31	dimensions	dimension	NOUN
ejpam-6139	433	32	by	by	ADP
ejpam-6139	433	33	varying	vary	VERB
ejpam-6139	433	34	α	α	PRON
ejpam-6139	433	35	∈	∈	PROPN
ejpam-6139	434	1	[	[	X
ejpam-6139	434	2	5	5	NUM
ejpam-6139	434	3	,	,	PUNCT
ejpam-6139	434	4	10	10	NUM
ejpam-6139	434	5	]	]	PUNCT
ejpam-6139	434	6	and	and	CCONJ
ejpam-6139	434	7	µ	µ	X
ejpam-6139	434	8	∈	∈	NOUN
ejpam-6139	434	9	(	(	PUNCT
ejpam-6139	434	10	0	0	NUM
ejpam-6139	434	11	,	,	PUNCT
ejpam-6139	434	12	1	1	NUM
ejpam-6139	434	13	]	]	PUNCT
ejpam-6139	434	14	.	.	PUNCT
ejpam-6139	435	1	figure	figure	NOUN
ejpam-6139	435	2	6	6	NUM
ejpam-6139	435	3	shows	show	VERB
ejpam-6139	435	4	a	a	DET
ejpam-6139	435	5	3d	3d	NUM
ejpam-6139	435	6	surface	surface	NOUN
ejpam-6139	435	7	plot	plot	NOUN
ejpam-6139	435	8	,	,	PUNCT
ejpam-6139	435	9	confirming	confirm	VERB
ejpam-6139	435	10	the	the	DET
ejpam-6139	435	11	robustness	robustness	NOUN
ejpam-6139	435	12	of	of	ADP
ejpam-6139	435	13	the	the	DET
ejpam-6139	435	14	inequality	inequality	NOUN
ejpam-6139	435	15	across	across	ADP
ejpam-6139	435	16	a	a	DET
ejpam-6139	435	17	broader	broad	ADJ
ejpam-6139	435	18	parameter	parameter	NOUN
ejpam-6139	435	19	range	range	NOUN
ejpam-6139	435	20	.	.	PUNCT
ejpam-6139	436	1	figure	figure	VERB
ejpam-6139	436	2	6	6	NUM
ejpam-6139	436	3	:	:	SYM
ejpam-6139	436	4	3d	3d	NUM
ejpam-6139	436	5	visualization	visualization	NOUN
ejpam-6139	436	6	validating	validate	VERB
ejpam-6139	436	7	the	the	DET
ejpam-6139	436	8	inequality	inequality	NOUN
ejpam-6139	436	9	in	in	ADP
ejpam-6139	436	10	theorem	theorem	NOUN
ejpam-6139	436	11	3	3	NUM
ejpam-6139	436	12	.	.	PUNCT
ejpam-6139	437	1	together	together	ADV
ejpam-6139	437	2	,	,	PUNCT
ejpam-6139	437	3	these	these	DET
ejpam-6139	437	4	analyses	analysis	NOUN
ejpam-6139	437	5	reinforce	reinforce	VERB
ejpam-6139	437	6	the	the	DET
ejpam-6139	437	7	accuracy	accuracy	NOUN
ejpam-6139	437	8	and	and	CCONJ
ejpam-6139	437	9	practical	practical	ADJ
ejpam-6139	437	10	relevance	relevance	NOUN
ejpam-6139	437	11	of	of	ADP
ejpam-6139	437	12	theorem	theorem	NOUN
ejpam-6139	437	13	3	3	NUM
ejpam-6139	437	14	in	in	ADP
ejpam-6139	437	15	characterizing	characterize	VERB
ejpam-6139	437	16	the	the	DET
ejpam-6139	437	17	behavior	behavior	NOUN
ejpam-6139	437	18	of	of	ADP
ejpam-6139	437	19	h(x	h(x	PROPN
ejpam-6139	437	20	)	)	PUNCT
ejpam-6139	437	21	under	under	ADP
ejpam-6139	437	22	the	the	DET
ejpam-6139	437	23	specified	specified	ADJ
ejpam-6139	437	24	conditions	condition	NOUN
ejpam-6139	437	25	.	.	PUNCT
ejpam-6139	438	1	m.	m.	NOUN
ejpam-6139	438	2	samraiz	samraiz	PROPN
ejpam-6139	438	3	et	et	PROPN
ejpam-6139	438	4	al	al	PROPN
ejpam-6139	438	5	.	.	PUNCT
ejpam-6139	438	6	/	/	SYM
ejpam-6139	438	7	eur	eur	PROPN
ejpam-6139	438	8	.	.	PUNCT
ejpam-6139	439	1	j.	j.	PROPN
ejpam-6139	439	2	pure	pure	PROPN
ejpam-6139	439	3	appl	appl	PROPN
ejpam-6139	439	4	.	.	PROPN
ejpam-6139	439	5	math	math	PROPN
ejpam-6139	439	6	,	,	PUNCT
ejpam-6139	439	7	18	18	NUM
ejpam-6139	439	8	(	(	PUNCT
ejpam-6139	439	9	4	4	NUM
ejpam-6139	439	10	)	)	PUNCT
ejpam-6139	439	11	(	(	PUNCT
ejpam-6139	439	12	2025	2025	NUM
ejpam-6139	439	13	)	)	PUNCT
ejpam-6139	439	14	,	,	PUNCT
ejpam-6139	439	15	6139	6139	NUM
ejpam-6139	439	16	18	18	NUM
ejpam-6139	439	17	of	of	ADP
ejpam-6139	439	18	34	34	NUM
ejpam-6139	439	19	4	4	NUM
ejpam-6139	439	20	.	.	PUNCT
ejpam-6139	439	21	mid	mid	ADJ
ejpam-6139	439	22	point	point	NOUN
ejpam-6139	439	23	type	type	NOUN
ejpam-6139	439	24	inequalities	inequality	NOUN
ejpam-6139	439	25	based	base	VERB
ejpam-6139	439	26	on	on	ADP
ejpam-6139	439	27	extended	extended	ADJ
ejpam-6139	439	28	conformable	conformable	ADJ
ejpam-6139	439	29	fractional	fractional	ADJ
ejpam-6139	439	30	operators	operator	NOUN
ejpam-6139	439	31	in	in	ADP
ejpam-6139	439	32	this	this	DET
ejpam-6139	439	33	section	section	NOUN
ejpam-6139	439	34	,	,	PUNCT
ejpam-6139	439	35	we	we	PRON
ejpam-6139	439	36	delve	delve	VERB
ejpam-6139	439	37	into	into	ADP
ejpam-6139	439	38	the	the	DET
ejpam-6139	439	39	study	study	NOUN
ejpam-6139	439	40	of	of	ADP
ejpam-6139	439	41	midpoint	midpoint	NOUN
ejpam-6139	439	42	inequalities	inequality	NOUN
ejpam-6139	439	43	derived	derive	VERB
ejpam-6139	439	44	from	from	ADP
ejpam-6139	439	45	twicedifferentiable	twicedifferentiable	ADJ
ejpam-6139	439	46	functions	function	NOUN
ejpam-6139	439	47	.	.	PUNCT
ejpam-6139	440	1	by	by	ADP
ejpam-6139	440	2	employing	employ	VERB
ejpam-6139	440	3	extended	extend	VERB
ejpam-6139	440	4	conformable	conformable	ADJ
ejpam-6139	440	5	fractional	fractional	ADJ
ejpam-6139	440	6	operators	operator	NOUN
ejpam-6139	440	7	and	and	CCONJ
ejpam-6139	440	8	twice	twice	ADV
ejpam-6139	440	9	-	-	PUNCT
ejpam-6139	440	10	differentiable	differentiable	ADJ
ejpam-6139	440	11	operators	operator	NOUN
ejpam-6139	440	12	,	,	PUNCT
ejpam-6139	440	13	we	we	PRON
ejpam-6139	440	14	aim	aim	VERB
ejpam-6139	440	15	to	to	PART
ejpam-6139	440	16	establish	establish	VERB
ejpam-6139	440	17	new	new	ADJ
ejpam-6139	440	18	insights	insight	NOUN
ejpam-6139	440	19	and	and	CCONJ
ejpam-6139	440	20	results	result	NOUN
ejpam-6139	440	21	in	in	ADP
ejpam-6139	440	22	this	this	DET
ejpam-6139	440	23	area	area	NOUN
ejpam-6139	440	24	.	.	PUNCT
ejpam-6139	441	1	our	our	PRON
ejpam-6139	441	2	approach	approach	NOUN
ejpam-6139	441	3	begins	begin	VERB
ejpam-6139	441	4	with	with	ADP
ejpam-6139	441	5	the	the	DET
ejpam-6139	441	6	formulation	formulation	NOUN
ejpam-6139	441	7	of	of	ADP
ejpam-6139	441	8	a	a	DET
ejpam-6139	441	9	fundamental	fundamental	ADJ
ejpam-6139	441	10	identity	identity	NOUN
ejpam-6139	441	11	,	,	PUNCT
ejpam-6139	441	12	which	which	PRON
ejpam-6139	441	13	serves	serve	VERB
ejpam-6139	441	14	as	as	ADP
ejpam-6139	441	15	the	the	DET
ejpam-6139	441	16	foundation	foundation	NOUN
ejpam-6139	441	17	for	for	ADP
ejpam-6139	441	18	deriving	derive	VERB
ejpam-6139	441	19	the	the	DET
ejpam-6139	441	20	desired	desire	VERB
ejpam-6139	441	21	inequalities.by	inequalities.by	X
ejpam-6139	441	22	leveraging	leverage	VERB
ejpam-6139	441	23	the	the	DET
ejpam-6139	441	24	capabilities	capability	NOUN
ejpam-6139	441	25	of	of	ADP
ejpam-6139	441	26	extended	extended	ADJ
ejpam-6139	441	27	conformable	conformable	ADJ
ejpam-6139	441	28	fractional	fractional	ADJ
ejpam-6139	441	29	operators	operator	NOUN
ejpam-6139	441	30	,	,	PUNCT
ejpam-6139	441	31	we	we	PRON
ejpam-6139	441	32	extend	extend	VERB
ejpam-6139	441	33	the	the	DET
ejpam-6139	441	34	applicability	applicability	NOUN
ejpam-6139	441	35	of	of	ADP
ejpam-6139	441	36	midpoint	midpoint	NOUN
ejpam-6139	441	37	inequalities	inequality	NOUN
ejpam-6139	441	38	to	to	ADP
ejpam-6139	441	39	a	a	DET
ejpam-6139	441	40	broader	broad	ADJ
ejpam-6139	441	41	class	class	NOUN
ejpam-6139	441	42	of	of	ADP
ejpam-6139	441	43	functions	function	NOUN
ejpam-6139	441	44	,	,	PUNCT
ejpam-6139	441	45	offering	offer	VERB
ejpam-6139	441	46	a	a	DET
ejpam-6139	441	47	more	more	ADV
ejpam-6139	441	48	comprehensive	comprehensive	ADJ
ejpam-6139	441	49	understanding	understanding	NOUN
ejpam-6139	441	50	of	of	ADP
ejpam-6139	441	51	their	their	PRON
ejpam-6139	441	52	behavior	behavior	NOUN
ejpam-6139	441	53	and	and	CCONJ
ejpam-6139	441	54	potential	potential	ADJ
ejpam-6139	441	55	applications	application	NOUN
ejpam-6139	441	56	.	.	PUNCT
ejpam-6139	442	1	the	the	DET
ejpam-6139	442	2	results	result	NOUN
ejpam-6139	442	3	obtained	obtain	VERB
ejpam-6139	442	4	in	in	ADP
ejpam-6139	442	5	this	this	DET
ejpam-6139	442	6	study	study	NOUN
ejpam-6139	442	7	not	not	PART
ejpam-6139	442	8	only	only	ADV
ejpam-6139	442	9	contribute	contribute	VERB
ejpam-6139	442	10	to	to	ADP
ejpam-6139	442	11	the	the	DET
ejpam-6139	442	12	theoretical	theoretical	ADJ
ejpam-6139	442	13	framework	framework	NOUN
ejpam-6139	442	14	but	but	CCONJ
ejpam-6139	442	15	also	also	ADV
ejpam-6139	442	16	pave	pave	VERB
ejpam-6139	442	17	the	the	DET
ejpam-6139	442	18	way	way	NOUN
ejpam-6139	442	19	for	for	ADP
ejpam-6139	442	20	future	future	ADJ
ejpam-6139	442	21	research	research	NOUN
ejpam-6139	442	22	in	in	ADP
ejpam-6139	442	23	related	related	ADJ
ejpam-6139	442	24	domains	domain	NOUN
ejpam-6139	442	25	.	.	PUNCT
ejpam-6139	443	1	lemma	lemma	PROPN
ejpam-6139	443	2	2	2	X
ejpam-6139	443	3	.	.	PUNCT
ejpam-6139	444	1	let	let	VERB
ejpam-6139	444	2	h	h	NOUN
ejpam-6139	444	3	:	:	PUNCT
ejpam-6139	445	1	[	[	X
ejpam-6139	445	2	ν	ν	X
ejpam-6139	445	3	,	,	PUNCT
ejpam-6139	445	4	ω	ω	NOUN
ejpam-6139	445	5	]	]	X
ejpam-6139	445	6	→	→	PUNCT
ejpam-6139	445	7	r	r	NOUN
ejpam-6139	445	8	be	be	AUX
ejpam-6139	445	9	a	a	DET
ejpam-6139	445	10	twice	twice	ADV
ejpam-6139	445	11	differentiable	differentiable	ADJ
ejpam-6139	445	12	mapping	mapping	NOUN
ejpam-6139	445	13	on	on	ADP
ejpam-6139	445	14	(	(	PUNCT
ejpam-6139	445	15	ν	ν	PROPN
ejpam-6139	445	16	,	,	PUNCT
ejpam-6139	445	17	ω	ω	NOUN
ejpam-6139	445	18	)	)	PUNCT
ejpam-6139	445	19	with	with	ADP
ejpam-6139	445	20	h′′	h′′	PROPN
ejpam-6139	445	21	∈	∈	PROPN
ejpam-6139	445	22	l1([ν	l1([ν	PROPN
ejpam-6139	445	23	,	,	PUNCT
ejpam-6139	445	24	ω	ω	NOUN
ejpam-6139	445	25	]	]	NOUN
ejpam-6139	445	26	)	)	PUNCT
ejpam-6139	445	27	.	.	PUNCT
ejpam-6139	446	1	then	then	ADV
ejpam-6139	446	2	the	the	DET
ejpam-6139	446	3	following	follow	VERB
ejpam-6139	446	4	equality	equality	NOUN
ejpam-6139	446	5	holds	hold	VERB
ejpam-6139	446	6	:	:	PUNCT
ejpam-6139	446	7	η	η	PROPN
ejpam-6139	446	8	µα	µα	ADP
ejpam-6139	446	9	k	k	PROPN
ejpam-6139	446	10	−1	−1	NOUN
ejpam-6139	446	11	(	(	PUNCT
ejpam-6139	446	12	ω	ω	NOUN
ejpam-6139	446	13	−	−	NOUN
ejpam-6139	447	1	ν	ν	NOUN
ejpam-6139	447	2	)	)	PUNCT
ejpam-6139	447	3	µα	µα	ADP
ejpam-6139	447	4	k	k	PROPN
ejpam-6139	447	5	(	(	PUNCT
ejpam-6139	447	6	kµ	kµ	PROPN
ejpam-6139	447	7	)	)	PUNCT
ejpam-6139	448	1	α	α	PROPN
ejpam-6139	448	2	k	k	PROPN
ejpam-6139	448	3	γ	γ	X
ejpam-6139	448	4	(	(	PUNCT
ejpam-6139	448	5	α	α	NOUN
ejpam-6139	448	6	k	k	PROPN
ejpam-6139	449	1	+	+	PROPN
ejpam-6139	449	2	1	1	X
ejpam-6139	449	3	)	)	PUNCT
ejpam-6139	449	4	(	(	PUNCT
ejpam-6139	449	5	α	α	PROPN
ejpam-6139	449	6	kj	kj	PROPN
ejpam-6139	449	7	µ	µ	PROPN
ejpam-6139	449	8	(	(	PUNCT
ejpam-6139	449	9	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	449	10	η	η	PROPN
ejpam-6139	449	11	−	−	PROPN
ejpam-6139	449	12	h(ν	h(ν	PROPN
ejpam-6139	449	13	)	)	PUNCT
ejpam-6139	450	1	+	+	NOUN
ejpam-6139	450	2	α	α	PROPN
ejpam-6139	450	3	k	k	X
ejpam-6139	450	4	jµ	jµ	PROPN
ejpam-6139	450	5	ν+(η−1)ω	ν+(η−1)ω	PROPN
ejpam-6139	450	6	η	η	PROPN
ejpam-6139	450	7	+	+	PROPN
ejpam-6139	450	8	h(ω	h(ω	PROPN
ejpam-6139	450	9	)	)	PUNCT
ejpam-6139	450	10	)	)	PUNCT
ejpam-6139	451	1	+	+	X
ejpam-6139	451	2	υk[µ	υk[µ	PROPN
ejpam-6139	451	3	,	,	PUNCT
ejpam-6139	451	4	α	α	NOUN
ejpam-6139	451	5	]	]	X
ejpam-6139	451	6	−	−	PROPN
ejpam-6139	451	7	1	1	NUM
ejpam-6139	451	8	η	η	PROPN
ejpam-6139	451	9	[	[	PUNCT
ejpam-6139	451	10	h	h	PROPN
ejpam-6139	451	11	(	(	PUNCT
ejpam-6139	451	12	η	η	PROPN
ejpam-6139	451	13	−	−	PROPN
ejpam-6139	451	14	1	1	NUM
ejpam-6139	451	15	η	η	PROPN
ejpam-6139	451	16	ν	ν	X
ejpam-6139	451	17	+	+	PROPN
ejpam-6139	451	18	1	1	NUM
ejpam-6139	451	19	η	η	PROPN
ejpam-6139	451	20	ω	ω	PROPN
ejpam-6139	451	21	)	)	PUNCT
ejpam-6139	452	1	+	+	CCONJ
ejpam-6139	452	2	h	h	NOUN
ejpam-6139	452	3	(	(	PUNCT
ejpam-6139	452	4	1	1	NUM
ejpam-6139	452	5	η	η	X
ejpam-6139	452	6	ν	ν	X
ejpam-6139	452	7	+	+	CCONJ
ejpam-6139	452	8	η	η	PROPN
ejpam-6139	452	9	−	−	PROPN
ejpam-6139	452	10	1	1	NUM
ejpam-6139	452	11	η	η	PROPN
ejpam-6139	452	12	ω	ω	PROPN
ejpam-6139	452	13	)	)	PUNCT
ejpam-6139	452	14	]	]	PUNCT
ejpam-6139	453	1	=	=	PUNCT
ejpam-6139	453	2	(	(	PUNCT
ejpam-6139	453	3	ω	ω	NUM
ejpam-6139	453	4	−	−	X
ejpam-6139	453	5	ν)2(kµ	ν)2(kµ	PROPN
ejpam-6139	453	6	)	)	PUNCT
ejpam-6139	453	7	α	α	PROPN
ejpam-6139	454	1	k	k	PROPN
ejpam-6139	454	2	η3	η3	PROPN
ejpam-6139	455	1	[	[	X
ejpam-6139	455	2	∫	∫	PROPN
ejpam-6139	455	3	1	1	NUM
ejpam-6139	455	4	0	0	NUM
ejpam-6139	456	1	[	[	X
ejpam-6139	456	2	∫	∫	X
ejpam-6139	456	3	t	t	PROPN
ejpam-6139	456	4	0	0	NUM
ejpam-6139	456	5	(	(	PUNCT
ejpam-6139	456	6	1−	1−	NUM
ejpam-6139	456	7	(	(	PUNCT
ejpam-6139	456	8	1−	1−	NUM
ejpam-6139	456	9	φ)µ	φ)µ	NOUN
ejpam-6139	456	10	kµ	kµ	NOUN
ejpam-6139	456	11	)	)	PUNCT
ejpam-6139	457	1	α	α	PROPN
ejpam-6139	457	2	k	k	X
ejpam-6139	458	1	dφ	dφ	X
ejpam-6139	458	2	]	]	PUNCT
ejpam-6139	458	3	h′′	h′′	PROPN
ejpam-6139	458	4	(	(	PUNCT
ejpam-6139	458	5	η	η	PROPN
ejpam-6139	458	6	−	−	PROPN
ejpam-6139	458	7	t	t	PROPN
ejpam-6139	458	8	η	η	PROPN
ejpam-6139	458	9	ν	ν	PROPN
ejpam-6139	458	10	+	+	PROPN
ejpam-6139	458	11	t	t	PROPN
ejpam-6139	458	12	η	η	PROPN
ejpam-6139	458	13	ω	ω	PROPN
ejpam-6139	458	14	)	)	PUNCT
ejpam-6139	458	15	dt	dt	PUNCT
ejpam-6139	459	1	+	+	CCONJ
ejpam-6139	459	2	∫	∫	PROPN
ejpam-6139	459	3	1	1	NUM
ejpam-6139	459	4	0	0	NUM
ejpam-6139	460	1	[	[	X
ejpam-6139	460	2	∫	∫	X
ejpam-6139	460	3	t	t	PROPN
ejpam-6139	460	4	0	0	NUM
ejpam-6139	460	5	(	(	PUNCT
ejpam-6139	460	6	1−	1−	NUM
ejpam-6139	460	7	(	(	PUNCT
ejpam-6139	460	8	1−	1−	NUM
ejpam-6139	460	9	φ)µ	φ)µ	NOUN
ejpam-6139	460	10	kµ	kµ	NOUN
ejpam-6139	460	11	)	)	PUNCT
ejpam-6139	461	1	α	α	PROPN
ejpam-6139	461	2	k	k	X
ejpam-6139	462	1	dφ	dφ	X
ejpam-6139	462	2	]	]	PUNCT
ejpam-6139	462	3	h′′	h′′	PROPN
ejpam-6139	462	4	(	(	PUNCT
ejpam-6139	462	5	t	t	PROPN
ejpam-6139	462	6	η	η	PROPN
ejpam-6139	462	7	ν	ν	PROPN
ejpam-6139	462	8	+	+	PROPN
ejpam-6139	462	9	η	η	PROPN
ejpam-6139	462	10	−	−	PROPN
ejpam-6139	462	11	t	t	PROPN
ejpam-6139	462	12	η	η	PROPN
ejpam-6139	462	13	ω	ω	PROPN
ejpam-6139	462	14	)	)	PUNCT
ejpam-6139	462	15	dt	dt	X
ejpam-6139	462	16	]	]	PUNCT
ejpam-6139	462	17	,	,	PUNCT
ejpam-6139	462	18	(	(	PUNCT
ejpam-6139	462	19	31	31	NUM
ejpam-6139	462	20	)	)	PUNCT
ejpam-6139	462	21	where	where	SCONJ
ejpam-6139	462	22	υk[µ	υk[µ	PROPN
ejpam-6139	462	23	,	,	PUNCT
ejpam-6139	462	24	α	α	NOUN
ejpam-6139	462	25	]	]	X
ejpam-6139	462	26	=	=	SYM
ejpam-6139	462	27	(	(	PUNCT
ejpam-6139	462	28	ω	ω	NUM
ejpam-6139	462	29	−	−	NOUN
ejpam-6139	462	30	ν	ν	NOUN
ejpam-6139	462	31	)	)	PUNCT
ejpam-6139	462	32	η2	η2	PROPN
ejpam-6139	462	33	(	(	PUNCT
ejpam-6139	462	34	kµ	kµ	PROPN
ejpam-6139	462	35	)	)	PUNCT
ejpam-6139	462	36	α	α	PROPN
ejpam-6139	462	37	k	k	PROPN
ejpam-6139	462	38	(	(	PUNCT
ejpam-6139	462	39	h′	h′	X
ejpam-6139	462	40	(	(	PUNCT
ejpam-6139	462	41	η	η	PROPN
ejpam-6139	462	42	−	−	PROPN
ejpam-6139	462	43	1	1	NUM
ejpam-6139	462	44	η	η	PROPN
ejpam-6139	462	45	ν	ν	X
ejpam-6139	462	46	+	+	PROPN
ejpam-6139	462	47	1	1	NUM
ejpam-6139	462	48	η	η	PROPN
ejpam-6139	462	49	ω	ω	PROPN
ejpam-6139	462	50	)	)	PUNCT
ejpam-6139	463	1	−	−	PROPN
ejpam-6139	463	2	h′	h′	PROPN
ejpam-6139	463	3	(	(	PUNCT
ejpam-6139	463	4	1	1	NUM
ejpam-6139	463	5	η	η	X
ejpam-6139	463	6	ν	ν	X
ejpam-6139	463	7	+	+	CCONJ
ejpam-6139	463	8	η	η	PROPN
ejpam-6139	463	9	−	−	PROPN
ejpam-6139	463	10	1	1	NUM
ejpam-6139	463	11	η	η	PROPN
ejpam-6139	463	12	ω	ω	PROPN
ejpam-6139	463	13	)	)	PUNCT
ejpam-6139	463	14	)	)	PUNCT
ejpam-6139	463	15	×	×	NOUN
ejpam-6139	464	1	[	[	X
ejpam-6139	464	2	∫	∫	PROPN
ejpam-6139	464	3	1	1	NUM
ejpam-6139	464	4	0	0	NUM
ejpam-6139	464	5	(	(	PUNCT
ejpam-6139	464	6	1−	1−	NUM
ejpam-6139	464	7	(	(	PUNCT
ejpam-6139	464	8	1−	1−	NUM
ejpam-6139	464	9	φ)µ	φ)µ	NOUN
ejpam-6139	464	10	kµ	kµ	NOUN
ejpam-6139	464	11	)	)	PUNCT
ejpam-6139	465	1	α	α	PROPN
ejpam-6139	465	2	k	k	X
ejpam-6139	466	1	dφ	dφ	ADP
ejpam-6139	466	2	]	]	PUNCT
ejpam-6139	466	3	.	.	PUNCT
ejpam-6139	467	1	proof	proof	NOUN
ejpam-6139	467	2	.	.	PUNCT
ejpam-6139	468	1	consider	consider	VERB
ejpam-6139	468	2	i3	i3	NOUN
ejpam-6139	468	3	=	=	SYM
ejpam-6139	468	4	∫	∫	PROPN
ejpam-6139	468	5	1	1	NUM
ejpam-6139	468	6	0	0	NUM
ejpam-6139	469	1	[	[	X
ejpam-6139	469	2	∫	∫	X
ejpam-6139	469	3	t	t	PROPN
ejpam-6139	469	4	0	0	NUM
ejpam-6139	469	5	(	(	PUNCT
ejpam-6139	469	6	1−	1−	NUM
ejpam-6139	469	7	(	(	PUNCT
ejpam-6139	469	8	1−	1−	NUM
ejpam-6139	469	9	φ)µ	φ)µ	NOUN
ejpam-6139	469	10	kµ	kµ	NOUN
ejpam-6139	469	11	)	)	PUNCT
ejpam-6139	470	1	α	α	PROPN
ejpam-6139	470	2	k	k	X
ejpam-6139	471	1	dφ	dφ	X
ejpam-6139	471	2	]	]	PUNCT
ejpam-6139	471	3	h′′	h′′	PROPN
ejpam-6139	471	4	(	(	PUNCT
ejpam-6139	471	5	η	η	PROPN
ejpam-6139	471	6	−	−	PROPN
ejpam-6139	471	7	t	t	PROPN
ejpam-6139	471	8	η	η	PROPN
ejpam-6139	471	9	ν	ν	PROPN
ejpam-6139	471	10	+	+	PROPN
ejpam-6139	471	11	t	t	PROPN
ejpam-6139	471	12	η	η	PROPN
ejpam-6139	471	13	ω	ω	PROPN
ejpam-6139	471	14	)	)	PUNCT
ejpam-6139	471	15	dt	dt	PROPN
ejpam-6139	471	16	,	,	PUNCT
ejpam-6139	471	17	utilizing	utilize	VERB
ejpam-6139	471	18	the	the	DET
ejpam-6139	471	19	technique	technique	NOUN
ejpam-6139	471	20	of	of	ADP
ejpam-6139	471	21	integration	integration	NOUN
ejpam-6139	471	22	by	by	ADP
ejpam-6139	471	23	parts	part	NOUN
ejpam-6139	471	24	,	,	PUNCT
ejpam-6139	471	25	we	we	PRON
ejpam-6139	471	26	obtain	obtain	VERB
ejpam-6139	471	27	i3	i3	NOUN
ejpam-6139	471	28	=	=	SYM
ejpam-6139	471	29	η	η	PROPN
ejpam-6139	471	30	ω	ω	PROPN
ejpam-6139	471	31	−	−	PROPN
ejpam-6139	471	32	ν	ν	X
ejpam-6139	471	33	h′	h′	X
ejpam-6139	471	34	(	(	PUNCT
ejpam-6139	471	35	η	η	PROPN
ejpam-6139	471	36	−	−	PROPN
ejpam-6139	471	37	t	t	PROPN
ejpam-6139	471	38	η	η	PROPN
ejpam-6139	471	39	ν	ν	PROPN
ejpam-6139	471	40	+	+	PROPN
ejpam-6139	471	41	t	t	PROPN
ejpam-6139	471	42	η	η	PROPN
ejpam-6139	471	43	ω	ω	PROPN
ejpam-6139	471	44	)	)	PUNCT
ejpam-6139	471	45	∫	∫	PROPN
ejpam-6139	471	46	t	t	PROPN
ejpam-6139	471	47	0	0	NUM
ejpam-6139	472	1	(	(	PUNCT
ejpam-6139	472	2	1−	1−	NUM
ejpam-6139	472	3	(	(	PUNCT
ejpam-6139	472	4	1−	1−	NUM
ejpam-6139	472	5	φ)µ	φ)µ	NOUN
ejpam-6139	472	6	kµ	kµ	NOUN
ejpam-6139	472	7	)	)	PUNCT
ejpam-6139	473	1	α	α	PROPN
ejpam-6139	473	2	k	k	X
ejpam-6139	473	3	dφ	dφ	ADP
ejpam-6139	473	4	∣∣∣∣1	∣∣∣∣1	PROPN
ejpam-6139	473	5	0	0	NUM
ejpam-6139	474	1	−	−	PROPN
ejpam-6139	474	2	η	η	PROPN
ejpam-6139	474	3	ω	ω	PROPN
ejpam-6139	474	4	−	−	PROPN
ejpam-6139	475	1	ν	ν	X
ejpam-6139	475	2	∫	∫	PROPN
ejpam-6139	475	3	1	1	NUM
ejpam-6139	475	4	0	0	NUM
ejpam-6139	475	5	(	(	PUNCT
ejpam-6139	475	6	1−	1−	NUM
ejpam-6139	475	7	(	(	PUNCT
ejpam-6139	475	8	1−	1−	NUM
ejpam-6139	475	9	t)µ	t)µ	NOUN
ejpam-6139	475	10	kµ	kµ	NOUN
ejpam-6139	475	11	)	)	PUNCT
ejpam-6139	476	1	α	α	PROPN
ejpam-6139	476	2	k	k	PROPN
ejpam-6139	476	3	h′	h′	PROPN
ejpam-6139	476	4	(	(	PUNCT
ejpam-6139	476	5	η	η	PROPN
ejpam-6139	476	6	−	−	PROPN
ejpam-6139	476	7	t	t	PROPN
ejpam-6139	476	8	η	η	PROPN
ejpam-6139	476	9	ν	ν	PROPN
ejpam-6139	476	10	+	+	PROPN
ejpam-6139	476	11	t	t	PROPN
ejpam-6139	476	12	η	η	PROPN
ejpam-6139	476	13	ω	ω	PROPN
ejpam-6139	476	14	)	)	PUNCT
ejpam-6139	476	15	dt	dt	PROPN
ejpam-6139	476	16	,	,	PUNCT
ejpam-6139	476	17	m.	m.	NOUN
ejpam-6139	476	18	samraiz	samraiz	PROPN
ejpam-6139	476	19	et	et	PROPN
ejpam-6139	476	20	al	al	PROPN
ejpam-6139	476	21	.	.	PUNCT
ejpam-6139	476	22	/	/	SYM
ejpam-6139	476	23	eur	eur	PROPN
ejpam-6139	476	24	.	.	PUNCT
ejpam-6139	477	1	j.	j.	PROPN
ejpam-6139	477	2	pure	pure	PROPN
ejpam-6139	477	3	appl	appl	PROPN
ejpam-6139	477	4	.	.	PROPN
ejpam-6139	477	5	math	math	PROPN
ejpam-6139	477	6	,	,	PUNCT
ejpam-6139	477	7	18	18	NUM
ejpam-6139	477	8	(	(	PUNCT
ejpam-6139	477	9	4	4	NUM
ejpam-6139	477	10	)	)	PUNCT
ejpam-6139	477	11	(	(	PUNCT
ejpam-6139	477	12	2025	2025	NUM
ejpam-6139	477	13	)	)	PUNCT
ejpam-6139	477	14	,	,	PUNCT
ejpam-6139	477	15	6139	6139	NUM
ejpam-6139	477	16	19	19	NUM
ejpam-6139	477	17	of	of	ADP
ejpam-6139	477	18	34	34	NUM
ejpam-6139	477	19	i3	i3	NOUN
ejpam-6139	477	20	=	=	SYM
ejpam-6139	477	21	η	η	PROPN
ejpam-6139	477	22	ω	ω	PROPN
ejpam-6139	477	23	−	−	PROPN
ejpam-6139	477	24	ν	ν	X
ejpam-6139	477	25	h′	h′	X
ejpam-6139	477	26	(	(	PUNCT
ejpam-6139	477	27	η	η	PROPN
ejpam-6139	477	28	−	−	PROPN
ejpam-6139	477	29	1	1	NUM
ejpam-6139	477	30	η	η	PROPN
ejpam-6139	477	31	ν	ν	X
ejpam-6139	477	32	+	+	PROPN
ejpam-6139	477	33	1	1	NUM
ejpam-6139	477	34	η	η	PROPN
ejpam-6139	477	35	ω	ω	PROPN
ejpam-6139	477	36	)	)	PUNCT
ejpam-6139	477	37	∫	∫	PROPN
ejpam-6139	477	38	1	1	NUM
ejpam-6139	477	39	0	0	NUM
ejpam-6139	477	40	(	(	PUNCT
ejpam-6139	477	41	1−	1−	NUM
ejpam-6139	477	42	(	(	PUNCT
ejpam-6139	477	43	1−	1−	NUM
ejpam-6139	477	44	φ)µ	φ)µ	NOUN
ejpam-6139	477	45	kµ	kµ	NOUN
ejpam-6139	477	46	)	)	PUNCT
ejpam-6139	478	1	α	α	PROPN
ejpam-6139	478	2	k	k	X
ejpam-6139	478	3	dφ	dφ	ADP
ejpam-6139	478	4	−	−	PROPN
ejpam-6139	478	5	η	η	PROPN
ejpam-6139	478	6	ω	ω	PROPN
ejpam-6139	478	7	−	−	PROPN
ejpam-6139	478	8	ν	ν	X
ejpam-6139	478	9	∫	∫	PROPN
ejpam-6139	478	10	1	1	NUM
ejpam-6139	478	11	0	0	NUM
ejpam-6139	478	12	(	(	PUNCT
ejpam-6139	478	13	1−	1−	NUM
ejpam-6139	478	14	(	(	PUNCT
ejpam-6139	478	15	1−	1−	NUM
ejpam-6139	478	16	t)µ	t)µ	NOUN
ejpam-6139	478	17	kµ	kµ	NOUN
ejpam-6139	478	18	)	)	PUNCT
ejpam-6139	479	1	α	α	PROPN
ejpam-6139	479	2	k	k	PROPN
ejpam-6139	479	3	h′	h′	PROPN
ejpam-6139	479	4	(	(	PUNCT
ejpam-6139	479	5	η	η	PROPN
ejpam-6139	479	6	−	−	PROPN
ejpam-6139	479	7	t	t	PROPN
ejpam-6139	479	8	η	η	PROPN
ejpam-6139	479	9	ν	ν	PROPN
ejpam-6139	479	10	+	+	PROPN
ejpam-6139	479	11	t	t	PROPN
ejpam-6139	479	12	η	η	PROPN
ejpam-6139	479	13	ω	ω	PROPN
ejpam-6139	479	14	)	)	PUNCT
ejpam-6139	479	15	dt	dt	X
ejpam-6139	479	16	,	,	PUNCT
ejpam-6139	479	17	again	again	ADV
ejpam-6139	479	18	employing	employ	VERB
ejpam-6139	479	19	integration	integration	NOUN
ejpam-6139	479	20	by	by	ADP
ejpam-6139	479	21	parts	part	NOUN
ejpam-6139	479	22	on	on	ADP
ejpam-6139	479	23	second	second	ADJ
ejpam-6139	479	24	term	term	NOUN
ejpam-6139	479	25	i3	i3	NOUN
ejpam-6139	479	26	=	=	SYM
ejpam-6139	479	27	η	η	PROPN
ejpam-6139	479	28	ω	ω	PROPN
ejpam-6139	479	29	−	−	PROPN
ejpam-6139	479	30	ν	ν	X
ejpam-6139	479	31	h′	h′	X
ejpam-6139	479	32	(	(	PUNCT
ejpam-6139	479	33	η	η	PROPN
ejpam-6139	479	34	−	−	PROPN
ejpam-6139	479	35	1	1	NUM
ejpam-6139	479	36	η	η	PROPN
ejpam-6139	479	37	ν	ν	X
ejpam-6139	479	38	+	+	PROPN
ejpam-6139	479	39	1	1	NUM
ejpam-6139	479	40	η	η	PROPN
ejpam-6139	479	41	ω	ω	PROPN
ejpam-6139	479	42	)	)	PUNCT
ejpam-6139	479	43	∫	∫	PROPN
ejpam-6139	479	44	1	1	NUM
ejpam-6139	479	45	0	0	NUM
ejpam-6139	479	46	(	(	PUNCT
ejpam-6139	479	47	1−	1−	NUM
ejpam-6139	479	48	(	(	PUNCT
ejpam-6139	479	49	1−	1−	NUM
ejpam-6139	479	50	φ)µ	φ)µ	NOUN
ejpam-6139	479	51	kµ	kµ	NOUN
ejpam-6139	479	52	)	)	PUNCT
ejpam-6139	480	1	α	α	PROPN
ejpam-6139	480	2	k	k	NOUN
ejpam-6139	481	1	dφ	dφ	ADP
ejpam-6139	481	2	−	−	PROPN
ejpam-6139	481	3	(	(	PUNCT
ejpam-6139	481	4	η	η	PROPN
ejpam-6139	481	5	ω	ω	PROPN
ejpam-6139	481	6	−	−	PROPN
ejpam-6139	481	7	ν	ν	NOUN
ejpam-6139	481	8	)	)	PUNCT
ejpam-6139	481	9	2(1−	2(1−	PROPN
ejpam-6139	481	10	(	(	PUNCT
ejpam-6139	481	11	1−	1−	NUM
ejpam-6139	481	12	t)µ	t)µ	NOUN
ejpam-6139	481	13	kµ	kµ	NOUN
ejpam-6139	481	14	)	)	PUNCT
ejpam-6139	482	1	α	α	PROPN
ejpam-6139	482	2	k	k	PROPN
ejpam-6139	482	3	h	h	PROPN
ejpam-6139	482	4	(	(	PUNCT
ejpam-6139	482	5	η	η	PROPN
ejpam-6139	482	6	−	−	PROPN
ejpam-6139	482	7	t	t	PROPN
ejpam-6139	482	8	η	η	PROPN
ejpam-6139	482	9	ν	ν	PROPN
ejpam-6139	482	10	+	+	PROPN
ejpam-6139	482	11	t	t	PROPN
ejpam-6139	482	12	η	η	PROPN
ejpam-6139	482	13	ω	ω	PROPN
ejpam-6139	482	14	)	)	PUNCT
ejpam-6139	482	15	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-6139	482	16	0	0	NUM
ejpam-6139	483	1	+	+	CCONJ
ejpam-6139	483	2	(	(	PUNCT
ejpam-6139	483	3	η	η	PROPN
ejpam-6139	483	4	ω	ω	PROPN
ejpam-6139	483	5	−	−	PROPN
ejpam-6139	483	6	ν	ν	NOUN
ejpam-6139	483	7	)	)	PUNCT
ejpam-6139	483	8	2	2	NUM
ejpam-6139	483	9	.	.	X
ejpam-6139	484	1	1	1	NUM
ejpam-6139	484	2	k	k	NOUN
ejpam-6139	484	3	(	(	PUNCT
ejpam-6139	484	4	α	α	NOUN
ejpam-6139	484	5	k	k	PROPN
ejpam-6139	484	6	)	)	PUNCT
ejpam-6139	484	7	∫	∫	PROPN
ejpam-6139	484	8	1	1	NUM
ejpam-6139	484	9	0	0	NUM
ejpam-6139	484	10	[	[	PUNCT
ejpam-6139	484	11	1−	1−	NUM
ejpam-6139	484	12	(	(	PUNCT
ejpam-6139	484	13	1−	1−	NUM
ejpam-6139	484	14	t)µ	t)µ	NOUN
ejpam-6139	484	15	kµ	kµ	PROPN
ejpam-6139	484	16	]	]	PUNCT
ejpam-6139	484	17	α	α	X
ejpam-6139	484	18	k	k	X
ejpam-6139	484	19	−1	−1	NOUN
ejpam-6139	484	20	(	(	PUNCT
ejpam-6139	484	21	1−	1−	NUM
ejpam-6139	484	22	t)µ−1	t)µ−1	NOUN
ejpam-6139	484	23	×	×	PROPN
ejpam-6139	484	24	h	h	PROPN
ejpam-6139	484	25	(	(	PUNCT
ejpam-6139	484	26	η	η	PROPN
ejpam-6139	484	27	−	−	PROPN
ejpam-6139	484	28	t	t	PROPN
ejpam-6139	484	29	η	η	PROPN
ejpam-6139	484	30	ν	ν	PROPN
ejpam-6139	484	31	+	+	PROPN
ejpam-6139	484	32	t	t	PROPN
ejpam-6139	484	33	η	η	PROPN
ejpam-6139	484	34	ω	ω	PROPN
ejpam-6139	484	35	)	)	PUNCT
ejpam-6139	484	36	dt	dt	PROPN
ejpam-6139	484	37	i3	i3	PROPN
ejpam-6139	484	38	=	=	SYM
ejpam-6139	484	39	η	η	PROPN
ejpam-6139	484	40	ω	ω	PROPN
ejpam-6139	484	41	−	−	PROPN
ejpam-6139	484	42	ν	ν	X
ejpam-6139	484	43	h′	h′	X
ejpam-6139	484	44	(	(	PUNCT
ejpam-6139	484	45	η	η	PROPN
ejpam-6139	484	46	−	−	PROPN
ejpam-6139	484	47	1	1	NUM
ejpam-6139	484	48	η	η	PROPN
ejpam-6139	484	49	ν	ν	X
ejpam-6139	484	50	+	+	PROPN
ejpam-6139	484	51	1	1	NUM
ejpam-6139	484	52	η	η	PROPN
ejpam-6139	484	53	ω	ω	PROPN
ejpam-6139	484	54	)	)	PUNCT
ejpam-6139	484	55	∫	∫	PROPN
ejpam-6139	484	56	1	1	NUM
ejpam-6139	484	57	0	0	NUM
ejpam-6139	484	58	(	(	PUNCT
ejpam-6139	484	59	1−	1−	NUM
ejpam-6139	484	60	(	(	PUNCT
ejpam-6139	484	61	1−	1−	NUM
ejpam-6139	484	62	φ)µ	φ)µ	NOUN
ejpam-6139	484	63	kµ	kµ	NOUN
ejpam-6139	484	64	)	)	PUNCT
ejpam-6139	485	1	α	α	PROPN
ejpam-6139	486	1	k	k	NOUN
ejpam-6139	487	1	dφ−	dφ−	PROPN
ejpam-6139	487	2	(	(	PUNCT
ejpam-6139	487	3	η	η	PROPN
ejpam-6139	487	4	ω	ω	PROPN
ejpam-6139	487	5	−	−	PROPN
ejpam-6139	487	6	ν	ν	NOUN
ejpam-6139	487	7	)	)	PUNCT
ejpam-6139	487	8	2	2	NUM
ejpam-6139	487	9	(	(	PUNCT
ejpam-6139	487	10	1	1	NUM
ejpam-6139	487	11	kµ	kµ	NOUN
ejpam-6139	487	12	)	)	PUNCT
ejpam-6139	488	1	α	α	PROPN
ejpam-6139	488	2	k	k	PROPN
ejpam-6139	488	3	h	h	PROPN
ejpam-6139	488	4	(	(	PUNCT
ejpam-6139	488	5	η	η	PROPN
ejpam-6139	488	6	−	−	PROPN
ejpam-6139	488	7	1	1	NUM
ejpam-6139	488	8	η	η	PROPN
ejpam-6139	488	9	ν	ν	X
ejpam-6139	488	10	+	+	PROPN
ejpam-6139	488	11	1	1	NUM
ejpam-6139	488	12	η	η	PROPN
ejpam-6139	488	13	ω	ω	PROPN
ejpam-6139	488	14	)	)	PUNCT
ejpam-6139	489	1	+	+	CCONJ
ejpam-6139	489	2	(	(	PUNCT
ejpam-6139	489	3	η	η	PROPN
ejpam-6139	489	4	ω	ω	PROPN
ejpam-6139	489	5	−	−	PROPN
ejpam-6139	489	6	ν	ν	NOUN
ejpam-6139	489	7	)	)	PUNCT
ejpam-6139	489	8	2	2	NUM
ejpam-6139	489	9	.	.	X
ejpam-6139	489	10	1	1	NUM
ejpam-6139	490	1	k	k	NOUN
ejpam-6139	490	2	1	1	NUM
ejpam-6139	490	3	k	k	NOUN
ejpam-6139	490	4	α	α	X
ejpam-6139	490	5	k	k	X
ejpam-6139	490	6	−1	−1	NOUN
ejpam-6139	490	7	(	(	PUNCT
ejpam-6139	490	8	α	α	NOUN
ejpam-6139	490	9	k	k	PROPN
ejpam-6139	490	10	)	)	PUNCT
ejpam-6139	490	11	∫	∫	PROPN
ejpam-6139	490	12	1	1	NUM
ejpam-6139	490	13	0	0	NUM
ejpam-6139	490	14	[	[	PUNCT
ejpam-6139	490	15	1−	1−	NUM
ejpam-6139	490	16	(	(	PUNCT
ejpam-6139	490	17	1−	1−	NUM
ejpam-6139	490	18	t)µ	t)µ	NOUN
ejpam-6139	490	19	kµ	kµ	PROPN
ejpam-6139	490	20	]	]	PUNCT
ejpam-6139	490	21	α	α	X
ejpam-6139	490	22	k	k	X
ejpam-6139	490	23	−1	−1	NOUN
ejpam-6139	490	24	(	(	PUNCT
ejpam-6139	490	25	1−	1−	NUM
ejpam-6139	490	26	t)µ−1	t)µ−1	NOUN
ejpam-6139	490	27	×	×	PROPN
ejpam-6139	490	28	h	h	PROPN
ejpam-6139	490	29	(	(	PUNCT
ejpam-6139	490	30	η	η	PROPN
ejpam-6139	490	31	−	−	PROPN
ejpam-6139	490	32	t	t	PROPN
ejpam-6139	490	33	η	η	PROPN
ejpam-6139	490	34	ν	ν	PROPN
ejpam-6139	490	35	+	+	PROPN
ejpam-6139	490	36	t	t	PROPN
ejpam-6139	490	37	η	η	PROPN
ejpam-6139	490	38	ω	ω	PROPN
ejpam-6139	490	39	)	)	PUNCT
ejpam-6139	490	40	dt	dt	X
ejpam-6139	490	41	.	.	PUNCT
ejpam-6139	491	1	substituting	substitute	VERB
ejpam-6139	491	2	x	x	PUNCT
ejpam-6139	491	3	=	=	SYM
ejpam-6139	491	4	η−t	η−t	PROPN
ejpam-6139	491	5	η	η	PROPN
ejpam-6139	491	6	ν	ν	PROPN
ejpam-6139	491	7	+	+	PROPN
ejpam-6139	491	8	t	t	PROPN
ejpam-6139	491	9	ηω	ηω	NOUN
ejpam-6139	491	10	,	,	PUNCT
ejpam-6139	491	11	we	we	PRON
ejpam-6139	491	12	can	can	AUX
ejpam-6139	491	13	write	write	VERB
ejpam-6139	491	14	i3	i3	NOUN
ejpam-6139	491	15	=	=	SYM
ejpam-6139	491	16	η	η	PROPN
ejpam-6139	491	17	ω	ω	PROPN
ejpam-6139	491	18	−	−	PROPN
ejpam-6139	491	19	ν	ν	X
ejpam-6139	491	20	h′	h′	X
ejpam-6139	491	21	(	(	PUNCT
ejpam-6139	491	22	η	η	PROPN
ejpam-6139	491	23	−	−	PROPN
ejpam-6139	491	24	1	1	NUM
ejpam-6139	491	25	η	η	PROPN
ejpam-6139	491	26	ν	ν	X
ejpam-6139	491	27	+	+	PROPN
ejpam-6139	491	28	1	1	NUM
ejpam-6139	491	29	η	η	PROPN
ejpam-6139	491	30	ω	ω	PROPN
ejpam-6139	491	31	)	)	PUNCT
ejpam-6139	491	32	∫	∫	PROPN
ejpam-6139	491	33	1	1	NUM
ejpam-6139	491	34	0	0	NUM
ejpam-6139	491	35	(	(	PUNCT
ejpam-6139	491	36	1−	1−	NUM
ejpam-6139	491	37	(	(	PUNCT
ejpam-6139	491	38	1−	1−	NUM
ejpam-6139	491	39	φ)µ	φ)µ	NOUN
ejpam-6139	491	40	kµ	kµ	NOUN
ejpam-6139	491	41	)	)	PUNCT
ejpam-6139	492	1	α	α	PROPN
ejpam-6139	492	2	k	k	NOUN
ejpam-6139	493	1	dφ	dφ	ADP
ejpam-6139	493	2	−	−	PROPN
ejpam-6139	493	3	(	(	PUNCT
ejpam-6139	493	4	m	m	PROPN
ejpam-6139	493	5	ω	ω	NUM
ejpam-6139	493	6	−	−	PROPN
ejpam-6139	493	7	ν	ν	NOUN
ejpam-6139	493	8	)	)	PUNCT
ejpam-6139	493	9	2	2	NUM
ejpam-6139	493	10	(	(	PUNCT
ejpam-6139	493	11	1	1	NUM
ejpam-6139	493	12	kµ	kµ	NOUN
ejpam-6139	493	13	)	)	PUNCT
ejpam-6139	493	14	α	α	PROPN
ejpam-6139	493	15	k	k	PROPN
ejpam-6139	493	16	h	h	PROPN
ejpam-6139	493	17	(	(	PUNCT
ejpam-6139	493	18	η	η	PROPN
ejpam-6139	493	19	−	−	PROPN
ejpam-6139	493	20	1	1	NUM
ejpam-6139	493	21	η	η	PROPN
ejpam-6139	493	22	ν	ν	X
ejpam-6139	493	23	+	+	PROPN
ejpam-6139	493	24	1	1	NUM
ejpam-6139	493	25	η	η	PROPN
ejpam-6139	493	26	ω	ω	PROPN
ejpam-6139	493	27	)	)	PUNCT
ejpam-6139	494	1	+	+	CCONJ
ejpam-6139	494	2	(	(	PUNCT
ejpam-6139	494	3	η	η	PROPN
ejpam-6139	494	4	ω	ω	PROPN
ejpam-6139	494	5	−	−	PROPN
ejpam-6139	494	6	ν	ν	NOUN
ejpam-6139	494	7	)	)	PUNCT
ejpam-6139	494	8	µα	µα	ADP
ejpam-6139	494	9	k	k	PROPN
ejpam-6139	494	10	+2	+2	PROPN
ejpam-6139	494	11	(	(	PUNCT
ejpam-6139	494	12	γ	γ	X
ejpam-6139	494	13	(	(	PUNCT
ejpam-6139	494	14	α	α	NOUN
ejpam-6139	494	15	k	k	PROPN
ejpam-6139	495	1	+	+	CCONJ
ejpam-6139	495	2	1	1	X
ejpam-6139	495	3	)	)	PUNCT
ejpam-6139	495	4	k.k	k.k	PROPN
ejpam-6139	495	5	α	α	PROPN
ejpam-6139	495	6	k	k	PROPN
ejpam-6139	495	7	−1γ(αk	−1γ(αk	PROPN
ejpam-6139	495	8	)	)	PUNCT
ejpam-6139	495	9	)	)	PUNCT
ejpam-6139	496	1	×	×	NOUN
ejpam-6139	496	2	∫	∫	INTJ
ejpam-6139	496	3	(	(	PUNCT
ejpam-6139	496	4	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	496	5	η	η	PROPN
ejpam-6139	496	6	ν	ν	ADP
ejpam-6139	496	7			PROPN
ejpam-6139	496	8	(	(	PUNCT
ejpam-6139	496	9	ω−ν	ω−ν	PROPN
ejpam-6139	496	10	η	η	PROPN
ejpam-6139	496	11	)	)	PUNCT
ejpam-6139	496	12	µ	µ	NOUN
ejpam-6139	496	13	−	−	PROPN
ejpam-6139	496	14	(	(	PUNCT
ejpam-6139	496	15	(	(	PUNCT
ejpam-6139	496	16	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	496	17	η	η	PROPN
ejpam-6139	496	18	−	−	PROPN
ejpam-6139	496	19	x	x	SYM
ejpam-6139	496	20	)	)	PUNCT
ejpam-6139	496	21	µ	µ	NOUN
ejpam-6139	496	22	µ	µ	X
ejpam-6139	496	23			NOUN
ejpam-6139	496	24	α	α	NOUN
ejpam-6139	496	25	k	k	NOUN
ejpam-6139	496	26	−1	−1	NOUN
ejpam-6139	496	27	[	[	PUNCT
ejpam-6139	496	28	(	(	PUNCT
ejpam-6139	496	29	η	η	X
ejpam-6139	496	30	−	−	PROPN
ejpam-6139	496	31	1)ν	1)ν	NUM
ejpam-6139	496	32	+	+	PROPN
ejpam-6139	496	33	ω	ω	NUM
ejpam-6139	496	34	η	η	NOUN
ejpam-6139	496	35	−	−	PROPN
ejpam-6139	496	36	x	x	SYM
ejpam-6139	496	37	]	]	X
ejpam-6139	496	38	µ−1	µ−1	PROPN
ejpam-6139	496	39	h(x)dx	h(x)dx	PART
ejpam-6139	496	40	.	.	PUNCT
ejpam-6139	497	1	by	by	ADP
ejpam-6139	497	2	using	use	VERB
ejpam-6139	497	3	relation	relation	NOUN
ejpam-6139	497	4	γkα	γkα	NOUN
ejpam-6139	497	5	=	=	PUNCT
ejpam-6139	497	6	k	k	PROPN
ejpam-6139	497	7	α	α	PROPN
ejpam-6139	497	8	k	k	X
ejpam-6139	498	1	−1γ	−1γ	X
ejpam-6139	498	2	(	(	PUNCT
ejpam-6139	498	3	α	α	NOUN
ejpam-6139	498	4	k	k	PROPN
ejpam-6139	498	5	)	)	PUNCT
ejpam-6139	498	6	,	,	PUNCT
ejpam-6139	498	7	we	we	PRON
ejpam-6139	498	8	can	can	AUX
ejpam-6139	498	9	write	write	VERB
ejpam-6139	498	10	i3	i3	NOUN
ejpam-6139	498	11	=	=	SYM
ejpam-6139	498	12	η	η	PROPN
ejpam-6139	498	13	ω	ω	PROPN
ejpam-6139	498	14	−	−	PROPN
ejpam-6139	498	15	ν	ν	X
ejpam-6139	498	16	h′	h′	X
ejpam-6139	498	17	(	(	PUNCT
ejpam-6139	498	18	η	η	PROPN
ejpam-6139	498	19	−	−	PROPN
ejpam-6139	498	20	1	1	NUM
ejpam-6139	498	21	η	η	PROPN
ejpam-6139	498	22	ν	ν	X
ejpam-6139	498	23	+	+	PROPN
ejpam-6139	498	24	1	1	NUM
ejpam-6139	498	25	η	η	PROPN
ejpam-6139	498	26	ω	ω	PROPN
ejpam-6139	498	27	)	)	PUNCT
ejpam-6139	498	28	∫	∫	PROPN
ejpam-6139	498	29	1	1	NUM
ejpam-6139	498	30	0	0	NUM
ejpam-6139	498	31	(	(	PUNCT
ejpam-6139	498	32	1−	1−	NUM
ejpam-6139	498	33	(	(	PUNCT
ejpam-6139	498	34	1−	1−	NUM
ejpam-6139	498	35	φ)µ	φ)µ	NOUN
ejpam-6139	498	36	kµ	kµ	NOUN
ejpam-6139	498	37	)	)	PUNCT
ejpam-6139	499	1	α	α	PROPN
ejpam-6139	500	1	k	k	NOUN
ejpam-6139	501	1	dφ−	dφ−	PROPN
ejpam-6139	501	2	(	(	PUNCT
ejpam-6139	501	3	η	η	PROPN
ejpam-6139	501	4	ω	ω	PROPN
ejpam-6139	501	5	−	−	PROPN
ejpam-6139	501	6	ν	ν	NOUN
ejpam-6139	501	7	)	)	PUNCT
ejpam-6139	501	8	2	2	NUM
ejpam-6139	501	9	(	(	PUNCT
ejpam-6139	501	10	1	1	NUM
ejpam-6139	501	11	kµ	kµ	NOUN
ejpam-6139	501	12	)	)	PUNCT
ejpam-6139	502	1	α	α	PROPN
ejpam-6139	502	2	k	k	PROPN
ejpam-6139	502	3	h	h	PROPN
ejpam-6139	502	4	(	(	PUNCT
ejpam-6139	502	5	η	η	PROPN
ejpam-6139	502	6	−	−	PROPN
ejpam-6139	502	7	1	1	NUM
ejpam-6139	502	8	η	η	PROPN
ejpam-6139	502	9	ν	ν	X
ejpam-6139	502	10	+	+	PROPN
ejpam-6139	502	11	1	1	NUM
ejpam-6139	502	12	η	η	PROPN
ejpam-6139	502	13	ω	ω	PROPN
ejpam-6139	502	14	)	)	PUNCT
ejpam-6139	503	1	+	+	CCONJ
ejpam-6139	503	2	(	(	PUNCT
ejpam-6139	503	3	η	η	PROPN
ejpam-6139	503	4	ω	ω	PROPN
ejpam-6139	503	5	−	−	PROPN
ejpam-6139	503	6	ν	ν	NOUN
ejpam-6139	503	7	)	)	PUNCT
ejpam-6139	503	8	µα	µα	ADP
ejpam-6139	503	9	k	k	PROPN
ejpam-6139	503	10	+2	+2	PROPN
ejpam-6139	503	11	γ	γ	X
ejpam-6139	503	12	(	(	PUNCT
ejpam-6139	503	13	α	α	NOUN
ejpam-6139	503	14	k	k	PROPN
ejpam-6139	504	1	+	+	PROPN
ejpam-6139	504	2	1	1	X
ejpam-6139	504	3	)	)	PUNCT
ejpam-6139	504	4	(	(	PUNCT
ejpam-6139	504	5	1	1	NUM
ejpam-6139	504	6	kγkα	kγkα	NOUN
ejpam-6139	504	7	)	)	PUNCT
ejpam-6139	504	8	∫	∫	PROPN
ejpam-6139	504	9	(	(	PUNCT
ejpam-6139	504	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	504	11	η	η	PROPN
ejpam-6139	504	12	ν	ν	ADP
ejpam-6139	504	13			PROPN
ejpam-6139	504	14	(	(	PUNCT
ejpam-6139	504	15	(	(	PUNCT
ejpam-6139	504	16	η−1)ν+ω	η−1)ν+ω	NOUN
ejpam-6139	504	17	η	η	NOUN
ejpam-6139	504	18	−	−	PROPN
ejpam-6139	504	19	ν	ν	PROPN
ejpam-6139	504	20	)	)	PUNCT
ejpam-6139	504	21	µ	µ	NOUN
ejpam-6139	504	22	−	−	PROPN
ejpam-6139	504	23	(	(	PUNCT
ejpam-6139	504	24	(	(	PUNCT
ejpam-6139	504	25	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	504	26	η	η	PROPN
ejpam-6139	504	27	−	−	PROPN
ejpam-6139	504	28	x	x	SYM
ejpam-6139	504	29	)	)	PUNCT
ejpam-6139	504	30	µ	µ	NOUN
ejpam-6139	504	31	µ	µ	X
ejpam-6139	504	32			NOUN
ejpam-6139	504	33	α	α	NOUN
ejpam-6139	504	34	k	k	NOUN
ejpam-6139	504	35	−1	−1	NOUN
ejpam-6139	504	36	(	(	PUNCT
ejpam-6139	504	37	32	32	NUM
ejpam-6139	504	38	)	)	PUNCT
ejpam-6139	504	39	m.	m.	NOUN
ejpam-6139	504	40	samraiz	samraiz	PROPN
ejpam-6139	504	41	et	et	PROPN
ejpam-6139	504	42	al	al	PROPN
ejpam-6139	504	43	.	.	PUNCT
ejpam-6139	504	44	/	/	SYM
ejpam-6139	504	45	eur	eur	PROPN
ejpam-6139	504	46	.	.	PUNCT
ejpam-6139	505	1	j.	j.	PROPN
ejpam-6139	505	2	pure	pure	PROPN
ejpam-6139	505	3	appl	appl	PROPN
ejpam-6139	505	4	.	.	PROPN
ejpam-6139	505	5	math	math	PROPN
ejpam-6139	505	6	,	,	PUNCT
ejpam-6139	505	7	18	18	NUM
ejpam-6139	505	8	(	(	PUNCT
ejpam-6139	505	9	4	4	NUM
ejpam-6139	505	10	)	)	PUNCT
ejpam-6139	505	11	(	(	PUNCT
ejpam-6139	505	12	2025	2025	NUM
ejpam-6139	505	13	)	)	PUNCT
ejpam-6139	505	14	,	,	PUNCT
ejpam-6139	505	15	6139	6139	NUM
ejpam-6139	505	16	20	20	NUM
ejpam-6139	505	17	of	of	ADP
ejpam-6139	505	18	34	34	NUM
ejpam-6139	505	19	×	×	NOUN
ejpam-6139	505	20			NOUN
ejpam-6139	505	21	h(ν)dx	h(ν)dx	ADP
ejpam-6139	505	22	[	[	PUNCT
ejpam-6139	505	23	(	(	PUNCT
ejpam-6139	505	24	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	505	25	η	η	PROPN
ejpam-6139	505	26	−	−	PROPN
ejpam-6139	505	27	x	x	SYM
ejpam-6139	505	28	]	]	X
ejpam-6139	505	29	1−µ	1−µ	X
ejpam-6139	505	30			PROPN
ejpam-6139	505	31	.	.	PUNCT
ejpam-6139	506	1	(	(	PUNCT
ejpam-6139	506	2	33	33	NUM
ejpam-6139	506	3	)	)	PUNCT
ejpam-6139	506	4	by	by	ADP
ejpam-6139	506	5	using	use	VERB
ejpam-6139	506	6	the	the	DET
ejpam-6139	506	7	definition	definition	NOUN
ejpam-6139	506	8	of	of	ADP
ejpam-6139	506	9	extended	extended	ADJ
ejpam-6139	506	10	conformable	conformable	ADJ
ejpam-6139	506	11	operator	operator	NOUN
ejpam-6139	506	12	(	(	PUNCT
ejpam-6139	506	13	4	4	NUM
ejpam-6139	506	14	)	)	PUNCT
ejpam-6139	506	15	,	,	PUNCT
ejpam-6139	506	16	we	we	PRON
ejpam-6139	506	17	can	can	AUX
ejpam-6139	506	18	write	write	VERB
ejpam-6139	506	19	i3	i3	NOUN
ejpam-6139	506	20	=	=	SYM
ejpam-6139	506	21	η	η	PROPN
ejpam-6139	506	22	ω	ω	PROPN
ejpam-6139	506	23	−	−	PROPN
ejpam-6139	506	24	ν	ν	X
ejpam-6139	506	25	h′	h′	X
ejpam-6139	506	26	(	(	PUNCT
ejpam-6139	506	27	η	η	PROPN
ejpam-6139	506	28	−	−	PROPN
ejpam-6139	506	29	1	1	NUM
ejpam-6139	506	30	η	η	PROPN
ejpam-6139	506	31	ν	ν	X
ejpam-6139	506	32	+	+	PROPN
ejpam-6139	506	33	1	1	NUM
ejpam-6139	506	34	η	η	PROPN
ejpam-6139	506	35	ω	ω	PROPN
ejpam-6139	506	36	)	)	PUNCT
ejpam-6139	506	37	∫	∫	PROPN
ejpam-6139	506	38	1	1	NUM
ejpam-6139	506	39	0	0	NUM
ejpam-6139	506	40	(	(	PUNCT
ejpam-6139	506	41	1−	1−	NUM
ejpam-6139	506	42	(	(	PUNCT
ejpam-6139	506	43	1−	1−	NUM
ejpam-6139	506	44	φ)µ	φ)µ	NOUN
ejpam-6139	506	45	kµ	kµ	NOUN
ejpam-6139	506	46	)	)	PUNCT
ejpam-6139	507	1	α	α	PROPN
ejpam-6139	507	2	k	k	NOUN
ejpam-6139	508	1	dφ	dφ	ADP
ejpam-6139	508	2	−	−	PROPN
ejpam-6139	508	3	(	(	PUNCT
ejpam-6139	508	4	η	η	PROPN
ejpam-6139	508	5	ω	ω	PROPN
ejpam-6139	508	6	−	−	PROPN
ejpam-6139	508	7	ν	ν	NOUN
ejpam-6139	508	8	)	)	PUNCT
ejpam-6139	508	9	2	2	NUM
ejpam-6139	508	10	(	(	PUNCT
ejpam-6139	508	11	1	1	NUM
ejpam-6139	508	12	kµ	kµ	NOUN
ejpam-6139	508	13	)	)	PUNCT
ejpam-6139	508	14	α	α	PROPN
ejpam-6139	508	15	k	k	PROPN
ejpam-6139	508	16	h	h	PROPN
ejpam-6139	508	17	(	(	PUNCT
ejpam-6139	508	18	η	η	PROPN
ejpam-6139	508	19	−	−	PROPN
ejpam-6139	508	20	1	1	NUM
ejpam-6139	508	21	η	η	PROPN
ejpam-6139	508	22	ν	ν	X
ejpam-6139	508	23	+	+	PROPN
ejpam-6139	508	24	1	1	NUM
ejpam-6139	508	25	η	η	PROPN
ejpam-6139	508	26	ω	ω	PROPN
ejpam-6139	508	27	)	)	PUNCT
ejpam-6139	509	1	+	+	CCONJ
ejpam-6139	509	2	(	(	PUNCT
ejpam-6139	509	3	η	η	PROPN
ejpam-6139	509	4	ω	ω	PROPN
ejpam-6139	509	5	−	−	PROPN
ejpam-6139	509	6	ν	ν	NOUN
ejpam-6139	509	7	)	)	PUNCT
ejpam-6139	509	8	µα	µα	ADP
ejpam-6139	509	9	k	k	PROPN
ejpam-6139	509	10	+2	+2	PROPN
ejpam-6139	509	11	γ	γ	X
ejpam-6139	509	12	(	(	PUNCT
ejpam-6139	509	13	α	α	NOUN
ejpam-6139	509	14	k	k	PROPN
ejpam-6139	510	1	+	+	CCONJ
ejpam-6139	510	2	1)αk	1)αk	VERB
ejpam-6139	510	3	j	j	PROPN
ejpam-6139	510	4	µ	µ	X
ejpam-6139	510	5	(	(	PUNCT
ejpam-6139	510	6	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	510	7	η	η	PROPN
ejpam-6139	510	8	−	−	PROPN
ejpam-6139	510	9	h(ν	h(ν	PROPN
ejpam-6139	510	10	)	)	PUNCT
ejpam-6139	510	11	.	.	PUNCT
ejpam-6139	511	1	(	(	PUNCT
ejpam-6139	511	2	34	34	NUM
ejpam-6139	511	3	)	)	PUNCT
ejpam-6139	511	4	similarly	similarly	ADV
ejpam-6139	511	5	i4	i4	PROPN
ejpam-6139	511	6	=	=	SYM
ejpam-6139	511	7	∫	∫	PROPN
ejpam-6139	511	8	1	1	NUM
ejpam-6139	511	9	0	0	NUM
ejpam-6139	512	1	[	[	X
ejpam-6139	512	2	∫	∫	X
ejpam-6139	512	3	t	t	PROPN
ejpam-6139	512	4	0	0	NUM
ejpam-6139	512	5	(	(	PUNCT
ejpam-6139	512	6	1−	1−	NUM
ejpam-6139	512	7	(	(	PUNCT
ejpam-6139	512	8	1−	1−	NUM
ejpam-6139	512	9	φ)µ	φ)µ	NOUN
ejpam-6139	512	10	kµ	kµ	NOUN
ejpam-6139	512	11	)	)	PUNCT
ejpam-6139	513	1	α	α	PROPN
ejpam-6139	513	2	k	k	X
ejpam-6139	514	1	dφ	dφ	X
ejpam-6139	514	2	]	]	PUNCT
ejpam-6139	514	3	h′′	h′′	PROPN
ejpam-6139	514	4	(	(	PUNCT
ejpam-6139	514	5	t	t	PROPN
ejpam-6139	514	6	η	η	PROPN
ejpam-6139	514	7	ν	ν	PROPN
ejpam-6139	514	8	+	+	PROPN
ejpam-6139	514	9	η	η	PROPN
ejpam-6139	514	10	−	−	PROPN
ejpam-6139	514	11	t	t	PROPN
ejpam-6139	514	12	η	η	PROPN
ejpam-6139	514	13	ω	ω	PROPN
ejpam-6139	514	14	)	)	PUNCT
ejpam-6139	514	15	dt	dt	PROPN
ejpam-6139	515	1	i4	i4	PROPN
ejpam-6139	515	2	=	=	SYM
ejpam-6139	515	3	−	−	PROPN
ejpam-6139	515	4	η	η	PROPN
ejpam-6139	515	5	ω	ω	PROPN
ejpam-6139	515	6	−	−	PROPN
ejpam-6139	515	7	ν	ν	X
ejpam-6139	515	8	h′	h′	X
ejpam-6139	515	9	(	(	PUNCT
ejpam-6139	515	10	1	1	NUM
ejpam-6139	515	11	η	η	X
ejpam-6139	515	12	ν	ν	X
ejpam-6139	515	13	+	+	CCONJ
ejpam-6139	515	14	η	η	PROPN
ejpam-6139	515	15	−	−	PROPN
ejpam-6139	515	16	1	1	NUM
ejpam-6139	515	17	η	η	PROPN
ejpam-6139	515	18	ω	ω	PROPN
ejpam-6139	515	19	)	)	PUNCT
ejpam-6139	515	20	∫	∫	PROPN
ejpam-6139	515	21	1	1	NUM
ejpam-6139	515	22	0	0	NUM
ejpam-6139	515	23	(	(	PUNCT
ejpam-6139	515	24	1−	1−	NUM
ejpam-6139	515	25	(	(	PUNCT
ejpam-6139	515	26	1−	1−	NUM
ejpam-6139	515	27	φ)µ	φ)µ	NOUN
ejpam-6139	515	28	kµ	kµ	NOUN
ejpam-6139	515	29	)	)	PUNCT
ejpam-6139	516	1	α	α	PROPN
ejpam-6139	516	2	k	k	NOUN
ejpam-6139	517	1	dφ	dφ	ADP
ejpam-6139	517	2	−	−	PROPN
ejpam-6139	517	3	(	(	PUNCT
ejpam-6139	517	4	η	η	PROPN
ejpam-6139	517	5	ω	ω	PROPN
ejpam-6139	517	6	−	−	PROPN
ejpam-6139	517	7	ν	ν	NOUN
ejpam-6139	517	8	)	)	PUNCT
ejpam-6139	517	9	2	2	NUM
ejpam-6139	517	10	h	h	NOUN
ejpam-6139	517	11	(	(	PUNCT
ejpam-6139	517	12	ν	ν	PROPN
ejpam-6139	517	13	η	η	PROPN
ejpam-6139	517	14	+	+	PROPN
ejpam-6139	517	15	η	η	PROPN
ejpam-6139	517	16	−	−	PROPN
ejpam-6139	517	17	1	1	NUM
ejpam-6139	517	18	η	η	PROPN
ejpam-6139	517	19	ω	ω	PROPN
ejpam-6139	517	20	)	)	PUNCT
ejpam-6139	517	21	1	1	NUM
ejpam-6139	517	22	(	(	PUNCT
ejpam-6139	517	23	ku	ku	PROPN
ejpam-6139	517	24	)	)	PUNCT
ejpam-6139	517	25	α	α	PROPN
ejpam-6139	517	26	k	k	X
ejpam-6139	518	1	+	+	CCONJ
ejpam-6139	518	2	(	(	PUNCT
ejpam-6139	518	3	η	η	PROPN
ejpam-6139	518	4	ω	ω	PROPN
ejpam-6139	518	5	−	−	PROPN
ejpam-6139	518	6	ν	ν	NOUN
ejpam-6139	518	7	)	)	PUNCT
ejpam-6139	518	8	µα	µα	ADP
ejpam-6139	518	9	k	k	PROPN
ejpam-6139	518	10	+2	+2	PROPN
ejpam-6139	518	11	γ	γ	X
ejpam-6139	518	12	(	(	PUNCT
ejpam-6139	518	13	α	α	NOUN
ejpam-6139	518	14	k	k	PROPN
ejpam-6139	519	1	+	+	CCONJ
ejpam-6139	519	2	1	1	X
ejpam-6139	519	3	)	)	PUNCT
ejpam-6139	519	4	α	α	NOUN
ejpam-6139	519	5	k	k	NOUN
ejpam-6139	519	6	jµν+(η−1)ω	jµν+(η−1)ω	X
ejpam-6139	519	7	η	η	PROPN
ejpam-6139	519	8	+	+	PROPN
ejpam-6139	519	9	h(ω	h(ω	PROPN
ejpam-6139	519	10	)	)	PUNCT
ejpam-6139	519	11	.	.	PUNCT
ejpam-6139	520	1	(	(	PUNCT
ejpam-6139	520	2	35	35	NUM
ejpam-6139	520	3	)	)	PUNCT
ejpam-6139	520	4	adding	add	VERB
ejpam-6139	520	5	equations	equation	NOUN
ejpam-6139	520	6	(	(	PUNCT
ejpam-6139	520	7	34	34	NUM
ejpam-6139	520	8	)	)	PUNCT
ejpam-6139	520	9	and	and	CCONJ
ejpam-6139	520	10	(	(	PUNCT
ejpam-6139	520	11	35	35	NUM
ejpam-6139	520	12	)	)	PUNCT
ejpam-6139	520	13	,	,	PUNCT
ejpam-6139	520	14	we	we	PRON
ejpam-6139	520	15	get	get	VERB
ejpam-6139	520	16	our	our	PRON
ejpam-6139	520	17	required	require	VERB
ejpam-6139	520	18	result	result	NOUN
ejpam-6139	520	19	.	.	PUNCT
ejpam-6139	521	1	remark	remark	VERB
ejpam-6139	521	2	7	7	NUM
ejpam-6139	521	3	.	.	PUNCT
ejpam-6139	521	4	by	by	ADP
ejpam-6139	521	5	considering	consider	VERB
ejpam-6139	521	6	η	η	PROPN
ejpam-6139	521	7	=	=	SYM
ejpam-6139	521	8	2	2	NUM
ejpam-6139	521	9	and	and	CCONJ
ejpam-6139	521	10	k=1	k=1	X
ejpam-6139	521	11	simultaneously	simultaneously	ADV
ejpam-6139	521	12	in	in	ADP
ejpam-6139	521	13	equation	equation	NOUN
ejpam-6139	521	14	(	(	PUNCT
ejpam-6139	521	15	31	31	NUM
ejpam-6139	521	16	)	)	PUNCT
ejpam-6139	521	17	,	,	PUNCT
ejpam-6139	521	18	that	that	PRON
ejpam-6139	521	19	directly	directly	ADV
ejpam-6139	521	20	leads	lead	VERB
ejpam-6139	521	21	to	to	ADP
ejpam-6139	521	22	[	[	X
ejpam-6139	521	23	[	[	X
ejpam-6139	521	24	44	44	NUM
ejpam-6139	521	25	]	]	PUNCT
ejpam-6139	521	26	,	,	PUNCT
ejpam-6139	521	27	lemma	lemma	PROPN
ejpam-6139	521	28	10	10	NUM
ejpam-6139	521	29	]	]	PUNCT
ejpam-6139	521	30	.	.	PUNCT
ejpam-6139	522	1	theorem	theorem	ADJ
ejpam-6139	522	2	4	4	NUM
ejpam-6139	522	3	.	.	PUNCT
ejpam-6139	522	4	assume	assume	VERB
ejpam-6139	522	5	that	that	SCONJ
ejpam-6139	522	6	h	h	NOUN
ejpam-6139	522	7	:	:	PUNCT
ejpam-6139	523	1	[	[	X
ejpam-6139	523	2	ν	ν	X
ejpam-6139	523	3	,	,	PUNCT
ejpam-6139	523	4	ω	ω	NOUN
ejpam-6139	523	5	]	]	X
ejpam-6139	523	6	→	→	SYM
ejpam-6139	523	7	r	r	NOUN
ejpam-6139	523	8	as	as	ADP
ejpam-6139	523	9	a	a	DET
ejpam-6139	523	10	twice	twice	ADV
ejpam-6139	523	11	differentiable	differentiable	ADJ
ejpam-6139	523	12	function	function	NOUN
ejpam-6139	523	13	on	on	ADP
ejpam-6139	523	14	(	(	PUNCT
ejpam-6139	523	15	ν	ν	PROPN
ejpam-6139	523	16	,	,	PUNCT
ejpam-6139	523	17	ω	ω	NOUN
ejpam-6139	523	18	)	)	PUNCT
ejpam-6139	523	19	such	such	ADJ
ejpam-6139	523	20	that	that	SCONJ
ejpam-6139	523	21	h′′	h′′	PROPN
ejpam-6139	523	22	∈	∈	PROPN
ejpam-6139	523	23	l1([ν	l1([ν	PROPN
ejpam-6139	523	24	,	,	PUNCT
ejpam-6139	523	25	ω	ω	NOUN
ejpam-6139	523	26	]	]	NOUN
ejpam-6139	523	27	)	)	PUNCT
ejpam-6139	523	28	.	.	PUNCT
ejpam-6139	524	1	by	by	ADP
ejpam-6139	524	2	considering	consider	VERB
ejpam-6139	524	3	the	the	DET
ejpam-6139	524	4	convexity	convexity	NOUN
ejpam-6139	524	5	|h′′|	|h′′|	VERB
ejpam-6139	524	6	on	on	ADP
ejpam-6139	524	7	[	[	X
ejpam-6139	524	8	ν	ν	X
ejpam-6139	524	9	,	,	PUNCT
ejpam-6139	524	10	ω	ω	PROPN
ejpam-6139	524	11	]	]	X
ejpam-6139	524	12	the	the	DET
ejpam-6139	524	13	inequality	inequality	NOUN
ejpam-6139	524	14	is	be	AUX
ejpam-6139	524	15	given	give	VERB
ejpam-6139	524	16	as,∣∣∣∣	as,∣∣∣∣	PROPN
ejpam-6139	524	17	ηµ	ηµ	VERB
ejpam-6139	524	18	α	α	PROPN
ejpam-6139	524	19	k	k	X
ejpam-6139	524	20	−1	−1	PROPN
ejpam-6139	524	21	(	(	PUNCT
ejpam-6139	524	22	ω	ω	PROPN
ejpam-6139	524	23	−	−	PROPN
ejpam-6139	524	24	ν)µ	ν)µ	ADV
ejpam-6139	524	25	α	α	PROPN
ejpam-6139	524	26	k	k	PROPN
ejpam-6139	524	27	(	(	PUNCT
ejpam-6139	524	28	kµ	kµ	PROPN
ejpam-6139	524	29	)	)	PUNCT
ejpam-6139	524	30	α	α	PROPN
ejpam-6139	525	1	k	k	PROPN
ejpam-6139	525	2	γ	γ	X
ejpam-6139	525	3	(	(	PUNCT
ejpam-6139	525	4	α	α	NOUN
ejpam-6139	525	5	k	k	PROPN
ejpam-6139	526	1	+	+	PROPN
ejpam-6139	526	2	1	1	X
ejpam-6139	526	3	)	)	PUNCT
ejpam-6139	526	4	(	(	PUNCT
ejpam-6139	526	5	α	α	PROPN
ejpam-6139	526	6	k	k	PROPN
ejpam-6139	526	7	j	j	PROPN
ejpam-6139	526	8	µ	µ	X
ejpam-6139	526	9	(	(	PUNCT
ejpam-6139	526	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	526	11	η	η	PROPN
ejpam-6139	526	12	−	−	PROPN
ejpam-6139	526	13	h(ν	h(ν	PROPN
ejpam-6139	526	14	)	)	PUNCT
ejpam-6139	526	15	+	+	NOUN
ejpam-6139	526	16	α	α	NOUN
ejpam-6139	526	17	k	k	X
ejpam-6139	526	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	526	19	η	η	PROPN
ejpam-6139	526	20	+	+	PROPN
ejpam-6139	526	21	h(ω	h(ω	PROPN
ejpam-6139	526	22	)	)	PUNCT
ejpam-6139	526	23	)	)	PUNCT
ejpam-6139	527	1	+	+	X
ejpam-6139	527	2	υk[µ	υk[µ	PROPN
ejpam-6139	527	3	,	,	PUNCT
ejpam-6139	527	4	α	α	NOUN
ejpam-6139	527	5	]	]	X
ejpam-6139	527	6	−	−	PROPN
ejpam-6139	527	7	1	1	NUM
ejpam-6139	527	8	η	η	PROPN
ejpam-6139	527	9	(	(	PUNCT
ejpam-6139	527	10	h	h	PROPN
ejpam-6139	527	11	(	(	PUNCT
ejpam-6139	527	12	η	η	PROPN
ejpam-6139	527	13	−	−	PROPN
ejpam-6139	527	14	1	1	NUM
ejpam-6139	527	15	η	η	PROPN
ejpam-6139	527	16	ν	ν	X
ejpam-6139	527	17	+	+	PROPN
ejpam-6139	527	18	1	1	NUM
ejpam-6139	527	19	η	η	PROPN
ejpam-6139	527	20	ω	ω	PROPN
ejpam-6139	527	21	)	)	PUNCT
ejpam-6139	528	1	+	+	CCONJ
ejpam-6139	528	2	h	h	NOUN
ejpam-6139	528	3	(	(	PUNCT
ejpam-6139	528	4	1	1	NUM
ejpam-6139	528	5	η	η	X
ejpam-6139	528	6	ν	ν	X
ejpam-6139	528	7	+	+	CCONJ
ejpam-6139	528	8	η	η	PROPN
ejpam-6139	528	9	−	−	PROPN
ejpam-6139	528	10	1	1	NUM
ejpam-6139	528	11	η	η	PROPN
ejpam-6139	528	12	ω	ω	PROPN
ejpam-6139	528	13	)	)	PUNCT
ejpam-6139	528	14	)	)	PUNCT
ejpam-6139	529	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	529	2	≤	≤	NOUN
ejpam-6139	529	3	(	(	PUNCT
ejpam-6139	529	4	ω	ω	NUM
ejpam-6139	529	5	−	−	PROPN
ejpam-6139	529	6	ν)2	ν)2	PROPN
ejpam-6139	529	7	η3	η3	PROPN
ejpam-6139	529	8	(	(	PUNCT
ejpam-6139	529	9	kµ	kµ	PROPN
ejpam-6139	529	10	)	)	PUNCT
ejpam-6139	529	11	α	α	PROPN
ejpam-6139	530	1	k	k	PROPN
ejpam-6139	530	2	1	1	NUM
ejpam-6139	530	3	µ	µ	PRON
ejpam-6139	530	4	∫	∫	NOUN
ejpam-6139	530	5	1	1	NUM
ejpam-6139	530	6	0	0	NUM
ejpam-6139	530	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	530	8	1	1	NUM
ejpam-6139	530	9	(	(	PUNCT
ejpam-6139	530	10	kµ	kµ	PROPN
ejpam-6139	530	11	)	)	PUNCT
ejpam-6139	530	12	α	α	PROPN
ejpam-6139	531	1	k	k	PROPN
ejpam-6139	531	2	b	b	PROPN
ejpam-6139	531	3	(	(	PUNCT
ejpam-6139	531	4	α	α	NOUN
ejpam-6139	531	5	k	k	PROPN
ejpam-6139	532	1	+	+	PROPN
ejpam-6139	532	2	1	1	NUM
ejpam-6139	532	3	,	,	PUNCT
ejpam-6139	532	4	1	1	NUM
ejpam-6139	532	5	µ	µ	NOUN
ejpam-6139	532	6	,	,	PUNCT
ejpam-6139	532	7	1−	1−	NUM
ejpam-6139	532	8	(	(	PUNCT
ejpam-6139	532	9	1−	1−	NUM
ejpam-6139	532	10	t)µ	t)µ	NOUN
ejpam-6139	532	11	)	)	PUNCT
ejpam-6139	533	1	∣∣∣∣(ts	∣∣∣∣(t	NOUN
ejpam-6139	533	2	+	+	CCONJ
ejpam-6139	533	3	(	(	PUNCT
ejpam-6139	533	4	η	η	PROPN
ejpam-6139	533	5	−	−	PROPN
ejpam-6139	533	6	t)s	t)s	ADV
ejpam-6139	533	7	)	)	PUNCT
ejpam-6139	533	8	dt	dt	X
ejpam-6139	534	1	×	×	NOUN
ejpam-6139	534	2	(	(	PUNCT
ejpam-6139	534	3	|h′′(ν)|+	|h′′(ν)|+	X
ejpam-6139	534	4	|h′′(ω)|	|h′′(ω)|	INTJ
ejpam-6139	534	5	ηs	ηs	NOUN
ejpam-6139	534	6	)	)	PUNCT
ejpam-6139	534	7	,	,	PUNCT
ejpam-6139	534	8	(	(	PUNCT
ejpam-6139	534	9	36	36	NUM
ejpam-6139	534	10	)	)	PUNCT
ejpam-6139	534	11	m.	m.	NOUN
ejpam-6139	534	12	samraiz	samraiz	PROPN
ejpam-6139	534	13	et	et	PROPN
ejpam-6139	534	14	al	al	PROPN
ejpam-6139	534	15	.	.	PUNCT
ejpam-6139	534	16	/	/	SYM
ejpam-6139	534	17	eur	eur	PROPN
ejpam-6139	534	18	.	.	PUNCT
ejpam-6139	535	1	j.	j.	PROPN
ejpam-6139	535	2	pure	pure	PROPN
ejpam-6139	535	3	appl	appl	PROPN
ejpam-6139	535	4	.	.	PROPN
ejpam-6139	535	5	math	math	PROPN
ejpam-6139	535	6	,	,	PUNCT
ejpam-6139	535	7	18	18	NUM
ejpam-6139	535	8	(	(	PUNCT
ejpam-6139	535	9	4	4	NUM
ejpam-6139	535	10	)	)	PUNCT
ejpam-6139	535	11	(	(	PUNCT
ejpam-6139	535	12	2025	2025	NUM
ejpam-6139	535	13	)	)	PUNCT
ejpam-6139	535	14	,	,	PUNCT
ejpam-6139	535	15	6139	6139	NUM
ejpam-6139	535	16	21	21	NUM
ejpam-6139	535	17	of	of	ADP
ejpam-6139	535	18	34	34	NUM
ejpam-6139	536	1	where	where	SCONJ
ejpam-6139	536	2	υk[µ	υk[µ	PROPN
ejpam-6139	536	3	,	,	PUNCT
ejpam-6139	536	4	α	α	NOUN
ejpam-6139	536	5	]	]	X
ejpam-6139	536	6	=	=	SYM
ejpam-6139	536	7	(	(	PUNCT
ejpam-6139	536	8	ω	ω	NUM
ejpam-6139	536	9	−	−	NOUN
ejpam-6139	536	10	ν	ν	NOUN
ejpam-6139	536	11	)	)	PUNCT
ejpam-6139	536	12	η2	η2	PROPN
ejpam-6139	536	13	(	(	PUNCT
ejpam-6139	536	14	kµ	kµ	PROPN
ejpam-6139	536	15	)	)	PUNCT
ejpam-6139	536	16	α	α	PROPN
ejpam-6139	536	17	k	k	PROPN
ejpam-6139	536	18	(	(	PUNCT
ejpam-6139	536	19	h′	h′	X
ejpam-6139	536	20	(	(	PUNCT
ejpam-6139	536	21	η	η	PROPN
ejpam-6139	536	22	−	−	PROPN
ejpam-6139	536	23	1	1	NUM
ejpam-6139	536	24	η	η	PROPN
ejpam-6139	536	25	ν	ν	X
ejpam-6139	536	26	+	+	PROPN
ejpam-6139	536	27	1	1	NUM
ejpam-6139	536	28	η	η	PROPN
ejpam-6139	536	29	ω	ω	PROPN
ejpam-6139	536	30	)	)	PUNCT
ejpam-6139	536	31	−	−	PROPN
ejpam-6139	536	32	h′	h′	PROPN
ejpam-6139	536	33	(	(	PUNCT
ejpam-6139	536	34	1	1	NUM
ejpam-6139	536	35	η	η	X
ejpam-6139	536	36	ν	ν	X
ejpam-6139	536	37	+	+	CCONJ
ejpam-6139	536	38	η	η	PROPN
ejpam-6139	536	39	−	−	PROPN
ejpam-6139	536	40	1	1	NUM
ejpam-6139	536	41	η	η	PROPN
ejpam-6139	536	42	ω	ω	PROPN
ejpam-6139	536	43	)	)	PUNCT
ejpam-6139	536	44	)	)	PUNCT
ejpam-6139	537	1	×	×	NOUN
ejpam-6139	538	1	[	[	X
ejpam-6139	538	2	∫	∫	PROPN
ejpam-6139	538	3	1	1	NUM
ejpam-6139	538	4	0	0	NUM
ejpam-6139	538	5	(	(	PUNCT
ejpam-6139	538	6	1−	1−	NUM
ejpam-6139	538	7	(	(	PUNCT
ejpam-6139	538	8	1−	1−	NUM
ejpam-6139	538	9	φ)µ	φ)µ	NOUN
ejpam-6139	538	10	kµ	kµ	NOUN
ejpam-6139	538	11	)	)	PUNCT
ejpam-6139	539	1	α	α	PROPN
ejpam-6139	539	2	k	k	X
ejpam-6139	540	1	dφ	dφ	ADP
ejpam-6139	540	2	]	]	PUNCT
ejpam-6139	540	3	.	.	PUNCT
ejpam-6139	541	1	proof	proof	NOUN
ejpam-6139	541	2	.	.	PUNCT
ejpam-6139	542	1	taking	take	VERB
ejpam-6139	542	2	absolute	absolute	ADJ
ejpam-6139	542	3	value	value	NOUN
ejpam-6139	542	4	on	on	ADP
ejpam-6139	542	5	both	both	DET
ejpam-6139	542	6	sides	side	NOUN
ejpam-6139	542	7	of	of	ADP
ejpam-6139	542	8	equation	equation	NOUN
ejpam-6139	542	9	(	(	PUNCT
ejpam-6139	542	10	31)∣∣∣∣	31)∣∣∣∣	NUM
ejpam-6139	542	11	ηµ	ηµ	VERB
ejpam-6139	542	12	α	α	PROPN
ejpam-6139	542	13	k	k	X
ejpam-6139	542	14	−1	−1	PROPN
ejpam-6139	542	15	(	(	PUNCT
ejpam-6139	542	16	ω	ω	PROPN
ejpam-6139	542	17	−	−	PROPN
ejpam-6139	542	18	ν)µ	ν)µ	ADV
ejpam-6139	542	19	α	α	PROPN
ejpam-6139	542	20	k	k	PROPN
ejpam-6139	542	21	(	(	PUNCT
ejpam-6139	542	22	kµ	kµ	PROPN
ejpam-6139	542	23	)	)	PUNCT
ejpam-6139	543	1	α	α	PROPN
ejpam-6139	543	2	k	k	PROPN
ejpam-6139	543	3	γ	γ	X
ejpam-6139	543	4	(	(	PUNCT
ejpam-6139	543	5	α	α	NOUN
ejpam-6139	543	6	k	k	PROPN
ejpam-6139	544	1	+	+	PROPN
ejpam-6139	544	2	1	1	X
ejpam-6139	544	3	)	)	PUNCT
ejpam-6139	544	4	(	(	PUNCT
ejpam-6139	544	5	α	α	PROPN
ejpam-6139	544	6	k	k	PROPN
ejpam-6139	544	7	j	j	PROPN
ejpam-6139	544	8	µ	µ	X
ejpam-6139	544	9	(	(	PUNCT
ejpam-6139	544	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	544	11	η	η	PROPN
ejpam-6139	544	12	−	−	PROPN
ejpam-6139	544	13	h(ν	h(ν	PROPN
ejpam-6139	544	14	)	)	PUNCT
ejpam-6139	544	15	+	+	NOUN
ejpam-6139	544	16	α	α	NOUN
ejpam-6139	544	17	k	k	X
ejpam-6139	544	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	544	19	η	η	PROPN
ejpam-6139	544	20	+	+	PROPN
ejpam-6139	544	21	h(ω	h(ω	PROPN
ejpam-6139	544	22	)	)	PUNCT
ejpam-6139	544	23	)	)	PUNCT
ejpam-6139	545	1	+	+	X
ejpam-6139	545	2	υk[µ	υk[µ	PROPN
ejpam-6139	545	3	,	,	PUNCT
ejpam-6139	545	4	α	α	NOUN
ejpam-6139	545	5	]	]	X
ejpam-6139	545	6	−	−	PROPN
ejpam-6139	545	7	1	1	NUM
ejpam-6139	545	8	η	η	PROPN
ejpam-6139	545	9	(	(	PUNCT
ejpam-6139	545	10	h	h	PROPN
ejpam-6139	545	11	(	(	PUNCT
ejpam-6139	545	12	η	η	PROPN
ejpam-6139	545	13	−	−	PROPN
ejpam-6139	545	14	1	1	NUM
ejpam-6139	545	15	η	η	PROPN
ejpam-6139	545	16	ν	ν	X
ejpam-6139	545	17	+	+	PROPN
ejpam-6139	545	18	1	1	NUM
ejpam-6139	545	19	η	η	PROPN
ejpam-6139	545	20	ω	ω	PROPN
ejpam-6139	545	21	)	)	PUNCT
ejpam-6139	546	1	+	+	CCONJ
ejpam-6139	546	2	h	h	NOUN
ejpam-6139	546	3	(	(	PUNCT
ejpam-6139	546	4	1	1	NUM
ejpam-6139	546	5	η	η	X
ejpam-6139	546	6	ν	ν	X
ejpam-6139	546	7	+	+	CCONJ
ejpam-6139	546	8	η	η	PROPN
ejpam-6139	546	9	−	−	PROPN
ejpam-6139	546	10	1	1	NUM
ejpam-6139	546	11	η	η	PROPN
ejpam-6139	546	12	ω	ω	PROPN
ejpam-6139	546	13	)	)	PUNCT
ejpam-6139	546	14	)	)	PUNCT
ejpam-6139	547	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	547	2	≤	≤	NOUN
ejpam-6139	547	3	(	(	PUNCT
ejpam-6139	547	4	ω	ω	NUM
ejpam-6139	547	5	−	−	PROPN
ejpam-6139	547	6	ν)2	ν)2	PROPN
ejpam-6139	547	7	η3	η3	PROPN
ejpam-6139	547	8	(	(	PUNCT
ejpam-6139	547	9	kµ	kµ	PROPN
ejpam-6139	547	10	)	)	PUNCT
ejpam-6139	547	11	α	α	PROPN
ejpam-6139	547	12	k	k	X
ejpam-6139	548	1	[	[	X
ejpam-6139	548	2	∫	∫	PROPN
ejpam-6139	548	3	1	1	NUM
ejpam-6139	548	4	0	0	NUM
ejpam-6139	548	5	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	548	6	t	t	NOUN
ejpam-6139	548	7	0	0	NUM
ejpam-6139	549	1	(	(	PUNCT
ejpam-6139	549	2	1−	1−	NUM
ejpam-6139	549	3	(	(	PUNCT
ejpam-6139	549	4	1−	1−	NUM
ejpam-6139	549	5	φ)µ	φ)µ	NOUN
ejpam-6139	549	6	kµ	kµ	NOUN
ejpam-6139	549	7	)	)	PUNCT
ejpam-6139	550	1	α	α	PROPN
ejpam-6139	550	2	k	k	X
ejpam-6139	551	1	dφ	dφ	ADP
ejpam-6139	551	2	∣∣∣∣∣∣∣∣h′′(η	∣∣∣∣∣∣∣∣h′′(η	PROPN
ejpam-6139	551	3	−	−	PROPN
ejpam-6139	551	4	t	t	PROPN
ejpam-6139	551	5	η	η	PROPN
ejpam-6139	551	6	ν	ν	PROPN
ejpam-6139	551	7	+	+	PROPN
ejpam-6139	551	8	t	t	PROPN
ejpam-6139	551	9	η	η	PROPN
ejpam-6139	551	10	ω	ω	PROPN
ejpam-6139	551	11	)	)	PUNCT
ejpam-6139	551	12	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	551	13	+	+	CCONJ
ejpam-6139	551	14	∫	∫	PROPN
ejpam-6139	551	15	1	1	NUM
ejpam-6139	551	16	0	0	NUM
ejpam-6139	551	17	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	551	18	t	t	NOUN
ejpam-6139	551	19	0	0	NUM
ejpam-6139	552	1	(	(	PUNCT
ejpam-6139	552	2	1−	1−	NUM
ejpam-6139	552	3	(	(	PUNCT
ejpam-6139	552	4	1−	1−	NUM
ejpam-6139	552	5	φ)µ	φ)µ	NOUN
ejpam-6139	552	6	kµ	kµ	NOUN
ejpam-6139	552	7	)	)	PUNCT
ejpam-6139	553	1	α	α	PROPN
ejpam-6139	553	2	k	k	X
ejpam-6139	553	3	dφ	dφ	X
ejpam-6139	553	4	∣∣∣∣∣∣∣∣h′′	∣∣∣∣∣∣∣∣h′′	PROPN
ejpam-6139	553	5	(	(	PUNCT
ejpam-6139	553	6	t	t	PROPN
ejpam-6139	553	7	η	η	PROPN
ejpam-6139	553	8	ν	ν	PROPN
ejpam-6139	553	9	+	+	PROPN
ejpam-6139	553	10	η	η	PROPN
ejpam-6139	553	11	−	−	PROPN
ejpam-6139	553	12	t	t	PROPN
ejpam-6139	553	13	η	η	PROPN
ejpam-6139	553	14	ω	ω	PROPN
ejpam-6139	553	15	)	)	PUNCT
ejpam-6139	553	16	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	553	17	]	]	PUNCT
ejpam-6139	553	18	.	.	PUNCT
ejpam-6139	554	1	(	(	PUNCT
ejpam-6139	554	2	37	37	NUM
ejpam-6139	554	3	)	)	PUNCT
ejpam-6139	554	4	by	by	ADP
ejpam-6139	554	5	considering	consider	VERB
ejpam-6139	554	6	s	s	NOUN
ejpam-6139	554	7	-	-	NOUN
ejpam-6139	554	8	convexity	convexity	NOUN
ejpam-6139	554	9	of	of	ADP
ejpam-6139	554	10	|h′′|	|h′′|	PROPN
ejpam-6139	554	11	in	in	ADP
ejpam-6139	554	12	second	second	ADJ
ejpam-6139	554	13	sense∣∣∣∣	sense∣∣∣∣	PROPN
ejpam-6139	554	14	ηµ	ηµ	VERB
ejpam-6139	554	15	α	α	PROPN
ejpam-6139	554	16	k	k	PROPN
ejpam-6139	554	17	−1	−1	PROPN
ejpam-6139	554	18	(	(	PUNCT
ejpam-6139	554	19	ω	ω	PROPN
ejpam-6139	554	20	−	−	PROPN
ejpam-6139	554	21	ν)µ	ν)µ	ADV
ejpam-6139	554	22	α	α	PROPN
ejpam-6139	554	23	k	k	PROPN
ejpam-6139	554	24	(	(	PUNCT
ejpam-6139	554	25	kµ	kµ	PROPN
ejpam-6139	554	26	)	)	PUNCT
ejpam-6139	554	27	α	α	PROPN
ejpam-6139	555	1	k	k	PROPN
ejpam-6139	555	2	γ	γ	X
ejpam-6139	555	3	(	(	PUNCT
ejpam-6139	555	4	α	α	NOUN
ejpam-6139	555	5	k	k	PROPN
ejpam-6139	556	1	+	+	PROPN
ejpam-6139	556	2	1	1	X
ejpam-6139	556	3	)	)	PUNCT
ejpam-6139	556	4	(	(	PUNCT
ejpam-6139	556	5	α	α	PROPN
ejpam-6139	556	6	k	k	PROPN
ejpam-6139	556	7	j	j	PROPN
ejpam-6139	556	8	µ	µ	X
ejpam-6139	556	9	(	(	PUNCT
ejpam-6139	556	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	556	11	η	η	PROPN
ejpam-6139	556	12	−	−	PROPN
ejpam-6139	556	13	h(ν	h(ν	PROPN
ejpam-6139	556	14	)	)	PUNCT
ejpam-6139	556	15	+	+	NOUN
ejpam-6139	556	16	α	α	NOUN
ejpam-6139	556	17	k	k	X
ejpam-6139	556	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	556	19	η	η	PROPN
ejpam-6139	556	20	+	+	PROPN
ejpam-6139	556	21	h(ω	h(ω	PROPN
ejpam-6139	556	22	)	)	PUNCT
ejpam-6139	556	23	)	)	PUNCT
ejpam-6139	557	1	+	+	X
ejpam-6139	557	2	υk[µ	υk[µ	PROPN
ejpam-6139	557	3	,	,	PUNCT
ejpam-6139	557	4	α	α	NOUN
ejpam-6139	557	5	]	]	X
ejpam-6139	557	6	−	−	PROPN
ejpam-6139	557	7	1	1	NUM
ejpam-6139	557	8	η	η	PROPN
ejpam-6139	557	9	(	(	PUNCT
ejpam-6139	557	10	h	h	PROPN
ejpam-6139	557	11	(	(	PUNCT
ejpam-6139	557	12	η	η	PROPN
ejpam-6139	557	13	−	−	PROPN
ejpam-6139	557	14	1	1	NUM
ejpam-6139	557	15	η	η	PROPN
ejpam-6139	557	16	ν	ν	X
ejpam-6139	557	17	+	+	PROPN
ejpam-6139	557	18	1	1	NUM
ejpam-6139	557	19	η	η	PROPN
ejpam-6139	557	20	ω	ω	PROPN
ejpam-6139	557	21	)	)	PUNCT
ejpam-6139	558	1	+	+	CCONJ
ejpam-6139	558	2	h	h	NOUN
ejpam-6139	558	3	(	(	PUNCT
ejpam-6139	558	4	1	1	NUM
ejpam-6139	558	5	η	η	X
ejpam-6139	558	6	ν	ν	X
ejpam-6139	558	7	+	+	CCONJ
ejpam-6139	558	8	η	η	PROPN
ejpam-6139	558	9	−	−	PROPN
ejpam-6139	558	10	1	1	NUM
ejpam-6139	558	11	η	η	PROPN
ejpam-6139	558	12	ω	ω	PROPN
ejpam-6139	558	13	)	)	PUNCT
ejpam-6139	558	14	)	)	PUNCT
ejpam-6139	559	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	559	2	≤	≤	NOUN
ejpam-6139	559	3	(	(	PUNCT
ejpam-6139	559	4	ω	ω	NUM
ejpam-6139	559	5	−	−	PROPN
ejpam-6139	559	6	ν)2	ν)2	PROPN
ejpam-6139	559	7	η3	η3	PROPN
ejpam-6139	559	8	(	(	PUNCT
ejpam-6139	559	9	kµ	kµ	PROPN
ejpam-6139	559	10	)	)	PUNCT
ejpam-6139	559	11	α	α	PROPN
ejpam-6139	559	12	k	k	X
ejpam-6139	560	1	[	[	X
ejpam-6139	560	2	∫	∫	PROPN
ejpam-6139	560	3	1	1	NUM
ejpam-6139	560	4	0	0	NUM
ejpam-6139	560	5	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	560	6	t	t	NOUN
ejpam-6139	560	7	0	0	NUM
ejpam-6139	561	1	(	(	PUNCT
ejpam-6139	561	2	1−	1−	NUM
ejpam-6139	561	3	(	(	PUNCT
ejpam-6139	561	4	1−	1−	NUM
ejpam-6139	561	5	φ)µ	φ)µ	NOUN
ejpam-6139	561	6	kµ	kµ	NOUN
ejpam-6139	561	7	)	)	PUNCT
ejpam-6139	562	1	α	α	PROPN
ejpam-6139	562	2	k	k	X
ejpam-6139	562	3	dφ	dφ	ADP
ejpam-6139	562	4	∣∣∣∣((η	∣∣∣∣((η	PRON
ejpam-6139	562	5	−	−	PROPN
ejpam-6139	562	6	t	t	PROPN
ejpam-6139	562	7	η	η	PROPN
ejpam-6139	562	8	)	)	PUNCT
ejpam-6139	562	9	s	s	PART
ejpam-6139	563	1	|h′′(ν)|+	|h′′(ν)|+	PROPN
ejpam-6139	563	2	(	(	PUNCT
ejpam-6139	563	3	t	t	PROPN
ejpam-6139	563	4	η	η	PROPN
ejpam-6139	563	5	)	)	PUNCT
ejpam-6139	563	6	s	s	PART
ejpam-6139	563	7	|h′′(ω)|	|h′′(ω)|	NOUN
ejpam-6139	563	8	)	)	PUNCT
ejpam-6139	563	9	dt	dt	VERB
ejpam-6139	564	1	+	+	CCONJ
ejpam-6139	564	2	∫	∫	PROPN
ejpam-6139	564	3	1	1	NUM
ejpam-6139	564	4	0	0	NUM
ejpam-6139	564	5	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	564	6	t	t	NOUN
ejpam-6139	564	7	0	0	NUM
ejpam-6139	565	1	(	(	PUNCT
ejpam-6139	565	2	1−	1−	NUM
ejpam-6139	565	3	(	(	PUNCT
ejpam-6139	565	4	1−	1−	NUM
ejpam-6139	565	5	φ)µ	φ)µ	NOUN
ejpam-6139	565	6	kµ	kµ	NOUN
ejpam-6139	565	7	)	)	PUNCT
ejpam-6139	566	1	α	α	PROPN
ejpam-6139	566	2	k	k	X
ejpam-6139	566	3	dφ	dφ	ADP
ejpam-6139	566	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	566	5	(	(	PUNCT
ejpam-6139	566	6	(	(	PUNCT
ejpam-6139	566	7	t	t	PROPN
ejpam-6139	566	8	η	η	PROPN
ejpam-6139	566	9	)	)	PUNCT
ejpam-6139	566	10	s	s	PART
ejpam-6139	567	1	|h′′(ν)|+	|h′′(ν)|+	PROPN
ejpam-6139	567	2	(	(	PUNCT
ejpam-6139	567	3	η	η	PROPN
ejpam-6139	567	4	−	−	PROPN
ejpam-6139	567	5	t	t	PROPN
ejpam-6139	567	6	η	η	PROPN
ejpam-6139	567	7	)	)	PUNCT
ejpam-6139	567	8	s	s	PART
ejpam-6139	567	9	|h′′(ω)|	|h′′(ω)|	NOUN
ejpam-6139	567	10	)	)	PUNCT
ejpam-6139	567	11	dt	dt	X
ejpam-6139	567	12	]	]	PUNCT
ejpam-6139	567	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	567	14	ηµ	ηµ	VERB
ejpam-6139	567	15	α	α	PROPN
ejpam-6139	567	16	k	k	X
ejpam-6139	567	17	−1	−1	PROPN
ejpam-6139	567	18	(	(	PUNCT
ejpam-6139	567	19	ω	ω	PROPN
ejpam-6139	567	20	−	−	PROPN
ejpam-6139	567	21	ν)µ	ν)µ	ADV
ejpam-6139	567	22	α	α	PROPN
ejpam-6139	567	23	k	k	PROPN
ejpam-6139	567	24	(	(	PUNCT
ejpam-6139	567	25	kµ	kµ	PROPN
ejpam-6139	567	26	)	)	PUNCT
ejpam-6139	568	1	α	α	PROPN
ejpam-6139	568	2	k	k	PROPN
ejpam-6139	568	3	γ	γ	X
ejpam-6139	568	4	(	(	PUNCT
ejpam-6139	568	5	α	α	NOUN
ejpam-6139	568	6	k	k	PROPN
ejpam-6139	569	1	+	+	PROPN
ejpam-6139	569	2	1	1	X
ejpam-6139	569	3	)	)	PUNCT
ejpam-6139	569	4	(	(	PUNCT
ejpam-6139	569	5	α	α	PROPN
ejpam-6139	569	6	k	k	PROPN
ejpam-6139	569	7	j	j	PROPN
ejpam-6139	569	8	µ	µ	X
ejpam-6139	569	9	(	(	PUNCT
ejpam-6139	569	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	569	11	η	η	PROPN
ejpam-6139	569	12	−	−	PROPN
ejpam-6139	569	13	h(ν	h(ν	PROPN
ejpam-6139	569	14	)	)	PUNCT
ejpam-6139	569	15	+	+	NOUN
ejpam-6139	569	16	α	α	NOUN
ejpam-6139	569	17	k	k	X
ejpam-6139	569	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	569	19	η	η	PROPN
ejpam-6139	569	20	+	+	PROPN
ejpam-6139	569	21	h(ω	h(ω	PROPN
ejpam-6139	569	22	)	)	PUNCT
ejpam-6139	569	23	)	)	PUNCT
ejpam-6139	570	1	+	+	X
ejpam-6139	570	2	υk[µ	υk[µ	PROPN
ejpam-6139	570	3	,	,	PUNCT
ejpam-6139	570	4	α	α	NOUN
ejpam-6139	570	5	]	]	X
ejpam-6139	570	6	−	−	PROPN
ejpam-6139	570	7	1	1	NUM
ejpam-6139	570	8	η	η	PROPN
ejpam-6139	570	9	(	(	PUNCT
ejpam-6139	570	10	h	h	PROPN
ejpam-6139	570	11	(	(	PUNCT
ejpam-6139	570	12	η	η	PROPN
ejpam-6139	570	13	−	−	PROPN
ejpam-6139	570	14	1	1	NUM
ejpam-6139	570	15	η	η	PROPN
ejpam-6139	570	16	ν	ν	X
ejpam-6139	570	17	+	+	PROPN
ejpam-6139	570	18	1	1	NUM
ejpam-6139	570	19	η	η	PROPN
ejpam-6139	570	20	ω	ω	PROPN
ejpam-6139	570	21	)	)	PUNCT
ejpam-6139	571	1	+	+	CCONJ
ejpam-6139	571	2	h	h	NOUN
ejpam-6139	571	3	(	(	PUNCT
ejpam-6139	571	4	1	1	NUM
ejpam-6139	571	5	η	η	X
ejpam-6139	571	6	ν	ν	X
ejpam-6139	571	7	+	+	CCONJ
ejpam-6139	571	8	η	η	PROPN
ejpam-6139	571	9	−	−	PROPN
ejpam-6139	571	10	1	1	NUM
ejpam-6139	571	11	η	η	PROPN
ejpam-6139	571	12	ω	ω	PROPN
ejpam-6139	571	13	)	)	PUNCT
ejpam-6139	571	14	)	)	PUNCT
ejpam-6139	572	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	572	2	(	(	PUNCT
ejpam-6139	572	3	38	38	NUM
ejpam-6139	572	4	)	)	PUNCT
ejpam-6139	572	5	≤	≤	NOUN
ejpam-6139	572	6	(	(	PUNCT
ejpam-6139	572	7	ω	ω	NUM
ejpam-6139	572	8	−	−	PROPN
ejpam-6139	572	9	ν)2	ν)2	PROPN
ejpam-6139	572	10	η3	η3	PROPN
ejpam-6139	572	11	(	(	PUNCT
ejpam-6139	572	12	kµ	kµ	PROPN
ejpam-6139	572	13	)	)	PUNCT
ejpam-6139	572	14	α	α	PROPN
ejpam-6139	573	1	k	k	NOUN
ejpam-6139	573	2	∫	∫	PROPN
ejpam-6139	573	3	1	1	NUM
ejpam-6139	573	4	0	0	NUM
ejpam-6139	573	5	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	573	6	t	t	NOUN
ejpam-6139	573	7	0	0	NUM
ejpam-6139	574	1	(	(	PUNCT
ejpam-6139	574	2	1−	1−	NUM
ejpam-6139	574	3	(	(	PUNCT
ejpam-6139	574	4	1−	1−	NUM
ejpam-6139	574	5	φ)µ	φ)µ	NOUN
ejpam-6139	574	6	kµ	kµ	NOUN
ejpam-6139	574	7	)	)	PUNCT
ejpam-6139	575	1	α	α	PROPN
ejpam-6139	575	2	k	k	X
ejpam-6139	575	3	dφ	dφ	ADP
ejpam-6139	575	4	∣∣∣∣(ts	∣∣∣∣(ts	PROPN
ejpam-6139	575	5	+	+	CCONJ
ejpam-6139	575	6	(	(	PUNCT
ejpam-6139	575	7	η	η	PROPN
ejpam-6139	575	8	−	−	PROPN
ejpam-6139	575	9	t)s	t)s	ADV
ejpam-6139	575	10	)	)	PUNCT
ejpam-6139	576	1	dt	dt	X
ejpam-6139	576	2	×	×	NOUN
ejpam-6139	576	3	(	(	PUNCT
ejpam-6139	576	4	|h′′(ν)|+	|h′′(ν)|+	X
ejpam-6139	576	5	|h′′(ω)|	|h′′(ω)|	INTJ
ejpam-6139	576	6	ηs	ηs	NOUN
ejpam-6139	576	7	)	)	PUNCT
ejpam-6139	576	8	.	.	PUNCT
ejpam-6139	577	1	(	(	PUNCT
ejpam-6139	577	2	39	39	NUM
ejpam-6139	577	3	)	)	PUNCT
ejpam-6139	577	4	consider	consider	VERB
ejpam-6139	577	5	ϖk[µ	ϖk[µ	PROPN
ejpam-6139	577	6	,	,	PUNCT
ejpam-6139	577	7	α	α	NOUN
ejpam-6139	577	8	]	]	X
ejpam-6139	577	9	=	=	X
ejpam-6139	577	10	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	577	11	t	t	NOUN
ejpam-6139	577	12	0	0	NUM
ejpam-6139	577	13	(	(	PUNCT
ejpam-6139	577	14	1−	1−	NUM
ejpam-6139	577	15	(	(	PUNCT
ejpam-6139	577	16	1−	1−	NUM
ejpam-6139	577	17	φ)µ	φ)µ	NOUN
ejpam-6139	577	18	kµ	kµ	NOUN
ejpam-6139	577	19	)	)	PUNCT
ejpam-6139	578	1	α	α	PROPN
ejpam-6139	578	2	k	k	NOUN
ejpam-6139	578	3	dφ	dφ	ADP
ejpam-6139	578	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	578	5	m.	m.	NOUN
ejpam-6139	578	6	samraiz	samraiz	PROPN
ejpam-6139	578	7	et	et	PROPN
ejpam-6139	578	8	al	al	PROPN
ejpam-6139	578	9	.	.	PUNCT
ejpam-6139	578	10	/	/	SYM
ejpam-6139	578	11	eur	eur	PROPN
ejpam-6139	578	12	.	.	PUNCT
ejpam-6139	579	1	j.	j.	PROPN
ejpam-6139	579	2	pure	pure	PROPN
ejpam-6139	579	3	appl	appl	PROPN
ejpam-6139	579	4	.	.	PROPN
ejpam-6139	579	5	math	math	PROPN
ejpam-6139	579	6	,	,	PUNCT
ejpam-6139	579	7	18	18	NUM
ejpam-6139	579	8	(	(	PUNCT
ejpam-6139	579	9	4	4	NUM
ejpam-6139	579	10	)	)	PUNCT
ejpam-6139	579	11	(	(	PUNCT
ejpam-6139	579	12	2025	2025	NUM
ejpam-6139	579	13	)	)	PUNCT
ejpam-6139	579	14	,	,	PUNCT
ejpam-6139	579	15	6139	6139	NUM
ejpam-6139	579	16	22	22	NUM
ejpam-6139	579	17	of	of	ADP
ejpam-6139	579	18	34	34	NUM
ejpam-6139	579	19	assuming	assume	VERB
ejpam-6139	579	20	p	p	PROPN
ejpam-6139	579	21	=	=	SYM
ejpam-6139	579	22	1−	1−	NUM
ejpam-6139	579	23	(	(	PUNCT
ejpam-6139	579	24	1−	1−	NUM
ejpam-6139	579	25	φ)µ	φ)µ	NOUN
ejpam-6139	579	26	dφ	dφ	X
ejpam-6139	579	27	=	=	SYM
ejpam-6139	579	28	1	1	NUM
ejpam-6139	579	29	µ	µ	X
ejpam-6139	579	30	(	(	PUNCT
ejpam-6139	579	31	1−	1−	NUM
ejpam-6139	579	32	p	p	NOUN
ejpam-6139	579	33	)	)	PUNCT
ejpam-6139	579	34	1	1	NUM
ejpam-6139	579	35	µ	µ	NUM
ejpam-6139	579	36	−1	−1	NOUN
ejpam-6139	579	37	dp	dp	NOUN
ejpam-6139	579	38	ϖk[µ	ϖk[µ	PROPN
ejpam-6139	579	39	,	,	PUNCT
ejpam-6139	579	40	α	α	NOUN
ejpam-6139	579	41	]	]	X
ejpam-6139	579	42	=	=	SYM
ejpam-6139	579	43	1	1	NUM
ejpam-6139	579	44	µ	µ	X
ejpam-6139	579	45	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	579	46	1	1	NUM
ejpam-6139	579	47	(	(	PUNCT
ejpam-6139	579	48	kµ	kµ	PROPN
ejpam-6139	579	49	)	)	PUNCT
ejpam-6139	579	50	α	α	PROPN
ejpam-6139	580	1	k	k	PROPN
ejpam-6139	580	2	∫	∫	PROPN
ejpam-6139	581	1	1−(1−t)µ	1−(1−t)µ	NUM
ejpam-6139	581	2	0	0	PUNCT
ejpam-6139	582	1	p	p	X
ejpam-6139	582	2	(	(	PUNCT
ejpam-6139	582	3	α	α	NOUN
ejpam-6139	582	4	k	k	NOUN
ejpam-6139	582	5	+1)−1(1−	+1)−1(1−	NUM
ejpam-6139	582	6	p	p	X
ejpam-6139	582	7	)	)	PUNCT
ejpam-6139	582	8	1	1	NUM
ejpam-6139	582	9	µ	µ	PRON
ejpam-6139	582	10	−1	−1	NOUN
ejpam-6139	582	11	dp	dp	NOUN
ejpam-6139	582	12	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	582	13	by	by	ADP
ejpam-6139	582	14	using	use	VERB
ejpam-6139	582	15	definition	definition	NOUN
ejpam-6139	582	16	of	of	ADP
ejpam-6139	582	17	incomplete	incomplete	ADJ
ejpam-6139	582	18	beta	beta	NOUN
ejpam-6139	582	19	function	function	NOUN
ejpam-6139	582	20	,	,	PUNCT
ejpam-6139	582	21	we	we	PRON
ejpam-6139	582	22	can	can	AUX
ejpam-6139	582	23	write	write	VERB
ejpam-6139	582	24	ϖk[µ	ϖk[µ	PROPN
ejpam-6139	582	25	,	,	PUNCT
ejpam-6139	582	26	α	α	NOUN
ejpam-6139	582	27	]	]	X
ejpam-6139	582	28	=	=	SYM
ejpam-6139	582	29	1	1	NUM
ejpam-6139	582	30	µ	µ	X
ejpam-6139	582	31	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	582	32	1	1	NUM
ejpam-6139	582	33	(	(	PUNCT
ejpam-6139	582	34	kµ	kµ	PROPN
ejpam-6139	582	35	)	)	PUNCT
ejpam-6139	582	36	α	α	PROPN
ejpam-6139	583	1	k	k	PROPN
ejpam-6139	583	2	b	b	PROPN
ejpam-6139	583	3	(	(	PUNCT
ejpam-6139	583	4	α	α	NOUN
ejpam-6139	583	5	k	k	PROPN
ejpam-6139	584	1	+	+	PROPN
ejpam-6139	584	2	1	1	NUM
ejpam-6139	584	3	,	,	PUNCT
ejpam-6139	584	4	1	1	NUM
ejpam-6139	584	5	µ	µ	NOUN
ejpam-6139	584	6	,	,	PUNCT
ejpam-6139	584	7	1−	1−	NUM
ejpam-6139	584	8	(	(	PUNCT
ejpam-6139	584	9	1−	1−	NUM
ejpam-6139	584	10	t)µ	t)µ	NOUN
ejpam-6139	584	11	)	)	PUNCT
ejpam-6139	584	12	∣∣∣∣.	∣∣∣∣.	NOUN
ejpam-6139	584	13	(	(	PUNCT
ejpam-6139	584	14	40	40	NUM
ejpam-6139	584	15	)	)	PUNCT
ejpam-6139	584	16	substituting	substitute	VERB
ejpam-6139	584	17	(	(	PUNCT
ejpam-6139	584	18	40	40	NUM
ejpam-6139	584	19	)	)	PUNCT
ejpam-6139	584	20	in	in	ADP
ejpam-6139	584	21	equation	equation	NOUN
ejpam-6139	584	22	(	(	PUNCT
ejpam-6139	584	23	38	38	NUM
ejpam-6139	584	24	)	)	PUNCT
ejpam-6139	584	25	,	,	PUNCT
ejpam-6139	584	26	we	we	PRON
ejpam-6139	584	27	obtained	obtain	VERB
ejpam-6139	584	28	≤	≤	NOUN
ejpam-6139	584	29	(	(	PUNCT
ejpam-6139	584	30	ω	ω	NUM
ejpam-6139	584	31	−	−	PROPN
ejpam-6139	584	32	ν)2	ν)2	PROPN
ejpam-6139	584	33	η3	η3	PROPN
ejpam-6139	584	34	(	(	PUNCT
ejpam-6139	584	35	kµ	kµ	PROPN
ejpam-6139	584	36	)	)	PUNCT
ejpam-6139	584	37	α	α	PROPN
ejpam-6139	585	1	k	k	NOUN
ejpam-6139	585	2	∫	∫	PROPN
ejpam-6139	585	3	1	1	NUM
ejpam-6139	585	4	0	0	NUM
ejpam-6139	585	5	1	1	NUM
ejpam-6139	585	6	µ	µ	PRON
ejpam-6139	585	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	585	8	1	1	NUM
ejpam-6139	585	9	(	(	PUNCT
ejpam-6139	585	10	kµ	kµ	PROPN
ejpam-6139	585	11	)	)	PUNCT
ejpam-6139	585	12	α	α	PROPN
ejpam-6139	586	1	k	k	PROPN
ejpam-6139	586	2	b	b	PROPN
ejpam-6139	586	3	(	(	PUNCT
ejpam-6139	586	4	α	α	NOUN
ejpam-6139	586	5	k	k	PROPN
ejpam-6139	587	1	+	+	PROPN
ejpam-6139	587	2	1	1	NUM
ejpam-6139	587	3	,	,	PUNCT
ejpam-6139	587	4	1	1	NUM
ejpam-6139	587	5	µ	µ	NOUN
ejpam-6139	587	6	,	,	PUNCT
ejpam-6139	587	7	1−	1−	NUM
ejpam-6139	587	8	(	(	PUNCT
ejpam-6139	587	9	1−	1−	NUM
ejpam-6139	587	10	t)µ	t)µ	NOUN
ejpam-6139	587	11	)	)	PUNCT
ejpam-6139	588	1	∣∣∣∣(ts	∣∣∣∣(t	NOUN
ejpam-6139	588	2	+	+	CCONJ
ejpam-6139	588	3	(	(	PUNCT
ejpam-6139	588	4	η	η	PROPN
ejpam-6139	588	5	−	−	PROPN
ejpam-6139	588	6	t)s	t)s	ADV
ejpam-6139	588	7	)	)	PUNCT
ejpam-6139	588	8	dt	dt	X
ejpam-6139	589	1	×	×	NOUN
ejpam-6139	589	2	(	(	PUNCT
ejpam-6139	589	3	|h′′(ν)|+	|h′′(ν)|+	X
ejpam-6139	589	4	|h′′(ω)|	|h′′(ω)|	INTJ
ejpam-6139	589	5	ηs	ηs	NOUN
ejpam-6139	589	6	)	)	PUNCT
ejpam-6139	589	7	.	.	PUNCT
ejpam-6139	590	1	(	(	PUNCT
ejpam-6139	590	2	41	41	NUM
ejpam-6139	590	3	)	)	PUNCT
ejpam-6139	590	4	ultimately	ultimately	ADV
ejpam-6139	590	5	,	,	PUNCT
ejpam-6139	590	6	the	the	DET
ejpam-6139	590	7	expected	expect	VERB
ejpam-6139	590	8	outcome	outcome	NOUN
ejpam-6139	590	9	has	have	AUX
ejpam-6139	590	10	been	be	AUX
ejpam-6139	590	11	reached	reach	VERB
ejpam-6139	590	12	.	.	PUNCT
ejpam-6139	591	1	remark	remark	NOUN
ejpam-6139	591	2	8	8	NUM
ejpam-6139	591	3	.	.	PUNCT
ejpam-6139	592	1	if	if	SCONJ
ejpam-6139	592	2	we	we	PRON
ejpam-6139	592	3	set	set	VERB
ejpam-6139	592	4	parameters	parameter	NOUN
ejpam-6139	592	5	as	as	ADP
ejpam-6139	592	6	η	η	PROPN
ejpam-6139	592	7	=	=	PROPN
ejpam-6139	592	8	2	2	NUM
ejpam-6139	592	9	,	,	PUNCT
ejpam-6139	592	10	s	s	NOUN
ejpam-6139	592	11	=	=	SYM
ejpam-6139	592	12	1	1	NUM
ejpam-6139	592	13	and	and	CCONJ
ejpam-6139	592	14	k=1	k=1	X
ejpam-6139	593	1	in	in	ADP
ejpam-6139	593	2	(	(	PUNCT
ejpam-6139	593	3	36	36	NUM
ejpam-6139	593	4	)	)	PUNCT
ejpam-6139	593	5	,	,	PUNCT
ejpam-6139	593	6	then	then	ADV
ejpam-6139	593	7	theorem	theorem	VERB
ejpam-6139	593	8	4	4	NUM
ejpam-6139	593	9	leads	lead	VERB
ejpam-6139	593	10	to	to	ADP
ejpam-6139	593	11	[	[	X
ejpam-6139	593	12	44	44	NUM
ejpam-6139	593	13	]	]	PUNCT
ejpam-6139	593	14	theorem	theorem	NOUN
ejpam-6139	593	15	11	11	NUM
ejpam-6139	593	16	.	.	PUNCT
ejpam-6139	593	17	remark	remark	NOUN
ejpam-6139	593	18	9	9	NUM
ejpam-6139	593	19	.	.	PUNCT
ejpam-6139	594	1	if	if	SCONJ
ejpam-6139	594	2	we	we	PRON
ejpam-6139	594	3	set	set	VERB
ejpam-6139	594	4	η	η	PROPN
ejpam-6139	594	5	=	=	PROPN
ejpam-6139	594	6	2	2	NUM
ejpam-6139	594	7	,	,	PUNCT
ejpam-6139	594	8	s	s	PART
ejpam-6139	594	9	=	=	SYM
ejpam-6139	594	10	1	1	NUM
ejpam-6139	594	11	,	,	PUNCT
ejpam-6139	594	12	k	k	NOUN
ejpam-6139	594	13	=	=	SYM
ejpam-6139	594	14	1	1	NUM
ejpam-6139	594	15	and	and	CCONJ
ejpam-6139	594	16	µ	µ	X
ejpam-6139	594	17	=	=	SYM
ejpam-6139	594	18	1	1	NUM
ejpam-6139	594	19	in	in	ADP
ejpam-6139	594	20	(	(	PUNCT
ejpam-6139	594	21	36	36	NUM
ejpam-6139	594	22	)	)	PUNCT
ejpam-6139	594	23	then	then	ADV
ejpam-6139	594	24	our	our	PRON
ejpam-6139	594	25	result	result	NOUN
ejpam-6139	594	26	reduced	reduce	VERB
ejpam-6139	594	27	to	to	ADP
ejpam-6139	594	28	[	[	X
ejpam-6139	594	29	46	46	NUM
ejpam-6139	594	30	]	]	PUNCT
ejpam-6139	594	31	theorem	theorem	VERB
ejpam-6139	594	32	1.5	1.5	NUM
ejpam-6139	594	33	.	.	PUNCT
ejpam-6139	595	1	remark	remark	NOUN
ejpam-6139	595	2	10	10	NUM
ejpam-6139	595	3	.	.	PUNCT
ejpam-6139	596	1	if	if	SCONJ
ejpam-6139	596	2	we	we	PRON
ejpam-6139	596	3	set	set	VERB
ejpam-6139	596	4	η	η	PROPN
ejpam-6139	596	5	=	=	PROPN
ejpam-6139	596	6	2	2	NUM
ejpam-6139	596	7	,	,	PUNCT
ejpam-6139	596	8	s	s	PART
ejpam-6139	596	9	=	=	SYM
ejpam-6139	596	10	1	1	NUM
ejpam-6139	596	11	,	,	PUNCT
ejpam-6139	596	12	k	k	NOUN
ejpam-6139	596	13	=	=	SYM
ejpam-6139	596	14	1	1	NUM
ejpam-6139	596	15	,	,	PUNCT
ejpam-6139	596	16	µ	µ	X
ejpam-6139	596	17	=	=	SYM
ejpam-6139	596	18	1	1	NUM
ejpam-6139	596	19	and	and	CCONJ
ejpam-6139	596	20	α	α	NOUN
ejpam-6139	596	21	=	=	NOUN
ejpam-6139	596	22	1	1	NUM
ejpam-6139	596	23	simultaneously	simultaneously	ADV
ejpam-6139	596	24	in	in	ADP
ejpam-6139	596	25	36	36	NUM
ejpam-6139	596	26	,	,	PUNCT
ejpam-6139	596	27	then	then	ADV
ejpam-6139	596	28	theorem	theorem	VERB
ejpam-6139	596	29	4	4	NUM
ejpam-6139	596	30	and	and	CCONJ
ejpam-6139	596	31	[	[	X
ejpam-6139	596	32	44	44	NUM
ejpam-6139	596	33	]	]	PUNCT
ejpam-6139	596	34	,	,	PUNCT
ejpam-6139	596	35	proposition	proposition	NOUN
ejpam-6139	596	36	1	1	NUM
ejpam-6139	596	37	become	become	VERB
ejpam-6139	596	38	identical	identical	ADJ
ejpam-6139	596	39	.	.	PUNCT
ejpam-6139	597	1	example	example	NOUN
ejpam-6139	598	1	4	4	NUM
ejpam-6139	598	2	.	.	PUNCT
ejpam-6139	598	3	this	this	DET
ejpam-6139	598	4	example	example	NOUN
ejpam-6139	598	5	demonstrates	demonstrate	VERB
ejpam-6139	598	6	the	the	DET
ejpam-6139	598	7	application	application	NOUN
ejpam-6139	598	8	of	of	ADP
ejpam-6139	598	9	theorem	theorem	NOUN
ejpam-6139	598	10	4	4	NUM
ejpam-6139	598	11	using	use	VERB
ejpam-6139	598	12	both	both	CCONJ
ejpam-6139	598	13	graphical	graphical	ADJ
ejpam-6139	598	14	and	and	CCONJ
ejpam-6139	598	15	numerical	numerical	ADJ
ejpam-6139	598	16	methods	method	NOUN
ejpam-6139	598	17	.	.	PUNCT
ejpam-6139	599	1	we	we	PRON
ejpam-6139	599	2	consider	consider	VERB
ejpam-6139	599	3	the	the	DET
ejpam-6139	599	4	function	function	NOUN
ejpam-6139	599	5	h(x	h(x	PROPN
ejpam-6139	599	6	)	)	PUNCT
ejpam-6139	599	7	=	=	PUNCT
ejpam-6139	600	1	x6	x6	PROPN
ejpam-6139	600	2	+	+	SYM
ejpam-6139	600	3	2x4	2x4	NUM
ejpam-6139	600	4	,	,	PUNCT
ejpam-6139	600	5	defined	define	VERB
ejpam-6139	600	6	on	on	ADP
ejpam-6139	600	7	the	the	DET
ejpam-6139	600	8	interval	interval	NOUN
ejpam-6139	600	9	[	[	X
ejpam-6139	600	10	2	2	NUM
ejpam-6139	600	11	,	,	PUNCT
ejpam-6139	600	12	7	7	NUM
ejpam-6139	600	13	]	]	PUNCT
ejpam-6139	600	14	,	,	PUNCT
ejpam-6139	600	15	and	and	CCONJ
ejpam-6139	600	16	evaluate	evaluate	VERB
ejpam-6139	600	17	the	the	DET
ejpam-6139	600	18	inequality	inequality	NOUN
ejpam-6139	600	19	under	under	ADP
ejpam-6139	600	20	specific	specific	ADJ
ejpam-6139	600	21	parameter	parameter	NOUN
ejpam-6139	600	22	values	value	NOUN
ejpam-6139	600	23	:	:	PUNCT
ejpam-6139	601	1	k	k	X
ejpam-6139	601	2	=	=	SYM
ejpam-6139	601	3	3,s	3,s	NUM
ejpam-6139	601	4	=	=	SYM
ejpam-6139	601	5	1	1	NUM
ejpam-6139	601	6	α	α	NOUN
ejpam-6139	601	7	=	=	SYM
ejpam-6139	601	8	4	4	NUM
ejpam-6139	601	9	,	,	PUNCT
ejpam-6139	601	10	and	and	CCONJ
ejpam-6139	601	11	η	η	PROPN
ejpam-6139	601	12	=	=	PROPN
ejpam-6139	601	13	8	8	PROPN
ejpam-6139	601	14	.	.	PUNCT
ejpam-6139	602	1	explanation	explanation	NOUN
ejpam-6139	602	2	:	:	PUNCT
ejpam-6139	602	3	figure	figure	VERB
ejpam-6139	602	4	7	7	NUM
ejpam-6139	602	5	presents	present	VERB
ejpam-6139	602	6	a	a	DET
ejpam-6139	602	7	2d	2d	NUM
ejpam-6139	602	8	plot	plot	NOUN
ejpam-6139	602	9	illustrating	illustrate	VERB
ejpam-6139	602	10	the	the	DET
ejpam-6139	602	11	behavior	behavior	NOUN
ejpam-6139	602	12	of	of	ADP
ejpam-6139	602	13	both	both	DET
ejpam-6139	602	14	sides	side	NOUN
ejpam-6139	602	15	of	of	ADP
ejpam-6139	602	16	the	the	DET
ejpam-6139	602	17	inequality	inequality	NOUN
ejpam-6139	602	18	(	(	PUNCT
ejpam-6139	602	19	36	36	NUM
ejpam-6139	602	20	)	)	PUNCT
ejpam-6139	602	21	as	as	SCONJ
ejpam-6139	602	22	µ	µ	NOUN
ejpam-6139	602	23	varies	vary	VERB
ejpam-6139	602	24	within	within	ADP
ejpam-6139	602	25	(	(	PUNCT
ejpam-6139	602	26	0	0	NUM
ejpam-6139	602	27	,	,	PUNCT
ejpam-6139	602	28	1	1	NUM
ejpam-6139	602	29	]	]	PUNCT
ejpam-6139	602	30	.	.	PUNCT
ejpam-6139	603	1	the	the	DET
ejpam-6139	603	2	graph	graph	NOUN
ejpam-6139	603	3	confirms	confirm	VERB
ejpam-6139	603	4	that	that	SCONJ
ejpam-6139	603	5	the	the	DET
ejpam-6139	603	6	left	left	ADJ
ejpam-6139	603	7	-	-	PUNCT
ejpam-6139	603	8	hand	hand	NOUN
ejpam-6139	603	9	side	side	NOUN
ejpam-6139	603	10	remains	remain	VERB
ejpam-6139	603	11	within	within	ADP
ejpam-6139	603	12	the	the	DET
ejpam-6139	603	13	bounds	bound	NOUN
ejpam-6139	603	14	set	set	VERB
ejpam-6139	603	15	by	by	ADP
ejpam-6139	603	16	the	the	DET
ejpam-6139	603	17	right	right	ADJ
ejpam-6139	603	18	-	-	PUNCT
ejpam-6139	603	19	hand	hand	NOUN
ejpam-6139	603	20	side	side	NOUN
ejpam-6139	603	21	,	,	PUNCT
ejpam-6139	603	22	visually	visually	ADV
ejpam-6139	603	23	supporting	support	VERB
ejpam-6139	603	24	the	the	DET
ejpam-6139	603	25	theorem	theorem	NOUN
ejpam-6139	603	26	’s	’s	PART
ejpam-6139	603	27	validity	validity	NOUN
ejpam-6139	603	28	.	.	PUNCT
ejpam-6139	604	1	numerical	numerical	PROPN
ejpam-6139	604	2	computations	computation	NOUN
ejpam-6139	604	3	were	be	AUX
ejpam-6139	604	4	performed	perform	VERB
ejpam-6139	604	5	to	to	PART
ejpam-6139	604	6	compare	compare	VERB
ejpam-6139	604	7	lhs	lhs	PROPN
ejpam-6139	604	8	and	and	CCONJ
ejpam-6139	604	9	rhs	rhs	PROPN
ejpam-6139	604	10	values	value	NOUN
ejpam-6139	604	11	for	for	ADP
ejpam-6139	604	12	selected	select	VERB
ejpam-6139	604	13	values	value	NOUN
ejpam-6139	604	14	of	of	ADP
ejpam-6139	604	15	µ.	µ.	NOUN
ejpam-6139	604	16	a	a	DET
ejpam-6139	604	17	table	table	NOUN
ejpam-6139	604	18	summarizing	summarize	VERB
ejpam-6139	604	19	these	these	DET
ejpam-6139	604	20	results	result	NOUN
ejpam-6139	604	21	is	be	AUX
ejpam-6139	604	22	shown	show	VERB
ejpam-6139	604	23	in	in	ADP
ejpam-6139	604	24	figure	figure	NOUN
ejpam-6139	604	25	6	6	NUM
ejpam-6139	604	26	,	,	PUNCT
ejpam-6139	604	27	demonstrating	demonstrate	VERB
ejpam-6139	604	28	consistency	consistency	NOUN
ejpam-6139	604	29	between	between	ADP
ejpam-6139	604	30	the	the	DET
ejpam-6139	604	31	computed	computed	ADJ
ejpam-6139	604	32	values	value	NOUN
ejpam-6139	604	33	and	and	CCONJ
ejpam-6139	604	34	the	the	DET
ejpam-6139	604	35	inequality	inequality	NOUN
ejpam-6139	604	36	constraints	constraint	NOUN
ejpam-6139	604	37	.	.	PUNCT
ejpam-6139	605	1	m.	m.	NOUN
ejpam-6139	605	2	samraiz	samraiz	PROPN
ejpam-6139	605	3	et	et	PROPN
ejpam-6139	605	4	al	al	PROPN
ejpam-6139	605	5	.	.	PUNCT
ejpam-6139	605	6	/	/	SYM
ejpam-6139	605	7	eur	eur	PROPN
ejpam-6139	605	8	.	.	PUNCT
ejpam-6139	606	1	j.	j.	PROPN
ejpam-6139	606	2	pure	pure	PROPN
ejpam-6139	606	3	appl	appl	PROPN
ejpam-6139	606	4	.	.	PROPN
ejpam-6139	606	5	math	math	PROPN
ejpam-6139	606	6	,	,	PUNCT
ejpam-6139	606	7	18	18	NUM
ejpam-6139	606	8	(	(	PUNCT
ejpam-6139	606	9	4	4	NUM
ejpam-6139	606	10	)	)	PUNCT
ejpam-6139	606	11	(	(	PUNCT
ejpam-6139	606	12	2025	2025	NUM
ejpam-6139	606	13	)	)	PUNCT
ejpam-6139	606	14	,	,	PUNCT
ejpam-6139	606	15	6139	6139	NUM
ejpam-6139	606	16	23	23	NUM
ejpam-6139	606	17	of	of	ADP
ejpam-6139	606	18	34	34	NUM
ejpam-6139	606	19	figure	figure	NOUN
ejpam-6139	606	20	7	7	NUM
ejpam-6139	606	21	:	:	PUNCT
ejpam-6139	606	22	this	this	DET
ejpam-6139	606	23	figure	figure	NOUN
ejpam-6139	606	24	provides	provide	VERB
ejpam-6139	606	25	a	a	DET
ejpam-6139	606	26	graphical	graphical	ADJ
ejpam-6139	606	27	illustration	illustration	NOUN
ejpam-6139	606	28	of	of	ADP
ejpam-6139	606	29	theorem	theorem	NOUN
ejpam-6139	606	30	4	4	NUM
ejpam-6139	606	31	for	for	ADP
ejpam-6139	606	32	µ	µ	X
ejpam-6139	606	33	∈	∈	NOUN
ejpam-6139	606	34	(	(	PUNCT
ejpam-6139	606	35	0	0	NUM
ejpam-6139	606	36	,	,	PUNCT
ejpam-6139	606	37	1	1	NUM
ejpam-6139	606	38	]	]	PUNCT
ejpam-6139	606	39	.	.	PUNCT
ejpam-6139	607	1	table	table	NOUN
ejpam-6139	607	2	6	6	NUM
ejpam-6139	607	3	:	:	PUNCT
ejpam-6139	607	4	the	the	DET
ejpam-6139	607	5	table	table	NOUN
ejpam-6139	607	6	displays	display	VERB
ejpam-6139	607	7	numerical	numerical	ADJ
ejpam-6139	607	8	values	value	NOUN
ejpam-6139	607	9	corresponding	correspond	VERB
ejpam-6139	607	10	to	to	ADP
ejpam-6139	607	11	equation	equation	NOUN
ejpam-6139	607	12	(	(	PUNCT
ejpam-6139	607	13	36	36	NUM
ejpam-6139	607	14	)	)	PUNCT
ejpam-6139	607	15	for	for	ADP
ejpam-6139	607	16	µ	µ	PRON
ejpam-6139	607	17	∈	∈	NOUN
ejpam-6139	607	18	(	(	PUNCT
ejpam-6139	607	19	0	0	NUM
ejpam-6139	607	20	,	,	PUNCT
ejpam-6139	607	21	1	1	NUM
ejpam-6139	607	22	]	]	PUNCT
ejpam-6139	607	23	which	which	PRON
ejpam-6139	607	24	is	be	AUX
ejpam-6139	607	25	supporting	support	VERB
ejpam-6139	607	26	our	our	PRON
ejpam-6139	607	27	results	result	NOUN
ejpam-6139	607	28	.	.	PUNCT
ejpam-6139	608	1	µ	µ	DET
ejpam-6139	608	2	0.2	0.2	NUM
ejpam-6139	608	3	0.4	0.4	NUM
ejpam-6139	608	4	0.6	0.6	NUM
ejpam-6139	608	5	0.8	0.8	NUM
ejpam-6139	608	6	1	1	NUM
ejpam-6139	608	7	lhs	lhs	PROPN
ejpam-6139	608	8	65.30	65.30	NUM
ejpam-6139	608	9	144.68	144.68	NUM
ejpam-6139	608	10	221	221	NUM
ejpam-6139	608	11	291.37	291.37	NUM
ejpam-6139	608	12	355.37	355.37	NUM
ejpam-6139	608	13	rhs	rh	NOUN
ejpam-6139	608	14	85.95	85.95	NUM
ejpam-6139	608	15	189.87	189.87	NUM
ejpam-6139	608	16	289.29	289.29	NUM
ejpam-6139	608	17	380.54	380.54	NUM
ejpam-6139	608	18	463.19	463.19	NUM
ejpam-6139	608	19	extending	extend	VERB
ejpam-6139	608	20	the	the	DET
ejpam-6139	608	21	analysis	analysis	NOUN
ejpam-6139	608	22	,	,	PUNCT
ejpam-6139	608	23	a	a	DET
ejpam-6139	608	24	3d	3d	NUM
ejpam-6139	608	25	visualization	visualization	NOUN
ejpam-6139	608	26	was	be	AUX
ejpam-6139	608	27	generated	generate	VERB
ejpam-6139	608	28	by	by	ADP
ejpam-6139	608	29	varying	vary	VERB
ejpam-6139	608	30	α	α	NOUN
ejpam-6139	608	31	over	over	ADP
ejpam-6139	608	32	[	[	X
ejpam-6139	608	33	5	5	NUM
ejpam-6139	608	34	,	,	PUNCT
ejpam-6139	608	35	10	10	NUM
ejpam-6139	608	36	]	]	PUNCT
ejpam-6139	608	37	and	and	CCONJ
ejpam-6139	608	38	µ	µ	X
ejpam-6139	608	39	within	within	X
ejpam-6139	608	40	(	(	PUNCT
ejpam-6139	608	41	0	0	NUM
ejpam-6139	608	42	,	,	PUNCT
ejpam-6139	608	43	1	1	NUM
ejpam-6139	608	44	]	]	PUNCT
ejpam-6139	608	45	.	.	PUNCT
ejpam-6139	609	1	the	the	DET
ejpam-6139	609	2	resulting	result	VERB
ejpam-6139	609	3	surface	surface	NOUN
ejpam-6139	609	4	plot	plot	NOUN
ejpam-6139	609	5	,	,	PUNCT
ejpam-6139	609	6	shown	show	VERB
ejpam-6139	609	7	in	in	ADP
ejpam-6139	609	8	figure	figure	NOUN
ejpam-6139	609	9	8	8	NUM
ejpam-6139	609	10	,	,	PUNCT
ejpam-6139	609	11	demonstrates	demonstrate	VERB
ejpam-6139	609	12	that	that	SCONJ
ejpam-6139	609	13	the	the	DET
ejpam-6139	609	14	inequality	inequality	NOUN
ejpam-6139	609	15	holds	hold	VERB
ejpam-6139	609	16	robustly	robustly	ADV
ejpam-6139	609	17	across	across	ADP
ejpam-6139	609	18	these	these	DET
ejpam-6139	609	19	parameter	parameter	NOUN
ejpam-6139	609	20	ranges	range	NOUN
ejpam-6139	609	21	.	.	PUNCT
ejpam-6139	610	1	this	this	DET
ejpam-6139	610	2	multi	multi	ADJ
ejpam-6139	610	3	-	-	ADJ
ejpam-6139	610	4	faceted	faceted	ADJ
ejpam-6139	610	5	approach	approach	NOUN
ejpam-6139	610	6	figure	figure	NOUN
ejpam-6139	610	7	8	8	NUM
ejpam-6139	610	8	:	:	PUNCT
ejpam-6139	610	9	three	three	NUM
ejpam-6139	610	10	-	-	PUNCT
ejpam-6139	610	11	dimensional	dimensional	ADJ
ejpam-6139	610	12	representation	representation	NOUN
ejpam-6139	610	13	of	of	ADP
ejpam-6139	610	14	theorem	theorem	NOUN
ejpam-6139	610	15	4	4	NUM
ejpam-6139	610	16	validating	validate	VERB
ejpam-6139	610	17	the	the	DET
ejpam-6139	610	18	inequality	inequality	NOUN
ejpam-6139	610	19	across	across	ADP
ejpam-6139	610	20	varying	vary	VERB
ejpam-6139	610	21	α	α	PROPN
ejpam-6139	610	22	and	and	CCONJ
ejpam-6139	610	23	µ.	µ.	PROPN
ejpam-6139	610	24	highlights	highlight	NOUN
ejpam-6139	610	25	the	the	DET
ejpam-6139	610	26	validity	validity	NOUN
ejpam-6139	610	27	and	and	CCONJ
ejpam-6139	610	28	practical	practical	ADJ
ejpam-6139	610	29	applicability	applicability	NOUN
ejpam-6139	610	30	of	of	ADP
ejpam-6139	610	31	theorem	theorem	NOUN
ejpam-6139	610	32	4	4	NUM
ejpam-6139	610	33	,	,	PUNCT
ejpam-6139	610	34	confirming	confirm	VERB
ejpam-6139	610	35	its	its	PRON
ejpam-6139	610	36	effectiveness	effectiveness	NOUN
ejpam-6139	610	37	in	in	ADP
ejpam-6139	610	38	bounding	bound	VERB
ejpam-6139	610	39	the	the	DET
ejpam-6139	610	40	behavior	behavior	NOUN
ejpam-6139	610	41	of	of	ADP
ejpam-6139	610	42	h(x	h(x	PROPN
ejpam-6139	610	43	)	)	PUNCT
ejpam-6139	610	44	under	under	ADP
ejpam-6139	610	45	the	the	DET
ejpam-6139	610	46	specified	specified	ADJ
ejpam-6139	610	47	conditions	condition	NOUN
ejpam-6139	610	48	.	.	PUNCT
ejpam-6139	611	1	theorem	theorem	NOUN
ejpam-6139	611	2	5	5	NUM
ejpam-6139	611	3	.	.	PUNCT
ejpam-6139	612	1	assume	assume	VERB
ejpam-6139	612	2	h	h	NOUN
ejpam-6139	612	3	:	:	PUNCT
ejpam-6139	613	1	[	[	X
ejpam-6139	613	2	ν	ν	X
ejpam-6139	613	3	,	,	PUNCT
ejpam-6139	613	4	ω	ω	NOUN
ejpam-6139	613	5	]	]	X
ejpam-6139	613	6	→	→	PUNCT
ejpam-6139	613	7	r	r	NOUN
ejpam-6139	613	8	is	be	AUX
ejpam-6139	613	9	a	a	DET
ejpam-6139	613	10	twice	twice	ADV
ejpam-6139	613	11	continuously	continuously	ADV
ejpam-6139	613	12	differentiable	differentiable	ADJ
ejpam-6139	613	13	function	function	NOUN
ejpam-6139	613	14	over	over	ADP
ejpam-6139	613	15	(	(	PUNCT
ejpam-6139	613	16	ν	ν	PROPN
ejpam-6139	613	17	,	,	PUNCT
ejpam-6139	613	18	ω	ω	NOUN
ejpam-6139	613	19	)	)	PUNCT
ejpam-6139	613	20	,	,	PUNCT
ejpam-6139	613	21	with	with	ADP
ejpam-6139	613	22	h′′	h′′	PROPN
ejpam-6139	613	23	∈	∈	PROPN
ejpam-6139	613	24	l1([ν	l1([ν	PROPN
ejpam-6139	613	25	,	,	PUNCT
ejpam-6139	613	26	ω	ω	NOUN
ejpam-6139	613	27	]	]	NOUN
ejpam-6139	613	28	)	)	PUNCT
ejpam-6139	613	29	.	.	PUNCT
ejpam-6139	614	1	let	let	VERB
ejpam-6139	614	2	|h′′|q	|h′′|q	NOUN
ejpam-6139	614	3	be	be	AUX
ejpam-6139	614	4	convex	convex	ADJ
ejpam-6139	614	5	on	on	ADP
ejpam-6139	614	6	[	[	X
ejpam-6139	614	7	ν	ν	X
ejpam-6139	614	8	,	,	PUNCT
ejpam-6139	614	9	ω	ω	NOUN
ejpam-6139	614	10	]	]	X
ejpam-6139	614	11	,	,	PUNCT
ejpam-6139	614	12	where	where	SCONJ
ejpam-6139	614	13	q	q	PUNCT
ejpam-6139	614	14	>	>	X
ejpam-6139	614	15	1	1	NUM
ejpam-6139	614	16	,	,	PUNCT
ejpam-6139	614	17	then∣∣∣∣	then∣∣∣∣	NOUN
ejpam-6139	614	18	ηµ	ηµ	ADP
ejpam-6139	614	19	α	α	PROPN
ejpam-6139	614	20	k	k	X
ejpam-6139	614	21	−1	−1	PROPN
ejpam-6139	614	22	(	(	PUNCT
ejpam-6139	614	23	ω	ω	PROPN
ejpam-6139	614	24	−	−	PROPN
ejpam-6139	614	25	ν)µ	ν)µ	ADV
ejpam-6139	614	26	α	α	PROPN
ejpam-6139	614	27	k	k	PROPN
ejpam-6139	614	28	(	(	PUNCT
ejpam-6139	614	29	kµ	kµ	PROPN
ejpam-6139	614	30	)	)	PUNCT
ejpam-6139	615	1	α	α	PROPN
ejpam-6139	615	2	k	k	PROPN
ejpam-6139	615	3	γ	γ	X
ejpam-6139	615	4	(	(	PUNCT
ejpam-6139	615	5	α	α	NOUN
ejpam-6139	615	6	k	k	PROPN
ejpam-6139	616	1	+	+	PROPN
ejpam-6139	616	2	1	1	X
ejpam-6139	616	3	)	)	PUNCT
ejpam-6139	616	4	(	(	PUNCT
ejpam-6139	616	5	α	α	PROPN
ejpam-6139	616	6	k	k	PROPN
ejpam-6139	616	7	j	j	PROPN
ejpam-6139	616	8	µ	µ	X
ejpam-6139	616	9	(	(	PUNCT
ejpam-6139	616	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	616	11	η	η	PROPN
ejpam-6139	616	12	−	−	PROPN
ejpam-6139	616	13	h(ν	h(ν	PROPN
ejpam-6139	616	14	)	)	PUNCT
ejpam-6139	616	15	+	+	NOUN
ejpam-6139	616	16	α	α	NOUN
ejpam-6139	616	17	k	k	X
ejpam-6139	616	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	616	19	η	η	PROPN
ejpam-6139	616	20	+	+	PROPN
ejpam-6139	616	21	h(ω	h(ω	PROPN
ejpam-6139	616	22	)	)	PUNCT
ejpam-6139	616	23	)	)	PUNCT
ejpam-6139	617	1	+	+	X
ejpam-6139	617	2	υk[µ	υk[µ	PROPN
ejpam-6139	617	3	,	,	PUNCT
ejpam-6139	617	4	α	α	NOUN
ejpam-6139	617	5	]	]	X
ejpam-6139	617	6	−	−	PROPN
ejpam-6139	617	7	1	1	NUM
ejpam-6139	617	8	η	η	PROPN
ejpam-6139	617	9	(	(	PUNCT
ejpam-6139	617	10	h	h	PROPN
ejpam-6139	617	11	(	(	PUNCT
ejpam-6139	617	12	η	η	PROPN
ejpam-6139	617	13	−	−	PROPN
ejpam-6139	617	14	1	1	NUM
ejpam-6139	617	15	η	η	PROPN
ejpam-6139	617	16	ν	ν	X
ejpam-6139	617	17	+	+	PROPN
ejpam-6139	617	18	1	1	NUM
ejpam-6139	617	19	η	η	PROPN
ejpam-6139	617	20	ω	ω	PROPN
ejpam-6139	617	21	)	)	PUNCT
ejpam-6139	617	22	+	+	CCONJ
ejpam-6139	617	23	h	h	NOUN
ejpam-6139	617	24	(	(	PUNCT
ejpam-6139	617	25	1	1	NUM
ejpam-6139	617	26	η	η	X
ejpam-6139	617	27	ν	ν	X
ejpam-6139	617	28	+	+	CCONJ
ejpam-6139	617	29	η	η	PROPN
ejpam-6139	617	30	−	−	PROPN
ejpam-6139	617	31	1	1	NUM
ejpam-6139	617	32	η	η	PROPN
ejpam-6139	617	33	ω	ω	PROPN
ejpam-6139	617	34	)	)	PUNCT
ejpam-6139	617	35	)	)	PUNCT
ejpam-6139	617	36	∣∣∣∣≤	∣∣∣∣≤	PROPN
ejpam-6139	617	37	(	(	PUNCT
ejpam-6139	617	38	ω	ω	NUM
ejpam-6139	617	39	−	−	PROPN
ejpam-6139	617	40	ν)2	ν)2	PROPN
ejpam-6139	617	41	η3	η3	PROPN
ejpam-6139	617	42	(	(	PUNCT
ejpam-6139	617	43	kµ	kµ	PROPN
ejpam-6139	617	44	)	)	PUNCT
ejpam-6139	617	45	α	α	PROPN
ejpam-6139	617	46	k	k	PROPN
ejpam-6139	617	47	×	×	PROPN
ejpam-6139	617	48	[	[	PUNCT
ejpam-6139	617	49	∫	∫	PROPN
ejpam-6139	617	50	1	1	NUM
ejpam-6139	617	51	0	0	NUM
ejpam-6139	617	52	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	617	53	t	t	NOUN
ejpam-6139	617	54	0	0	NUM
ejpam-6139	617	55	(	(	PUNCT
ejpam-6139	617	56	1−	1−	NUM
ejpam-6139	617	57	(	(	PUNCT
ejpam-6139	617	58	1−	1−	NUM
ejpam-6139	617	59	φ)µ	φ)µ	NOUN
ejpam-6139	617	60	kµ	kµ	NOUN
ejpam-6139	617	61	)	)	PUNCT
ejpam-6139	618	1	α	α	PROPN
ejpam-6139	618	2	k	k	X
ejpam-6139	618	3	dφ	dφ	ADP
ejpam-6139	618	4	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	618	5	]	]	X
ejpam-6139	618	6	1	1	NUM
ejpam-6139	618	7	p	p	X
ejpam-6139	618	8	[	[	X
ejpam-6139	618	9	(	(	PUNCT
ejpam-6139	618	10	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	618	11	ηs(s+	ηs(s+	NOUN
ejpam-6139	618	12	1	1	NUM
ejpam-6139	618	13	)	)	PUNCT
ejpam-6139	618	14	−	−	PROPN
ejpam-6139	618	15	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	618	16	ηs(s+	ηs(s+	PROPN
ejpam-6139	618	17	1	1	NUM
ejpam-6139	618	18	)	)	PUNCT
ejpam-6139	618	19	(	(	PUNCT
ejpam-6139	618	20	(	(	PUNCT
ejpam-6139	618	21	η	η	PROPN
ejpam-6139	618	22	−	−	PROPN
ejpam-6139	618	23	1)s+1	1)s+1	NUM
ejpam-6139	618	24	−	−	PROPN
ejpam-6139	618	25	ηs+1	ηs+1	PROPN
ejpam-6139	618	26	)	)	PUNCT
ejpam-6139	618	27	)	)	PUNCT
ejpam-6139	619	1	1	1	NUM
ejpam-6139	619	2	q	q	NOUN
ejpam-6139	619	3	m.	m.	NOUN
ejpam-6139	619	4	samraiz	samraiz	PROPN
ejpam-6139	619	5	et	et	PROPN
ejpam-6139	619	6	al	al	PROPN
ejpam-6139	619	7	.	.	PUNCT
ejpam-6139	619	8	/	/	SYM
ejpam-6139	619	9	eur	eur	PROPN
ejpam-6139	619	10	.	.	PUNCT
ejpam-6139	620	1	j.	j.	PROPN
ejpam-6139	620	2	pure	pure	PROPN
ejpam-6139	620	3	appl	appl	PROPN
ejpam-6139	620	4	.	.	PROPN
ejpam-6139	620	5	math	math	PROPN
ejpam-6139	620	6	,	,	PUNCT
ejpam-6139	620	7	18	18	NUM
ejpam-6139	620	8	(	(	PUNCT
ejpam-6139	620	9	4	4	NUM
ejpam-6139	620	10	)	)	PUNCT
ejpam-6139	620	11	(	(	PUNCT
ejpam-6139	620	12	2025	2025	NUM
ejpam-6139	620	13	)	)	PUNCT
ejpam-6139	620	14	,	,	PUNCT
ejpam-6139	620	15	6139	6139	NUM
ejpam-6139	620	16	24	24	NUM
ejpam-6139	620	17	of	of	ADP
ejpam-6139	620	18	34	34	NUM
ejpam-6139	620	19	+	+	CCONJ
ejpam-6139	620	20	(	(	PUNCT
ejpam-6139	620	21	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	620	22	ηs(s+	ηs(s+	PROPN
ejpam-6139	620	23	1	1	NUM
ejpam-6139	620	24	)	)	PUNCT
ejpam-6139	620	25	−	−	PROPN
ejpam-6139	620	26	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	620	27	ηs(s+	ηs(s+	PROPN
ejpam-6139	620	28	1	1	NUM
ejpam-6139	620	29	)	)	PUNCT
ejpam-6139	620	30	(	(	PUNCT
ejpam-6139	620	31	(	(	PUNCT
ejpam-6139	620	32	η	η	PROPN
ejpam-6139	620	33	−	−	PROPN
ejpam-6139	620	34	1)s+1	1)s+1	NUM
ejpam-6139	620	35	−	−	PROPN
ejpam-6139	620	36	ηs+1	ηs+1	PROPN
ejpam-6139	620	37	)	)	PUNCT
ejpam-6139	620	38	)	)	PUNCT
ejpam-6139	620	39	1	1	NUM
ejpam-6139	620	40	q	q	NOUN
ejpam-6139	620	41	]	]	PUNCT
ejpam-6139	620	42	.	.	PUNCT
ejpam-6139	621	1	(	(	PUNCT
ejpam-6139	621	2	42	42	X
ejpam-6139	621	3	)	)	PUNCT
ejpam-6139	621	4	proof	proof	NOUN
ejpam-6139	621	5	.	.	PUNCT
ejpam-6139	622	1	by	by	ADP
ejpam-6139	622	2	employing	employ	VERB
ejpam-6139	622	3	hölder	hölder	NOUN
ejpam-6139	622	4	inequality	inequality	NOUN
ejpam-6139	622	5	on	on	ADP
ejpam-6139	622	6	equation	equation	NOUN
ejpam-6139	622	7	(	(	PUNCT
ejpam-6139	622	8	37)∣∣∣∣	37)∣∣∣∣	NUM
ejpam-6139	622	9	ηµ	ηµ	VERB
ejpam-6139	622	10	α	α	PROPN
ejpam-6139	622	11	k	k	X
ejpam-6139	622	12	−1	−1	PROPN
ejpam-6139	622	13	(	(	PUNCT
ejpam-6139	622	14	ω	ω	PROPN
ejpam-6139	622	15	−	−	PROPN
ejpam-6139	622	16	ν)µ	ν)µ	ADV
ejpam-6139	622	17	α	α	PROPN
ejpam-6139	622	18	k	k	PROPN
ejpam-6139	622	19	(	(	PUNCT
ejpam-6139	622	20	kµ	kµ	PROPN
ejpam-6139	622	21	)	)	PUNCT
ejpam-6139	622	22	α	α	PROPN
ejpam-6139	622	23	k	k	PROPN
ejpam-6139	622	24	γ	γ	X
ejpam-6139	622	25	(	(	PUNCT
ejpam-6139	622	26	α	α	NOUN
ejpam-6139	622	27	k	k	PROPN
ejpam-6139	623	1	+	+	PROPN
ejpam-6139	623	2	1	1	X
ejpam-6139	623	3	)	)	PUNCT
ejpam-6139	623	4	(	(	PUNCT
ejpam-6139	623	5	α	α	PROPN
ejpam-6139	623	6	k	k	PROPN
ejpam-6139	623	7	j	j	PROPN
ejpam-6139	623	8	µ	µ	X
ejpam-6139	623	9	(	(	PUNCT
ejpam-6139	623	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	623	11	η	η	PROPN
ejpam-6139	623	12	−	−	PROPN
ejpam-6139	623	13	h(ν	h(ν	PROPN
ejpam-6139	623	14	)	)	PUNCT
ejpam-6139	623	15	+	+	NOUN
ejpam-6139	623	16	α	α	NOUN
ejpam-6139	623	17	k	k	X
ejpam-6139	623	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	623	19	η	η	PROPN
ejpam-6139	623	20	+	+	PROPN
ejpam-6139	623	21	h(ω	h(ω	PROPN
ejpam-6139	623	22	)	)	PUNCT
ejpam-6139	623	23	)	)	PUNCT
ejpam-6139	624	1	+	+	X
ejpam-6139	624	2	υk[µ	υk[µ	PROPN
ejpam-6139	624	3	,	,	PUNCT
ejpam-6139	624	4	α	α	NOUN
ejpam-6139	624	5	]	]	X
ejpam-6139	624	6	−	−	PROPN
ejpam-6139	624	7	1	1	NUM
ejpam-6139	624	8	η	η	PROPN
ejpam-6139	624	9	(	(	PUNCT
ejpam-6139	624	10	h	h	PROPN
ejpam-6139	624	11	(	(	PUNCT
ejpam-6139	624	12	η	η	PROPN
ejpam-6139	624	13	−	−	PROPN
ejpam-6139	624	14	1	1	NUM
ejpam-6139	624	15	η	η	PROPN
ejpam-6139	624	16	ν	ν	X
ejpam-6139	624	17	+	+	PROPN
ejpam-6139	624	18	1	1	NUM
ejpam-6139	624	19	η	η	PROPN
ejpam-6139	624	20	ω	ω	PROPN
ejpam-6139	624	21	)	)	PUNCT
ejpam-6139	624	22	+	+	CCONJ
ejpam-6139	624	23	h	h	NOUN
ejpam-6139	624	24	(	(	PUNCT
ejpam-6139	624	25	1	1	NUM
ejpam-6139	624	26	η	η	X
ejpam-6139	624	27	ν	ν	X
ejpam-6139	624	28	+	+	CCONJ
ejpam-6139	624	29	η	η	PROPN
ejpam-6139	624	30	−	−	PROPN
ejpam-6139	624	31	1	1	NUM
ejpam-6139	624	32	η	η	PROPN
ejpam-6139	624	33	ω	ω	PROPN
ejpam-6139	624	34	)	)	PUNCT
ejpam-6139	624	35	)	)	PUNCT
ejpam-6139	624	36	∣∣∣∣≤	∣∣∣∣≤	PROPN
ejpam-6139	624	37	(	(	PUNCT
ejpam-6139	624	38	ω	ω	NUM
ejpam-6139	624	39	−	−	PROPN
ejpam-6139	624	40	ν)2	ν)2	PROPN
ejpam-6139	624	41	η3	η3	PROPN
ejpam-6139	624	42	(	(	PUNCT
ejpam-6139	624	43	kµ	kµ	PROPN
ejpam-6139	624	44	)	)	PUNCT
ejpam-6139	624	45	α	α	PROPN
ejpam-6139	625	1	k	k	NOUN
ejpam-6139	625	2	×	×	PROPN
ejpam-6139	625	3	[	[	X
ejpam-6139	625	4	(	(	PUNCT
ejpam-6139	625	5	∫	∫	PROPN
ejpam-6139	625	6	1	1	NUM
ejpam-6139	625	7	0	0	NUM
ejpam-6139	625	8	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	625	9	t	t	NOUN
ejpam-6139	625	10	0	0	NUM
ejpam-6139	626	1	(	(	PUNCT
ejpam-6139	626	2	1−	1−	NUM
ejpam-6139	626	3	(	(	PUNCT
ejpam-6139	626	4	1−	1−	NUM
ejpam-6139	626	5	φ)µ	φ)µ	NOUN
ejpam-6139	626	6	kµ	kµ	NOUN
ejpam-6139	626	7	)	)	PUNCT
ejpam-6139	627	1	α	α	PROPN
ejpam-6139	627	2	k	k	X
ejpam-6139	627	3	dφ	dφ	X
ejpam-6139	627	4	∣∣∣∣pdt	∣∣∣∣pdt	PROPN
ejpam-6139	627	5	)	)	PUNCT
ejpam-6139	627	6	1	1	NUM
ejpam-6139	628	1	p	p	NOUN
ejpam-6139	628	2	∣∣∣∣(∫	∣∣∣∣(∫	NOUN
ejpam-6139	628	3	1	1	NUM
ejpam-6139	628	4	0	0	NUM
ejpam-6139	628	5	∣∣∣∣h′′(η	∣∣∣∣h′′(η	ADV
ejpam-6139	628	6	−	−	PROPN
ejpam-6139	628	7	t	t	PROPN
ejpam-6139	628	8	η	η	PROPN
ejpam-6139	628	9	ν	ν	PROPN
ejpam-6139	628	10	+	+	PROPN
ejpam-6139	628	11	t	t	PROPN
ejpam-6139	628	12	η	η	PROPN
ejpam-6139	628	13	ω	ω	PROPN
ejpam-6139	628	14	)	)	PUNCT
ejpam-6139	628	15	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	628	16	)	)	PUNCT
ejpam-6139	628	17	1	1	NUM
ejpam-6139	628	18	q	q	NOUN
ejpam-6139	628	19	+	+	CCONJ
ejpam-6139	628	20	(	(	PUNCT
ejpam-6139	628	21	∫	∫	PROPN
ejpam-6139	628	22	1	1	NUM
ejpam-6139	628	23	0	0	NUM
ejpam-6139	628	24	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	628	25	t	t	NOUN
ejpam-6139	628	26	0	0	NUM
ejpam-6139	629	1	(	(	PUNCT
ejpam-6139	629	2	1−	1−	NUM
ejpam-6139	629	3	(	(	PUNCT
ejpam-6139	629	4	1−	1−	NUM
ejpam-6139	629	5	φ)µ	φ)µ	NOUN
ejpam-6139	629	6	kµ	kµ	NOUN
ejpam-6139	629	7	)	)	PUNCT
ejpam-6139	630	1	α	α	PROPN
ejpam-6139	630	2	k	k	X
ejpam-6139	630	3	dφ	dφ	X
ejpam-6139	630	4	∣∣∣∣pdt	∣∣∣∣pdt	PROPN
ejpam-6139	630	5	)	)	PUNCT
ejpam-6139	630	6	1	1	NUM
ejpam-6139	630	7	p	p	NOUN
ejpam-6139	630	8	(	(	PUNCT
ejpam-6139	630	9	∫	∫	PROPN
ejpam-6139	630	10	1	1	NUM
ejpam-6139	630	11	0	0	NUM
ejpam-6139	630	12	∣∣∣∣h′′	∣∣∣∣h′′	NOUN
ejpam-6139	630	13	(	(	PUNCT
ejpam-6139	630	14	t	t	PROPN
ejpam-6139	630	15	η	η	PROPN
ejpam-6139	630	16	ν	ν	PROPN
ejpam-6139	630	17	+	+	PROPN
ejpam-6139	630	18	η	η	PROPN
ejpam-6139	630	19	−	−	PROPN
ejpam-6139	630	20	t	t	PROPN
ejpam-6139	630	21	η	η	PROPN
ejpam-6139	630	22	ω	ω	PROPN
ejpam-6139	630	23	)	)	PUNCT
ejpam-6139	630	24	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	630	25	)	)	PUNCT
ejpam-6139	630	26	1	1	NUM
ejpam-6139	630	27	q	q	NOUN
ejpam-6139	630	28	.	.	PUNCT
ejpam-6139	631	1	(	(	PUNCT
ejpam-6139	631	2	43	43	NUM
ejpam-6139	631	3	)	)	PUNCT
ejpam-6139	631	4	by	by	ADP
ejpam-6139	631	5	taking	take	VERB
ejpam-6139	631	6	advantage	advantage	NOUN
ejpam-6139	631	7	of	of	ADP
ejpam-6139	631	8	s	s	NOUN
ejpam-6139	631	9	-	-	NOUN
ejpam-6139	631	10	convexity	convexity	NOUN
ejpam-6139	631	11	of	of	ADP
ejpam-6139	631	12	|h′′(x)|q	|h′′(x)|q	PROPN
ejpam-6139	631	13	on	on	ADP
ejpam-6139	631	14	following	follow	VERB
ejpam-6139	631	15	equations	equation	NOUN
ejpam-6139	631	16	,	,	PUNCT
ejpam-6139	631	17	consider(∫	consider(∫	VERB
ejpam-6139	631	18	1	1	NUM
ejpam-6139	631	19	0	0	NUM
ejpam-6139	632	1	∣∣∣∣h′′(η	∣∣∣∣h′′(η	ADV
ejpam-6139	632	2	−	−	PROPN
ejpam-6139	632	3	t	t	PROPN
ejpam-6139	632	4	η	η	PROPN
ejpam-6139	632	5	ν	ν	PROPN
ejpam-6139	632	6	+	+	PROPN
ejpam-6139	632	7	t	t	PROPN
ejpam-6139	632	8	η	η	PROPN
ejpam-6139	632	9	ω	ω	PROPN
ejpam-6139	632	10	)	)	PUNCT
ejpam-6139	632	11	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	632	12	)	)	PUNCT
ejpam-6139	632	13	1	1	NUM
ejpam-6139	632	14	q	q	NOUN
ejpam-6139	632	15	≤	≤	NUM
ejpam-6139	632	16	(	(	PUNCT
ejpam-6139	632	17	∫	∫	PROPN
ejpam-6139	632	18	1	1	NUM
ejpam-6139	632	19	0	0	NUM
ejpam-6139	633	1	[	[	X
ejpam-6139	633	2	(	(	PUNCT
ejpam-6139	633	3	η	η	PROPN
ejpam-6139	633	4	−	−	PROPN
ejpam-6139	633	5	t	t	PROPN
ejpam-6139	633	6	η	η	PROPN
ejpam-6139	633	7	)	)	PUNCT
ejpam-6139	633	8	s	s	PART
ejpam-6139	633	9	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	633	10	+	+	CCONJ
ejpam-6139	633	11	(	(	PUNCT
ejpam-6139	633	12	t	t	PROPN
ejpam-6139	633	13	η	η	PROPN
ejpam-6139	633	14	)	)	PUNCT
ejpam-6139	633	15	s	s	PART
ejpam-6139	633	16	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	633	17	]	]	PUNCT
ejpam-6139	633	18	dt	dt	X
ejpam-6139	633	19	)	)	PUNCT
ejpam-6139	633	20	1	1	NUM
ejpam-6139	633	21	q	q	NOUN
ejpam-6139	633	22	(	(	PUNCT
ejpam-6139	633	23	∫	∫	PROPN
ejpam-6139	633	24	1	1	NUM
ejpam-6139	633	25	0	0	NUM
ejpam-6139	633	26	∣∣∣∣h′′(η	∣∣∣∣h′′(η	ADV
ejpam-6139	633	27	−	−	PROPN
ejpam-6139	633	28	t	t	PROPN
ejpam-6139	633	29	η	η	PROPN
ejpam-6139	633	30	ν	ν	PROPN
ejpam-6139	633	31	+	+	PROPN
ejpam-6139	633	32	t	t	PROPN
ejpam-6139	633	33	η	η	PROPN
ejpam-6139	633	34	ω	ω	PROPN
ejpam-6139	633	35	)	)	PUNCT
ejpam-6139	633	36	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	633	37	)	)	PUNCT
ejpam-6139	633	38	1	1	NUM
ejpam-6139	633	39	q	q	NOUN
ejpam-6139	633	40	≤	≤	NUM
ejpam-6139	633	41	(	(	PUNCT
ejpam-6139	633	42	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	633	43	1	1	NUM
ejpam-6139	633	44	ηs	ηs	NOUN
ejpam-6139	633	45	(	(	PUNCT
ejpam-6139	633	46	ts+1	ts+1	PROPN
ejpam-6139	633	47	s+	s+	PUNCT
ejpam-6139	633	48	1	1	NUM
ejpam-6139	633	49	)	)	PUNCT
ejpam-6139	633	50	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-6139	633	51	0	0	NUM
ejpam-6139	633	52	−	−	PROPN
ejpam-6139	633	53	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	633	54	ηs(s+	ηs(s+	PROPN
ejpam-6139	633	55	1	1	NUM
ejpam-6139	633	56	)	)	PUNCT
ejpam-6139	633	57	(	(	PUNCT
ejpam-6139	633	58	η	η	PROPN
ejpam-6139	633	59	−	−	PROPN
ejpam-6139	633	60	t)s+1	t)s+1	PROPN
ejpam-6139	633	61	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-6139	633	62	0	0	NUM
ejpam-6139	633	63	)	)	PUNCT
ejpam-6139	633	64	1	1	NUM
ejpam-6139	633	65	q	q	NOUN
ejpam-6139	633	66	(	(	PUNCT
ejpam-6139	633	67	∫	∫	PROPN
ejpam-6139	633	68	1	1	NUM
ejpam-6139	633	69	0	0	NUM
ejpam-6139	633	70	∣∣∣∣h′′(η	∣∣∣∣h′′(η	ADV
ejpam-6139	633	71	−	−	PROPN
ejpam-6139	633	72	t	t	PROPN
ejpam-6139	633	73	η	η	PROPN
ejpam-6139	633	74	ν	ν	PROPN
ejpam-6139	633	75	+	+	PROPN
ejpam-6139	633	76	t	t	PROPN
ejpam-6139	633	77	η	η	PROPN
ejpam-6139	633	78	ω	ω	PROPN
ejpam-6139	633	79	)	)	PUNCT
ejpam-6139	633	80	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	633	81	)	)	PUNCT
ejpam-6139	633	82	1	1	NUM
ejpam-6139	633	83	q	q	NOUN
ejpam-6139	633	84	≤	≤	NUM
ejpam-6139	633	85	(	(	PUNCT
ejpam-6139	633	86	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	633	87	ηs(s+	ηs(s+	PROPN
ejpam-6139	633	88	1	1	NUM
ejpam-6139	633	89	)	)	PUNCT
ejpam-6139	633	90	−	−	PROPN
ejpam-6139	633	91	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	633	92	ηs(s+	ηs(s+	PROPN
ejpam-6139	633	93	1	1	NUM
ejpam-6139	633	94	)	)	PUNCT
ejpam-6139	633	95	(	(	PUNCT
ejpam-6139	633	96	(	(	PUNCT
ejpam-6139	633	97	η	η	PROPN
ejpam-6139	633	98	−	−	PROPN
ejpam-6139	633	99	1)s+1	1)s+1	NUM
ejpam-6139	633	100	−	−	PROPN
ejpam-6139	633	101	ηs+1	ηs+1	PROPN
ejpam-6139	633	102	)	)	PUNCT
ejpam-6139	633	103	)	)	PUNCT
ejpam-6139	633	104	1	1	NUM
ejpam-6139	633	105	q	q	NOUN
ejpam-6139	633	106	.	.	PUNCT
ejpam-6139	634	1	(	(	PUNCT
ejpam-6139	634	2	44	44	NUM
ejpam-6139	634	3	)	)	PUNCT
ejpam-6139	634	4	similarly(∫	similarly(∫	VERB
ejpam-6139	634	5	1	1	NUM
ejpam-6139	634	6	0	0	NUM
ejpam-6139	634	7	∣∣∣∣h′′	∣∣∣∣h′′	NOUN
ejpam-6139	634	8	(	(	PUNCT
ejpam-6139	634	9	t	t	PROPN
ejpam-6139	634	10	η	η	PROPN
ejpam-6139	634	11	ν	ν	PROPN
ejpam-6139	634	12	+	+	PROPN
ejpam-6139	634	13	η	η	PROPN
ejpam-6139	634	14	−	−	PROPN
ejpam-6139	634	15	t	t	PROPN
ejpam-6139	634	16	η	η	PROPN
ejpam-6139	634	17	ω	ω	PROPN
ejpam-6139	634	18	)	)	PUNCT
ejpam-6139	634	19	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	634	20	)	)	PUNCT
ejpam-6139	634	21	1	1	NUM
ejpam-6139	634	22	q	q	NOUN
ejpam-6139	634	23	≤	≤	NUM
ejpam-6139	634	24	(	(	PUNCT
ejpam-6139	634	25	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	634	26	ηs(s+	ηs(s+	PROPN
ejpam-6139	634	27	1	1	NUM
ejpam-6139	634	28	)	)	PUNCT
ejpam-6139	634	29	−	−	PROPN
ejpam-6139	634	30	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	634	31	ηs(s+	ηs(s+	PROPN
ejpam-6139	634	32	1	1	NUM
ejpam-6139	634	33	)	)	PUNCT
ejpam-6139	634	34	(	(	PUNCT
ejpam-6139	634	35	(	(	PUNCT
ejpam-6139	634	36	η	η	PROPN
ejpam-6139	634	37	−	−	PROPN
ejpam-6139	634	38	1)s+1	1)s+1	NUM
ejpam-6139	634	39	−	−	PROPN
ejpam-6139	634	40	ηs+1	ηs+1	PROPN
ejpam-6139	634	41	)	)	PUNCT
ejpam-6139	634	42	)	)	PUNCT
ejpam-6139	634	43	1	1	NUM
ejpam-6139	634	44	q	q	NOUN
ejpam-6139	634	45	.	.	PUNCT
ejpam-6139	635	1	(	(	PUNCT
ejpam-6139	635	2	45	45	NUM
ejpam-6139	635	3	)	)	PUNCT
ejpam-6139	635	4	substituting	substituting	NOUN
ejpam-6139	635	5	(	(	PUNCT
ejpam-6139	635	6	44	44	NUM
ejpam-6139	635	7	)	)	PUNCT
ejpam-6139	635	8	and	and	CCONJ
ejpam-6139	635	9	(	(	PUNCT
ejpam-6139	635	10	45	45	NUM
ejpam-6139	635	11	)	)	PUNCT
ejpam-6139	635	12	in	in	ADP
ejpam-6139	635	13	(	(	PUNCT
ejpam-6139	635	14	43	43	NUM
ejpam-6139	635	15	)	)	PUNCT
ejpam-6139	635	16	,	,	PUNCT
ejpam-6139	635	17	we	we	PRON
ejpam-6139	635	18	get∣∣∣∣	get∣∣∣∣	VERB
ejpam-6139	635	19	ηµ	ηµ	VERB
ejpam-6139	635	20	α	α	PROPN
ejpam-6139	635	21	k	k	X
ejpam-6139	635	22	−1	−1	PROPN
ejpam-6139	635	23	(	(	PUNCT
ejpam-6139	635	24	ω	ω	PROPN
ejpam-6139	635	25	−	−	PROPN
ejpam-6139	635	26	ν)µ	ν)µ	ADV
ejpam-6139	635	27	α	α	PROPN
ejpam-6139	635	28	k	k	PROPN
ejpam-6139	635	29	(	(	PUNCT
ejpam-6139	635	30	kµ	kµ	PROPN
ejpam-6139	635	31	)	)	PUNCT
ejpam-6139	635	32	α	α	PROPN
ejpam-6139	636	1	k	k	PROPN
ejpam-6139	636	2	γ	γ	X
ejpam-6139	636	3	(	(	PUNCT
ejpam-6139	636	4	α	α	NOUN
ejpam-6139	636	5	k	k	PROPN
ejpam-6139	637	1	+	+	PROPN
ejpam-6139	637	2	1	1	X
ejpam-6139	637	3	)	)	PUNCT
ejpam-6139	637	4	(	(	PUNCT
ejpam-6139	637	5	α	α	PROPN
ejpam-6139	637	6	k	k	PROPN
ejpam-6139	637	7	j	j	PROPN
ejpam-6139	637	8	µ	µ	X
ejpam-6139	637	9	(	(	PUNCT
ejpam-6139	637	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	637	11	η	η	PROPN
ejpam-6139	637	12	−	−	PROPN
ejpam-6139	637	13	h(ν	h(ν	PROPN
ejpam-6139	637	14	)	)	PUNCT
ejpam-6139	637	15	+	+	NOUN
ejpam-6139	637	16	α	α	NOUN
ejpam-6139	637	17	k	k	X
ejpam-6139	637	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	637	19	η	η	PROPN
ejpam-6139	637	20	+	+	PROPN
ejpam-6139	637	21	h(ω	h(ω	PROPN
ejpam-6139	637	22	)	)	PUNCT
ejpam-6139	637	23	)	)	PUNCT
ejpam-6139	638	1	+	+	X
ejpam-6139	638	2	υk[µ	υk[µ	PROPN
ejpam-6139	638	3	,	,	PUNCT
ejpam-6139	638	4	α	α	NOUN
ejpam-6139	638	5	]	]	X
ejpam-6139	638	6	−	−	PROPN
ejpam-6139	638	7	1	1	NUM
ejpam-6139	638	8	η	η	PROPN
ejpam-6139	638	9	(	(	PUNCT
ejpam-6139	638	10	h	h	PROPN
ejpam-6139	638	11	(	(	PUNCT
ejpam-6139	638	12	η	η	PROPN
ejpam-6139	638	13	−	−	PROPN
ejpam-6139	638	14	1	1	NUM
ejpam-6139	638	15	η	η	PROPN
ejpam-6139	638	16	ν	ν	X
ejpam-6139	638	17	+	+	PROPN
ejpam-6139	638	18	1	1	NUM
ejpam-6139	638	19	η	η	PROPN
ejpam-6139	638	20	ω	ω	PROPN
ejpam-6139	638	21	)	)	PUNCT
ejpam-6139	638	22	+	+	CCONJ
ejpam-6139	638	23	h	h	NOUN
ejpam-6139	638	24	(	(	PUNCT
ejpam-6139	638	25	1	1	NUM
ejpam-6139	638	26	η	η	X
ejpam-6139	638	27	ν	ν	X
ejpam-6139	638	28	+	+	CCONJ
ejpam-6139	638	29	η	η	PROPN
ejpam-6139	638	30	−	−	PROPN
ejpam-6139	638	31	1	1	NUM
ejpam-6139	638	32	η	η	PROPN
ejpam-6139	638	33	ω	ω	PROPN
ejpam-6139	638	34	)	)	PUNCT
ejpam-6139	638	35	)	)	PUNCT
ejpam-6139	638	36	∣∣∣∣≤	∣∣∣∣≤	PROPN
ejpam-6139	638	37	(	(	PUNCT
ejpam-6139	638	38	ω	ω	NUM
ejpam-6139	638	39	−	−	PROPN
ejpam-6139	638	40	ν)2	ν)2	PROPN
ejpam-6139	638	41	η3	η3	PROPN
ejpam-6139	638	42	(	(	PUNCT
ejpam-6139	638	43	kµ	kµ	PROPN
ejpam-6139	638	44	)	)	PUNCT
ejpam-6139	638	45	α	α	PROPN
ejpam-6139	638	46	k	k	PROPN
ejpam-6139	638	47	×	×	PROPN
ejpam-6139	638	48	[	[	PUNCT
ejpam-6139	638	49	∫	∫	PROPN
ejpam-6139	638	50	1	1	NUM
ejpam-6139	638	51	0	0	NUM
ejpam-6139	638	52	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	638	53	t	t	NOUN
ejpam-6139	638	54	0	0	NUM
ejpam-6139	638	55	(	(	PUNCT
ejpam-6139	638	56	1−	1−	NUM
ejpam-6139	638	57	(	(	PUNCT
ejpam-6139	638	58	1−	1−	NUM
ejpam-6139	638	59	φ)µ	φ)µ	NOUN
ejpam-6139	638	60	kµ	kµ	NOUN
ejpam-6139	638	61	)	)	PUNCT
ejpam-6139	639	1	α	α	PROPN
ejpam-6139	639	2	k	k	X
ejpam-6139	639	3	dφ	dφ	ADP
ejpam-6139	639	4	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	639	5	]	]	X
ejpam-6139	639	6	1	1	NUM
ejpam-6139	639	7	p	p	X
ejpam-6139	639	8	[	[	X
ejpam-6139	639	9	(	(	PUNCT
ejpam-6139	639	10	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	639	11	ηs(s+	ηs(s+	NOUN
ejpam-6139	639	12	1	1	NUM
ejpam-6139	639	13	)	)	PUNCT
ejpam-6139	639	14	−	−	PROPN
ejpam-6139	639	15	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	639	16	ηs(s+	ηs(s+	PROPN
ejpam-6139	639	17	1	1	NUM
ejpam-6139	639	18	)	)	PUNCT
ejpam-6139	639	19	(	(	PUNCT
ejpam-6139	639	20	(	(	PUNCT
ejpam-6139	639	21	η	η	PROPN
ejpam-6139	639	22	−	−	PROPN
ejpam-6139	639	23	1)s+1	1)s+1	NUM
ejpam-6139	639	24	−	−	PROPN
ejpam-6139	639	25	ηs+1	ηs+1	PROPN
ejpam-6139	639	26	)	)	PUNCT
ejpam-6139	639	27	)	)	PUNCT
ejpam-6139	640	1	1	1	NUM
ejpam-6139	640	2	q	q	NOUN
ejpam-6139	640	3	+	+	CCONJ
ejpam-6139	640	4	(	(	PUNCT
ejpam-6139	640	5	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	640	6	ηs(s+	ηs(s+	PROPN
ejpam-6139	640	7	1	1	NUM
ejpam-6139	640	8	)	)	PUNCT
ejpam-6139	640	9	−	−	PROPN
ejpam-6139	640	10	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	640	11	ηs(s+	ηs(s+	PROPN
ejpam-6139	640	12	1	1	NUM
ejpam-6139	640	13	)	)	PUNCT
ejpam-6139	640	14	(	(	PUNCT
ejpam-6139	640	15	(	(	PUNCT
ejpam-6139	640	16	η	η	PROPN
ejpam-6139	640	17	−	−	PROPN
ejpam-6139	640	18	1)s+1	1)s+1	NUM
ejpam-6139	640	19	−	−	PROPN
ejpam-6139	640	20	ηs+1	ηs+1	PROPN
ejpam-6139	640	21	)	)	PUNCT
ejpam-6139	640	22	)	)	PUNCT
ejpam-6139	640	23	1	1	NUM
ejpam-6139	640	24	q	q	NOUN
ejpam-6139	640	25	]	]	PUNCT
ejpam-6139	640	26	.	.	PUNCT
ejpam-6139	641	1	(	(	PUNCT
ejpam-6139	641	2	46	46	NUM
ejpam-6139	641	3	)	)	PUNCT
ejpam-6139	641	4	therefore	therefore	ADV
ejpam-6139	641	5	,	,	PUNCT
ejpam-6139	641	6	the	the	DET
ejpam-6139	641	7	calculations	calculation	NOUN
ejpam-6139	641	8	produce	produce	VERB
ejpam-6139	641	9	the	the	DET
ejpam-6139	641	10	anticipated	anticipate	VERB
ejpam-6139	641	11	result	result	NOUN
ejpam-6139	641	12	.	.	PUNCT
ejpam-6139	642	1	m.	m.	NOUN
ejpam-6139	642	2	samraiz	samraiz	PROPN
ejpam-6139	642	3	et	et	PROPN
ejpam-6139	642	4	al	al	PROPN
ejpam-6139	642	5	.	.	PUNCT
ejpam-6139	642	6	/	/	SYM
ejpam-6139	642	7	eur	eur	PROPN
ejpam-6139	642	8	.	.	PUNCT
ejpam-6139	643	1	j.	j.	PROPN
ejpam-6139	643	2	pure	pure	PROPN
ejpam-6139	643	3	appl	appl	PROPN
ejpam-6139	643	4	.	.	PROPN
ejpam-6139	643	5	math	math	PROPN
ejpam-6139	643	6	,	,	PUNCT
ejpam-6139	643	7	18	18	NUM
ejpam-6139	643	8	(	(	PUNCT
ejpam-6139	643	9	4	4	NUM
ejpam-6139	643	10	)	)	PUNCT
ejpam-6139	643	11	(	(	PUNCT
ejpam-6139	643	12	2025	2025	NUM
ejpam-6139	643	13	)	)	PUNCT
ejpam-6139	643	14	,	,	PUNCT
ejpam-6139	643	15	6139	6139	NUM
ejpam-6139	643	16	25	25	NUM
ejpam-6139	643	17	of	of	ADP
ejpam-6139	643	18	34	34	NUM
ejpam-6139	643	19	remark	remark	NOUN
ejpam-6139	643	20	11	11	NUM
ejpam-6139	643	21	.	.	PUNCT
ejpam-6139	644	1	by	by	ADP
ejpam-6139	644	2	substituting	substitute	VERB
ejpam-6139	644	3	k=1,s=1and	k=1,s=1and	PROPN
ejpam-6139	644	4	η	η	PROPN
ejpam-6139	644	5	=	=	PROPN
ejpam-6139	644	6	2	2	NUM
ejpam-6139	644	7	in	in	ADP
ejpam-6139	644	8	(	(	PUNCT
ejpam-6139	644	9	42	42	NUM
ejpam-6139	644	10	)	)	PUNCT
ejpam-6139	644	11	we	we	PRON
ejpam-6139	644	12	conclude∣∣∣∣	conclude∣∣∣∣	VERB
ejpam-6139	644	13	2µα−1	2µα−1	NUM
ejpam-6139	644	14	(	(	PUNCT
ejpam-6139	644	15	ω	ω	NOUN
ejpam-6139	644	16	−	−	X
ejpam-6139	644	17	ν)µα	ν)µα	PROPN
ejpam-6139	644	18	(	(	PUNCT
ejpam-6139	644	19	µ)αγ	µ)αγ	PROPN
ejpam-6139	644	20	(	(	PUNCT
ejpam-6139	644	21	α+	α+	NOUN
ejpam-6139	644	22	1	1	NUM
ejpam-6139	644	23	)	)	PUNCT
ejpam-6139	644	24	(	(	PUNCT
ejpam-6139	644	25	αjµν+ω	αjµν+ω	PROPN
ejpam-6139	644	26	2	2	NUM
ejpam-6139	644	27	−h(ν	−h(ν	NOUN
ejpam-6139	644	28	)	)	PUNCT
ejpam-6139	644	29	+	+	CCONJ
ejpam-6139	644	30	α	α	PROPN
ejpam-6139	644	31	jµν+ω	jµν+ω	PROPN
ejpam-6139	644	32	2	2	NUM
ejpam-6139	644	33	+	+	NUM
ejpam-6139	644	34	h(ω	h(ω	PROPN
ejpam-6139	644	35	)	)	PUNCT
ejpam-6139	644	36	)	)	PUNCT
ejpam-6139	645	1	−	−	PROPN
ejpam-6139	645	2	h	h	NOUN
ejpam-6139	645	3	(	(	PUNCT
ejpam-6139	645	4	ν	ν	X
ejpam-6139	645	5	+	+	X
ejpam-6139	645	6	ω	ω	NUM
ejpam-6139	645	7	2	2	NUM
ejpam-6139	645	8	)	)	PUNCT
ejpam-6139	645	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	645	10	≤	≤	NOUN
ejpam-6139	645	11	(	(	PUNCT
ejpam-6139	645	12	ω	ω	NUM
ejpam-6139	645	13	−	−	PROPN
ejpam-6139	645	14	ν)2	ν)2	NOUN
ejpam-6139	645	15	8	8	NUM
ejpam-6139	645	16	µα	µα	ADP
ejpam-6139	645	17	[	[	PUNCT
ejpam-6139	645	18	∫	∫	PROPN
ejpam-6139	645	19	1	1	NUM
ejpam-6139	645	20	0	0	NUM
ejpam-6139	645	21	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	645	22	t	t	NOUN
ejpam-6139	645	23	0	0	NUM
ejpam-6139	646	1	(	(	PUNCT
ejpam-6139	646	2	1−	1−	NUM
ejpam-6139	646	3	(	(	PUNCT
ejpam-6139	646	4	1−	1−	NUM
ejpam-6139	646	5	φ)µ	φ)µ	X
ejpam-6139	646	6	µ	µ	X
ejpam-6139	646	7	)	)	PUNCT
ejpam-6139	646	8	α	α	NOUN
ejpam-6139	646	9	dφ	dφ	ADP
ejpam-6139	646	10	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	646	11	]	]	X
ejpam-6139	646	12	1	1	NUM
ejpam-6139	646	13	p	p	X
ejpam-6139	646	14	[	[	X
ejpam-6139	646	15	(	(	PUNCT
ejpam-6139	646	16	3|h′′(ν)|q	3|h′′(ν)|q	PROPN
ejpam-6139	646	17	+	+	NUM
ejpam-6139	646	18	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	646	19	4	4	NUM
ejpam-6139	646	20	)	)	PUNCT
ejpam-6139	646	21	1	1	NUM
ejpam-6139	646	22	q	q	NOUN
ejpam-6139	647	1	+	+	CCONJ
ejpam-6139	647	2	(	(	PUNCT
ejpam-6139	647	3	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	647	4	+	+	CCONJ
ejpam-6139	647	5	3|h′′(ω)|q	3|h′′(ω)|q	NUM
ejpam-6139	647	6	4	4	NUM
ejpam-6139	647	7	)	)	PUNCT
ejpam-6139	647	8	1	1	NUM
ejpam-6139	647	9	q	q	NOUN
ejpam-6139	647	10	]	]	PUNCT
ejpam-6139	647	11	.	.	PUNCT
ejpam-6139	648	1	(	(	PUNCT
ejpam-6139	648	2	47	47	NUM
ejpam-6139	648	3	)	)	PUNCT
ejpam-6139	648	4	remark	remark	NOUN
ejpam-6139	648	5	12	12	NUM
ejpam-6139	648	6	.	.	PUNCT
ejpam-6139	649	1	by	by	ADP
ejpam-6139	649	2	taking	take	VERB
ejpam-6139	649	3	values	value	NOUN
ejpam-6139	649	4	µ	µ	X
ejpam-6139	649	5	=	=	SYM
ejpam-6139	649	6	1	1	NUM
ejpam-6139	649	7	in	in	ADP
ejpam-6139	649	8	(	(	PUNCT
ejpam-6139	649	9	47	47	NUM
ejpam-6139	649	10	)	)	PUNCT
ejpam-6139	649	11	,	,	PUNCT
ejpam-6139	649	12	result	result	VERB
ejpam-6139	649	13	reduced	reduce	VERB
ejpam-6139	649	14	to∣∣∣∣	to∣∣∣∣	PROPN
ejpam-6139	649	15	2α−1	2α−1	NUM
ejpam-6139	649	16	(	(	PUNCT
ejpam-6139	649	17	ω	ω	NUM
ejpam-6139	649	18	−	−	PROPN
ejpam-6139	649	19	ν)α	ν)α	NOUN
ejpam-6139	649	20	γ	γ	X
ejpam-6139	649	21	(	(	PUNCT
ejpam-6139	649	22	α+	α+	PROPN
ejpam-6139	649	23	1	1	NUM
ejpam-6139	649	24	)	)	PUNCT
ejpam-6139	649	25	(	(	PUNCT
ejpam-6139	649	26	αj	αj	NOUN
ejpam-6139	649	27	ν+ω	ν+ω	NUM
ejpam-6139	649	28	2	2	NUM
ejpam-6139	649	29	−h(ν	−h(ν	NOUN
ejpam-6139	649	30	)	)	PUNCT
ejpam-6139	649	31	+	+	CCONJ
ejpam-6139	650	1	α	α	PRON
ejpam-6139	650	2	j	j	NOUN
ejpam-6139	650	3	ν+ω	ν+ω	NUM
ejpam-6139	650	4	2	2	NUM
ejpam-6139	650	5	+	+	NOUN
ejpam-6139	650	6	h(ω	h(ω	X
ejpam-6139	650	7	)	)	PUNCT
ejpam-6139	650	8	)	)	PUNCT
ejpam-6139	651	1	−	−	PROPN
ejpam-6139	651	2	h	h	NOUN
ejpam-6139	651	3	(	(	PUNCT
ejpam-6139	651	4	ν	ν	X
ejpam-6139	651	5	+	+	X
ejpam-6139	651	6	ω	ω	NUM
ejpam-6139	651	7	2	2	NUM
ejpam-6139	651	8	)	)	PUNCT
ejpam-6139	651	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	651	10	≤	≤	NOUN
ejpam-6139	651	11	(	(	PUNCT
ejpam-6139	651	12	ω	ω	NUM
ejpam-6139	651	13	−	−	PROPN
ejpam-6139	651	14	ν)2	ν)2	NOUN
ejpam-6139	651	15	8	8	NUM
ejpam-6139	651	16	[	[	PUNCT
ejpam-6139	651	17	∫	∫	PROPN
ejpam-6139	651	18	1	1	NUM
ejpam-6139	651	19	0	0	NUM
ejpam-6139	651	20	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	651	21	t	t	NOUN
ejpam-6139	651	22	0	0	NUM
ejpam-6139	651	23	sαdφ	sαdφ	PROPN
ejpam-6139	651	24	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	651	25	]	]	X
ejpam-6139	651	26	1	1	NUM
ejpam-6139	651	27	p	p	X
ejpam-6139	651	28	[	[	X
ejpam-6139	651	29	(	(	PUNCT
ejpam-6139	651	30	3|h′′(ν)|q	3|h′′(ν)|q	PROPN
ejpam-6139	651	31	+	+	NUM
ejpam-6139	651	32	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	651	33	4	4	NUM
ejpam-6139	651	34	)	)	PUNCT
ejpam-6139	651	35	1	1	NUM
ejpam-6139	651	36	q	q	NOUN
ejpam-6139	651	37	+	+	CCONJ
ejpam-6139	651	38	(	(	PUNCT
ejpam-6139	651	39	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	651	40	+	+	CCONJ
ejpam-6139	651	41	3|h′′(ω)|q	3|h′′(ω)|q	NUM
ejpam-6139	651	42	4	4	NUM
ejpam-6139	651	43	)	)	PUNCT
ejpam-6139	651	44	1	1	NUM
ejpam-6139	651	45	q	q	NOUN
ejpam-6139	651	46	]	]	PUNCT
ejpam-6139	651	47	.	.	PUNCT
ejpam-6139	652	1	(	(	PUNCT
ejpam-6139	652	2	48	48	NUM
ejpam-6139	652	3	)	)	PUNCT
ejpam-6139	652	4	consider	consider	VERB
ejpam-6139	652	5	the	the	DET
ejpam-6139	652	6	term	term	NOUN
ejpam-6139	652	7	[	[	PUNCT
ejpam-6139	652	8	∫	∫	PROPN
ejpam-6139	652	9	1	1	NUM
ejpam-6139	652	10	0	0	NUM
ejpam-6139	652	11	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	652	12	t	t	NOUN
ejpam-6139	652	13	0	0	NUM
ejpam-6139	652	14	sαdφ	sαdφ	PROPN
ejpam-6139	652	15	∣∣∣∣pdt	∣∣∣∣pdt	PROPN
ejpam-6139	652	16	]	]	X
ejpam-6139	652	17	1	1	NUM
ejpam-6139	652	18	p	p	NOUN
ejpam-6139	652	19	=	=	X
ejpam-6139	652	20	[	[	PUNCT
ejpam-6139	652	21	∫	∫	PROPN
ejpam-6139	652	22	1	1	NUM
ejpam-6139	652	23	0	0	NUM
ejpam-6139	652	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	652	25	tα+1	tα+1	NOUN
ejpam-6139	652	26	α+	α+	PUNCT
ejpam-6139	652	27	1	1	NUM
ejpam-6139	652	28	∣∣∣∣pdt	∣∣∣∣pdt	NOUN
ejpam-6139	652	29	]	]	X
ejpam-6139	652	30	1	1	NUM
ejpam-6139	652	31	p	p	NOUN
ejpam-6139	652	32	[	[	PUNCT
ejpam-6139	652	33	∫	∫	PROPN
ejpam-6139	652	34	1	1	NUM
ejpam-6139	652	35	0	0	NUM
ejpam-6139	652	36	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	652	37	t	t	NOUN
ejpam-6139	652	38	0	0	NUM
ejpam-6139	652	39	sαdφ	sαdφ	PROPN
ejpam-6139	652	40	∣∣∣∣pdt	∣∣∣∣pdt	PROPN
ejpam-6139	652	41	]	]	X
ejpam-6139	652	42	1	1	NUM
ejpam-6139	652	43	p	p	NOUN
ejpam-6139	652	44	=	=	PUNCT
ejpam-6139	652	45	(	(	PUNCT
ejpam-6139	652	46	1	1	NUM
ejpam-6139	652	47	(	(	PUNCT
ejpam-6139	652	48	α+	α+	NOUN
ejpam-6139	652	49	1)p	1)p	NUM
ejpam-6139	652	50	∫	∫	NOUN
ejpam-6139	652	51	1	1	NUM
ejpam-6139	652	52	0	0	NUM
ejpam-6139	652	53	tpα+pdt	tpα+pdt	NOUN
ejpam-6139	652	54	)	)	PUNCT
ejpam-6139	652	55	1	1	NUM
ejpam-6139	652	56	p	p	NOUN
ejpam-6139	652	57	[	[	PUNCT
ejpam-6139	652	58	∫	∫	PROPN
ejpam-6139	652	59	1	1	NUM
ejpam-6139	652	60	0	0	NUM
ejpam-6139	652	61	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6139	652	62	t	t	NOUN
ejpam-6139	652	63	0	0	NUM
ejpam-6139	652	64	sαdφ	sαdφ	PROPN
ejpam-6139	652	65	∣∣∣∣pdt	∣∣∣∣pdt	PROPN
ejpam-6139	652	66	]	]	X
ejpam-6139	652	67	1	1	NUM
ejpam-6139	652	68	p	p	NOUN
ejpam-6139	652	69	=	=	PUNCT
ejpam-6139	652	70	(	(	PUNCT
ejpam-6139	652	71	1	1	NUM
ejpam-6139	652	72	(	(	PUNCT
ejpam-6139	652	73	α+	α+	X
ejpam-6139	652	74	1)p(pα+	1)p(pα+	NUM
ejpam-6139	652	75	p+	p+	NOUN
ejpam-6139	652	76	1	1	NUM
ejpam-6139	652	77	)	)	PUNCT
ejpam-6139	652	78	)	)	PUNCT
ejpam-6139	653	1	1	1	NUM
ejpam-6139	653	2	p	p	NOUN
ejpam-6139	653	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	653	4	2α−1	2α−1	NUM
ejpam-6139	653	5	(	(	PUNCT
ejpam-6139	653	6	ω	ω	NOUN
ejpam-6139	653	7	−	−	NOUN
ejpam-6139	653	8	ν)α	ν)α	X
ejpam-6139	653	9	γ(α+	γ(α+	X
ejpam-6139	653	10	1	1	NUM
ejpam-6139	653	11	)	)	PUNCT
ejpam-6139	653	12	(	(	PUNCT
ejpam-6139	653	13	αj	αj	NOUN
ejpam-6139	653	14	ν+ω	ν+ω	NUM
ejpam-6139	653	15	2	2	NUM
ejpam-6139	653	16	−h(ν	−h(ν	NOUN
ejpam-6139	653	17	)	)	PUNCT
ejpam-6139	653	18	+	+	CCONJ
ejpam-6139	653	19	α	α	PRON
ejpam-6139	653	20	j	j	NOUN
ejpam-6139	653	21	ν+ω	ν+ω	NUM
ejpam-6139	653	22	2	2	NUM
ejpam-6139	653	23	+	+	NOUN
ejpam-6139	653	24	h(ω	h(ω	X
ejpam-6139	653	25	)	)	PUNCT
ejpam-6139	653	26	)	)	PUNCT
ejpam-6139	654	1	−	−	PROPN
ejpam-6139	654	2	h	h	NOUN
ejpam-6139	654	3	(	(	PUNCT
ejpam-6139	654	4	ν	ν	X
ejpam-6139	654	5	+	+	X
ejpam-6139	654	6	ω	ω	NUM
ejpam-6139	654	7	2	2	NUM
ejpam-6139	654	8	)	)	PUNCT
ejpam-6139	654	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	654	10	≤	≤	NOUN
ejpam-6139	654	11	(	(	PUNCT
ejpam-6139	654	12	ω	ω	NUM
ejpam-6139	654	13	−	−	PROPN
ejpam-6139	654	14	ν)2	ν)2	NOUN
ejpam-6139	654	15	8	8	NUM
ejpam-6139	654	16	(	(	PUNCT
ejpam-6139	654	17	1	1	NUM
ejpam-6139	654	18	(	(	PUNCT
ejpam-6139	654	19	α+	α+	X
ejpam-6139	654	20	1)p(pα+	1)p(pα+	NUM
ejpam-6139	654	21	p+	p+	NOUN
ejpam-6139	654	22	1	1	NUM
ejpam-6139	654	23	)	)	PUNCT
ejpam-6139	654	24	)	)	PUNCT
ejpam-6139	655	1	1	1	NUM
ejpam-6139	655	2	p	p	NOUN
ejpam-6139	655	3	[	[	X
ejpam-6139	655	4	(	(	PUNCT
ejpam-6139	655	5	3|h′′(ν)|q	3|h′′(ν)|q	PROPN
ejpam-6139	655	6	+	+	NUM
ejpam-6139	655	7	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	655	8	4	4	NUM
ejpam-6139	655	9	)	)	PUNCT
ejpam-6139	655	10	1	1	NUM
ejpam-6139	655	11	q	q	NOUN
ejpam-6139	656	1	+	+	CCONJ
ejpam-6139	656	2	(	(	PUNCT
ejpam-6139	656	3	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	656	4	+	+	CCONJ
ejpam-6139	656	5	3|h′′(ω)|q	3|h′′(ω)|q	NUM
ejpam-6139	656	6	4	4	NUM
ejpam-6139	656	7	)	)	PUNCT
ejpam-6139	656	8	1	1	NUM
ejpam-6139	656	9	q	q	NOUN
ejpam-6139	656	10	]	]	PUNCT
ejpam-6139	656	11	.	.	PUNCT
ejpam-6139	657	1	remark	remark	PROPN
ejpam-6139	657	2	13	13	NUM
ejpam-6139	657	3	.	.	PUNCT
ejpam-6139	658	1	assuming	assume	VERB
ejpam-6139	658	2	α	α	PROPN
ejpam-6139	658	3	=	=	SYM
ejpam-6139	658	4	1	1	NUM
ejpam-6139	658	5	in	in	ADP
ejpam-6139	658	6	(	(	PUNCT
ejpam-6139	658	7	48	48	NUM
ejpam-6139	658	8	)	)	PUNCT
ejpam-6139	658	9	,	,	PUNCT
ejpam-6139	658	10	we	we	PRON
ejpam-6139	658	11	obtain	obtain	VERB
ejpam-6139	658	12	following	follow	VERB
ejpam-6139	658	13	result∣∣∣∣	result∣∣∣∣	PROPN
ejpam-6139	658	14	1	1	NUM
ejpam-6139	658	15	ω	ω	NUM
ejpam-6139	658	16	−	−	NOUN
ejpam-6139	658	17	ν	ν	PROPN
ejpam-6139	658	18	∫	∫	PROPN
ejpam-6139	658	19	ω	ω	PROPN
ejpam-6139	658	20	ν	ν	X
ejpam-6139	658	21	h(x)dx−	h(x)dx−	PROPN
ejpam-6139	658	22	h	h	NOUN
ejpam-6139	658	23	(	(	PUNCT
ejpam-6139	658	24	ν	ν	X
ejpam-6139	658	25	+	+	X
ejpam-6139	658	26	ω	ω	NUM
ejpam-6139	658	27	2	2	NUM
ejpam-6139	658	28	)	)	PUNCT
ejpam-6139	658	29	∣∣∣∣≤	∣∣∣∣≤	PROPN
ejpam-6139	658	30	(	(	PUNCT
ejpam-6139	658	31	ω	ω	NUM
ejpam-6139	658	32	−	−	PROPN
ejpam-6139	658	33	ν)2	ν)2	NOUN
ejpam-6139	658	34	16	16	NUM
ejpam-6139	658	35	(	(	PUNCT
ejpam-6139	658	36	1	1	NUM
ejpam-6139	658	37	2p+	2p+	NUM
ejpam-6139	658	38	1	1	NUM
ejpam-6139	658	39	)	)	PUNCT
ejpam-6139	658	40	1	1	NUM
ejpam-6139	658	41	p	p	NOUN
ejpam-6139	658	42	×	×	NOUN
ejpam-6139	658	43	[	[	X
ejpam-6139	658	44	(	(	PUNCT
ejpam-6139	658	45	3|h′′(ν)|q	3|h′′(ν)|q	PROPN
ejpam-6139	658	46	+	+	NUM
ejpam-6139	658	47	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	658	48	4	4	NUM
ejpam-6139	658	49	)	)	PUNCT
ejpam-6139	658	50	1	1	NUM
ejpam-6139	658	51	q	q	NOUN
ejpam-6139	658	52	+	+	CCONJ
ejpam-6139	658	53	(	(	PUNCT
ejpam-6139	658	54	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	658	55	+	+	CCONJ
ejpam-6139	658	56	3|h′′(ω)|q	3|h′′(ω)|q	NUM
ejpam-6139	658	57	4	4	NUM
ejpam-6139	658	58	)	)	PUNCT
ejpam-6139	658	59	1	1	NUM
ejpam-6139	658	60	q	q	NOUN
ejpam-6139	658	61	]	]	PUNCT
ejpam-6139	658	62	.	.	PUNCT
ejpam-6139	659	1	(	(	PUNCT
ejpam-6139	659	2	49	49	NUM
ejpam-6139	659	3	)	)	PUNCT
ejpam-6139	659	4	m.	m.	NOUN
ejpam-6139	659	5	samraiz	samraiz	PROPN
ejpam-6139	659	6	et	et	PROPN
ejpam-6139	659	7	al	al	PROPN
ejpam-6139	659	8	.	.	PUNCT
ejpam-6139	659	9	/	/	SYM
ejpam-6139	659	10	eur	eur	PROPN
ejpam-6139	659	11	.	.	PUNCT
ejpam-6139	660	1	j.	j.	PROPN
ejpam-6139	660	2	pure	pure	PROPN
ejpam-6139	660	3	appl	appl	PROPN
ejpam-6139	660	4	.	.	PROPN
ejpam-6139	660	5	math	math	PROPN
ejpam-6139	660	6	,	,	PUNCT
ejpam-6139	660	7	18	18	NUM
ejpam-6139	660	8	(	(	PUNCT
ejpam-6139	660	9	4	4	NUM
ejpam-6139	660	10	)	)	PUNCT
ejpam-6139	660	11	(	(	PUNCT
ejpam-6139	660	12	2025	2025	NUM
ejpam-6139	660	13	)	)	PUNCT
ejpam-6139	660	14	,	,	PUNCT
ejpam-6139	660	15	6139	6139	NUM
ejpam-6139	660	16	26	26	NUM
ejpam-6139	660	17	of	of	ADP
ejpam-6139	660	18	34	34	NUM
ejpam-6139	660	19	example	example	NOUN
ejpam-6139	660	20	5	5	NUM
ejpam-6139	660	21	.	.	PUNCT
ejpam-6139	661	1	this	this	DET
ejpam-6139	661	2	example	example	NOUN
ejpam-6139	661	3	illustrates	illustrate	VERB
ejpam-6139	661	4	the	the	DET
ejpam-6139	661	5	use	use	NOUN
ejpam-6139	661	6	of	of	ADP
ejpam-6139	661	7	theorem	theorem	NOUN
ejpam-6139	661	8	5	5	NUM
ejpam-6139	661	9	through	through	ADP
ejpam-6139	661	10	a	a	DET
ejpam-6139	661	11	combination	combination	NOUN
ejpam-6139	661	12	of	of	ADP
ejpam-6139	661	13	graphical	graphical	ADJ
ejpam-6139	661	14	and	and	CCONJ
ejpam-6139	661	15	numerical	numerical	ADJ
ejpam-6139	661	16	techniques	technique	NOUN
ejpam-6139	661	17	.	.	PUNCT
ejpam-6139	662	1	the	the	DET
ejpam-6139	662	2	function	function	NOUN
ejpam-6139	662	3	under	under	ADP
ejpam-6139	662	4	consideration	consideration	NOUN
ejpam-6139	662	5	is	be	AUX
ejpam-6139	662	6	h(x	h(x	PROPN
ejpam-6139	662	7	)	)	PUNCT
ejpam-6139	662	8	=	=	SYM
ejpam-6139	663	1	x6	x6	PROPN
ejpam-6139	663	2	+	+	SYM
ejpam-6139	663	3	2x4	2x4	NUM
ejpam-6139	663	4	,	,	PUNCT
ejpam-6139	663	5	defined	define	VERB
ejpam-6139	663	6	on	on	ADP
ejpam-6139	663	7	the	the	DET
ejpam-6139	663	8	interval	interval	NOUN
ejpam-6139	663	9	[	[	X
ejpam-6139	663	10	2	2	NUM
ejpam-6139	663	11	,	,	PUNCT
ejpam-6139	663	12	7	7	NUM
ejpam-6139	663	13	]	]	PUNCT
ejpam-6139	663	14	,	,	PUNCT
ejpam-6139	663	15	with	with	SCONJ
ejpam-6139	663	16	the	the	DET
ejpam-6139	663	17	inequality	inequality	NOUN
ejpam-6139	663	18	evaluated	evaluate	VERB
ejpam-6139	663	19	using	use	VERB
ejpam-6139	663	20	the	the	DET
ejpam-6139	663	21	parameters	parameter	NOUN
ejpam-6139	663	22	k	k	X
ejpam-6139	664	1	=	=	SYM
ejpam-6139	664	2	3	3	NUM
ejpam-6139	664	3	,	,	PUNCT
ejpam-6139	664	4	α	α	NOUN
ejpam-6139	664	5	=	=	SYM
ejpam-6139	664	6	4,s=1	4,s=1	PROPN
ejpam-6139	664	7	,	,	PUNCT
ejpam-6139	664	8	1	1	NUM
ejpam-6139	664	9	p	p	NOUN
ejpam-6139	664	10	=	=	SYM
ejpam-6139	664	11	0.6	0.6	NUM
ejpam-6139	664	12	,	,	PUNCT
ejpam-6139	664	13	1	1	NUM
ejpam-6139	664	14	q	q	NOUN
ejpam-6139	664	15	=	=	NUM
ejpam-6139	664	16	0.4	0.4	NUM
ejpam-6139	664	17	,	,	PUNCT
ejpam-6139	664	18	and	and	CCONJ
ejpam-6139	664	19	η	η	PROPN
ejpam-6139	664	20	=	=	PROPN
ejpam-6139	664	21	8	8	PROPN
ejpam-6139	664	22	.	.	PUNCT
ejpam-6139	665	1	explanation	explanation	NOUN
ejpam-6139	665	2	:	:	PUNCT
ejpam-6139	665	3	figure	figure	NOUN
ejpam-6139	665	4	9	9	NUM
ejpam-6139	665	5	provides	provide	VERB
ejpam-6139	665	6	a	a	DET
ejpam-6139	665	7	2d	2d	NUM
ejpam-6139	665	8	visualization	visualization	NOUN
ejpam-6139	665	9	of	of	ADP
ejpam-6139	665	10	the	the	DET
ejpam-6139	665	11	inequality	inequality	NOUN
ejpam-6139	665	12	(	(	PUNCT
ejpam-6139	665	13	42	42	NUM
ejpam-6139	665	14	)	)	PUNCT
ejpam-6139	665	15	,	,	PUNCT
ejpam-6139	665	16	depicting	depict	VERB
ejpam-6139	665	17	the	the	DET
ejpam-6139	665	18	behavior	behavior	NOUN
ejpam-6139	665	19	of	of	ADP
ejpam-6139	665	20	the	the	DET
ejpam-6139	665	21	left	left	ADJ
ejpam-6139	665	22	-	-	PUNCT
ejpam-6139	665	23	hand	hand	NOUN
ejpam-6139	665	24	side	side	NOUN
ejpam-6139	665	25	and	and	CCONJ
ejpam-6139	665	26	right	right	ADJ
ejpam-6139	665	27	-	-	PUNCT
ejpam-6139	665	28	hand	hand	NOUN
ejpam-6139	665	29	side	side	NOUN
ejpam-6139	665	30	as	as	ADP
ejpam-6139	665	31	µ	µ	NOUN
ejpam-6139	665	32	varies	vary	VERB
ejpam-6139	665	33	in	in	ADP
ejpam-6139	665	34	(	(	PUNCT
ejpam-6139	665	35	0	0	NUM
ejpam-6139	665	36	,	,	PUNCT
ejpam-6139	665	37	1	1	NUM
ejpam-6139	665	38	]	]	PUNCT
ejpam-6139	665	39	.	.	PUNCT
ejpam-6139	666	1	the	the	DET
ejpam-6139	666	2	graph	graph	NOUN
ejpam-6139	666	3	demonstrates	demonstrate	VERB
ejpam-6139	666	4	that	that	SCONJ
ejpam-6139	666	5	the	the	DET
ejpam-6139	666	6	lhs	lhs	PROPN
ejpam-6139	666	7	consistently	consistently	ADV
ejpam-6139	666	8	adheres	adhere	VERB
ejpam-6139	666	9	to	to	ADP
ejpam-6139	666	10	the	the	DET
ejpam-6139	666	11	bounds	bound	NOUN
ejpam-6139	666	12	imposed	impose	VERB
ejpam-6139	666	13	by	by	ADP
ejpam-6139	666	14	the	the	DET
ejpam-6139	666	15	rhs	rhs	PROPN
ejpam-6139	666	16	,	,	PUNCT
ejpam-6139	666	17	supporting	support	VERB
ejpam-6139	666	18	the	the	DET
ejpam-6139	666	19	validity	validity	NOUN
ejpam-6139	666	20	of	of	ADP
ejpam-6139	666	21	the	the	DET
ejpam-6139	666	22	theorem	theorem	NOUN
ejpam-6139	666	23	.	.	PROPN
ejpam-6139	666	24	to	to	PART
ejpam-6139	666	25	complement	complement	VERB
ejpam-6139	666	26	the	the	DET
ejpam-6139	666	27	graphical	graphical	ADJ
ejpam-6139	666	28	analysis	analysis	NOUN
ejpam-6139	666	29	,	,	PUNCT
ejpam-6139	666	30	numerical	numerical	ADJ
ejpam-6139	666	31	evaluations	evaluation	NOUN
ejpam-6139	666	32	of	of	ADP
ejpam-6139	666	33	the	the	DET
ejpam-6139	666	34	lhs	lhs	PROPN
ejpam-6139	666	35	and	and	CCONJ
ejpam-6139	666	36	rhs	rhs	PROPN
ejpam-6139	666	37	were	be	AUX
ejpam-6139	666	38	conducted	conduct	VERB
ejpam-6139	666	39	for	for	ADP
ejpam-6139	666	40	specific	specific	ADJ
ejpam-6139	666	41	values	value	NOUN
ejpam-6139	666	42	of	of	ADP
ejpam-6139	666	43	µ.	µ.	NOUN
ejpam-6139	666	44	the	the	DET
ejpam-6139	666	45	results	result	NOUN
ejpam-6139	666	46	,	,	PUNCT
ejpam-6139	666	47	displayed	display	VERB
ejpam-6139	666	48	in	in	ADP
ejpam-6139	666	49	a	a	DET
ejpam-6139	666	50	table	table	NOUN
ejpam-6139	666	51	7	7	NUM
ejpam-6139	666	52	,	,	PUNCT
ejpam-6139	666	53	confirm	confirm	VERB
ejpam-6139	666	54	that	that	SCONJ
ejpam-6139	666	55	the	the	DET
ejpam-6139	666	56	inequality	inequality	NOUN
ejpam-6139	666	57	holds	hold	VERB
ejpam-6139	666	58	under	under	ADP
ejpam-6139	666	59	the	the	DET
ejpam-6139	666	60	given	give	VERB
ejpam-6139	666	61	parameters	parameter	NOUN
ejpam-6139	666	62	.	.	PUNCT
ejpam-6139	667	1	figure	figure	VERB
ejpam-6139	667	2	9	9	NUM
ejpam-6139	667	3	:	:	PUNCT
ejpam-6139	667	4	this	this	DET
ejpam-6139	667	5	figure	figure	NOUN
ejpam-6139	667	6	is	be	AUX
ejpam-6139	667	7	illustrating	illustrate	VERB
ejpam-6139	667	8	the	the	DET
ejpam-6139	667	9	2d	2d	NOUN
ejpam-6139	667	10	visualization	visualization	NOUN
ejpam-6139	667	11	of	of	ADP
ejpam-6139	667	12	the	the	DET
ejpam-6139	667	13	inequality	inequality	NOUN
ejpam-6139	667	14	(	(	PUNCT
ejpam-6139	667	15	42	42	NUM
ejpam-6139	667	16	)	)	PUNCT
ejpam-6139	667	17	confirming	confirm	VERB
ejpam-6139	667	18	the	the	DET
ejpam-6139	667	19	validity	validity	NOUN
ejpam-6139	667	20	its	its	PRON
ejpam-6139	667	21	validity	validity	NOUN
ejpam-6139	667	22	.	.	PUNCT
ejpam-6139	668	1	table	table	NOUN
ejpam-6139	668	2	7	7	NUM
ejpam-6139	668	3	:	:	PUNCT
ejpam-6139	668	4	this	this	DET
ejpam-6139	668	5	table	table	NOUN
ejpam-6139	668	6	summarizes	summarize	VERB
ejpam-6139	668	7	the	the	DET
ejpam-6139	668	8	numerical	numerical	ADJ
ejpam-6139	668	9	results	result	NOUN
ejpam-6139	668	10	of	of	ADP
ejpam-6139	668	11	(	(	PUNCT
ejpam-6139	668	12	42	42	NUM
ejpam-6139	668	13	)	)	PUNCT
ejpam-6139	668	14	.	.	PUNCT
ejpam-6139	669	1	µ	µ	X
ejpam-6139	669	2	0.2	0.2	NUM
ejpam-6139	669	3	0.4	0.4	NUM
ejpam-6139	669	4	0.6	0.6	NUM
ejpam-6139	669	5	0.8	0.8	NUM
ejpam-6139	669	6	1	1	NUM
ejpam-6139	669	7	lhs	lhs	PROPN
ejpam-6139	669	8	65.30	65.30	NUM
ejpam-6139	669	9	144.68	144.68	NUM
ejpam-6139	669	10	221	221	NUM
ejpam-6139	669	11	291.37	291.37	NUM
ejpam-6139	669	12	355.37	355.37	NUM
ejpam-6139	669	13	rhs	rhs	PROPN
ejpam-6139	669	14	151.38	151.38	NUM
ejpam-6139	669	15	328.386	328.386	NUM
ejpam-6139	669	16	492.93	492.93	NUM
ejpam-6139	669	17	640.33	640.33	NUM
ejpam-6139	669	18	771.12	771.12	NUM
ejpam-6139	669	19	further	further	ADJ
ejpam-6139	669	20	validation	validation	NOUN
ejpam-6139	669	21	was	be	AUX
ejpam-6139	669	22	performed	perform	VERB
ejpam-6139	669	23	by	by	ADP
ejpam-6139	669	24	generating	generate	VERB
ejpam-6139	669	25	a	a	DET
ejpam-6139	669	26	3d	3d	NOUN
ejpam-6139	669	27	representation	representation	NOUN
ejpam-6139	669	28	of	of	ADP
ejpam-6139	669	29	the	the	DET
ejpam-6139	669	30	inequality	inequality	NOUN
ejpam-6139	669	31	as	as	SCONJ
ejpam-6139	669	32	α	α	PROPN
ejpam-6139	669	33	ranges	range	VERB
ejpam-6139	669	34	within	within	ADP
ejpam-6139	669	35	[	[	X
ejpam-6139	669	36	5	5	NUM
ejpam-6139	669	37	,	,	PUNCT
ejpam-6139	669	38	10	10	NUM
ejpam-6139	669	39	]	]	PUNCT
ejpam-6139	669	40	and	and	CCONJ
ejpam-6139	669	41	µ	µ	X
ejpam-6139	669	42	within	within	X
ejpam-6139	669	43	(	(	PUNCT
ejpam-6139	669	44	0	0	NUM
ejpam-6139	669	45	,	,	PUNCT
ejpam-6139	669	46	1	1	NUM
ejpam-6139	669	47	]	]	PUNCT
ejpam-6139	669	48	.	.	PUNCT
ejpam-6139	670	1	the	the	DET
ejpam-6139	670	2	resulting	result	VERB
ejpam-6139	670	3	surface	surface	NOUN
ejpam-6139	670	4	plot	plot	NOUN
ejpam-6139	670	5	,	,	PUNCT
ejpam-6139	670	6	presented	present	VERB
ejpam-6139	670	7	in	in	ADP
ejpam-6139	670	8	figure	figure	NOUN
ejpam-6139	670	9	10	10	NUM
ejpam-6139	670	10	,	,	PUNCT
ejpam-6139	670	11	illustrates	illustrate	VERB
ejpam-6139	670	12	that	that	SCONJ
ejpam-6139	670	13	the	the	DET
ejpam-6139	670	14	inequality	inequality	NOUN
ejpam-6139	670	15	remains	remain	VERB
ejpam-6139	670	16	valid	valid	ADJ
ejpam-6139	670	17	across	across	ADP
ejpam-6139	670	18	the	the	DET
ejpam-6139	670	19	explored	explore	VERB
ejpam-6139	670	20	parameter	parameter	NOUN
ejpam-6139	670	21	space	space	NOUN
ejpam-6139	670	22	.	.	PUNCT
ejpam-6139	671	1	this	this	DET
ejpam-6139	671	2	figure	figure	NOUN
ejpam-6139	671	3	10	10	NUM
ejpam-6139	671	4	:	:	PUNCT
ejpam-6139	671	5	three	three	NUM
ejpam-6139	671	6	-	-	PUNCT
ejpam-6139	671	7	dimensional	dimensional	ADJ
ejpam-6139	671	8	validation	validation	NOUN
ejpam-6139	671	9	of	of	ADP
ejpam-6139	671	10	theorem	theorem	NOUN
ejpam-6139	671	11	5	5	NUM
ejpam-6139	671	12	across	across	ADP
ejpam-6139	671	13	different	different	ADJ
ejpam-6139	671	14	values	value	NOUN
ejpam-6139	671	15	of	of	ADP
ejpam-6139	671	16	α	α	PROPN
ejpam-6139	671	17	and	and	CCONJ
ejpam-6139	671	18	µ.	µ.	PROPN
ejpam-6139	671	19	m.	m.	PROPN
ejpam-6139	671	20	samraiz	samraiz	PROPN
ejpam-6139	671	21	et	et	PROPN
ejpam-6139	671	22	al	al	PROPN
ejpam-6139	671	23	.	.	PUNCT
ejpam-6139	671	24	/	/	SYM
ejpam-6139	671	25	eur	eur	PROPN
ejpam-6139	671	26	.	.	PUNCT
ejpam-6139	672	1	j.	j.	PROPN
ejpam-6139	672	2	pure	pure	PROPN
ejpam-6139	672	3	appl	appl	PROPN
ejpam-6139	672	4	.	.	PROPN
ejpam-6139	672	5	math	math	PROPN
ejpam-6139	672	6	,	,	PUNCT
ejpam-6139	672	7	18	18	NUM
ejpam-6139	672	8	(	(	PUNCT
ejpam-6139	672	9	4	4	NUM
ejpam-6139	672	10	)	)	PUNCT
ejpam-6139	672	11	(	(	PUNCT
ejpam-6139	672	12	2025	2025	NUM
ejpam-6139	672	13	)	)	PUNCT
ejpam-6139	672	14	,	,	PUNCT
ejpam-6139	672	15	6139	6139	NUM
ejpam-6139	672	16	27	27	NUM
ejpam-6139	672	17	of	of	ADP
ejpam-6139	672	18	34	34	NUM
ejpam-6139	672	19	comprehensive	comprehensive	ADJ
ejpam-6139	672	20	analysis	analysis	NOUN
ejpam-6139	672	21	underscores	underscore	VERB
ejpam-6139	672	22	the	the	DET
ejpam-6139	672	23	utility	utility	NOUN
ejpam-6139	672	24	and	and	CCONJ
ejpam-6139	672	25	reliability	reliability	NOUN
ejpam-6139	672	26	of	of	ADP
ejpam-6139	672	27	theorem	theorem	NOUN
ejpam-6139	672	28	5	5	NUM
ejpam-6139	672	29	,	,	PUNCT
ejpam-6139	672	30	verifying	verify	VERB
ejpam-6139	672	31	its	its	PRON
ejpam-6139	672	32	capacity	capacity	NOUN
ejpam-6139	672	33	to	to	PART
ejpam-6139	672	34	constrain	constrain	VERB
ejpam-6139	672	35	the	the	DET
ejpam-6139	672	36	behavior	behavior	NOUN
ejpam-6139	672	37	of	of	ADP
ejpam-6139	672	38	h(x	h(x	PROPN
ejpam-6139	672	39	)	)	PUNCT
ejpam-6139	672	40	under	under	ADP
ejpam-6139	672	41	the	the	DET
ejpam-6139	672	42	specified	specified	ADJ
ejpam-6139	672	43	conditions	condition	NOUN
ejpam-6139	672	44	.	.	PUNCT
ejpam-6139	673	1	theorem	theorem	NOUN
ejpam-6139	673	2	6	6	NUM
ejpam-6139	673	3	.	.	PUNCT
ejpam-6139	674	1	let	let	VERB
ejpam-6139	674	2	h	h	NOUN
ejpam-6139	674	3	:	:	PUNCT
ejpam-6139	675	1	[	[	X
ejpam-6139	675	2	ν	ν	X
ejpam-6139	675	3	,	,	PUNCT
ejpam-6139	675	4	ω	ω	NOUN
ejpam-6139	675	5	]	]	X
ejpam-6139	675	6	→	→	PUNCT
ejpam-6139	675	7	r	r	NOUN
ejpam-6139	675	8	be	be	AUX
ejpam-6139	675	9	a	a	DET
ejpam-6139	675	10	twice	twice	ADV
ejpam-6139	675	11	differentiable	differentiable	ADJ
ejpam-6139	675	12	mapping	mapping	NOUN
ejpam-6139	675	13	on	on	ADP
ejpam-6139	675	14	(	(	PUNCT
ejpam-6139	675	15	ν	ν	PROPN
ejpam-6139	675	16	,	,	PUNCT
ejpam-6139	675	17	ω	ω	NOUN
ejpam-6139	675	18	)	)	PUNCT
ejpam-6139	675	19	such	such	ADJ
ejpam-6139	675	20	that	that	DET
ejpam-6139	675	21	h′′l1([ν	h′′l1([ν	PROPN
ejpam-6139	675	22	,	,	PUNCT
ejpam-6139	675	23	ω	ω	NOUN
ejpam-6139	675	24	]	]	NOUN
ejpam-6139	675	25	)	)	PUNCT
ejpam-6139	675	26	.	.	PUNCT
ejpam-6139	676	1	let	let	VERB
ejpam-6139	676	2	|h′′|q	|h′′|q	NOUN
ejpam-6139	676	3	be	be	AUX
ejpam-6139	676	4	a	a	DET
ejpam-6139	676	5	s	s	NOUN
ejpam-6139	676	6	-	-	NOUN
ejpam-6139	676	7	convex	convex	NOUN
ejpam-6139	676	8	in	in	ADP
ejpam-6139	676	9	second	second	ADJ
ejpam-6139	676	10	sense	sense	NOUN
ejpam-6139	676	11	on	on	ADP
ejpam-6139	676	12	[	[	X
ejpam-6139	676	13	ν	ν	X
ejpam-6139	676	14	,	,	PUNCT
ejpam-6139	676	15	ω	ω	NOUN
ejpam-6139	676	16	]	]	PUNCT
ejpam-6139	676	17	with	with	ADP
ejpam-6139	676	18	q	q	PROPN
ejpam-6139	676	19	>	>	X
ejpam-6139	676	20	1	1	NUM
ejpam-6139	676	21	then,∣∣∣∣	then,∣∣∣∣	NUM
ejpam-6139	676	22	ηµ	ηµ	VERB
ejpam-6139	676	23	α	α	PROPN
ejpam-6139	676	24	k	k	X
ejpam-6139	676	25	−1	−1	PROPN
ejpam-6139	676	26	(	(	PUNCT
ejpam-6139	676	27	ω	ω	PROPN
ejpam-6139	676	28	−	−	PROPN
ejpam-6139	677	1	ν)µ	ν)µ	ADV
ejpam-6139	677	2	α	α	PROPN
ejpam-6139	677	3	k	k	PROPN
ejpam-6139	677	4	(	(	PUNCT
ejpam-6139	677	5	kµ	kµ	PROPN
ejpam-6139	677	6	)	)	PUNCT
ejpam-6139	678	1	α	α	PROPN
ejpam-6139	678	2	k	k	PROPN
ejpam-6139	678	3	γ	γ	X
ejpam-6139	678	4	(	(	PUNCT
ejpam-6139	678	5	α	α	NOUN
ejpam-6139	678	6	k	k	PROPN
ejpam-6139	679	1	+	+	PROPN
ejpam-6139	679	2	1	1	X
ejpam-6139	679	3	)	)	PUNCT
ejpam-6139	679	4	(	(	PUNCT
ejpam-6139	679	5	α	α	PROPN
ejpam-6139	679	6	k	k	PROPN
ejpam-6139	679	7	j	j	PROPN
ejpam-6139	679	8	µ	µ	X
ejpam-6139	679	9	(	(	PUNCT
ejpam-6139	679	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	679	11	η	η	PROPN
ejpam-6139	679	12	−	−	PROPN
ejpam-6139	679	13	h(ν	h(ν	PROPN
ejpam-6139	679	14	)	)	PUNCT
ejpam-6139	679	15	+	+	NOUN
ejpam-6139	679	16	α	α	NOUN
ejpam-6139	679	17	k	k	X
ejpam-6139	679	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	679	19	η	η	PROPN
ejpam-6139	679	20	+	+	PROPN
ejpam-6139	679	21	h(ω	h(ω	PROPN
ejpam-6139	679	22	)	)	PUNCT
ejpam-6139	679	23	)	)	PUNCT
ejpam-6139	680	1	+	+	X
ejpam-6139	680	2	υk[µ	υk[µ	PROPN
ejpam-6139	680	3	,	,	PUNCT
ejpam-6139	680	4	α	α	NOUN
ejpam-6139	680	5	]	]	X
ejpam-6139	680	6	−	−	PROPN
ejpam-6139	680	7	1	1	NUM
ejpam-6139	680	8	η	η	PROPN
ejpam-6139	680	9	(	(	PUNCT
ejpam-6139	680	10	h	h	PROPN
ejpam-6139	680	11	(	(	PUNCT
ejpam-6139	680	12	η	η	PROPN
ejpam-6139	680	13	−	−	PROPN
ejpam-6139	680	14	1	1	NUM
ejpam-6139	680	15	η	η	PROPN
ejpam-6139	680	16	ν	ν	X
ejpam-6139	680	17	+	+	PROPN
ejpam-6139	680	18	1	1	NUM
ejpam-6139	680	19	η	η	PROPN
ejpam-6139	680	20	ω	ω	PROPN
ejpam-6139	680	21	)	)	PUNCT
ejpam-6139	680	22	+	+	CCONJ
ejpam-6139	680	23	h	h	NOUN
ejpam-6139	680	24	(	(	PUNCT
ejpam-6139	680	25	1	1	NUM
ejpam-6139	680	26	η	η	X
ejpam-6139	680	27	ν	ν	X
ejpam-6139	680	28	+	+	CCONJ
ejpam-6139	680	29	η	η	PROPN
ejpam-6139	680	30	−	−	PROPN
ejpam-6139	680	31	1	1	NUM
ejpam-6139	680	32	η	η	PROPN
ejpam-6139	680	33	ω	ω	PROPN
ejpam-6139	680	34	)	)	PUNCT
ejpam-6139	680	35	)	)	PUNCT
ejpam-6139	680	36	∣∣∣∣≤	∣∣∣∣≤	PROPN
ejpam-6139	680	37	(	(	PUNCT
ejpam-6139	680	38	ω	ω	NUM
ejpam-6139	680	39	−	−	PROPN
ejpam-6139	680	40	ν)2	ν)2	PROPN
ejpam-6139	680	41	η3	η3	PROPN
ejpam-6139	680	42	(	(	PUNCT
ejpam-6139	680	43	kµ	kµ	PROPN
ejpam-6139	680	44	)	)	PUNCT
ejpam-6139	680	45	α	α	PROPN
ejpam-6139	680	46	k	k	PROPN
ejpam-6139	680	47	×	×	PROPN
ejpam-6139	680	48	(	(	PUNCT
ejpam-6139	680	49	∫	∫	PROPN
ejpam-6139	680	50	1	1	NUM
ejpam-6139	680	51	0	0	NUM
ejpam-6139	680	52	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	680	53	∫	∫	PROPN
ejpam-6139	680	54	t	t	PROPN
ejpam-6139	680	55	0	0	NUM
ejpam-6139	680	56	(	(	PUNCT
ejpam-6139	680	57	1−	1−	NUM
ejpam-6139	680	58	(	(	PUNCT
ejpam-6139	680	59	1−	1−	NUM
ejpam-6139	680	60	φ)µ	φ)µ	NOUN
ejpam-6139	680	61	ku	ku	PROPN
ejpam-6139	680	62	)	)	PUNCT
ejpam-6139	681	1	α	α	PROPN
ejpam-6139	681	2	k	k	X
ejpam-6139	681	3	dφ	dφ	ADP
ejpam-6139	681	4	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	681	5	)	)	PUNCT
ejpam-6139	682	1	1−	1−	PROPN
ejpam-6139	682	2	1	1	NUM
ejpam-6139	682	3	q	q	NOUN
ejpam-6139	683	1	[	[	X
ejpam-6139	683	2	(	(	PUNCT
ejpam-6139	683	3	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	683	4	ηs	ηs	ADP
ejpam-6139	683	5	ξ2k(µ	ξ2k(µ	PROPN
ejpam-6139	683	6	,	,	PUNCT
ejpam-6139	683	7	α	α	X
ejpam-6139	683	8	)	)	PUNCT
ejpam-6139	683	9	+	+	NUM
ejpam-6139	683	10	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	683	11	ηs	ηs	ADP
ejpam-6139	683	12	ξ1k(µ	ξ1k(µ	PROPN
ejpam-6139	683	13	,	,	PUNCT
ejpam-6139	683	14	α	α	NOUN
ejpam-6139	683	15	)	)	PUNCT
ejpam-6139	683	16	)	)	PUNCT
ejpam-6139	683	17	1	1	NUM
ejpam-6139	683	18	q	q	NOUN
ejpam-6139	683	19	+	+	CCONJ
ejpam-6139	683	20	(	(	PUNCT
ejpam-6139	683	21	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	683	22	ηs	ηs	ADP
ejpam-6139	683	23	ξ1k(µ	ξ1k(µ	PROPN
ejpam-6139	683	24	,	,	PUNCT
ejpam-6139	683	25	α	α	X
ejpam-6139	683	26	)	)	PUNCT
ejpam-6139	683	27	+	+	NUM
ejpam-6139	683	28	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	683	29	ηs	ηs	ADP
ejpam-6139	683	30	ξ2k(µ	ξ2k(µ	PROPN
ejpam-6139	683	31	,	,	PUNCT
ejpam-6139	683	32	α	α	NOUN
ejpam-6139	683	33	)	)	PUNCT
ejpam-6139	683	34	)	)	PUNCT
ejpam-6139	683	35	1	1	NUM
ejpam-6139	683	36	q	q	NOUN
ejpam-6139	683	37	]	]	PUNCT
ejpam-6139	683	38	(	(	PUNCT
ejpam-6139	683	39	50	50	NUM
ejpam-6139	683	40	)	)	PUNCT
ejpam-6139	683	41	where	where	SCONJ
ejpam-6139	683	42	ξ1k(µ	ξ1k(µ	PROPN
ejpam-6139	683	43	,	,	PUNCT
ejpam-6139	683	44	α	α	X
ejpam-6139	683	45	)	)	PUNCT
ejpam-6139	683	46	=	=	SYM
ejpam-6139	683	47	∫	∫	PROPN
ejpam-6139	683	48	1	1	NUM
ejpam-6139	683	49	0	0	NUM
ejpam-6139	683	50	ts	ts	ADP
ejpam-6139	683	51	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	683	52	∫	∫	PROPN
ejpam-6139	683	53	t	t	PROPN
ejpam-6139	683	54	0	0	NUM
ejpam-6139	683	55	(	(	PUNCT
ejpam-6139	683	56	1−	1−	NUM
ejpam-6139	683	57	(	(	PUNCT
ejpam-6139	683	58	1−	1−	NUM
ejpam-6139	683	59	φ)µ	φ)µ	NOUN
ejpam-6139	683	60	ku	ku	PROPN
ejpam-6139	683	61	)	)	PUNCT
ejpam-6139	683	62	α	α	PROPN
ejpam-6139	683	63	k	k	X
ejpam-6139	683	64	dφ	dφ	ADP
ejpam-6139	683	65	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	683	66	,	,	PUNCT
ejpam-6139	683	67	ξ2k(µ	ξ2k(µ	PROPN
ejpam-6139	683	68	,	,	PUNCT
ejpam-6139	683	69	α	α	X
ejpam-6139	683	70	)	)	PUNCT
ejpam-6139	683	71	=	=	SYM
ejpam-6139	683	72	∫	∫	PROPN
ejpam-6139	683	73	1	1	NUM
ejpam-6139	683	74	0	0	NUM
ejpam-6139	683	75	(	(	PUNCT
ejpam-6139	683	76	η	η	PROPN
ejpam-6139	683	77	−	−	PROPN
ejpam-6139	683	78	t)s	t)s	ADJ
ejpam-6139	683	79	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	683	80	∫	∫	PROPN
ejpam-6139	683	81	t	t	PROPN
ejpam-6139	683	82	0	0	NUM
ejpam-6139	684	1	(	(	PUNCT
ejpam-6139	684	2	1−	1−	NUM
ejpam-6139	684	3	(	(	PUNCT
ejpam-6139	684	4	1−	1−	NUM
ejpam-6139	684	5	φ)µ	φ)µ	NOUN
ejpam-6139	684	6	ku	ku	PROPN
ejpam-6139	684	7	)	)	PUNCT
ejpam-6139	684	8	α	α	PROPN
ejpam-6139	684	9	k	k	X
ejpam-6139	684	10	dφ	dφ	ADP
ejpam-6139	684	11	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	684	12	.	.	PUNCT
ejpam-6139	685	1	proof	proof	NOUN
ejpam-6139	685	2	.	.	PUNCT
ejpam-6139	686	1	by	by	ADP
ejpam-6139	686	2	employing	employ	VERB
ejpam-6139	686	3	power	power	NOUN
ejpam-6139	686	4	mean	mean	VERB
ejpam-6139	686	5	inequality	inequality	NOUN
ejpam-6139	686	6	on	on	ADP
ejpam-6139	686	7	equation	equation	NOUN
ejpam-6139	686	8	(	(	PUNCT
ejpam-6139	686	9	37),∣∣∣∣	37),∣∣∣∣	NUM
ejpam-6139	686	10	ηµ	ηµ	VERB
ejpam-6139	686	11	α	α	PROPN
ejpam-6139	686	12	k	k	X
ejpam-6139	686	13	−1	−1	PROPN
ejpam-6139	686	14	(	(	PUNCT
ejpam-6139	686	15	ω	ω	PROPN
ejpam-6139	686	16	−	−	PROPN
ejpam-6139	686	17	ν)µ	ν)µ	ADV
ejpam-6139	686	18	α	α	PROPN
ejpam-6139	686	19	k	k	PROPN
ejpam-6139	686	20	(	(	PUNCT
ejpam-6139	686	21	kµ	kµ	PROPN
ejpam-6139	686	22	)	)	PUNCT
ejpam-6139	686	23	α	α	PROPN
ejpam-6139	686	24	k	k	PROPN
ejpam-6139	686	25	γ	γ	X
ejpam-6139	686	26	(	(	PUNCT
ejpam-6139	686	27	α	α	NOUN
ejpam-6139	686	28	k	k	PROPN
ejpam-6139	687	1	+	+	PROPN
ejpam-6139	687	2	1	1	X
ejpam-6139	687	3	)	)	PUNCT
ejpam-6139	687	4	(	(	PUNCT
ejpam-6139	687	5	α	α	PROPN
ejpam-6139	687	6	k	k	PROPN
ejpam-6139	687	7	j	j	PROPN
ejpam-6139	687	8	µ	µ	X
ejpam-6139	687	9	(	(	PUNCT
ejpam-6139	687	10	η−1)ν+ω	η−1)ν+ω	PROPN
ejpam-6139	687	11	η	η	PROPN
ejpam-6139	687	12	−	−	PROPN
ejpam-6139	687	13	h(ν	h(ν	PROPN
ejpam-6139	687	14	)	)	PUNCT
ejpam-6139	687	15	+	+	NOUN
ejpam-6139	687	16	α	α	NOUN
ejpam-6139	687	17	k	k	X
ejpam-6139	687	18	jµν+(η−1)ω	jµν+(η−1)ω	PRON
ejpam-6139	687	19	η	η	PROPN
ejpam-6139	687	20	+	+	PROPN
ejpam-6139	687	21	h(ω	h(ω	PROPN
ejpam-6139	687	22	)	)	PUNCT
ejpam-6139	687	23	)	)	PUNCT
ejpam-6139	688	1	+	+	X
ejpam-6139	688	2	υk[µ	υk[µ	PROPN
ejpam-6139	688	3	,	,	PUNCT
ejpam-6139	688	4	α	α	NOUN
ejpam-6139	688	5	]	]	X
ejpam-6139	688	6	−	−	PROPN
ejpam-6139	688	7	1	1	NUM
ejpam-6139	688	8	η	η	PROPN
ejpam-6139	688	9	(	(	PUNCT
ejpam-6139	688	10	h	h	PROPN
ejpam-6139	688	11	(	(	PUNCT
ejpam-6139	688	12	η	η	PROPN
ejpam-6139	688	13	−	−	PROPN
ejpam-6139	688	14	1	1	NUM
ejpam-6139	688	15	η	η	PROPN
ejpam-6139	688	16	ν	ν	X
ejpam-6139	688	17	+	+	PROPN
ejpam-6139	688	18	1	1	NUM
ejpam-6139	688	19	η	η	PROPN
ejpam-6139	688	20	ω	ω	PROPN
ejpam-6139	688	21	)	)	PUNCT
ejpam-6139	688	22	+	+	CCONJ
ejpam-6139	688	23	h	h	NOUN
ejpam-6139	688	24	(	(	PUNCT
ejpam-6139	688	25	1	1	NUM
ejpam-6139	688	26	η	η	X
ejpam-6139	688	27	ν	ν	X
ejpam-6139	688	28	+	+	CCONJ
ejpam-6139	688	29	η	η	PROPN
ejpam-6139	688	30	−	−	PROPN
ejpam-6139	688	31	1	1	NUM
ejpam-6139	688	32	η	η	PROPN
ejpam-6139	688	33	ω	ω	PROPN
ejpam-6139	688	34	)	)	PUNCT
ejpam-6139	688	35	)	)	PUNCT
ejpam-6139	688	36	∣∣∣∣≤	∣∣∣∣≤	PROPN
ejpam-6139	688	37	(	(	PUNCT
ejpam-6139	688	38	ω	ω	NUM
ejpam-6139	688	39	−	−	PROPN
ejpam-6139	688	40	ν)2	ν)2	PROPN
ejpam-6139	688	41	η3	η3	PROPN
ejpam-6139	688	42	(	(	PUNCT
ejpam-6139	688	43	kµ	kµ	PROPN
ejpam-6139	688	44	)	)	PUNCT
ejpam-6139	688	45	α	α	PROPN
ejpam-6139	689	1	k	k	NOUN
ejpam-6139	689	2	×	×	PROPN
ejpam-6139	690	1	[	[	X
ejpam-6139	690	2	(	(	PUNCT
ejpam-6139	690	3	∫	∫	PROPN
ejpam-6139	690	4	1	1	NUM
ejpam-6139	690	5	0	0	NUM
ejpam-6139	690	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	690	7	∫	∫	PROPN
ejpam-6139	690	8	t	t	PROPN
ejpam-6139	690	9	0	0	NUM
ejpam-6139	690	10	(	(	PUNCT
ejpam-6139	690	11	1−	1−	NUM
ejpam-6139	690	12	(	(	PUNCT
ejpam-6139	690	13	1−	1−	NUM
ejpam-6139	690	14	φ)µ	φ)µ	NOUN
ejpam-6139	690	15	ku	ku	PROPN
ejpam-6139	690	16	)	)	PUNCT
ejpam-6139	690	17	α	α	PROPN
ejpam-6139	690	18	k	k	X
ejpam-6139	690	19	dφ	dφ	ADP
ejpam-6139	690	20	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	690	21	)	)	PUNCT
ejpam-6139	690	22	1−	1−	NUM
ejpam-6139	691	1	1	1	NUM
ejpam-6139	691	2	q	q	NOUN
ejpam-6139	691	3	×	×	NOUN
ejpam-6139	691	4	(	(	PUNCT
ejpam-6139	691	5	∫	∫	PROPN
ejpam-6139	691	6	1	1	NUM
ejpam-6139	691	7	0	0	NUM
ejpam-6139	691	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	691	9	∫	∫	PROPN
ejpam-6139	691	10	t	t	PROPN
ejpam-6139	691	11	0	0	NUM
ejpam-6139	691	12	(	(	PUNCT
ejpam-6139	691	13	1−	1−	NUM
ejpam-6139	691	14	(	(	PUNCT
ejpam-6139	691	15	1−	1−	NUM
ejpam-6139	691	16	φ)µ	φ)µ	NOUN
ejpam-6139	691	17	ku	ku	PROPN
ejpam-6139	691	18	)	)	PUNCT
ejpam-6139	691	19	α	α	PROPN
ejpam-6139	692	1	k	k	X
ejpam-6139	692	2	dφ	dφ	X
ejpam-6139	692	3	∣∣∣∣.∣∣∣∣h′′(η	∣∣∣∣.∣∣∣∣h′′(η	ADP
ejpam-6139	692	4	−	−	PROPN
ejpam-6139	692	5	t	t	PROPN
ejpam-6139	692	6	η	η	PROPN
ejpam-6139	692	7	ν	ν	PROPN
ejpam-6139	692	8	+	+	PROPN
ejpam-6139	692	9	t	t	PROPN
ejpam-6139	692	10	η	η	PROPN
ejpam-6139	692	11	ω	ω	PROPN
ejpam-6139	692	12	)	)	PUNCT
ejpam-6139	692	13	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	692	14	)	)	PUNCT
ejpam-6139	692	15	1	1	NUM
ejpam-6139	692	16	q	q	NOUN
ejpam-6139	693	1	+	+	CCONJ
ejpam-6139	693	2	(	(	PUNCT
ejpam-6139	693	3	∫	∫	PROPN
ejpam-6139	693	4	1	1	NUM
ejpam-6139	693	5	0	0	NUM
ejpam-6139	693	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	693	7	∫	∫	PROPN
ejpam-6139	693	8	t	t	PROPN
ejpam-6139	693	9	0	0	NUM
ejpam-6139	693	10	(	(	PUNCT
ejpam-6139	693	11	1−	1−	NUM
ejpam-6139	693	12	(	(	PUNCT
ejpam-6139	693	13	1−	1−	NUM
ejpam-6139	693	14	φ)µ	φ)µ	NOUN
ejpam-6139	693	15	ku	ku	PROPN
ejpam-6139	693	16	)	)	PUNCT
ejpam-6139	693	17	α	α	PROPN
ejpam-6139	694	1	k	k	X
ejpam-6139	694	2	dφ	dφ	ADP
ejpam-6139	694	3	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	694	4	)	)	PUNCT
ejpam-6139	694	5	1−	1−	NUM
ejpam-6139	695	1	1	1	NUM
ejpam-6139	695	2	q	q	NOUN
ejpam-6139	695	3	×	×	NOUN
ejpam-6139	695	4	(	(	PUNCT
ejpam-6139	695	5	∫	∫	PROPN
ejpam-6139	695	6	1	1	NUM
ejpam-6139	695	7	0	0	NUM
ejpam-6139	695	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	695	9	∫	∫	PROPN
ejpam-6139	695	10	t	t	PROPN
ejpam-6139	695	11	0	0	NUM
ejpam-6139	695	12	(	(	PUNCT
ejpam-6139	695	13	1−	1−	NUM
ejpam-6139	695	14	(	(	PUNCT
ejpam-6139	695	15	1−	1−	NUM
ejpam-6139	695	16	φ)µ	φ)µ	NOUN
ejpam-6139	695	17	ku	ku	PROPN
ejpam-6139	695	18	)	)	PUNCT
ejpam-6139	695	19	α	α	PROPN
ejpam-6139	695	20	k	k	X
ejpam-6139	695	21	dφ	dφ	ADP
ejpam-6139	695	22	∣∣∣∣.∣∣∣∣h′′	∣∣∣∣.∣∣∣∣h′′	PROPN
ejpam-6139	695	23	(	(	PUNCT
ejpam-6139	695	24	t	t	PROPN
ejpam-6139	695	25	η	η	PROPN
ejpam-6139	695	26	ν	ν	PROPN
ejpam-6139	695	27	+	+	PROPN
ejpam-6139	695	28	η	η	PROPN
ejpam-6139	695	29	−	−	PROPN
ejpam-6139	695	30	t	t	PROPN
ejpam-6139	695	31	η	η	PROPN
ejpam-6139	695	32	ω	ω	PROPN
ejpam-6139	695	33	)	)	PUNCT
ejpam-6139	695	34	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	695	35	)	)	PUNCT
ejpam-6139	695	36	1	1	NUM
ejpam-6139	695	37	q	q	NOUN
ejpam-6139	695	38	]	]	PUNCT
ejpam-6139	695	39	.	.	PUNCT
ejpam-6139	696	1	(	(	PUNCT
ejpam-6139	696	2	51	51	NUM
ejpam-6139	696	3	)	)	PUNCT
ejpam-6139	696	4	by	by	ADP
ejpam-6139	696	5	considering	consider	VERB
ejpam-6139	696	6	s	s	NOUN
ejpam-6139	696	7	-	-	NOUN
ejpam-6139	696	8	convexity	convexity	NOUN
ejpam-6139	696	9	of	of	ADP
ejpam-6139	696	10	|h′′(x)|q	|h′′(x)|q	PROPN
ejpam-6139	696	11	in	in	ADP
ejpam-6139	696	12	second	second	ADJ
ejpam-6139	696	13	sense	sense	NOUN
ejpam-6139	696	14	,	,	PUNCT
ejpam-6139	696	15	consider∫	consider∫	NOUN
ejpam-6139	696	16	1	1	NUM
ejpam-6139	696	17	0	0	NUM
ejpam-6139	696	18	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	696	19	∫	∫	PROPN
ejpam-6139	696	20	t	t	PROPN
ejpam-6139	696	21	0	0	NUM
ejpam-6139	696	22	(	(	PUNCT
ejpam-6139	696	23	1−	1−	NUM
ejpam-6139	696	24	(	(	PUNCT
ejpam-6139	696	25	1−	1−	NUM
ejpam-6139	696	26	φ)µ	φ)µ	NOUN
ejpam-6139	696	27	ku	ku	PROPN
ejpam-6139	696	28	)	)	PUNCT
ejpam-6139	697	1	α	α	PROPN
ejpam-6139	697	2	k	k	X
ejpam-6139	697	3	dφ	dφ	X
ejpam-6139	697	4	∣∣∣∣.∣∣∣∣h′′(η	∣∣∣∣.∣∣∣∣h′′(η	ADP
ejpam-6139	697	5	−	−	PROPN
ejpam-6139	697	6	t	t	PROPN
ejpam-6139	697	7	η	η	PROPN
ejpam-6139	697	8	ν	ν	PROPN
ejpam-6139	697	9	+	+	PROPN
ejpam-6139	697	10	t	t	PROPN
ejpam-6139	697	11	η	η	PROPN
ejpam-6139	697	12	ω	ω	PROPN
ejpam-6139	697	13	)	)	PUNCT
ejpam-6139	698	1	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	698	2	m.	m.	NOUN
ejpam-6139	698	3	samraiz	samraiz	PROPN
ejpam-6139	698	4	et	et	PROPN
ejpam-6139	698	5	al	al	PROPN
ejpam-6139	698	6	.	.	PUNCT
ejpam-6139	698	7	/	/	SYM
ejpam-6139	698	8	eur	eur	PROPN
ejpam-6139	698	9	.	.	PUNCT
ejpam-6139	699	1	j.	j.	PROPN
ejpam-6139	699	2	pure	pure	PROPN
ejpam-6139	699	3	appl	appl	PROPN
ejpam-6139	699	4	.	.	PROPN
ejpam-6139	699	5	math	math	PROPN
ejpam-6139	699	6	,	,	PUNCT
ejpam-6139	699	7	18	18	NUM
ejpam-6139	699	8	(	(	PUNCT
ejpam-6139	699	9	4	4	NUM
ejpam-6139	699	10	)	)	PUNCT
ejpam-6139	699	11	(	(	PUNCT
ejpam-6139	699	12	2025	2025	NUM
ejpam-6139	699	13	)	)	PUNCT
ejpam-6139	699	14	,	,	PUNCT
ejpam-6139	699	15	6139	6139	NUM
ejpam-6139	699	16	28	28	NUM
ejpam-6139	699	17	of	of	ADP
ejpam-6139	699	18	34	34	NUM
ejpam-6139	699	19	≤	≤	NUM
ejpam-6139	699	20	∫	∫	PROPN
ejpam-6139	699	21	1	1	NUM
ejpam-6139	699	22	0	0	NUM
ejpam-6139	699	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	699	24	∫	∫	PROPN
ejpam-6139	699	25	t	t	PROPN
ejpam-6139	699	26	0	0	NUM
ejpam-6139	700	1	(	(	PUNCT
ejpam-6139	700	2	1−	1−	NUM
ejpam-6139	700	3	(	(	PUNCT
ejpam-6139	700	4	1−	1−	NUM
ejpam-6139	700	5	φ)µ	φ)µ	NOUN
ejpam-6139	700	6	ku	ku	PROPN
ejpam-6139	700	7	)	)	PUNCT
ejpam-6139	701	1	α	α	PROPN
ejpam-6139	701	2	k	k	NOUN
ejpam-6139	701	3	dφ	dφ	X
ejpam-6139	701	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	701	5	(	(	PUNCT
ejpam-6139	701	6	|h′′(ν)|(η	|h′′(ν)|(η	PROPN
ejpam-6139	701	7	−	−	PROPN
ejpam-6139	701	8	t	t	PROPN
ejpam-6139	701	9	η	η	PROPN
ejpam-6139	701	10	)	)	PUNCT
ejpam-6139	701	11	s	s	PART
ejpam-6139	702	1	+	+	CCONJ
ejpam-6139	702	2	(	(	PUNCT
ejpam-6139	702	3	t	t	PROPN
ejpam-6139	702	4	η	η	PROPN
ejpam-6139	702	5	)	)	PUNCT
ejpam-6139	702	6	s	s	PART
ejpam-6139	702	7	|h′′(ω)|	|h′′(ω)|	NOUN
ejpam-6139	702	8	)	)	PUNCT
ejpam-6139	702	9	dt	dt	X
ejpam-6139	702	10	∫	∫	PROPN
ejpam-6139	702	11	1	1	NUM
ejpam-6139	702	12	0	0	NUM
ejpam-6139	702	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	702	14	∫	∫	PROPN
ejpam-6139	702	15	t	t	PROPN
ejpam-6139	702	16	0	0	NUM
ejpam-6139	702	17	(	(	PUNCT
ejpam-6139	702	18	1−	1−	NUM
ejpam-6139	702	19	(	(	PUNCT
ejpam-6139	702	20	1−	1−	NUM
ejpam-6139	702	21	φ)µ	φ)µ	NOUN
ejpam-6139	702	22	ku	ku	PROPN
ejpam-6139	702	23	)	)	PUNCT
ejpam-6139	703	1	α	α	PROPN
ejpam-6139	703	2	k	k	X
ejpam-6139	703	3	dφ	dφ	X
ejpam-6139	703	4	∣∣∣∣.∣∣∣∣h′′(η	∣∣∣∣.∣∣∣∣h′′(η	ADP
ejpam-6139	703	5	−	−	PROPN
ejpam-6139	703	6	t	t	PROPN
ejpam-6139	703	7	η	η	PROPN
ejpam-6139	703	8	ν	ν	PROPN
ejpam-6139	703	9	+	+	PROPN
ejpam-6139	703	10	t	t	PROPN
ejpam-6139	703	11	η	η	PROPN
ejpam-6139	703	12	ω	ω	PROPN
ejpam-6139	703	13	)	)	PUNCT
ejpam-6139	703	14	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	703	15	≤	≤	NUM
ejpam-6139	703	16	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	703	17	ηs	ηs	ADP
ejpam-6139	703	18	∫	∫	PROPN
ejpam-6139	703	19	1	1	NUM
ejpam-6139	703	20	0	0	NUM
ejpam-6139	703	21	(	(	PUNCT
ejpam-6139	703	22	η	η	PROPN
ejpam-6139	703	23	−	−	PROPN
ejpam-6139	703	24	t)s	t)s	ADJ
ejpam-6139	703	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	703	26	∫	∫	PROPN
ejpam-6139	703	27	t	t	PROPN
ejpam-6139	703	28	0	0	NUM
ejpam-6139	704	1	(	(	PUNCT
ejpam-6139	704	2	1−	1−	NUM
ejpam-6139	704	3	(	(	PUNCT
ejpam-6139	704	4	1−	1−	NUM
ejpam-6139	704	5	φ)µ	φ)µ	NOUN
ejpam-6139	704	6	ku	ku	PROPN
ejpam-6139	704	7	)	)	PUNCT
ejpam-6139	704	8	α	α	PROPN
ejpam-6139	704	9	k	k	X
ejpam-6139	704	10	dφ	dφ	ADP
ejpam-6139	704	11	∣∣∣∣dt	∣∣∣∣dt	PROPN
ejpam-6139	704	12	+	+	CCONJ
ejpam-6139	704	13	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	704	14	ηs	ηs	ADP
ejpam-6139	704	15	∫	∫	PROPN
ejpam-6139	704	16	1	1	NUM
ejpam-6139	704	17	0	0	NUM
ejpam-6139	704	18	ts	ts	ADP
ejpam-6139	704	19	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	704	20	∫	∫	PROPN
ejpam-6139	704	21	t	t	PROPN
ejpam-6139	704	22	0	0	NUM
ejpam-6139	704	23	(	(	PUNCT
ejpam-6139	704	24	1−	1−	NUM
ejpam-6139	704	25	(	(	PUNCT
ejpam-6139	704	26	1−	1−	NUM
ejpam-6139	704	27	φ)µ	φ)µ	NOUN
ejpam-6139	704	28	ku	ku	PROPN
ejpam-6139	704	29	)	)	PUNCT
ejpam-6139	704	30	α	α	PROPN
ejpam-6139	705	1	k	k	X
ejpam-6139	705	2	dφ	dφ	ADP
ejpam-6139	705	3	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	705	4	.	.	PUNCT
ejpam-6139	706	1	(	(	PUNCT
ejpam-6139	706	2	52	52	NUM
ejpam-6139	706	3	)	)	PUNCT
ejpam-6139	706	4	assuming	assume	VERB
ejpam-6139	706	5	ξ1k(µ	ξ1k(µ	PROPN
ejpam-6139	706	6	,	,	PUNCT
ejpam-6139	706	7	α	α	X
ejpam-6139	706	8	)	)	PUNCT
ejpam-6139	707	1	=	=	SYM
ejpam-6139	707	2	∫	∫	PROPN
ejpam-6139	708	1	1	1	NUM
ejpam-6139	708	2	0	0	NUM
ejpam-6139	708	3	ts	ts	ADP
ejpam-6139	708	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	708	5	∫	∫	PROPN
ejpam-6139	708	6	t	t	PROPN
ejpam-6139	708	7	0	0	NUM
ejpam-6139	708	8	(	(	PUNCT
ejpam-6139	708	9	1−	1−	NUM
ejpam-6139	708	10	(	(	PUNCT
ejpam-6139	708	11	1−	1−	NUM
ejpam-6139	708	12	φ)µ	φ)µ	NOUN
ejpam-6139	708	13	ku	ku	PROPN
ejpam-6139	708	14	)	)	PUNCT
ejpam-6139	708	15	α	α	PROPN
ejpam-6139	708	16	k	k	X
ejpam-6139	708	17	dφ	dφ	ADP
ejpam-6139	708	18	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	708	19	,	,	PUNCT
ejpam-6139	708	20	(	(	PUNCT
ejpam-6139	708	21	53	53	NUM
ejpam-6139	708	22	)	)	PUNCT
ejpam-6139	708	23	ξ2k(µ	ξ2k(µ	PROPN
ejpam-6139	708	24	,	,	PUNCT
ejpam-6139	708	25	α	α	X
ejpam-6139	708	26	)	)	PUNCT
ejpam-6139	708	27	=	=	SYM
ejpam-6139	709	1	∫	∫	PROPN
ejpam-6139	709	2	1	1	NUM
ejpam-6139	709	3	0	0	NUM
ejpam-6139	709	4	(	(	PUNCT
ejpam-6139	709	5	η	η	PROPN
ejpam-6139	709	6	−	−	PROPN
ejpam-6139	709	7	t)s	t)s	ADJ
ejpam-6139	709	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6139	709	9	∫	∫	PROPN
ejpam-6139	709	10	t	t	PROPN
ejpam-6139	709	11	0	0	NUM
ejpam-6139	709	12	(	(	PUNCT
ejpam-6139	709	13	1−	1−	NUM
ejpam-6139	709	14	(	(	PUNCT
ejpam-6139	709	15	1−	1−	NUM
ejpam-6139	709	16	φ)µ	φ)µ	NOUN
ejpam-6139	709	17	ku	ku	PROPN
ejpam-6139	709	18	)	)	PUNCT
ejpam-6139	710	1	α	α	PROPN
ejpam-6139	710	2	k	k	X
ejpam-6139	710	3	dφ	dφ	ADP
ejpam-6139	710	4	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-6139	710	5	.	.	PUNCT
ejpam-6139	711	1	(	(	PUNCT
ejpam-6139	711	2	54	54	NUM
ejpam-6139	711	3	)	)	PUNCT
ejpam-6139	711	4	substituting	substitute	VERB
ejpam-6139	711	5	(	(	PUNCT
ejpam-6139	711	6	53	53	NUM
ejpam-6139	711	7	)	)	PUNCT
ejpam-6139	711	8	and	and	CCONJ
ejpam-6139	711	9	(	(	PUNCT
ejpam-6139	711	10	54	54	NUM
ejpam-6139	711	11	)	)	PUNCT
ejpam-6139	711	12	in	in	ADP
ejpam-6139	711	13	(	(	PUNCT
ejpam-6139	711	14	52	52	NUM
ejpam-6139	711	15	)	)	PUNCT
ejpam-6139	711	16	,	,	PUNCT
ejpam-6139	711	17	we	we	PRON
ejpam-6139	711	18	obtain∫	obtain∫	VERB
ejpam-6139	711	19	1	1	NUM
ejpam-6139	711	20	0	0	NUM
ejpam-6139	711	21	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	711	22	∫	∫	PROPN
ejpam-6139	711	23	t	t	PROPN
ejpam-6139	711	24	0	0	NUM
ejpam-6139	711	25	(	(	PUNCT
ejpam-6139	711	26	1−	1−	NUM
ejpam-6139	711	27	(	(	PUNCT
ejpam-6139	711	28	1−	1−	NUM
ejpam-6139	711	29	φ)µ	φ)µ	NOUN
ejpam-6139	711	30	ku	ku	PROPN
ejpam-6139	711	31	)	)	PUNCT
ejpam-6139	712	1	α	α	PROPN
ejpam-6139	713	1	k	k	X
ejpam-6139	714	1	dφ	dφ	X
ejpam-6139	714	2	∣∣∣∣.∣∣∣∣h′′(η	∣∣∣∣.∣∣∣∣h′′(η	ADP
ejpam-6139	714	3	−	−	PROPN
ejpam-6139	714	4	t	t	PROPN
ejpam-6139	714	5	η	η	PROPN
ejpam-6139	714	6	ν	ν	PROPN
ejpam-6139	714	7	+	+	PROPN
ejpam-6139	714	8	t	t	PROPN
ejpam-6139	714	9	η	η	PROPN
ejpam-6139	714	10	ω	ω	PROPN
ejpam-6139	714	11	)	)	PUNCT
ejpam-6139	714	12	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	714	13	≤	≤	NUM
ejpam-6139	714	14	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	714	15	ηs	ηs	ADP
ejpam-6139	714	16	ξ2k(µ	ξ2k(µ	PROPN
ejpam-6139	714	17	,	,	PUNCT
ejpam-6139	714	18	α	α	X
ejpam-6139	714	19	)	)	PUNCT
ejpam-6139	714	20	+	+	NUM
ejpam-6139	714	21	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	714	22	ηs	ηs	ADP
ejpam-6139	714	23	ξ1k(µ	ξ1k(µ	PROPN
ejpam-6139	714	24	,	,	PUNCT
ejpam-6139	714	25	α	α	X
ejpam-6139	714	26	)	)	PUNCT
ejpam-6139	714	27	(	(	PUNCT
ejpam-6139	714	28	55	55	NUM
ejpam-6139	714	29	)	)	PUNCT
ejpam-6139	714	30	similarly	similarly	ADV
ejpam-6139	714	31	∫	∫	PROPN
ejpam-6139	714	32	1	1	NUM
ejpam-6139	714	33	0	0	NUM
ejpam-6139	714	34	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6139	714	35	∫	∫	PROPN
ejpam-6139	714	36	t	t	PROPN
ejpam-6139	714	37	0	0	NUM
ejpam-6139	714	38	(	(	PUNCT
ejpam-6139	714	39	1−	1−	NUM
ejpam-6139	714	40	(	(	PUNCT
ejpam-6139	714	41	1−	1−	NUM
ejpam-6139	714	42	φ)µ	φ)µ	NOUN
ejpam-6139	714	43	ku	ku	PROPN
ejpam-6139	714	44	)	)	PUNCT
ejpam-6139	714	45	α	α	PROPN
ejpam-6139	715	1	k	k	X
ejpam-6139	715	2	dφ	dφ	ADP
ejpam-6139	715	3	∣∣∣∣.∣∣∣∣h′′	∣∣∣∣.∣∣∣∣h′′	PROPN
ejpam-6139	715	4	(	(	PUNCT
ejpam-6139	715	5	t	t	PROPN
ejpam-6139	715	6	η	η	PROPN
ejpam-6139	715	7	ν	ν	PROPN
ejpam-6139	715	8	+	+	PROPN
ejpam-6139	715	9	η	η	PROPN
ejpam-6139	715	10	−	−	PROPN
ejpam-6139	715	11	t	t	PROPN
ejpam-6139	715	12	η	η	PROPN
ejpam-6139	715	13	ω	ω	PROPN
ejpam-6139	715	14	)	)	PUNCT
ejpam-6139	715	15	∣∣∣∣qdt	∣∣∣∣qdt	NOUN
ejpam-6139	715	16	≤	≤	NUM
ejpam-6139	715	17	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	715	18	ηs	ηs	ADP
ejpam-6139	715	19	ξ1k(µ	ξ1k(µ	PROPN
ejpam-6139	715	20	,	,	PUNCT
ejpam-6139	715	21	α	α	X
ejpam-6139	715	22	)	)	PUNCT
ejpam-6139	716	1	+	+	NUM
ejpam-6139	716	2	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	716	3	ηs	ηs	ADP
ejpam-6139	716	4	ξ2k(µ	ξ2k(µ	PROPN
ejpam-6139	716	5	,	,	PUNCT
ejpam-6139	716	6	α	α	NOUN
ejpam-6139	716	7	)	)	PUNCT
ejpam-6139	716	8	.	.	PUNCT
ejpam-6139	717	1	(	(	PUNCT
ejpam-6139	717	2	56	56	X
ejpam-6139	717	3	)	)	PUNCT
ejpam-6139	717	4	substituting	substituting	NOUN
ejpam-6139	717	5	(	(	PUNCT
ejpam-6139	717	6	55	55	NUM
ejpam-6139	717	7	)	)	PUNCT
ejpam-6139	717	8	and	and	CCONJ
ejpam-6139	717	9	(	(	PUNCT
ejpam-6139	717	10	56	56	NUM
ejpam-6139	717	11	)	)	PUNCT
ejpam-6139	717	12	in	in	ADP
ejpam-6139	717	13	equation	equation	NOUN
ejpam-6139	717	14	(	(	PUNCT
ejpam-6139	717	15	51	51	NUM
ejpam-6139	717	16	)	)	PUNCT
ejpam-6139	717	17	,	,	PUNCT
ejpam-6139	717	18	we	we	PRON
ejpam-6139	717	19	obtain	obtain	VERB
ejpam-6139	717	20	required	required	ADJ
ejpam-6139	717	21	result	result	NOUN
ejpam-6139	717	22	.	.	PUNCT
ejpam-6139	718	1	remark	remark	PROPN
ejpam-6139	718	2	14	14	NUM
ejpam-6139	718	3	.	.	PUNCT
ejpam-6139	719	1	by	by	ADP
ejpam-6139	719	2	assuming	assume	VERB
ejpam-6139	719	3	the	the	DET
ejpam-6139	719	4	values	value	NOUN
ejpam-6139	719	5	of	of	ADP
ejpam-6139	719	6	η	η	PROPN
ejpam-6139	719	7	=	=	PROPN
ejpam-6139	719	8	2,s=1	2,s=1	PROPN
ejpam-6139	719	9	and	and	CCONJ
ejpam-6139	719	10	k	k	NOUN
ejpam-6139	719	11	=	=	SYM
ejpam-6139	719	12	1	1	NUM
ejpam-6139	719	13	in	in	ADP
ejpam-6139	719	14	(	(	PUNCT
ejpam-6139	719	15	51	51	NUM
ejpam-6139	719	16	)	)	PUNCT
ejpam-6139	719	17	,	,	PUNCT
ejpam-6139	719	18	the	the	DET
ejpam-6139	719	19	resulting	result	VERB
ejpam-6139	719	20	outcome	outcome	NOUN
ejpam-6139	719	21	is	be	AUX
ejpam-6139	719	22	obtained	obtain	VERB
ejpam-6139	719	23	as	as	ADP
ejpam-6139	719	24	follow∣∣∣∣	follow∣∣∣∣	PROPN
ejpam-6139	719	25	2µα−1	2µα−1	PROPN
ejpam-6139	719	26	(	(	PUNCT
ejpam-6139	719	27	ω	ω	NOUN
ejpam-6139	720	1	−	−	X
ejpam-6139	720	2	ν)µα	ν)µα	PROPN
ejpam-6139	720	3	µαγ	µαγ	NOUN
ejpam-6139	720	4	(	(	PUNCT
ejpam-6139	720	5	α+	α+	NOUN
ejpam-6139	720	6	1	1	NUM
ejpam-6139	720	7	)	)	PUNCT
ejpam-6139	720	8	(	(	PUNCT
ejpam-6139	720	9	αjµν+ω	αjµν+ω	PROPN
ejpam-6139	720	10	η	η	NOUN
ejpam-6139	720	11	−h(ν	−h(ν	PROPN
ejpam-6139	720	12	)	)	PUNCT
ejpam-6139	720	13	+	+	CCONJ
ejpam-6139	720	14	α	α	PROPN
ejpam-6139	720	15	jµν+ω	jµν+ω	PROPN
ejpam-6139	720	16	η	η	PROPN
ejpam-6139	720	17	+	+	PROPN
ejpam-6139	720	18	h(ω	h(ω	PROPN
ejpam-6139	720	19	)	)	PUNCT
ejpam-6139	720	20	)	)	PUNCT
ejpam-6139	721	1	−	−	PROPN
ejpam-6139	721	2	h	h	NOUN
ejpam-6139	721	3	(	(	PUNCT
ejpam-6139	721	4	ν	ν	X
ejpam-6139	721	5	+	+	X
ejpam-6139	721	6	ω	ω	NUM
ejpam-6139	721	7	2	2	NUM
ejpam-6139	721	8	)	)	PUNCT
ejpam-6139	721	9	∣∣∣∣≤	∣∣∣∣≤	PROPN
ejpam-6139	721	10	(	(	PUNCT
ejpam-6139	721	11	ω	ω	NUM
ejpam-6139	721	12	−	−	PROPN
ejpam-6139	721	13	ν)2	ν)2	NOUN
ejpam-6139	721	14	8	8	NUM
ejpam-6139	721	15	µα	µα	ADP
ejpam-6139	721	16	×	×	NOUN
ejpam-6139	721	17	(	(	PUNCT
ejpam-6139	721	18	ξ1(µ	ξ1(µ	NOUN
ejpam-6139	721	19	,	,	PUNCT
ejpam-6139	721	20	α	α	NOUN
ejpam-6139	721	21	)	)	PUNCT
ejpam-6139	721	22	)	)	PUNCT
ejpam-6139	721	23	1−	1−	NUM
ejpam-6139	722	1	1	1	NUM
ejpam-6139	722	2	q	q	NOUN
ejpam-6139	722	3	[	[	X
ejpam-6139	722	4	(	(	PUNCT
ejpam-6139	722	5	2ξ1(µ	2ξ1(µ	ADV
ejpam-6139	722	6	,	,	PUNCT
ejpam-6139	722	7	α)−	α)−	PROPN
ejpam-6139	722	8	ξ2(µ	ξ2(µ	PROPN
ejpam-6139	722	9	,	,	PUNCT
ejpam-6139	722	10	α	α	NOUN
ejpam-6139	722	11	)	)	PUNCT
ejpam-6139	722	12	2	2	NUM
ejpam-6139	722	13	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	722	14	+	+	CCONJ
ejpam-6139	722	15	ξ2(µ	ξ2(µ	NUM
ejpam-6139	722	16	,	,	PUNCT
ejpam-6139	722	17	α	α	NOUN
ejpam-6139	722	18	)	)	PUNCT
ejpam-6139	722	19	2	2	NUM
ejpam-6139	722	20	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	722	21	)	)	PUNCT
ejpam-6139	722	22	1	1	NUM
ejpam-6139	722	23	q	q	NOUN
ejpam-6139	722	24	+	+	CCONJ
ejpam-6139	722	25	(	(	PUNCT
ejpam-6139	722	26	ξ2(µ	ξ2(µ	PROPN
ejpam-6139	722	27	,	,	PUNCT
ejpam-6139	722	28	α	α	NOUN
ejpam-6139	722	29	)	)	PUNCT
ejpam-6139	722	30	2	2	NUM
ejpam-6139	722	31	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	722	32	+	+	CCONJ
ejpam-6139	722	33	2ξ1(µ	2ξ1(µ	NUM
ejpam-6139	722	34	,	,	PUNCT
ejpam-6139	722	35	α)−	α)−	PROPN
ejpam-6139	722	36	ξ2(µ	ξ2(µ	PROPN
ejpam-6139	722	37	,	,	PUNCT
ejpam-6139	722	38	α	α	NOUN
ejpam-6139	722	39	)	)	PUNCT
ejpam-6139	722	40	2	2	NUM
ejpam-6139	722	41	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	722	42	)	)	PUNCT
ejpam-6139	722	43	1	1	NUM
ejpam-6139	722	44	q	q	NOUN
ejpam-6139	722	45	]	]	PUNCT
ejpam-6139	722	46	.	.	PUNCT
ejpam-6139	723	1	(	(	PUNCT
ejpam-6139	723	2	57	57	NUM
ejpam-6139	723	3	)	)	PUNCT
ejpam-6139	723	4	m.	m.	NOUN
ejpam-6139	723	5	samraiz	samraiz	PROPN
ejpam-6139	723	6	et	et	PROPN
ejpam-6139	723	7	al	al	PROPN
ejpam-6139	723	8	.	.	PUNCT
ejpam-6139	723	9	/	/	SYM
ejpam-6139	723	10	eur	eur	PROPN
ejpam-6139	723	11	.	.	PUNCT
ejpam-6139	724	1	j.	j.	PROPN
ejpam-6139	724	2	pure	pure	PROPN
ejpam-6139	724	3	appl	appl	PROPN
ejpam-6139	724	4	.	.	PROPN
ejpam-6139	724	5	math	math	PROPN
ejpam-6139	724	6	,	,	PUNCT
ejpam-6139	724	7	18	18	NUM
ejpam-6139	724	8	(	(	PUNCT
ejpam-6139	724	9	4	4	NUM
ejpam-6139	724	10	)	)	PUNCT
ejpam-6139	724	11	(	(	PUNCT
ejpam-6139	724	12	2025	2025	NUM
ejpam-6139	724	13	)	)	PUNCT
ejpam-6139	724	14	,	,	PUNCT
ejpam-6139	724	15	6139	6139	NUM
ejpam-6139	724	16	29	29	NUM
ejpam-6139	724	17	of	of	ADP
ejpam-6139	724	18	34	34	NUM
ejpam-6139	724	19	remark	remark	NOUN
ejpam-6139	724	20	15	15	NUM
ejpam-6139	724	21	.	.	PUNCT
ejpam-6139	725	1	substituting	substitute	VERB
ejpam-6139	725	2	α	α	NOUN
ejpam-6139	725	3	=	=	SYM
ejpam-6139	725	4	1	1	NUM
ejpam-6139	725	5	and	and	CCONJ
ejpam-6139	725	6	µ	µ	X
ejpam-6139	725	7	=	=	SYM
ejpam-6139	725	8	1	1	NUM
ejpam-6139	725	9	in	in	ADP
ejpam-6139	725	10	(	(	PUNCT
ejpam-6139	725	11	57	57	NUM
ejpam-6139	725	12	)	)	PUNCT
ejpam-6139	725	13	,	,	PUNCT
ejpam-6139	725	14	we	we	PRON
ejpam-6139	725	15	get	get	VERB
ejpam-6139	725	16	the	the	DET
ejpam-6139	725	17	following	follow	VERB
ejpam-6139	725	18	inequality∣∣∣∣	inequality∣∣∣∣	PROPN
ejpam-6139	725	19	1	1	NUM
ejpam-6139	725	20	(	(	PUNCT
ejpam-6139	725	21	ω	ω	NOUN
ejpam-6139	725	22	−	−	NOUN
ejpam-6139	725	23	ν	ν	PROPN
ejpam-6139	725	24	)	)	PUNCT
ejpam-6139	725	25	∫	∫	PROPN
ejpam-6139	725	26	ω	ω	PROPN
ejpam-6139	725	27	ν	ν	X
ejpam-6139	725	28	h(x)dx−	h(x)dx−	PROPN
ejpam-6139	725	29	h′	h′	PROPN
ejpam-6139	725	30	(	(	PUNCT
ejpam-6139	725	31	ν	ν	PROPN
ejpam-6139	725	32	+	+	X
ejpam-6139	725	33	ω	ω	NUM
ejpam-6139	725	34	2	2	NUM
ejpam-6139	725	35	)	)	PUNCT
ejpam-6139	725	36	∣∣∣∣≤	∣∣∣∣≤	PROPN
ejpam-6139	726	1	(	(	PUNCT
ejpam-6139	726	2	ω	ω	NUM
ejpam-6139	726	3	−	−	PROPN
ejpam-6139	726	4	ν)2	ν)2	NOUN
ejpam-6139	726	5	8	8	NUM
ejpam-6139	726	6	(	(	PUNCT
ejpam-6139	726	7	1	1	NUM
ejpam-6139	726	8	6	6	NUM
ejpam-6139	726	9	)	)	PUNCT
ejpam-6139	726	10	1−	1−	NUM
ejpam-6139	726	11	1	1	NUM
ejpam-6139	726	12	q	q	NOUN
ejpam-6139	727	1	[	[	X
ejpam-6139	727	2	(	(	PUNCT
ejpam-6139	727	3	5	5	NUM
ejpam-6139	727	4	8	8	NUM
ejpam-6139	727	5	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	727	6	+	+	CCONJ
ejpam-6139	727	7	3	3	NUM
ejpam-6139	727	8	8	8	NUM
ejpam-6139	727	9	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	727	10	)	)	PUNCT
ejpam-6139	727	11	1	1	NUM
ejpam-6139	727	12	q	q	NOUN
ejpam-6139	727	13	+	+	CCONJ
ejpam-6139	727	14	(	(	PUNCT
ejpam-6139	727	15	3	3	NUM
ejpam-6139	727	16	8	8	NUM
ejpam-6139	727	17	|h′′(ν)|q	|h′′(ν)|q	PROPN
ejpam-6139	727	18	+	+	CCONJ
ejpam-6139	727	19	5	5	NUM
ejpam-6139	727	20	8	8	NUM
ejpam-6139	727	21	|h′′(ω)|q	|h′′(ω)|q	PROPN
ejpam-6139	727	22	)	)	PUNCT
ejpam-6139	727	23	1	1	NUM
ejpam-6139	727	24	q	q	NOUN
ejpam-6139	727	25	]	]	PUNCT
ejpam-6139	727	26	.	.	PUNCT
ejpam-6139	728	1	(	(	PUNCT
ejpam-6139	728	2	58	58	NUM
ejpam-6139	728	3	)	)	PUNCT
ejpam-6139	728	4	example	example	NOUN
ejpam-6139	728	5	6	6	NUM
ejpam-6139	728	6	.	.	PUNCT
ejpam-6139	729	1	this	this	DET
ejpam-6139	729	2	example	example	NOUN
ejpam-6139	729	3	illustrates	illustrate	VERB
ejpam-6139	729	4	the	the	DET
ejpam-6139	729	5	use	use	NOUN
ejpam-6139	729	6	of	of	ADP
ejpam-6139	729	7	theorem	theorem	NOUN
ejpam-6139	729	8	6	6	NUM
ejpam-6139	729	9	through	through	ADP
ejpam-6139	729	10	a	a	DET
ejpam-6139	729	11	combination	combination	NOUN
ejpam-6139	729	12	of	of	ADP
ejpam-6139	729	13	graphical	graphical	ADJ
ejpam-6139	729	14	and	and	CCONJ
ejpam-6139	729	15	numerical	numerical	ADJ
ejpam-6139	729	16	techniques	technique	NOUN
ejpam-6139	729	17	.	.	PUNCT
ejpam-6139	730	1	the	the	DET
ejpam-6139	730	2	function	function	NOUN
ejpam-6139	730	3	under	under	ADP
ejpam-6139	730	4	consideration	consideration	NOUN
ejpam-6139	730	5	is	be	AUX
ejpam-6139	730	6	h(x	h(x	PROPN
ejpam-6139	730	7	)	)	PUNCT
ejpam-6139	730	8	=	=	SYM
ejpam-6139	731	1	x6	x6	PROPN
ejpam-6139	731	2	+	+	SYM
ejpam-6139	731	3	2x4	2x4	NUM
ejpam-6139	731	4	,	,	PUNCT
ejpam-6139	731	5	defined	define	VERB
ejpam-6139	731	6	on	on	ADP
ejpam-6139	731	7	the	the	DET
ejpam-6139	731	8	interval	interval	NOUN
ejpam-6139	731	9	[	[	X
ejpam-6139	731	10	2	2	NUM
ejpam-6139	731	11	,	,	PUNCT
ejpam-6139	731	12	7	7	NUM
ejpam-6139	731	13	]	]	PUNCT
ejpam-6139	731	14	,	,	PUNCT
ejpam-6139	731	15	with	with	SCONJ
ejpam-6139	731	16	the	the	DET
ejpam-6139	731	17	inequality	inequality	NOUN
ejpam-6139	731	18	evaluated	evaluate	VERB
ejpam-6139	731	19	using	use	VERB
ejpam-6139	731	20	the	the	DET
ejpam-6139	731	21	parameters	parameter	NOUN
ejpam-6139	731	22	k	k	X
ejpam-6139	732	1	=	=	SYM
ejpam-6139	732	2	3	3	NUM
ejpam-6139	732	3	,	,	PUNCT
ejpam-6139	732	4	α	α	NOUN
ejpam-6139	732	5	=	=	SYM
ejpam-6139	732	6	4,s=1	4,s=1	PROPN
ejpam-6139	732	7	,	,	PUNCT
ejpam-6139	732	8	1	1	NUM
ejpam-6139	732	9	p	p	NOUN
ejpam-6139	732	10	=	=	SYM
ejpam-6139	732	11	0.6	0.6	NUM
ejpam-6139	732	12	,	,	PUNCT
ejpam-6139	732	13	1	1	NUM
ejpam-6139	732	14	q	q	NOUN
ejpam-6139	732	15	=	=	NUM
ejpam-6139	732	16	0.4	0.4	NUM
ejpam-6139	732	17	,	,	PUNCT
ejpam-6139	732	18	and	and	CCONJ
ejpam-6139	732	19	η	η	PROPN
ejpam-6139	732	20	=	=	PROPN
ejpam-6139	732	21	8	8	PROPN
ejpam-6139	732	22	.	.	PUNCT
ejpam-6139	733	1	explanation	explanation	NOUN
ejpam-6139	733	2	:	:	PUNCT
ejpam-6139	733	3	figure	figure	NOUN
ejpam-6139	733	4	11	11	NUM
ejpam-6139	733	5	provides	provide	VERB
ejpam-6139	733	6	a	a	DET
ejpam-6139	733	7	2d	2d	NUM
ejpam-6139	733	8	visualization	visualization	NOUN
ejpam-6139	733	9	of	of	ADP
ejpam-6139	733	10	the	the	DET
ejpam-6139	733	11	inequality	inequality	NOUN
ejpam-6139	733	12	(	(	PUNCT
ejpam-6139	733	13	51	51	NUM
ejpam-6139	733	14	)	)	PUNCT
ejpam-6139	733	15	,	,	PUNCT
ejpam-6139	733	16	depicting	depict	VERB
ejpam-6139	733	17	the	the	DET
ejpam-6139	733	18	behavior	behavior	NOUN
ejpam-6139	733	19	of	of	ADP
ejpam-6139	733	20	the	the	DET
ejpam-6139	733	21	left	left	ADJ
ejpam-6139	733	22	-	-	PUNCT
ejpam-6139	733	23	hand	hand	NOUN
ejpam-6139	733	24	side	side	NOUN
ejpam-6139	733	25	and	and	CCONJ
ejpam-6139	733	26	right	right	ADJ
ejpam-6139	733	27	-	-	PUNCT
ejpam-6139	733	28	hand	hand	NOUN
ejpam-6139	733	29	side	side	NOUN
ejpam-6139	733	30	as	as	ADP
ejpam-6139	733	31	µ	µ	NOUN
ejpam-6139	733	32	varies	vary	VERB
ejpam-6139	733	33	in	in	ADP
ejpam-6139	733	34	(	(	PUNCT
ejpam-6139	733	35	0	0	NUM
ejpam-6139	733	36	,	,	PUNCT
ejpam-6139	733	37	1	1	NUM
ejpam-6139	733	38	]	]	PUNCT
ejpam-6139	733	39	.	.	PUNCT
ejpam-6139	734	1	the	the	DET
ejpam-6139	734	2	graph	graph	NOUN
ejpam-6139	734	3	demonstrates	demonstrate	VERB
ejpam-6139	734	4	the	the	DET
ejpam-6139	734	5	validity	validity	NOUN
ejpam-6139	734	6	of	of	ADP
ejpam-6139	734	7	the	the	DET
ejpam-6139	734	8	theorem	theorem	NOUN
ejpam-6139	734	9	.	.	PROPN
ejpam-6139	734	10	to	to	PART
ejpam-6139	734	11	complement	complement	VERB
ejpam-6139	734	12	the	the	DET
ejpam-6139	734	13	graphical	graphical	ADJ
ejpam-6139	734	14	analysis	analysis	NOUN
ejpam-6139	734	15	,	,	PUNCT
ejpam-6139	734	16	numerical	numerical	ADJ
ejpam-6139	734	17	evaluations	evaluation	NOUN
ejpam-6139	734	18	of	of	ADP
ejpam-6139	734	19	the	the	DET
ejpam-6139	734	20	lhs	lhs	PROPN
ejpam-6139	734	21	and	and	CCONJ
ejpam-6139	734	22	rhs	rhs	PROPN
ejpam-6139	734	23	were	be	AUX
ejpam-6139	734	24	conducted	conduct	VERB
ejpam-6139	734	25	for	for	ADP
ejpam-6139	734	26	specific	specific	ADJ
ejpam-6139	734	27	values	value	NOUN
ejpam-6139	734	28	of	of	ADP
ejpam-6139	734	29	µ.	µ.	NOUN
ejpam-6139	734	30	the	the	DET
ejpam-6139	734	31	results	result	NOUN
ejpam-6139	734	32	,	,	PUNCT
ejpam-6139	734	33	displayed	display	VERB
ejpam-6139	734	34	in	in	ADP
ejpam-6139	734	35	a	a	DET
ejpam-6139	734	36	table	table	NOUN
ejpam-6139	734	37	8	8	NUM
ejpam-6139	734	38	,	,	PUNCT
ejpam-6139	734	39	confirm	confirm	VERB
ejpam-6139	734	40	that	that	SCONJ
ejpam-6139	734	41	the	the	DET
ejpam-6139	734	42	inequality	inequality	NOUN
ejpam-6139	734	43	holds	hold	VERB
ejpam-6139	734	44	under	under	ADP
ejpam-6139	734	45	the	the	DET
ejpam-6139	734	46	given	give	VERB
ejpam-6139	734	47	parameters	parameter	NOUN
ejpam-6139	734	48	.	.	PUNCT
ejpam-6139	735	1	figure	figure	VERB
ejpam-6139	735	2	11	11	NUM
ejpam-6139	735	3	:	:	PUNCT
ejpam-6139	735	4	verification	verification	NOUN
ejpam-6139	735	5	of	of	ADP
ejpam-6139	735	6	theorem	theorem	NOUN
ejpam-6139	735	7	6	6	NUM
ejpam-6139	735	8	using	use	VERB
ejpam-6139	735	9	graphical	graphical	ADJ
ejpam-6139	735	10	and	and	CCONJ
ejpam-6139	735	11	numerical	numerical	ADJ
ejpam-6139	735	12	data	datum	NOUN
ejpam-6139	735	13	for	for	ADP
ejpam-6139	735	14	µ	µ	X
ejpam-6139	735	15	∈	∈	NOUN
ejpam-6139	735	16	(	(	PUNCT
ejpam-6139	735	17	0	0	NUM
ejpam-6139	735	18	,	,	PUNCT
ejpam-6139	735	19	1	1	NUM
ejpam-6139	735	20	]	]	PUNCT
ejpam-6139	735	21	.	.	PUNCT
ejpam-6139	736	1	table	table	NOUN
ejpam-6139	736	2	8	8	NUM
ejpam-6139	736	3	:	:	PUNCT
ejpam-6139	736	4	this	this	DET
ejpam-6139	736	5	table	table	NOUN
ejpam-6139	736	6	offers	offer	VERB
ejpam-6139	736	7	numerical	numerical	ADJ
ejpam-6139	736	8	data	datum	NOUN
ejpam-6139	736	9	for	for	ADP
ejpam-6139	736	10	comparison	comparison	NOUN
ejpam-6139	736	11	of	of	ADP
ejpam-6139	736	12	left	left	ADJ
ejpam-6139	736	13	hand	hand	NOUN
ejpam-6139	736	14	side	side	NOUN
ejpam-6139	736	15	and	and	CCONJ
ejpam-6139	736	16	right	right	ADJ
ejpam-6139	736	17	hand	hand	NOUN
ejpam-6139	736	18	side	side	NOUN
ejpam-6139	736	19	of	of	ADP
ejpam-6139	736	20	inequality	inequality	NOUN
ejpam-6139	736	21	(	(	PUNCT
ejpam-6139	736	22	51	51	NUM
ejpam-6139	736	23	)	)	PUNCT
ejpam-6139	736	24	.	.	PUNCT
ejpam-6139	737	1	µ	µ	X
ejpam-6139	737	2	0.2	0.2	NUM
ejpam-6139	737	3	0.4	0.4	NUM
ejpam-6139	737	4	0.6	0.6	NUM
ejpam-6139	737	5	0.8	0.8	NUM
ejpam-6139	737	6	1	1	NUM
ejpam-6139	737	7	lhs	lhs	PROPN
ejpam-6139	737	8	65.30	65.30	NUM
ejpam-6139	737	9	144.68	144.68	NUM
ejpam-6139	737	10	221	221	NUM
ejpam-6139	737	11	291.37	291.37	NUM
ejpam-6139	737	12	355.37	355.37	NUM
ejpam-6139	737	13	rhs	rhs	PROPN
ejpam-6139	737	14	115.67	115.67	NUM
ejpam-6139	737	15	255.29	255.29	NUM
ejpam-6139	737	16	388.67	388.67	NUM
ejpam-6139	737	17	510.90	510.90	NUM
ejpam-6139	737	18	621.48	621.48	NUM
ejpam-6139	737	19	further	further	ADJ
ejpam-6139	737	20	validation	validation	NOUN
ejpam-6139	737	21	was	be	AUX
ejpam-6139	737	22	performed	perform	VERB
ejpam-6139	737	23	by	by	ADP
ejpam-6139	737	24	generating	generate	VERB
ejpam-6139	737	25	a	a	DET
ejpam-6139	737	26	3d	3d	NOUN
ejpam-6139	737	27	representation	representation	NOUN
ejpam-6139	737	28	of	of	ADP
ejpam-6139	737	29	the	the	DET
ejpam-6139	737	30	inequality	inequality	NOUN
ejpam-6139	737	31	as	as	SCONJ
ejpam-6139	737	32	α	α	PROPN
ejpam-6139	737	33	ranges	range	VERB
ejpam-6139	737	34	within	within	ADP
ejpam-6139	737	35	[	[	X
ejpam-6139	737	36	5	5	NUM
ejpam-6139	737	37	,	,	PUNCT
ejpam-6139	737	38	10	10	NUM
ejpam-6139	737	39	]	]	PUNCT
ejpam-6139	737	40	and	and	CCONJ
ejpam-6139	737	41	µ	µ	X
ejpam-6139	737	42	within	within	X
ejpam-6139	737	43	(	(	PUNCT
ejpam-6139	737	44	0	0	NUM
ejpam-6139	737	45	,	,	PUNCT
ejpam-6139	737	46	1	1	NUM
ejpam-6139	737	47	]	]	PUNCT
ejpam-6139	737	48	.	.	PUNCT
ejpam-6139	738	1	the	the	DET
ejpam-6139	738	2	resulting	result	VERB
ejpam-6139	738	3	surface	surface	NOUN
ejpam-6139	738	4	plot	plot	NOUN
ejpam-6139	738	5	,	,	PUNCT
ejpam-6139	738	6	presented	present	VERB
ejpam-6139	738	7	in	in	ADP
ejpam-6139	738	8	figure	figure	NOUN
ejpam-6139	738	9	12	12	NUM
ejpam-6139	738	10	,	,	PUNCT
ejpam-6139	738	11	illustrates	illustrate	VERB
ejpam-6139	738	12	that	that	SCONJ
ejpam-6139	738	13	the	the	DET
ejpam-6139	738	14	inequality	inequality	NOUN
ejpam-6139	738	15	remains	remain	VERB
ejpam-6139	738	16	valid	valid	ADJ
ejpam-6139	738	17	across	across	ADP
ejpam-6139	738	18	the	the	DET
ejpam-6139	738	19	explored	explore	VERB
ejpam-6139	738	20	parameter	parameter	NOUN
ejpam-6139	738	21	space	space	NOUN
ejpam-6139	738	22	.	.	PUNCT
ejpam-6139	739	1	m.	m.	NOUN
ejpam-6139	739	2	samraiz	samraiz	PROPN
ejpam-6139	739	3	et	et	PROPN
ejpam-6139	739	4	al	al	PROPN
ejpam-6139	739	5	.	.	PUNCT
ejpam-6139	739	6	/	/	SYM
ejpam-6139	739	7	eur	eur	PROPN
ejpam-6139	739	8	.	.	PUNCT
ejpam-6139	740	1	j.	j.	PROPN
ejpam-6139	740	2	pure	pure	PROPN
ejpam-6139	740	3	appl	appl	PROPN
ejpam-6139	740	4	.	.	PROPN
ejpam-6139	740	5	math	math	PROPN
ejpam-6139	740	6	,	,	PUNCT
ejpam-6139	740	7	18	18	NUM
ejpam-6139	740	8	(	(	PUNCT
ejpam-6139	740	9	4	4	NUM
ejpam-6139	740	10	)	)	PUNCT
ejpam-6139	740	11	(	(	PUNCT
ejpam-6139	740	12	2025	2025	NUM
ejpam-6139	740	13	)	)	PUNCT
ejpam-6139	740	14	,	,	PUNCT
ejpam-6139	740	15	6139	6139	NUM
ejpam-6139	740	16	30	30	NUM
ejpam-6139	740	17	of	of	ADP
ejpam-6139	740	18	34	34	NUM
ejpam-6139	740	19	figure	figure	NOUN
ejpam-6139	740	20	12	12	NUM
ejpam-6139	740	21	:	:	PUNCT
ejpam-6139	740	22	three	three	NUM
ejpam-6139	740	23	-	-	PUNCT
ejpam-6139	740	24	dimensional	dimensional	ADJ
ejpam-6139	740	25	validation	validation	NOUN
ejpam-6139	740	26	of	of	ADP
ejpam-6139	740	27	theorem	theorem	NOUN
ejpam-6139	740	28	6	6	NUM
ejpam-6139	740	29	across	across	ADP
ejpam-6139	740	30	different	different	ADJ
ejpam-6139	740	31	values	value	NOUN
ejpam-6139	740	32	of	of	ADP
ejpam-6139	740	33	α	α	NOUN
ejpam-6139	740	34	and	and	CCONJ
ejpam-6139	740	35	µ.	µ.	NOUN
ejpam-6139	740	36	this	this	DET
ejpam-6139	740	37	comprehensive	comprehensive	ADJ
ejpam-6139	740	38	analysis	analysis	NOUN
ejpam-6139	740	39	underscores	underscore	VERB
ejpam-6139	740	40	the	the	DET
ejpam-6139	740	41	utility	utility	NOUN
ejpam-6139	740	42	and	and	CCONJ
ejpam-6139	740	43	reliability	reliability	NOUN
ejpam-6139	740	44	of	of	ADP
ejpam-6139	740	45	theorem	theorem	NOUN
ejpam-6139	740	46	6	6	NUM
ejpam-6139	740	47	,	,	PUNCT
ejpam-6139	740	48	verifying	verify	VERB
ejpam-6139	740	49	its	its	PRON
ejpam-6139	740	50	capacity	capacity	NOUN
ejpam-6139	740	51	to	to	PART
ejpam-6139	740	52	constrain	constrain	VERB
ejpam-6139	740	53	the	the	DET
ejpam-6139	740	54	behavior	behavior	NOUN
ejpam-6139	740	55	of	of	ADP
ejpam-6139	740	56	h(x	h(x	PROPN
ejpam-6139	740	57	)	)	PUNCT
ejpam-6139	740	58	under	under	ADP
ejpam-6139	740	59	the	the	DET
ejpam-6139	740	60	specified	specified	ADJ
ejpam-6139	740	61	conditions	condition	NOUN
ejpam-6139	740	62	.	.	PUNCT
ejpam-6139	741	1	5	5	X
ejpam-6139	741	2	.	.	X
ejpam-6139	741	3	conclusion	conclusion	NOUN
ejpam-6139	741	4	in	in	ADP
ejpam-6139	741	5	this	this	DET
ejpam-6139	741	6	paper	paper	NOUN
ejpam-6139	741	7	,	,	PUNCT
ejpam-6139	741	8	we	we	PRON
ejpam-6139	741	9	have	have	AUX
ejpam-6139	741	10	successfully	successfully	ADV
ejpam-6139	741	11	extended	extend	VERB
ejpam-6139	741	12	the	the	DET
ejpam-6139	741	13	understanding	understanding	NOUN
ejpam-6139	741	14	of	of	ADP
ejpam-6139	741	15	inequalities	inequality	NOUN
ejpam-6139	741	16	associated	associate	VERB
ejpam-6139	741	17	with	with	ADP
ejpam-6139	741	18	twice	twice	ADJ
ejpam-6139	741	19	differentiable	differentiable	ADJ
ejpam-6139	741	20	functions	function	NOUN
ejpam-6139	741	21	through	through	ADP
ejpam-6139	741	22	the	the	DET
ejpam-6139	741	23	lens	lens	NOUN
ejpam-6139	741	24	of	of	ADP
ejpam-6139	741	25	extended	extended	ADJ
ejpam-6139	741	26	conformable	conformable	ADJ
ejpam-6139	741	27	fractional	fractional	ADJ
ejpam-6139	741	28	operators	operator	NOUN
ejpam-6139	741	29	.	.	PUNCT
ejpam-6139	742	1	the	the	DET
ejpam-6139	742	2	establishment	establishment	NOUN
ejpam-6139	742	3	of	of	ADP
ejpam-6139	742	4	new	new	ADJ
ejpam-6139	742	5	equalities	equality	NOUN
ejpam-6139	742	6	and	and	CCONJ
ejpam-6139	742	7	the	the	DET
ejpam-6139	742	8	derivation	derivation	NOUN
ejpam-6139	742	9	of	of	ADP
ejpam-6139	742	10	novel	novel	ADJ
ejpam-6139	742	11	trapezoidaltype	trapezoidaltype	NOUN
ejpam-6139	742	12	and	and	CCONJ
ejpam-6139	742	13	midpoint	midpoint	NOUN
ejpam-6139	742	14	-	-	PUNCT
ejpam-6139	742	15	type	type	NOUN
ejpam-6139	742	16	inequalities	inequality	NOUN
ejpam-6139	742	17	highlight	highlight	VERB
ejpam-6139	742	18	the	the	DET
ejpam-6139	742	19	significance	significance	NOUN
ejpam-6139	742	20	convexity	convexity	NOUN
ejpam-6139	742	21	.	.	PUNCT
ejpam-6139	743	1	the	the	DET
ejpam-6139	743	2	applications	application	NOUN
ejpam-6139	743	3	of	of	ADP
ejpam-6139	743	4	established	establish	VERB
ejpam-6139	743	5	inequalities	inequality	NOUN
ejpam-6139	743	6	,	,	PUNCT
ejpam-6139	743	7	such	such	ADJ
ejpam-6139	743	8	as	as	ADP
ejpam-6139	743	9	the	the	DET
ejpam-6139	743	10	power	power	NOUN
ejpam-6139	743	11	mean	mean	VERB
ejpam-6139	743	12	inequality	inequality	NOUN
ejpam-6139	743	13	and	and	CCONJ
ejpam-6139	743	14	hölder	hölder	PROPN
ejpam-6139	743	15	’s	’s	PART
ejpam-6139	743	16	inequality	inequality	NOUN
ejpam-6139	743	17	has	have	AUX
ejpam-6139	743	18	led	lead	VERB
ejpam-6139	743	19	to	to	ADP
ejpam-6139	743	20	the	the	DET
ejpam-6139	743	21	development	development	NOUN
ejpam-6139	743	22	of	of	ADP
ejpam-6139	743	23	a	a	DET
ejpam-6139	743	24	new	new	ADJ
ejpam-6139	743	25	class	class	NOUN
ejpam-6139	743	26	of	of	ADP
ejpam-6139	743	27	inequalities	inequality	NOUN
ejpam-6139	743	28	,	,	PUNCT
ejpam-6139	743	29	further	far	ADV
ejpam-6139	743	30	enriching	enrich	VERB
ejpam-6139	743	31	the	the	DET
ejpam-6139	743	32	existing	exist	VERB
ejpam-6139	743	33	body	body	NOUN
ejpam-6139	743	34	of	of	ADP
ejpam-6139	743	35	knowledge	knowledge	NOUN
ejpam-6139	743	36	.	.	PUNCT
ejpam-6139	744	1	these	these	DET
ejpam-6139	744	2	findings	finding	NOUN
ejpam-6139	744	3	not	not	PART
ejpam-6139	744	4	only	only	ADV
ejpam-6139	744	5	generalize	generalize	VERB
ejpam-6139	744	6	previous	previous	ADJ
ejpam-6139	744	7	research	research	NOUN
ejpam-6139	744	8	but	but	CCONJ
ejpam-6139	744	9	also	also	ADV
ejpam-6139	744	10	open	open	ADJ
ejpam-6139	744	11	avenues	avenue	NOUN
ejpam-6139	744	12	for	for	ADP
ejpam-6139	744	13	future	future	ADJ
ejpam-6139	744	14	exploration	exploration	NOUN
ejpam-6139	744	15	in	in	ADP
ejpam-6139	744	16	the	the	DET
ejpam-6139	744	17	field	field	NOUN
ejpam-6139	744	18	of	of	ADP
ejpam-6139	744	19	fractional	fractional	ADJ
ejpam-6139	744	20	calculus	calculus	NOUN
ejpam-6139	744	21	.	.	PUNCT
ejpam-6139	745	1	importantly	importantly	ADV
ejpam-6139	745	2	,	,	PUNCT
ejpam-6139	745	3	this	this	DET
ejpam-6139	745	4	research	research	NOUN
ejpam-6139	745	5	bridges	bridge	VERB
ejpam-6139	745	6	a	a	DET
ejpam-6139	745	7	gap	gap	NOUN
ejpam-6139	745	8	between	between	ADP
ejpam-6139	745	9	classical	classical	ADJ
ejpam-6139	745	10	convex	convex	NOUN
ejpam-6139	745	11	analysis	analysis	NOUN
ejpam-6139	745	12	and	and	CCONJ
ejpam-6139	745	13	the	the	DET
ejpam-6139	745	14	modern	modern	ADJ
ejpam-6139	745	15	framework	framework	NOUN
ejpam-6139	745	16	of	of	ADP
ejpam-6139	745	17	fractional	fractional	ADJ
ejpam-6139	745	18	calculus	calculus	NOUN
ejpam-6139	745	19	,	,	PUNCT
ejpam-6139	745	20	emphasizing	emphasize	VERB
ejpam-6139	745	21	the	the	DET
ejpam-6139	745	22	role	role	NOUN
ejpam-6139	745	23	of	of	ADP
ejpam-6139	745	24	extended	extended	ADJ
ejpam-6139	745	25	operators	operator	NOUN
ejpam-6139	745	26	in	in	ADP
ejpam-6139	745	27	advancing	advance	VERB
ejpam-6139	745	28	mathematical	mathematical	ADJ
ejpam-6139	745	29	theory	theory	NOUN
ejpam-6139	745	30	.	.	PUNCT
ejpam-6139	746	1	furthermore	furthermore	ADV
ejpam-6139	746	2	,	,	PUNCT
ejpam-6139	746	3	the	the	DET
ejpam-6139	746	4	insights	insight	NOUN
ejpam-6139	746	5	gained	gain	VERB
ejpam-6139	746	6	from	from	ADP
ejpam-6139	746	7	this	this	DET
ejpam-6139	746	8	study	study	NOUN
ejpam-6139	746	9	may	may	AUX
ejpam-6139	746	10	inspire	inspire	VERB
ejpam-6139	746	11	researchers	researcher	NOUN
ejpam-6139	746	12	to	to	PART
ejpam-6139	746	13	investigate	investigate	VERB
ejpam-6139	746	14	the	the	DET
ejpam-6139	746	15	application	application	NOUN
ejpam-6139	746	16	of	of	ADP
ejpam-6139	746	17	these	these	DET
ejpam-6139	746	18	concepts	concept	NOUN
ejpam-6139	746	19	to	to	ADP
ejpam-6139	746	20	other	other	ADJ
ejpam-6139	746	21	fractional	fractional	ADJ
ejpam-6139	746	22	operators	operator	NOUN
ejpam-6139	746	23	.	.	PUNCT
ejpam-6139	747	1	this	this	DET
ejpam-6139	747	2	study	study	NOUN
ejpam-6139	747	3	lays	lay	VERB
ejpam-6139	747	4	a	a	DET
ejpam-6139	747	5	solid	solid	ADJ
ejpam-6139	747	6	foundation	foundation	NOUN
ejpam-6139	747	7	for	for	ADP
ejpam-6139	747	8	future	future	ADJ
ejpam-6139	747	9	investigations	investigation	NOUN
ejpam-6139	747	10	,	,	PUNCT
ejpam-6139	747	11	particularly	particularly	ADV
ejpam-6139	747	12	in	in	ADP
ejpam-6139	747	13	applying	apply	VERB
ejpam-6139	747	14	extended	extended	ADJ
ejpam-6139	747	15	conformable	conformable	ADJ
ejpam-6139	747	16	fractional	fractional	ADJ
ejpam-6139	747	17	operators	operator	NOUN
ejpam-6139	747	18	to	to	ADP
ejpam-6139	747	19	other	other	ADJ
ejpam-6139	747	20	forms	form	NOUN
ejpam-6139	747	21	of	of	ADP
ejpam-6139	747	22	inequalities	inequality	NOUN
ejpam-6139	747	23	or	or	CCONJ
ejpam-6139	747	24	to	to	ADP
ejpam-6139	747	25	different	different	ADJ
ejpam-6139	747	26	classes	class	NOUN
ejpam-6139	747	27	of	of	ADP
ejpam-6139	747	28	functions	function	NOUN
ejpam-6139	747	29	beyond	beyond	ADP
ejpam-6139	747	30	the	the	DET
ejpam-6139	747	31	twice	twice	ADV
ejpam-6139	747	32	differentiable	differentiable	ADJ
ejpam-6139	747	33	case	case	NOUN
ejpam-6139	747	34	.	.	PUNCT
ejpam-6139	748	1	this	this	DET
ejpam-6139	748	2	work	work	NOUN
ejpam-6139	748	3	encourages	encourage	VERB
ejpam-6139	748	4	applying	apply	VERB
ejpam-6139	748	5	these	these	DET
ejpam-6139	748	6	concepts	concept	NOUN
ejpam-6139	748	7	to	to	ADP
ejpam-6139	748	8	other	other	ADJ
ejpam-6139	748	9	fractional	fractional	ADJ
ejpam-6139	748	10	operators	operator	NOUN
ejpam-6139	748	11	and	and	CCONJ
ejpam-6139	748	12	highlights	highlight	NOUN
ejpam-6139	748	13	the	the	DET
ejpam-6139	748	14	link	link	NOUN
ejpam-6139	748	15	between	between	ADP
ejpam-6139	748	16	convexity	convexity	NOUN
ejpam-6139	748	17	,	,	PUNCT
ejpam-6139	748	18	differentiability	differentiability	NOUN
ejpam-6139	748	19	,	,	PUNCT
ejpam-6139	748	20	and	and	CCONJ
ejpam-6139	748	21	fractional	fractional	ADJ
ejpam-6139	748	22	calculus	calculus	NOUN
ejpam-6139	748	23	.	.	PUNCT
ejpam-6139	749	1	acknowledgements	acknowledgement	NOUN
ejpam-6139	749	2	authors	author	NOUN
ejpam-6139	749	3	m.sarwar	m.sarwar	VERB
ejpam-6139	749	4	,	,	PUNCT
ejpam-6139	749	5	n.fatima	n.fatima	NUM
ejpam-6139	749	6	and	and	CCONJ
ejpam-6139	749	7	k.	k.	PROPN
ejpam-6139	749	8	abodayeh	abodayeh	PROPN
ejpam-6139	749	9	are	be	AUX
ejpam-6139	749	10	thankful	thankful	ADJ
ejpam-6139	749	11	to	to	ADP
ejpam-6139	749	12	prince	prince	PROPN
ejpam-6139	749	13	sultan	sultan	PROPN
ejpam-6139	749	14	university	university	PROPN
ejpam-6139	749	15	for	for	ADP
ejpam-6139	749	16	apc	apc	PROPN
ejpam-6139	749	17	and	and	CCONJ
ejpam-6139	749	18	support	support	VERB
ejpam-6139	749	19	through	through	ADP
ejpam-6139	749	20	tas	ta	NOUN
ejpam-6139	749	21	research	research	NOUN
ejpam-6139	749	22	lab	lab	PROPN
ejpam-6139	749	23	.	.	PUNCT
ejpam-6139	750	1	m.	m.	NOUN
ejpam-6139	750	2	samraiz	samraiz	PROPN
ejpam-6139	750	3	et	et	PROPN
ejpam-6139	750	4	al	al	PROPN
ejpam-6139	750	5	.	.	PUNCT
ejpam-6139	750	6	/	/	SYM
ejpam-6139	750	7	eur	eur	PROPN
ejpam-6139	750	8	.	.	PUNCT
ejpam-6139	751	1	j.	j.	PROPN
ejpam-6139	751	2	pure	pure	PROPN
ejpam-6139	751	3	appl	appl	PROPN
ejpam-6139	751	4	.	.	PROPN
ejpam-6139	751	5	math	math	PROPN
ejpam-6139	751	6	,	,	PUNCT
ejpam-6139	751	7	18	18	NUM
ejpam-6139	751	8	(	(	PUNCT
ejpam-6139	751	9	4	4	NUM
ejpam-6139	751	10	)	)	PUNCT
ejpam-6139	751	11	(	(	PUNCT
ejpam-6139	751	12	2025	2025	NUM
ejpam-6139	751	13	)	)	PUNCT
ejpam-6139	751	14	,	,	PUNCT
ejpam-6139	751	15	6139	6139	NUM
ejpam-6139	751	16	31	31	NUM
ejpam-6139	751	17	of	of	ADP
ejpam-6139	751	18	34	34	NUM
ejpam-6139	751	19	declarations	declaration	NOUN
ejpam-6139	751	20	:	:	PUNCT
ejpam-6139	751	21	availability	availability	NOUN
ejpam-6139	751	22	of	of	ADP
ejpam-6139	751	23	data	datum	NOUN
ejpam-6139	751	24	and	and	CCONJ
ejpam-6139	751	25	material	material	NOUN
ejpam-6139	751	26	the	the	DET
ejpam-6139	751	27	data	datum	NOUN
ejpam-6139	751	28	used	use	VERB
ejpam-6139	751	29	to	to	PART
ejpam-6139	751	30	support	support	VERB
ejpam-6139	751	31	the	the	DET
ejpam-6139	751	32	findings	finding	NOUN
ejpam-6139	751	33	of	of	ADP
ejpam-6139	751	34	this	this	DET
ejpam-6139	751	35	study	study	NOUN
ejpam-6139	751	36	are	be	AUX
ejpam-6139	751	37	available	available	ADJ
ejpam-6139	751	38	from	from	ADP
ejpam-6139	751	39	the	the	DET
ejpam-6139	751	40	corresponding	corresponding	ADJ
ejpam-6139	751	41	author	author	NOUN
ejpam-6139	751	42	upon	upon	SCONJ
ejpam-6139	751	43	request	request	NOUN
ejpam-6139	751	44	.	.	PUNCT
ejpam-6139	752	1	funding	fund	VERB
ejpam-6139	752	2	this	this	DET
ejpam-6139	752	3	work	work	NOUN
ejpam-6139	752	4	does	do	AUX
ejpam-6139	752	5	not	not	PART
ejpam-6139	752	6	receive	receive	VERB
ejpam-6139	752	7	any	any	DET
ejpam-6139	752	8	external	external	ADJ
ejpam-6139	752	9	funding	funding	NOUN
ejpam-6139	752	10	.	.	PUNCT
ejpam-6139	753	1	authors	author	NOUN
ejpam-6139	753	2	’	'	PUNCT
ejpam-6139	753	3	contributions	contribution	NOUN
ejpam-6139	753	4	all	all	DET
ejpam-6139	753	5	authors	author	NOUN
ejpam-6139	753	6	contributed	contribute	VERB
ejpam-6139	753	7	equally	equally	ADV
ejpam-6139	753	8	and	and	CCONJ
ejpam-6139	753	9	significantly	significantly	ADV
ejpam-6139	753	10	in	in	ADP
ejpam-6139	753	11	writing	write	VERB
ejpam-6139	753	12	this	this	DET
ejpam-6139	753	13	article	article	NOUN
ejpam-6139	753	14	.	.	PUNCT
ejpam-6139	754	1	all	all	DET
ejpam-6139	754	2	authors	author	NOUN
ejpam-6139	754	3	read	read	VERB
ejpam-6139	754	4	and	and	CCONJ
ejpam-6139	754	5	approved	approve	VERB
ejpam-6139	754	6	the	the	DET
ejpam-6139	754	7	final	final	ADJ
ejpam-6139	754	8	version	version	NOUN
ejpam-6139	754	9	.	.	PUNCT
ejpam-6139	755	1	competing	compete	VERB
ejpam-6139	755	2	interests	interest	NOUN
ejpam-6139	755	3	the	the	DET
ejpam-6139	755	4	authors	author	NOUN
ejpam-6139	755	5	declare	declare	VERB
ejpam-6139	755	6	that	that	SCONJ
ejpam-6139	755	7	they	they	PRON
ejpam-6139	755	8	have	have	VERB
ejpam-6139	755	9	no	no	DET
ejpam-6139	755	10	conflicts	conflict	NOUN
ejpam-6139	755	11	of	of	ADP
ejpam-6139	755	12	interest	interest	NOUN
ejpam-6139	755	13	.	.	PUNCT
ejpam-6139	756	1	references	reference	NOUN
ejpam-6139	756	2	[	[	X
ejpam-6139	756	3	1	1	NUM
ejpam-6139	756	4	]	]	PUNCT
ejpam-6139	756	5	ohta	ohta	NOUN
ejpam-6139	756	6	and	and	CCONJ
ejpam-6139	756	7	shin	shin	NOUN
ejpam-6139	756	8	-	-	PUNCT
ejpam-6139	756	9	ichi	ichi	PROPN
ejpam-6139	756	10	.	.	PUNCT
ejpam-6139	757	1	uniform	uniform	PROPN
ejpam-6139	757	2	convexity	convexity	NOUN
ejpam-6139	757	3	and	and	CCONJ
ejpam-6139	757	4	smoothness	smoothness	NOUN
ejpam-6139	757	5	,	,	PUNCT
ejpam-6139	757	6	and	and	CCONJ
ejpam-6139	757	7	their	their	PRON
ejpam-6139	757	8	applications	application	NOUN
ejpam-6139	757	9	in	in	ADP
ejpam-6139	757	10	finsler	finsler	NOUN
ejpam-6139	757	11	geometry	geometry	NOUN
ejpam-6139	757	12	.	.	PUNCT
ejpam-6139	758	1	mathematische	mathematische	PROPN
ejpam-6139	758	2	annalen	annalen	PROPN
ejpam-6139	758	3	,	,	PUNCT
ejpam-6139	758	4	343:669–699	343:669–699	NUM
ejpam-6139	758	5	,	,	PUNCT
ejpam-6139	758	6	2009	2009	NUM
ejpam-6139	758	7	.	.	PUNCT
ejpam-6139	759	1	[	[	X
ejpam-6139	759	2	2	2	NUM
ejpam-6139	759	3	]	]	X
ejpam-6139	759	4	mecke	mecke	NOUN
ejpam-6139	759	5	and	and	CCONJ
ejpam-6139	759	6	klaus	klaus	PROPN
ejpam-6139	759	7	r.	r.	PROPN
ejpam-6139	759	8	additivity	additivity	PROPN
ejpam-6139	759	9	,	,	PUNCT
ejpam-6139	759	10	convexity	convexity	NOUN
ejpam-6139	759	11	,	,	PUNCT
ejpam-6139	759	12	and	and	CCONJ
ejpam-6139	759	13	beyond	beyond	ADP
ejpam-6139	759	14	:	:	PUNCT
ejpam-6139	759	15	applications	application	NOUN
ejpam-6139	759	16	of	of	ADP
ejpam-6139	759	17	minkowski	minkowski	ADJ
ejpam-6139	759	18	functionals	functional	NOUN
ejpam-6139	759	19	in	in	ADP
ejpam-6139	759	20	statistical	statistical	ADJ
ejpam-6139	759	21	physics	physic	NOUN
ejpam-6139	759	22	.	.	PUNCT
ejpam-6139	760	1	statistical	statistical	ADJ
ejpam-6139	760	2	physics	physics	NOUN
ejpam-6139	760	3	and	and	CCONJ
ejpam-6139	760	4	spatial	spatial	ADJ
ejpam-6139	760	5	statistics	statistic	NOUN
ejpam-6139	760	6	:	:	PUNCT
ejpam-6139	760	7	the	the	DET
ejpam-6139	760	8	art	art	NOUN
ejpam-6139	760	9	of	of	ADP
ejpam-6139	760	10	analyzing	analyze	VERB
ejpam-6139	760	11	and	and	CCONJ
ejpam-6139	760	12	modeling	model	VERB
ejpam-6139	760	13	spatial	spatial	ADJ
ejpam-6139	760	14	structures	structure	NOUN
ejpam-6139	760	15	and	and	CCONJ
ejpam-6139	760	16	pattern	pattern	NOUN
ejpam-6139	760	17	formation	formation	NOUN
ejpam-6139	760	18	.	.	PUNCT
ejpam-6139	761	1	berlin	berlin	PROPN
ejpam-6139	761	2	,	,	PUNCT
ejpam-6139	761	3	heidelberg	heidelberg	PROPN
ejpam-6139	761	4	:	:	PUNCT
ejpam-6139	761	5	springer	springer	PROPN
ejpam-6139	761	6	berlin	berlin	PROPN
ejpam-6139	761	7	heidelberg	heidelberg	PROPN
ejpam-6139	761	8	,	,	PUNCT
ejpam-6139	761	9	pages	page	VERB
ejpam-6139	761	10	111–184	111–184	NUM
ejpam-6139	761	11	,	,	PUNCT
ejpam-6139	761	12	2000	2000	NUM
ejpam-6139	761	13	.	.	PUNCT
ejpam-6139	762	1	[	[	X
ejpam-6139	762	2	3	3	X
ejpam-6139	762	3	]	]	X
ejpam-6139	762	4	michael	michael	PROPN
ejpam-6139	762	5	hirsch	hirsch	PROPN
ejpam-6139	762	6	and	and	CCONJ
ejpam-6139	762	7	wolfgang	wolfgang	PROPN
ejpam-6139	762	8	quapp	quapp	PROPN
ejpam-6139	762	9	.	.	PUNCT
ejpam-6139	763	1	reaction	reaction	NOUN
ejpam-6139	763	2	pathways	pathway	NOUN
ejpam-6139	763	3	and	and	CCONJ
ejpam-6139	763	4	convexity	convexity	NOUN
ejpam-6139	763	5	of	of	ADP
ejpam-6139	763	6	the	the	DET
ejpam-6139	763	7	potential	potential	ADJ
ejpam-6139	763	8	energy	energy	NOUN
ejpam-6139	763	9	surface	surface	NOUN
ejpam-6139	763	10	:	:	PUNCT
ejpam-6139	763	11	application	application	NOUN
ejpam-6139	763	12	of	of	ADP
ejpam-6139	763	13	newton	newton	PROPN
ejpam-6139	763	14	trajectories	trajectories	PROPN
ejpam-6139	763	15	.	.	PUNCT
ejpam-6139	764	1	journal	journal	PROPN
ejpam-6139	764	2	of	of	ADP
ejpam-6139	764	3	mathematical	mathematical	ADJ
ejpam-6139	764	4	chemistry	chemistry	NOUN
ejpam-6139	764	5	,	,	PUNCT
ejpam-6139	764	6	36:307–340	36:307–340	NUM
ejpam-6139	764	7	,	,	PUNCT
ejpam-6139	764	8	2004	2004	NUM
ejpam-6139	764	9	.	.	PUNCT
ejpam-6139	765	1	[	[	X
ejpam-6139	765	2	4	4	NUM
ejpam-6139	765	3	]	]	X
ejpam-6139	765	4	el	el	PROPN
ejpam-6139	765	5	-	-	PUNCT
ejpam-6139	765	6	shahed	shahed	ADJ
ejpam-6139	765	7	and	and	CCONJ
ejpam-6139	765	8	moustafa	moustafa	NOUN
ejpam-6139	765	9	.	.	PUNCT
ejpam-6139	766	1	fractional	fractional	ADJ
ejpam-6139	766	2	calculus	calculus	NOUN
ejpam-6139	766	3	model	model	NOUN
ejpam-6139	766	4	of	of	ADP
ejpam-6139	766	5	the	the	DET
ejpam-6139	766	6	semilunar	semilunar	NOUN
ejpam-6139	766	7	heart	heart	NOUN
ejpam-6139	766	8	valve	valve	VERB
ejpam-6139	766	9	vibrations	vibration	NOUN
ejpam-6139	766	10	.	.	PUNCT
ejpam-6139	767	1	international	international	ADJ
ejpam-6139	767	2	design	design	NOUN
ejpam-6139	767	3	engineering	engineering	NOUN
ejpam-6139	767	4	technical	technical	ADJ
ejpam-6139	767	5	conferences	conference	NOUN
ejpam-6139	767	6	and	and	CCONJ
ejpam-6139	767	7	computers	computer	NOUN
ejpam-6139	767	8	and	and	CCONJ
ejpam-6139	767	9	information	information	NOUN
ejpam-6139	767	10	in	in	ADP
ejpam-6139	767	11	engineering	engineering	NOUN
ejpam-6139	767	12	conference	conference	NOUN
ejpam-6139	767	13	.	.	PUNCT
ejpam-6139	767	14	,	,	PUNCT
ejpam-6139	767	15	37033	37033	NUM
ejpam-6139	767	16	,	,	PUNCT
ejpam-6139	767	17	2003	2003	NUM
ejpam-6139	767	18	.	.	PUNCT
ejpam-6139	768	1	[	[	X
ejpam-6139	768	2	5	5	NUM
ejpam-6139	768	3	]	]	X
ejpam-6139	768	4	alberto	alberto	PROPN
ejpam-6139	768	5	cambini	cambini	PROPN
ejpam-6139	768	6	and	and	CCONJ
ejpam-6139	768	7	laura	laura	NOUN
ejpam-6139	768	8	martein	martein	PROPN
ejpam-6139	768	9	.	.	PUNCT
ejpam-6139	769	1	generalized	generalized	ADJ
ejpam-6139	769	2	convexity	convexity	NOUN
ejpam-6139	769	3	and	and	CCONJ
ejpam-6139	769	4	optimization	optimization	NOUN
ejpam-6139	769	5	:	:	PUNCT
ejpam-6139	769	6	theory	theory	NOUN
ejpam-6139	769	7	and	and	CCONJ
ejpam-6139	769	8	applications	application	NOUN
ejpam-6139	769	9	.	.	PUNCT
ejpam-6139	770	1	springer	springer	NOUN
ejpam-6139	770	2	science	science	PROPN
ejpam-6139	770	3	and	and	CCONJ
ejpam-6139	770	4	business	business	NOUN
ejpam-6139	770	5	media	medium	NOUN
ejpam-6139	770	6	.	.	PUNCT
ejpam-6139	770	7	,	,	PUNCT
ejpam-6139	770	8	616	616	NUM
ejpam-6139	770	9	,	,	PUNCT
ejpam-6139	770	10	2008	2008	NUM
ejpam-6139	770	11	.	.	PUNCT
ejpam-6139	771	1	[	[	X
ejpam-6139	771	2	6	6	NUM
ejpam-6139	771	3	]	]	SYM
ejpam-6139	771	4	magin	magin	NOUN
ejpam-6139	771	5	and	and	CCONJ
ejpam-6139	771	6	r	r	NOUN
ejpam-6139	771	7	l.	l.	NOUN
ejpam-6139	771	8	fractional	fractional	PROPN
ejpam-6139	771	9	calculus	calculus	NOUN
ejpam-6139	771	10	in	in	ADP
ejpam-6139	771	11	bioengineering	bioengineering	NOUN
ejpam-6139	771	12	begell	begell	NOUN
ejpam-6139	771	13	house	house	NOUN
ejpam-6139	771	14	publishers	publisher	NOUN
ejpam-6139	771	15	.	.	PUNCT
ejpam-6139	772	1	inc	inc	PROPN
ejpam-6139	772	2	.	.	PROPN
ejpam-6139	772	3	,	,	PUNCT
ejpam-6139	772	4	connecticut	connecticut	PROPN
ejpam-6139	772	5	.	.	PUNCT
ejpam-6139	772	6	,	,	PUNCT
ejpam-6139	772	7	2006	2006	NUM
ejpam-6139	772	8	.	.	PUNCT
ejpam-6139	773	1	[	[	X
ejpam-6139	773	2	7	7	X
ejpam-6139	773	3	]	]	X
ejpam-6139	773	4	pham	pham	PROPN
ejpam-6139	773	5	dinh	dinh	PROPN
ejpam-6139	773	6	tao	tao	PROPN
ejpam-6139	773	7	and	and	CCONJ
ejpam-6139	773	8	lt	lt	PRON
ejpam-6139	773	9	hoai	hoai	PROPN
ejpam-6139	773	10	an	an	PROPN
ejpam-6139	773	11	.	.	PUNCT
ejpam-6139	773	12	convex	convex	PROPN
ejpam-6139	773	13	analysis	analysis	NOUN
ejpam-6139	773	14	approach	approach	NOUN
ejpam-6139	773	15	to	to	ADP
ejpam-6139	773	16	dc	dc	PROPN
ejpam-6139	773	17	programming	programming	NOUN
ejpam-6139	773	18	:	:	PUNCT
ejpam-6139	774	1	theory	theory	NOUN
ejpam-6139	774	2	,	,	PUNCT
ejpam-6139	774	3	algorithms	algorithm	NOUN
ejpam-6139	774	4	and	and	CCONJ
ejpam-6139	774	5	applications	application	NOUN
ejpam-6139	774	6	.	.	PUNCT
ejpam-6139	775	1	acta	acta	PROPN
ejpam-6139	775	2	mathematica	mathematica	PROPN
ejpam-6139	775	3	vietnamica	vietnamica	PROPN
ejpam-6139	775	4	.	.	PUNCT
ejpam-6139	775	5	,	,	PUNCT
ejpam-6139	775	6	22(1):289–355	22(1):289–355	PROPN
ejpam-6139	775	7	,	,	PUNCT
ejpam-6139	775	8	1997	1997	NUM
ejpam-6139	775	9	.	.	PUNCT
ejpam-6139	776	1	[	[	X
ejpam-6139	776	2	8	8	X
ejpam-6139	776	3	]	]	PUNCT
ejpam-6139	776	4	xinyue	xinyue	PROPN
ejpam-6139	776	5	shen	shen	PROPN
ejpam-6139	776	6	and	and	CCONJ
ejpam-6139	776	7	et	et	PROPN
ejpam-6139	776	8	al	al	PROPN
ejpam-6139	776	9	.	.	PROPN
ejpam-6139	776	10	disciplined	discipline	VERB
ejpam-6139	776	11	multi	multi	ADJ
ejpam-6139	776	12	-	-	ADJ
ejpam-6139	776	13	convex	convex	ADJ
ejpam-6139	776	14	programming	programming	NOUN
ejpam-6139	776	15	.	.	PUNCT
ejpam-6139	777	1	29th	29th	ADJ
ejpam-6139	777	2	chinese	chinese	ADJ
ejpam-6139	777	3	control	control	NOUN
ejpam-6139	777	4	and	and	CCONJ
ejpam-6139	777	5	decision	decision	NOUN
ejpam-6139	777	6	conference	conference	NOUN
ejpam-6139	777	7	(	(	PUNCT
ejpam-6139	777	8	ccdc	ccdc	PROPN
ejpam-6139	777	9	)	)	PUNCT
ejpam-6139	777	10	ieee	ieee	PROPN
ejpam-6139	777	11	.	.	PROPN
ejpam-6139	777	12	,	,	PUNCT
ejpam-6139	777	13	2017	2017	NUM
ejpam-6139	777	14	.	.	PUNCT
ejpam-6139	778	1	[	[	X
ejpam-6139	778	2	9	9	NUM
ejpam-6139	778	3	]	]	X
ejpam-6139	778	4	asimow	asimow	NOUN
ejpam-6139	778	5	and	and	CCONJ
ejpam-6139	778	6	leonhard	leonhard	PROPN
ejpam-6139	778	7	.	.	PUNCT
ejpam-6139	779	1	convexity	convexity	NOUN
ejpam-6139	779	2	theory	theory	NOUN
ejpam-6139	779	3	and	and	CCONJ
ejpam-6139	779	4	its	its	PRON
ejpam-6139	779	5	applications	application	NOUN
ejpam-6139	779	6	in	in	ADP
ejpam-6139	779	7	functional	functional	ADJ
ejpam-6139	779	8	analysis	analysis	NOUN
ejpam-6139	779	9	.	.	PUNCT
ejpam-6139	780	1	elsevier	elsevier	NOUN
ejpam-6139	780	2	.	.	PUNCT
ejpam-6139	781	1	,	,	PUNCT
ejpam-6139	781	2	16	16	NUM
ejpam-6139	781	3	,	,	PUNCT
ejpam-6139	781	4	2014	2014	NUM
ejpam-6139	781	5	.	.	PUNCT
ejpam-6139	782	1	m.	m.	NOUN
ejpam-6139	782	2	samraiz	samraiz	PROPN
ejpam-6139	782	3	et	et	PROPN
ejpam-6139	782	4	al	al	PROPN
ejpam-6139	782	5	.	.	PUNCT
ejpam-6139	782	6	/	/	SYM
ejpam-6139	782	7	eur	eur	PROPN
ejpam-6139	782	8	.	.	PUNCT
ejpam-6139	783	1	j.	j.	PROPN
ejpam-6139	783	2	pure	pure	PROPN
ejpam-6139	783	3	appl	appl	PROPN
ejpam-6139	783	4	.	.	PROPN
ejpam-6139	783	5	math	math	PROPN
ejpam-6139	783	6	,	,	PUNCT
ejpam-6139	783	7	18	18	NUM
ejpam-6139	783	8	(	(	PUNCT
ejpam-6139	783	9	4	4	NUM
ejpam-6139	783	10	)	)	PUNCT
ejpam-6139	783	11	(	(	PUNCT
ejpam-6139	783	12	2025	2025	NUM
ejpam-6139	783	13	)	)	PUNCT
ejpam-6139	783	14	,	,	PUNCT
ejpam-6139	783	15	6139	6139	NUM
ejpam-6139	783	16	32	32	NUM
ejpam-6139	783	17	of	of	ADP
ejpam-6139	783	18	34	34	NUM
ejpam-6139	783	19	[	[	SYM
ejpam-6139	783	20	10	10	NUM
ejpam-6139	783	21	]	]	X
ejpam-6139	783	22	hasanov	hasanov	NOUN
ejpam-6139	783	23	and	and	CCONJ
ejpam-6139	783	24	alemdar	alemdar	NOUN
ejpam-6139	783	25	.	.	PUNCT
ejpam-6139	784	1	convexity	convexity	NOUN
ejpam-6139	784	2	argument	argument	NOUN
ejpam-6139	784	3	for	for	ADP
ejpam-6139	784	4	monotone	monotone	ADJ
ejpam-6139	784	5	potential	potential	ADJ
ejpam-6139	784	6	operators	operator	NOUN
ejpam-6139	784	7	and	and	CCONJ
ejpam-6139	784	8	its	its	PRON
ejpam-6139	784	9	application	application	NOUN
ejpam-6139	784	10	.	.	PUNCT
ejpam-6139	785	1	nonlinear	nonlinear	ADJ
ejpam-6139	785	2	analysis	analysis	NOUN
ejpam-6139	785	3	-	-	PUNCT
ejpam-6139	785	4	series	series	NOUN
ejpam-6139	785	5	a	a	DET
ejpam-6139	785	6	theory	theory	NOUN
ejpam-6139	785	7	and	and	CCONJ
ejpam-6139	785	8	methods	method	NOUN
ejpam-6139	785	9	and	and	CCONJ
ejpam-6139	785	10	series	series	PROPN
ejpam-6139	785	11	b	b	PROPN
ejpam-6139	785	12	real	real	ADJ
ejpam-6139	785	13	world	world	NOUN
ejpam-6139	785	14	applications	application	NOUN
ejpam-6139	785	15	.	.	PUNCT
ejpam-6139	785	16	,	,	PUNCT
ejpam-6139	785	17	41(7):907–920	41(7):907–920	NOUN
ejpam-6139	785	18	,	,	PUNCT
ejpam-6139	785	19	2000	2000	NUM
ejpam-6139	785	20	.	.	PUNCT
ejpam-6139	786	1	[	[	X
ejpam-6139	786	2	11	11	NUM
ejpam-6139	786	3	]	]	SYM
ejpam-6139	786	4	soĺıs	soĺıs	NUM
ejpam-6139	786	5	-	-	PUNCT
ejpam-6139	786	6	pérez	pérez	PROPN
ejpam-6139	786	7	j.	j.	PROPN
ejpam-6139	786	8	e.	e.	PROPN
ejpam-6139	786	9	gomez	gomez	PROPN
ejpam-6139	786	10	-	-	PUNCT
ejpam-6139	786	11	aguilar	aguilar	PROPN
ejpam-6139	786	12	j.	j.	PROPN
ejpam-6139	786	13	f.	f.	PROPN
ejpam-6139	786	14	razo	razo	PROPN
ejpam-6139	786	15	-	-	PUNCT
ejpam-6139	786	16	hernández	hernández	PROPN
ejpam-6139	786	17	j.	j.	PROPN
ejpam-6139	786	18	r.	r.	PROPN
ejpam-6139	786	19	etemad	etemad	PROPN
ejpam-6139	786	20	s.	s.	PROPN
ejpam-6139	786	21	lav́ındelgado	lav́ındelgado	PROPN
ejpam-6139	786	22	,	,	PUNCT
ejpam-6139	786	23	j.	j.	PROPN
ejpam-6139	786	24	e.	e.	PROPN
ejpam-6139	786	25	and	and	CCONJ
ejpam-6139	786	26	s.	s.	PROPN
ejpam-6139	786	27	rezapour	rezapour	PROPN
ejpam-6139	786	28	.	.	PUNCT
ejpam-6139	787	1	an	an	DET
ejpam-6139	787	2	improved	improved	ADJ
ejpam-6139	787	3	object	object	NOUN
ejpam-6139	787	4	detection	detection	NOUN
ejpam-6139	787	5	algorithm	algorithm	NOUN
ejpam-6139	787	6	based	base	VERB
ejpam-6139	787	7	on	on	ADP
ejpam-6139	787	8	the	the	DET
ejpam-6139	787	9	hessian	hessian	ADJ
ejpam-6139	787	10	matrix	matrix	NOUN
ejpam-6139	787	11	and	and	CCONJ
ejpam-6139	787	12	conformable	conformable	ADJ
ejpam-6139	787	13	derivative	derivative	ADJ
ejpam-6139	787	14	.	.	PUNCT
ejpam-6139	788	1	circuits	circuit	NOUN
ejpam-6139	788	2	,	,	PUNCT
ejpam-6139	788	3	systems	system	NOUN
ejpam-6139	788	4	,	,	PUNCT
ejpam-6139	788	5	and	and	CCONJ
ejpam-6139	788	6	signal	signal	NOUN
ejpam-6139	788	7	processing	processing	NOUN
ejpam-6139	788	8	.	.	PUNCT
ejpam-6139	788	9	,	,	PUNCT
ejpam-6139	788	10	43(8):4991–5047	43(8):4991–5047	NUM
ejpam-6139	788	11	,	,	PUNCT
ejpam-6139	788	12	2024	2024	NUM
ejpam-6139	788	13	.	.	PUNCT
ejpam-6139	789	1	[	[	X
ejpam-6139	789	2	12	12	NUM
ejpam-6139	789	3	]	]	X
ejpam-6139	789	4	krantz	krantz	PROPN
ejpam-6139	789	5	and	and	CCONJ
ejpam-6139	789	6	steven	steven	PROPN
ejpam-6139	789	7	g.	g.	PROPN
ejpam-6139	789	8	convexity	convexity	PROPN
ejpam-6139	789	9	in	in	ADP
ejpam-6139	789	10	complex	complex	ADJ
ejpam-6139	789	11	analysis	analysis	NOUN
ejpam-6139	789	12	.	.	PUNCT
ejpam-6139	790	1	proc	proc	NOUN
ejpam-6139	790	2	.	.	PUNCT
ejpam-6139	791	1	symp	symp	PROPN
ejpam-6139	791	2	.	.	PUNCT
ejpam-6139	792	1	pure	pure	ADJ
ejpam-6139	792	2	math	math	NOUN
ejpam-6139	792	3	.	.	PUNCT
ejpam-6139	792	4	,	,	PUNCT
ejpam-6139	792	5	52	52	NUM
ejpam-6139	792	6	,	,	PUNCT
ejpam-6139	792	7	1991	1991	NUM
ejpam-6139	792	8	.	.	PUNCT
ejpam-6139	793	1	[	[	X
ejpam-6139	793	2	13	13	NUM
ejpam-6139	793	3	]	]	X
ejpam-6139	793	4	archimedes	archimede	NOUN
ejpam-6139	793	5	and	and	CCONJ
ejpam-6139	793	6	sir	sir	PROPN
ejpam-6139	793	7	thomas	thomas	PROPN
ejpam-6139	793	8	little	little	ADJ
ejpam-6139	793	9	heath	heath	PROPN
ejpam-6139	793	10	.	.	PUNCT
ejpam-6139	794	1	the	the	DET
ejpam-6139	794	2	works	work	NOUN
ejpam-6139	794	3	of	of	ADP
ejpam-6139	794	4	archimedes	archimedes	PROPN
ejpam-6139	794	5	.	.	PUNCT
ejpam-6139	795	1	cup	cup	PROPN
ejpam-6139	795	2	archive	archive	NOUN
ejpam-6139	795	3	,	,	PUNCT
ejpam-6139	795	4	2004	2004	NUM
ejpam-6139	795	5	.	.	PUNCT
ejpam-6139	796	1	[	[	X
ejpam-6139	796	2	14	14	NUM
ejpam-6139	796	3	]	]	X
ejpam-6139	796	4	kjeldsen	kjeldsen	PROPN
ejpam-6139	796	5	and	and	CCONJ
ejpam-6139	796	6	tinne	tinne	PROPN
ejpam-6139	796	7	hoff	hoff	PROPN
ejpam-6139	796	8	.	.	PUNCT
ejpam-6139	797	1	from	from	ADP
ejpam-6139	797	2	measuring	measure	VERB
ejpam-6139	797	3	tool	tool	NOUN
ejpam-6139	797	4	to	to	ADP
ejpam-6139	797	5	geometrical	geometrical	ADJ
ejpam-6139	797	6	object	object	NOUN
ejpam-6139	797	7	:	:	PUNCT
ejpam-6139	797	8	minkowski	minkowski	PROPN
ejpam-6139	797	9	’s	’s	PART
ejpam-6139	797	10	development	development	NOUN
ejpam-6139	797	11	of	of	ADP
ejpam-6139	797	12	the	the	DET
ejpam-6139	797	13	concept	concept	NOUN
ejpam-6139	797	14	of	of	ADP
ejpam-6139	797	15	convex	convex	NOUN
ejpam-6139	797	16	bodies	body	NOUN
ejpam-6139	797	17	.	.	PUNCT
ejpam-6139	798	1	archive	archive	NOUN
ejpam-6139	798	2	for	for	ADP
ejpam-6139	798	3	history	history	NOUN
ejpam-6139	798	4	of	of	ADP
ejpam-6139	798	5	exact	exact	ADJ
ejpam-6139	798	6	sciences	science	NOUN
ejpam-6139	798	7	.	.	PUNCT
ejpam-6139	798	8	,	,	PUNCT
ejpam-6139	798	9	62(1):59–89	62(1):59–89	NUM
ejpam-6139	798	10	,	,	PUNCT
ejpam-6139	798	11	2008	2008	NUM
ejpam-6139	798	12	.	.	PUNCT
ejpam-6139	799	1	[	[	X
ejpam-6139	799	2	15	15	NUM
ejpam-6139	799	3	]	]	X
ejpam-6139	799	4	steele	steele	PROPN
ejpam-6139	799	5	and	and	CCONJ
ejpam-6139	799	6	j.	j.	PROPN
ejpam-6139	799	7	michael	michael	PROPN
ejpam-6139	799	8	.	.	PUNCT
ejpam-6139	800	1	the	the	DET
ejpam-6139	800	2	cauchy	cauchy	PROPN
ejpam-6139	800	3	-	-	PUNCT
ejpam-6139	800	4	schwarz	schwarz	PROPN
ejpam-6139	800	5	master	master	NOUN
ejpam-6139	800	6	class	class	NOUN
ejpam-6139	800	7	:	:	PUNCT
ejpam-6139	800	8	an	an	DET
ejpam-6139	800	9	introduction	introduction	NOUN
ejpam-6139	800	10	to	to	ADP
ejpam-6139	800	11	the	the	DET
ejpam-6139	800	12	art	art	NOUN
ejpam-6139	800	13	of	of	ADP
ejpam-6139	800	14	mathematical	mathematical	ADJ
ejpam-6139	800	15	inequalities	inequality	NOUN
ejpam-6139	800	16	.	.	PUNCT
ejpam-6139	801	1	cambridge	cambridge	PROPN
ejpam-6139	801	2	university	university	PROPN
ejpam-6139	801	3	press	press	NOUN
ejpam-6139	801	4	,	,	PUNCT
ejpam-6139	801	5	2004	2004	NUM
ejpam-6139	801	6	.	.	PUNCT
ejpam-6139	802	1	[	[	X
ejpam-6139	802	2	16	16	NUM
ejpam-6139	802	3	]	]	X
ejpam-6139	802	4	smallwood	smallwood	PROPN
ejpam-6139	802	5	and	and	CCONJ
ejpam-6139	802	6	peter	peter	PROPN
ejpam-6139	802	7	d.	d.	PROPN
ejpam-6139	802	8	an	an	DET
ejpam-6139	802	9	introduction	introduction	NOUN
ejpam-6139	802	10	to	to	PART
ejpam-6139	802	11	risk	risk	VERB
ejpam-6139	802	12	sensitivity	sensitivity	NOUN
ejpam-6139	802	13	:	:	PUNCT
ejpam-6139	802	14	the	the	DET
ejpam-6139	802	15	use	use	NOUN
ejpam-6139	802	16	of	of	ADP
ejpam-6139	802	17	jensen	jensen	PROPN
ejpam-6139	802	18	’s	’s	PART
ejpam-6139	802	19	inequality	inequality	NOUN
ejpam-6139	802	20	to	to	PART
ejpam-6139	802	21	clarify	clarify	VERB
ejpam-6139	802	22	evolutionary	evolutionary	ADJ
ejpam-6139	802	23	arguments	argument	NOUN
ejpam-6139	802	24	of	of	ADP
ejpam-6139	802	25	adaptation	adaptation	NOUN
ejpam-6139	802	26	and	and	CCONJ
ejpam-6139	802	27	constraint	constraint	NOUN
ejpam-6139	802	28	.	.	PUNCT
ejpam-6139	803	1	american	american	PROPN
ejpam-6139	803	2	zoologist	zoologist	PROPN
ejpam-6139	803	3	.	.	PUNCT
ejpam-6139	803	4	,	,	PUNCT
ejpam-6139	803	5	36(4):392–401	36(4):392–401	PROPN
ejpam-6139	803	6	,	,	PUNCT
ejpam-6139	803	7	1996	1996	NUM
ejpam-6139	803	8	.	.	PUNCT
ejpam-6139	804	1	[	[	X
ejpam-6139	804	2	17	17	NUM
ejpam-6139	804	3	]	]	X
ejpam-6139	804	4	miao	miao	NOUN
ejpam-6139	804	5	-	-	PUNCT
ejpam-6139	804	6	kun	kun	NOUN
ejpam-6139	804	7	wang	wang	PROPN
ejpam-6139	804	8	and	and	CCONJ
ejpam-6139	804	9	et	et	PROPN
ejpam-6139	804	10	al	al	PROPN
ejpam-6139	804	11	.	.	PUNCT
ejpam-6139	805	1	an	an	DET
ejpam-6139	805	2	optimal	optimal	ADJ
ejpam-6139	805	3	power	power	NOUN
ejpam-6139	805	4	mean	mean	VERB
ejpam-6139	805	5	inequality	inequality	NOUN
ejpam-6139	805	6	for	for	ADP
ejpam-6139	805	7	the	the	DET
ejpam-6139	805	8	complete	complete	ADJ
ejpam-6139	805	9	elliptic	elliptic	ADJ
ejpam-6139	805	10	integrals	integral	NOUN
ejpam-6139	805	11	.	.	PUNCT
ejpam-6139	806	1	applied	apply	VERB
ejpam-6139	806	2	mathematics	mathematics	NOUN
ejpam-6139	806	3	letters	letter	NOUN
ejpam-6139	806	4	.	.	PUNCT
ejpam-6139	806	5	,	,	PUNCT
ejpam-6139	806	6	24(6):887–890	24(6):887–890	NOUN
ejpam-6139	806	7	,	,	PUNCT
ejpam-6139	806	8	2011	2011	NUM
ejpam-6139	806	9	.	.	PUNCT
ejpam-6139	807	1	[	[	X
ejpam-6139	807	2	18	18	NUM
ejpam-6139	807	3	]	]	X
ejpam-6139	807	4	roger	roger	PROPN
ejpam-6139	807	5	a.	a.	NOUN
ejpam-6139	807	6	horn	horn	PROPN
ejpam-6139	807	7	and	and	CCONJ
ejpam-6139	807	8	roy	roy	PROPN
ejpam-6139	807	9	mathias	mathias	PROPN
ejpam-6139	807	10	.	.	PUNCT
ejpam-6139	808	1	cauchy	cauchy	PROPN
ejpam-6139	808	2	-	-	PUNCT
ejpam-6139	808	3	schwarz	schwarz	PROPN
ejpam-6139	808	4	inequalities	inequality	NOUN
ejpam-6139	808	5	associated	associate	VERB
ejpam-6139	808	6	with	with	ADP
ejpam-6139	808	7	positive	positive	ADJ
ejpam-6139	808	8	semidefinite	semidefinite	NOUN
ejpam-6139	808	9	matrices	matrix	NOUN
ejpam-6139	808	10	.	.	PUNCT
ejpam-6139	809	1	linear	linear	ADJ
ejpam-6139	809	2	algebra	algebra	NOUN
ejpam-6139	809	3	and	and	CCONJ
ejpam-6139	809	4	its	its	PRON
ejpam-6139	809	5	applications	application	NOUN
ejpam-6139	809	6	.	.	PUNCT
ejpam-6139	809	7	,	,	PUNCT
ejpam-6139	809	8	142:63–82	142:63–82	NUM
ejpam-6139	809	9	,	,	PUNCT
ejpam-6139	809	10	1990	1990	NUM
ejpam-6139	809	11	.	.	PUNCT
ejpam-6139	810	1	[	[	X
ejpam-6139	810	2	19	19	NUM
ejpam-6139	810	3	]	]	X
ejpam-6139	810	4	khrennikov	khrennikov	NOUN
ejpam-6139	810	5	and	and	CCONJ
ejpam-6139	810	6	a.	a.	PROPN
ejpam-6139	810	7	yu	yu	PROPN
ejpam-6139	810	8	.	.	PUNCT
ejpam-6139	810	9	epr	epr	PROPN
ejpam-6139	810	10	-	-	PUNCT
ejpam-6139	810	11	bohm	bohm	PROPN
ejpam-6139	810	12	experiment	experiment	NOUN
ejpam-6139	810	13	and	and	CCONJ
ejpam-6139	810	14	bell	bell	PROPN
ejpam-6139	810	15	’s	’s	PART
ejpam-6139	810	16	inequality	inequality	NOUN
ejpam-6139	810	17	:	:	PUNCT
ejpam-6139	810	18	quantum	quantum	ADJ
ejpam-6139	810	19	physics	physics	NOUN
ejpam-6139	810	20	meets	meet	VERB
ejpam-6139	810	21	probability	probability	NOUN
ejpam-6139	810	22	theory	theory	NOUN
ejpam-6139	810	23	.	.	PUNCT
ejpam-6139	811	1	theoretical	theoretical	ADJ
ejpam-6139	811	2	and	and	CCONJ
ejpam-6139	811	3	mathematical	mathematical	ADJ
ejpam-6139	811	4	physics	physics	NOUN
ejpam-6139	811	5	.	.	PUNCT
ejpam-6139	811	6	,	,	PUNCT
ejpam-6139	811	7	157:1448–1460	157:1448–1460	NUM
ejpam-6139	811	8	,	,	PUNCT
ejpam-6139	811	9	2008	2008	NUM
ejpam-6139	811	10	.	.	PUNCT
ejpam-6139	812	1	[	[	X
ejpam-6139	812	2	20	20	NUM
ejpam-6139	812	3	]	]	PUNCT
ejpam-6139	812	4	karl	karl	PROPN
ejpam-6139	812	5	hess	hess	PROPN
ejpam-6139	812	6	de	de	PROPN
ejpam-6139	812	7	raedt	raedt	PROPN
ejpam-6139	812	8	,	,	PUNCT
ejpam-6139	812	9	hans	hans	PROPN
ejpam-6139	812	10	and	and	CCONJ
ejpam-6139	812	11	kristel	kristel	PROPN
ejpam-6139	812	12	michielsen	michielsen	PROPN
ejpam-6139	812	13	.	.	PROPN
ejpam-6139	812	14	extended	extend	VERB
ejpam-6139	812	15	boole	boole	PROPN
ejpam-6139	812	16	-	-	PUNCT
ejpam-6139	812	17	bell	bell	PROPN
ejpam-6139	812	18	inequalities	inequality	NOUN
ejpam-6139	812	19	applicable	applicable	ADJ
ejpam-6139	812	20	to	to	ADP
ejpam-6139	812	21	quantum	quantum	ADJ
ejpam-6139	812	22	theory	theory	NOUN
ejpam-6139	812	23	.	.	PUNCT
ejpam-6139	813	1	journal	journal	NOUN
ejpam-6139	813	2	of	of	ADP
ejpam-6139	813	3	computational	computational	ADJ
ejpam-6139	813	4	and	and	CCONJ
ejpam-6139	813	5	theoretical	theoretical	ADJ
ejpam-6139	813	6	nanoscience	nanoscience	NOUN
ejpam-6139	813	7	.	.	PUNCT
ejpam-6139	813	8	,	,	PUNCT
ejpam-6139	813	9	8(6):1011–1039	8(6):1011–1039	PROPN
ejpam-6139	813	10	,	,	PUNCT
ejpam-6139	813	11	2011	2011	NUM
ejpam-6139	813	12	.	.	PUNCT
ejpam-6139	814	1	[	[	X
ejpam-6139	814	2	21	21	NUM
ejpam-6139	814	3	]	]	X
ejpam-6139	814	4	wu	wu	PROPN
ejpam-6139	814	5	and	and	CCONJ
ejpam-6139	814	6	liming	liming	NOUN
ejpam-6139	814	7	.	.	PUNCT
ejpam-6139	815	1	a	a	DET
ejpam-6139	815	2	new	new	ADJ
ejpam-6139	815	3	modified	modify	VERB
ejpam-6139	815	4	logarithmic	logarithmic	ADJ
ejpam-6139	815	5	sobolev	sobolev	NOUN
ejpam-6139	815	6	inequality	inequality	NOUN
ejpam-6139	815	7	for	for	ADP
ejpam-6139	815	8	poisson	poisson	NOUN
ejpam-6139	815	9	point	point	NOUN
ejpam-6139	815	10	processes	process	NOUN
ejpam-6139	815	11	and	and	CCONJ
ejpam-6139	815	12	several	several	ADJ
ejpam-6139	815	13	applications	application	NOUN
ejpam-6139	815	14	.	.	PUNCT
ejpam-6139	816	1	probability	probability	NOUN
ejpam-6139	816	2	theory	theory	NOUN
ejpam-6139	816	3	and	and	CCONJ
ejpam-6139	816	4	related	related	ADJ
ejpam-6139	816	5	fields	field	NOUN
ejpam-6139	816	6	.	.	PUNCT
ejpam-6139	816	7	,	,	PUNCT
ejpam-6139	816	8	118(3):427	118(3):427	NUM
ejpam-6139	816	9	–	–	PUNCT
ejpam-6139	816	10	438	438	NUM
ejpam-6139	816	11	,	,	PUNCT
ejpam-6139	816	12	2000	2000	NUM
ejpam-6139	816	13	.	.	PUNCT
ejpam-6139	817	1	[	[	X
ejpam-6139	817	2	22	22	NUM
ejpam-6139	817	3	]	]	SYM
ejpam-6139	817	4	gr	gr	PROPN
ejpam-6139	817	5	mohtashami	mohtashami	NOUN
ejpam-6139	817	6	borzadaran	borzadaran	NOUN
ejpam-6139	817	7	and	and	CCONJ
ejpam-6139	817	8	d.	d.	PROPN
ejpam-6139	817	9	n.	n.	PROPN
ejpam-6139	817	10	shanbhag	shanbhag	PROPN
ejpam-6139	817	11	.	.	PUNCT
ejpam-6139	818	1	further	further	ADJ
ejpam-6139	818	2	results	result	NOUN
ejpam-6139	818	3	based	base	VERB
ejpam-6139	818	4	on	on	ADP
ejpam-6139	818	5	chernofftype	chernofftype	NOUN
ejpam-6139	818	6	inequalities	inequality	NOUN
ejpam-6139	818	7	.	.	PUNCT
ejpam-6139	819	1	statistics	statistic	NOUN
ejpam-6139	819	2	and	and	CCONJ
ejpam-6139	819	3	probability	probability	NOUN
ejpam-6139	819	4	letters	letter	NOUN
ejpam-6139	819	5	.	.	PUNCT
ejpam-6139	819	6	,	,	PUNCT
ejpam-6139	819	7	39(2):109–117	39(2):109–117	PROPN
ejpam-6139	819	8	,	,	PUNCT
ejpam-6139	819	9	1998	1998	NUM
ejpam-6139	819	10	.	.	PUNCT
ejpam-6139	820	1	[	[	X
ejpam-6139	820	2	23	23	NUM
ejpam-6139	820	3	]	]	PUNCT
ejpam-6139	820	4	sever	sever	PROPN
ejpam-6139	820	5	s.	s.	PROPN
ejpam-6139	820	6	dragomir	dragomir	PROPN
ejpam-6139	820	7	and	and	CCONJ
ejpam-6139	820	8	charles	charles	PROPN
ejpam-6139	820	9	em	em	PROPN
ejpam-6139	820	10	pearce	pearce	PROPN
ejpam-6139	820	11	.	.	PUNCT
ejpam-6139	821	1	selected	select	VERB
ejpam-6139	821	2	topics	topic	NOUN
ejpam-6139	821	3	on	on	ADP
ejpam-6139	821	4	hermite	hermite	ADJ
ejpam-6139	821	5	-	-	PUNCT
ejpam-6139	821	6	hadamard	hadamard	ADJ
ejpam-6139	821	7	inequalities	inequality	NOUN
ejpam-6139	821	8	and	and	CCONJ
ejpam-6139	821	9	applications	application	NOUN
ejpam-6139	821	10	.	.	PUNCT
ejpam-6139	822	1	ssrn	ssrn	PROPN
ejpam-6139	822	2	,	,	PUNCT
ejpam-6139	822	3	melbourne	melbourne	PROPN
ejpam-6139	822	4	city	city	PROPN
ejpam-6139	822	5	mc	mc	PROPN
ejpam-6139	822	6	,	,	PUNCT
ejpam-6139	822	7	victoria	victoria	PROPN
ejpam-6139	822	8	,	,	PUNCT
ejpam-6139	822	9	australia	australia	PROPN
ejpam-6139	822	10	,	,	PUNCT
ejpam-6139	822	11	2018	2018	NUM
ejpam-6139	822	12	.	.	PUNCT
ejpam-6139	823	1	[	[	X
ejpam-6139	823	2	24	24	NUM
ejpam-6139	823	3	]	]	PUNCT
ejpam-6139	823	4	muhammad	muhammad	PROPN
ejpam-6139	823	5	samraiz	samraiz	PROPN
ejpam-6139	823	6	cetin	cetin	PROPN
ejpam-6139	823	7	yıldız	yıldız	PROPN
ejpam-6139	823	8	maryam	maryam	PROPN
ejpam-6139	823	9	ali	ali	PROPN
ejpam-6139	823	10	alghafli	alghafli	PROPN
ejpam-6139	823	11	rahman	rahman	PROPN
ejpam-6139	823	12	,	,	PUNCT
ejpam-6139	823	13	gauhar	gauhar	PROPN
ejpam-6139	823	14	and	and	CCONJ
ejpam-6139	823	15	nabil	nabil	PROPN
ejpam-6139	823	16	mlaiki	mlaiki	PROPN
ejpam-6139	823	17	.	.	PUNCT
ejpam-6139	824	1	advancements	advancement	NOUN
ejpam-6139	824	2	in	in	ADP
ejpam-6139	824	3	ostrowski	ostrowski	ADJ
ejpam-6139	824	4	type	type	NOUN
ejpam-6139	824	5	fractional	fractional	ADJ
ejpam-6139	824	6	integral	integral	ADJ
ejpam-6139	824	7	inequalities	inequality	NOUN
ejpam-6139	824	8	via	via	ADP
ejpam-6139	824	9	applications	application	NOUN
ejpam-6139	824	10	of	of	ADP
ejpam-6139	824	11	jensen	jensen	PROPN
ejpam-6139	824	12	’s	’s	PART
ejpam-6139	824	13	and	and	CCONJ
ejpam-6139	824	14	young	young	ADJ
ejpam-6139	824	15	’s	’s	PART
ejpam-6139	824	16	inequalities	inequality	NOUN
ejpam-6139	824	17	.	.	PUNCT
ejpam-6139	825	1	european	european	PROPN
ejpam-6139	825	2	journal	journal	PROPN
ejpam-6139	825	3	of	of	ADP
ejpam-6139	825	4	pure	pure	ADJ
ejpam-6139	825	5	and	and	CCONJ
ejpam-6139	825	6	applied	applied	ADJ
ejpam-6139	825	7	mathematics	mathematic	NOUN
ejpam-6139	825	8	,	,	PUNCT
ejpam-6139	825	9	18(2):5816–5816	18(2):5816–5816	NUM
ejpam-6139	825	10	,	,	PUNCT
ejpam-6139	825	11	2025	2025	NUM
ejpam-6139	825	12	.	.	PUNCT
ejpam-6139	826	1	[	[	X
ejpam-6139	826	2	25	25	NUM
ejpam-6139	826	3	]	]	X
ejpam-6139	826	4	kirmaci	kirmaci	NOUN
ejpam-6139	826	5	and	and	CCONJ
ejpam-6139	826	6	ugur	ugur	PROPN
ejpam-6139	826	7	s.	s.	PROPN
ejpam-6139	826	8	inequalities	inequality	NOUN
ejpam-6139	826	9	for	for	ADP
ejpam-6139	826	10	differentiable	differentiable	ADJ
ejpam-6139	826	11	mappings	mapping	NOUN
ejpam-6139	826	12	and	and	CCONJ
ejpam-6139	826	13	applications	application	NOUN
ejpam-6139	826	14	to	to	ADP
ejpam-6139	826	15	special	special	ADJ
ejpam-6139	826	16	means	mean	NOUN
ejpam-6139	826	17	of	of	ADP
ejpam-6139	826	18	real	real	ADJ
ejpam-6139	826	19	numbers	number	NOUN
ejpam-6139	826	20	and	and	CCONJ
ejpam-6139	826	21	to	to	PART
ejpam-6139	826	22	midpoint	midpoint	NOUN
ejpam-6139	826	23	formula	formula	NOUN
ejpam-6139	826	24	.	.	PUNCT
ejpam-6139	827	1	applied	apply	VERB
ejpam-6139	827	2	mathematics	mathematic	NOUN
ejpam-6139	827	3	and	and	CCONJ
ejpam-6139	827	4	computation	computation	NOUN
ejpam-6139	827	5	.	.	PUNCT
ejpam-6139	827	6	,	,	PUNCT
ejpam-6139	827	7	147(1):137–146	147(1):137–146	NUM
ejpam-6139	827	8	,	,	PUNCT
ejpam-6139	827	9	2004	2004	NUM
ejpam-6139	827	10	.	.	PUNCT
ejpam-6139	828	1	m.	m.	NOUN
ejpam-6139	828	2	samraiz	samraiz	PROPN
ejpam-6139	828	3	et	et	PROPN
ejpam-6139	828	4	al	al	PROPN
ejpam-6139	828	5	.	.	PUNCT
ejpam-6139	828	6	/	/	SYM
ejpam-6139	828	7	eur	eur	PROPN
ejpam-6139	828	8	.	.	PUNCT
ejpam-6139	829	1	j.	j.	PROPN
ejpam-6139	829	2	pure	pure	PROPN
ejpam-6139	829	3	appl	appl	PROPN
ejpam-6139	829	4	.	.	PROPN
ejpam-6139	829	5	math	math	PROPN
ejpam-6139	829	6	,	,	PUNCT
ejpam-6139	829	7	18	18	NUM
ejpam-6139	829	8	(	(	PUNCT
ejpam-6139	829	9	4	4	NUM
ejpam-6139	829	10	)	)	PUNCT
ejpam-6139	829	11	(	(	PUNCT
ejpam-6139	829	12	2025	2025	NUM
ejpam-6139	829	13	)	)	PUNCT
ejpam-6139	829	14	,	,	PUNCT
ejpam-6139	829	15	6139	6139	NUM
ejpam-6139	829	16	33	33	NUM
ejpam-6139	829	17	of	of	ADP
ejpam-6139	829	18	34	34	NUM
ejpam-6139	830	1	[	[	X
ejpam-6139	830	2	26	26	NUM
ejpam-6139	830	3	]	]	SYM
ejpam-6139	830	4	s	s	PART
ejpam-6139	830	5	s	s	X
ejpam-6139	830	6	agarwal	agarwal	PROPN
ejpam-6139	830	7	dragomir	dragomir	NOUN
ejpam-6139	830	8	and	and	CCONJ
ejpam-6139	830	9	r.	r.	PROPN
ejpam-6139	830	10	two	two	NUM
ejpam-6139	830	11	inequalities	inequality	NOUN
ejpam-6139	830	12	for	for	ADP
ejpam-6139	830	13	differentiable	differentiable	ADJ
ejpam-6139	830	14	mappings	mapping	NOUN
ejpam-6139	830	15	and	and	CCONJ
ejpam-6139	830	16	applications	application	NOUN
ejpam-6139	830	17	to	to	ADP
ejpam-6139	830	18	special	special	ADJ
ejpam-6139	830	19	means	mean	NOUN
ejpam-6139	830	20	of	of	ADP
ejpam-6139	830	21	real	real	ADJ
ejpam-6139	830	22	numbers	number	NOUN
ejpam-6139	830	23	and	and	CCONJ
ejpam-6139	830	24	to	to	ADP
ejpam-6139	830	25	trapezoidal	trapezoidal	ADJ
ejpam-6139	830	26	formula	formula	NOUN
ejpam-6139	830	27	.	.	PUNCT
ejpam-6139	831	1	applied	apply	VERB
ejpam-6139	831	2	mathematics	mathematics	NOUN
ejpam-6139	831	3	letters	letter	NOUN
ejpam-6139	831	4	.	.	PUNCT
ejpam-6139	831	5	,	,	PUNCT
ejpam-6139	831	6	11(5):91–95	11(5):91–95	NUM
ejpam-6139	831	7	,	,	PUNCT
ejpam-6139	831	8	1998	1998	NUM
ejpam-6139	831	9	.	.	PUNCT
ejpam-6139	832	1	[	[	X
ejpam-6139	832	2	27	27	NUM
ejpam-6139	832	3	]	]	X
ejpam-6139	832	4	rajpar	rajpar	PROPN
ejpam-6139	832	5	a.	a.	PROPN
ejpam-6139	832	6	h.	h.	PROPN
ejpam-6139	832	7	alzabut	alzabut	PROPN
ejpam-6139	832	8	j.	j.	PROPN
ejpam-6139	832	9	aslam	aslam	PROPN
ejpam-6139	832	10	m.-etemad	m.-etemad	PROPN
ejpam-6139	832	11	s.	s.	PROPN
ejpam-6139	832	12	rezapour	rezapour	PROPN
ejpam-6139	832	13	khan	khan	PROPN
ejpam-6139	832	14	,	,	PUNCT
ejpam-6139	832	15	h.	h.	PROPN
ejpam-6139	832	16	and	and	CCONJ
ejpam-6139	832	17	s.	s.	PROPN
ejpam-6139	832	18	on	on	ADP
ejpam-6139	832	19	a	a	DET
ejpam-6139	832	20	fractal	fractal	ADJ
ejpam-6139	832	21	–	–	PUNCT
ejpam-6139	832	22	fractional	fractional	ADJ
ejpam-6139	832	23	-	-	PUNCT
ejpam-6139	832	24	based	base	VERB
ejpam-6139	832	25	modeling	modeling	NOUN
ejpam-6139	832	26	for	for	ADP
ejpam-6139	832	27	influenza	influenza	NOUN
ejpam-6139	832	28	and	and	CCONJ
ejpam-6139	832	29	its	its	PRON
ejpam-6139	832	30	analytical	analytical	ADJ
ejpam-6139	832	31	results	result	NOUN
ejpam-6139	832	32	.	.	PUNCT
ejpam-6139	833	1	qualitative	qualitative	ADJ
ejpam-6139	833	2	theory	theory	NOUN
ejpam-6139	833	3	of	of	ADP
ejpam-6139	833	4	dynamical	dynamical	ADJ
ejpam-6139	833	5	systems	system	NOUN
ejpam-6139	833	6	.	.	PUNCT
ejpam-6139	833	7	,	,	PUNCT
ejpam-6139	833	8	23(2):70	23(2):70	PROPN
ejpam-6139	833	9	,	,	PUNCT
ejpam-6139	833	10	2024	2024	NUM
ejpam-6139	833	11	.	.	PUNCT
ejpam-6139	834	1	[	[	X
ejpam-6139	834	2	28	28	NUM
ejpam-6139	834	3	]	]	X
ejpam-6139	834	4	lav́ın	lav́ın	NUM
ejpam-6139	834	5	-	-	PUNCT
ejpam-6139	834	6	delgado	delgado	PROPN
ejpam-6139	834	7	j.	j.	PROPN
ejpam-6139	834	8	e.	e.	PROPN
ejpam-6139	834	9	gómez	gómez	PROPN
ejpam-6139	834	10	-	-	PUNCT
ejpam-6139	834	11	aguilar	aguilar	PROPN
ejpam-6139	834	12	-	-	PUNCT
ejpam-6139	834	13	j.	j.	PROPN
ejpam-6139	834	14	f.	f.	PROPN
ejpam-6139	834	15	razo	razo	PROPN
ejpam-6139	834	16	-	-	PUNCT
ejpam-6139	834	17	hernández	hernández	PROPN
ejpam-6139	834	18	-	-	PUNCT
ejpam-6139	834	19	j.	j.	PROPN
ejpam-6139	834	20	r.	r.	PROPN
ejpam-6139	834	21	etemad	etemad	PROPN
ejpam-6139	834	22	s.	s.	PROPN
ejpam-6139	834	23	rezapour	rezapour	PROPN
ejpam-6139	834	24	chávez	chávez	PROPN
ejpam-6139	834	25	-	-	PUNCT
ejpam-6139	834	26	vázquez	vázquez	PROPN
ejpam-6139	834	27	,	,	PUNCT
ejpam-6139	834	28	s.	s.	PROPN
ejpam-6139	834	29	and	and	CCONJ
ejpam-6139	834	30	s.	s.	PROPN
ejpam-6139	834	31	trajectory	trajectory	PROPN
ejpam-6139	834	32	tracking	tracking	PROPN
ejpam-6139	834	33	of	of	ADP
ejpam-6139	834	34	stanford	stanford	PROPN
ejpam-6139	834	35	robot	robot	NOUN
ejpam-6139	834	36	manipulator	manipulator	NOUN
ejpam-6139	834	37	by	by	ADP
ejpam-6139	834	38	fractional	fractional	ADJ
ejpam-6139	834	39	-	-	PUNCT
ejpam-6139	834	40	order	order	NOUN
ejpam-6139	834	41	sliding	slide	VERB
ejpam-6139	834	42	mode	mode	NOUN
ejpam-6139	834	43	control	control	NOUN
ejpam-6139	834	44	.	.	PUNCT
ejpam-6139	835	1	applied	apply	VERB
ejpam-6139	835	2	mathematical	mathematical	ADJ
ejpam-6139	835	3	modelling	modelling	NOUN
ejpam-6139	835	4	.	.	PUNCT
ejpam-6139	835	5	,	,	PUNCT
ejpam-6139	835	6	120:436–462	120:436–462	NUM
ejpam-6139	835	7	,	,	PUNCT
ejpam-6139	835	8	2023	2023	NUM
ejpam-6139	835	9	.	.	PUNCT
ejpam-6139	836	1	[	[	X
ejpam-6139	836	2	29	29	NUM
ejpam-6139	836	3	]	]	X
ejpam-6139	836	4	hari	hari	PROPN
ejpam-6139	836	5	m	m	PROPN
ejpam-6139	836	6	srivastava	srivastava	PROPN
ejpam-6139	836	7	kilbas	kilbas	PROPN
ejpam-6139	836	8	,	,	PUNCT
ejpam-6139	836	9	anatolĭı	anatolĭı	PROPN
ejpam-6139	836	10	aleksandrovich	aleksandrovich	PROPN
ejpam-6139	836	11	and	and	CCONJ
ejpam-6139	836	12	juan	juan	PROPN
ejpam-6139	836	13	j	j	PROPN
ejpam-6139	836	14	trujillo	trujillo	PROPN
ejpam-6139	836	15	.	.	PUNCT
ejpam-6139	836	16	theory	theory	NOUN
ejpam-6139	836	17	and	and	CCONJ
ejpam-6139	836	18	applications	application	NOUN
ejpam-6139	836	19	of	of	ADP
ejpam-6139	836	20	fractional	fractional	ADJ
ejpam-6139	836	21	differential	differential	ADJ
ejpam-6139	836	22	equations	equation	NOUN
ejpam-6139	836	23	.	.	PUNCT
ejpam-6139	837	1	elsevier	elsevier	NOUN
ejpam-6139	837	2	,	,	PUNCT
ejpam-6139	837	3	2006	2006	NUM
ejpam-6139	837	4	.	.	PUNCT
ejpam-6139	838	1	[	[	X
ejpam-6139	838	2	30	30	NUM
ejpam-6139	838	3	]	]	X
ejpam-6139	838	4	soubhagya	soubhagya	PROPN
ejpam-6139	838	5	kumar	kumar	PROPN
ejpam-6139	838	6	et	et	PROPN
ejpam-6139	838	7	al	al	PROPN
ejpam-6139	838	8	.	.	PROPN
ejpam-6139	839	1	sahoo	sahoo	PROPN
ejpam-6139	839	2	.	.	PUNCT
ejpam-6139	840	1	new	new	ADJ
ejpam-6139	840	2	fractional	fractional	ADJ
ejpam-6139	840	3	integral	integral	ADJ
ejpam-6139	840	4	inequalities	inequality	NOUN
ejpam-6139	840	5	for	for	ADP
ejpam-6139	840	6	convex	convex	NOUN
ejpam-6139	840	7	functions	function	NOUN
ejpam-6139	840	8	pertaining	pertain	VERB
ejpam-6139	840	9	to	to	ADP
ejpam-6139	840	10	caputo	caputo	PROPN
ejpam-6139	840	11	–	–	PUNCT
ejpam-6139	840	12	fabrizio	fabrizio	NOUN
ejpam-6139	840	13	operator	operator	NOUN
ejpam-6139	840	14	.	.	PUNCT
ejpam-6139	841	1	fractal	fractal	PROPN
ejpam-6139	841	2	and	and	CCONJ
ejpam-6139	841	3	fractional	fractional	ADJ
ejpam-6139	841	4	.	.	PUNCT
ejpam-6139	841	5	,	,	PUNCT
ejpam-6139	841	6	6(3):171	6(3):171	NUM
ejpam-6139	841	7	,	,	PUNCT
ejpam-6139	841	8	2022	2022	NUM
ejpam-6139	841	9	.	.	PUNCT
ejpam-6139	842	1	[	[	X
ejpam-6139	842	2	31	31	NUM
ejpam-6139	842	3	]	]	PUNCT
ejpam-6139	842	4	rudolf	rudolf	NOUN
ejpam-6139	842	5	hilfer	hilfer	NOUN
ejpam-6139	842	6	and	and	CCONJ
ejpam-6139	842	7	ed	ed	NOUN
ejpam-6139	842	8	.	.	PUNCT
ejpam-6139	843	1	applications	application	NOUN
ejpam-6139	843	2	of	of	ADP
ejpam-6139	843	3	fractional	fractional	ADJ
ejpam-6139	843	4	calculus	calculus	NOUN
ejpam-6139	843	5	in	in	ADP
ejpam-6139	843	6	physics	physics	PROPN
ejpam-6139	843	7	.	.	PUNCT
ejpam-6139	844	1	world	world	PROPN
ejpam-6139	844	2	scientific	scientific	PROPN
ejpam-6139	844	3	.	.	PUNCT
ejpam-6139	844	4	,	,	PUNCT
ejpam-6139	844	5	shelton	shelton	PROPN
ejpam-6139	844	6	street	street	PROPN
ejpam-6139	844	7	,	,	PUNCT
ejpam-6139	844	8	covent	covent	PROPN
ejpam-6139	844	9	garden	garden	PROPN
ejpam-6139	844	10	,	,	PUNCT
ejpam-6139	844	11	london	london	PROPN
ejpam-6139	844	12	.	.	PROPN
ejpam-6139	844	13	,	,	PUNCT
ejpam-6139	844	14	2000	2000	NUM
ejpam-6139	844	15	.	.	PUNCT
ejpam-6139	845	1	[	[	X
ejpam-6139	845	2	32	32	NUM
ejpam-6139	845	3	]	]	SYM
ejpam-6139	845	4	kilbas	kilbas	PROPN
ejpam-6139	845	5	and	and	CCONJ
ejpam-6139	845	6	anatoly	anatoly	PROPN
ejpam-6139	845	7	a.	a.	PROPN
ejpam-6139	845	8	hadamard	hadamard	NOUN
ejpam-6139	845	9	-	-	PUNCT
ejpam-6139	845	10	type	type	NOUN
ejpam-6139	845	11	fractional	fractional	ADJ
ejpam-6139	845	12	calculus	calculus	NOUN
ejpam-6139	845	13	.	.	PUNCT
ejpam-6139	846	1	journal	journal	NOUN
ejpam-6139	846	2	of	of	ADP
ejpam-6139	846	3	the	the	DET
ejpam-6139	846	4	korean	korean	PROPN
ejpam-6139	846	5	mathematical	mathematical	ADJ
ejpam-6139	846	6	society	society	NOUN
ejpam-6139	846	7	.	.	PUNCT
ejpam-6139	846	8	,	,	PUNCT
ejpam-6139	846	9	38(6):1191–1204	38(6):1191–1204	NUM
ejpam-6139	846	10	,	,	PUNCT
ejpam-6139	846	11	2001	2001	NUM
ejpam-6139	846	12	.	.	PUNCT
ejpam-6139	847	1	[	[	X
ejpam-6139	847	2	33	33	NUM
ejpam-6139	847	3	]	]	X
ejpam-6139	847	4	katugampola	katugampola	PROPN
ejpam-6139	847	5	and	and	CCONJ
ejpam-6139	847	6	udita	udita	PROPN
ejpam-6139	847	7	n.	n.	PROPN
ejpam-6139	847	8	a	a	DET
ejpam-6139	847	9	new	new	ADJ
ejpam-6139	847	10	approach	approach	NOUN
ejpam-6139	847	11	to	to	ADP
ejpam-6139	847	12	generalized	generalized	ADJ
ejpam-6139	847	13	fractional	fractional	ADJ
ejpam-6139	847	14	derivatives	derivative	NOUN
ejpam-6139	847	15	.	.	PUNCT
ejpam-6139	848	1	arxiv	arxiv	PROPN
ejpam-6139	848	2	preprint	preprint	PROPN
ejpam-6139	848	3	arxiv	arxiv	PROPN
ejpam-6139	848	4	.	.	PUNCT
ejpam-6139	848	5	,	,	PUNCT
ejpam-6139	848	6	1106.0965	1106.0965	NUM
ejpam-6139	848	7	,	,	PUNCT
ejpam-6139	848	8	2011	2011	NUM
ejpam-6139	848	9	.	.	PUNCT
ejpam-6139	849	1	[	[	X
ejpam-6139	849	2	34	34	NUM
ejpam-6139	849	3	]	]	X
ejpam-6139	849	4	jarad	jarad	PROPN
ejpam-6139	849	5	and	and	CCONJ
ejpam-6139	849	6	fahd	fahd	PROPN
ejpam-6139	849	7	et	et	PROPN
ejpam-6139	849	8	al	al	PROPN
ejpam-6139	849	9	.	.	PROPN
ejpam-6139	850	1	on	on	ADP
ejpam-6139	850	2	a	a	DET
ejpam-6139	850	3	new	new	ADJ
ejpam-6139	850	4	class	class	NOUN
ejpam-6139	850	5	of	of	ADP
ejpam-6139	850	6	fractional	fractional	ADJ
ejpam-6139	850	7	operators	operator	NOUN
ejpam-6139	850	8	.	.	PUNCT
ejpam-6139	851	1	advances	advance	NOUN
ejpam-6139	851	2	in	in	ADP
ejpam-6139	851	3	difference	difference	NOUN
ejpam-6139	851	4	equations	equation	NOUN
ejpam-6139	851	5	.	.	PUNCT
ejpam-6139	852	1	,	,	PUNCT
ejpam-6139	852	2	pages	page	VERB
ejpam-6139	852	3	1–16	1–16	PROPN
ejpam-6139	852	4	,	,	PUNCT
ejpam-6139	852	5	2017	2017	NUM
ejpam-6139	852	6	.	.	PUNCT
ejpam-6139	853	1	[	[	X
ejpam-6139	853	2	35	35	NUM
ejpam-6139	853	3	]	]	PUNCT
ejpam-6139	853	4	samraiz	samraiz	PROPN
ejpam-6139	853	5	m.	m.	PROPN
ejpam-6139	853	6	haque	haque	PROPN
ejpam-6139	853	7	s.	s.	PROPN
ejpam-6139	853	8	rahman	rahman	PROPN
ejpam-6139	853	9	,	,	PUNCT
ejpam-6139	853	10	g.	g.	PROPN
ejpam-6139	853	11	and	and	CCONJ
ejpam-6139	853	12	n.	n.	PROPN
ejpam-6139	853	13	mlaiki	mlaiki	PROPN
ejpam-6139	853	14	.	.	PUNCT
ejpam-6139	854	1	exploration	exploration	NOUN
ejpam-6139	854	2	of	of	ADP
ejpam-6139	854	3	some	some	DET
ejpam-6139	854	4	novel	novel	ADJ
ejpam-6139	854	5	integral	integral	ADJ
ejpam-6139	854	6	inequalities	inequality	NOUN
ejpam-6139	854	7	pertaining	pertain	VERB
ejpam-6139	854	8	to	to	ADP
ejpam-6139	854	9	the	the	DET
ejpam-6139	854	10	new	new	ADJ
ejpam-6139	854	11	class	class	NOUN
ejpam-6139	854	12	of	of	ADP
ejpam-6139	854	13	(	(	PUNCT
ejpam-6139	854	14	k	k	X
ejpam-6139	854	15	,	,	PUNCT
ejpam-6139	854	16	ρ)−conformable	ρ)−conformable	ADJ
ejpam-6139	854	17	fractional	fractional	ADJ
ejpam-6139	854	18	integrals	integral	NOUN
ejpam-6139	854	19	.	.	PUNCT
ejpam-6139	855	1	contemporary	contemporary	ADJ
ejpam-6139	855	2	mathematics	mathematic	NOUN
ejpam-6139	855	3	.	.	PUNCT
ejpam-6139	855	4	,	,	PUNCT
ejpam-6139	855	5	pages	page	NOUN
ejpam-6139	855	6	2853–2877	2853–2877	NUM
ejpam-6139	855	7	,	,	PUNCT
ejpam-6139	855	8	2025	2025	NUM
ejpam-6139	855	9	.	.	PUNCT
ejpam-6139	856	1	[	[	X
ejpam-6139	856	2	36	36	NUM
ejpam-6139	856	3	]	]	PUNCT
ejpam-6139	856	4	samraiz	samraiz	PROPN
ejpam-6139	856	5	m	m	PROPN
ejpam-6139	856	6	rahman	rahman	PROPN
ejpam-6139	856	7	g	g	PROPN
ejpam-6139	856	8	-	-	PUNCT
ejpam-6139	856	9	haque	haque	PROPN
ejpam-6139	856	10	s	s	X
ejpam-6139	856	11	aloqaily	aloqaily	ADV
ejpam-6139	856	12	a	a	DET
ejpam-6139	856	13	-	-	PUNCT
ejpam-6139	856	14	mlaiki	mlaiki	ADJ
ejpam-6139	856	15	n.	n.	PROPN
ejpam-6139	856	16	younis	younis	PROPN
ejpam-6139	856	17	m	m	PROPN
ejpam-6139	856	18	,	,	PUNCT
ejpam-6139	856	19	mehmood	mehmood	PROPN
ejpam-6139	856	20	a.	a.	PROPN
ejpam-6139	856	21	computational	computational	ADJ
ejpam-6139	856	22	representation	representation	NOUN
ejpam-6139	856	23	of	of	ADP
ejpam-6139	856	24	fractional	fractional	ADJ
ejpam-6139	856	25	inequalities	inequality	NOUN
ejpam-6139	856	26	through	through	ADP
ejpam-6139	856	27	2d	2d	NUM
ejpam-6139	856	28	and	and	CCONJ
ejpam-6139	856	29	3d	3d	NUM
ejpam-6139	856	30	graphs	graph	NOUN
ejpam-6139	856	31	with	with	ADP
ejpam-6139	856	32	applications	application	NOUN
ejpam-6139	856	33	.	.	PUNCT
ejpam-6139	857	1	computation	computation	NOUN
ejpam-6139	857	2	.	.	PUNCT
ejpam-6139	857	3	,	,	PUNCT
ejpam-6139	857	4	13(2):46	13(2):46	NUM
ejpam-6139	857	5	,	,	PUNCT
ejpam-6139	857	6	2025	2025	NUM
ejpam-6139	857	7	.	.	PUNCT
ejpam-6139	858	1	[	[	X
ejpam-6139	858	2	37	37	NUM
ejpam-6139	858	3	]	]	X
ejpam-6139	858	4	josip	josip	PROPN
ejpam-6139	858	5	pecaric	pecaric	PROPN
ejpam-6139	858	6	mitrinovic	mitrinovic	PROPN
ejpam-6139	858	7	,	,	PUNCT
ejpam-6139	858	8	dragoslav	dragoslav	PROPN
ejpam-6139	858	9	s.	s.	PROPN
ejpam-6139	858	10	and	and	CCONJ
ejpam-6139	858	11	arlington	arlington	PROPN
ejpam-6139	858	12	m.	m.	PROPN
ejpam-6139	858	13	fink	fink	PROPN
ejpam-6139	858	14	.	.	PUNCT
ejpam-6139	859	1	classical	classical	ADJ
ejpam-6139	859	2	and	and	CCONJ
ejpam-6139	859	3	new	new	ADJ
ejpam-6139	859	4	inequalities	inequality	NOUN
ejpam-6139	859	5	in	in	ADP
ejpam-6139	859	6	analysis	analysis	NOUN
ejpam-6139	859	7	.	.	PUNCT
ejpam-6139	860	1	springer	springer	NOUN
ejpam-6139	860	2	science	science	NOUN
ejpam-6139	860	3	and	and	CCONJ
ejpam-6139	860	4	business	business	NOUN
ejpam-6139	860	5	media	medium	NOUN
ejpam-6139	860	6	.	.	PUNCT
ejpam-6139	860	7	,	,	PUNCT
ejpam-6139	860	8	61	61	NUM
ejpam-6139	860	9	,	,	PUNCT
ejpam-6139	860	10	2013	2013	NUM
ejpam-6139	860	11	.	.	PUNCT
ejpam-6139	861	1	[	[	X
ejpam-6139	861	2	38	38	NUM
ejpam-6139	861	3	]	]	X
ejpam-6139	861	4	srivastava	srivastava	PROPN
ejpam-6139	861	5	h.m	h.m	PROPN
ejpam-6139	861	6	.	.	PROPN
ejpam-6139	861	7	trujillo	trujillo	PROPN
ejpam-6139	861	8	kilbas	kilbas	PROPN
ejpam-6139	861	9	,	,	PUNCT
ejpam-6139	861	10	a.	a.	PROPN
ejpam-6139	861	11	and	and	CCONJ
ejpam-6139	861	12	j.j	j.j	PROPN
ejpam-6139	861	13	.	.	PROPN
ejpam-6139	861	14	theory	theory	NOUN
ejpam-6139	861	15	and	and	CCONJ
ejpam-6139	861	16	application	application	NOUN
ejpam-6139	861	17	of	of	ADP
ejpam-6139	861	18	fractional	fractional	ADJ
ejpam-6139	861	19	differential	differential	ADJ
ejpam-6139	861	20	equations	equation	NOUN
ejpam-6139	861	21	.	.	PUNCT
ejpam-6139	862	1	north	north	NOUN
ejpam-6139	862	2	holland	holland	PROPN
ejpam-6139	862	3	:	:	PUNCT
ejpam-6139	863	1	elsevier	elsevier	PROPN
ejpam-6139	863	2	.	.	PUNCT
ejpam-6139	863	3	,	,	PUNCT
ejpam-6139	863	4	2006	2006	NUM
ejpam-6139	863	5	.	.	PUNCT
ejpam-6139	864	1	[	[	X
ejpam-6139	864	2	39	39	NUM
ejpam-6139	864	3	]	]	PUNCT
ejpam-6139	864	4	habib	habib	PROPN
ejpam-6139	864	5	s.	s.	PROPN
ejpam-6139	864	6	mubeen	mubeen	PROPN
ejpam-6139	864	7	s.	s.	PROPN
ejpam-6139	864	8	qi	qi	PROPN
ejpam-6139	864	9	,	,	PUNCT
ejpam-6139	864	10	f.	f.	PROPN
ejpam-6139	864	11	and	and	CCONJ
ejpam-6139	864	12	naeem	naeem	PROPN
ejpam-6139	864	13	m.	m.	PROPN
ejpam-6139	864	14	n.	n.	PROPN
ejpam-6139	864	15	generalized	generalize	VERB
ejpam-6139	864	16	k	k	ADJ
ejpam-6139	864	17	-	-	ADJ
ejpam-6139	864	18	fractional	fractional	ADJ
ejpam-6139	864	19	conformable	conformable	ADJ
ejpam-6139	864	20	integrals	integral	NOUN
ejpam-6139	864	21	and	and	CCONJ
ejpam-6139	864	22	related	related	ADJ
ejpam-6139	864	23	inequalities	inequality	NOUN
ejpam-6139	864	24	.	.	PUNCT
ejpam-6139	865	1	aims	aim	VERB
ejpam-6139	865	2	mathematics	mathematic	NOUN
ejpam-6139	865	3	.	.	PUNCT
ejpam-6139	865	4	,	,	PUNCT
ejpam-6139	865	5	4(3):343–358	4(3):343–358	NOUN
ejpam-6139	865	6	,	,	PUNCT
ejpam-6139	865	7	2019	2019	NUM
ejpam-6139	865	8	.	.	PUNCT
ejpam-6139	866	1	[	[	X
ejpam-6139	866	2	40	40	NUM
ejpam-6139	866	3	]	]	PUNCT
ejpam-6139	866	4	kenneth	kenneth	PROPN
ejpam-6139	866	5	s.	s.	PROPN
ejpam-6139	866	6	miller	miller	PROPN
ejpam-6139	866	7	and	and	CCONJ
ejpam-6139	866	8	bertram	bertram	PROPN
ejpam-6139	866	9	ross	ross	PROPN
ejpam-6139	866	10	.	.	PUNCT
ejpam-6139	867	1	an	an	DET
ejpam-6139	867	2	introduction	introduction	NOUN
ejpam-6139	867	3	to	to	ADP
ejpam-6139	867	4	the	the	DET
ejpam-6139	867	5	fractional	fractional	ADJ
ejpam-6139	867	6	calculus	calculus	NOUN
ejpam-6139	867	7	and	and	CCONJ
ejpam-6139	867	8	fractional	fractional	ADJ
ejpam-6139	867	9	differential	differential	ADJ
ejpam-6139	867	10	equations	equation	NOUN
ejpam-6139	867	11	.	.	PUNCT
ejpam-6139	868	1	john	john	PROPN
ejpam-6139	868	2	wiley	wiley	PROPN
ejpam-6139	868	3	and	and	CCONJ
ejpam-6139	868	4	sons	son	NOUN
ejpam-6139	868	5	.	.	PUNCT
ejpam-6139	868	6	,	,	PUNCT
ejpam-6139	868	7	1993	1993	NUM
ejpam-6139	868	8	.	.	PUNCT
ejpam-6139	869	1	[	[	X
ejpam-6139	869	2	41	41	NUM
ejpam-6139	869	3	]	]	X
ejpam-6139	869	4	miller	miller	PROPN
ejpam-6139	869	5	s.	s.	PROPN
ejpam-6139	869	6	ross	ross	PROPN
ejpam-6139	869	7	and	and	CCONJ
ejpam-6139	869	8	b.	b.	PROPN
ejpam-6139	869	9	an	an	DET
ejpam-6139	869	10	introduction	introduction	NOUN
ejpam-6139	869	11	to	to	ADP
ejpam-6139	869	12	the	the	DET
ejpam-6139	869	13	fractional	fractional	ADJ
ejpam-6139	869	14	calculus	calculus	NOUN
ejpam-6139	869	15	and	and	CCONJ
ejpam-6139	869	16	fractional	fractional	ADJ
ejpam-6139	869	17	differential	differential	ADJ
ejpam-6139	869	18	equations	equation	NOUN
ejpam-6139	869	19	.	.	PUNCT
ejpam-6139	870	1	john	john	PROPN
ejpam-6139	870	2	wiley	wiley	PROPN
ejpam-6139	870	3	and	and	CCONJ
ejpam-6139	870	4	sons	son	NOUN
ejpam-6139	870	5	.	.	PUNCT
ejpam-6139	870	6	,	,	PUNCT
ejpam-6139	870	7	1993	1993	NUM
ejpam-6139	870	8	.	.	PUNCT
ejpam-6139	871	1	[	[	X
ejpam-6139	871	2	42	42	NUM
ejpam-6139	871	3	]	]	PUNCT
ejpam-6139	871	4	sever	sever	PROPN
ejpam-6139	871	5	s.	s.	PROPN
ejpam-6139	871	6	dragomir	dragomir	PROPN
ejpam-6139	871	7	and	and	CCONJ
ejpam-6139	871	8	charles	charles	PROPN
ejpam-6139	871	9	em	em	PROPN
ejpam-6139	871	10	pearce	pearce	PROPN
ejpam-6139	871	11	.	.	PUNCT
ejpam-6139	872	1	selected	select	VERB
ejpam-6139	872	2	topics	topic	NOUN
ejpam-6139	872	3	on	on	ADP
ejpam-6139	872	4	hermite	hermite	ADJ
ejpam-6139	872	5	-	-	PUNCT
ejpam-6139	872	6	hadamard	hadamard	ADJ
ejpam-6139	872	7	inequalities	inequality	NOUN
ejpam-6139	872	8	and	and	CCONJ
ejpam-6139	872	9	applications	application	NOUN
ejpam-6139	872	10	.	.	PUNCT
ejpam-6139	873	1	ssrn	ssrn	PROPN
ejpam-6139	873	2	.	.	PUNCT
ejpam-6139	873	3	,	,	PUNCT
ejpam-6139	873	4	2018	2018	NUM
ejpam-6139	873	5	.	.	PUNCT
ejpam-6139	874	1	[	[	X
ejpam-6139	874	2	43	43	NUM
ejpam-6139	874	3	]	]	X
ejpam-6139	874	4	kavurmaci	kavurmaci	NOUN
ejpam-6139	874	5	h.	h.	PROPN
ejpam-6139	874	6	avci	avci	PROPN
ejpam-6139	874	7	,	,	PUNCT
ejpam-6139	874	8	m.	m.	NOUN
ejpam-6139	874	9	,	,	PUNCT
ejpam-6139	874	10	özdemir	özdemir	PROPN
ejpam-6139	874	11	,	,	PUNCT
ejpam-6139	874	12	and	and	CCONJ
ejpam-6139	874	13	m.e	m.e	PROPN
ejpam-6139	874	14	.	.	PROPN
ejpam-6139	874	15	new	new	ADJ
ejpam-6139	874	16	inequalities	inequality	NOUN
ejpam-6139	874	17	of	of	ADP
ejpam-6139	874	18	hermite	hermite	ADJ
ejpam-6139	874	19	–	–	PUNCT
ejpam-6139	874	20	hadamard	hadamard	ADJ
ejpam-6139	874	21	type	type	NOUN
ejpam-6139	874	22	via	via	ADP
ejpam-6139	874	23	s	s	ADJ
ejpam-6139	874	24	-	-	PUNCT
ejpam-6139	874	25	convex	convex	ADJ
ejpam-6139	874	26	functions	function	NOUN
ejpam-6139	874	27	in	in	ADP
ejpam-6139	874	28	the	the	DET
ejpam-6139	874	29	second	second	ADJ
ejpam-6139	874	30	sense	sense	NOUN
ejpam-6139	874	31	with	with	ADP
ejpam-6139	874	32	applications	application	NOUN
ejpam-6139	874	33	.	.	PUNCT
ejpam-6139	875	1	applied	apply	VERB
ejpam-6139	875	2	mathematics	mathematic	NOUN
ejpam-6139	875	3	and	and	CCONJ
ejpam-6139	875	4	computation	computation	NOUN
ejpam-6139	875	5	.	.	PUNCT
ejpam-6139	875	6	,	,	PUNCT
ejpam-6139	875	7	217(12):5171–5176	217(12):5171–5176	NUM
ejpam-6139	875	8	,	,	PUNCT
ejpam-6139	875	9	2011	2011	NUM
ejpam-6139	875	10	.	.	PUNCT
ejpam-6139	876	1	m.	m.	NOUN
ejpam-6139	876	2	samraiz	samraiz	PROPN
ejpam-6139	876	3	et	et	PROPN
ejpam-6139	876	4	al	al	PROPN
ejpam-6139	876	5	.	.	PUNCT
ejpam-6139	876	6	/	/	SYM
ejpam-6139	876	7	eur	eur	PROPN
ejpam-6139	876	8	.	.	PUNCT
ejpam-6139	877	1	j.	j.	PROPN
ejpam-6139	877	2	pure	pure	PROPN
ejpam-6139	877	3	appl	appl	PROPN
ejpam-6139	877	4	.	.	PROPN
ejpam-6139	877	5	math	math	PROPN
ejpam-6139	877	6	,	,	PUNCT
ejpam-6139	877	7	18	18	NUM
ejpam-6139	877	8	(	(	PUNCT
ejpam-6139	877	9	4	4	NUM
ejpam-6139	877	10	)	)	PUNCT
ejpam-6139	877	11	(	(	PUNCT
ejpam-6139	877	12	2025	2025	NUM
ejpam-6139	877	13	)	)	PUNCT
ejpam-6139	877	14	,	,	PUNCT
ejpam-6139	877	15	6139	6139	NUM
ejpam-6139	877	16	34	34	NUM
ejpam-6139	877	17	of	of	ADP
ejpam-6139	877	18	34	34	NUM
ejpam-6139	877	19	[	[	X
ejpam-6139	877	20	44	44	NUM
ejpam-6139	877	21	]	]	X
ejpam-6139	877	22	budak	budak	PROPN
ejpam-6139	877	23	h.	h.	PROPN
ejpam-6139	877	24	etemad	etemad	PROPN
ejpam-6139	877	25	s.	s.	PROPN
ejpam-6139	877	26	rezapour	rezapour	PROPN
ejpam-6139	877	27	s.-ahmad	s.-ahmad	PUNCT
ejpam-6139	877	28	h.	h.	PROPN
ejpam-6139	877	29	kaabar	kaabar	PROPN
ejpam-6139	877	30	kara	kara	PROPN
ejpam-6139	877	31	,	,	PUNCT
ejpam-6139	877	32	h.	h.	PROPN
ejpam-6139	877	33	and	and	CCONJ
ejpam-6139	877	34	m.	m.	PROPN
ejpam-6139	877	35	k.	k.	PROPN
ejpam-6139	878	1	a	a	DET
ejpam-6139	878	2	study	study	NOUN
ejpam-6139	878	3	on	on	ADP
ejpam-6139	878	4	the	the	DET
ejpam-6139	878	5	new	new	ADJ
ejpam-6139	878	6	class	class	NOUN
ejpam-6139	878	7	of	of	ADP
ejpam-6139	878	8	inequalities	inequality	NOUN
ejpam-6139	878	9	of	of	ADP
ejpam-6139	878	10	midpoint	midpoint	NOUN
ejpam-6139	878	11	-	-	PUNCT
ejpam-6139	878	12	type	type	NOUN
ejpam-6139	878	13	and	and	CCONJ
ejpam-6139	878	14	trapezoidal	trapezoidal	NOUN
ejpam-6139	878	15	-	-	PUNCT
ejpam-6139	878	16	type	type	NOUN
ejpam-6139	878	17	based	base	VERB
ejpam-6139	878	18	on	on	ADP
ejpam-6139	878	19	twice	twice	ADJ
ejpam-6139	878	20	differentiable	differentiable	ADJ
ejpam-6139	878	21	functions	function	NOUN
ejpam-6139	878	22	with	with	ADP
ejpam-6139	878	23	conformable	conformable	ADJ
ejpam-6139	878	24	operators	operator	NOUN
ejpam-6139	878	25	.	.	PUNCT
ejpam-6139	879	1	journal	journal	NOUN
ejpam-6139	879	2	of	of	ADP
ejpam-6139	879	3	function	function	NOUN
ejpam-6139	879	4	spaces	space	NOUN
ejpam-6139	879	5	.	.	PUNCT
ejpam-6139	879	6	,	,	PUNCT
ejpam-6139	879	7	page	page	NOUN
ejpam-6139	879	8	4624604	4624604	NUM
ejpam-6139	879	9	,	,	PUNCT
ejpam-6139	879	10	2023(1	2023(1	NUM
ejpam-6139	879	11	)	)	PUNCT
ejpam-6139	879	12	.	.	PUNCT
ejpam-6139	880	1	[	[	X
ejpam-6139	880	2	45	45	NUM
ejpam-6139	880	3	]	]	PUNCT
ejpam-6139	880	4	pshtiwan	pshtiwan	PROPN
ejpam-6139	880	5	othman	othman	PROPN
ejpam-6139	880	6	mohammed	mohammed	PROPN
ejpam-6139	880	7	and	and	CCONJ
ejpam-6139	880	8	mehmet	mehmet	PROPN
ejpam-6139	880	9	zeki	zeki	PROPN
ejpam-6139	880	10	sarikaya	sarikaya	PROPN
ejpam-6139	880	11	.	.	PUNCT
ejpam-6139	881	1	on	on	ADP
ejpam-6139	881	2	generalized	generalized	ADJ
ejpam-6139	881	3	fractional	fractional	ADJ
ejpam-6139	881	4	integral	integral	ADJ
ejpam-6139	881	5	inequalities	inequality	NOUN
ejpam-6139	881	6	for	for	ADP
ejpam-6139	881	7	twice	twice	ADV
ejpam-6139	881	8	differentiable	differentiable	ADJ
ejpam-6139	881	9	convex	convex	NOUN
ejpam-6139	881	10	functions	function	NOUN
ejpam-6139	881	11	.	.	PUNCT
ejpam-6139	882	1	journal	journal	NOUN
ejpam-6139	882	2	of	of	ADP
ejpam-6139	882	3	computational	computational	ADJ
ejpam-6139	882	4	and	and	CCONJ
ejpam-6139	882	5	applied	applied	ADJ
ejpam-6139	882	6	mathematics	mathematic	NOUN
ejpam-6139	882	7	.	.	PUNCT
ejpam-6139	882	8	,	,	PUNCT
ejpam-6139	882	9	372:112740	372:112740	NUM
ejpam-6139	882	10	,	,	PUNCT
ejpam-6139	882	11	2020	2020	NUM
ejpam-6139	882	12	.	.	PUNCT
ejpam-6139	883	1	[	[	X
ejpam-6139	883	2	46	46	NUM
ejpam-6139	883	3	]	]	X
ejpam-6139	883	4	mehmet	mehmet	PROPN
ejpam-6139	883	5	zeki	zeki	PROPN
ejpam-6139	883	6	sarikaya	sarikaya	PROPN
ejpam-6139	883	7	and	and	CCONJ
ejpam-6139	883	8	nesip	nesip	PROPN
ejpam-6139	883	9	aktan	aktan	PROPN
ejpam-6139	883	10	.	.	PUNCT
ejpam-6139	884	1	on	on	ADP
ejpam-6139	884	2	the	the	DET
ejpam-6139	884	3	generalization	generalization	NOUN
ejpam-6139	884	4	of	of	ADP
ejpam-6139	884	5	some	some	DET
ejpam-6139	884	6	integral	integral	ADJ
ejpam-6139	884	7	inequalities	inequality	NOUN
ejpam-6139	884	8	and	and	CCONJ
ejpam-6139	884	9	their	their	PRON
ejpam-6139	884	10	applications	application	NOUN
ejpam-6139	884	11	.	.	PUNCT
ejpam-6139	885	1	mathematical	mathematical	ADJ
ejpam-6139	885	2	and	and	CCONJ
ejpam-6139	885	3	computer	computer	NOUN
ejpam-6139	885	4	modelling	modelling	NOUN
ejpam-6139	885	5	.	.	PUNCT
ejpam-6139	885	6	,	,	PUNCT
ejpam-6139	885	7	54.910:2175–2182	54.910:2175–2182	NOUN
ejpam-6139	885	8	,	,	PUNCT
ejpam-6139	885	9	2011	2011	NUM
ejpam-6139	885	10	.	.	PUNCT