id	sid	tid	token	lemma	pos
ejpam-4784	1	1	european	european	PROPN
ejpam-4784	1	2	journal	journal	PROPN
ejpam-4784	1	3	of	of	ADP
ejpam-4784	1	4	pure	pure	ADJ
ejpam-4784	1	5	and	and	CCONJ
ejpam-4784	1	6	applied	apply	VERB
ejpam-4784	1	7	mathematics	mathematic	NOUN
ejpam-4784	1	8	vol	vol	NOUN
ejpam-4784	1	9	.	.	PUNCT
ejpam-4784	2	1	16	16	NUM
ejpam-4784	2	2	,	,	PUNCT
ejpam-4784	2	3	no	no	INTJ
ejpam-4784	2	4	.	.	NOUN
ejpam-4784	2	5	3	3	NUM
ejpam-4784	2	6	,	,	PUNCT
ejpam-4784	2	7	2023	2023	NUM
ejpam-4784	2	8	,	,	PUNCT
ejpam-4784	2	9	1448	1448	NUM
ejpam-4784	2	10	-	-	SYM
ejpam-4784	2	11	1463	1463	NUM
ejpam-4784	2	12	issn	issn	PROPN
ejpam-4784	2	13	1307	1307	NUM
ejpam-4784	2	14	-	-	SYM
ejpam-4784	2	15	5543	5543	NUM
ejpam-4784	2	16	–	–	PUNCT
ejpam-4784	3	1	ejpam.com	ejpam.com	X
ejpam-4784	3	2	published	publish	VERB
ejpam-4784	3	3	by	by	ADP
ejpam-4784	3	4	new	new	PROPN
ejpam-4784	3	5	york	york	PROPN
ejpam-4784	3	6	business	business	PROPN
ejpam-4784	3	7	global	global	ADJ
ejpam-4784	3	8	generalization	generalization	NOUN
ejpam-4784	3	9	of	of	ADP
ejpam-4784	3	10	jensen	jensen	PROPN
ejpam-4784	3	11	mercer	mercer	PROPN
ejpam-4784	3	12	inequality	inequality	PROPN
ejpam-4784	3	13	on	on	ADP
ejpam-4784	3	14	delta	delta	PROPN
ejpam-4784	3	15	integral	integral	ADJ
ejpam-4784	3	16	with	with	ADP
ejpam-4784	3	17	applications	application	NOUN
ejpam-4784	3	18	sadia	sadia	PROPN
ejpam-4784	3	19	chanan1,2	chanan1,2	PROPN
ejpam-4784	3	20	,	,	PUNCT
ejpam-4784	3	21	nazia	nazia	PROPN
ejpam-4784	3	22	irshad3,∗	irshad3,∗	PROPN
ejpam-4784	3	23	,	,	PUNCT
ejpam-4784	3	24	afshan	afshan	NOUN
ejpam-4784	3	25	khan4	khan4	NOUN
ejpam-4784	3	26	1	1	NUM
ejpam-4784	3	27	department	department	NOUN
ejpam-4784	3	28	of	of	ADP
ejpam-4784	3	29	mathematics	mathematic	NOUN
ejpam-4784	3	30	,	,	PUNCT
ejpam-4784	3	31	university	university	PROPN
ejpam-4784	3	32	of	of	ADP
ejpam-4784	3	33	karachi	karachi	PROPN
ejpam-4784	3	34	,	,	PUNCT
ejpam-4784	3	35	university	university	NOUN
ejpam-4784	3	36	road	road	NOUN
ejpam-4784	3	37	,	,	PUNCT
ejpam-4784	3	38	karachi-75270	karachi-75270	X
ejpam-4784	3	39	,	,	PUNCT
ejpam-4784	3	40	pakistan	pakistan	PROPN
ejpam-4784	3	41	2	2	NUM
ejpam-4784	3	42	sir	sir	PROPN
ejpam-4784	3	43	syed	syed	PROPN
ejpam-4784	3	44	university	university	PROPN
ejpam-4784	3	45	of	of	ADP
ejpam-4784	3	46	engineering	engineering	NOUN
ejpam-4784	3	47	and	and	CCONJ
ejpam-4784	3	48	technology	technology	NOUN
ejpam-4784	3	49	,	,	PUNCT
ejpam-4784	3	50	main	main	ADJ
ejpam-4784	3	51	university	university	NOUN
ejpam-4784	3	52	road	road	NOUN
ejpam-4784	3	53	,	,	PUNCT
ejpam-4784	3	54	karachi	karachi	PROPN
ejpam-4784	3	55	75300	75300	NUM
ejpam-4784	3	56	,	,	PUNCT
ejpam-4784	3	57	pakistan	pakistan	PROPN
ejpam-4784	3	58	3	3	NUM
ejpam-4784	3	59	department	department	NOUN
ejpam-4784	3	60	of	of	ADP
ejpam-4784	3	61	mathematics	mathematics	PROPN
ejpam-4784	3	62	,	,	PUNCT
ejpam-4784	3	63	dawood	dawood	PROPN
ejpam-4784	3	64	university	university	PROPN
ejpam-4784	3	65	of	of	ADP
ejpam-4784	3	66	engineering	engineering	NOUN
ejpam-4784	3	67	and	and	CCONJ
ejpam-4784	3	68	technology	technology	NOUN
ejpam-4784	3	69	,	,	PUNCT
ejpam-4784	3	70	m.	m.	NOUN
ejpam-4784	3	71	a	a	DET
ejpam-4784	3	72	jinnah	jinnah	PROPN
ejpam-4784	3	73	road	road	PROPN
ejpam-4784	3	74	,	,	PUNCT
ejpam-4784	3	75	karachi-74800	karachi-74800	PROPN
ejpam-4784	3	76	,	,	PUNCT
ejpam-4784	3	77	pakistan	pakistan	PROPN
ejpam-4784	3	78	4	4	NUM
ejpam-4784	3	79	department	department	NOUN
ejpam-4784	3	80	of	of	ADP
ejpam-4784	3	81	mathematics	mathematic	NOUN
ejpam-4784	3	82	,	,	PUNCT
ejpam-4784	3	83	nazeer	nazeer	PROPN
ejpam-4784	3	84	hussain	hussain	PROPN
ejpam-4784	3	85	university	university	PROPN
ejpam-4784	3	86	,	,	PUNCT
ejpam-4784	3	87	karachi	karachi	PROPN
ejpam-4784	3	88	,	,	PUNCT
ejpam-4784	3	89	pakistan	pakistan	PROPN
ejpam-4784	3	90	abstract	abstract	NOUN
ejpam-4784	3	91	.	.	PUNCT
ejpam-4784	4	1	the	the	DET
ejpam-4784	4	2	aim	aim	NOUN
ejpam-4784	4	3	of	of	ADP
ejpam-4784	4	4	this	this	DET
ejpam-4784	4	5	article	article	NOUN
ejpam-4784	4	6	is	be	AUX
ejpam-4784	4	7	to	to	PART
ejpam-4784	4	8	give	give	VERB
ejpam-4784	4	9	generalization	generalization	NOUN
ejpam-4784	4	10	of	of	ADP
ejpam-4784	4	11	jensen	jensen	PROPN
ejpam-4784	4	12	mercer	mercer	PROPN
ejpam-4784	4	13	inequality	inequality	PROPN
ejpam-4784	4	14	on	on	ADP
ejpam-4784	4	15	delta	delta	NOUN
ejpam-4784	4	16	integral	integral	ADJ
ejpam-4784	4	17	along	along	ADP
ejpam-4784	4	18	with	with	ADP
ejpam-4784	4	19	applications	application	NOUN
ejpam-4784	4	20	to	to	ADP
ejpam-4784	4	21	ky	ky	PROPN
ejpam-4784	4	22	fan	fan	PROPN
ejpam-4784	4	23	inequality	inequality	PROPN
ejpam-4784	4	24	and	and	CCONJ
ejpam-4784	4	25	related	related	ADJ
ejpam-4784	4	26	results	result	NOUN
ejpam-4784	4	27	.	.	PUNCT
ejpam-4784	5	1	2020	2020	NUM
ejpam-4784	5	2	mathematics	mathematic	NOUN
ejpam-4784	5	3	subject	subject	NOUN
ejpam-4784	5	4	classifications	classification	NOUN
ejpam-4784	5	5	:	:	PUNCT
ejpam-4784	5	6	26a51,26d10	26a51,26d10	NUM
ejpam-4784	5	7	key	key	ADJ
ejpam-4784	5	8	words	word	NOUN
ejpam-4784	5	9	and	and	CCONJ
ejpam-4784	5	10	phrases	phrase	NOUN
ejpam-4784	5	11	:	:	PUNCT
ejpam-4784	5	12	jensen	jensen	PROPN
ejpam-4784	5	13	mercer	mercer	PROPN
ejpam-4784	5	14	inequality	inequality	PROPN
ejpam-4784	5	15	,	,	PUNCT
ejpam-4784	5	16	time	time	NOUN
ejpam-4784	5	17	scale	scale	NOUN
ejpam-4784	5	18	calculus	calculus	NOUN
ejpam-4784	5	19	,	,	PUNCT
ejpam-4784	5	20	ky	ky	PROPN
ejpam-4784	5	21	fan	fan	PROPN
ejpam-4784	5	22	inequality	inequality	PROPN
ejpam-4784	5	23	1	1	NUM
ejpam-4784	5	24	.	.	PUNCT
ejpam-4784	6	1	introduction	introduction	NOUN
ejpam-4784	6	2	one	one	NUM
ejpam-4784	6	3	of	of	ADP
ejpam-4784	6	4	the	the	DET
ejpam-4784	6	5	most	most	ADV
ejpam-4784	6	6	well	well	ADV
ejpam-4784	6	7	-	-	PUNCT
ejpam-4784	6	8	known	know	VERB
ejpam-4784	6	9	inequality	inequality	NOUN
ejpam-4784	6	10	in	in	ADP
ejpam-4784	6	11	mathematics	mathematic	NOUN
ejpam-4784	6	12	and	and	CCONJ
ejpam-4784	6	13	statistics	statistic	NOUN
ejpam-4784	6	14	is	be	AUX
ejpam-4784	6	15	jensen	jensen	PROPN
ejpam-4784	6	16	’s	’s	PART
ejpam-4784	6	17	inequality	inequality	NOUN
ejpam-4784	6	18	for	for	ADP
ejpam-4784	6	19	convex	convex	NOUN
ejpam-4784	6	20	functions	function	NOUN
ejpam-4784	6	21	.	.	PUNCT
ejpam-4784	7	1	because	because	SCONJ
ejpam-4784	7	2	of	of	ADP
ejpam-4784	7	3	their	their	PRON
ejpam-4784	7	4	importance	importance	NOUN
ejpam-4784	7	5	,	,	PUNCT
ejpam-4784	7	6	jensen	jensen	PROPN
ejpam-4784	7	7	’s	’s	PART
ejpam-4784	7	8	inequality	inequality	NOUN
ejpam-4784	7	9	has	have	AUX
ejpam-4784	7	10	received	receive	VERB
ejpam-4784	7	11	numerous	numerous	ADJ
ejpam-4784	7	12	variants	variant	NOUN
ejpam-4784	7	13	,	,	PUNCT
ejpam-4784	7	14	generalizations	generalization	NOUN
ejpam-4784	7	15	,	,	PUNCT
ejpam-4784	7	16	and	and	CCONJ
ejpam-4784	7	17	refinements	refinement	NOUN
ejpam-4784	7	18	(	(	PUNCT
ejpam-4784	7	19	for	for	ADP
ejpam-4784	7	20	reference	reference	NOUN
ejpam-4784	7	21	see	see	VERB
ejpam-4784	7	22	[	[	X
ejpam-4784	7	23	1	1	NUM
ejpam-4784	7	24	,	,	PUNCT
ejpam-4784	7	25	3	3	NUM
ejpam-4784	7	26	,	,	PUNCT
ejpam-4784	7	27	7	7	NUM
ejpam-4784	7	28	,	,	PUNCT
ejpam-4784	7	29	9–12	9–12	NOUN
ejpam-4784	7	30	,	,	PUNCT
ejpam-4784	7	31	14	14	NUM
ejpam-4784	7	32	–	–	SYM
ejpam-4784	7	33	18	18	NUM
ejpam-4784	7	34	,	,	PUNCT
ejpam-4784	7	35	21	21	NUM
ejpam-4784	7	36	,	,	PUNCT
ejpam-4784	7	37	22	22	NUM
ejpam-4784	7	38	]	]	PUNCT
ejpam-4784	7	39	)	)	PUNCT
ejpam-4784	7	40	.	.	PUNCT
ejpam-4784	8	1	in	in	ADP
ejpam-4784	8	2	2003	2003	NUM
ejpam-4784	8	3	,	,	PUNCT
ejpam-4784	8	4	mercer	mercer	PROPN
ejpam-4784	8	5	established	establish	VERB
ejpam-4784	8	6	a	a	DET
ejpam-4784	8	7	variant	variant	NOUN
ejpam-4784	8	8	of	of	ADP
ejpam-4784	8	9	jensen	jensen	PROPN
ejpam-4784	8	10	’s	’s	PART
ejpam-4784	8	11	inequality	inequality	NOUN
ejpam-4784	8	12	known	know	VERB
ejpam-4784	8	13	as	as	ADP
ejpam-4784	8	14	the	the	DET
ejpam-4784	8	15	jensen	jensen	PROPN
ejpam-4784	8	16	-	-	PUNCT
ejpam-4784	8	17	mercer	mercer	PROPN
ejpam-4784	8	18	inequality	inequality	NOUN
ejpam-4784	8	19	[	[	X
ejpam-4784	8	20	19	19	NUM
ejpam-4784	8	21	]	]	PUNCT
ejpam-4784	8	22	,	,	PUNCT
ejpam-4784	8	23	which	which	PRON
ejpam-4784	8	24	as	as	SCONJ
ejpam-4784	8	25	follows	follow	VERB
ejpam-4784	8	26	:	:	PUNCT
ejpam-4784	8	27	proposition	proposition	NOUN
ejpam-4784	8	28	1	1	NUM
ejpam-4784	8	29	.	.	PUNCT
ejpam-4784	8	30	let	let	VERB
ejpam-4784	8	31	ζ	ζ	NOUN
ejpam-4784	8	32	:	:	PUNCT
ejpam-4784	9	1	[	[	X
ejpam-4784	9	2	µ	µ	X
ejpam-4784	9	3	,	,	PUNCT
ejpam-4784	9	4	ν	ν	X
ejpam-4784	9	5	]	]	X
ejpam-4784	9	6	⊂	⊂	PROPN
ejpam-4784	10	1	i	i	PRON
ejpam-4784	10	2	→	→	PUNCT
ejpam-4784	10	3	r	r	NOUN
ejpam-4784	10	4	be	be	AUX
ejpam-4784	10	5	a	a	DET
ejpam-4784	10	6	convex	convex	NOUN
ejpam-4784	10	7	function	function	NOUN
ejpam-4784	10	8	and	and	CCONJ
ejpam-4784	10	9	xi	xi	ADP
ejpam-4784	10	10	∈	∈	PROPN
ejpam-4784	11	1	[	[	X
ejpam-4784	11	2	µ	µ	X
ejpam-4784	11	3	,	,	PUNCT
ejpam-4784	11	4	ν	ν	X
ejpam-4784	11	5	]	]	PUNCT
ejpam-4784	11	6	,	,	PUNCT
ejpam-4784	11	7	s.	s.	PROPN
ejpam-4784	11	8	t.	t.	PROPN
ejpam-4784	11	9	n∑	n∑	PROPN
ejpam-4784	11	10	i=1	i=1	PROPN
ejpam-4784	11	11	ωi	ωi	PROPN
ejpam-4784	11	12	=	=	NOUN
ejpam-4784	11	13	1	1	NUM
ejpam-4784	11	14	,	,	PUNCT
ejpam-4784	11	15	for	for	ADP
ejpam-4784	11	16	1	1	NUM
ejpam-4784	11	17	≤	≤	NUM
ejpam-4784	11	18	i	i	PRON
ejpam-4784	11	19	≤	≤	PROPN
ejpam-4784	11	20	n	n	CCONJ
ejpam-4784	11	21	,	,	PUNCT
ejpam-4784	11	22	then	then	ADV
ejpam-4784	11	23	ζ	ζ	X
ejpam-4784	11	24	(	(	PUNCT
ejpam-4784	11	25	µ+	µ+	NOUN
ejpam-4784	11	26	ν	ν	NOUN
ejpam-4784	12	1	−	−	PROPN
ejpam-4784	12	2	n∑	n∑	PROPN
ejpam-4784	12	3	i=1	i=1	PROPN
ejpam-4784	12	4	ωixi	ωixi	ADJ
ejpam-4784	12	5	)	)	PUNCT
ejpam-4784	12	6	≤	≤	NUM
ejpam-4784	12	7	ζ	ζ	X
ejpam-4784	12	8	(	(	PUNCT
ejpam-4784	12	9	µ	µ	NOUN
ejpam-4784	12	10	)	)	PUNCT
ejpam-4784	13	1	+	+	CCONJ
ejpam-4784	13	2	ζ	ζ	X
ejpam-4784	13	3	(	(	PUNCT
ejpam-4784	13	4	v)−	v)−	PROPN
ejpam-4784	13	5	n∑	n∑	PROPN
ejpam-4784	13	6	i=1	i=1	PROPN
ejpam-4784	13	7	ωiζ	ωiζ	PROPN
ejpam-4784	13	8	(	(	PUNCT
ejpam-4784	13	9	xi	xi	PROPN
ejpam-4784	13	10	)	)	PUNCT
ejpam-4784	13	11	.	.	PUNCT
ejpam-4784	14	1	∗corresponding	∗corresponde	VERB
ejpam-4784	14	2	author	author	NOUN
ejpam-4784	14	3	.	.	PUNCT
ejpam-4784	15	1	doi	doi	NOUN
ejpam-4784	15	2	:	:	PUNCT
ejpam-4784	15	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4784	https://doi.org/10.29020/nybg.ejpam.v16i3.4784	NOUN
ejpam-4784	15	4	email	email	NOUN
ejpam-4784	15	5	addresses	address	NOUN
ejpam-4784	15	6	:	:	PUNCT
ejpam-4784	15	7	sadiachanankhan@yahoo.com	sadiachanankhan@yahoo.com	X
ejpam-4784	16	1	sadia.khan@ssuet.edu.pk	sadia.khan@ssuet.edu.pk	PROPN
ejpam-4784	16	2	(	(	PUNCT
ejpam-4784	16	3	s.	s.	PROPN
ejpam-4784	16	4	chanan	chanan	PROPN
ejpam-4784	16	5	)	)	PUNCT
ejpam-4784	16	6	,	,	PUNCT
ejpam-4784	16	7	nazia.irshad@duet.edu.pk	nazia.irshad@duet.edu.pk	PROPN
ejpam-4784	16	8	(	(	PUNCT
ejpam-4784	16	9	n.	n.	PROPN
ejpam-4784	16	10	irshad	irshad	PROPN
ejpam-4784	16	11	)	)	PUNCT
ejpam-4784	16	12	,	,	PUNCT
ejpam-4784	16	13	afshan	afshan	NOUN
ejpam-4784	16	14	khan19@hotmail.com	khan19@hotmail.com	X
ejpam-4784	16	15	(	(	PUNCT
ejpam-4784	16	16	a.	a.	PROPN
ejpam-4784	16	17	khan	khan	PROPN
ejpam-4784	16	18	)	)	PUNCT
ejpam-4784	16	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4784	16	20	1448	1448	NUM
ejpam-4784	16	21	©	©	PROPN
ejpam-4784	16	22	2023	2023	NUM
ejpam-4784	16	23	ejpam	ejpam	NOUN
ejpam-4784	16	24	all	all	DET
ejpam-4784	16	25	rights	right	NOUN
ejpam-4784	16	26	reserved	reserve	VERB
ejpam-4784	16	27	.	.	PUNCT
ejpam-4784	17	1	s.	s.	PROPN
ejpam-4784	17	2	chanan	chanan	PROPN
ejpam-4784	17	3	,	,	PUNCT
ejpam-4784	17	4	n.	n.	PROPN
ejpam-4784	17	5	irshad	irshad	PROPN
ejpam-4784	17	6	,	,	PUNCT
ejpam-4784	17	7	a.	a.	PROPN
ejpam-4784	17	8	khan	khan	PROPN
ejpam-4784	17	9	/	/	SYM
ejpam-4784	17	10	eur	eur	PROPN
ejpam-4784	17	11	.	.	PUNCT
ejpam-4784	18	1	j.	j.	PROPN
ejpam-4784	18	2	pure	pure	PROPN
ejpam-4784	18	3	appl	appl	PROPN
ejpam-4784	18	4	.	.	PROPN
ejpam-4784	18	5	math	math	PROPN
ejpam-4784	18	6	,	,	PUNCT
ejpam-4784	18	7	16	16	NUM
ejpam-4784	18	8	(	(	PUNCT
ejpam-4784	18	9	3	3	NUM
ejpam-4784	18	10	)	)	PUNCT
ejpam-4784	18	11	(	(	PUNCT
ejpam-4784	18	12	2023	2023	NUM
ejpam-4784	18	13	)	)	PUNCT
ejpam-4784	18	14	,	,	PUNCT
ejpam-4784	18	15	1448	1448	NUM
ejpam-4784	18	16	-	-	SYM
ejpam-4784	18	17	1463	1463	NUM
ejpam-4784	18	18	1449	1449	NUM
ejpam-4784	18	19	in	in	ADP
ejpam-4784	18	20	1988	1988	NUM
ejpam-4784	19	1	,	,	PUNCT
ejpam-4784	19	2	stefan	stefan	PROPN
ejpam-4784	19	3	hilger	hilger	PROPN
ejpam-4784	19	4	introduced	introduce	VERB
ejpam-4784	19	5	the	the	DET
ejpam-4784	19	6	idea	idea	NOUN
ejpam-4784	19	7	of	of	ADP
ejpam-4784	19	8	theory	theory	NOUN
ejpam-4784	19	9	of	of	ADP
ejpam-4784	19	10	time	time	NOUN
ejpam-4784	19	11	scale	scale	NOUN
ejpam-4784	19	12	calculus	calculus	NOUN
ejpam-4784	19	13	in	in	ADP
ejpam-4784	19	14	order	order	NOUN
ejpam-4784	19	15	to	to	PART
ejpam-4784	19	16	unify	unify	VERB
ejpam-4784	19	17	discrete	discrete	ADJ
ejpam-4784	19	18	and	and	CCONJ
ejpam-4784	19	19	continuous	continuous	ADJ
ejpam-4784	19	20	analysis	analysis	NOUN
ejpam-4784	19	21	and	and	CCONJ
ejpam-4784	19	22	also	also	ADV
ejpam-4784	19	23	extend	extend	VERB
ejpam-4784	19	24	the	the	DET
ejpam-4784	19	25	traditional	traditional	ADJ
ejpam-4784	19	26	differential	differential	NOUN
ejpam-4784	19	27	and	and	CCONJ
ejpam-4784	19	28	difference	difference	NOUN
ejpam-4784	19	29	equations	equation	NOUN
ejpam-4784	19	30	in	in	ADP
ejpam-4784	19	31	[	[	X
ejpam-4784	19	32	13	13	NUM
ejpam-4784	19	33	]	]	PUNCT
ejpam-4784	19	34	.	.	PUNCT
ejpam-4784	20	1	there	there	PRON
ejpam-4784	20	2	have	have	AUX
ejpam-4784	20	3	been	be	AUX
ejpam-4784	20	4	over	over	ADP
ejpam-4784	20	5	a	a	DET
ejpam-4784	20	6	thousand	thousand	NUM
ejpam-4784	20	7	publications	publication	NOUN
ejpam-4784	20	8	in	in	ADP
ejpam-4784	20	9	this	this	DET
ejpam-4784	20	10	field	field	NOUN
ejpam-4784	20	11	,	,	PUNCT
ejpam-4784	20	12	with	with	ADP
ejpam-4784	20	13	numerous	numerous	ADJ
ejpam-4784	20	14	applications	application	NOUN
ejpam-4784	20	15	[	[	X
ejpam-4784	20	16	5	5	NUM
ejpam-4784	20	17	]	]	PUNCT
ejpam-4784	20	18	in	in	ADP
ejpam-4784	20	19	all	all	DET
ejpam-4784	20	20	branches	branch	NOUN
ejpam-4784	20	21	of	of	ADP
ejpam-4784	20	22	science	science	NOUN
ejpam-4784	20	23	.	.	PUNCT
ejpam-4784	21	1	for	for	ADP
ejpam-4784	21	2	interest	interest	NOUN
ejpam-4784	21	3	,	,	PUNCT
ejpam-4784	21	4	readers	reader	NOUN
ejpam-4784	21	5	can	can	AUX
ejpam-4784	21	6	see	see	VERB
ejpam-4784	21	7	bohner	bohner	NOUN
ejpam-4784	21	8	and	and	CCONJ
ejpam-4784	21	9	peterson	peterson	PROPN
ejpam-4784	21	10	’s	’s	PART
ejpam-4784	21	11	monograph	monograph	NOUN
ejpam-4784	22	1	[	[	X
ejpam-4784	22	2	6	6	NUM
ejpam-4784	22	3	]	]	PUNCT
ejpam-4784	22	4	for	for	ADP
ejpam-4784	22	5	an	an	DET
ejpam-4784	22	6	introduction	introduction	NOUN
ejpam-4784	22	7	to	to	ADP
ejpam-4784	22	8	single	single	ADJ
ejpam-4784	22	9	-	-	PUNCT
ejpam-4784	22	10	variable	variable	ADJ
ejpam-4784	22	11	time	time	NOUN
ejpam-4784	22	12	scale	scale	NOUN
ejpam-4784	22	13	calculus	calculus	NOUN
ejpam-4784	22	14	and	and	CCONJ
ejpam-4784	22	15	its	its	PRON
ejpam-4784	22	16	applications	application	NOUN
ejpam-4784	22	17	.	.	PUNCT
ejpam-4784	23	1	definition	definition	NOUN
ejpam-4784	23	2	1	1	NUM
ejpam-4784	23	3	.	.	PUNCT
ejpam-4784	24	1	a	a	DET
ejpam-4784	24	2	time	time	NOUN
ejpam-4784	24	3	scale	scale	NOUN
ejpam-4784	24	4	is	be	AUX
ejpam-4784	24	5	an	an	DET
ejpam-4784	24	6	arbitrary	arbitrary	ADJ
ejpam-4784	24	7	nonempty	nonempty	NOUN
ejpam-4784	24	8	closed	close	VERB
ejpam-4784	24	9	subset	subset	NOUN
ejpam-4784	24	10	of	of	ADP
ejpam-4784	24	11	the	the	DET
ejpam-4784	24	12	real	real	ADJ
ejpam-4784	24	13	numbers	number	NOUN
ejpam-4784	24	14	.	.	PUNCT
ejpam-4784	25	1	examples	example	NOUN
ejpam-4784	25	2	of	of	ADP
ejpam-4784	25	3	time	time	NOUN
ejpam-4784	25	4	scales	scale	NOUN
ejpam-4784	25	5	are	be	AUX
ejpam-4784	25	6	r	r	NOUN
ejpam-4784	25	7	,	,	PUNCT
ejpam-4784	25	8	z	z	NOUN
ejpam-4784	25	9	and	and	CCONJ
ejpam-4784	25	10	qn0	qn0	ADJ
ejpam-4784	25	11	:	:	PUNCT
ejpam-4784	25	12	=	=	SYM
ejpam-4784	25	13	{	{	PUNCT
ejpam-4784	25	14	qk|k	qk|k	PROPN
ejpam-4784	25	15	∈	∈	PROPN
ejpam-4784	25	16	n0	n0	NUM
ejpam-4784	25	17	}	}	PUNCT
ejpam-4784	25	18	.	.	PUNCT
ejpam-4784	26	1	the	the	DET
ejpam-4784	26	2	complex	complex	ADJ
ejpam-4784	26	3	number	number	NOUN
ejpam-4784	26	4	are	be	AUX
ejpam-4784	26	5	not	not	PART
ejpam-4784	26	6	time	time	NOUN
ejpam-4784	26	7	scale	scale	NOUN
ejpam-4784	26	8	.	.	PUNCT
ejpam-4784	27	1	definition	definition	NOUN
ejpam-4784	27	2	2	2	NUM
ejpam-4784	27	3	.	.	PUNCT
ejpam-4784	28	1	if	if	SCONJ
ejpam-4784	28	2	t	t	PROPN
ejpam-4784	28	3	is	be	AUX
ejpam-4784	28	4	a	a	DET
ejpam-4784	28	5	time	time	NOUN
ejpam-4784	28	6	scale	scale	NOUN
ejpam-4784	28	7	,	,	PUNCT
ejpam-4784	28	8	then	then	ADV
ejpam-4784	28	9	we	we	PRON
ejpam-4784	28	10	define	define	VERB
ejpam-4784	28	11	forward	forward	ADV
ejpam-4784	28	12	jump	jump	NOUN
ejpam-4784	28	13	operator	operator	NOUN
ejpam-4784	28	14	σ	σ	NOUN
ejpam-4784	28	15	:	:	PUNCT
ejpam-4784	28	16	t	t	PROPN
ejpam-4784	28	17	→	→	SYM
ejpam-4784	28	18	r	r	NOUN
ejpam-4784	28	19	by	by	ADP
ejpam-4784	28	20	σ(θ̂	σ(θ̂	NOUN
ejpam-4784	28	21	)	)	PUNCT
ejpam-4784	28	22	:	:	PUNCT
ejpam-4784	29	1	=	=	PUNCT
ejpam-4784	29	2	inf{τ	inf{τ	PROPN
ejpam-4784	29	3	∈	∈	PROPN
ejpam-4784	29	4	t|τ	t|τ	ADV
ejpam-4784	29	5	>	>	X
ejpam-4784	29	6	θ̂	θ̂	NUM
ejpam-4784	29	7	}	}	PUNCT
ejpam-4784	29	8	for	for	ADP
ejpam-4784	29	9	all	all	DET
ejpam-4784	29	10	θ̂	θ̂	NUM
ejpam-4784	29	11	∈	∈	PROPN
ejpam-4784	29	12	t	t	PROPN
ejpam-4784	29	13	,	,	PUNCT
ejpam-4784	29	14	the	the	DET
ejpam-4784	29	15	backward	backward	ADJ
ejpam-4784	29	16	jump	jump	NOUN
ejpam-4784	29	17	operator	operator	NOUN
ejpam-4784	29	18	ρ	ρ	NOUN
ejpam-4784	29	19	:	:	PUNCT
ejpam-4784	29	20	t	t	PROPN
ejpam-4784	29	21	→	→	SYM
ejpam-4784	29	22	r	r	NOUN
ejpam-4784	29	23	by	by	ADP
ejpam-4784	29	24	ρ(θ̂	ρ(θ̂	NOUN
ejpam-4784	29	25	)	)	PUNCT
ejpam-4784	29	26	:	:	PUNCT
ejpam-4784	29	27	=	=	PROPN
ejpam-4784	29	28	sup{τ	sup{τ	VERB
ejpam-4784	29	29	∈	∈	PROPN
ejpam-4784	29	30	t|τ	t|τ	ADV
ejpam-4784	29	31	<	<	X
ejpam-4784	29	32	θ̂	θ̂	NUM
ejpam-4784	29	33	}	}	PUNCT
ejpam-4784	29	34	for	for	ADP
ejpam-4784	29	35	all	all	DET
ejpam-4784	29	36	θ̂	θ̂	NUM
ejpam-4784	29	37	∈	∈	PROPN
ejpam-4784	29	38	t	t	PROPN
ejpam-4784	29	39	,	,	PUNCT
ejpam-4784	29	40	and	and	CCONJ
ejpam-4784	29	41	the	the	DET
ejpam-4784	29	42	graininess	graininess	NOUN
ejpam-4784	29	43	function	function	VERB
ejpam-4784	29	44	µ	µ	X
ejpam-4784	29	45	:	:	PUNCT
ejpam-4784	29	46	t	t	PROPN
ejpam-4784	29	47	→	→	PUNCT
ejpam-4784	30	1	[	[	X
ejpam-4784	30	2	0,∞	0,∞	NOUN
ejpam-4784	30	3	)	)	PUNCT
ejpam-4784	30	4	by	by	ADP
ejpam-4784	30	5	µ(θ̂	µ(θ̂	NOUN
ejpam-4784	30	6	)	)	PUNCT
ejpam-4784	30	7	:	:	PUNCT
ejpam-4784	31	1	=	=	SYM
ejpam-4784	31	2	σ(θ̂	σ(θ̂	PROPN
ejpam-4784	31	3	)	)	PUNCT
ejpam-4784	31	4	−	−	PROPN
ejpam-4784	31	5	θ̂	θ̂	PUNCT
ejpam-4784	31	6	for	for	ADP
ejpam-4784	31	7	all	all	PRON
ejpam-4784	31	8	θ̂	θ̂	PUNCT
ejpam-4784	31	9	∈	∈	PROPN
ejpam-4784	31	10	t.	t.	NOUN
ejpam-4784	31	11	furthermore	furthermore	ADV
ejpam-4784	31	12	for	for	ADP
ejpam-4784	31	13	a	a	DET
ejpam-4784	31	14	function	function	NOUN
ejpam-4784	31	15	g	g	NOUN
ejpam-4784	31	16	:	:	PUNCT
ejpam-4784	31	17	t	t	PROPN
ejpam-4784	31	18	→	→	SYM
ejpam-4784	31	19	r	r	NOUN
ejpam-4784	31	20	,	,	PUNCT
ejpam-4784	31	21	we	we	PRON
ejpam-4784	31	22	define	define	VERB
ejpam-4784	31	23	gσ(θ̂	gσ(θ̂	NOUN
ejpam-4784	31	24	)	)	PUNCT
ejpam-4784	31	25	=	=	SYM
ejpam-4784	31	26	g(σ(θ̂	g(σ(θ̂	PROPN
ejpam-4784	31	27	)	)	PUNCT
ejpam-4784	31	28	)	)	PUNCT
ejpam-4784	31	29	for	for	ADP
ejpam-4784	31	30	all	all	DET
ejpam-4784	31	31	θ̂	θ̂	PUNCT
ejpam-4784	31	32	∈	∈	PROPN
ejpam-4784	31	33	t	t	NOUN
ejpam-4784	31	34	and	and	CCONJ
ejpam-4784	31	35	gρ(θ̂	gρ(θ̂	NOUN
ejpam-4784	31	36	)	)	PUNCT
ejpam-4784	31	37	=	=	NUM
ejpam-4784	31	38	g(ρ(θ̂	g(ρ(θ̂	VERB
ejpam-4784	31	39	)	)	PUNCT
ejpam-4784	31	40	)	)	PUNCT
ejpam-4784	31	41	for	for	ADP
ejpam-4784	31	42	all	all	DET
ejpam-4784	31	43	θ̂	θ̂	VERB
ejpam-4784	31	44	∈	∈	PROPN
ejpam-4784	31	45	t.	t.	NOUN
ejpam-4784	31	46	in	in	ADP
ejpam-4784	31	47	this	this	DET
ejpam-4784	31	48	definition	definition	NOUN
ejpam-4784	31	49	we	we	PRON
ejpam-4784	31	50	use	use	VERB
ejpam-4784	31	51	inf	inf	NOUN
ejpam-4784	31	52	∅	∅	NOUN
ejpam-4784	31	53	=	=	SYM
ejpam-4784	31	54	supt	supt	X
ejpam-4784	31	55	(	(	PUNCT
ejpam-4784	31	56	i.e.	i.e.	X
ejpam-4784	31	57	,	,	PUNCT
ejpam-4784	31	58	ρ(θ̂	ρ(θ̂	NOUN
ejpam-4784	31	59	)	)	PUNCT
ejpam-4784	31	60	=	=	SYM
ejpam-4784	31	61	θ̂	θ̂	PUNCT
ejpam-4784	31	62	if	if	SCONJ
ejpam-4784	31	63	θ̂	θ̂	NUM
ejpam-4784	31	64	is	be	AUX
ejpam-4784	31	65	the	the	DET
ejpam-4784	31	66	maximum	maximum	NOUN
ejpam-4784	31	67	of	of	ADP
ejpam-4784	31	68	t	t	PROPN
ejpam-4784	31	69	)	)	PUNCT
ejpam-4784	31	70	and	and	CCONJ
ejpam-4784	31	71	sup	sup	NOUN
ejpam-4784	31	72	∅	∅	NOUN
ejpam-4784	31	73	=	=	SYM
ejpam-4784	31	74	inf	inf	PROPN
ejpam-4784	31	75	t	t	PROPN
ejpam-4784	31	76	(	(	PUNCT
ejpam-4784	31	77	i.e.	i.e.	X
ejpam-4784	31	78	,	,	PUNCT
ejpam-4784	31	79	ρ(θ̂	ρ(θ̂	NOUN
ejpam-4784	31	80	)	)	PUNCT
ejpam-4784	31	81	=	=	SYM
ejpam-4784	31	82	θ̂	θ̂	PUNCT
ejpam-4784	31	83	if	if	SCONJ
ejpam-4784	31	84	θ̂	θ̂	NUM
ejpam-4784	31	85	is	be	AUX
ejpam-4784	31	86	the	the	DET
ejpam-4784	31	87	minimum	minimum	NOUN
ejpam-4784	31	88	of	of	ADP
ejpam-4784	31	89	t	t	PROPN
ejpam-4784	31	90	)	)	PUNCT
ejpam-4784	31	91	.	.	PUNCT
ejpam-4784	32	1	these	these	DET
ejpam-4784	32	2	definitions	definition	NOUN
ejpam-4784	32	3	allow	allow	VERB
ejpam-4784	32	4	us	we	PRON
ejpam-4784	32	5	to	to	PART
ejpam-4784	32	6	characterize	characterize	VERB
ejpam-4784	32	7	every	every	DET
ejpam-4784	32	8	point	point	NOUN
ejpam-4784	32	9	in	in	ADP
ejpam-4784	32	10	a	a	DET
ejpam-4784	32	11	time	time	NOUN
ejpam-4784	32	12	scale	scale	NOUN
ejpam-4784	32	13	as	as	ADP
ejpam-4784	32	14	following	follow	VERB
ejpam-4784	32	15	classification	classification	NOUN
ejpam-4784	32	16	of	of	ADP
ejpam-4784	32	17	points	point	NOUN
ejpam-4784	32	18	:	:	PUNCT
ejpam-4784	32	19	(	(	PUNCT
ejpam-4784	32	20	i	i	NOUN
ejpam-4784	32	21	)	)	PUNCT
ejpam-4784	32	22	θ̂	θ̂	VERB
ejpam-4784	32	23	right	right	ADV
ejpam-4784	32	24	-	-	PUNCT
ejpam-4784	32	25	scattered	scatter	VERB
ejpam-4784	32	26	=	=	NOUN
ejpam-4784	32	27	⇒	⇒	NOUN
ejpam-4784	32	28	θ̂	θ̂	X
ejpam-4784	32	29	<	<	X
ejpam-4784	32	30	σ(θ̂	σ(θ̂	PROPN
ejpam-4784	32	31	)	)	PUNCT
ejpam-4784	32	32	,	,	PUNCT
ejpam-4784	32	33	(	(	PUNCT
ejpam-4784	32	34	ii	ii	NOUN
ejpam-4784	32	35	)	)	PUNCT
ejpam-4784	32	36	θ̂	θ̂	VERB
ejpam-4784	32	37	right	right	ADJ
ejpam-4784	32	38	-	-	PUNCT
ejpam-4784	32	39	dense	dense	ADJ
ejpam-4784	32	40	=	=	NOUN
ejpam-4784	32	41	⇒	⇒	NOUN
ejpam-4784	32	42	θ̂	θ̂	NUM
ejpam-4784	32	43	=	=	SYM
ejpam-4784	32	44	σ(θ̂	σ(θ̂	ADJ
ejpam-4784	32	45	)	)	PUNCT
ejpam-4784	32	46	,	,	PUNCT
ejpam-4784	32	47	(	(	PUNCT
ejpam-4784	32	48	iii	iii	X
ejpam-4784	32	49	)	)	PUNCT
ejpam-4784	32	50	θ̂	θ̂	X
ejpam-4784	32	51	left	leave	VERB
ejpam-4784	32	52	-	-	PUNCT
ejpam-4784	32	53	scattered	scatter	VERB
ejpam-4784	32	54	=	=	NOUN
ejpam-4784	32	55	⇒	⇒	NOUN
ejpam-4784	32	56	ρ(θ̂	ρ(θ̂	NOUN
ejpam-4784	32	57	)	)	PUNCT
ejpam-4784	32	58	<	<	X
ejpam-4784	32	59	θ̂	θ̂	NUM
ejpam-4784	32	60	,	,	PUNCT
ejpam-4784	32	61	(	(	PUNCT
ejpam-4784	32	62	iv	iv	X
ejpam-4784	32	63	)	)	PUNCT
ejpam-4784	32	64	θ̂	θ̂	X
ejpam-4784	32	65	left	leave	VERB
ejpam-4784	32	66	-	-	PUNCT
ejpam-4784	32	67	dense	dense	ADJ
ejpam-4784	32	68	=	=	NOUN
ejpam-4784	32	69	⇒	⇒	NOUN
ejpam-4784	32	70	ρ(θ̂	ρ(θ̂	NOUN
ejpam-4784	32	71	)	)	PUNCT
ejpam-4784	32	72	=	=	PUNCT
ejpam-4784	32	73	θ̂	θ̂	NUM
ejpam-4784	32	74	,	,	PUNCT
ejpam-4784	32	75	(	(	PUNCT
ejpam-4784	32	76	v	v	NOUN
ejpam-4784	32	77	)	)	PUNCT
ejpam-4784	32	78	θ̂	θ̂	X
ejpam-4784	32	79	isolated	isolate	VERB
ejpam-4784	32	80	=	=	X
ejpam-4784	32	81	⇒	⇒	NOUN
ejpam-4784	32	82	ρ(θ̂	ρ(θ̂	NOUN
ejpam-4784	32	83	)	)	PUNCT
ejpam-4784	32	84	<	<	X
ejpam-4784	32	85	θ̂	θ̂	X
ejpam-4784	32	86	<	<	X
ejpam-4784	32	87	σ(θ̂	σ(θ̂	NOUN
ejpam-4784	32	88	)	)	PUNCT
ejpam-4784	32	89	,	,	PUNCT
ejpam-4784	32	90	(	(	PUNCT
ejpam-4784	32	91	vi	vi	NOUN
ejpam-4784	32	92	)	)	PUNCT
ejpam-4784	32	93	θ̂	θ̂	VERB
ejpam-4784	32	94	dense	dense	ADJ
ejpam-4784	32	95	=	=	PRON
ejpam-4784	32	96	⇒	⇒	NOUN
ejpam-4784	32	97	ρ(θ̂	ρ(θ̂	NOUN
ejpam-4784	32	98	)	)	PUNCT
ejpam-4784	32	99	=	=	SYM
ejpam-4784	32	100	θ̂	θ̂	X
ejpam-4784	32	101	=	=	SYM
ejpam-4784	32	102	σ(θ̂	σ(θ̂	X
ejpam-4784	32	103	)	)	PUNCT
ejpam-4784	32	104	.	.	PUNCT
ejpam-4784	33	1	we	we	PRON
ejpam-4784	33	2	define	define	VERB
ejpam-4784	33	3	,	,	PUNCT
ejpam-4784	33	4	if	if	SCONJ
ejpam-4784	33	5	t	t	PROPN
ejpam-4784	33	6	has	have	VERB
ejpam-4784	33	7	a	a	DET
ejpam-4784	33	8	left	left	ADJ
ejpam-4784	33	9	scattered	scatter	VERB
ejpam-4784	33	10	maximum	maximum	ADJ
ejpam-4784	33	11	m1	m1	NOUN
ejpam-4784	33	12	,	,	PUNCT
ejpam-4784	33	13	then	then	ADV
ejpam-4784	33	14	we	we	PRON
ejpam-4784	33	15	define	define	VERB
ejpam-4784	33	16	tk	tk	PROPN
ejpam-4784	33	17	=	=	PROPN
ejpam-4784	33	18	t	t	PROPN
ejpam-4784	33	19	/	/	SYM
ejpam-4784	33	20	m1	m1	NOUN
ejpam-4784	33	21	;	;	PUNCT
ejpam-4784	33	22	otherwise	otherwise	ADV
ejpam-4784	33	23	tk	tk	PROPN
ejpam-4784	34	1	=	=	PUNCT
ejpam-4784	34	2	t.	t.	PROPN
ejpam-4784	34	3	if	if	SCONJ
ejpam-4784	34	4	t	t	PROPN
ejpam-4784	34	5	has	have	VERB
ejpam-4784	34	6	a	a	DET
ejpam-4784	34	7	right	right	ADJ
ejpam-4784	34	8	scattered	scatter	VERB
ejpam-4784	34	9	maximum	maximum	ADJ
ejpam-4784	34	10	m2	m2	PROPN
ejpam-4784	34	11	,	,	PUNCT
ejpam-4784	34	12	then	then	ADV
ejpam-4784	34	13	we	we	PRON
ejpam-4784	34	14	define	define	VERB
ejpam-4784	34	15	tk	tk	PROPN
ejpam-4784	34	16	=	=	PROPN
ejpam-4784	34	17	t	t	PROPN
ejpam-4784	34	18	/	/	SYM
ejpam-4784	34	19	m2	m2	PROPN
ejpam-4784	34	20	;	;	PUNCT
ejpam-4784	34	21	otherwise	otherwise	ADV
ejpam-4784	34	22	tk	tk	PROPN
ejpam-4784	34	23	=	=	PROPN
ejpam-4784	34	24	t.	t.	PROPN
ejpam-4784	34	25	finally	finally	ADV
ejpam-4784	34	26	we	we	PRON
ejpam-4784	34	27	define	define	VERB
ejpam-4784	34	28	t∗	t∗	NOUN
ejpam-4784	34	29	=	=	SYM
ejpam-4784	34	30	tk	tk	PROPN
ejpam-4784	34	31	⋂	⋂	PROPN
ejpam-4784	34	32	tk	tk	PROPN
ejpam-4784	34	33	.	.	PUNCT
ejpam-4784	35	1	the	the	DET
ejpam-4784	35	2	mapping	mapping	PROPN
ejpam-4784	35	3	µ	µ	NOUN
ejpam-4784	35	4	,	,	PUNCT
ejpam-4784	35	5	ν	ν	X
ejpam-4784	35	6	:	:	PUNCT
ejpam-4784	35	7	t	t	X
ejpam-4784	35	8	→	→	PUNCT
ejpam-4784	36	1	[	[	X
ejpam-4784	36	2	0,∞	0,∞	NOUN
ejpam-4784	36	3	)	)	PUNCT
ejpam-4784	36	4	defined	define	VERB
ejpam-4784	36	5	by	by	ADP
ejpam-4784	36	6	µ(t	µ(t	ADJ
ejpam-4784	36	7	)	)	PUNCT
ejpam-4784	36	8	=	=	SYM
ejpam-4784	36	9	σ(t)−	σ(t)−	PROPN
ejpam-4784	36	10	t	t	PROPN
ejpam-4784	36	11	and	and	CCONJ
ejpam-4784	36	12	ν(t	ν(t	NOUN
ejpam-4784	36	13	)	)	PUNCT
ejpam-4784	37	1	=	=	SYM
ejpam-4784	37	2	t−	t−	PROPN
ejpam-4784	37	3	ρ(t	ρ(t	NUM
ejpam-4784	37	4	)	)	PUNCT
ejpam-4784	37	5	are	be	AUX
ejpam-4784	37	6	called	call	VERB
ejpam-4784	37	7	the	the	DET
ejpam-4784	37	8	forward	forward	ADJ
ejpam-4784	37	9	and	and	CCONJ
ejpam-4784	37	10	backward	backward	ADJ
ejpam-4784	37	11	graininess	graininess	NOUN
ejpam-4784	37	12	functions	function	NOUN
ejpam-4784	37	13	,	,	PUNCT
ejpam-4784	37	14	respectively	respectively	ADV
ejpam-4784	37	15	.	.	PUNCT
ejpam-4784	38	1	in	in	ADP
ejpam-4784	38	2	the	the	DET
ejpam-4784	38	3	following	follow	VERB
ejpam-4784	38	4	consideration	consideration	NOUN
ejpam-4784	38	5	,	,	PUNCT
ejpam-4784	38	6	it	it	PRON
ejpam-4784	38	7	=	=	PUNCT
ejpam-4784	39	1	i	i	PRON
ejpam-4784	39	2	⋂	⋂	PROPN
ejpam-4784	39	3	t	t	PROPN
ejpam-4784	39	4	will	will	AUX
ejpam-4784	39	5	denote	denote	VERB
ejpam-4784	39	6	a	a	DET
ejpam-4784	39	7	time	time	NOUN
ejpam-4784	39	8	scale	scale	NOUN
ejpam-4784	39	9	interval	interval	NOUN
ejpam-4784	39	10	.	.	PUNCT
ejpam-4784	40	1	s.	s.	PROPN
ejpam-4784	40	2	chanan	chanan	PROPN
ejpam-4784	40	3	,	,	PUNCT
ejpam-4784	40	4	n.	n.	PROPN
ejpam-4784	40	5	irshad	irshad	PROPN
ejpam-4784	40	6	,	,	PUNCT
ejpam-4784	40	7	a.	a.	PROPN
ejpam-4784	40	8	khan	khan	PROPN
ejpam-4784	40	9	/	/	SYM
ejpam-4784	40	10	eur	eur	PROPN
ejpam-4784	40	11	.	.	PUNCT
ejpam-4784	41	1	j.	j.	PROPN
ejpam-4784	41	2	pure	pure	PROPN
ejpam-4784	41	3	appl	appl	PROPN
ejpam-4784	41	4	.	.	PROPN
ejpam-4784	41	5	math	math	PROPN
ejpam-4784	41	6	,	,	PUNCT
ejpam-4784	41	7	16	16	NUM
ejpam-4784	41	8	(	(	PUNCT
ejpam-4784	41	9	3	3	NUM
ejpam-4784	41	10	)	)	PUNCT
ejpam-4784	41	11	(	(	PUNCT
ejpam-4784	41	12	2023	2023	NUM
ejpam-4784	41	13	)	)	PUNCT
ejpam-4784	41	14	,	,	PUNCT
ejpam-4784	41	15	1448	1448	NUM
ejpam-4784	41	16	-	-	SYM
ejpam-4784	41	17	1463	1463	NUM
ejpam-4784	41	18	1450	1450	NUM
ejpam-4784	41	19	definition	definition	NOUN
ejpam-4784	41	20	3	3	X
ejpam-4784	41	21	.	.	PUNCT
ejpam-4784	42	1	let	let	VERB
ejpam-4784	42	2	f	f	PROPN
ejpam-4784	42	3	:	:	PUNCT
ejpam-4784	42	4	t	t	PROPN
ejpam-4784	42	5	→	→	SYM
ejpam-4784	42	6	r	r	NOUN
ejpam-4784	42	7	be	be	AUX
ejpam-4784	42	8	a	a	DET
ejpam-4784	42	9	real	real	ADJ
ejpam-4784	42	10	function	function	NOUN
ejpam-4784	42	11	on	on	ADP
ejpam-4784	42	12	time	time	NOUN
ejpam-4784	42	13	scale	scale	NOUN
ejpam-4784	42	14	t.	t.	PROPN
ejpam-4784	42	15	then	then	ADV
ejpam-4784	42	16	for	for	ADP
ejpam-4784	42	17	t	t	PROPN
ejpam-4784	42	18	∈	∈	PROPN
ejpam-4784	42	19	tk	tk	PROPN
ejpam-4784	42	20	,	,	PUNCT
ejpam-4784	42	21	we	we	PRON
ejpam-4784	42	22	define	define	VERB
ejpam-4784	42	23	a	a	DET
ejpam-4784	42	24	f∆(t	f∆(t	NOUN
ejpam-4784	42	25	)	)	PUNCT
ejpam-4784	42	26	to	to	PART
ejpam-4784	42	27	be	be	AUX
ejpam-4784	42	28	a	a	DET
ejpam-4784	42	29	number	number	NOUN
ejpam-4784	42	30	with	with	ADP
ejpam-4784	42	31	the	the	DET
ejpam-4784	42	32	property	property	NOUN
ejpam-4784	42	33	that	that	PRON
ejpam-4784	42	34	given	give	VERB
ejpam-4784	42	35	any	any	DET
ejpam-4784	42	36	ε	ε	PROPN
ejpam-4784	42	37	>	>	X
ejpam-4784	42	38	0	0	PROPN
ejpam-4784	42	39	,	,	PUNCT
ejpam-4784	42	40	there	there	PRON
ejpam-4784	42	41	is	be	VERB
ejpam-4784	42	42	a	a	DET
ejpam-4784	42	43	neighbour	neighbour	ADJ
ejpam-4784	42	44	hood	hood	NOUN
ejpam-4784	42	45	ut	ut	PROPN
ejpam-4784	42	46	of	of	ADP
ejpam-4784	42	47	t	t	PROPN
ejpam-4784	42	48	such	such	ADJ
ejpam-4784	42	49	that	that	DET
ejpam-4784	42	50	|(f(ρ(t))−	|(f(ρ(t))−	NOUN
ejpam-4784	42	51	f(s))−	f(s))−	NOUN
ejpam-4784	42	52	f∆(t)[ρ(t)−	f∆(t)[ρ(t)−	PROPN
ejpam-4784	42	53	s]|	s]|	VERB
ejpam-4784	42	54	≤	≤	NUM
ejpam-4784	42	55	ε|ρ(t)−	ε|ρ(t)−	PROPN
ejpam-4784	42	56	s|	s|	VERB
ejpam-4784	42	57	for	for	ADP
ejpam-4784	42	58	all	all	DET
ejpam-4784	42	59	s	s	PART
ejpam-4784	42	60	∈	∈	ADJ
ejpam-4784	42	61	ut	ut	NOUN
ejpam-4784	42	62	we	we	PRON
ejpam-4784	42	63	call	call	VERB
ejpam-4784	42	64	f∆(t	f∆(t	NOUN
ejpam-4784	42	65	)	)	PUNCT
ejpam-4784	42	66	the	the	DET
ejpam-4784	42	67	delta	delta	NOUN
ejpam-4784	42	68	derivative	derivative	NOUN
ejpam-4784	42	69	of	of	ADP
ejpam-4784	42	70	f	f	PROPN
ejpam-4784	42	71	at	at	ADP
ejpam-4784	42	72	t.	t.	PROPN
ejpam-4784	42	73	for	for	ADP
ejpam-4784	42	74	f	f	PROPN
ejpam-4784	42	75	:	:	PUNCT
ejpam-4784	42	76	t	t	PROPN
ejpam-4784	42	77	→	→	SYM
ejpam-4784	42	78	r	r	NOUN
ejpam-4784	42	79	,	,	PUNCT
ejpam-4784	42	80	then	then	ADV
ejpam-4784	42	81	we	we	PRON
ejpam-4784	42	82	define	define	VERB
ejpam-4784	42	83	fσ	fσ	X
ejpam-4784	42	84	:	:	PUNCT
ejpam-4784	42	85	t	t	PROPN
ejpam-4784	42	86	→	→	SYM
ejpam-4784	42	87	r	r	NOUN
ejpam-4784	42	88	by	by	ADP
ejpam-4784	42	89	fσ(t	fσ(t	NOUN
ejpam-4784	42	90	)	)	PUNCT
ejpam-4784	43	1	=	=	SYM
ejpam-4784	43	2	f(σ(t	f(σ(t	PROPN
ejpam-4784	43	3	)	)	PUNCT
ejpam-4784	43	4	)	)	PUNCT
ejpam-4784	43	5	for	for	ADP
ejpam-4784	43	6	t	t	PROPN
ejpam-4784	43	7	∈	∈	PROPN
ejpam-4784	43	8	t.	t.	NOUN
ejpam-4784	43	9	we	we	PRON
ejpam-4784	43	10	define	define	VERB
ejpam-4784	43	11	fρ	fρ	ADP
ejpam-4784	43	12	:	:	PUNCT
ejpam-4784	43	13	t	t	PROPN
ejpam-4784	43	14	→	→	SYM
ejpam-4784	43	15	r	r	NOUN
ejpam-4784	43	16	by	by	ADP
ejpam-4784	43	17	fρ(t	fρ(t	NOUN
ejpam-4784	43	18	)	)	PUNCT
ejpam-4784	43	19	=	=	SYM
ejpam-4784	43	20	f(ρ(t	f(ρ(t	NOUN
ejpam-4784	43	21	)	)	PUNCT
ejpam-4784	43	22	)	)	PUNCT
ejpam-4784	43	23	for	for	ADP
ejpam-4784	43	24	t	t	PROPN
ejpam-4784	43	25	∈	∈	PROPN
ejpam-4784	43	26	t.	t.	NOUN
ejpam-4784	43	27	following	follow	VERB
ejpam-4784	43	28	properties	property	NOUN
ejpam-4784	43	29	holds	hold	VERB
ejpam-4784	43	30	for	for	ADP
ejpam-4784	43	31	t	t	PROPN
ejpam-4784	43	32	∈	∈	PROPN
ejpam-4784	43	33	tk	tk	PROPN
ejpam-4784	43	34	.	.	PUNCT
ejpam-4784	44	1	(	(	PUNCT
ejpam-4784	44	2	i	i	NOUN
ejpam-4784	44	3	)	)	PUNCT
ejpam-4784	44	4	if	if	SCONJ
ejpam-4784	44	5	f	f	PROPN
ejpam-4784	44	6	is	be	AUX
ejpam-4784	44	7	∆	∆	PROPN
ejpam-4784	44	8	differentiable	differentiable	NOUN
ejpam-4784	44	9	at	at	ADP
ejpam-4784	44	10	t	t	PROPN
ejpam-4784	44	11	,	,	PUNCT
ejpam-4784	44	12	then	then	ADV
ejpam-4784	44	13	f	f	PROPN
ejpam-4784	44	14	is	be	AUX
ejpam-4784	44	15	continuous	continuous	ADJ
ejpam-4784	44	16	at	at	ADP
ejpam-4784	44	17	t.	t.	PROPN
ejpam-4784	44	18	(	(	PUNCT
ejpam-4784	44	19	ii	ii	PROPN
ejpam-4784	44	20	)	)	PUNCT
ejpam-4784	44	21	if	if	SCONJ
ejpam-4784	44	22	f	f	PROPN
ejpam-4784	44	23	is	be	AUX
ejpam-4784	44	24	continuous	continuous	ADJ
ejpam-4784	44	25	at	at	ADP
ejpam-4784	44	26	t	t	PROPN
ejpam-4784	44	27	and	and	CCONJ
ejpam-4784	44	28	t	t	PROPN
ejpam-4784	44	29	is	be	AUX
ejpam-4784	44	30	right	right	ADV
ejpam-4784	44	31	-	-	PUNCT
ejpam-4784	44	32	scattered	scatter	VERB
ejpam-4784	44	33	,	,	PUNCT
ejpam-4784	44	34	then	then	ADV
ejpam-4784	44	35	f	f	PROPN
ejpam-4784	44	36	is	be	AUX
ejpam-4784	44	37	delta	delta	NOUN
ejpam-4784	44	38	differentiable	differentiable	ADJ
ejpam-4784	44	39	at	at	ADP
ejpam-4784	44	40	t	t	PROPN
ejpam-4784	44	41	with	with	ADP
ejpam-4784	44	42	f∆(t	f∆(t	NOUN
ejpam-4784	44	43	)	)	PUNCT
ejpam-4784	44	44	=	=	PRON
ejpam-4784	45	1	(	(	PUNCT
ejpam-4784	45	2	f(t)−	f(t)−	PROPN
ejpam-4784	45	3	f(σ(t))/υ(t	f(σ(t))/υ(t	PROPN
ejpam-4784	45	4	)	)	PUNCT
ejpam-4784	45	5	)	)	PUNCT
ejpam-4784	45	6	(	(	PUNCT
ejpam-4784	45	7	iii	iii	X
ejpam-4784	45	8	)	)	PUNCT
ejpam-4784	45	9	if	if	SCONJ
ejpam-4784	45	10	f	f	PROPN
ejpam-4784	45	11	is	be	AUX
ejpam-4784	45	12	right	right	ADJ
ejpam-4784	45	13	-	-	PUNCT
ejpam-4784	45	14	dense	dense	ADJ
ejpam-4784	45	15	,	,	PUNCT
ejpam-4784	45	16	then	then	ADV
ejpam-4784	45	17	f	f	PROPN
ejpam-4784	45	18	is	be	AUX
ejpam-4784	45	19	delta	delta	NOUN
ejpam-4784	45	20	differentiable	differentiable	ADJ
ejpam-4784	45	21	at	at	ADP
ejpam-4784	45	22	t	t	PROPN
ejpam-4784	45	23	if	if	SCONJ
ejpam-4784	45	24	and	and	CCONJ
ejpam-4784	45	25	only	only	ADV
ejpam-4784	45	26	if	if	SCONJ
ejpam-4784	45	27	the	the	DET
ejpam-4784	45	28	lims→t(f(t)−	lims→t(f(t)−	PROPN
ejpam-4784	45	29	f(s))/(t−	f(s))/(t−	PROPN
ejpam-4784	45	30	s	s	PROPN
ejpam-4784	45	31	)	)	PUNCT
ejpam-4784	45	32	exit	exit	NOUN
ejpam-4784	45	33	,	,	PUNCT
ejpam-4784	45	34	then	then	ADV
ejpam-4784	45	35	f∆(t	f∆(t	NOUN
ejpam-4784	45	36	)	)	PUNCT
ejpam-4784	45	37	=	=	SYM
ejpam-4784	45	38	lims→t(f(t)−	lims→t(f(t)−	PROPN
ejpam-4784	46	1	f(s))/(t−	f(s))/(t−	PROPN
ejpam-4784	46	2	s	s	PROPN
ejpam-4784	46	3	)	)	PUNCT
ejpam-4784	46	4	.	.	PUNCT
ejpam-4784	47	1	(	(	PUNCT
ejpam-4784	47	2	iv	iv	X
ejpam-4784	47	3	)	)	PUNCT
ejpam-4784	47	4	if	if	SCONJ
ejpam-4784	47	5	f	f	PROPN
ejpam-4784	47	6	is	be	AUX
ejpam-4784	47	7	∆	∆	PROPN
ejpam-4784	47	8	differentiable	differentiable	NOUN
ejpam-4784	47	9	at	at	ADP
ejpam-4784	47	10	t	t	PROPN
ejpam-4784	47	11	,	,	PUNCT
ejpam-4784	47	12	then	then	ADV
ejpam-4784	47	13	fρ(t	fρ(t	PUNCT
ejpam-4784	47	14	)	)	PUNCT
ejpam-4784	47	15	=	=	SYM
ejpam-4784	47	16	f(t	f(t	NOUN
ejpam-4784	47	17	)	)	PUNCT
ejpam-4784	48	1	+	+	NUM
ejpam-4784	48	2	f∆(t)υ(t	f∆(t)υ(t	NOUN
ejpam-4784	48	3	)	)	PUNCT
ejpam-4784	48	4	)	)	PUNCT
ejpam-4784	48	5	.	.	PUNCT
ejpam-4784	49	1	for	for	ADP
ejpam-4784	49	2	more	more	ADJ
ejpam-4784	49	3	details	detail	NOUN
ejpam-4784	49	4	on	on	ADP
ejpam-4784	49	5	time	time	NOUN
ejpam-4784	49	6	scale	scale	NOUN
ejpam-4784	49	7	,	,	PUNCT
ejpam-4784	49	8	we	we	PRON
ejpam-4784	49	9	refer	refer	VERB
ejpam-4784	49	10	the	the	DET
ejpam-4784	49	11	reader	reader	NOUN
ejpam-4784	49	12	to	to	ADP
ejpam-4784	49	13	[	[	X
ejpam-4784	49	14	20	20	NUM
ejpam-4784	49	15	]	]	PUNCT
ejpam-4784	49	16	.	.	PUNCT
ejpam-4784	50	1	in	in	ADP
ejpam-4784	50	2	[	[	X
ejpam-4784	50	3	23	23	NUM
ejpam-4784	50	4	]	]	PUNCT
ejpam-4784	50	5	,	,	PUNCT
ejpam-4784	50	6	jensen	jensen	PROPN
ejpam-4784	50	7	inequality	inequality	PROPN
ejpam-4784	50	8	on	on	ADP
ejpam-4784	50	9	delta	delta	PROPN
ejpam-4784	50	10	integral	integral	ADJ
ejpam-4784	50	11	is	be	AUX
ejpam-4784	50	12	given	give	VERB
ejpam-4784	50	13	as	as	ADP
ejpam-4784	50	14	follow	follow	VERB
ejpam-4784	50	15	:	:	PUNCT
ejpam-4784	50	16	proposition	proposition	NOUN
ejpam-4784	50	17	2	2	NUM
ejpam-4784	50	18	.	.	PUNCT
ejpam-4784	51	1	let	let	VERB
ejpam-4784	51	2	a	a	DET
ejpam-4784	51	3	,	,	PUNCT
ejpam-4784	51	4	b	b	PROPN
ejpam-4784	51	5	∈	∈	PROPN
ejpam-4784	51	6	t	t	PROPN
ejpam-4784	51	7	,	,	PUNCT
ejpam-4784	51	8	a	a	DET
ejpam-4784	51	9	<	<	X
ejpam-4784	51	10	b	b	NOUN
ejpam-4784	51	11	and	and	CCONJ
ejpam-4784	51	12	i	i	PRON
ejpam-4784	51	13	⊂	⊂	PROPN
ejpam-4784	51	14	r	r	X
ejpam-4784	51	15	,	,	PUNCT
ejpam-4784	51	16	g	g	PROPN
ejpam-4784	51	17	∈	∈	PROPN
ejpam-4784	51	18	c([a	c([a	NOUN
ejpam-4784	51	19	,	,	PUNCT
ejpam-4784	51	20	b]t	b]t	NOUN
ejpam-4784	51	21	,	,	PUNCT
ejpam-4784	51	22	i	i	PROPN
ejpam-4784	51	23	)	)	PUNCT
ejpam-4784	51	24	and	and	CCONJ
ejpam-4784	51	25	ω	ω	NUM
ejpam-4784	51	26	∈	∈	PROPN
ejpam-4784	51	27	c([a	c([a	NOUN
ejpam-4784	51	28	,	,	PUNCT
ejpam-4784	51	29	b]t	b]t	NOUN
ejpam-4784	51	30	,	,	PUNCT
ejpam-4784	51	31	r	r	NOUN
ejpam-4784	51	32	)	)	PUNCT
ejpam-4784	51	33	is	be	AUX
ejpam-4784	51	34	a	a	DET
ejpam-4784	51	35	probability	probability	NOUN
ejpam-4784	51	36	density	density	NOUN
ejpam-4784	51	37	function	function	NOUN
ejpam-4784	51	38	and	and	CCONJ
ejpam-4784	51	39	also	also	ADV
ejpam-4784	51	40	ζ	ζ	PROPN
ejpam-4784	51	41	∈	∈	PROPN
ejpam-4784	51	42	c(i	c(i	NOUN
ejpam-4784	51	43	,	,	PUNCT
ejpam-4784	51	44	r	r	NOUN
ejpam-4784	51	45	)	)	PUNCT
ejpam-4784	51	46	is	be	AUX
ejpam-4784	51	47	convex	convex	PROPN
ejpam-4784	51	48	,	,	PUNCT
ejpam-4784	51	49	then	then	ADV
ejpam-4784	51	50	ζ	ζ	PROPN
ejpam-4784	51	51	(	(	PUNCT
ejpam-4784	51	52	∫	∫	PROPN
ejpam-4784	51	53	b	b	PROPN
ejpam-4784	51	54	a	a	DET
ejpam-4784	51	55	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	51	56	)	)	PUNCT
ejpam-4784	51	57	≤	≤	NUM
ejpam-4784	52	1	∫	∫	PROPN
ejpam-4784	52	2	b	b	PROPN
ejpam-4784	52	3	a	a	DET
ejpam-4784	52	4	ω(†)ζ	ω(†)ζ	ADJ
ejpam-4784	52	5	(	(	PUNCT
ejpam-4784	52	6	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	52	7	.	.	PUNCT
ejpam-4784	53	1	(	(	PUNCT
ejpam-4784	53	2	1	1	X
ejpam-4784	53	3	)	)	PUNCT
ejpam-4784	53	4	in	in	ADP
ejpam-4784	53	5	this	this	DET
ejpam-4784	53	6	article	article	NOUN
ejpam-4784	53	7	we	we	PRON
ejpam-4784	53	8	generalize	generalize	VERB
ejpam-4784	53	9	jensen	jensen	PROPN
ejpam-4784	53	10	mercer	mercer	PROPN
ejpam-4784	53	11	inequality	inequality	PROPN
ejpam-4784	53	12	for	for	ADP
ejpam-4784	53	13	∆−integral	∆−integral	PROPN
ejpam-4784	53	14	.	.	PUNCT
ejpam-4784	54	1	also	also	ADV
ejpam-4784	54	2	give	give	VERB
ejpam-4784	54	3	generalization	generalization	NOUN
ejpam-4784	54	4	and	and	CCONJ
ejpam-4784	54	5	refinement	refinement	NOUN
ejpam-4784	54	6	of	of	ADP
ejpam-4784	54	7	ky	ky	PROPN
ejpam-4784	54	8	fan	fan	PROPN
ejpam-4784	54	9	inequality	inequality	PROPN
ejpam-4784	54	10	and	and	CCONJ
ejpam-4784	54	11	its	its	PRON
ejpam-4784	54	12	related	related	ADJ
ejpam-4784	54	13	results	result	NOUN
ejpam-4784	54	14	for	for	ADP
ejpam-4784	54	15	∆−integral	∆−integral	ADJ
ejpam-4784	54	16	.	.	PUNCT
ejpam-4784	55	1	we	we	PRON
ejpam-4784	55	2	establish	establish	VERB
ejpam-4784	55	3	a	a	DET
ejpam-4784	55	4	jensen	jensen	PROPN
ejpam-4784	55	5	mercer	mercer	PROPN
ejpam-4784	55	6	∆−integral	∆−integral	PROPN
ejpam-4784	55	7	inequality	inequality	NOUN
ejpam-4784	55	8	.	.	PUNCT
ejpam-4784	56	1	before	before	SCONJ
ejpam-4784	56	2	we	we	PRON
ejpam-4784	56	3	further	far	ADV
ejpam-4784	56	4	proceed	proceed	VERB
ejpam-4784	56	5	we	we	PRON
ejpam-4784	56	6	recall	recall	VERB
ejpam-4784	56	7	here	here	ADV
ejpam-4784	56	8	a	a	DET
ejpam-4784	56	9	lemma	lemma	PROPN
ejpam-4784	56	10	from	from	ADP
ejpam-4784	56	11	[	[	X
ejpam-4784	56	12	19	19	NUM
ejpam-4784	56	13	]	]	PUNCT
ejpam-4784	56	14	stated	state	VERB
ejpam-4784	56	15	as	as	ADP
ejpam-4784	56	16	under	under	ADV
ejpam-4784	56	17	:	:	PUNCT
ejpam-4784	56	18	lemma	lemma	PROPN
ejpam-4784	56	19	1	1	X
ejpam-4784	56	20	.	.	PUNCT
ejpam-4784	57	1	let	let	VERB
ejpam-4784	57	2	ζ	ζ	NOUN
ejpam-4784	57	3	:	:	PUNCT
ejpam-4784	58	1	[	[	X
ejpam-4784	58	2	µ	µ	X
ejpam-4784	58	3	,	,	PUNCT
ejpam-4784	58	4	ν	ν	X
ejpam-4784	58	5	]	]	X
ejpam-4784	58	6	⊂	⊂	PROPN
ejpam-4784	59	1	i	i	PRON
ejpam-4784	59	2	→	→	PUNCT
ejpam-4784	59	3	r	r	NOUN
ejpam-4784	59	4	be	be	AUX
ejpam-4784	59	5	a	a	DET
ejpam-4784	59	6	convex	convex	NOUN
ejpam-4784	59	7	function	function	NOUN
ejpam-4784	59	8	and	and	CCONJ
ejpam-4784	59	9	xi	xi	ADP
ejpam-4784	59	10	∈	∈	PROPN
ejpam-4784	60	1	[	[	X
ejpam-4784	60	2	µ	µ	X
ejpam-4784	60	3	,	,	PUNCT
ejpam-4784	60	4	ν	ν	X
ejpam-4784	60	5	]	]	PUNCT
ejpam-4784	60	6	.	.	PUNCT
ejpam-4784	61	1	then	then	ADV
ejpam-4784	61	2	ζ	ζ	X
ejpam-4784	61	3	(	(	PUNCT
ejpam-4784	61	4	µ+	µ+	NOUN
ejpam-4784	61	5	ν	ν	X
ejpam-4784	61	6	−	−	NOUN
ejpam-4784	61	7	xi	xi	NOUN
ejpam-4784	61	8	)	)	PUNCT
ejpam-4784	61	9	≤	≤	NOUN
ejpam-4784	61	10	ζ	ζ	X
ejpam-4784	61	11	(	(	PUNCT
ejpam-4784	61	12	µ	µ	NOUN
ejpam-4784	61	13	)	)	PUNCT
ejpam-4784	61	14	+	+	CCONJ
ejpam-4784	61	15	ζ	ζ	X
ejpam-4784	61	16	(	(	PUNCT
ejpam-4784	61	17	v)−	v)−	NOUN
ejpam-4784	61	18	ζ	ζ	X
ejpam-4784	61	19	(	(	PUNCT
ejpam-4784	61	20	xi	xi	PROPN
ejpam-4784	61	21	)	)	PUNCT
ejpam-4784	61	22	,	,	PUNCT
ejpam-4784	61	23	1	1	NUM
ejpam-4784	61	24	≤	≤	NUM
ejpam-4784	61	25	i	i	PRON
ejpam-4784	61	26	≤	≤	PROPN
ejpam-4784	61	27	n.	n.	NOUN
ejpam-4784	61	28	theorem	theorem	VERB
ejpam-4784	61	29	1	1	NUM
ejpam-4784	61	30	.	.	PUNCT
ejpam-4784	62	1	if	if	SCONJ
ejpam-4784	62	2	g	g	PROPN
ejpam-4784	62	3	∈	∈	PROPN
ejpam-4784	62	4	c([a	c([a	PROPN
ejpam-4784	62	5	,	,	PUNCT
ejpam-4784	62	6	b]t	b]t	NOUN
ejpam-4784	62	7	,	,	PUNCT
ejpam-4784	62	8	[	[	X
ejpam-4784	62	9	µ	µ	X
ejpam-4784	62	10	,	,	PUNCT
ejpam-4784	62	11	ν	ν	NOUN
ejpam-4784	62	12	]	]	PUNCT
ejpam-4784	62	13	)	)	PUNCT
ejpam-4784	62	14	and	and	CCONJ
ejpam-4784	62	15	ω	ω	NUM
ejpam-4784	62	16	∈	∈	PROPN
ejpam-4784	62	17	c([a	c([a	NOUN
ejpam-4784	62	18	,	,	PUNCT
ejpam-4784	62	19	b]t	b]t	NOUN
ejpam-4784	62	20	,	,	PUNCT
ejpam-4784	62	21	[	[	X
ejpam-4784	62	22	µ	µ	X
ejpam-4784	62	23	,	,	PUNCT
ejpam-4784	62	24	ν	ν	X
ejpam-4784	62	25	]	]	PUNCT
ejpam-4784	62	26	)	)	PUNCT
ejpam-4784	62	27	is	be	AUX
ejpam-4784	62	28	a	a	DET
ejpam-4784	62	29	probability	probability	NOUN
ejpam-4784	62	30	density	density	NOUN
ejpam-4784	62	31	function	function	NOUN
ejpam-4784	62	32	and	and	CCONJ
ejpam-4784	62	33	also	also	ADV
ejpam-4784	62	34	ζ	ζ	PROPN
ejpam-4784	62	35	∈	∈	PROPN
ejpam-4784	62	36	c([µ	c([µ	NOUN
ejpam-4784	62	37	,	,	PUNCT
ejpam-4784	62	38	ν],r	ν],r	NOUN
ejpam-4784	62	39	)	)	PUNCT
ejpam-4784	62	40	is	be	AUX
ejpam-4784	62	41	convex	convex	PROPN
ejpam-4784	62	42	,	,	PUNCT
ejpam-4784	62	43	then	then	ADV
ejpam-4784	62	44	ζ	ζ	X
ejpam-4784	62	45	(	(	PUNCT
ejpam-4784	62	46	µ+	µ+	NOUN
ejpam-4784	62	47	ν	ν	X
ejpam-4784	62	48	−	−	PROPN
ejpam-4784	63	1	∫	∫	PROPN
ejpam-4784	63	2	b	b	PROPN
ejpam-4784	63	3	a	a	DET
ejpam-4784	63	4	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	63	5	)	)	PUNCT
ejpam-4784	63	6	≤	≤	NOUN
ejpam-4784	63	7	ζ	ζ	X
ejpam-4784	63	8	(	(	PUNCT
ejpam-4784	63	9	µ	µ	NOUN
ejpam-4784	63	10	)	)	PUNCT
ejpam-4784	63	11	+	+	CCONJ
ejpam-4784	63	12	ζ	ζ	X
ejpam-4784	63	13	(	(	PUNCT
ejpam-4784	63	14	v	v	NOUN
ejpam-4784	63	15	)	)	PUNCT
ejpam-4784	63	16	−	−	PROPN
ejpam-4784	64	1	∫	∫	PROPN
ejpam-4784	64	2	b	b	PROPN
ejpam-4784	64	3	a	a	DET
ejpam-4784	64	4	ω(†)ζ	ω(†)ζ	ADJ
ejpam-4784	64	5	(	(	PUNCT
ejpam-4784	64	6	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	64	7	.	.	PUNCT
ejpam-4784	65	1	(	(	PUNCT
ejpam-4784	65	2	2	2	X
ejpam-4784	65	3	)	)	PUNCT
ejpam-4784	65	4	s.	s.	PROPN
ejpam-4784	65	5	chanan	chanan	PROPN
ejpam-4784	65	6	,	,	PUNCT
ejpam-4784	65	7	n.	n.	PROPN
ejpam-4784	65	8	irshad	irshad	PROPN
ejpam-4784	65	9	,	,	PUNCT
ejpam-4784	65	10	a.	a.	PROPN
ejpam-4784	65	11	khan	khan	PROPN
ejpam-4784	65	12	/	/	SYM
ejpam-4784	65	13	eur	eur	PROPN
ejpam-4784	65	14	.	.	PUNCT
ejpam-4784	66	1	j.	j.	PROPN
ejpam-4784	66	2	pure	pure	PROPN
ejpam-4784	66	3	appl	appl	PROPN
ejpam-4784	66	4	.	.	PROPN
ejpam-4784	66	5	math	math	PROPN
ejpam-4784	66	6	,	,	PUNCT
ejpam-4784	66	7	16	16	NUM
ejpam-4784	66	8	(	(	PUNCT
ejpam-4784	66	9	3	3	NUM
ejpam-4784	66	10	)	)	PUNCT
ejpam-4784	66	11	(	(	PUNCT
ejpam-4784	66	12	2023	2023	NUM
ejpam-4784	66	13	)	)	PUNCT
ejpam-4784	66	14	,	,	PUNCT
ejpam-4784	66	15	1448	1448	NUM
ejpam-4784	66	16	-	-	SYM
ejpam-4784	66	17	1463	1463	NUM
ejpam-4784	66	18	1451	1451	NUM
ejpam-4784	66	19	proof	proof	NOUN
ejpam-4784	66	20	.	.	PUNCT
ejpam-4784	67	1	since	since	SCONJ
ejpam-4784	67	2	ζ	ζ	NOUN
ejpam-4784	67	3	is	be	AUX
ejpam-4784	67	4	convex	convex	ADJ
ejpam-4784	67	5	function	function	NOUN
ejpam-4784	67	6	and	and	CCONJ
ejpam-4784	67	7	(	(	PUNCT
ejpam-4784	67	8	µ+	µ+	ADP
ejpam-4784	67	9	ν	ν	X
ejpam-4784	67	10	−	−	PROPN
ejpam-4784	67	11	∫	∫	PROPN
ejpam-4784	67	12	b	b	PROPN
ejpam-4784	67	13	a	a	DET
ejpam-4784	67	14	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	67	15	)	)	PUNCT
ejpam-4784	67	16	∈	∈	PROPN
ejpam-4784	68	1	[	[	X
ejpam-4784	68	2	µ	µ	X
ejpam-4784	68	3	,	,	PUNCT
ejpam-4784	68	4	ν	ν	X
ejpam-4784	68	5	]	]	PUNCT
ejpam-4784	68	6	,	,	PUNCT
ejpam-4784	68	7	therefore	therefore	ADV
ejpam-4784	68	8	by	by	ADP
ejpam-4784	68	9	inequality	inequality	NOUN
ejpam-4784	68	10	(	(	PUNCT
ejpam-4784	68	11	1	1	NUM
ejpam-4784	68	12	)	)	PUNCT
ejpam-4784	68	13	and	and	CCONJ
ejpam-4784	68	14	lemma	lemma	PROPN
ejpam-4784	68	15	1	1	NUM
ejpam-4784	68	16	,	,	PUNCT
ejpam-4784	68	17	we	we	PRON
ejpam-4784	68	18	have	have	VERB
ejpam-4784	68	19	ζ	ζ	NOUN
ejpam-4784	68	20	(	(	PUNCT
ejpam-4784	68	21	µ+	µ+	NOUN
ejpam-4784	68	22	ν	ν	X
ejpam-4784	68	23	−	−	PROPN
ejpam-4784	68	24	∫	∫	PROPN
ejpam-4784	68	25	b	b	PROPN
ejpam-4784	68	26	a	a	DET
ejpam-4784	68	27	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	68	28	)	)	PUNCT
ejpam-4784	68	29	=	=	SYM
ejpam-4784	68	30	ζ	ζ	NOUN
ejpam-4784	68	31	(	(	PUNCT
ejpam-4784	68	32	∫	∫	PROPN
ejpam-4784	68	33	b	b	PROPN
ejpam-4784	68	34	a	a	DET
ejpam-4784	68	35	ω(†)(µ+	ω(†)(µ+	ADP
ejpam-4784	68	36	ν	ν	X
ejpam-4784	68	37	−	−	PROPN
ejpam-4784	68	38	g(η))∆η	g(η))∆η	PROPN
ejpam-4784	68	39	)	)	PUNCT
ejpam-4784	68	40	≤	≤	NUM
ejpam-4784	69	1	∫	∫	PROPN
ejpam-4784	70	1	b	b	PROPN
ejpam-4784	70	2	a	a	DET
ejpam-4784	70	3	ω(†	ω(†	NOUN
ejpam-4784	70	4	)	)	PUNCT
ejpam-4784	71	1	[	[	X
ejpam-4784	71	2	ζ	ζ	X
ejpam-4784	71	3	(	(	PUNCT
ejpam-4784	71	4	µ+	µ+	NOUN
ejpam-4784	71	5	ν	ν	X
ejpam-4784	71	6	−	−	X
ejpam-4784	71	7	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	71	8	]	]	X
ejpam-4784	71	9	=	=	SYM
ejpam-4784	71	10	ζ	ζ	X
ejpam-4784	71	11	(	(	PUNCT
ejpam-4784	71	12	µ	µ	NOUN
ejpam-4784	71	13	)	)	PUNCT
ejpam-4784	71	14	+	+	CCONJ
ejpam-4784	71	15	ζ	ζ	X
ejpam-4784	71	16	(	(	PUNCT
ejpam-4784	71	17	v)−	v)−	PROPN
ejpam-4784	71	18	∫	∫	PROPN
ejpam-4784	71	19	b	b	PROPN
ejpam-4784	71	20	a	a	DET
ejpam-4784	71	21	ω(†)ζ	ω(†)ζ	ADJ
ejpam-4784	71	22	(	(	PUNCT
ejpam-4784	71	23	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	71	24	.	.	PUNCT
ejpam-4784	71	25	corollary	corollary	ADJ
ejpam-4784	71	26	1	1	NUM
ejpam-4784	71	27	.	.	PUNCT
ejpam-4784	72	1	let	let	VERB
ejpam-4784	72	2	t	t	NOUN
ejpam-4784	72	3	=	=	SYM
ejpam-4784	72	4	r	r	NOUN
ejpam-4784	72	5	and	and	CCONJ
ejpam-4784	72	6	by	by	ADP
ejpam-4784	72	7	considering	consider	VERB
ejpam-4784	72	8	assumptions	assumption	NOUN
ejpam-4784	72	9	of	of	ADP
ejpam-4784	72	10	theorem	theorem	NOUN
ejpam-4784	72	11	1	1	NUM
ejpam-4784	72	12	.	.	PUNCT
ejpam-4784	73	1	then	then	ADV
ejpam-4784	73	2	ζ	ζ	X
ejpam-4784	73	3	(	(	PUNCT
ejpam-4784	73	4	µ+	µ+	NOUN
ejpam-4784	73	5	ν	ν	X
ejpam-4784	73	6	−	−	PROPN
ejpam-4784	73	7	∫	∫	PROPN
ejpam-4784	73	8	b	b	PROPN
ejpam-4784	73	9	a	a	PRON
ejpam-4784	73	10	ω(†)g(η)dη	ω(†)g(η)dη	NUM
ejpam-4784	73	11	)	)	PUNCT
ejpam-4784	73	12	≤	≤	NUM
ejpam-4784	73	13	ζ	ζ	X
ejpam-4784	73	14	(	(	PUNCT
ejpam-4784	73	15	µ	µ	NOUN
ejpam-4784	73	16	)	)	PUNCT
ejpam-4784	73	17	+	+	CCONJ
ejpam-4784	73	18	ζ	ζ	X
ejpam-4784	73	19	(	(	PUNCT
ejpam-4784	73	20	v	v	NOUN
ejpam-4784	73	21	)	)	PUNCT
ejpam-4784	73	22	−	−	PROPN
ejpam-4784	74	1	∫	∫	PROPN
ejpam-4784	74	2	b	b	PROPN
ejpam-4784	74	3	a	a	DET
ejpam-4784	74	4	ω(†)ζ	ω(†)ζ	ADJ
ejpam-4784	74	5	(	(	PUNCT
ejpam-4784	74	6	g(η	g(η	VERB
ejpam-4784	74	7	)	)	PUNCT
ejpam-4784	74	8	)	)	PUNCT
ejpam-4784	75	1	dη	dη	NOUN
ejpam-4784	75	2	.	.	PUNCT
ejpam-4784	76	1	(	(	PUNCT
ejpam-4784	76	2	3	3	X
ejpam-4784	76	3	)	)	PUNCT
ejpam-4784	76	4	1.1	1.1	NUM
ejpam-4784	76	5	.	.	PUNCT
ejpam-4784	77	1	cases	case	NOUN
ejpam-4784	77	2	(	(	PUNCT
ejpam-4784	77	3	i	i	NOUN
ejpam-4784	77	4	)	)	PUNCT
ejpam-4784	77	5	let	let	VERB
ejpam-4784	77	6	g(η	g(η	VERB
ejpam-4784	77	7	)	)	PUNCT
ejpam-4784	77	8	>	>	X
ejpam-4784	77	9	0	0	PUNCT
ejpam-4784	78	1	on	on	ADP
ejpam-4784	78	2	[	[	X
ejpam-4784	78	3	a	a	DET
ejpam-4784	78	4	,	,	PUNCT
ejpam-4784	78	5	b]t	b]t	NOUN
ejpam-4784	78	6	and	and	CCONJ
ejpam-4784	78	7	ζ(†	ζ(†	NOUN
ejpam-4784	78	8	)	)	PUNCT
ejpam-4784	78	9	=	=	SYM
ejpam-4784	78	10	tβ	tβ	PROPN
ejpam-4784	78	11	is	be	AUX
ejpam-4784	78	12	convex	convex	ADJ
ejpam-4784	78	13	and	and	CCONJ
ejpam-4784	78	14	concave	concave	VERB
ejpam-4784	78	15	on	on	ADP
ejpam-4784	78	16	(	(	PUNCT
ejpam-4784	78	17	0,+∞	0,+∞	NUM
ejpam-4784	78	18	)	)	PUNCT
ejpam-4784	78	19	for	for	ADP
ejpam-4784	78	20	β	β	X
ejpam-4784	78	21	<	<	X
ejpam-4784	78	22	0	0	NUM
ejpam-4784	78	23	or	or	CCONJ
ejpam-4784	78	24	β	β	ADJ
ejpam-4784	78	25	>	>	X
ejpam-4784	78	26	1	1	NUM
ejpam-4784	78	27	and	and	CCONJ
ejpam-4784	78	28	for	for	ADP
ejpam-4784	78	29	β	β	X
ejpam-4784	78	30	∈	∈	PROPN
ejpam-4784	78	31	(	(	PUNCT
ejpam-4784	78	32	0	0	NUM
ejpam-4784	78	33	,	,	PUNCT
ejpam-4784	78	34	1	1	NUM
ejpam-4784	78	35	)	)	PUNCT
ejpam-4784	78	36	respectively	respectively	ADV
ejpam-4784	78	37	.	.	PUNCT
ejpam-4784	79	1	then	then	ADV
ejpam-4784	79	2	ζ	ζ	X
ejpam-4784	79	3	(	(	PUNCT
ejpam-4784	79	4	µ+	µ+	NOUN
ejpam-4784	79	5	ν	ν	X
ejpam-4784	79	6	−	−	PROPN
ejpam-4784	79	7	∫	∫	PROPN
ejpam-4784	79	8	b	b	PROPN
ejpam-4784	79	9	a	a	DET
ejpam-4784	79	10	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	79	11	)	)	PUNCT
ejpam-4784	79	12	β	β	NOUN
ejpam-4784	79	13	≤	≤	ADJ
ejpam-4784	79	14	ζ	ζ	NOUN
ejpam-4784	79	15	(	(	PUNCT
ejpam-4784	79	16	µ)β	µ)β	PUNCT
ejpam-4784	79	17	+	+	CCONJ
ejpam-4784	79	18	ζ	ζ	NOUN
ejpam-4784	79	19	(	(	PUNCT
ejpam-4784	79	20	v)β	v)β	NOUN
ejpam-4784	79	21	−	−	PROPN
ejpam-4784	79	22	∫	∫	PROPN
ejpam-4784	79	23	b	b	PROPN
ejpam-4784	79	24	a	a	DET
ejpam-4784	79	25	ω(†)ζ	ω(†)ζ	ADJ
ejpam-4784	79	26	(	(	PUNCT
ejpam-4784	79	27	g(η))β	g(η))β	NOUN
ejpam-4784	79	28	∆η	∆η	PROPN
ejpam-4784	79	29	,	,	PUNCT
ejpam-4784	79	30	β	β	X
ejpam-4784	79	31	<	<	X
ejpam-4784	79	32	0	0	NUM
ejpam-4784	79	33	or	or	CCONJ
ejpam-4784	79	34	β	β	ADJ
ejpam-4784	79	35	>	>	X
ejpam-4784	79	36	1	1	NUM
ejpam-4784	79	37	,	,	PUNCT
ejpam-4784	79	38	(	(	PUNCT
ejpam-4784	79	39	4	4	X
ejpam-4784	79	40	)	)	PUNCT
ejpam-4784	79	41	ζ	ζ	NOUN
ejpam-4784	79	42	(	(	PUNCT
ejpam-4784	79	43	µ+	µ+	NOUN
ejpam-4784	79	44	ν	ν	X
ejpam-4784	79	45	−	−	PROPN
ejpam-4784	79	46	∫	∫	PROPN
ejpam-4784	79	47	b	b	PROPN
ejpam-4784	79	48	a	a	DET
ejpam-4784	79	49	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	79	50	)	)	PUNCT
ejpam-4784	79	51	β	β	X
ejpam-4784	79	52	≥	≥	PROPN
ejpam-4784	79	53	ζ	ζ	NOUN
ejpam-4784	79	54	(	(	PUNCT
ejpam-4784	79	55	µ)β	µ)β	NOUN
ejpam-4784	79	56	+	+	CCONJ
ejpam-4784	79	57	ζ	ζ	NOUN
ejpam-4784	79	58	(	(	PUNCT
ejpam-4784	79	59	v)β	v)β	NOUN
ejpam-4784	79	60	−	−	PROPN
ejpam-4784	79	61	∫	∫	PROPN
ejpam-4784	79	62	b	b	PROPN
ejpam-4784	79	63	a	a	DET
ejpam-4784	79	64	ω(†)ζ	ω(†)ζ	ADJ
ejpam-4784	79	65	(	(	PUNCT
ejpam-4784	79	66	g(η))β	g(η))β	NOUN
ejpam-4784	79	67	∆η	∆η	PROPN
ejpam-4784	79	68	,	,	PUNCT
ejpam-4784	79	69	β	β	X
ejpam-4784	79	70	∈	∈	PROPN
ejpam-4784	79	71	(	(	PUNCT
ejpam-4784	79	72	0	0	NUM
ejpam-4784	79	73	,	,	PUNCT
ejpam-4784	79	74	1	1	NUM
ejpam-4784	79	75	)	)	PUNCT
ejpam-4784	79	76	.	.	PUNCT
ejpam-4784	80	1	(	(	PUNCT
ejpam-4784	80	2	5	5	NUM
ejpam-4784	80	3	)	)	PUNCT
ejpam-4784	80	4	(	(	PUNCT
ejpam-4784	80	5	ii	ii	NOUN
ejpam-4784	80	6	)	)	PUNCT
ejpam-4784	80	7	let	let	VERB
ejpam-4784	80	8	g(η	g(η	VERB
ejpam-4784	80	9	)	)	PUNCT
ejpam-4784	80	10	>	>	X
ejpam-4784	80	11	0	0	PUNCT
ejpam-4784	81	1	on	on	ADP
ejpam-4784	81	2	[	[	X
ejpam-4784	81	3	a	a	DET
ejpam-4784	81	4	,	,	PUNCT
ejpam-4784	81	5	b]t	b]t	NOUN
ejpam-4784	81	6	and	and	CCONJ
ejpam-4784	81	7	ζ(†	ζ(†	NOUN
ejpam-4784	81	8	)	)	PUNCT
ejpam-4784	81	9	=	=	SYM
ejpam-4784	81	10	ln(†	ln(†	X
ejpam-4784	81	11	)	)	PUNCT
ejpam-4784	81	12	is	be	AUX
ejpam-4784	81	13	concave	concave	VERB
ejpam-4784	81	14	on	on	ADP
ejpam-4784	81	15	(	(	PUNCT
ejpam-4784	81	16	0,+∞	0,+∞	NUM
ejpam-4784	81	17	)	)	PUNCT
ejpam-4784	81	18	.	.	PUNCT
ejpam-4784	82	1	then	then	ADV
ejpam-4784	82	2	ln	ln	INTJ
ejpam-4784	82	3	(	(	PUNCT
ejpam-4784	82	4	µ+	µ+	ADP
ejpam-4784	82	5	ν	ν	X
ejpam-4784	82	6	−	−	PROPN
ejpam-4784	82	7	∫	∫	PROPN
ejpam-4784	82	8	b	b	PROPN
ejpam-4784	82	9	a	a	DET
ejpam-4784	82	10	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	82	11	)	)	PUNCT
ejpam-4784	82	12	≤	≤	NOUN
ejpam-4784	82	13	ln	ln	ADJ
ejpam-4784	82	14	(	(	PUNCT
ejpam-4784	82	15	µ	µ	NOUN
ejpam-4784	82	16	)	)	PUNCT
ejpam-4784	82	17	+	+	CCONJ
ejpam-4784	82	18	ln	ln	ADJ
ejpam-4784	82	19	(	(	PUNCT
ejpam-4784	82	20	v)−	v)−	PROPN
ejpam-4784	82	21	∫	∫	PROPN
ejpam-4784	82	22	b	b	PROPN
ejpam-4784	82	23	a	a	DET
ejpam-4784	82	24	ω(†	ω(†	NOUN
ejpam-4784	82	25	)	)	PUNCT
ejpam-4784	82	26	ln	ln	NOUN
ejpam-4784	82	27	(	(	PUNCT
ejpam-4784	82	28	g(η))∆η	g(η))∆η	PROPN
ejpam-4784	82	29	.	.	PUNCT
ejpam-4784	83	1	s.	s.	PROPN
ejpam-4784	83	2	chanan	chanan	PROPN
ejpam-4784	83	3	,	,	PUNCT
ejpam-4784	83	4	n.	n.	PROPN
ejpam-4784	83	5	irshad	irshad	PROPN
ejpam-4784	83	6	,	,	PUNCT
ejpam-4784	83	7	a.	a.	PROPN
ejpam-4784	83	8	khan	khan	PROPN
ejpam-4784	83	9	/	/	SYM
ejpam-4784	83	10	eur	eur	PROPN
ejpam-4784	83	11	.	.	PUNCT
ejpam-4784	84	1	j.	j.	PROPN
ejpam-4784	84	2	pure	pure	PROPN
ejpam-4784	84	3	appl	appl	PROPN
ejpam-4784	84	4	.	.	PROPN
ejpam-4784	84	5	math	math	PROPN
ejpam-4784	84	6	,	,	PUNCT
ejpam-4784	84	7	16	16	NUM
ejpam-4784	84	8	(	(	PUNCT
ejpam-4784	84	9	3	3	NUM
ejpam-4784	84	10	)	)	PUNCT
ejpam-4784	84	11	(	(	PUNCT
ejpam-4784	84	12	2023	2023	NUM
ejpam-4784	84	13	)	)	PUNCT
ejpam-4784	84	14	,	,	PUNCT
ejpam-4784	84	15	1448	1448	NUM
ejpam-4784	84	16	-	-	SYM
ejpam-4784	84	17	1463	1463	NUM
ejpam-4784	84	18	1452	1452	NUM
ejpam-4784	84	19	(	(	PUNCT
ejpam-4784	84	20	iii	iii	NOUN
ejpam-4784	84	21	)	)	PUNCT
ejpam-4784	84	22	let	let	VERB
ejpam-4784	84	23	t	t	NOUN
ejpam-4784	84	24	=	=	PUNCT
ejpam-4784	84	25	z	z	PROPN
ejpam-4784	84	26	and	and	CCONJ
ejpam-4784	84	27	m	m	PROPN
ejpam-4784	84	28	∈	∈	PROPN
ejpam-4784	84	29	n.	n.	NOUN
ejpam-4784	84	30	fix	fix	VERB
ejpam-4784	84	31	a	a	DET
ejpam-4784	84	32	=	=	SYM
ejpam-4784	84	33	1	1	NUM
ejpam-4784	84	34	and	and	CCONJ
ejpam-4784	84	35	b	b	X
ejpam-4784	84	36	=	=	NOUN
ejpam-4784	84	37	m	m	VERB
ejpam-4784	84	38	+	+	ADJ
ejpam-4784	84	39	1	1	NUM
ejpam-4784	84	40	,	,	PUNCT
ejpam-4784	84	41	let	let	VERB
ejpam-4784	84	42	g	g	NOUN
ejpam-4784	84	43	:	:	PUNCT
ejpam-4784	84	44	{	{	PUNCT
ejpam-4784	84	45	1	1	NUM
ejpam-4784	84	46	,	,	PUNCT
ejpam-4784	84	47	.	.	PUNCT
ejpam-4784	84	48	.	.	PUNCT
ejpam-4784	84	49	.	.	PUNCT
ejpam-4784	85	1	,	,	PUNCT
ejpam-4784	85	2	m	m	VERB
ejpam-4784	85	3	+	+	ADJ
ejpam-4784	85	4	1	1	NUM
ejpam-4784	85	5	}	}	PUNCT
ejpam-4784	85	6	→	→	X
ejpam-4784	85	7	(	(	PUNCT
ejpam-4784	85	8	0,∞	0,∞	NUM
ejpam-4784	85	9	)	)	PUNCT
ejpam-4784	85	10	,	,	PUNCT
ejpam-4784	85	11	ζ	ζ	NOUN
ejpam-4784	85	12	=	=	SYM
ejpam-4784	85	13	−	−	PROPN
ejpam-4784	85	14	lnx	lnx	PROPN
ejpam-4784	85	15	is	be	AUX
ejpam-4784	85	16	convex	convex	ADJ
ejpam-4784	85	17	on	on	ADP
ejpam-4784	85	18	(	(	PUNCT
ejpam-4784	85	19	0,+∞	0,+∞	NUM
ejpam-4784	85	20	)	)	PUNCT
ejpam-4784	85	21	and	and	CCONJ
ejpam-4784	85	22	by	by	ADP
ejpam-4784	85	23	using	use	VERB
ejpam-4784	85	24	theorem	theorem	NOUN
ejpam-4784	85	25	1	1	NUM
ejpam-4784	85	26	,	,	PUNCT
ejpam-4784	85	27	we	we	PRON
ejpam-4784	85	28	get	get	VERB
ejpam-4784	85	29	ln	ln	ADJ
ejpam-4784	85	30	µ+	µ+	NOUN
ejpam-4784	85	31	ν	ν	NOUN
ejpam-4784	85	32	−	−	NOUN
ejpam-4784	85	33	m∑	m∑	ADV
ejpam-4784	85	34	†=1	†=1	CCONJ
ejpam-4784	85	35	g(†	g(†	NOUN
ejpam-4784	85	36	)	)	PUNCT
ejpam-4784	86	1			PROPN
ejpam-4784	86	2	=	=	SYM
ejpam-4784	86	3	ln	ln	NOUN
ejpam-4784	86	4	(	(	PUNCT
ejpam-4784	86	5	µ+	µ+	NOUN
ejpam-4784	86	6	ν	ν	NOUN
ejpam-4784	86	7	−	−	PROPN
ejpam-4784	86	8	∫	∫	NOUN
ejpam-4784	86	9	m+1	m+1	NUM
ejpam-4784	86	10	1	1	NUM
ejpam-4784	86	11	g(η)∆η	g(η)∆η	PROPN
ejpam-4784	86	12	)	)	PUNCT
ejpam-4784	86	13	≥	≥	NOUN
ejpam-4784	86	14	ln	ln	X
ejpam-4784	86	15	(	(	PUNCT
ejpam-4784	86	16	µ	µ	NOUN
ejpam-4784	86	17	)	)	PUNCT
ejpam-4784	86	18	+	+	CCONJ
ejpam-4784	86	19	ln	ln	ADJ
ejpam-4784	86	20	(	(	PUNCT
ejpam-4784	86	21	v)−	v)−	PROPN
ejpam-4784	86	22	∫	∫	PROPN
ejpam-4784	87	1	m+1	m+1	NUM
ejpam-4784	87	2	1	1	NUM
ejpam-4784	87	3	ln	ln	ADJ
ejpam-4784	87	4	(	(	PUNCT
ejpam-4784	87	5	g(η))∆η	g(η))∆η	PROPN
ejpam-4784	87	6	=	=	SYM
ejpam-4784	87	7	ln	ln	ADJ
ejpam-4784	87	8	(	(	PUNCT
ejpam-4784	87	9	µν)−	µν)−	ADJ
ejpam-4784	87	10			NOUN
ejpam-4784	87	11	m∑	m∑	ADV
ejpam-4784	87	12	†=1	†=1	NOUN
ejpam-4784	87	13	ln(g(†	ln(g(†	NOUN
ejpam-4784	87	14	)	)	PUNCT
ejpam-4784	87	15	)	)	PUNCT
ejpam-4784	87	16			NOUN
ejpam-4784	87	17	=	=	PUNCT
ejpam-4784	87	18	ln	ln	ADJ
ejpam-4784	87	19	(	(	PUNCT
ejpam-4784	87	20	µν)−	µν)−	ADV
ejpam-4784	87	21	ln	ln	PROPN
ejpam-4784	87	22			PROPN
ejpam-4784	87	23	m∏	m∏	PROPN
ejpam-4784	87	24	†=1	†=1	NOUN
ejpam-4784	87	25	g(†	g(†	NOUN
ejpam-4784	87	26	)	)	PUNCT
ejpam-4784	87	27			NOUN
ejpam-4784	87	28	,	,	PUNCT
ejpam-4784	87	29	and	and	CCONJ
ejpam-4784	87	30	hence	hence	ADV
ejpam-4784	87	31	ln	ln	ADJ
ejpam-4784	87	32	µ+	µ+	ADJ
ejpam-4784	87	33	ν	ν	NOUN
ejpam-4784	87	34	−	−	NOUN
ejpam-4784	87	35	m∑	m∑	ADV
ejpam-4784	87	36	†=1	†=1	CCONJ
ejpam-4784	87	37	g(†	g(†	NOUN
ejpam-4784	87	38	)	)	PUNCT
ejpam-4784	87	39			PROPN
ejpam-4784	87	40	≥	≥	PUNCT
ejpam-4784	87	41	ln	ln	NOUN
ejpam-4784	88	1	(	(	PUNCT
ejpam-4784	89	1	µν)	µν)	PROPN
ejpam-4784	89	2	m∏	m∏	PROPN
ejpam-4784	89	3	†=1	†=1	NOUN
ejpam-4784	89	4	g(†	g(†	NOUN
ejpam-4784	89	5	)	)	PUNCT
ejpam-4784	89	6			PROPN
ejpam-4784	89	7	.	.	PUNCT
ejpam-4784	90	1	(	(	PUNCT
ejpam-4784	90	2	iv	iv	X
ejpam-4784	90	3	)	)	PUNCT
ejpam-4784	90	4	let	let	VERB
ejpam-4784	90	5	t	t	NOUN
ejpam-4784	90	6	=	=	SYM
ejpam-4784	90	7	2m⊬	2m⊬	PROPN
ejpam-4784	90	8	and	and	CCONJ
ejpam-4784	90	9	m	m	PROPN
ejpam-4784	90	10	∈	∈	PROPN
ejpam-4784	90	11	n.	n.	NOUN
ejpam-4784	90	12	fix	fix	VERB
ejpam-4784	90	13	a	a	DET
ejpam-4784	90	14	=	=	SYM
ejpam-4784	90	15	1	1	NUM
ejpam-4784	90	16	and	and	CCONJ
ejpam-4784	90	17	b	b	NOUN
ejpam-4784	91	1	=	=	SYM
ejpam-4784	91	2	2	2	NUM
ejpam-4784	91	3	m	m	NOUN
ejpam-4784	92	1	and	and	CCONJ
ejpam-4784	92	2	consider	consider	VERB
ejpam-4784	92	3	a	a	DET
ejpam-4784	92	4	function	function	NOUN
ejpam-4784	92	5	g	g	NOUN
ejpam-4784	92	6	:	:	PUNCT
ejpam-4784	92	7	{	{	PUNCT
ejpam-4784	92	8	2l	2l	NOUN
ejpam-4784	92	9	:	:	PUNCT
ejpam-4784	92	10	0	0	NUM
ejpam-4784	92	11	≤	≤	NUM
ejpam-4784	92	12	l	l	NOUN
ejpam-4784	92	13	≤	≤	NOUN
ejpam-4784	92	14	n	n	CCONJ
ejpam-4784	92	15	}	}	PUNCT
ejpam-4784	92	16	→	→	X
ejpam-4784	92	17	(	(	PUNCT
ejpam-4784	92	18	0,∞	0,∞	NUM
ejpam-4784	92	19	)	)	PUNCT
ejpam-4784	92	20	by	by	ADP
ejpam-4784	92	21	using	use	VERB
ejpam-4784	92	22	theorem	theorem	NOUN
ejpam-4784	92	23	1	1	NUM
ejpam-4784	92	24	,	,	PUNCT
ejpam-4784	92	25	we	we	PRON
ejpam-4784	92	26	get	get	VERB
ejpam-4784	92	27	ln	ln	ADJ
ejpam-4784	92	28	(	(	PUNCT
ejpam-4784	92	29	µ+	µ+	NOUN
ejpam-4784	93	1	ν	ν	NOUN
ejpam-4784	93	2	−	−	PROPN
ejpam-4784	93	3	∫	∫	PROPN
ejpam-4784	93	4	2	2	NUM
ejpam-4784	93	5	m	m	PROPN
ejpam-4784	93	6	1	1	NUM
ejpam-4784	93	7	g(†)∆	g(†)∆	NOUN
ejpam-4784	93	8	)	)	PUNCT
ejpam-4784	94	1	=	=	PUNCT
ejpam-4784	94	2	ln	ln	ADJ
ejpam-4784	94	3	(	(	PUNCT
ejpam-4784	94	4	µ+	µ+	NOUN
ejpam-4784	94	5	ν	ν	X
ejpam-4784	94	6	−	−	PROPN
ejpam-4784	94	7	m−1∑	m−1∑	NUM
ejpam-4784	94	8	l=0	l=0	PROPN
ejpam-4784	94	9	2lg(2l	2lg(2l	PROPN
ejpam-4784	94	10	)	)	PUNCT
ejpam-4784	94	11	)	)	PUNCT
ejpam-4784	95	1	=	=	PUNCT
ejpam-4784	95	2	ln	ln	ADJ
ejpam-4784	95	3	(	(	PUNCT
ejpam-4784	95	4	µ+	µ+	NOUN
ejpam-4784	95	5	ν	ν	NOUN
ejpam-4784	95	6	−	−	PROPN
ejpam-4784	95	7	∫	∫	PROPN
ejpam-4784	95	8	2	2	NUM
ejpam-4784	95	9	m	m	PROPN
ejpam-4784	95	10	1	1	NUM
ejpam-4784	95	11	g(η)∆η	g(η)∆η	PROPN
ejpam-4784	95	12	)	)	PUNCT
ejpam-4784	95	13	≥	≥	NOUN
ejpam-4784	95	14	ln	ln	X
ejpam-4784	95	15	(	(	PUNCT
ejpam-4784	95	16	µ	µ	NOUN
ejpam-4784	95	17	)	)	PUNCT
ejpam-4784	95	18	+	+	CCONJ
ejpam-4784	95	19	ln	ln	ADJ
ejpam-4784	95	20	(	(	PUNCT
ejpam-4784	95	21	v)−	v)−	PROPN
ejpam-4784	95	22	∫	∫	PROPN
ejpam-4784	95	23	2	2	NUM
ejpam-4784	95	24	m	m	PROPN
ejpam-4784	95	25	1	1	NUM
ejpam-4784	95	26	ln	ln	ADJ
ejpam-4784	95	27	(	(	PUNCT
ejpam-4784	95	28	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	95	29	.	.	PUNCT
ejpam-4784	96	1	=	=	SYM
ejpam-4784	96	2	ln	ln	ADJ
ejpam-4784	96	3	(	(	PUNCT
ejpam-4784	96	4	µν)−	µν)−	ADJ
ejpam-4784	96	5	∫	∫	NOUN
ejpam-4784	96	6	2	2	NUM
ejpam-4784	96	7	m	m	NOUN
ejpam-4784	96	8	1	1	NUM
ejpam-4784	96	9	ln	ln	NOUN
ejpam-4784	96	10	(	(	PUNCT
ejpam-4784	96	11	g(†))∆†	g(†))∆†	PROPN
ejpam-4784	96	12	=	=	SYM
ejpam-4784	96	13	ln	ln	ADJ
ejpam-4784	96	14	(	(	PUNCT
ejpam-4784	96	15	µν)−	µν)−	ADJ
ejpam-4784	96	16	m−1∑	m−1∑	NUM
ejpam-4784	96	17	l=0	l=0	PROPN
ejpam-4784	96	18	2l	2l	PROPN
ejpam-4784	96	19	ln	ln	X
ejpam-4784	96	20	(	(	PUNCT
ejpam-4784	96	21	g(2l	g(2l	PROPN
ejpam-4784	96	22	)	)	PUNCT
ejpam-4784	96	23	)	)	PUNCT
ejpam-4784	97	1	s.	s.	PROPN
ejpam-4784	97	2	chanan	chanan	PROPN
ejpam-4784	97	3	,	,	PUNCT
ejpam-4784	97	4	n.	n.	PROPN
ejpam-4784	97	5	irshad	irshad	PROPN
ejpam-4784	97	6	,	,	PUNCT
ejpam-4784	97	7	a.	a.	PROPN
ejpam-4784	97	8	khan	khan	PROPN
ejpam-4784	97	9	/	/	SYM
ejpam-4784	97	10	eur	eur	PROPN
ejpam-4784	97	11	.	.	PUNCT
ejpam-4784	98	1	j.	j.	PROPN
ejpam-4784	98	2	pure	pure	PROPN
ejpam-4784	98	3	appl	appl	PROPN
ejpam-4784	98	4	.	.	PROPN
ejpam-4784	98	5	math	math	PROPN
ejpam-4784	98	6	,	,	PUNCT
ejpam-4784	98	7	16	16	NUM
ejpam-4784	98	8	(	(	PUNCT
ejpam-4784	98	9	3	3	NUM
ejpam-4784	98	10	)	)	PUNCT
ejpam-4784	98	11	(	(	PUNCT
ejpam-4784	98	12	2023	2023	NUM
ejpam-4784	98	13	)	)	PUNCT
ejpam-4784	98	14	,	,	PUNCT
ejpam-4784	98	15	1448	1448	NUM
ejpam-4784	98	16	-	-	SYM
ejpam-4784	98	17	1463	1463	NUM
ejpam-4784	98	18	1453	1453	NUM
ejpam-4784	98	19	=	=	SYM
ejpam-4784	98	20	ln	ln	ADJ
ejpam-4784	98	21	(	(	PUNCT
ejpam-4784	98	22	µν)−	µν)−	ADJ
ejpam-4784	98	23	[	[	PUNCT
ejpam-4784	98	24	ln	ln	ADJ
ejpam-4784	98	25	m−1∏	m−1∏	PROPN
ejpam-4784	98	26	l=0	l=0	PROPN
ejpam-4784	98	27	(	(	PUNCT
ejpam-4784	98	28	g(2l))2	g(2l))2	NOUN
ejpam-4784	98	29	l	l	NOUN
ejpam-4784	98	30	]	]	PUNCT
ejpam-4784	98	31	and	and	CCONJ
ejpam-4784	98	32	hence	hence	ADV
ejpam-4784	98	33	µ+	µ+	ADJ
ejpam-4784	98	34	ν	ν	X
ejpam-4784	98	35	−	−	PROPN
ejpam-4784	98	36	(	(	PUNCT
ejpam-4784	98	37	m−1∑	m−1∑	NUM
ejpam-4784	98	38	l=0	l=0	PROPN
ejpam-4784	98	39	2lg(2l	2lg(2l	PROPN
ejpam-4784	98	40	)	)	PUNCT
ejpam-4784	98	41	)	)	PUNCT
ejpam-4784	98	42	≥	≥	NOUN
ejpam-4784	99	1	µν	µν	ADP
ejpam-4784	99	2	m−1∏	m−1∏	PROPN
ejpam-4784	99	3	l=0	l=0	PROPN
ejpam-4784	99	4	(	(	PUNCT
ejpam-4784	99	5	g(2l	g(2l	PROPN
ejpam-4784	99	6	)	)	PUNCT
ejpam-4784	99	7	)	)	PUNCT
ejpam-4784	99	8	2l	2l	NOUN
ejpam-4784	99	9	.	.	PUNCT
ejpam-4784	100	1	2	2	X
ejpam-4784	100	2	.	.	X
ejpam-4784	100	3	ky	ky	PROPN
ejpam-4784	100	4	fan	fan	PROPN
ejpam-4784	100	5	inequality	inequality	PROPN
ejpam-4784	100	6	and	and	CCONJ
ejpam-4784	100	7	related	related	ADJ
ejpam-4784	100	8	results	result	NOUN
ejpam-4784	100	9	in	in	ADP
ejpam-4784	100	10	1961	1961	NUM
ejpam-4784	100	11	,	,	PUNCT
ejpam-4784	100	12	the	the	DET
ejpam-4784	100	13	ky	ky	PROPN
ejpam-4784	100	14	fan	fan	PROPN
ejpam-4784	100	15	inequality	inequality	PROPN
ejpam-4784	100	16	was	be	AUX
ejpam-4784	100	17	given	give	VERB
ejpam-4784	100	18	in	in	ADP
ejpam-4784	100	19	the	the	DET
ejpam-4784	100	20	famous	famous	ADJ
ejpam-4784	100	21	monograph	monograph	NOUN
ejpam-4784	100	22	‘	'	PUNCT
ejpam-4784	100	23	inequalities	inequality	NOUN
ejpam-4784	100	24	’	'	PUNCT
ejpam-4784	100	25	in	in	ADP
ejpam-4784	100	26	[	[	X
ejpam-4784	100	27	4	4	NUM
ejpam-4784	100	28	]	]	PUNCT
ejpam-4784	100	29	as	as	SCONJ
ejpam-4784	100	30	follow	follow	VERB
ejpam-4784	100	31	:	:	PUNCT
ejpam-4784	100	32	ǧn	ǧn	PROPN
ejpam-4784	100	33	ǧ′	ǧ′	PROPN
ejpam-4784	100	34	n	n	CCONJ
ejpam-4784	100	35	≤	≤	X
ejpam-4784	100	36	ǎn	ǎn	VERB
ejpam-4784	100	37	ǎ′	ǎ′	VERB
ejpam-4784	100	38	n	n	PROPN
ejpam-4784	100	39	,	,	PUNCT
ejpam-4784	100	40	xj	xj	PROPN
ejpam-4784	100	41	∈	∈	PROPN
ejpam-4784	100	42	(	(	PUNCT
ejpam-4784	100	43	0	0	NUM
ejpam-4784	100	44	,	,	PUNCT
ejpam-4784	100	45	1	1	NUM
ejpam-4784	100	46	2	2	NUM
ejpam-4784	100	47	]	]	PUNCT
ejpam-4784	100	48	(	(	PUNCT
ejpam-4784	100	49	6	6	X
ejpam-4784	100	50	)	)	PUNCT
ejpam-4784	100	51	equality	equality	NOUN
ejpam-4784	100	52	holds	hold	VERB
ejpam-4784	100	53	iff	iff	PROPN
ejpam-4784	100	54	x1	x1	PROPN
ejpam-4784	100	55	=	=	SYM
ejpam-4784	100	56	·	·	PUNCT
ejpam-4784	100	57	·	·	PUNCT
ejpam-4784	100	58	·	·	PUNCT
ejpam-4784	101	1	=	=	SYM
ejpam-4784	101	2	xn	xn	PROPN
ejpam-4784	101	3	,	,	PUNCT
ejpam-4784	101	4	which	which	PRON
ejpam-4784	101	5	magnetize	magnetize	VERB
ejpam-4784	101	6	the	the	DET
ejpam-4784	101	7	attention	attention	NOUN
ejpam-4784	101	8	of	of	ADP
ejpam-4784	101	9	several	several	ADJ
ejpam-4784	101	10	mathematician	mathematician	NOUN
ejpam-4784	101	11	.	.	PUNCT
ejpam-4784	102	1	for	for	ADP
ejpam-4784	102	2	generalization	generalization	NOUN
ejpam-4784	102	3	and	and	CCONJ
ejpam-4784	102	4	refinement	refinement	NOUN
ejpam-4784	102	5	of	of	ADP
ejpam-4784	102	6	the	the	DET
ejpam-4784	102	7	ky	ky	PROPN
ejpam-4784	102	8	fan	fan	PROPN
ejpam-4784	102	9	inequality	inequality	PROPN
ejpam-4784	102	10	see	see	VERB
ejpam-4784	102	11	papers	paper	NOUN
ejpam-4784	102	12	[	[	X
ejpam-4784	102	13	2	2	NUM
ejpam-4784	102	14	,	,	PUNCT
ejpam-4784	102	15	8	8	NUM
ejpam-4784	102	16	]	]	PUNCT
ejpam-4784	102	17	.	.	PUNCT
ejpam-4784	103	1	(	(	PUNCT
ejpam-4784	103	2	and	and	CCONJ
ejpam-4784	103	3	references	reference	NOUN
ejpam-4784	103	4	therein	therein	ADV
ejpam-4784	103	5	)	)	PUNCT
ejpam-4784	103	6	in	in	ADP
ejpam-4784	103	7	this	this	DET
ejpam-4784	103	8	section	section	NOUN
ejpam-4784	103	9	,	,	PUNCT
ejpam-4784	103	10	we	we	PRON
ejpam-4784	103	11	are	be	AUX
ejpam-4784	103	12	improving	improve	VERB
ejpam-4784	103	13	ky	ky	PROPN
ejpam-4784	103	14	fan	fan	PROPN
ejpam-4784	103	15	inequality	inequality	PROPN
ejpam-4784	103	16	and	and	CCONJ
ejpam-4784	103	17	related	relate	VERB
ejpam-4784	103	18	results	result	NOUN
ejpam-4784	103	19	for	for	ADP
ejpam-4784	103	20	time	time	NOUN
ejpam-4784	103	21	scale	scale	NOUN
ejpam-4784	103	22	calculus	calculus	NOUN
ejpam-4784	103	23	.	.	PUNCT
ejpam-4784	104	1	by	by	ADP
ejpam-4784	104	2	considering	consider	VERB
ejpam-4784	104	3	assumptions	assumption	NOUN
ejpam-4784	104	4	of	of	ADP
ejpam-4784	104	5	theorem	theorem	NOUN
ejpam-4784	104	6	1	1	NUM
ejpam-4784	104	7	,	,	PUNCT
ejpam-4784	104	8	we	we	PRON
ejpam-4784	104	9	define	define	VERB
ejpam-4784	104	10	the	the	DET
ejpam-4784	104	11	generalized	generalize	VERB
ejpam-4784	104	12	weighted	weight	VERB
ejpam-4784	104	13	arithmetic	arithmetic	ADJ
ejpam-4784	104	14	mean	mean	NOUN
ejpam-4784	104	15	of	of	ADP
ejpam-4784	104	16	g	g	PROPN
ejpam-4784	104	17	∈	∈	PROPN
ejpam-4784	104	18	c([a	c([a	PROPN
ejpam-4784	104	19	,	,	PUNCT
ejpam-4784	104	20	b]t	b]t	NOUN
ejpam-4784	104	21	,	,	PUNCT
ejpam-4784	104	22	[	[	X
ejpam-4784	104	23	µ	µ	X
ejpam-4784	104	24	,	,	PUNCT
ejpam-4784	104	25	ν	ν	NOUN
ejpam-4784	104	26	]	]	PUNCT
ejpam-4784	104	27	)	)	PUNCT
ejpam-4784	104	28	with	with	ADP
ejpam-4784	104	29	weight	weight	NOUN
ejpam-4784	104	30	ω	ω	PROPN
ejpam-4784	104	31	:	:	PUNCT
ejpam-4784	104	32	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	104	33	,	,	PUNCT
ejpam-4784	104	34	ω	ω	NOUN
ejpam-4784	104	35	)	)	PUNCT
ejpam-4784	104	36	=	=	SYM
ejpam-4784	104	37	µ+	µ+	PUNCT
ejpam-4784	104	38	ν	ν	NOUN
ejpam-4784	104	39	−	−	PROPN
ejpam-4784	104	40	∫	∫	PROPN
ejpam-4784	104	41	b	b	PROPN
ejpam-4784	104	42	a	a	DET
ejpam-4784	104	43	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	104	44	,	,	PUNCT
ejpam-4784	104	45	(	(	PUNCT
ejpam-4784	104	46	7	7	X
ejpam-4784	104	47	)	)	PUNCT
ejpam-4784	104	48	the	the	DET
ejpam-4784	104	49	generalized	generalize	VERB
ejpam-4784	104	50	weighted	weight	VERB
ejpam-4784	104	51	geometric	geometric	ADJ
ejpam-4784	104	52	mean	mean	NOUN
ejpam-4784	104	53	of	of	ADP
ejpam-4784	104	54	the	the	DET
ejpam-4784	104	55	g	g	PROPN
ejpam-4784	104	56	∈	∈	PROPN
ejpam-4784	104	57	c([a	c([a	PROPN
ejpam-4784	104	58	,	,	PUNCT
ejpam-4784	104	59	b]t	b]t	NOUN
ejpam-4784	104	60	,	,	PUNCT
ejpam-4784	104	61	[	[	X
ejpam-4784	104	62	µ	µ	X
ejpam-4784	104	63	,	,	PUNCT
ejpam-4784	104	64	ν	ν	NOUN
ejpam-4784	104	65	]	]	PUNCT
ejpam-4784	104	66	)	)	PUNCT
ejpam-4784	104	67	of	of	ADP
ejpam-4784	104	68	weight	weight	NOUN
ejpam-4784	104	69	ω	ω	PROPN
ejpam-4784	104	70	:	:	PUNCT
ejpam-4784	104	71	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	104	72	,	,	PUNCT
ejpam-4784	104	73	ω	ω	NOUN
ejpam-4784	104	74	)	)	PUNCT
ejpam-4784	104	75	=	=	SYM
ejpam-4784	104	76	exp	exp	NOUN
ejpam-4784	104	77	[	[	PUNCT
ejpam-4784	104	78	ln	ln	ADJ
ejpam-4784	104	79	(	(	PUNCT
ejpam-4784	104	80	µν)−	µν)−	ADJ
ejpam-4784	104	81	∫	∫	PROPN
ejpam-4784	104	82	b	b	PROPN
ejpam-4784	104	83	a	a	DET
ejpam-4784	104	84	ω(†	ω(†	NOUN
ejpam-4784	104	85	)	)	PUNCT
ejpam-4784	104	86	ln	ln	NOUN
ejpam-4784	104	87	(	(	PUNCT
ejpam-4784	104	88	g(η))∆η	g(η))∆η	PROPN
ejpam-4784	104	89	]	]	PUNCT
ejpam-4784	104	90	,	,	PUNCT
ejpam-4784	104	91	(	(	PUNCT
ejpam-4784	104	92	8)	8)	NUM
ejpam-4784	104	93	the	the	DET
ejpam-4784	104	94	generalized	generalized	ADJ
ejpam-4784	104	95	weighted	weight	VERB
ejpam-4784	104	96	harmonic	harmonic	ADJ
ejpam-4784	104	97	mean	mean	NOUN
ejpam-4784	104	98	of	of	ADP
ejpam-4784	104	99	the	the	DET
ejpam-4784	104	100	g	g	PROPN
ejpam-4784	104	101	∈	∈	PROPN
ejpam-4784	104	102	c([a	c([a	PROPN
ejpam-4784	104	103	,	,	PUNCT
ejpam-4784	104	104	b]t	b]t	NOUN
ejpam-4784	104	105	,	,	PUNCT
ejpam-4784	104	106	[	[	X
ejpam-4784	104	107	µ	µ	X
ejpam-4784	104	108	,	,	PUNCT
ejpam-4784	104	109	ν	ν	NOUN
ejpam-4784	104	110	]	]	PUNCT
ejpam-4784	104	111	)	)	PUNCT
ejpam-4784	104	112	of	of	ADP
ejpam-4784	104	113	weight	weight	NOUN
ejpam-4784	104	114	ω	ω	PROPN
ejpam-4784	104	115	:	:	PUNCT
ejpam-4784	104	116	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	104	117	,	,	PUNCT
ejpam-4784	104	118	ω	ω	NOUN
ejpam-4784	104	119	)	)	PUNCT
ejpam-4784	104	120	=	=	PUNCT
ejpam-4784	104	121	(	(	PUNCT
ejpam-4784	104	122	1	1	NUM
ejpam-4784	104	123	µ	µ	NOUN
ejpam-4784	104	124	+	+	CCONJ
ejpam-4784	105	1	1	1	NUM
ejpam-4784	105	2	ν	ν	NOUN
ejpam-4784	105	3	−	−	PROPN
ejpam-4784	105	4	∫	∫	PROPN
ejpam-4784	105	5	b	b	PROPN
ejpam-4784	105	6	a	a	DET
ejpam-4784	105	7	ω(†	ω(†	NOUN
ejpam-4784	105	8	)	)	PUNCT
ejpam-4784	105	9	1	1	NUM
ejpam-4784	105	10	(	(	PUNCT
ejpam-4784	105	11	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	105	12	)	)	PUNCT
ejpam-4784	105	13	−1	−1	NOUN
ejpam-4784	105	14	.	.	PUNCT
ejpam-4784	106	1	(	(	PUNCT
ejpam-4784	106	2	9	9	X
ejpam-4784	106	3	)	)	PUNCT
ejpam-4784	106	4	examples	example	NOUN
ejpam-4784	106	5	(	(	PUNCT
ejpam-4784	106	6	i	i	NOUN
ejpam-4784	106	7	)	)	PUNCT
ejpam-4784	106	8	let	let	VERB
ejpam-4784	106	9	t	t	PROPN
ejpam-4784	106	10	=	=	SYM
ejpam-4784	106	11	r.	r.	PROPN
ejpam-4784	106	12	then	then	ADV
ejpam-4784	106	13	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	106	14	,	,	PUNCT
ejpam-4784	106	15	ω	ω	NOUN
ejpam-4784	106	16	)	)	PUNCT
ejpam-4784	106	17	=	=	SYM
ejpam-4784	106	18	µ+	µ+	PUNCT
ejpam-4784	106	19	ν	ν	NOUN
ejpam-4784	106	20	−	−	PROPN
ejpam-4784	106	21	∫	∫	PROPN
ejpam-4784	106	22	b	b	PROPN
ejpam-4784	106	23	a	a	DET
ejpam-4784	106	24	ω(†)g(η)dη	ω(†)g(η)dη	X
ejpam-4784	106	25	,	,	PUNCT
ejpam-4784	106	26	(	(	PUNCT
ejpam-4784	106	27	10	10	NUM
ejpam-4784	106	28	)	)	PUNCT
ejpam-4784	106	29	s.	s.	PROPN
ejpam-4784	106	30	chanan	chanan	PROPN
ejpam-4784	106	31	,	,	PUNCT
ejpam-4784	106	32	n.	n.	PROPN
ejpam-4784	106	33	irshad	irshad	PROPN
ejpam-4784	106	34	,	,	PUNCT
ejpam-4784	106	35	a.	a.	PROPN
ejpam-4784	106	36	khan	khan	PROPN
ejpam-4784	106	37	/	/	SYM
ejpam-4784	106	38	eur	eur	PROPN
ejpam-4784	106	39	.	.	PUNCT
ejpam-4784	107	1	j.	j.	PROPN
ejpam-4784	107	2	pure	pure	PROPN
ejpam-4784	107	3	appl	appl	PROPN
ejpam-4784	107	4	.	.	PROPN
ejpam-4784	107	5	math	math	PROPN
ejpam-4784	107	6	,	,	PUNCT
ejpam-4784	107	7	16	16	NUM
ejpam-4784	107	8	(	(	PUNCT
ejpam-4784	107	9	3	3	NUM
ejpam-4784	107	10	)	)	PUNCT
ejpam-4784	107	11	(	(	PUNCT
ejpam-4784	107	12	2023	2023	NUM
ejpam-4784	107	13	)	)	PUNCT
ejpam-4784	107	14	,	,	PUNCT
ejpam-4784	107	15	1448	1448	NUM
ejpam-4784	107	16	-	-	SYM
ejpam-4784	107	17	1463	1463	NUM
ejpam-4784	107	18	1454	1454	NUM
ejpam-4784	107	19	g[µ,ν](g	g[µ,ν](g	PROPN
ejpam-4784	107	20	,	,	PUNCT
ejpam-4784	107	21	ω	ω	NOUN
ejpam-4784	107	22	)	)	PUNCT
ejpam-4784	107	23	=	=	SYM
ejpam-4784	107	24	exp	exp	NOUN
ejpam-4784	107	25	[	[	PUNCT
ejpam-4784	107	26	ln	ln	ADJ
ejpam-4784	107	27	(	(	PUNCT
ejpam-4784	107	28	µν)−	µν)−	ADJ
ejpam-4784	107	29	∫	∫	PROPN
ejpam-4784	107	30	b	b	PROPN
ejpam-4784	107	31	a	a	DET
ejpam-4784	107	32	ω(†	ω(†	NOUN
ejpam-4784	107	33	)	)	PUNCT
ejpam-4784	107	34	ln	ln	NOUN
ejpam-4784	107	35	(	(	PUNCT
ejpam-4784	107	36	g(η	g(η	NOUN
ejpam-4784	107	37	)	)	PUNCT
ejpam-4784	107	38	)	)	PUNCT
ejpam-4784	107	39	dη	dη	ADP
ejpam-4784	107	40	]	]	PUNCT
ejpam-4784	107	41	,	,	PUNCT
ejpam-4784	107	42	(	(	PUNCT
ejpam-4784	107	43	11	11	NUM
ejpam-4784	107	44	)	)	PUNCT
ejpam-4784	107	45	and	and	CCONJ
ejpam-4784	107	46	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	107	47	,	,	PUNCT
ejpam-4784	107	48	ω	ω	NOUN
ejpam-4784	107	49	)	)	PUNCT
ejpam-4784	107	50	=	=	PUNCT
ejpam-4784	107	51	(	(	PUNCT
ejpam-4784	107	52	1	1	NUM
ejpam-4784	107	53	µ	µ	NOUN
ejpam-4784	107	54	+	+	CCONJ
ejpam-4784	107	55	1	1	NUM
ejpam-4784	107	56	ν	ν	NOUN
ejpam-4784	108	1	−	−	PROPN
ejpam-4784	109	1	∫	∫	PROPN
ejpam-4784	110	1	b	b	PROPN
ejpam-4784	110	2	a	a	DET
ejpam-4784	110	3	ω(†	ω(†	NOUN
ejpam-4784	110	4	)	)	PUNCT
ejpam-4784	110	5	1	1	NUM
ejpam-4784	110	6	(	(	PUNCT
ejpam-4784	110	7	g(η	g(η	VERB
ejpam-4784	110	8	)	)	PUNCT
ejpam-4784	110	9	)	)	PUNCT
ejpam-4784	111	1	dη	dη	NOUN
ejpam-4784	111	2	)	)	PUNCT
ejpam-4784	111	3	−1	−1	NOUN
ejpam-4784	111	4	.	.	PUNCT
ejpam-4784	112	1	(	(	PUNCT
ejpam-4784	112	2	12	12	NUM
ejpam-4784	112	3	)	)	PUNCT
ejpam-4784	112	4	(	(	PUNCT
ejpam-4784	112	5	ii	ii	NOUN
ejpam-4784	112	6	)	)	PUNCT
ejpam-4784	112	7	let	let	VERB
ejpam-4784	112	8	t	t	NOUN
ejpam-4784	112	9	=	=	SYM
ejpam-4784	112	10	z	z	PROPN
ejpam-4784	112	11	,	,	PUNCT
ejpam-4784	112	12	a	a	DET
ejpam-4784	112	13	=	=	SYM
ejpam-4784	112	14	1	1	NUM
ejpam-4784	112	15	and	and	CCONJ
ejpam-4784	112	16	b	b	X
ejpam-4784	112	17	=	=	SYM
ejpam-4784	112	18	n	n	PROPN
ejpam-4784	112	19	+	+	NOUN
ejpam-4784	112	20	1	1	NUM
ejpam-4784	112	21	,	,	PUNCT
ejpam-4784	112	22	we	we	PRON
ejpam-4784	112	23	define	define	VERB
ejpam-4784	112	24	ω(i	ω(i	NOUN
ejpam-4784	112	25	)	)	PUNCT
ejpam-4784	112	26	=	=	SYM
ejpam-4784	112	27	ωi	ωi	X
ejpam-4784	112	28	and	and	CCONJ
ejpam-4784	112	29	g(i	g(i	PROPN
ejpam-4784	112	30	)	)	PUNCT
ejpam-4784	113	1	=	=	SYM
ejpam-4784	113	2	gi	gi	X
ejpam-4784	113	3	.	.	PUNCT
ejpam-4784	114	1	the	the	DET
ejpam-4784	114	2	condition	condition	NOUN
ejpam-4784	114	3	for	for	ADP
ejpam-4784	114	4	weight	weight	NOUN
ejpam-4784	114	5	for	for	ADP
ejpam-4784	114	6	ω	ω	PROPN
ejpam-4784	114	7	means	mean	VERB
ejpam-4784	114	8	that	that	SCONJ
ejpam-4784	114	9	n∑	n∑	NOUN
ejpam-4784	114	10	i=1	i=1	X
ejpam-4784	114	11	ωi	ωi	X
ejpam-4784	114	12	>	>	X
ejpam-4784	114	13	0	0	X
ejpam-4784	114	14	.	.	PUNCT
ejpam-4784	115	1	then	then	ADV
ejpam-4784	115	2	,	,	PUNCT
ejpam-4784	115	3	we	we	PRON
ejpam-4784	115	4	have	have	VERB
ejpam-4784	115	5	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	115	6	,	,	PUNCT
ejpam-4784	115	7	ω	ω	NOUN
ejpam-4784	115	8	)	)	PUNCT
ejpam-4784	115	9	=	=	SYM
ejpam-4784	115	10	ǎn(g	ǎn(g	X
ejpam-4784	115	11	,	,	PUNCT
ejpam-4784	115	12	ω	ω	NOUN
ejpam-4784	115	13	)	)	PUNCT
ejpam-4784	115	14	=	=	SYM
ejpam-4784	116	1	µ+	µ+	PUNCT
ejpam-4784	116	2	ν	ν	NOUN
ejpam-4784	116	3	−	−	PROPN
ejpam-4784	116	4	n∑	n∑	PROPN
ejpam-4784	116	5	i=1	i=1	PROPN
ejpam-4784	116	6	ωigi	ωigi	NOUN
ejpam-4784	116	7	,	,	PUNCT
ejpam-4784	116	8	(	(	PUNCT
ejpam-4784	116	9	13	13	NUM
ejpam-4784	116	10	)	)	PUNCT
ejpam-4784	116	11	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	116	12	,	,	PUNCT
ejpam-4784	116	13	ω	ω	NOUN
ejpam-4784	116	14	)	)	PUNCT
ejpam-4784	116	15	=	=	SYM
ejpam-4784	117	1	ḡn(g	ḡn(g	PROPN
ejpam-4784	117	2	,	,	PUNCT
ejpam-4784	117	3	ω	ω	NOUN
ejpam-4784	117	4	)	)	PUNCT
ejpam-4784	117	5	=	=	SYM
ejpam-4784	117	6	(	(	PUNCT
ejpam-4784	117	7	µν	µν	ADJ
ejpam-4784	117	8	)	)	PUNCT
ejpam-4784	117	9	n∏	n∏	PROPN
ejpam-4784	117	10	i=1	i=1	PROPN
ejpam-4784	118	1	gωi	gωi	INTJ
ejpam-4784	119	1	i	i	PRON
ejpam-4784	119	2	,	,	PUNCT
ejpam-4784	119	3	(	(	PUNCT
ejpam-4784	119	4	14	14	NUM
ejpam-4784	119	5	)	)	PUNCT
ejpam-4784	119	6	and	and	CCONJ
ejpam-4784	119	7	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	119	8	,	,	PUNCT
ejpam-4784	119	9	ω	ω	NOUN
ejpam-4784	119	10	)	)	PUNCT
ejpam-4784	119	11	=	=	SYM
ejpam-4784	119	12	ȟn(g	ȟn(g	NUM
ejpam-4784	119	13	,	,	PUNCT
ejpam-4784	119	14	ω	ω	NOUN
ejpam-4784	119	15	)	)	PUNCT
ejpam-4784	119	16	=	=	PUNCT
ejpam-4784	119	17	(	(	PUNCT
ejpam-4784	119	18	1	1	NUM
ejpam-4784	119	19	µ	µ	NOUN
ejpam-4784	119	20	+	+	CCONJ
ejpam-4784	119	21	1	1	NUM
ejpam-4784	119	22	ν	ν	NOUN
ejpam-4784	119	23	−	−	PROPN
ejpam-4784	119	24	n∑	n∑	NOUN
ejpam-4784	119	25	i=1	i=1	PROPN
ejpam-4784	119	26	ωi	ωi	INTJ
ejpam-4784	119	27	1	1	NUM
ejpam-4784	119	28	(	(	PUNCT
ejpam-4784	119	29	gi	gi	NOUN
ejpam-4784	119	30	)	)	PUNCT
ejpam-4784	119	31	)	)	PUNCT
ejpam-4784	119	32	−1	−1	NOUN
ejpam-4784	119	33	.	.	PUNCT
ejpam-4784	120	1	(	(	PUNCT
ejpam-4784	120	2	15	15	NUM
ejpam-4784	120	3	)	)	PUNCT
ejpam-4784	120	4	now	now	ADV
ejpam-4784	120	5	we	we	PRON
ejpam-4784	120	6	establish	establish	VERB
ejpam-4784	120	7	generalized	generalized	ADJ
ejpam-4784	120	8	ky	ky	PROPN
ejpam-4784	120	9	fan	fan	PROPN
ejpam-4784	120	10	inequality	inequality	PROPN
ejpam-4784	120	11	for	for	ADP
ejpam-4784	120	12	time	time	NOUN
ejpam-4784	120	13	scale	scale	NOUN
ejpam-4784	120	14	.	.	PUNCT
ejpam-4784	121	1	theorem	theorem	NOUN
ejpam-4784	121	2	2	2	NUM
ejpam-4784	121	3	.	.	PUNCT
ejpam-4784	121	4	by	by	ADP
ejpam-4784	121	5	considering	consider	VERB
ejpam-4784	121	6	assumptions	assumption	NOUN
ejpam-4784	121	7	of	of	ADP
ejpam-4784	121	8	theorem	theorem	NOUN
ejpam-4784	121	9	1	1	NUM
ejpam-4784	121	10	,	,	PUNCT
ejpam-4784	121	11	and	and	CCONJ
ejpam-4784	121	12	g(η	g(η	VERB
ejpam-4784	121	13	)	)	PUNCT
ejpam-4784	121	14	∈	∈	PROPN
ejpam-4784	121	15	(	(	PUNCT
ejpam-4784	121	16	0	0	NUM
ejpam-4784	121	17	,	,	PUNCT
ejpam-4784	121	18	γ2	γ2	NOUN
ejpam-4784	121	19	]	]	PUNCT
ejpam-4784	121	20	,	,	PUNCT
ejpam-4784	121	21	where	where	SCONJ
ejpam-4784	121	22	0	0	NUM
ejpam-4784	121	23	<	<	X
ejpam-4784	121	24	r	r	X
ejpam-4784	121	25	<	<	X
ejpam-4784	121	26	γ	γ	X
ejpam-4784	121	27	<	<	X
ejpam-4784	121	28	1	1	NUM
ejpam-4784	121	29	,	,	PUNCT
ejpam-4784	121	30	then	then	ADV
ejpam-4784	121	31	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	121	32	,	,	PUNCT
ejpam-4784	121	33	ω	ω	NOUN
ejpam-4784	121	34	)	)	PUNCT
ejpam-4784	121	35	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	121	36	,	,	PUNCT
ejpam-4784	121	37	ω	ω	NUM
ejpam-4784	121	38	)	)	PUNCT
ejpam-4784	121	39	≥	≥	NOUN
ejpam-4784	121	40	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	121	41	−	−	PUNCT
ejpam-4784	121	42	g	g	PROPN
ejpam-4784	121	43	,	,	PUNCT
ejpam-4784	121	44	ω	ω	NOUN
ejpam-4784	121	45	)	)	PUNCT
ejpam-4784	121	46	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	121	47	−	−	PROPN
ejpam-4784	121	48	g	g	NOUN
ejpam-4784	121	49	,	,	PUNCT
ejpam-4784	121	50	ω	ω	NOUN
ejpam-4784	121	51	)	)	PUNCT
ejpam-4784	121	52	.	.	PUNCT
ejpam-4784	122	1	proof	proof	NOUN
ejpam-4784	122	2	.	.	PUNCT
ejpam-4784	123	1	by	by	ADP
ejpam-4784	123	2	applying	apply	VERB
ejpam-4784	123	3	ζ(x	ζ(x	NOUN
ejpam-4784	123	4	)	)	PUNCT
ejpam-4784	123	5	=	=	SYM
ejpam-4784	123	6	ln	ln	ADJ
ejpam-4784	123	7	γ−x	γ−x	NOUN
ejpam-4784	123	8	x	x	X
ejpam-4784	123	9	,	,	PUNCT
ejpam-4784	123	10	x	x	SYM
ejpam-4784	123	11	∈	∈	PROPN
ejpam-4784	123	12	(	(	PUNCT
ejpam-4784	123	13	0	0	NUM
ejpam-4784	123	14	,	,	PUNCT
ejpam-4784	123	15	γ2	γ2	NOUN
ejpam-4784	123	16	]	]	PUNCT
ejpam-4784	123	17	to	to	ADP
ejpam-4784	123	18	the	the	DET
ejpam-4784	123	19	theorem	theorem	NOUN
ejpam-4784	123	20	1	1	NUM
ejpam-4784	123	21	,	,	PUNCT
ejpam-4784	123	22	we	we	PRON
ejpam-4784	123	23	obtain	obtain	VERB
ejpam-4784	123	24	required	require	VERB
ejpam-4784	123	25	results	result	NOUN
ejpam-4784	123	26	.	.	PUNCT
ejpam-4784	124	1	in	in	ADP
ejpam-4784	124	2	next	next	ADJ
ejpam-4784	124	3	theorem	theorem	NOUN
ejpam-4784	124	4	we	we	PRON
ejpam-4784	124	5	provide	provide	VERB
ejpam-4784	124	6	refinement	refinement	NOUN
ejpam-4784	124	7	of	of	ADP
ejpam-4784	124	8	the	the	DET
ejpam-4784	124	9	ky	ky	PROPN
ejpam-4784	124	10	fan	fan	PROPN
ejpam-4784	124	11	inequality	inequality	PROPN
ejpam-4784	124	12	as	as	ADP
ejpam-4784	124	13	follow	follow	NOUN
ejpam-4784	124	14	:	:	PUNCT
ejpam-4784	124	15	theorem	theorem	NOUN
ejpam-4784	124	16	3	3	NUM
ejpam-4784	124	17	.	.	PUNCT
ejpam-4784	124	18	by	by	ADP
ejpam-4784	124	19	considering	consider	VERB
ejpam-4784	124	20	assumptions	assumption	NOUN
ejpam-4784	124	21	of	of	ADP
ejpam-4784	124	22	theorem	theorem	NOUN
ejpam-4784	124	23	1	1	NUM
ejpam-4784	124	24	and	and	CCONJ
ejpam-4784	124	25	0	0	NUM
ejpam-4784	124	26	<	<	X
ejpam-4784	124	27	n	n	PRON
ejpam-4784	124	28	≤	≤	ADV
ejpam-4784	124	29	g(η	g(η	VERB
ejpam-4784	124	30	)	)	PUNCT
ejpam-4784	124	31	≤	≤	NOUN
ejpam-4784	124	32	n	n	CCONJ
ejpam-4784	124	33	,	,	PUNCT
ejpam-4784	124	34	γ	γ	X
ejpam-4784	124	35	>	>	X
ejpam-4784	124	36	0	0	NUM
ejpam-4784	124	37	,	,	PUNCT
ejpam-4784	124	38	then	then	ADV
ejpam-4784	124	39	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	124	40	,	,	PUNCT
ejpam-4784	124	41	ω	ω	NOUN
ejpam-4784	124	42	)	)	PUNCT
ejpam-4784	124	43	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	124	44	,	,	PUNCT
ejpam-4784	124	45	ω	ω	NUM
ejpam-4784	124	46	)	)	PUNCT
ejpam-4784	124	47	≥	≥	NOUN
ejpam-4784	124	48	[	[	PUNCT
ejpam-4784	124	49	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	124	50	,	,	PUNCT
ejpam-4784	124	51	ω	ω	NOUN
ejpam-4784	124	52	)	)	PUNCT
ejpam-4784	124	53	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	124	54	,	,	PUNCT
ejpam-4784	124	55	ω	ω	PROPN
ejpam-4784	124	56	)	)	PUNCT
ejpam-4784	124	57	]	]	PUNCT
ejpam-4784	125	1	n2	n2	NOUN
ejpam-4784	125	2	(	(	PUNCT
ejpam-4784	125	3	γ	γ	X
ejpam-4784	125	4	−n)2	−n)2	VERB
ejpam-4784	125	5	≥	≥	PUNCT
ejpam-4784	125	6	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	125	7	−	−	NOUN
ejpam-4784	125	8	x	x	SYM
ejpam-4784	125	9	,	,	PUNCT
ejpam-4784	125	10	ω	ω	NOUN
ejpam-4784	125	11	)	)	PUNCT
ejpam-4784	125	12	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	125	13	−	−	NUM
ejpam-4784	125	14	x	x	SYM
ejpam-4784	125	15	,	,	PUNCT
ejpam-4784	125	16	ω	ω	PROPN
ejpam-4784	125	17	)	)	PUNCT
ejpam-4784	125	18	s.	s.	PROPN
ejpam-4784	125	19	chanan	chanan	PROPN
ejpam-4784	125	20	,	,	PUNCT
ejpam-4784	125	21	n.	n.	PROPN
ejpam-4784	125	22	irshad	irshad	PROPN
ejpam-4784	125	23	,	,	PUNCT
ejpam-4784	125	24	a.	a.	PROPN
ejpam-4784	125	25	khan	khan	PROPN
ejpam-4784	125	26	/	/	SYM
ejpam-4784	125	27	eur	eur	PROPN
ejpam-4784	125	28	.	.	PUNCT
ejpam-4784	126	1	j.	j.	PROPN
ejpam-4784	126	2	pure	pure	PROPN
ejpam-4784	126	3	appl	appl	PROPN
ejpam-4784	126	4	.	.	PROPN
ejpam-4784	126	5	math	math	PROPN
ejpam-4784	126	6	,	,	PUNCT
ejpam-4784	126	7	16	16	NUM
ejpam-4784	126	8	(	(	PUNCT
ejpam-4784	126	9	3	3	NUM
ejpam-4784	126	10	)	)	PUNCT
ejpam-4784	126	11	(	(	PUNCT
ejpam-4784	126	12	2023	2023	NUM
ejpam-4784	126	13	)	)	PUNCT
ejpam-4784	126	14	,	,	PUNCT
ejpam-4784	126	15	1448	1448	NUM
ejpam-4784	126	16	-	-	SYM
ejpam-4784	126	17	1463	1463	NUM
ejpam-4784	126	18	1455	1455	NUM
ejpam-4784	126	19	≥	≥	NOUN
ejpam-4784	126	20	[	[	PUNCT
ejpam-4784	126	21	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	126	22	,	,	PUNCT
ejpam-4784	126	23	ω	ω	NOUN
ejpam-4784	126	24	)	)	PUNCT
ejpam-4784	126	25	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	126	26	,	,	PUNCT
ejpam-4784	126	27	ω	ω	PROPN
ejpam-4784	126	28	)	)	PUNCT
ejpam-4784	126	29	]	]	PUNCT
ejpam-4784	126	30	n2	n2	NOUN
ejpam-4784	126	31	(	(	PUNCT
ejpam-4784	126	32	γ	γ	PROPN
ejpam-4784	126	33	−	−	PROPN
ejpam-4784	126	34	n)2	n)2	PROPN
ejpam-4784	126	35	≥	≥	NOUN
ejpam-4784	126	36	1	1	NUM
ejpam-4784	126	37	.	.	PUNCT
ejpam-4784	127	1	(	(	PUNCT
ejpam-4784	127	2	16	16	NUM
ejpam-4784	127	3	)	)	PUNCT
ejpam-4784	127	4	proof	proof	NOUN
ejpam-4784	127	5	.	.	PUNCT
ejpam-4784	128	1	from	from	ADP
ejpam-4784	128	2	the	the	DET
ejpam-4784	128	3	inequality	inequality	NOUN
ejpam-4784	128	4	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	128	5	,	,	PUNCT
ejpam-4784	128	6	ω	ω	NOUN
ejpam-4784	128	7	)	)	PUNCT
ejpam-4784	128	8	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	128	9	,	,	PUNCT
ejpam-4784	128	10	ω	ω	NUM
ejpam-4784	128	11	)	)	PUNCT
ejpam-4784	128	12	≥	≥	NOUN
ejpam-4784	128	13	1	1	NUM
ejpam-4784	128	14	and	and	CCONJ
ejpam-4784	128	15	n	n	CCONJ
ejpam-4784	128	16	,	,	PUNCT
ejpam-4784	128	17	n	n	PRON
ejpam-4784	128	18	∈	∈	PROPN
ejpam-4784	128	19	(	(	PUNCT
ejpam-4784	128	20	0	0	NUM
ejpam-4784	128	21	,	,	PUNCT
ejpam-4784	128	22	γ2	γ2	NOUN
ejpam-4784	128	23	]	]	PUNCT
ejpam-4784	128	24	,	,	PUNCT
ejpam-4784	128	25	the	the	DET
ejpam-4784	128	26	first	first	ADJ
ejpam-4784	128	27	and	and	CCONJ
ejpam-4784	128	28	last	last	ADJ
ejpam-4784	128	29	inequalities	inequality	NOUN
ejpam-4784	128	30	deduced	deduce	VERB
ejpam-4784	128	31	directly	directly	ADV
ejpam-4784	128	32	.	.	PUNCT
ejpam-4784	129	1	let	let	VERB
ejpam-4784	129	2	ϕ	ϕ	NOUN
ejpam-4784	129	3	:	:	PUNCT
ejpam-4784	129	4	(	(	PUNCT
ejpam-4784	129	5	0	0	NUM
ejpam-4784	129	6	,	,	PUNCT
ejpam-4784	129	7	γ	γ	NOUN
ejpam-4784	129	8	)	)	PUNCT
ejpam-4784	129	9	→	→	SYM
ejpam-4784	129	10	r	r	NOUN
ejpam-4784	129	11	,	,	PUNCT
ejpam-4784	129	12	ϕ(r	ϕ(r	PROPN
ejpam-4784	129	13	)	)	PUNCT
ejpam-4784	130	1	=	=	SYM
ejpam-4784	130	2	ln[(γ−r	ln[(γ−r	NOUN
ejpam-4784	130	3	r	r	NOUN
ejpam-4784	130	4	)	)	PUNCT
ejpam-4784	130	5	]	]	PUNCT
ejpam-4784	131	1	+	+	CCONJ
ejpam-4784	131	2	α	α	PRON
ejpam-4784	131	3	ln(r	ln(r	NOUN
ejpam-4784	131	4	)	)	PUNCT
ejpam-4784	131	5	with	with	ADP
ejpam-4784	131	6	α	α	PROPN
ejpam-4784	131	7	∈	∈	PROPN
ejpam-4784	131	8	r	r	NOUN
ejpam-4784	131	9	,	,	PUNCT
ejpam-4784	131	10	we	we	PRON
ejpam-4784	131	11	have	have	VERB
ejpam-4784	131	12	ϕ′(r	ϕ′(r	PRON
ejpam-4784	131	13	)	)	PUNCT
ejpam-4784	132	1	=	=	SYM
ejpam-4784	132	2	−	−	PROPN
ejpam-4784	132	3	1	1	NUM
ejpam-4784	132	4	r(γ	r(γ	NOUN
ejpam-4784	132	5	−	−	NOUN
ejpam-4784	132	6	r	r	NOUN
ejpam-4784	132	7	)	)	PUNCT
ejpam-4784	132	8	+	+	NOUN
ejpam-4784	132	9	α	α	NOUN
ejpam-4784	132	10	r	r	NOUN
ejpam-4784	132	11	,	,	PUNCT
ejpam-4784	132	12	r	r	NOUN
ejpam-4784	132	13	∈	∈	PROPN
ejpam-4784	132	14	(	(	PUNCT
ejpam-4784	132	15	0	0	NUM
ejpam-4784	132	16	,	,	PUNCT
ejpam-4784	132	17	γ	γ	NOUN
ejpam-4784	132	18	)	)	PUNCT
ejpam-4784	132	19	,	,	PUNCT
ejpam-4784	132	20	ϕ′′(r	ϕ′′(r	NOUN
ejpam-4784	132	21	)	)	PUNCT
ejpam-4784	132	22	=	=	SYM
ejpam-4784	132	23	1	1	NUM
ejpam-4784	132	24	r2	r2	NOUN
ejpam-4784	132	25	[	[	PUNCT
ejpam-4784	132	26	γ(γ	γ(γ	PROPN
ejpam-4784	132	27	−	−	PROPN
ejpam-4784	132	28	2r	2r	NUM
ejpam-4784	132	29	)	)	PUNCT
ejpam-4784	132	30	(	(	PUNCT
ejpam-4784	132	31	γ	γ	PROPN
ejpam-4784	132	32	−	−	PROPN
ejpam-4784	132	33	r)2	r)2	NOUN
ejpam-4784	132	34	−	−	PROPN
ejpam-4784	132	35	α	α	NOUN
ejpam-4784	132	36	]	]	PUNCT
ejpam-4784	132	37	,	,	PUNCT
ejpam-4784	132	38	r	r	NOUN
ejpam-4784	132	39	∈	∈	PROPN
ejpam-4784	132	40	(	(	PUNCT
ejpam-4784	132	41	0	0	NUM
ejpam-4784	132	42	,	,	PUNCT
ejpam-4784	132	43	γ	γ	NOUN
ejpam-4784	132	44	)	)	PUNCT
ejpam-4784	132	45	.	.	PUNCT
ejpam-4784	133	1	if	if	SCONJ
ejpam-4784	133	2	φ	φ	PROPN
ejpam-4784	133	3	:	:	PUNCT
ejpam-4784	133	4	(	(	PUNCT
ejpam-4784	133	5	0	0	NUM
ejpam-4784	133	6	,	,	PUNCT
ejpam-4784	133	7	γ	γ	NOUN
ejpam-4784	133	8	)	)	PUNCT
ejpam-4784	133	9	→	→	SYM
ejpam-4784	133	10	r	r	NOUN
ejpam-4784	133	11	,	,	PUNCT
ejpam-4784	133	12	defined	define	VERB
ejpam-4784	133	13	as	as	ADP
ejpam-4784	133	14	φ(r	φ(r	ADJ
ejpam-4784	133	15	)	)	PUNCT
ejpam-4784	133	16	=	=	SYM
ejpam-4784	133	17	γ(γ−2r	γ(γ−2r	NOUN
ejpam-4784	133	18	)	)	PUNCT
ejpam-4784	133	19	(	(	PUNCT
ejpam-4784	133	20	γ−r)2	γ−r)2	X
ejpam-4784	133	21	,	,	PUNCT
ejpam-4784	133	22	then	then	ADV
ejpam-4784	133	23	φ′(r	φ′(r	PROPN
ejpam-4784	133	24	)	)	PUNCT
ejpam-4784	133	25	=	=	SYM
ejpam-4784	133	26	2r(r−1	2r(r−1	NUM
ejpam-4784	133	27	)	)	PUNCT
ejpam-4784	133	28	(	(	PUNCT
ejpam-4784	133	29	1−r)4	1−r)4	NUM
ejpam-4784	133	30	,	,	PUNCT
ejpam-4784	133	31	indicating	indicate	VERB
ejpam-4784	133	32	φ	φ	PROPN
ejpam-4784	133	33	is	be	AUX
ejpam-4784	133	34	monotonically	monotonically	ADV
ejpam-4784	133	35	strictly	strictly	ADV
ejpam-4784	133	36	decreasing	decrease	VERB
ejpam-4784	133	37	on	on	ADP
ejpam-4784	133	38	(	(	PUNCT
ejpam-4784	133	39	0	0	NUM
ejpam-4784	133	40	,	,	PUNCT
ejpam-4784	133	41	γ	γ	NOUN
ejpam-4784	133	42	)	)	PUNCT
ejpam-4784	133	43	.	.	PUNCT
ejpam-4784	134	1	consequently	consequently	ADV
ejpam-4784	134	2	for	for	ADP
ejpam-4784	134	3	r	r	PROPN
ejpam-4784	134	4	∈	∈	PROPN
ejpam-4784	134	5	(	(	PUNCT
ejpam-4784	134	6	n	n	X
ejpam-4784	134	7	,	,	PUNCT
ejpam-4784	134	8	n	n	CCONJ
ejpam-4784	134	9	)	)	PUNCT
ejpam-4784	134	10	,	,	PUNCT
ejpam-4784	134	11	we	we	PRON
ejpam-4784	134	12	have	have	VERB
ejpam-4784	134	13	1−	1−	NUM
ejpam-4784	134	14	2n	2n	NUM
ejpam-4784	134	15	(	(	PUNCT
ejpam-4784	134	16	1−n)2	1−n)2	NUM
ejpam-4784	134	17	=	=	SYM
ejpam-4784	134	18	φ(n	φ(n	ADJ
ejpam-4784	134	19	)	)	PUNCT
ejpam-4784	134	20	≤	≤	NOUN
ejpam-4784	134	21	φ(r	φ(r	ADJ
ejpam-4784	134	22	)	)	PUNCT
ejpam-4784	134	23	≤	≤	NOUN
ejpam-4784	134	24	φ(n	φ(n	NOUN
ejpam-4784	134	25	)	)	PUNCT
ejpam-4784	134	26	=	=	SYM
ejpam-4784	134	27	1−	1−	NUM
ejpam-4784	134	28	2n	2n	NUM
ejpam-4784	134	29	(	(	PUNCT
ejpam-4784	134	30	1−	1−	NUM
ejpam-4784	134	31	n)2	n)2	NOUN
ejpam-4784	134	32	.	.	PUNCT
ejpam-4784	135	1	(	(	PUNCT
ejpam-4784	135	2	17	17	NUM
ejpam-4784	135	3	)	)	PUNCT
ejpam-4784	135	4	if	if	SCONJ
ejpam-4784	135	5	α	α	PRON
ejpam-4784	135	6	≤	≤	ADJ
ejpam-4784	135	7	γ(γ−2n	γ(γ−2n	NUM
ejpam-4784	135	8	)	)	PUNCT
ejpam-4784	135	9	(	(	PUNCT
ejpam-4784	135	10	γ−n)2	γ−n)2	ADV
ejpam-4784	135	11	,	,	PUNCT
ejpam-4784	135	12	we	we	PRON
ejpam-4784	135	13	conclude	conclude	VERB
ejpam-4784	135	14	from	from	ADP
ejpam-4784	135	15	(	(	PUNCT
ejpam-4784	135	16	17	17	NUM
ejpam-4784	135	17	)	)	PUNCT
ejpam-4784	135	18	that	that	SCONJ
ejpam-4784	135	19	the	the	DET
ejpam-4784	135	20	function	function	NOUN
ejpam-4784	135	21	φ	φ	PROPN
ejpam-4784	135	22	is	be	AUX
ejpam-4784	135	23	strictly	strictly	ADV
ejpam-4784	135	24	convex	convex	ADJ
ejpam-4784	135	25	on	on	ADP
ejpam-4784	135	26	(	(	PUNCT
ejpam-4784	135	27	n	n	CCONJ
ejpam-4784	135	28	,	,	PUNCT
ejpam-4784	135	29	n	n	CCONJ
ejpam-4784	135	30	)	)	PUNCT
ejpam-4784	135	31	.	.	PUNCT
ejpam-4784	136	1	applying	apply	VERB
ejpam-4784	136	2	theorem	theorem	NOUN
ejpam-4784	136	3	1	1	NUM
ejpam-4784	136	4	to	to	ADP
ejpam-4784	136	5	the	the	DET
ejpam-4784	136	6	function	function	NOUN
ejpam-4784	136	7	ϕ	ϕ	NOUN
ejpam-4784	136	8	:	:	PUNCT
ejpam-4784	136	9	(	(	PUNCT
ejpam-4784	136	10	n	n	X
ejpam-4784	136	11	,	,	PUNCT
ejpam-4784	136	12	n	n	CCONJ
ejpam-4784	136	13	)	)	PUNCT
ejpam-4784	136	14	→	→	SYM
ejpam-4784	136	15	r	r	NOUN
ejpam-4784	136	16	,	,	PUNCT
ejpam-4784	136	17	ϕ(r	ϕ(r	PROPN
ejpam-4784	136	18	)	)	PUNCT
ejpam-4784	137	1	=	=	PUNCT
ejpam-4784	137	2	ln	ln	NOUN
ejpam-4784	138	1	[	[	X
ejpam-4784	138	2	(	(	PUNCT
ejpam-4784	138	3	γ	γ	X
ejpam-4784	138	4	−	−	NOUN
ejpam-4784	138	5	r	r	NOUN
ejpam-4784	138	6	r	r	NOUN
ejpam-4784	138	7	)	)	PUNCT
ejpam-4784	138	8	]	]	PUNCT
ejpam-4784	139	1	+	+	CCONJ
ejpam-4784	139	2	α	α	X
ejpam-4784	139	3	ln	ln	ADJ
ejpam-4784	139	4	(	(	PUNCT
ejpam-4784	139	5	r	r	NOUN
ejpam-4784	139	6	)	)	PUNCT
ejpam-4784	139	7	,	,	PUNCT
ejpam-4784	139	8	with	with	ADP
ejpam-4784	139	9	α	α	NOUN
ejpam-4784	139	10	≤	≤	ADJ
ejpam-4784	139	11	γ(γ−2n	γ(γ−2n	NUM
ejpam-4784	139	12	)	)	PUNCT
ejpam-4784	139	13	(	(	PUNCT
ejpam-4784	139	14	γ−n)2	γ−n)2	ADV
ejpam-4784	139	15	,	,	PUNCT
ejpam-4784	139	16	we	we	PRON
ejpam-4784	139	17	conclude	conclude	VERB
ejpam-4784	139	18	that	that	SCONJ
ejpam-4784	139	19	ln	ln	INTJ
ejpam-4784	139	20	(	(	PUNCT
ejpam-4784	139	21	γ	γ	PROPN
ejpam-4784	139	22	−	−	PROPN
ejpam-4784	139	23	u	u	PROPN
ejpam-4784	139	24	u	u	PROPN
ejpam-4784	139	25	)	)	PUNCT
ejpam-4784	140	1	+	+	CCONJ
ejpam-4784	140	2	α	α	PROPN
ejpam-4784	140	3	lnu+	lnu+	ADJ
ejpam-4784	140	4	ln	ln	X
ejpam-4784	140	5	(	(	PUNCT
ejpam-4784	140	6	γ−ν	γ−ν	X
ejpam-4784	140	7	ν	ν	NOUN
ejpam-4784	140	8	)	)	PUNCT
ejpam-4784	141	1	+	+	CCONJ
ejpam-4784	141	2	α	α	PROPN
ejpam-4784	141	3	ln	ln	NOUN
ejpam-4784	141	4	v	v	NOUN
ejpam-4784	141	5	−	−	PROPN
ejpam-4784	141	6	∫	∫	PROPN
ejpam-4784	141	7	b	b	PROPN
ejpam-4784	141	8	a	a	DET
ejpam-4784	141	9	ω(†	ω(†	NOUN
ejpam-4784	141	10	)	)	PUNCT
ejpam-4784	141	11	[	[	PUNCT
ejpam-4784	141	12	ln	ln	X
ejpam-4784	141	13	(	(	PUNCT
ejpam-4784	141	14	γ	γ	X
ejpam-4784	141	15	−	−	PROPN
ejpam-4784	141	16	g(η	g(η	PROPN
ejpam-4784	141	17	)	)	PUNCT
ejpam-4784	141	18	g(η	g(η	PROPN
ejpam-4784	141	19	)	)	PUNCT
ejpam-4784	141	20	)	)	PUNCT
ejpam-4784	142	1	+	+	CCONJ
ejpam-4784	142	2	α	α	PRON
ejpam-4784	142	3	ln(g(η	ln(g(η	NUM
ejpam-4784	142	4	)	)	PUNCT
ejpam-4784	142	5	)	)	PUNCT
ejpam-4784	142	6	]	]	PUNCT
ejpam-4784	143	1	∆η	∆η	NOUN
ejpam-4784	143	2	≥	≥	X
ejpam-4784	143	3	ln	ln	ADV
ejpam-4784	143	4	γ	γ	NOUN
ejpam-4784	143	5	−	−	PROPN
ejpam-4784	143	6	u−ν	u−ν	NOUN
ejpam-4784	143	7	+	+	CCONJ
ejpam-4784	143	8	∫	∫	PROPN
ejpam-4784	143	9	b	b	PROPN
ejpam-4784	143	10	a	a	DET
ejpam-4784	143	11	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	143	12	µ+	µ+	NOUN
ejpam-4784	143	13	ν	ν	NOUN
ejpam-4784	143	14	−	−	PROPN
ejpam-4784	143	15	∫	∫	PROPN
ejpam-4784	143	16	b	b	PROPN
ejpam-4784	143	17	a	a	DET
ejpam-4784	143	18	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	143	19	+	+	NOUN
ejpam-4784	143	20	α	α	NOUN
ejpam-4784	143	21	ln	ln	NOUN
ejpam-4784	144	1	(	(	PUNCT
ejpam-4784	144	2	µ+	µ+	NOUN
ejpam-4784	144	3	ν	ν	X
ejpam-4784	144	4	−	−	PROPN
ejpam-4784	144	5	∫	∫	PROPN
ejpam-4784	144	6	b	b	PROPN
ejpam-4784	144	7	a	a	DET
ejpam-4784	144	8	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	144	9	)	)	PUNCT
ejpam-4784	144	10	ln	ln	ADJ
ejpam-4784	144	11	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	144	12	−	−	PROPN
ejpam-4784	144	13	g	g	PROPN
ejpam-4784	144	14	,	,	PUNCT
ejpam-4784	144	15	ω	ω	NOUN
ejpam-4784	144	16	)	)	PUNCT
ejpam-4784	144	17	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	144	18	,	,	PUNCT
ejpam-4784	144	19	ω	ω	NOUN
ejpam-4784	144	20	)	)	PUNCT
ejpam-4784	144	21	+	+	CCONJ
ejpam-4784	144	22	α	α	PROPN
ejpam-4784	144	23	ln	ln	ADJ
ejpam-4784	144	24	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	144	25	,	,	PUNCT
ejpam-4784	144	26	ω	ω	NUM
ejpam-4784	144	27	)	)	PUNCT
ejpam-4784	144	28	≥	≥	X
ejpam-4784	144	29	ln	ln	ADV
ejpam-4784	144	30	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	144	31	−	−	PROPN
ejpam-4784	144	32	g	g	PROPN
ejpam-4784	144	33	,	,	PUNCT
ejpam-4784	144	34	ω	ω	NOUN
ejpam-4784	144	35	)	)	PUNCT
ejpam-4784	144	36	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	144	37	,	,	PUNCT
ejpam-4784	144	38	ω	ω	NOUN
ejpam-4784	144	39	)	)	PUNCT
ejpam-4784	144	40	+	+	CCONJ
ejpam-4784	144	41	α	α	PROPN
ejpam-4784	144	42	ln	ln	ADJ
ejpam-4784	144	43	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	144	44	,	,	PUNCT
ejpam-4784	144	45	ω	ω	NOUN
ejpam-4784	144	46	)	)	PUNCT
ejpam-4784	144	47	(	(	PUNCT
ejpam-4784	144	48	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	144	49	,	,	PUNCT
ejpam-4784	144	50	ω	ω	NOUN
ejpam-4784	144	51	)	)	PUNCT
ejpam-4784	144	52	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	144	53	,	,	PUNCT
ejpam-4784	144	54	ω	ω	NOUN
ejpam-4784	144	55	)	)	PUNCT
ejpam-4784	144	56	)	)	PUNCT
ejpam-4784	145	1	α	α	PRON
ejpam-4784	145	2	≥	≥	NOUN
ejpam-4784	145	3	ǎ[µ,ν](γ	ǎ[µ,ν](γ	VERB
ejpam-4784	145	4	−	−	PUNCT
ejpam-4784	145	5	g	g	PROPN
ejpam-4784	145	6	,	,	PUNCT
ejpam-4784	145	7	ω	ω	NOUN
ejpam-4784	145	8	)	)	PUNCT
ejpam-4784	145	9	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	145	10	,	,	PUNCT
ejpam-4784	145	11	ω	ω	NOUN
ejpam-4784	145	12	)	)	PUNCT
ejpam-4784	145	13	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	145	14	,	,	PUNCT
ejpam-4784	145	15	ω	ω	NOUN
ejpam-4784	145	16	)	)	PUNCT
ejpam-4784	145	17	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	145	18	−	−	PROPN
ejpam-4784	145	19	g	g	NOUN
ejpam-4784	145	20	,	,	PUNCT
ejpam-4784	145	21	ω	ω	NOUN
ejpam-4784	145	22	)	)	PUNCT
ejpam-4784	145	23	(	(	PUNCT
ejpam-4784	145	24	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	145	25	,	,	PUNCT
ejpam-4784	145	26	ω	ω	NOUN
ejpam-4784	145	27	)	)	PUNCT
ejpam-4784	145	28	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	145	29	,	,	PUNCT
ejpam-4784	145	30	ω	ω	NOUN
ejpam-4784	145	31	)	)	PUNCT
ejpam-4784	145	32	)	)	PUNCT
ejpam-4784	145	33	α−1	α−1	PROPN
ejpam-4784	145	34	≥	≥	NUM
ejpam-4784	145	35	(	(	PUNCT
ejpam-4784	145	36	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	145	37	−	−	NOUN
ejpam-4784	145	38	x	x	SYM
ejpam-4784	145	39	,	,	PUNCT
ejpam-4784	145	40	ω	ω	NOUN
ejpam-4784	145	41	)	)	PUNCT
ejpam-4784	145	42	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	145	43	−	−	NUM
ejpam-4784	145	44	x	x	SYM
ejpam-4784	145	45	,	,	PUNCT
ejpam-4784	145	46	ω	ω	NUM
ejpam-4784	145	47	)	)	PUNCT
ejpam-4784	145	48	)	)	PUNCT
ejpam-4784	145	49	(	(	PUNCT
ejpam-4784	145	50	18	18	NUM
ejpam-4784	145	51	)	)	PUNCT
ejpam-4784	145	52	s.	s.	PROPN
ejpam-4784	145	53	chanan	chanan	PROPN
ejpam-4784	145	54	,	,	PUNCT
ejpam-4784	145	55	n.	n.	PROPN
ejpam-4784	145	56	irshad	irshad	PROPN
ejpam-4784	145	57	,	,	PUNCT
ejpam-4784	145	58	a.	a.	PROPN
ejpam-4784	145	59	khan	khan	PROPN
ejpam-4784	145	60	/	/	SYM
ejpam-4784	145	61	eur	eur	PROPN
ejpam-4784	145	62	.	.	PUNCT
ejpam-4784	146	1	j.	j.	PROPN
ejpam-4784	146	2	pure	pure	PROPN
ejpam-4784	146	3	appl	appl	PROPN
ejpam-4784	146	4	.	.	PROPN
ejpam-4784	146	5	math	math	PROPN
ejpam-4784	146	6	,	,	PUNCT
ejpam-4784	146	7	16	16	NUM
ejpam-4784	146	8	(	(	PUNCT
ejpam-4784	146	9	3	3	NUM
ejpam-4784	146	10	)	)	PUNCT
ejpam-4784	146	11	(	(	PUNCT
ejpam-4784	146	12	2023	2023	NUM
ejpam-4784	146	13	)	)	PUNCT
ejpam-4784	146	14	,	,	PUNCT
ejpam-4784	146	15	1448	1448	NUM
ejpam-4784	146	16	-	-	SYM
ejpam-4784	146	17	1463	1463	NUM
ejpam-4784	146	18	1456	1456	NUM
ejpam-4784	146	19	from	from	ADP
ejpam-4784	146	20	(	(	PUNCT
ejpam-4784	146	21	18	18	NUM
ejpam-4784	146	22	)	)	PUNCT
ejpam-4784	146	23	we	we	PRON
ejpam-4784	146	24	observe	observe	VERB
ejpam-4784	146	25	that	that	SCONJ
ejpam-4784	146	26	this	this	DET
ejpam-4784	146	27	inequality	inequality	NOUN
ejpam-4784	146	28	is	be	AUX
ejpam-4784	146	29	best	well	ADV
ejpam-4784	146	30	possible	possible	ADJ
ejpam-4784	146	31	if	if	SCONJ
ejpam-4784	146	32	we	we	PRON
ejpam-4784	146	33	have	have	VERB
ejpam-4784	146	34	α	α	PROPN
ejpam-4784	146	35	is	be	AUX
ejpam-4784	146	36	maximal	maximal	ADJ
ejpam-4784	146	37	,	,	PUNCT
ejpam-4784	146	38	i.e	i.e	PROPN
ejpam-4784	146	39	,	,	PUNCT
ejpam-4784	147	1	α	α	PROPN
ejpam-4784	147	2	=	=	SYM
ejpam-4784	147	3	γ−2n	γ−2n	PROPN
ejpam-4784	147	4	(	(	PUNCT
ejpam-4784	147	5	γ−n)2	γ−n)2	ADV
ejpam-4784	147	6	,	,	PUNCT
ejpam-4784	147	7	that	that	PRON
ejpam-4784	147	8	leads	lead	VERB
ejpam-4784	147	9	(	(	PUNCT
ejpam-4784	147	10	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	147	11	,	,	PUNCT
ejpam-4784	147	12	ω	ω	NOUN
ejpam-4784	147	13	)	)	PUNCT
ejpam-4784	147	14	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	147	15	,	,	PUNCT
ejpam-4784	147	16	ω	ω	NOUN
ejpam-4784	147	17	)	)	PUNCT
ejpam-4784	147	18	)	)	PUNCT
ejpam-4784	148	1	γ−2n	γ−2n	INTJ
ejpam-4784	148	2	(	(	PUNCT
ejpam-4784	148	3	γ−n)2	γ−n)2	NUM
ejpam-4784	148	4	−1	−1	NOUN
ejpam-4784	148	5	≥	≥	NOUN
ejpam-4784	148	6	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	148	7	−	−	NOUN
ejpam-4784	148	8	x	x	SYM
ejpam-4784	148	9	,	,	PUNCT
ejpam-4784	148	10	ω	ω	NOUN
ejpam-4784	148	11	)	)	PUNCT
ejpam-4784	148	12	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	148	13	−	−	NUM
ejpam-4784	148	14	x	x	SYM
ejpam-4784	148	15	,	,	PUNCT
ejpam-4784	148	16	ω	ω	PROPN
ejpam-4784	148	17	)	)	PUNCT
ejpam-4784	148	18	which	which	PRON
ejpam-4784	148	19	yield	yield	VERB
ejpam-4784	148	20	to	to	ADP
ejpam-4784	148	21	the	the	DET
ejpam-4784	148	22	second	second	ADJ
ejpam-4784	148	23	inequality	inequality	NOUN
ejpam-4784	148	24	in	in	ADP
ejpam-4784	148	25	(	(	PUNCT
ejpam-4784	148	26	16	16	NUM
ejpam-4784	148	27	)	)	PUNCT
ejpam-4784	148	28	.	.	PUNCT
ejpam-4784	149	1	we	we	PRON
ejpam-4784	149	2	established	establish	VERB
ejpam-4784	149	3	the	the	DET
ejpam-4784	149	4	third	third	ADJ
ejpam-4784	149	5	inequality	inequality	NOUN
ejpam-4784	149	6	by	by	ADP
ejpam-4784	149	7	using	use	VERB
ejpam-4784	149	8	the	the	DET
ejpam-4784	149	9	function	function	NOUN
ejpam-4784	149	10	f	f	PROPN
ejpam-4784	149	11	(	(	PUNCT
ejpam-4784	149	12	r	r	NOUN
ejpam-4784	149	13	)	)	PUNCT
ejpam-4784	149	14	=	=	SYM
ejpam-4784	149	15	β	β	PROPN
ejpam-4784	149	16	ln	ln	PROPN
ejpam-4784	149	17	r−	r−	PROPN
ejpam-4784	149	18	ln	ln	PROPN
ejpam-4784	149	19	[	[	PUNCT
ejpam-4784	149	20	(	(	PUNCT
ejpam-4784	149	21	γ−r	γ−r	NUM
ejpam-4784	149	22	)	)	PUNCT
ejpam-4784	149	23	r	r	NOUN
ejpam-4784	149	24	]	]	PUNCT
ejpam-4784	149	25	and	and	CCONJ
ejpam-4784	149	26	the	the	DET
ejpam-4784	149	27	same	same	ADJ
ejpam-4784	149	28	technique	technique	NOUN
ejpam-4784	149	29	.	.	PUNCT
ejpam-4784	150	1	if	if	SCONJ
ejpam-4784	150	2	β	β	X
ejpam-4784	150	3	≥	≥	NUM
ejpam-4784	150	4	γ−2n	γ−2n	X
ejpam-4784	150	5	(	(	PUNCT
ejpam-4784	150	6	γ−n)2	γ−n)2	ADV
ejpam-4784	150	7	is	be	AUX
ejpam-4784	150	8	true	true	ADJ
ejpam-4784	150	9	,	,	PUNCT
ejpam-4784	150	10	then	then	ADV
ejpam-4784	150	11	the	the	DET
ejpam-4784	150	12	function	function	NOUN
ejpam-4784	150	13	is	be	AUX
ejpam-4784	150	14	strictly	strictly	ADV
ejpam-4784	150	15	convex	convex	ADJ
ejpam-4784	150	16	on	on	ADP
ejpam-4784	150	17	(	(	PUNCT
ejpam-4784	150	18	n	n	CCONJ
ejpam-4784	150	19	,	,	PUNCT
ejpam-4784	150	20	n	n	CCONJ
ejpam-4784	150	21	)	)	PUNCT
ejpam-4784	150	22	.	.	PUNCT
ejpam-4784	151	1	remark	remark	PROPN
ejpam-4784	151	2	1	1	NUM
ejpam-4784	151	3	.	.	PUNCT
ejpam-4784	152	1	since	since	SCONJ
ejpam-4784	152	2	the	the	DET
ejpam-4784	152	3	ky	ky	PROPN
ejpam-4784	152	4	fan	fan	PROPN
ejpam-4784	152	5	inequality	inequality	PROPN
ejpam-4784	152	6	is	be	AUX
ejpam-4784	152	7	also	also	ADV
ejpam-4784	152	8	equivalent	equivalent	ADJ
ejpam-4784	152	9	to	to	ADP
ejpam-4784	152	10	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	152	11	,	,	PUNCT
ejpam-4784	152	12	ω	ω	NOUN
ejpam-4784	152	13	)	)	PUNCT
ejpam-4784	152	14	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	152	15	,	,	PUNCT
ejpam-4784	152	16	ω	ω	NUM
ejpam-4784	152	17	)	)	PUNCT
ejpam-4784	152	18	≥	≥	NOUN
ejpam-4784	152	19	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	152	20	−	−	PUNCT
ejpam-4784	152	21	g	g	PROPN
ejpam-4784	152	22	,	,	PUNCT
ejpam-4784	152	23	ω	ω	NOUN
ejpam-4784	152	24	)	)	PUNCT
ejpam-4784	152	25	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	152	26	−	−	PROPN
ejpam-4784	152	27	g	g	NOUN
ejpam-4784	152	28	,	,	PUNCT
ejpam-4784	152	29	ω	ω	PROPN
ejpam-4784	152	30	)	)	PUNCT
ejpam-4784	152	31	,	,	PUNCT
ejpam-4784	152	32	then	then	ADV
ejpam-4784	152	33	the	the	DET
ejpam-4784	152	34	first	first	ADJ
ejpam-4784	152	35	part	part	NOUN
ejpam-4784	152	36	of	of	ADP
ejpam-4784	152	37	the	the	DET
ejpam-4784	152	38	inequality	inequality	NOUN
ejpam-4784	152	39	may	may	AUX
ejpam-4784	152	40	be	be	AUX
ejpam-4784	152	41	seen	see	VERB
ejpam-4784	152	42	as	as	ADP
ejpam-4784	152	43	refinement	refinement	NOUN
ejpam-4784	152	44	of	of	ADP
ejpam-4784	152	45	the	the	DET
ejpam-4784	152	46	ky	ky	PROPN
ejpam-4784	152	47	fan	fan	PROPN
ejpam-4784	152	48	inequality	inequality	PROPN
ejpam-4784	152	49	while	while	SCONJ
ejpam-4784	152	50	the	the	DET
ejpam-4784	152	51	second	second	ADJ
ejpam-4784	152	52	part	part	NOUN
ejpam-4784	152	53	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	152	54	−	−	PROPN
ejpam-4784	152	55	g	g	PROPN
ejpam-4784	152	56	,	,	PUNCT
ejpam-4784	152	57	ω	ω	NOUN
ejpam-4784	152	58	)	)	PUNCT
ejpam-4784	152	59	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	152	60	−	−	PROPN
ejpam-4784	152	61	g	g	NOUN
ejpam-4784	152	62	,	,	PUNCT
ejpam-4784	152	63	ω	ω	PROPN
ejpam-4784	152	64	)	)	PUNCT
ejpam-4784	152	65	≥	≥	PROPN
ejpam-4784	152	66	(	(	PUNCT
ejpam-4784	152	67	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	152	68	,	,	PUNCT
ejpam-4784	152	69	ω	ω	NOUN
ejpam-4784	152	70	)	)	PUNCT
ejpam-4784	152	71	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	152	72	,	,	PUNCT
ejpam-4784	152	73	ω	ω	NOUN
ejpam-4784	152	74	)	)	PUNCT
ejpam-4784	152	75	)	)	PUNCT
ejpam-4784	152	76	n2	n2	NOUN
ejpam-4784	152	77	(	(	PUNCT
ejpam-4784	152	78	γ−n)2	γ−n)2	NUM
ejpam-4784	152	79	can	can	AUX
ejpam-4784	152	80	be	be	AUX
ejpam-4784	152	81	considered	consider	VERB
ejpam-4784	152	82	as	as	ADP
ejpam-4784	152	83	a	a	DET
ejpam-4784	152	84	counter	counter	ADJ
ejpam-4784	152	85	part	part	NOUN
ejpam-4784	152	86	of	of	ADP
ejpam-4784	152	87	the	the	DET
ejpam-4784	152	88	ky	ky	PROPN
ejpam-4784	152	89	fan	fan	PROPN
ejpam-4784	152	90	inequality	inequality	PROPN
ejpam-4784	152	91	.	.	PUNCT
ejpam-4784	153	1	remark	remark	PROPN
ejpam-4784	153	2	2	2	NUM
ejpam-4784	153	3	.	.	PUNCT
ejpam-4784	154	1	(	(	PUNCT
ejpam-4784	154	2	i	i	NOUN
ejpam-4784	154	3	)	)	PUNCT
ejpam-4784	154	4	let	let	VERB
ejpam-4784	154	5	t	t	NOUN
ejpam-4784	154	6	=	=	SYM
ejpam-4784	154	7	z	z	PROPN
ejpam-4784	154	8	,	,	PUNCT
ejpam-4784	154	9	a	a	DET
ejpam-4784	154	10	=	=	SYM
ejpam-4784	154	11	1	1	NUM
ejpam-4784	154	12	and	and	CCONJ
ejpam-4784	154	13	b	b	X
ejpam-4784	154	14	=	=	SYM
ejpam-4784	154	15	n+1	n+1	PROPN
ejpam-4784	154	16	,	,	PUNCT
ejpam-4784	154	17	we	we	PRON
ejpam-4784	154	18	define	define	VERB
ejpam-4784	154	19	ω(i	ω(i	NOUN
ejpam-4784	154	20	)	)	PUNCT
ejpam-4784	154	21	=	=	SYM
ejpam-4784	154	22	ωi	ωi	X
ejpam-4784	154	23	and	and	CCONJ
ejpam-4784	154	24	g(i	g(i	PROPN
ejpam-4784	154	25	)	)	PUNCT
ejpam-4784	155	1	=	=	SYM
ejpam-4784	155	2	gi	gi	X
ejpam-4784	155	3	.	.	PUNCT
ejpam-4784	156	1	the	the	DET
ejpam-4784	156	2	condition	condition	NOUN
ejpam-4784	156	3	for	for	ADP
ejpam-4784	156	4	ω	ω	PROPN
ejpam-4784	156	5	means	mean	VERB
ejpam-4784	156	6	that	that	SCONJ
ejpam-4784	156	7	n∑	n∑	NOUN
ejpam-4784	156	8	i=1	i=1	X
ejpam-4784	156	9	ωi	ωi	X
ejpam-4784	156	10	>	>	X
ejpam-4784	156	11	0	0	X
ejpam-4784	156	12	.	.	PUNCT
ejpam-4784	157	1	then	then	ADV
ejpam-4784	157	2	,	,	PUNCT
ejpam-4784	157	3	we	we	PRON
ejpam-4784	157	4	have	have	VERB
ejpam-4784	157	5	ǎn(g	ǎn(g	NUM
ejpam-4784	157	6	,	,	PUNCT
ejpam-4784	157	7	ω	ω	NUM
ejpam-4784	157	8	)	)	PUNCT
ejpam-4784	157	9	ǧn(g	ǧn(g	PROPN
ejpam-4784	157	10	,	,	PUNCT
ejpam-4784	157	11	ω	ω	NUM
ejpam-4784	157	12	)	)	PUNCT
ejpam-4784	157	13	≥	≥	NOUN
ejpam-4784	157	14	[	[	PUNCT
ejpam-4784	157	15	ǎn(g	ǎn(g	NUM
ejpam-4784	157	16	,	,	PUNCT
ejpam-4784	157	17	ω	ω	NOUN
ejpam-4784	157	18	)	)	PUNCT
ejpam-4784	158	1	ǧn(g	ǧn(g	PROPN
ejpam-4784	158	2	,	,	PUNCT
ejpam-4784	158	3	ω	ω	NOUN
ejpam-4784	158	4	)	)	PUNCT
ejpam-4784	158	5	]	]	PUNCT
ejpam-4784	158	6	n2	n2	NOUN
ejpam-4784	158	7	(	(	PUNCT
ejpam-4784	158	8	γ	γ	X
ejpam-4784	158	9	−n)2	−n)2	VERB
ejpam-4784	158	10	≥	≥	NOUN
ejpam-4784	158	11	ǎn(γ	ǎn(γ	PRON
ejpam-4784	158	12	−	−	PUNCT
ejpam-4784	158	13	g	g	PROPN
ejpam-4784	158	14	,	,	PUNCT
ejpam-4784	158	15	ω	ω	PROPN
ejpam-4784	158	16	)	)	PUNCT
ejpam-4784	158	17	ǧn(γ	ǧn(γ	X
ejpam-4784	158	18	−	−	PROPN
ejpam-4784	158	19	g	g	PROPN
ejpam-4784	158	20	,	,	PUNCT
ejpam-4784	158	21	ω	ω	PROPN
ejpam-4784	158	22	)	)	PUNCT
ejpam-4784	158	23	≥	≥	NOUN
ejpam-4784	158	24	[	[	PUNCT
ejpam-4784	158	25	ǎn(g	ǎn(g	NUM
ejpam-4784	158	26	,	,	PUNCT
ejpam-4784	158	27	ω	ω	NOUN
ejpam-4784	158	28	)	)	PUNCT
ejpam-4784	158	29	ǧn(g	ǧn(g	PROPN
ejpam-4784	158	30	,	,	PUNCT
ejpam-4784	158	31	ω	ω	NOUN
ejpam-4784	158	32	)	)	PUNCT
ejpam-4784	158	33	]	]	PUNCT
ejpam-4784	158	34	n2	n2	NOUN
ejpam-4784	158	35	(	(	PUNCT
ejpam-4784	158	36	γ	γ	PROPN
ejpam-4784	158	37	−	−	PROPN
ejpam-4784	158	38	n)2	n)2	PROPN
ejpam-4784	158	39	≥	≥	NOUN
ejpam-4784	158	40	1	1	NUM
ejpam-4784	158	41	.	.	PUNCT
ejpam-4784	158	42	(	(	PUNCT
ejpam-4784	158	43	ii	ii	NOUN
ejpam-4784	158	44	)	)	PUNCT
ejpam-4784	158	45	let	let	VERB
ejpam-4784	158	46	t	t	PROPN
ejpam-4784	158	47	=	=	SYM
ejpam-4784	158	48	r.	r.	PROPN
ejpam-4784	158	49	then	then	ADV
ejpam-4784	158	50	for	for	ADP
ejpam-4784	158	51	weight	weight	NOUN
ejpam-4784	158	52	ω	ω	NOUN
ejpam-4784	158	53	:	:	PUNCT
ejpam-4784	158	54	r	r	NOUN
ejpam-4784	158	55	→	→	SYM
ejpam-4784	158	56	r	r	NOUN
ejpam-4784	158	57	and	and	CCONJ
ejpam-4784	158	58	for	for	ADP
ejpam-4784	158	59	continuous	continuous	ADJ
ejpam-4784	158	60	function	function	NOUN
ejpam-4784	158	61	g	g	NOUN
ejpam-4784	158	62	:	:	PUNCT
ejpam-4784	158	63	r	r	NOUN
ejpam-4784	158	64	→	→	SYM
ejpam-4784	158	65	r	r	NOUN
ejpam-4784	158	66	with	with	ADP
ejpam-4784	158	67	g([µ	g([µ	PROPN
ejpam-4784	158	68	,	,	PUNCT
ejpam-4784	158	69	ν	ν	NOUN
ejpam-4784	158	70	]	]	PUNCT
ejpam-4784	158	71	)	)	PUNCT
ejpam-4784	158	72	⊂	⊂	PROPN
ejpam-4784	159	1	[	[	X
ejpam-4784	159	2	n	n	CCONJ
ejpam-4784	159	3	,	,	PUNCT
ejpam-4784	159	4	n	n	X
ejpam-4784	159	5	]	]	PUNCT
ejpam-4784	159	6	⊂	⊂	X
ejpam-4784	159	7	(	(	PUNCT
ejpam-4784	159	8	0	0	NUM
ejpam-4784	159	9	,	,	PUNCT
ejpam-4784	159	10	γ2	γ2	NOUN
ejpam-4784	159	11	]	]	PUNCT
ejpam-4784	159	12	,	,	PUNCT
ejpam-4784	159	13	we	we	PRON
ejpam-4784	159	14	have	have	VERB
ejpam-4784	159	15	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	159	16	,	,	PUNCT
ejpam-4784	159	17	ω	ω	NOUN
ejpam-4784	159	18	)	)	PUNCT
ejpam-4784	159	19	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	159	20	,	,	PUNCT
ejpam-4784	159	21	ω	ω	NUM
ejpam-4784	159	22	)	)	PUNCT
ejpam-4784	159	23	≥	≥	NOUN
ejpam-4784	159	24	[	[	PUNCT
ejpam-4784	159	25	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	159	26	,	,	PUNCT
ejpam-4784	159	27	ω	ω	NOUN
ejpam-4784	159	28	)	)	PUNCT
ejpam-4784	159	29	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	159	30	,	,	PUNCT
ejpam-4784	159	31	ω	ω	PROPN
ejpam-4784	159	32	)	)	PUNCT
ejpam-4784	159	33	]	]	PUNCT
ejpam-4784	159	34	n2	n2	NOUN
ejpam-4784	159	35	(	(	PUNCT
ejpam-4784	159	36	γ	γ	X
ejpam-4784	159	37	−n)2	−n)2	VERB
ejpam-4784	159	38	≥	≥	PUNCT
ejpam-4784	159	39	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	159	40	−	−	PUNCT
ejpam-4784	159	41	g	g	PROPN
ejpam-4784	159	42	,	,	PUNCT
ejpam-4784	159	43	ω	ω	NOUN
ejpam-4784	159	44	)	)	PUNCT
ejpam-4784	159	45	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	159	46	−	−	PROPN
ejpam-4784	159	47	g	g	NOUN
ejpam-4784	159	48	,	,	PUNCT
ejpam-4784	159	49	ω	ω	PROPN
ejpam-4784	159	50	)	)	PUNCT
ejpam-4784	159	51	≥	≥	NOUN
ejpam-4784	159	52	[	[	PUNCT
ejpam-4784	159	53	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	159	54	,	,	PUNCT
ejpam-4784	159	55	ω	ω	NOUN
ejpam-4784	159	56	)	)	PUNCT
ejpam-4784	159	57	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	159	58	,	,	PUNCT
ejpam-4784	159	59	ω	ω	PROPN
ejpam-4784	159	60	)	)	PUNCT
ejpam-4784	159	61	]	]	PUNCT
ejpam-4784	159	62	n2	n2	NOUN
ejpam-4784	159	63	(	(	PUNCT
ejpam-4784	159	64	γ	γ	PROPN
ejpam-4784	159	65	−	−	PROPN
ejpam-4784	159	66	n)2	n)2	PROPN
ejpam-4784	159	67	≥	≥	NOUN
ejpam-4784	159	68	1	1	NUM
ejpam-4784	159	69	.	.	PUNCT
ejpam-4784	160	1	s.	s.	PROPN
ejpam-4784	160	2	chanan	chanan	PROPN
ejpam-4784	160	3	,	,	PUNCT
ejpam-4784	160	4	n.	n.	PROPN
ejpam-4784	160	5	irshad	irshad	PROPN
ejpam-4784	160	6	,	,	PUNCT
ejpam-4784	160	7	a.	a.	PROPN
ejpam-4784	160	8	khan	khan	PROPN
ejpam-4784	160	9	/	/	SYM
ejpam-4784	160	10	eur	eur	PROPN
ejpam-4784	160	11	.	.	PUNCT
ejpam-4784	161	1	j.	j.	PROPN
ejpam-4784	161	2	pure	pure	PROPN
ejpam-4784	161	3	appl	appl	PROPN
ejpam-4784	161	4	.	.	PROPN
ejpam-4784	161	5	math	math	PROPN
ejpam-4784	161	6	,	,	PUNCT
ejpam-4784	161	7	16	16	NUM
ejpam-4784	161	8	(	(	PUNCT
ejpam-4784	161	9	3	3	NUM
ejpam-4784	161	10	)	)	PUNCT
ejpam-4784	161	11	(	(	PUNCT
ejpam-4784	161	12	2023	2023	NUM
ejpam-4784	161	13	)	)	PUNCT
ejpam-4784	161	14	,	,	PUNCT
ejpam-4784	161	15	1448	1448	NUM
ejpam-4784	161	16	-	-	SYM
ejpam-4784	161	17	1463	1463	NUM
ejpam-4784	161	18	1457	1457	NUM
ejpam-4784	161	19	now	now	ADV
ejpam-4784	161	20	,	,	PUNCT
ejpam-4784	161	21	we	we	PRON
ejpam-4784	161	22	will	will	AUX
ejpam-4784	161	23	prove	prove	VERB
ejpam-4784	161	24	a	a	DET
ejpam-4784	161	25	result	result	NOUN
ejpam-4784	161	26	related	relate	VERB
ejpam-4784	161	27	to	to	ADP
ejpam-4784	161	28	the	the	DET
ejpam-4784	161	29	inequality	inequality	NOUN
ejpam-4784	161	30	ǎ[µ,ν](γ−x	ǎ[µ,ν](γ−x	PROPN
ejpam-4784	161	31	,	,	PUNCT
ejpam-4784	161	32	ω	ω	NUM
ejpam-4784	161	33	)	)	PUNCT
ejpam-4784	161	34	≥	≥	PROPN
ejpam-4784	161	35	ǧ[µ,ν](γ−x	ǧ[µ,ν](γ−x	PROPN
ejpam-4784	161	36	,	,	PUNCT
ejpam-4784	161	37	ω	ω	NUM
ejpam-4784	161	38	)	)	PUNCT
ejpam-4784	161	39	.	.	PUNCT
ejpam-4784	162	1	theorem	theorem	ADJ
ejpam-4784	162	2	4	4	NUM
ejpam-4784	162	3	.	.	PUNCT
ejpam-4784	162	4	by	by	ADP
ejpam-4784	162	5	considering	consider	VERB
ejpam-4784	162	6	the	the	DET
ejpam-4784	162	7	assumptions	assumption	NOUN
ejpam-4784	162	8	of	of	ADP
ejpam-4784	162	9	theorem	theorem	ADJ
ejpam-4784	162	10	1	1	NUM
ejpam-4784	162	11	and	and	CCONJ
ejpam-4784	162	12	also	also	ADV
ejpam-4784	162	13	ζ	ζ	PROPN
ejpam-4784	162	14	∈	∈	PROPN
ejpam-4784	162	15	c([µ	c([µ	NOUN
ejpam-4784	162	16	,	,	PUNCT
ejpam-4784	162	17	ν],r	ν],r	NOUN
ejpam-4784	162	18	)	)	PUNCT
ejpam-4784	162	19	is	be	AUX
ejpam-4784	162	20	convex	convex	ADJ
ejpam-4784	162	21	and	and	CCONJ
ejpam-4784	162	22	γ	γ	X
ejpam-4784	162	23	>	>	X
ejpam-4784	162	24	0	0	NUM
ejpam-4784	162	25	,	,	PUNCT
ejpam-4784	162	26	then	then	ADV
ejpam-4784	162	27	ǎ[µ,ν](γ	ǎ[µ,ν](γ	VERB
ejpam-4784	162	28	−	−	PROPN
ejpam-4784	162	29	g	g	PROPN
ejpam-4784	162	30	,	,	PUNCT
ejpam-4784	162	31	ω	ω	PROPN
ejpam-4784	162	32	)	)	PUNCT
ejpam-4784	162	33	≥	≥	NOUN
ejpam-4784	162	34	ǧ[µ,ν](γ	ǧ[µ,ν](γ	VERB
ejpam-4784	162	35	−	−	PROPN
ejpam-4784	162	36	g	g	NOUN
ejpam-4784	162	37	,	,	PUNCT
ejpam-4784	162	38	ω	ω	NOUN
ejpam-4784	162	39	)	)	PUNCT
ejpam-4784	162	40	.	.	PUNCT
ejpam-4784	163	1	proof	proof	NOUN
ejpam-4784	163	2	.	.	PUNCT
ejpam-4784	164	1	by	by	ADP
ejpam-4784	164	2	applying	apply	VERB
ejpam-4784	164	3	ζ(x	ζ(x	NOUN
ejpam-4784	164	4	)	)	PUNCT
ejpam-4784	164	5	=	=	SYM
ejpam-4784	164	6	x	x	X
ejpam-4784	164	7	−	−	NOUN
ejpam-4784	164	8	ln(γ	ln(γ	PUNCT
ejpam-4784	164	9	−	−	NOUN
ejpam-4784	164	10	x	x	X
ejpam-4784	164	11	)	)	PUNCT
ejpam-4784	164	12	for	for	ADP
ejpam-4784	164	13	all	all	DET
ejpam-4784	164	14	x	x	SYM
ejpam-4784	164	15	∈	∈	PROPN
ejpam-4784	164	16	(	(	PUNCT
ejpam-4784	164	17	0	0	NUM
ejpam-4784	164	18	,	,	PUNCT
ejpam-4784	164	19	γ2	γ2	NOUN
ejpam-4784	164	20	]	]	PUNCT
ejpam-4784	164	21	to	to	ADP
ejpam-4784	164	22	the	the	DET
ejpam-4784	164	23	theorem	theorem	NOUN
ejpam-4784	164	24	1	1	NUM
ejpam-4784	164	25	,	,	PUNCT
ejpam-4784	164	26	we	we	PRON
ejpam-4784	164	27	get	get	VERB
ejpam-4784	164	28	required	require	VERB
ejpam-4784	164	29	result	result	NOUN
ejpam-4784	164	30	.	.	PUNCT
ejpam-4784	165	1	now	now	ADV
ejpam-4784	165	2	,	,	PUNCT
ejpam-4784	165	3	we	we	PRON
ejpam-4784	165	4	present	present	VERB
ejpam-4784	165	5	refinement	refinement	NOUN
ejpam-4784	165	6	of	of	ADP
ejpam-4784	165	7	ky	ky	PROPN
ejpam-4784	165	8	fan	fan	PROPN
ejpam-4784	165	9	inequality	inequality	PROPN
ejpam-4784	165	10	via	via	ADP
ejpam-4784	165	11	convexity	convexity	NOUN
ejpam-4784	165	12	.	.	PUNCT
ejpam-4784	166	1	theorem	theorem	NOUN
ejpam-4784	166	2	5	5	NUM
ejpam-4784	166	3	.	.	PUNCT
ejpam-4784	166	4	by	by	ADP
ejpam-4784	166	5	considering	consider	VERB
ejpam-4784	166	6	the	the	DET
ejpam-4784	166	7	assumptions	assumption	NOUN
ejpam-4784	166	8	of	of	ADP
ejpam-4784	166	9	theorem	theorem	NOUN
ejpam-4784	166	10	1	1	NUM
ejpam-4784	166	11	,	,	PUNCT
ejpam-4784	166	12	we	we	PRON
ejpam-4784	166	13	get	get	VERB
ejpam-4784	166	14	ǎ[µ,ν](γ	ǎ[µ,ν](γ	NOUN
ejpam-4784	166	15	−	−	NOUN
ejpam-4784	166	16	g	g	PROPN
ejpam-4784	166	17	,	,	PUNCT
ejpam-4784	166	18	ω	ω	NOUN
ejpam-4784	166	19	)	)	PUNCT
ejpam-4784	166	20	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	166	21	−	−	NUM
ejpam-4784	166	22	x	x	SYM
ejpam-4784	166	23	,	,	PUNCT
ejpam-4784	166	24	ω	ω	NOUN
ejpam-4784	166	25	)	)	PUNCT
ejpam-4784	166	26	≤	≤	NOUN
ejpam-4784	166	27	1	1	NUM
ejpam-4784	166	28	ǧ[µ,ν](g	ǧ[µ,ν](g	NOUN
ejpam-4784	166	29	,	,	PUNCT
ejpam-4784	166	30	ω	ω	NOUN
ejpam-4784	166	31	)	)	PUNCT
ejpam-4784	167	1	+	+	CCONJ
ejpam-4784	167	2	ǧ[µ,ν](γ	ǧ[µ,ν](γ	VERB
ejpam-4784	167	3	−	−	NOUN
ejpam-4784	167	4	g	g	NOUN
ejpam-4784	167	5	,	,	PUNCT
ejpam-4784	167	6	ω	ω	NOUN
ejpam-4784	167	7	)	)	PUNCT
ejpam-4784	167	8	≤	≤	PROPN
ejpam-4784	167	9	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	167	10	,	,	PUNCT
ejpam-4784	167	11	ω	ω	NOUN
ejpam-4784	167	12	)	)	PUNCT
ejpam-4784	167	13	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	167	14	,	,	PUNCT
ejpam-4784	167	15	ω	ω	NOUN
ejpam-4784	167	16	)	)	PUNCT
ejpam-4784	167	17	.	.	PUNCT
ejpam-4784	168	1	(	(	PUNCT
ejpam-4784	168	2	19	19	NUM
ejpam-4784	168	3	)	)	PUNCT
ejpam-4784	168	4	proof	proof	NOUN
ejpam-4784	168	5	.	.	PUNCT
ejpam-4784	169	1	by	by	ADP
ejpam-4784	169	2	using	use	VERB
ejpam-4784	169	3	ζ	ζ	NOUN
ejpam-4784	169	4	(	(	PUNCT
ejpam-4784	169	5	x	x	NOUN
ejpam-4784	169	6	)	)	PUNCT
ejpam-4784	169	7	=	=	SYM
ejpam-4784	169	8	1	1	NUM
ejpam-4784	169	9	1	1	NUM
ejpam-4784	169	10	+	+	CCONJ
ejpam-4784	169	11	ex	ex	PRON
ejpam-4784	169	12	,	,	PUNCT
ejpam-4784	169	13	for	for	ADP
ejpam-4784	169	14	strictly	strictly	ADV
ejpam-4784	169	15	convex	convex	VERB
ejpam-4784	169	16	on	on	ADP
ejpam-4784	169	17	[	[	X
ejpam-4784	169	18	0,∞	0,∞	NOUN
ejpam-4784	169	19	)	)	PUNCT
ejpam-4784	169	20	and	and	CCONJ
ejpam-4784	169	21	strictly	strictly	ADV
ejpam-4784	169	22	concave	concave	VERB
ejpam-4784	169	23	on	on	ADP
ejpam-4784	169	24	(	(	PUNCT
ejpam-4784	169	25	−∞	−∞	NOUN
ejpam-4784	169	26	,	,	PUNCT
ejpam-4784	169	27	0	0	NUM
ejpam-4784	169	28	]	]	PUNCT
ejpam-4784	169	29	.	.	PUNCT
ejpam-4784	170	1	we	we	PRON
ejpam-4784	170	2	apply	apply	VERB
ejpam-4784	170	3	convex	convex	NOUN
ejpam-4784	170	4	function	function	NOUN
ejpam-4784	170	5	to	to	ADP
ejpam-4784	170	6	the	the	DET
ejpam-4784	170	7	inequality	inequality	NOUN
ejpam-4784	170	8	(	(	PUNCT
ejpam-4784	170	9	2	2	NUM
ejpam-4784	170	10	)	)	PUNCT
ejpam-4784	170	11	and	and	CCONJ
ejpam-4784	170	12	we	we	PRON
ejpam-4784	170	13	define	define	VERB
ejpam-4784	170	14	g(η	g(η	ADJ
ejpam-4784	170	15	)	)	PUNCT
ejpam-4784	170	16	=	=	SYM
ejpam-4784	170	17	ln	ln	ADJ
ejpam-4784	170	18	γ	γ	PROPN
ejpam-4784	170	19	−	−	PROPN
ejpam-4784	170	20	g(η	g(η	PROPN
ejpam-4784	170	21	)	)	PUNCT
ejpam-4784	170	22	g(η	g(η	PROPN
ejpam-4784	170	23	)	)	PUNCT
ejpam-4784	170	24	≥	≥	NOUN
ejpam-4784	170	25	0	0	NUM
ejpam-4784	170	26	,	,	PUNCT
ejpam-4784	170	27	µ	µ	X
ejpam-4784	170	28	=	=	SYM
ejpam-4784	170	29	ln	ln	NOUN
ejpam-4784	170	30	(	(	PUNCT
ejpam-4784	170	31	γ	γ	PROPN
ejpam-4784	170	32	−	−	PROPN
ejpam-4784	170	33	µ	µ	X
ejpam-4784	170	34	µ	µ	X
ejpam-4784	170	35	)	)	PUNCT
ejpam-4784	170	36	,	,	PUNCT
ejpam-4784	170	37	ν	ν	X
ejpam-4784	170	38	=	=	SYM
ejpam-4784	170	39	ln	ln	ADJ
ejpam-4784	170	40	(	(	PUNCT
ejpam-4784	170	41	γ	γ	NOUN
ejpam-4784	170	42	−	−	PROPN
ejpam-4784	170	43	ν	ν	NOUN
ejpam-4784	170	44	ν	ν	NOUN
ejpam-4784	170	45	)	)	PUNCT
ejpam-4784	170	46	,	,	PUNCT
ejpam-4784	170	47	by	by	ADP
ejpam-4784	170	48	which	which	PRON
ejpam-4784	170	49	we	we	PRON
ejpam-4784	170	50	get	get	VERB
ejpam-4784	170	51	,	,	PUNCT
ejpam-4784	170	52	1	1	NUM
ejpam-4784	170	53	1	1	NUM
ejpam-4784	170	54	+	+	NUM
ejpam-4784	170	55	e	e	X
ejpam-4784	170	56	(	(	PUNCT
ejpam-4784	170	57	µ+	µ+	NOUN
ejpam-4784	170	58	ν	ν	X
ejpam-4784	170	59	−	−	PROPN
ejpam-4784	170	60	∫	∫	PROPN
ejpam-4784	170	61	b	b	PROPN
ejpam-4784	170	62	a	a	DET
ejpam-4784	170	63	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	170	64	)	)	PUNCT
ejpam-4784	170	65	≤	≤	NUM
ejpam-4784	170	66	1	1	NUM
ejpam-4784	170	67	1	1	NUM
ejpam-4784	170	68	+	+	CCONJ
ejpam-4784	170	69	eu	eu	PROPN
ejpam-4784	171	1	+	+	NOUN
ejpam-4784	171	2	1	1	NUM
ejpam-4784	171	3	1	1	NUM
ejpam-4784	171	4	+	+	NUM
ejpam-4784	171	5	eν	eν	PROPN
ejpam-4784	171	6	−	−	PROPN
ejpam-4784	171	7	∫	∫	PROPN
ejpam-4784	171	8	b	b	PROPN
ejpam-4784	171	9	a	a	DET
ejpam-4784	171	10	ω(†	ω(†	NOUN
ejpam-4784	171	11	)	)	PUNCT
ejpam-4784	171	12	1	1	NUM
ejpam-4784	171	13	1	1	NUM
ejpam-4784	171	14	+	+	CCONJ
ejpam-4784	171	15	eg(η	eg(η	NUM
ejpam-4784	171	16	)	)	PUNCT
ejpam-4784	171	17	1	1	NUM
ejpam-4784	171	18	1	1	NUM
ejpam-4784	171	19	+	+	NUM
ejpam-4784	171	20	exp	exp	NOUN
ejpam-4784	171	21	(	(	PUNCT
ejpam-4784	171	22	ln	ln	X
ejpam-4784	171	23	(	(	PUNCT
ejpam-4784	171	24	γ−µ	γ−µ	PROPN
ejpam-4784	171	25	µ	µ	X
ejpam-4784	171	26	)	)	PUNCT
ejpam-4784	172	1	+	+	CCONJ
ejpam-4784	172	2	ln	ln	ADJ
ejpam-4784	172	3	(	(	PUNCT
ejpam-4784	172	4	γ−ν	γ−ν	ADP
ejpam-4784	172	5	ν	ν	NOUN
ejpam-4784	172	6	)	)	PUNCT
ejpam-4784	173	1	−	−	PROPN
ejpam-4784	173	2	∫	∫	PROPN
ejpam-4784	173	3	b	b	PROPN
ejpam-4784	173	4	a	a	DET
ejpam-4784	173	5	ω(†	ω(†	NOUN
ejpam-4784	173	6	)	)	PUNCT
ejpam-4784	173	7	ln	ln	NOUN
ejpam-4784	173	8	(	(	PUNCT
ejpam-4784	173	9	γ	γ	X
ejpam-4784	173	10	−	−	PROPN
ejpam-4784	173	11	g(η	g(η	PROPN
ejpam-4784	173	12	)	)	PUNCT
ejpam-4784	173	13	g(η	g(η	PROPN
ejpam-4784	173	14	)	)	PUNCT
ejpam-4784	173	15	)	)	PUNCT
ejpam-4784	174	1	∆η	∆η	NOUN
ejpam-4784	174	2	)	)	PUNCT
ejpam-4784	174	3	≤	≤	NUM
ejpam-4784	175	1	1	1	NUM
ejpam-4784	175	2	1	1	NUM
ejpam-4784	175	3	+	+	NUM
ejpam-4784	175	4	exp	exp	NOUN
ejpam-4784	175	5	(	(	PUNCT
ejpam-4784	175	6	ln	ln	PROPN
ejpam-4784	175	7	(	(	PUNCT
ejpam-4784	175	8	γ	γ	X
ejpam-4784	175	9	−	−	PROPN
ejpam-4784	175	10	µ	µ	PROPN
ejpam-4784	175	11	u	u	NOUN
ejpam-4784	175	12	)	)	PUNCT
ejpam-4784	175	13	)	)	PUNCT
ejpam-4784	176	1	+	+	CCONJ
ejpam-4784	176	2	1	1	NUM
ejpam-4784	176	3	1	1	NUM
ejpam-4784	176	4	+	+	NUM
ejpam-4784	176	5	exp	exp	NOUN
ejpam-4784	176	6	(	(	PUNCT
ejpam-4784	176	7	ln	ln	X
ejpam-4784	176	8	(	(	PUNCT
ejpam-4784	176	9	γ	γ	NOUN
ejpam-4784	176	10	−	−	NOUN
ejpam-4784	176	11	ν	ν	NOUN
ejpam-4784	176	12	ν	ν	NOUN
ejpam-4784	176	13	)	)	PUNCT
ejpam-4784	176	14	)	)	PUNCT
ejpam-4784	177	1	−	−	NUM
ejpam-4784	178	1	∫	∫	PROPN
ejpam-4784	178	2	b	b	PROPN
ejpam-4784	178	3	a	a	DET
ejpam-4784	178	4	ω(†	ω(†	NOUN
ejpam-4784	178	5	)	)	PUNCT
ejpam-4784	178	6			PROPN
ejpam-4784	178	7	1	1	NUM
ejpam-4784	178	8	1	1	NUM
ejpam-4784	178	9	+	+	NUM
ejpam-4784	178	10	exp	exp	NOUN
ejpam-4784	178	11	(	(	PUNCT
ejpam-4784	178	12	ln	ln	PROPN
ejpam-4784	178	13	(	(	PUNCT
ejpam-4784	178	14	γ−g(η	γ−g(η	NOUN
ejpam-4784	178	15	)	)	PUNCT
ejpam-4784	178	16	g(η	g(η	PROPN
ejpam-4784	178	17	)	)	PUNCT
ejpam-4784	178	18	)	)	PUNCT
ejpam-4784	178	19	)	)	PUNCT
ejpam-4784	179	1	∆η	∆η	NUM
ejpam-4784	179	2	which	which	PRON
ejpam-4784	179	3	gives	give	VERB
ejpam-4784	179	4	,	,	PUNCT
ejpam-4784	179	5	1	1	NUM
ejpam-4784	179	6	1	1	NUM
ejpam-4784	179	7	+	+	NUM
ejpam-4784	179	8	exp	exp	NOUN
ejpam-4784	179	9	(	(	PUNCT
ejpam-4784	179	10	ln(γ	ln(γ	NOUN
ejpam-4784	179	11	−	−	PROPN
ejpam-4784	179	12	µ)(γ	µ)(γ	NOUN
ejpam-4784	179	13	−	−	PROPN
ejpam-4784	179	14	ν)−	ν)−	PROPN
ejpam-4784	179	15	∫	∫	PROPN
ejpam-4784	179	16	b	b	PROPN
ejpam-4784	179	17	a	a	DET
ejpam-4784	179	18	ω(†	ω(†	NOUN
ejpam-4784	179	19	)	)	PUNCT
ejpam-4784	179	20	ln(γ	ln(γ	PUNCT
ejpam-4784	179	21	−	−	PROPN
ejpam-4784	179	22	g(η))∆η	g(η))∆η	PROPN
ejpam-4784	179	23	)	)	PUNCT
ejpam-4784	179	24	−	−	PRON
ejpam-4784	179	25	ln(µν	ln(µν	PROPN
ejpam-4784	179	26	)	)	PUNCT
ejpam-4784	179	27	+	+	CCONJ
ejpam-4784	180	1	∫	∫	PROPN
ejpam-4784	180	2	b	b	X
ejpam-4784	180	3	a	a	DET
ejpam-4784	180	4	ω(†	ω(†	NOUN
ejpam-4784	180	5	)	)	PUNCT
ejpam-4784	180	6	ln(g(η))∆η	ln(g(η))∆η	PROPN
ejpam-4784	180	7	≤	≤	PROPN
ejpam-4784	180	8	(	(	PUNCT
ejpam-4784	180	9	µ+	µ+	NOUN
ejpam-4784	180	10	ν	ν	X
ejpam-4784	180	11	−	−	PROPN
ejpam-4784	180	12	∫	∫	PROPN
ejpam-4784	180	13	b	b	PROPN
ejpam-4784	180	14	a	a	DET
ejpam-4784	180	15	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	181	1	)	)	PUNCT
ejpam-4784	181	2	s.	s.	PROPN
ejpam-4784	181	3	chanan	chanan	PROPN
ejpam-4784	181	4	,	,	PUNCT
ejpam-4784	181	5	n.	n.	PROPN
ejpam-4784	181	6	irshad	irshad	PROPN
ejpam-4784	181	7	,	,	PUNCT
ejpam-4784	181	8	a.	a.	PROPN
ejpam-4784	181	9	khan	khan	PROPN
ejpam-4784	181	10	/	/	SYM
ejpam-4784	181	11	eur	eur	PROPN
ejpam-4784	181	12	.	.	PUNCT
ejpam-4784	182	1	j.	j.	PROPN
ejpam-4784	182	2	pure	pure	PROPN
ejpam-4784	182	3	appl	appl	PROPN
ejpam-4784	182	4	.	.	PROPN
ejpam-4784	182	5	math	math	PROPN
ejpam-4784	182	6	,	,	PUNCT
ejpam-4784	182	7	16	16	NUM
ejpam-4784	182	8	(	(	PUNCT
ejpam-4784	182	9	3	3	NUM
ejpam-4784	182	10	)	)	PUNCT
ejpam-4784	182	11	(	(	PUNCT
ejpam-4784	182	12	2023	2023	NUM
ejpam-4784	182	13	)	)	PUNCT
ejpam-4784	182	14	,	,	PUNCT
ejpam-4784	182	15	1448	1448	NUM
ejpam-4784	182	16	-	-	SYM
ejpam-4784	182	17	1463	1463	NUM
ejpam-4784	182	18	1458	1458	NUM
ejpam-4784	182	19	consequently	consequently	ADV
ejpam-4784	182	20	,	,	PUNCT
ejpam-4784	182	21	1	1	NUM
ejpam-4784	182	22	1	1	NUM
ejpam-4784	182	23	+	+	NUM
ejpam-4784	182	24	exp	exp	NOUN
ejpam-4784	182	25	(	(	PUNCT
ejpam-4784	182	26	ln	ln	ADJ
ejpam-4784	182	27	g[µ,ν]((γ	g[µ,ν]((γ	NOUN
ejpam-4784	182	28	−	−	PROPN
ejpam-4784	182	29	g	g	NOUN
ejpam-4784	182	30	)	)	PUNCT
ejpam-4784	182	31	,	,	PUNCT
ejpam-4784	182	32	ω	ω	X
ejpam-4784	182	33	)	)	PUNCT
ejpam-4784	182	34	g[µ,ν](g	g[µ,ν](g	PROPN
ejpam-4784	182	35	,	,	PUNCT
ejpam-4784	182	36	ω	ω	NOUN
ejpam-4784	182	37	)	)	PUNCT
ejpam-4784	182	38	)	)	PUNCT
ejpam-4784	182	39	≤	≤	NOUN
ejpam-4784	182	40	a[µ,ν](g	a[µ,ν](g	NUM
ejpam-4784	182	41	,	,	PUNCT
ejpam-4784	182	42	ω	ω	NOUN
ejpam-4784	182	43	)	)	PUNCT
ejpam-4784	182	44	or	or	CCONJ
ejpam-4784	182	45	1	1	NUM
ejpam-4784	182	46	ǧ[µ,ν](g	ǧ[µ,ν](g	NOUN
ejpam-4784	182	47	,	,	PUNCT
ejpam-4784	182	48	ω	ω	NOUN
ejpam-4784	182	49	)	)	PUNCT
ejpam-4784	182	50	+	+	CCONJ
ejpam-4784	182	51	ǧ[µ,ν](γ	ǧ[µ,ν](γ	VERB
ejpam-4784	182	52	−	−	NOUN
ejpam-4784	182	53	g	g	NOUN
ejpam-4784	182	54	,	,	PUNCT
ejpam-4784	182	55	ω	ω	NOUN
ejpam-4784	182	56	)	)	PUNCT
ejpam-4784	182	57	≤	≤	PROPN
ejpam-4784	182	58	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	182	59	,	,	PUNCT
ejpam-4784	182	60	ω	ω	NOUN
ejpam-4784	182	61	)	)	PUNCT
ejpam-4784	182	62	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	182	63	,	,	PUNCT
ejpam-4784	182	64	ω	ω	NOUN
ejpam-4784	182	65	)	)	PUNCT
ejpam-4784	182	66	,	,	PUNCT
ejpam-4784	182	67	this	this	PRON
ejpam-4784	182	68	gives	give	VERB
ejpam-4784	182	69	the	the	DET
ejpam-4784	182	70	right	right	ADJ
ejpam-4784	182	71	hand	hand	NOUN
ejpam-4784	182	72	side	side	NOUN
ejpam-4784	182	73	of	of	ADP
ejpam-4784	182	74	(	(	PUNCT
ejpam-4784	182	75	19	19	NUM
ejpam-4784	182	76	)	)	PUNCT
ejpam-4784	182	77	.	.	PUNCT
ejpam-4784	183	1	now	now	ADV
ejpam-4784	183	2	by	by	ADP
ejpam-4784	183	3	applying	apply	VERB
ejpam-4784	183	4	the	the	DET
ejpam-4784	183	5	theorem	theorem	NOUN
ejpam-4784	183	6	1	1	NUM
ejpam-4784	183	7	for	for	ADP
ejpam-4784	183	8	the	the	DET
ejpam-4784	183	9	convex	convex	PROPN
ejpam-4784	183	10	function	function	NOUN
ejpam-4784	183	11	−ζ	−ζ	NOUN
ejpam-4784	183	12	on	on	ADP
ejpam-4784	183	13	(	(	PUNCT
ejpam-4784	183	14	−∞	−∞	NOUN
ejpam-4784	183	15	,	,	PUNCT
ejpam-4784	183	16	0	0	NUM
ejpam-4784	183	17	]	]	PUNCT
ejpam-4784	183	18	with	with	ADP
ejpam-4784	183	19	g(η	g(η	PROPN
ejpam-4784	183	20	)	)	PUNCT
ejpam-4784	183	21	=	=	SYM
ejpam-4784	183	22	ln	ln	PROPN
ejpam-4784	183	23	g(η	g(η	PROPN
ejpam-4784	183	24	)	)	PUNCT
ejpam-4784	183	25	γ	γ	PROPN
ejpam-4784	183	26	−	−	PROPN
ejpam-4784	183	27	g(η	g(η	PROPN
ejpam-4784	183	28	)	)	PUNCT
ejpam-4784	183	29	≤	≤	NOUN
ejpam-4784	183	30	0	0	NUM
ejpam-4784	183	31	,	,	PUNCT
ejpam-4784	183	32	we	we	PRON
ejpam-4784	183	33	get	get	AUX
ejpam-4784	183	34	left	leave	VERB
ejpam-4784	183	35	side	side	NOUN
ejpam-4784	183	36	of	of	ADP
ejpam-4784	183	37	the	the	DET
ejpam-4784	183	38	inequality	inequality	NOUN
ejpam-4784	183	39	(	(	PUNCT
ejpam-4784	183	40	19	19	NUM
ejpam-4784	183	41	)	)	PUNCT
ejpam-4784	183	42	.	.	PUNCT
ejpam-4784	184	1	now	now	ADV
ejpam-4784	184	2	,	,	PUNCT
ejpam-4784	184	3	we	we	PRON
ejpam-4784	184	4	will	will	AUX
ejpam-4784	184	5	establish	establish	VERB
ejpam-4784	184	6	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	184	7	,	,	PUNCT
ejpam-4784	184	8	ω	ω	NUM
ejpam-4784	184	9	)	)	PUNCT
ejpam-4784	184	10	≥	≥	NOUN
ejpam-4784	184	11	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	184	12	,	,	PUNCT
ejpam-4784	184	13	ω	ω	NOUN
ejpam-4784	184	14	)	)	PUNCT
ejpam-4784	184	15	and	and	CCONJ
ejpam-4784	184	16	ǎ[µ,ν](1−	ǎ[µ,ν](1−	VERB
ejpam-4784	184	17	g	g	PROPN
ejpam-4784	184	18	,	,	PUNCT
ejpam-4784	184	19	ω	ω	PROPN
ejpam-4784	184	20	)	)	PUNCT
ejpam-4784	184	21	≥	≥	NOUN
ejpam-4784	184	22	ȟ[µ,ν](1−	ȟ[µ,ν](1−	ADJ
ejpam-4784	184	23	g	g	PROPN
ejpam-4784	184	24	,	,	PUNCT
ejpam-4784	184	25	ω	ω	NOUN
ejpam-4784	184	26	)	)	PUNCT
ejpam-4784	184	27	.	.	PUNCT
ejpam-4784	185	1	theorem	theorem	ADJ
ejpam-4784	185	2	6	6	NUM
ejpam-4784	185	3	.	.	PUNCT
ejpam-4784	185	4	by	by	ADP
ejpam-4784	185	5	considering	consider	VERB
ejpam-4784	185	6	the	the	DET
ejpam-4784	185	7	assumptions	assumption	NOUN
ejpam-4784	185	8	of	of	ADP
ejpam-4784	185	9	theorem	theorem	NOUN
ejpam-4784	185	10	1	1	NUM
ejpam-4784	185	11	also	also	ADV
ejpam-4784	185	12	by	by	ADP
ejpam-4784	185	13	considering	consider	VERB
ejpam-4784	185	14	g(η	g(η	VERB
ejpam-4784	185	15	)	)	PUNCT
ejpam-4784	185	16	∈	∈	PROPN
ejpam-4784	185	17	(	(	PUNCT
ejpam-4784	185	18	0	0	NUM
ejpam-4784	185	19	,	,	PUNCT
ejpam-4784	185	20	γ2	γ2	PROPN
ejpam-4784	185	21	]	]	PUNCT
ejpam-4784	185	22	⊂	⊂	PROPN
ejpam-4784	186	1	[	[	X
ejpam-4784	186	2	µ	µ	X
ejpam-4784	186	3	,	,	PUNCT
ejpam-4784	186	4	ν	ν	X
ejpam-4784	186	5	]	]	PUNCT
ejpam-4784	186	6	,	,	PUNCT
ejpam-4784	186	7	then	then	ADV
ejpam-4784	186	8	(	(	PUNCT
ejpam-4784	186	9	i	i	NOUN
ejpam-4784	186	10	)	)	PUNCT
ejpam-4784	186	11	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	186	12	,	,	PUNCT
ejpam-4784	186	13	ω	ω	NUM
ejpam-4784	186	14	)	)	PUNCT
ejpam-4784	186	15	≥	≥	NOUN
ejpam-4784	186	16	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	186	17	,	,	PUNCT
ejpam-4784	186	18	ω	ω	NOUN
ejpam-4784	186	19	)	)	PUNCT
ejpam-4784	186	20	.	.	PUNCT
ejpam-4784	187	1	(	(	PUNCT
ejpam-4784	187	2	ii	ii	NOUN
ejpam-4784	187	3	)	)	PUNCT
ejpam-4784	187	4	ǎ[µ,ν](γ	ǎ[µ,ν](γ	PROPN
ejpam-4784	187	5	−	−	PROPN
ejpam-4784	187	6	g	g	PROPN
ejpam-4784	187	7	,	,	PUNCT
ejpam-4784	187	8	ω	ω	NOUN
ejpam-4784	187	9	)	)	PUNCT
ejpam-4784	187	10	≥	≥	PRON
ejpam-4784	187	11	ȟ[µ,ν](γ	ȟ[µ,ν](γ	VERB
ejpam-4784	187	12	−	−	PROPN
ejpam-4784	187	13	g	g	PROPN
ejpam-4784	187	14	,	,	PUNCT
ejpam-4784	187	15	ω	ω	NOUN
ejpam-4784	187	16	)	)	PUNCT
ejpam-4784	187	17	.	.	PUNCT
ejpam-4784	188	1	proof	proof	NOUN
ejpam-4784	188	2	.	.	PUNCT
ejpam-4784	189	1	(	(	PUNCT
ejpam-4784	189	2	i	i	NOUN
ejpam-4784	189	3	)	)	PUNCT
ejpam-4784	189	4	by	by	ADP
ejpam-4784	189	5	using	use	VERB
ejpam-4784	189	6	ζ(x	ζ(x	NOUN
ejpam-4784	189	7	)	)	PUNCT
ejpam-4784	189	8	=	=	SYM
ejpam-4784	189	9	1	1	NUM
ejpam-4784	189	10	x	x	PUNCT
ejpam-4784	189	11	for	for	ADP
ejpam-4784	189	12	all	all	DET
ejpam-4784	189	13	x	x	SYM
ejpam-4784	189	14	∈	∈	PROPN
ejpam-4784	189	15	(	(	PUNCT
ejpam-4784	189	16	0	0	NUM
ejpam-4784	189	17	,	,	PUNCT
ejpam-4784	189	18	γ2	γ2	NOUN
ejpam-4784	189	19	]	]	PUNCT
ejpam-4784	189	20	to	to	ADP
ejpam-4784	189	21	the	the	DET
ejpam-4784	189	22	inequality	inequality	NOUN
ejpam-4784	189	23	(	(	PUNCT
ejpam-4784	189	24	2	2	X
ejpam-4784	189	25	)	)	PUNCT
ejpam-4784	189	26	we	we	PRON
ejpam-4784	189	27	get	get	VERB
ejpam-4784	189	28	,	,	PUNCT
ejpam-4784	189	29	1	1	NUM
ejpam-4784	189	30	µ+	µ+	PRON
ejpam-4784	189	31	ν	ν	NOUN
ejpam-4784	189	32	−	−	PROPN
ejpam-4784	189	33	∫	∫	PROPN
ejpam-4784	189	34	b	b	PROPN
ejpam-4784	189	35	a	a	DET
ejpam-4784	189	36	ω(†)g(η)∆η	ω(†)g(η)∆η	ADJ
ejpam-4784	189	37	≤	≤	NUM
ejpam-4784	189	38	1	1	NUM
ejpam-4784	189	39	µ	µ	NOUN
ejpam-4784	189	40	+	+	CCONJ
ejpam-4784	189	41	1	1	NUM
ejpam-4784	189	42	ν	ν	NOUN
ejpam-4784	189	43	−	−	PROPN
ejpam-4784	189	44	∫	∫	PROPN
ejpam-4784	189	45	b	b	PROPN
ejpam-4784	189	46	a	a	DET
ejpam-4784	189	47	ω(†	ω(†	NOUN
ejpam-4784	189	48	)	)	PUNCT
ejpam-4784	189	49	(	(	PUNCT
ejpam-4784	189	50	1	1	NUM
ejpam-4784	189	51	g(η	g(η	NOUN
ejpam-4784	189	52	)	)	PUNCT
ejpam-4784	189	53	)	)	PUNCT
ejpam-4784	190	1	∆η	∆η	PROPN
ejpam-4784	190	2	a[µ,ν](g	a[µ,ν](g	NUM
ejpam-4784	190	3	,	,	PUNCT
ejpam-4784	190	4	ω	ω	NOUN
ejpam-4784	190	5	)	)	PUNCT
ejpam-4784	190	6	≥	≥	NOUN
ejpam-4784	190	7	1	1	NUM
ejpam-4784	190	8	1	1	NUM
ejpam-4784	190	9	µ	µ	X
ejpam-4784	190	10	+	+	CCONJ
ejpam-4784	190	11	1	1	NUM
ejpam-4784	190	12	ν	ν	NOUN
ejpam-4784	190	13	−	−	PROPN
ejpam-4784	190	14	∫	∫	PROPN
ejpam-4784	190	15	b	b	PROPN
ejpam-4784	190	16	a	a	DET
ejpam-4784	190	17	ω(†	ω(†	NOUN
ejpam-4784	190	18	)	)	PUNCT
ejpam-4784	190	19	(	(	PUNCT
ejpam-4784	190	20	1	1	NUM
ejpam-4784	190	21	g(η	g(η	NOUN
ejpam-4784	190	22	)	)	PUNCT
ejpam-4784	190	23	)	)	PUNCT
ejpam-4784	191	1	∆η	∆η	PROPN
ejpam-4784	191	2	a[µ,ν](g	a[µ,ν](g	NUM
ejpam-4784	191	3	,	,	PUNCT
ejpam-4784	191	4	ω	ω	NUM
ejpam-4784	191	5	)	)	PUNCT
ejpam-4784	191	6	≥	≥	NOUN
ejpam-4784	191	7	h[µ,ν](g	h[µ,ν](g	NUM
ejpam-4784	191	8	,	,	PUNCT
ejpam-4784	191	9	ω	ω	NOUN
ejpam-4784	191	10	)	)	PUNCT
ejpam-4784	191	11	.	.	PUNCT
ejpam-4784	192	1	proof	proof	NOUN
ejpam-4784	192	2	.	.	PUNCT
ejpam-4784	193	1	(	(	PUNCT
ejpam-4784	193	2	ii	ii	NOUN
ejpam-4784	193	3	)	)	PUNCT
ejpam-4784	193	4	by	by	ADP
ejpam-4784	193	5	using	use	VERB
ejpam-4784	193	6	ϕ(x	ϕ(x	X
ejpam-4784	193	7	)	)	PUNCT
ejpam-4784	193	8	=	=	SYM
ejpam-4784	193	9	1	1	NUM
ejpam-4784	193	10	γ−x	γ−x	NOUN
ejpam-4784	193	11	for	for	ADP
ejpam-4784	193	12	all	all	DET
ejpam-4784	193	13	x	x	SYM
ejpam-4784	193	14	∈	∈	PROPN
ejpam-4784	193	15	(	(	PUNCT
ejpam-4784	193	16	0	0	NUM
ejpam-4784	193	17	,	,	PUNCT
ejpam-4784	193	18	γ2	γ2	NOUN
ejpam-4784	193	19	]	]	PUNCT
ejpam-4784	193	20	to	to	ADP
ejpam-4784	193	21	the	the	DET
ejpam-4784	193	22	inequality	inequality	NOUN
ejpam-4784	193	23	(	(	PUNCT
ejpam-4784	193	24	2	2	NUM
ejpam-4784	193	25	)	)	PUNCT
ejpam-4784	193	26	,	,	PUNCT
ejpam-4784	193	27	we	we	PRON
ejpam-4784	193	28	get	get	VERB
ejpam-4784	193	29	,	,	PUNCT
ejpam-4784	193	30	1	1	NUM
ejpam-4784	193	31	γ	γ	NOUN
ejpam-4784	193	32	−	−	PROPN
ejpam-4784	193	33	(	(	PUNCT
ejpam-4784	193	34	µ+	µ+	NOUN
ejpam-4784	193	35	ν	ν	X
ejpam-4784	193	36	−	−	PROPN
ejpam-4784	193	37	∫	∫	PROPN
ejpam-4784	193	38	b	b	PROPN
ejpam-4784	193	39	a	a	DET
ejpam-4784	193	40	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	193	41	)	)	PUNCT
ejpam-4784	193	42	≤	≤	NUM
ejpam-4784	194	1	1	1	NUM
ejpam-4784	194	2	γ	γ	PROPN
ejpam-4784	194	3	−	−	PROPN
ejpam-4784	194	4	µ	µ	PROPN
ejpam-4784	194	5	+	+	CCONJ
ejpam-4784	194	6	1	1	NUM
ejpam-4784	194	7	γ	γ	NOUN
ejpam-4784	194	8	−	−	ADP
ejpam-4784	194	9	ν	ν	NOUN
ejpam-4784	194	10	−	−	PROPN
ejpam-4784	194	11	∫	∫	PROPN
ejpam-4784	194	12	b	b	PROPN
ejpam-4784	194	13	a	a	DET
ejpam-4784	194	14	ω(†	ω(†	NOUN
ejpam-4784	194	15	)	)	PUNCT
ejpam-4784	194	16	(	(	PUNCT
ejpam-4784	194	17	1	1	NUM
ejpam-4784	194	18	γ	γ	PRON
ejpam-4784	194	19	−	−	PROPN
ejpam-4784	194	20	g(η	g(η	PROPN
ejpam-4784	194	21	)	)	PUNCT
ejpam-4784	194	22	)	)	PUNCT
ejpam-4784	195	1	∆η	∆η	NOUN
ejpam-4784	195	2	1	1	NUM
ejpam-4784	195	3	(	(	PUNCT
ejpam-4784	195	4	γ	γ	PROPN
ejpam-4784	195	5	−	−	PROPN
ejpam-4784	195	6	µ	µ	NUM
ejpam-4784	195	7	)	)	PUNCT
ejpam-4784	195	8	+	+	CCONJ
ejpam-4784	195	9	(	(	PUNCT
ejpam-4784	195	10	γ	γ	X
ejpam-4784	195	11	−	−	PROPN
ejpam-4784	195	12	ν)−	ν)−	PROPN
ejpam-4784	195	13	∫	∫	PROPN
ejpam-4784	195	14	b	b	PROPN
ejpam-4784	195	15	a	a	DET
ejpam-4784	195	16	ω(†)(γ	ω(†)(γ	ADJ
ejpam-4784	195	17	−	−	NOUN
ejpam-4784	195	18	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	195	19	≤	≤	ADJ
ejpam-4784	195	20	1	1	NUM
ejpam-4784	195	21	γ	γ	PROPN
ejpam-4784	195	22	−	−	PROPN
ejpam-4784	195	23	µ	µ	PROPN
ejpam-4784	195	24	+	+	CCONJ
ejpam-4784	195	25	1	1	NUM
ejpam-4784	195	26	γ	γ	NOUN
ejpam-4784	195	27	−	−	ADP
ejpam-4784	195	28	ν	ν	NOUN
ejpam-4784	195	29	−	−	PROPN
ejpam-4784	195	30	∫	∫	PROPN
ejpam-4784	195	31	b	b	PROPN
ejpam-4784	195	32	a	a	DET
ejpam-4784	195	33	ω(†	ω(†	NOUN
ejpam-4784	195	34	)	)	PUNCT
ejpam-4784	195	35	(	(	PUNCT
ejpam-4784	195	36	1	1	NUM
ejpam-4784	195	37	γ	γ	PRON
ejpam-4784	195	38	−	−	PROPN
ejpam-4784	195	39	g(η	g(η	PROPN
ejpam-4784	195	40	)	)	PUNCT
ejpam-4784	195	41	)	)	PUNCT
ejpam-4784	196	1	∆η	∆η	NOUN
ejpam-4784	196	2	ǎ[µ,ν](γ	ǎ[µ,ν](γ	VERB
ejpam-4784	196	3	−	−	NOUN
ejpam-4784	196	4	g	g	PROPN
ejpam-4784	196	5	,	,	PUNCT
ejpam-4784	196	6	ω	ω	NOUN
ejpam-4784	196	7	)	)	PUNCT
ejpam-4784	196	8	≥	≥	PRON
ejpam-4784	196	9	ȟ[µ,ν](γ	ȟ[µ,ν](γ	VERB
ejpam-4784	196	10	−	−	PROPN
ejpam-4784	196	11	g	g	PROPN
ejpam-4784	196	12	,	,	PUNCT
ejpam-4784	196	13	ω	ω	NOUN
ejpam-4784	196	14	)	)	PUNCT
ejpam-4784	196	15	.	.	PUNCT
ejpam-4784	197	1	now	now	ADV
ejpam-4784	197	2	,	,	PUNCT
ejpam-4784	197	3	we	we	PRON
ejpam-4784	197	4	present	present	VERB
ejpam-4784	197	5	arithmetic	arithmetic	ADJ
ejpam-4784	197	6	and	and	CCONJ
ejpam-4784	197	7	harmonic	harmonic	ADJ
ejpam-4784	197	8	mean	mean	NOUN
ejpam-4784	197	9	inequality	inequality	NOUN
ejpam-4784	197	10	.	.	PUNCT
ejpam-4784	198	1	s.	s.	PROPN
ejpam-4784	198	2	chanan	chanan	PROPN
ejpam-4784	198	3	,	,	PUNCT
ejpam-4784	198	4	n.	n.	PROPN
ejpam-4784	198	5	irshad	irshad	PROPN
ejpam-4784	198	6	,	,	PUNCT
ejpam-4784	198	7	a.	a.	PROPN
ejpam-4784	198	8	khan	khan	PROPN
ejpam-4784	198	9	/	/	SYM
ejpam-4784	198	10	eur	eur	PROPN
ejpam-4784	198	11	.	.	PUNCT
ejpam-4784	199	1	j.	j.	PROPN
ejpam-4784	199	2	pure	pure	PROPN
ejpam-4784	199	3	appl	appl	PROPN
ejpam-4784	199	4	.	.	PROPN
ejpam-4784	199	5	math	math	PROPN
ejpam-4784	199	6	,	,	PUNCT
ejpam-4784	199	7	16	16	NUM
ejpam-4784	199	8	(	(	PUNCT
ejpam-4784	199	9	3	3	NUM
ejpam-4784	199	10	)	)	PUNCT
ejpam-4784	199	11	(	(	PUNCT
ejpam-4784	199	12	2023	2023	NUM
ejpam-4784	199	13	)	)	PUNCT
ejpam-4784	199	14	,	,	PUNCT
ejpam-4784	199	15	1448	1448	NUM
ejpam-4784	199	16	-	-	SYM
ejpam-4784	199	17	1463	1463	NUM
ejpam-4784	199	18	1459	1459	NUM
ejpam-4784	199	19	theorem	theorem	VERB
ejpam-4784	199	20	7	7	NUM
ejpam-4784	199	21	.	.	PUNCT
ejpam-4784	199	22	by	by	ADP
ejpam-4784	199	23	considering	consider	VERB
ejpam-4784	199	24	the	the	DET
ejpam-4784	199	25	assumptions	assumption	NOUN
ejpam-4784	199	26	of	of	ADP
ejpam-4784	199	27	theorem	theorem	NOUN
ejpam-4784	199	28	1	1	NUM
ejpam-4784	199	29	,	,	PUNCT
ejpam-4784	199	30	we	we	PRON
ejpam-4784	199	31	get	get	VERB
ejpam-4784	199	32	1	1	NUM
ejpam-4784	199	33	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	199	34	,	,	PUNCT
ejpam-4784	199	35	ω	ω	NOUN
ejpam-4784	199	36	)	)	PUNCT
ejpam-4784	199	37	−	−	PROPN
ejpam-4784	199	38	1	1	NUM
ejpam-4784	199	39	ǎ[µ,ν](γ	ǎ[µ,ν](γ	NOUN
ejpam-4784	199	40	−	−	PROPN
ejpam-4784	199	41	g	g	PROPN
ejpam-4784	199	42	,	,	PUNCT
ejpam-4784	199	43	ω	ω	NOUN
ejpam-4784	199	44	)	)	PUNCT
ejpam-4784	199	45	≤	≤	NOUN
ejpam-4784	199	46	1	1	NUM
ejpam-4784	199	47	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	199	48	,	,	PUNCT
ejpam-4784	199	49	ω	ω	NOUN
ejpam-4784	199	50	)	)	PUNCT
ejpam-4784	199	51	−	−	PROPN
ejpam-4784	199	52	1	1	NUM
ejpam-4784	199	53	ȟ[µ,ν](γ	ȟ[µ,ν](γ	PROPN
ejpam-4784	199	54	−	−	PROPN
ejpam-4784	199	55	g	g	PROPN
ejpam-4784	199	56	,	,	PUNCT
ejpam-4784	199	57	ω	ω	NOUN
ejpam-4784	199	58	)	)	PUNCT
ejpam-4784	199	59	.	.	PUNCT
ejpam-4784	200	1	proof	proof	NOUN
ejpam-4784	200	2	.	.	PUNCT
ejpam-4784	201	1	we	we	PRON
ejpam-4784	201	2	establish	establish	VERB
ejpam-4784	201	3	it	it	PRON
ejpam-4784	201	4	by	by	ADP
ejpam-4784	201	5	applying	apply	VERB
ejpam-4784	201	6	the	the	DET
ejpam-4784	201	7	theorem	theorem	NOUN
ejpam-4784	201	8	1	1	NUM
ejpam-4784	201	9	to	to	ADP
ejpam-4784	201	10	the	the	DET
ejpam-4784	201	11	function	function	NOUN
ejpam-4784	201	12	,	,	PUNCT
ejpam-4784	201	13	ζ	ζ	X
ejpam-4784	201	14	(	(	PUNCT
ejpam-4784	201	15	z	z	NOUN
ejpam-4784	201	16	)	)	PUNCT
ejpam-4784	201	17	=	=	SYM
ejpam-4784	201	18	1	1	NUM
ejpam-4784	201	19	z	z	NOUN
ejpam-4784	201	20	−	−	NUM
ejpam-4784	201	21	1	1	NUM
ejpam-4784	201	22	γ	γ	NOUN
ejpam-4784	201	23	−	−	PROPN
ejpam-4784	201	24	z	z	NOUN
ejpam-4784	201	25	,	,	PUNCT
ejpam-4784	201	26	(	(	PUNCT
ejpam-4784	201	27	0	0	PUNCT
ejpam-4784	201	28	<	<	X
ejpam-4784	201	29	z	z	NOUN
ejpam-4784	201	30	≤	≤	NUM
ejpam-4784	201	31	γ	γ	X
ejpam-4784	201	32	2	2	NUM
ejpam-4784	201	33	)	)	PUNCT
ejpam-4784	201	34	.	.	PUNCT
ejpam-4784	202	1	by	by	ADP
ejpam-4784	202	2	which	which	PRON
ejpam-4784	202	3	we	we	PRON
ejpam-4784	202	4	get,	get,	VERB
ejpam-4784	202	5	1	1	NUM
ejpam-4784	202	6	µ+	µ+	PUNCT
ejpam-4784	202	7	ν	ν	NOUN
ejpam-4784	202	8	−	−	PROPN
ejpam-4784	202	9	∫	∫	PROPN
ejpam-4784	202	10	b	b	PROPN
ejpam-4784	202	11	a	a	DET
ejpam-4784	202	12	ω(†)g(η)∆η	ω(†)g(η)∆η	ADJ
ejpam-4784	202	13	−	−	NOUN
ejpam-4784	202	14			ADJ
ejpam-4784	202	15	1	1	NUM
ejpam-4784	202	16	(	(	PUNCT
ejpam-4784	202	17	γ	γ	PROPN
ejpam-4784	202	18	−	−	PROPN
ejpam-4784	202	19	µ	µ	NUM
ejpam-4784	202	20	)	)	PUNCT
ejpam-4784	202	21	+	+	CCONJ
ejpam-4784	202	22	(	(	PUNCT
ejpam-4784	202	23	γ	γ	X
ejpam-4784	202	24	−	−	PROPN
ejpam-4784	202	25	ν)−	ν)−	PROPN
ejpam-4784	202	26	∫	∫	PROPN
ejpam-4784	202	27	b	b	PROPN
ejpam-4784	202	28	a	a	DET
ejpam-4784	202	29	ω(†	ω(†	NOUN
ejpam-4784	202	30	)	)	PUNCT
ejpam-4784	202	31	(	(	PUNCT
ejpam-4784	202	32	γ	γ	PROPN
ejpam-4784	202	33	−	−	PROPN
ejpam-4784	202	34	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	202	35			NOUN
ejpam-4784	202	36	≤	≤	NUM
ejpam-4784	202	37	(	(	PUNCT
ejpam-4784	203	1	1	1	NUM
ejpam-4784	203	2	µ	µ	NOUN
ejpam-4784	203	3	−	−	NOUN
ejpam-4784	203	4	1	1	NUM
ejpam-4784	203	5	1−	1−	NUM
ejpam-4784	203	6	µ	µ	X
ejpam-4784	203	7	+	+	CCONJ
ejpam-4784	203	8	1	1	NUM
ejpam-4784	203	9	ν	ν	NOUN
ejpam-4784	203	10	−	−	PROPN
ejpam-4784	203	11	1	1	NUM
ejpam-4784	203	12	γ	γ	NOUN
ejpam-4784	203	13	−	−	ADP
ejpam-4784	203	14	ν	ν	NOUN
ejpam-4784	203	15	−	−	PROPN
ejpam-4784	203	16	∫	∫	PROPN
ejpam-4784	203	17	b	b	PROPN
ejpam-4784	203	18	a	a	DET
ejpam-4784	203	19	ω(†	ω(†	NOUN
ejpam-4784	203	20	)	)	PUNCT
ejpam-4784	203	21	(	(	PUNCT
ejpam-4784	203	22	1	1	NUM
ejpam-4784	203	23	g(η	g(η	NOUN
ejpam-4784	203	24	)	)	PUNCT
ejpam-4784	204	1	−	−	PROPN
ejpam-4784	204	2	1	1	NUM
ejpam-4784	204	3	γ	γ	NOUN
ejpam-4784	204	4	−	−	PROPN
ejpam-4784	204	5	g(η	g(η	PROPN
ejpam-4784	204	6	)	)	PUNCT
ejpam-4784	204	7	)	)	PUNCT
ejpam-4784	205	1	∆η	∆η	NOUN
ejpam-4784	205	2	)	)	PUNCT
ejpam-4784	205	3	left	leave	VERB
ejpam-4784	205	4	side	side	NOUN
ejpam-4784	205	5	of	of	ADP
ejpam-4784	205	6	inequality	inequality	NOUN
ejpam-4784	205	7	gives	give	VERB
ejpam-4784	205	8	,	,	PUNCT
ejpam-4784	205	9	1	1	NUM
ejpam-4784	205	10	ǎ[µ,ν](g	ǎ[µ,ν](g	PROPN
ejpam-4784	205	11	,	,	PUNCT
ejpam-4784	205	12	ω	ω	NOUN
ejpam-4784	205	13	)	)	PUNCT
ejpam-4784	205	14	−	−	PROPN
ejpam-4784	205	15	1	1	NUM
ejpam-4784	205	16	ǎ[µ,ν](γ	ǎ[µ,ν](γ	NOUN
ejpam-4784	205	17	−	−	PROPN
ejpam-4784	205	18	g	g	PROPN
ejpam-4784	205	19	,	,	PUNCT
ejpam-4784	205	20	ω	ω	NOUN
ejpam-4784	205	21	)	)	PUNCT
ejpam-4784	205	22	from	from	ADP
ejpam-4784	205	23	the	the	DET
ejpam-4784	205	24	right	right	ADJ
ejpam-4784	205	25	side	side	NOUN
ejpam-4784	205	26	of	of	ADP
ejpam-4784	205	27	the	the	DET
ejpam-4784	205	28	inequality	inequality	NOUN
ejpam-4784	205	29	we	we	PRON
ejpam-4784	205	30	obtain	obtain	VERB
ejpam-4784	205	31	,	,	PUNCT
ejpam-4784	205	32	[	[	PUNCT
ejpam-4784	205	33	1	1	NUM
ejpam-4784	205	34	µ	µ	NOUN
ejpam-4784	205	35	+	+	CCONJ
ejpam-4784	205	36	1	1	NUM
ejpam-4784	205	37	ν	ν	NOUN
ejpam-4784	205	38	−	−	PROPN
ejpam-4784	205	39	∫	∫	PROPN
ejpam-4784	205	40	b	b	PROPN
ejpam-4784	205	41	a	a	DET
ejpam-4784	205	42	ω(†	ω(†	NOUN
ejpam-4784	205	43	)	)	PUNCT
ejpam-4784	205	44	1	1	NUM
ejpam-4784	205	45	g(η	g(η	VERB
ejpam-4784	205	46	)	)	PUNCT
ejpam-4784	205	47	∆η	∆η	PROPN
ejpam-4784	205	48	]	]	PUNCT
ejpam-4784	206	1	−	−	PROPN
ejpam-4784	206	2	[	[	PUNCT
ejpam-4784	206	3	1	1	NUM
ejpam-4784	206	4	γ	γ	PROPN
ejpam-4784	206	5	−	−	PROPN
ejpam-4784	206	6	µ	µ	NOUN
ejpam-4784	206	7	+	+	CCONJ
ejpam-4784	206	8	1	1	NUM
ejpam-4784	206	9	γ	γ	NOUN
ejpam-4784	206	10	−	−	ADP
ejpam-4784	206	11	ν	ν	NOUN
ejpam-4784	207	1	−	−	PROPN
ejpam-4784	207	2	∫	∫	PROPN
ejpam-4784	207	3	b	b	PROPN
ejpam-4784	207	4	a	a	DET
ejpam-4784	207	5	ω(†	ω(†	NOUN
ejpam-4784	207	6	)	)	PUNCT
ejpam-4784	207	7	(	(	PUNCT
ejpam-4784	207	8	1	1	NUM
ejpam-4784	207	9	(	(	PUNCT
ejpam-4784	207	10	γ	γ	X
ejpam-4784	207	11	−	−	PROPN
ejpam-4784	207	12	g(η	g(η	PROPN
ejpam-4784	207	13	)	)	PUNCT
ejpam-4784	207	14	)	)	PUNCT
ejpam-4784	207	15	)	)	PUNCT
ejpam-4784	208	1	∆η	∆η	NOUN
ejpam-4784	208	2	]	]	PUNCT
ejpam-4784	208	3	1	1	NUM
ejpam-4784	208	4	[	[	SYM
ejpam-4784	208	5	1	1	NUM
ejpam-4784	208	6	µ	µ	NOUN
ejpam-4784	208	7	+	+	CCONJ
ejpam-4784	208	8	1	1	NUM
ejpam-4784	208	9	ν	ν	NOUN
ejpam-4784	208	10	−	−	PROPN
ejpam-4784	208	11	∫	∫	PROPN
ejpam-4784	208	12	b	b	PROPN
ejpam-4784	208	13	a	a	DET
ejpam-4784	208	14	ω(†	ω(†	NOUN
ejpam-4784	208	15	)	)	PUNCT
ejpam-4784	208	16	1	1	NUM
ejpam-4784	208	17	g(η	g(η	VERB
ejpam-4784	208	18	)	)	PUNCT
ejpam-4784	208	19	∆η	∆η	PROPN
ejpam-4784	208	20	]	]	SYM
ejpam-4784	208	21	−1	−1	NOUN
ejpam-4784	208	22	−	−	NOUN
ejpam-4784	208	23	1	1	NUM
ejpam-4784	208	24	[	[	SYM
ejpam-4784	208	25	1	1	NUM
ejpam-4784	208	26	γ	γ	PROPN
ejpam-4784	208	27	−	−	PROPN
ejpam-4784	208	28	µ	µ	NOUN
ejpam-4784	208	29	+	+	CCONJ
ejpam-4784	208	30	1	1	NUM
ejpam-4784	208	31	γ	γ	NOUN
ejpam-4784	208	32	−	−	ADP
ejpam-4784	208	33	ν	ν	NOUN
ejpam-4784	208	34	−	−	PROPN
ejpam-4784	208	35	∫	∫	PROPN
ejpam-4784	208	36	b	b	PROPN
ejpam-4784	208	37	a	a	DET
ejpam-4784	208	38	ω(†	ω(†	NOUN
ejpam-4784	208	39	)	)	PUNCT
ejpam-4784	208	40	(	(	PUNCT
ejpam-4784	208	41	1	1	NUM
ejpam-4784	208	42	γ	γ	PRON
ejpam-4784	208	43	−	−	PROPN
ejpam-4784	208	44	g(η	g(η	PROPN
ejpam-4784	208	45	)	)	PUNCT
ejpam-4784	208	46	)	)	PUNCT
ejpam-4784	209	1	∆η	∆η	NOUN
ejpam-4784	209	2	]	]	PUNCT
ejpam-4784	209	3	−1	−1	NOUN
ejpam-4784	209	4	=	=	SYM
ejpam-4784	209	5	1	1	NUM
ejpam-4784	209	6	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	209	7	,	,	PUNCT
ejpam-4784	209	8	ω	ω	NOUN
ejpam-4784	209	9	)	)	PUNCT
ejpam-4784	209	10	−	−	PROPN
ejpam-4784	209	11	1	1	NUM
ejpam-4784	209	12	ȟ[µ,ν](γ	ȟ[µ,ν](γ	PROPN
ejpam-4784	209	13	−	−	PROPN
ejpam-4784	209	14	g	g	PROPN
ejpam-4784	209	15	,	,	PUNCT
ejpam-4784	209	16	ω	ω	NOUN
ejpam-4784	209	17	)	)	PUNCT
ejpam-4784	209	18	that	that	PRON
ejpam-4784	209	19	completes	complete	VERB
ejpam-4784	209	20	the	the	DET
ejpam-4784	209	21	proof	proof	NOUN
ejpam-4784	209	22	.	.	PUNCT
ejpam-4784	210	1	now	now	ADV
ejpam-4784	210	2	,	,	PUNCT
ejpam-4784	210	3	we	we	PRON
ejpam-4784	210	4	establish	establish	VERB
ejpam-4784	210	5	geometric	geometric	ADJ
ejpam-4784	210	6	and	and	CCONJ
ejpam-4784	210	7	harmonic	harmonic	ADJ
ejpam-4784	210	8	mean	mean	NOUN
ejpam-4784	210	9	inequality	inequality	NOUN
ejpam-4784	210	10	for	for	ADP
ejpam-4784	210	11	time	time	NOUN
ejpam-4784	210	12	scale	scale	NOUN
ejpam-4784	210	13	.	.	PUNCT
ejpam-4784	211	1	theorem	theorem	ADJ
ejpam-4784	211	2	8	8	NUM
ejpam-4784	211	3	.	.	PUNCT
ejpam-4784	211	4	by	by	ADP
ejpam-4784	211	5	considering	consider	VERB
ejpam-4784	211	6	the	the	DET
ejpam-4784	211	7	assumptions	assumption	NOUN
ejpam-4784	211	8	of	of	ADP
ejpam-4784	211	9	theorem	theorem	NOUN
ejpam-4784	211	10	1	1	NUM
ejpam-4784	211	11	,	,	PUNCT
ejpam-4784	211	12	we	we	PRON
ejpam-4784	211	13	get	get	VERB
ejpam-4784	211	14	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	211	15	,	,	PUNCT
ejpam-4784	211	16	ω	ω	NOUN
ejpam-4784	211	17	)	)	PUNCT
ejpam-4784	211	18	≤	≤	NOUN
ejpam-4784	211	19	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	211	20	,	,	PUNCT
ejpam-4784	211	21	ω	ω	NOUN
ejpam-4784	211	22	)	)	PUNCT
ejpam-4784	211	23	.	.	PUNCT
ejpam-4784	212	1	proof	proof	NOUN
ejpam-4784	212	2	.	.	PUNCT
ejpam-4784	213	1	by	by	ADP
ejpam-4784	213	2	using	use	VERB
ejpam-4784	213	3	ϕ(x	ϕ(x	X
ejpam-4784	213	4	)	)	PUNCT
ejpam-4784	213	5	=	=	SYM
ejpam-4784	213	6	ex	ex	X
ejpam-4784	213	7	for	for	ADP
ejpam-4784	213	8	all	all	DET
ejpam-4784	213	9	x	x	SYM
ejpam-4784	213	10	∈	∈	PROPN
ejpam-4784	213	11	[	[	X
ejpam-4784	213	12	−∞,∞	−∞,∞	X
ejpam-4784	213	13	)	)	PUNCT
ejpam-4784	213	14	to	to	ADP
ejpam-4784	213	15	the	the	DET
ejpam-4784	213	16	inequality	inequality	NOUN
ejpam-4784	213	17	(	(	PUNCT
ejpam-4784	213	18	2	2	X
ejpam-4784	213	19	)	)	PUNCT
ejpam-4784	213	20	we	we	PRON
ejpam-4784	213	21	get	get	VERB
ejpam-4784	213	22	exp	exp	NOUN
ejpam-4784	213	23	(	(	PUNCT
ejpam-4784	213	24	µ+	µ+	NOUN
ejpam-4784	213	25	ν	ν	NOUN
ejpam-4784	213	26	−	−	PROPN
ejpam-4784	213	27	∫	∫	PROPN
ejpam-4784	213	28	b	b	PROPN
ejpam-4784	213	29	a	a	DET
ejpam-4784	213	30	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	213	31	)	)	PUNCT
ejpam-4784	213	32	≤	≤	NUM
ejpam-4784	213	33	exp	exp	NOUN
ejpam-4784	213	34	(	(	PUNCT
ejpam-4784	213	35	µ	µ	NOUN
ejpam-4784	213	36	)	)	PUNCT
ejpam-4784	214	1	+	+	NUM
ejpam-4784	214	2	exp	exp	NOUN
ejpam-4784	214	3	(	(	PUNCT
ejpam-4784	214	4	ν)−	ν)−	PROPN
ejpam-4784	214	5	∫	∫	PROPN
ejpam-4784	214	6	b	b	PROPN
ejpam-4784	214	7	a	a	DET
ejpam-4784	214	8	ω(†	ω(†	NOUN
ejpam-4784	214	9	)	)	PUNCT
ejpam-4784	214	10	exp	exp	NOUN
ejpam-4784	214	11	(	(	PUNCT
ejpam-4784	214	12	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	214	13	.	.	PUNCT
ejpam-4784	214	14	by	by	ADP
ejpam-4784	214	15	replacing	replace	VERB
ejpam-4784	214	16	µ	µ	PRON
ejpam-4784	214	17	by	by	ADP
ejpam-4784	214	18	ln	ln	ADJ
ejpam-4784	214	19	(	(	PUNCT
ejpam-4784	214	20	1	1	NUM
ejpam-4784	214	21	µ	µ	NOUN
ejpam-4784	214	22	)	)	PUNCT
ejpam-4784	214	23	,	,	PUNCT
ejpam-4784	214	24	ν	ν	NOUN
ejpam-4784	214	25	by	by	ADP
ejpam-4784	214	26	ln	ln	NOUN
ejpam-4784	214	27	(	(	PUNCT
ejpam-4784	214	28	1	1	NUM
ejpam-4784	214	29	ν	ν	NOUN
ejpam-4784	214	30	)	)	PUNCT
ejpam-4784	214	31	and	and	CCONJ
ejpam-4784	214	32	g(η	g(η	VERB
ejpam-4784	214	33	)	)	PUNCT
ejpam-4784	214	34	by	by	ADP
ejpam-4784	214	35	ln	ln	NOUN
ejpam-4784	214	36	(	(	PUNCT
ejpam-4784	214	37	1	1	NUM
ejpam-4784	214	38	g(η	g(η	NOUN
ejpam-4784	214	39	)	)	PUNCT
ejpam-4784	214	40	)	)	PUNCT
ejpam-4784	214	41	,	,	PUNCT
ejpam-4784	214	42	then	then	ADV
ejpam-4784	214	43	we	we	PRON
ejpam-4784	214	44	obtained	obtain	VERB
ejpam-4784	214	45	result	result	NOUN
ejpam-4784	214	46	.	.	PUNCT
ejpam-4784	215	1	s.	s.	PROPN
ejpam-4784	215	2	chanan	chanan	PROPN
ejpam-4784	215	3	,	,	PUNCT
ejpam-4784	215	4	n.	n.	PROPN
ejpam-4784	215	5	irshad	irshad	PROPN
ejpam-4784	215	6	,	,	PUNCT
ejpam-4784	215	7	a.	a.	PROPN
ejpam-4784	215	8	khan	khan	PROPN
ejpam-4784	215	9	/	/	SYM
ejpam-4784	215	10	eur	eur	PROPN
ejpam-4784	215	11	.	.	PUNCT
ejpam-4784	216	1	j.	j.	PROPN
ejpam-4784	216	2	pure	pure	PROPN
ejpam-4784	216	3	appl	appl	PROPN
ejpam-4784	216	4	.	.	PROPN
ejpam-4784	216	5	math	math	PROPN
ejpam-4784	216	6	,	,	PUNCT
ejpam-4784	216	7	16	16	NUM
ejpam-4784	216	8	(	(	PUNCT
ejpam-4784	216	9	3	3	NUM
ejpam-4784	216	10	)	)	PUNCT
ejpam-4784	216	11	(	(	PUNCT
ejpam-4784	216	12	2023	2023	NUM
ejpam-4784	216	13	)	)	PUNCT
ejpam-4784	216	14	,	,	PUNCT
ejpam-4784	216	15	1448	1448	NUM
ejpam-4784	216	16	-	-	SYM
ejpam-4784	216	17	1463	1463	NUM
ejpam-4784	216	18	1460	1460	NUM
ejpam-4784	216	19	theorem	theorem	NOUN
ejpam-4784	216	20	9	9	NUM
ejpam-4784	216	21	.	.	PUNCT
ejpam-4784	216	22	by	by	ADP
ejpam-4784	216	23	considering	consider	VERB
ejpam-4784	216	24	the	the	DET
ejpam-4784	216	25	assumptions	assumption	NOUN
ejpam-4784	216	26	of	of	ADP
ejpam-4784	216	27	theorem	theorem	NOUN
ejpam-4784	216	28	1	1	NUM
ejpam-4784	216	29	,	,	PUNCT
ejpam-4784	216	30	we	we	PRON
ejpam-4784	216	31	get	get	VERB
ejpam-4784	216	32	ȟ[µ,ν](γ	ȟ[µ,ν](γ	ADJ
ejpam-4784	216	33	−	−	NOUN
ejpam-4784	216	34	g	g	PROPN
ejpam-4784	216	35	,	,	PUNCT
ejpam-4784	216	36	ω	ω	NOUN
ejpam-4784	216	37	)	)	PUNCT
ejpam-4784	216	38	≤	≤	NOUN
ejpam-4784	216	39	ǧ[µ,ν](γ	ǧ[µ,ν](γ	VERB
ejpam-4784	216	40	−	−	PROPN
ejpam-4784	216	41	g	g	PROPN
ejpam-4784	216	42	,	,	PUNCT
ejpam-4784	216	43	ω	ω	NOUN
ejpam-4784	216	44	)	)	PUNCT
ejpam-4784	216	45	.	.	PUNCT
ejpam-4784	217	1	proof	proof	NOUN
ejpam-4784	217	2	.	.	PUNCT
ejpam-4784	218	1	by	by	ADP
ejpam-4784	218	2	applying	apply	VERB
ejpam-4784	218	3	ϕ(x	ϕ(x	NOUN
ejpam-4784	218	4	)	)	PUNCT
ejpam-4784	218	5	=	=	SYM
ejpam-4784	218	6	ex	ex	X
ejpam-4784	218	7	for	for	ADP
ejpam-4784	218	8	all	all	DET
ejpam-4784	218	9	x	x	SYM
ejpam-4784	218	10	∈	∈	PROPN
ejpam-4784	218	11	(	(	PUNCT
ejpam-4784	218	12	0	0	NUM
ejpam-4784	218	13	,	,	PUNCT
ejpam-4784	218	14	γ2	γ2	NOUN
ejpam-4784	218	15	]	]	PUNCT
ejpam-4784	218	16	to	to	ADP
ejpam-4784	218	17	the	the	DET
ejpam-4784	218	18	inequality	inequality	NOUN
ejpam-4784	218	19	(	(	PUNCT
ejpam-4784	218	20	2	2	NUM
ejpam-4784	218	21	)	)	PUNCT
ejpam-4784	218	22	,	,	PUNCT
ejpam-4784	218	23	exp	exp	NOUN
ejpam-4784	218	24	(	(	PUNCT
ejpam-4784	218	25	µ+	µ+	NOUN
ejpam-4784	218	26	ν	ν	NOUN
ejpam-4784	218	27	−	−	PROPN
ejpam-4784	218	28	∫	∫	PROPN
ejpam-4784	218	29	b	b	PROPN
ejpam-4784	218	30	a	a	DET
ejpam-4784	218	31	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	218	32	)	)	PUNCT
ejpam-4784	218	33	≤	≤	NUM
ejpam-4784	218	34	exp	exp	NOUN
ejpam-4784	218	35	(	(	PUNCT
ejpam-4784	218	36	µ	µ	NOUN
ejpam-4784	218	37	)	)	PUNCT
ejpam-4784	218	38	+	+	NUM
ejpam-4784	218	39	exp	exp	NOUN
ejpam-4784	218	40	(	(	PUNCT
ejpam-4784	218	41	ν)−	ν)−	PROPN
ejpam-4784	218	42	∫	∫	PROPN
ejpam-4784	218	43	b	b	PROPN
ejpam-4784	218	44	a	a	DET
ejpam-4784	218	45	ω(†	ω(†	NOUN
ejpam-4784	218	46	)	)	PUNCT
ejpam-4784	218	47	exp	exp	NOUN
ejpam-4784	218	48	(	(	PUNCT
ejpam-4784	218	49	g(η))∆η	g(η))∆η	ADJ
ejpam-4784	218	50	.	.	PUNCT
ejpam-4784	218	51	by	by	ADP
ejpam-4784	218	52	using	use	VERB
ejpam-4784	218	53	µ	µ	NOUN
ejpam-4784	218	54	=	=	SYM
ejpam-4784	218	55	ln	ln	ADJ
ejpam-4784	218	56	(	(	PUNCT
ejpam-4784	218	57	1	1	NUM
ejpam-4784	218	58	γ−µ	γ−µ	PROPN
ejpam-4784	218	59	)	)	PUNCT
ejpam-4784	218	60	,	,	PUNCT
ejpam-4784	218	61	ν	ν	X
ejpam-4784	218	62	=	=	SYM
ejpam-4784	218	63	ln	ln	ADJ
ejpam-4784	218	64	(	(	PUNCT
ejpam-4784	218	65	1	1	NUM
ejpam-4784	218	66	γ−ν	γ−ν	ADV
ejpam-4784	218	67	)	)	PUNCT
ejpam-4784	218	68	and	and	CCONJ
ejpam-4784	218	69	g(η	g(η	VERB
ejpam-4784	218	70	)	)	PUNCT
ejpam-4784	218	71	=	=	PUNCT
ejpam-4784	218	72	ln	ln	ADJ
ejpam-4784	218	73	(	(	PUNCT
ejpam-4784	218	74	1	1	NUM
ejpam-4784	218	75	γ−g(η	γ−g(η	NOUN
ejpam-4784	218	76	)	)	PUNCT
ejpam-4784	218	77	)	)	PUNCT
ejpam-4784	218	78	,	,	PUNCT
ejpam-4784	218	79	then	then	ADV
ejpam-4784	218	80	we	we	PRON
ejpam-4784	218	81	get	get	VERB
ejpam-4784	218	82	required	require	VERB
ejpam-4784	218	83	result	result	NOUN
ejpam-4784	218	84	.	.	PUNCT
ejpam-4784	219	1	theorem	theorem	ADJ
ejpam-4784	219	2	10	10	NUM
ejpam-4784	219	3	.	.	PUNCT
ejpam-4784	219	4	by	by	ADP
ejpam-4784	219	5	considering	consider	VERB
ejpam-4784	219	6	the	the	DET
ejpam-4784	219	7	assumptions	assumption	NOUN
ejpam-4784	219	8	of	of	ADP
ejpam-4784	219	9	theorem	theorem	NOUN
ejpam-4784	219	10	1	1	NUM
ejpam-4784	219	11	,	,	PUNCT
ejpam-4784	219	12	we	we	PRON
ejpam-4784	219	13	get	get	VERB
ejpam-4784	219	14	ȟ[µ,ν](γ	ȟ[µ,ν](γ	ADJ
ejpam-4784	219	15	−	−	NOUN
ejpam-4784	219	16	g	g	PROPN
ejpam-4784	219	17	,	,	PUNCT
ejpam-4784	219	18	ω	ω	NOUN
ejpam-4784	219	19	)	)	PUNCT
ejpam-4784	219	20	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	219	21	,	,	PUNCT
ejpam-4784	219	22	ω	ω	NOUN
ejpam-4784	219	23	)	)	PUNCT
ejpam-4784	219	24	≤	≤	NOUN
ejpam-4784	219	25	ǧ[µ,ν](γ	ǧ[µ,ν](γ	VERB
ejpam-4784	219	26	−	−	PROPN
ejpam-4784	219	27	g	g	PROPN
ejpam-4784	219	28	,	,	PUNCT
ejpam-4784	219	29	ω	ω	NOUN
ejpam-4784	219	30	)	)	PUNCT
ejpam-4784	219	31	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	219	32	,	,	PUNCT
ejpam-4784	219	33	ω	ω	NOUN
ejpam-4784	219	34	)	)	PUNCT
ejpam-4784	219	35	.	.	PUNCT
ejpam-4784	220	1	(	(	PUNCT
ejpam-4784	220	2	20	20	X
ejpam-4784	220	3	)	)	PUNCT
ejpam-4784	220	4	proof	proof	NOUN
ejpam-4784	220	5	.	.	PUNCT
ejpam-4784	221	1	without	without	ADP
ejpam-4784	221	2	loss	loss	NOUN
ejpam-4784	221	3	of	of	ADP
ejpam-4784	221	4	generality	generality	NOUN
ejpam-4784	221	5	we	we	PRON
ejpam-4784	221	6	suppose	suppose	VERB
ejpam-4784	221	7	that	that	SCONJ
ejpam-4784	221	8	g′js	g′js	PROPN
ejpam-4784	221	9	are	be	AUX
ejpam-4784	221	10	not	not	PART
ejpam-4784	221	11	equal	equal	ADJ
ejpam-4784	221	12	and	and	CCONJ
ejpam-4784	221	13	by	by	ADP
ejpam-4784	221	14	using	use	VERB
ejpam-4784	221	15	the	the	DET
ejpam-4784	221	16	strictly	strictly	ADV
ejpam-4784	221	17	convex	convex	ADJ
ejpam-4784	221	18	function	function	NOUN
ejpam-4784	221	19	ϕ	ϕ	X
ejpam-4784	221	20	(	(	PUNCT
ejpam-4784	221	21	z	z	NOUN
ejpam-4784	221	22	)	)	PUNCT
ejpam-4784	222	1	=	=	SYM
ejpam-4784	222	2	ln	ln	ADJ
ejpam-4784	222	3	(	(	PUNCT
ejpam-4784	222	4	γ	γ	X
ejpam-4784	222	5	−	−	PROPN
ejpam-4784	222	6	z	z	PROPN
ejpam-4784	222	7	z	z	PROPN
ejpam-4784	222	8	)	)	PUNCT
ejpam-4784	222	9	,	,	PUNCT
ejpam-4784	222	10	for	for	ADP
ejpam-4784	222	11	all	all	DET
ejpam-4784	222	12	z	z	NOUN
ejpam-4784	222	13	∈	∈	PROPN
ejpam-4784	222	14	(	(	PUNCT
ejpam-4784	222	15	0	0	NUM
ejpam-4784	222	16	,	,	PUNCT
ejpam-4784	222	17	γ2	γ2	NOUN
ejpam-4784	222	18	]	]	PUNCT
ejpam-4784	222	19	.	.	PUNCT
ejpam-4784	223	1	we	we	PRON
ejpam-4784	223	2	set	set	VERB
ejpam-4784	223	3	,	,	PUNCT
ejpam-4784	223	4	y	y	PROPN
ejpam-4784	223	5	=	=	SYM
ejpam-4784	223	6	h[µ,ν](g	h[µ,ν](g	PROPN
ejpam-4784	223	7	,	,	PUNCT
ejpam-4784	223	8	ω	ω	NOUN
ejpam-4784	223	9	)	)	PUNCT
ejpam-4784	223	10	h[µ,ν](g	h[µ,ν](g	PROPN
ejpam-4784	223	11	,	,	PUNCT
ejpam-4784	223	12	ω	ω	NOUN
ejpam-4784	223	13	)	)	PUNCT
ejpam-4784	224	1	+	+	VERB
ejpam-4784	224	2	h[µ,ν](γ	h[µ,ν](γ	PROPN
ejpam-4784	224	3	−	−	NOUN
ejpam-4784	224	4	g	g	PROPN
ejpam-4784	224	5	,	,	PUNCT
ejpam-4784	224	6	ω	ω	PROPN
ejpam-4784	224	7	)	)	PUNCT
ejpam-4784	224	8	,	,	PUNCT
ejpam-4784	224	9	y	y	PROPN
ejpam-4784	224	10	∈	∈	PROPN
ejpam-4784	224	11	(	(	PUNCT
ejpam-4784	224	12	0	0	NUM
ejpam-4784	224	13	,	,	PUNCT
ejpam-4784	224	14	γ	γ	X
ejpam-4784	224	15	2	2	NUM
ejpam-4784	224	16	]	]	PUNCT
ejpam-4784	224	17	.	.	PUNCT
ejpam-4784	225	1	then	then	ADV
ejpam-4784	225	2	we	we	PRON
ejpam-4784	225	3	get	get	VERB
ejpam-4784	225	4	,	,	PUNCT
ejpam-4784	225	5	ln	ln	ADJ
ejpam-4784	225	6			NOUN
ejpam-4784	225	7	1−	1−	NUM
ejpam-4784	225	8	h[µ,ν](g	h[µ,ν](g	NUM
ejpam-4784	225	9	,	,	PUNCT
ejpam-4784	225	10	ω	ω	NOUN
ejpam-4784	225	11	)	)	PUNCT
ejpam-4784	225	12	h[µ,ν](g	h[µ,ν](g	PROPN
ejpam-4784	225	13	,	,	PUNCT
ejpam-4784	225	14	ω	ω	NOUN
ejpam-4784	225	15	)	)	PUNCT
ejpam-4784	226	1	+	+	VERB
ejpam-4784	226	2	h[µ,ν](γ	h[µ,ν](γ	PROPN
ejpam-4784	226	3	−	−	NOUN
ejpam-4784	226	4	g	g	PROPN
ejpam-4784	226	5	,	,	PUNCT
ejpam-4784	226	6	ω	ω	NOUN
ejpam-4784	226	7	)	)	PUNCT
ejpam-4784	226	8	h[µ,ν](g	h[µ,ν](g	PROPN
ejpam-4784	226	9	,	,	PUNCT
ejpam-4784	226	10	ω	ω	NOUN
ejpam-4784	226	11	)	)	PUNCT
ejpam-4784	226	12	h[µ,ν](g	h[µ,ν](g	PROPN
ejpam-4784	226	13	,	,	PUNCT
ejpam-4784	226	14	ω	ω	NOUN
ejpam-4784	226	15	)	)	PUNCT
ejpam-4784	227	1	+	+	VERB
ejpam-4784	227	2	h[µ,ν](γ	h[µ,ν](γ	PROPN
ejpam-4784	227	3	−	−	NOUN
ejpam-4784	227	4	g	g	PROPN
ejpam-4784	227	5	,	,	PUNCT
ejpam-4784	227	6	ω	ω	NOUN
ejpam-4784	227	7	)	)	PUNCT
ejpam-4784	227	8			PROPN
ejpam-4784	227	9	=	=	SYM
ejpam-4784	227	10	ln	ln	ADJ
ejpam-4784	227	11	(	(	PUNCT
ejpam-4784	227	12	h[µ,ν](γ	h[µ,ν](γ	PROPN
ejpam-4784	227	13	−	−	ADP
ejpam-4784	227	14	g	g	PROPN
ejpam-4784	227	15	,	,	PUNCT
ejpam-4784	227	16	ω	ω	NOUN
ejpam-4784	227	17	)	)	PUNCT
ejpam-4784	227	18	h[µ,ν](g	h[µ,ν](g	PROPN
ejpam-4784	227	19	,	,	PUNCT
ejpam-4784	227	20	ω	ω	NOUN
ejpam-4784	227	21	)	)	PUNCT
ejpam-4784	227	22	)	)	PUNCT
ejpam-4784	228	1	=	=	PUNCT
ejpam-4784	228	2	ln	ln	ADJ
ejpam-4784	228	3			NOUN
ejpam-4784	228	4	1	1	NUM
ejpam-4784	228	5	µ	µ	NOUN
ejpam-4784	228	6	+	+	CCONJ
ejpam-4784	228	7	1	1	NUM
ejpam-4784	228	8	ν	ν	NOUN
ejpam-4784	228	9	−	−	PROPN
ejpam-4784	228	10	∫	∫	PROPN
ejpam-4784	228	11	b	b	PROPN
ejpam-4784	228	12	a	a	DET
ejpam-4784	228	13	ω(†	ω(†	NOUN
ejpam-4784	228	14	)	)	PUNCT
ejpam-4784	228	15	1	1	NUM
ejpam-4784	228	16	g(η	g(η	VERB
ejpam-4784	228	17	)	)	PUNCT
ejpam-4784	228	18	∆η	∆η	PROPN
ejpam-4784	228	19	1	1	NUM
ejpam-4784	228	20	γ−µ	γ−µ	NOUN
ejpam-4784	228	21	+	+	CCONJ
ejpam-4784	228	22	1	1	NUM
ejpam-4784	228	23	γ−ν	γ−ν	ADP
ejpam-4784	228	24	−	−	ADP
ejpam-4784	228	25	∫	∫	PROPN
ejpam-4784	228	26	b	b	PROPN
ejpam-4784	228	27	a	a	DET
ejpam-4784	228	28	ω(†	ω(†	NOUN
ejpam-4784	228	29	)	)	PUNCT
ejpam-4784	228	30	1	1	NUM
ejpam-4784	228	31	γ	γ	PROPN
ejpam-4784	228	32	−	−	PROPN
ejpam-4784	228	33	g(η	g(η	PROPN
ejpam-4784	228	34	)	)	PUNCT
ejpam-4784	228	35	∆η	∆η	NOUN
ejpam-4784	229	1			NOUN
ejpam-4784	229	2	=	=	SYM
ejpam-4784	229	3	ln	ln	ADJ
ejpam-4784	229	4	(	(	PUNCT
ejpam-4784	229	5	1	1	NUM
ejpam-4784	229	6	µ	µ	NOUN
ejpam-4784	229	7	+	+	CCONJ
ejpam-4784	229	8	1	1	NUM
ejpam-4784	229	9	ν	ν	NOUN
ejpam-4784	229	10	−	−	PROPN
ejpam-4784	229	11	∫	∫	PROPN
ejpam-4784	229	12	b	b	PROPN
ejpam-4784	229	13	a	a	DET
ejpam-4784	229	14	ω(†	ω(†	NOUN
ejpam-4784	229	15	)	)	PUNCT
ejpam-4784	229	16	1	1	NUM
ejpam-4784	229	17	g(η	g(η	VERB
ejpam-4784	229	18	)	)	PUNCT
ejpam-4784	229	19	∆η	∆η	PROPN
ejpam-4784	229	20	)	)	PUNCT
ejpam-4784	230	1	−	−	PROPN
ejpam-4784	230	2	ln	ln	INTJ
ejpam-4784	230	3	(	(	PUNCT
ejpam-4784	230	4	1	1	NUM
ejpam-4784	230	5	γ	γ	PROPN
ejpam-4784	230	6	−	−	PROPN
ejpam-4784	230	7	µ	µ	NOUN
ejpam-4784	230	8	+	+	CCONJ
ejpam-4784	230	9	1	1	NUM
ejpam-4784	230	10	γ	γ	NOUN
ejpam-4784	230	11	−	−	PROPN
ejpam-4784	230	12	µν	µν	ADP
ejpam-4784	230	13	−	−	PROPN
ejpam-4784	230	14	∫	∫	PROPN
ejpam-4784	230	15	b	b	PROPN
ejpam-4784	230	16	a	a	DET
ejpam-4784	230	17	ω(†	ω(†	NOUN
ejpam-4784	230	18	)	)	PUNCT
ejpam-4784	230	19	1	1	NUM
ejpam-4784	230	20	γ	γ	PROPN
ejpam-4784	230	21	−	−	PROPN
ejpam-4784	230	22	g(η	g(η	PROPN
ejpam-4784	230	23	)	)	PUNCT
ejpam-4784	230	24	∆η	∆η	PROPN
ejpam-4784	230	25	)	)	PUNCT
ejpam-4784	230	26	≤	≤	NUM
ejpam-4784	230	27	(	(	PUNCT
ejpam-4784	230	28	ln	ln	NOUN
ejpam-4784	230	29	1	1	NUM
ejpam-4784	230	30	µν	µν	ADP
ejpam-4784	230	31	−	−	PROPN
ejpam-4784	230	32	∫	∫	PROPN
ejpam-4784	230	33	b	b	PROPN
ejpam-4784	230	34	a	a	DET
ejpam-4784	230	35	ω(†	ω(†	NOUN
ejpam-4784	230	36	)	)	PUNCT
ejpam-4784	230	37	ln	ln	ADJ
ejpam-4784	230	38	(	(	PUNCT
ejpam-4784	230	39	1	1	NUM
ejpam-4784	230	40	g(η	g(η	NOUN
ejpam-4784	230	41	)	)	PUNCT
ejpam-4784	230	42	)	)	PUNCT
ejpam-4784	230	43	∆η	∆η	NOUN
ejpam-4784	230	44	)	)	PUNCT
ejpam-4784	230	45	−	−	PROPN
ejpam-4784	231	1	(	(	PUNCT
ejpam-4784	231	2	ln	ln	NOUN
ejpam-4784	231	3	1	1	NUM
ejpam-4784	231	4	(	(	PUNCT
ejpam-4784	231	5	γ	γ	NOUN
ejpam-4784	231	6	−	−	PROPN
ejpam-4784	231	7	µ)(γ	µ)(γ	NOUN
ejpam-4784	231	8	−	−	NOUN
ejpam-4784	231	9	ν	ν	NOUN
ejpam-4784	231	10	)	)	PUNCT
ejpam-4784	231	11	−	−	PROPN
ejpam-4784	231	12	∫	∫	PROPN
ejpam-4784	231	13	b	b	PROPN
ejpam-4784	231	14	a	a	DET
ejpam-4784	231	15	ω(†	ω(†	NOUN
ejpam-4784	231	16	)	)	PUNCT
ejpam-4784	231	17	ln	ln	NOUN
ejpam-4784	231	18	(	(	PUNCT
ejpam-4784	231	19	1	1	NUM
ejpam-4784	231	20	γ	γ	PRON
ejpam-4784	231	21	−	−	PROPN
ejpam-4784	231	22	g(η	g(η	PROPN
ejpam-4784	231	23	)	)	PUNCT
ejpam-4784	231	24	)	)	PUNCT
ejpam-4784	232	1	∆η	∆η	NOUN
ejpam-4784	232	2	)	)	PUNCT
ejpam-4784	232	3	references	reference	VERB
ejpam-4784	232	4	1461	1461	NUM
ejpam-4784	232	5	right	right	ADJ
ejpam-4784	232	6	side	side	NOUN
ejpam-4784	232	7	of	of	ADP
ejpam-4784	232	8	the	the	DET
ejpam-4784	232	9	inequality	inequality	NOUN
ejpam-4784	232	10	gives	give	VERB
ejpam-4784	232	11	,	,	PUNCT
ejpam-4784	232	12	ln	ln	ADV
ejpam-4784	232	13	(	(	PUNCT
ejpam-4784	232	14	ǧ[µ,ν](γ	ǧ[µ,ν](γ	PROPN
ejpam-4784	232	15	−	−	PROPN
ejpam-4784	232	16	g	g	NOUN
ejpam-4784	232	17	,	,	PUNCT
ejpam-4784	232	18	ω	ω	NOUN
ejpam-4784	232	19	)	)	PUNCT
ejpam-4784	232	20	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	232	21	,	,	PUNCT
ejpam-4784	232	22	ω	ω	NOUN
ejpam-4784	232	23	)	)	PUNCT
ejpam-4784	232	24	)	)	PUNCT
ejpam-4784	232	25	.	.	PUNCT
ejpam-4784	233	1	we	we	PRON
ejpam-4784	233	2	get	get	VERB
ejpam-4784	233	3	required	require	VERB
ejpam-4784	233	4	inequality	inequality	NOUN
ejpam-4784	233	5	(	(	PUNCT
ejpam-4784	233	6	20	20	NUM
ejpam-4784	233	7	)	)	PUNCT
ejpam-4784	233	8	by	by	ADP
ejpam-4784	233	9	taking	take	VERB
ejpam-4784	233	10	exponential	exponential	NOUN
ejpam-4784	233	11	on	on	ADP
ejpam-4784	233	12	both	both	DET
ejpam-4784	233	13	sides	side	NOUN
ejpam-4784	233	14	.	.	PUNCT
ejpam-4784	234	1	theorem	theorem	VERB
ejpam-4784	234	2	11	11	NUM
ejpam-4784	234	3	.	.	PUNCT
ejpam-4784	235	1	by	by	ADP
ejpam-4784	235	2	considering	consider	VERB
ejpam-4784	235	3	the	the	DET
ejpam-4784	235	4	assumptions	assumption	NOUN
ejpam-4784	235	5	of	of	ADP
ejpam-4784	235	6	theorem	theorem	NOUN
ejpam-4784	235	7	1	1	NUM
ejpam-4784	235	8	,	,	PUNCT
ejpam-4784	235	9	we	we	PRON
ejpam-4784	235	10	get	get	VERB
ejpam-4784	235	11	ȟ[µ,ν](γ	ȟ[µ,ν](γ	ADJ
ejpam-4784	235	12	−	−	NOUN
ejpam-4784	235	13	g	g	PROPN
ejpam-4784	235	14	,	,	PUNCT
ejpam-4784	235	15	ω	ω	NOUN
ejpam-4784	235	16	)	)	PUNCT
ejpam-4784	235	17	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	235	18	−	−	PROPN
ejpam-4784	235	19	g	g	NOUN
ejpam-4784	235	20	,	,	PUNCT
ejpam-4784	235	21	ω	ω	NOUN
ejpam-4784	235	22	)	)	PUNCT
ejpam-4784	235	23	≤	≤	NOUN
ejpam-4784	235	24	1	1	NUM
ejpam-4784	235	25	ǧ[µ,ν](g	ǧ[µ,ν](g	NOUN
ejpam-4784	235	26	,	,	PUNCT
ejpam-4784	235	27	ω	ω	NOUN
ejpam-4784	235	28	)	)	PUNCT
ejpam-4784	235	29	+	+	CCONJ
ejpam-4784	235	30	ǧ[µ,ν](γ	ǧ[µ,ν](γ	VERB
ejpam-4784	235	31	−	−	NOUN
ejpam-4784	235	32	g	g	NOUN
ejpam-4784	235	33	,	,	PUNCT
ejpam-4784	235	34	ω	ω	NOUN
ejpam-4784	235	35	)	)	PUNCT
ejpam-4784	235	36	≤	≤	NOUN
ejpam-4784	235	37	ȟ[µ,ν](g	ȟ[µ,ν](g	PROPN
ejpam-4784	235	38	,	,	PUNCT
ejpam-4784	235	39	ω	ω	NOUN
ejpam-4784	235	40	)	)	PUNCT
ejpam-4784	235	41	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	235	42	,	,	PUNCT
ejpam-4784	235	43	ω	ω	NOUN
ejpam-4784	235	44	)	)	PUNCT
ejpam-4784	235	45	.	.	PUNCT
ejpam-4784	236	1	(	(	PUNCT
ejpam-4784	236	2	21	21	NUM
ejpam-4784	236	3	)	)	PUNCT
ejpam-4784	236	4	proof	proof	NOUN
ejpam-4784	236	5	.	.	PUNCT
ejpam-4784	237	1	for	for	ADP
ejpam-4784	237	2	the	the	DET
ejpam-4784	237	3	left	left	ADJ
ejpam-4784	237	4	hand	hand	NOUN
ejpam-4784	237	5	inequality	inequality	NOUN
ejpam-4784	237	6	we	we	PRON
ejpam-4784	237	7	apply	apply	VERB
ejpam-4784	237	8	function	function	NOUN
ejpam-4784	237	9	ζ(x	ζ(x	NOUN
ejpam-4784	237	10	)	)	PUNCT
ejpam-4784	237	11	=	=	SYM
ejpam-4784	238	1	1	1	NUM
ejpam-4784	238	2	ex	ex	ADJ
ejpam-4784	238	3	+1	+1	X
ejpam-4784	238	4	on	on	ADP
ejpam-4784	238	5	(	(	PUNCT
ejpam-4784	238	6	−∞,∞	−∞,∞	NOUN
ejpam-4784	238	7	]	]	PUNCT
ejpam-4784	238	8	to	to	ADP
ejpam-4784	238	9	the	the	DET
ejpam-4784	238	10	inequality	inequality	NOUN
ejpam-4784	238	11	(	(	PUNCT
ejpam-4784	238	12	2	2	NUM
ejpam-4784	238	13	)	)	PUNCT
ejpam-4784	238	14	that	that	PRON
ejpam-4784	238	15	is	be	AUX
ejpam-4784	238	16	,	,	PUNCT
ejpam-4784	238	17	1	1	NUM
ejpam-4784	238	18	exp	exp	NOUN
ejpam-4784	238	19	(	(	PUNCT
ejpam-4784	238	20	µ+	µ+	NOUN
ejpam-4784	238	21	ν	ν	NOUN
ejpam-4784	238	22	−	−	PROPN
ejpam-4784	238	23	∫	∫	PROPN
ejpam-4784	238	24	b	b	PROPN
ejpam-4784	238	25	a	a	DET
ejpam-4784	238	26	ω(†)g(η)∆η	ω(†)g(η)∆η	NOUN
ejpam-4784	238	27	)	)	PUNCT
ejpam-4784	238	28	+	+	CCONJ
ejpam-4784	238	29	1	1	NUM
ejpam-4784	238	30	≤	≤	NOUN
ejpam-4784	238	31	(	(	PUNCT
ejpam-4784	238	32	1	1	NUM
ejpam-4784	238	33	exp(µ	exp(µ	NOUN
ejpam-4784	238	34	)	)	PUNCT
ejpam-4784	238	35	+	+	CCONJ
ejpam-4784	238	36	1	1	X
ejpam-4784	238	37	)	)	PUNCT
ejpam-4784	238	38	+	+	CCONJ
ejpam-4784	238	39	(	(	PUNCT
ejpam-4784	238	40	1	1	NUM
ejpam-4784	238	41	exp(ν	exp(ν	NOUN
ejpam-4784	238	42	)	)	PUNCT
ejpam-4784	239	1	+	+	CCONJ
ejpam-4784	239	2	1	1	X
ejpam-4784	239	3	)	)	PUNCT
ejpam-4784	239	4	−	−	ADP
ejpam-4784	239	5	∫	∫	PROPN
ejpam-4784	239	6	b	b	PROPN
ejpam-4784	239	7	a	a	DET
ejpam-4784	239	8	ω(†	ω(†	NOUN
ejpam-4784	239	9	)	)	PUNCT
ejpam-4784	239	10	1	1	NUM
ejpam-4784	239	11	exp(g(η	exp(g(η	NOUN
ejpam-4784	239	12	)	)	PUNCT
ejpam-4784	239	13	)	)	PUNCT
ejpam-4784	240	1	+	+	CCONJ
ejpam-4784	240	2	1	1	NUM
ejpam-4784	240	3	∆η	∆η	NOUN
ejpam-4784	240	4	by	by	ADP
ejpam-4784	240	5	replacing	replace	VERB
ejpam-4784	240	6	g(η	g(η	VERB
ejpam-4784	240	7	)	)	PUNCT
ejpam-4784	240	8	=	=	SYM
ejpam-4784	240	9	ln(γ−g(η	ln(γ−g(η	VERB
ejpam-4784	240	10	)	)	PUNCT
ejpam-4784	240	11	g(η	g(η	PROPN
ejpam-4784	240	12	)	)	PUNCT
ejpam-4784	240	13	)	)	PUNCT
ejpam-4784	240	14	≥	≥	NOUN
ejpam-4784	240	15	0	0	NUM
ejpam-4784	240	16	,	,	PUNCT
ejpam-4784	240	17	µ	µ	X
ejpam-4784	240	18	by	by	ADP
ejpam-4784	240	19	ln(γ−µ	ln(γ−µ	PROPN
ejpam-4784	240	20	µ	µ	PROPN
ejpam-4784	240	21	)	)	PUNCT
ejpam-4784	240	22	and	and	CCONJ
ejpam-4784	240	23	ν	ν	NOUN
ejpam-4784	240	24	by	by	ADP
ejpam-4784	240	25	ln(γ−ν	ln(γ−ν	PROPN
ejpam-4784	240	26	ν	ν	PROPN
ejpam-4784	240	27	)	)	PUNCT
ejpam-4784	240	28	,	,	PUNCT
ejpam-4784	240	29	we	we	PRON
ejpam-4784	240	30	get	get	VERB
ejpam-4784	240	31	1	1	NUM
ejpam-4784	240	32	exp	exp	NOUN
ejpam-4784	240	33	[	[	PUNCT
ejpam-4784	240	34	ln	ln	NOUN
ejpam-4784	240	35	(	(	PUNCT
ejpam-4784	240	36	ǧ[µ,ν](γ−g	ǧ[µ,ν](γ−g	PROPN
ejpam-4784	240	37	,	,	PUNCT
ejpam-4784	240	38	ω	ω	PROPN
ejpam-4784	240	39	)	)	PUNCT
ejpam-4784	240	40	ǧ[µ,ν](γ−g	ǧ[µ,ν](γ−g	PROPN
ejpam-4784	240	41	,	,	PUNCT
ejpam-4784	240	42	ω	ω	NOUN
ejpam-4784	240	43	)	)	PUNCT
ejpam-4784	240	44	)	)	PUNCT
ejpam-4784	240	45	]	]	PUNCT
ejpam-4784	241	1	+	+	CCONJ
ejpam-4784	241	2	1	1	NUM
ejpam-4784	241	3	≤	≤	NOUN
ejpam-4784	241	4	(	(	PUNCT
ejpam-4784	241	5	1	1	NUM
ejpam-4784	241	6	γ	γ	PROPN
ejpam-4784	241	7	−	−	PROPN
ejpam-4784	241	8	µ	µ	NOUN
ejpam-4784	241	9	+	+	CCONJ
ejpam-4784	241	10	1	1	NUM
ejpam-4784	241	11	γ	γ	NOUN
ejpam-4784	241	12	−	−	ADP
ejpam-4784	241	13	ν	ν	NOUN
ejpam-4784	241	14	−	−	PROPN
ejpam-4784	241	15	∫	∫	PROPN
ejpam-4784	241	16	b	b	PROPN
ejpam-4784	241	17	a	a	DET
ejpam-4784	241	18	ω(†	ω(†	NOUN
ejpam-4784	241	19	)	)	PUNCT
ejpam-4784	241	20	1	1	NUM
ejpam-4784	241	21	(	(	PUNCT
ejpam-4784	241	22	γ	γ	X
ejpam-4784	241	23	−	−	PROPN
ejpam-4784	241	24	g(η	g(η	PROPN
ejpam-4784	241	25	)	)	PUNCT
ejpam-4784	241	26	)	)	PUNCT
ejpam-4784	241	27	∆η	∆η	PROPN
ejpam-4784	241	28	)	)	PUNCT
ejpam-4784	241	29	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	241	30	,	,	PUNCT
ejpam-4784	241	31	ω	ω	NOUN
ejpam-4784	241	32	)	)	PUNCT
ejpam-4784	241	33	+	+	CCONJ
ejpam-4784	241	34	ǧ[µ,ν](γ	ǧ[µ,ν](γ	VERB
ejpam-4784	241	35	−	−	NOUN
ejpam-4784	241	36	g	g	NOUN
ejpam-4784	241	37	,	,	PUNCT
ejpam-4784	241	38	ω	ω	NOUN
ejpam-4784	241	39	)	)	PUNCT
ejpam-4784	241	40	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	241	41	−	−	PROPN
ejpam-4784	241	42	g	g	NOUN
ejpam-4784	241	43	,	,	PUNCT
ejpam-4784	241	44	ω	ω	NOUN
ejpam-4784	241	45	)	)	PUNCT
ejpam-4784	241	46	≤	≤	NOUN
ejpam-4784	241	47	(	(	PUNCT
ejpam-4784	241	48	1	1	NUM
ejpam-4784	241	49	γ	γ	PROPN
ejpam-4784	241	50	−	−	PROPN
ejpam-4784	241	51	µ	µ	NOUN
ejpam-4784	241	52	+	+	CCONJ
ejpam-4784	241	53	1	1	NUM
ejpam-4784	241	54	γ	γ	NOUN
ejpam-4784	241	55	−	−	ADP
ejpam-4784	241	56	ν	ν	NOUN
ejpam-4784	241	57	−	−	PROPN
ejpam-4784	241	58	∫	∫	PROPN
ejpam-4784	241	59	b	b	PROPN
ejpam-4784	241	60	a	a	DET
ejpam-4784	241	61	ω(†	ω(†	NOUN
ejpam-4784	241	62	)	)	PUNCT
ejpam-4784	241	63	1	1	NUM
ejpam-4784	241	64	(	(	PUNCT
ejpam-4784	241	65	γ	γ	X
ejpam-4784	241	66	−	−	PROPN
ejpam-4784	241	67	g(η	g(η	PROPN
ejpam-4784	241	68	)	)	PUNCT
ejpam-4784	241	69	)	)	PUNCT
ejpam-4784	242	1	∆η	∆η	PROPN
ejpam-4784	242	2	)	)	PUNCT
ejpam-4784	242	3	ȟ[µ,ν](γ	ȟ[µ,ν](γ	PROPN
ejpam-4784	242	4	−	−	PROPN
ejpam-4784	242	5	g	g	PROPN
ejpam-4784	242	6	,	,	PUNCT
ejpam-4784	242	7	ω	ω	NOUN
ejpam-4784	242	8	)	)	PUNCT
ejpam-4784	242	9	ǧ[µ,ν](γ	ǧ[µ,ν](γ	NOUN
ejpam-4784	242	10	−	−	PROPN
ejpam-4784	242	11	g	g	NOUN
ejpam-4784	242	12	,	,	PUNCT
ejpam-4784	242	13	ω	ω	NOUN
ejpam-4784	242	14	)	)	PUNCT
ejpam-4784	242	15	≤	≤	NOUN
ejpam-4784	242	16	1	1	NUM
ejpam-4784	242	17	ǧ[µ,ν](γ	ǧ[µ,ν](γ	ADJ
ejpam-4784	242	18	−	−	PROPN
ejpam-4784	242	19	g	g	NOUN
ejpam-4784	242	20	,	,	PUNCT
ejpam-4784	242	21	ω	ω	NOUN
ejpam-4784	242	22	)	)	PUNCT
ejpam-4784	242	23	+	+	CCONJ
ejpam-4784	242	24	ǧ[µ,ν](g	ǧ[µ,ν](g	PROPN
ejpam-4784	242	25	,	,	PUNCT
ejpam-4784	242	26	ω	ω	NOUN
ejpam-4784	242	27	)	)	PUNCT
ejpam-4784	242	28	.	.	PUNCT
ejpam-4784	243	1	to	to	PART
ejpam-4784	243	2	prove	prove	VERB
ejpam-4784	243	3	right	right	ADJ
ejpam-4784	243	4	-	-	PUNCT
ejpam-4784	243	5	hand	hand	NOUN
ejpam-4784	243	6	of	of	ADP
ejpam-4784	243	7	the	the	DET
ejpam-4784	243	8	inequality	inequality	NOUN
ejpam-4784	243	9	(	(	PUNCT
ejpam-4784	243	10	21	21	NUM
ejpam-4784	243	11	)	)	PUNCT
ejpam-4784	243	12	we	we	PRON
ejpam-4784	243	13	apply	apply	VERB
ejpam-4784	243	14	inequality	inequality	NOUN
ejpam-4784	243	15	(	(	PUNCT
ejpam-4784	243	16	2	2	NUM
ejpam-4784	243	17	)	)	PUNCT
ejpam-4784	243	18	to	to	ADP
ejpam-4784	243	19	the	the	DET
ejpam-4784	243	20	convex	convex	PROPN
ejpam-4784	243	21	function	function	NOUN
ejpam-4784	243	22	−ζ	−ζ	NOUN
ejpam-4784	243	23	on	on	ADP
ejpam-4784	243	24	(	(	PUNCT
ejpam-4784	243	25	−∞,∞	−∞,∞	NOUN
ejpam-4784	243	26	]	]	PUNCT
ejpam-4784	243	27	with	with	ADP
ejpam-4784	243	28	g(η	g(η	PROPN
ejpam-4784	243	29	)	)	PUNCT
ejpam-4784	244	1	=	=	SYM
ejpam-4784	244	2	ln	ln	ADJ
ejpam-4784	244	3	(	(	PUNCT
ejpam-4784	244	4	g(η	g(η	PROPN
ejpam-4784	244	5	)	)	PUNCT
ejpam-4784	244	6	γ−g(η	γ−g(η	PROPN
ejpam-4784	244	7	)	)	PUNCT
ejpam-4784	244	8	)	)	PUNCT
ejpam-4784	245	1	≤	≤	ADV
ejpam-4784	245	2	0	0	NUM
ejpam-4784	245	3	,	,	PUNCT
ejpam-4784	245	4	µ	µ	X
ejpam-4784	245	5	=	=	SYM
ejpam-4784	245	6	ln	ln	X
ejpam-4784	245	7	(	(	PUNCT
ejpam-4784	245	8	µ	µ	X
ejpam-4784	245	9	γ−µ	γ−µ	PROPN
ejpam-4784	245	10	)	)	PUNCT
ejpam-4784	245	11	,	,	PUNCT
ejpam-4784	245	12	ν	ν	X
ejpam-4784	245	13	=	=	X
ejpam-4784	245	14	ln	ln	PROPN
ejpam-4784	245	15	(	(	PUNCT
ejpam-4784	245	16	ν	ν	X
ejpam-4784	245	17	γ−ν	γ−ν	ADV
ejpam-4784	245	18	)	)	PUNCT
ejpam-4784	245	19	.	.	PUNCT
ejpam-4784	246	1	references	reference	NOUN
ejpam-4784	246	2	[	[	X
ejpam-4784	246	3	1	1	NUM
ejpam-4784	246	4	]	]	PUNCT
ejpam-4784	246	5	m.	m.	NOUN
ejpam-4784	246	6	m.	m.	PROPN
ejpam-4784	246	7	ali	ali	PROPN
ejpam-4784	246	8	and	and	CCONJ
ejpam-4784	246	9	a.	a.	PROPN
ejpam-4784	246	10	r.	r.	PROPN
ejpam-4784	246	11	khan	khan	PROPN
ejpam-4784	246	12	.	.	PUNCT
ejpam-4784	247	1	generalized	generalize	VERB
ejpam-4784	247	2	integral	integral	ADJ
ejpam-4784	247	3	mercer	mercer	PROPN
ejpam-4784	247	4	’s	’s	PART
ejpam-4784	247	5	inequality	inequality	NOUN
ejpam-4784	247	6	and	and	CCONJ
ejpam-4784	247	7	integral	integral	ADJ
ejpam-4784	247	8	means	mean	NOUN
ejpam-4784	247	9	.	.	PUNCT
ejpam-4784	248	1	j.	j.	PROPN
ejpam-4784	248	2	inequal	inequal	PROPN
ejpam-4784	248	3	.	.	PUNCT
ejpam-4784	249	1	special	special	ADJ
ejpam-4784	249	2	funct	funct	NOUN
ejpam-4784	249	3	.	.	PUNCT
ejpam-4784	249	4	,	,	PUNCT
ejpam-4784	249	5	10(1):60–76	10(1):60–76	NUM
ejpam-4784	249	6	,	,	PUNCT
ejpam-4784	249	7	2019	2019	NUM
ejpam-4784	249	8	.	.	PUNCT
ejpam-4784	250	1	references	reference	NOUN
ejpam-4784	250	2	1462	1462	NUM
ejpam-4784	250	3	[	[	X
ejpam-4784	250	4	2	2	NUM
ejpam-4784	250	5	]	]	PUNCT
ejpam-4784	250	6	h.	h.	PROPN
ejpam-4784	250	7	alzer	alzer	PROPN
ejpam-4784	250	8	.	.	PUNCT
ejpam-4784	251	1	the	the	DET
ejpam-4784	251	2	inequality	inequality	NOUN
ejpam-4784	251	3	of	of	ADP
ejpam-4784	251	4	ky	ky	PROPN
ejpam-4784	251	5	fan	fan	PROPN
ejpam-4784	251	6	’s	’s	PART
ejpam-4784	251	7	and	and	CCONJ
ejpam-4784	251	8	related	related	ADJ
ejpam-4784	251	9	results	result	NOUN
ejpam-4784	251	10	.	.	PUNCT
ejpam-4784	252	1	acta	acta	PROPN
ejpam-4784	252	2	app	app	PROPN
ejpam-4784	252	3	.	.	PROPN
ejpam-4784	252	4	math	math	PROPN
ejpam-4784	252	5	.	.	PUNCT
ejpam-4784	252	6	,	,	PUNCT
ejpam-4784	253	1	38:305–354	38:305–354	PROPN
ejpam-4784	253	2	,	,	PUNCT
ejpam-4784	253	3	1995	1995	NUM
ejpam-4784	253	4	.	.	PUNCT
ejpam-4784	254	1	[	[	X
ejpam-4784	254	2	3	3	X
ejpam-4784	254	3	]	]	PUNCT
ejpam-4784	254	4	m.	m.	NOUN
ejpam-4784	254	5	k.	k.	PROPN
ejpam-4784	254	6	bakula	bakula	PROPN
ejpam-4784	254	7	and	and	CCONJ
ejpam-4784	254	8	j.	j.	PROPN
ejpam-4784	254	9	pečarić.	pečarić.	PROPN
ejpam-4784	254	10	on	on	ADP
ejpam-4784	254	11	the	the	DET
ejpam-4784	254	12	jensen	jensen	PROPN
ejpam-4784	254	13	’s	’s	PART
ejpam-4784	254	14	inequality	inequality	NOUN
ejpam-4784	254	15	for	for	ADP
ejpam-4784	254	16	convex	convex	NOUN
ejpam-4784	254	17	functions	function	NOUN
ejpam-4784	254	18	on	on	ADP
ejpam-4784	254	19	the	the	DET
ejpam-4784	254	20	co	co	NOUN
ejpam-4784	254	21	-	-	NOUN
ejpam-4784	254	22	ordinates	ordinate	NOUN
ejpam-4784	254	23	in	in	ADP
ejpam-4784	254	24	a	a	DET
ejpam-4784	254	25	rectangle	rectangle	NOUN
ejpam-4784	254	26	from	from	ADP
ejpam-4784	254	27	the	the	DET
ejpam-4784	254	28	plane	plane	NOUN
ejpam-4784	254	29	.	.	PUNCT
ejpam-4784	255	1	taiwanese	taiwanese	ADJ
ejpam-4784	255	2	j.	j.	PROPN
ejpam-4784	255	3	math	math	PROPN
ejpam-4784	255	4	.	.	PUNCT
ejpam-4784	255	5	,	,	PUNCT
ejpam-4784	255	6	10(5):1271–1292	10(5):1271–1292	NUM
ejpam-4784	255	7	,	,	PUNCT
ejpam-4784	255	8	2006	2006	NUM
ejpam-4784	255	9	.	.	PUNCT
ejpam-4784	256	1	[	[	X
ejpam-4784	256	2	4	4	X
ejpam-4784	256	3	]	]	PUNCT
ejpam-4784	256	4	e.	e.	PROPN
ejpam-4784	256	5	f.	f.	PROPN
ejpam-4784	256	6	beckenback	beckenback	PROPN
ejpam-4784	256	7	and	and	CCONJ
ejpam-4784	256	8	r.	r.	PROPN
ejpam-4784	256	9	bellman	bellman	PROPN
ejpam-4784	256	10	.	.	PUNCT
ejpam-4784	257	1	inequalities	inequality	NOUN
ejpam-4784	257	2	.	.	PUNCT
ejpam-4784	258	1	springer	springer	PROPN
ejpam-4784	258	2	verlag	verlag	PROPN
ejpam-4784	258	3	,	,	PUNCT
ejpam-4784	258	4	berlin	berlin	PROPN
ejpam-4784	258	5	,	,	PUNCT
ejpam-4784	258	6	berlin	berlin	PROPN
ejpam-4784	258	7	,	,	PUNCT
ejpam-4784	258	8	1961	1961	NUM
ejpam-4784	258	9	.	.	PUNCT
ejpam-4784	259	1	[	[	X
ejpam-4784	259	2	5	5	NUM
ejpam-4784	259	3	]	]	PUNCT
ejpam-4784	259	4	m.	m.	NOUN
ejpam-4784	259	5	bohner	bohner	NOUN
ejpam-4784	259	6	and	and	CCONJ
ejpam-4784	259	7	s.	s.	PROPN
ejpam-4784	259	8	g.	g.	PROPN
ejpam-4784	259	9	georgiev	georgiev	PROPN
ejpam-4784	259	10	.	.	PUNCT
ejpam-4784	260	1	multivariable	multivariable	ADJ
ejpam-4784	260	2	dynamic	dynamic	ADJ
ejpam-4784	260	3	calculus	calculus	NOUN
ejpam-4784	260	4	on	on	ADP
ejpam-4784	260	5	time	time	NOUN
ejpam-4784	260	6	scales	scale	NOUN
ejpam-4784	260	7	.	.	PUNCT
ejpam-4784	261	1	springer	springer	NOUN
ejpam-4784	261	2	international	international	PROPN
ejpam-4784	261	3	publishing	publishing	PROPN
ejpam-4784	261	4	switzerland	switzerland	PROPN
ejpam-4784	261	5	,	,	PUNCT
ejpam-4784	261	6	switzerland	switzerland	PROPN
ejpam-4784	261	7	,	,	PUNCT
ejpam-4784	261	8	2016	2016	NUM
ejpam-4784	261	9	.	.	PUNCT
ejpam-4784	262	1	[	[	X
ejpam-4784	262	2	6	6	NUM
ejpam-4784	262	3	]	]	PUNCT
ejpam-4784	262	4	m.	m.	NOUN
ejpam-4784	262	5	bohner	bohner	NOUN
ejpam-4784	262	6	and	and	CCONJ
ejpam-4784	262	7	a.	a.	PROPN
ejpam-4784	262	8	peterson	peterson	PROPN
ejpam-4784	262	9	.	.	PUNCT
ejpam-4784	263	1	dynamic	dynamic	ADJ
ejpam-4784	263	2	equations	equation	NOUN
ejpam-4784	263	3	on	on	ADP
ejpam-4784	263	4	time	time	NOUN
ejpam-4784	263	5	scales	scale	NOUN
ejpam-4784	263	6	.	.	PUNCT
ejpam-4784	264	1	ma	ma	PROPN
ejpam-4784	264	2	:	:	PUNCT
ejpam-4784	264	3	birkhäuser	birkhäuser	PROPN
ejpam-4784	264	4	boston	boston	PROPN
ejpam-4784	264	5	inc	inc	PROPN
ejpam-4784	264	6	.	.	PROPN
ejpam-4784	264	7	,	,	PUNCT
ejpam-4784	264	8	boston	boston	PROPN
ejpam-4784	264	9	,	,	PUNCT
ejpam-4784	264	10	2011	2011	NUM
ejpam-4784	264	11	.	.	PUNCT
ejpam-4784	265	1	[	[	X
ejpam-4784	265	2	7	7	X
ejpam-4784	265	3	]	]	X
ejpam-4784	265	4	i.	i.	NOUN
ejpam-4784	265	5	brentic	brentic	PROPN
ejpam-4784	265	6	,	,	PUNCT
ejpam-4784	265	7	k.	k.	PROPN
ejpam-4784	265	8	a.	a.	PROPN
ejpam-4784	265	9	khan	khan	PROPN
ejpam-4784	265	10	,	,	PUNCT
ejpam-4784	265	11	and	and	CCONJ
ejpam-4784	265	12	j.	j.	PROPN
ejpam-4784	265	13	pečarić.	pečarić.	PROPN
ejpam-4784	265	14	refinements	refinement	NOUN
ejpam-4784	265	15	of	of	ADP
ejpam-4784	265	16	jensen	jensen	PROPN
ejpam-4784	265	17	’s	’s	PART
ejpam-4784	265	18	inequality	inequality	NOUN
ejpam-4784	265	19	with	with	ADP
ejpam-4784	265	20	applications	application	NOUN
ejpam-4784	265	21	to	to	ADP
ejpam-4784	265	22	cyclic	cyclic	ADJ
ejpam-4784	265	23	mixed	mixed	ADJ
ejpam-4784	265	24	symmetric	symmetric	ADJ
ejpam-4784	265	25	means	mean	NOUN
ejpam-4784	265	26	and	and	CCONJ
ejpam-4784	265	27	cauchy	cauchy	PROPN
ejpam-4784	265	28	means	mean	NOUN
ejpam-4784	265	29	.	.	PUNCT
ejpam-4784	266	1	j.	j.	PROPN
ejpam-4784	266	2	math	math	PROPN
ejpam-4784	266	3	.	.	PUNCT
ejpam-4784	267	1	ineqaul	ineqaul	PROPN
ejpam-4784	267	2	.	.	PUNCT
ejpam-4784	267	3	,	,	PUNCT
ejpam-4784	267	4	9(4):1309–1321	9(4):1309–1321	PROPN
ejpam-4784	267	5	,	,	PUNCT
ejpam-4784	267	6	2015	2015	NUM
ejpam-4784	267	7	.	.	PUNCT
ejpam-4784	268	1	[	[	X
ejpam-4784	268	2	8	8	NUM
ejpam-4784	268	3	]	]	PUNCT
ejpam-4784	268	4	s.	s.	PROPN
ejpam-4784	268	5	chanan	chanan	PROPN
ejpam-4784	268	6	,	,	PUNCT
ejpam-4784	268	7	s.	s.	PROPN
ejpam-4784	268	8	ahmed	ahmed	PROPN
ejpam-4784	268	9	a.r	a.r	PROPN
ejpam-4784	268	10	.	.	PROPN
ejpam-4784	268	11	khan	khan	PROPN
ejpam-4784	268	12	,	,	PUNCT
ejpam-4784	268	13	and	and	CCONJ
ejpam-4784	268	14	n.	n.	PROPN
ejpam-4784	268	15	raisat	raisat	PROPN
ejpam-4784	268	16	.	.	PUNCT
ejpam-4784	269	1	generalizations	generalization	NOUN
ejpam-4784	269	2	of	of	ADP
ejpam-4784	269	3	ky	ky	PROPN
ejpam-4784	269	4	fan	fan	PROPN
ejpam-4784	269	5	inequality	inequality	PROPN
ejpam-4784	269	6	and	and	CCONJ
ejpam-4784	269	7	related	related	ADJ
ejpam-4784	269	8	results	result	NOUN
ejpam-4784	269	9	.	.	PUNCT
ejpam-4784	270	1	j.	j.	PROPN
ejpam-4784	270	2	inequal	inequal	PROPN
ejpam-4784	270	3	.	.	PUNCT
ejpam-4784	270	4	and	and	CCONJ
ejpam-4784	270	5	special	special	ADJ
ejpam-4784	270	6	functions	function	NOUN
ejpam-4784	270	7	,	,	PUNCT
ejpam-4784	270	8	10:123–142	10:123–142	NUM
ejpam-4784	270	9	,	,	PUNCT
ejpam-4784	270	10	2019	2019	NUM
ejpam-4784	270	11	.	.	PUNCT
ejpam-4784	271	1	[	[	X
ejpam-4784	271	2	9	9	NUM
ejpam-4784	271	3	]	]	PUNCT
ejpam-4784	271	4	s.	s.	PROPN
ejpam-4784	271	5	chanan	chanan	PROPN
ejpam-4784	271	6	,	,	PUNCT
ejpam-4784	271	7	a.	a.	PROPN
ejpam-4784	271	8	r.	r.	PROPN
ejpam-4784	271	9	khan	khan	PROPN
ejpam-4784	271	10	,	,	PUNCT
ejpam-4784	271	11	and	and	CCONJ
ejpam-4784	271	12	i.	i.	PROPN
ejpam-4784	271	13	khan	khan	PROPN
ejpam-4784	271	14	.	.	PUNCT
ejpam-4784	272	1	gabler	gabler	PROPN
ejpam-4784	272	2	inequality	inequality	PROPN
ejpam-4784	272	3	for	for	ADP
ejpam-4784	272	4	functions	function	NOUN
ejpam-4784	272	5	with	with	ADP
ejpam-4784	272	6	nondecreasing	nondecreasing	ADJ
ejpam-4784	272	7	increments	increment	NOUN
ejpam-4784	272	8	of	of	ADP
ejpam-4784	272	9	convex	convex	ADJ
ejpam-4784	272	10	type	type	NOUN
ejpam-4784	272	11	.	.	PUNCT
ejpam-4784	273	1	adv	adv	PROPN
ejpam-4784	273	2	.	.	PUNCT
ejpam-4784	273	3	inequal	inequal	PROPN
ejpam-4784	273	4	.	.	PUNCT
ejpam-4784	274	1	appl	appl	PROPN
ejpam-4784	274	2	.	.	PROPN
ejpam-4784	274	3	,	,	PUNCT
ejpam-4784	274	4	10(3	10(3	NUM
ejpam-4784	274	5	)	)	PUNCT
ejpam-4784	274	6	,	,	PUNCT
ejpam-4784	274	7	2020	2020	NUM
ejpam-4784	274	8	.	.	PUNCT
ejpam-4784	275	1	[	[	X
ejpam-4784	275	2	10	10	NUM
ejpam-4784	275	3	]	]	X
ejpam-4784	275	4	w.	w.	PROPN
ejpam-4784	275	5	s.	s.	PROPN
ejpam-4784	275	6	cheung	cheung	PROPN
ejpam-4784	275	7	,	,	PUNCT
ejpam-4784	275	8	a.	a.	NOUN
ejpam-4784	275	9	matković	matković	NOUN
ejpam-4784	275	10	,	,	PUNCT
ejpam-4784	275	11	and	and	CCONJ
ejpam-4784	275	12	j.	j.	PROPN
ejpam-4784	275	13	pečarić.	pečarić.	PROPN
ejpam-4784	275	14	a	a	DET
ejpam-4784	275	15	variant	variant	NOUN
ejpam-4784	275	16	of	of	ADP
ejpam-4784	275	17	jessen	jessen	PROPN
ejpam-4784	275	18	’s	’s	PART
ejpam-4784	275	19	inequality	inequality	NOUN
ejpam-4784	275	20	and	and	CCONJ
ejpam-4784	275	21	generalized	generalized	ADJ
ejpam-4784	275	22	means	mean	NOUN
ejpam-4784	275	23	.	.	PUNCT
ejpam-4784	276	1	j.	j.	PROPN
ejpam-4784	276	2	ineq	ineq	PROPN
ejpam-4784	276	3	.	.	PUNCT
ejpam-4784	277	1	pure	pure	ADJ
ejpam-4784	277	2	appl	appl	PROPN
ejpam-4784	277	3	.	.	PUNCT
ejpam-4784	277	4	math	math	PROPN
ejpam-4784	277	5	.	.	PUNCT
ejpam-4784	278	1	,	,	PUNCT
ejpam-4784	278	2	7(1):article	7(1):article	NUM
ejpam-4784	278	3	10	10	NUM
ejpam-4784	278	4	,	,	PUNCT
ejpam-4784	278	5	2006	2006	NUM
ejpam-4784	278	6	.	.	PUNCT
ejpam-4784	279	1	[	[	X
ejpam-4784	279	2	11	11	NUM
ejpam-4784	279	3	]	]	PUNCT
ejpam-4784	279	4	s.	s.	PROPN
ejpam-4784	279	5	s.	s.	PROPN
ejpam-4784	279	6	dragomir	dragomir	PROPN
ejpam-4784	279	7	.	.	PUNCT
ejpam-4784	280	1	some	some	DET
ejpam-4784	280	2	refinements	refinement	NOUN
ejpam-4784	280	3	of	of	ADP
ejpam-4784	280	4	jensen	jensen	PROPN
ejpam-4784	280	5	’s	’s	PART
ejpam-4784	280	6	inequality	inequality	NOUN
ejpam-4784	280	7	.	.	PUNCT
ejpam-4784	281	1	j.	j.	PROPN
ejpam-4784	281	2	math	math	PROPN
ejpam-4784	281	3	.	.	PUNCT
ejpam-4784	282	1	anal	anal	PROPN
ejpam-4784	282	2	.	.	PUNCT
ejpam-4784	283	1	appl	appl	PROPN
ejpam-4784	283	2	.	.	PROPN
ejpam-4784	283	3	,	,	PUNCT
ejpam-4784	283	4	168(2):518–522	168(2):518–522	NUM
ejpam-4784	283	5	,	,	PUNCT
ejpam-4784	283	6	1992	1992	NUM
ejpam-4784	283	7	.	.	PUNCT
ejpam-4784	284	1	[	[	X
ejpam-4784	284	2	12	12	NUM
ejpam-4784	284	3	]	]	PUNCT
ejpam-4784	284	4	s.	s.	PROPN
ejpam-4784	284	5	s.	s.	PROPN
ejpam-4784	284	6	dragomir	dragomir	PROPN
ejpam-4784	284	7	.	.	PUNCT
ejpam-4784	285	1	a	a	DET
ejpam-4784	285	2	new	new	ADJ
ejpam-4784	285	3	refinement	refinement	NOUN
ejpam-4784	285	4	of	of	ADP
ejpam-4784	285	5	jensen	jensen	PROPN
ejpam-4784	285	6	’s	’s	PART
ejpam-4784	285	7	inequality	inequality	NOUN
ejpam-4784	285	8	in	in	ADP
ejpam-4784	285	9	linear	linear	PROPN
ejpam-4784	285	10	spaces	space	NOUN
ejpam-4784	285	11	with	with	ADP
ejpam-4784	285	12	applications	application	NOUN
ejpam-4784	285	13	.	.	PUNCT
ejpam-4784	286	1	mathematical	mathematical	ADJ
ejpam-4784	286	2	and	and	CCONJ
ejpam-4784	286	3	computer	computer	NOUN
ejpam-4784	286	4	modelling	modelling	NOUN
ejpam-4784	286	5	,	,	PUNCT
ejpam-4784	286	6	52:153–163	52:153–163	NUM
ejpam-4784	286	7	,	,	PUNCT
ejpam-4784	286	8	2010	2010	NUM
ejpam-4784	286	9	.	.	PUNCT
ejpam-4784	287	1	[	[	X
ejpam-4784	287	2	13	13	NUM
ejpam-4784	287	3	]	]	PUNCT
ejpam-4784	287	4	s.	s.	PROPN
ejpam-4784	287	5	hilger	hilger	PROPN
ejpam-4784	287	6	.	.	PUNCT
ejpam-4784	288	1	ein	ein	PROPN
ejpam-4784	288	2	maßkettenkalkül	maßkettenkalkül	PROPN
ejpam-4784	288	3	mit	mit	PROPN
ejpam-4784	288	4	anwendung	anwendung	PROPN
ejpam-4784	288	5	auf	auf	PROPN
ejpam-4784	288	6	zentrumsmannigfaltigkeiten	zentrumsmannigfaltigkeiten	PROPN
ejpam-4784	288	7	.	.	PUNCT
ejpam-4784	289	1	phd	phd	NOUN
ejpam-4784	289	2	thesis	thesis	PROPN
ejpam-4784	289	3	,	,	PUNCT
ejpam-4784	289	4	universität	universität	PROPN
ejpam-4784	289	5	würzburg	würzburg	NOUN
ejpam-4784	289	6	,	,	PUNCT
ejpam-4784	289	7	1988	1988	NUM
ejpam-4784	289	8	.	.	PUNCT
ejpam-4784	290	1	[	[	X
ejpam-4784	290	2	14	14	NUM
ejpam-4784	290	3	]	]	X
ejpam-4784	290	4	s.	s.	PROPN
ejpam-4784	290	5	hussain	hussain	PROPN
ejpam-4784	290	6	and	and	CCONJ
ejpam-4784	290	7	j.	j.	PROPN
ejpam-4784	290	8	pečarić.	pečarić.	PROPN
ejpam-4784	290	9	an	an	DET
ejpam-4784	290	10	improvement	improvement	NOUN
ejpam-4784	290	11	of	of	ADP
ejpam-4784	290	12	jensen	jensen	PROPN
ejpam-4784	290	13	’s	’s	PART
ejpam-4784	290	14	inequality	inequality	NOUN
ejpam-4784	290	15	with	with	ADP
ejpam-4784	290	16	some	some	DET
ejpam-4784	290	17	applications	application	NOUN
ejpam-4784	290	18	.	.	PUNCT
ejpam-4784	291	1	asian	asian	ADJ
ejpam-4784	291	2	-	-	PUNCT
ejpam-4784	291	3	european	european	PROPN
ejpam-4784	291	4	j.	j.	PROPN
ejpam-4784	291	5	math	math	PROPN
ejpam-4784	291	6	.	.	PROPN
ejpam-4784	291	7	,	,	PUNCT
ejpam-4784	291	8	2(1):85–94	2(1):85–94	NUM
ejpam-4784	291	9	,	,	PUNCT
ejpam-4784	291	10	2009	2009	NUM
ejpam-4784	291	11	.	.	PUNCT
ejpam-4784	292	1	[	[	X
ejpam-4784	292	2	15	15	NUM
ejpam-4784	292	3	]	]	X
ejpam-4784	292	4	a.	a.	PROPN
ejpam-4784	292	5	r.	r.	PROPN
ejpam-4784	292	6	khan	khan	PROPN
ejpam-4784	292	7	and	and	CCONJ
ejpam-4784	292	8	i.	i.	PROPN
ejpam-4784	292	9	khan	khan	PROPN
ejpam-4784	292	10	.	.	PUNCT
ejpam-4784	293	1	an	an	DET
ejpam-4784	293	2	extension	extension	NOUN
ejpam-4784	293	3	of	of	ADP
ejpam-4784	293	4	jensen	jensen	PROPN
ejpam-4784	293	5	-	-	PUNCT
ejpam-4784	293	6	mercer	mercer	PROPN
ejpam-4784	293	7	inequality	inequality	NOUN
ejpam-4784	293	8	for	for	ADP
ejpam-4784	293	9	functions	function	NOUN
ejpam-4784	293	10	with	with	ADP
ejpam-4784	293	11	nondecreasing	nondecreasing	ADJ
ejpam-4784	293	12	increments	increment	NOUN
ejpam-4784	293	13	.	.	PUNCT
ejpam-4784	294	1	j.	j.	PROPN
ejpam-4784	294	2	inequal	inequal	PROPN
ejpam-4784	294	3	.	.	PUNCT
ejpam-4784	295	1	special	special	ADJ
ejpam-4784	295	2	funct	funct	NOUN
ejpam-4784	295	3	,	,	PUNCT
ejpam-4784	295	4	10(3):1–15	10(3):1–15	NUM
ejpam-4784	295	5	,	,	PUNCT
ejpam-4784	295	6	2019	2019	NUM
ejpam-4784	295	7	.	.	PUNCT
ejpam-4784	296	1	[	[	X
ejpam-4784	296	2	16	16	NUM
ejpam-4784	296	3	]	]	PUNCT
ejpam-4784	296	4	a.	a.	PROPN
ejpam-4784	296	5	r.	r.	PROPN
ejpam-4784	296	6	khan	khan	PROPN
ejpam-4784	296	7	,	,	PUNCT
ejpam-4784	296	8	i.	i.	PROPN
ejpam-4784	296	9	khan	khan	PROPN
ejpam-4784	296	10	,	,	PUNCT
ejpam-4784	296	11	and	and	CCONJ
ejpam-4784	296	12	s.	s.	PROPN
ejpam-4784	296	13	s.	s.	PROPN
ejpam-4784	296	14	a.	a.	PROPN
ejpam-4784	296	15	ramji	ramji	PROPN
ejpam-4784	296	16	.	.	PUNCT
ejpam-4784	297	1	generalization	generalization	NOUN
ejpam-4784	297	2	and	and	CCONJ
ejpam-4784	297	3	refinements	refinement	NOUN
ejpam-4784	297	4	of	of	ADP
ejpam-4784	297	5	jensenmercer	jensenmercer	NOUN
ejpam-4784	297	6	inequality	inequality	NOUN
ejpam-4784	297	7	with	with	ADP
ejpam-4784	297	8	applications	application	NOUN
ejpam-4784	297	9	.	.	PUNCT
ejpam-4784	298	1	j.	j.	PROPN
ejpam-4784	298	2	math	math	PROPN
ejpam-4784	298	3	.	.	PUNCT
ejpam-4784	299	1	inequal	inequal	ADJ
ejpam-4784	299	2	.	.	PUNCT
ejpam-4784	299	3	,	,	PUNCT
ejpam-4784	299	4	15(4):1341–1360	15(4):1341–1360	NUM
ejpam-4784	299	5	,	,	PUNCT
ejpam-4784	299	6	2021	2021	NUM
ejpam-4784	299	7	.	.	PUNCT
ejpam-4784	300	1	[	[	X
ejpam-4784	300	2	17	17	NUM
ejpam-4784	300	3	]	]	PUNCT
ejpam-4784	300	4	a.	a.	PROPN
ejpam-4784	300	5	r.	r.	PROPN
ejpam-4784	300	6	khan	khan	PROPN
ejpam-4784	300	7	,	,	PUNCT
ejpam-4784	300	8	j.	j.	PROPN
ejpam-4784	300	9	pečarić	pečarić	PROPN
ejpam-4784	300	10	,	,	PUNCT
ejpam-4784	300	11	and	and	CCONJ
ejpam-4784	300	12	m.	m.	NOUN
ejpam-4784	300	13	praljak	praljak	ADV
ejpam-4784	300	14	.	.	PUNCT
ejpam-4784	301	1	a	a	DET
ejpam-4784	301	2	note	note	NOUN
ejpam-4784	301	3	on	on	ADP
ejpam-4784	301	4	generalized	generalized	ADJ
ejpam-4784	301	5	mercer	mercer	PROPN
ejpam-4784	301	6	’s	’s	PART
ejpam-4784	301	7	inequality	inequality	NOUN
ejpam-4784	301	8	.	.	PUNCT
ejpam-4784	302	1	bull	bull	NOUN
ejpam-4784	302	2	.	.	PUNCT
ejpam-4784	303	1	malays	malays	PROPN
ejpam-4784	303	2	.	.	PUNCT
ejpam-4784	304	1	math	math	NOUN
ejpam-4784	304	2	.	.	PUNCT
ejpam-4784	305	1	sci	sci	PROPN
ejpam-4784	305	2	.	.	PROPN
ejpam-4784	305	3	soc	soc	PROPN
ejpam-4784	305	4	.	.	PROPN
ejpam-4784	305	5	,	,	PUNCT
ejpam-4784	305	6	40:881–889	40:881–889	PROPN
ejpam-4784	305	7	,	,	PUNCT
ejpam-4784	305	8	2017	2017	NUM
ejpam-4784	305	9	.	.	PUNCT
ejpam-4784	306	1	references	reference	NOUN
ejpam-4784	306	2	1463	1463	NUM
ejpam-4784	306	3	[	[	X
ejpam-4784	306	4	18	18	NUM
ejpam-4784	306	5	]	]	PUNCT
ejpam-4784	306	6	m.	m.	NOUN
ejpam-4784	306	7	a.	a.	PROPN
ejpam-4784	306	8	khan	khan	PROPN
ejpam-4784	306	9	,	,	PUNCT
ejpam-4784	306	10	a.	a.	PROPN
ejpam-4784	306	11	r.	r.	PROPN
ejpam-4784	306	12	khan	khan	PROPN
ejpam-4784	306	13	,	,	PUNCT
ejpam-4784	306	14	and	and	CCONJ
ejpam-4784	306	15	j.	j.	PROPN
ejpam-4784	306	16	pečarić.	pečarić.	PROPN
ejpam-4784	306	17	on	on	ADP
ejpam-4784	306	18	the	the	DET
ejpam-4784	306	19	refinements	refinement	NOUN
ejpam-4784	306	20	of	of	ADP
ejpam-4784	306	21	jensen	jensen	PROPN
ejpam-4784	306	22	-	-	PUNCT
ejpam-4784	306	23	mercer	mercer	PROPN
ejpam-4784	306	24	’s	’s	PART
ejpam-4784	306	25	inequality	inequality	NOUN
ejpam-4784	306	26	.	.	PUNCT
ejpam-4784	307	1	rev	rev	PROPN
ejpam-4784	307	2	.	.	PROPN
ejpam-4784	307	3	anal	anal	PROPN
ejpam-4784	307	4	.	.	PUNCT
ejpam-4784	308	1	numer	numer	PROPN
ejpam-4784	308	2	.	.	PUNCT
ejpam-4784	309	1	theor	theor	PROPN
ejpam-4784	309	2	.	.	PUNCT
ejpam-4784	310	1	approx	approx	PROPN
ejpam-4784	310	2	.	.	PUNCT
ejpam-4784	310	3	,	,	PUNCT
ejpam-4784	310	4	41(1):62–81	41(1):62–81	NUM
ejpam-4784	310	5	,	,	PUNCT
ejpam-4784	310	6	2012	2012	NUM
ejpam-4784	310	7	.	.	PUNCT
ejpam-4784	311	1	[	[	X
ejpam-4784	311	2	19	19	NUM
ejpam-4784	311	3	]	]	PUNCT
ejpam-4784	311	4	a.	a.	NOUN
ejpam-4784	311	5	mcd	mcd	PROPN
ejpam-4784	311	6	.	.	PUNCT
ejpam-4784	312	1	mercer	mercer	PROPN
ejpam-4784	312	2	.	.	PUNCT
ejpam-4784	313	1	a	a	DET
ejpam-4784	313	2	variant	variant	NOUN
ejpam-4784	313	3	of	of	ADP
ejpam-4784	313	4	jensen	jensen	PROPN
ejpam-4784	313	5	’s	’s	PART
ejpam-4784	313	6	inequality	inequality	NOUN
ejpam-4784	313	7	.	.	PUNCT
ejpam-4784	314	1	j.	j.	PROPN
ejpam-4784	314	2	ineq	ineq	PROPN
ejpam-4784	314	3	.	.	PUNCT
ejpam-4784	315	1	pure	pure	ADJ
ejpam-4784	315	2	and	and	CCONJ
ejpam-4784	315	3	appl	appl	PROPN
ejpam-4784	315	4	.	.	PROPN
ejpam-4784	315	5	math	math	PROPN
ejpam-4784	315	6	.	.	PUNCT
ejpam-4784	316	1	,	,	PUNCT
ejpam-4784	317	1	4	4	NUM
ejpam-4784	317	2	,	,	PUNCT
ejpam-4784	317	3	2013	2013	NUM
ejpam-4784	317	4	.	.	PUNCT
ejpam-4784	318	1	[	[	X
ejpam-4784	318	2	20	20	NUM
ejpam-4784	318	3	]	]	PUNCT
ejpam-4784	318	4	q.	q.	PROPN
ejpam-4784	318	5	sheng	sheng	PROPN
ejpam-4784	318	6	,	,	PUNCT
ejpam-4784	318	7	m.	m.	PROPN
ejpam-4784	318	8	fadag	fadag	PROPN
ejpam-4784	318	9	,	,	PUNCT
ejpam-4784	318	10	j.	j.	PROPN
ejpam-4784	318	11	henderson	henderson	PROPN
ejpam-4784	318	12	,	,	PUNCT
ejpam-4784	318	13	and	and	CCONJ
ejpam-4784	318	14	j.	j.	PROPN
ejpam-4784	318	15	m.	m.	PROPN
ejpam-4784	318	16	davis	davis	PROPN
ejpam-4784	318	17	.	.	PUNCT
ejpam-4784	319	1	an	an	DET
ejpam-4784	319	2	exploration	exploration	NOUN
ejpam-4784	319	3	of	of	ADP
ejpam-4784	319	4	combined	combine	VERB
ejpam-4784	319	5	dynamic	dynamic	ADJ
ejpam-4784	319	6	derivativeson	derivativeson	NOUN
ejpam-4784	319	7	time	time	NOUN
ejpam-4784	319	8	scales	scale	NOUN
ejpam-4784	319	9	and	and	CCONJ
ejpam-4784	319	10	their	their	PRON
ejpam-4784	319	11	applications	application	NOUN
ejpam-4784	319	12	,	,	PUNCT
ejpam-4784	319	13	.	.	PUNCT
ejpam-4784	320	1	nonlinear	nonlinear	ADJ
ejpam-4784	320	2	analysis	analysis	NOUN
ejpam-4784	320	3	:	:	PUNCT
ejpam-4784	320	4	real	real	ADJ
ejpam-4784	320	5	world	world	NOUN
ejpam-4784	320	6	applications	application	NOUN
ejpam-4784	320	7	,	,	PUNCT
ejpam-4784	320	8	7(3):395–413	7(3):395–413	NUM
ejpam-4784	320	9	,	,	PUNCT
ejpam-4784	320	10	2006	2006	NUM
ejpam-4784	320	11	.	.	PUNCT
ejpam-4784	321	1	[	[	X
ejpam-4784	321	2	21	21	NUM
ejpam-4784	321	3	]	]	PUNCT
ejpam-4784	321	4	x.	x.	PROPN
ejpam-4784	321	5	l.	l.	PROPN
ejpam-4784	321	6	tang	tang	PROPN
ejpam-4784	321	7	and	and	CCONJ
ejpam-4784	321	8	j.	j.	PROPN
ejpam-4784	321	9	j.	j.	PROPN
ejpam-4784	321	10	wen	wen	PROPN
ejpam-4784	321	11	.	.	PUNCT
ejpam-4784	322	1	some	some	DET
ejpam-4784	322	2	developments	development	NOUN
ejpam-4784	322	3	of	of	ADP
ejpam-4784	322	4	refined	refined	ADJ
ejpam-4784	322	5	jensen	jensen	PROPN
ejpam-4784	322	6	’s	’s	PART
ejpam-4784	322	7	inequality	inequality	NOUN
ejpam-4784	322	8	,	,	PUNCT
ejpam-4784	322	9	.	.	PUNCT
ejpam-4784	323	1	j.	j.	PROPN
ejpam-4784	323	2	southwest	southwest	PROPN
ejpam-4784	323	3	univ	univ	PROPN
ejpam-4784	323	4	.	.	PUNCT
ejpam-4784	324	1	nationalities	nationality	NOUN
ejpam-4784	324	2	,	,	PUNCT
ejpam-4784	324	3	29	29	NUM
ejpam-4784	324	4	.	.	PUNCT
ejpam-4784	325	1	[	[	X
ejpam-4784	325	2	22	22	NUM
ejpam-4784	325	3	]	]	X
ejpam-4784	325	4	l.	l.	PROPN
ejpam-4784	325	5	c.	c.	PROPN
ejpam-4784	325	6	wang	wang	PROPN
ejpam-4784	325	7	,	,	PUNCT
ejpam-4784	325	8	x.	x.	PROPN
ejpam-4784	325	9	f.	f.	PROPN
ejpam-4784	325	10	ma	ma	PROPN
ejpam-4784	325	11	,	,	PUNCT
ejpam-4784	325	12	and	and	CCONJ
ejpam-4784	325	13	l.	l.	PROPN
ejpam-4784	325	14	h.	h.	PROPN
ejpam-4784	325	15	liu	liu	PROPN
ejpam-4784	325	16	.	.	PUNCT
ejpam-4784	326	1	a	a	DET
ejpam-4784	326	2	note	note	NOUN
ejpam-4784	326	3	on	on	ADP
ejpam-4784	326	4	some	some	DET
ejpam-4784	326	5	new	new	ADJ
ejpam-4784	326	6	refinements	refinement	NOUN
ejpam-4784	326	7	of	of	ADP
ejpam-4784	326	8	jensen	jensen	PROPN
ejpam-4784	326	9	’s	’s	PART
ejpam-4784	326	10	inequality	inequality	NOUN
ejpam-4784	326	11	for	for	ADP
ejpam-4784	326	12	convex	convex	NOUN
ejpam-4784	326	13	functions	function	NOUN
ejpam-4784	326	14	,	,	PUNCT
ejpam-4784	326	15	.	.	PUNCT
ejpam-4784	327	1	j.	j.	PROPN
ejpam-4784	327	2	ineq	ineq	PROPN
ejpam-4784	327	3	.	.	PUNCT
ejpam-4784	328	1	pure	pure	ADJ
ejpam-4784	328	2	appl	appl	PROPN
ejpam-4784	328	3	.	.	PUNCT
ejpam-4784	328	4	math	math	PROPN
ejpam-4784	328	5	.	.	PUNCT
ejpam-4784	328	6	,	,	PUNCT
ejpam-4784	328	7	10(2):article	10(2):article	PROPN
ejpam-4784	328	8	48	48	NUM
ejpam-4784	328	9	,	,	PUNCT
ejpam-4784	328	10	2006	2006	NUM
ejpam-4784	328	11	.	.	PUNCT
ejpam-4784	329	1	[	[	X
ejpam-4784	329	2	23	23	NUM
ejpam-4784	329	3	]	]	PUNCT
ejpam-4784	329	4	f.-h	f.-h	NOUN
ejpam-4784	329	5	.	.	PUNCT
ejpam-4784	330	1	wong	wong	PROPN
ejpam-4784	330	2	,	,	PUNCT
ejpam-4784	330	3	c.-c	c.-c	PROPN
ejpam-4784	330	4	.	.	PUNCT
ejpam-4784	331	1	yeh	yeh	PROPN
ejpam-4784	331	2	,	,	PUNCT
ejpam-4784	331	3	and	and	CCONJ
ejpam-4784	331	4	w.-c	w.-c	NOUN
ejpam-4784	331	5	.	.	PUNCT
ejpam-4784	332	1	lian	lian	PROPN
ejpam-4784	332	2	.	.	PROPN
ejpam-4784	333	1	advances	advance	NOUN
ejpam-4784	333	2	in	in	ADP
ejpam-4784	333	3	dynamical	dynamical	ADJ
ejpam-4784	333	4	systems	system	NOUN
ejpam-4784	333	5	and	and	CCONJ
ejpam-4784	333	6	applications	application	NOUN
ejpam-4784	333	7	.	.	PUNCT
ejpam-4784	334	1	nonlinear	nonlinear	ADJ
ejpam-4784	334	2	functional	functional	ADJ
ejpam-4784	334	3	anal	anal	NOUN
ejpam-4784	334	4	.	.	PUNCT
ejpam-4784	335	1	appl	appl	PROPN
ejpam-4784	335	2	.	.	PROPN
ejpam-4784	335	3	,	,	PUNCT
ejpam-4784	335	4	1(1):113–120	1(1):113–120	NUM
ejpam-4784	335	5	,	,	PUNCT
ejpam-4784	335	6	2006	2006	NUM
ejpam-4784	335	7	.	.	PUNCT