id	sid	tid	token	lemma	pos
ejpam-4444	1	1	european	european	PROPN
ejpam-4444	1	2	journal	journal	PROPN
ejpam-4444	1	3	of	of	ADP
ejpam-4444	1	4	pure	pure	ADJ
ejpam-4444	1	5	and	and	CCONJ
ejpam-4444	1	6	applied	apply	VERB
ejpam-4444	1	7	mathematics	mathematic	NOUN
ejpam-4444	1	8	vol	vol	NOUN
ejpam-4444	1	9	.	.	PROPN
ejpam-4444	2	1	15	15	NUM
ejpam-4444	2	2	,	,	PUNCT
ejpam-4444	2	3	no	no	INTJ
ejpam-4444	2	4	.	.	NOUN
ejpam-4444	2	5	3	3	NUM
ejpam-4444	2	6	,	,	PUNCT
ejpam-4444	2	7	2022	2022	NUM
ejpam-4444	2	8	,	,	PUNCT
ejpam-4444	2	9	1120	1120	NUM
ejpam-4444	2	10	-	-	SYM
ejpam-4444	2	11	1143	1143	NUM
ejpam-4444	2	12	issn	issn	PROPN
ejpam-4444	2	13	1307	1307	NUM
ejpam-4444	2	14	-	-	SYM
ejpam-4444	2	15	5543	5543	NUM
ejpam-4444	2	16	–	–	PUNCT
ejpam-4444	2	17	ejpam.com	ejpam.com	X
ejpam-4444	2	18	published	publish	VERB
ejpam-4444	2	19	by	by	ADP
ejpam-4444	2	20	new	new	PROPN
ejpam-4444	2	21	york	york	PROPN
ejpam-4444	2	22	business	business	PROPN
ejpam-4444	2	23	global	global	ADJ
ejpam-4444	2	24	bounds	bound	NOUN
ejpam-4444	2	25	for	for	ADP
ejpam-4444	2	26	the	the	DET
ejpam-4444	2	27	convex	convex	ADJ
ejpam-4444	2	28	combination	combination	NOUN
ejpam-4444	2	29	of	of	ADP
ejpam-4444	2	30	contra	contra	PROPN
ejpam-4444	2	31	-	-	ADJ
ejpam-4444	2	32	harmonic	harmonic	ADJ
ejpam-4444	2	33	and	and	CCONJ
ejpam-4444	2	34	harmonic	harmonic	ADJ
ejpam-4444	2	35	means	mean	NOUN
ejpam-4444	2	36	by	by	ADP
ejpam-4444	2	37	the	the	DET
ejpam-4444	2	38	generalized	generalize	VERB
ejpam-4444	2	39	logarithmic	logarithmic	ADJ
ejpam-4444	2	40	mean	mean	NOUN
ejpam-4444	2	41	annop	annop	PROPN
ejpam-4444	2	42	sonubon1	sonubon1	PROPN
ejpam-4444	2	43	,	,	PUNCT
ejpam-4444	2	44	somsak	somsak	ADJ
ejpam-4444	2	45	orankitjaroen1,∗	orankitjaroen1,∗	NOUN
ejpam-4444	2	46	,	,	PUNCT
ejpam-4444	2	47	kamsing	kamse	VERB
ejpam-4444	2	48	nonlaopon2	nonlaopon2	NOUN
ejpam-4444	2	49	1	1	NUM
ejpam-4444	2	50	department	department	NOUN
ejpam-4444	2	51	of	of	ADP
ejpam-4444	2	52	mathematics	mathematic	NOUN
ejpam-4444	2	53	,	,	PUNCT
ejpam-4444	2	54	faculty	faculty	NOUN
ejpam-4444	2	55	of	of	ADP
ejpam-4444	2	56	science	science	NOUN
ejpam-4444	2	57	,	,	PUNCT
ejpam-4444	2	58	mahidol	mahidol	PROPN
ejpam-4444	2	59	university	university	PROPN
ejpam-4444	2	60	,	,	PUNCT
ejpam-4444	2	61	bangkok	bangkok	PROPN
ejpam-4444	2	62	,	,	PUNCT
ejpam-4444	2	63	10400	10400	NUM
ejpam-4444	2	64	,	,	PUNCT
ejpam-4444	2	65	thailand	thailand	PROPN
ejpam-4444	2	66	2	2	NUM
ejpam-4444	2	67	department	department	NOUN
ejpam-4444	2	68	of	of	ADP
ejpam-4444	2	69	mathematics	mathematic	NOUN
ejpam-4444	2	70	,	,	PUNCT
ejpam-4444	2	71	faculty	faculty	NOUN
ejpam-4444	2	72	of	of	ADP
ejpam-4444	2	73	science	science	NOUN
ejpam-4444	2	74	,	,	PUNCT
ejpam-4444	2	75	khon	khon	PROPN
ejpam-4444	2	76	kaen	kaen	PROPN
ejpam-4444	2	77	university	university	PROPN
ejpam-4444	2	78	,	,	PUNCT
ejpam-4444	2	79	khon	khon	PROPN
ejpam-4444	2	80	kaen	kaen	PROPN
ejpam-4444	2	81	,	,	PUNCT
ejpam-4444	2	82	40002	40002	NUM
ejpam-4444	2	83	,	,	PUNCT
ejpam-4444	2	84	thailand	thailand	PROPN
ejpam-4444	2	85	abstract	abstract	NOUN
ejpam-4444	2	86	.	.	PUNCT
ejpam-4444	3	1	we	we	PRON
ejpam-4444	3	2	verify	verify	VERB
ejpam-4444	3	3	the	the	DET
ejpam-4444	3	4	optimal	optimal	ADJ
ejpam-4444	3	5	upper	upper	ADJ
ejpam-4444	3	6	bound	bind	VERB
ejpam-4444	3	7	and	and	CCONJ
ejpam-4444	3	8	optimal	optimal	ADJ
ejpam-4444	3	9	lower	lower	ADV
ejpam-4444	3	10	bound	bind	VERB
ejpam-4444	3	11	for	for	ADP
ejpam-4444	3	12	the	the	DET
ejpam-4444	3	13	convex	convex	ADJ
ejpam-4444	3	14	combination	combination	NOUN
ejpam-4444	3	15	of	of	ADP
ejpam-4444	3	16	contra	contra	PROPN
ejpam-4444	3	17	-	-	ADJ
ejpam-4444	3	18	harmonic	harmonic	ADJ
ejpam-4444	3	19	and	and	CCONJ
ejpam-4444	3	20	harmonic	harmonic	ADJ
ejpam-4444	3	21	means	mean	NOUN
ejpam-4444	3	22	by	by	ADP
ejpam-4444	3	23	the	the	DET
ejpam-4444	3	24	generalized	generalize	VERB
ejpam-4444	3	25	logarithmic	logarithmic	ADJ
ejpam-4444	3	26	mean	mean	NOUN
ejpam-4444	3	27	lp	lp	NOUN
ejpam-4444	3	28	when	when	SCONJ
ejpam-4444	3	29	p	p	NOUN
ejpam-4444	3	30	is	be	AUX
ejpam-4444	3	31	of	of	ADP
ejpam-4444	3	32	the	the	DET
ejpam-4444	3	33	linear	linear	ADJ
ejpam-4444	3	34	form	form	NOUN
ejpam-4444	3	35	p	p	NOUN
ejpam-4444	3	36	=	=	SYM
ejpam-4444	3	37	2(1	2(1	NUM
ejpam-4444	3	38	−	−	NOUN
ejpam-4444	3	39	c)α	c)α	NOUN
ejpam-4444	4	1	+	+	CCONJ
ejpam-4444	4	2	c	c	NOUN
ejpam-4444	4	3	and	and	CCONJ
ejpam-4444	4	4	p	p	NOUN
ejpam-4444	4	5	is	be	AUX
ejpam-4444	4	6	of	of	ADP
ejpam-4444	4	7	the	the	DET
ejpam-4444	4	8	reciprocal	reciprocal	NOUN
ejpam-4444	4	9	of	of	ADP
ejpam-4444	4	10	linear	linear	ADJ
ejpam-4444	4	11	form	form	NOUN
ejpam-4444	4	12	p	p	NOUN
ejpam-4444	4	13	=	=	SYM
ejpam-4444	4	14	1/[2(1	1/[2(1	NUM
ejpam-4444	4	15	−	−	NOUN
ejpam-4444	4	16	c)α	c)α	NOUN
ejpam-4444	5	1	+	+	CCONJ
ejpam-4444	6	1	c	c	X
ejpam-4444	6	2	]	]	PUNCT
ejpam-4444	6	3	respectively	respectively	ADV
ejpam-4444	6	4	.	.	PUNCT
ejpam-4444	7	1	we	we	PRON
ejpam-4444	7	2	prove	prove	VERB
ejpam-4444	7	3	that	that	SCONJ
ejpam-4444	7	4	1	1	NUM
ejpam-4444	7	5	)	)	PUNCT
ejpam-4444	7	6	l4α−1	l4α−1	NOUN
ejpam-4444	7	7	=	=	SYM
ejpam-4444	7	8	minc	minc	PROPN
ejpam-4444	7	9	{	{	PUNCT
ejpam-4444	7	10	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	7	11	|	|	ADV
ejpam-4444	7	12	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	7	13	>	>	X
ejpam-4444	7	14	αc	αc	PROPN
ejpam-4444	8	1	+	+	CCONJ
ejpam-4444	8	2	(	(	PUNCT
ejpam-4444	8	3	1−	1−	NUM
ejpam-4444	8	4	α)h	α)h	NOUN
ejpam-4444	8	5	}	}	PUNCT
ejpam-4444	8	6	for	for	ADP
ejpam-4444	8	7	α	α	PRON
ejpam-4444	8	8	∈	∈	PROPN
ejpam-4444	8	9	(	(	PUNCT
ejpam-4444	8	10	0	0	NUM
ejpam-4444	8	11	,	,	PUNCT
ejpam-4444	8	12	1/2	1/2	NUM
ejpam-4444	8	13	)	)	PUNCT
ejpam-4444	8	14	,	,	PUNCT
ejpam-4444	8	15	2	2	X
ejpam-4444	8	16	)	)	PUNCT
ejpam-4444	8	17	l	l	NOUN
ejpam-4444	8	18	7	7	NUM
ejpam-4444	8	19	13−12α	13−12α	NOUN
ejpam-4444	8	20	=	=	SYM
ejpam-4444	8	21	maxc	maxc	NOUN
ejpam-4444	8	22	{	{	PUNCT
ejpam-4444	8	23	l	l	PROPN
ejpam-4444	8	24	1	1	NUM
ejpam-4444	8	25	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	8	26	∣∣∣l	∣∣∣l	NOUN
ejpam-4444	8	27	1	1	NUM
ejpam-4444	8	28	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	8	29	<	<	X
ejpam-4444	8	30	αc	αc	NOUN
ejpam-4444	9	1	+	+	CCONJ
ejpam-4444	10	1	(	(	PUNCT
ejpam-4444	10	2	1−	1−	NUM
ejpam-4444	10	3	α)h	α)h	NOUN
ejpam-4444	10	4	}	}	PUNCT
ejpam-4444	10	5	for	for	ADP
ejpam-4444	10	6	α	α	PRON
ejpam-4444	10	7	∈	∈	PROPN
ejpam-4444	10	8	(	(	PUNCT
ejpam-4444	10	9	1/2	1/2	NUM
ejpam-4444	10	10	,	,	PUNCT
ejpam-4444	10	11	1	1	NUM
ejpam-4444	10	12	)	)	PUNCT
ejpam-4444	10	13	where	where	SCONJ
ejpam-4444	10	14	c(a	c(a	PROPN
ejpam-4444	10	15	,	,	PUNCT
ejpam-4444	10	16	b	b	NOUN
ejpam-4444	10	17	)	)	PUNCT
ejpam-4444	10	18	and	and	CCONJ
ejpam-4444	10	19	h(a	h(a	PROPN
ejpam-4444	10	20	,	,	PUNCT
ejpam-4444	10	21	b	b	X
ejpam-4444	10	22	)	)	PUNCT
ejpam-4444	10	23	are	be	AUX
ejpam-4444	10	24	contra	contra	ADJ
ejpam-4444	10	25	-	-	ADJ
ejpam-4444	10	26	harmonic	harmonic	ADJ
ejpam-4444	10	27	and	and	CCONJ
ejpam-4444	10	28	harmonic	harmonic	ADJ
ejpam-4444	10	29	means	mean	NOUN
ejpam-4444	10	30	.	.	PUNCT
ejpam-4444	11	1	2020	2020	NUM
ejpam-4444	11	2	mathematics	mathematic	NOUN
ejpam-4444	11	3	subject	subject	NOUN
ejpam-4444	11	4	classifications	classification	NOUN
ejpam-4444	11	5	:	:	PUNCT
ejpam-4444	11	6	26d15	26d15	NUM
ejpam-4444	11	7	,	,	PUNCT
ejpam-4444	11	8	26d20	26d20	NUM
ejpam-4444	11	9	,	,	PUNCT
ejpam-4444	11	10	26e20	26e20	NUM
ejpam-4444	11	11	key	key	ADJ
ejpam-4444	11	12	words	word	NOUN
ejpam-4444	11	13	and	and	CCONJ
ejpam-4444	11	14	phrases	phrase	NOUN
ejpam-4444	11	15	:	:	PUNCT
ejpam-4444	11	16	inequality	inequality	NOUN
ejpam-4444	11	17	,	,	PUNCT
ejpam-4444	11	18	generalized	generalized	ADJ
ejpam-4444	11	19	logarithmic	logarithmic	ADJ
ejpam-4444	11	20	mean	mean	NOUN
ejpam-4444	11	21	,	,	PUNCT
ejpam-4444	11	22	weighted	weight	VERB
ejpam-4444	11	23	arithmetic	arithmetic	ADJ
ejpam-4444	11	24	mean	mean	NOUN
ejpam-4444	11	25	,	,	PUNCT
ejpam-4444	11	26	harmonic	harmonic	ADJ
ejpam-4444	11	27	mean	mean	NOUN
ejpam-4444	11	28	,	,	PUNCT
ejpam-4444	11	29	contra	contra	PROPN
ejpam-4444	11	30	-	-	ADJ
ejpam-4444	11	31	harmonic	harmonic	ADJ
ejpam-4444	11	32	mean	mean	NOUN
ejpam-4444	11	33	1	1	NUM
ejpam-4444	11	34	.	.	X
ejpam-4444	11	35	introduction	introduction	NOUN
ejpam-4444	11	36	for	for	ADP
ejpam-4444	11	37	any	any	DET
ejpam-4444	11	38	real	real	ADJ
ejpam-4444	11	39	number	number	NOUN
ejpam-4444	11	40	p	p	NOUN
ejpam-4444	11	41	,	,	PUNCT
ejpam-4444	11	42	generalized	generalize	VERB
ejpam-4444	11	43	logarithmic	logarithmic	ADJ
ejpam-4444	11	44	mean	mean	NOUN
ejpam-4444	11	45	lp(a	lp(a	NOUN
ejpam-4444	11	46	,	,	PUNCT
ejpam-4444	11	47	b	b	NOUN
ejpam-4444	11	48	)	)	PUNCT
ejpam-4444	11	49	of	of	ADP
ejpam-4444	11	50	two	two	NUM
ejpam-4444	11	51	positive	positive	ADJ
ejpam-4444	11	52	numbers	number	NOUN
ejpam-4444	11	53	a	a	PRON
ejpam-4444	11	54	and	and	CCONJ
ejpam-4444	11	55	b	b	NOUN
ejpam-4444	11	56	is	be	AUX
ejpam-4444	11	57	defined	define	VERB
ejpam-4444	11	58	by	by	ADP
ejpam-4444	11	59	lp(a	lp(a	PROPN
ejpam-4444	11	60	,	,	PUNCT
ejpam-4444	11	61	b	b	NOUN
ejpam-4444	11	62	)	)	PUNCT
ejpam-4444	11	63	=	=	SYM
ejpam-4444	11	64			PROPN
ejpam-4444	11	65	[	[	PUNCT
ejpam-4444	11	66	ap+1	ap+1	NOUN
ejpam-4444	12	1	−	−	NOUN
ejpam-4444	12	2	bp+1	bp+1	NOUN
ejpam-4444	12	3	(	(	PUNCT
ejpam-4444	12	4	p+	p+	PROPN
ejpam-4444	12	5	1)(a−	1)(a−	PROPN
ejpam-4444	12	6	b	b	NOUN
ejpam-4444	12	7	)	)	PUNCT
ejpam-4444	12	8	]	]	PUNCT
ejpam-4444	12	9	1	1	X
ejpam-4444	12	10	/	/	SYM
ejpam-4444	12	11	p	p	NOUN
ejpam-4444	12	12	,	,	PUNCT
ejpam-4444	12	13	a	a	DET
ejpam-4444	12	14	̸=	̸=	PROPN
ejpam-4444	12	15	b	b	PROPN
ejpam-4444	12	16	,	,	PUNCT
ejpam-4444	12	17	p	p	PROPN
ejpam-4444	12	18	̸=	̸=	PROPN
ejpam-4444	12	19	0	0	NUM
ejpam-4444	12	20	,	,	PUNCT
ejpam-4444	12	21	p	p	PROPN
ejpam-4444	12	22	̸=	̸=	PROPN
ejpam-4444	12	23	−1	−1	NOUN
ejpam-4444	12	24	;	;	PUNCT
ejpam-4444	12	25	1	1	NUM
ejpam-4444	12	26	e	e	X
ejpam-4444	12	27	(	(	PUNCT
ejpam-4444	12	28	bb	bb	NOUN
ejpam-4444	12	29	aa	aa	ADJ
ejpam-4444	12	30	)	)	PUNCT
ejpam-4444	12	31	1/(b−a	1/(b−a	NUM
ejpam-4444	12	32	)	)	PUNCT
ejpam-4444	12	33	,	,	PUNCT
ejpam-4444	12	34	a	a	DET
ejpam-4444	12	35	̸=	̸=	PROPN
ejpam-4444	12	36	b	b	PROPN
ejpam-4444	12	37	,	,	PUNCT
ejpam-4444	12	38	p	p	X
ejpam-4444	12	39	=	=	NOUN
ejpam-4444	12	40	0	0	NUM
ejpam-4444	12	41	;	;	PUNCT
ejpam-4444	12	42	b−	b−	PROPN
ejpam-4444	12	43	a	a	DET
ejpam-4444	12	44	log	log	NOUN
ejpam-4444	12	45	b−	b−	PROPN
ejpam-4444	12	46	log	log	VERB
ejpam-4444	12	47	a	a	PRON
ejpam-4444	12	48	,	,	PUNCT
ejpam-4444	12	49	a	a	DET
ejpam-4444	12	50	̸=	̸=	PROPN
ejpam-4444	12	51	b	b	PROPN
ejpam-4444	12	52	,	,	PUNCT
ejpam-4444	12	53	p	p	NOUN
ejpam-4444	12	54	=	=	NOUN
ejpam-4444	12	55	−1	−1	NOUN
ejpam-4444	12	56	;	;	PUNCT
ejpam-4444	12	57	a	a	PRON
ejpam-4444	12	58	,	,	PUNCT
ejpam-4444	12	59	a	a	DET
ejpam-4444	12	60	=	=	X
ejpam-4444	12	61	b.	b.	PROPN
ejpam-4444	12	62	∗corresponding	∗corresponde	VERB
ejpam-4444	12	63	author	author	NOUN
ejpam-4444	12	64	.	.	PUNCT
ejpam-4444	13	1	doi	doi	NOUN
ejpam-4444	13	2	:	:	PUNCT
ejpam-4444	13	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4444	https://doi.org/10.29020/nybg.ejpam.v15i3.4444	NOUN
ejpam-4444	13	4	email	email	NOUN
ejpam-4444	13	5	addresses	address	NOUN
ejpam-4444	13	6	:	:	PUNCT
ejpam-4444	13	7	murfy.pm@gmail.com	murfy.pm@gmail.com	X
ejpam-4444	13	8	(	(	PUNCT
ejpam-4444	13	9	a.	a.	NOUN
ejpam-4444	13	10	sonubon	sonubon	PROPN
ejpam-4444	13	11	)	)	PUNCT
ejpam-4444	13	12	,	,	PUNCT
ejpam-4444	13	13	,	,	PUNCT
ejpam-4444	13	14	,	,	PUNCT
ejpam-4444	13	15	somsak.ora@mahidol.ac.th	somsak.ora@mahidol.ac.th	PROPN
ejpam-4444	13	16	(	(	PUNCT
ejpam-4444	13	17	s.	s.	PROPN
ejpam-4444	13	18	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	13	19	)	)	PUNCT
ejpam-4444	13	20	,	,	PUNCT
ejpam-4444	13	21	nkamsi@kku.ac.th	nkamsi@kku.ac.th	PROPN
ejpam-4444	13	22	(	(	PUNCT
ejpam-4444	13	23	k.	k.	NOUN
ejpam-4444	13	24	nonlaopon	nonlaopon	NOUN
ejpam-4444	13	25	)	)	PUNCT
ejpam-4444	13	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4444	14	1	1120	1120	NUM
ejpam-4444	15	1	©	©	ADP
ejpam-4444	15	2	2022	2022	NUM
ejpam-4444	15	3	ejpam	ejpam	VERB
ejpam-4444	15	4	all	all	DET
ejpam-4444	15	5	rights	right	NOUN
ejpam-4444	15	6	reserved	reserve	VERB
ejpam-4444	15	7	.	.	PUNCT
ejpam-4444	16	1	a.	a.	PROPN
ejpam-4444	16	2	sonubon	sonubon	PROPN
ejpam-4444	16	3	,	,	PUNCT
ejpam-4444	16	4	s.	s.	PROPN
ejpam-4444	16	5	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	16	6	,	,	PUNCT
ejpam-4444	16	7	k.	k.	PROPN
ejpam-4444	16	8	nonlaopon	nonlaopon	ADV
ejpam-4444	16	9	/	/	SYM
ejpam-4444	16	10	eur	eur	PROPN
ejpam-4444	16	11	.	.	PUNCT
ejpam-4444	17	1	j.	j.	PROPN
ejpam-4444	17	2	pure	pure	PROPN
ejpam-4444	17	3	appl	appl	PROPN
ejpam-4444	17	4	.	.	PROPN
ejpam-4444	17	5	math	math	PROPN
ejpam-4444	17	6	,	,	PUNCT
ejpam-4444	17	7	15	15	NUM
ejpam-4444	17	8	(	(	PUNCT
ejpam-4444	17	9	3	3	NUM
ejpam-4444	17	10	)	)	PUNCT
ejpam-4444	17	11	(	(	PUNCT
ejpam-4444	17	12	2022	2022	NUM
ejpam-4444	17	13	)	)	PUNCT
ejpam-4444	17	14	,	,	PUNCT
ejpam-4444	17	15	1120	1120	NUM
ejpam-4444	17	16	-	-	SYM
ejpam-4444	17	17	1143	1143	NUM
ejpam-4444	17	18	1121	1121	NUM
ejpam-4444	17	19	mean	mean	NOUN
ejpam-4444	17	20	lp	lp	PROPN
ejpam-4444	17	21	is	be	AUX
ejpam-4444	17	22	continuous	continuous	ADJ
ejpam-4444	17	23	and	and	CCONJ
ejpam-4444	17	24	strictly	strictly	ADV
ejpam-4444	17	25	increasing	increase	VERB
ejpam-4444	17	26	with	with	ADP
ejpam-4444	17	27	respect	respect	NOUN
ejpam-4444	17	28	to	to	ADP
ejpam-4444	17	29	p.	p.	NOUN
ejpam-4444	17	30	it	it	PRON
ejpam-4444	17	31	has	have	VERB
ejpam-4444	17	32	many	many	ADJ
ejpam-4444	17	33	applications	application	NOUN
ejpam-4444	17	34	in	in	ADP
ejpam-4444	17	35	physics	physics	NOUN
ejpam-4444	17	36	involving	involve	VERB
ejpam-4444	17	37	a	a	DET
ejpam-4444	17	38	heat	heat	NOUN
ejpam-4444	17	39	conductor	conductor	NOUN
ejpam-4444	17	40	problem	problem	NOUN
ejpam-4444	17	41	and	and	CCONJ
ejpam-4444	17	42	a	a	DET
ejpam-4444	17	43	mean	mean	ADJ
ejpam-4444	17	44	temperature	temperature	NOUN
ejpam-4444	17	45	between	between	ADP
ejpam-4444	17	46	two	two	NUM
ejpam-4444	17	47	points	point	NOUN
ejpam-4444	17	48	at	at	ADP
ejpam-4444	17	49	different	different	ADJ
ejpam-4444	17	50	temperature	temperature	NOUN
ejpam-4444	17	51	[	[	X
ejpam-4444	17	52	6	6	NUM
ejpam-4444	17	53	,	,	PUNCT
ejpam-4444	17	54	10	10	NUM
ejpam-4444	17	55	]	]	PUNCT
ejpam-4444	17	56	.	.	PUNCT
ejpam-4444	18	1	many	many	ADJ
ejpam-4444	18	2	classical	classical	ADJ
ejpam-4444	18	3	bivariate	bivariate	ADJ
ejpam-4444	18	4	means	mean	NOUN
ejpam-4444	18	5	are	be	AUX
ejpam-4444	18	6	special	special	ADJ
ejpam-4444	18	7	cases	case	NOUN
ejpam-4444	18	8	of	of	ADP
ejpam-4444	18	9	generalized	generalized	ADJ
ejpam-4444	18	10	logarithmic	logarithmic	ADJ
ejpam-4444	18	11	means	mean	NOUN
ejpam-4444	18	12	such	such	ADJ
ejpam-4444	18	13	as	as	ADP
ejpam-4444	18	14	g(a	g(a	PROPN
ejpam-4444	18	15	,	,	PUNCT
ejpam-4444	18	16	b	b	NOUN
ejpam-4444	18	17	)	)	PUNCT
ejpam-4444	18	18	=	=	SYM
ejpam-4444	18	19	l−2(a	l−2(a	PROPN
ejpam-4444	18	20	,	,	PUNCT
ejpam-4444	18	21	b	b	NOUN
ejpam-4444	18	22	)	)	PUNCT
ejpam-4444	18	23	,	,	PUNCT
ejpam-4444	18	24	l(a	l(a	PROPN
ejpam-4444	18	25	,	,	PUNCT
ejpam-4444	18	26	b	b	NOUN
ejpam-4444	18	27	)	)	PUNCT
ejpam-4444	18	28	=	=	SYM
ejpam-4444	18	29	l−1(a	l−1(a	PROPN
ejpam-4444	18	30	,	,	PUNCT
ejpam-4444	18	31	b	b	NOUN
ejpam-4444	18	32	)	)	PUNCT
ejpam-4444	18	33	,	,	PUNCT
ejpam-4444	18	34	n(a	n(a	PROPN
ejpam-4444	18	35	,	,	PUNCT
ejpam-4444	18	36	b	b	X
ejpam-4444	18	37	)	)	PUNCT
ejpam-4444	18	38	=	=	SYM
ejpam-4444	18	39	l−1/2(a	l−1/2(a	NOUN
ejpam-4444	18	40	,	,	PUNCT
ejpam-4444	18	41	b	b	NOUN
ejpam-4444	18	42	)	)	PUNCT
ejpam-4444	18	43	,	,	PUNCT
ejpam-4444	18	44	i(a	i(a	PROPN
ejpam-4444	18	45	,	,	PUNCT
ejpam-4444	18	46	b	b	NOUN
ejpam-4444	18	47	)	)	PUNCT
ejpam-4444	18	48	=	=	SYM
ejpam-4444	18	49	l0(a	l0(a	PROPN
ejpam-4444	18	50	,	,	PUNCT
ejpam-4444	18	51	b	b	NOUN
ejpam-4444	18	52	)	)	PUNCT
ejpam-4444	18	53	,	,	PUNCT
ejpam-4444	18	54	and	and	CCONJ
ejpam-4444	18	55	a(a	a(a	PROPN
ejpam-4444	18	56	,	,	PUNCT
ejpam-4444	18	57	b	b	X
ejpam-4444	18	58	)	)	PUNCT
ejpam-4444	18	59	=	=	SYM
ejpam-4444	18	60	l1(a	l1(a	PROPN
ejpam-4444	18	61	,	,	PUNCT
ejpam-4444	18	62	b	b	NOUN
ejpam-4444	18	63	)	)	PUNCT
ejpam-4444	18	64	,	,	PUNCT
ejpam-4444	18	65	where	where	SCONJ
ejpam-4444	18	66	g	g	NOUN
ejpam-4444	18	67	,	,	PUNCT
ejpam-4444	18	68	l	l	NOUN
ejpam-4444	18	69	,	,	PUNCT
ejpam-4444	18	70	n	n	CCONJ
ejpam-4444	18	71	,	,	PUNCT
ejpam-4444	18	72	i	i	PRON
ejpam-4444	18	73	,	,	PUNCT
ejpam-4444	18	74	and	and	CCONJ
ejpam-4444	18	75	a	a	PRON
ejpam-4444	18	76	are	be	AUX
ejpam-4444	18	77	geometric	geometric	ADJ
ejpam-4444	18	78	,	,	PUNCT
ejpam-4444	18	79	logarithmic	logarithmic	ADJ
ejpam-4444	18	80	,	,	PUNCT
ejpam-4444	18	81	square	square	ADJ
ejpam-4444	18	82	-	-	PUNCT
ejpam-4444	18	83	root	root	NOUN
ejpam-4444	18	84	,	,	PUNCT
ejpam-4444	18	85	identric	identric	ADJ
ejpam-4444	18	86	and	and	CCONJ
ejpam-4444	18	87	arithmetic	arithmetic	ADJ
ejpam-4444	18	88	means	mean	NOUN
ejpam-4444	18	89	,	,	PUNCT
ejpam-4444	18	90	respectively	respectively	ADV
ejpam-4444	18	91	.	.	PUNCT
ejpam-4444	19	1	in	in	ADP
ejpam-4444	19	2	view	view	NOUN
ejpam-4444	19	3	of	of	ADP
ejpam-4444	19	4	generalized	generalized	ADJ
ejpam-4444	19	5	logarithmic	logarithmic	ADJ
ejpam-4444	19	6	means	mean	NOUN
ejpam-4444	19	7	we	we	PRON
ejpam-4444	19	8	have	have	VERB
ejpam-4444	19	9	a	a	DET
ejpam-4444	19	10	well	well	ADV
ejpam-4444	19	11	-	-	PUNCT
ejpam-4444	19	12	known	know	VERB
ejpam-4444	19	13	string	string	NOUN
ejpam-4444	19	14	of	of	ADP
ejpam-4444	19	15	inequalities	inequality	NOUN
ejpam-4444	19	16	min{a	min{a	PROPN
ejpam-4444	19	17	,	,	PUNCT
ejpam-4444	19	18	b	b	AUX
ejpam-4444	19	19	}	}	PUNCT
ejpam-4444	19	20	<	<	X
ejpam-4444	19	21	h(a	h(a	PROPN
ejpam-4444	19	22	,	,	PUNCT
ejpam-4444	19	23	b	b	NOUN
ejpam-4444	19	24	)	)	PUNCT
ejpam-4444	19	25	<	<	X
ejpam-4444	19	26	l−2(a	l−2(a	PROPN
ejpam-4444	19	27	,	,	PUNCT
ejpam-4444	19	28	b	b	NOUN
ejpam-4444	19	29	)	)	PUNCT
ejpam-4444	19	30	<	<	X
ejpam-4444	19	31	l1(a	l1(a	PROPN
ejpam-4444	19	32	,	,	PUNCT
ejpam-4444	19	33	b	b	NOUN
ejpam-4444	19	34	)	)	PUNCT
ejpam-4444	19	35	<	<	X
ejpam-4444	19	36	s(a	s(a	PROPN
ejpam-4444	19	37	,	,	PUNCT
ejpam-4444	19	38	b	b	NOUN
ejpam-4444	19	39	)	)	PUNCT
ejpam-4444	19	40	<	<	X
ejpam-4444	19	41	c(a	c(a	PROPN
ejpam-4444	19	42	,	,	PUNCT
ejpam-4444	19	43	b	b	NOUN
ejpam-4444	19	44	)	)	PUNCT
ejpam-4444	19	45	<	<	X
ejpam-4444	19	46	max{a	max{a	PROPN
ejpam-4444	19	47	,	,	PUNCT
ejpam-4444	19	48	b	b	NOUN
ejpam-4444	19	49	}	}	PUNCT
ejpam-4444	19	50	for	for	ADP
ejpam-4444	19	51	all	all	DET
ejpam-4444	19	52	distinct	distinct	ADJ
ejpam-4444	19	53	positive	positive	ADJ
ejpam-4444	19	54	numbers	number	NOUN
ejpam-4444	19	55	a	a	DET
ejpam-4444	19	56	,	,	PUNCT
ejpam-4444	19	57	b	b	NOUN
ejpam-4444	19	58	;	;	PUNCT
ejpam-4444	19	59	here	here	ADV
ejpam-4444	19	60	h(a	h(a	PROPN
ejpam-4444	19	61	,	,	PUNCT
ejpam-4444	19	62	b	b	NOUN
ejpam-4444	19	63	)	)	PUNCT
ejpam-4444	19	64	=	=	SYM
ejpam-4444	19	65	2ab	2ab	NOUN
ejpam-4444	19	66	a+	a+	PRON
ejpam-4444	19	67	b	b	NOUN
ejpam-4444	19	68	,	,	PUNCT
ejpam-4444	19	69	s(a	s(a	PROPN
ejpam-4444	19	70	,	,	PUNCT
ejpam-4444	19	71	b	b	NOUN
ejpam-4444	19	72	)	)	PUNCT
ejpam-4444	19	73	=	=	SYM
ejpam-4444	19	74	√	√	NUM
ejpam-4444	19	75	a2	a2	PROPN
ejpam-4444	19	76	+	+	CCONJ
ejpam-4444	19	77	b2	b2	PROPN
ejpam-4444	19	78	2	2	NUM
ejpam-4444	19	79	,	,	PUNCT
ejpam-4444	19	80	c(a	c(a	PROPN
ejpam-4444	19	81	,	,	PUNCT
ejpam-4444	19	82	b	b	NOUN
ejpam-4444	19	83	)	)	PUNCT
ejpam-4444	19	84	=	=	SYM
ejpam-4444	19	85	a2	a2	PROPN
ejpam-4444	19	86	+	+	CCONJ
ejpam-4444	19	87	b2	b2	PROPN
ejpam-4444	19	88	a+	a+	PRON
ejpam-4444	19	89	b	b	NOUN
ejpam-4444	19	90	are	be	AUX
ejpam-4444	19	91	harmonic	harmonic	ADJ
ejpam-4444	19	92	,	,	PUNCT
ejpam-4444	19	93	root	root	NOUN
ejpam-4444	19	94	-	-	PUNCT
ejpam-4444	19	95	square	square	NOUN
ejpam-4444	19	96	,	,	PUNCT
ejpam-4444	19	97	and	and	CCONJ
ejpam-4444	19	98	contra	contra	ADJ
ejpam-4444	19	99	-	-	ADJ
ejpam-4444	19	100	harmonic	harmonic	ADJ
ejpam-4444	19	101	means	mean	NOUN
ejpam-4444	19	102	,	,	PUNCT
ejpam-4444	19	103	respectively	respectively	ADV
ejpam-4444	19	104	.	.	PUNCT
ejpam-4444	20	1	generalized	generalize	VERB
ejpam-4444	20	2	logarithmic	logarithmic	ADJ
ejpam-4444	20	3	mean	mean	NOUN
ejpam-4444	20	4	has	have	AUX
ejpam-4444	20	5	been	be	AUX
ejpam-4444	20	6	the	the	DET
ejpam-4444	20	7	subject	subject	NOUN
ejpam-4444	20	8	of	of	ADP
ejpam-4444	20	9	intensive	intensive	ADJ
ejpam-4444	20	10	research	research	NOUN
ejpam-4444	20	11	in	in	ADP
ejpam-4444	20	12	particular	particular	ADJ
ejpam-4444	20	13	those	those	PRON
ejpam-4444	20	14	involving	involve	VERB
ejpam-4444	20	15	inequalities	inequality	NOUN
ejpam-4444	20	16	and	and	CCONJ
ejpam-4444	20	17	monotonicity	monotonicity	NOUN
ejpam-4444	21	1	[	[	X
ejpam-4444	21	2	1–4	1–4	PROPN
ejpam-4444	21	3	,	,	PUNCT
ejpam-4444	21	4	11–13	11–13	NUM
ejpam-4444	21	5	,	,	PUNCT
ejpam-4444	21	6	18	18	NUM
ejpam-4444	21	7	,	,	PUNCT
ejpam-4444	21	8	19	19	NUM
ejpam-4444	21	9	]	]	PUNCT
ejpam-4444	21	10	.	.	PUNCT
ejpam-4444	22	1	below	below	ADP
ejpam-4444	22	2	we	we	PRON
ejpam-4444	22	3	present	present	VERB
ejpam-4444	22	4	some	some	DET
ejpam-4444	22	5	recent	recent	ADJ
ejpam-4444	22	6	works	work	NOUN
ejpam-4444	22	7	concerning	concern	VERB
ejpam-4444	22	8	the	the	DET
ejpam-4444	22	9	optimal	optimal	ADJ
ejpam-4444	22	10	bound	bind	VERB
ejpam-4444	22	11	of	of	ADP
ejpam-4444	22	12	certain	certain	ADJ
ejpam-4444	22	13	means	mean	NOUN
ejpam-4444	22	14	by	by	ADP
ejpam-4444	22	15	generalized	generalized	ADJ
ejpam-4444	22	16	logarithmic	logarithmic	ADJ
ejpam-4444	22	17	means	mean	NOUN
ejpam-4444	22	18	in	in	ADP
ejpam-4444	22	19	one	one	NUM
ejpam-4444	22	20	direction	direction	NOUN
ejpam-4444	22	21	and	and	CCONJ
ejpam-4444	22	22	weighted	weight	VERB
ejpam-4444	22	23	means	mean	NOUN
ejpam-4444	22	24	by	by	ADP
ejpam-4444	22	25	generalized	generalized	ADJ
ejpam-4444	22	26	logarithmic	logarithmic	ADJ
ejpam-4444	22	27	means	mean	NOUN
ejpam-4444	22	28	in	in	ADP
ejpam-4444	22	29	another	another	PRON
ejpam-4444	22	30	.	.	PUNCT
ejpam-4444	23	1	for	for	ADP
ejpam-4444	23	2	a	a	DET
ejpam-4444	23	3	problem	problem	NOUN
ejpam-4444	23	4	of	of	ADP
ejpam-4444	23	5	finding	find	VERB
ejpam-4444	23	6	sharp	sharp	ADJ
ejpam-4444	23	7	double	double	ADJ
ejpam-4444	23	8	inequalities	inequality	NOUN
ejpam-4444	23	9	between	between	ADP
ejpam-4444	23	10	generalized	generalized	ADJ
ejpam-4444	23	11	logarithmic	logarithmic	ADJ
ejpam-4444	23	12	means	mean	NOUN
ejpam-4444	23	13	and	and	CCONJ
ejpam-4444	23	14	other	other	ADJ
ejpam-4444	23	15	means	mean	NOUN
ejpam-4444	23	16	,	,	PUNCT
ejpam-4444	23	17	recently	recently	ADV
ejpam-4444	23	18	it	it	PRON
ejpam-4444	23	19	was	be	AUX
ejpam-4444	23	20	found	find	VERB
ejpam-4444	23	21	possible	possible	ADJ
ejpam-4444	23	22	for	for	ADP
ejpam-4444	23	23	neuman	neuman	NOUN
ejpam-4444	23	24	-	-	PUNCT
ejpam-4444	23	25	sándor	sándor	NOUN
ejpam-4444	23	26	mean	mean	NOUN
ejpam-4444	23	27	m	m	NOUN
ejpam-4444	23	28	and	and	CCONJ
ejpam-4444	23	29	yang	yang	PROPN
ejpam-4444	23	30	mean	mean	VERB
ejpam-4444	23	31	u	u	PRON
ejpam-4444	23	32	which	which	PRON
ejpam-4444	23	33	are	be	AUX
ejpam-4444	23	34	defined	define	VERB
ejpam-4444	23	35	by	by	ADP
ejpam-4444	23	36	m(a	m(a	PROPN
ejpam-4444	23	37	,	,	PUNCT
ejpam-4444	23	38	b	b	NOUN
ejpam-4444	23	39	)	)	PUNCT
ejpam-4444	23	40	=	=	SYM
ejpam-4444	23	41			PUNCT
ejpam-4444	23	42	a−	a−	PROPN
ejpam-4444	23	43	b	b	NOUN
ejpam-4444	23	44	2	2	NUM
ejpam-4444	23	45	sinh−1	sinh−1	PROPN
ejpam-4444	23	46	(	(	PUNCT
ejpam-4444	23	47	a−b	a−b	PROPN
ejpam-4444	23	48	a+b	a+b	NUM
ejpam-4444	23	49	)	)	PUNCT
ejpam-4444	23	50	,	,	PUNCT
ejpam-4444	23	51	a	a	DET
ejpam-4444	23	52	̸=	̸=	PROPN
ejpam-4444	23	53	b	b	NOUN
ejpam-4444	23	54	;	;	PUNCT
ejpam-4444	23	55	a	a	PRON
ejpam-4444	23	56	,	,	PUNCT
ejpam-4444	23	57	a	a	PRON
ejpam-4444	23	58	=	=	SYM
ejpam-4444	23	59	b	b	PROPN
ejpam-4444	23	60	,	,	PUNCT
ejpam-4444	23	61	u(a	u(a	PROPN
ejpam-4444	23	62	,	,	PUNCT
ejpam-4444	23	63	b	b	NOUN
ejpam-4444	23	64	)	)	PUNCT
ejpam-4444	23	65	=	=	SYM
ejpam-4444	23	66			PUNCT
ejpam-4444	23	67	a−	a−	PROPN
ejpam-4444	23	68	b	b	PROPN
ejpam-4444	23	69	√	√	PROPN
ejpam-4444	23	70	2tan−1	2tan−1	NUM
ejpam-4444	23	71	(	(	PUNCT
ejpam-4444	23	72	a−b√	a−b√	PROPN
ejpam-4444	23	73	2ab	2ab	NOUN
ejpam-4444	23	74	)	)	PUNCT
ejpam-4444	23	75	,	,	PUNCT
ejpam-4444	23	76	a	a	DET
ejpam-4444	23	77	̸=	̸=	PROPN
ejpam-4444	23	78	b	b	NOUN
ejpam-4444	23	79	;	;	PUNCT
ejpam-4444	23	80	a	a	PRON
ejpam-4444	23	81	,	,	PUNCT
ejpam-4444	23	82	a	a	DET
ejpam-4444	23	83	=	=	X
ejpam-4444	23	84	b.	b.	PROPN
ejpam-4444	23	85	in	in	ADP
ejpam-4444	23	86	case	case	NOUN
ejpam-4444	23	87	of	of	ADP
ejpam-4444	23	88	neuman	neuman	NOUN
ejpam-4444	23	89	-	-	PUNCT
ejpam-4444	23	90	sándor	sándor	NOUN
ejpam-4444	23	91	mean	mean	NOUN
ejpam-4444	23	92	,	,	PUNCT
ejpam-4444	23	93	li	li	PROPN
ejpam-4444	23	94	,	,	PUNCT
ejpam-4444	23	95	long	long	ADJ
ejpam-4444	23	96	and	and	CCONJ
ejpam-4444	23	97	chu	chu	VERB
ejpam-4444	24	1	[	[	X
ejpam-4444	24	2	8	8	NUM
ejpam-4444	24	3	]	]	PUNCT
ejpam-4444	24	4	in	in	ADP
ejpam-4444	24	5	2012	2012	NUM
ejpam-4444	24	6	found	find	VERB
ejpam-4444	24	7	the	the	DET
ejpam-4444	24	8	best	well	ADV
ejpam-4444	24	9	largest	large	ADJ
ejpam-4444	24	10	value	value	NOUN
ejpam-4444	24	11	p	p	X
ejpam-4444	24	12	=	=	PROPN
ejpam-4444	24	13	1.8435	1.8435	NUM
ejpam-4444	24	14	.	.	PUNCT
ejpam-4444	24	15	.	.	PUNCT
ejpam-4444	25	1	.	.	PUNCT
ejpam-4444	26	1	and	and	CCONJ
ejpam-4444	26	2	smallest	small	ADJ
ejpam-4444	26	3	value	value	NOUN
ejpam-4444	26	4	q	q	NOUN
ejpam-4444	27	1	=	=	SYM
ejpam-4444	27	2	2	2	NUM
ejpam-4444	27	3	,	,	PUNCT
ejpam-4444	27	4	where	where	SCONJ
ejpam-4444	27	5	p	p	NOUN
ejpam-4444	27	6	is	be	AUX
ejpam-4444	27	7	the	the	DET
ejpam-4444	27	8	unique	unique	ADJ
ejpam-4444	27	9	solution	solution	NOUN
ejpam-4444	27	10	of	of	ADP
ejpam-4444	27	11	the	the	DET
ejpam-4444	27	12	equation	equation	NOUN
ejpam-4444	27	13	(	(	PUNCT
ejpam-4444	27	14	p+	p+	NOUN
ejpam-4444	27	15	1)1	1)1	NUM
ejpam-4444	27	16	/	/	SYM
ejpam-4444	27	17	p	p	NOUN
ejpam-4444	27	18	=	=	SYM
ejpam-4444	27	19	2	2	NUM
ejpam-4444	27	20	log(1	log(1	NOUN
ejpam-4444	28	1	+	+	CCONJ
ejpam-4444	28	2	√	√	NUM
ejpam-4444	28	3	2	2	NUM
ejpam-4444	28	4	)	)	PUNCT
ejpam-4444	29	1	such	such	ADJ
ejpam-4444	29	2	that	that	SCONJ
ejpam-4444	29	3	the	the	DET
ejpam-4444	29	4	double	double	ADJ
ejpam-4444	29	5	inequalities	inequality	NOUN
ejpam-4444	29	6	lp(a	lp(a	ADP
ejpam-4444	29	7	,	,	PUNCT
ejpam-4444	29	8	b	b	NOUN
ejpam-4444	29	9	)	)	PUNCT
ejpam-4444	29	10	<	<	X
ejpam-4444	29	11	m(a	m(a	PROPN
ejpam-4444	29	12	,	,	PUNCT
ejpam-4444	29	13	b	b	NOUN
ejpam-4444	29	14	)	)	PUNCT
ejpam-4444	29	15	<	<	X
ejpam-4444	29	16	lq(a	lq(a	X
ejpam-4444	29	17	,	,	PUNCT
ejpam-4444	29	18	b	b	X
ejpam-4444	29	19	)	)	PUNCT
ejpam-4444	29	20	hold	hold	VERB
ejpam-4444	29	21	for	for	ADP
ejpam-4444	29	22	all	all	DET
ejpam-4444	29	23	distinct	distinct	ADJ
ejpam-4444	29	24	positive	positive	ADJ
ejpam-4444	29	25	numbers	number	NOUN
ejpam-4444	29	26	a	a	DET
ejpam-4444	29	27	,	,	PUNCT
ejpam-4444	29	28	b.	b.	PROPN
ejpam-4444	30	1	in	in	ADP
ejpam-4444	30	2	case	case	NOUN
ejpam-4444	30	3	of	of	ADP
ejpam-4444	30	4	yang	yang	PROPN
ejpam-4444	30	5	mean	mean	PROPN
ejpam-4444	30	6	,	,	PUNCT
ejpam-4444	30	7	qian	qian	PROPN
ejpam-4444	30	8	and	and	CCONJ
ejpam-4444	30	9	chu	chu	PROPN
ejpam-4444	30	10	[	[	X
ejpam-4444	30	11	14	14	NUM
ejpam-4444	30	12	]	]	X
ejpam-4444	30	13	in	in	ADP
ejpam-4444	30	14	2016	2016	NUM
ejpam-4444	30	15	found	find	VERB
ejpam-4444	30	16	the	the	DET
ejpam-4444	30	17	best	good	ADJ
ejpam-4444	30	18	possible	possible	ADJ
ejpam-4444	30	19	parameters	parameter	NOUN
ejpam-4444	30	20	p	p	X
ejpam-4444	30	21	=	=	PUNCT
ejpam-4444	30	22	0.5451	0.5451	NUM
ejpam-4444	30	23	.	.	PUNCT
ejpam-4444	30	24	.	.	PUNCT
ejpam-4444	31	1	.	.	PUNCT
ejpam-4444	32	1	and	and	CCONJ
ejpam-4444	32	2	q	q	X
ejpam-4444	32	3	=	=	SYM
ejpam-4444	32	4	2	2	NUM
ejpam-4444	32	5	,	,	PUNCT
ejpam-4444	32	6	where	where	SCONJ
ejpam-4444	32	7	p	p	NOUN
ejpam-4444	32	8	is	be	AUX
ejpam-4444	32	9	the	the	DET
ejpam-4444	32	10	unique	unique	ADJ
ejpam-4444	32	11	solution	solution	NOUN
ejpam-4444	32	12	of	of	ADP
ejpam-4444	32	13	the	the	DET
ejpam-4444	32	14	equation	equation	NOUN
ejpam-4444	32	15	(	(	PUNCT
ejpam-4444	32	16	p+1)1	p+1)1	NOUN
ejpam-4444	32	17	/	/	SYM
ejpam-4444	33	1	p	p	NOUN
ejpam-4444	33	2	=	=	NOUN
ejpam-4444	33	3	√	√	PROPN
ejpam-4444	33	4	2π/2	2π/2	NUM
ejpam-4444	33	5	such	such	ADJ
ejpam-4444	33	6	that	that	SCONJ
ejpam-4444	33	7	the	the	DET
ejpam-4444	33	8	double	double	ADJ
ejpam-4444	33	9	inequalities	inequality	NOUN
ejpam-4444	33	10	lp(a	lp(a	ADP
ejpam-4444	33	11	,	,	PUNCT
ejpam-4444	33	12	b	b	X
ejpam-4444	33	13	)	)	PUNCT
ejpam-4444	33	14	<	<	X
ejpam-4444	33	15	u(a	u(a	PROPN
ejpam-4444	33	16	,	,	PUNCT
ejpam-4444	33	17	b	b	NOUN
ejpam-4444	33	18	)	)	PUNCT
ejpam-4444	33	19	<	<	X
ejpam-4444	33	20	lq(a	lq(a	X
ejpam-4444	33	21	,	,	PUNCT
ejpam-4444	33	22	b	b	NOUN
ejpam-4444	33	23	)	)	PUNCT
ejpam-4444	33	24	a.	a.	NOUN
ejpam-4444	33	25	sonubon	sonubon	PROPN
ejpam-4444	33	26	,	,	PUNCT
ejpam-4444	33	27	s.	s.	PROPN
ejpam-4444	33	28	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	33	29	,	,	PUNCT
ejpam-4444	33	30	k.	k.	PROPN
ejpam-4444	33	31	nonlaopon	nonlaopon	ADV
ejpam-4444	33	32	/	/	SYM
ejpam-4444	33	33	eur	eur	PROPN
ejpam-4444	33	34	.	.	PUNCT
ejpam-4444	34	1	j.	j.	PROPN
ejpam-4444	34	2	pure	pure	PROPN
ejpam-4444	34	3	appl	appl	PROPN
ejpam-4444	34	4	.	.	PROPN
ejpam-4444	34	5	math	math	PROPN
ejpam-4444	34	6	,	,	PUNCT
ejpam-4444	34	7	15	15	NUM
ejpam-4444	34	8	(	(	PUNCT
ejpam-4444	34	9	3	3	NUM
ejpam-4444	34	10	)	)	PUNCT
ejpam-4444	34	11	(	(	PUNCT
ejpam-4444	34	12	2022	2022	NUM
ejpam-4444	34	13	)	)	PUNCT
ejpam-4444	34	14	,	,	PUNCT
ejpam-4444	34	15	1120	1120	NUM
ejpam-4444	34	16	-	-	SYM
ejpam-4444	34	17	1143	1143	NUM
ejpam-4444	34	18	1122	1122	NUM
ejpam-4444	34	19	hold	hold	VERB
ejpam-4444	34	20	for	for	ADP
ejpam-4444	34	21	all	all	DET
ejpam-4444	34	22	distinct	distinct	ADJ
ejpam-4444	34	23	positive	positive	ADJ
ejpam-4444	34	24	numbers	number	NOUN
ejpam-4444	34	25	a	a	DET
ejpam-4444	34	26	,	,	PUNCT
ejpam-4444	34	27	b.	b.	PROPN
ejpam-4444	34	28	for	for	ADP
ejpam-4444	34	29	a	a	DET
ejpam-4444	34	30	problem	problem	NOUN
ejpam-4444	34	31	of	of	ADP
ejpam-4444	34	32	finding	find	VERB
ejpam-4444	34	33	optimal	optimal	ADJ
ejpam-4444	34	34	bound	bind	VERB
ejpam-4444	34	35	of	of	ADP
ejpam-4444	34	36	weight	weight	NOUN
ejpam-4444	34	37	either	either	CCONJ
ejpam-4444	34	38	geometric	geometric	ADJ
ejpam-4444	34	39	or	or	CCONJ
ejpam-4444	34	40	arithmetic	arithmetic	ADJ
ejpam-4444	34	41	means	mean	NOUN
ejpam-4444	34	42	by	by	ADP
ejpam-4444	34	43	generalized	generalized	ADJ
ejpam-4444	34	44	logarithmic	logarithmic	ADJ
ejpam-4444	34	45	means	mean	NOUN
ejpam-4444	34	46	,	,	PUNCT
ejpam-4444	34	47	there	there	PRON
ejpam-4444	34	48	are	be	VERB
ejpam-4444	34	49	many	many	ADJ
ejpam-4444	34	50	recent	recent	ADJ
ejpam-4444	34	51	works	work	NOUN
ejpam-4444	34	52	in	in	ADP
ejpam-4444	34	53	this	this	DET
ejpam-4444	34	54	direction	direction	NOUN
ejpam-4444	34	55	.	.	PUNCT
ejpam-4444	35	1	in	in	ADP
ejpam-4444	35	2	case	case	NOUN
ejpam-4444	35	3	of	of	ADP
ejpam-4444	35	4	weighted	weight	VERB
ejpam-4444	35	5	geometric	geometric	ADJ
ejpam-4444	35	6	mean	mean	NOUN
ejpam-4444	35	7	,	,	PUNCT
ejpam-4444	35	8	for	for	ADP
ejpam-4444	35	9	α	α	NOUN
ejpam-4444	35	10	,	,	PUNCT
ejpam-4444	35	11	β	β	X
ejpam-4444	35	12	,	,	PUNCT
ejpam-4444	35	13	γ	γ	PROPN
ejpam-4444	35	14	∈	∈	PROPN
ejpam-4444	35	15	(	(	PUNCT
ejpam-4444	35	16	0	0	NUM
ejpam-4444	35	17	,	,	PUNCT
ejpam-4444	35	18	1	1	NUM
ejpam-4444	35	19	)	)	PUNCT
ejpam-4444	35	20	and	and	CCONJ
ejpam-4444	35	21	α	α	PRON
ejpam-4444	35	22	+	+	X
ejpam-4444	35	23	β	β	X
ejpam-4444	35	24	+	+	X
ejpam-4444	35	25	γ	γ	X
ejpam-4444	35	26	=	=	SYM
ejpam-4444	35	27	1	1	NUM
ejpam-4444	35	28	,	,	PUNCT
ejpam-4444	35	29	chu	chu	NOUN
ejpam-4444	35	30	and	and	CCONJ
ejpam-4444	35	31	long	long	ADJ
ejpam-4444	35	32	[	[	X
ejpam-4444	35	33	4	4	X
ejpam-4444	35	34	]	]	PUNCT
ejpam-4444	35	35	in	in	ADP
ejpam-4444	35	36	2010	2010	NUM
ejpam-4444	35	37	found	find	VERB
ejpam-4444	35	38	the	the	DET
ejpam-4444	35	39	optimal	optimal	ADJ
ejpam-4444	35	40	bound	bind	VERB
ejpam-4444	35	41	for	for	ADP
ejpam-4444	35	42	aα(a	aα(a	NOUN
ejpam-4444	35	43	,	,	PUNCT
ejpam-4444	35	44	b)gβ(a	b)gβ(a	PROPN
ejpam-4444	35	45	,	,	PUNCT
ejpam-4444	35	46	b)hγ(a	b)hγ(a	ADJ
ejpam-4444	35	47	,	,	PUNCT
ejpam-4444	35	48	b	b	NOUN
ejpam-4444	35	49	)	)	PUNCT
ejpam-4444	35	50	.	.	PUNCT
ejpam-4444	36	1	that	that	PRON
ejpam-4444	36	2	is	be	AUX
ejpam-4444	36	3	,	,	PUNCT
ejpam-4444	36	4	they	they	PRON
ejpam-4444	36	5	discovered	discover	VERB
ejpam-4444	36	6	that	that	SCONJ
ejpam-4444	36	7	the	the	DET
ejpam-4444	36	8	largest	large	ADJ
ejpam-4444	36	9	value	value	NOUN
ejpam-4444	36	10	p	p	NOUN
ejpam-4444	36	11	=	=	NOUN
ejpam-4444	36	12	6α+3β	6α+3β	NUM
ejpam-4444	36	13	−	−	NUM
ejpam-4444	36	14	5	5	NUM
ejpam-4444	36	15	and	and	CCONJ
ejpam-4444	36	16	the	the	DET
ejpam-4444	36	17	smallest	small	ADJ
ejpam-4444	36	18	value	value	NOUN
ejpam-4444	36	19	q	q	NOUN
ejpam-4444	36	20	=	=	SYM
ejpam-4444	36	21	−2/(2α+	−2/(2α+	NUM
ejpam-4444	36	22	β	β	NOUN
ejpam-4444	36	23	)	)	PUNCT
ejpam-4444	36	24	are	be	AUX
ejpam-4444	36	25	the	the	DET
ejpam-4444	36	26	optimal	optimal	ADJ
ejpam-4444	36	27	values	value	NOUN
ejpam-4444	36	28	such	such	ADJ
ejpam-4444	36	29	that	that	SCONJ
ejpam-4444	36	30	the	the	DET
ejpam-4444	36	31	double	double	ADJ
ejpam-4444	36	32	inequalities	inequality	NOUN
ejpam-4444	36	33	lp(a	lp(a	ADP
ejpam-4444	36	34	,	,	PUNCT
ejpam-4444	36	35	b	b	NOUN
ejpam-4444	36	36	)	)	PUNCT
ejpam-4444	36	37	<	<	X
ejpam-4444	36	38	aα(a	aα(a	NOUN
ejpam-4444	36	39	,	,	PUNCT
ejpam-4444	36	40	b)gβ(a	b)gβ(a	PROPN
ejpam-4444	36	41	,	,	PUNCT
ejpam-4444	36	42	b)hγ(a	b)hγ(a	ADJ
ejpam-4444	36	43	,	,	PUNCT
ejpam-4444	36	44	b	b	NOUN
ejpam-4444	36	45	)	)	PUNCT
ejpam-4444	36	46	<	<	X
ejpam-4444	36	47	lq(a	lq(a	X
ejpam-4444	36	48	,	,	PUNCT
ejpam-4444	36	49	b	b	X
ejpam-4444	36	50	)	)	PUNCT
ejpam-4444	36	51	hold	hold	VERB
ejpam-4444	36	52	for	for	ADP
ejpam-4444	36	53	all	all	DET
ejpam-4444	36	54	distinct	distinct	ADJ
ejpam-4444	36	55	positive	positive	ADJ
ejpam-4444	36	56	numbers	number	NOUN
ejpam-4444	36	57	a	a	PRON
ejpam-4444	36	58	,	,	PUNCT
ejpam-4444	36	59	b.	b.	PROPN
ejpam-4444	36	60	in	in	ADP
ejpam-4444	36	61	2011	2011	NUM
ejpam-4444	36	62	,	,	PUNCT
ejpam-4444	36	63	qian	qian	ADJ
ejpam-4444	36	64	and	and	CCONJ
ejpam-4444	36	65	long	long	ADJ
ejpam-4444	37	1	[	[	X
ejpam-4444	37	2	16	16	NUM
ejpam-4444	37	3	]	]	PUNCT
ejpam-4444	37	4	presented	present	VERB
ejpam-4444	37	5	the	the	DET
ejpam-4444	37	6	sharp	sharp	ADJ
ejpam-4444	37	7	upper	upper	ADJ
ejpam-4444	37	8	and	and	CCONJ
ejpam-4444	37	9	lower	lower	ADV
ejpam-4444	37	10	bound	bind	VERB
ejpam-4444	37	11	for	for	ADP
ejpam-4444	37	12	the	the	DET
ejpam-4444	37	13	weighted	weight	VERB
ejpam-4444	37	14	geometric	geometric	ADJ
ejpam-4444	37	15	mean	mean	NOUN
ejpam-4444	37	16	of	of	ADP
ejpam-4444	37	17	geometric	geometric	ADJ
ejpam-4444	37	18	and	and	CCONJ
ejpam-4444	37	19	harmonic	harmonic	ADJ
ejpam-4444	37	20	means	mean	NOUN
ejpam-4444	37	21	by	by	ADP
ejpam-4444	37	22	generalized	generalized	ADJ
ejpam-4444	37	23	logarithmic	logarithmic	ADJ
ejpam-4444	37	24	means	mean	NOUN
ejpam-4444	37	25	:	:	PUNCT
ejpam-4444	37	26	for	for	ADP
ejpam-4444	37	27	all	all	DET
ejpam-4444	37	28	positive	positive	ADJ
ejpam-4444	37	29	numbers	number	NOUN
ejpam-4444	37	30	a	a	PRON
ejpam-4444	37	31	and	and	CCONJ
ejpam-4444	37	32	b	b	NOUN
ejpam-4444	37	33	1	1	NUM
ejpam-4444	37	34	)	)	PUNCT
ejpam-4444	37	35	l3α−5(a	l3α−5(a	NOUN
ejpam-4444	37	36	,	,	PUNCT
ejpam-4444	37	37	b	b	NOUN
ejpam-4444	37	38	)	)	PUNCT
ejpam-4444	37	39	=	=	SYM
ejpam-4444	37	40	gα(a	gα(a	NOUN
ejpam-4444	37	41	,	,	PUNCT
ejpam-4444	37	42	b)h1−α(a	b)h1−α(a	NOUN
ejpam-4444	37	43	,	,	PUNCT
ejpam-4444	37	44	b	b	NOUN
ejpam-4444	37	45	)	)	PUNCT
ejpam-4444	37	46	=	=	SYM
ejpam-4444	38	1	l−2	l−2	NOUN
ejpam-4444	38	2	/	/	SYM
ejpam-4444	38	3	α(a	α(a	PROPN
ejpam-4444	38	4	,	,	PUNCT
ejpam-4444	38	5	b	b	NOUN
ejpam-4444	38	6	)	)	PUNCT
ejpam-4444	38	7	for	for	ADP
ejpam-4444	38	8	α	α	NOUN
ejpam-4444	38	9	=	=	SYM
ejpam-4444	38	10	2/3	2/3	NUM
ejpam-4444	38	11	,	,	PUNCT
ejpam-4444	38	12	2	2	NUM
ejpam-4444	38	13	)	)	PUNCT
ejpam-4444	38	14	l3α−5(a	l3α−5(a	NOUN
ejpam-4444	38	15	,	,	PUNCT
ejpam-4444	38	16	b	b	NOUN
ejpam-4444	38	17	)	)	PUNCT
ejpam-4444	38	18	⩾	⩾	NOUN
ejpam-4444	38	19	gα(a	gα(a	NOUN
ejpam-4444	38	20	,	,	PUNCT
ejpam-4444	38	21	b)h1−α(a	b)h1−α(a	NOUN
ejpam-4444	38	22	,	,	PUNCT
ejpam-4444	38	23	b	b	NOUN
ejpam-4444	38	24	)	)	PUNCT
ejpam-4444	38	25	⩾	⩾	PROPN
ejpam-4444	39	1	l−2	l−2	NOUN
ejpam-4444	39	2	/	/	SYM
ejpam-4444	39	3	α(a	α(a	PROPN
ejpam-4444	39	4	,	,	PUNCT
ejpam-4444	39	5	b	b	NOUN
ejpam-4444	39	6	)	)	PUNCT
ejpam-4444	39	7	for	for	ADP
ejpam-4444	39	8	α	α	PRON
ejpam-4444	39	9	∈	∈	PROPN
ejpam-4444	39	10	(	(	PUNCT
ejpam-4444	39	11	0	0	NUM
ejpam-4444	39	12	,	,	PUNCT
ejpam-4444	39	13	2/3	2/3	NUM
ejpam-4444	39	14	)	)	PUNCT
ejpam-4444	39	15	,	,	PUNCT
ejpam-4444	39	16	and	and	CCONJ
ejpam-4444	39	17	l3α−5(a	l3α−5(a	NUM
ejpam-4444	39	18	,	,	PUNCT
ejpam-4444	39	19	b	b	NOUN
ejpam-4444	39	20	)	)	PUNCT
ejpam-4444	39	21	⩽	⩽	NOUN
ejpam-4444	39	22	gα(a	gα(a	PROPN
ejpam-4444	39	23	,	,	PUNCT
ejpam-4444	39	24	b)h1−α(a	b)h1−α(a	NOUN
ejpam-4444	39	25	,	,	PUNCT
ejpam-4444	39	26	b	b	NOUN
ejpam-4444	39	27	)	)	PUNCT
ejpam-4444	39	28	⩽	⩽	NOUN
ejpam-4444	39	29	l−2	l−2	PROPN
ejpam-4444	39	30	/	/	SYM
ejpam-4444	39	31	α	α	PROPN
ejpam-4444	39	32	for	for	ADP
ejpam-4444	39	33	α	α	PRON
ejpam-4444	39	34	∈	∈	PROPN
ejpam-4444	39	35	(	(	PUNCT
ejpam-4444	39	36	2/3	2/3	NUM
ejpam-4444	39	37	,	,	PUNCT
ejpam-4444	39	38	1	1	NUM
ejpam-4444	39	39	)	)	PUNCT
ejpam-4444	39	40	,	,	PUNCT
ejpam-4444	39	41	with	with	ADP
ejpam-4444	39	42	equality	equality	NOUN
ejpam-4444	39	43	if	if	SCONJ
ejpam-4444	39	44	and	and	CCONJ
ejpam-4444	39	45	only	only	ADV
ejpam-4444	39	46	if	if	SCONJ
ejpam-4444	39	47	a	a	DET
ejpam-4444	39	48	=	=	SYM
ejpam-4444	39	49	b	b	NOUN
ejpam-4444	39	50	,	,	PUNCT
ejpam-4444	39	51	and	and	CCONJ
ejpam-4444	39	52	the	the	DET
ejpam-4444	39	53	parameters	parameter	NOUN
ejpam-4444	39	54	3α−	3α−	NUM
ejpam-4444	39	55	5	5	NUM
ejpam-4444	39	56	and	and	CCONJ
ejpam-4444	39	57	−2	−2	NOUN
ejpam-4444	39	58	/	/	SYM
ejpam-4444	39	59	α	α	PROPN
ejpam-4444	39	60	can	can	AUX
ejpam-4444	39	61	not	not	PART
ejpam-4444	39	62	be	be	AUX
ejpam-4444	39	63	improved	improve	VERB
ejpam-4444	39	64	in	in	ADP
ejpam-4444	39	65	either	either	DET
ejpam-4444	39	66	case	case	NOUN
ejpam-4444	39	67	.	.	PUNCT
ejpam-4444	40	1	chunrong	chunrong	ADJ
ejpam-4444	40	2	and	and	CCONJ
ejpam-4444	40	3	siqi	siqi	NOUN
ejpam-4444	41	1	[	[	X
ejpam-4444	41	2	5	5	NUM
ejpam-4444	41	3	]	]	PUNCT
ejpam-4444	41	4	established	establish	VERB
ejpam-4444	41	5	the	the	DET
ejpam-4444	41	6	optimal	optimal	ADJ
ejpam-4444	41	7	bounds	bound	NOUN
ejpam-4444	41	8	for	for	ADP
ejpam-4444	41	9	gα(a	gα(a	NOUN
ejpam-4444	41	10	,	,	PUNCT
ejpam-4444	41	11	b)n1−α(a	b)n1−α(a	NOUN
ejpam-4444	41	12	,	,	PUNCT
ejpam-4444	41	13	b	b	NOUN
ejpam-4444	41	14	)	)	PUNCT
ejpam-4444	41	15	in	in	ADP
ejpam-4444	41	16	term	term	NOUN
ejpam-4444	41	17	of	of	ADP
ejpam-4444	41	18	lp(a	lp(a	PRON
ejpam-4444	41	19	,	,	PUNCT
ejpam-4444	41	20	b	b	NOUN
ejpam-4444	41	21	)	)	PUNCT
ejpam-4444	41	22	.	.	PUNCT
ejpam-4444	42	1	they	they	PRON
ejpam-4444	42	2	found	find	VERB
ejpam-4444	42	3	that	that	SCONJ
ejpam-4444	42	4	for	for	ADP
ejpam-4444	42	5	any	any	DET
ejpam-4444	42	6	positive	positive	ADJ
ejpam-4444	42	7	numbers	number	NOUN
ejpam-4444	42	8	a	a	DET
ejpam-4444	42	9	and	and	CCONJ
ejpam-4444	42	10	b	b	NOUN
ejpam-4444	42	11	1	1	X
ejpam-4444	42	12	)	)	PUNCT
ejpam-4444	42	13	l−(1	l−(1	PROPN
ejpam-4444	42	14	+	+	PROPN
ejpam-4444	42	15	3α)/2(a	3α)/2(a	NOUN
ejpam-4444	42	16	,	,	PUNCT
ejpam-4444	42	17	b	b	NOUN
ejpam-4444	42	18	)	)	PUNCT
ejpam-4444	42	19	=	=	SYM
ejpam-4444	42	20	gα(a	gα(a	NOUN
ejpam-4444	42	21	,	,	PUNCT
ejpam-4444	42	22	b)n1−α(a	b)n1−α(a	NOUN
ejpam-4444	42	23	,	,	PUNCT
ejpam-4444	42	24	b	b	NOUN
ejpam-4444	42	25	)	)	PUNCT
ejpam-4444	42	26	=	=	SYM
ejpam-4444	42	27	l2/(α−2)(a	l2/(α−2)(a	PROPN
ejpam-4444	42	28	,	,	PUNCT
ejpam-4444	42	29	b	b	NOUN
ejpam-4444	42	30	)	)	PUNCT
ejpam-4444	42	31	for	for	ADP
ejpam-4444	42	32	α	α	NOUN
ejpam-4444	42	33	=	=	SYM
ejpam-4444	42	34	2/3	2/3	NUM
ejpam-4444	42	35	,	,	PUNCT
ejpam-4444	42	36	2	2	NUM
ejpam-4444	42	37	)	)	PUNCT
ejpam-4444	42	38	l−(1	l−(1	PROPN
ejpam-4444	42	39	+	+	PROPN
ejpam-4444	42	40	3α)/2(a	3α)/2(a	NOUN
ejpam-4444	42	41	,	,	PUNCT
ejpam-4444	42	42	b	b	NOUN
ejpam-4444	42	43	)	)	PUNCT
ejpam-4444	42	44	>	>	X
ejpam-4444	42	45	gα(a	gα(a	PROPN
ejpam-4444	42	46	,	,	PUNCT
ejpam-4444	42	47	b)n1−α(a	b)n1−α(a	NOUN
ejpam-4444	42	48	,	,	PUNCT
ejpam-4444	42	49	b	b	NOUN
ejpam-4444	42	50	)	)	PUNCT
ejpam-4444	42	51	>	>	X
ejpam-4444	43	1	l2/(α−2)(a	l2/(α−2)(a	PROPN
ejpam-4444	43	2	,	,	PUNCT
ejpam-4444	43	3	b	b	NOUN
ejpam-4444	43	4	)	)	PUNCT
ejpam-4444	43	5	for	for	ADP
ejpam-4444	43	6	α	α	PRON
ejpam-4444	43	7	∈	∈	PROPN
ejpam-4444	43	8	(	(	PUNCT
ejpam-4444	43	9	0	0	NUM
ejpam-4444	43	10	,	,	PUNCT
ejpam-4444	43	11	2/3	2/3	NUM
ejpam-4444	43	12	)	)	PUNCT
ejpam-4444	43	13	,	,	PUNCT
ejpam-4444	43	14	and	and	CCONJ
ejpam-4444	43	15	l−(1	l−(1	PROPN
ejpam-4444	43	16	+	+	PROPN
ejpam-4444	43	17	3α)/2(a	3α)/2(a	PROPN
ejpam-4444	43	18	,	,	PUNCT
ejpam-4444	43	19	b	b	NOUN
ejpam-4444	43	20	)	)	PUNCT
ejpam-4444	43	21	<	<	X
ejpam-4444	43	22	gα(a	gα(a	NOUN
ejpam-4444	43	23	,	,	PUNCT
ejpam-4444	43	24	b)n1−α(a	b)n1−α(a	NOUN
ejpam-4444	43	25	,	,	PUNCT
ejpam-4444	43	26	b	b	X
ejpam-4444	43	27	)	)	PUNCT
ejpam-4444	43	28	<	<	X
ejpam-4444	43	29	l2/(α−2)(a	l2/(α−2)(a	PROPN
ejpam-4444	43	30	,	,	PUNCT
ejpam-4444	43	31	b	b	NOUN
ejpam-4444	43	32	)	)	PUNCT
ejpam-4444	43	33	for	for	ADP
ejpam-4444	43	34	α	α	PRON
ejpam-4444	43	35	∈	∈	PROPN
ejpam-4444	43	36	(	(	PUNCT
ejpam-4444	43	37	2/3	2/3	NUM
ejpam-4444	43	38	,	,	PUNCT
ejpam-4444	43	39	1	1	NUM
ejpam-4444	43	40	)	)	PUNCT
ejpam-4444	43	41	,	,	PUNCT
ejpam-4444	43	42	and	and	CCONJ
ejpam-4444	43	43	the	the	DET
ejpam-4444	43	44	parameters	parameter	NOUN
ejpam-4444	43	45	−(1	−(1	PROPN
ejpam-4444	44	1	+	+	CCONJ
ejpam-4444	44	2	3α)/2	3α)/2	NUM
ejpam-4444	44	3	and	and	CCONJ
ejpam-4444	44	4	2/(α−	2/(α−	NUM
ejpam-4444	44	5	2	2	NUM
ejpam-4444	44	6	)	)	PUNCT
ejpam-4444	44	7	can	can	AUX
ejpam-4444	44	8	not	not	PART
ejpam-4444	44	9	be	be	AUX
ejpam-4444	44	10	improved	improve	VERB
ejpam-4444	44	11	in	in	ADP
ejpam-4444	44	12	either	either	DET
ejpam-4444	44	13	case	case	NOUN
ejpam-4444	44	14	.	.	PUNCT
ejpam-4444	45	1	in	in	ADP
ejpam-4444	45	2	the	the	DET
ejpam-4444	45	3	case	case	NOUN
ejpam-4444	45	4	of	of	ADP
ejpam-4444	45	5	weighted	weight	VERB
ejpam-4444	45	6	arithmetic	arithmetic	ADJ
ejpam-4444	45	7	mean	mean	NOUN
ejpam-4444	45	8	,	,	PUNCT
ejpam-4444	45	9	long	long	ADJ
ejpam-4444	45	10	and	and	CCONJ
ejpam-4444	45	11	chu	chu	VERB
ejpam-4444	46	1	[	[	X
ejpam-4444	46	2	9	9	NUM
ejpam-4444	46	3	]	]	PUNCT
ejpam-4444	46	4	in	in	ADP
ejpam-4444	46	5	2010	2010	NUM
ejpam-4444	46	6	proposed	propose	VERB
ejpam-4444	46	7	the	the	DET
ejpam-4444	46	8	inequalities	inequality	NOUN
ejpam-4444	46	9	involving	involve	VERB
ejpam-4444	46	10	generalized	generalize	VERB
ejpam-4444	46	11	logarithmic	logarithmic	ADJ
ejpam-4444	46	12	means	mean	NOUN
ejpam-4444	46	13	and	and	CCONJ
ejpam-4444	46	14	weighted	weight	VERB
ejpam-4444	46	15	arithmetic	arithmetic	ADJ
ejpam-4444	46	16	means	mean	NOUN
ejpam-4444	46	17	of	of	ADP
ejpam-4444	46	18	arithmetic	arithmetic	ADJ
ejpam-4444	46	19	and	and	CCONJ
ejpam-4444	46	20	geometric	geometric	ADJ
ejpam-4444	46	21	means	mean	NOUN
ejpam-4444	46	22	:	:	PUNCT
ejpam-4444	46	23	1	1	NUM
ejpam-4444	46	24	)	)	PUNCT
ejpam-4444	46	25	l3α−2(a	l3α−2(a	NOUN
ejpam-4444	46	26	,	,	PUNCT
ejpam-4444	46	27	b	b	NOUN
ejpam-4444	46	28	)	)	PUNCT
ejpam-4444	46	29	=	=	SYM
ejpam-4444	46	30	αa(a	αa(a	NOUN
ejpam-4444	46	31	,	,	PUNCT
ejpam-4444	46	32	b	b	NOUN
ejpam-4444	46	33	)	)	PUNCT
ejpam-4444	47	1	+	+	CCONJ
ejpam-4444	47	2	(	(	PUNCT
ejpam-4444	47	3	1−	1−	NUM
ejpam-4444	47	4	α)g(a	α)g(a	NOUN
ejpam-4444	47	5	,	,	PUNCT
ejpam-4444	47	6	b	b	NOUN
ejpam-4444	47	7	)	)	PUNCT
ejpam-4444	47	8	for	for	ADP
ejpam-4444	47	9	α	α	NOUN
ejpam-4444	47	10	=	=	SYM
ejpam-4444	47	11	1/2	1/2	NUM
ejpam-4444	47	12	,	,	PUNCT
ejpam-4444	47	13	2	2	NUM
ejpam-4444	47	14	)	)	PUNCT
ejpam-4444	47	15	l3α−2(a	l3α−2(a	NOUN
ejpam-4444	47	16	,	,	PUNCT
ejpam-4444	47	17	b	b	NOUN
ejpam-4444	47	18	)	)	PUNCT
ejpam-4444	47	19	<	<	X
ejpam-4444	47	20	αa(a	αa(a	NOUN
ejpam-4444	47	21	,	,	PUNCT
ejpam-4444	47	22	b	b	NOUN
ejpam-4444	47	23	)	)	PUNCT
ejpam-4444	48	1	+	+	CCONJ
ejpam-4444	48	2	(	(	PUNCT
ejpam-4444	48	3	1−	1−	NUM
ejpam-4444	48	4	α)g(a	α)g(a	NOUN
ejpam-4444	48	5	,	,	PUNCT
ejpam-4444	48	6	b	b	NOUN
ejpam-4444	48	7	)	)	PUNCT
ejpam-4444	48	8	for	for	ADP
ejpam-4444	48	9	α	α	PRON
ejpam-4444	48	10	∈	∈	PROPN
ejpam-4444	48	11	(	(	PUNCT
ejpam-4444	48	12	0	0	NUM
ejpam-4444	48	13	,	,	PUNCT
ejpam-4444	48	14	1/2	1/2	NUM
ejpam-4444	48	15	)	)	PUNCT
ejpam-4444	48	16	,	,	PUNCT
ejpam-4444	48	17	3	3	X
ejpam-4444	48	18	)	)	PUNCT
ejpam-4444	48	19	l3α−2(a	l3α−2(a	PROPN
ejpam-4444	48	20	,	,	PUNCT
ejpam-4444	48	21	b	b	NOUN
ejpam-4444	48	22	)	)	PUNCT
ejpam-4444	48	23	>	>	X
ejpam-4444	48	24	αa(a	αa(a	NOUN
ejpam-4444	48	25	,	,	PUNCT
ejpam-4444	48	26	b	b	NOUN
ejpam-4444	48	27	)	)	PUNCT
ejpam-4444	49	1	+	+	CCONJ
ejpam-4444	49	2	(	(	PUNCT
ejpam-4444	49	3	1−	1−	NUM
ejpam-4444	49	4	α)g(a	α)g(a	NOUN
ejpam-4444	49	5	,	,	PUNCT
ejpam-4444	49	6	b	b	NOUN
ejpam-4444	49	7	)	)	PUNCT
ejpam-4444	49	8	for	for	ADP
ejpam-4444	49	9	α	α	PRON
ejpam-4444	49	10	∈	∈	PROPN
ejpam-4444	49	11	(	(	PUNCT
ejpam-4444	49	12	1/2	1/2	NUM
ejpam-4444	49	13	,	,	PUNCT
ejpam-4444	49	14	1	1	NUM
ejpam-4444	49	15	)	)	PUNCT
ejpam-4444	49	16	.	.	PUNCT
ejpam-4444	50	1	moreover	moreover	ADV
ejpam-4444	50	2	,	,	PUNCT
ejpam-4444	50	3	in	in	ADP
ejpam-4444	50	4	each	each	DET
ejpam-4444	50	5	case	case	NOUN
ejpam-4444	50	6	,	,	PUNCT
ejpam-4444	50	7	the	the	DET
ejpam-4444	50	8	bound	bind	VERB
ejpam-4444	50	9	l3α−2(a	l3α−2(a	NOUN
ejpam-4444	50	10	,	,	PUNCT
ejpam-4444	50	11	b	b	NOUN
ejpam-4444	50	12	)	)	PUNCT
ejpam-4444	50	13	for	for	ADP
ejpam-4444	50	14	the	the	DET
ejpam-4444	50	15	sum	sum	NOUN
ejpam-4444	50	16	of	of	ADP
ejpam-4444	50	17	αa(a	αa(a	NUM
ejpam-4444	50	18	,	,	PUNCT
ejpam-4444	50	19	b	b	NOUN
ejpam-4444	50	20	)	)	PUNCT
ejpam-4444	51	1	+	+	CCONJ
ejpam-4444	51	2	(	(	PUNCT
ejpam-4444	51	3	1−α)g(a	1−α)g(a	NUM
ejpam-4444	51	4	,	,	PUNCT
ejpam-4444	51	5	b	b	NOUN
ejpam-4444	51	6	)	)	PUNCT
ejpam-4444	51	7	is	be	AUX
ejpam-4444	51	8	optimal	optimal	ADJ
ejpam-4444	51	9	.	.	PUNCT
ejpam-4444	52	1	the	the	DET
ejpam-4444	52	2	harmonic	harmonic	NOUN
ejpam-4444	52	3	and	and	CCONJ
ejpam-4444	52	4	contra	contra	ADJ
ejpam-4444	52	5	-	-	ADJ
ejpam-4444	52	6	harmonic	harmonic	ADJ
ejpam-4444	52	7	means	mean	NOUN
ejpam-4444	52	8	have	have	AUX
ejpam-4444	52	9	recently	recently	ADV
ejpam-4444	52	10	been	be	AUX
ejpam-4444	52	11	used	use	VERB
ejpam-4444	52	12	to	to	PART
ejpam-4444	52	13	investigate	investigate	VERB
ejpam-4444	52	14	the	the	DET
ejpam-4444	52	15	optimal	optimal	ADJ
ejpam-4444	52	16	bounds	bound	NOUN
ejpam-4444	52	17	for	for	ADP
ejpam-4444	52	18	means	mean	NOUN
ejpam-4444	52	19	inequalities	inequality	NOUN
ejpam-4444	52	20	as	as	SCONJ
ejpam-4444	52	21	mentioned	mention	VERB
ejpam-4444	52	22	in	in	ADP
ejpam-4444	52	23	the	the	DET
ejpam-4444	52	24	following	following	NOUN
ejpam-4444	52	25	.	.	PUNCT
ejpam-4444	53	1	in	in	ADP
ejpam-4444	53	2	2017	2017	NUM
ejpam-4444	53	3	,	,	PUNCT
ejpam-4444	53	4	qian	qian	PROPN
ejpam-4444	53	5	,	,	PUNCT
ejpam-4444	53	6	zhang	zhang	PROPN
ejpam-4444	53	7	and	and	CCONJ
ejpam-4444	53	8	chu	chu	PROPN
ejpam-4444	54	1	[	[	X
ejpam-4444	54	2	17	17	NUM
ejpam-4444	54	3	]	]	PUNCT
ejpam-4444	54	4	discovered	discover	VERB
ejpam-4444	54	5	the	the	DET
ejpam-4444	54	6	greatest	great	ADJ
ejpam-4444	54	7	values	value	NOUN
ejpam-4444	54	8	α	α	NOUN
ejpam-4444	54	9	and	and	CCONJ
ejpam-4444	54	10	λ	λ	PROPN
ejpam-4444	54	11	,	,	PUNCT
ejpam-4444	54	12	and	and	CCONJ
ejpam-4444	54	13	the	the	DET
ejpam-4444	54	14	smallest	small	ADJ
ejpam-4444	54	15	values	value	NOUN
ejpam-4444	54	16	β	β	X
ejpam-4444	54	17	and	and	CCONJ
ejpam-4444	54	18	µ	µ	X
ejpam-4444	54	19	in	in	ADP
ejpam-4444	54	20	[	[	X
ejpam-4444	54	21	0,1/2	0,1/2	NOUN
ejpam-4444	54	22	]	]	PUNCT
ejpam-4444	54	23	such	such	ADJ
ejpam-4444	54	24	that	that	SCONJ
ejpam-4444	54	25	h[αa+	h[αa+	X
ejpam-4444	54	26	(	(	PUNCT
ejpam-4444	54	27	1−	1−	NUM
ejpam-4444	54	28	α)b	α)b	ADJ
ejpam-4444	54	29	,	,	PUNCT
ejpam-4444	54	30	αb+	αb+	PROPN
ejpam-4444	54	31	(	(	PUNCT
ejpam-4444	54	32	1−	1−	NUM
ejpam-4444	54	33	α)a	α)a	NOUN
ejpam-4444	54	34	]	]	PUNCT
ejpam-4444	54	35	<	<	X
ejpam-4444	54	36	tq(a	tq(a	NOUN
ejpam-4444	54	37	,	,	PUNCT
ejpam-4444	54	38	b	b	X
ejpam-4444	54	39	)	)	PUNCT
ejpam-4444	54	40	<	<	X
ejpam-4444	54	41	h[βa+	h[βa+	X
ejpam-4444	54	42	(	(	PUNCT
ejpam-4444	54	43	1−	1−	NUM
ejpam-4444	54	44	β)b	β)b	NUM
ejpam-4444	54	45	,	,	PUNCT
ejpam-4444	54	46	βb+	βb+	NOUN
ejpam-4444	54	47	(	(	PUNCT
ejpam-4444	54	48	1−	1−	NUM
ejpam-4444	54	49	β)a	β)a	NOUN
ejpam-4444	54	50	]	]	PUNCT
ejpam-4444	54	51	,	,	PUNCT
ejpam-4444	54	52	a.	a.	NOUN
ejpam-4444	54	53	sonubon	sonubon	PROPN
ejpam-4444	54	54	,	,	PUNCT
ejpam-4444	54	55	s.	s.	PROPN
ejpam-4444	54	56	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	54	57	,	,	PUNCT
ejpam-4444	54	58	k.	k.	PROPN
ejpam-4444	54	59	nonlaopon	nonlaopon	ADV
ejpam-4444	54	60	/	/	SYM
ejpam-4444	54	61	eur	eur	PROPN
ejpam-4444	54	62	.	.	PUNCT
ejpam-4444	55	1	j.	j.	PROPN
ejpam-4444	55	2	pure	pure	PROPN
ejpam-4444	55	3	appl	appl	PROPN
ejpam-4444	55	4	.	.	PROPN
ejpam-4444	55	5	math	math	PROPN
ejpam-4444	55	6	,	,	PUNCT
ejpam-4444	55	7	15	15	NUM
ejpam-4444	55	8	(	(	PUNCT
ejpam-4444	55	9	3	3	NUM
ejpam-4444	55	10	)	)	PUNCT
ejpam-4444	55	11	(	(	PUNCT
ejpam-4444	55	12	2022	2022	NUM
ejpam-4444	55	13	)	)	PUNCT
ejpam-4444	55	14	,	,	PUNCT
ejpam-4444	55	15	1120	1120	NUM
ejpam-4444	55	16	-	-	SYM
ejpam-4444	55	17	1143	1143	NUM
ejpam-4444	55	18	1123	1123	NUM
ejpam-4444	55	19	g[λa+	g[λa+	NOUN
ejpam-4444	55	20	(	(	PUNCT
ejpam-4444	55	21	1−	1−	NUM
ejpam-4444	55	22	λ)b	λ)b	NOUN
ejpam-4444	55	23	,	,	PUNCT
ejpam-4444	55	24	λb+	λb+	NOUN
ejpam-4444	55	25	(	(	PUNCT
ejpam-4444	55	26	1−	1−	NUM
ejpam-4444	55	27	λ)a	λ)a	X
ejpam-4444	55	28	]	]	X
ejpam-4444	55	29	<	<	X
ejpam-4444	55	30	tq(a	tq(a	NOUN
ejpam-4444	55	31	,	,	PUNCT
ejpam-4444	55	32	b	b	X
ejpam-4444	55	33	)	)	PUNCT
ejpam-4444	55	34	<	<	X
ejpam-4444	55	35	h[µa+	h[µa+	PROPN
ejpam-4444	55	36	(	(	PUNCT
ejpam-4444	55	37	1−	1−	NUM
ejpam-4444	55	38	µ)b	µ)b	NOUN
ejpam-4444	55	39	,	,	PUNCT
ejpam-4444	55	40	µb+	µb+	NOUN
ejpam-4444	55	41	(	(	PUNCT
ejpam-4444	55	42	1−	1−	NUM
ejpam-4444	55	43	µ)a	µ)a	NOUN
ejpam-4444	55	44	]	]	PUNCT
ejpam-4444	55	45	hold	hold	VERB
ejpam-4444	55	46	for	for	ADP
ejpam-4444	55	47	all	all	DET
ejpam-4444	55	48	a	a	PRON
ejpam-4444	55	49	,	,	PUNCT
ejpam-4444	55	50	b	b	X
ejpam-4444	55	51	>	>	X
ejpam-4444	55	52	0	0	PUNCT
ejpam-4444	55	53	with	with	ADP
ejpam-4444	55	54	a	a	DET
ejpam-4444	55	55	̸=	̸=	PROPN
ejpam-4444	55	56	b	b	PROPN
ejpam-4444	55	57	,	,	PUNCT
ejpam-4444	55	58	where	where	SCONJ
ejpam-4444	55	59	tq(a	tq(a	NOUN
ejpam-4444	55	60	,	,	PUNCT
ejpam-4444	55	61	b	b	X
ejpam-4444	55	62	)	)	PUNCT
ejpam-4444	55	63	=	=	SYM
ejpam-4444	55	64	2	2	NUM
ejpam-4444	55	65	π	π	X
ejpam-4444	55	66	∫	∫	PROPN
ejpam-4444	55	67	π/2	π/2	PROPN
ejpam-4444	55	68	0	0	NUM
ejpam-4444	55	69	acos	acos	PROPN
ejpam-4444	55	70	2	2	NUM
ejpam-4444	55	71	θbsin	θbsin	NOUN
ejpam-4444	55	72	2	2	NUM
ejpam-4444	55	73	θdθ	θdθ	NOUN
ejpam-4444	55	74	is	be	AUX
ejpam-4444	55	75	the	the	DET
ejpam-4444	55	76	toader	toader	ADJ
ejpam-4444	55	77	-	-	PUNCT
ejpam-4444	55	78	qi	qi	NOUN
ejpam-4444	55	79	mean	mean	NOUN
ejpam-4444	55	80	of	of	ADP
ejpam-4444	55	81	a	a	PRON
ejpam-4444	55	82	and	and	CCONJ
ejpam-4444	55	83	b.	b.	PROPN
ejpam-4444	55	84	in	in	ADP
ejpam-4444	55	85	2018	2018	NUM
ejpam-4444	55	86	,	,	PUNCT
ejpam-4444	55	87	xu	xu	PROPN
ejpam-4444	55	88	,	,	PUNCT
ejpam-4444	55	89	chu	chu	PROPN
ejpam-4444	55	90	and	and	CCONJ
ejpam-4444	55	91	qian	qian	PROPN
ejpam-4444	56	1	[	[	X
ejpam-4444	56	2	20	20	NUM
ejpam-4444	56	3	]	]	PUNCT
ejpam-4444	56	4	found	find	VERB
ejpam-4444	56	5	the	the	DET
ejpam-4444	56	6	optimal	optimal	ADJ
ejpam-4444	56	7	parameters	parameter	NOUN
ejpam-4444	56	8	αi	αi	ADP
ejpam-4444	56	9	,	,	PUNCT
ejpam-4444	56	10	βi	βi	PROPN
ejpam-4444	56	11	∈	∈	PROPN
ejpam-4444	56	12	(	(	PUNCT
ejpam-4444	56	13	0	0	NUM
ejpam-4444	56	14	,	,	PUNCT
ejpam-4444	56	15	1	1	NUM
ejpam-4444	56	16	)	)	PUNCT
ejpam-4444	56	17	(	(	PUNCT
ejpam-4444	56	18	i	i	NOUN
ejpam-4444	56	19	=	=	NOUN
ejpam-4444	56	20	1	1	NUM
ejpam-4444	56	21	,	,	PUNCT
ejpam-4444	56	22	2	2	NUM
ejpam-4444	56	23	,	,	PUNCT
ejpam-4444	56	24	3	3	NUM
ejpam-4444	56	25	,	,	PUNCT
ejpam-4444	56	26	4	4	NUM
ejpam-4444	56	27	)	)	PUNCT
ejpam-4444	56	28	to	to	PART
ejpam-4444	56	29	ensure	ensure	VERB
ejpam-4444	56	30	that	that	SCONJ
ejpam-4444	56	31	four	four	NUM
ejpam-4444	56	32	double	double	ADJ
ejpam-4444	56	33	inequalities	inequality	NOUN
ejpam-4444	56	34	cα1(a	cα1(a	PROPN
ejpam-4444	56	35	,	,	PUNCT
ejpam-4444	56	36	b)a1−α1(a	b)a1−α1(a	PROPN
ejpam-4444	56	37	,	,	PUNCT
ejpam-4444	56	38	b	b	NOUN
ejpam-4444	56	39	)	)	PUNCT
ejpam-4444	56	40	<	<	X
ejpam-4444	56	41	rsa(a	rsa(a	PROPN
ejpam-4444	56	42	,	,	PUNCT
ejpam-4444	56	43	b	b	NOUN
ejpam-4444	56	44	)	)	PUNCT
ejpam-4444	56	45	<	<	X
ejpam-4444	56	46	cβ1(a	cβ1(a	PROPN
ejpam-4444	56	47	,	,	PUNCT
ejpam-4444	56	48	b)a1−β1(a	b)a1−β1(a	PROPN
ejpam-4444	56	49	,	,	PUNCT
ejpam-4444	56	50	b	b	NOUN
ejpam-4444	56	51	)	)	PUNCT
ejpam-4444	56	52	,	,	PUNCT
ejpam-4444	56	53	cα2(a	cα2(a	PROPN
ejpam-4444	56	54	,	,	PUNCT
ejpam-4444	56	55	b)a1−α2(a	b)a1−α2(a	PROPN
ejpam-4444	56	56	,	,	PUNCT
ejpam-4444	56	57	b	b	NOUN
ejpam-4444	56	58	)	)	PUNCT
ejpam-4444	56	59	<	<	X
ejpam-4444	56	60	ras(a	ras(a	PROPN
ejpam-4444	56	61	,	,	PUNCT
ejpam-4444	56	62	b	b	NOUN
ejpam-4444	56	63	)	)	PUNCT
ejpam-4444	56	64	<	<	X
ejpam-4444	56	65	cβ2(a	cβ2(a	PROPN
ejpam-4444	56	66	,	,	PUNCT
ejpam-4444	56	67	b)a1−β2(a	b)a1−β2(a	PROPN
ejpam-4444	56	68	,	,	PUNCT
ejpam-4444	56	69	b	b	NOUN
ejpam-4444	56	70	)	)	PUNCT
ejpam-4444	56	71	,	,	PUNCT
ejpam-4444	56	72	α3	α3	NOUN
ejpam-4444	56	73	[	[	PUNCT
ejpam-4444	56	74	1	1	NUM
ejpam-4444	56	75	3	3	NUM
ejpam-4444	56	76	c(a	c(a	PROPN
ejpam-4444	56	77	,	,	PUNCT
ejpam-4444	56	78	b	b	NOUN
ejpam-4444	56	79	)	)	PUNCT
ejpam-4444	56	80	+	+	CCONJ
ejpam-4444	56	81	2	2	NUM
ejpam-4444	56	82	3	3	NUM
ejpam-4444	56	83	a(a	a(a	PROPN
ejpam-4444	56	84	,	,	PUNCT
ejpam-4444	56	85	b	b	NOUN
ejpam-4444	56	86	)	)	PUNCT
ejpam-4444	56	87	]	]	PUNCT
ejpam-4444	57	1	+	+	CCONJ
ejpam-4444	57	2	(	(	PUNCT
ejpam-4444	57	3	1−	1−	NUM
ejpam-4444	57	4	α3)c	α3)c	NOUN
ejpam-4444	57	5	1/3(a	1/3(a	PROPN
ejpam-4444	57	6	,	,	PUNCT
ejpam-4444	57	7	b)a2/3(a	b)a2/3(a	PROPN
ejpam-4444	57	8	,	,	PUNCT
ejpam-4444	57	9	b	b	NOUN
ejpam-4444	57	10	)	)	PUNCT
ejpam-4444	57	11	<	<	X
ejpam-4444	57	12	rsa(a	rsa(a	PROPN
ejpam-4444	57	13	,	,	PUNCT
ejpam-4444	57	14	b	b	NOUN
ejpam-4444	57	15	)	)	PUNCT
ejpam-4444	57	16	<	<	X
ejpam-4444	57	17	β3	β3	PROPN
ejpam-4444	57	18	[	[	PUNCT
ejpam-4444	57	19	1	1	NUM
ejpam-4444	57	20	3	3	NUM
ejpam-4444	57	21	c(a	c(a	PROPN
ejpam-4444	57	22	,	,	PUNCT
ejpam-4444	57	23	b	b	NOUN
ejpam-4444	57	24	)	)	PUNCT
ejpam-4444	57	25	+	+	CCONJ
ejpam-4444	57	26	2	2	NUM
ejpam-4444	57	27	3	3	NUM
ejpam-4444	57	28	a(a	a(a	PROPN
ejpam-4444	57	29	,	,	PUNCT
ejpam-4444	57	30	b	b	NOUN
ejpam-4444	57	31	)	)	PUNCT
ejpam-4444	57	32	]	]	PUNCT
ejpam-4444	58	1	+	+	CCONJ
ejpam-4444	58	2	(	(	PUNCT
ejpam-4444	58	3	1−	1−	NUM
ejpam-4444	58	4	β3)c	β3)c	NOUN
ejpam-4444	58	5	1/3(a	1/3(a	NUM
ejpam-4444	58	6	,	,	PUNCT
ejpam-4444	58	7	b)a2/3(a	b)a2/3(a	PROPN
ejpam-4444	58	8	,	,	PUNCT
ejpam-4444	58	9	b	b	NOUN
ejpam-4444	58	10	)	)	PUNCT
ejpam-4444	58	11	,	,	PUNCT
ejpam-4444	58	12	α4	α4	NOUN
ejpam-4444	58	13	[	[	PUNCT
ejpam-4444	58	14	1	1	NUM
ejpam-4444	58	15	6	6	NUM
ejpam-4444	58	16	c(a	c(a	PROPN
ejpam-4444	58	17	,	,	PUNCT
ejpam-4444	58	18	b	b	NOUN
ejpam-4444	58	19	)	)	PUNCT
ejpam-4444	58	20	+	+	CCONJ
ejpam-4444	58	21	5	5	NUM
ejpam-4444	58	22	6	6	NUM
ejpam-4444	58	23	a(a	a(a	PROPN
ejpam-4444	58	24	,	,	PUNCT
ejpam-4444	58	25	b	b	NOUN
ejpam-4444	58	26	)	)	PUNCT
ejpam-4444	58	27	]	]	PUNCT
ejpam-4444	59	1	+	+	CCONJ
ejpam-4444	59	2	(	(	PUNCT
ejpam-4444	59	3	1−	1−	NUM
ejpam-4444	59	4	α4)c	α4)c	NOUN
ejpam-4444	59	5	1/6(a	1/6(a	NUM
ejpam-4444	59	6	,	,	PUNCT
ejpam-4444	59	7	b)a5/6(a	b)a5/6(a	NOUN
ejpam-4444	59	8	,	,	PUNCT
ejpam-4444	59	9	b	b	NOUN
ejpam-4444	59	10	)	)	PUNCT
ejpam-4444	59	11	<	<	X
ejpam-4444	59	12	ras(a	ras(a	PROPN
ejpam-4444	59	13	,	,	PUNCT
ejpam-4444	59	14	b	b	NOUN
ejpam-4444	59	15	)	)	PUNCT
ejpam-4444	59	16	<	<	X
ejpam-4444	59	17	β4	β4	PROPN
ejpam-4444	59	18	[	[	PUNCT
ejpam-4444	59	19	1	1	NUM
ejpam-4444	59	20	6	6	NUM
ejpam-4444	59	21	c(a	c(a	PROPN
ejpam-4444	59	22	,	,	PUNCT
ejpam-4444	59	23	b	b	NOUN
ejpam-4444	59	24	)	)	PUNCT
ejpam-4444	59	25	+	+	CCONJ
ejpam-4444	59	26	5	5	NUM
ejpam-4444	59	27	6	6	NUM
ejpam-4444	59	28	a(a	a(a	PROPN
ejpam-4444	59	29	,	,	PUNCT
ejpam-4444	59	30	b	b	NOUN
ejpam-4444	59	31	)	)	PUNCT
ejpam-4444	59	32	]	]	PUNCT
ejpam-4444	60	1	+	+	CCONJ
ejpam-4444	60	2	(	(	PUNCT
ejpam-4444	60	3	1−	1−	NUM
ejpam-4444	60	4	β4)c	β4)c	NOUN
ejpam-4444	60	5	1/6(a	1/6(a	NUM
ejpam-4444	60	6	,	,	PUNCT
ejpam-4444	60	7	b)a5/6(a	b)a5/6(a	NOUN
ejpam-4444	60	8	,	,	PUNCT
ejpam-4444	60	9	b	b	NOUN
ejpam-4444	60	10	)	)	PUNCT
ejpam-4444	60	11	hold	hold	VERB
ejpam-4444	60	12	for	for	ADP
ejpam-4444	60	13	all	all	DET
ejpam-4444	60	14	distinct	distinct	ADJ
ejpam-4444	60	15	positive	positive	ADJ
ejpam-4444	60	16	numbers	number	NOUN
ejpam-4444	60	17	a	a	PRON
ejpam-4444	60	18	,	,	PUNCT
ejpam-4444	60	19	b	b	PROPN
ejpam-4444	60	20	and	and	CCONJ
ejpam-4444	60	21	rsa(a	rsa(a	PROPN
ejpam-4444	60	22	,	,	PUNCT
ejpam-4444	60	23	b	b	NOUN
ejpam-4444	60	24	)	)	PUNCT
ejpam-4444	60	25	=	=	SYM
ejpam-4444	60	26	1	1	NUM
ejpam-4444	60	27	2	2	NUM
ejpam-4444	60	28	a(a	a(a	PROPN
ejpam-4444	60	29	,	,	PUNCT
ejpam-4444	60	30	b	b	X
ejpam-4444	60	31	)	)	PUNCT
ejpam-4444	61	1	[	[	X
ejpam-4444	61	2	√	√	ADJ
ejpam-4444	61	3	1	1	NUM
ejpam-4444	61	4	+	+	CCONJ
ejpam-4444	61	5	u2	u2	PROPN
ejpam-4444	61	6	+	+	CCONJ
ejpam-4444	61	7	sinh−1(u	sinh−1(u	NOUN
ejpam-4444	61	8	)	)	PUNCT
ejpam-4444	61	9	u	u	NOUN
ejpam-4444	61	10	]	]	PUNCT
ejpam-4444	61	11	,	,	PUNCT
ejpam-4444	61	12	ras(a	ras(a	PROPN
ejpam-4444	61	13	,	,	PUNCT
ejpam-4444	61	14	b	b	NOUN
ejpam-4444	61	15	)	)	PUNCT
ejpam-4444	61	16	=	=	SYM
ejpam-4444	61	17	1	1	NUM
ejpam-4444	61	18	2	2	NUM
ejpam-4444	61	19	a(a	a(a	PROPN
ejpam-4444	61	20	,	,	PUNCT
ejpam-4444	61	21	b	b	X
ejpam-4444	61	22	)	)	PUNCT
ejpam-4444	61	23	[	[	PUNCT
ejpam-4444	61	24	1	1	NUM
ejpam-4444	61	25	+	+	CCONJ
ejpam-4444	61	26	(	(	PUNCT
ejpam-4444	61	27	1	1	NUM
ejpam-4444	61	28	+	+	CCONJ
ejpam-4444	61	29	u2	u2	NOUN
ejpam-4444	61	30	)	)	PUNCT
ejpam-4444	61	31	tan−1(u	tan−1(u	NOUN
ejpam-4444	61	32	)	)	PUNCT
ejpam-4444	61	33	u	u	NOUN
ejpam-4444	61	34	]	]	PUNCT
ejpam-4444	61	35	,	,	PUNCT
ejpam-4444	61	36	where	where	SCONJ
ejpam-4444	61	37	a	a	DET
ejpam-4444	61	38	>	>	X
ejpam-4444	61	39	b	b	X
ejpam-4444	61	40	>	>	X
ejpam-4444	61	41	0	0	PUNCT
ejpam-4444	61	42	and	and	CCONJ
ejpam-4444	61	43	u	u	NOUN
ejpam-4444	61	44	=	=	PUNCT
ejpam-4444	61	45	(	(	PUNCT
ejpam-4444	61	46	a−	a−	PROPN
ejpam-4444	61	47	b)/(a+	b)/(a+	NOUN
ejpam-4444	61	48	b	b	NOUN
ejpam-4444	61	49	)	)	PUNCT
ejpam-4444	61	50	.	.	PUNCT
ejpam-4444	62	1	in	in	ADP
ejpam-4444	62	2	2019	2019	NUM
ejpam-4444	62	3	,	,	PUNCT
ejpam-4444	62	4	qian	qian	PROPN
ejpam-4444	62	5	,	,	PUNCT
ejpam-4444	62	6	he	he	PRON
ejpam-4444	62	7	,	,	PUNCT
ejpam-4444	62	8	zhang	zhang	PROPN
ejpam-4444	62	9	and	and	CCONJ
ejpam-4444	62	10	chu	chu	PROPN
ejpam-4444	63	1	[	[	X
ejpam-4444	63	2	15	15	NUM
ejpam-4444	63	3	]	]	PUNCT
ejpam-4444	63	4	found	find	VERB
ejpam-4444	63	5	the	the	DET
ejpam-4444	63	6	best	good	ADJ
ejpam-4444	63	7	values	value	NOUN
ejpam-4444	63	8	λ1	λ1	X
ejpam-4444	63	9	=	=	SYM
ejpam-4444	63	10	λ1(ν	λ1(ν	PROPN
ejpam-4444	63	11	)	)	PUNCT
ejpam-4444	63	12	,	,	PUNCT
ejpam-4444	63	13	µ1	µ1	PROPN
ejpam-4444	63	14	=	=	SYM
ejpam-4444	63	15	µ1(ν	µ1(ν	PROPN
ejpam-4444	63	16	)	)	PUNCT
ejpam-4444	63	17	,	,	PUNCT
ejpam-4444	63	18	λ2	λ2	NOUN
ejpam-4444	63	19	=	=	SYM
ejpam-4444	63	20	λ2(ν	λ2(ν	NUM
ejpam-4444	63	21	)	)	PUNCT
ejpam-4444	63	22	and	and	CCONJ
ejpam-4444	63	23	µ2	µ2	PROPN
ejpam-4444	63	24	=	=	SYM
ejpam-4444	63	25	µ2(ν	µ2(ν	NUM
ejpam-4444	63	26	)	)	PUNCT
ejpam-4444	63	27	on	on	ADP
ejpam-4444	63	28	the	the	DET
ejpam-4444	63	29	interval	interval	NOUN
ejpam-4444	63	30	[	[	X
ejpam-4444	63	31	1/2	1/2	NUM
ejpam-4444	63	32	,	,	PUNCT
ejpam-4444	63	33	1	1	NUM
ejpam-4444	63	34	]	]	PUNCT
ejpam-4444	63	35	such	such	ADJ
ejpam-4444	63	36	that	that	SCONJ
ejpam-4444	63	37	the	the	DET
ejpam-4444	63	38	double	double	ADJ
ejpam-4444	63	39	inequalities	inequality	NOUN
ejpam-4444	63	40	wλ1,ν(a	wλ1,ν(a	PROPN
ejpam-4444	63	41	,	,	PUNCT
ejpam-4444	63	42	b	b	X
ejpam-4444	63	43	)	)	PUNCT
ejpam-4444	63	44	<	<	X
ejpam-4444	63	45	rsa(a	rsa(a	PROPN
ejpam-4444	63	46	,	,	PUNCT
ejpam-4444	63	47	b	b	NOUN
ejpam-4444	63	48	)	)	PUNCT
ejpam-4444	63	49	<	<	X
ejpam-4444	63	50	wµ1,ν(a	wµ1,ν(a	PROPN
ejpam-4444	63	51	,	,	PUNCT
ejpam-4444	63	52	b	b	NOUN
ejpam-4444	63	53	)	)	PUNCT
ejpam-4444	63	54	,	,	PUNCT
ejpam-4444	63	55	wλ2,ν(a	wλ2,ν(a	NOUN
ejpam-4444	63	56	,	,	PUNCT
ejpam-4444	63	57	b	b	NOUN
ejpam-4444	63	58	)	)	PUNCT
ejpam-4444	63	59	<	<	X
ejpam-4444	63	60	ras(a	ras(a	PROPN
ejpam-4444	63	61	,	,	PUNCT
ejpam-4444	63	62	b	b	NOUN
ejpam-4444	63	63	)	)	PUNCT
ejpam-4444	63	64	<	<	X
ejpam-4444	63	65	wµ2,ν(a	wµ2,ν(a	PROPN
ejpam-4444	63	66	,	,	PUNCT
ejpam-4444	63	67	b	b	NOUN
ejpam-4444	63	68	)	)	PUNCT
ejpam-4444	63	69	hold	hold	VERB
ejpam-4444	63	70	for	for	ADP
ejpam-4444	63	71	all	all	DET
ejpam-4444	63	72	distinct	distinct	ADJ
ejpam-4444	63	73	positive	positive	ADJ
ejpam-4444	63	74	numbers	number	NOUN
ejpam-4444	63	75	a	a	DET
ejpam-4444	63	76	,	,	PUNCT
ejpam-4444	63	77	b	b	NOUN
ejpam-4444	63	78	and	and	CCONJ
ejpam-4444	63	79	ν	ν	PROPN
ejpam-4444	63	80	≥	≥	NOUN
ejpam-4444	63	81	1/2	1/2	NUM
ejpam-4444	63	82	where	where	SCONJ
ejpam-4444	63	83	wλ	wλ	NOUN
ejpam-4444	63	84	,	,	PUNCT
ejpam-4444	63	85	ν(a	ν(a	PROPN
ejpam-4444	63	86	,	,	PUNCT
ejpam-4444	63	87	b	b	NOUN
ejpam-4444	63	88	)	)	PUNCT
ejpam-4444	64	1	=	=	VERB
ejpam-4444	64	2	cν	cν	NOUN
ejpam-4444	65	1	[	[	X
ejpam-4444	65	2	λa+	λa+	NOUN
ejpam-4444	65	3	(	(	PUNCT
ejpam-4444	65	4	1−	1−	NUM
ejpam-4444	65	5	λ)b	λ)b	NOUN
ejpam-4444	65	6	,	,	PUNCT
ejpam-4444	65	7	λb+	λb+	NOUN
ejpam-4444	65	8	(	(	PUNCT
ejpam-4444	65	9	1−	1−	NUM
ejpam-4444	65	10	λ)a]a1−ν(a	λ)a]a1−ν(a	PROPN
ejpam-4444	65	11	,	,	PUNCT
ejpam-4444	65	12	b	b	NOUN
ejpam-4444	65	13	)	)	PUNCT
ejpam-4444	65	14	.	.	PUNCT
ejpam-4444	66	1	in	in	ADP
ejpam-4444	66	2	2022	2022	NUM
ejpam-4444	66	3	,	,	PUNCT
ejpam-4444	66	4	li	li	PROPN
ejpam-4444	66	5	,	,	PUNCT
ejpam-4444	66	6	miao	miao	NOUN
ejpam-4444	66	7	and	and	CCONJ
ejpam-4444	66	8	guo	guo	PROPN
ejpam-4444	66	9	[	[	X
ejpam-4444	66	10	7	7	NUM
ejpam-4444	66	11	]	]	PUNCT
ejpam-4444	66	12	discovered	discover	VERB
ejpam-4444	66	13	the	the	DET
ejpam-4444	66	14	largest	large	ADJ
ejpam-4444	66	15	values	value	NOUN
ejpam-4444	66	16	αi	αi	VERB
ejpam-4444	66	17	and	and	CCONJ
ejpam-4444	66	18	the	the	DET
ejpam-4444	66	19	smallest	small	ADJ
ejpam-4444	66	20	values	value	NOUN
ejpam-4444	67	1	βi	βi	PRON
ejpam-4444	68	1	(	(	PUNCT
ejpam-4444	68	2	i	i	NOUN
ejpam-4444	68	3	=	=	NOUN
ejpam-4444	68	4	1	1	NUM
ejpam-4444	68	5	,	,	PUNCT
ejpam-4444	68	6	2	2	NUM
ejpam-4444	68	7	,	,	PUNCT
ejpam-4444	68	8	3	3	NUM
ejpam-4444	68	9	)	)	PUNCT
ejpam-4444	68	10	such	such	ADJ
ejpam-4444	68	11	that	that	SCONJ
ejpam-4444	68	12	the	the	DET
ejpam-4444	68	13	inequalities	inequality	NOUN
ejpam-4444	68	14	α1	α1	PROPN
ejpam-4444	68	15	c(a	c(a	PROPN
ejpam-4444	68	16	,	,	PUNCT
ejpam-4444	68	17	b	b	NOUN
ejpam-4444	68	18	)	)	PUNCT
ejpam-4444	68	19	+	+	NUM
ejpam-4444	68	20	1−	1−	NUM
ejpam-4444	68	21	α1	α1	PROPN
ejpam-4444	68	22	a(a	a(a	PROPN
ejpam-4444	68	23	,	,	PUNCT
ejpam-4444	68	24	b	b	X
ejpam-4444	68	25	)	)	PUNCT
ejpam-4444	68	26	<	<	X
ejpam-4444	68	27	1	1	NUM
ejpam-4444	68	28	m(a	m(a	PROPN
ejpam-4444	68	29	,	,	PUNCT
ejpam-4444	68	30	b	b	NOUN
ejpam-4444	68	31	)	)	PUNCT
ejpam-4444	68	32	<	<	X
ejpam-4444	68	33	β1	β1	PROPN
ejpam-4444	68	34	c(a	c(a	PROPN
ejpam-4444	68	35	,	,	PUNCT
ejpam-4444	68	36	b	b	NOUN
ejpam-4444	68	37	)	)	PUNCT
ejpam-4444	68	38	+	+	SYM
ejpam-4444	68	39	1−	1−	NUM
ejpam-4444	68	40	β1	β1	PROPN
ejpam-4444	68	41	a(a	a(a	PROPN
ejpam-4444	68	42	,	,	PUNCT
ejpam-4444	68	43	b	b	NOUN
ejpam-4444	68	44	)	)	PUNCT
ejpam-4444	68	45	,	,	PUNCT
ejpam-4444	68	46	α2	α2	PROPN
ejpam-4444	68	47	c2(a	c2(a	PROPN
ejpam-4444	68	48	,	,	PUNCT
ejpam-4444	68	49	b	b	NOUN
ejpam-4444	68	50	)	)	PUNCT
ejpam-4444	68	51	+	+	CCONJ
ejpam-4444	68	52	1−	1−	NUM
ejpam-4444	68	53	α2	α2	NOUN
ejpam-4444	68	54	a2(a	a2(a	PROPN
ejpam-4444	68	55	,	,	PUNCT
ejpam-4444	68	56	b	b	NOUN
ejpam-4444	68	57	)	)	PUNCT
ejpam-4444	68	58	<	<	X
ejpam-4444	68	59	1	1	NUM
ejpam-4444	68	60	m2(a	m2(a	NOUN
ejpam-4444	68	61	,	,	PUNCT
ejpam-4444	68	62	b	b	NOUN
ejpam-4444	68	63	)	)	PUNCT
ejpam-4444	68	64	<	<	X
ejpam-4444	69	1	β2	β2	PROPN
ejpam-4444	69	2	c2(a	c2(a	PROPN
ejpam-4444	69	3	,	,	PUNCT
ejpam-4444	69	4	b	b	NOUN
ejpam-4444	69	5	)	)	PUNCT
ejpam-4444	69	6	+	+	NUM
ejpam-4444	69	7	1−	1−	NUM
ejpam-4444	69	8	β2	β2	NOUN
ejpam-4444	69	9	a2(a	a2(a	PROPN
ejpam-4444	69	10	,	,	PUNCT
ejpam-4444	69	11	b	b	NOUN
ejpam-4444	69	12	)	)	PUNCT
ejpam-4444	69	13	,	,	PUNCT
ejpam-4444	69	14	a.	a.	NOUN
ejpam-4444	69	15	sonubon	sonubon	PROPN
ejpam-4444	69	16	,	,	PUNCT
ejpam-4444	69	17	s.	s.	PROPN
ejpam-4444	69	18	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	69	19	,	,	PUNCT
ejpam-4444	69	20	k.	k.	PROPN
ejpam-4444	69	21	nonlaopon	nonlaopon	ADV
ejpam-4444	69	22	/	/	SYM
ejpam-4444	69	23	eur	eur	PROPN
ejpam-4444	69	24	.	.	PUNCT
ejpam-4444	70	1	j.	j.	PROPN
ejpam-4444	70	2	pure	pure	PROPN
ejpam-4444	70	3	appl	appl	PROPN
ejpam-4444	70	4	.	.	PROPN
ejpam-4444	70	5	math	math	PROPN
ejpam-4444	70	6	,	,	PUNCT
ejpam-4444	70	7	15	15	NUM
ejpam-4444	70	8	(	(	PUNCT
ejpam-4444	70	9	3	3	NUM
ejpam-4444	70	10	)	)	PUNCT
ejpam-4444	70	11	(	(	PUNCT
ejpam-4444	70	12	2022	2022	NUM
ejpam-4444	70	13	)	)	PUNCT
ejpam-4444	70	14	,	,	PUNCT
ejpam-4444	70	15	1120	1120	NUM
ejpam-4444	70	16	-	-	SYM
ejpam-4444	70	17	1143	1143	NUM
ejpam-4444	70	18	1124	1124	NUM
ejpam-4444	70	19	and	and	CCONJ
ejpam-4444	70	20	α3c	α3c	NUM
ejpam-4444	70	21	2(a	2(a	NUM
ejpam-4444	70	22	,	,	PUNCT
ejpam-4444	70	23	b	b	NOUN
ejpam-4444	70	24	)	)	PUNCT
ejpam-4444	71	1	+	+	CCONJ
ejpam-4444	71	2	(	(	PUNCT
ejpam-4444	71	3	1−	1−	NUM
ejpam-4444	71	4	α3)a	α3)a	NOUN
ejpam-4444	71	5	2(a	2(a	NUM
ejpam-4444	71	6	,	,	PUNCT
ejpam-4444	71	7	b	b	NOUN
ejpam-4444	71	8	)	)	PUNCT
ejpam-4444	71	9	<	<	X
ejpam-4444	71	10	m2(a	m2(a	PROPN
ejpam-4444	71	11	,	,	PUNCT
ejpam-4444	71	12	b	b	NOUN
ejpam-4444	71	13	)	)	PUNCT
ejpam-4444	71	14	<	<	X
ejpam-4444	71	15	β3c	β3c	NOUN
ejpam-4444	71	16	2(a	2(a	NUM
ejpam-4444	71	17	,	,	PUNCT
ejpam-4444	71	18	b	b	NOUN
ejpam-4444	71	19	)	)	PUNCT
ejpam-4444	71	20	+	+	CCONJ
ejpam-4444	71	21	(	(	PUNCT
ejpam-4444	71	22	1−	1−	NUM
ejpam-4444	71	23	β3)a	β3)a	PROPN
ejpam-4444	71	24	2(a	2(a	NUM
ejpam-4444	71	25	,	,	PUNCT
ejpam-4444	71	26	b	b	X
ejpam-4444	71	27	)	)	PUNCT
ejpam-4444	71	28	hold	hold	VERB
ejpam-4444	71	29	for	for	ADP
ejpam-4444	71	30	all	all	DET
ejpam-4444	71	31	positive	positive	ADJ
ejpam-4444	71	32	real	real	ADJ
ejpam-4444	71	33	numbers	number	NOUN
ejpam-4444	71	34	a	a	PRON
ejpam-4444	71	35	and	and	CCONJ
ejpam-4444	71	36	b	b	NOUN
ejpam-4444	71	37	with	with	ADP
ejpam-4444	71	38	a	a	DET
ejpam-4444	71	39	̸=	̸=	PROPN
ejpam-4444	71	40	b.	b.	NOUN
ejpam-4444	71	41	the	the	DET
ejpam-4444	71	42	purpose	purpose	NOUN
ejpam-4444	71	43	of	of	ADP
ejpam-4444	71	44	this	this	DET
ejpam-4444	71	45	paper	paper	NOUN
ejpam-4444	71	46	is	be	AUX
ejpam-4444	71	47	to	to	PART
ejpam-4444	71	48	present	present	VERB
ejpam-4444	71	49	the	the	DET
ejpam-4444	71	50	inequalities	inequality	NOUN
ejpam-4444	71	51	with	with	ADP
ejpam-4444	71	52	optimal	optimal	ADJ
ejpam-4444	71	53	upper	upper	ADJ
ejpam-4444	71	54	bound	bind	VERB
ejpam-4444	71	55	and	and	CCONJ
ejpam-4444	71	56	optimal	optimal	ADJ
ejpam-4444	71	57	lower	lower	ADV
ejpam-4444	71	58	bound	bind	VERB
ejpam-4444	71	59	of	of	ADP
ejpam-4444	71	60	weighted	weight	VERB
ejpam-4444	71	61	arithmetic	arithmetic	ADJ
ejpam-4444	71	62	means	mean	NOUN
ejpam-4444	71	63	of	of	ADP
ejpam-4444	71	64	contra	contra	PROPN
ejpam-4444	71	65	-	-	ADJ
ejpam-4444	71	66	harmonic	harmonic	ADJ
ejpam-4444	71	67	and	and	CCONJ
ejpam-4444	71	68	harmonic	harmonic	ADJ
ejpam-4444	71	69	means	mean	NOUN
ejpam-4444	71	70	by	by	ADP
ejpam-4444	71	71	generalized	generalize	VERB
ejpam-4444	71	72	logarithmic	logarithmic	ADJ
ejpam-4444	71	73	means	mean	NOUN
ejpam-4444	71	74	lp	lp	ADV
ejpam-4444	71	75	when	when	SCONJ
ejpam-4444	71	76	p	p	NOUN
ejpam-4444	71	77	is	be	AUX
ejpam-4444	71	78	of	of	ADP
ejpam-4444	71	79	the	the	DET
ejpam-4444	71	80	linear	linear	ADJ
ejpam-4444	71	81	form	form	NOUN
ejpam-4444	71	82	p	p	NOUN
ejpam-4444	71	83	=	=	NOUN
ejpam-4444	71	84	2(1−	2(1−	NUM
ejpam-4444	71	85	c)α+	c)α+	NOUN
ejpam-4444	71	86	c	c	NOUN
ejpam-4444	72	1	and	and	CCONJ
ejpam-4444	72	2	p	p	NOUN
ejpam-4444	72	3	is	be	AUX
ejpam-4444	72	4	of	of	ADP
ejpam-4444	72	5	the	the	DET
ejpam-4444	72	6	reciprocal	reciprocal	NOUN
ejpam-4444	72	7	of	of	ADP
ejpam-4444	72	8	linear	linear	ADJ
ejpam-4444	72	9	form	form	NOUN
ejpam-4444	72	10	p	p	NOUN
ejpam-4444	72	11	=	=	SYM
ejpam-4444	72	12	1/[2(1	1/[2(1	NUM
ejpam-4444	72	13	−	−	NOUN
ejpam-4444	72	14	c)α	c)α	NOUN
ejpam-4444	72	15	+	+	CCONJ
ejpam-4444	73	1	c	c	X
ejpam-4444	73	2	]	]	PUNCT
ejpam-4444	73	3	respectively	respectively	ADV
ejpam-4444	73	4	and	and	CCONJ
ejpam-4444	73	5	c	c	NOUN
ejpam-4444	73	6	is	be	AUX
ejpam-4444	73	7	the	the	DET
ejpam-4444	73	8	value	value	NOUN
ejpam-4444	73	9	to	to	PART
ejpam-4444	73	10	be	be	AUX
ejpam-4444	73	11	determined	determine	VERB
ejpam-4444	73	12	in	in	ADP
ejpam-4444	73	13	both	both	DET
ejpam-4444	73	14	cases	case	NOUN
ejpam-4444	73	15	.	.	PUNCT
ejpam-4444	74	1	precisely	precisely	ADV
ejpam-4444	74	2	,	,	PUNCT
ejpam-4444	74	3	we	we	PRON
ejpam-4444	74	4	prove	prove	VERB
ejpam-4444	74	5	that	that	SCONJ
ejpam-4444	74	6	1	1	NUM
ejpam-4444	74	7	)	)	PUNCT
ejpam-4444	74	8	l4α−1	l4α−1	NOUN
ejpam-4444	74	9	=	=	SYM
ejpam-4444	74	10	minc	minc	PROPN
ejpam-4444	74	11	{	{	PUNCT
ejpam-4444	74	12	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	74	13	|	|	ADV
ejpam-4444	74	14	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	74	15	>	>	X
ejpam-4444	74	16	αc	αc	PROPN
ejpam-4444	75	1	+	+	CCONJ
ejpam-4444	75	2	(	(	PUNCT
ejpam-4444	75	3	1−	1−	NUM
ejpam-4444	75	4	α)h	α)h	NOUN
ejpam-4444	75	5	}	}	PUNCT
ejpam-4444	75	6	for	for	ADP
ejpam-4444	75	7	α	α	PRON
ejpam-4444	75	8	∈	∈	PROPN
ejpam-4444	75	9	(	(	PUNCT
ejpam-4444	75	10	0	0	NUM
ejpam-4444	75	11	,	,	PUNCT
ejpam-4444	75	12	1/2	1/2	NUM
ejpam-4444	75	13	)	)	PUNCT
ejpam-4444	75	14	,	,	PUNCT
ejpam-4444	75	15	2	2	X
ejpam-4444	75	16	)	)	PUNCT
ejpam-4444	75	17	l	l	NOUN
ejpam-4444	75	18	7	7	NUM
ejpam-4444	75	19	13−12α	13−12α	NOUN
ejpam-4444	75	20	=	=	SYM
ejpam-4444	75	21	maxc	maxc	NOUN
ejpam-4444	75	22	{	{	PUNCT
ejpam-4444	75	23	l	l	PROPN
ejpam-4444	75	24	1	1	NUM
ejpam-4444	75	25	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	75	26	∣∣∣l	∣∣∣l	NOUN
ejpam-4444	75	27	1	1	NUM
ejpam-4444	75	28	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	75	29	<	<	X
ejpam-4444	75	30	αc	αc	NOUN
ejpam-4444	76	1	+	+	CCONJ
ejpam-4444	77	1	(	(	PUNCT
ejpam-4444	77	2	1−	1−	NUM
ejpam-4444	77	3	α)h	α)h	NOUN
ejpam-4444	77	4	}	}	PUNCT
ejpam-4444	77	5	for	for	ADP
ejpam-4444	77	6	α	α	PRON
ejpam-4444	77	7	∈	∈	PROPN
ejpam-4444	77	8	(	(	PUNCT
ejpam-4444	77	9	1/2	1/2	NUM
ejpam-4444	77	10	,	,	PUNCT
ejpam-4444	77	11	1	1	NUM
ejpam-4444	77	12	)	)	PUNCT
ejpam-4444	77	13	.	.	PUNCT
ejpam-4444	78	1	details	detail	NOUN
ejpam-4444	78	2	of	of	ADP
ejpam-4444	78	3	the	the	DET
ejpam-4444	78	4	results	result	NOUN
ejpam-4444	78	5	are	be	AUX
ejpam-4444	78	6	theorem	theorem	VERB
ejpam-4444	78	7	1	1	NUM
ejpam-4444	78	8	and	and	CCONJ
ejpam-4444	78	9	theorem	theorem	VERB
ejpam-4444	78	10	2	2	NUM
ejpam-4444	78	11	in	in	ADP
ejpam-4444	78	12	section	section	NOUN
ejpam-4444	78	13	3	3	NUM
ejpam-4444	78	14	.	.	PUNCT
ejpam-4444	79	1	some	some	DET
ejpam-4444	79	2	complicated	complicated	ADJ
ejpam-4444	79	3	computations	computation	NOUN
ejpam-4444	79	4	are	be	AUX
ejpam-4444	79	5	carried	carry	VERB
ejpam-4444	79	6	out	out	ADP
ejpam-4444	79	7	using	use	VERB
ejpam-4444	79	8	matlabr2021a	matlabr2021a	ADJ
ejpam-4444	79	9	software	software	NOUN
ejpam-4444	79	10	computer	computer	NOUN
ejpam-4444	79	11	system	system	NOUN
ejpam-4444	79	12	.	.	PUNCT
ejpam-4444	80	1	2	2	X
ejpam-4444	80	2	.	.	X
ejpam-4444	80	3	preliminaries	preliminary	NOUN
ejpam-4444	80	4	in	in	ADP
ejpam-4444	80	5	this	this	DET
ejpam-4444	80	6	section	section	NOUN
ejpam-4444	80	7	,	,	PUNCT
ejpam-4444	80	8	we	we	PRON
ejpam-4444	80	9	present	present	VERB
ejpam-4444	80	10	four	four	NUM
ejpam-4444	80	11	lemmas	lemma	NOUN
ejpam-4444	80	12	necessary	necessary	ADJ
ejpam-4444	80	13	in	in	ADP
ejpam-4444	80	14	the	the	DET
ejpam-4444	80	15	proof	proof	NOUN
ejpam-4444	80	16	of	of	ADP
ejpam-4444	80	17	our	our	PRON
ejpam-4444	80	18	main	main	ADJ
ejpam-4444	80	19	results	result	NOUN
ejpam-4444	80	20	in	in	ADP
ejpam-4444	80	21	section	section	NOUN
ejpam-4444	80	22	3	3	NUM
ejpam-4444	80	23	.	.	PUNCT
ejpam-4444	81	1	more	more	ADV
ejpam-4444	81	2	specifically	specifically	ADV
ejpam-4444	81	3	lemma	lemma	PROPN
ejpam-4444	81	4	1	1	NUM
ejpam-4444	81	5	is	be	AUX
ejpam-4444	81	6	used	use	VERB
ejpam-4444	81	7	in	in	ADP
ejpam-4444	81	8	all	all	DET
ejpam-4444	81	9	theorems	theorem	NOUN
ejpam-4444	81	10	whereas	whereas	SCONJ
ejpam-4444	81	11	lemma	lemma	PROPN
ejpam-4444	81	12	2	2	NUM
ejpam-4444	81	13	to	to	PART
ejpam-4444	81	14	lemma	lemma	PROPN
ejpam-4444	81	15	4	4	NUM
ejpam-4444	81	16	are	be	AUX
ejpam-4444	81	17	used	use	VERB
ejpam-4444	81	18	only	only	ADV
ejpam-4444	81	19	in	in	ADP
ejpam-4444	81	20	theorem	theorem	NOUN
ejpam-4444	81	21	1	1	NUM
ejpam-4444	81	22	.	.	PUNCT
ejpam-4444	82	1	lemma	lemma	PROPN
ejpam-4444	82	2	1	1	NUM
ejpam-4444	82	3	.	.	PUNCT
ejpam-4444	83	1	if	if	SCONJ
ejpam-4444	83	2	p	p	X
ejpam-4444	83	3	∈	∈	PROPN
ejpam-4444	83	4	r	r	PROPN
ejpam-4444	83	5	,	,	PUNCT
ejpam-4444	83	6	t	t	X
ejpam-4444	83	7	>	>	X
ejpam-4444	83	8	1	1	NUM
ejpam-4444	83	9	and	and	CCONJ
ejpam-4444	83	10	f	f	PROPN
ejpam-4444	83	11	(	(	PUNCT
ejpam-4444	83	12	t	t	PROPN
ejpam-4444	83	13	)	)	PUNCT
ejpam-4444	83	14	:	:	PUNCT
ejpam-4444	84	1	=	=	SYM
ejpam-4444	84	2	1	1	NUM
ejpam-4444	84	3	p	p	X
ejpam-4444	84	4	[	[	PUNCT
ejpam-4444	84	5	ln	ln	ADJ
ejpam-4444	84	6	(	(	PUNCT
ejpam-4444	84	7	tp+1	tp+1	NOUN
ejpam-4444	84	8	−	−	NOUN
ejpam-4444	84	9	1	1	NUM
ejpam-4444	84	10	)	)	PUNCT
ejpam-4444	84	11	−	−	PROPN
ejpam-4444	85	1	ln(p+	ln(p+	PROPN
ejpam-4444	85	2	1)−	1)−	PROPN
ejpam-4444	85	3	ln(t−	ln(t−	PROPN
ejpam-4444	85	4	1	1	NUM
ejpam-4444	85	5	)	)	PUNCT
ejpam-4444	85	6	]	]	PUNCT
ejpam-4444	86	1	−	−	PROPN
ejpam-4444	86	2	ln	ln	ADV
ejpam-4444	86	3	[	[	PUNCT
ejpam-4444	86	4	α(t2	α(t2	ADJ
ejpam-4444	86	5	+	+	NOUN
ejpam-4444	86	6	1	1	NUM
ejpam-4444	86	7	)	)	PUNCT
ejpam-4444	86	8	+	+	CCONJ
ejpam-4444	86	9	2(1−	2(1−	NUM
ejpam-4444	86	10	α)t	α)t	NOUN
ejpam-4444	86	11	]	]	PUNCT
ejpam-4444	87	1	+	+	CCONJ
ejpam-4444	87	2	ln(t+	ln(t+	PROPN
ejpam-4444	87	3	1	1	NUM
ejpam-4444	87	4	)	)	PUNCT
ejpam-4444	87	5	,	,	PUNCT
ejpam-4444	87	6	(	(	PUNCT
ejpam-4444	87	7	1	1	X
ejpam-4444	87	8	)	)	PUNCT
ejpam-4444	87	9	then	then	ADV
ejpam-4444	87	10	f	f	PROPN
ejpam-4444	87	11	′(t	′(t	PROPN
ejpam-4444	87	12	)	)	PUNCT
ejpam-4444	87	13	=	=	SYM
ejpam-4444	87	14	g(t	g(t	PROPN
ejpam-4444	87	15	)	)	PUNCT
ejpam-4444	88	1	p	p	X
ejpam-4444	88	2	(	(	PUNCT
ejpam-4444	88	3	tp+1	tp+1	NOUN
ejpam-4444	88	4	−	−	NOUN
ejpam-4444	88	5	1	1	NUM
ejpam-4444	88	6	)	)	PUNCT
ejpam-4444	88	7	(	(	PUNCT
ejpam-4444	88	8	t2	t2	NOUN
ejpam-4444	88	9	−	−	PROPN
ejpam-4444	88	10	1	1	NUM
ejpam-4444	88	11	)	)	PUNCT
ejpam-4444	89	1	[	[	X
ejpam-4444	89	2	α(t2	α(t2	ADJ
ejpam-4444	89	3	+	+	NOUN
ejpam-4444	89	4	1	1	NUM
ejpam-4444	89	5	)	)	PUNCT
ejpam-4444	89	6	+	+	CCONJ
ejpam-4444	89	7	2(1−	2(1−	NUM
ejpam-4444	89	8	α)t	α)t	NOUN
ejpam-4444	89	9	]	]	PUNCT
ejpam-4444	89	10	,	,	PUNCT
ejpam-4444	89	11	(	(	PUNCT
ejpam-4444	89	12	2	2	X
ejpam-4444	89	13	)	)	PUNCT
ejpam-4444	89	14	where	where	SCONJ
ejpam-4444	89	15	g(t	g(t	NOUN
ejpam-4444	89	16	)	)	PUNCT
ejpam-4444	90	1	=	=	PUNCT
ejpam-4444	90	2	(	(	PUNCT
ejpam-4444	90	3	−3αp+	−3αp+	PROPN
ejpam-4444	90	4	2p−	2p−	NUM
ejpam-4444	90	5	α	α	NOUN
ejpam-4444	90	6	)	)	PUNCT
ejpam-4444	90	7	(	(	PUNCT
ejpam-4444	90	8	tp+3	tp+3	NOUN
ejpam-4444	90	9	−	−	NOUN
ejpam-4444	90	10	1	1	NUM
ejpam-4444	90	11	)	)	PUNCT
ejpam-4444	91	1	+	+	CCONJ
ejpam-4444	91	2	(	(	PUNCT
ejpam-4444	91	3	5αp−	5αp−	NUM
ejpam-4444	91	4	2p+	2p+	NUM
ejpam-4444	91	5	α−	α−	ADP
ejpam-4444	91	6	2	2	NUM
ejpam-4444	91	7	)	)	PUNCT
ejpam-4444	91	8	(	(	PUNCT
ejpam-4444	91	9	tp+2	tp+2	NUM
ejpam-4444	91	10	−	−	PROPN
ejpam-4444	91	11	t	t	PROPN
ejpam-4444	91	12	)	)	PUNCT
ejpam-4444	92	1	+	+	CCONJ
ejpam-4444	92	2	(	(	PUNCT
ejpam-4444	92	3	−αp+	−αp+	INTJ
ejpam-4444	92	4	α−	α−	ADP
ejpam-4444	92	5	2	2	NUM
ejpam-4444	92	6	)	)	PUNCT
ejpam-4444	92	7	(	(	PUNCT
ejpam-4444	92	8	tp+1	tp+1	NOUN
ejpam-4444	92	9	−	−	PROPN
ejpam-4444	92	10	t2	t2	NOUN
ejpam-4444	92	11	)	)	PUNCT
ejpam-4444	92	12	−	−	PUNCT
ejpam-4444	93	1	α(p+	α(p+	NOUN
ejpam-4444	93	2	1	1	NUM
ejpam-4444	93	3	)	)	PUNCT
ejpam-4444	93	4	(	(	PUNCT
ejpam-4444	93	5	tp	tp	ADP
ejpam-4444	93	6	−	−	PROPN
ejpam-4444	93	7	t3	t3	PROPN
ejpam-4444	93	8	)	)	PUNCT
ejpam-4444	93	9	.	.	PUNCT
ejpam-4444	94	1	furthermore	furthermore	ADV
ejpam-4444	94	2	,	,	PUNCT
ejpam-4444	94	3	g(1	g(1	NOUN
ejpam-4444	94	4	)	)	PUNCT
ejpam-4444	94	5	=	=	PUNCT
ejpam-4444	95	1	g′(1	g′(1	ADJ
ejpam-4444	95	2	)	)	PUNCT
ejpam-4444	95	3	=	=	SYM
ejpam-4444	95	4	g′′(1	g′′(1	NOUN
ejpam-4444	95	5	)	)	PUNCT
ejpam-4444	96	1	=	=	SYM
ejpam-4444	96	2	0	0	X
ejpam-4444	96	3	.	.	PUNCT
ejpam-4444	97	1	proof	proof	NOUN
ejpam-4444	97	2	.	.	PUNCT
ejpam-4444	98	1	differentiating	differentiate	VERB
ejpam-4444	98	2	f	f	PROPN
ejpam-4444	98	3	(	(	PUNCT
ejpam-4444	98	4	t	t	PROPN
ejpam-4444	98	5	)	)	PUNCT
ejpam-4444	98	6	yields	yield	NOUN
ejpam-4444	98	7	(	(	PUNCT
ejpam-4444	98	8	2	2	NUM
ejpam-4444	98	9	)	)	PUNCT
ejpam-4444	98	10	and	and	CCONJ
ejpam-4444	98	11	by	by	ADP
ejpam-4444	98	12	taking	take	VERB
ejpam-4444	98	13	derivative	derivative	NOUN
ejpam-4444	98	14	of	of	ADP
ejpam-4444	98	15	g	g	PROPN
ejpam-4444	98	16	,	,	PUNCT
ejpam-4444	98	17	we	we	PRON
ejpam-4444	98	18	obtain	obtain	VERB
ejpam-4444	98	19	g′(t	g′(t	NOUN
ejpam-4444	98	20	)	)	PUNCT
ejpam-4444	98	21	=	=	PUNCT
ejpam-4444	98	22	(	(	PUNCT
ejpam-4444	98	23	−3αp+	−3αp+	PROPN
ejpam-4444	98	24	2p−	2p−	NUM
ejpam-4444	98	25	α)(p+	α)(p+	PROPN
ejpam-4444	98	26	3)tp+2	3)tp+2	NUM
ejpam-4444	99	1	+	+	CCONJ
ejpam-4444	99	2	(	(	PUNCT
ejpam-4444	99	3	5αp−	5αp−	NUM
ejpam-4444	99	4	2p+	2p+	NUM
ejpam-4444	99	5	α−	α−	ADP
ejpam-4444	99	6	2	2	NUM
ejpam-4444	99	7	)	)	PUNCT
ejpam-4444	99	8	[	[	PUNCT
ejpam-4444	99	9	(	(	PUNCT
ejpam-4444	99	10	p+	p+	NOUN
ejpam-4444	99	11	2)tp+1	2)tp+1	NUM
ejpam-4444	99	12	−	−	NOUN
ejpam-4444	99	13	1	1	NUM
ejpam-4444	99	14	]	]	PUNCT
ejpam-4444	99	15	+	+	CCONJ
ejpam-4444	99	16	(	(	PUNCT
ejpam-4444	99	17	−αp+	−αp+	X
ejpam-4444	99	18	α−	α−	ADP
ejpam-4444	99	19	2	2	NUM
ejpam-4444	99	20	)	)	PUNCT
ejpam-4444	99	21	[	[	X
ejpam-4444	99	22	(	(	PUNCT
ejpam-4444	99	23	p+	p+	VERB
ejpam-4444	99	24	1)tp	1)tp	PROPN
ejpam-4444	99	25	−	−	PROPN
ejpam-4444	99	26	2t]−	2t]−	NUM
ejpam-4444	99	27	α(p+	α(p+	NOUN
ejpam-4444	99	28	1	1	NUM
ejpam-4444	99	29	)	)	PUNCT
ejpam-4444	99	30	(	(	PUNCT
ejpam-4444	99	31	ptp−1	ptp−1	PROPN
ejpam-4444	99	32	−	−	PROPN
ejpam-4444	99	33	3t2	3t2	NUM
ejpam-4444	99	34	)	)	PUNCT
ejpam-4444	99	35	,	,	PUNCT
ejpam-4444	99	36	g′′(t	g′′(t	NOUN
ejpam-4444	99	37	)	)	PUNCT
ejpam-4444	99	38	=	=	PUNCT
ejpam-4444	100	1	(	(	PUNCT
ejpam-4444	100	2	−3αp+	−3αp+	PROPN
ejpam-4444	100	3	2p−	2p−	PROPN
ejpam-4444	100	4	α)(p+	α)(p+	PROPN
ejpam-4444	100	5	3)(p+	3)(p+	NUM
ejpam-4444	100	6	2)tp+1	2)tp+1	NUM
ejpam-4444	100	7	+	+	CCONJ
ejpam-4444	100	8	(	(	PUNCT
ejpam-4444	100	9	5αp−	5αp−	NUM
ejpam-4444	100	10	2p+	2p+	NUM
ejpam-4444	100	11	α−	α−	ADP
ejpam-4444	100	12	2)(p+	2)(p+	NUM
ejpam-4444	100	13	2)(p+	2)(p+	NUM
ejpam-4444	100	14	1)tp	1)tp	NOUN
ejpam-4444	101	1	+	+	CCONJ
ejpam-4444	101	2	(	(	PUNCT
ejpam-4444	101	3	−αp+	−αp+	X
ejpam-4444	101	4	α−	α−	ADP
ejpam-4444	101	5	2	2	NUM
ejpam-4444	101	6	)	)	PUNCT
ejpam-4444	101	7	[	[	PUNCT
ejpam-4444	101	8	(	(	PUNCT
ejpam-4444	101	9	p+	p+	NOUN
ejpam-4444	101	10	1)ptp−1	1)ptp−1	NUM
ejpam-4444	101	11	−	−	NOUN
ejpam-4444	101	12	2	2	NUM
ejpam-4444	101	13	]	]	PUNCT
ejpam-4444	101	14	−	−	PUNCT
ejpam-4444	101	15	α(p+	α(p+	NOUN
ejpam-4444	101	16	1	1	NUM
ejpam-4444	101	17	)	)	PUNCT
ejpam-4444	101	18	[	[	PUNCT
ejpam-4444	101	19	p(p−	p(p−	VERB
ejpam-4444	101	20	1)tp−2	1)tp−2	NUM
ejpam-4444	101	21	−	−	PROPN
ejpam-4444	101	22	6	6	NUM
ejpam-4444	101	23	t	t	NOUN
ejpam-4444	101	24	]	]	PUNCT
ejpam-4444	101	25	,	,	PUNCT
ejpam-4444	101	26	respectively	respectively	ADV
ejpam-4444	101	27	.	.	PUNCT
ejpam-4444	102	1	it	it	PRON
ejpam-4444	102	2	follows	follow	VERB
ejpam-4444	102	3	immediately	immediately	ADV
ejpam-4444	102	4	that	that	SCONJ
ejpam-4444	102	5	g(1	g(1	NOUN
ejpam-4444	102	6	)	)	PUNCT
ejpam-4444	103	1	=	=	SYM
ejpam-4444	103	2	g	g	NOUN
ejpam-4444	103	3	′	′	NUM
ejpam-4444	104	1	(	(	PUNCT
ejpam-4444	104	2	1	1	NUM
ejpam-4444	104	3	)	)	PUNCT
ejpam-4444	104	4	=	=	SYM
ejpam-4444	104	5	g	g	PROPN
ejpam-4444	104	6	′′	′′	PROPN
ejpam-4444	104	7	(	(	PUNCT
ejpam-4444	104	8	1	1	NUM
ejpam-4444	104	9	)	)	PUNCT
ejpam-4444	104	10	=	=	SYM
ejpam-4444	104	11	0	0	X
ejpam-4444	104	12	.	.	PUNCT
ejpam-4444	104	13	a.	a.	NOUN
ejpam-4444	104	14	sonubon	sonubon	PROPN
ejpam-4444	104	15	,	,	PUNCT
ejpam-4444	104	16	s.	s.	PROPN
ejpam-4444	104	17	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	104	18	,	,	PUNCT
ejpam-4444	104	19	k.	k.	PROPN
ejpam-4444	104	20	nonlaopon	nonlaopon	ADV
ejpam-4444	104	21	/	/	SYM
ejpam-4444	104	22	eur	eur	PROPN
ejpam-4444	104	23	.	.	PUNCT
ejpam-4444	105	1	j.	j.	PROPN
ejpam-4444	105	2	pure	pure	PROPN
ejpam-4444	105	3	appl	appl	PROPN
ejpam-4444	105	4	.	.	PROPN
ejpam-4444	105	5	math	math	PROPN
ejpam-4444	105	6	,	,	PUNCT
ejpam-4444	105	7	15	15	NUM
ejpam-4444	105	8	(	(	PUNCT
ejpam-4444	105	9	3	3	NUM
ejpam-4444	105	10	)	)	PUNCT
ejpam-4444	105	11	(	(	PUNCT
ejpam-4444	105	12	2022	2022	NUM
ejpam-4444	105	13	)	)	PUNCT
ejpam-4444	105	14	,	,	PUNCT
ejpam-4444	105	15	1120	1120	NUM
ejpam-4444	105	16	-	-	SYM
ejpam-4444	105	17	1143	1143	NUM
ejpam-4444	105	18	1125	1125	NUM
ejpam-4444	105	19	lemma	lemma	PROPN
ejpam-4444	105	20	2	2	NUM
ejpam-4444	105	21	.	.	PUNCT
ejpam-4444	106	1	let	let	VERB
ejpam-4444	106	2	α	α	PRON
ejpam-4444	106	3	∈	∈	PROPN
ejpam-4444	106	4	(	(	PUNCT
ejpam-4444	106	5	0	0	NUM
ejpam-4444	106	6	,	,	PUNCT
ejpam-4444	106	7	1/8	1/8	NUM
ejpam-4444	106	8	)	)	PUNCT
ejpam-4444	106	9	and	and	CCONJ
ejpam-4444	106	10	t	t	X
ejpam-4444	106	11	>	>	X
ejpam-4444	106	12	1	1	NUM
ejpam-4444	106	13	and	and	CCONJ
ejpam-4444	106	14	f(t	f(t	NOUN
ejpam-4444	106	15	)	)	PUNCT
ejpam-4444	106	16	=	=	SYM
ejpam-4444	106	17	1	1	NUM
ejpam-4444	106	18	t	t	NOUN
ejpam-4444	106	19	exp	exp	NOUN
ejpam-4444	106	20	[	[	PUNCT
ejpam-4444	106	21	t2	t2	NOUN
ejpam-4444	106	22	−	−	PROPN
ejpam-4444	106	23	1	1	NUM
ejpam-4444	106	24	α(t2	α(t2	NOUN
ejpam-4444	106	25	+	+	ADP
ejpam-4444	106	26	1	1	NUM
ejpam-4444	106	27	)	)	PUNCT
ejpam-4444	107	1	+	+	CCONJ
ejpam-4444	107	2	2(1−	2(1−	NUM
ejpam-4444	107	3	α)t	α)t	NOUN
ejpam-4444	107	4	]	]	PUNCT
ejpam-4444	107	5	.	.	PUNCT
ejpam-4444	108	1	function	function	PROPN
ejpam-4444	108	2	f	f	PROPN
ejpam-4444	108	3	is	be	AUX
ejpam-4444	108	4	strictly	strictly	ADV
ejpam-4444	108	5	increasing	increase	VERB
ejpam-4444	108	6	for	for	ADP
ejpam-4444	108	7	t	t	NOUN
ejpam-4444	108	8	satisfying	satisfy	VERB
ejpam-4444	108	9	the	the	DET
ejpam-4444	108	10	inequality	inequality	NOUN
ejpam-4444	108	11	α2t2	α2t2	PRON
ejpam-4444	108	12	−	−	PROPN
ejpam-4444	108	13	2(α2	2(α2	NUM
ejpam-4444	108	14	−	−	NOUN
ejpam-4444	108	15	3α+	3α+	NUM
ejpam-4444	108	16	1)t+	1)t+	NUM
ejpam-4444	108	17	α2	α2	NOUN
ejpam-4444	108	18	<	<	X
ejpam-4444	108	19	0	0	X
ejpam-4444	108	20	.	.	PUNCT
ejpam-4444	109	1	proof	proof	NOUN
ejpam-4444	109	2	.	.	PUNCT
ejpam-4444	110	1	differentiating	differentiate	VERB
ejpam-4444	110	2	f(t	f(t	NOUN
ejpam-4444	110	3	)	)	PUNCT
ejpam-4444	110	4	with	with	ADP
ejpam-4444	110	5	respect	respect	NOUN
ejpam-4444	110	6	to	to	ADP
ejpam-4444	110	7	t	t	PROPN
ejpam-4444	110	8	yields	yield	NOUN
ejpam-4444	110	9	f	f	PROPN
ejpam-4444	110	10	′(t	′(t	PROPN
ejpam-4444	110	11	)	)	PUNCT
ejpam-4444	110	12	=	=	SYM
ejpam-4444	110	13	t−1e	t−1e	NOUN
ejpam-4444	110	14	t2−1	t2−1	ADP
ejpam-4444	110	15	α(t2	α(t2	ADJ
ejpam-4444	110	16	+	+	NOUN
ejpam-4444	110	17	1)+2(1−α)t	1)+2(1−α)t	NUM
ejpam-4444	110	18	{	{	PUNCT
ejpam-4444	110	19	[	[	PUNCT
ejpam-4444	110	20	α(t2	α(t2	ADJ
ejpam-4444	110	21	+	+	NOUN
ejpam-4444	110	22	1	1	NUM
ejpam-4444	110	23	)	)	PUNCT
ejpam-4444	110	24	+	+	CCONJ
ejpam-4444	110	25	2(1−	2(1−	NUM
ejpam-4444	110	26	α)t	α)t	NOUN
ejpam-4444	110	27	]	]	PUNCT
ejpam-4444	110	28	(	(	PUNCT
ejpam-4444	110	29	2t)−	2t)−	INTJ
ejpam-4444	110	30	(	(	PUNCT
ejpam-4444	110	31	t2	t2	NOUN
ejpam-4444	110	32	−	−	PROPN
ejpam-4444	110	33	1	1	NUM
ejpam-4444	110	34	)	)	PUNCT
ejpam-4444	110	35	[	[	PUNCT
ejpam-4444	110	36	2αt+	2αt+	NUM
ejpam-4444	110	37	2(1−	2(1−	NUM
ejpam-4444	110	38	α	α	NOUN
ejpam-4444	110	39	)	)	PUNCT
ejpam-4444	110	40	]	]	PUNCT
ejpam-4444	110	41	[	[	PUNCT
ejpam-4444	110	42	α(t2	α(t2	ADJ
ejpam-4444	110	43	+	+	NOUN
ejpam-4444	110	44	1	1	NUM
ejpam-4444	110	45	)	)	PUNCT
ejpam-4444	110	46	+	+	CCONJ
ejpam-4444	110	47	2(1−	2(1−	NUM
ejpam-4444	110	48	α)t	α)t	NOUN
ejpam-4444	110	49	]	]	SYM
ejpam-4444	110	50	2	2	NUM
ejpam-4444	110	51	}	}	PUNCT
ejpam-4444	110	52	−	−	PROPN
ejpam-4444	110	53	t−2e	t−2e	NOUN
ejpam-4444	110	54	t2−1	t2−1	ADP
ejpam-4444	110	55	α(t2	α(t2	ADJ
ejpam-4444	110	56	+	+	NOUN
ejpam-4444	110	57	1)+2(1−α)t	1)+2(1−α)t	NUM
ejpam-4444	110	58	.	.	PUNCT
ejpam-4444	111	1	simplifying	simplify	VERB
ejpam-4444	111	2	f	f	PROPN
ejpam-4444	111	3	′(t	′(t	PROPN
ejpam-4444	111	4	)	)	PUNCT
ejpam-4444	111	5	and	and	CCONJ
ejpam-4444	111	6	setting	set	VERB
ejpam-4444	111	7	f	f	PROPN
ejpam-4444	111	8	′(t	′(t	PROPN
ejpam-4444	111	9	)	)	PUNCT
ejpam-4444	111	10	>	>	X
ejpam-4444	111	11	0	0	NUM
ejpam-4444	111	12	,	,	PUNCT
ejpam-4444	111	13	we	we	PRON
ejpam-4444	111	14	obtain	obtain	VERB
ejpam-4444	111	15	2[α(t2	2[α(t2	NUM
ejpam-4444	111	16	+	+	CCONJ
ejpam-4444	111	17	1	1	NUM
ejpam-4444	111	18	)	)	PUNCT
ejpam-4444	111	19	+	+	CCONJ
ejpam-4444	111	20	2(1−	2(1−	NUM
ejpam-4444	111	21	α)t]t2	α)t]t2	NOUN
ejpam-4444	111	22	−	−	PROPN
ejpam-4444	111	23	t(t2	t(t2	NOUN
ejpam-4444	111	24	−	−	NOUN
ejpam-4444	111	25	1	1	NUM
ejpam-4444	111	26	)	)	PUNCT
ejpam-4444	111	27	[	[	PUNCT
ejpam-4444	111	28	2αt+	2αt+	NUM
ejpam-4444	111	29	2(1−	2(1−	NUM
ejpam-4444	111	30	α	α	NOUN
ejpam-4444	111	31	)	)	PUNCT
ejpam-4444	111	32	]	]	PUNCT
ejpam-4444	112	1	−	−	PROPN
ejpam-4444	112	2	[	[	PUNCT
ejpam-4444	112	3	α(t2	α(t2	ADJ
ejpam-4444	112	4	+	+	NOUN
ejpam-4444	112	5	1	1	NUM
ejpam-4444	112	6	)	)	PUNCT
ejpam-4444	112	7	+	+	CCONJ
ejpam-4444	112	8	2(1−	2(1−	NUM
ejpam-4444	112	9	α)t	α)t	NOUN
ejpam-4444	112	10	]	]	SYM
ejpam-4444	112	11	2	2	NUM
ejpam-4444	112	12	>	>	SYM
ejpam-4444	112	13	0	0	NUM
ejpam-4444	112	14	or	or	CCONJ
ejpam-4444	112	15	α2t2	α2t2	PRON
ejpam-4444	112	16	−	−	PROPN
ejpam-4444	112	17	(	(	PUNCT
ejpam-4444	112	18	2α2	2α2	NUM
ejpam-4444	113	1	−	−	NUM
ejpam-4444	113	2	6α+	6α+	NUM
ejpam-4444	113	3	2)t+	2)t+	NUM
ejpam-4444	113	4	α2	α2	ADV
ejpam-4444	113	5	<	<	X
ejpam-4444	113	6	0	0	X
ejpam-4444	113	7	.	.	PUNCT
ejpam-4444	114	1	lemma	lemma	PROPN
ejpam-4444	114	2	3	3	X
ejpam-4444	114	3	.	.	PUNCT
ejpam-4444	115	1	for	for	ADP
ejpam-4444	115	2	a	a	DET
ejpam-4444	115	3	,	,	PUNCT
ejpam-4444	115	4	b	b	X
ejpam-4444	115	5	>	>	X
ejpam-4444	115	6	0	0	PROPN
ejpam-4444	115	7	and	and	CCONJ
ejpam-4444	115	8	α	α	NOUN
ejpam-4444	115	9	,	,	PUNCT
ejpam-4444	115	10	β	β	X
ejpam-4444	115	11	∈	∈	PROPN
ejpam-4444	115	12	(	(	PUNCT
ejpam-4444	115	13	0	0	NUM
ejpam-4444	115	14	,	,	PUNCT
ejpam-4444	115	15	1	1	NUM
ejpam-4444	115	16	)	)	PUNCT
ejpam-4444	115	17	with	with	ADP
ejpam-4444	115	18	α	α	PROPN
ejpam-4444	115	19	>	>	X
ejpam-4444	115	20	β	β	X
ejpam-4444	115	21	,	,	PUNCT
ejpam-4444	115	22	we	we	PRON
ejpam-4444	115	23	have	have	VERB
ejpam-4444	115	24	αc(a	αc(a	NOUN
ejpam-4444	115	25	,	,	PUNCT
ejpam-4444	115	26	b	b	NOUN
ejpam-4444	115	27	)	)	PUNCT
ejpam-4444	116	1	+	+	CCONJ
ejpam-4444	116	2	(	(	PUNCT
ejpam-4444	116	3	1−	1−	NUM
ejpam-4444	116	4	α)h(a	α)h(a	NOUN
ejpam-4444	116	5	,	,	PUNCT
ejpam-4444	116	6	b	b	NOUN
ejpam-4444	116	7	)	)	PUNCT
ejpam-4444	116	8	>	>	X
ejpam-4444	116	9	βc(a	βc(a	PROPN
ejpam-4444	116	10	,	,	PUNCT
ejpam-4444	116	11	b	b	NOUN
ejpam-4444	116	12	)	)	PUNCT
ejpam-4444	116	13	+	+	CCONJ
ejpam-4444	116	14	(	(	PUNCT
ejpam-4444	116	15	1−	1−	NUM
ejpam-4444	116	16	β)h(a	β)h(a	NOUN
ejpam-4444	116	17	,	,	PUNCT
ejpam-4444	116	18	b	b	NOUN
ejpam-4444	116	19	)	)	PUNCT
ejpam-4444	116	20	.	.	PUNCT
ejpam-4444	117	1	proof	proof	NOUN
ejpam-4444	117	2	.	.	PUNCT
ejpam-4444	118	1	because	because	SCONJ
ejpam-4444	118	2	c(a	c(a	PROPN
ejpam-4444	118	3	,	,	PUNCT
ejpam-4444	118	4	b	b	NOUN
ejpam-4444	118	5	)	)	PUNCT
ejpam-4444	118	6	>	>	X
ejpam-4444	119	1	h(a	h(a	PROPN
ejpam-4444	119	2	,	,	PUNCT
ejpam-4444	119	3	b	b	NOUN
ejpam-4444	119	4	)	)	PUNCT
ejpam-4444	119	5	and	and	CCONJ
ejpam-4444	119	6	α	α	X
ejpam-4444	119	7	>	>	X
ejpam-4444	119	8	β	β	X
ejpam-4444	119	9	,	,	PUNCT
ejpam-4444	119	10	the	the	DET
ejpam-4444	119	11	result	result	NOUN
ejpam-4444	119	12	follows	follow	VERB
ejpam-4444	119	13	immediately	immediately	ADV
ejpam-4444	119	14	from	from	ADP
ejpam-4444	119	15	the	the	DET
ejpam-4444	119	16	inequality	inequality	NOUN
ejpam-4444	119	17	(	(	PUNCT
ejpam-4444	119	18	α−	α−	ADP
ejpam-4444	119	19	β)c(a	β)c(a	NUM
ejpam-4444	119	20	,	,	PUNCT
ejpam-4444	119	21	b	b	NOUN
ejpam-4444	119	22	)	)	PUNCT
ejpam-4444	119	23	>	>	X
ejpam-4444	120	1	(	(	PUNCT
ejpam-4444	120	2	α−	α−	ADP
ejpam-4444	120	3	β)h(a	β)h(a	ADJ
ejpam-4444	120	4	,	,	PUNCT
ejpam-4444	120	5	b	b	NOUN
ejpam-4444	120	6	)	)	PUNCT
ejpam-4444	120	7	.	.	PUNCT
ejpam-4444	121	1	lemma	lemma	PROPN
ejpam-4444	121	2	4	4	NUM
ejpam-4444	121	3	.	.	PUNCT
ejpam-4444	122	1	for	for	ADP
ejpam-4444	122	2	t	t	PROPN
ejpam-4444	122	3	>	>	X
ejpam-4444	122	4	1	1	NUM
ejpam-4444	122	5	,	,	PUNCT
ejpam-4444	122	6	we	we	PRON
ejpam-4444	122	7	have	have	VERB
ejpam-4444	122	8	l−1/2(1	l−1/2(1	PROPN
ejpam-4444	122	9	,	,	PUNCT
ejpam-4444	122	10	t	t	PROPN
ejpam-4444	122	11	)	)	PUNCT
ejpam-4444	122	12	>	>	X
ejpam-4444	122	13	1	1	NUM
ejpam-4444	122	14	4	4	NUM
ejpam-4444	122	15	c(1	c(1	PROPN
ejpam-4444	122	16	,	,	PUNCT
ejpam-4444	122	17	t	t	PROPN
ejpam-4444	122	18	)	)	PUNCT
ejpam-4444	123	1	+	+	CCONJ
ejpam-4444	123	2	3	3	NUM
ejpam-4444	123	3	4	4	NUM
ejpam-4444	123	4	h(1	h(1	PROPN
ejpam-4444	123	5	,	,	PUNCT
ejpam-4444	123	6	t	t	PROPN
ejpam-4444	123	7	)	)	PUNCT
ejpam-4444	123	8	.	.	PUNCT
ejpam-4444	124	1	proof	proof	NOUN
ejpam-4444	124	2	.	.	PUNCT
ejpam-4444	125	1	the	the	DET
ejpam-4444	125	2	proposed	propose	VERB
ejpam-4444	125	3	inequality	inequality	NOUN
ejpam-4444	125	4	is	be	AUX
ejpam-4444	125	5	1	1	NUM
ejpam-4444	125	6	+	+	CCONJ
ejpam-4444	125	7	2	2	NUM
ejpam-4444	125	8	√	√	NUM
ejpam-4444	125	9	t+	t+	NOUN
ejpam-4444	125	10	t	t	PROPN
ejpam-4444	125	11	4	4	NUM
ejpam-4444	125	12	>	>	SYM
ejpam-4444	125	13	1	1	NUM
ejpam-4444	125	14	4	4	NUM
ejpam-4444	125	15	(	(	PUNCT
ejpam-4444	125	16	t2	t2	NOUN
ejpam-4444	125	17	+	+	CCONJ
ejpam-4444	125	18	1	1	NUM
ejpam-4444	125	19	t+	t+	NUM
ejpam-4444	125	20	1	1	NUM
ejpam-4444	125	21	)	)	PUNCT
ejpam-4444	125	22	+	+	CCONJ
ejpam-4444	125	23	3	3	NUM
ejpam-4444	125	24	4	4	NUM
ejpam-4444	125	25	(	(	PUNCT
ejpam-4444	125	26	2	2	NUM
ejpam-4444	125	27	t	t	NOUN
ejpam-4444	125	28	t+	t+	PUNCT
ejpam-4444	125	29	1	1	NUM
ejpam-4444	125	30	)	)	PUNCT
ejpam-4444	125	31	which	which	PRON
ejpam-4444	125	32	is	be	AUX
ejpam-4444	125	33	equivalent	equivalent	ADJ
ejpam-4444	125	34	to	to	ADP
ejpam-4444	125	35	(	(	PUNCT
ejpam-4444	125	36	√	√	INTJ
ejpam-4444	125	37	t−	t−	PROPN
ejpam-4444	125	38	1)2	1)2	NUM
ejpam-4444	125	39	>	>	X
ejpam-4444	125	40	0	0	X
ejpam-4444	125	41	.	.	PUNCT
ejpam-4444	125	42	a.	a.	NOUN
ejpam-4444	125	43	sonubon	sonubon	PROPN
ejpam-4444	125	44	,	,	PUNCT
ejpam-4444	125	45	s.	s.	PROPN
ejpam-4444	125	46	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	125	47	,	,	PUNCT
ejpam-4444	125	48	k.	k.	PROPN
ejpam-4444	125	49	nonlaopon	nonlaopon	ADV
ejpam-4444	125	50	/	/	SYM
ejpam-4444	125	51	eur	eur	PROPN
ejpam-4444	125	52	.	.	PUNCT
ejpam-4444	126	1	j.	j.	PROPN
ejpam-4444	126	2	pure	pure	PROPN
ejpam-4444	126	3	appl	appl	PROPN
ejpam-4444	126	4	.	.	PROPN
ejpam-4444	126	5	math	math	PROPN
ejpam-4444	126	6	,	,	PUNCT
ejpam-4444	126	7	15	15	NUM
ejpam-4444	126	8	(	(	PUNCT
ejpam-4444	126	9	3	3	NUM
ejpam-4444	126	10	)	)	PUNCT
ejpam-4444	126	11	(	(	PUNCT
ejpam-4444	126	12	2022	2022	NUM
ejpam-4444	126	13	)	)	PUNCT
ejpam-4444	126	14	,	,	PUNCT
ejpam-4444	126	15	1120	1120	NUM
ejpam-4444	126	16	-	-	SYM
ejpam-4444	126	17	1143	1143	NUM
ejpam-4444	126	18	1126	1126	NUM
ejpam-4444	126	19	3	3	NUM
ejpam-4444	126	20	.	.	X
ejpam-4444	126	21	main	main	ADJ
ejpam-4444	126	22	results	result	NOUN
ejpam-4444	126	23	we	we	PRON
ejpam-4444	126	24	first	first	ADV
ejpam-4444	126	25	establish	establish	VERB
ejpam-4444	126	26	the	the	DET
ejpam-4444	126	27	optimal	optimal	ADJ
ejpam-4444	126	28	upper	upper	ADJ
ejpam-4444	126	29	bound	bind	VERB
ejpam-4444	126	30	for	for	ADP
ejpam-4444	126	31	the	the	DET
ejpam-4444	126	32	weighted	weight	VERB
ejpam-4444	126	33	arithmetic	arithmetic	ADJ
ejpam-4444	126	34	mean	mean	NOUN
ejpam-4444	126	35	of	of	ADP
ejpam-4444	126	36	contraharmonic	contraharmonic	NOUN
ejpam-4444	126	37	and	and	CCONJ
ejpam-4444	126	38	harmonic	harmonic	ADJ
ejpam-4444	126	39	means	mean	NOUN
ejpam-4444	126	40	by	by	ADP
ejpam-4444	126	41	generalized	generalize	VERB
ejpam-4444	126	42	logarithmic	logarithmic	ADJ
ejpam-4444	126	43	means	mean	NOUN
ejpam-4444	126	44	lp	lp	ADV
ejpam-4444	126	45	where	where	SCONJ
ejpam-4444	126	46	p	p	NOUN
ejpam-4444	126	47	has	have	VERB
ejpam-4444	126	48	the	the	DET
ejpam-4444	126	49	linear	linear	ADJ
ejpam-4444	126	50	form	form	NOUN
ejpam-4444	126	51	p	p	NOUN
ejpam-4444	126	52	=	=	NOUN
ejpam-4444	126	53	2(1−	2(1−	NUM
ejpam-4444	126	54	c)α+	c)α+	NOUN
ejpam-4444	126	55	c	c	NOUN
ejpam-4444	126	56	and	and	CCONJ
ejpam-4444	126	57	α	α	PRON
ejpam-4444	126	58	∈	∈	PROPN
ejpam-4444	126	59	(	(	PUNCT
ejpam-4444	126	60	0	0	NUM
ejpam-4444	126	61	,	,	PUNCT
ejpam-4444	126	62	1/2	1/2	NUM
ejpam-4444	126	63	)	)	PUNCT
ejpam-4444	126	64	.	.	PUNCT
ejpam-4444	127	1	precisely	precisely	ADV
ejpam-4444	127	2	,	,	PUNCT
ejpam-4444	127	3	we	we	PRON
ejpam-4444	127	4	have	have	AUX
ejpam-4444	127	5	theorem	theorem	VERB
ejpam-4444	127	6	1	1	NUM
ejpam-4444	127	7	.	.	PUNCT
ejpam-4444	128	1	let	let	VERB
ejpam-4444	128	2	a	a	DET
ejpam-4444	128	3	,	,	PUNCT
ejpam-4444	128	4	b	b	X
ejpam-4444	128	5	>	>	X
ejpam-4444	128	6	0	0	PUNCT
ejpam-4444	128	7	with	with	ADP
ejpam-4444	128	8	a	a	DET
ejpam-4444	128	9	̸=	̸=	PROPN
ejpam-4444	128	10	b.	b.	NOUN
ejpam-4444	128	11	then	then	ADV
ejpam-4444	128	12	1	1	NUM
ejpam-4444	128	13	)	)	PUNCT
ejpam-4444	128	14	l4α−1(a	l4α−1(a	NUM
ejpam-4444	128	15	,	,	PUNCT
ejpam-4444	128	16	b	b	NOUN
ejpam-4444	128	17	)	)	PUNCT
ejpam-4444	128	18	=	=	SYM
ejpam-4444	128	19	αc(a	αc(a	NOUN
ejpam-4444	128	20	,	,	PUNCT
ejpam-4444	128	21	b	b	NOUN
ejpam-4444	128	22	)	)	PUNCT
ejpam-4444	129	1	+	+	CCONJ
ejpam-4444	129	2	(	(	PUNCT
ejpam-4444	129	3	1−	1−	NUM
ejpam-4444	129	4	α)h(a	α)h(a	NOUN
ejpam-4444	129	5	,	,	PUNCT
ejpam-4444	129	6	b	b	NOUN
ejpam-4444	129	7	)	)	PUNCT
ejpam-4444	129	8	for	for	ADP
ejpam-4444	129	9	α	α	NOUN
ejpam-4444	129	10	=	=	SYM
ejpam-4444	129	11	1/2	1/2	NUM
ejpam-4444	129	12	;	;	PUNCT
ejpam-4444	129	13	2	2	NUM
ejpam-4444	129	14	)	)	PUNCT
ejpam-4444	129	15	l4α−1(a	l4α−1(a	NUM
ejpam-4444	129	16	,	,	PUNCT
ejpam-4444	129	17	b	b	NOUN
ejpam-4444	129	18	)	)	PUNCT
ejpam-4444	129	19	>	>	X
ejpam-4444	129	20	αc(a	αc(a	NUM
ejpam-4444	129	21	,	,	PUNCT
ejpam-4444	129	22	b	b	NOUN
ejpam-4444	129	23	)	)	PUNCT
ejpam-4444	129	24	+	+	CCONJ
ejpam-4444	129	25	(	(	PUNCT
ejpam-4444	129	26	1−	1−	NUM
ejpam-4444	129	27	α)h(a	α)h(a	NOUN
ejpam-4444	129	28	,	,	PUNCT
ejpam-4444	129	29	b	b	NOUN
ejpam-4444	129	30	)	)	PUNCT
ejpam-4444	129	31	for	for	ADP
ejpam-4444	129	32	α	α	PRON
ejpam-4444	129	33	∈	∈	PROPN
ejpam-4444	129	34	(	(	PUNCT
ejpam-4444	129	35	0	0	NUM
ejpam-4444	129	36	,	,	PUNCT
ejpam-4444	129	37	1/2	1/2	NUM
ejpam-4444	129	38	)	)	PUNCT
ejpam-4444	129	39	,	,	PUNCT
ejpam-4444	129	40	and	and	CCONJ
ejpam-4444	129	41	the	the	DET
ejpam-4444	129	42	parameter	parameter	NOUN
ejpam-4444	129	43	4α−	4α−	PROPN
ejpam-4444	129	44	1	1	NUM
ejpam-4444	129	45	can	can	AUX
ejpam-4444	129	46	not	not	PART
ejpam-4444	129	47	be	be	AUX
ejpam-4444	129	48	improved	improve	VERB
ejpam-4444	129	49	in	in	ADP
ejpam-4444	129	50	the	the	DET
ejpam-4444	129	51	sense	sense	NOUN
ejpam-4444	129	52	that	that	SCONJ
ejpam-4444	129	53	l4α−1	l4α−1	NOUN
ejpam-4444	129	54	=	=	PUNCT
ejpam-4444	129	55	min	min	PROPN
ejpam-4444	129	56	c	c	PROPN
ejpam-4444	129	57	{	{	PUNCT
ejpam-4444	129	58	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	129	59	|	|	ADV
ejpam-4444	129	60	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	129	61	>	>	X
ejpam-4444	129	62	αc	αc	PROPN
ejpam-4444	130	1	+	+	CCONJ
ejpam-4444	130	2	(	(	PUNCT
ejpam-4444	130	3	1−	1−	NUM
ejpam-4444	130	4	α)h	α)h	NOUN
ejpam-4444	130	5	}	}	PUNCT
ejpam-4444	130	6	for	for	ADP
ejpam-4444	130	7	α	α	PRON
ejpam-4444	130	8	∈	∈	PROPN
ejpam-4444	130	9	(	(	PUNCT
ejpam-4444	130	10	0	0	NUM
ejpam-4444	130	11	,	,	PUNCT
ejpam-4444	130	12	1/2	1/2	NUM
ejpam-4444	130	13	)	)	PUNCT
ejpam-4444	130	14	i.e.	i.e.	X
ejpam-4444	130	15	c	c	NOUN
ejpam-4444	130	16	=	=	SYM
ejpam-4444	130	17	−1	−1	NOUN
ejpam-4444	130	18	;	;	PUNCT
ejpam-4444	130	19	3	3	X
ejpam-4444	130	20	)	)	PUNCT
ejpam-4444	130	21	l4α−1(a	l4α−1(a	NUM
ejpam-4444	130	22	,	,	PUNCT
ejpam-4444	130	23	b	b	NOUN
ejpam-4444	130	24	)	)	PUNCT
ejpam-4444	130	25	<	<	X
ejpam-4444	130	26	αc(a	αc(a	NOUN
ejpam-4444	130	27	,	,	PUNCT
ejpam-4444	130	28	b	b	NOUN
ejpam-4444	130	29	)	)	PUNCT
ejpam-4444	130	30	+	+	CCONJ
ejpam-4444	130	31	(	(	PUNCT
ejpam-4444	130	32	1−	1−	NUM
ejpam-4444	130	33	α)h(a	α)h(a	NOUN
ejpam-4444	130	34	,	,	PUNCT
ejpam-4444	130	35	b	b	NOUN
ejpam-4444	130	36	)	)	PUNCT
ejpam-4444	130	37	for	for	ADP
ejpam-4444	130	38	α	α	PRON
ejpam-4444	130	39	∈	∈	PROPN
ejpam-4444	130	40	(	(	PUNCT
ejpam-4444	130	41	1/2	1/2	NUM
ejpam-4444	130	42	,	,	PUNCT
ejpam-4444	130	43	1	1	NUM
ejpam-4444	130	44	)	)	PUNCT
ejpam-4444	130	45	.	.	PUNCT
ejpam-4444	131	1	proof	proof	NOUN
ejpam-4444	131	2	.	.	PUNCT
ejpam-4444	132	1	1	1	X
ejpam-4444	132	2	)	)	PUNCT
ejpam-4444	132	3	for	for	ADP
ejpam-4444	132	4	α	α	NOUN
ejpam-4444	132	5	=	=	SYM
ejpam-4444	132	6	1/2	1/2	NUM
ejpam-4444	132	7	,	,	PUNCT
ejpam-4444	132	8	on	on	ADP
ejpam-4444	132	9	one	one	NUM
ejpam-4444	132	10	hand	hand	NOUN
ejpam-4444	132	11	we	we	PRON
ejpam-4444	132	12	have	have	VERB
ejpam-4444	132	13	l4	l4	PROPN
ejpam-4444	132	14	(	(	PUNCT
ejpam-4444	132	15	1	1	NUM
ejpam-4444	132	16	2)−1(a	2)−1(a	NUM
ejpam-4444	132	17	,	,	PUNCT
ejpam-4444	132	18	b	b	NOUN
ejpam-4444	132	19	)	)	PUNCT
ejpam-4444	132	20	=	=	SYM
ejpam-4444	133	1	l1(a	l1(a	PROPN
ejpam-4444	133	2	,	,	PUNCT
ejpam-4444	133	3	b	b	NOUN
ejpam-4444	133	4	)	)	PUNCT
ejpam-4444	133	5	=	=	SYM
ejpam-4444	133	6	a+	a+	PUNCT
ejpam-4444	133	7	b	b	NOUN
ejpam-4444	133	8	2	2	NUM
ejpam-4444	133	9	.	.	PUNCT
ejpam-4444	134	1	on	on	ADP
ejpam-4444	134	2	the	the	DET
ejpam-4444	134	3	other	other	ADJ
ejpam-4444	134	4	hand	hand	NOUN
ejpam-4444	134	5	,	,	PUNCT
ejpam-4444	134	6	we	we	PRON
ejpam-4444	134	7	have	have	AUX
ejpam-4444	134	8	c(a	c(a	PROPN
ejpam-4444	134	9	,	,	PUNCT
ejpam-4444	134	10	b	b	NOUN
ejpam-4444	134	11	)	)	PUNCT
ejpam-4444	134	12	+	+	PROPN
ejpam-4444	134	13	h(a	h(a	PROPN
ejpam-4444	134	14	,	,	PUNCT
ejpam-4444	134	15	b	b	NOUN
ejpam-4444	134	16	)	)	PUNCT
ejpam-4444	134	17	2	2	NUM
ejpam-4444	134	18	=	=	SYM
ejpam-4444	134	19	a2+b2	a2+b2	PROPN
ejpam-4444	134	20	a+b	a+b	NUM
ejpam-4444	134	21	+	+	CCONJ
ejpam-4444	134	22	2ab	2ab	ADJ
ejpam-4444	134	23	a+b	a+b	NUM
ejpam-4444	134	24	2	2	NUM
ejpam-4444	134	25	=	=	SYM
ejpam-4444	134	26	a+	a+	PUNCT
ejpam-4444	134	27	b	b	PROPN
ejpam-4444	134	28	2	2	NUM
ejpam-4444	134	29	.	.	NOUN
ejpam-4444	134	30	2	2	NUM
ejpam-4444	134	31	)	)	PUNCT
ejpam-4444	134	32	without	without	ADP
ejpam-4444	134	33	loss	loss	NOUN
ejpam-4444	134	34	of	of	ADP
ejpam-4444	134	35	generality	generality	NOUN
ejpam-4444	134	36	,	,	PUNCT
ejpam-4444	134	37	we	we	PRON
ejpam-4444	134	38	assume	assume	VERB
ejpam-4444	134	39	that	that	SCONJ
ejpam-4444	134	40	b	b	X
ejpam-4444	134	41	>	>	X
ejpam-4444	134	42	a	a	DET
ejpam-4444	134	43	>	>	X
ejpam-4444	134	44	0	0	PUNCT
ejpam-4444	134	45	and	and	CCONJ
ejpam-4444	134	46	set	set	VERB
ejpam-4444	134	47	t	t	NOUN
ejpam-4444	134	48	=	=	SYM
ejpam-4444	134	49	b	b	X
ejpam-4444	134	50	/	/	SYM
ejpam-4444	134	51	a	a	PRON
ejpam-4444	134	52	>	>	X
ejpam-4444	134	53	1	1	NUM
ejpam-4444	134	54	.	.	PUNCT
ejpam-4444	135	1	the	the	DET
ejpam-4444	135	2	proposed	propose	VERB
ejpam-4444	135	3	inequality	inequality	NOUN
ejpam-4444	135	4	becomes	become	VERB
ejpam-4444	135	5	[	[	PUNCT
ejpam-4444	135	6	t4α	t4α	NOUN
ejpam-4444	135	7	−	−	PROPN
ejpam-4444	135	8	1	1	NUM
ejpam-4444	135	9	4α(t−	4α(t−	NUM
ejpam-4444	135	10	1	1	NUM
ejpam-4444	135	11	)	)	PUNCT
ejpam-4444	135	12	]	]	PUNCT
ejpam-4444	135	13	1/(4α−1	1/(4α−1	NUM
ejpam-4444	135	14	)	)	PUNCT
ejpam-4444	135	15	>	>	X
ejpam-4444	136	1	α	α	PROPN
ejpam-4444	136	2	(	(	PUNCT
ejpam-4444	136	3	t2	t2	NOUN
ejpam-4444	136	4	+	+	CCONJ
ejpam-4444	136	5	1	1	NUM
ejpam-4444	136	6	t+	t+	NUM
ejpam-4444	136	7	1	1	NUM
ejpam-4444	136	8	)	)	PUNCT
ejpam-4444	136	9	+	+	CCONJ
ejpam-4444	136	10	(	(	PUNCT
ejpam-4444	136	11	1−	1−	NUM
ejpam-4444	136	12	α	α	NOUN
ejpam-4444	136	13	)	)	PUNCT
ejpam-4444	136	14	(	(	PUNCT
ejpam-4444	136	15	2	2	NUM
ejpam-4444	136	16	t	t	NOUN
ejpam-4444	136	17	t+	t+	PUNCT
ejpam-4444	136	18	1	1	NUM
ejpam-4444	136	19	)	)	PUNCT
ejpam-4444	136	20	α	α	PROPN
ejpam-4444	136	21	∈	∈	PROPN
ejpam-4444	136	22	(	(	PUNCT
ejpam-4444	136	23	0	0	NUM
ejpam-4444	136	24	,	,	PUNCT
ejpam-4444	136	25	1/2	1/2	NUM
ejpam-4444	136	26	)	)	PUNCT
ejpam-4444	136	27	.	.	PUNCT
ejpam-4444	137	1	(	(	PUNCT
ejpam-4444	137	2	3	3	X
ejpam-4444	137	3	)	)	PUNCT
ejpam-4444	137	4	inequality	inequality	NOUN
ejpam-4444	137	5	(	(	PUNCT
ejpam-4444	137	6	3	3	NUM
ejpam-4444	137	7	)	)	PUNCT
ejpam-4444	137	8	is	be	AUX
ejpam-4444	137	9	equivalent	equivalent	ADJ
ejpam-4444	137	10	to	to	ADP
ejpam-4444	137	11	f	f	PROPN
ejpam-4444	137	12	(	(	PUNCT
ejpam-4444	137	13	t	t	PROPN
ejpam-4444	137	14	)	)	PUNCT
ejpam-4444	137	15	>	>	X
ejpam-4444	137	16	0	0	PUNCT
ejpam-4444	138	1	in	in	ADP
ejpam-4444	138	2	(	(	PUNCT
ejpam-4444	138	3	1	1	NUM
ejpam-4444	138	4	)	)	PUNCT
ejpam-4444	138	5	with	with	ADP
ejpam-4444	138	6	p	p	NOUN
ejpam-4444	138	7	=	=	PUNCT
ejpam-4444	138	8	4α−	4α−	PROPN
ejpam-4444	138	9	1	1	NUM
ejpam-4444	138	10	.	.	PUNCT
ejpam-4444	138	11	using	use	VERB
ejpam-4444	138	12	lemma	lemma	PROPN
ejpam-4444	138	13	1	1	NUM
ejpam-4444	138	14	,	,	PUNCT
ejpam-4444	138	15	we	we	PRON
ejpam-4444	138	16	have	have	VERB
ejpam-4444	138	17	a	a	DET
ejpam-4444	138	18	formula	formula	NOUN
ejpam-4444	138	19	for	for	ADP
ejpam-4444	138	20	f	f	PROPN
ejpam-4444	138	21	′(t	′(t	PROPN
ejpam-4444	138	22	)	)	PUNCT
ejpam-4444	138	23	,	,	PUNCT
ejpam-4444	138	24	g′(t	g′(t	PROPN
ejpam-4444	138	25	)	)	PUNCT
ejpam-4444	138	26	,	,	PUNCT
ejpam-4444	138	27	g′′(t	g′′(t	NOUN
ejpam-4444	138	28	)	)	PUNCT
ejpam-4444	138	29	where	where	SCONJ
ejpam-4444	138	30	g(t	g(t	PROPN
ejpam-4444	138	31	)	)	PUNCT
ejpam-4444	138	32	is	be	AUX
ejpam-4444	138	33	the	the	DET
ejpam-4444	138	34	numerator	numerator	NOUN
ejpam-4444	138	35	of	of	ADP
ejpam-4444	138	36	f	f	PROPN
ejpam-4444	138	37	′(t	′(t	PROPN
ejpam-4444	138	38	)	)	PUNCT
ejpam-4444	138	39	appearing	appear	VERB
ejpam-4444	138	40	in	in	ADP
ejpam-4444	138	41	(	(	PUNCT
ejpam-4444	138	42	2	2	NUM
ejpam-4444	138	43	)	)	PUNCT
ejpam-4444	138	44	.	.	PUNCT
ejpam-4444	139	1	taking	take	VERB
ejpam-4444	139	2	derivative	derivative	NOUN
ejpam-4444	139	3	of	of	ADP
ejpam-4444	139	4	g′′(t	g′′(t	NOUN
ejpam-4444	139	5	)	)	PUNCT
ejpam-4444	139	6	,	,	PUNCT
ejpam-4444	139	7	we	we	PRON
ejpam-4444	139	8	have	have	VERB
ejpam-4444	139	9	g	g	PROPN
ejpam-4444	139	10	′′′	′′′	PROPN
ejpam-4444	139	11	(	(	PUNCT
ejpam-4444	139	12	t	t	PROPN
ejpam-4444	139	13	)	)	PUNCT
ejpam-4444	139	14	8αt4α−4	8αt4α−4	NUM
ejpam-4444	139	15	=	=	SYM
ejpam-4444	139	16	(	(	PUNCT
ejpam-4444	139	17	4α+	4α+	NUM
ejpam-4444	139	18	2)(4α+	2)(4α+	NUM
ejpam-4444	139	19	1)(3α−	1)(3α−	NUM
ejpam-4444	139	20	1)(1−	1)(1−	NUM
ejpam-4444	139	21	2α)t3	2α)t3	NUM
ejpam-4444	139	22	−	−	ADP
ejpam-4444	139	23	2α(4α+	2α(4α+	NUM
ejpam-4444	139	24	1)(4α−	1)(4α−	NUM
ejpam-4444	139	25	1)(3−	1)(3−	NUM
ejpam-4444	139	26	5α)t2	5α)t2	PROPN
ejpam-4444	139	27	+	+	CCONJ
ejpam-4444	139	28	2(2α2	2(2α2	NUM
ejpam-4444	139	29	−	−	NOUN
ejpam-4444	140	1	α+	α+	PUNCT
ejpam-4444	140	2	1)(4α−	1)(4α−	NUM
ejpam-4444	140	3	1)(1−	1)(1−	NUM
ejpam-4444	140	4	2α)t	2α)t	NUM
ejpam-4444	140	5	−	−	PROPN
ejpam-4444	140	6	α(4α−	α(4α−	PROPN
ejpam-4444	140	7	1)(1−	1)(1−	NUM
ejpam-4444	140	8	2α)(3−	2α)(3−	NUM
ejpam-4444	140	9	4α	4α	NOUN
ejpam-4444	140	10	)	)	PUNCT
ejpam-4444	141	1	+	+	CCONJ
ejpam-4444	142	1	3αt4−4α	3αt4−4α	NUM
ejpam-4444	142	2	.	.	PUNCT
ejpam-4444	143	1	(	(	PUNCT
ejpam-4444	143	2	4	4	X
ejpam-4444	143	3	)	)	PUNCT
ejpam-4444	143	4	we	we	PRON
ejpam-4444	143	5	divide	divide	VERB
ejpam-4444	143	6	our	our	PRON
ejpam-4444	143	7	proof	proof	NOUN
ejpam-4444	143	8	into	into	ADP
ejpam-4444	143	9	four	four	NUM
ejpam-4444	143	10	cases	case	NOUN
ejpam-4444	143	11	:	:	PUNCT
ejpam-4444	143	12	α	α	X
ejpam-4444	143	13	∈	∈	PROPN
ejpam-4444	144	1	[	[	X
ejpam-4444	144	2	1/3	1/3	NUM
ejpam-4444	144	3	,	,	PUNCT
ejpam-4444	144	4	1/2	1/2	NUM
ejpam-4444	144	5	)	)	PUNCT
ejpam-4444	144	6	,	,	PUNCT
ejpam-4444	144	7	α	α	PROPN
ejpam-4444	144	8	∈	∈	PROPN
ejpam-4444	145	1	[	[	X
ejpam-4444	145	2	1/8	1/8	NUM
ejpam-4444	145	3	,	,	PUNCT
ejpam-4444	145	4	1/4	1/4	NUM
ejpam-4444	145	5	)	)	PUNCT
ejpam-4444	146	1	,	,	PUNCT
ejpam-4444	146	2	α	α	PROPN
ejpam-4444	146	3	∈	∈	PROPN
ejpam-4444	147	1	[	[	X
ejpam-4444	147	2	1/4	1/4	NUM
ejpam-4444	147	3	,	,	PUNCT
ejpam-4444	147	4	1/3	1/3	NUM
ejpam-4444	147	5	)	)	PUNCT
ejpam-4444	147	6	and	and	CCONJ
ejpam-4444	147	7	α	α	PRON
ejpam-4444	147	8	∈	∈	PROPN
ejpam-4444	147	9	(	(	PUNCT
ejpam-4444	147	10	0	0	NUM
ejpam-4444	147	11	,	,	PUNCT
ejpam-4444	147	12	1/8	1/8	NUM
ejpam-4444	147	13	)	)	PUNCT
ejpam-4444	147	14	.	.	PUNCT
ejpam-4444	148	1	a.	a.	PROPN
ejpam-4444	148	2	sonubon	sonubon	PROPN
ejpam-4444	148	3	,	,	PUNCT
ejpam-4444	148	4	s.	s.	PROPN
ejpam-4444	148	5	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	148	6	,	,	PUNCT
ejpam-4444	148	7	k.	k.	PROPN
ejpam-4444	148	8	nonlaopon	nonlaopon	ADV
ejpam-4444	148	9	/	/	SYM
ejpam-4444	148	10	eur	eur	PROPN
ejpam-4444	148	11	.	.	PUNCT
ejpam-4444	149	1	j.	j.	PROPN
ejpam-4444	149	2	pure	pure	PROPN
ejpam-4444	149	3	appl	appl	PROPN
ejpam-4444	149	4	.	.	PROPN
ejpam-4444	149	5	math	math	PROPN
ejpam-4444	149	6	,	,	PUNCT
ejpam-4444	149	7	15	15	NUM
ejpam-4444	149	8	(	(	PUNCT
ejpam-4444	149	9	3	3	NUM
ejpam-4444	149	10	)	)	PUNCT
ejpam-4444	149	11	(	(	PUNCT
ejpam-4444	149	12	2022	2022	NUM
ejpam-4444	149	13	)	)	PUNCT
ejpam-4444	149	14	,	,	PUNCT
ejpam-4444	149	15	1120	1120	NUM
ejpam-4444	149	16	-	-	SYM
ejpam-4444	149	17	1143	1143	NUM
ejpam-4444	149	18	1127	1127	NUM
ejpam-4444	149	19	2.1	2.1	NUM
ejpam-4444	149	20	)	)	PUNCT
ejpam-4444	149	21	case	case	NOUN
ejpam-4444	149	22	α	α	X
ejpam-4444	149	23	∈	∈	PROPN
ejpam-4444	150	1	[	[	X
ejpam-4444	150	2	1/3	1/3	NUM
ejpam-4444	150	3	,	,	PUNCT
ejpam-4444	150	4	1/2	1/2	NUM
ejpam-4444	150	5	):	):	PUNCT
ejpam-4444	150	6	observe	observe	VERB
ejpam-4444	150	7	that	that	SCONJ
ejpam-4444	150	8	the	the	DET
ejpam-4444	150	9	coefficients	coefficient	NOUN
ejpam-4444	150	10	of	of	ADP
ejpam-4444	150	11	t3	t3	PROPN
ejpam-4444	150	12	and	and	CCONJ
ejpam-4444	150	13	t	t	PROPN
ejpam-4444	150	14	in	in	ADP
ejpam-4444	150	15	(	(	PUNCT
ejpam-4444	150	16	4	4	X
ejpam-4444	150	17	)	)	PUNCT
ejpam-4444	150	18	are	be	AUX
ejpam-4444	150	19	positive	positive	ADJ
ejpam-4444	150	20	while	while	SCONJ
ejpam-4444	150	21	that	that	PRON
ejpam-4444	150	22	of	of	ADP
ejpam-4444	150	23	t2	t2	NOUN
ejpam-4444	150	24	and	and	CCONJ
ejpam-4444	150	25	constant	constant	ADJ
ejpam-4444	150	26	term	term	NOUN
ejpam-4444	150	27	are	be	AUX
ejpam-4444	150	28	negative	negative	ADJ
ejpam-4444	150	29	for	for	ADP
ejpam-4444	150	30	α	α	PRON
ejpam-4444	150	31	∈	∈	PROPN
ejpam-4444	151	1	[	[	X
ejpam-4444	151	2	1/3	1/3	NUM
ejpam-4444	151	3	,	,	PUNCT
ejpam-4444	151	4	1/2	1/2	NUM
ejpam-4444	151	5	)	)	PUNCT
ejpam-4444	151	6	.	.	PUNCT
ejpam-4444	152	1	since	since	SCONJ
ejpam-4444	152	2	t	t	PROPN
ejpam-4444	152	3	>	>	X
ejpam-4444	152	4	1	1	NUM
ejpam-4444	152	5	,	,	PUNCT
ejpam-4444	152	6	we	we	PRON
ejpam-4444	152	7	have	have	VERB
ejpam-4444	152	8	t2	t2	NOUN
ejpam-4444	152	9	<	<	X
ejpam-4444	152	10	t4−4α	t4−4α	PROPN
ejpam-4444	152	11	<	<	X
ejpam-4444	152	12	t3	t3	NOUN
ejpam-4444	152	13	and	and	CCONJ
ejpam-4444	152	14	consequently	consequently	ADV
ejpam-4444	152	15	g	g	PROPN
ejpam-4444	152	16	′′′	′′′	PROPN
ejpam-4444	152	17	(	(	PUNCT
ejpam-4444	152	18	t	t	PROPN
ejpam-4444	152	19	)	)	PUNCT
ejpam-4444	152	20	8αt4α−4	8αt4α−4	NUM
ejpam-4444	152	21	>	>	X
ejpam-4444	153	1	[	[	PUNCT
ejpam-4444	153	2	(	(	PUNCT
ejpam-4444	153	3	4α+	4α+	NUM
ejpam-4444	153	4	2)(4α+	2)(4α+	NUM
ejpam-4444	153	5	1)(3α−	1)(3α−	NUM
ejpam-4444	153	6	1)(1−	1)(1−	NUM
ejpam-4444	153	7	2α)−	2α)−	NUM
ejpam-4444	153	8	2α(4α+	2α(4α+	NUM
ejpam-4444	153	9	1)(4α−	1)(4α−	NUM
ejpam-4444	153	10	1)(3−	1)(3−	NUM
ejpam-4444	153	11	5α	5α	NUM
ejpam-4444	153	12	)	)	PUNCT
ejpam-4444	154	1	+	+	NUM
ejpam-4444	154	2	3α	3α	NOUN
ejpam-4444	154	3	]	]	PUNCT
ejpam-4444	154	4	t4−4α	t4−4α	PROPN
ejpam-4444	155	1	+	+	PUNCT
ejpam-4444	155	2	[	[	PUNCT
ejpam-4444	155	3	2(2α2	2(2α2	NUM
ejpam-4444	155	4	−	−	ADP
ejpam-4444	155	5	α+	α+	PUNCT
ejpam-4444	155	6	1)(4α−	1)(4α−	NUM
ejpam-4444	155	7	1)(1−	1)(1−	NUM
ejpam-4444	155	8	2α)−	2α)−	NUM
ejpam-4444	155	9	α(4α−	α(4α−	PROPN
ejpam-4444	155	10	1)(1−	1)(1−	NUM
ejpam-4444	155	11	2α)(3−	2α)(3−	NUM
ejpam-4444	155	12	4α	4α	NOUN
ejpam-4444	155	13	)	)	PUNCT
ejpam-4444	155	14	]	]	PUNCT
ejpam-4444	156	1	t	t	X
ejpam-4444	156	2	>	>	X
ejpam-4444	156	3	(	(	PUNCT
ejpam-4444	156	4	1−	1−	NUM
ejpam-4444	156	5	2α)(4α−	2α)(4α−	NUM
ejpam-4444	156	6	1)(−8α2	1)(−8α2	NUM
ejpam-4444	156	7	+	+	CCONJ
ejpam-4444	156	8	5α+	5α+	NUM
ejpam-4444	156	9	2	2	NUM
ejpam-4444	156	10	)	)	PUNCT
ejpam-4444	156	11	(	(	PUNCT
ejpam-4444	156	12	t4−4α	t4−4α	PROPN
ejpam-4444	156	13	−	−	PROPN
ejpam-4444	156	14	t	t	PROPN
ejpam-4444	156	15	)	)	PUNCT
ejpam-4444	156	16	>	>	X
ejpam-4444	157	1	0	0	X
ejpam-4444	157	2	.	.	PUNCT
ejpam-4444	158	1	together	together	ADV
ejpam-4444	158	2	with	with	ADP
ejpam-4444	158	3	g(1	g(1	NOUN
ejpam-4444	158	4	)	)	PUNCT
ejpam-4444	158	5	=	=	PUNCT
ejpam-4444	158	6	g′(1	g′(1	ADJ
ejpam-4444	158	7	)	)	PUNCT
ejpam-4444	158	8	=	=	SYM
ejpam-4444	158	9	g′′(1	g′′(1	NOUN
ejpam-4444	158	10	)	)	PUNCT
ejpam-4444	158	11	from	from	ADP
ejpam-4444	158	12	lemma	lemma	PROPN
ejpam-4444	158	13	1	1	NUM
ejpam-4444	158	14	,	,	PUNCT
ejpam-4444	158	15	we	we	PRON
ejpam-4444	158	16	conclude	conclude	VERB
ejpam-4444	158	17	that	that	SCONJ
ejpam-4444	158	18	f	f	PROPN
ejpam-4444	158	19	(	(	PUNCT
ejpam-4444	158	20	t	t	PROPN
ejpam-4444	158	21	)	)	PUNCT
ejpam-4444	158	22	>	>	X
ejpam-4444	158	23	0	0	PUNCT
ejpam-4444	159	1	for	for	ADP
ejpam-4444	159	2	all	all	DET
ejpam-4444	159	3	α	α	PRON
ejpam-4444	159	4	∈	∈	PROPN
ejpam-4444	159	5	[	[	X
ejpam-4444	159	6	1/3	1/3	NUM
ejpam-4444	159	7	,	,	PUNCT
ejpam-4444	159	8	1/2	1/2	NUM
ejpam-4444	159	9	)	)	PUNCT
ejpam-4444	159	10	.	.	PUNCT
ejpam-4444	159	11	2.2	2.2	NUM
ejpam-4444	159	12	)	)	PUNCT
ejpam-4444	159	13	case	case	NOUN
ejpam-4444	159	14	α	α	X
ejpam-4444	159	15	∈	∈	PROPN
ejpam-4444	160	1	[	[	X
ejpam-4444	160	2	1/8	1/8	NUM
ejpam-4444	160	3	,	,	PUNCT
ejpam-4444	160	4	1/4	1/4	NUM
ejpam-4444	160	5	):	):	PUNCT
ejpam-4444	160	6	since	since	SCONJ
ejpam-4444	160	7	monotonicity	monotonicity	NOUN
ejpam-4444	160	8	property	property	NOUN
ejpam-4444	160	9	of	of	ADP
ejpam-4444	160	10	lp	lp	PROPN
ejpam-4444	160	11	implies	imply	VERB
ejpam-4444	160	12	that	that	SCONJ
ejpam-4444	160	13	l4α−1(1	l4α−1(1	NOUN
ejpam-4444	160	14	,	,	PUNCT
ejpam-4444	160	15	t	t	PROPN
ejpam-4444	160	16	)	)	PUNCT
ejpam-4444	160	17	≥	≥	PROPN
ejpam-4444	160	18	l−1/2(1	l−1/2(1	PROPN
ejpam-4444	160	19	,	,	PUNCT
ejpam-4444	160	20	t	t	PROPN
ejpam-4444	160	21	)	)	PUNCT
ejpam-4444	160	22	for	for	ADP
ejpam-4444	160	23	α	α	DET
ejpam-4444	160	24	≥	≥	NUM
ejpam-4444	160	25	1/8	1/8	NUM
ejpam-4444	160	26	,	,	PUNCT
ejpam-4444	160	27	it	it	PRON
ejpam-4444	160	28	is	be	AUX
ejpam-4444	160	29	sufficient	sufficient	ADJ
ejpam-4444	160	30	to	to	PART
ejpam-4444	160	31	prove	prove	VERB
ejpam-4444	160	32	instead	instead	ADV
ejpam-4444	160	33	the	the	DET
ejpam-4444	160	34	inequality	inequality	PROPN
ejpam-4444	160	35	l−1/2(1	l−1/2(1	PROPN
ejpam-4444	160	36	,	,	PUNCT
ejpam-4444	160	37	t	t	PROPN
ejpam-4444	160	38	)	)	PUNCT
ejpam-4444	160	39	>	>	X
ejpam-4444	161	1	αc(1	αc(1	PROPN
ejpam-4444	161	2	,	,	PUNCT
ejpam-4444	161	3	t	t	PROPN
ejpam-4444	161	4	)	)	PUNCT
ejpam-4444	162	1	+	+	CCONJ
ejpam-4444	162	2	(	(	PUNCT
ejpam-4444	162	3	1−	1−	NUM
ejpam-4444	162	4	α)h(1	α)h(1	NOUN
ejpam-4444	162	5	,	,	PUNCT
ejpam-4444	162	6	t	t	PROPN
ejpam-4444	162	7	)	)	PUNCT
ejpam-4444	162	8	or	or	CCONJ
ejpam-4444	162	9	(	(	PUNCT
ejpam-4444	162	10	1−	1−	NUM
ejpam-4444	162	11	4α	4α	NOUN
ejpam-4444	162	12	)	)	PUNCT
ejpam-4444	163	1	√	√	PROPN
ejpam-4444	163	2	t	t	NOUN
ejpam-4444	163	3	2	2	NUM
ejpam-4444	164	1	+	+	CCONJ
ejpam-4444	164	2	4(1−	4(1−	NUM
ejpam-4444	164	3	2α	2α	NOUN
ejpam-4444	164	4	)	)	PUNCT
ejpam-4444	164	5	√	√	NUM
ejpam-4444	164	6	t+	t+	PRON
ejpam-4444	164	7	(	(	PUNCT
ejpam-4444	164	8	1−	1−	NUM
ejpam-4444	164	9	4α	4α	NOUN
ejpam-4444	164	10	)	)	PUNCT
ejpam-4444	164	11	>	>	X
ejpam-4444	165	1	0	0	X
ejpam-4444	165	2	.	.	NOUN
ejpam-4444	165	3	which	which	PRON
ejpam-4444	165	4	is	be	AUX
ejpam-4444	165	5	true	true	ADJ
ejpam-4444	165	6	for	for	ADP
ejpam-4444	165	7	t	t	PROPN
ejpam-4444	165	8	>	>	X
ejpam-4444	165	9	1	1	NUM
ejpam-4444	165	10	and	and	CCONJ
ejpam-4444	165	11	α	α	NOUN
ejpam-4444	165	12	∈	∈	PROPN
ejpam-4444	166	1	[	[	X
ejpam-4444	166	2	1/8	1/8	NUM
ejpam-4444	166	3	,	,	PUNCT
ejpam-4444	166	4	1/4	1/4	NUM
ejpam-4444	166	5	)	)	PUNCT
ejpam-4444	166	6	.	.	PUNCT
ejpam-4444	167	1	2.3	2.3	NUM
ejpam-4444	167	2	)	)	PUNCT
ejpam-4444	167	3	case	case	NOUN
ejpam-4444	167	4	α	α	X
ejpam-4444	167	5	∈	∈	PROPN
ejpam-4444	168	1	[	[	X
ejpam-4444	168	2	1/4	1/4	NUM
ejpam-4444	168	3	,	,	PUNCT
ejpam-4444	168	4	1/3	1/3	NUM
ejpam-4444	168	5	):	):	PUNCT
ejpam-4444	168	6	monotonicity	monotonicity	NOUN
ejpam-4444	168	7	of	of	ADP
ejpam-4444	168	8	lp	lp	PROPN
ejpam-4444	168	9	and	and	CCONJ
ejpam-4444	168	10	lemma	lemma	PROPN
ejpam-4444	168	11	3	3	NUM
ejpam-4444	168	12	imply	imply	NOUN
ejpam-4444	168	13	that	that	PRON
ejpam-4444	168	14	l4α−1(1	l4α−1(1	NOUN
ejpam-4444	168	15	,	,	PUNCT
ejpam-4444	168	16	t	t	PROPN
ejpam-4444	168	17	)	)	PUNCT
ejpam-4444	168	18	≥	≥	NOUN
ejpam-4444	168	19	l0(1	l0(1	PROPN
ejpam-4444	168	20	,	,	PUNCT
ejpam-4444	168	21	t	t	PROPN
ejpam-4444	168	22	)	)	PUNCT
ejpam-4444	168	23	>	>	X
ejpam-4444	169	1	l−1/2(1	l−1/2(1	PROPN
ejpam-4444	169	2	,	,	PUNCT
ejpam-4444	169	3	t	t	PROPN
ejpam-4444	169	4	)	)	PUNCT
ejpam-4444	169	5	for	for	ADP
ejpam-4444	169	6	α	α	PRON
ejpam-4444	169	7	≥	≥	NUM
ejpam-4444	169	8	1/4	1/4	NUM
ejpam-4444	169	9	,	,	PUNCT
ejpam-4444	169	10	l0(1	l0(1	PROPN
ejpam-4444	169	11	,	,	PUNCT
ejpam-4444	169	12	t	t	PROPN
ejpam-4444	169	13	)	)	PUNCT
ejpam-4444	169	14	=	=	PUNCT
ejpam-4444	169	15	(	(	PUNCT
ejpam-4444	169	16	1	1	NUM
ejpam-4444	169	17	/	/	SYM
ejpam-4444	169	18	e)t1	e)t1	NOUN
ejpam-4444	169	19	+	+	CCONJ
ejpam-4444	169	20	1	1	NUM
ejpam-4444	169	21	t−1	t−1	PROPN
ejpam-4444	169	22	>	>	X
ejpam-4444	169	23	t	t	PROPN
ejpam-4444	169	24	/	/	SYM
ejpam-4444	169	25	e	e	PROPN
ejpam-4444	169	26	,	,	PUNCT
ejpam-4444	169	27	(	(	PUNCT
ejpam-4444	169	28	1/3)c(1	1/3)c(1	NUM
ejpam-4444	169	29	,	,	PUNCT
ejpam-4444	169	30	t	t	PROPN
ejpam-4444	169	31	)	)	PUNCT
ejpam-4444	169	32	+	+	CCONJ
ejpam-4444	169	33	(	(	PUNCT
ejpam-4444	169	34	2/3)h(1	2/3)h(1	NUM
ejpam-4444	169	35	,	,	PUNCT
ejpam-4444	169	36	t	t	PROPN
ejpam-4444	169	37	)	)	PUNCT
ejpam-4444	169	38	>	>	X
ejpam-4444	169	39	αc(1	αc(1	PROPN
ejpam-4444	169	40	,	,	PUNCT
ejpam-4444	169	41	t	t	PROPN
ejpam-4444	169	42	)	)	PUNCT
ejpam-4444	169	43	+	+	CCONJ
ejpam-4444	169	44	(	(	PUNCT
ejpam-4444	169	45	1−	1−	NUM
ejpam-4444	169	46	α)h(1	α)h(1	NOUN
ejpam-4444	169	47	,	,	PUNCT
ejpam-4444	169	48	t	t	PROPN
ejpam-4444	169	49	)	)	PUNCT
ejpam-4444	169	50	for	for	ADP
ejpam-4444	169	51	α	α	PRON
ejpam-4444	169	52	∈	∈	PROPN
ejpam-4444	170	1	[	[	X
ejpam-4444	170	2	1/4	1/4	NUM
ejpam-4444	170	3	,	,	PUNCT
ejpam-4444	170	4	1/3	1/3	NUM
ejpam-4444	170	5	)	)	PUNCT
ejpam-4444	170	6	.	.	PUNCT
ejpam-4444	171	1	to	to	PART
ejpam-4444	171	2	prove	prove	VERB
ejpam-4444	171	3	this	this	DET
ejpam-4444	171	4	case	case	NOUN
ejpam-4444	171	5	,	,	PUNCT
ejpam-4444	171	6	it	it	PRON
ejpam-4444	171	7	is	be	AUX
ejpam-4444	171	8	thus	thus	ADV
ejpam-4444	171	9	sufficient	sufficient	ADJ
ejpam-4444	171	10	to	to	PART
ejpam-4444	171	11	show	show	VERB
ejpam-4444	171	12	that	that	SCONJ
ejpam-4444	171	13	there	there	PRON
ejpam-4444	171	14	exist	exist	VERB
ejpam-4444	171	15	t1	t1	NOUN
ejpam-4444	171	16	<	<	X
ejpam-4444	171	17	t2	t2	PROPN
ejpam-4444	171	18	<	<	X
ejpam-4444	171	19	t3	t3	PROPN
ejpam-4444	171	20	s.t	s.t	PROPN
ejpam-4444	171	21	.	.	PUNCT
ejpam-4444	172	1	(	(	PUNCT
ejpam-4444	172	2	i	i	NOUN
ejpam-4444	172	3	)	)	PUNCT
ejpam-4444	172	4	l−1/2(1	l−1/2(1	PROPN
ejpam-4444	172	5	,	,	PUNCT
ejpam-4444	172	6	t	t	PROPN
ejpam-4444	172	7	)	)	PUNCT
ejpam-4444	172	8	>	>	X
ejpam-4444	172	9	(	(	PUNCT
ejpam-4444	172	10	1/3)c(1	1/3)c(1	NUM
ejpam-4444	172	11	,	,	PUNCT
ejpam-4444	172	12	t	t	PROPN
ejpam-4444	172	13	)	)	PUNCT
ejpam-4444	173	1	+	+	CCONJ
ejpam-4444	173	2	(	(	PUNCT
ejpam-4444	173	3	2/3)h(1	2/3)h(1	NUM
ejpam-4444	173	4	,	,	PUNCT
ejpam-4444	173	5	t	t	PROPN
ejpam-4444	173	6	)	)	PUNCT
ejpam-4444	173	7	,	,	PUNCT
ejpam-4444	173	8	1	1	NUM
ejpam-4444	173	9	<	<	X
ejpam-4444	173	10	t	t	X
ejpam-4444	173	11	<	<	X
ejpam-4444	173	12	t2	t2	PROPN
ejpam-4444	173	13	;	;	PUNCT
ejpam-4444	173	14	(	(	PUNCT
ejpam-4444	173	15	ii	ii	NOUN
ejpam-4444	173	16	)	)	PUNCT
ejpam-4444	173	17	t	t	PROPN
ejpam-4444	173	18	/	/	SYM
ejpam-4444	173	19	e	e	X
ejpam-4444	173	20	>	>	X
ejpam-4444	173	21	(	(	PUNCT
ejpam-4444	173	22	1/3)c(1	1/3)c(1	NUM
ejpam-4444	173	23	,	,	PUNCT
ejpam-4444	173	24	t	t	PROPN
ejpam-4444	173	25	)	)	PUNCT
ejpam-4444	173	26	+	+	CCONJ
ejpam-4444	173	27	(	(	PUNCT
ejpam-4444	173	28	2/3)h(1	2/3)h(1	NUM
ejpam-4444	173	29	,	,	PUNCT
ejpam-4444	173	30	t	t	PROPN
ejpam-4444	173	31	)	)	PUNCT
ejpam-4444	173	32	,	,	PUNCT
ejpam-4444	173	33	t3	t3	PROPN
ejpam-4444	173	34	<	<	X
ejpam-4444	173	35	t	t	PROPN
ejpam-4444	173	36	;	;	PUNCT
ejpam-4444	173	37	(	(	PUNCT
ejpam-4444	173	38	iii	iii	X
ejpam-4444	173	39	)	)	PUNCT
ejpam-4444	173	40	l0(1	l0(1	PROPN
ejpam-4444	173	41	,	,	PUNCT
ejpam-4444	173	42	t	t	PROPN
ejpam-4444	173	43	)	)	PUNCT
ejpam-4444	173	44	>	>	X
ejpam-4444	173	45	(	(	PUNCT
ejpam-4444	173	46	1/3)c(1	1/3)c(1	NUM
ejpam-4444	173	47	,	,	PUNCT
ejpam-4444	173	48	t	t	PROPN
ejpam-4444	173	49	)	)	PUNCT
ejpam-4444	173	50	+	+	CCONJ
ejpam-4444	173	51	(	(	PUNCT
ejpam-4444	173	52	2/3)h(1	2/3)h(1	NUM
ejpam-4444	173	53	,	,	PUNCT
ejpam-4444	173	54	t	t	PROPN
ejpam-4444	173	55	)	)	PUNCT
ejpam-4444	173	56	,	,	PUNCT
ejpam-4444	173	57	t1	t1	NOUN
ejpam-4444	173	58	<	<	X
ejpam-4444	173	59	t	t	PROPN
ejpam-4444	173	60	≤	≤	PUNCT
ejpam-4444	173	61	t3	t3	PROPN
ejpam-4444	173	62	.	.	PUNCT
ejpam-4444	174	1	since	since	SCONJ
ejpam-4444	174	2	the	the	DET
ejpam-4444	174	3	inequality	inequality	NOUN
ejpam-4444	174	4	in	in	ADP
ejpam-4444	174	5	(	(	PUNCT
ejpam-4444	174	6	i	i	NOUN
ejpam-4444	174	7	)	)	PUNCT
ejpam-4444	174	8	is	be	AUX
ejpam-4444	174	9	just	just	ADV
ejpam-4444	174	10	1	1	NUM
ejpam-4444	174	11	+	+	SYM
ejpam-4444	174	12	2	2	NUM
ejpam-4444	174	13	√	√	NUM
ejpam-4444	174	14	t+	t+	NOUN
ejpam-4444	174	15	t	t	PROPN
ejpam-4444	174	16	4	4	NUM
ejpam-4444	174	17	>	>	NOUN
ejpam-4444	174	18	t2	t2	PROPN
ejpam-4444	174	19	+	+	CCONJ
ejpam-4444	174	20	4t+	4t+	NUM
ejpam-4444	174	21	1	1	NUM
ejpam-4444	174	22	3(t+	3(t+	NUM
ejpam-4444	174	23	1	1	NUM
ejpam-4444	174	24	)	)	PUNCT
ejpam-4444	174	25	or	or	CCONJ
ejpam-4444	174	26	√	√	NUM
ejpam-4444	174	27	t	t	NOUN
ejpam-4444	174	28	2	2	NUM
ejpam-4444	174	29	−	−	PROPN
ejpam-4444	174	30	4	4	NUM
ejpam-4444	174	31	√	√	NOUN
ejpam-4444	174	32	t+	t+	NOUN
ejpam-4444	174	33	1	1	NUM
ejpam-4444	174	34	<	<	X
ejpam-4444	174	35	0	0	NUM
ejpam-4444	174	36	,	,	PUNCT
ejpam-4444	174	37	which	which	PRON
ejpam-4444	174	38	is	be	AUX
ejpam-4444	174	39	true	true	ADJ
ejpam-4444	174	40	for	for	ADP
ejpam-4444	174	41	1	1	NUM
ejpam-4444	174	42	<	<	X
ejpam-4444	174	43	t	t	X
ejpam-4444	174	44	<	<	X
ejpam-4444	174	45	(	(	PUNCT
ejpam-4444	174	46	2	2	NUM
ejpam-4444	174	47	+	+	CCONJ
ejpam-4444	174	48	√	√	NUM
ejpam-4444	174	49	3)2	3)2	NUM
ejpam-4444	175	1	and	and	CCONJ
ejpam-4444	175	2	we	we	PRON
ejpam-4444	175	3	choose	choose	VERB
ejpam-4444	175	4	t2	t2	NOUN
ejpam-4444	175	5	=	=	SYM
ejpam-4444	175	6	(	(	PUNCT
ejpam-4444	175	7	2	2	NUM
ejpam-4444	175	8	+	+	CCONJ
ejpam-4444	175	9	√	√	PROPN
ejpam-4444	175	10	3)2	3)2	NUM
ejpam-4444	176	1	≈	≈	PROPN
ejpam-4444	176	2	13.92	13.92	NUM
ejpam-4444	176	3	so	so	SCONJ
ejpam-4444	176	4	that	that	SCONJ
ejpam-4444	176	5	(	(	PUNCT
ejpam-4444	176	6	i	i	NOUN
ejpam-4444	176	7	)	)	PUNCT
ejpam-4444	176	8	is	be	AUX
ejpam-4444	176	9	valid	valid	ADJ
ejpam-4444	176	10	.	.	PUNCT
ejpam-4444	177	1	now	now	ADV
ejpam-4444	177	2	,	,	PUNCT
ejpam-4444	177	3	consider	consider	VERB
ejpam-4444	177	4	the	the	DET
ejpam-4444	177	5	inequality	inequality	NOUN
ejpam-4444	177	6	in	in	ADP
ejpam-4444	177	7	(	(	PUNCT
ejpam-4444	177	8	ii	ii	NOUN
ejpam-4444	177	9	)	)	PUNCT
ejpam-4444	177	10	or	or	CCONJ
ejpam-4444	177	11	t	t	PROPN
ejpam-4444	177	12	e	e	X
ejpam-4444	177	13	>	>	X
ejpam-4444	177	14	t2	t2	PROPN
ejpam-4444	177	15	+	+	CCONJ
ejpam-4444	177	16	4t+	4t+	NUM
ejpam-4444	177	17	1	1	NUM
ejpam-4444	177	18	3(t+	3(t+	NUM
ejpam-4444	177	19	1	1	NUM
ejpam-4444	177	20	)	)	PUNCT
ejpam-4444	177	21	or	or	CCONJ
ejpam-4444	177	22	(	(	PUNCT
ejpam-4444	177	23	3−	3−	NUM
ejpam-4444	177	24	e)t2	e)t2	PROPN
ejpam-4444	177	25	+	+	CCONJ
ejpam-4444	177	26	(	(	PUNCT
ejpam-4444	177	27	3−	3−	NUM
ejpam-4444	177	28	4e)t−	4e)t−	NUM
ejpam-4444	177	29	e	e	NOUN
ejpam-4444	177	30	>	>	X
ejpam-4444	177	31	0	0	PROPN
ejpam-4444	177	32	,	,	PUNCT
ejpam-4444	177	33	which	which	PRON
ejpam-4444	177	34	is	be	AUX
ejpam-4444	177	35	true	true	ADJ
ejpam-4444	177	36	for	for	ADP
ejpam-4444	177	37	t	t	PROPN
ejpam-4444	177	38	>	>	X
ejpam-4444	178	1	4e−	4e−	NUM
ejpam-4444	178	2	3	3	NUM
ejpam-4444	178	3	+	+	CCONJ
ejpam-4444	178	4	√	√	PROPN
ejpam-4444	178	5	12e2	12e2	NUM
ejpam-4444	178	6	−	−	NOUN
ejpam-4444	178	7	12e+	12e+	NUM
ejpam-4444	178	8	9	9	NUM
ejpam-4444	178	9	6−	6−	NUM
ejpam-4444	178	10	2e	2e	NOUN
ejpam-4444	178	11	≈	≈	PROPN
ejpam-4444	178	12	28.28	28.28	NUM
ejpam-4444	178	13	.	.	PUNCT
ejpam-4444	179	1	a.	a.	NOUN
ejpam-4444	179	2	sonubon	sonubon	PROPN
ejpam-4444	179	3	,	,	PUNCT
ejpam-4444	179	4	s.	s.	PROPN
ejpam-4444	179	5	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	179	6	,	,	PUNCT
ejpam-4444	179	7	k.	k.	PROPN
ejpam-4444	179	8	nonlaopon	nonlaopon	ADV
ejpam-4444	179	9	/	/	SYM
ejpam-4444	179	10	eur	eur	PROPN
ejpam-4444	179	11	.	.	PUNCT
ejpam-4444	180	1	j.	j.	PROPN
ejpam-4444	180	2	pure	pure	PROPN
ejpam-4444	180	3	appl	appl	PROPN
ejpam-4444	180	4	.	.	PROPN
ejpam-4444	180	5	math	math	PROPN
ejpam-4444	180	6	,	,	PUNCT
ejpam-4444	180	7	15	15	NUM
ejpam-4444	180	8	(	(	PUNCT
ejpam-4444	180	9	3	3	NUM
ejpam-4444	180	10	)	)	PUNCT
ejpam-4444	180	11	(	(	PUNCT
ejpam-4444	180	12	2022	2022	NUM
ejpam-4444	180	13	)	)	PUNCT
ejpam-4444	180	14	,	,	PUNCT
ejpam-4444	180	15	1120	1120	NUM
ejpam-4444	180	16	-	-	SYM
ejpam-4444	180	17	1143	1143	NUM
ejpam-4444	180	18	1128	1128	NUM
ejpam-4444	180	19	hence	hence	ADV
ejpam-4444	180	20	,	,	PUNCT
ejpam-4444	180	21	we	we	PRON
ejpam-4444	180	22	choose	choose	VERB
ejpam-4444	180	23	t3	t3	PROPN
ejpam-4444	180	24	to	to	PART
ejpam-4444	180	25	be	be	AUX
ejpam-4444	180	26	the	the	DET
ejpam-4444	180	27	right	right	ADJ
ejpam-4444	180	28	-	-	PUNCT
ejpam-4444	180	29	side	side	NOUN
ejpam-4444	180	30	number	number	NOUN
ejpam-4444	180	31	so	so	SCONJ
ejpam-4444	180	32	that	that	SCONJ
ejpam-4444	180	33	(	(	PUNCT
ejpam-4444	180	34	ii	ii	NOUN
ejpam-4444	180	35	)	)	PUNCT
ejpam-4444	180	36	is	be	AUX
ejpam-4444	180	37	valid	valid	ADJ
ejpam-4444	180	38	.	.	PUNCT
ejpam-4444	181	1	now	now	ADV
ejpam-4444	181	2	,	,	PUNCT
ejpam-4444	181	3	we	we	PRON
ejpam-4444	181	4	consider	consider	VERB
ejpam-4444	181	5	t	t	NOUN
ejpam-4444	181	6	≤	≤	NUM
ejpam-4444	181	7	t3	t3	PROPN
ejpam-4444	181	8	.	.	PUNCT
ejpam-4444	182	1	since	since	SCONJ
ejpam-4444	182	2	t1/(t−1	t1/(t−1	NUM
ejpam-4444	182	3	)	)	PUNCT
ejpam-4444	182	4	is	be	AUX
ejpam-4444	182	5	a	a	DET
ejpam-4444	182	6	decreasing	decrease	VERB
ejpam-4444	182	7	function	function	NOUN
ejpam-4444	182	8	for	for	ADP
ejpam-4444	182	9	t	t	PROPN
ejpam-4444	182	10	>	>	X
ejpam-4444	182	11	1	1	NUM
ejpam-4444	182	12	,	,	PUNCT
ejpam-4444	182	13	we	we	PRON
ejpam-4444	182	14	have	have	VERB
ejpam-4444	182	15	(	(	PUNCT
ejpam-4444	182	16	1	1	NUM
ejpam-4444	182	17	/	/	SYM
ejpam-4444	182	18	e)t1	e)t1	PRON
ejpam-4444	182	19	+	+	CCONJ
ejpam-4444	182	20	1	1	NUM
ejpam-4444	182	21	t−1	t−1	PROPN
ejpam-4444	182	22	≥	≥	NOUN
ejpam-4444	182	23	t	t	PROPN
ejpam-4444	182	24	/	/	SYM
ejpam-4444	182	25	c	c	PROPN
ejpam-4444	182	26	where	where	SCONJ
ejpam-4444	182	27	c	c	NOUN
ejpam-4444	182	28	=	=	SYM
ejpam-4444	182	29	e	e	X
ejpam-4444	182	30	/	/	SYM
ejpam-4444	182	31	t3	t3	PROPN
ejpam-4444	182	32	1/(t3−1	1/(t3−1	NUM
ejpam-4444	182	33	)	)	PUNCT
ejpam-4444	182	34	.	.	PUNCT
ejpam-4444	183	1	to	to	PART
ejpam-4444	183	2	find	find	VERB
ejpam-4444	183	3	t1	t1	NOUN
ejpam-4444	183	4	for	for	ADP
ejpam-4444	183	5	(	(	PUNCT
ejpam-4444	183	6	iii	iii	NOUN
ejpam-4444	183	7	)	)	PUNCT
ejpam-4444	183	8	,	,	PUNCT
ejpam-4444	183	9	it	it	PRON
ejpam-4444	183	10	is	be	AUX
ejpam-4444	183	11	enough	enough	ADJ
ejpam-4444	183	12	to	to	PART
ejpam-4444	183	13	find	find	VERB
ejpam-4444	183	14	it	it	PRON
ejpam-4444	183	15	from	from	ADP
ejpam-4444	183	16	t	t	PROPN
ejpam-4444	183	17	c	c	PROPN
ejpam-4444	183	18	>	>	X
ejpam-4444	183	19	t2	t2	PROPN
ejpam-4444	183	20	+	+	CCONJ
ejpam-4444	183	21	4t+	4t+	NUM
ejpam-4444	183	22	1	1	NUM
ejpam-4444	183	23	3(t+	3(t+	NUM
ejpam-4444	183	24	1	1	NUM
ejpam-4444	183	25	)	)	PUNCT
ejpam-4444	183	26	or	or	CCONJ
ejpam-4444	183	27	(	(	PUNCT
ejpam-4444	183	28	3−	3−	PROPN
ejpam-4444	183	29	c)t2	c)t2	PROPN
ejpam-4444	183	30	+	+	CCONJ
ejpam-4444	183	31	(	(	PUNCT
ejpam-4444	183	32	3−	3−	NUM
ejpam-4444	183	33	4c)t−	4c)t−	NUM
ejpam-4444	183	34	e	e	NOUN
ejpam-4444	183	35	>	>	X
ejpam-4444	183	36	0	0	PROPN
ejpam-4444	183	37	,	,	PUNCT
ejpam-4444	183	38	which	which	PRON
ejpam-4444	183	39	is	be	AUX
ejpam-4444	183	40	true	true	ADJ
ejpam-4444	183	41	for	for	ADP
ejpam-4444	183	42	t	t	PROPN
ejpam-4444	183	43	>	>	X
ejpam-4444	183	44	4c−	4c−	PROPN
ejpam-4444	183	45	3	3	NUM
ejpam-4444	183	46	+	+	CCONJ
ejpam-4444	183	47	√	√	PROPN
ejpam-4444	184	1	12c2	12c2	NUM
ejpam-4444	184	2	−	−	NUM
ejpam-4444	184	3	12c+	12c+	NUM
ejpam-4444	184	4	9	9	NUM
ejpam-4444	184	5	6−	6−	NUM
ejpam-4444	184	6	2c	2c	NUM
ejpam-4444	185	1	≈	≈	PROPN
ejpam-4444	185	2	11.47	11.47	NUM
ejpam-4444	185	3	.	.	PUNCT
ejpam-4444	186	1	we	we	PRON
ejpam-4444	186	2	therefore	therefore	ADV
ejpam-4444	186	3	choose	choose	VERB
ejpam-4444	186	4	t1	t1	PROPN
ejpam-4444	186	5	=	=	PUNCT
ejpam-4444	186	6	4c−3	4c−3	NUM
ejpam-4444	187	1	+	+	CCONJ
ejpam-4444	187	2	√	√	NUM
ejpam-4444	187	3	12c2−12c+9	12c2−12c+9	NUM
ejpam-4444	187	4	6−2c	6−2c	NUM
ejpam-4444	187	5	so	so	SCONJ
ejpam-4444	187	6	that	that	SCONJ
ejpam-4444	187	7	(	(	PUNCT
ejpam-4444	187	8	iii	iii	NOUN
ejpam-4444	187	9	)	)	PUNCT
ejpam-4444	187	10	is	be	AUX
ejpam-4444	187	11	valid	valid	ADJ
ejpam-4444	187	12	.	.	PUNCT
ejpam-4444	188	1	now	now	ADV
ejpam-4444	188	2	t1	t1	VERB
ejpam-4444	188	3	<	<	X
ejpam-4444	188	4	t2	t2	PROPN
ejpam-4444	188	5	<	<	X
ejpam-4444	188	6	t3	t3	PROPN
ejpam-4444	188	7	and	and	CCONJ
ejpam-4444	188	8	satisfy	satisfy	NOUN
ejpam-4444	188	9	(	(	PUNCT
ejpam-4444	188	10	i	i	NOUN
ejpam-4444	188	11	)	)	PUNCT
ejpam-4444	188	12	,	,	PUNCT
ejpam-4444	188	13	(	(	PUNCT
ejpam-4444	188	14	ii	ii	NOUN
ejpam-4444	188	15	)	)	PUNCT
ejpam-4444	188	16	and	and	CCONJ
ejpam-4444	188	17	(	(	PUNCT
ejpam-4444	188	18	iii	iii	NOUN
ejpam-4444	188	19	)	)	PUNCT
ejpam-4444	188	20	.	.	PUNCT
ejpam-4444	189	1	2.4	2.4	NUM
ejpam-4444	189	2	)	)	PUNCT
ejpam-4444	189	3	case	case	NOUN
ejpam-4444	189	4	α	α	X
ejpam-4444	189	5	∈	∈	PROPN
ejpam-4444	189	6	(	(	PUNCT
ejpam-4444	189	7	0	0	NUM
ejpam-4444	189	8	,	,	PUNCT
ejpam-4444	189	9	1/8	1/8	NUM
ejpam-4444	189	10	):	):	PUNCT
ejpam-4444	189	11	monotonicity	monotonicity	NOUN
ejpam-4444	189	12	of	of	ADP
ejpam-4444	189	13	lp	lp	PROPN
ejpam-4444	189	14	implies	imply	VERB
ejpam-4444	189	15	that	that	SCONJ
ejpam-4444	189	16	l4α−1(1	l4α−1(1	NOUN
ejpam-4444	189	17	,	,	PUNCT
ejpam-4444	189	18	t	t	PROPN
ejpam-4444	189	19	)	)	PUNCT
ejpam-4444	189	20	>	>	X
ejpam-4444	189	21	l−1(1	l−1(1	PROPN
ejpam-4444	189	22	,	,	PUNCT
ejpam-4444	189	23	t	t	PROPN
ejpam-4444	189	24	)	)	PUNCT
ejpam-4444	189	25	for	for	ADP
ejpam-4444	189	26	α	α	PROPN
ejpam-4444	189	27	>	>	X
ejpam-4444	189	28	0	0	PROPN
ejpam-4444	189	29	.	.	PUNCT
ejpam-4444	190	1	hence	hence	ADV
ejpam-4444	190	2	we	we	PRON
ejpam-4444	190	3	will	will	AUX
ejpam-4444	190	4	seek	seek	VERB
ejpam-4444	190	5	t	t	NOUN
ejpam-4444	190	6	which	which	PRON
ejpam-4444	190	7	satisfies	satisfie	NOUN
ejpam-4444	190	8	l−1(1	l−1(1	PROPN
ejpam-4444	190	9	,	,	PUNCT
ejpam-4444	190	10	t	t	PROPN
ejpam-4444	190	11	)	)	PUNCT
ejpam-4444	190	12	>	>	X
ejpam-4444	191	1	αc(1	αc(1	PROPN
ejpam-4444	191	2	,	,	PUNCT
ejpam-4444	191	3	t	t	PROPN
ejpam-4444	191	4	)	)	PUNCT
ejpam-4444	192	1	+	+	CCONJ
ejpam-4444	192	2	(	(	PUNCT
ejpam-4444	192	3	1−	1−	NUM
ejpam-4444	192	4	α)h(1	α)h(1	NOUN
ejpam-4444	192	5	,	,	PUNCT
ejpam-4444	192	6	t	t	PROPN
ejpam-4444	192	7	)	)	PUNCT
ejpam-4444	192	8	or	or	CCONJ
ejpam-4444	192	9	t−	t−	PROPN
ejpam-4444	192	10	1	1	NUM
ejpam-4444	192	11	ln	ln	NOUN
ejpam-4444	192	12	t	t	X
ejpam-4444	192	13	>	>	X
ejpam-4444	192	14	α	α	PROPN
ejpam-4444	192	15	(	(	PUNCT
ejpam-4444	192	16	t2	t2	NOUN
ejpam-4444	192	17	+	+	CCONJ
ejpam-4444	192	18	1	1	NUM
ejpam-4444	192	19	t+	t+	NUM
ejpam-4444	192	20	1	1	NUM
ejpam-4444	192	21	)	)	PUNCT
ejpam-4444	192	22	+	+	CCONJ
ejpam-4444	192	23	(	(	PUNCT
ejpam-4444	192	24	1−	1−	NUM
ejpam-4444	192	25	α	α	NOUN
ejpam-4444	192	26	)	)	PUNCT
ejpam-4444	192	27	(	(	PUNCT
ejpam-4444	192	28	2	2	NUM
ejpam-4444	192	29	t	t	NOUN
ejpam-4444	192	30	t+	t+	PUNCT
ejpam-4444	192	31	1	1	NUM
ejpam-4444	192	32	)	)	PUNCT
ejpam-4444	192	33	or	or	CCONJ
ejpam-4444	192	34	1	1	NUM
ejpam-4444	192	35	t	t	NOUN
ejpam-4444	192	36	exp	exp	NOUN
ejpam-4444	192	37	[	[	PUNCT
ejpam-4444	192	38	t2	t2	NOUN
ejpam-4444	192	39	−	−	PROPN
ejpam-4444	192	40	1	1	NUM
ejpam-4444	192	41	α(t2	α(t2	NOUN
ejpam-4444	192	42	+	+	ADP
ejpam-4444	192	43	1	1	NUM
ejpam-4444	192	44	)	)	PUNCT
ejpam-4444	193	1	+	+	CCONJ
ejpam-4444	193	2	2(1−	2(1−	NUM
ejpam-4444	193	3	α)t	α)t	NOUN
ejpam-4444	193	4	]	]	PUNCT
ejpam-4444	193	5	>	>	X
ejpam-4444	193	6	1	1	X
ejpam-4444	193	7	.	.	X
ejpam-4444	194	1	setting	set	VERB
ejpam-4444	194	2	f(t	f(t	NOUN
ejpam-4444	194	3	)	)	PUNCT
ejpam-4444	195	1	:	:	PUNCT
ejpam-4444	195	2	=	=	SYM
ejpam-4444	195	3	t−1	t−1	PROPN
ejpam-4444	195	4	exp	exp	NOUN
ejpam-4444	195	5	[	[	PUNCT
ejpam-4444	195	6	t2−1	t2−1	ADP
ejpam-4444	195	7	α(t2	α(t2	ADJ
ejpam-4444	195	8	+	+	NOUN
ejpam-4444	195	9	1)+2(1−α)t	1)+2(1−α)t	NUM
ejpam-4444	195	10	]	]	PUNCT
ejpam-4444	195	11	,	,	PUNCT
ejpam-4444	195	12	we	we	PRON
ejpam-4444	195	13	can	can	AUX
ejpam-4444	195	14	see	see	VERB
ejpam-4444	195	15	that	that	DET
ejpam-4444	195	16	f(1	f(1	PROPN
ejpam-4444	195	17	)	)	PUNCT
ejpam-4444	195	18	=	=	SYM
ejpam-4444	195	19	1	1	NUM
ejpam-4444	195	20	and	and	CCONJ
ejpam-4444	195	21	use	use	VERB
ejpam-4444	195	22	lemma	lemma	PROPN
ejpam-4444	195	23	2	2	NUM
ejpam-4444	195	24	to	to	PART
ejpam-4444	195	25	conclude	conclude	VERB
ejpam-4444	195	26	that	that	SCONJ
ejpam-4444	195	27	f	f	PROPN
ejpam-4444	195	28	′(t	′(t	PROPN
ejpam-4444	195	29	)	)	PUNCT
ejpam-4444	195	30	>	>	X
ejpam-4444	195	31	0	0	PUNCT
ejpam-4444	196	1	where	where	SCONJ
ejpam-4444	196	2	α2t2	α2t2	PRON
ejpam-4444	196	3	−	−	PROPN
ejpam-4444	196	4	2(α2	2(α2	NUM
ejpam-4444	197	1	−	−	NOUN
ejpam-4444	198	1	3α	3α	NOUN
ejpam-4444	199	1	+	+	CCONJ
ejpam-4444	199	2	1)t	1)t	PROPN
ejpam-4444	199	3	+	+	CCONJ
ejpam-4444	199	4	α2	α2	ADJ
ejpam-4444	199	5	<	<	X
ejpam-4444	199	6	0	0	X
ejpam-4444	199	7	.	.	PUNCT
ejpam-4444	199	8	function	function	NOUN
ejpam-4444	199	9	f(t	f(t	PROPN
ejpam-4444	199	10	)	)	PUNCT
ejpam-4444	199	11	is	be	AUX
ejpam-4444	199	12	an	an	DET
ejpam-4444	199	13	increasing	increase	VERB
ejpam-4444	199	14	function	function	NOUN
ejpam-4444	199	15	when	when	SCONJ
ejpam-4444	199	16	a.	a.	NOUN
ejpam-4444	199	17	sonubon	sonubon	PROPN
ejpam-4444	199	18	,	,	PUNCT
ejpam-4444	199	19	s.	s.	PROPN
ejpam-4444	199	20	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	199	21	,	,	PUNCT
ejpam-4444	199	22	k.	k.	PROPN
ejpam-4444	199	23	nonlaopon	nonlaopon	ADV
ejpam-4444	199	24	/	/	SYM
ejpam-4444	199	25	eur	eur	PROPN
ejpam-4444	199	26	.	.	PUNCT
ejpam-4444	200	1	j.	j.	PROPN
ejpam-4444	200	2	pure	pure	PROPN
ejpam-4444	200	3	appl	appl	PROPN
ejpam-4444	200	4	.	.	PROPN
ejpam-4444	200	5	math	math	PROPN
ejpam-4444	200	6	,	,	PUNCT
ejpam-4444	200	7	15	15	NUM
ejpam-4444	200	8	(	(	PUNCT
ejpam-4444	200	9	3	3	NUM
ejpam-4444	200	10	)	)	PUNCT
ejpam-4444	200	11	(	(	PUNCT
ejpam-4444	200	12	2022	2022	NUM
ejpam-4444	200	13	)	)	PUNCT
ejpam-4444	200	14	,	,	PUNCT
ejpam-4444	200	15	1120	1120	NUM
ejpam-4444	200	16	-	-	SYM
ejpam-4444	200	17	1143	1143	NUM
ejpam-4444	200	18	1129	1129	NUM
ejpam-4444	200	19	t	t	PROPN
ejpam-4444	200	20	∈	∈	PROPN
ejpam-4444	200	21	(	(	PUNCT
ejpam-4444	200	22	(	(	PUNCT
ejpam-4444	200	23	α2	α2	ADJ
ejpam-4444	200	24	−	−	PROPN
ejpam-4444	200	25	3α+	3α+	PROPN
ejpam-4444	200	26	1)−	1)−	NUM
ejpam-4444	200	27	√	√	NOUN
ejpam-4444	200	28	−6α3	−6α3	NUM
ejpam-4444	200	29	+	+	CCONJ
ejpam-4444	200	30	11α2	11α2	NUM
ejpam-4444	200	31	−	−	NUM
ejpam-4444	200	32	6α+	6α+	NUM
ejpam-4444	200	33	1	1	NUM
ejpam-4444	200	34	α2	α2	ADJ
ejpam-4444	200	35	,	,	PUNCT
ejpam-4444	200	36	(	(	PUNCT
ejpam-4444	200	37	α2	α2	ADV
ejpam-4444	200	38	−	−	PROPN
ejpam-4444	200	39	3α+	3α+	NUM
ejpam-4444	200	40	1	1	NUM
ejpam-4444	200	41	)	)	PUNCT
ejpam-4444	201	1	+	+	CCONJ
ejpam-4444	201	2	√	√	VERB
ejpam-4444	201	3	−6α3	−6α3	NUM
ejpam-4444	201	4	+	+	CCONJ
ejpam-4444	201	5	11α2	11α2	NUM
ejpam-4444	201	6	−	−	NUM
ejpam-4444	201	7	6α+	6α+	NUM
ejpam-4444	201	8	1	1	NUM
ejpam-4444	201	9	α2	α2	ADJ
ejpam-4444	201	10	)	)	PUNCT
ejpam-4444	201	11	,	,	PUNCT
ejpam-4444	201	12	which	which	PRON
ejpam-4444	201	13	implies	imply	VERB
ejpam-4444	201	14	that	that	SCONJ
ejpam-4444	201	15	for	for	ADP
ejpam-4444	201	16	α	α	DET
ejpam-4444	201	17	∈	∈	PROPN
ejpam-4444	201	18	(	(	PUNCT
ejpam-4444	201	19	0	0	NUM
ejpam-4444	201	20	,	,	PUNCT
ejpam-4444	201	21	1/8	1/8	NUM
ejpam-4444	201	22	)	)	PUNCT
ejpam-4444	201	23	,	,	PUNCT
ejpam-4444	201	24	f(t	f(t	PROPN
ejpam-4444	201	25	)	)	PUNCT
ejpam-4444	201	26	>	>	X
ejpam-4444	201	27	1	1	NUM
ejpam-4444	201	28	when	when	SCONJ
ejpam-4444	201	29	t	t	PROPN
ejpam-4444	201	30	∈	∈	PROPN
ejpam-4444	201	31	(	(	PUNCT
ejpam-4444	201	32	1	1	NUM
ejpam-4444	201	33	,	,	PUNCT
ejpam-4444	201	34	α2	α2	ADJ
ejpam-4444	201	35	−	−	PROPN
ejpam-4444	201	36	3α+	3α+	NUM
ejpam-4444	201	37	1	1	NUM
ejpam-4444	201	38	α2	α2	ADJ
ejpam-4444	201	39	]	]	PUNCT
ejpam-4444	201	40	.	.	PUNCT
ejpam-4444	202	1	hence	hence	ADV
ejpam-4444	202	2	l4α−1(1	l4α−1(1	NOUN
ejpam-4444	202	3	,	,	PUNCT
ejpam-4444	202	4	t	t	PROPN
ejpam-4444	202	5	)	)	PUNCT
ejpam-4444	202	6	>	>	X
ejpam-4444	203	1	αc(1	αc(1	PROPN
ejpam-4444	203	2	,	,	PUNCT
ejpam-4444	203	3	t	t	PROPN
ejpam-4444	203	4	)	)	PUNCT
ejpam-4444	204	1	+	+	CCONJ
ejpam-4444	204	2	(	(	PUNCT
ejpam-4444	204	3	1−	1−	NUM
ejpam-4444	204	4	α)h(1	α)h(1	NOUN
ejpam-4444	204	5	,	,	PUNCT
ejpam-4444	204	6	t	t	PROPN
ejpam-4444	204	7	)	)	PUNCT
ejpam-4444	204	8	for	for	ADP
ejpam-4444	204	9	1	1	NUM
ejpam-4444	204	10	<	<	X
ejpam-4444	204	11	t	t	NOUN
ejpam-4444	204	12	≤	≤	NOUN
ejpam-4444	204	13	(	(	PUNCT
ejpam-4444	204	14	α2	α2	ADJ
ejpam-4444	204	15	−	−	PROPN
ejpam-4444	204	16	3α+	3α+	NUM
ejpam-4444	204	17	1)/α2	1)/α2	NUM
ejpam-4444	204	18	.	.	PUNCT
ejpam-4444	205	1	(	(	PUNCT
ejpam-4444	205	2	5	5	NUM
ejpam-4444	205	3	)	)	PUNCT
ejpam-4444	205	4	now	now	ADV
ejpam-4444	205	5	,	,	PUNCT
ejpam-4444	205	6	observe	observe	VERB
ejpam-4444	205	7	that	that	SCONJ
ejpam-4444	205	8	the	the	DET
ejpam-4444	205	9	qualities	quality	NOUN
ejpam-4444	205	10	[	[	PUNCT
ejpam-4444	205	11	t4α	t4α	NOUN
ejpam-4444	205	12	−	−	PROPN
ejpam-4444	205	13	1	1	NUM
ejpam-4444	205	14	4α(t−	4α(t−	NUM
ejpam-4444	205	15	1	1	NUM
ejpam-4444	205	16	)	)	PUNCT
ejpam-4444	205	17	]	]	PUNCT
ejpam-4444	205	18	1	1	NUM
ejpam-4444	205	19	4α−1	4α−1	NUM
ejpam-4444	205	20	>	>	X
ejpam-4444	205	21	t	t	PROPN
ejpam-4444	205	22	(	(	PUNCT
ejpam-4444	205	23	1	1	NUM
ejpam-4444	205	24	4α	4α	NOUN
ejpam-4444	205	25	)	)	PUNCT
ejpam-4444	205	26	1	1	NUM
ejpam-4444	205	27	4α−1	4α−1	NUM
ejpam-4444	205	28	and	and	CCONJ
ejpam-4444	205	29	αt+	αt+	ADJ
ejpam-4444	205	30	(	(	PUNCT
ejpam-4444	205	31	2−	2−	NUM
ejpam-4444	205	32	α	α	NOUN
ejpam-4444	205	33	)	)	PUNCT
ejpam-4444	205	34	>	>	X
ejpam-4444	206	1	α(1	α(1	PROPN
ejpam-4444	206	2	+	+	SYM
ejpam-4444	206	3	t2	t2	NOUN
ejpam-4444	206	4	)	)	PUNCT
ejpam-4444	207	1	+	+	CCONJ
ejpam-4444	207	2	(	(	PUNCT
ejpam-4444	207	3	1−	1−	NUM
ejpam-4444	207	4	α)(2	α)(2	NUM
ejpam-4444	207	5	t	t	NOUN
ejpam-4444	207	6	)	)	PUNCT
ejpam-4444	207	7	1	1	NUM
ejpam-4444	208	1	+	+	NUM
ejpam-4444	208	2	t	t	PROPN
ejpam-4444	208	3	hold	hold	NOUN
ejpam-4444	208	4	for	for	ADP
ejpam-4444	208	5	all	all	DET
ejpam-4444	208	6	α	α	PRON
ejpam-4444	208	7	∈	∈	NOUN
ejpam-4444	208	8	(	(	PUNCT
ejpam-4444	208	9	0	0	NUM
ejpam-4444	208	10	,	,	PUNCT
ejpam-4444	208	11	1/8	1/8	NUM
ejpam-4444	208	12	)	)	PUNCT
ejpam-4444	208	13	.	.	PUNCT
ejpam-4444	209	1	we	we	PRON
ejpam-4444	209	2	will	will	AUX
ejpam-4444	209	3	show	show	VERB
ejpam-4444	209	4	that	that	SCONJ
ejpam-4444	209	5	t	t	NOUN
ejpam-4444	209	6	(	(	PUNCT
ejpam-4444	209	7	1	1	NUM
ejpam-4444	209	8	4α	4α	NOUN
ejpam-4444	209	9	)	)	PUNCT
ejpam-4444	209	10	1	1	NUM
ejpam-4444	209	11	4α−1	4α−1	NUM
ejpam-4444	209	12	>	>	X
ejpam-4444	209	13	αt+	αt+	NOUN
ejpam-4444	209	14	(	(	PUNCT
ejpam-4444	209	15	2−	2−	NUM
ejpam-4444	209	16	α	α	NOUN
ejpam-4444	209	17	)	)	PUNCT
ejpam-4444	209	18	or	or	CCONJ
ejpam-4444	209	19	t	t	X
ejpam-4444	210	1	[	[	X
ejpam-4444	210	2	(	(	PUNCT
ejpam-4444	210	3	1	1	NUM
ejpam-4444	210	4	4α	4α	NOUN
ejpam-4444	210	5	)	)	PUNCT
ejpam-4444	210	6	1	1	NUM
ejpam-4444	210	7	4α−1	4α−1	NUM
ejpam-4444	210	8	−	−	PROPN
ejpam-4444	211	1	α	α	NOUN
ejpam-4444	211	2	]	]	PUNCT
ejpam-4444	211	3	>	>	X
ejpam-4444	211	4	2−	2−	NUM
ejpam-4444	211	5	α	α	NOUN
ejpam-4444	211	6	for	for	ADP
ejpam-4444	211	7	all	all	DET
ejpam-4444	211	8	t	t	NOUN
ejpam-4444	211	9	>	>	X
ejpam-4444	211	10	(	(	PUNCT
ejpam-4444	211	11	α2	α2	ADJ
ejpam-4444	211	12	−	−	PROPN
ejpam-4444	211	13	3α+	3α+	NUM
ejpam-4444	211	14	1)/α2	1)/α2	NUM
ejpam-4444	211	15	.	.	PUNCT
ejpam-4444	212	1	it	it	PRON
ejpam-4444	212	2	is	be	AUX
ejpam-4444	212	3	sufficient	sufficient	ADJ
ejpam-4444	212	4	to	to	PART
ejpam-4444	212	5	show	show	VERB
ejpam-4444	212	6	that	that	SCONJ
ejpam-4444	212	7	(	(	PUNCT
ejpam-4444	212	8	α2	α2	ADJ
ejpam-4444	212	9	−	−	PROPN
ejpam-4444	212	10	3α+	3α+	NUM
ejpam-4444	212	11	1	1	NUM
ejpam-4444	212	12	α2	α2	ADJ
ejpam-4444	212	13	)	)	PUNCT
ejpam-4444	213	1	[	[	X
ejpam-4444	213	2	(	(	PUNCT
ejpam-4444	213	3	1	1	NUM
ejpam-4444	213	4	4α	4α	NOUN
ejpam-4444	213	5	)	)	PUNCT
ejpam-4444	213	6	1	1	NUM
ejpam-4444	213	7	4α−1	4α−1	NUM
ejpam-4444	214	1	−	−	PROPN
ejpam-4444	214	2	α	α	NOUN
ejpam-4444	214	3	]	]	PUNCT
ejpam-4444	214	4	>	>	X
ejpam-4444	214	5	2−	2−	NUM
ejpam-4444	214	6	α	α	NOUN
ejpam-4444	214	7	or	or	CCONJ
ejpam-4444	214	8	(	(	PUNCT
ejpam-4444	214	9	1	1	NUM
ejpam-4444	214	10	4α	4α	NOUN
ejpam-4444	214	11	)	)	PUNCT
ejpam-4444	214	12	1	1	NUM
ejpam-4444	214	13	4α−1	4α−1	NUM
ejpam-4444	214	14	>	>	X
ejpam-4444	214	15	α−	α−	ADP
ejpam-4444	214	16	α2	α2	ADJ
ejpam-4444	214	17	α2	α2	PROPN
ejpam-4444	215	1	−	−	PROPN
ejpam-4444	216	1	3α+	3α+	NUM
ejpam-4444	216	2	1	1	NUM
ejpam-4444	216	3	.	.	PUNCT
ejpam-4444	217	1	however	however	ADV
ejpam-4444	217	2	,	,	PUNCT
ejpam-4444	217	3	this	this	PRON
ejpam-4444	217	4	is	be	AUX
ejpam-4444	217	5	a	a	DET
ejpam-4444	217	6	direct	direct	ADJ
ejpam-4444	217	7	consequence	consequence	NOUN
ejpam-4444	217	8	of	of	ADP
ejpam-4444	217	9	a	a	DET
ejpam-4444	217	10	simple	simple	ADJ
ejpam-4444	217	11	string	string	NOUN
ejpam-4444	217	12	of	of	ADP
ejpam-4444	217	13	inequalities	inequality	NOUN
ejpam-4444	217	14	,	,	PUNCT
ejpam-4444	217	15	(	(	PUNCT
ejpam-4444	217	16	1	1	NUM
ejpam-4444	217	17	4α	4α	NOUN
ejpam-4444	217	18	)	)	PUNCT
ejpam-4444	217	19	1	1	NUM
ejpam-4444	217	20	4α−1	4α−1	NUM
ejpam-4444	217	21	>	>	X
ejpam-4444	217	22	2α	2α	X
ejpam-4444	217	23	>	>	X
ejpam-4444	217	24	α−	α−	ADP
ejpam-4444	217	25	α2	α2	ADJ
ejpam-4444	217	26	α2	α2	PROPN
ejpam-4444	218	1	−	−	PROPN
ejpam-4444	219	1	3α+	3α+	NUM
ejpam-4444	219	2	1	1	NUM
ejpam-4444	219	3	for	for	ADP
ejpam-4444	219	4	all	all	PRON
ejpam-4444	219	5	α	α	PRON
ejpam-4444	219	6	∈	∈	NOUN
ejpam-4444	219	7	(	(	PUNCT
ejpam-4444	219	8	0	0	NUM
ejpam-4444	219	9	,	,	PUNCT
ejpam-4444	219	10	1/8	1/8	NUM
ejpam-4444	219	11	)	)	PUNCT
ejpam-4444	219	12	.	.	PUNCT
ejpam-4444	220	1	thus	thus	ADV
ejpam-4444	220	2	l4α−1(1	l4α−1(1	NOUN
ejpam-4444	220	3	,	,	PUNCT
ejpam-4444	220	4	t	t	PROPN
ejpam-4444	220	5	)	)	PUNCT
ejpam-4444	220	6	>	>	X
ejpam-4444	221	1	αc(1	αc(1	PROPN
ejpam-4444	221	2	,	,	PUNCT
ejpam-4444	221	3	t	t	PROPN
ejpam-4444	221	4	)	)	PUNCT
ejpam-4444	222	1	+	+	CCONJ
ejpam-4444	222	2	(	(	PUNCT
ejpam-4444	222	3	1−	1−	NUM
ejpam-4444	222	4	α)h(1	α)h(1	NOUN
ejpam-4444	222	5	,	,	PUNCT
ejpam-4444	222	6	t	t	PROPN
ejpam-4444	222	7	)	)	PUNCT
ejpam-4444	222	8	for	for	ADP
ejpam-4444	222	9	t	t	PROPN
ejpam-4444	222	10	>	>	X
ejpam-4444	222	11	(	(	PUNCT
ejpam-4444	222	12	α2	α2	ADJ
ejpam-4444	222	13	−	−	PROPN
ejpam-4444	222	14	3α+	3α+	NUM
ejpam-4444	222	15	1)/α2	1)/α2	NUM
ejpam-4444	222	16	.	.	PUNCT
ejpam-4444	223	1	(	(	PUNCT
ejpam-4444	223	2	6	6	NUM
ejpam-4444	223	3	)	)	PUNCT
ejpam-4444	223	4	from	from	ADP
ejpam-4444	223	5	inequalities	inequality	NOUN
ejpam-4444	223	6	(	(	PUNCT
ejpam-4444	223	7	5	5	NUM
ejpam-4444	223	8	)	)	PUNCT
ejpam-4444	223	9	and	and	CCONJ
ejpam-4444	223	10	(	(	PUNCT
ejpam-4444	223	11	6	6	NUM
ejpam-4444	223	12	)	)	PUNCT
ejpam-4444	223	13	,	,	PUNCT
ejpam-4444	223	14	we	we	PRON
ejpam-4444	223	15	conclude	conclude	VERB
ejpam-4444	223	16	that	that	PRON
ejpam-4444	223	17	for	for	ADP
ejpam-4444	223	18	α	α	PRON
ejpam-4444	223	19	∈	∈	PROPN
ejpam-4444	223	20	(	(	PUNCT
ejpam-4444	223	21	0	0	NUM
ejpam-4444	223	22	,	,	PUNCT
ejpam-4444	223	23	1/8	1/8	NUM
ejpam-4444	223	24	)	)	PUNCT
ejpam-4444	223	25	l4α−1(1	l4α−1(1	NOUN
ejpam-4444	223	26	,	,	PUNCT
ejpam-4444	223	27	t	t	PROPN
ejpam-4444	223	28	)	)	PUNCT
ejpam-4444	223	29	>	>	X
ejpam-4444	224	1	αc(1	αc(1	PROPN
ejpam-4444	224	2	,	,	PUNCT
ejpam-4444	224	3	t	t	PROPN
ejpam-4444	224	4	)	)	PUNCT
ejpam-4444	225	1	+	+	CCONJ
ejpam-4444	225	2	(	(	PUNCT
ejpam-4444	225	3	1−	1−	NUM
ejpam-4444	225	4	α)h(1	α)h(1	NOUN
ejpam-4444	225	5	,	,	PUNCT
ejpam-4444	225	6	t	t	PROPN
ejpam-4444	225	7	)	)	PUNCT
ejpam-4444	225	8	for	for	ADP
ejpam-4444	225	9	all	all	DET
ejpam-4444	225	10	t	t	PROPN
ejpam-4444	225	11	>	>	X
ejpam-4444	225	12	1	1	X
ejpam-4444	225	13	.	.	PUNCT
ejpam-4444	225	14	(	(	PUNCT
ejpam-4444	225	15	7	7	X
ejpam-4444	225	16	)	)	PUNCT
ejpam-4444	225	17	finally	finally	ADV
ejpam-4444	225	18	,	,	PUNCT
ejpam-4444	225	19	we	we	PRON
ejpam-4444	225	20	will	will	AUX
ejpam-4444	225	21	prove	prove	VERB
ejpam-4444	225	22	that	that	SCONJ
ejpam-4444	225	23	the	the	DET
ejpam-4444	225	24	parameter	parameter	NOUN
ejpam-4444	225	25	4α−	4α−	PROPN
ejpam-4444	225	26	1	1	NUM
ejpam-4444	225	27	can	can	AUX
ejpam-4444	225	28	not	not	PART
ejpam-4444	225	29	be	be	AUX
ejpam-4444	225	30	improved	improve	VERB
ejpam-4444	225	31	in	in	ADP
ejpam-4444	225	32	this	this	DET
ejpam-4444	225	33	case	case	NOUN
ejpam-4444	225	34	.	.	PUNCT
ejpam-4444	226	1	suppose	suppose	VERB
ejpam-4444	226	2	,	,	PUNCT
ejpam-4444	226	3	to	to	ADP
ejpam-4444	226	4	the	the	DET
ejpam-4444	226	5	contrary	contrary	NOUN
ejpam-4444	226	6	,	,	PUNCT
ejpam-4444	226	7	that	that	DET
ejpam-4444	226	8	inequality	inequality	NOUN
ejpam-4444	226	9	(	(	PUNCT
ejpam-4444	226	10	7	7	NUM
ejpam-4444	226	11	)	)	PUNCT
ejpam-4444	226	12	is	be	AUX
ejpam-4444	226	13	true	true	ADJ
ejpam-4444	226	14	with	with	ADP
ejpam-4444	226	15	parameter	parameter	NOUN
ejpam-4444	227	1	2[1−	2[1−	NOUN
ejpam-4444	227	2	(	(	PUNCT
ejpam-4444	227	3	−1−	−1−	NOUN
ejpam-4444	227	4	ϵ)]α+	ϵ)]α+	PROPN
ejpam-4444	227	5	(	(	PUNCT
ejpam-4444	227	6	−1−	−1−	PROPN
ejpam-4444	227	7	ϵ	ϵ	NUM
ejpam-4444	227	8	)	)	PUNCT
ejpam-4444	227	9	for	for	ADP
ejpam-4444	227	10	a	a	DET
ejpam-4444	227	11	sufficiently	sufficiently	ADV
ejpam-4444	227	12	small	small	ADJ
ejpam-4444	227	13	ϵ	ϵ	X
ejpam-4444	227	14	>	>	X
ejpam-4444	227	15	0	0	NUM
ejpam-4444	227	16	.	.	PUNCT
ejpam-4444	228	1	that	that	PRON
ejpam-4444	228	2	is	be	AUX
ejpam-4444	228	3	l2[1−(−1−ϵ)]α+(−1−ϵ)(1	l2[1−(−1−ϵ)]α+(−1−ϵ)(1	PROPN
ejpam-4444	228	4	,	,	PUNCT
ejpam-4444	228	5	t)−	t)−	PROPN
ejpam-4444	228	6	[	[	PUNCT
ejpam-4444	228	7	αc(1	αc(1	PROPN
ejpam-4444	228	8	,	,	PUNCT
ejpam-4444	228	9	t	t	PROPN
ejpam-4444	228	10	)	)	PUNCT
ejpam-4444	229	1	+	+	CCONJ
ejpam-4444	229	2	(	(	PUNCT
ejpam-4444	229	3	1−	1−	NUM
ejpam-4444	229	4	α)h(1	α)h(1	NOUN
ejpam-4444	229	5	,	,	PUNCT
ejpam-4444	229	6	t	t	PROPN
ejpam-4444	229	7	)	)	PUNCT
ejpam-4444	229	8	]	]	PUNCT
ejpam-4444	230	1	>	>	X
ejpam-4444	230	2	0	0	PUNCT
ejpam-4444	231	1	for	for	ADP
ejpam-4444	231	2	all	all	DET
ejpam-4444	231	3	t	t	PROPN
ejpam-4444	231	4	>	>	X
ejpam-4444	231	5	1	1	X
ejpam-4444	231	6	.	.	PUNCT
ejpam-4444	231	7	a.	a.	NOUN
ejpam-4444	231	8	sonubon	sonubon	PROPN
ejpam-4444	231	9	,	,	PUNCT
ejpam-4444	231	10	s.	s.	PROPN
ejpam-4444	231	11	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	231	12	,	,	PUNCT
ejpam-4444	231	13	k.	k.	PROPN
ejpam-4444	231	14	nonlaopon	nonlaopon	ADV
ejpam-4444	231	15	/	/	SYM
ejpam-4444	231	16	eur	eur	PROPN
ejpam-4444	231	17	.	.	PUNCT
ejpam-4444	232	1	j.	j.	PROPN
ejpam-4444	232	2	pure	pure	PROPN
ejpam-4444	232	3	appl	appl	PROPN
ejpam-4444	232	4	.	.	PROPN
ejpam-4444	232	5	math	math	PROPN
ejpam-4444	232	6	,	,	PUNCT
ejpam-4444	232	7	15	15	NUM
ejpam-4444	232	8	(	(	PUNCT
ejpam-4444	232	9	3	3	NUM
ejpam-4444	232	10	)	)	PUNCT
ejpam-4444	232	11	(	(	PUNCT
ejpam-4444	232	12	2022	2022	NUM
ejpam-4444	232	13	)	)	PUNCT
ejpam-4444	232	14	,	,	PUNCT
ejpam-4444	232	15	1120	1120	NUM
ejpam-4444	232	16	-	-	SYM
ejpam-4444	232	17	1143	1143	NUM
ejpam-4444	232	18	1130	1130	NUM
ejpam-4444	232	19	hence	hence	ADV
ejpam-4444	232	20	l2[1−(−1−ϵ)]α+(−1−ϵ)(1	l2[1−(−1−ϵ)]α+(−1−ϵ)(1	PROPN
ejpam-4444	232	21	,	,	PUNCT
ejpam-4444	232	22	t)−	t)−	PROPN
ejpam-4444	232	23	[	[	PUNCT
ejpam-4444	232	24	αc(1	αc(1	PROPN
ejpam-4444	232	25	,	,	PUNCT
ejpam-4444	232	26	t	t	PROPN
ejpam-4444	232	27	)	)	PUNCT
ejpam-4444	233	1	+	+	CCONJ
ejpam-4444	233	2	(	(	PUNCT
ejpam-4444	233	3	1−	1−	NUM
ejpam-4444	233	4	α)h(1	α)h(1	NOUN
ejpam-4444	233	5	,	,	PUNCT
ejpam-4444	233	6	t	t	PROPN
ejpam-4444	233	7	)	)	PUNCT
ejpam-4444	233	8	]	]	PUNCT
ejpam-4444	234	1	t	t	X
ejpam-4444	234	2	>	>	X
ejpam-4444	234	3	0	0	PUNCT
ejpam-4444	235	1	for	for	ADP
ejpam-4444	235	2	all	all	DET
ejpam-4444	235	3	t	t	PROPN
ejpam-4444	235	4	>	>	X
ejpam-4444	235	5	1	1	X
ejpam-4444	235	6	.	.	PUNCT
ejpam-4444	235	7	taking	take	VERB
ejpam-4444	235	8	limits	limit	NOUN
ejpam-4444	235	9	to	to	ADP
ejpam-4444	235	10	both	both	DET
ejpam-4444	235	11	sides	side	NOUN
ejpam-4444	235	12	of	of	ADP
ejpam-4444	235	13	the	the	DET
ejpam-4444	235	14	above	above	ADJ
ejpam-4444	235	15	inequality	inequality	NOUN
ejpam-4444	235	16	leads	lead	VERB
ejpam-4444	235	17	to	to	ADP
ejpam-4444	235	18	lim	lim	PROPN
ejpam-4444	235	19	α→	α→	PROPN
ejpam-4444	236	1	[	[	PUNCT
ejpam-4444	236	2	ϵ	ϵ	NOUN
ejpam-4444	236	3	2(2+ϵ	2(2+ϵ	NUM
ejpam-4444	236	4	)	)	PUNCT
ejpam-4444	236	5	]	]	PUNCT
ejpam-4444	237	1	+	+	CCONJ
ejpam-4444	237	2	(	(	PUNCT
ejpam-4444	237	3	lim	lim	PROPN
ejpam-4444	237	4	t→+∞	t→+∞	PROPN
ejpam-4444	237	5	l2[1−(−1−ϵ)]α+(−1−ϵ)(1	l2[1−(−1−ϵ)]α+(−1−ϵ)(1	PROPN
ejpam-4444	237	6	,	,	PUNCT
ejpam-4444	237	7	t)−	t)−	PROPN
ejpam-4444	237	8	[	[	PUNCT
ejpam-4444	237	9	αc(1	αc(1	PROPN
ejpam-4444	237	10	,	,	PUNCT
ejpam-4444	237	11	t	t	PROPN
ejpam-4444	237	12	)	)	PUNCT
ejpam-4444	237	13	+	+	CCONJ
ejpam-4444	237	14	(	(	PUNCT
ejpam-4444	237	15	1−	1−	NUM
ejpam-4444	237	16	α)h(1	α)h(1	NOUN
ejpam-4444	237	17	,	,	PUNCT
ejpam-4444	237	18	t	t	PROPN
ejpam-4444	237	19	)	)	PUNCT
ejpam-4444	237	20	]	]	PUNCT
ejpam-4444	237	21	t	t	X
ejpam-4444	237	22	)	)	PUNCT
ejpam-4444	237	23	=	=	PUNCT
ejpam-4444	238	1	−	−	PROPN
ejpam-4444	239	1	ϵ	ϵ	SYM
ejpam-4444	239	2	2(2	2(2	NUM
ejpam-4444	240	1	+	+	CCONJ
ejpam-4444	240	2	ϵ	ϵ	X
ejpam-4444	240	3	)	)	PUNCT
ejpam-4444	240	4	<	<	X
ejpam-4444	240	5	0	0	NUM
ejpam-4444	240	6	,	,	PUNCT
ejpam-4444	240	7	which	which	PRON
ejpam-4444	240	8	is	be	AUX
ejpam-4444	240	9	a	a	DET
ejpam-4444	240	10	contradiction	contradiction	NOUN
ejpam-4444	240	11	.	.	PUNCT
ejpam-4444	241	1	3	3	X
ejpam-4444	241	2	)	)	PUNCT
ejpam-4444	241	3	as	as	ADP
ejpam-4444	241	4	in	in	ADP
ejpam-4444	241	5	2	2	NUM
ejpam-4444	241	6	)	)	PUNCT
ejpam-4444	241	7	,	,	PUNCT
ejpam-4444	241	8	the	the	DET
ejpam-4444	241	9	proposed	propose	VERB
ejpam-4444	241	10	inequality	inequality	NOUN
ejpam-4444	241	11	becomes	become	VERB
ejpam-4444	241	12	[	[	PUNCT
ejpam-4444	241	13	t4α	t4α	NOUN
ejpam-4444	241	14	−	−	PROPN
ejpam-4444	241	15	1	1	NUM
ejpam-4444	241	16	4α(t−	4α(t−	NUM
ejpam-4444	241	17	1	1	NUM
ejpam-4444	241	18	)	)	PUNCT
ejpam-4444	241	19	]	]	PUNCT
ejpam-4444	241	20	1/(4α−1	1/(4α−1	NUM
ejpam-4444	241	21	)	)	PUNCT
ejpam-4444	241	22	<	<	X
ejpam-4444	241	23	α	α	PROPN
ejpam-4444	241	24	(	(	PUNCT
ejpam-4444	241	25	t2	t2	NOUN
ejpam-4444	241	26	+	+	CCONJ
ejpam-4444	241	27	1	1	NUM
ejpam-4444	241	28	t+	t+	NUM
ejpam-4444	241	29	1	1	NUM
ejpam-4444	241	30	)	)	PUNCT
ejpam-4444	241	31	+	+	CCONJ
ejpam-4444	241	32	(	(	PUNCT
ejpam-4444	241	33	1−	1−	NUM
ejpam-4444	241	34	α	α	NOUN
ejpam-4444	241	35	)	)	PUNCT
ejpam-4444	241	36	(	(	PUNCT
ejpam-4444	241	37	2	2	NUM
ejpam-4444	241	38	t	t	NOUN
ejpam-4444	241	39	t+	t+	PUNCT
ejpam-4444	241	40	1	1	NUM
ejpam-4444	241	41	)	)	PUNCT
ejpam-4444	241	42	α	α	PROPN
ejpam-4444	241	43	∈	∈	PROPN
ejpam-4444	241	44	(	(	PUNCT
ejpam-4444	241	45	1/2	1/2	NUM
ejpam-4444	241	46	,	,	PUNCT
ejpam-4444	241	47	1	1	NUM
ejpam-4444	241	48	)	)	PUNCT
ejpam-4444	241	49	.	.	PUNCT
ejpam-4444	242	1	(	(	PUNCT
ejpam-4444	242	2	8)	8)	NUM
ejpam-4444	242	3	inequality	inequality	NOUN
ejpam-4444	242	4	(	(	PUNCT
ejpam-4444	242	5	8)	8)	NUM
ejpam-4444	242	6	is	be	AUX
ejpam-4444	242	7	equivalent	equivalent	ADJ
ejpam-4444	242	8	to	to	ADP
ejpam-4444	242	9	f	f	PROPN
ejpam-4444	242	10	(	(	PUNCT
ejpam-4444	242	11	t	t	PROPN
ejpam-4444	242	12	)	)	PUNCT
ejpam-4444	242	13	<	<	X
ejpam-4444	242	14	0	0	PUNCT
ejpam-4444	243	1	and	and	CCONJ
ejpam-4444	243	2	the	the	DET
ejpam-4444	243	3	term	term	NOUN
ejpam-4444	243	4	g′′′(t	g′′′(t	NOUN
ejpam-4444	243	5	)	)	PUNCT
ejpam-4444	243	6	is	be	AUX
ejpam-4444	243	7	still	still	ADV
ejpam-4444	243	8	that	that	PRON
ejpam-4444	243	9	in	in	ADP
ejpam-4444	243	10	(	(	PUNCT
ejpam-4444	243	11	4	4	NUM
ejpam-4444	243	12	)	)	PUNCT
ejpam-4444	243	13	.	.	PUNCT
ejpam-4444	244	1	it	it	PRON
ejpam-4444	244	2	is	be	AUX
ejpam-4444	244	3	sufficient	sufficient	ADJ
ejpam-4444	244	4	to	to	PART
ejpam-4444	244	5	show	show	VERB
ejpam-4444	244	6	that	that	SCONJ
ejpam-4444	244	7	g′′′(t	g′′′(t	VERB
ejpam-4444	244	8	)	)	PUNCT
ejpam-4444	244	9	<	<	X
ejpam-4444	244	10	0	0	NUM
ejpam-4444	244	11	for	for	ADP
ejpam-4444	244	12	all	all	DET
ejpam-4444	244	13	α	α	PRON
ejpam-4444	244	14	∈	∈	PROPN
ejpam-4444	244	15	(	(	PUNCT
ejpam-4444	244	16	1/2	1/2	NUM
ejpam-4444	244	17	,	,	PUNCT
ejpam-4444	244	18	1	1	NUM
ejpam-4444	244	19	)	)	PUNCT
ejpam-4444	244	20	.	.	PUNCT
ejpam-4444	245	1	to	to	ADP
ejpam-4444	245	2	that	that	DET
ejpam-4444	245	3	end	end	NOUN
ejpam-4444	245	4	,	,	PUNCT
ejpam-4444	245	5	we	we	PRON
ejpam-4444	245	6	divide	divide	VERB
ejpam-4444	245	7	our	our	PRON
ejpam-4444	245	8	proof	proof	NOUN
ejpam-4444	245	9	into	into	ADP
ejpam-4444	245	10	three	three	NUM
ejpam-4444	245	11	cases	case	NOUN
ejpam-4444	245	12	:	:	PUNCT
ejpam-4444	245	13	α	α	PROPN
ejpam-4444	245	14	∈	∈	PROPN
ejpam-4444	245	15	(	(	PUNCT
ejpam-4444	245	16	1/2	1/2	NUM
ejpam-4444	245	17	,	,	PUNCT
ejpam-4444	245	18	3/5	3/5	NUM
ejpam-4444	245	19	]	]	PUNCT
ejpam-4444	245	20	,	,	PUNCT
ejpam-4444	245	21	α	α	PROPN
ejpam-4444	245	22	∈	∈	PROPN
ejpam-4444	245	23	(	(	PUNCT
ejpam-4444	245	24	3/5	3/5	NUM
ejpam-4444	245	25	,	,	PUNCT
ejpam-4444	245	26	3/4	3/4	NUM
ejpam-4444	245	27	]	]	PUNCT
ejpam-4444	245	28	and	and	CCONJ
ejpam-4444	245	29	α	α	PRON
ejpam-4444	245	30	∈	∈	PROPN
ejpam-4444	245	31	(	(	PUNCT
ejpam-4444	245	32	3/4	3/4	NUM
ejpam-4444	245	33	,	,	PUNCT
ejpam-4444	245	34	1	1	NUM
ejpam-4444	245	35	)	)	PUNCT
ejpam-4444	245	36	.	.	PUNCT
ejpam-4444	246	1	(	(	PUNCT
ejpam-4444	246	2	a	a	X
ejpam-4444	246	3	)	)	PUNCT
ejpam-4444	246	4	case	case	NOUN
ejpam-4444	246	5	α	α	X
ejpam-4444	246	6	∈	∈	PROPN
ejpam-4444	246	7	(	(	PUNCT
ejpam-4444	246	8	1/2	1/2	NUM
ejpam-4444	246	9	,	,	PUNCT
ejpam-4444	246	10	3/5	3/5	NUM
ejpam-4444	246	11	]	]	X
ejpam-4444	246	12	:	:	PUNCT
ejpam-4444	246	13	in	in	ADP
ejpam-4444	246	14	(	(	PUNCT
ejpam-4444	246	15	4	4	NUM
ejpam-4444	246	16	)	)	PUNCT
ejpam-4444	246	17	,	,	PUNCT
ejpam-4444	246	18	observe	observe	VERB
ejpam-4444	246	19	that	that	SCONJ
ejpam-4444	246	20	the	the	DET
ejpam-4444	246	21	constant	constant	ADJ
ejpam-4444	246	22	term	term	NOUN
ejpam-4444	246	23	is	be	AUX
ejpam-4444	246	24	positive	positive	ADJ
ejpam-4444	246	25	while	while	SCONJ
ejpam-4444	246	26	the	the	DET
ejpam-4444	246	27	coefficients	coefficient	NOUN
ejpam-4444	246	28	of	of	ADP
ejpam-4444	246	29	t3	t3	PROPN
ejpam-4444	246	30	,	,	PUNCT
ejpam-4444	246	31	t2	t2	PROPN
ejpam-4444	246	32	and	and	CCONJ
ejpam-4444	246	33	t	t	NOUN
ejpam-4444	246	34	are	be	AUX
ejpam-4444	246	35	negative	negative	ADJ
ejpam-4444	246	36	for	for	ADP
ejpam-4444	246	37	α	α	PRON
ejpam-4444	246	38	∈	∈	PROPN
ejpam-4444	246	39	(	(	PUNCT
ejpam-4444	246	40	1/2	1/2	NUM
ejpam-4444	246	41	,	,	PUNCT
ejpam-4444	246	42	3/5	3/5	NUM
ejpam-4444	246	43	]	]	PUNCT
ejpam-4444	246	44	.	.	PUNCT
ejpam-4444	247	1	since	since	SCONJ
ejpam-4444	247	2	t	t	PROPN
ejpam-4444	247	3	>	>	X
ejpam-4444	247	4	1	1	NUM
ejpam-4444	247	5	,	,	PUNCT
ejpam-4444	247	6	it	it	PRON
ejpam-4444	247	7	follows	follow	VERB
ejpam-4444	247	8	that	that	SCONJ
ejpam-4444	247	9	t4−4α	t4−4α	PROPN
ejpam-4444	247	10	<	<	X
ejpam-4444	247	11	t2	t2	PROPN
ejpam-4444	247	12	<	<	X
ejpam-4444	247	13	t3	t3	PROPN
ejpam-4444	247	14	and	and	CCONJ
ejpam-4444	247	15	consequently	consequently	ADV
ejpam-4444	247	16	g	g	PROPN
ejpam-4444	247	17	′′′	′′′	PROPN
ejpam-4444	247	18	(	(	PUNCT
ejpam-4444	247	19	t	t	PROPN
ejpam-4444	247	20	)	)	PUNCT
ejpam-4444	247	21	8αt4α−4	8αt4α−4	NUM
ejpam-4444	247	22	<	<	X
ejpam-4444	247	23	[	[	PUNCT
ejpam-4444	247	24	−	−	X
ejpam-4444	247	25	(	(	PUNCT
ejpam-4444	247	26	4α+	4α+	NUM
ejpam-4444	247	27	2)(4α+	2)(4α+	NUM
ejpam-4444	247	28	1)(3α−	1)(3α−	NUM
ejpam-4444	247	29	1)(2α−	1)(2α−	NUM
ejpam-4444	247	30	1	1	NUM
ejpam-4444	247	31	)	)	PUNCT
ejpam-4444	247	32	+	+	NUM
ejpam-4444	247	33	2α(5α−	2α(5α−	NUM
ejpam-4444	247	34	3)(4α+	3)(4α+	NUM
ejpam-4444	247	35	1)(4α−	1)(4α−	NUM
ejpam-4444	247	36	1	1	NUM
ejpam-4444	247	37	)	)	PUNCT
ejpam-4444	247	38	+	+	NUM
ejpam-4444	247	39	3α	3α	NOUN
ejpam-4444	247	40	]	]	PUNCT
ejpam-4444	247	41	t4−4α	t4−4α	PROPN
ejpam-4444	247	42	+	+	PUNCT
ejpam-4444	247	43	[	[	PUNCT
ejpam-4444	247	44	−	−	NUM
ejpam-4444	247	45	2(2α2	2(2α2	NOUN
ejpam-4444	248	1	−	−	PRON
ejpam-4444	249	1	α+	α+	PUNCT
ejpam-4444	249	2	1)(4α−	1)(4α−	NUM
ejpam-4444	249	3	1)(2α−	1)(2α−	NUM
ejpam-4444	249	4	1	1	NUM
ejpam-4444	249	5	)	)	PUNCT
ejpam-4444	249	6	+	+	CCONJ
ejpam-4444	249	7	α(4α−	α(4α−	PROPN
ejpam-4444	249	8	1)(2α−	1)(2α−	NUM
ejpam-4444	249	9	1)(3−	1)(3−	NUM
ejpam-4444	249	10	4α	4α	NOUN
ejpam-4444	249	11	)	)	PUNCT
ejpam-4444	249	12	]	]	PUNCT
ejpam-4444	250	1	<	<	X
ejpam-4444	250	2	(	(	PUNCT
ejpam-4444	250	3	2α−	2α−	NUM
ejpam-4444	250	4	1)(4α−	1)(4α−	NUM
ejpam-4444	250	5	1	1	NUM
ejpam-4444	250	6	)	)	PUNCT
ejpam-4444	250	7	[	[	PUNCT
ejpam-4444	250	8	−	−	PROPN
ejpam-4444	250	9	(	(	PUNCT
ejpam-4444	250	10	−8α2	−8α2	X
ejpam-4444	250	11	+	+	CCONJ
ejpam-4444	250	12	5α+	5α+	NUM
ejpam-4444	250	13	2)t4−4α	2)t4−4α	NUM
ejpam-4444	250	14	−	−	PROPN
ejpam-4444	251	1	(	(	PUNCT
ejpam-4444	251	2	8α2	8α2	NUM
ejpam-4444	251	3	−	−	PROPN
ejpam-4444	251	4	5α+	5α+	NUM
ejpam-4444	251	5	2	2	NUM
ejpam-4444	251	6	)	)	PUNCT
ejpam-4444	251	7	]	]	PUNCT
ejpam-4444	251	8	<	<	X
ejpam-4444	251	9	(	(	PUNCT
ejpam-4444	251	10	2α−	2α−	NUM
ejpam-4444	251	11	1)(4α−	1)(4α−	NUM
ejpam-4444	251	12	1	1	NUM
ejpam-4444	251	13	)	)	PUNCT
ejpam-4444	251	14	[	[	PUNCT
ejpam-4444	251	15	−	−	PROPN
ejpam-4444	251	16	(	(	PUNCT
ejpam-4444	251	17	−8α2	−8α2	X
ejpam-4444	251	18	+	+	CCONJ
ejpam-4444	251	19	5α+	5α+	NUM
ejpam-4444	251	20	2)−	2)−	NUM
ejpam-4444	251	21	(	(	PUNCT
ejpam-4444	251	22	8α2	8α2	NUM
ejpam-4444	251	23	−	−	PROPN
ejpam-4444	251	24	5α+	5α+	NUM
ejpam-4444	251	25	2	2	NUM
ejpam-4444	251	26	)	)	PUNCT
ejpam-4444	251	27	]	]	PUNCT
ejpam-4444	252	1	=	=	PUNCT
ejpam-4444	252	2	−4(2α−	−4(2α−	NUM
ejpam-4444	252	3	1)(4α−	1)(4α−	NUM
ejpam-4444	252	4	1	1	NUM
ejpam-4444	252	5	)	)	PUNCT
ejpam-4444	252	6	<	<	X
ejpam-4444	252	7	0	0	X
ejpam-4444	252	8	.	.	PUNCT
ejpam-4444	252	9	(	(	PUNCT
ejpam-4444	252	10	b	b	X
ejpam-4444	252	11	)	)	PUNCT
ejpam-4444	252	12	case	case	NOUN
ejpam-4444	252	13	α	α	X
ejpam-4444	252	14	∈	∈	PROPN
ejpam-4444	252	15	(	(	PUNCT
ejpam-4444	252	16	3/5	3/5	NUM
ejpam-4444	252	17	,	,	PUNCT
ejpam-4444	252	18	3/4	3/4	NUM
ejpam-4444	252	19	]	]	PUNCT
ejpam-4444	252	20	:	:	PUNCT
ejpam-4444	252	21	for	for	ADP
ejpam-4444	252	22	such	such	ADJ
ejpam-4444	252	23	α	α	NOUN
ejpam-4444	252	24	,	,	PUNCT
ejpam-4444	252	25	the	the	DET
ejpam-4444	252	26	coefficient	coefficient	NOUN
ejpam-4444	252	27	of	of	ADP
ejpam-4444	252	28	t2	t2	NOUN
ejpam-4444	252	29	and	and	CCONJ
ejpam-4444	252	30	the	the	DET
ejpam-4444	252	31	constant	constant	ADJ
ejpam-4444	252	32	term	term	NOUN
ejpam-4444	252	33	in	in	ADP
ejpam-4444	252	34	(	(	PUNCT
ejpam-4444	252	35	4	4	X
ejpam-4444	252	36	)	)	PUNCT
ejpam-4444	252	37	are	be	AUX
ejpam-4444	252	38	positive	positive	ADJ
ejpam-4444	252	39	while	while	SCONJ
ejpam-4444	252	40	the	the	DET
ejpam-4444	252	41	coefficients	coefficient	NOUN
ejpam-4444	252	42	of	of	ADP
ejpam-4444	252	43	t3	t3	PROPN
ejpam-4444	252	44	and	and	CCONJ
ejpam-4444	252	45	t	t	PROPN
ejpam-4444	252	46	are	be	AUX
ejpam-4444	252	47	negative	negative	ADJ
ejpam-4444	252	48	.	.	PUNCT
ejpam-4444	253	1	since	since	SCONJ
ejpam-4444	253	2	t	t	PROPN
ejpam-4444	253	3	>	>	X
ejpam-4444	253	4	1	1	NUM
ejpam-4444	253	5	,	,	PUNCT
ejpam-4444	253	6	we	we	PRON
ejpam-4444	253	7	have	have	VERB
ejpam-4444	253	8	t2	t2	PROPN
ejpam-4444	253	9	<	<	X
ejpam-4444	253	10	t3	t3	PROPN
ejpam-4444	253	11	and	and	CCONJ
ejpam-4444	253	12	consequently	consequently	ADV
ejpam-4444	253	13	g	g	PROPN
ejpam-4444	253	14	′′′	′′′	PROPN
ejpam-4444	253	15	(	(	PUNCT
ejpam-4444	253	16	t	t	PROPN
ejpam-4444	253	17	)	)	PUNCT
ejpam-4444	253	18	8αt4α−4	8αt4α−4	NUM
ejpam-4444	253	19	<	<	X
ejpam-4444	253	20	[	[	PUNCT
ejpam-4444	253	21	−	−	X
ejpam-4444	253	22	(	(	PUNCT
ejpam-4444	253	23	4α+	4α+	NUM
ejpam-4444	253	24	2)(4α+	2)(4α+	NUM
ejpam-4444	253	25	1)(3α−	1)(3α−	NUM
ejpam-4444	253	26	1)(2α−	1)(2α−	NUM
ejpam-4444	253	27	1	1	NUM
ejpam-4444	253	28	)	)	PUNCT
ejpam-4444	253	29	+	+	NUM
ejpam-4444	253	30	2α(5α−	2α(5α−	NUM
ejpam-4444	253	31	3)(4α+	3)(4α+	NUM
ejpam-4444	253	32	1)(4α−	1)(4α−	NUM
ejpam-4444	253	33	1	1	NUM
ejpam-4444	253	34	)	)	PUNCT
ejpam-4444	253	35	]	]	PUNCT
ejpam-4444	254	1	t2	t2	PROPN
ejpam-4444	254	2	a.	a.	NOUN
ejpam-4444	254	3	sonubon	sonubon	PROPN
ejpam-4444	254	4	,	,	PUNCT
ejpam-4444	254	5	s.	s.	PROPN
ejpam-4444	254	6	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	254	7	,	,	PUNCT
ejpam-4444	254	8	k.	k.	PROPN
ejpam-4444	254	9	nonlaopon	nonlaopon	ADV
ejpam-4444	254	10	/	/	SYM
ejpam-4444	254	11	eur	eur	PROPN
ejpam-4444	254	12	.	.	PUNCT
ejpam-4444	255	1	j.	j.	PROPN
ejpam-4444	255	2	pure	pure	PROPN
ejpam-4444	255	3	appl	appl	PROPN
ejpam-4444	255	4	.	.	PROPN
ejpam-4444	255	5	math	math	PROPN
ejpam-4444	255	6	,	,	PUNCT
ejpam-4444	255	7	15	15	NUM
ejpam-4444	255	8	(	(	PUNCT
ejpam-4444	255	9	3	3	NUM
ejpam-4444	255	10	)	)	PUNCT
ejpam-4444	255	11	(	(	PUNCT
ejpam-4444	255	12	2022	2022	NUM
ejpam-4444	255	13	)	)	PUNCT
ejpam-4444	255	14	,	,	PUNCT
ejpam-4444	255	15	1120	1120	NUM
ejpam-4444	255	16	-	-	SYM
ejpam-4444	255	17	1143	1143	NUM
ejpam-4444	255	18	1131	1131	NUM
ejpam-4444	255	19	+	+	CCONJ
ejpam-4444	256	1	[	[	X
ejpam-4444	256	2	−2(2α2	−2(2α2	NOUN
ejpam-4444	256	3	−	−	PROPN
ejpam-4444	256	4	α+	α+	PUNCT
ejpam-4444	256	5	1)(4α−	1)(4α−	NUM
ejpam-4444	256	6	1)(2α−	1)(2α−	NUM
ejpam-4444	256	7	1	1	NUM
ejpam-4444	256	8	)	)	PUNCT
ejpam-4444	256	9	+	+	CCONJ
ejpam-4444	256	10	α(4α−	α(4α−	PROPN
ejpam-4444	256	11	1)(2α−	1)(2α−	NUM
ejpam-4444	256	12	1)(3−	1)(3−	NUM
ejpam-4444	256	13	4α	4α	NOUN
ejpam-4444	256	14	)	)	PUNCT
ejpam-4444	256	15	]	]	PUNCT
ejpam-4444	257	1	+	+	CCONJ
ejpam-4444	257	2	3αt4−4α	3αt4−4α	NUM
ejpam-4444	257	3	=	=	PUNCT
ejpam-4444	258	1	−2(1−	−2(1−	PROPN
ejpam-4444	258	2	α)(4α+	α)(4α+	PROPN
ejpam-4444	258	3	1)(8α2	1)(8α2	NUM
ejpam-4444	258	4	−	−	PROPN
ejpam-4444	258	5	5α+	5α+	NUM
ejpam-4444	258	6	1)t2	1)t2	NUM
ejpam-4444	258	7	−	−	PROPN
ejpam-4444	258	8	(	(	PUNCT
ejpam-4444	258	9	2α−	2α−	NUM
ejpam-4444	258	10	1)(4α−	1)(4α−	NUM
ejpam-4444	258	11	1)(8α2	1)(8α2	NUM
ejpam-4444	258	12	−	−	PROPN
ejpam-4444	258	13	5α+	5α+	NUM
ejpam-4444	258	14	2	2	NUM
ejpam-4444	258	15	)	)	PUNCT
ejpam-4444	258	16	+	+	CCONJ
ejpam-4444	258	17	3αt4−4α	3αt4−4α	PROPN
ejpam-4444	258	18	.	.	PUNCT
ejpam-4444	259	1	now	now	ADV
ejpam-4444	259	2	,	,	PUNCT
ejpam-4444	259	3	consider	consider	VERB
ejpam-4444	259	4	the	the	DET
ejpam-4444	259	5	term	term	NOUN
ejpam-4444	259	6	on	on	ADP
ejpam-4444	259	7	the	the	DET
ejpam-4444	259	8	right	right	ADJ
ejpam-4444	259	9	side	side	NOUN
ejpam-4444	259	10	of	of	ADP
ejpam-4444	259	11	the	the	DET
ejpam-4444	259	12	above	above	ADJ
ejpam-4444	259	13	inequality	inequality	NOUN
ejpam-4444	259	14	.	.	PUNCT
ejpam-4444	260	1	since	since	SCONJ
ejpam-4444	260	2	the	the	DET
ejpam-4444	260	3	coefficient	coefficient	NOUN
ejpam-4444	260	4	−2(1−	−2(1−	PROPN
ejpam-4444	260	5	α)(4α	α)(4α	PROPN
ejpam-4444	261	1	+	+	PROPN
ejpam-4444	261	2	1)(8α2	1)(8α2	NUM
ejpam-4444	261	3	−	−	NOUN
ejpam-4444	261	4	5α	5α	NOUN
ejpam-4444	262	1	+	+	CCONJ
ejpam-4444	262	2	1	1	X
ejpam-4444	262	3	)	)	PUNCT
ejpam-4444	262	4	of	of	ADP
ejpam-4444	262	5	t2	t2	NOUN
ejpam-4444	262	6	is	be	AUX
ejpam-4444	262	7	negative	negative	ADJ
ejpam-4444	262	8	for	for	ADP
ejpam-4444	262	9	α	α	PRON
ejpam-4444	262	10	∈	∈	PROPN
ejpam-4444	262	11	(	(	PUNCT
ejpam-4444	262	12	3/5	3/5	NUM
ejpam-4444	262	13	,	,	PUNCT
ejpam-4444	262	14	3/4	3/4	NUM
ejpam-4444	262	15	]	]	PUNCT
ejpam-4444	262	16	and	and	CCONJ
ejpam-4444	262	17	t4−4α	t4−4α	PROPN
ejpam-4444	262	18	<	<	X
ejpam-4444	262	19	t2	t2	PROPN
ejpam-4444	262	20	,	,	PUNCT
ejpam-4444	262	21	we	we	PRON
ejpam-4444	262	22	get	get	VERB
ejpam-4444	262	23	g	g	PROPN
ejpam-4444	262	24	′′′	′′′	PROPN
ejpam-4444	262	25	(	(	PUNCT
ejpam-4444	262	26	t	t	PROPN
ejpam-4444	262	27	)	)	PUNCT
ejpam-4444	262	28	8αt4α−4	8αt4α−4	NUM
ejpam-4444	262	29	<	<	X
ejpam-4444	262	30	[	[	PUNCT
ejpam-4444	262	31	−	−	PROPN
ejpam-4444	262	32	2(1−	2(1−	NUM
ejpam-4444	262	33	α)(4α+	α)(4α+	PROPN
ejpam-4444	262	34	1)(8α2	1)(8α2	NUM
ejpam-4444	262	35	−	−	PROPN
ejpam-4444	262	36	5α+	5α+	NUM
ejpam-4444	262	37	1	1	NUM
ejpam-4444	262	38	)	)	PUNCT
ejpam-4444	263	1	+	+	NUM
ejpam-4444	263	2	3α	3α	NOUN
ejpam-4444	263	3	]	]	PUNCT
ejpam-4444	263	4	t4−4α	t4−4α	PROPN
ejpam-4444	263	5	−	−	PROPN
ejpam-4444	263	6	(	(	PUNCT
ejpam-4444	263	7	2α−	2α−	NUM
ejpam-4444	263	8	1)(4α−	1)(4α−	NUM
ejpam-4444	263	9	1)(8α2	1)(8α2	NUM
ejpam-4444	264	1	−	−	PROPN
ejpam-4444	264	2	5α+	5α+	NUM
ejpam-4444	264	3	2	2	NUM
ejpam-4444	264	4	)	)	PUNCT
ejpam-4444	264	5	=	=	NOUN
ejpam-4444	264	6	(	(	PUNCT
ejpam-4444	264	7	2α−	2α−	NUM
ejpam-4444	264	8	1)(4α−	1)(4α−	NUM
ejpam-4444	264	9	1	1	NUM
ejpam-4444	264	10	)	)	PUNCT
ejpam-4444	264	11	[	[	PUNCT
ejpam-4444	264	12	(	(	PUNCT
ejpam-4444	264	13	8α2	8α2	NUM
ejpam-4444	264	14	−	−	PROPN
ejpam-4444	265	1	5α−	5α−	NUM
ejpam-4444	265	2	2)t4−4α	2)t4−4α	NUM
ejpam-4444	265	3	−	−	PROPN
ejpam-4444	265	4	(	(	PUNCT
ejpam-4444	265	5	8α2	8α2	NUM
ejpam-4444	265	6	−	−	PROPN
ejpam-4444	265	7	5α+	5α+	NUM
ejpam-4444	265	8	2	2	NUM
ejpam-4444	265	9	)	)	PUNCT
ejpam-4444	265	10	]	]	PUNCT
ejpam-4444	266	1	<	<	X
ejpam-4444	266	2	(	(	PUNCT
ejpam-4444	266	3	2α−	2α−	NUM
ejpam-4444	266	4	1)(4α−	1)(4α−	NUM
ejpam-4444	266	5	1	1	NUM
ejpam-4444	266	6	)	)	PUNCT
ejpam-4444	266	7	[	[	PUNCT
ejpam-4444	266	8	(	(	PUNCT
ejpam-4444	266	9	8α2	8α2	NUM
ejpam-4444	266	10	−	−	PROPN
ejpam-4444	267	1	5α−	5α−	PROPN
ejpam-4444	267	2	2)−	2)−	PROPN
ejpam-4444	267	3	(	(	PUNCT
ejpam-4444	267	4	8α2	8α2	NUM
ejpam-4444	267	5	−	−	PROPN
ejpam-4444	267	6	5α+	5α+	NUM
ejpam-4444	267	7	2	2	NUM
ejpam-4444	267	8	)	)	PUNCT
ejpam-4444	267	9	]	]	PUNCT
ejpam-4444	268	1	=	=	PUNCT
ejpam-4444	268	2	−4(2α−	−4(2α−	NUM
ejpam-4444	268	3	1)(4α−	1)(4α−	NUM
ejpam-4444	268	4	1	1	NUM
ejpam-4444	268	5	)	)	PUNCT
ejpam-4444	268	6	<	<	X
ejpam-4444	268	7	0	0	X
ejpam-4444	268	8	.	.	PUNCT
ejpam-4444	269	1	(	(	PUNCT
ejpam-4444	269	2	c	c	X
ejpam-4444	269	3	)	)	PUNCT
ejpam-4444	269	4	case	case	NOUN
ejpam-4444	269	5	α	α	X
ejpam-4444	269	6	∈	∈	PROPN
ejpam-4444	269	7	(	(	PUNCT
ejpam-4444	269	8	3/4	3/4	NUM
ejpam-4444	269	9	,	,	PUNCT
ejpam-4444	269	10	1	1	NUM
ejpam-4444	269	11	):	):	PUNCT
ejpam-4444	269	12	for	for	ADP
ejpam-4444	269	13	α	α	NOUN
ejpam-4444	269	14	in	in	ADP
ejpam-4444	269	15	this	this	DET
ejpam-4444	269	16	interval	interval	NOUN
ejpam-4444	269	17	the	the	DET
ejpam-4444	269	18	coefficients	coefficient	NOUN
ejpam-4444	269	19	of	of	ADP
ejpam-4444	269	20	t3	t3	PROPN
ejpam-4444	269	21	and	and	CCONJ
ejpam-4444	269	22	t	t	PROPN
ejpam-4444	269	23	in	in	ADP
ejpam-4444	269	24	(	(	PUNCT
ejpam-4444	269	25	4	4	X
ejpam-4444	269	26	)	)	PUNCT
ejpam-4444	269	27	are	be	AUX
ejpam-4444	269	28	negative	negative	ADJ
ejpam-4444	269	29	while	while	SCONJ
ejpam-4444	269	30	the	the	DET
ejpam-4444	269	31	coefficient	coefficient	NOUN
ejpam-4444	269	32	of	of	ADP
ejpam-4444	269	33	t2	t2	NOUN
ejpam-4444	269	34	is	be	AUX
ejpam-4444	269	35	positive	positive	ADJ
ejpam-4444	269	36	.	.	PUNCT
ejpam-4444	270	1	because	because	SCONJ
ejpam-4444	270	2	t	t	PROPN
ejpam-4444	270	3	>	>	X
ejpam-4444	270	4	1	1	NUM
ejpam-4444	270	5	,	,	PUNCT
ejpam-4444	270	6	we	we	PRON
ejpam-4444	270	7	have	have	VERB
ejpam-4444	270	8	t4−4α	t4−4α	PROPN
ejpam-4444	270	9	<	<	X
ejpam-4444	270	10	t2	t2	PROPN
ejpam-4444	270	11	<	<	X
ejpam-4444	270	12	t3	t3	PROPN
ejpam-4444	270	13	.	.	PUNCT
ejpam-4444	271	1	thus	thus	ADV
ejpam-4444	271	2	g	g	PROPN
ejpam-4444	271	3	′′′	′′′	PROPN
ejpam-4444	271	4	(	(	PUNCT
ejpam-4444	271	5	t	t	PROPN
ejpam-4444	271	6	)	)	PUNCT
ejpam-4444	271	7	8αt4α−4	8αt4α−4	NUM
ejpam-4444	271	8	<	<	X
ejpam-4444	271	9	[	[	PUNCT
ejpam-4444	271	10	−	−	PROPN
ejpam-4444	271	11	α(4α+	α(4α+	NOUN
ejpam-4444	271	12	2)(4α+	2)(4α+	PROPN
ejpam-4444	271	13	1)(3α−	1)(3α−	NUM
ejpam-4444	271	14	1)(2α−	1)(2α−	NUM
ejpam-4444	271	15	1	1	NUM
ejpam-4444	271	16	)	)	PUNCT
ejpam-4444	271	17	+	+	NUM
ejpam-4444	271	18	2α(5α−	2α(5α−	NUM
ejpam-4444	271	19	3)(4α+	3)(4α+	NUM
ejpam-4444	271	20	1)(4α−	1)(4α−	NUM
ejpam-4444	271	21	1	1	NUM
ejpam-4444	271	22	)	)	PUNCT
ejpam-4444	271	23	]	]	PUNCT
ejpam-4444	272	1	t2	t2	NOUN
ejpam-4444	272	2	+	+	CCONJ
ejpam-4444	272	3	[	[	PUNCT
ejpam-4444	272	4	−	−	NUM
ejpam-4444	272	5	2(2α2	2(2α2	NOUN
ejpam-4444	272	6	−	−	PRON
ejpam-4444	273	1	α+	α+	PUNCT
ejpam-4444	273	2	1)(4α−	1)(4α−	NUM
ejpam-4444	273	3	1)(2α−	1)(2α−	NUM
ejpam-4444	273	4	1	1	NUM
ejpam-4444	273	5	)	)	PUNCT
ejpam-4444	273	6	+	+	NUM
ejpam-4444	273	7	3α	3α	NOUN
ejpam-4444	273	8	]	]	PUNCT
ejpam-4444	273	9	t4−4α	t4−4α	PROPN
ejpam-4444	273	10	−	−	PROPN
ejpam-4444	273	11	α(4α−	α(4α−	PROPN
ejpam-4444	273	12	1)(2α−	1)(2α−	NUM
ejpam-4444	273	13	1)(4α−	1)(4α−	NUM
ejpam-4444	273	14	3	3	NUM
ejpam-4444	273	15	)	)	PUNCT
ejpam-4444	273	16	=	=	PUNCT
ejpam-4444	274	1	−2(1−	−2(1−	PROPN
ejpam-4444	274	2	α)(4α+	α)(4α+	PROPN
ejpam-4444	274	3	1)(8α2	1)(8α2	NUM
ejpam-4444	274	4	−	−	PROPN
ejpam-4444	274	5	5α+	5α+	NUM
ejpam-4444	274	6	1)t2	1)t2	NUM
ejpam-4444	274	7	+	+	CCONJ
ejpam-4444	274	8	(	(	PUNCT
ejpam-4444	274	9	−32α4	−32α4	NUM
ejpam-4444	274	10	+	+	CCONJ
ejpam-4444	274	11	40α3	40α3	NUM
ejpam-4444	274	12	−	−	NUM
ejpam-4444	274	13	32α2	32α2	NUM
ejpam-4444	275	1	+	+	NUM
ejpam-4444	275	2	17α−	17α−	NUM
ejpam-4444	275	3	2)t4−4α	2)t4−4α	NUM
ejpam-4444	275	4	−	−	PROPN
ejpam-4444	275	5	α(4α−	α(4α−	PROPN
ejpam-4444	275	6	1)(2α−	1)(2α−	NUM
ejpam-4444	275	7	1)(4α−	1)(4α−	NUM
ejpam-4444	275	8	3	3	NUM
ejpam-4444	275	9	)	)	PUNCT
ejpam-4444	275	10	.	.	PUNCT
ejpam-4444	276	1	now	now	ADV
ejpam-4444	276	2	consider	consider	VERB
ejpam-4444	276	3	the	the	DET
ejpam-4444	276	4	term	term	NOUN
ejpam-4444	276	5	on	on	ADP
ejpam-4444	276	6	the	the	DET
ejpam-4444	276	7	right	right	ADJ
ejpam-4444	276	8	side	side	NOUN
ejpam-4444	276	9	of	of	ADP
ejpam-4444	276	10	the	the	DET
ejpam-4444	276	11	last	last	ADJ
ejpam-4444	276	12	equality	equality	NOUN
ejpam-4444	276	13	sign	sign	NOUN
ejpam-4444	276	14	above	above	ADV
ejpam-4444	276	15	.	.	PUNCT
ejpam-4444	277	1	the	the	DET
ejpam-4444	277	2	coefficient	coefficient	NOUN
ejpam-4444	277	3	−2(1	−2(1	NOUN
ejpam-4444	277	4	−	−	PROPN
ejpam-4444	277	5	α)(4α	α)(4α	PROPN
ejpam-4444	278	1	+	+	PROPN
ejpam-4444	278	2	1)(8α2	1)(8α2	NUM
ejpam-4444	278	3	−	−	NOUN
ejpam-4444	278	4	5α	5α	NOUN
ejpam-4444	279	1	+	+	CCONJ
ejpam-4444	279	2	1	1	X
ejpam-4444	279	3	)	)	PUNCT
ejpam-4444	279	4	of	of	ADP
ejpam-4444	279	5	t2	t2	NOUN
ejpam-4444	279	6	is	be	AUX
ejpam-4444	279	7	negative	negative	ADJ
ejpam-4444	279	8	and	and	CCONJ
ejpam-4444	279	9	t4−4α	t4−4α	PROPN
ejpam-4444	279	10	<	<	X
ejpam-4444	279	11	t2	t2	PROPN
ejpam-4444	279	12	as	as	ADP
ejpam-4444	279	13	α	α	PROPN
ejpam-4444	279	14	∈	∈	PROPN
ejpam-4444	279	15	(	(	PUNCT
ejpam-4444	279	16	3/4	3/4	NUM
ejpam-4444	279	17	,	,	PUNCT
ejpam-4444	279	18	1	1	NUM
ejpam-4444	279	19	)	)	PUNCT
ejpam-4444	279	20	.	.	PUNCT
ejpam-4444	280	1	hence	hence	ADV
ejpam-4444	280	2	g	g	PROPN
ejpam-4444	280	3	′′′	′′′	PROPN
ejpam-4444	280	4	(	(	PUNCT
ejpam-4444	280	5	t	t	PROPN
ejpam-4444	280	6	)	)	PUNCT
ejpam-4444	280	7	8αt4α−4	8αt4α−4	NUM
ejpam-4444	280	8	<	<	X
ejpam-4444	280	9	[	[	PUNCT
ejpam-4444	280	10	−	−	PROPN
ejpam-4444	280	11	2(1−	2(1−	NUM
ejpam-4444	280	12	α)(4α+	α)(4α+	PROPN
ejpam-4444	280	13	1)(8α2	1)(8α2	NUM
ejpam-4444	281	1	−	−	PROPN
ejpam-4444	281	2	5α+	5α+	NUM
ejpam-4444	281	3	1	1	NUM
ejpam-4444	281	4	)	)	PUNCT
ejpam-4444	281	5	+	+	CCONJ
ejpam-4444	281	6	(	(	PUNCT
ejpam-4444	281	7	−32α4	−32α4	NUM
ejpam-4444	281	8	+	+	CCONJ
ejpam-4444	281	9	40α3	40α3	NUM
ejpam-4444	281	10	−	−	NOUN
ejpam-4444	281	11	32α2	32α2	NUM
ejpam-4444	281	12	+	+	NUM
ejpam-4444	281	13	17α−	17α−	NUM
ejpam-4444	281	14	2	2	NUM
ejpam-4444	281	15	)	)	PUNCT
ejpam-4444	281	16	]	]	PUNCT
ejpam-4444	282	1	t4−4α	t4−4α	PROPN
ejpam-4444	282	2	−	−	PROPN
ejpam-4444	282	3	α(4α−	α(4α−	PROPN
ejpam-4444	282	4	1)(2α−	1)(2α−	NUM
ejpam-4444	282	5	1)(4α−	1)(4α−	NUM
ejpam-4444	282	6	3	3	NUM
ejpam-4444	282	7	)	)	PUNCT
ejpam-4444	282	8	=	=	NOUN
ejpam-4444	282	9	(	(	PUNCT
ejpam-4444	282	10	2α−	2α−	NUM
ejpam-4444	282	11	1)(4α−	1)(4α−	NUM
ejpam-4444	282	12	1	1	NUM
ejpam-4444	282	13	)	)	PUNCT
ejpam-4444	282	14	[	[	PUNCT
ejpam-4444	282	15	−	−	PROPN
ejpam-4444	282	16	(	(	PUNCT
ejpam-4444	282	17	−4α2	−4α2	SYM
ejpam-4444	282	18	+	+	SYM
ejpam-4444	282	19	3α+	3α+	NUM
ejpam-4444	282	20	4)t4−4α	4)t4−4α	NUM
ejpam-4444	282	21	−	−	PROPN
ejpam-4444	282	22	α(4α−	α(4α−	PROPN
ejpam-4444	282	23	1)(2α−	1)(2α−	NUM
ejpam-4444	282	24	1)(4α−	1)(4α−	NUM
ejpam-4444	282	25	3	3	NUM
ejpam-4444	282	26	)	)	PUNCT
ejpam-4444	282	27	]	]	PUNCT
ejpam-4444	282	28	<	<	X
ejpam-4444	282	29	(	(	PUNCT
ejpam-4444	282	30	2α−	2α−	NUM
ejpam-4444	282	31	1)(4α−	1)(4α−	NUM
ejpam-4444	282	32	1	1	NUM
ejpam-4444	282	33	)	)	PUNCT
ejpam-4444	282	34	[	[	PUNCT
ejpam-4444	282	35	−	−	PROPN
ejpam-4444	282	36	(	(	PUNCT
ejpam-4444	282	37	−4α2	−4α2	SYM
ejpam-4444	282	38	+	+	SYM
ejpam-4444	282	39	3α+	3α+	NUM
ejpam-4444	282	40	4	4	NUM
ejpam-4444	282	41	)	)	PUNCT
ejpam-4444	282	42	−	−	PROPN
ejpam-4444	282	43	α(4α−	α(4α−	PROPN
ejpam-4444	282	44	1)(2α−	1)(2α−	NUM
ejpam-4444	282	45	1)(4α−	1)(4α−	NUM
ejpam-4444	282	46	3	3	NUM
ejpam-4444	282	47	)	)	PUNCT
ejpam-4444	282	48	]	]	PUNCT
ejpam-4444	283	1	=	=	PUNCT
ejpam-4444	283	2	−4(2α−	−4(2α−	NUM
ejpam-4444	283	3	1)(4α−	1)(4α−	NUM
ejpam-4444	283	4	1	1	NUM
ejpam-4444	283	5	)	)	PUNCT
ejpam-4444	283	6	<	<	X
ejpam-4444	283	7	0	0	X
ejpam-4444	283	8	.	.	PUNCT
ejpam-4444	283	9	a.	a.	NOUN
ejpam-4444	283	10	sonubon	sonubon	PROPN
ejpam-4444	283	11	,	,	PUNCT
ejpam-4444	283	12	s.	s.	PROPN
ejpam-4444	283	13	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	283	14	,	,	PUNCT
ejpam-4444	283	15	k.	k.	PROPN
ejpam-4444	283	16	nonlaopon	nonlaopon	ADV
ejpam-4444	283	17	/	/	SYM
ejpam-4444	283	18	eur	eur	PROPN
ejpam-4444	283	19	.	.	PUNCT
ejpam-4444	284	1	j.	j.	PROPN
ejpam-4444	284	2	pure	pure	PROPN
ejpam-4444	284	3	appl	appl	PROPN
ejpam-4444	284	4	.	.	PROPN
ejpam-4444	284	5	math	math	PROPN
ejpam-4444	284	6	,	,	PUNCT
ejpam-4444	284	7	15	15	NUM
ejpam-4444	284	8	(	(	PUNCT
ejpam-4444	284	9	3	3	NUM
ejpam-4444	284	10	)	)	PUNCT
ejpam-4444	284	11	(	(	PUNCT
ejpam-4444	284	12	2022	2022	NUM
ejpam-4444	284	13	)	)	PUNCT
ejpam-4444	284	14	,	,	PUNCT
ejpam-4444	284	15	1120	1120	NUM
ejpam-4444	284	16	-	-	SYM
ejpam-4444	284	17	1143	1143	NUM
ejpam-4444	284	18	1132	1132	NUM
ejpam-4444	284	19	the	the	DET
ejpam-4444	284	20	proof	proof	NOUN
ejpam-4444	284	21	is	be	AUX
ejpam-4444	284	22	complete	complete	ADJ
ejpam-4444	284	23	.	.	PUNCT
ejpam-4444	285	1	the	the	DET
ejpam-4444	285	2	next	next	ADJ
ejpam-4444	285	3	theorem	theorem	NOUN
ejpam-4444	285	4	is	be	AUX
ejpam-4444	285	5	concerned	concern	VERB
ejpam-4444	285	6	with	with	ADP
ejpam-4444	285	7	determining	determine	VERB
ejpam-4444	285	8	the	the	DET
ejpam-4444	285	9	optimal	optimal	ADJ
ejpam-4444	285	10	lower	lower	ADV
ejpam-4444	285	11	bound	bind	VERB
ejpam-4444	285	12	for	for	ADP
ejpam-4444	285	13	the	the	DET
ejpam-4444	285	14	weighted	weight	VERB
ejpam-4444	285	15	arithmetic	arithmetic	ADJ
ejpam-4444	285	16	mean	mean	NOUN
ejpam-4444	285	17	of	of	ADP
ejpam-4444	285	18	contra	contra	PROPN
ejpam-4444	285	19	-	-	ADJ
ejpam-4444	285	20	harmonic	harmonic	ADJ
ejpam-4444	285	21	and	and	CCONJ
ejpam-4444	285	22	harmonic	harmonic	ADJ
ejpam-4444	285	23	means	mean	NOUN
ejpam-4444	285	24	by	by	ADP
ejpam-4444	285	25	generalized	generalize	VERB
ejpam-4444	285	26	logarithmic	logarithmic	ADJ
ejpam-4444	285	27	means	mean	NOUN
ejpam-4444	285	28	lp	lp	ADP
ejpam-4444	285	29	,	,	PUNCT
ejpam-4444	285	30	where	where	SCONJ
ejpam-4444	285	31	p	p	NOUN
ejpam-4444	285	32	is	be	AUX
ejpam-4444	285	33	of	of	ADP
ejpam-4444	285	34	the	the	DET
ejpam-4444	285	35	reciprocal	reciprocal	NOUN
ejpam-4444	285	36	of	of	ADP
ejpam-4444	285	37	linear	linear	ADJ
ejpam-4444	285	38	form	form	NOUN
ejpam-4444	285	39	p	p	NOUN
ejpam-4444	285	40	=	=	NOUN
ejpam-4444	286	1	1/[2(1−	1/[2(1−	NUM
ejpam-4444	286	2	c)α+	c)α+	NOUN
ejpam-4444	286	3	c	c	NOUN
ejpam-4444	286	4	]	]	PUNCT
ejpam-4444	286	5	where	where	SCONJ
ejpam-4444	286	6	α	α	PROPN
ejpam-4444	286	7	∈	∈	PROPN
ejpam-4444	286	8	(	(	PUNCT
ejpam-4444	286	9	1/2	1/2	NUM
ejpam-4444	286	10	,	,	PUNCT
ejpam-4444	286	11	1	1	NUM
ejpam-4444	286	12	)	)	PUNCT
ejpam-4444	286	13	.	.	PUNCT
ejpam-4444	287	1	theorem	theorem	NOUN
ejpam-4444	287	2	2	2	NUM
ejpam-4444	287	3	.	.	PUNCT
ejpam-4444	287	4	let	let	VERB
ejpam-4444	287	5	a	a	DET
ejpam-4444	287	6	,	,	PUNCT
ejpam-4444	287	7	b	b	X
ejpam-4444	287	8	>	>	X
ejpam-4444	287	9	0	0	PUNCT
ejpam-4444	287	10	with	with	ADP
ejpam-4444	287	11	a	a	DET
ejpam-4444	287	12	̸=	̸=	PROPN
ejpam-4444	287	13	b.	b.	NOUN
ejpam-4444	287	14	then	then	ADV
ejpam-4444	287	15	1	1	X
ejpam-4444	287	16	)	)	PUNCT
ejpam-4444	287	17	l7/(13−12α)(a	l7/(13−12α)(a	NOUN
ejpam-4444	287	18	,	,	PUNCT
ejpam-4444	287	19	b	b	NOUN
ejpam-4444	287	20	)	)	PUNCT
ejpam-4444	287	21	=	=	SYM
ejpam-4444	287	22	αc(a	αc(a	NOUN
ejpam-4444	287	23	,	,	PUNCT
ejpam-4444	287	24	b	b	NOUN
ejpam-4444	287	25	)	)	PUNCT
ejpam-4444	288	1	+	+	CCONJ
ejpam-4444	288	2	(	(	PUNCT
ejpam-4444	288	3	1−	1−	NUM
ejpam-4444	288	4	α)h(a	α)h(a	NOUN
ejpam-4444	288	5	,	,	PUNCT
ejpam-4444	288	6	b	b	NOUN
ejpam-4444	288	7	)	)	PUNCT
ejpam-4444	288	8	for	for	ADP
ejpam-4444	288	9	α	α	NOUN
ejpam-4444	288	10	=	=	SYM
ejpam-4444	288	11	1/2	1/2	NUM
ejpam-4444	288	12	;	;	PUNCT
ejpam-4444	288	13	2	2	NUM
ejpam-4444	288	14	)	)	PUNCT
ejpam-4444	288	15	l7/(13−12α)(a	l7/(13−12α)(a	NOUN
ejpam-4444	288	16	,	,	PUNCT
ejpam-4444	288	17	b	b	NOUN
ejpam-4444	288	18	)	)	PUNCT
ejpam-4444	288	19	>	>	X
ejpam-4444	288	20	αc(a	αc(a	NUM
ejpam-4444	288	21	,	,	PUNCT
ejpam-4444	288	22	b	b	NOUN
ejpam-4444	288	23	)	)	PUNCT
ejpam-4444	288	24	+	+	CCONJ
ejpam-4444	288	25	(	(	PUNCT
ejpam-4444	288	26	1−	1−	NUM
ejpam-4444	288	27	α)h(a	α)h(a	NOUN
ejpam-4444	288	28	,	,	PUNCT
ejpam-4444	288	29	b	b	NOUN
ejpam-4444	288	30	)	)	PUNCT
ejpam-4444	288	31	for	for	ADP
ejpam-4444	288	32	α	α	PRON
ejpam-4444	288	33	∈	∈	PROPN
ejpam-4444	288	34	(	(	PUNCT
ejpam-4444	288	35	0	0	NUM
ejpam-4444	288	36	,	,	PUNCT
ejpam-4444	288	37	1/2	1/2	NUM
ejpam-4444	288	38	)	)	PUNCT
ejpam-4444	288	39	;	;	PUNCT
ejpam-4444	288	40	3	3	X
ejpam-4444	288	41	)	)	PUNCT
ejpam-4444	288	42	l7/(13−12α)(a	l7/(13−12α)(a	NOUN
ejpam-4444	288	43	,	,	PUNCT
ejpam-4444	288	44	b	b	NOUN
ejpam-4444	288	45	)	)	PUNCT
ejpam-4444	288	46	<	<	X
ejpam-4444	288	47	αc(a	αc(a	NOUN
ejpam-4444	288	48	,	,	PUNCT
ejpam-4444	288	49	b	b	NOUN
ejpam-4444	288	50	)	)	PUNCT
ejpam-4444	289	1	+	+	CCONJ
ejpam-4444	289	2	(	(	PUNCT
ejpam-4444	289	3	1	1	NUM
ejpam-4444	289	4	−	−	PROPN
ejpam-4444	289	5	α)h(a	α)h(a	NOUN
ejpam-4444	289	6	,	,	PUNCT
ejpam-4444	289	7	b	b	NOUN
ejpam-4444	289	8	)	)	PUNCT
ejpam-4444	289	9	for	for	ADP
ejpam-4444	289	10	α	α	PRON
ejpam-4444	289	11	∈	∈	PROPN
ejpam-4444	289	12	(	(	PUNCT
ejpam-4444	289	13	1/2	1/2	NUM
ejpam-4444	289	14	,	,	PUNCT
ejpam-4444	289	15	1	1	NUM
ejpam-4444	289	16	)	)	PUNCT
ejpam-4444	289	17	,	,	PUNCT
ejpam-4444	289	18	and	and	CCONJ
ejpam-4444	289	19	the	the	DET
ejpam-4444	289	20	parameter	parameter	NOUN
ejpam-4444	289	21	7/(13−	7/(13−	PROPN
ejpam-4444	289	22	12α	12α	NOUN
ejpam-4444	289	23	)	)	PUNCT
ejpam-4444	289	24	can	can	AUX
ejpam-4444	289	25	not	not	PART
ejpam-4444	289	26	be	be	AUX
ejpam-4444	289	27	improved	improve	VERB
ejpam-4444	289	28	in	in	ADP
ejpam-4444	289	29	the	the	DET
ejpam-4444	289	30	sense	sense	NOUN
ejpam-4444	289	31	that	that	SCONJ
ejpam-4444	289	32	l	l	NOUN
ejpam-4444	289	33	7	7	NUM
ejpam-4444	289	34	13−12α	13−12α	NOUN
ejpam-4444	289	35	=	=	SYM
ejpam-4444	289	36	max	max	PROPN
ejpam-4444	289	37	c	c	PROPN
ejpam-4444	289	38	{	{	PUNCT
ejpam-4444	289	39	l	l	NOUN
ejpam-4444	289	40	1	1	NUM
ejpam-4444	289	41	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	289	42	∣∣∣l	∣∣∣l	NOUN
ejpam-4444	289	43	1	1	NUM
ejpam-4444	289	44	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	289	45	<	<	X
ejpam-4444	289	46	αc	αc	NOUN
ejpam-4444	290	1	+	+	CCONJ
ejpam-4444	291	1	(	(	PUNCT
ejpam-4444	291	2	1−	1−	NUM
ejpam-4444	291	3	α)h	α)h	NOUN
ejpam-4444	291	4	}	}	PUNCT
ejpam-4444	291	5	for	for	ADP
ejpam-4444	291	6	α	α	PRON
ejpam-4444	291	7	∈	∈	PROPN
ejpam-4444	291	8	(	(	PUNCT
ejpam-4444	291	9	1/2	1/2	NUM
ejpam-4444	291	10	,	,	PUNCT
ejpam-4444	291	11	1	1	NUM
ejpam-4444	291	12	)	)	PUNCT
ejpam-4444	291	13	i.e.	i.e.	X
ejpam-4444	291	14	c	c	NOUN
ejpam-4444	291	15	=	=	SYM
ejpam-4444	291	16	13/7	13/7	NOUN
ejpam-4444	291	17	.	.	PUNCT
ejpam-4444	292	1	proof	proof	NOUN
ejpam-4444	292	2	.	.	PUNCT
ejpam-4444	293	1	1	1	X
ejpam-4444	293	2	)	)	PUNCT
ejpam-4444	293	3	for	for	ADP
ejpam-4444	293	4	α	α	NOUN
ejpam-4444	293	5	=	=	SYM
ejpam-4444	293	6	1/2	1/2	NUM
ejpam-4444	293	7	,	,	PUNCT
ejpam-4444	293	8	we	we	PRON
ejpam-4444	293	9	have	have	VERB
ejpam-4444	293	10	l7/[13−12(1/2)](a	l7/[13−12(1/2)](a	NOUN
ejpam-4444	293	11	,	,	PUNCT
ejpam-4444	293	12	b	b	X
ejpam-4444	293	13	)	)	PUNCT
ejpam-4444	294	1	=	=	SYM
ejpam-4444	294	2	l1(a	l1(a	PROPN
ejpam-4444	294	3	,	,	PUNCT
ejpam-4444	294	4	b	b	NOUN
ejpam-4444	294	5	)	)	PUNCT
ejpam-4444	294	6	=	=	SYM
ejpam-4444	294	7	a+	a+	PUNCT
ejpam-4444	294	8	b	b	X
ejpam-4444	294	9	2	2	NUM
ejpam-4444	294	10	=	=	SYM
ejpam-4444	294	11	c(a	c(a	PROPN
ejpam-4444	294	12	,	,	PUNCT
ejpam-4444	294	13	b	b	NOUN
ejpam-4444	294	14	)	)	PUNCT
ejpam-4444	295	1	+	+	PROPN
ejpam-4444	295	2	h(a	h(a	PROPN
ejpam-4444	295	3	,	,	PUNCT
ejpam-4444	295	4	b	b	NOUN
ejpam-4444	295	5	)	)	PUNCT
ejpam-4444	295	6	2	2	NUM
ejpam-4444	295	7	.	.	NOUN
ejpam-4444	295	8	2	2	X
ejpam-4444	295	9	)	)	PUNCT
ejpam-4444	295	10	treated	treat	VERB
ejpam-4444	295	11	as	as	ADP
ejpam-4444	295	12	in	in	ADP
ejpam-4444	295	13	theorem	theorem	ADJ
ejpam-4444	295	14	1.2	1.2	NUM
ejpam-4444	295	15	)	)	PUNCT
ejpam-4444	295	16	,	,	PUNCT
ejpam-4444	295	17	the	the	DET
ejpam-4444	295	18	proposed	propose	VERB
ejpam-4444	295	19	inequality	inequality	NOUN
ejpam-4444	295	20	becomes	become	VERB
ejpam-4444	295	21	[	[	PUNCT
ejpam-4444	295	22	t	t	NOUN
ejpam-4444	295	23	20−12α	20−12α	NUM
ejpam-4444	295	24	13−12α	13−12α	NUM
ejpam-4444	295	25	−	−	NOUN
ejpam-4444	295	26	1	1	NUM
ejpam-4444	295	27	(	(	PUNCT
ejpam-4444	295	28	20−12α	20−12α	NUM
ejpam-4444	295	29	13−12α	13−12α	NUM
ejpam-4444	295	30	)	)	PUNCT
ejpam-4444	296	1	(	(	PUNCT
ejpam-4444	296	2	t−	t−	PROPN
ejpam-4444	296	3	1	1	NUM
ejpam-4444	296	4	)	)	PUNCT
ejpam-4444	296	5	]	]	X
ejpam-4444	296	6	(	(	PUNCT
ejpam-4444	296	7	13−12α)/7	13−12α)/7	NUM
ejpam-4444	296	8	>	>	X
ejpam-4444	296	9	α	α	PROPN
ejpam-4444	296	10	(	(	PUNCT
ejpam-4444	296	11	t2	t2	NOUN
ejpam-4444	296	12	+	+	CCONJ
ejpam-4444	296	13	1	1	NUM
ejpam-4444	296	14	t+	t+	NUM
ejpam-4444	296	15	1	1	NUM
ejpam-4444	296	16	)	)	PUNCT
ejpam-4444	296	17	+	+	CCONJ
ejpam-4444	296	18	(	(	PUNCT
ejpam-4444	296	19	1−	1−	NUM
ejpam-4444	296	20	α	α	NOUN
ejpam-4444	296	21	)	)	PUNCT
ejpam-4444	296	22	(	(	PUNCT
ejpam-4444	296	23	2	2	NUM
ejpam-4444	296	24	t	t	NOUN
ejpam-4444	296	25	t+	t+	PUNCT
ejpam-4444	296	26	1	1	NUM
ejpam-4444	296	27	)	)	PUNCT
ejpam-4444	296	28	α	α	PROPN
ejpam-4444	296	29	∈	∈	PROPN
ejpam-4444	296	30	(	(	PUNCT
ejpam-4444	296	31	0	0	NUM
ejpam-4444	296	32	,	,	PUNCT
ejpam-4444	296	33	1/2	1/2	NUM
ejpam-4444	296	34	)	)	PUNCT
ejpam-4444	296	35	,	,	PUNCT
ejpam-4444	296	36	(	(	PUNCT
ejpam-4444	296	37	9	9	X
ejpam-4444	296	38	)	)	PUNCT
ejpam-4444	296	39	for	for	ADP
ejpam-4444	296	40	t	t	NOUN
ejpam-4444	296	41	=	=	SYM
ejpam-4444	296	42	b	b	X
ejpam-4444	296	43	/	/	SYM
ejpam-4444	296	44	a	a	PRON
ejpam-4444	296	45	>	>	X
ejpam-4444	296	46	1	1	X
ejpam-4444	296	47	.	.	X
ejpam-4444	296	48	inequality	inequality	NOUN
ejpam-4444	296	49	(	(	PUNCT
ejpam-4444	296	50	9	9	NUM
ejpam-4444	296	51	)	)	PUNCT
ejpam-4444	296	52	is	be	AUX
ejpam-4444	296	53	equivalent	equivalent	ADJ
ejpam-4444	296	54	to	to	ADP
ejpam-4444	296	55	f	f	PROPN
ejpam-4444	296	56	(	(	PUNCT
ejpam-4444	296	57	t	t	PROPN
ejpam-4444	296	58	)	)	PUNCT
ejpam-4444	296	59	>	>	X
ejpam-4444	296	60	0	0	PUNCT
ejpam-4444	297	1	in	in	ADP
ejpam-4444	297	2	(	(	PUNCT
ejpam-4444	297	3	1	1	NUM
ejpam-4444	297	4	)	)	PUNCT
ejpam-4444	297	5	with	with	ADP
ejpam-4444	297	6	p	p	NOUN
ejpam-4444	297	7	=	=	PROPN
ejpam-4444	297	8	7/(13	7/(13	NUM
ejpam-4444	297	9	−	−	NOUN
ejpam-4444	297	10	12α	12α	NUM
ejpam-4444	297	11	)	)	PUNCT
ejpam-4444	297	12	.	.	PUNCT
ejpam-4444	298	1	using	use	VERB
ejpam-4444	298	2	lemma	lemma	PROPN
ejpam-4444	298	3	1	1	NUM
ejpam-4444	298	4	,	,	PUNCT
ejpam-4444	298	5	we	we	PRON
ejpam-4444	298	6	have	have	VERB
ejpam-4444	298	7	a	a	DET
ejpam-4444	298	8	formula	formula	NOUN
ejpam-4444	298	9	for	for	ADP
ejpam-4444	298	10	f	f	PROPN
ejpam-4444	298	11	′(t	′(t	PROPN
ejpam-4444	298	12	)	)	PUNCT
ejpam-4444	298	13	,	,	PUNCT
ejpam-4444	298	14	g′(t	g′(t	PROPN
ejpam-4444	298	15	)	)	PUNCT
ejpam-4444	298	16	,	,	PUNCT
ejpam-4444	298	17	g′′(t	g′′(t	NOUN
ejpam-4444	298	18	)	)	PUNCT
ejpam-4444	298	19	and	and	CCONJ
ejpam-4444	298	20	by	by	ADP
ejpam-4444	298	21	taking	take	VERB
ejpam-4444	298	22	derivative	derivative	NOUN
ejpam-4444	298	23	of	of	ADP
ejpam-4444	298	24	g′′(t	g′′(t	NOUN
ejpam-4444	298	25	)	)	PUNCT
ejpam-4444	298	26	,	,	PUNCT
ejpam-4444	298	27	we	we	PRON
ejpam-4444	298	28	obtain	obtain	VERB
ejpam-4444	298	29	g′′′(t	g′′′(t	NOUN
ejpam-4444	298	30	)	)	PUNCT
ejpam-4444	299	1	=	=	NUM
ejpam-4444	300	1	6ata−4	6ata−4	NOUN
ejpam-4444	300	2	(	(	PUNCT
ejpam-4444	300	3	13−	13−	NUM
ejpam-4444	300	4	12α)3	12α)3	NUM
ejpam-4444	300	5	h(t	h(t	PROPN
ejpam-4444	300	6	)	)	PUNCT
ejpam-4444	300	7	,	,	PUNCT
ejpam-4444	300	8	(	(	PUNCT
ejpam-4444	300	9	10	10	NUM
ejpam-4444	300	10	)	)	PUNCT
ejpam-4444	300	11	where	where	SCONJ
ejpam-4444	300	12	a	a	DET
ejpam-4444	300	13	=	=	ADJ
ejpam-4444	300	14	20−	20−	NUM
ejpam-4444	300	15	12α	12α	NOUN
ejpam-4444	300	16	13−	13−	NUM
ejpam-4444	300	17	12α	12α	NOUN
ejpam-4444	300	18	,	,	PUNCT
ejpam-4444	300	19	(	(	PUNCT
ejpam-4444	300	20	11	11	NUM
ejpam-4444	300	21	)	)	PUNCT
ejpam-4444	300	22	and	and	CCONJ
ejpam-4444	300	23	h(t	h(t	NUM
ejpam-4444	300	24	)	)	PUNCT
ejpam-4444	300	25	=	=	PUNCT
ejpam-4444	301	1	2(1−	2(1−	NUM
ejpam-4444	301	2	2α)(7−	2α)(7−	NUM
ejpam-4444	301	3	3α)(23−	3α)(23−	NUM
ejpam-4444	302	1	18α)(11−	18α)(11−	NUM
ejpam-4444	302	2	8α)t3	8α)t3	NUM
ejpam-4444	302	3	−	−	NOUN
ejpam-4444	303	1	14(3α2	14(3α2	NUM
ejpam-4444	303	2	−	−	ADP
ejpam-4444	303	3	18α+	18α+	NUM
ejpam-4444	303	4	10)(11−	10)(11−	NUM
ejpam-4444	303	5	8α)t2	8α)t2	NUM
ejpam-4444	303	6	+	+	CCONJ
ejpam-4444	304	1	14(6α2	14(6α2	NUM
ejpam-4444	304	2	−	−	PROPN
ejpam-4444	304	3	15α+	15α+	NOUN
ejpam-4444	304	4	13)(1−	13)(1−	NUM
ejpam-4444	304	5	2α)t	2α)t	NUM
ejpam-4444	304	6	a.	a.	NOUN
ejpam-4444	304	7	sonubon	sonubon	NOUN
ejpam-4444	304	8	,	,	PUNCT
ejpam-4444	304	9	s.	s.	PROPN
ejpam-4444	304	10	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	304	11	,	,	PUNCT
ejpam-4444	304	12	k.	k.	PROPN
ejpam-4444	304	13	nonlaopon	nonlaopon	ADV
ejpam-4444	304	14	/	/	SYM
ejpam-4444	304	15	eur	eur	PROPN
ejpam-4444	304	16	.	.	PUNCT
ejpam-4444	305	1	j.	j.	PROPN
ejpam-4444	305	2	pure	pure	PROPN
ejpam-4444	305	3	appl	appl	PROPN
ejpam-4444	305	4	.	.	PROPN
ejpam-4444	305	5	math	math	PROPN
ejpam-4444	305	6	,	,	PUNCT
ejpam-4444	305	7	15	15	NUM
ejpam-4444	305	8	(	(	PUNCT
ejpam-4444	305	9	3	3	NUM
ejpam-4444	305	10	)	)	PUNCT
ejpam-4444	305	11	(	(	PUNCT
ejpam-4444	305	12	2022	2022	NUM
ejpam-4444	305	13	)	)	PUNCT
ejpam-4444	305	14	,	,	PUNCT
ejpam-4444	305	15	1120	1120	NUM
ejpam-4444	305	16	-	-	SYM
ejpam-4444	305	17	1143	1143	NUM
ejpam-4444	305	18	1133	1133	NUM
ejpam-4444	305	19	−	−	PROPN
ejpam-4444	305	20	7α(1−	7α(1−	PROPN
ejpam-4444	305	21	2α)(19−	2α)(19−	NUM
ejpam-4444	305	22	24α	24α	NOUN
ejpam-4444	305	23	)	)	PUNCT
ejpam-4444	306	1	+	+	CCONJ
ejpam-4444	306	2	α(13−	α(13−	PROPN
ejpam-4444	306	3	12α)3t4−a	12α)3t4−a	NUM
ejpam-4444	306	4	.	.	PUNCT
ejpam-4444	307	1	(	(	PUNCT
ejpam-4444	307	2	12	12	NUM
ejpam-4444	307	3	)	)	PUNCT
ejpam-4444	307	4	note	note	NOUN
ejpam-4444	307	5	that	that	SCONJ
ejpam-4444	307	6	the	the	DET
ejpam-4444	307	7	coefficients	coefficient	NOUN
ejpam-4444	307	8	of	of	ADP
ejpam-4444	307	9	t3	t3	NOUN
ejpam-4444	307	10	and	and	CCONJ
ejpam-4444	307	11	t4−a	t4−a	PROPN
ejpam-4444	307	12	in	in	ADP
ejpam-4444	307	13	(	(	PUNCT
ejpam-4444	307	14	12	12	NUM
ejpam-4444	307	15	)	)	PUNCT
ejpam-4444	307	16	are	be	AUX
ejpam-4444	307	17	positive	positive	ADJ
ejpam-4444	307	18	but	but	CCONJ
ejpam-4444	307	19	that	that	PRON
ejpam-4444	307	20	of	of	ADP
ejpam-4444	307	21	t2	t2	NOUN
ejpam-4444	307	22	is	be	AUX
ejpam-4444	307	23	negative	negative	ADJ
ejpam-4444	307	24	for	for	ADP
ejpam-4444	307	25	α	α	PRON
ejpam-4444	307	26	∈	∈	PROPN
ejpam-4444	307	27	(	(	PUNCT
ejpam-4444	307	28	0	0	NUM
ejpam-4444	307	29	,	,	PUNCT
ejpam-4444	307	30	1/2	1/2	NUM
ejpam-4444	307	31	)	)	PUNCT
ejpam-4444	307	32	.	.	PUNCT
ejpam-4444	308	1	since	since	SCONJ
ejpam-4444	308	2	t4−a	t4−a	PROPN
ejpam-4444	308	3	>	>	X
ejpam-4444	308	4	t2	t2	PROPN
ejpam-4444	308	5	and	and	CCONJ
ejpam-4444	308	6	t2	t2	PROPN
ejpam-4444	308	7	>	>	X
ejpam-4444	308	8	2t−	2t−	PROPN
ejpam-4444	308	9	1	1	NUM
ejpam-4444	308	10	,	,	PUNCT
ejpam-4444	308	11	we	we	PRON
ejpam-4444	308	12	further	far	ADV
ejpam-4444	308	13	have	have	VERB
ejpam-4444	308	14	h(t	h(t	PROPN
ejpam-4444	308	15	)	)	PUNCT
ejpam-4444	308	16	>	>	X
ejpam-4444	309	1	2(1−	2(1−	NUM
ejpam-4444	309	2	2α)(7−	2α)(7−	NUM
ejpam-4444	309	3	3α)(23−	3α)(23−	NUM
ejpam-4444	309	4	18α)(11−	18α)(11−	NUM
ejpam-4444	309	5	8α)t(2t−	8α)t(2t−	NUM
ejpam-4444	309	6	1	1	NUM
ejpam-4444	309	7	)	)	PUNCT
ejpam-4444	309	8	+	+	CCONJ
ejpam-4444	310	1	[	[	X
ejpam-4444	310	2	α(13−	α(13−	PROPN
ejpam-4444	310	3	12α)3	12α)3	NUM
ejpam-4444	310	4	−	−	PROPN
ejpam-4444	311	1	14(3α2	14(3α2	NUM
ejpam-4444	311	2	−	−	ADP
ejpam-4444	311	3	18α+	18α+	NUM
ejpam-4444	311	4	10)(11−	10)(11−	NUM
ejpam-4444	311	5	8α)]t2	8α)]t2	NUM
ejpam-4444	311	6	+	+	CCONJ
ejpam-4444	311	7	14(6α2	14(6α2	NUM
ejpam-4444	311	8	−	−	PROPN
ejpam-4444	311	9	15α+	15α+	NOUN
ejpam-4444	311	10	13)(1−	13)(1−	NUM
ejpam-4444	311	11	2α)t−	2α)t−	NUM
ejpam-4444	311	12	7α(1−	7α(1−	NUM
ejpam-4444	311	13	2α)(19−	2α)(19−	NUM
ejpam-4444	311	14	24α	24α	NOUN
ejpam-4444	311	15	)	)	PUNCT
ejpam-4444	311	16	=	=	SYM
ejpam-4444	311	17	(	(	PUNCT
ejpam-4444	311	18	1−	1−	NUM
ejpam-4444	311	19	2α	2α	NOUN
ejpam-4444	311	20	)	)	PUNCT
ejpam-4444	311	21	[	[	PUNCT
ejpam-4444	311	22	(	(	PUNCT
ejpam-4444	311	23	−864α3	−864α3	NOUN
ejpam-4444	311	24	+	+	NOUN
ejpam-4444	311	25	6	6	NUM
ejpam-4444	311	26	,	,	PUNCT
ejpam-4444	311	27	072α2	072α2	NUM
ejpam-4444	311	28	−	−	NOUN
ejpam-4444	311	29	10	10	NUM
ejpam-4444	311	30	,	,	PUNCT
ejpam-4444	311	31	723α+	723α+	NUM
ejpam-4444	311	32	5	5	NUM
ejpam-4444	311	33	,	,	PUNCT
ejpam-4444	311	34	544)t2	544)t2	NUM
ejpam-4444	311	35	−	−	PROPN
ejpam-4444	311	36	32(5−	32(5−	NUM
ejpam-4444	311	37	3α)(9α2	3α)(9α2	NUM
ejpam-4444	311	38	−	−	NOUN
ejpam-4444	311	39	29α+	29α+	NUM
ejpam-4444	311	40	21)t−	21)t−	NUM
ejpam-4444	311	41	7α(19−	7α(19−	NUM
ejpam-4444	311	42	24α	24α	NOUN
ejpam-4444	311	43	)	)	PUNCT
ejpam-4444	311	44	]	]	PUNCT
ejpam-4444	311	45	.	.	PUNCT
ejpam-4444	312	1	now	now	ADV
ejpam-4444	312	2	consider	consider	VERB
ejpam-4444	312	3	the	the	DET
ejpam-4444	312	4	term	term	NOUN
ejpam-4444	312	5	on	on	ADP
ejpam-4444	312	6	the	the	DET
ejpam-4444	312	7	right	right	ADJ
ejpam-4444	312	8	side	side	NOUN
ejpam-4444	312	9	of	of	ADP
ejpam-4444	312	10	the	the	DET
ejpam-4444	312	11	above	above	ADJ
ejpam-4444	312	12	equality	equality	NOUN
ejpam-4444	312	13	sign	sign	NOUN
ejpam-4444	312	14	.	.	PUNCT
ejpam-4444	313	1	the	the	DET
ejpam-4444	313	2	coefficient	coefficient	NOUN
ejpam-4444	313	3	(	(	PUNCT
ejpam-4444	313	4	1	1	NUM
ejpam-4444	313	5	−	−	NUM
ejpam-4444	313	6	2α)(−864α3	2α)(−864α3	NUM
ejpam-4444	313	7	+	+	NOUN
ejpam-4444	313	8	6	6	NUM
ejpam-4444	313	9	,	,	PUNCT
ejpam-4444	313	10	072α2−10	072α2−10	PROPN
ejpam-4444	313	11	,	,	PUNCT
ejpam-4444	313	12	723α+5	723α+5	ADJ
ejpam-4444	313	13	,	,	PUNCT
ejpam-4444	313	14	544	544	NUM
ejpam-4444	313	15	)	)	PUNCT
ejpam-4444	313	16	of	of	ADP
ejpam-4444	313	17	t2	t2	NOUN
ejpam-4444	313	18	becomes	become	VERB
ejpam-4444	313	19	positive	positive	ADJ
ejpam-4444	313	20	for	for	ADP
ejpam-4444	313	21	α	α	PRON
ejpam-4444	313	22	∈	∈	PROPN
ejpam-4444	313	23	(	(	PUNCT
ejpam-4444	313	24	0	0	NUM
ejpam-4444	313	25	,	,	PUNCT
ejpam-4444	313	26	1/2	1/2	NUM
ejpam-4444	313	27	)	)	PUNCT
ejpam-4444	313	28	.	.	PUNCT
ejpam-4444	314	1	together	together	ADV
ejpam-4444	314	2	with	with	ADP
ejpam-4444	314	3	t	t	PROPN
ejpam-4444	314	4	<	<	X
ejpam-4444	314	5	t2	t2	PROPN
ejpam-4444	314	6	,	,	PUNCT
ejpam-4444	314	7	we	we	PRON
ejpam-4444	314	8	finally	finally	ADV
ejpam-4444	314	9	have	have	VERB
ejpam-4444	314	10	h(t	h(t	PROPN
ejpam-4444	314	11	)	)	PUNCT
ejpam-4444	314	12	>	>	X
ejpam-4444	315	1	(	(	PUNCT
ejpam-4444	315	2	1−	1−	NUM
ejpam-4444	315	3	2α	2α	NOUN
ejpam-4444	315	4	)	)	PUNCT
ejpam-4444	315	5	[	[	PUNCT
ejpam-4444	315	6	(	(	PUNCT
ejpam-4444	315	7	−864α3	−864α3	NOUN
ejpam-4444	315	8	+	+	NOUN
ejpam-4444	315	9	6	6	NUM
ejpam-4444	315	10	,	,	PUNCT
ejpam-4444	315	11	072α2	072α2	NUM
ejpam-4444	315	12	−	−	NOUN
ejpam-4444	315	13	10	10	NUM
ejpam-4444	315	14	,	,	PUNCT
ejpam-4444	315	15	723α+	723α+	NUM
ejpam-4444	315	16	5	5	NUM
ejpam-4444	315	17	,	,	PUNCT
ejpam-4444	315	18	544	544	NUM
ejpam-4444	315	19	)	)	PUNCT
ejpam-4444	315	20	−	−	PROPN
ejpam-4444	316	1	32(5−	32(5−	NUM
ejpam-4444	316	2	3α)(9α2	3α)(9α2	NUM
ejpam-4444	316	3	−	−	NUM
ejpam-4444	316	4	29α+	29α+	NUM
ejpam-4444	316	5	21)−	21)−	NUM
ejpam-4444	316	6	7α(19−	7α(19−	NUM
ejpam-4444	316	7	24α	24α	NOUN
ejpam-4444	316	8	)	)	PUNCT
ejpam-4444	316	9	]	]	PUNCT
ejpam-4444	317	1	t	t	NOUN
ejpam-4444	317	2	=	=	SYM
ejpam-4444	317	3	168(1−	168(1−	NUM
ejpam-4444	317	4	α)(13−	α)(13−	NUM
ejpam-4444	317	5	12α)(1−	12α)(1−	PROPN
ejpam-4444	317	6	2α)t	2α)t	NUM
ejpam-4444	317	7	>	>	X
ejpam-4444	317	8	0	0	X
ejpam-4444	317	9	.	.	PUNCT
ejpam-4444	318	1	therefore	therefore	ADV
ejpam-4444	318	2	g′′′(t	g′′′(t	VERB
ejpam-4444	318	3	)	)	PUNCT
ejpam-4444	318	4	>	>	X
ejpam-4444	318	5	0	0	PUNCT
ejpam-4444	319	1	for	for	ADP
ejpam-4444	319	2	all	all	DET
ejpam-4444	319	3	α	α	PRON
ejpam-4444	319	4	∈	∈	NOUN
ejpam-4444	319	5	(	(	PUNCT
ejpam-4444	319	6	0	0	NUM
ejpam-4444	319	7	,	,	PUNCT
ejpam-4444	319	8	1/2	1/2	NUM
ejpam-4444	319	9	)	)	PUNCT
ejpam-4444	319	10	.	.	PUNCT
ejpam-4444	320	1	3	3	X
ejpam-4444	320	2	)	)	PUNCT
ejpam-4444	320	3	here	here	ADV
ejpam-4444	320	4	the	the	DET
ejpam-4444	320	5	proposed	propose	VERB
ejpam-4444	320	6	inequality	inequality	NOUN
ejpam-4444	320	7	becomes	become	VERB
ejpam-4444	320	8	[	[	PUNCT
ejpam-4444	320	9	t	t	NOUN
ejpam-4444	320	10	20−12α	20−12α	NUM
ejpam-4444	320	11	13−12α	13−12α	NUM
ejpam-4444	320	12	−	−	NOUN
ejpam-4444	320	13	1	1	NUM
ejpam-4444	320	14	(	(	PUNCT
ejpam-4444	320	15	20−12α	20−12α	NUM
ejpam-4444	320	16	13−12α	13−12α	NUM
ejpam-4444	320	17	)	)	PUNCT
ejpam-4444	320	18	(	(	PUNCT
ejpam-4444	320	19	t−	t−	PROPN
ejpam-4444	320	20	1	1	NUM
ejpam-4444	320	21	)	)	PUNCT
ejpam-4444	320	22	]	]	X
ejpam-4444	320	23	(	(	PUNCT
ejpam-4444	320	24	13−12α)/7	13−12α)/7	NUM
ejpam-4444	320	25	<	<	X
ejpam-4444	320	26	α	α	PROPN
ejpam-4444	320	27	(	(	PUNCT
ejpam-4444	320	28	t2	t2	NOUN
ejpam-4444	320	29	+	+	CCONJ
ejpam-4444	320	30	1	1	NUM
ejpam-4444	320	31	t+	t+	NUM
ejpam-4444	320	32	1	1	NUM
ejpam-4444	320	33	)	)	PUNCT
ejpam-4444	321	1	+	+	CCONJ
ejpam-4444	321	2	(	(	PUNCT
ejpam-4444	321	3	1−	1−	NUM
ejpam-4444	321	4	α	α	NOUN
ejpam-4444	321	5	)	)	PUNCT
ejpam-4444	321	6	(	(	PUNCT
ejpam-4444	321	7	2	2	NUM
ejpam-4444	321	8	t	t	NOUN
ejpam-4444	321	9	t+	t+	PUNCT
ejpam-4444	321	10	1	1	NUM
ejpam-4444	321	11	)	)	PUNCT
ejpam-4444	321	12	α	α	PROPN
ejpam-4444	321	13	∈	∈	PROPN
ejpam-4444	321	14	(	(	PUNCT
ejpam-4444	321	15	1/2	1/2	NUM
ejpam-4444	321	16	,	,	PUNCT
ejpam-4444	321	17	1	1	NUM
ejpam-4444	321	18	)	)	PUNCT
ejpam-4444	321	19	,	,	PUNCT
ejpam-4444	321	20	(	(	PUNCT
ejpam-4444	321	21	13	13	NUM
ejpam-4444	321	22	)	)	PUNCT
ejpam-4444	321	23	for	for	ADP
ejpam-4444	321	24	t	t	NOUN
ejpam-4444	321	25	=	=	SYM
ejpam-4444	321	26	b	b	X
ejpam-4444	321	27	/	/	SYM
ejpam-4444	321	28	a	a	PRON
ejpam-4444	321	29	>	>	X
ejpam-4444	321	30	1	1	X
ejpam-4444	321	31	.	.	X
ejpam-4444	321	32	inequality	inequality	NOUN
ejpam-4444	321	33	(	(	PUNCT
ejpam-4444	321	34	13	13	NUM
ejpam-4444	321	35	)	)	PUNCT
ejpam-4444	321	36	is	be	AUX
ejpam-4444	321	37	equivalent	equivalent	ADJ
ejpam-4444	321	38	to	to	ADP
ejpam-4444	321	39	f	f	PROPN
ejpam-4444	321	40	(	(	PUNCT
ejpam-4444	321	41	t	t	PROPN
ejpam-4444	321	42	)	)	PUNCT
ejpam-4444	321	43	<	<	X
ejpam-4444	321	44	0	0	PUNCT
ejpam-4444	322	1	in	in	ADP
ejpam-4444	322	2	(	(	PUNCT
ejpam-4444	322	3	1	1	NUM
ejpam-4444	322	4	)	)	PUNCT
ejpam-4444	322	5	.	.	PUNCT
ejpam-4444	323	1	terms	term	NOUN
ejpam-4444	323	2	g′′′(t	g′′′(t	VERB
ejpam-4444	323	3	)	)	PUNCT
ejpam-4444	323	4	,	,	PUNCT
ejpam-4444	323	5	a	a	PRON
ejpam-4444	323	6	and	and	CCONJ
ejpam-4444	323	7	h(t	h(t	NUM
ejpam-4444	323	8	)	)	PUNCT
ejpam-4444	323	9	are	be	AUX
ejpam-4444	323	10	still	still	ADV
ejpam-4444	323	11	of	of	ADP
ejpam-4444	323	12	the	the	DET
ejpam-4444	323	13	forms	form	NOUN
ejpam-4444	323	14	(	(	PUNCT
ejpam-4444	323	15	10	10	NUM
ejpam-4444	323	16	)	)	PUNCT
ejpam-4444	323	17	,	,	PUNCT
ejpam-4444	323	18	(	(	PUNCT
ejpam-4444	323	19	11	11	NUM
ejpam-4444	323	20	)	)	PUNCT
ejpam-4444	323	21	and	and	CCONJ
ejpam-4444	323	22	(	(	PUNCT
ejpam-4444	323	23	12	12	NUM
ejpam-4444	323	24	)	)	PUNCT
ejpam-4444	323	25	,	,	PUNCT
ejpam-4444	323	26	respectively	respectively	ADV
ejpam-4444	323	27	.	.	PUNCT
ejpam-4444	324	1	it	it	PRON
ejpam-4444	324	2	is	be	AUX
ejpam-4444	324	3	then	then	ADV
ejpam-4444	324	4	sufficient	sufficient	ADJ
ejpam-4444	324	5	to	to	PART
ejpam-4444	324	6	show	show	VERB
ejpam-4444	324	7	that	that	SCONJ
ejpam-4444	324	8	h(t	h(t	PROPN
ejpam-4444	324	9	)	)	PUNCT
ejpam-4444	324	10	<	<	X
ejpam-4444	324	11	0	0	PUNCT
ejpam-4444	324	12	for	for	ADP
ejpam-4444	324	13	all	all	DET
ejpam-4444	324	14	α	α	PRON
ejpam-4444	324	15	∈	∈	PROPN
ejpam-4444	324	16	(	(	PUNCT
ejpam-4444	324	17	1/2	1/2	NUM
ejpam-4444	324	18	,	,	PUNCT
ejpam-4444	324	19	1	1	NUM
ejpam-4444	324	20	)	)	PUNCT
ejpam-4444	324	21	.	.	PUNCT
ejpam-4444	325	1	to	to	ADP
ejpam-4444	325	2	that	that	DET
ejpam-4444	325	3	end	end	NOUN
ejpam-4444	325	4	,	,	PUNCT
ejpam-4444	325	5	we	we	PRON
ejpam-4444	325	6	divide	divide	VERB
ejpam-4444	325	7	our	our	PRON
ejpam-4444	325	8	proof	proof	NOUN
ejpam-4444	325	9	into	into	ADP
ejpam-4444	325	10	two	two	NUM
ejpam-4444	325	11	cases	case	NOUN
ejpam-4444	325	12	α	α	X
ejpam-4444	325	13	∈	∈	NOUN
ejpam-4444	325	14	(	(	PUNCT
ejpam-4444	325	15	8/9	8/9	NUM
ejpam-4444	325	16	,	,	PUNCT
ejpam-4444	325	17	1	1	NUM
ejpam-4444	325	18	)	)	PUNCT
ejpam-4444	325	19	and	and	CCONJ
ejpam-4444	325	20	α	α	PRON
ejpam-4444	325	21	∈	∈	PROPN
ejpam-4444	325	22	(	(	PUNCT
ejpam-4444	325	23	1/2	1/2	NUM
ejpam-4444	325	24	,	,	PUNCT
ejpam-4444	325	25	8/9	8/9	NUM
ejpam-4444	325	26	]	]	PUNCT
ejpam-4444	325	27	.	.	NOUN
ejpam-4444	326	1	3.1	3.1	NUM
ejpam-4444	326	2	)	)	PUNCT
ejpam-4444	326	3	case	case	NOUN
ejpam-4444	326	4	α	α	X
ejpam-4444	326	5	∈	∈	PROPN
ejpam-4444	326	6	(	(	PUNCT
ejpam-4444	326	7	8/9	8/9	NUM
ejpam-4444	326	8	,	,	PUNCT
ejpam-4444	326	9	1	1	NUM
ejpam-4444	326	10	):	):	PUNCT
ejpam-4444	326	11	for	for	ADP
ejpam-4444	326	12	such	such	ADJ
ejpam-4444	326	13	α	α	NOUN
ejpam-4444	326	14	,	,	PUNCT
ejpam-4444	326	15	we	we	PRON
ejpam-4444	326	16	have	have	VERB
ejpam-4444	326	17	4−a	4−a	NUM
ejpam-4444	326	18	∈	∈	NOUN
ejpam-4444	326	19	(	(	PUNCT
ejpam-4444	326	20	−4	−4	PROPN
ejpam-4444	326	21	,	,	PUNCT
ejpam-4444	326	22	0	0	NUM
ejpam-4444	326	23	)	)	PUNCT
ejpam-4444	326	24	and	and	CCONJ
ejpam-4444	326	25	t4−a	t4−a	PROPN
ejpam-4444	326	26	<	<	X
ejpam-4444	326	27	1	1	NUM
ejpam-4444	326	28	<	<	SYM
ejpam-4444	326	29	1	1	NUM
ejpam-4444	326	30	+	+	CCONJ
ejpam-4444	326	31	(	(	PUNCT
ejpam-4444	326	32	4−a)(t−	4−a)(t−	PROPN
ejpam-4444	326	33	1	1	NUM
ejpam-4444	326	34	)	)	PUNCT
ejpam-4444	326	35	+	+	CCONJ
ejpam-4444	326	36	(	(	PUNCT
ejpam-4444	326	37	4−a)(3−a	4−a)(3−a	NOUN
ejpam-4444	326	38	)	)	PUNCT
ejpam-4444	326	39	2	2	NUM
ejpam-4444	326	40	(	(	PUNCT
ejpam-4444	326	41	t−	t−	PROPN
ejpam-4444	326	42	1)2	1)2	NUM
ejpam-4444	326	43	=	=	SYM
ejpam-4444	326	44	(	(	PUNCT
ejpam-4444	326	45	432α2	432α2	NOUN
ejpam-4444	326	46	−	−	NUM
ejpam-4444	326	47	726α+	726α+	NUM
ejpam-4444	326	48	304)t2	304)t2	NUM
ejpam-4444	326	49	+	+	CCONJ
ejpam-4444	326	50	(	(	PUNCT
ejpam-4444	326	51	−432α2	−432α2	PROPN
ejpam-4444	326	52	+	+	NUM
ejpam-4444	326	53	600α−	600α−	NUM
ejpam-4444	326	54	192)t+	192)t+	NUM
ejpam-4444	326	55	(	(	PUNCT
ejpam-4444	326	56	144α2	144α2	NUM
ejpam-4444	326	57	−	−	NOUN
ejpam-4444	326	58	186α+	186α+	NUM
ejpam-4444	326	59	57	57	NUM
ejpam-4444	326	60	)	)	PUNCT
ejpam-4444	326	61	(	(	PUNCT
ejpam-4444	326	62	13−	13−	NUM
ejpam-4444	326	63	12α)2	12α)2	NUM
ejpam-4444	326	64	.	.	PUNCT
ejpam-4444	327	1	a.	a.	NOUN
ejpam-4444	327	2	sonubon	sonubon	PROPN
ejpam-4444	327	3	,	,	PUNCT
ejpam-4444	327	4	s.	s.	PROPN
ejpam-4444	327	5	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	327	6	,	,	PUNCT
ejpam-4444	327	7	k.	k.	PROPN
ejpam-4444	327	8	nonlaopon	nonlaopon	ADV
ejpam-4444	327	9	/	/	SYM
ejpam-4444	327	10	eur	eur	PROPN
ejpam-4444	327	11	.	.	PUNCT
ejpam-4444	328	1	j.	j.	PROPN
ejpam-4444	328	2	pure	pure	PROPN
ejpam-4444	328	3	appl	appl	PROPN
ejpam-4444	328	4	.	.	PROPN
ejpam-4444	328	5	math	math	PROPN
ejpam-4444	328	6	,	,	PUNCT
ejpam-4444	328	7	15	15	NUM
ejpam-4444	328	8	(	(	PUNCT
ejpam-4444	328	9	3	3	NUM
ejpam-4444	328	10	)	)	PUNCT
ejpam-4444	328	11	(	(	PUNCT
ejpam-4444	328	12	2022	2022	NUM
ejpam-4444	328	13	)	)	PUNCT
ejpam-4444	328	14	,	,	PUNCT
ejpam-4444	328	15	1120	1120	NUM
ejpam-4444	328	16	-	-	SYM
ejpam-4444	328	17	1143	1143	NUM
ejpam-4444	328	18	1134	1134	NUM
ejpam-4444	328	19	hence	hence	ADV
ejpam-4444	328	20	h(t	h(t	NUM
ejpam-4444	328	21	)	)	PUNCT
ejpam-4444	328	22	<	<	X
ejpam-4444	328	23	2(2α−	2(2α−	NUM
ejpam-4444	328	24	1	1	NUM
ejpam-4444	328	25	)	)	PUNCT
ejpam-4444	328	26	[	[	PUNCT
ejpam-4444	328	27	−	−	PROPN
ejpam-4444	328	28	(	(	PUNCT
ejpam-4444	328	29	7−	7−	NUM
ejpam-4444	328	30	3α)(23−	3α)(23−	NUM
ejpam-4444	328	31	18α)(11−	18α)(11−	NUM
ejpam-4444	328	32	8α)t3	8α)t3	NUM
ejpam-4444	328	33	+	+	CCONJ
ejpam-4444	328	34	2(−648α3	2(−648α3	NUM
ejpam-4444	328	35	+	+	CCONJ
ejpam-4444	328	36	1	1	NUM
ejpam-4444	328	37	,	,	PUNCT
ejpam-4444	328	38	509α2	509α2	NUM
ejpam-4444	328	39	−	−	NOUN
ejpam-4444	328	40	1	1	NUM
ejpam-4444	328	41	,	,	PUNCT
ejpam-4444	328	42	191α+	191α+	NUM
ejpam-4444	328	43	385)t2	385)t2	NUM
ejpam-4444	328	44	−	−	PROPN
ejpam-4444	328	45	(	(	PUNCT
ejpam-4444	328	46	−1	−1	NOUN
ejpam-4444	328	47	,	,	PUNCT
ejpam-4444	328	48	296α3	296α3	NUM
ejpam-4444	328	49	+	+	CCONJ
ejpam-4444	328	50	2	2	NUM
ejpam-4444	328	51	,	,	PUNCT
ejpam-4444	328	52	598α2	598α2	NUM
ejpam-4444	328	53	−	−	PROPN
ejpam-4444	328	54	1	1	NUM
ejpam-4444	328	55	,	,	PUNCT
ejpam-4444	328	56	353α+	353α+	NUM
ejpam-4444	328	57	91)t	91)t	NUM
ejpam-4444	329	1	−	−	NUM
ejpam-4444	330	1	2α(24α−	2α(24α−	NUM
ejpam-4444	330	2	19)(9α−	19)(9α−	NUM
ejpam-4444	330	3	8)	8)	NUM
ejpam-4444	330	4	]	]	PUNCT
ejpam-4444	330	5	.	.	PUNCT
ejpam-4444	331	1	now	now	ADV
ejpam-4444	331	2	consider	consider	VERB
ejpam-4444	331	3	the	the	DET
ejpam-4444	331	4	term	term	NOUN
ejpam-4444	331	5	on	on	ADP
ejpam-4444	331	6	the	the	DET
ejpam-4444	331	7	right	right	ADJ
ejpam-4444	331	8	side	side	NOUN
ejpam-4444	331	9	of	of	ADP
ejpam-4444	331	10	the	the	DET
ejpam-4444	331	11	above	above	ADJ
ejpam-4444	331	12	inequality	inequality	NOUN
ejpam-4444	331	13	sign	sign	NOUN
ejpam-4444	331	14	.	.	PUNCT
ejpam-4444	332	1	as	as	SCONJ
ejpam-4444	332	2	the	the	DET
ejpam-4444	332	3	coefficient	coefficient	NOUN
ejpam-4444	332	4	of	of	ADP
ejpam-4444	332	5	t3	t3	PROPN
ejpam-4444	332	6	is	be	AUX
ejpam-4444	332	7	negative	negative	ADJ
ejpam-4444	332	8	for	for	ADP
ejpam-4444	332	9	α	α	PRON
ejpam-4444	332	10	∈	∈	PROPN
ejpam-4444	332	11	(	(	PUNCT
ejpam-4444	332	12	1/2	1/2	NUM
ejpam-4444	332	13	,	,	PUNCT
ejpam-4444	332	14	1	1	NUM
ejpam-4444	332	15	)	)	PUNCT
ejpam-4444	332	16	and	and	CCONJ
ejpam-4444	332	17	t3	t3	PROPN
ejpam-4444	332	18	>	>	X
ejpam-4444	332	19	t(2t−	t(2t−	PROPN
ejpam-4444	332	20	1	1	NUM
ejpam-4444	332	21	)	)	PUNCT
ejpam-4444	332	22	,	,	PUNCT
ejpam-4444	332	23	we	we	PRON
ejpam-4444	332	24	have	have	VERB
ejpam-4444	332	25	h(t	h(t	NUM
ejpam-4444	332	26	)	)	PUNCT
ejpam-4444	332	27	<	<	X
ejpam-4444	332	28	2(2α−	2(2α−	NUM
ejpam-4444	332	29	1	1	NUM
ejpam-4444	332	30	)	)	PUNCT
ejpam-4444	332	31	[	[	PUNCT
ejpam-4444	332	32	−	−	PROPN
ejpam-4444	332	33	(	(	PUNCT
ejpam-4444	332	34	7−	7−	NUM
ejpam-4444	332	35	3α)(23−	3α)(23−	NUM
ejpam-4444	332	36	18α)(11−	18α)(11−	NUM
ejpam-4444	332	37	8α)t(2t−	8α)t(2t−	NUM
ejpam-4444	332	38	1	1	NUM
ejpam-4444	332	39	)	)	PUNCT
ejpam-4444	332	40	+	+	CCONJ
ejpam-4444	333	1	2(−648α3	2(−648α3	NUM
ejpam-4444	333	2	+	+	CCONJ
ejpam-4444	333	3	1	1	NUM
ejpam-4444	333	4	,	,	PUNCT
ejpam-4444	333	5	509α2	509α2	NUM
ejpam-4444	333	6	−	−	NOUN
ejpam-4444	333	7	1	1	NUM
ejpam-4444	333	8	,	,	PUNCT
ejpam-4444	333	9	191α+	191α+	NUM
ejpam-4444	333	10	385)t2	385)t2	NUM
ejpam-4444	334	1	−	−	PROPN
ejpam-4444	334	2	(	(	PUNCT
ejpam-4444	334	3	−1	−1	NOUN
ejpam-4444	334	4	,	,	PUNCT
ejpam-4444	334	5	296α3	296α3	NUM
ejpam-4444	334	6	+	+	CCONJ
ejpam-4444	334	7	2	2	NUM
ejpam-4444	334	8	,	,	PUNCT
ejpam-4444	334	9	598α2	598α2	NUM
ejpam-4444	334	10	−	−	PROPN
ejpam-4444	334	11	1	1	NUM
ejpam-4444	334	12	,	,	PUNCT
ejpam-4444	334	13	353α+	353α+	NUM
ejpam-4444	334	14	91)t	91)t	NUM
ejpam-4444	334	15	−	−	NUM
ejpam-4444	335	1	2α(24α−	2α(24α−	NUM
ejpam-4444	335	2	19)(9α−	19)(9α−	NUM
ejpam-4444	335	3	8)	8)	NUM
ejpam-4444	335	4	]	]	PUNCT
ejpam-4444	335	5	=	=	SYM
ejpam-4444	335	6	2(2α−	2(2α−	NUM
ejpam-4444	335	7	1	1	NUM
ejpam-4444	335	8	)	)	PUNCT
ejpam-4444	335	9	[	[	PUNCT
ejpam-4444	335	10	(	(	PUNCT
ejpam-4444	335	11	−432α3	−432α3	PROPN
ejpam-4444	335	12	−	−	PROPN
ejpam-4444	335	13	1	1	NUM
ejpam-4444	335	14	,	,	PUNCT
ejpam-4444	335	15	290α2	290α2	NUM
ejpam-4444	335	16	+	+	CCONJ
ejpam-4444	335	17	4	4	NUM
ejpam-4444	335	18	,	,	PUNCT
ejpam-4444	335	19	484α−	484α−	NUM
ejpam-4444	335	20	2	2	NUM
ejpam-4444	335	21	,	,	PUNCT
ejpam-4444	335	22	772)t2	772)t2	NUM
ejpam-4444	335	23	+	+	CCONJ
ejpam-4444	335	24	(	(	PUNCT
ejpam-4444	335	25	864α3	864α3	NUM
ejpam-4444	335	26	−	−	NOUN
ejpam-4444	335	27	444α2	444α2	NUM
ejpam-4444	335	28	−	−	NOUN
ejpam-4444	335	29	2	2	NUM
ejpam-4444	335	30	,	,	PUNCT
ejpam-4444	335	31	080α+	080α+	NUM
ejpam-4444	335	32	1	1	NUM
ejpam-4444	335	33	,	,	PUNCT
ejpam-4444	335	34	680)t	680)t	NUM
ejpam-4444	335	35	−	−	PROPN
ejpam-4444	335	36	2α(24α−	2α(24α−	NUM
ejpam-4444	335	37	19)(9α−	19)(9α−	NUM
ejpam-4444	335	38	8)	8)	NUM
ejpam-4444	335	39	]	]	PUNCT
ejpam-4444	335	40	.	.	PUNCT
ejpam-4444	336	1	examine	examine	VERB
ejpam-4444	336	2	the	the	DET
ejpam-4444	336	3	term	term	NOUN
ejpam-4444	336	4	on	on	ADP
ejpam-4444	336	5	the	the	DET
ejpam-4444	336	6	right	right	ADJ
ejpam-4444	336	7	side	side	NOUN
ejpam-4444	336	8	of	of	ADP
ejpam-4444	336	9	the	the	DET
ejpam-4444	336	10	equality	equality	NOUN
ejpam-4444	336	11	sign	sign	NOUN
ejpam-4444	336	12	above	above	ADV
ejpam-4444	336	13	.	.	PUNCT
ejpam-4444	337	1	the	the	DET
ejpam-4444	337	2	coefficient	coefficient	NOUN
ejpam-4444	337	3	−432α3	−432α3	PROPN
ejpam-4444	337	4	−	−	PROPN
ejpam-4444	337	5	1	1	NUM
ejpam-4444	337	6	,	,	PUNCT
ejpam-4444	337	7	290α2	290α2	NUM
ejpam-4444	337	8	+	+	CCONJ
ejpam-4444	337	9	4	4	NUM
ejpam-4444	337	10	,	,	PUNCT
ejpam-4444	337	11	484α	484α	NOUN
ejpam-4444	337	12	−	−	NOUN
ejpam-4444	337	13	2	2	NUM
ejpam-4444	337	14	,	,	PUNCT
ejpam-4444	337	15	772	772	NUM
ejpam-4444	337	16	is	be	AUX
ejpam-4444	337	17	an	an	DET
ejpam-4444	337	18	increasing	increase	VERB
ejpam-4444	337	19	function	function	NOUN
ejpam-4444	337	20	of	of	ADP
ejpam-4444	337	21	α	α	PROPN
ejpam-4444	337	22	∈	∈	PROPN
ejpam-4444	337	23	(	(	PUNCT
ejpam-4444	337	24	1/2	1/2	NUM
ejpam-4444	337	25	,	,	PUNCT
ejpam-4444	337	26	1	1	NUM
ejpam-4444	337	27	)	)	PUNCT
ejpam-4444	337	28	with	with	ADP
ejpam-4444	337	29	negative	negative	ADJ
ejpam-4444	337	30	value	value	NOUN
ejpam-4444	337	31	(	(	PUNCT
ejpam-4444	337	32	-10	-10	NUM
ejpam-4444	337	33	)	)	PUNCT
ejpam-4444	337	34	at	at	ADP
ejpam-4444	337	35	α	α	NOUN
ejpam-4444	337	36	=	=	SYM
ejpam-4444	337	37	1	1	X
ejpam-4444	337	38	.	.	PUNCT
ejpam-4444	338	1	since	since	SCONJ
ejpam-4444	338	2	the	the	DET
ejpam-4444	338	3	coefficient	coefficient	NOUN
ejpam-4444	338	4	of	of	ADP
ejpam-4444	338	5	t2	t2	NOUN
ejpam-4444	338	6	is	be	AUX
ejpam-4444	338	7	negative	negative	ADJ
ejpam-4444	338	8	for	for	ADP
ejpam-4444	338	9	α	α	PRON
ejpam-4444	338	10	∈	∈	PROPN
ejpam-4444	338	11	(	(	PUNCT
ejpam-4444	338	12	8/9	8/9	NUM
ejpam-4444	338	13	,	,	PUNCT
ejpam-4444	338	14	1	1	NUM
ejpam-4444	338	15	)	)	PUNCT
ejpam-4444	338	16	and	and	CCONJ
ejpam-4444	338	17	t2	t2	PROPN
ejpam-4444	338	18	>	>	X
ejpam-4444	338	19	2	2	NUM
ejpam-4444	338	20	t	t	NOUN
ejpam-4444	338	21	−	−	NOUN
ejpam-4444	338	22	1	1	NUM
ejpam-4444	338	23	,	,	PUNCT
ejpam-4444	338	24	we	we	PRON
ejpam-4444	338	25	obtain	obtain	VERB
ejpam-4444	338	26	h(t	h(t	NUM
ejpam-4444	338	27	)	)	PUNCT
ejpam-4444	338	28	<	<	X
ejpam-4444	338	29	2(2α−	2(2α−	NUM
ejpam-4444	338	30	1	1	NUM
ejpam-4444	338	31	)	)	PUNCT
ejpam-4444	338	32	[	[	PUNCT
ejpam-4444	338	33	(	(	PUNCT
ejpam-4444	338	34	−432α3	−432α3	PROPN
ejpam-4444	338	35	−	−	PROPN
ejpam-4444	338	36	1	1	NUM
ejpam-4444	338	37	,	,	PUNCT
ejpam-4444	338	38	290α2	290α2	NUM
ejpam-4444	338	39	+	+	CCONJ
ejpam-4444	338	40	4	4	NUM
ejpam-4444	338	41	,	,	PUNCT
ejpam-4444	338	42	484α−	484α−	NUM
ejpam-4444	338	43	2	2	NUM
ejpam-4444	338	44	,	,	PUNCT
ejpam-4444	338	45	772)(2t−	772)(2t−	NOUN
ejpam-4444	338	46	1	1	NUM
ejpam-4444	338	47	)	)	PUNCT
ejpam-4444	338	48	+	+	CCONJ
ejpam-4444	338	49	(	(	PUNCT
ejpam-4444	338	50	864α3	864α3	NUM
ejpam-4444	338	51	−	−	NOUN
ejpam-4444	338	52	444α2	444α2	NUM
ejpam-4444	338	53	−	−	NOUN
ejpam-4444	338	54	2	2	NUM
ejpam-4444	338	55	,	,	PUNCT
ejpam-4444	338	56	080α+	080α+	NUM
ejpam-4444	338	57	1	1	NUM
ejpam-4444	338	58	,	,	PUNCT
ejpam-4444	338	59	680)t	680)t	NUM
ejpam-4444	338	60	−	−	PROPN
ejpam-4444	338	61	2α(24α−	2α(24α−	NUM
ejpam-4444	338	62	19)(9α−	19)(9α−	NUM
ejpam-4444	338	63	8)	8)	NUM
ejpam-4444	338	64	]	]	PUNCT
ejpam-4444	338	65	=	=	SYM
ejpam-4444	338	66	2(2α−	2(2α−	NUM
ejpam-4444	338	67	1	1	NUM
ejpam-4444	338	68	)	)	PUNCT
ejpam-4444	338	69	[	[	PUNCT
ejpam-4444	338	70	−	−	PROPN
ejpam-4444	338	71	168(1−	168(1−	NUM
ejpam-4444	338	72	α)(23−	α)(23−	NOUN
ejpam-4444	338	73	18α)t+	18α)t+	NUM
ejpam-4444	338	74	252(1−	252(1−	NUM
ejpam-4444	338	75	α)(11−	α)(11−	NUM
ejpam-4444	338	76	8α	8α	NUM
ejpam-4444	338	77	)	)	PUNCT
ejpam-4444	338	78	]	]	PUNCT
ejpam-4444	338	79	.	.	PUNCT
ejpam-4444	339	1	look	look	VERB
ejpam-4444	339	2	at	at	ADP
ejpam-4444	339	3	the	the	DET
ejpam-4444	339	4	term	term	NOUN
ejpam-4444	339	5	on	on	ADP
ejpam-4444	339	6	the	the	DET
ejpam-4444	339	7	right	right	ADJ
ejpam-4444	339	8	side	side	NOUN
ejpam-4444	339	9	of	of	ADP
ejpam-4444	339	10	the	the	DET
ejpam-4444	339	11	above	above	ADJ
ejpam-4444	339	12	inequality	inequality	NOUN
ejpam-4444	339	13	sign	sign	NOUN
ejpam-4444	339	14	.	.	PUNCT
ejpam-4444	340	1	since	since	SCONJ
ejpam-4444	340	2	the	the	DET
ejpam-4444	340	3	coefficient	coefficient	NOUN
ejpam-4444	340	4	−168(1−	−168(1−	PROPN
ejpam-4444	340	5	α)(23−	α)(23−	PROPN
ejpam-4444	340	6	18α	18α	NUM
ejpam-4444	340	7	)	)	PUNCT
ejpam-4444	340	8	of	of	ADP
ejpam-4444	340	9	t	t	PROPN
ejpam-4444	340	10	is	be	AUX
ejpam-4444	340	11	negative	negative	ADJ
ejpam-4444	340	12	and	and	CCONJ
ejpam-4444	340	13	t	t	X
ejpam-4444	340	14	>	>	X
ejpam-4444	340	15	1	1	NUM
ejpam-4444	340	16	,	,	PUNCT
ejpam-4444	340	17	we	we	PRON
ejpam-4444	340	18	finally	finally	ADV
ejpam-4444	340	19	have	have	VERB
ejpam-4444	340	20	h(t	h(t	NUM
ejpam-4444	340	21	)	)	PUNCT
ejpam-4444	340	22	<	<	X
ejpam-4444	340	23	2(2α−	2(2α−	NUM
ejpam-4444	340	24	1	1	NUM
ejpam-4444	340	25	)	)	PUNCT
ejpam-4444	340	26	[	[	PUNCT
ejpam-4444	340	27	−	−	PROPN
ejpam-4444	340	28	168(1−	168(1−	NUM
ejpam-4444	340	29	α)(23−	α)(23−	NOUN
ejpam-4444	340	30	18α)t+	18α)t+	NUM
ejpam-4444	340	31	252(1−	252(1−	NUM
ejpam-4444	340	32	α)(11−	α)(11−	NUM
ejpam-4444	340	33	8α	8α	NUM
ejpam-4444	340	34	)	)	PUNCT
ejpam-4444	340	35	]	]	PUNCT
ejpam-4444	341	1	<	<	X
ejpam-4444	341	2	−168(2α−	−168(2α−	X
ejpam-4444	341	3	1)(1−	1)(1−	NUM
ejpam-4444	341	4	α)(13−	α)(13−	NUM
ejpam-4444	341	5	12α	12α	NOUN
ejpam-4444	341	6	)	)	PUNCT
ejpam-4444	341	7	<	<	X
ejpam-4444	341	8	0	0	NUM
ejpam-4444	341	9	.	.	NOUN
ejpam-4444	341	10	3.2	3.2	NUM
ejpam-4444	341	11	)	)	PUNCT
ejpam-4444	341	12	case	case	NOUN
ejpam-4444	341	13	α	α	X
ejpam-4444	341	14	∈	∈	PROPN
ejpam-4444	341	15	(	(	PUNCT
ejpam-4444	341	16	1/2	1/2	NUM
ejpam-4444	341	17	,	,	PUNCT
ejpam-4444	341	18	8/9	8/9	NUM
ejpam-4444	341	19	]	]	PUNCT
ejpam-4444	341	20	:	:	PUNCT
ejpam-4444	341	21	for	for	ADP
ejpam-4444	341	22	α	α	NOUN
ejpam-4444	341	23	in	in	ADP
ejpam-4444	341	24	this	this	DET
ejpam-4444	341	25	interval	interval	NOUN
ejpam-4444	341	26	,	,	PUNCT
ejpam-4444	341	27	the	the	DET
ejpam-4444	341	28	coefficient	coefficient	NOUN
ejpam-4444	341	29	of	of	ADP
ejpam-4444	341	30	t3	t3	PROPN
ejpam-4444	341	31	in	in	ADP
ejpam-4444	341	32	(	(	PUNCT
ejpam-4444	341	33	12	12	NUM
ejpam-4444	341	34	)	)	PUNCT
ejpam-4444	341	35	is	be	AUX
ejpam-4444	341	36	negative	negative	ADJ
ejpam-4444	341	37	and	and	CCONJ
ejpam-4444	341	38	4−a	4−a	NUM
ejpam-4444	341	39	∈	∈	PROPN
ejpam-4444	342	1	[	[	X
ejpam-4444	342	2	0	0	NUM
ejpam-4444	342	3	,	,	PUNCT
ejpam-4444	342	4	2	2	NUM
ejpam-4444	342	5	)	)	PUNCT
ejpam-4444	342	6	.	.	PUNCT
ejpam-4444	343	1	hence	hence	ADV
ejpam-4444	343	2	t4−a	t4−a	PROPN
ejpam-4444	343	3	<	<	X
ejpam-4444	343	4	t2	t2	PROPN
ejpam-4444	343	5	.	.	PUNCT
ejpam-4444	344	1	these	these	DET
ejpam-4444	344	2	consequences	consequence	NOUN
ejpam-4444	344	3	and	and	CCONJ
ejpam-4444	344	4	t3	t3	PROPN
ejpam-4444	344	5	>	>	X
ejpam-4444	344	6	t(2t−	t(2t−	PROPN
ejpam-4444	344	7	1	1	NUM
ejpam-4444	344	8	)	)	PUNCT
ejpam-4444	344	9	imply	imply	VERB
ejpam-4444	344	10	that	that	SCONJ
ejpam-4444	344	11	a.	a.	NOUN
ejpam-4444	344	12	sonubon	sonubon	PROPN
ejpam-4444	344	13	,	,	PUNCT
ejpam-4444	344	14	s.	s.	PROPN
ejpam-4444	344	15	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	344	16	,	,	PUNCT
ejpam-4444	344	17	k.	k.	PROPN
ejpam-4444	345	1	nonlaopon	nonlaopon	ADV
ejpam-4444	345	2	/	/	SYM
ejpam-4444	345	3	eur	eur	PROPN
ejpam-4444	345	4	.	.	PUNCT
ejpam-4444	346	1	j.	j.	PROPN
ejpam-4444	346	2	pure	pure	PROPN
ejpam-4444	346	3	appl	appl	PROPN
ejpam-4444	346	4	.	.	PROPN
ejpam-4444	346	5	math	math	PROPN
ejpam-4444	346	6	,	,	PUNCT
ejpam-4444	346	7	15	15	NUM
ejpam-4444	346	8	(	(	PUNCT
ejpam-4444	346	9	3	3	NUM
ejpam-4444	346	10	)	)	PUNCT
ejpam-4444	346	11	(	(	PUNCT
ejpam-4444	346	12	2022	2022	NUM
ejpam-4444	346	13	)	)	PUNCT
ejpam-4444	346	14	,	,	PUNCT
ejpam-4444	346	15	1120	1120	NUM
ejpam-4444	346	16	-	-	SYM
ejpam-4444	346	17	1143	1143	NUM
ejpam-4444	346	18	1135	1135	NUM
ejpam-4444	346	19	h(t	h(t	PROPN
ejpam-4444	346	20	)	)	PUNCT
ejpam-4444	346	21	<	<	X
ejpam-4444	346	22	−2(2α−	−2(2α−	NUM
ejpam-4444	346	23	1)(7−	1)(7−	NUM
ejpam-4444	346	24	3α)(23−	3α)(23−	NUM
ejpam-4444	346	25	18α)(11−	18α)(11−	NUM
ejpam-4444	346	26	8α)t(2t−	8α)t(2t−	NUM
ejpam-4444	346	27	1	1	NUM
ejpam-4444	346	28	)	)	PUNCT
ejpam-4444	346	29	+	+	CCONJ
ejpam-4444	346	30	[	[	PUNCT
ejpam-4444	346	31	α(13−	α(13−	PROPN
ejpam-4444	346	32	12α)3	12α)3	NUM
ejpam-4444	346	33	−	−	PROPN
ejpam-4444	347	1	14(3α2	14(3α2	NUM
ejpam-4444	347	2	−	−	ADP
ejpam-4444	347	3	18α+	18α+	NUM
ejpam-4444	347	4	10)(11−	10)(11−	NUM
ejpam-4444	347	5	8α	8α	NUM
ejpam-4444	347	6	)	)	PUNCT
ejpam-4444	347	7	]	]	PUNCT
ejpam-4444	348	1	t2	t2	NOUN
ejpam-4444	348	2	−	−	PROPN
ejpam-4444	349	1	14(6α2	14(6α2	NUM
ejpam-4444	349	2	−	−	PROPN
ejpam-4444	349	3	15α+	15α+	NOUN
ejpam-4444	349	4	13)(2α−	13)(2α−	NUM
ejpam-4444	349	5	1)t−	1)t−	NUM
ejpam-4444	349	6	7α(2α−	7α(2α−	NUM
ejpam-4444	349	7	1)(24α−	1)(24α−	NOUN
ejpam-4444	349	8	19	19	NUM
ejpam-4444	349	9	)	)	PUNCT
ejpam-4444	349	10	=	=	PUNCT
ejpam-4444	349	11	(	(	PUNCT
ejpam-4444	349	12	864α3	864α3	NUM
ejpam-4444	349	13	−	−	NOUN
ejpam-4444	349	14	6	6	NUM
ejpam-4444	349	15	,	,	PUNCT
ejpam-4444	349	16	072α2	072α2	NUM
ejpam-4444	349	17	+	+	CCONJ
ejpam-4444	349	18	10	10	NUM
ejpam-4444	349	19	,	,	PUNCT
ejpam-4444	349	20	723α−	723α−	NUM
ejpam-4444	349	21	5	5	NUM
ejpam-4444	349	22	,	,	PUNCT
ejpam-4444	349	23	544)t2	544)t2	NUM
ejpam-4444	349	24	+	+	CCONJ
ejpam-4444	349	25	32(5−	32(5−	NUM
ejpam-4444	349	26	3α)(9α2	3α)(9α2	NUM
ejpam-4444	349	27	−	−	NOUN
ejpam-4444	349	28	29α+	29α+	NUM
ejpam-4444	350	1	21)t−	21)t−	NUM
ejpam-4444	350	2	7α(24α−	7α(24α−	NOUN
ejpam-4444	350	3	19	19	NUM
ejpam-4444	350	4	)	)	PUNCT
ejpam-4444	350	5	.	.	PUNCT
ejpam-4444	351	1	examine	examine	VERB
ejpam-4444	351	2	the	the	DET
ejpam-4444	351	3	term	term	NOUN
ejpam-4444	351	4	on	on	ADP
ejpam-4444	351	5	the	the	DET
ejpam-4444	351	6	right	right	ADJ
ejpam-4444	351	7	side	side	NOUN
ejpam-4444	351	8	of	of	ADP
ejpam-4444	351	9	the	the	DET
ejpam-4444	351	10	inequality	inequality	NOUN
ejpam-4444	351	11	sign	sign	NOUN
ejpam-4444	351	12	shown	show	VERB
ejpam-4444	351	13	above	above	ADV
ejpam-4444	351	14	.	.	PUNCT
ejpam-4444	352	1	notice	notice	VERB
ejpam-4444	352	2	that	that	SCONJ
ejpam-4444	352	3	the	the	DET
ejpam-4444	352	4	coefficient	coefficient	NOUN
ejpam-4444	352	5	864α3	864α3	NUM
ejpam-4444	352	6	−	−	NOUN
ejpam-4444	352	7	6	6	NUM
ejpam-4444	352	8	,	,	PUNCT
ejpam-4444	352	9	072α2	072α2	NUM
ejpam-4444	352	10	+	+	CCONJ
ejpam-4444	352	11	10	10	NUM
ejpam-4444	352	12	,	,	PUNCT
ejpam-4444	352	13	723α	723α	NOUN
ejpam-4444	352	14	−	−	PROPN
ejpam-4444	352	15	5	5	NUM
ejpam-4444	352	16	,	,	PUNCT
ejpam-4444	352	17	544	544	NUM
ejpam-4444	352	18	is	be	AUX
ejpam-4444	352	19	an	an	DET
ejpam-4444	352	20	increasing	increase	VERB
ejpam-4444	352	21	function	function	NOUN
ejpam-4444	352	22	for	for	ADP
ejpam-4444	352	23	α	α	PRON
ejpam-4444	352	24	∈	∈	PROPN
ejpam-4444	352	25	(	(	PUNCT
ejpam-4444	352	26	1/2	1/2	NUM
ejpam-4444	352	27	,	,	PUNCT
ejpam-4444	352	28	1	1	NUM
ejpam-4444	352	29	)	)	PUNCT
ejpam-4444	352	30	with	with	ADP
ejpam-4444	352	31	negative	negative	ADJ
ejpam-4444	352	32	value	value	NOUN
ejpam-4444	352	33	(	(	PUNCT
ejpam-4444	352	34	-29	-29	NUM
ejpam-4444	352	35	)	)	PUNCT
ejpam-4444	352	36	at	at	ADP
ejpam-4444	352	37	α	α	NOUN
ejpam-4444	352	38	=	=	SYM
ejpam-4444	352	39	1	1	NUM
ejpam-4444	352	40	.	.	PUNCT
ejpam-4444	353	1	the	the	DET
ejpam-4444	353	2	coefficient	coefficient	NOUN
ejpam-4444	353	3	of	of	ADP
ejpam-4444	353	4	t2	t2	NOUN
ejpam-4444	353	5	is	be	AUX
ejpam-4444	353	6	negative	negative	ADJ
ejpam-4444	353	7	for	for	ADP
ejpam-4444	353	8	α	α	PRON
ejpam-4444	353	9	∈	∈	PROPN
ejpam-4444	353	10	(	(	PUNCT
ejpam-4444	353	11	1/2	1/2	NUM
ejpam-4444	353	12	,	,	PUNCT
ejpam-4444	353	13	8/9	8/9	NUM
ejpam-4444	353	14	]	]	PUNCT
ejpam-4444	353	15	.	.	PUNCT
ejpam-4444	354	1	we	we	PRON
ejpam-4444	354	2	have	have	VERB
ejpam-4444	354	3	t2	t2	PROPN
ejpam-4444	354	4	>	>	PUNCT
ejpam-4444	354	5	t	t	PROPN
ejpam-4444	354	6	and	and	CCONJ
ejpam-4444	354	7	then	then	ADV
ejpam-4444	354	8	h(t	h(t	PROPN
ejpam-4444	354	9	)	)	PUNCT
ejpam-4444	354	10	<	<	X
ejpam-4444	355	1	[	[	PUNCT
ejpam-4444	355	2	(	(	PUNCT
ejpam-4444	355	3	864α3	864α3	NUM
ejpam-4444	355	4	−	−	NOUN
ejpam-4444	355	5	6	6	NUM
ejpam-4444	355	6	,	,	PUNCT
ejpam-4444	355	7	072α2	072α2	NUM
ejpam-4444	355	8	+	+	CCONJ
ejpam-4444	355	9	10	10	NUM
ejpam-4444	355	10	,	,	PUNCT
ejpam-4444	355	11	723α−	723α−	NUM
ejpam-4444	355	12	5	5	NUM
ejpam-4444	355	13	,	,	PUNCT
ejpam-4444	355	14	544	544	NUM
ejpam-4444	355	15	)	)	PUNCT
ejpam-4444	355	16	+	+	CCONJ
ejpam-4444	355	17	32(5−	32(5−	NUM
ejpam-4444	355	18	3α)(9α2	3α)(9α2	NUM
ejpam-4444	355	19	−	−	NOUN
ejpam-4444	355	20	29α+	29α+	NUM
ejpam-4444	355	21	21	21	NUM
ejpam-4444	355	22	)	)	PUNCT
ejpam-4444	355	23	]	]	PUNCT
ejpam-4444	356	1	t−	t−	PROPN
ejpam-4444	356	2	7α(24α−	7α(24α−	PROPN
ejpam-4444	356	3	19	19	NUM
ejpam-4444	356	4	)	)	PUNCT
ejpam-4444	356	5	=	=	PRON
ejpam-4444	356	6	(	(	PUNCT
ejpam-4444	356	7	−1	−1	NOUN
ejpam-4444	356	8	,	,	PUNCT
ejpam-4444	356	9	848α2	848α2	NUM
ejpam-4444	356	10	+	+	CCONJ
ejpam-4444	356	11	4	4	NUM
ejpam-4444	356	12	,	,	PUNCT
ejpam-4444	356	13	067α−	067α−	NUM
ejpam-4444	356	14	2	2	NUM
ejpam-4444	356	15	,	,	PUNCT
ejpam-4444	356	16	184)t−	184)t−	NUM
ejpam-4444	356	17	7α(24α−	7α(24α−	NUM
ejpam-4444	356	18	19	19	NUM
ejpam-4444	356	19	)	)	PUNCT
ejpam-4444	356	20	.	.	PUNCT
ejpam-4444	357	1	consider	consider	VERB
ejpam-4444	357	2	the	the	DET
ejpam-4444	357	3	term	term	NOUN
ejpam-4444	357	4	on	on	ADP
ejpam-4444	357	5	the	the	DET
ejpam-4444	357	6	right	right	ADJ
ejpam-4444	357	7	side	side	NOUN
ejpam-4444	357	8	of	of	ADP
ejpam-4444	357	9	the	the	DET
ejpam-4444	357	10	equality	equality	NOUN
ejpam-4444	357	11	sign	sign	NOUN
ejpam-4444	357	12	above	above	ADV
ejpam-4444	357	13	.	.	PUNCT
ejpam-4444	358	1	coefficient	coefficient	PROPN
ejpam-4444	358	2	−1	−1	NOUN
ejpam-4444	358	3	,	,	PUNCT
ejpam-4444	358	4	848α2	848α2	NUM
ejpam-4444	358	5	+	+	CCONJ
ejpam-4444	358	6	4	4	NUM
ejpam-4444	358	7	,	,	PUNCT
ejpam-4444	358	8	067α−	067α−	NUM
ejpam-4444	358	9	2	2	NUM
ejpam-4444	358	10	,	,	PUNCT
ejpam-4444	358	11	184	184	NUM
ejpam-4444	358	12	is	be	AUX
ejpam-4444	358	13	increasing	increase	VERB
ejpam-4444	358	14	for	for	ADP
ejpam-4444	358	15	α	α	PRON
ejpam-4444	358	16	∈	∈	PROPN
ejpam-4444	358	17	(	(	PUNCT
ejpam-4444	358	18	1/2	1/2	NUM
ejpam-4444	358	19	,	,	PUNCT
ejpam-4444	358	20	8/9	8/9	NUM
ejpam-4444	358	21	]	]	PUNCT
ejpam-4444	358	22	with	with	ADP
ejpam-4444	358	23	negative	negative	ADJ
ejpam-4444	358	24	value	value	NOUN
ejpam-4444	358	25	(	(	PUNCT
ejpam-4444	358	26	-29.03	-29.03	NUM
ejpam-4444	358	27	)	)	PUNCT
ejpam-4444	358	28	at	at	ADP
ejpam-4444	358	29	α	α	NOUN
ejpam-4444	358	30	=	=	SYM
ejpam-4444	358	31	8/9	8/9	NUM
ejpam-4444	358	32	,	,	PUNCT
ejpam-4444	358	33	it	it	PRON
ejpam-4444	358	34	is	be	AUX
ejpam-4444	358	35	therefore	therefore	ADV
ejpam-4444	358	36	negative	negative	ADJ
ejpam-4444	358	37	on	on	ADP
ejpam-4444	358	38	the	the	DET
ejpam-4444	358	39	whole	whole	ADJ
ejpam-4444	358	40	interval	interval	NOUN
ejpam-4444	358	41	(	(	PUNCT
ejpam-4444	358	42	1/2	1/2	NUM
ejpam-4444	358	43	,	,	PUNCT
ejpam-4444	358	44	8/9	8/9	NUM
ejpam-4444	358	45	]	]	PUNCT
ejpam-4444	358	46	.	.	PUNCT
ejpam-4444	359	1	since	since	SCONJ
ejpam-4444	359	2	t	t	PROPN
ejpam-4444	359	3	>	>	X
ejpam-4444	359	4	1	1	NUM
ejpam-4444	359	5	,	,	PUNCT
ejpam-4444	359	6	we	we	PRON
ejpam-4444	359	7	get	get	VERB
ejpam-4444	359	8	h(t	h(t	PRON
ejpam-4444	359	9	)	)	PUNCT
ejpam-4444	359	10	<	<	X
ejpam-4444	359	11	(	(	PUNCT
ejpam-4444	359	12	−1	−1	NOUN
ejpam-4444	359	13	,	,	PUNCT
ejpam-4444	359	14	848α2	848α2	NUM
ejpam-4444	359	15	+	+	CCONJ
ejpam-4444	359	16	4	4	NUM
ejpam-4444	359	17	,	,	PUNCT
ejpam-4444	359	18	067α−	067α−	NUM
ejpam-4444	359	19	2	2	NUM
ejpam-4444	359	20	,	,	PUNCT
ejpam-4444	359	21	184)−	184)−	NUM
ejpam-4444	359	22	7α(24α−	7α(24α−	NUM
ejpam-4444	359	23	19	19	NUM
ejpam-4444	359	24	)	)	PUNCT
ejpam-4444	359	25	<	<	X
ejpam-4444	359	26	−168(1−	−168(1−	X
ejpam-4444	359	27	α)(13−	α)(13−	NUM
ejpam-4444	359	28	12α	12α	NOUN
ejpam-4444	359	29	)	)	PUNCT
ejpam-4444	359	30	<	<	X
ejpam-4444	360	1	0	0	X
ejpam-4444	360	2	.	.	PUNCT
ejpam-4444	361	1	finally	finally	ADV
ejpam-4444	361	2	,	,	PUNCT
ejpam-4444	361	3	we	we	PRON
ejpam-4444	361	4	will	will	AUX
ejpam-4444	361	5	prove	prove	VERB
ejpam-4444	361	6	that	that	SCONJ
ejpam-4444	361	7	the	the	DET
ejpam-4444	361	8	parameter	parameter	NOUN
ejpam-4444	361	9	7/(13−	7/(13−	PROPN
ejpam-4444	361	10	12α	12α	NOUN
ejpam-4444	361	11	)	)	PUNCT
ejpam-4444	361	12	can	can	AUX
ejpam-4444	361	13	not	not	PART
ejpam-4444	361	14	be	be	AUX
ejpam-4444	361	15	improved	improve	VERB
ejpam-4444	361	16	in	in	ADP
ejpam-4444	361	17	this	this	DET
ejpam-4444	361	18	case	case	NOUN
ejpam-4444	361	19	.	.	PUNCT
ejpam-4444	362	1	suppose	suppose	VERB
ejpam-4444	362	2	,	,	PUNCT
ejpam-4444	362	3	to	to	ADP
ejpam-4444	362	4	the	the	DET
ejpam-4444	362	5	contrary	contrary	NOUN
ejpam-4444	362	6	,	,	PUNCT
ejpam-4444	362	7	that	that	DET
ejpam-4444	362	8	inequality	inequality	NOUN
ejpam-4444	362	9	(	(	PUNCT
ejpam-4444	362	10	13	13	NUM
ejpam-4444	362	11	)	)	PUNCT
ejpam-4444	362	12	is	be	AUX
ejpam-4444	362	13	true	true	ADJ
ejpam-4444	362	14	for	for	ADP
ejpam-4444	362	15	the	the	DET
ejpam-4444	362	16	parameter	parameter	NOUN
ejpam-4444	362	17	1	1	NUM
ejpam-4444	362	18	2[1−	2[1−	NOUN
ejpam-4444	362	19	(	(	PUNCT
ejpam-4444	362	20	1	1	NUM
ejpam-4444	363	1	+	+	CCONJ
ejpam-4444	363	2	k	k	PROPN
ejpam-4444	364	1	+	+	CCONJ
ejpam-4444	364	2	ϵ)]α+	ϵ)]α+	PROPN
ejpam-4444	364	3	(	(	PUNCT
ejpam-4444	364	4	1	1	NUM
ejpam-4444	364	5	+	+	CCONJ
ejpam-4444	364	6	k	k	NOUN
ejpam-4444	364	7	+	+	CCONJ
ejpam-4444	364	8	ϵ	ϵ	X
ejpam-4444	364	9	)	)	PUNCT
ejpam-4444	364	10	for	for	ADP
ejpam-4444	364	11	a	a	DET
ejpam-4444	364	12	sufficiently	sufficiently	ADV
ejpam-4444	364	13	small	small	ADJ
ejpam-4444	364	14	ϵ	ϵ	X
ejpam-4444	364	15	>	>	X
ejpam-4444	364	16	0	0	NUM
ejpam-4444	364	17	.	.	PUNCT
ejpam-4444	365	1	that	that	PRON
ejpam-4444	365	2	is	be	AUX
ejpam-4444	365	3	l	l	NOUN
ejpam-4444	365	4	1	1	NUM
ejpam-4444	365	5	2[1−(1+k+ϵ)]α+(1+k+ϵ	2[1−(1+k+ϵ)]α+(1+k+ϵ	NUM
ejpam-4444	365	6	)	)	PUNCT
ejpam-4444	365	7	(	(	PUNCT
ejpam-4444	365	8	1	1	NUM
ejpam-4444	365	9	,	,	PUNCT
ejpam-4444	365	10	t	t	PROPN
ejpam-4444	365	11	)	)	PUNCT
ejpam-4444	365	12	<	<	X
ejpam-4444	365	13	αc(1	αc(1	PROPN
ejpam-4444	365	14	,	,	PUNCT
ejpam-4444	365	15	t	t	PROPN
ejpam-4444	365	16	)	)	PUNCT
ejpam-4444	366	1	+	+	CCONJ
ejpam-4444	366	2	(	(	PUNCT
ejpam-4444	366	3	1−	1−	NUM
ejpam-4444	366	4	α)h(1	α)h(1	NOUN
ejpam-4444	366	5	,	,	PUNCT
ejpam-4444	366	6	t	t	PROPN
ejpam-4444	366	7	)	)	PUNCT
ejpam-4444	366	8	for	for	ADP
ejpam-4444	366	9	all	all	DET
ejpam-4444	366	10	t	t	PROPN
ejpam-4444	366	11	>	>	X
ejpam-4444	366	12	1	1	X
ejpam-4444	366	13	.	.	PUNCT
ejpam-4444	367	1	taking	take	VERB
ejpam-4444	367	2	logarithm	logarithm	NOUN
ejpam-4444	367	3	of	of	ADP
ejpam-4444	367	4	both	both	DET
ejpam-4444	367	5	sides	side	NOUN
ejpam-4444	367	6	of	of	ADP
ejpam-4444	367	7	the	the	DET
ejpam-4444	367	8	above	above	ADJ
ejpam-4444	367	9	inequality	inequality	NOUN
ejpam-4444	367	10	,	,	PUNCT
ejpam-4444	367	11	we	we	PRON
ejpam-4444	367	12	get	get	VERB
ejpam-4444	367	13	ln	ln	ADJ
ejpam-4444	368	1	[	[	PUNCT
ejpam-4444	368	2	l	l	NOUN
ejpam-4444	368	3	1	1	NUM
ejpam-4444	368	4	2[1−(13/7+ϵ)]α+(13/7+ϵ	2[1−(13/7+ϵ)]α+(13/7+ϵ	NUM
ejpam-4444	368	5	)	)	PUNCT
ejpam-4444	368	6	(	(	PUNCT
ejpam-4444	368	7	1	1	NUM
ejpam-4444	368	8	,	,	PUNCT
ejpam-4444	368	9	t	t	PROPN
ejpam-4444	368	10	)	)	PUNCT
ejpam-4444	368	11	]	]	PUNCT
ejpam-4444	369	1	−	−	PROPN
ejpam-4444	369	2	ln	ln	INTJ
ejpam-4444	369	3	[	[	PUNCT
ejpam-4444	369	4	αc(1	αc(1	PROPN
ejpam-4444	369	5	,	,	PUNCT
ejpam-4444	369	6	t	t	PROPN
ejpam-4444	369	7	)	)	PUNCT
ejpam-4444	370	1	+	+	CCONJ
ejpam-4444	370	2	(	(	PUNCT
ejpam-4444	370	3	1−	1−	NUM
ejpam-4444	370	4	α)h(1	α)h(1	NOUN
ejpam-4444	370	5	,	,	PUNCT
ejpam-4444	370	6	t	t	PROPN
ejpam-4444	370	7	)	)	PUNCT
ejpam-4444	370	8	]	]	PUNCT
ejpam-4444	371	1	<	<	X
ejpam-4444	371	2	0	0	X
ejpam-4444	371	3	.	.	PUNCT
ejpam-4444	372	1	with	with	ADP
ejpam-4444	372	2	the	the	DET
ejpam-4444	372	3	notation	notation	NOUN
ejpam-4444	372	4	in	in	ADP
ejpam-4444	372	5	lemma	lemma	PROPN
ejpam-4444	372	6	1	1	NUM
ejpam-4444	372	7	,	,	PUNCT
ejpam-4444	372	8	this	this	PRON
ejpam-4444	372	9	is	be	AUX
ejpam-4444	372	10	just	just	ADV
ejpam-4444	372	11	f	f	PROPN
ejpam-4444	372	12	(	(	PUNCT
ejpam-4444	372	13	t	t	PROPN
ejpam-4444	372	14	)	)	PUNCT
ejpam-4444	372	15	<	<	X
ejpam-4444	372	16	0	0	NUM
ejpam-4444	372	17	for	for	ADP
ejpam-4444	372	18	all	all	DET
ejpam-4444	372	19	t	t	NOUN
ejpam-4444	372	20	>	>	X
ejpam-4444	372	21	1	1	NUM
ejpam-4444	372	22	where	where	SCONJ
ejpam-4444	372	23	p	p	NOUN
ejpam-4444	372	24	=	=	NOUN
ejpam-4444	372	25	1	1	NUM
ejpam-4444	372	26	2	2	NUM
ejpam-4444	372	27	[	[	X
ejpam-4444	372	28	1−	1−	NUM
ejpam-4444	372	29	(	(	PUNCT
ejpam-4444	372	30	13/7	13/7	NOUN
ejpam-4444	372	31	+	+	NUM
ejpam-4444	372	32	ϵ)]α+	ϵ)]α+	PROPN
ejpam-4444	372	33	(	(	PUNCT
ejpam-4444	372	34	13/7	13/7	NOUN
ejpam-4444	372	35	+	+	CCONJ
ejpam-4444	372	36	ϵ	ϵ	NUM
ejpam-4444	372	37	)	)	PUNCT
ejpam-4444	372	38	.	.	PUNCT
ejpam-4444	373	1	(	(	PUNCT
ejpam-4444	373	2	14	14	NUM
ejpam-4444	373	3	)	)	PUNCT
ejpam-4444	373	4	from	from	ADP
ejpam-4444	373	5	lemma	lemma	PROPN
ejpam-4444	373	6	1	1	NUM
ejpam-4444	373	7	,	,	PUNCT
ejpam-4444	373	8	g(1	g(1	NOUN
ejpam-4444	373	9	)	)	PUNCT
ejpam-4444	373	10	=	=	PUNCT
ejpam-4444	373	11	g′(1	g′(1	ADJ
ejpam-4444	373	12	)	)	PUNCT
ejpam-4444	373	13	=	=	SYM
ejpam-4444	373	14	g′′(1	g′′(1	NOUN
ejpam-4444	373	15	)	)	PUNCT
ejpam-4444	374	1	=	=	SYM
ejpam-4444	374	2	0	0	X
ejpam-4444	374	3	.	.	PUNCT
ejpam-4444	375	1	taking	take	VERB
ejpam-4444	375	2	derivative	derivative	NOUN
ejpam-4444	375	3	of	of	ADP
ejpam-4444	375	4	g′′(t	g′′(t	NOUN
ejpam-4444	375	5	)	)	PUNCT
ejpam-4444	375	6	,	,	PUNCT
ejpam-4444	375	7	we	we	PRON
ejpam-4444	375	8	have	have	VERB
ejpam-4444	375	9	a.	a.	NOUN
ejpam-4444	375	10	sonubon	sonubon	PROPN
ejpam-4444	375	11	,	,	PUNCT
ejpam-4444	375	12	s.	s.	PROPN
ejpam-4444	375	13	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	375	14	,	,	PUNCT
ejpam-4444	375	15	k.	k.	PROPN
ejpam-4444	376	1	nonlaopon	nonlaopon	ADV
ejpam-4444	376	2	/	/	SYM
ejpam-4444	376	3	eur	eur	PROPN
ejpam-4444	376	4	.	.	PUNCT
ejpam-4444	377	1	j.	j.	PROPN
ejpam-4444	377	2	pure	pure	PROPN
ejpam-4444	377	3	appl	appl	PROPN
ejpam-4444	377	4	.	.	PROPN
ejpam-4444	377	5	math	math	PROPN
ejpam-4444	377	6	,	,	PUNCT
ejpam-4444	377	7	15	15	NUM
ejpam-4444	377	8	(	(	PUNCT
ejpam-4444	377	9	3	3	NUM
ejpam-4444	377	10	)	)	PUNCT
ejpam-4444	377	11	(	(	PUNCT
ejpam-4444	377	12	2022	2022	NUM
ejpam-4444	377	13	)	)	PUNCT
ejpam-4444	377	14	,	,	PUNCT
ejpam-4444	377	15	1120	1120	NUM
ejpam-4444	377	16	-	-	SYM
ejpam-4444	377	17	1143	1143	NUM
ejpam-4444	377	18	1136	1136	NUM
ejpam-4444	377	19	g′′′(t	g′′′(t	NOUN
ejpam-4444	377	20	)	)	PUNCT
ejpam-4444	377	21	=	=	PUNCT
ejpam-4444	377	22	(	(	PUNCT
ejpam-4444	377	23	−3αp+	−3αp+	PROPN
ejpam-4444	377	24	2p−	2p−	PROPN
ejpam-4444	377	25	α)(p+	α)(p+	PROPN
ejpam-4444	377	26	3)(p+	3)(p+	NUM
ejpam-4444	377	27	2)(p+	2)(p+	NUM
ejpam-4444	377	28	1)tp	1)tp	NOUN
ejpam-4444	378	1	+	+	CCONJ
ejpam-4444	378	2	(	(	PUNCT
ejpam-4444	378	3	5αp−	5αp−	NUM
ejpam-4444	378	4	2p+	2p+	NUM
ejpam-4444	378	5	α−	α−	ADP
ejpam-4444	378	6	2)(p+	2)(p+	NUM
ejpam-4444	378	7	2)(p+	2)(p+	NUM
ejpam-4444	378	8	1)ptp−1	1)ptp−1	NUM
ejpam-4444	378	9	+	+	CCONJ
ejpam-4444	378	10	(	(	PUNCT
ejpam-4444	378	11	−αp+	−αp+	X
ejpam-4444	378	12	α−	α−	ADP
ejpam-4444	378	13	2)(p+	2)(p+	NUM
ejpam-4444	378	14	1)p(p−	1)p(p−	NUM
ejpam-4444	378	15	1)tp−2	1)tp−2	NUM
ejpam-4444	378	16	−	−	NUM
ejpam-4444	378	17	α(p+	α(p+	NOUN
ejpam-4444	378	18	1	1	NUM
ejpam-4444	378	19	)	)	PUNCT
ejpam-4444	378	20	[	[	PUNCT
ejpam-4444	378	21	p(p−	p(p−	VERB
ejpam-4444	378	22	1)(p−	1)(p−	NUM
ejpam-4444	378	23	2)tp−3	2)tp−3	NOUN
ejpam-4444	378	24	−	−	NUM
ejpam-4444	378	25	6	6	NUM
ejpam-4444	378	26	]	]	PUNCT
ejpam-4444	378	27	.	.	PUNCT
ejpam-4444	379	1	hence	hence	ADV
ejpam-4444	379	2	g′′′(1	g′′′(1	PROPN
ejpam-4444	379	3	)	)	PUNCT
ejpam-4444	380	1	=	=	SYM
ejpam-4444	380	2	2(p+	2(p+	NUM
ejpam-4444	380	3	1)p(p−	1)p(p−	NUM
ejpam-4444	380	4	12α+	12α+	NUM
ejpam-4444	380	5	5	5	NUM
ejpam-4444	380	6	)	)	PUNCT
ejpam-4444	380	7	for	for	ADP
ejpam-4444	380	8	α	α	DET
ejpam-4444	380	9	∈	∈	PROPN
ejpam-4444	380	10	(	(	PUNCT
ejpam-4444	380	11	1/2	1/2	NUM
ejpam-4444	380	12	,	,	PUNCT
ejpam-4444	380	13	1	1	NUM
ejpam-4444	380	14	)	)	PUNCT
ejpam-4444	380	15	.	.	PUNCT
ejpam-4444	381	1	however	however	ADV
ejpam-4444	381	2	,	,	PUNCT
ejpam-4444	381	3	lim	lim	PROPN
ejpam-4444	381	4	α→1−	α→1−	PROPN
ejpam-4444	381	5	2(p+	2(p+	NUM
ejpam-4444	381	6	1)p(p−	1)p(p−	NUM
ejpam-4444	381	7	12α+	12α+	NUM
ejpam-4444	381	8	5	5	NUM
ejpam-4444	381	9	)	)	PUNCT
ejpam-4444	381	10	=	=	SYM
ejpam-4444	382	1	686(7ϵ−	686(7ϵ−	NUM
ejpam-4444	382	2	8)ϵ	8)ϵ	NOUN
ejpam-4444	382	3	(	(	PUNCT
ejpam-4444	382	4	7ϵ−	7ϵ−	PROPN
ejpam-4444	382	5	1)3	1)3	PROPN
ejpam-4444	382	6	>	>	X
ejpam-4444	382	7	0	0	X
ejpam-4444	382	8	.	.	PUNCT
ejpam-4444	383	1	therefore	therefore	ADV
ejpam-4444	383	2	g(t	g(t	PROPN
ejpam-4444	383	3	)	)	PUNCT
ejpam-4444	383	4	<	<	X
ejpam-4444	383	5	0	0	PUNCT
ejpam-4444	383	6	or	or	CCONJ
ejpam-4444	383	7	f	f	PROPN
ejpam-4444	383	8	(	(	PUNCT
ejpam-4444	383	9	t	t	PROPN
ejpam-4444	383	10	)	)	PUNCT
ejpam-4444	383	11	<	<	X
ejpam-4444	383	12	0	0	NUM
ejpam-4444	383	13	in	in	ADP
ejpam-4444	383	14	a	a	DET
ejpam-4444	383	15	small	small	ADJ
ejpam-4444	383	16	neighborhood	neighborhood	NOUN
ejpam-4444	383	17	of	of	ADP
ejpam-4444	383	18	1	1	NUM
ejpam-4444	383	19	if	if	SCONJ
ejpam-4444	383	20	ϵ	ϵ	X
ejpam-4444	383	21	<	<	X
ejpam-4444	383	22	1/7	1/7	NUM
ejpam-4444	383	23	.	.	PUNCT
ejpam-4444	384	1	this	this	PRON
ejpam-4444	384	2	contradict	contradict	VERB
ejpam-4444	384	3	to	to	ADP
ejpam-4444	384	4	statement	statement	NOUN
ejpam-4444	384	5	(	(	PUNCT
ejpam-4444	384	6	14	14	NUM
ejpam-4444	384	7	)	)	PUNCT
ejpam-4444	384	8	.	.	PUNCT
ejpam-4444	385	1	the	the	DET
ejpam-4444	385	2	proof	proof	NOUN
ejpam-4444	385	3	is	be	AUX
ejpam-4444	385	4	complete	complete	ADJ
ejpam-4444	385	5	.	.	PUNCT
ejpam-4444	386	1	remark	remark	PROPN
ejpam-4444	386	2	1	1	NUM
ejpam-4444	386	3	.	.	PUNCT
ejpam-4444	387	1	in	in	ADP
ejpam-4444	387	2	statement	statement	NOUN
ejpam-4444	387	3	3	3	NUM
ejpam-4444	387	4	)	)	PUNCT
ejpam-4444	387	5	of	of	ADP
ejpam-4444	387	6	theorem	theorem	NOUN
ejpam-4444	387	7	1	1	NUM
ejpam-4444	387	8	,	,	PUNCT
ejpam-4444	387	9	l4α−1	l4α−1	NOUN
ejpam-4444	387	10	is	be	AUX
ejpam-4444	387	11	not	not	PART
ejpam-4444	387	12	the	the	DET
ejpam-4444	387	13	optimal	optimal	ADJ
ejpam-4444	387	14	lower	low	ADJ
ejpam-4444	387	15	bound	bind	VERB
ejpam-4444	387	16	of	of	ADP
ejpam-4444	387	17	the	the	DET
ejpam-4444	387	18	considered	consider	VERB
ejpam-4444	387	19	weighted	weight	VERB
ejpam-4444	387	20	arithmetic	arithmetic	ADJ
ejpam-4444	387	21	mean	mean	NOUN
ejpam-4444	387	22	for	for	ADP
ejpam-4444	387	23	α	α	PROPN
ejpam-4444	387	24	∈	∈	PROPN
ejpam-4444	387	25	(	(	PUNCT
ejpam-4444	387	26	1/2	1/2	NUM
ejpam-4444	387	27	,	,	PUNCT
ejpam-4444	387	28	1	1	NUM
ejpam-4444	387	29	)	)	PUNCT
ejpam-4444	387	30	.	.	PUNCT
ejpam-4444	388	1	neither	neither	PRON
ejpam-4444	388	2	is	be	AUX
ejpam-4444	388	3	l7/(13−12α	l7/(13−12α	ADV
ejpam-4444	388	4	)	)	PUNCT
ejpam-4444	388	5	the	the	DET
ejpam-4444	388	6	optimal	optimal	ADJ
ejpam-4444	388	7	upper	upper	ADJ
ejpam-4444	388	8	bound	bind	VERB
ejpam-4444	388	9	of	of	ADP
ejpam-4444	388	10	the	the	DET
ejpam-4444	388	11	one	one	NOUN
ejpam-4444	388	12	for	for	ADP
ejpam-4444	388	13	α	α	PRON
ejpam-4444	388	14	∈	∈	PROPN
ejpam-4444	388	15	(	(	PUNCT
ejpam-4444	388	16	0	0	NUM
ejpam-4444	388	17	,	,	PUNCT
ejpam-4444	388	18	1/2	1/2	NUM
ejpam-4444	388	19	)	)	PUNCT
ejpam-4444	388	20	in	in	ADP
ejpam-4444	388	21	statement	statement	NOUN
ejpam-4444	388	22	2	2	NUM
ejpam-4444	388	23	)	)	PUNCT
ejpam-4444	388	24	of	of	ADP
ejpam-4444	388	25	theorem	theorem	NOUN
ejpam-4444	388	26	2	2	NUM
ejpam-4444	388	27	.	.	PUNCT
ejpam-4444	388	28	due	due	ADP
ejpam-4444	388	29	to	to	ADP
ejpam-4444	388	30	monotonicity	monotonicity	NOUN
ejpam-4444	388	31	property	property	NOUN
ejpam-4444	388	32	of	of	ADP
ejpam-4444	388	33	generalized	generalized	ADJ
ejpam-4444	388	34	logarithmic	logarithmic	ADJ
ejpam-4444	388	35	means	mean	NOUN
ejpam-4444	388	36	,	,	PUNCT
ejpam-4444	388	37	we	we	PRON
ejpam-4444	388	38	expect	expect	VERB
ejpam-4444	388	39	a	a	DET
ejpam-4444	388	40	sharper	sharp	ADJ
ejpam-4444	388	41	result	result	NOUN
ejpam-4444	388	42	.	.	PUNCT
ejpam-4444	389	1	partial	partial	ADJ
ejpam-4444	389	2	results	result	NOUN
ejpam-4444	389	3	are	be	AUX
ejpam-4444	389	4	shown	show	VERB
ejpam-4444	389	5	in	in	ADP
ejpam-4444	389	6	the	the	DET
ejpam-4444	389	7	following	follow	VERB
ejpam-4444	389	8	theorem	theorem	PROPN
ejpam-4444	389	9	.	.	PUNCT
ejpam-4444	389	10	theorem	theorem	NOUN
ejpam-4444	389	11	3	3	X
ejpam-4444	389	12	.	.	PUNCT
ejpam-4444	390	1	let	let	VERB
ejpam-4444	390	2	a	a	DET
ejpam-4444	390	3	,	,	PUNCT
ejpam-4444	390	4	b	b	X
ejpam-4444	390	5	>	>	X
ejpam-4444	390	6	0	0	PUNCT
ejpam-4444	390	7	with	with	ADP
ejpam-4444	390	8	a	a	DET
ejpam-4444	390	9	̸=	̸=	PROPN
ejpam-4444	390	10	b	b	PROPN
ejpam-4444	390	11	and	and	CCONJ
ejpam-4444	390	12	k	k	PROPN
ejpam-4444	391	1	=	=	SYM
ejpam-4444	391	2	2/(2	2/(2	NUM
ejpam-4444	391	3	ln	ln	ADJ
ejpam-4444	391	4	2−	2−	NUM
ejpam-4444	391	5	1	1	NUM
ejpam-4444	391	6	)	)	PUNCT
ejpam-4444	391	7	.	.	PUNCT
ejpam-4444	392	1	then	then	ADV
ejpam-4444	392	2	1	1	X
ejpam-4444	392	3	)	)	PUNCT
ejpam-4444	392	4	l1/[−2kα+(k+1)](a	l1/[−2kα+(k+1)](a	NOUN
ejpam-4444	392	5	,	,	PUNCT
ejpam-4444	392	6	b	b	NOUN
ejpam-4444	392	7	)	)	PUNCT
ejpam-4444	392	8	=	=	SYM
ejpam-4444	392	9	αc(a	αc(a	NOUN
ejpam-4444	392	10	,	,	PUNCT
ejpam-4444	392	11	b	b	NOUN
ejpam-4444	392	12	)	)	PUNCT
ejpam-4444	393	1	+	+	CCONJ
ejpam-4444	393	2	(	(	PUNCT
ejpam-4444	393	3	1−	1−	NUM
ejpam-4444	393	4	α)h(a	α)h(a	NOUN
ejpam-4444	393	5	,	,	PUNCT
ejpam-4444	393	6	b	b	NOUN
ejpam-4444	393	7	)	)	PUNCT
ejpam-4444	393	8	=	=	SYM
ejpam-4444	393	9	l2kα+(1−k)(a	l2kα+(1−k)(a	PROPN
ejpam-4444	393	10	,	,	PUNCT
ejpam-4444	393	11	b	b	NOUN
ejpam-4444	393	12	)	)	PUNCT
ejpam-4444	393	13	for	for	ADP
ejpam-4444	393	14	α	α	NOUN
ejpam-4444	393	15	=	=	SYM
ejpam-4444	393	16	1/2	1/2	NUM
ejpam-4444	393	17	;	;	PUNCT
ejpam-4444	393	18	2	2	NUM
ejpam-4444	393	19	)	)	PUNCT
ejpam-4444	393	20	l1/[−2kα+(k+1)](a	l1/[−2kα+(k+1)](a	NOUN
ejpam-4444	393	21	,	,	PUNCT
ejpam-4444	393	22	b	b	NOUN
ejpam-4444	393	23	)	)	PUNCT
ejpam-4444	393	24	>	>	X
ejpam-4444	393	25	αc(a	αc(a	NUM
ejpam-4444	393	26	,	,	PUNCT
ejpam-4444	393	27	b	b	NOUN
ejpam-4444	393	28	)	)	PUNCT
ejpam-4444	393	29	+	+	CCONJ
ejpam-4444	393	30	(	(	PUNCT
ejpam-4444	393	31	1−	1−	NUM
ejpam-4444	393	32	α)h(a	α)h(a	NOUN
ejpam-4444	393	33	,	,	PUNCT
ejpam-4444	393	34	b	b	NOUN
ejpam-4444	393	35	)	)	PUNCT
ejpam-4444	393	36	for	for	ADP
ejpam-4444	393	37	α	α	PRON
ejpam-4444	393	38	∈	∈	PROPN
ejpam-4444	393	39	(	(	PUNCT
ejpam-4444	393	40	0	0	NUM
ejpam-4444	393	41	,	,	PUNCT
ejpam-4444	393	42	2	2	NUM
ejpam-4444	393	43	/	/	SYM
ejpam-4444	393	44	k	k	NOUN
ejpam-4444	393	45	)	)	PUNCT
ejpam-4444	394	1	≈	≈	PROPN
ejpam-4444	394	2	(	(	PUNCT
ejpam-4444	394	3	0	0	NUM
ejpam-4444	394	4	,	,	PUNCT
ejpam-4444	394	5	0.38	0.38	NUM
ejpam-4444	394	6	)	)	PUNCT
ejpam-4444	394	7	;	;	PUNCT
ejpam-4444	394	8	3	3	X
ejpam-4444	394	9	)	)	PUNCT
ejpam-4444	394	10	l2kα+(1−k)(a	l2kα+(1−k)(a	NOUN
ejpam-4444	394	11	,	,	PUNCT
ejpam-4444	394	12	b	b	NOUN
ejpam-4444	394	13	)	)	PUNCT
ejpam-4444	394	14	<	<	X
ejpam-4444	394	15	αc(a	αc(a	NOUN
ejpam-4444	394	16	,	,	PUNCT
ejpam-4444	394	17	b	b	NOUN
ejpam-4444	394	18	)	)	PUNCT
ejpam-4444	394	19	+	+	CCONJ
ejpam-4444	394	20	(	(	PUNCT
ejpam-4444	394	21	1−	1−	NUM
ejpam-4444	394	22	α)h(a	α)h(a	NOUN
ejpam-4444	394	23	,	,	PUNCT
ejpam-4444	394	24	b	b	NOUN
ejpam-4444	394	25	)	)	PUNCT
ejpam-4444	394	26	for	for	ADP
ejpam-4444	394	27	α	α	PRON
ejpam-4444	394	28	∈	∈	PROPN
ejpam-4444	394	29	(	(	PUNCT
ejpam-4444	394	30	(	(	PUNCT
ejpam-4444	394	31	k	k	X
ejpam-4444	394	32	+	+	NOUN
ejpam-4444	394	33	2)/2k	2)/2k	NUM
ejpam-4444	394	34	,	,	PUNCT
ejpam-4444	394	35	1	1	NUM
ejpam-4444	394	36	)	)	PUNCT
ejpam-4444	394	37	≈	≈	PROPN
ejpam-4444	394	38	(	(	PUNCT
ejpam-4444	394	39	0.7	0.7	NUM
ejpam-4444	394	40	,	,	PUNCT
ejpam-4444	394	41	1	1	NUM
ejpam-4444	394	42	)	)	PUNCT
ejpam-4444	394	43	.	.	PUNCT
ejpam-4444	395	1	proof	proof	NOUN
ejpam-4444	395	2	.	.	PUNCT
ejpam-4444	396	1	1	1	X
ejpam-4444	396	2	)	)	PUNCT
ejpam-4444	396	3	this	this	PRON
ejpam-4444	396	4	is	be	AUX
ejpam-4444	396	5	obvious	obvious	ADJ
ejpam-4444	396	6	after	after	ADP
ejpam-4444	396	7	inserting	insert	VERB
ejpam-4444	396	8	α	α	NOUN
ejpam-4444	396	9	=	=	NOUN
ejpam-4444	396	10	1/2	1/2	NUM
ejpam-4444	396	11	into	into	ADP
ejpam-4444	396	12	the	the	DET
ejpam-4444	396	13	left	left	ADJ
ejpam-4444	396	14	and	and	CCONJ
ejpam-4444	396	15	right	right	ADJ
ejpam-4444	396	16	sides	side	NOUN
ejpam-4444	396	17	of	of	ADP
ejpam-4444	396	18	the	the	DET
ejpam-4444	396	19	statement	statement	NOUN
ejpam-4444	396	20	.	.	PUNCT
ejpam-4444	397	1	2	2	X
ejpam-4444	397	2	)	)	PUNCT
ejpam-4444	397	3	treated	treat	VERB
ejpam-4444	397	4	as	as	ADP
ejpam-4444	397	5	in	in	ADP
ejpam-4444	397	6	theorem	theorem	ADJ
ejpam-4444	397	7	1(2	1(2	NUM
ejpam-4444	397	8	)	)	PUNCT
ejpam-4444	397	9	,	,	PUNCT
ejpam-4444	397	10	the	the	DET
ejpam-4444	397	11	proposed	propose	VERB
ejpam-4444	397	12	inequality	inequality	NOUN
ejpam-4444	397	13	becomes	becomes	X
ejpam-4444	397	14	t1	t1	NOUN
ejpam-4444	397	15	+	+	CCONJ
ejpam-4444	397	16	{	{	PUNCT
ejpam-4444	397	17	1/[−2kα+(k+1	1/[−2kα+(k+1	NUM
ejpam-4444	397	18	)	)	PUNCT
ejpam-4444	397	19	]	]	PUNCT
ejpam-4444	398	1	}	}	PUNCT
ejpam-4444	398	2	−	−	PROPN
ejpam-4444	398	3	1	1	NUM
ejpam-4444	398	4	(	(	PUNCT
ejpam-4444	398	5	1	1	NUM
ejpam-4444	398	6	+	+	CCONJ
ejpam-4444	398	7	{	{	PUNCT
ejpam-4444	398	8	1/	1/	NUM
ejpam-4444	398	9	[	[	X
ejpam-4444	398	10	−2kα+	−2kα+	X
ejpam-4444	398	11	(	(	PUNCT
ejpam-4444	398	12	k	k	PROPN
ejpam-4444	398	13	+	+	PROPN
ejpam-4444	398	14	1	1	NUM
ejpam-4444	398	15	)	)	PUNCT
ejpam-4444	398	16	]	]	PUNCT
ejpam-4444	398	17	}	}	PUNCT
ejpam-4444	398	18	)	)	PUNCT
ejpam-4444	398	19	(	(	PUNCT
ejpam-4444	398	20	t−	t−	PROPN
ejpam-4444	398	21	1	1	NUM
ejpam-4444	398	22	)	)	PUNCT
ejpam-4444	398	23	−2kα+(k+1	−2kα+(k+1	PROPN
ejpam-4444	398	24	)	)	PUNCT
ejpam-4444	398	25	>	>	X
ejpam-4444	398	26	(	(	PUNCT
ejpam-4444	398	27	α	α	NOUN
ejpam-4444	398	28	)	)	PUNCT
ejpam-4444	398	29	t2	t2	NOUN
ejpam-4444	398	30	+	+	CCONJ
ejpam-4444	398	31	1	1	NUM
ejpam-4444	398	32	t+	t+	NUM
ejpam-4444	398	33	1	1	NUM
ejpam-4444	398	34	+	+	CCONJ
ejpam-4444	398	35	(	(	PUNCT
ejpam-4444	398	36	1−	1−	NUM
ejpam-4444	398	37	α	α	NOUN
ejpam-4444	398	38	)	)	PUNCT
ejpam-4444	398	39	2	2	NUM
ejpam-4444	398	40	t	t	NOUN
ejpam-4444	398	41	t+	t+	PUNCT
ejpam-4444	398	42	1	1	NUM
ejpam-4444	398	43	(	(	PUNCT
ejpam-4444	398	44	15	15	NUM
ejpam-4444	398	45	)	)	PUNCT
ejpam-4444	398	46	for	for	ADP
ejpam-4444	398	47	all	all	PRON
ejpam-4444	398	48	α	α	PRON
ejpam-4444	398	49	∈	∈	PROPN
ejpam-4444	398	50	(	(	PUNCT
ejpam-4444	398	51	0	0	NUM
ejpam-4444	398	52	,	,	PUNCT
ejpam-4444	398	53	2	2	NUM
ejpam-4444	398	54	/	/	SYM
ejpam-4444	398	55	k	k	NOUN
ejpam-4444	398	56	)	)	PUNCT
ejpam-4444	398	57	and	and	CCONJ
ejpam-4444	398	58	t	t	X
ejpam-4444	398	59	=	=	SYM
ejpam-4444	398	60	b	b	X
ejpam-4444	398	61	/	/	SYM
ejpam-4444	398	62	a	a	PRON
ejpam-4444	398	63	>	>	X
ejpam-4444	398	64	1	1	X
ejpam-4444	398	65	.	.	X
ejpam-4444	398	66	inequality	inequality	NOUN
ejpam-4444	398	67	(	(	PUNCT
ejpam-4444	398	68	15	15	NUM
ejpam-4444	398	69	)	)	PUNCT
ejpam-4444	398	70	is	be	AUX
ejpam-4444	398	71	equivalent	equivalent	ADJ
ejpam-4444	398	72	to	to	ADP
ejpam-4444	398	73	f	f	PROPN
ejpam-4444	398	74	(	(	PUNCT
ejpam-4444	398	75	t	t	PROPN
ejpam-4444	398	76	)	)	PUNCT
ejpam-4444	398	77	>	>	X
ejpam-4444	398	78	0	0	PUNCT
ejpam-4444	399	1	in	in	ADP
ejpam-4444	399	2	(	(	PUNCT
ejpam-4444	399	3	1	1	NUM
ejpam-4444	399	4	)	)	PUNCT
ejpam-4444	399	5	with	with	ADP
ejpam-4444	399	6	p	p	NOUN
ejpam-4444	399	7	=	=	SYM
ejpam-4444	399	8	1/	1/	NUM
ejpam-4444	399	9	[	[	X
ejpam-4444	399	10	−2kα+	−2kα+	X
ejpam-4444	399	11	(	(	PUNCT
ejpam-4444	399	12	k	k	PROPN
ejpam-4444	399	13	+	+	PROPN
ejpam-4444	399	14	1	1	NUM
ejpam-4444	399	15	)	)	PUNCT
ejpam-4444	399	16	]	]	PUNCT
ejpam-4444	399	17	.	.	PUNCT
ejpam-4444	400	1	using	use	VERB
ejpam-4444	400	2	lemma	lemma	PROPN
ejpam-4444	400	3	1	1	NUM
ejpam-4444	400	4	,	,	PUNCT
ejpam-4444	400	5	we	we	PRON
ejpam-4444	400	6	have	have	AUX
ejpam-4444	400	7	formulae	formulae	NOUN
ejpam-4444	400	8	for	for	ADP
ejpam-4444	400	9	f	f	PROPN
ejpam-4444	400	10	′(t	′(t	PROPN
ejpam-4444	400	11	)	)	PUNCT
ejpam-4444	400	12	,	,	PUNCT
ejpam-4444	400	13	g′(t	g′(t	PROPN
ejpam-4444	400	14	)	)	PUNCT
ejpam-4444	400	15	,	,	PUNCT
ejpam-4444	400	16	g′′(t	g′′(t	NOUN
ejpam-4444	400	17	)	)	PUNCT
ejpam-4444	400	18	.	.	PUNCT
ejpam-4444	401	1	taking	take	VERB
ejpam-4444	401	2	derivative	derivative	NOUN
ejpam-4444	401	3	of	of	ADP
ejpam-4444	401	4	g′′(t	g′′(t	NOUN
ejpam-4444	401	5	)	)	PUNCT
ejpam-4444	401	6	,	,	PUNCT
ejpam-4444	401	7	we	we	PRON
ejpam-4444	401	8	have	have	AUX
ejpam-4444	401	9	g′′′(t	g′′′(t	VERB
ejpam-4444	401	10	)	)	PUNCT
ejpam-4444	401	11	=	=	SYM
ejpam-4444	402	1	2	2	NUM
ejpam-4444	402	2	+	+	CCONJ
ejpam-4444	402	3	k	k	PROPN
ejpam-4444	402	4	−	−	PROPN
ejpam-4444	402	5	2kα	2kα	NOUN
ejpam-4444	402	6	(	(	PUNCT
ejpam-4444	402	7	2kα−	2kα−	NUM
ejpam-4444	402	8	k	k	PROPN
ejpam-4444	402	9	−	−	PROPN
ejpam-4444	402	10	1)4	1)4	PROPN
ejpam-4444	402	11	t	t	PROPN
ejpam-4444	402	12	−2+(6α−3)k	−2+(6α−3)k	PROPN
ejpam-4444	402	13	−1+(2α−1)k	−1+(2α−1)k	PROPN
ejpam-4444	402	14	j(t	j(t	PROPN
ejpam-4444	402	15	)	)	PUNCT
ejpam-4444	402	16	,	,	PUNCT
ejpam-4444	402	17	a.	a.	NOUN
ejpam-4444	402	18	sonubon	sonubon	PROPN
ejpam-4444	402	19	,	,	PUNCT
ejpam-4444	402	20	s.	s.	PROPN
ejpam-4444	402	21	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	402	22	,	,	PUNCT
ejpam-4444	402	23	k.	k.	PROPN
ejpam-4444	402	24	nonlaopon	nonlaopon	ADV
ejpam-4444	402	25	/	/	SYM
ejpam-4444	402	26	eur	eur	PROPN
ejpam-4444	402	27	.	.	PUNCT
ejpam-4444	403	1	j.	j.	PROPN
ejpam-4444	403	2	pure	pure	PROPN
ejpam-4444	403	3	appl	appl	PROPN
ejpam-4444	403	4	.	.	PROPN
ejpam-4444	403	5	math	math	PROPN
ejpam-4444	403	6	,	,	PUNCT
ejpam-4444	403	7	15	15	NUM
ejpam-4444	403	8	(	(	PUNCT
ejpam-4444	403	9	3	3	NUM
ejpam-4444	403	10	)	)	PUNCT
ejpam-4444	403	11	(	(	PUNCT
ejpam-4444	403	12	2022	2022	NUM
ejpam-4444	403	13	)	)	PUNCT
ejpam-4444	403	14	,	,	PUNCT
ejpam-4444	403	15	1120	1120	NUM
ejpam-4444	403	16	-	-	SYM
ejpam-4444	403	17	1143	1143	NUM
ejpam-4444	403	18	1137	1137	NUM
ejpam-4444	403	19	where	where	SCONJ
ejpam-4444	403	20	j(t	j(t	PROPN
ejpam-4444	403	21	)	)	PUNCT
ejpam-4444	403	22	=	=	PUNCT
ejpam-4444	403	23	(	(	PUNCT
ejpam-4444	403	24	1−	1−	NUM
ejpam-4444	403	25	2α)(2−	2α)(2−	NUM
ejpam-4444	403	26	kα)(6kα−	kα)(6kα−	NOUN
ejpam-4444	403	27	3k	3k	PROPN
ejpam-4444	403	28	−	−	PROPN
ejpam-4444	403	29	4)(4kα−	4)(4kα−	NUM
ejpam-4444	403	30	2k	2k	NOUN
ejpam-4444	403	31	−	−	PROPN
ejpam-4444	403	32	3)t3	3)t3	NUM
ejpam-4444	403	33	−	−	PROPN
ejpam-4444	404	1	(	(	PUNCT
ejpam-4444	404	2	2α2k	2α2k	ADV
ejpam-4444	404	3	−	−	X
ejpam-4444	404	4	5kα−	5kα−	NUM
ejpam-4444	404	5	6α+	6α+	NUM
ejpam-4444	404	6	2k	2k	NOUN
ejpam-4444	404	7	+	+	CCONJ
ejpam-4444	404	8	4)(−4kα+	4)(−4kα+	NUM
ejpam-4444	404	9	2k	2k	NOUN
ejpam-4444	404	10	+	+	CCONJ
ejpam-4444	404	11	3)t2	3)t2	PROPN
ejpam-4444	404	12	+	+	CCONJ
ejpam-4444	404	13	(	(	PUNCT
ejpam-4444	404	14	1−	1−	NUM
ejpam-4444	404	15	2α)k(2α2k	2α)k(2α2k	NUM
ejpam-4444	404	16	−	−	PROPN
ejpam-4444	405	1	5kα+	5kα+	NUM
ejpam-4444	405	2	2k	2k	NOUN
ejpam-4444	405	3	+	+	CCONJ
ejpam-4444	405	4	2)t−	2)t−	NUM
ejpam-4444	405	5	α(1−	α(1−	PROPN
ejpam-4444	405	6	2α)k(−4kα+	2α)k(−4kα+	NUM
ejpam-4444	405	7	2k	2k	NOUN
ejpam-4444	405	8	+	+	CCONJ
ejpam-4444	405	9	1	1	NUM
ejpam-4444	405	10	)	)	PUNCT
ejpam-4444	405	11	+	+	SYM
ejpam-4444	405	12	6α(1	6α(1	X
ejpam-4444	406	1	+	+	CCONJ
ejpam-4444	406	2	k	k	PROPN
ejpam-4444	407	1	−	−	PROPN
ejpam-4444	407	2	2kα)3	2kα)3	NUM
ejpam-4444	407	3	t	t	NOUN
ejpam-4444	407	4	−2+(6α−3)k	−2+(6α−3)k	PROPN
ejpam-4444	407	5	−1+(2α−1)k	−1+(2α−1)k	PROPN
ejpam-4444	407	6	.	.	PUNCT
ejpam-4444	408	1	for	for	ADP
ejpam-4444	408	2	α	α	PRON
ejpam-4444	408	3	∈	∈	PROPN
ejpam-4444	408	4	(	(	PUNCT
ejpam-4444	408	5	0	0	NUM
ejpam-4444	408	6	,	,	PUNCT
ejpam-4444	408	7	2	2	NUM
ejpam-4444	408	8	/	/	SYM
ejpam-4444	408	9	k	k	NOUN
ejpam-4444	408	10	)	)	PUNCT
ejpam-4444	408	11	,	,	PUNCT
ejpam-4444	408	12	exponent	exponent	NOUN
ejpam-4444	409	1	[	[	X
ejpam-4444	409	2	−1	−1	NOUN
ejpam-4444	409	3	+	+	PUNCT
ejpam-4444	409	4	(	(	PUNCT
ejpam-4444	409	5	4α−	4α−	PROPN
ejpam-4444	409	6	2)k]/[−1	2)k]/[−1	NUM
ejpam-4444	409	7	+	+	CCONJ
ejpam-4444	409	8	(	(	PUNCT
ejpam-4444	409	9	2α−	2α−	NUM
ejpam-4444	409	10	1)k	1)k	NUM
ejpam-4444	409	11	]	]	PUNCT
ejpam-4444	409	12	>	>	X
ejpam-4444	409	13	1	1	NUM
ejpam-4444	409	14	and	and	CCONJ
ejpam-4444	409	15	hence	hence	ADV
ejpam-4444	409	16	t	t	PROPN
ejpam-4444	409	17	−2+(6α−3)k	−2+(6α−3)k	PROPN
ejpam-4444	409	18	−1+(2α−1)k	−1+(2α−1)k	PROPN
ejpam-4444	409	19	=	=	SYM
ejpam-4444	409	20	t	t	PROPN
ejpam-4444	409	21	[	[	PUNCT
ejpam-4444	409	22	t	t	X
ejpam-4444	409	23	−1+(4α−2)k	−1+(4α−2)k	PROPN
ejpam-4444	409	24	−1+(2α−1)k	−1+(2α−1)k	PROPN
ejpam-4444	409	25	]	]	PUNCT
ejpam-4444	409	26	>	>	X
ejpam-4444	409	27	t	t	X
ejpam-4444	409	28	{	{	PUNCT
ejpam-4444	409	29	1	1	NUM
ejpam-4444	410	1	+	+	CCONJ
ejpam-4444	410	2	[	[	X
ejpam-4444	410	3	−1	−1	NOUN
ejpam-4444	410	4	+	+	PUNCT
ejpam-4444	410	5	(	(	PUNCT
ejpam-4444	410	6	4α−	4α−	NOUN
ejpam-4444	410	7	2)k	2)k	NUM
ejpam-4444	410	8	−1	−1	NOUN
ejpam-4444	410	9	+	+	PUNCT
ejpam-4444	410	10	(	(	PUNCT
ejpam-4444	410	11	2α−	2α−	NUM
ejpam-4444	410	12	1)k	1)k	NUM
ejpam-4444	410	13	]	]	PUNCT
ejpam-4444	410	14	(	(	PUNCT
ejpam-4444	410	15	t−	t−	PROPN
ejpam-4444	410	16	1	1	NUM
ejpam-4444	410	17	)	)	PUNCT
ejpam-4444	410	18	}	}	PUNCT
ejpam-4444	411	1	=	=	PUNCT
ejpam-4444	412	1	[	[	X
ejpam-4444	412	2	−1	−1	NOUN
ejpam-4444	412	3	+	+	PUNCT
ejpam-4444	412	4	(	(	PUNCT
ejpam-4444	412	5	4α−	4α−	NOUN
ejpam-4444	412	6	2)k	2)k	NUM
ejpam-4444	412	7	−1	−1	NOUN
ejpam-4444	412	8	+	+	PUNCT
ejpam-4444	412	9	(	(	PUNCT
ejpam-4444	412	10	2α−	2α−	NUM
ejpam-4444	412	11	1)k	1)k	NUM
ejpam-4444	412	12	]	]	PUNCT
ejpam-4444	412	13	t2	t2	NOUN
ejpam-4444	412	14	+	+	CCONJ
ejpam-4444	412	15	[	[	PUNCT
ejpam-4444	412	16	(	(	PUNCT
ejpam-4444	412	17	1−	1−	NUM
ejpam-4444	412	18	2α)k	2α)k	NUM
ejpam-4444	412	19	−1	−1	NOUN
ejpam-4444	412	20	+	+	PUNCT
ejpam-4444	412	21	(	(	PUNCT
ejpam-4444	412	22	2α−	2α−	NUM
ejpam-4444	412	23	1)k	1)k	NUM
ejpam-4444	412	24	]	]	PUNCT
ejpam-4444	413	1	t.	t.	X
ejpam-4444	413	2	furthermore	furthermore	ADV
ejpam-4444	413	3	coefficient	coefficient	NOUN
ejpam-4444	413	4	6α(1	6α(1	PUNCT
ejpam-4444	414	1	+	+	CCONJ
ejpam-4444	414	2	k	k	PROPN
ejpam-4444	415	1	−	−	PROPN
ejpam-4444	415	2	2kα)3	2kα)3	NUM
ejpam-4444	415	3	>	>	X
ejpam-4444	415	4	0	0	NUM
ejpam-4444	416	1	for	for	ADP
ejpam-4444	416	2	such	such	ADJ
ejpam-4444	416	3	α	α	NOUN
ejpam-4444	416	4	.	.	PUNCT
ejpam-4444	416	5	therefore	therefore	ADV
ejpam-4444	416	6	j(t	j(t	PROPN
ejpam-4444	416	7	)	)	PUNCT
ejpam-4444	416	8	>	>	X
ejpam-4444	416	9	(	(	PUNCT
ejpam-4444	416	10	1−	1−	NUM
ejpam-4444	416	11	2α	2α	NOUN
ejpam-4444	416	12	)	)	PUNCT
ejpam-4444	416	13	[	[	PUNCT
ejpam-4444	416	14	(	(	PUNCT
ejpam-4444	416	15	2−	2−	NUM
ejpam-4444	416	16	kα)(6kα−	kα)(6kα−	NOUN
ejpam-4444	416	17	3k	3k	PROPN
ejpam-4444	416	18	−	−	PROPN
ejpam-4444	416	19	4)(4kα−	4)(4kα−	NUM
ejpam-4444	416	20	2k	2k	NOUN
ejpam-4444	416	21	−	−	PROPN
ejpam-4444	416	22	3)t3	3)t3	NUM
ejpam-4444	416	23	+	+	CCONJ
ejpam-4444	416	24	(	(	PUNCT
ejpam-4444	416	25	48α3k3	48α3k3	NUM
ejpam-4444	416	26	−	−	PROPN
ejpam-4444	416	27	48α2k3	48α2k3	NUM
ejpam-4444	416	28	−	−	PROPN
ejpam-4444	416	29	64α2k2	64α2k2	NOUN
ejpam-4444	416	30	+	+	CCONJ
ejpam-4444	416	31	12αk3	12αk3	X
ejpam-4444	416	32	+	+	CCONJ
ejpam-4444	416	33	40αk2	40αk2	NOUN
ejpam-4444	416	34	+	+	CCONJ
ejpam-4444	416	35	39kα−	39kα−	NUM
ejpam-4444	416	36	4k2	4k2	NUM
ejpam-4444	416	37	−	−	PROPN
ejpam-4444	416	38	14k	14k	NOUN
ejpam-4444	416	39	−	−	PROPN
ejpam-4444	416	40	12)t2	12)t2	NUM
ejpam-4444	416	41	−	−	PROPN
ejpam-4444	417	1	k(24α3k2	k(24α3k2	PROPN
ejpam-4444	417	2	−	−	PROPN
ejpam-4444	417	3	24α2k2	24α2k2	NOUN
ejpam-4444	417	4	−	−	PROPN
ejpam-4444	417	5	26α2k	26α2k	PROPN
ejpam-4444	417	6	+	+	CCONJ
ejpam-4444	417	7	6αk2	6αk2	NUM
ejpam-4444	418	1	+	+	NUM
ejpam-4444	418	2	17kα+	17kα+	NUM
ejpam-4444	418	3	6α−	6α−	NUM
ejpam-4444	418	4	2k	2k	NUM
ejpam-4444	418	5	−	−	NOUN
ejpam-4444	418	6	2)t	2)t	NUM
ejpam-4444	418	7	−	−	ADP
ejpam-4444	418	8	αk(−4kα+	αk(−4kα+	ADJ
ejpam-4444	418	9	2k	2k	NOUN
ejpam-4444	418	10	+	+	CCONJ
ejpam-4444	418	11	1	1	NUM
ejpam-4444	418	12	)	)	PUNCT
ejpam-4444	418	13	]	]	PUNCT
ejpam-4444	418	14	.	.	PUNCT
ejpam-4444	419	1	consider	consider	VERB
ejpam-4444	419	2	the	the	DET
ejpam-4444	419	3	term	term	NOUN
ejpam-4444	419	4	on	on	ADP
ejpam-4444	419	5	the	the	DET
ejpam-4444	419	6	right	right	ADJ
ejpam-4444	419	7	side	side	NOUN
ejpam-4444	419	8	of	of	ADP
ejpam-4444	419	9	the	the	DET
ejpam-4444	419	10	inequality	inequality	NOUN
ejpam-4444	419	11	sign	sign	NOUN
ejpam-4444	419	12	above	above	ADV
ejpam-4444	419	13	.	.	PUNCT
ejpam-4444	420	1	since	since	SCONJ
ejpam-4444	420	2	t2	t2	PROPN
ejpam-4444	420	3	>	>	X
ejpam-4444	420	4	2	2	NUM
ejpam-4444	420	5	t	t	NOUN
ejpam-4444	420	6	−	−	NOUN
ejpam-4444	420	7	1	1	NUM
ejpam-4444	420	8	and	and	CCONJ
ejpam-4444	420	9	coefficient	coefficient	NOUN
ejpam-4444	420	10	(	(	PUNCT
ejpam-4444	420	11	2−	2−	NUM
ejpam-4444	420	12	kα)(6kα−	kα)(6kα−	NOUN
ejpam-4444	420	13	3k	3k	PROPN
ejpam-4444	420	14	−	−	PROPN
ejpam-4444	420	15	4)(4kα−	4)(4kα−	NUM
ejpam-4444	420	16	2k	2k	NOUN
ejpam-4444	420	17	−	−	NOUN
ejpam-4444	420	18	3	3	NUM
ejpam-4444	420	19	)	)	PUNCT
ejpam-4444	420	20	of	of	ADP
ejpam-4444	420	21	t3	t3	PROPN
ejpam-4444	420	22	is	be	AUX
ejpam-4444	420	23	positive	positive	ADJ
ejpam-4444	420	24	,	,	PUNCT
ejpam-4444	420	25	we	we	PRON
ejpam-4444	420	26	have	have	VERB
ejpam-4444	420	27	j(t	j(t	PROPN
ejpam-4444	420	28	)	)	PUNCT
ejpam-4444	420	29	>	>	X
ejpam-4444	421	1	(	(	PUNCT
ejpam-4444	421	2	1−	1−	NUM
ejpam-4444	421	3	2α	2α	NOUN
ejpam-4444	421	4	)	)	PUNCT
ejpam-4444	421	5	[	[	PUNCT
ejpam-4444	421	6	(	(	PUNCT
ejpam-4444	421	7	100α2k2	100α2k2	NUM
ejpam-4444	421	8	−	−	NOUN
ejpam-4444	421	9	90αk2	90αk2	NOUN
ejpam-4444	421	10	−	−	PROPN
ejpam-4444	421	11	121kα+	121kα+	NOUN
ejpam-4444	421	12	20k2	20k2	NUM
ejpam-4444	422	1	+	+	NUM
ejpam-4444	422	2	54k	54k	NOUN
ejpam-4444	422	3	+	+	CCONJ
ejpam-4444	422	4	36)t2	36)t2	NUM
ejpam-4444	423	1	+	+	CCONJ
ejpam-4444	423	2	(	(	PUNCT
ejpam-4444	423	3	−56α2k2	−56α2k2	NOUN
ejpam-4444	423	4	+	+	CCONJ
ejpam-4444	423	5	48αk2	48αk2	NOUN
ejpam-4444	423	6	+	+	CCONJ
ejpam-4444	423	7	74kα−	74kα−	NUM
ejpam-4444	423	8	10k2	10k2	NUM
ejpam-4444	423	9	−	−	NOUN
ejpam-4444	423	10	32k	32k	NOUN
ejpam-4444	423	11	−	−	PROPN
ejpam-4444	423	12	24)t−	24)t−	NUM
ejpam-4444	423	13	αk(−4kα+	αk(−4kα+	ADJ
ejpam-4444	423	14	2k	2k	NUM
ejpam-4444	423	15	+	+	CCONJ
ejpam-4444	423	16	1	1	NUM
ejpam-4444	423	17	)	)	PUNCT
ejpam-4444	423	18	]	]	PUNCT
ejpam-4444	423	19	.	.	PUNCT
ejpam-4444	424	1	because	because	SCONJ
ejpam-4444	424	2	t2	t2	PROPN
ejpam-4444	424	3	>	>	X
ejpam-4444	424	4	t	t	PROPN
ejpam-4444	424	5	and	and	CCONJ
ejpam-4444	424	6	coefficient	coefficient	NOUN
ejpam-4444	424	7	100α2k2	100α2k2	NUM
ejpam-4444	424	8	−	−	PROPN
ejpam-4444	424	9	90αk2	90αk2	NOUN
ejpam-4444	425	1	−	−	PROPN
ejpam-4444	426	1	121kα	121kα	PROPN
ejpam-4444	427	1	+	+	CCONJ
ejpam-4444	427	2	20k2	20k2	NUM
ejpam-4444	427	3	+	+	NUM
ejpam-4444	427	4	54k	54k	NOUN
ejpam-4444	427	5	+	+	CCONJ
ejpam-4444	427	6	36	36	NUM
ejpam-4444	427	7	of	of	ADP
ejpam-4444	427	8	t2	t2	NOUN
ejpam-4444	427	9	on	on	ADP
ejpam-4444	427	10	the	the	DET
ejpam-4444	427	11	right	right	ADJ
ejpam-4444	427	12	side	side	NOUN
ejpam-4444	427	13	of	of	ADP
ejpam-4444	427	14	the	the	DET
ejpam-4444	427	15	above	above	ADJ
ejpam-4444	427	16	inequality	inequality	NOUN
ejpam-4444	427	17	is	be	AUX
ejpam-4444	427	18	positive	positive	ADJ
ejpam-4444	427	19	for	for	ADP
ejpam-4444	427	20	α	α	PRON
ejpam-4444	427	21	∈	∈	PROPN
ejpam-4444	427	22	(	(	PUNCT
ejpam-4444	427	23	0	0	NUM
ejpam-4444	427	24	,	,	PUNCT
ejpam-4444	427	25	2	2	NUM
ejpam-4444	427	26	/	/	SYM
ejpam-4444	427	27	k	k	NOUN
ejpam-4444	427	28	)	)	PUNCT
ejpam-4444	427	29	,	,	PUNCT
ejpam-4444	427	30	we	we	PRON
ejpam-4444	427	31	obtain	obtain	VERB
ejpam-4444	427	32	j(t	j(t	PROPN
ejpam-4444	427	33	)	)	PUNCT
ejpam-4444	427	34	>	>	X
ejpam-4444	428	1	(	(	PUNCT
ejpam-4444	428	2	1−	1−	NUM
ejpam-4444	428	3	2α	2α	NOUN
ejpam-4444	428	4	)	)	PUNCT
ejpam-4444	428	5	[	[	PUNCT
ejpam-4444	428	6	(	(	PUNCT
ejpam-4444	428	7	44α2k2	44α2k2	NOUN
ejpam-4444	428	8	−	−	PROPN
ejpam-4444	428	9	42αk2	42αk2	NOUN
ejpam-4444	428	10	−	−	PROPN
ejpam-4444	429	1	47kα+	47kα+	NUM
ejpam-4444	429	2	10k2	10k2	NUM
ejpam-4444	429	3	+	+	NUM
ejpam-4444	429	4	22k	22k	NOUN
ejpam-4444	429	5	+	+	CCONJ
ejpam-4444	429	6	12)t	12)t	NUM
ejpam-4444	429	7	−	−	NOUN
ejpam-4444	429	8	αk(−4kα+	αk(−4kα+	ADJ
ejpam-4444	429	9	2k	2k	NOUN
ejpam-4444	429	10	+	+	CCONJ
ejpam-4444	429	11	1	1	NUM
ejpam-4444	429	12	)	)	PUNCT
ejpam-4444	429	13	]	]	PUNCT
ejpam-4444	429	14	.	.	PUNCT
ejpam-4444	430	1	observe	observe	VERB
ejpam-4444	430	2	that	that	PRON
ejpam-4444	430	3	coefficient	coefficient	NOUN
ejpam-4444	430	4	44α2k2	44α2k2	X
ejpam-4444	430	5	−	−	PROPN
ejpam-4444	430	6	42αk2	42αk2	NOUN
ejpam-4444	430	7	−	−	PROPN
ejpam-4444	430	8	47kα+10k2	47kα+10k2	NUM
ejpam-4444	430	9	+22k+12	+22k+12	PRON
ejpam-4444	430	10	of	of	ADP
ejpam-4444	430	11	t	t	PROPN
ejpam-4444	430	12	is	be	AUX
ejpam-4444	430	13	positive	positive	ADJ
ejpam-4444	430	14	for	for	ADP
ejpam-4444	430	15	such	such	ADJ
ejpam-4444	430	16	α	α	X
ejpam-4444	430	17	.	.	PUNCT
ejpam-4444	431	1	since	since	SCONJ
ejpam-4444	431	2	t	t	PROPN
ejpam-4444	431	3	>	>	X
ejpam-4444	431	4	1	1	NUM
ejpam-4444	431	5	,	,	PUNCT
ejpam-4444	431	6	we	we	PRON
ejpam-4444	431	7	finally	finally	ADV
ejpam-4444	431	8	have	have	VERB
ejpam-4444	431	9	j(t	j(t	PROPN
ejpam-4444	431	10	)	)	PUNCT
ejpam-4444	431	11	>	>	X
ejpam-4444	432	1	2(1−	2(1−	NUM
ejpam-4444	432	2	2α)(12kα−	2α)(12kα−	NUM
ejpam-4444	432	3	5k	5k	NUM
ejpam-4444	432	4	−	−	NOUN
ejpam-4444	432	5	6)(2kα−	6)(2kα−	NOUN
ejpam-4444	432	6	k	k	PROPN
ejpam-4444	432	7	−	−	PROPN
ejpam-4444	432	8	1	1	NUM
ejpam-4444	432	9	)	)	PUNCT
ejpam-4444	432	10	>	>	X
ejpam-4444	433	1	0	0	X
ejpam-4444	433	2	.	.	PUNCT
ejpam-4444	433	3	therefore	therefore	ADV
ejpam-4444	433	4	g′′′(t	g′′′(t	VERB
ejpam-4444	433	5	)	)	PUNCT
ejpam-4444	433	6	>	>	X
ejpam-4444	433	7	0	0	PUNCT
ejpam-4444	434	1	for	for	ADP
ejpam-4444	434	2	all	all	DET
ejpam-4444	434	3	α	α	PRON
ejpam-4444	434	4	∈	∈	NOUN
ejpam-4444	434	5	(	(	PUNCT
ejpam-4444	434	6	0	0	NUM
ejpam-4444	434	7	,	,	PUNCT
ejpam-4444	434	8	2	2	NUM
ejpam-4444	434	9	/	/	SYM
ejpam-4444	434	10	k	k	NOUN
ejpam-4444	434	11	)	)	PUNCT
ejpam-4444	434	12	.	.	PUNCT
ejpam-4444	435	1	a.	a.	PROPN
ejpam-4444	435	2	sonubon	sonubon	PROPN
ejpam-4444	435	3	,	,	PUNCT
ejpam-4444	435	4	s.	s.	PROPN
ejpam-4444	435	5	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	435	6	,	,	PUNCT
ejpam-4444	435	7	k.	k.	PROPN
ejpam-4444	435	8	nonlaopon	nonlaopon	ADV
ejpam-4444	435	9	/	/	SYM
ejpam-4444	435	10	eur	eur	PROPN
ejpam-4444	435	11	.	.	PUNCT
ejpam-4444	436	1	j.	j.	PROPN
ejpam-4444	436	2	pure	pure	PROPN
ejpam-4444	436	3	appl	appl	PROPN
ejpam-4444	436	4	.	.	PROPN
ejpam-4444	436	5	math	math	PROPN
ejpam-4444	436	6	,	,	PUNCT
ejpam-4444	436	7	15	15	NUM
ejpam-4444	436	8	(	(	PUNCT
ejpam-4444	436	9	3	3	NUM
ejpam-4444	436	10	)	)	PUNCT
ejpam-4444	436	11	(	(	PUNCT
ejpam-4444	436	12	2022	2022	NUM
ejpam-4444	436	13	)	)	PUNCT
ejpam-4444	436	14	,	,	PUNCT
ejpam-4444	436	15	1120	1120	NUM
ejpam-4444	436	16	-	-	SYM
ejpam-4444	436	17	1143	1143	NUM
ejpam-4444	436	18	1138	1138	NUM
ejpam-4444	436	19	3	3	NUM
ejpam-4444	436	20	)	)	PUNCT
ejpam-4444	436	21	treated	treat	VERB
ejpam-4444	436	22	as	as	ADP
ejpam-4444	436	23	in	in	ADP
ejpam-4444	436	24	theorem	theorem	ADJ
ejpam-4444	436	25	1(2	1(2	NUM
ejpam-4444	436	26	)	)	PUNCT
ejpam-4444	437	1	,	,	PUNCT
ejpam-4444	437	2	the	the	DET
ejpam-4444	437	3	proposed	propose	VERB
ejpam-4444	437	4	inequality	inequality	NOUN
ejpam-4444	437	5	becomes	become	VERB
ejpam-4444	437	6	{	{	PUNCT
ejpam-4444	437	7	t2kα+(2−k	t2kα+(2−k	NOUN
ejpam-4444	437	8	)	)	PUNCT
ejpam-4444	437	9	−	−	PROPN
ejpam-4444	437	10	1	1	NUM
ejpam-4444	437	11	[	[	PUNCT
ejpam-4444	437	12	2kα+	2kα+	NUM
ejpam-4444	437	13	(	(	PUNCT
ejpam-4444	437	14	2−	2−	NUM
ejpam-4444	437	15	k	k	NOUN
ejpam-4444	437	16	)	)	PUNCT
ejpam-4444	437	17	]	]	PUNCT
ejpam-4444	438	1	(	(	PUNCT
ejpam-4444	438	2	t−	t−	PROPN
ejpam-4444	438	3	1	1	NUM
ejpam-4444	438	4	)	)	PUNCT
ejpam-4444	438	5	}	}	PUNCT
ejpam-4444	438	6	1/[2kα+(1−k	1/[2kα+(1−k	NUM
ejpam-4444	438	7	)	)	PUNCT
ejpam-4444	438	8	]	]	PUNCT
ejpam-4444	438	9	<	<	X
ejpam-4444	438	10	α	α	X
ejpam-4444	438	11	(	(	PUNCT
ejpam-4444	438	12	t2	t2	NOUN
ejpam-4444	438	13	+	+	CCONJ
ejpam-4444	438	14	1	1	NUM
ejpam-4444	438	15	t+	t+	NUM
ejpam-4444	438	16	1	1	NUM
ejpam-4444	438	17	)	)	PUNCT
ejpam-4444	438	18	+	+	CCONJ
ejpam-4444	438	19	(	(	PUNCT
ejpam-4444	438	20	1−	1−	NUM
ejpam-4444	438	21	α	α	NOUN
ejpam-4444	438	22	)	)	PUNCT
ejpam-4444	438	23	(	(	PUNCT
ejpam-4444	438	24	2	2	NUM
ejpam-4444	438	25	t	t	NOUN
ejpam-4444	438	26	t+	t+	PUNCT
ejpam-4444	438	27	1	1	NUM
ejpam-4444	438	28	)	)	PUNCT
ejpam-4444	438	29	(	(	PUNCT
ejpam-4444	438	30	16	16	NUM
ejpam-4444	438	31	)	)	PUNCT
ejpam-4444	438	32	for	for	ADP
ejpam-4444	438	33	all	all	DET
ejpam-4444	438	34	α	α	PRON
ejpam-4444	438	35	∈	∈	NOUN
ejpam-4444	438	36	(	(	PUNCT
ejpam-4444	438	37	(	(	PUNCT
ejpam-4444	438	38	k	k	X
ejpam-4444	438	39	+	+	NOUN
ejpam-4444	438	40	2)/2k	2)/2k	NUM
ejpam-4444	438	41	,	,	PUNCT
ejpam-4444	438	42	1	1	NUM
ejpam-4444	438	43	)	)	PUNCT
ejpam-4444	438	44	and	and	CCONJ
ejpam-4444	438	45	t	t	X
ejpam-4444	439	1	=	=	SYM
ejpam-4444	439	2	b	b	X
ejpam-4444	439	3	/	/	SYM
ejpam-4444	439	4	a	a	PRON
ejpam-4444	439	5	>	>	X
ejpam-4444	439	6	1	1	X
ejpam-4444	439	7	.	.	X
ejpam-4444	439	8	inequality	inequality	NOUN
ejpam-4444	439	9	(	(	PUNCT
ejpam-4444	439	10	16	16	NUM
ejpam-4444	439	11	)	)	PUNCT
ejpam-4444	439	12	is	be	AUX
ejpam-4444	439	13	equivalent	equivalent	ADJ
ejpam-4444	439	14	to	to	ADP
ejpam-4444	439	15	f	f	PROPN
ejpam-4444	439	16	(	(	PUNCT
ejpam-4444	439	17	t	t	PROPN
ejpam-4444	439	18	)	)	PUNCT
ejpam-4444	439	19	>	>	X
ejpam-4444	439	20	0	0	PUNCT
ejpam-4444	440	1	in	in	ADP
ejpam-4444	440	2	(	(	PUNCT
ejpam-4444	440	3	1	1	NUM
ejpam-4444	440	4	)	)	PUNCT
ejpam-4444	440	5	with	with	ADP
ejpam-4444	440	6	p	p	PROPN
ejpam-4444	440	7	=	=	PROPN
ejpam-4444	440	8	2kα+(1−k	2kα+(1−k	NUM
ejpam-4444	440	9	)	)	PUNCT
ejpam-4444	440	10	.	.	PUNCT
ejpam-4444	441	1	using	use	VERB
ejpam-4444	441	2	lemma	lemma	PROPN
ejpam-4444	441	3	1	1	NUM
ejpam-4444	441	4	,	,	PUNCT
ejpam-4444	441	5	we	we	PRON
ejpam-4444	441	6	have	have	AUX
ejpam-4444	441	7	formulae	formulae	NOUN
ejpam-4444	441	8	for	for	ADP
ejpam-4444	441	9	f	f	PROPN
ejpam-4444	441	10	′(t	′(t	PROPN
ejpam-4444	441	11	)	)	PUNCT
ejpam-4444	441	12	,	,	PUNCT
ejpam-4444	441	13	g′(t	g′(t	PROPN
ejpam-4444	441	14	)	)	PUNCT
ejpam-4444	441	15	,	,	PUNCT
ejpam-4444	441	16	g′′(t	g′′(t	NOUN
ejpam-4444	441	17	)	)	PUNCT
ejpam-4444	441	18	.	.	PUNCT
ejpam-4444	442	1	taking	take	VERB
ejpam-4444	442	2	derivative	derivative	NOUN
ejpam-4444	442	3	of	of	ADP
ejpam-4444	442	4	g′′(t	g′′(t	NOUN
ejpam-4444	442	5	)	)	PUNCT
ejpam-4444	442	6	,	,	PUNCT
ejpam-4444	442	7	we	we	PRON
ejpam-4444	442	8	have	have	AUX
ejpam-4444	442	9	g′′′(t	g′′′(t	VERB
ejpam-4444	442	10	)	)	PUNCT
ejpam-4444	442	11	=	=	PUNCT
ejpam-4444	442	12	(	(	PUNCT
ejpam-4444	442	13	2kα−	2kα−	NUM
ejpam-4444	442	14	k	k	X
ejpam-4444	442	15	+	+	NUM
ejpam-4444	442	16	2)t2kα−k−2k(t	2)t2kα−k−2k(t	NUM
ejpam-4444	442	17	)	)	PUNCT
ejpam-4444	442	18	,	,	PUNCT
ejpam-4444	442	19	where	where	SCONJ
ejpam-4444	442	20	k(t	k(t	VERB
ejpam-4444	442	21	)	)	PUNCT
ejpam-4444	442	22	=	=	NOUN
ejpam-4444	442	23	−(2α−	−(2α−	X
ejpam-4444	442	24	1)(3kα−	1)(3kα−	NUM
ejpam-4444	442	25	2k	2k	NOUN
ejpam-4444	442	26	+	+	CCONJ
ejpam-4444	442	27	2)(2kα−	2)(2kα−	NOUN
ejpam-4444	442	28	k	k	NOUN
ejpam-4444	443	1	+	+	NUM
ejpam-4444	443	2	4)(2kα−	4)(2kα−	NOUN
ejpam-4444	443	3	k	k	NOUN
ejpam-4444	444	1	+	+	CCONJ
ejpam-4444	444	2	3)t3	3)t3	NUM
ejpam-4444	444	3	+	+	CCONJ
ejpam-4444	444	4	(	(	PUNCT
ejpam-4444	444	5	10α2k	10α2k	NUM
ejpam-4444	444	6	−	−	PROPN
ejpam-4444	444	7	9kα+	9kα+	NUM
ejpam-4444	444	8	6α+	6α+	NUM
ejpam-4444	444	9	2k	2k	NOUN
ejpam-4444	444	10	−	−	PROPN
ejpam-4444	444	11	4)(2kα−	4)(2kα−	NOUN
ejpam-4444	444	12	k	k	PROPN
ejpam-4444	445	1	+	+	CCONJ
ejpam-4444	445	2	3)(2kα−	3)(2kα−	NUM
ejpam-4444	445	3	k	k	PROPN
ejpam-4444	446	1	+	+	CCONJ
ejpam-4444	446	2	1)t2	1)t2	NUM
ejpam-4444	446	3	−	−	PROPN
ejpam-4444	447	1	(	(	PUNCT
ejpam-4444	447	2	2α2k	2α2k	ADV
ejpam-4444	447	3	−	−	ADP
ejpam-4444	447	4	kα+	kα+	NOUN
ejpam-4444	447	5	2)(2kα−	2)(2kα−	NOUN
ejpam-4444	447	6	k	k	PROPN
ejpam-4444	447	7	+	+	CCONJ
ejpam-4444	447	8	1)(2α−	1)(2α−	NUM
ejpam-4444	447	9	1)kt	1)kt	NUM
ejpam-4444	447	10	−	−	PROPN
ejpam-4444	448	1	α(2kα−	α(2kα−	NUM
ejpam-4444	448	2	k	k	NOUN
ejpam-4444	449	1	+	+	PROPN
ejpam-4444	449	2	1)(2kα−	1)(2kα−	NUM
ejpam-4444	449	3	k	k	NOUN
ejpam-4444	449	4	−	−	ADP
ejpam-4444	449	5	1)(2α−	1)(2α−	NUM
ejpam-4444	449	6	1)k	1)k	NUM
ejpam-4444	449	7	+	+	CCONJ
ejpam-4444	449	8	6αtk−2kα+2	6αtk−2kα+2	NUM
ejpam-4444	449	9	.	.	PUNCT
ejpam-4444	450	1	(	(	PUNCT
ejpam-4444	450	2	17	17	NUM
ejpam-4444	450	3	)	)	PUNCT
ejpam-4444	450	4	since	since	SCONJ
ejpam-4444	450	5	t3	t3	PROPN
ejpam-4444	450	6	>	>	X
ejpam-4444	450	7	t(2t−	t(2t−	PROPN
ejpam-4444	450	8	1	1	NUM
ejpam-4444	450	9	)	)	PUNCT
ejpam-4444	450	10	and	and	CCONJ
ejpam-4444	450	11	the	the	DET
ejpam-4444	450	12	coefficient	coefficient	NOUN
ejpam-4444	450	13	of	of	ADP
ejpam-4444	450	14	t3	t3	PROPN
ejpam-4444	450	15	in	in	ADP
ejpam-4444	450	16	(	(	PUNCT
ejpam-4444	450	17	17	17	NUM
ejpam-4444	450	18	)	)	PUNCT
ejpam-4444	450	19	is	be	AUX
ejpam-4444	450	20	negative	negative	ADJ
ejpam-4444	450	21	for	for	ADP
ejpam-4444	450	22	α	α	PRON
ejpam-4444	450	23	∈	∈	PROPN
ejpam-4444	450	24	(	(	PUNCT
ejpam-4444	450	25	(	(	PUNCT
ejpam-4444	450	26	k	k	X
ejpam-4444	450	27	+	+	NOUN
ejpam-4444	450	28	2)/2k	2)/2k	NUM
ejpam-4444	450	29	,	,	PUNCT
ejpam-4444	450	30	1	1	NUM
ejpam-4444	450	31	)	)	PUNCT
ejpam-4444	450	32	,	,	PUNCT
ejpam-4444	450	33	we	we	PRON
ejpam-4444	450	34	have	have	VERB
ejpam-4444	450	35	k(t	k(t	VERB
ejpam-4444	450	36	)	)	PUNCT
ejpam-4444	450	37	<	<	X
ejpam-4444	451	1	−(2kα−	−(2kα−	PROPN
ejpam-4444	451	2	k	k	PROPN
ejpam-4444	451	3	+	+	PROPN
ejpam-4444	451	4	3	3	X
ejpam-4444	451	5	)	)	PUNCT
ejpam-4444	451	6	(	(	PUNCT
ejpam-4444	451	7	4α3k2	4α3k2	NOUN
ejpam-4444	451	8	−	−	NOUN
ejpam-4444	451	9	12α2k2	12α2k2	PROPN
ejpam-4444	451	10	+	+	NUM
ejpam-4444	451	11	42α2k	42α2k	NOUN
ejpam-4444	451	12	+	+	CCONJ
ejpam-4444	451	13	9αk2	9αk2	NUM
ejpam-4444	451	14	−	−	ADP
ejpam-4444	451	15	49kα−	49kα−	NUM
ejpam-4444	451	16	2k2	2k2	NUM
ejpam-4444	451	17	+	+	NUM
ejpam-4444	451	18	26α+	26α+	NUM
ejpam-4444	451	19	14k	14k	NOUN
ejpam-4444	451	20	−	−	PROPN
ejpam-4444	451	21	2)t2	2)t2	NUM
ejpam-4444	451	22	+	+	CCONJ
ejpam-4444	451	23	2(2α−	2(2α−	NUM
ejpam-4444	451	24	1)(2kα−	1)(2kα−	NUM
ejpam-4444	451	25	k	k	PROPN
ejpam-4444	452	1	+	+	PROPN
ejpam-4444	452	2	2)(2α2k2	2)(2α2k2	NUM
ejpam-4444	452	3	−	−	NOUN
ejpam-4444	452	4	3αk2	3αk2	NUM
ejpam-4444	453	1	+	+	CCONJ
ejpam-4444	453	2	10kα+	10kα+	NUM
ejpam-4444	453	3	k2	k2	NOUN
ejpam-4444	453	4	−	−	PROPN
ejpam-4444	453	5	7k	7k	PROPN
ejpam-4444	453	6	+	+	CCONJ
ejpam-4444	453	7	6)t	6)t	NUM
ejpam-4444	453	8	−	−	PROPN
ejpam-4444	453	9	α(2kα−	α(2kα−	NUM
ejpam-4444	453	10	k	k	NOUN
ejpam-4444	454	1	+	+	PROPN
ejpam-4444	454	2	1)(2kα−	1)(2kα−	NUM
ejpam-4444	454	3	k	k	NOUN
ejpam-4444	454	4	−	−	ADP
ejpam-4444	454	5	1)(2α−	1)(2α−	NUM
ejpam-4444	454	6	1)k	1)k	NUM
ejpam-4444	454	7	+	+	CCONJ
ejpam-4444	454	8	6αtk−2kα+2	6αtk−2kα+2	NUM
ejpam-4444	454	9	.	.	PUNCT
ejpam-4444	455	1	(	(	PUNCT
ejpam-4444	455	2	18	18	NUM
ejpam-4444	455	3	)	)	PUNCT
ejpam-4444	455	4	since	since	SCONJ
ejpam-4444	455	5	t2	t2	PROPN
ejpam-4444	455	6	>	>	X
ejpam-4444	455	7	2	2	NUM
ejpam-4444	455	8	t	t	NOUN
ejpam-4444	455	9	−	−	NOUN
ejpam-4444	455	10	1	1	NUM
ejpam-4444	455	11	and	and	CCONJ
ejpam-4444	455	12	the	the	DET
ejpam-4444	455	13	coefficient	coefficient	NOUN
ejpam-4444	455	14	of	of	ADP
ejpam-4444	455	15	t2	t2	PROPN
ejpam-4444	455	16	in	in	ADP
ejpam-4444	455	17	(	(	PUNCT
ejpam-4444	455	18	18	18	NUM
ejpam-4444	455	19	)	)	PUNCT
ejpam-4444	455	20	is	be	AUX
ejpam-4444	455	21	negative	negative	ADJ
ejpam-4444	455	22	for	for	ADP
ejpam-4444	455	23	α	α	PRON
ejpam-4444	455	24	∈	∈	PROPN
ejpam-4444	455	25	(	(	PUNCT
ejpam-4444	455	26	(	(	PUNCT
ejpam-4444	455	27	k	k	X
ejpam-4444	455	28	+	+	NOUN
ejpam-4444	455	29	2)/2k	2)/2k	NUM
ejpam-4444	455	30	,	,	PUNCT
ejpam-4444	455	31	1	1	NUM
ejpam-4444	455	32	)	)	PUNCT
ejpam-4444	455	33	,	,	PUNCT
ejpam-4444	455	34	it	it	PRON
ejpam-4444	455	35	follows	follow	VERB
ejpam-4444	455	36	that	that	SCONJ
ejpam-4444	455	37	k(t	k(t	NOUN
ejpam-4444	455	38	)	)	PUNCT
ejpam-4444	455	39	<	<	X
ejpam-4444	456	1	(	(	PUNCT
ejpam-4444	456	2	16α3k3	16α3k3	NUM
ejpam-4444	456	3	−	−	PROPN
ejpam-4444	456	4	96α3k2	96α3k2	PROPN
ejpam-4444	456	5	−	−	PROPN
ejpam-4444	456	6	24α2k3	24α2k3	NUM
ejpam-4444	456	7	+	+	CCONJ
ejpam-4444	456	8	184α2k2	184α2k2	NUM
ejpam-4444	456	9	+	+	CCONJ
ejpam-4444	456	10	12αk3	12αk3	ADV
ejpam-4444	456	11	−	−	PROPN
ejpam-4444	456	12	228α2k	228α2k	NUM
ejpam-4444	456	13	−	−	PROPN
ejpam-4444	456	14	112αk2	112αk2	NUM
ejpam-4444	456	15	−	−	PROPN
ejpam-4444	456	16	2k3	2k3	NUM
ejpam-4444	456	17	+	+	CCONJ
ejpam-4444	456	18	250kα+	250kα+	NUM
ejpam-4444	456	19	22k2	22k2	NUM
ejpam-4444	456	20	−	−	NUM
ejpam-4444	456	21	108α−	108α−	NUM
ejpam-4444	456	22	68k	68k	NOUN
ejpam-4444	456	23	+	+	CCONJ
ejpam-4444	456	24	48)t	48)t	NUM
ejpam-4444	456	25	+	+	CCONJ
ejpam-4444	456	26	(	(	PUNCT
ejpam-4444	456	27	−16α3k3	−16α3k3	PROPN
ejpam-4444	456	28	+	+	CCONJ
ejpam-4444	456	29	96α3k2	96α3k2	NOUN
ejpam-4444	456	30	+	+	CCONJ
ejpam-4444	456	31	24α2k3	24α2k3	NUM
ejpam-4444	456	32	−	−	PROPN
ejpam-4444	456	33	176α2k2	176α2k2	NUM
ejpam-4444	456	34	−	−	PROPN
ejpam-4444	456	35	12αk3	12αk3	NOUN
ejpam-4444	457	1	+	+	NUM
ejpam-4444	457	2	180α2k	180α2k	NUM
ejpam-4444	457	3	+	+	NUM
ejpam-4444	457	4	104αk2	104αk2	NUM
ejpam-4444	458	1	+	+	CCONJ
ejpam-4444	458	2	2k3	2k3	NUM
ejpam-4444	458	3	−	−	PROPN
ejpam-4444	458	4	198kα−	198kα−	NUM
ejpam-4444	458	5	20k2	20k2	NUM
ejpam-4444	458	6	+	+	NUM
ejpam-4444	458	7	78α+	78α+	NUM
ejpam-4444	458	8	54k	54k	NOUN
ejpam-4444	458	9	−	−	PROPN
ejpam-4444	458	10	36	36	NUM
ejpam-4444	458	11	)	)	PUNCT
ejpam-4444	459	1	+	+	CCONJ
ejpam-4444	459	2	6αtk−2kα+2	6αtk−2kα+2	NUM
ejpam-4444	459	3	.	.	PUNCT
ejpam-4444	460	1	(	(	PUNCT
ejpam-4444	460	2	19	19	NUM
ejpam-4444	460	3	)	)	PUNCT
ejpam-4444	460	4	the	the	DET
ejpam-4444	460	5	coefficient	coefficient	NOUN
ejpam-4444	460	6	of	of	ADP
ejpam-4444	460	7	t	t	PROPN
ejpam-4444	460	8	in	in	ADP
ejpam-4444	460	9	(	(	PUNCT
ejpam-4444	460	10	19	19	NUM
ejpam-4444	460	11	)	)	PUNCT
ejpam-4444	460	12	is	be	AUX
ejpam-4444	460	13	negative	negative	ADJ
ejpam-4444	460	14	and	and	CCONJ
ejpam-4444	460	15	tk−2kα+2	tk−2kα+2	X
ejpam-4444	460	16	<	<	X
ejpam-4444	460	17	1	1	NUM
ejpam-4444	460	18	for	for	ADP
ejpam-4444	460	19	α	α	PRON
ejpam-4444	460	20	∈	∈	PROPN
ejpam-4444	460	21	(	(	PUNCT
ejpam-4444	460	22	(	(	PUNCT
ejpam-4444	460	23	k	k	X
ejpam-4444	460	24	+	+	NOUN
ejpam-4444	460	25	2)/2k	2)/2k	NUM
ejpam-4444	460	26	,	,	PUNCT
ejpam-4444	460	27	1	1	NUM
ejpam-4444	460	28	)	)	PUNCT
ejpam-4444	460	29	.	.	PUNCT
ejpam-4444	461	1	therefore	therefore	ADV
ejpam-4444	461	2	,	,	PUNCT
ejpam-4444	461	3	k(t	k(t	PROPN
ejpam-4444	461	4	)	)	PUNCT
ejpam-4444	461	5	<	<	X
ejpam-4444	461	6	(	(	PUNCT
ejpam-4444	461	7	8α2k2	8α2k2	NOUN
ejpam-4444	461	8	−	−	PROPN
ejpam-4444	461	9	48α2k	48α2k	NUM
ejpam-4444	461	10	−	−	PROPN
ejpam-4444	461	11	8αk2	8αk2	NUM
ejpam-4444	461	12	+	+	CCONJ
ejpam-4444	461	13	52kα+	52kα+	NUM
ejpam-4444	461	14	2k2	2k2	NUM
ejpam-4444	461	15	−	−	NUM
ejpam-4444	461	16	30α−	30α−	NUM
ejpam-4444	461	17	14k	14k	NOUN
ejpam-4444	461	18	+	+	ADV
ejpam-4444	461	19	12	12	NUM
ejpam-4444	461	20	)	)	PUNCT
ejpam-4444	461	21	+	+	CCONJ
ejpam-4444	461	22	6αtk−2kα+2	6αtk−2kα+2	ADJ
ejpam-4444	461	23	<	<	X
ejpam-4444	461	24	(	(	PUNCT
ejpam-4444	461	25	8α2k2	8α2k2	NOUN
ejpam-4444	461	26	−	−	PROPN
ejpam-4444	461	27	48α2k	48α2k	NUM
ejpam-4444	461	28	−	−	PROPN
ejpam-4444	461	29	8αk2	8αk2	NUM
ejpam-4444	461	30	+	+	CCONJ
ejpam-4444	461	31	52kα+	52kα+	NUM
ejpam-4444	461	32	2k2	2k2	NUM
ejpam-4444	461	33	−	−	NUM
ejpam-4444	461	34	30α−	30α−	NUM
ejpam-4444	461	35	14k	14k	NOUN
ejpam-4444	461	36	+	+	ADV
ejpam-4444	461	37	12	12	NUM
ejpam-4444	461	38	)	)	PUNCT
ejpam-4444	462	1	+	+	NUM
ejpam-4444	462	2	6α	6α	NOUN
ejpam-4444	462	3	=	=	NOUN
ejpam-4444	462	4	2(k	2(k	NUM
ejpam-4444	463	1	−	−	NOUN
ejpam-4444	463	2	6)(2α−	6)(2α−	NUM
ejpam-4444	463	3	1)(2kα−	1)(2kα−	NUM
ejpam-4444	463	4	k	k	NOUN
ejpam-4444	464	1	+	+	CCONJ
ejpam-4444	464	2	1	1	X
ejpam-4444	464	3	)	)	PUNCT
ejpam-4444	464	4	<	<	X
ejpam-4444	464	5	0	0	X
ejpam-4444	464	6	.	.	PUNCT
ejpam-4444	465	1	as	as	ADP
ejpam-4444	465	2	a	a	DET
ejpam-4444	465	3	result	result	NOUN
ejpam-4444	465	4	,	,	PUNCT
ejpam-4444	465	5	g′′′(t	g′′′(t	VERB
ejpam-4444	465	6	)	)	PUNCT
ejpam-4444	465	7	<	<	X
ejpam-4444	465	8	0	0	NUM
ejpam-4444	465	9	for	for	ADP
ejpam-4444	465	10	all	all	DET
ejpam-4444	465	11	α	α	PRON
ejpam-4444	465	12	∈	∈	NOUN
ejpam-4444	465	13	(	(	PUNCT
ejpam-4444	465	14	(	(	PUNCT
ejpam-4444	465	15	k	k	X
ejpam-4444	465	16	+	+	NOUN
ejpam-4444	465	17	2)/2k	2)/2k	NUM
ejpam-4444	465	18	,	,	PUNCT
ejpam-4444	465	19	1	1	NUM
ejpam-4444	465	20	)	)	PUNCT
ejpam-4444	465	21	.	.	PUNCT
ejpam-4444	466	1	a.	a.	PROPN
ejpam-4444	466	2	sonubon	sonubon	PROPN
ejpam-4444	466	3	,	,	PUNCT
ejpam-4444	466	4	s.	s.	PROPN
ejpam-4444	466	5	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	466	6	,	,	PUNCT
ejpam-4444	466	7	k.	k.	PROPN
ejpam-4444	466	8	nonlaopon	nonlaopon	ADV
ejpam-4444	466	9	/	/	SYM
ejpam-4444	466	10	eur	eur	PROPN
ejpam-4444	466	11	.	.	PUNCT
ejpam-4444	467	1	j.	j.	PROPN
ejpam-4444	467	2	pure	pure	PROPN
ejpam-4444	467	3	appl	appl	PROPN
ejpam-4444	467	4	.	.	PROPN
ejpam-4444	467	5	math	math	PROPN
ejpam-4444	467	6	,	,	PUNCT
ejpam-4444	467	7	15	15	NUM
ejpam-4444	467	8	(	(	PUNCT
ejpam-4444	467	9	3	3	NUM
ejpam-4444	467	10	)	)	PUNCT
ejpam-4444	467	11	(	(	PUNCT
ejpam-4444	467	12	2022	2022	NUM
ejpam-4444	467	13	)	)	PUNCT
ejpam-4444	467	14	,	,	PUNCT
ejpam-4444	467	15	1120	1120	NUM
ejpam-4444	467	16	-	-	SYM
ejpam-4444	467	17	1143	1143	NUM
ejpam-4444	467	18	1139	1139	NUM
ejpam-4444	467	19	conjecture	conjecture	NOUN
ejpam-4444	467	20	1	1	NUM
ejpam-4444	467	21	.	.	PUNCT
ejpam-4444	468	1	let	let	VERB
ejpam-4444	468	2	a	a	DET
ejpam-4444	468	3	,	,	PUNCT
ejpam-4444	468	4	b	b	X
ejpam-4444	468	5	>	>	X
ejpam-4444	468	6	0	0	PUNCT
ejpam-4444	468	7	with	with	ADP
ejpam-4444	468	8	a	a	DET
ejpam-4444	468	9	̸=	̸=	PROPN
ejpam-4444	468	10	b	b	PROPN
ejpam-4444	468	11	and	and	CCONJ
ejpam-4444	468	12	k	k	PROPN
ejpam-4444	469	1	=	=	SYM
ejpam-4444	469	2	2/(2	2/(2	NUM
ejpam-4444	469	3	ln	ln	ADJ
ejpam-4444	469	4	2−	2−	NUM
ejpam-4444	469	5	1	1	NUM
ejpam-4444	469	6	)	)	PUNCT
ejpam-4444	469	7	.	.	PUNCT
ejpam-4444	470	1	1	1	X
ejpam-4444	470	2	)	)	PUNCT
ejpam-4444	470	3	l1/[−2kα+(k+1)](a	l1/[−2kα+(k+1)](a	NOUN
ejpam-4444	470	4	,	,	PUNCT
ejpam-4444	470	5	b	b	NOUN
ejpam-4444	470	6	)	)	PUNCT
ejpam-4444	470	7	>	>	X
ejpam-4444	470	8	αc(a	αc(a	NUM
ejpam-4444	470	9	,	,	PUNCT
ejpam-4444	470	10	b	b	NOUN
ejpam-4444	470	11	)	)	PUNCT
ejpam-4444	470	12	+	+	CCONJ
ejpam-4444	470	13	(	(	PUNCT
ejpam-4444	470	14	1−	1−	NUM
ejpam-4444	470	15	α)h(a	α)h(a	NOUN
ejpam-4444	470	16	,	,	PUNCT
ejpam-4444	470	17	b	b	NOUN
ejpam-4444	470	18	)	)	PUNCT
ejpam-4444	470	19	for	for	ADP
ejpam-4444	470	20	α	α	PRON
ejpam-4444	470	21	∈	∈	PROPN
ejpam-4444	470	22	(	(	PUNCT
ejpam-4444	470	23	0	0	NUM
ejpam-4444	470	24	,	,	PUNCT
ejpam-4444	470	25	1/2	1/2	NUM
ejpam-4444	470	26	)	)	PUNCT
ejpam-4444	470	27	;	;	PUNCT
ejpam-4444	470	28	2	2	X
ejpam-4444	470	29	)	)	PUNCT
ejpam-4444	470	30	l2kα+(1−k)(a	l2kα+(1−k)(a	NOUN
ejpam-4444	470	31	,	,	PUNCT
ejpam-4444	470	32	b	b	NOUN
ejpam-4444	470	33	)	)	PUNCT
ejpam-4444	470	34	<	<	X
ejpam-4444	470	35	αc(a	αc(a	NOUN
ejpam-4444	470	36	,	,	PUNCT
ejpam-4444	470	37	b	b	NOUN
ejpam-4444	470	38	)	)	PUNCT
ejpam-4444	471	1	+	+	CCONJ
ejpam-4444	471	2	(	(	PUNCT
ejpam-4444	471	3	1−	1−	NUM
ejpam-4444	471	4	α)h(a	α)h(a	NOUN
ejpam-4444	471	5	,	,	PUNCT
ejpam-4444	471	6	b	b	NOUN
ejpam-4444	471	7	)	)	PUNCT
ejpam-4444	471	8	for	for	ADP
ejpam-4444	471	9	α	α	PRON
ejpam-4444	471	10	∈	∈	PROPN
ejpam-4444	471	11	(	(	PUNCT
ejpam-4444	471	12	1/2	1/2	NUM
ejpam-4444	471	13	,	,	PUNCT
ejpam-4444	471	14	1	1	NUM
ejpam-4444	471	15	)	)	PUNCT
ejpam-4444	471	16	.	.	PUNCT
ejpam-4444	472	1	if	if	SCONJ
ejpam-4444	472	2	conjecture	conjecture	NOUN
ejpam-4444	472	3	1	1	NUM
ejpam-4444	472	4	is	be	AUX
ejpam-4444	472	5	correct	correct	ADJ
ejpam-4444	472	6	,	,	PUNCT
ejpam-4444	472	7	l1/[−2kα+(k+1	l1/[−2kα+(k+1	ADJ
ejpam-4444	472	8	)	)	PUNCT
ejpam-4444	472	9	]	]	PUNCT
ejpam-4444	472	10	will	will	AUX
ejpam-4444	472	11	be	be	AUX
ejpam-4444	472	12	the	the	DET
ejpam-4444	472	13	optimal	optimal	ADJ
ejpam-4444	472	14	upper	upper	ADJ
ejpam-4444	472	15	bound	bind	VERB
ejpam-4444	472	16	for	for	ADP
ejpam-4444	472	17	the	the	DET
ejpam-4444	472	18	considered	consider	VERB
ejpam-4444	472	19	weighted	weight	VERB
ejpam-4444	472	20	arithmetic	arithmetic	ADJ
ejpam-4444	472	21	mean	mean	NOUN
ejpam-4444	472	22	forα	forα	VERB
ejpam-4444	472	23	∈	∈	PROPN
ejpam-4444	472	24	(	(	PUNCT
ejpam-4444	472	25	0	0	NUM
ejpam-4444	472	26	,	,	PUNCT
ejpam-4444	472	27	1/2	1/2	NUM
ejpam-4444	472	28	)	)	PUNCT
ejpam-4444	472	29	and	and	CCONJ
ejpam-4444	472	30	l2kα+(1−k	l2kα+(1−k	PROPN
ejpam-4444	472	31	)	)	PUNCT
ejpam-4444	472	32	will	will	AUX
ejpam-4444	472	33	be	be	AUX
ejpam-4444	472	34	the	the	DET
ejpam-4444	472	35	optimal	optimal	ADJ
ejpam-4444	472	36	lower	lower	ADV
ejpam-4444	472	37	bound	bind	VERB
ejpam-4444	472	38	for	for	ADP
ejpam-4444	472	39	the	the	DET
ejpam-4444	472	40	considered	consider	VERB
ejpam-4444	472	41	weighted	weight	VERB
ejpam-4444	472	42	arithmetic	arithmetic	ADJ
ejpam-4444	472	43	mean	mean	NOUN
ejpam-4444	472	44	for	for	ADP
ejpam-4444	472	45	α	α	PROPN
ejpam-4444	472	46	∈	∈	PROPN
ejpam-4444	472	47	(	(	PUNCT
ejpam-4444	472	48	1/2	1/2	NUM
ejpam-4444	472	49	,	,	PUNCT
ejpam-4444	472	50	1	1	NUM
ejpam-4444	472	51	)	)	PUNCT
ejpam-4444	472	52	,	,	PUNCT
ejpam-4444	472	53	as	as	SCONJ
ejpam-4444	472	54	shown	show	VERB
ejpam-4444	472	55	in	in	ADP
ejpam-4444	472	56	the	the	DET
ejpam-4444	472	57	following	follow	VERB
ejpam-4444	472	58	theorem	theorem	NOUN
ejpam-4444	472	59	.	.	PUNCT
ejpam-4444	472	60	theorem	theorem	NOUN
ejpam-4444	472	61	4	4	NUM
ejpam-4444	472	62	.	.	PUNCT
ejpam-4444	473	1	let	let	VERB
ejpam-4444	473	2	a	a	DET
ejpam-4444	473	3	,	,	PUNCT
ejpam-4444	473	4	b	b	X
ejpam-4444	473	5	>	>	X
ejpam-4444	473	6	0	0	PUNCT
ejpam-4444	473	7	with	with	ADP
ejpam-4444	473	8	a	a	DET
ejpam-4444	473	9	̸=	̸=	PROPN
ejpam-4444	473	10	b	b	PROPN
ejpam-4444	473	11	and	and	CCONJ
ejpam-4444	473	12	k	k	PROPN
ejpam-4444	474	1	=	=	SYM
ejpam-4444	474	2	2/(2	2/(2	NUM
ejpam-4444	474	3	ln	ln	ADJ
ejpam-4444	474	4	2−	2−	NUM
ejpam-4444	474	5	1	1	NUM
ejpam-4444	474	6	)	)	PUNCT
ejpam-4444	474	7	.	.	PUNCT
ejpam-4444	475	1	1	1	X
ejpam-4444	475	2	)	)	PUNCT
ejpam-4444	475	3	if	if	SCONJ
ejpam-4444	475	4	l1/[−2kα+(k+1)](a	l1/[−2kα+(k+1)](a	NOUN
ejpam-4444	475	5	,	,	PUNCT
ejpam-4444	475	6	b	b	NOUN
ejpam-4444	475	7	)	)	PUNCT
ejpam-4444	475	8	>	>	X
ejpam-4444	475	9	αc(a	αc(a	NUM
ejpam-4444	475	10	,	,	PUNCT
ejpam-4444	475	11	b	b	NOUN
ejpam-4444	475	12	)	)	PUNCT
ejpam-4444	475	13	+	+	CCONJ
ejpam-4444	475	14	(	(	PUNCT
ejpam-4444	475	15	1−α)h(a	1−α)h(a	NUM
ejpam-4444	475	16	,	,	PUNCT
ejpam-4444	475	17	b	b	NOUN
ejpam-4444	475	18	)	)	PUNCT
ejpam-4444	475	19	for	for	ADP
ejpam-4444	475	20	α	α	DET
ejpam-4444	475	21	∈	∈	PROPN
ejpam-4444	475	22	(	(	PUNCT
ejpam-4444	475	23	0	0	NUM
ejpam-4444	475	24	,	,	PUNCT
ejpam-4444	475	25	1/2	1/2	NUM
ejpam-4444	475	26	)	)	PUNCT
ejpam-4444	475	27	,	,	PUNCT
ejpam-4444	475	28	then	then	ADV
ejpam-4444	475	29	the	the	DET
ejpam-4444	475	30	parameter	parameter	NOUN
ejpam-4444	475	31	1/	1/	NUM
ejpam-4444	476	1	[	[	X
ejpam-4444	476	2	−2kα+	−2kα+	X
ejpam-4444	476	3	(	(	PUNCT
ejpam-4444	476	4	k	k	PROPN
ejpam-4444	476	5	+	+	PROPN
ejpam-4444	476	6	1	1	NUM
ejpam-4444	476	7	)	)	PUNCT
ejpam-4444	476	8	]	]	PUNCT
ejpam-4444	476	9	can	can	AUX
ejpam-4444	476	10	not	not	PART
ejpam-4444	476	11	be	be	AUX
ejpam-4444	476	12	improved	improve	VERB
ejpam-4444	476	13	in	in	ADP
ejpam-4444	476	14	the	the	DET
ejpam-4444	476	15	sense	sense	NOUN
ejpam-4444	476	16	that	that	SCONJ
ejpam-4444	476	17	l	l	NOUN
ejpam-4444	476	18	1	1	NUM
ejpam-4444	476	19	−2kα+(k+1	−2kα+(k+1	PUNCT
ejpam-4444	476	20	)	)	PUNCT
ejpam-4444	476	21	=	=	SYM
ejpam-4444	476	22	min	min	NOUN
ejpam-4444	476	23	c	c	NOUN
ejpam-4444	476	24	{	{	PUNCT
ejpam-4444	476	25	l	l	NOUN
ejpam-4444	476	26	1	1	NUM
ejpam-4444	476	27	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	476	28	∣∣∣l	∣∣∣l	NOUN
ejpam-4444	476	29	1	1	NUM
ejpam-4444	476	30	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	476	31	>	>	X
ejpam-4444	476	32	αc	αc	PROPN
ejpam-4444	477	1	+	+	CCONJ
ejpam-4444	477	2	(	(	PUNCT
ejpam-4444	477	3	1−	1−	NUM
ejpam-4444	477	4	α)h	α)h	NOUN
ejpam-4444	477	5	}	}	PUNCT
ejpam-4444	477	6	for	for	ADP
ejpam-4444	477	7	α	α	PRON
ejpam-4444	477	8	∈	∈	PROPN
ejpam-4444	477	9	(	(	PUNCT
ejpam-4444	477	10	0	0	NUM
ejpam-4444	477	11	,	,	PUNCT
ejpam-4444	477	12	1/2	1/2	NUM
ejpam-4444	477	13	)	)	PUNCT
ejpam-4444	478	1	i.e.	i.e.	X
ejpam-4444	478	2	c	c	NOUN
ejpam-4444	478	3	=	=	SYM
ejpam-4444	478	4	1	1	NUM
ejpam-4444	478	5	+	+	CCONJ
ejpam-4444	478	6	k	k	NOUN
ejpam-4444	478	7	;	;	PUNCT
ejpam-4444	478	8	2	2	X
ejpam-4444	478	9	)	)	PUNCT
ejpam-4444	478	10	if	if	SCONJ
ejpam-4444	478	11	l2kα+(1−k)(a	l2kα+(1−k)(a	PROPN
ejpam-4444	478	12	,	,	PUNCT
ejpam-4444	478	13	b	b	NOUN
ejpam-4444	478	14	)	)	PUNCT
ejpam-4444	478	15	<	<	X
ejpam-4444	478	16	αc(a	αc(a	NOUN
ejpam-4444	478	17	,	,	PUNCT
ejpam-4444	478	18	b	b	NOUN
ejpam-4444	478	19	)	)	PUNCT
ejpam-4444	478	20	+	+	CCONJ
ejpam-4444	478	21	(	(	PUNCT
ejpam-4444	478	22	1	1	NUM
ejpam-4444	478	23	−	−	PROPN
ejpam-4444	478	24	α)h(a	α)h(a	NOUN
ejpam-4444	478	25	,	,	PUNCT
ejpam-4444	478	26	b	b	NOUN
ejpam-4444	478	27	)	)	PUNCT
ejpam-4444	478	28	for	for	ADP
ejpam-4444	478	29	α	α	PRON
ejpam-4444	478	30	∈	∈	PROPN
ejpam-4444	478	31	(	(	PUNCT
ejpam-4444	478	32	1/2	1/2	NUM
ejpam-4444	478	33	,	,	PUNCT
ejpam-4444	478	34	1	1	NUM
ejpam-4444	478	35	)	)	PUNCT
ejpam-4444	478	36	,	,	PUNCT
ejpam-4444	478	37	then	then	ADV
ejpam-4444	478	38	the	the	DET
ejpam-4444	478	39	parameter	parameter	NOUN
ejpam-4444	478	40	2kα+	2kα+	NUM
ejpam-4444	478	41	(	(	PUNCT
ejpam-4444	478	42	1−	1−	NUM
ejpam-4444	478	43	k	k	NOUN
ejpam-4444	478	44	)	)	PUNCT
ejpam-4444	478	45	can	can	AUX
ejpam-4444	478	46	not	not	PART
ejpam-4444	478	47	be	be	AUX
ejpam-4444	478	48	improved	improve	VERB
ejpam-4444	478	49	in	in	ADP
ejpam-4444	478	50	the	the	DET
ejpam-4444	478	51	sense	sense	NOUN
ejpam-4444	478	52	that	that	SCONJ
ejpam-4444	478	53	l2kα+(1−k	l2kα+(1−k	NOUN
ejpam-4444	478	54	)	)	PUNCT
ejpam-4444	479	1	=	=	SYM
ejpam-4444	479	2	max	max	PROPN
ejpam-4444	479	3	c	c	PROPN
ejpam-4444	479	4	{	{	PUNCT
ejpam-4444	479	5	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	479	6	|	|	ADV
ejpam-4444	479	7	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	479	8	<	<	X
ejpam-4444	479	9	αc	αc	PROPN
ejpam-4444	480	1	+	+	CCONJ
ejpam-4444	481	1	(	(	PUNCT
ejpam-4444	481	2	1−	1−	NUM
ejpam-4444	481	3	α)h	α)h	NOUN
ejpam-4444	481	4	}	}	PUNCT
ejpam-4444	481	5	for	for	ADP
ejpam-4444	481	6	α	α	PRON
ejpam-4444	481	7	∈	∈	PROPN
ejpam-4444	481	8	(	(	PUNCT
ejpam-4444	481	9	1/2	1/2	NUM
ejpam-4444	481	10	,	,	PUNCT
ejpam-4444	481	11	1	1	NUM
ejpam-4444	481	12	)	)	PUNCT
ejpam-4444	482	1	i.e.	i.e.	X
ejpam-4444	482	2	c	c	X
ejpam-4444	482	3	=	=	SYM
ejpam-4444	482	4	1−	1−	NUM
ejpam-4444	482	5	k.	k.	PROPN
ejpam-4444	482	6	proof	proof	NOUN
ejpam-4444	482	7	.	.	PUNCT
ejpam-4444	483	1	1	1	X
ejpam-4444	483	2	)	)	PUNCT
ejpam-4444	483	3	suppose	suppose	VERB
ejpam-4444	483	4	,	,	PUNCT
ejpam-4444	483	5	to	to	ADP
ejpam-4444	483	6	the	the	DET
ejpam-4444	483	7	contrary	contrary	NOUN
ejpam-4444	483	8	,	,	PUNCT
ejpam-4444	483	9	that	that	DET
ejpam-4444	483	10	inequality	inequality	NOUN
ejpam-4444	483	11	(	(	PUNCT
ejpam-4444	483	12	15	15	NUM
ejpam-4444	483	13	)	)	PUNCT
ejpam-4444	483	14	is	be	AUX
ejpam-4444	483	15	true	true	ADJ
ejpam-4444	483	16	for	for	ADP
ejpam-4444	483	17	the	the	DET
ejpam-4444	483	18	parameter	parameter	NOUN
ejpam-4444	483	19	1	1	NUM
ejpam-4444	483	20	2[1−	2[1−	NOUN
ejpam-4444	483	21	(	(	PUNCT
ejpam-4444	483	22	1	1	NUM
ejpam-4444	484	1	+	+	CCONJ
ejpam-4444	484	2	k	k	PROPN
ejpam-4444	485	1	+	+	CCONJ
ejpam-4444	485	2	ϵ)]α+	ϵ)]α+	PROPN
ejpam-4444	485	3	(	(	PUNCT
ejpam-4444	485	4	1	1	NUM
ejpam-4444	485	5	+	+	CCONJ
ejpam-4444	485	6	k	k	NOUN
ejpam-4444	485	7	+	+	CCONJ
ejpam-4444	485	8	ϵ	ϵ	X
ejpam-4444	485	9	)	)	PUNCT
ejpam-4444	485	10	for	for	ADP
ejpam-4444	485	11	a	a	DET
ejpam-4444	485	12	sufficiently	sufficiently	ADV
ejpam-4444	485	13	small	small	ADJ
ejpam-4444	485	14	ϵ	ϵ	X
ejpam-4444	485	15	>	>	X
ejpam-4444	485	16	0	0	NUM
ejpam-4444	485	17	.	.	PUNCT
ejpam-4444	486	1	that	that	PRON
ejpam-4444	486	2	is	be	AUX
ejpam-4444	486	3	l	l	NOUN
ejpam-4444	486	4	1	1	NUM
ejpam-4444	486	5	2[1−(1+k+ϵ)]α+(1+k+ϵ	2[1−(1+k+ϵ)]α+(1+k+ϵ	NUM
ejpam-4444	486	6	)	)	PUNCT
ejpam-4444	486	7	(	(	PUNCT
ejpam-4444	486	8	1	1	NUM
ejpam-4444	486	9	,	,	PUNCT
ejpam-4444	486	10	t	t	PROPN
ejpam-4444	486	11	)	)	PUNCT
ejpam-4444	486	12	>	>	X
ejpam-4444	487	1	αc(1	αc(1	PROPN
ejpam-4444	487	2	,	,	PUNCT
ejpam-4444	487	3	t	t	PROPN
ejpam-4444	487	4	)	)	PUNCT
ejpam-4444	488	1	+	+	CCONJ
ejpam-4444	488	2	(	(	PUNCT
ejpam-4444	488	3	1−	1−	NUM
ejpam-4444	488	4	α)h(1	α)h(1	NOUN
ejpam-4444	488	5	,	,	PUNCT
ejpam-4444	488	6	t	t	PROPN
ejpam-4444	488	7	)	)	PUNCT
ejpam-4444	488	8	for	for	ADP
ejpam-4444	488	9	all	all	DET
ejpam-4444	488	10	t	t	PROPN
ejpam-4444	488	11	>	>	X
ejpam-4444	488	12	1	1	X
ejpam-4444	488	13	.	.	PUNCT
ejpam-4444	489	1	hence	hence	ADV
ejpam-4444	489	2	1	1	NUM
ejpam-4444	489	3	t	t	NOUN
ejpam-4444	489	4	{	{	PUNCT
ejpam-4444	489	5	l	l	NOUN
ejpam-4444	489	6	1	1	NUM
ejpam-4444	489	7	2[1−(1+k+ϵ)]α+(1+k+ϵ	2[1−(1+k+ϵ)]α+(1+k+ϵ	NUM
ejpam-4444	489	8	)	)	PUNCT
ejpam-4444	489	9	(	(	PUNCT
ejpam-4444	489	10	1	1	NUM
ejpam-4444	489	11	,	,	PUNCT
ejpam-4444	489	12	t	t	PROPN
ejpam-4444	489	13	)	)	PUNCT
ejpam-4444	489	14	}	}	PUNCT
ejpam-4444	489	15	≥	≥	VERB
ejpam-4444	489	16	1	1	NUM
ejpam-4444	489	17	t	t	PROPN
ejpam-4444	489	18	{	{	PUNCT
ejpam-4444	489	19	αc(1	αc(1	PROPN
ejpam-4444	489	20	,	,	PUNCT
ejpam-4444	489	21	t	t	PROPN
ejpam-4444	489	22	)	)	PUNCT
ejpam-4444	490	1	+	+	CCONJ
ejpam-4444	490	2	(	(	PUNCT
ejpam-4444	490	3	1−	1−	NUM
ejpam-4444	490	4	α)h(1	α)h(1	NOUN
ejpam-4444	490	5	,	,	PUNCT
ejpam-4444	490	6	t	t	PROPN
ejpam-4444	490	7	)	)	PUNCT
ejpam-4444	490	8	}	}	PUNCT
ejpam-4444	490	9	for	for	ADP
ejpam-4444	490	10	all	all	DET
ejpam-4444	490	11	t	t	PROPN
ejpam-4444	490	12	>	>	X
ejpam-4444	490	13	1	1	X
ejpam-4444	490	14	.	.	PUNCT
ejpam-4444	491	1	taking	take	VERB
ejpam-4444	491	2	limits	limit	NOUN
ejpam-4444	491	3	on	on	ADP
ejpam-4444	491	4	both	both	DET
ejpam-4444	491	5	sides	side	NOUN
ejpam-4444	491	6	of	of	ADP
ejpam-4444	491	7	the	the	DET
ejpam-4444	491	8	above	above	ADJ
ejpam-4444	491	9	inequality	inequality	NOUN
ejpam-4444	491	10	lead	lead	VERB
ejpam-4444	491	11	to	to	ADP
ejpam-4444	491	12	lim	lim	PROPN
ejpam-4444	491	13	t→+∞	t→+∞	PROPN
ejpam-4444	491	14	1	1	NUM
ejpam-4444	491	15	t	t	NOUN
ejpam-4444	491	16	{	{	PUNCT
ejpam-4444	491	17	l	l	NOUN
ejpam-4444	491	18	1	1	NUM
ejpam-4444	491	19	2[1−(1+k+ϵ)]α+(1+k+ϵ	2[1−(1+k+ϵ)]α+(1+k+ϵ	NUM
ejpam-4444	491	20	)	)	PUNCT
ejpam-4444	491	21	(	(	PUNCT
ejpam-4444	491	22	1	1	NUM
ejpam-4444	491	23	,	,	PUNCT
ejpam-4444	491	24	t	t	PROPN
ejpam-4444	491	25	)	)	PUNCT
ejpam-4444	491	26	}	}	PUNCT
ejpam-4444	491	27	≥	≥	PROPN
ejpam-4444	491	28	lim	lim	NOUN
ejpam-4444	491	29	t→+∞	t→+∞	VERB
ejpam-4444	491	30	1	1	NUM
ejpam-4444	491	31	t	t	NOUN
ejpam-4444	491	32	[	[	PUNCT
ejpam-4444	491	33	αc(1	αc(1	PROPN
ejpam-4444	491	34	,	,	PUNCT
ejpam-4444	491	35	t	t	PROPN
ejpam-4444	491	36	)	)	PUNCT
ejpam-4444	492	1	+	+	CCONJ
ejpam-4444	492	2	(	(	PUNCT
ejpam-4444	492	3	1−	1−	NUM
ejpam-4444	492	4	α)h(1	α)h(1	NOUN
ejpam-4444	492	5	,	,	PUNCT
ejpam-4444	492	6	t	t	PROPN
ejpam-4444	492	7	)	)	PUNCT
ejpam-4444	492	8	]	]	PUNCT
ejpam-4444	492	9	,	,	PUNCT
ejpam-4444	492	10	a.	a.	NOUN
ejpam-4444	492	11	sonubon	sonubon	PROPN
ejpam-4444	492	12	,	,	PUNCT
ejpam-4444	492	13	s.	s.	PROPN
ejpam-4444	492	14	orankitjaroen	orankitjaroen	PROPN
ejpam-4444	492	15	,	,	PUNCT
ejpam-4444	492	16	k.	k.	PROPN
ejpam-4444	492	17	nonlaopon	nonlaopon	ADV
ejpam-4444	492	18	/	/	SYM
ejpam-4444	492	19	eur	eur	PROPN
ejpam-4444	492	20	.	.	PUNCT
ejpam-4444	493	1	j.	j.	PROPN
ejpam-4444	493	2	pure	pure	PROPN
ejpam-4444	493	3	appl	appl	PROPN
ejpam-4444	493	4	.	.	PROPN
ejpam-4444	493	5	math	math	PROPN
ejpam-4444	493	6	,	,	PUNCT
ejpam-4444	493	7	15	15	NUM
ejpam-4444	493	8	(	(	PUNCT
ejpam-4444	493	9	3	3	NUM
ejpam-4444	493	10	)	)	PUNCT
ejpam-4444	493	11	(	(	PUNCT
ejpam-4444	493	12	2022	2022	NUM
ejpam-4444	493	13	)	)	PUNCT
ejpam-4444	493	14	,	,	PUNCT
ejpam-4444	493	15	1120	1120	NUM
ejpam-4444	493	16	-	-	SYM
ejpam-4444	493	17	1143	1143	NUM
ejpam-4444	493	18	1140	1140	NUM
ejpam-4444	493	19	which	which	PRON
ejpam-4444	493	20	is	be	AUX
ejpam-4444	493	21	equivalent	equivalent	ADJ
ejpam-4444	493	22	to	to	ADP
ejpam-4444	493	23	[	[	PUNCT
ejpam-4444	493	24	(	(	PUNCT
ejpam-4444	493	25	1−	1−	NUM
ejpam-4444	493	26	2α)(k	2α)(k	NUM
ejpam-4444	493	27	+	+	CCONJ
ejpam-4444	493	28	ϵ	ϵ	X
ejpam-4444	493	29	)	)	PUNCT
ejpam-4444	493	30	+	+	CCONJ
ejpam-4444	493	31	1	1	NUM
ejpam-4444	493	32	(	(	PUNCT
ejpam-4444	493	33	1−	1−	NUM
ejpam-4444	493	34	2α)(k	2α)(k	NUM
ejpam-4444	493	35	+	+	CCONJ
ejpam-4444	493	36	ϵ	ϵ	X
ejpam-4444	493	37	)	)	PUNCT
ejpam-4444	494	1	+	+	CCONJ
ejpam-4444	494	2	2	2	NUM
ejpam-4444	494	3	]	]	SYM
ejpam-4444	494	4	(	(	PUNCT
ejpam-4444	494	5	1−2α)(k+ϵ)+1	1−2α)(k+ϵ)+1	NUM
ejpam-4444	494	6	≥	≥	NOUN
ejpam-4444	494	7	α	α	NOUN
ejpam-4444	494	8	.	.	PUNCT
ejpam-4444	494	9	taking	take	VERB
ejpam-4444	494	10	logarithm	logarithm	NOUN
ejpam-4444	494	11	of	of	ADP
ejpam-4444	494	12	both	both	DET
ejpam-4444	494	13	sides	side	NOUN
ejpam-4444	494	14	of	of	ADP
ejpam-4444	494	15	the	the	DET
ejpam-4444	494	16	above	above	ADJ
ejpam-4444	494	17	inequality	inequality	NOUN
ejpam-4444	494	18	,	,	PUNCT
ejpam-4444	494	19	we	we	PRON
ejpam-4444	494	20	get	get	VERB
ejpam-4444	494	21	q(α	q(α	PROPN
ejpam-4444	494	22	)	)	PUNCT
ejpam-4444	494	23	:	:	PUNCT
ejpam-4444	495	1	=	=	PUNCT
ejpam-4444	496	1	[	[	X
ejpam-4444	496	2	(	(	PUNCT
ejpam-4444	496	3	1−	1−	NUM
ejpam-4444	496	4	2α)(k	2α)(k	NUM
ejpam-4444	496	5	+	+	CCONJ
ejpam-4444	496	6	ϵ	ϵ	X
ejpam-4444	496	7	)	)	PUNCT
ejpam-4444	496	8	+	+	CCONJ
ejpam-4444	496	9	1	1	X
ejpam-4444	496	10	]	]	X
ejpam-4444	496	11	ln	ln	NOUN
ejpam-4444	496	12	[	[	PUNCT
ejpam-4444	496	13	(	(	PUNCT
ejpam-4444	496	14	1−	1−	NUM
ejpam-4444	496	15	2α)(k	2α)(k	NUM
ejpam-4444	496	16	+	+	CCONJ
ejpam-4444	496	17	ϵ	ϵ	X
ejpam-4444	496	18	)	)	PUNCT
ejpam-4444	496	19	+	+	CCONJ
ejpam-4444	496	20	1	1	NUM
ejpam-4444	496	21	(	(	PUNCT
ejpam-4444	496	22	1−	1−	NUM
ejpam-4444	496	23	2α)(k	2α)(k	NUM
ejpam-4444	496	24	+	+	CCONJ
ejpam-4444	496	25	ϵ	ϵ	X
ejpam-4444	496	26	)	)	PUNCT
ejpam-4444	496	27	+	+	CCONJ
ejpam-4444	496	28	2	2	X
ejpam-4444	496	29	]	]	PUNCT
ejpam-4444	496	30	−	−	NOUN
ejpam-4444	496	31	lnα	lnα	NOUN
ejpam-4444	496	32	≥	≥	NOUN
ejpam-4444	496	33	0	0	NUM
ejpam-4444	496	34	.	.	PUNCT
ejpam-4444	497	1	sine	sine	PROPN
ejpam-4444	497	2	q(α	q(α	PROPN
ejpam-4444	497	3	)	)	PUNCT
ejpam-4444	497	4	≥	≥	NOUN
ejpam-4444	497	5	0	0	NUM
ejpam-4444	497	6	for	for	ADP
ejpam-4444	497	7	all	all	DET
ejpam-4444	497	8	α	α	PRON
ejpam-4444	497	9	∈	∈	NOUN
ejpam-4444	497	10	(	(	PUNCT
ejpam-4444	497	11	0	0	NUM
ejpam-4444	497	12	,	,	PUNCT
ejpam-4444	497	13	1/2	1/2	NUM
ejpam-4444	497	14	)	)	PUNCT
ejpam-4444	497	15	and	and	CCONJ
ejpam-4444	497	16	q((1/2)−	q((1/2)−	NOUN
ejpam-4444	497	17	)	)	PUNCT
ejpam-4444	498	1	=	=	SYM
ejpam-4444	498	2	0	0	NUM
ejpam-4444	498	3	,	,	PUNCT
ejpam-4444	498	4	it	it	PRON
ejpam-4444	498	5	immediately	immediately	ADV
ejpam-4444	498	6	follows	follow	VERB
ejpam-4444	498	7	that	that	SCONJ
ejpam-4444	498	8	q′((1/2)−	q′((1/2)−	VERB
ejpam-4444	498	9	)	)	PUNCT
ejpam-4444	498	10	≤	≤	NUM
ejpam-4444	498	11	0	0	NUM
ejpam-4444	498	12	.	.	PUNCT
ejpam-4444	499	1	however	however	ADV
ejpam-4444	499	2	,	,	PUNCT
ejpam-4444	499	3	q′(α	q′(α	NOUN
ejpam-4444	499	4	)	)	PUNCT
ejpam-4444	499	5	=	=	SYM
ejpam-4444	499	6	−2(k	−2(k	NOUN
ejpam-4444	499	7	+	+	CCONJ
ejpam-4444	499	8	ϵ	ϵ	X
ejpam-4444	499	9	)	)	PUNCT
ejpam-4444	499	10	(	(	PUNCT
ejpam-4444	499	11	1−	1−	NUM
ejpam-4444	499	12	2α)(k	2α)(k	NUM
ejpam-4444	499	13	+	+	CCONJ
ejpam-4444	499	14	ϵ	ϵ	X
ejpam-4444	499	15	)	)	PUNCT
ejpam-4444	500	1	+	+	CCONJ
ejpam-4444	500	2	2	2	NUM
ejpam-4444	500	3	−	−	NOUN
ejpam-4444	500	4	2(k	2(k	NUM
ejpam-4444	501	1	+	+	CCONJ
ejpam-4444	501	2	ϵ	ϵ	X
ejpam-4444	501	3	)	)	PUNCT
ejpam-4444	501	4	ln	ln	NOUN
ejpam-4444	501	5	[	[	PUNCT
ejpam-4444	501	6	(	(	PUNCT
ejpam-4444	501	7	1−	1−	NUM
ejpam-4444	501	8	2α)(k	2α)(k	NUM
ejpam-4444	502	1	+	+	CCONJ
ejpam-4444	502	2	ϵ	ϵ	X
ejpam-4444	502	3	)	)	PUNCT
ejpam-4444	503	1	+	+	CCONJ
ejpam-4444	503	2	1	1	NUM
ejpam-4444	503	3	(	(	PUNCT
ejpam-4444	503	4	1−	1−	NUM
ejpam-4444	503	5	2α)(k	2α)(k	NUM
ejpam-4444	503	6	+	+	CCONJ
ejpam-4444	503	7	ϵ	ϵ	X
ejpam-4444	503	8	)	)	PUNCT
ejpam-4444	503	9	+	+	CCONJ
ejpam-4444	503	10	2	2	X
ejpam-4444	503	11	]	]	SYM
ejpam-4444	503	12	−	−	PROPN
ejpam-4444	503	13	1	1	NUM
ejpam-4444	503	14	α	α	NOUN
ejpam-4444	503	15	leading	lead	VERB
ejpam-4444	503	16	to	to	ADP
ejpam-4444	503	17	lim	lim	PROPN
ejpam-4444	503	18	α→(1/2)−	α→(1/2)−	VERB
ejpam-4444	503	19	q′(α	q′(α	NOUN
ejpam-4444	503	20	)	)	PUNCT
ejpam-4444	503	21	=	=	VERB
ejpam-4444	503	22	2ϵ	2ϵ	NUM
ejpam-4444	504	1	k	k	X
ejpam-4444	504	2	>	>	X
ejpam-4444	504	3	0	0	PROPN
ejpam-4444	504	4	,	,	PUNCT
ejpam-4444	504	5	which	which	PRON
ejpam-4444	504	6	is	be	AUX
ejpam-4444	504	7	a	a	DET
ejpam-4444	504	8	contradiction	contradiction	NOUN
ejpam-4444	504	9	.	.	PUNCT
ejpam-4444	505	1	2	2	X
ejpam-4444	505	2	)	)	PUNCT
ejpam-4444	505	3	suppose	suppose	VERB
ejpam-4444	505	4	,	,	PUNCT
ejpam-4444	505	5	to	to	ADP
ejpam-4444	505	6	the	the	DET
ejpam-4444	505	7	contrary	contrary	NOUN
ejpam-4444	505	8	,	,	PUNCT
ejpam-4444	505	9	that	that	DET
ejpam-4444	505	10	inequality	inequality	NOUN
ejpam-4444	505	11	(	(	PUNCT
ejpam-4444	505	12	16	16	NUM
ejpam-4444	505	13	)	)	PUNCT
ejpam-4444	505	14	is	be	AUX
ejpam-4444	505	15	true	true	ADJ
ejpam-4444	505	16	for	for	ADP
ejpam-4444	505	17	the	the	DET
ejpam-4444	505	18	parameter	parameter	NOUN
ejpam-4444	505	19	2[1−	2[1−	NOUN
ejpam-4444	505	20	(	(	PUNCT
ejpam-4444	505	21	1−	1−	NUM
ejpam-4444	506	1	k	k	NOUN
ejpam-4444	506	2	−	−	X
ejpam-4444	507	1	ϵ)]α+	ϵ)]α+	PROPN
ejpam-4444	507	2	(	(	PUNCT
ejpam-4444	507	3	1−	1−	NUM
ejpam-4444	507	4	k	k	NOUN
ejpam-4444	507	5	−	−	PROPN
ejpam-4444	507	6	ϵ	ϵ	X
ejpam-4444	507	7	)	)	PUNCT
ejpam-4444	507	8	for	for	ADP
ejpam-4444	507	9	a	a	DET
ejpam-4444	507	10	sufficiently	sufficiently	ADV
ejpam-4444	507	11	small	small	ADJ
ejpam-4444	507	12	ϵ	ϵ	X
ejpam-4444	507	13	>	>	X
ejpam-4444	507	14	0	0	NUM
ejpam-4444	507	15	.	.	PUNCT
ejpam-4444	508	1	that	that	PRON
ejpam-4444	508	2	is	be	AUX
ejpam-4444	508	3	l2[1−(1−k−ϵ)]α+(1−k−ϵ)(1	l2[1−(1−k−ϵ)]α+(1−k−ϵ)(1	ADJ
ejpam-4444	508	4	,	,	PUNCT
ejpam-4444	508	5	t	t	PROPN
ejpam-4444	508	6	)	)	PUNCT
ejpam-4444	508	7	<	<	X
ejpam-4444	508	8	αc(1	αc(1	PROPN
ejpam-4444	508	9	,	,	PUNCT
ejpam-4444	508	10	t	t	PROPN
ejpam-4444	508	11	)	)	PUNCT
ejpam-4444	509	1	+	+	CCONJ
ejpam-4444	509	2	(	(	PUNCT
ejpam-4444	509	3	1−	1−	NUM
ejpam-4444	509	4	α)h(1	α)h(1	NOUN
ejpam-4444	509	5	,	,	PUNCT
ejpam-4444	509	6	t	t	PROPN
ejpam-4444	509	7	)	)	PUNCT
ejpam-4444	509	8	for	for	ADP
ejpam-4444	509	9	all	all	DET
ejpam-4444	509	10	t	t	PROPN
ejpam-4444	509	11	>	>	X
ejpam-4444	509	12	1	1	X
ejpam-4444	509	13	.	.	PUNCT
ejpam-4444	510	1	hence	hence	ADV
ejpam-4444	510	2	1	1	NUM
ejpam-4444	510	3	t	t	NOUN
ejpam-4444	510	4	{	{	PUNCT
ejpam-4444	510	5	l2[1−(1−k−ϵ)]α+(1−k−ϵ)(1	l2[1−(1−k−ϵ)]α+(1−k−ϵ)(1	PROPN
ejpam-4444	510	6	,	,	PUNCT
ejpam-4444	510	7	t	t	PROPN
ejpam-4444	510	8	)	)	PUNCT
ejpam-4444	510	9	}	}	PUNCT
ejpam-4444	510	10	<	<	X
ejpam-4444	510	11	1	1	NUM
ejpam-4444	510	12	t	t	PROPN
ejpam-4444	510	13	[	[	PUNCT
ejpam-4444	510	14	αc(1	αc(1	PROPN
ejpam-4444	510	15	,	,	PUNCT
ejpam-4444	510	16	t	t	PROPN
ejpam-4444	510	17	)	)	PUNCT
ejpam-4444	511	1	+	+	CCONJ
ejpam-4444	511	2	(	(	PUNCT
ejpam-4444	511	3	1−	1−	NUM
ejpam-4444	511	4	α)h(1	α)h(1	NOUN
ejpam-4444	511	5	,	,	PUNCT
ejpam-4444	511	6	t	t	PROPN
ejpam-4444	511	7	)	)	PUNCT
ejpam-4444	511	8	]	]	PUNCT
ejpam-4444	511	9	for	for	ADP
ejpam-4444	511	10	all	all	DET
ejpam-4444	511	11	t	t	PROPN
ejpam-4444	511	12	>	>	X
ejpam-4444	511	13	1	1	X
ejpam-4444	511	14	.	.	PUNCT
ejpam-4444	512	1	taking	take	VERB
ejpam-4444	512	2	limits	limit	NOUN
ejpam-4444	512	3	on	on	ADP
ejpam-4444	512	4	both	both	DET
ejpam-4444	512	5	sides	side	NOUN
ejpam-4444	512	6	of	of	ADP
ejpam-4444	512	7	the	the	DET
ejpam-4444	512	8	above	above	ADJ
ejpam-4444	512	9	inequality	inequality	NOUN
ejpam-4444	512	10	lead	lead	VERB
ejpam-4444	512	11	to	to	ADP
ejpam-4444	512	12	lim	lim	PROPN
ejpam-4444	512	13	t→+∞	t→+∞	PROPN
ejpam-4444	512	14	1	1	NUM
ejpam-4444	512	15	t	t	NOUN
ejpam-4444	512	16	{	{	PUNCT
ejpam-4444	512	17	l2[1−(−1−ϵ)]α+(−1−ϵ)(1	l2[1−(−1−ϵ)]α+(−1−ϵ)(1	PROPN
ejpam-4444	512	18	,	,	PUNCT
ejpam-4444	512	19	t	t	PROPN
ejpam-4444	512	20	)	)	PUNCT
ejpam-4444	512	21	}	}	PUNCT
ejpam-4444	512	22	≤	≤	NUM
ejpam-4444	513	1	lim	lim	NOUN
ejpam-4444	513	2	t→+∞	t→+∞	VERB
ejpam-4444	513	3	1	1	NUM
ejpam-4444	513	4	t	t	NOUN
ejpam-4444	513	5	[	[	PUNCT
ejpam-4444	513	6	αc(1	αc(1	PROPN
ejpam-4444	513	7	,	,	PUNCT
ejpam-4444	513	8	t	t	PROPN
ejpam-4444	513	9	)	)	PUNCT
ejpam-4444	514	1	+	+	CCONJ
ejpam-4444	514	2	(	(	PUNCT
ejpam-4444	514	3	1−	1−	NUM
ejpam-4444	514	4	α)h(1	α)h(1	NOUN
ejpam-4444	514	5	,	,	PUNCT
ejpam-4444	514	6	t	t	PROPN
ejpam-4444	514	7	)	)	PUNCT
ejpam-4444	514	8	]	]	PUNCT
ejpam-4444	514	9	,	,	PUNCT
ejpam-4444	514	10	which	which	PRON
ejpam-4444	514	11	is	be	AUX
ejpam-4444	514	12	equivalent	equivalent	ADJ
ejpam-4444	514	13	to	to	ADP
ejpam-4444	514	14	[	[	PUNCT
ejpam-4444	514	15	1	1	NUM
ejpam-4444	514	16	(	(	PUNCT
ejpam-4444	514	17	2α−	2α−	NUM
ejpam-4444	514	18	1)(k	1)(k	NUM
ejpam-4444	514	19	+	+	CCONJ
ejpam-4444	514	20	ϵ)α+	ϵ)α+	PROPN
ejpam-4444	514	21	2	2	NUM
ejpam-4444	514	22	]	]	PUNCT
ejpam-4444	514	23	1/[(2α−1)(k+ϵ)α+1	1/[(2α−1)(k+ϵ)α+1	X
ejpam-4444	514	24	]	]	PUNCT
ejpam-4444	514	25	≤	≤	NUM
ejpam-4444	514	26	α	α	X
ejpam-4444	514	27	.	.	PUNCT
ejpam-4444	515	1	taking	take	VERB
ejpam-4444	515	2	logarithm	logarithm	NOUN
ejpam-4444	515	3	of	of	ADP
ejpam-4444	515	4	both	both	DET
ejpam-4444	515	5	sides	side	NOUN
ejpam-4444	515	6	of	of	ADP
ejpam-4444	515	7	the	the	DET
ejpam-4444	515	8	above	above	ADJ
ejpam-4444	515	9	inequality	inequality	NOUN
ejpam-4444	515	10	,	,	PUNCT
ejpam-4444	515	11	we	we	PRON
ejpam-4444	515	12	get	get	VERB
ejpam-4444	515	13	r(α	r(α	VERB
ejpam-4444	515	14	)	)	PUNCT
ejpam-4444	515	15	:	:	PUNCT
ejpam-4444	516	1	=	=	PUNCT
ejpam-4444	516	2	−	−	PROPN
ejpam-4444	516	3	ln	ln	NOUN
ejpam-4444	517	1	[	[	X
ejpam-4444	517	2	(	(	PUNCT
ejpam-4444	517	3	2α−	2α−	NUM
ejpam-4444	517	4	1)(k	1)(k	NUM
ejpam-4444	517	5	+	+	CCONJ
ejpam-4444	517	6	ϵ	ϵ	X
ejpam-4444	517	7	)	)	PUNCT
ejpam-4444	517	8	+	+	CCONJ
ejpam-4444	518	1	2]−	2]−	NUM
ejpam-4444	518	2	[	[	X
ejpam-4444	518	3	(	(	PUNCT
ejpam-4444	518	4	2α−	2α−	NUM
ejpam-4444	518	5	1)(k	1)(k	NUM
ejpam-4444	518	6	+	+	CCONJ
ejpam-4444	518	7	ϵ	ϵ	X
ejpam-4444	518	8	)	)	PUNCT
ejpam-4444	518	9	+	+	CCONJ
ejpam-4444	518	10	1	1	X
ejpam-4444	518	11	]	]	PUNCT
ejpam-4444	518	12	ln(α	ln(α	PROPN
ejpam-4444	518	13	)	)	PUNCT
ejpam-4444	518	14	≤	≤	NOUN
ejpam-4444	518	15	0	0	NUM
ejpam-4444	518	16	.	.	PUNCT
ejpam-4444	519	1	sine	sine	ADJ
ejpam-4444	519	2	r(α	r(α	NOUN
ejpam-4444	519	3	)	)	PUNCT
ejpam-4444	519	4	≤	≤	NOUN
ejpam-4444	519	5	0	0	NUM
ejpam-4444	520	1	for	for	ADP
ejpam-4444	520	2	all	all	DET
ejpam-4444	520	3	α	α	PRON
ejpam-4444	520	4	∈	∈	PROPN
ejpam-4444	520	5	(	(	PUNCT
ejpam-4444	520	6	1/2	1/2	NUM
ejpam-4444	520	7	,	,	PUNCT
ejpam-4444	520	8	1	1	NUM
ejpam-4444	520	9	)	)	PUNCT
ejpam-4444	520	10	and	and	CCONJ
ejpam-4444	520	11	r((1/2)+	r((1/2)+	PROPN
ejpam-4444	520	12	)	)	PUNCT
ejpam-4444	520	13	=	=	SYM
ejpam-4444	520	14	0	0	NUM
ejpam-4444	520	15	,	,	PUNCT
ejpam-4444	520	16	it	it	PRON
ejpam-4444	520	17	immediately	immediately	ADV
ejpam-4444	520	18	follows	follow	VERB
ejpam-4444	520	19	that	that	SCONJ
ejpam-4444	520	20	r′((1/2)+	r′((1/2)+	NOUN
ejpam-4444	520	21	)	)	PUNCT
ejpam-4444	520	22	≤	≤	NOUN
ejpam-4444	520	23	0	0	NUM
ejpam-4444	520	24	.	.	PUNCT
ejpam-4444	521	1	however	however	ADV
ejpam-4444	521	2	,	,	PUNCT
ejpam-4444	521	3	references	reference	NOUN
ejpam-4444	521	4	1141	1141	NUM
ejpam-4444	521	5	r′(α	r′(α	SYM
ejpam-4444	521	6	)	)	PUNCT
ejpam-4444	521	7	=	=	SYM
ejpam-4444	522	1	−	−	PROPN
ejpam-4444	522	2	(	(	PUNCT
ejpam-4444	522	3	k	k	PROPN
ejpam-4444	522	4	+	+	CCONJ
ejpam-4444	522	5	ϵ	ϵ	X
ejpam-4444	522	6	)	)	PUNCT
ejpam-4444	522	7	{	{	PUNCT
ejpam-4444	522	8	4α	4α	NOUN
ejpam-4444	522	9	[	[	PUNCT
ejpam-4444	522	10	1	1	NUM
ejpam-4444	522	11	+	+	CCONJ
ejpam-4444	522	12	(	(	PUNCT
ejpam-4444	522	13	α−	α−	ADP
ejpam-4444	522	14	1/2)(k	1/2)(k	NUM
ejpam-4444	522	15	+	+	CCONJ
ejpam-4444	522	16	ϵ	ϵ	X
ejpam-4444	522	17	)	)	PUNCT
ejpam-4444	522	18	]	]	PUNCT
ejpam-4444	522	19	ln(α	ln(α	ADV
ejpam-4444	522	20	)	)	PUNCT
ejpam-4444	523	1	+	+	CCONJ
ejpam-4444	524	1	4(α−	4(α−	NUM
ejpam-4444	524	2	1/2)2(k	1/2)2(k	NUM
ejpam-4444	525	1	+	+	CCONJ
ejpam-4444	525	2	ϵ	ϵ	X
ejpam-4444	525	3	)	)	PUNCT
ejpam-4444	526	1	+	+	CCONJ
ejpam-4444	526	2	(	(	PUNCT
ejpam-4444	526	3	8α−	8α−	PROPN
ejpam-4444	526	4	3	3	NUM
ejpam-4444	526	5	)	)	PUNCT
ejpam-4444	526	6	}	}	PUNCT
ejpam-4444	526	7	+	+	CCONJ
ejpam-4444	526	8	2	2	NUM
ejpam-4444	526	9	α	α	NOUN
ejpam-4444	526	10	[	[	X
ejpam-4444	526	11	(	(	PUNCT
ejpam-4444	526	12	2α−	2α−	NUM
ejpam-4444	526	13	1)(k	1)(k	NUM
ejpam-4444	526	14	+	+	CCONJ
ejpam-4444	526	15	ϵ	ϵ	X
ejpam-4444	526	16	)	)	PUNCT
ejpam-4444	526	17	+	+	CCONJ
ejpam-4444	526	18	2	2	X
ejpam-4444	526	19	]	]	PUNCT
ejpam-4444	526	20	leading	lead	VERB
ejpam-4444	526	21	to	to	ADP
ejpam-4444	526	22	lim	lim	PROPN
ejpam-4444	526	23	α→(1/2)+	α→(1/2)+	PROPN
ejpam-4444	526	24	r′(α	r′(α	PROPN
ejpam-4444	526	25	)	)	PUNCT
ejpam-4444	527	1	=	=	PRON
ejpam-4444	527	2	2ϵ	2ϵ	VERB
ejpam-4444	528	1	k	k	X
ejpam-4444	528	2	>	>	X
ejpam-4444	528	3	0	0	PROPN
ejpam-4444	528	4	,	,	PUNCT
ejpam-4444	528	5	which	which	PRON
ejpam-4444	528	6	is	be	AUX
ejpam-4444	528	7	a	a	DET
ejpam-4444	528	8	contradiction	contradiction	NOUN
ejpam-4444	528	9	.	.	PUNCT
ejpam-4444	529	1	4	4	X
ejpam-4444	529	2	.	.	X
ejpam-4444	529	3	conclusions	conclusion	NOUN
ejpam-4444	529	4	in	in	ADP
ejpam-4444	529	5	this	this	DET
ejpam-4444	529	6	paper	paper	NOUN
ejpam-4444	529	7	,	,	PUNCT
ejpam-4444	529	8	we	we	PRON
ejpam-4444	529	9	seek	seek	VERB
ejpam-4444	529	10	the	the	DET
ejpam-4444	529	11	optimal	optimal	ADJ
ejpam-4444	529	12	upper	upper	ADJ
ejpam-4444	529	13	and	and	CCONJ
ejpam-4444	529	14	lower	low	ADJ
ejpam-4444	529	15	bounds	bound	NOUN
ejpam-4444	529	16	of	of	ADP
ejpam-4444	529	17	weighted	weight	VERB
ejpam-4444	529	18	arithmetic	arithmetic	ADJ
ejpam-4444	529	19	means	mean	NOUN
ejpam-4444	529	20	of	of	ADP
ejpam-4444	529	21	contra	contra	PROPN
ejpam-4444	529	22	-	-	ADJ
ejpam-4444	529	23	harmonic	harmonic	ADJ
ejpam-4444	529	24	and	and	CCONJ
ejpam-4444	529	25	harmonic	harmonic	ADJ
ejpam-4444	529	26	means	mean	NOUN
ejpam-4444	529	27	by	by	ADP
ejpam-4444	529	28	generalized	generalize	VERB
ejpam-4444	529	29	logarithmic	logarithmic	ADJ
ejpam-4444	529	30	means	mean	NOUN
ejpam-4444	529	31	lp	lp	ADV
ejpam-4444	529	32	when	when	SCONJ
ejpam-4444	529	33	p	p	NOUN
ejpam-4444	529	34	is	be	AUX
ejpam-4444	529	35	of	of	ADP
ejpam-4444	529	36	the	the	DET
ejpam-4444	529	37	linear	linear	ADJ
ejpam-4444	529	38	form	form	NOUN
ejpam-4444	530	1	p	p	NOUN
ejpam-4444	530	2	=	=	SYM
ejpam-4444	530	3	2(1	2(1	NUM
ejpam-4444	530	4	−	−	NOUN
ejpam-4444	530	5	c)α	c)α	NOUN
ejpam-4444	530	6	+	+	CCONJ
ejpam-4444	531	1	c	c	NOUN
ejpam-4444	531	2	and	and	CCONJ
ejpam-4444	531	3	p	p	NOUN
ejpam-4444	531	4	is	be	AUX
ejpam-4444	531	5	of	of	ADP
ejpam-4444	531	6	the	the	DET
ejpam-4444	531	7	reciprocal	reciprocal	NOUN
ejpam-4444	531	8	of	of	ADP
ejpam-4444	531	9	linear	linear	ADJ
ejpam-4444	531	10	form	form	NOUN
ejpam-4444	531	11	p	p	NOUN
ejpam-4444	531	12	=	=	NOUN
ejpam-4444	532	1	1/[2(1−	1/[2(1−	NUM
ejpam-4444	532	2	c)α+	c)α+	NOUN
ejpam-4444	532	3	c	c	NOUN
ejpam-4444	532	4	]	]	PUNCT
ejpam-4444	532	5	respectively	respectively	ADV
ejpam-4444	532	6	.	.	PUNCT
ejpam-4444	533	1	when	when	SCONJ
ejpam-4444	533	2	p	p	NOUN
ejpam-4444	533	3	has	have	VERB
ejpam-4444	533	4	a	a	DET
ejpam-4444	533	5	linear	linear	ADJ
ejpam-4444	533	6	form	form	NOUN
ejpam-4444	533	7	,	,	PUNCT
ejpam-4444	533	8	we	we	PRON
ejpam-4444	533	9	found	find	VERB
ejpam-4444	533	10	that	that	SCONJ
ejpam-4444	533	11	l4α−1	l4α−1	NOUN
ejpam-4444	533	12	=	=	PUNCT
ejpam-4444	533	13	min	min	PROPN
ejpam-4444	533	14	c	c	PROPN
ejpam-4444	533	15	{	{	PUNCT
ejpam-4444	533	16	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	533	17	|	|	ADV
ejpam-4444	533	18	l2(1−c)α+c	l2(1−c)α+c	PROPN
ejpam-4444	533	19	>	>	X
ejpam-4444	533	20	αc	αc	PROPN
ejpam-4444	534	1	+	+	CCONJ
ejpam-4444	534	2	(	(	PUNCT
ejpam-4444	534	3	1−	1−	NUM
ejpam-4444	534	4	α)h	α)h	NOUN
ejpam-4444	534	5	}	}	PUNCT
ejpam-4444	534	6	for	for	ADP
ejpam-4444	534	7	α	α	PRON
ejpam-4444	534	8	∈	∈	PROPN
ejpam-4444	534	9	(	(	PUNCT
ejpam-4444	534	10	0	0	NUM
ejpam-4444	534	11	,	,	PUNCT
ejpam-4444	534	12	1/2	1/2	NUM
ejpam-4444	534	13	)	)	PUNCT
ejpam-4444	534	14	.	.	PUNCT
ejpam-4444	535	1	when	when	SCONJ
ejpam-4444	535	2	p	p	NOUN
ejpam-4444	535	3	has	have	VERB
ejpam-4444	535	4	a	a	DET
ejpam-4444	535	5	reciprocal	reciprocal	NOUN
ejpam-4444	535	6	of	of	ADP
ejpam-4444	535	7	linear	linear	PROPN
ejpam-4444	535	8	form	form	NOUN
ejpam-4444	535	9	,	,	PUNCT
ejpam-4444	535	10	we	we	PRON
ejpam-4444	535	11	found	find	VERB
ejpam-4444	535	12	that	that	SCONJ
ejpam-4444	535	13	l	l	NOUN
ejpam-4444	535	14	7	7	NUM
ejpam-4444	535	15	13−12α	13−12α	NOUN
ejpam-4444	535	16	=	=	SYM
ejpam-4444	535	17	max	max	PROPN
ejpam-4444	535	18	c	c	PROPN
ejpam-4444	535	19	{	{	PUNCT
ejpam-4444	535	20	l	l	NOUN
ejpam-4444	535	21	1	1	NUM
ejpam-4444	535	22	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	535	23	∣∣∣l	∣∣∣l	NOUN
ejpam-4444	535	24	1	1	NUM
ejpam-4444	535	25	2(1−c)α+c	2(1−c)α+c	NUM
ejpam-4444	535	26	<	<	X
ejpam-4444	535	27	αc	αc	NOUN
ejpam-4444	536	1	+	+	CCONJ
ejpam-4444	537	1	(	(	PUNCT
ejpam-4444	537	2	1−	1−	NUM
ejpam-4444	537	3	α)h	α)h	NOUN
ejpam-4444	537	4	}	}	PUNCT
ejpam-4444	537	5	for	for	ADP
ejpam-4444	537	6	α	α	PRON
ejpam-4444	537	7	∈	∈	PROPN
ejpam-4444	537	8	(	(	PUNCT
ejpam-4444	537	9	1/2	1/2	NUM
ejpam-4444	537	10	,	,	PUNCT
ejpam-4444	537	11	1	1	NUM
ejpam-4444	537	12	)	)	PUNCT
ejpam-4444	537	13	.	.	PUNCT
ejpam-4444	538	1	we	we	PRON
ejpam-4444	538	2	also	also	ADV
ejpam-4444	538	3	show	show	VERB
ejpam-4444	538	4	that	that	SCONJ
ejpam-4444	538	5	,	,	PUNCT
ejpam-4444	538	6	if	if	SCONJ
ejpam-4444	538	7	conjecture	conjecture	NOUN
ejpam-4444	538	8	1	1	NUM
ejpam-4444	538	9	is	be	AUX
ejpam-4444	538	10	correct	correct	ADJ
ejpam-4444	538	11	,	,	PUNCT
ejpam-4444	538	12	then	then	ADV
ejpam-4444	538	13	l1/[−2kα+(k+1	l1/[−2kα+(k+1	ADJ
ejpam-4444	538	14	)	)	PUNCT
ejpam-4444	538	15	]	]	PUNCT
ejpam-4444	538	16	will	will	AUX
ejpam-4444	538	17	be	be	AUX
ejpam-4444	538	18	the	the	DET
ejpam-4444	538	19	optimal	optimal	ADJ
ejpam-4444	538	20	upper	upper	ADJ
ejpam-4444	538	21	bound	bind	VERB
ejpam-4444	538	22	for	for	ADP
ejpam-4444	538	23	the	the	DET
ejpam-4444	538	24	considered	consider	VERB
ejpam-4444	538	25	weighted	weight	VERB
ejpam-4444	538	26	arithmetic	arithmetic	ADJ
ejpam-4444	538	27	mean	mean	NOUN
ejpam-4444	538	28	for	for	ADP
ejpam-4444	538	29	α	α	PROPN
ejpam-4444	538	30	∈	∈	PROPN
ejpam-4444	538	31	(	(	PUNCT
ejpam-4444	538	32	0	0	NUM
ejpam-4444	538	33	,	,	PUNCT
ejpam-4444	538	34	1/2	1/2	NUM
ejpam-4444	538	35	)	)	PUNCT
ejpam-4444	538	36	and	and	CCONJ
ejpam-4444	538	37	l2kα+(1−k	l2kα+(1−k	PROPN
ejpam-4444	538	38	)	)	PUNCT
ejpam-4444	538	39	will	will	AUX
ejpam-4444	538	40	be	be	AUX
ejpam-4444	538	41	the	the	DET
ejpam-4444	538	42	optimal	optimal	ADJ
ejpam-4444	538	43	lower	lower	ADV
ejpam-4444	538	44	bound	bind	VERB
ejpam-4444	538	45	for	for	ADP
ejpam-4444	538	46	the	the	DET
ejpam-4444	538	47	considered	consider	VERB
ejpam-4444	538	48	weighted	weight	VERB
ejpam-4444	538	49	arithmetic	arithmetic	ADJ
ejpam-4444	538	50	mean	mean	NOUN
ejpam-4444	538	51	for	for	ADP
ejpam-4444	538	52	α	α	PROPN
ejpam-4444	538	53	∈	∈	PROPN
ejpam-4444	538	54	(	(	PUNCT
ejpam-4444	538	55	1/2	1/2	NUM
ejpam-4444	538	56	,	,	PUNCT
ejpam-4444	538	57	1	1	NUM
ejpam-4444	538	58	)	)	PUNCT
ejpam-4444	538	59	.	.	PUNCT
ejpam-4444	539	1	acknowledgements	acknowledgement	NOUN
ejpam-4444	539	2	the	the	DET
ejpam-4444	539	3	first	first	ADJ
ejpam-4444	539	4	author	author	NOUN
ejpam-4444	539	5	would	would	AUX
ejpam-4444	539	6	like	like	VERB
ejpam-4444	539	7	to	to	PART
ejpam-4444	539	8	thank	thank	VERB
ejpam-4444	539	9	the	the	DET
ejpam-4444	539	10	development	development	NOUN
ejpam-4444	539	11	and	and	CCONJ
ejpam-4444	539	12	promotion	promotion	NOUN
ejpam-4444	539	13	for	for	ADP
ejpam-4444	539	14	science	science	NOUN
ejpam-4444	539	15	and	and	CCONJ
ejpam-4444	539	16	technology	technology	NOUN
ejpam-4444	539	17	talents	talent	NOUN
ejpam-4444	539	18	project	project	NOUN
ejpam-4444	539	19	(	(	PUNCT
ejpam-4444	539	20	dpst	dpst	NOUN
ejpam-4444	539	21	)	)	PUNCT
ejpam-4444	539	22	in	in	ADP
ejpam-4444	539	23	thailand	thailand	PROPN
ejpam-4444	539	24	for	for	ADP
ejpam-4444	539	25	the	the	DET
ejpam-4444	539	26	support	support	NOUN
ejpam-4444	539	27	in	in	ADP
ejpam-4444	539	28	this	this	DET
ejpam-4444	539	29	work	work	NOUN
ejpam-4444	539	30	.	.	PUNCT
ejpam-4444	540	1	references	reference	NOUN
ejpam-4444	540	2	[	[	X
ejpam-4444	540	3	1	1	X
ejpam-4444	540	4	]	]	PUNCT
ejpam-4444	540	5	a	a	DET
ejpam-4444	540	6	a	a	DET
ejpam-4444	540	7	k	k	PROPN
ejpam-4444	540	8	abuhany	abuhany	PROPN
ejpam-4444	540	9	,	,	PUNCT
ejpam-4444	540	10	s	s	PART
ejpam-4444	540	11	salem	salem	NOUN
ejpam-4444	540	12	,	,	PUNCT
ejpam-4444	540	13	and	and	CCONJ
ejpam-4444	540	14	i	i	PRON
ejpam-4444	540	15	m	m	PROPN
ejpam-4444	540	16	salman	salman	PROPN
ejpam-4444	540	17	.	.	PUNCT
ejpam-4444	541	1	on	on	ADP
ejpam-4444	541	2	steffensen	steffensen	PROPN
ejpam-4444	541	3	’s	’s	PART
ejpam-4444	541	4	integral	integral	ADJ
ejpam-4444	541	5	inequality	inequality	NOUN
ejpam-4444	541	6	with	with	ADP
ejpam-4444	541	7	applications	application	NOUN
ejpam-4444	541	8	,	,	PUNCT
ejpam-4444	541	9	estimation	estimation	NOUN
ejpam-4444	541	10	and	and	CCONJ
ejpam-4444	541	11	testing	testing	NOUN
ejpam-4444	541	12	.	.	PUNCT
ejpam-4444	542	1	j.	j.	PROPN
ejpam-4444	542	2	rajasthan	rajasthan	PROPN
ejpam-4444	542	3	acad	acad	PROPN
ejpam-4444	542	4	.	.	PUNCT
ejpam-4444	543	1	phys	phy	NOUN
ejpam-4444	543	2	.	.	PUNCT
ejpam-4444	544	1	sci	sci	PROPN
ejpam-4444	544	2	.	.	PROPN
ejpam-4444	544	3	,	,	PUNCT
ejpam-4444	544	4	5:1–12	5:1–12	NUM
ejpam-4444	544	5	,	,	PUNCT
ejpam-4444	544	6	2006	2006	NUM
ejpam-4444	544	7	.	.	PUNCT
ejpam-4444	545	1	[	[	X
ejpam-4444	545	2	2	2	NUM
ejpam-4444	545	3	]	]	X
ejpam-4444	545	4	c	c	PROPN
ejpam-4444	545	5	p	p	PROPN
ejpam-4444	545	6	chen	chen	PROPN
ejpam-4444	545	7	.	.	PUNCT
ejpam-4444	546	1	the	the	DET
ejpam-4444	546	2	monotonicity	monotonicity	NOUN
ejpam-4444	546	3	of	of	ADP
ejpam-4444	546	4	the	the	DET
ejpam-4444	546	5	ratio	ratio	NOUN
ejpam-4444	546	6	between	between	ADP
ejpam-4444	546	7	generalized	generalized	ADJ
ejpam-4444	546	8	logarithmic	logarithmic	ADJ
ejpam-4444	546	9	means	mean	NOUN
ejpam-4444	546	10	.	.	PUNCT
ejpam-4444	547	1	j.	j.	PROPN
ejpam-4444	547	2	math	math	PROPN
ejpam-4444	547	3	.	.	PUNCT
ejpam-4444	548	1	anal	anal	PROPN
ejpam-4444	548	2	.	.	PUNCT
ejpam-4444	549	1	appl	appl	PROPN
ejpam-4444	549	2	.	.	PROPN
ejpam-4444	549	3	,	,	PUNCT
ejpam-4444	549	4	345:86–89	345:86–89	NUM
ejpam-4444	549	5	,	,	PUNCT
ejpam-4444	549	6	2008	2008	NUM
ejpam-4444	549	7	.	.	PUNCT
ejpam-4444	550	1	[	[	X
ejpam-4444	550	2	3	3	X
ejpam-4444	550	3	]	]	X
ejpam-4444	550	4	c	c	PROPN
ejpam-4444	550	5	p	p	PROPN
ejpam-4444	550	6	chen	chen	PROPN
ejpam-4444	550	7	and	and	CCONJ
ejpam-4444	550	8	f	f	PROPN
ejpam-4444	550	9	qi	qi	PROPN
ejpam-4444	550	10	.	.	PUNCT
ejpam-4444	551	1	monotonicity	monotonicity	NOUN
ejpam-4444	551	2	properties	property	NOUN
ejpam-4444	551	3	for	for	ADP
ejpam-4444	551	4	generalized	generalized	ADJ
ejpam-4444	551	5	logarithmic	logarithmic	ADJ
ejpam-4444	551	6	means	mean	NOUN
ejpam-4444	551	7	.	.	PUNCT
ejpam-4444	552	1	aust	aust	PROPN
ejpam-4444	552	2	.	.	PUNCT
ejpam-4444	553	1	j.	j.	PROPN
ejpam-4444	553	2	math	math	PROPN
ejpam-4444	553	3	.	.	PUNCT
ejpam-4444	554	1	anal	anal	PROPN
ejpam-4444	554	2	.	.	PROPN
ejpam-4444	554	3	,	,	PUNCT
ejpam-4444	554	4	1:1–4	1:1–4	NUM
ejpam-4444	554	5	,	,	PUNCT
ejpam-4444	554	6	2004	2004	NUM
ejpam-4444	554	7	.	.	PUNCT
ejpam-4444	555	1	references	reference	NOUN
ejpam-4444	555	2	1142	1142	NUM
ejpam-4444	555	3	[	[	X
ejpam-4444	555	4	4	4	NUM
ejpam-4444	555	5	]	]	X
ejpam-4444	555	6	y	y	PROPN
ejpam-4444	555	7	m	m	PROPN
ejpam-4444	555	8	chu	chu	PROPN
ejpam-4444	555	9	and	and	CCONJ
ejpam-4444	555	10	b	b	PROPN
ejpam-4444	555	11	y	y	PROPN
ejpam-4444	555	12	long	long	ADV
ejpam-4444	555	13	.	.	PUNCT
ejpam-4444	556	1	best	good	ADJ
ejpam-4444	556	2	possible	possible	ADJ
ejpam-4444	556	3	inequalities	inequality	NOUN
ejpam-4444	556	4	between	between	ADP
ejpam-4444	556	5	generalized	generalized	ADJ
ejpam-4444	556	6	logarithmic	logarithmic	ADJ
ejpam-4444	556	7	mean	mean	NOUN
ejpam-4444	556	8	and	and	CCONJ
ejpam-4444	556	9	classical	classical	ADJ
ejpam-4444	556	10	means	mean	NOUN
ejpam-4444	556	11	.	.	PUNCT
ejpam-4444	557	1	abstr	abstr	PROPN
ejpam-4444	557	2	.	.	PUNCT
ejpam-4444	557	3	appl	appl	PROPN
ejpam-4444	557	4	.	.	PUNCT
ejpam-4444	558	1	anal	anal	PROPN
ejpam-4444	558	2	.	.	PUNCT
ejpam-4444	558	3	,	,	PUNCT
ejpam-4444	558	4	article	article	NOUN
ejpam-4444	558	5	i	i	PROPN
ejpam-4444	558	6	d	d	PROPN
ejpam-4444	558	7	303286:13	303286:13	NUM
ejpam-4444	558	8	pages	page	NOUN
ejpam-4444	558	9	,	,	PUNCT
ejpam-4444	558	10	2010	2010	NUM
ejpam-4444	558	11	.	.	PUNCT
ejpam-4444	559	1	[	[	X
ejpam-4444	559	2	5	5	NUM
ejpam-4444	559	3	]	]	X
ejpam-4444	559	4	l	l	NOUN
ejpam-4444	559	5	chunrong	chunrong	NOUN
ejpam-4444	559	6	and	and	CCONJ
ejpam-4444	559	7	l	l	PROPN
ejpam-4444	559	8	siqi	siqi	NOUN
ejpam-4444	559	9	.	.	PUNCT
ejpam-4444	560	1	best	good	ADJ
ejpam-4444	560	2	possible	possible	ADJ
ejpam-4444	560	3	inequalities	inequality	NOUN
ejpam-4444	560	4	between	between	ADP
ejpam-4444	560	5	generalized	generalized	ADJ
ejpam-4444	560	6	logarithmic	logarithmic	ADJ
ejpam-4444	560	7	mean	mean	NOUN
ejpam-4444	560	8	and	and	CCONJ
ejpam-4444	560	9	weighted	weight	VERB
ejpam-4444	560	10	geometric	geometric	ADJ
ejpam-4444	560	11	mean	mean	NOUN
ejpam-4444	560	12	of	of	ADP
ejpam-4444	560	13	geometric	geometric	ADJ
ejpam-4444	560	14	,	,	PUNCT
ejpam-4444	560	15	square	square	ADJ
ejpam-4444	560	16	-	-	PUNCT
ejpam-4444	560	17	root	root	NOUN
ejpam-4444	560	18	,	,	PUNCT
ejpam-4444	560	19	and	and	CCONJ
ejpam-4444	560	20	root	root	NOUN
ejpam-4444	560	21	-	-	PUNCT
ejpam-4444	560	22	square	square	NOUN
ejpam-4444	560	23	means	mean	NOUN
ejpam-4444	560	24	.	.	PUNCT
ejpam-4444	561	1	j.	j.	PROPN
ejpam-4444	561	2	math	math	PROPN
ejpam-4444	561	3	.	.	PUNCT
ejpam-4444	562	1	inequal	inequal	ADJ
ejpam-4444	562	2	.	.	PUNCT
ejpam-4444	562	3	,	,	PUNCT
ejpam-4444	562	4	8:899–914	8:899–914	PROPN
ejpam-4444	562	5	,	,	PUNCT
ejpam-4444	562	6	2014	2014	NUM
ejpam-4444	562	7	.	.	PUNCT
ejpam-4444	563	1	[	[	X
ejpam-4444	563	2	6	6	NUM
ejpam-4444	563	3	]	]	PUNCT
ejpam-4444	563	4	p	p	X
ejpam-4444	563	5	kahlig	kahlig	PROPN
ejpam-4444	563	6	and	and	CCONJ
ejpam-4444	563	7	j	j	PROPN
ejpam-4444	563	8	matkowski	matkowski	PROPN
ejpam-4444	563	9	.	.	PUNCT
ejpam-4444	564	1	functional	functional	ADJ
ejpam-4444	564	2	equations	equation	NOUN
ejpam-4444	564	3	involving	involve	VERB
ejpam-4444	564	4	the	the	DET
ejpam-4444	564	5	logarithmic	logarithmic	ADJ
ejpam-4444	564	6	mean	mean	NOUN
ejpam-4444	564	7	.	.	PUNCT
ejpam-4444	565	1	zeithchür	zeithchür	PROPN
ejpam-4444	565	2	angewandte	angewandte	PROPN
ejpam-4444	565	3	mathematik	mathematik	PROPN
ejpam-4444	565	4	und	und	PROPN
ejpam-4444	565	5	mechanik	mechanik	PROPN
ejpam-4444	565	6	,	,	PUNCT
ejpam-4444	565	7	76:385–390	76:385–390	PROPN
ejpam-4444	565	8	,	,	PUNCT
ejpam-4444	565	9	1996	1996	NUM
ejpam-4444	565	10	.	.	PUNCT
ejpam-4444	566	1	[	[	X
ejpam-4444	566	2	7	7	X
ejpam-4444	566	3	]	]	X
ejpam-4444	566	4	w	w	PROPN
ejpam-4444	566	5	h	h	PROPN
ejpam-4444	566	6	li	li	PROPN
ejpam-4444	566	7	,	,	PUNCT
ejpam-4444	566	8	p	p	NOUN
ejpam-4444	566	9	miao	miao	NOUN
ejpam-4444	566	10	,	,	PUNCT
ejpam-4444	566	11	and	and	CCONJ
ejpam-4444	566	12	b	b	X
ejpam-4444	566	13	n	n	X
ejpam-4444	566	14	guo	guo	PROPN
ejpam-4444	566	15	.	.	PUNCT
ejpam-4444	566	16	bounds	bound	VERB
ejpam-4444	566	17	for	for	ADP
ejpam-4444	566	18	the	the	DET
ejpam-4444	566	19	neuman	neuman	NOUN
ejpam-4444	566	20	–	–	PUNCT
ejpam-4444	566	21	sándor	sándor	INTJ
ejpam-4444	566	22	mean	mean	NOUN
ejpam-4444	566	23	in	in	ADP
ejpam-4444	566	24	terms	term	NOUN
ejpam-4444	566	25	of	of	ADP
ejpam-4444	566	26	the	the	DET
ejpam-4444	566	27	arithmetic	arithmetic	ADJ
ejpam-4444	566	28	and	and	CCONJ
ejpam-4444	566	29	contraharmonic	contraharmonic	PROPN
ejpam-4444	566	30	mean	mean	NOUN
ejpam-4444	566	31	.	.	PUNCT
ejpam-4444	567	1	axioms	axiom	NOUN
ejpam-4444	567	2	.	.	PUNCT
ejpam-4444	568	1	,	,	PUNCT
ejpam-4444	568	2	11:12	11:12	NUM
ejpam-4444	568	3	pages	page	NOUN
ejpam-4444	568	4	,	,	PUNCT
ejpam-4444	568	5	2022	2022	NUM
ejpam-4444	568	6	.	.	PUNCT
ejpam-4444	569	1	[	[	X
ejpam-4444	569	2	8	8	NUM
ejpam-4444	569	3	]	]	X
ejpam-4444	569	4	y	y	PROPN
ejpam-4444	569	5	m	m	PROPN
ejpam-4444	569	6	li	li	PROPN
ejpam-4444	569	7	,	,	PUNCT
ejpam-4444	569	8	b	b	PROPN
ejpam-4444	569	9	y	y	NOUN
ejpam-4444	569	10	long	long	ADV
ejpam-4444	569	11	,	,	PUNCT
ejpam-4444	569	12	and	and	CCONJ
ejpam-4444	569	13	y	y	PROPN
ejpam-4444	569	14	m	m	PROPN
ejpam-4444	569	15	chu	chu	PROPN
ejpam-4444	569	16	.	.	PUNCT
ejpam-4444	570	1	sharp	sharp	ADJ
ejpam-4444	570	2	bounds	bound	NOUN
ejpam-4444	570	3	for	for	ADP
ejpam-4444	570	4	the	the	DET
ejpam-4444	570	5	neuman	neuman	NOUN
ejpam-4444	570	6	-	-	PUNCT
ejpam-4444	570	7	sándor	sándor	NOUN
ejpam-4444	570	8	mean	mean	NOUN
ejpam-4444	570	9	in	in	ADP
ejpam-4444	570	10	terms	term	NOUN
ejpam-4444	570	11	of	of	ADP
ejpam-4444	570	12	generalized	generalized	ADJ
ejpam-4444	570	13	logarithmic	logarithmic	ADJ
ejpam-4444	570	14	mean	mean	NOUN
ejpam-4444	570	15	.	.	PUNCT
ejpam-4444	571	1	j.	j.	PROPN
ejpam-4444	571	2	math	math	PROPN
ejpam-4444	571	3	.	.	PUNCT
ejpam-4444	572	1	inequal	inequal	ADJ
ejpam-4444	572	2	.	.	PUNCT
ejpam-4444	572	3	,	,	PUNCT
ejpam-4444	572	4	6:567–577	6:567–577	NUM
ejpam-4444	572	5	,	,	PUNCT
ejpam-4444	572	6	2012	2012	NUM
ejpam-4444	572	7	.	.	PUNCT
ejpam-4444	573	1	[	[	X
ejpam-4444	573	2	9	9	NUM
ejpam-4444	573	3	]	]	SYM
ejpam-4444	573	4	b	b	NOUN
ejpam-4444	573	5	y	y	PROPN
ejpam-4444	573	6	long	long	ADV
ejpam-4444	573	7	and	and	CCONJ
ejpam-4444	573	8	y	y	PROPN
ejpam-4444	573	9	m	m	PROPN
ejpam-4444	573	10	chu	chu	PROPN
ejpam-4444	573	11	.	.	PUNCT
ejpam-4444	574	1	optimal	optimal	ADJ
ejpam-4444	574	2	inequalities	inequality	NOUN
ejpam-4444	574	3	for	for	ADP
ejpam-4444	574	4	generalized	generalized	ADJ
ejpam-4444	574	5	logarithmic	logarithmic	ADJ
ejpam-4444	574	6	,	,	PUNCT
ejpam-4444	574	7	arithmetic	arithmetic	ADJ
ejpam-4444	574	8	,	,	PUNCT
ejpam-4444	574	9	and	and	CCONJ
ejpam-4444	574	10	geometric	geometric	ADJ
ejpam-4444	574	11	means	mean	NOUN
ejpam-4444	574	12	.	.	PUNCT
ejpam-4444	575	1	j.	j.	PROPN
ejpam-4444	575	2	inequal	inequal	PROPN
ejpam-4444	575	3	.	.	PUNCT
ejpam-4444	576	1	appl	appl	PROPN
ejpam-4444	576	2	.	.	PROPN
ejpam-4444	576	3	,	,	PUNCT
ejpam-4444	576	4	article	article	NOUN
ejpam-4444	576	5	i	i	PROPN
ejpam-4444	576	6	d	d	PROPN
ejpam-4444	576	7	806825:10	806825:10	NUM
ejpam-4444	576	8	pages	page	NOUN
ejpam-4444	576	9	,	,	PUNCT
ejpam-4444	576	10	2010	2010	NUM
ejpam-4444	576	11	.	.	PUNCT
ejpam-4444	577	1	[	[	X
ejpam-4444	577	2	10	10	NUM
ejpam-4444	577	3	]	]	X
ejpam-4444	577	4	w	w	PROPN
ejpam-4444	577	5	h	h	PROPN
ejpam-4444	577	6	mcadam	mcadam	PROPN
ejpam-4444	577	7	.	.	PUNCT
ejpam-4444	578	1	heat	heat	PROPN
ejpam-4444	578	2	transmission	transmission	NOUN
ejpam-4444	578	3	.	.	PUNCT
ejpam-4444	579	1	mcgraw	mcgraw	PROPN
ejpam-4444	579	2	-	-	PUNCT
ejpam-4444	579	3	hill	hill	PROPN
ejpam-4444	579	4	,	,	PUNCT
ejpam-4444	579	5	new	new	PROPN
ejpam-4444	579	6	york	york	PROPN
ejpam-4444	579	7	,	,	PUNCT
ejpam-4444	579	8	1954	1954	NUM
ejpam-4444	579	9	.	.	PUNCT
ejpam-4444	580	1	[	[	X
ejpam-4444	580	2	11	11	NUM
ejpam-4444	580	3	]	]	SYM
ejpam-4444	580	4	b	b	X
ejpam-4444	580	5	mond	mond	NOUN
ejpam-4444	580	6	,	,	PUNCT
ejpam-4444	580	7	c	c	PROPN
ejpam-4444	580	8	e	e	PROPN
ejpam-4444	580	9	m	m	PROPN
ejpam-4444	580	10	pearce	pearce	PROPN
ejpam-4444	580	11	,	,	PUNCT
ejpam-4444	580	12	and	and	CCONJ
ejpam-4444	580	13	j	j	PROPN
ejpam-4444	580	14	pec̆arić.	pec̆arić.	NOUN
ejpam-4444	580	15	the	the	DET
ejpam-4444	580	16	logarithmic	logarithmic	ADJ
ejpam-4444	580	17	mean	mean	NOUN
ejpam-4444	580	18	is	be	AUX
ejpam-4444	580	19	a	a	DET
ejpam-4444	580	20	mean	mean	NOUN
ejpam-4444	580	21	.	.	PUNCT
ejpam-4444	581	1	j.	j.	PROPN
ejpam-4444	581	2	math	math	PROPN
ejpam-4444	581	3	.	.	PUNCT
ejpam-4444	582	1	commun	commun	PROPN
ejpam-4444	582	2	.	.	PROPN
ejpam-4444	582	3	,	,	PUNCT
ejpam-4444	582	4	345:86–89	345:86–89	NUM
ejpam-4444	582	5	,	,	PUNCT
ejpam-4444	582	6	2008	2008	NUM
ejpam-4444	582	7	.	.	PUNCT
ejpam-4444	583	1	[	[	X
ejpam-4444	583	2	12	12	NUM
ejpam-4444	583	3	]	]	X
ejpam-4444	583	4	f	f	PROPN
ejpam-4444	583	5	qi	qi	PROPN
ejpam-4444	583	6	.	.	PROPN
ejpam-4444	583	7	refinement	refinement	NOUN
ejpam-4444	583	8	,	,	PUNCT
ejpam-4444	583	9	extensions	extension	NOUN
ejpam-4444	583	10	and	and	CCONJ
ejpam-4444	583	11	generalizations	generalization	NOUN
ejpam-4444	583	12	of	of	ADP
ejpam-4444	583	13	the	the	DET
ejpam-4444	583	14	second	second	ADJ
ejpam-4444	583	15	kershaw	kershaw	PROPN
ejpam-4444	583	16	’s	’s	PART
ejpam-4444	583	17	double	double	ADJ
ejpam-4444	583	18	inequality	inequality	NOUN
ejpam-4444	583	19	.	.	PUNCT
ejpam-4444	584	1	math	math	NOUN
ejpam-4444	584	2	.	.	PUNCT
ejpam-4444	585	1	inequalities	inequalities	PROPN
ejpam-4444	585	2	appl	appl	PROPN
ejpam-4444	585	3	.	.	PROPN
ejpam-4444	585	4	,	,	PUNCT
ejpam-4444	585	5	11:457–465	11:457–465	NUM
ejpam-4444	585	6	,	,	PUNCT
ejpam-4444	585	7	2008	2008	NUM
ejpam-4444	585	8	.	.	PUNCT
ejpam-4444	586	1	[	[	X
ejpam-4444	586	2	13	13	NUM
ejpam-4444	586	3	]	]	X
ejpam-4444	586	4	f	f	PROPN
ejpam-4444	586	5	qi	qi	PROPN
ejpam-4444	586	6	,	,	PUNCT
ejpam-4444	586	7	s	s	PART
ejpam-4444	586	8	x	x	SYM
ejpam-4444	586	9	chen	chen	PROPN
ejpam-4444	586	10	,	,	PUNCT
ejpam-4444	586	11	and	and	CCONJ
ejpam-4444	586	12	c	c	X
ejpam-4444	586	13	p	p	PROPN
ejpam-4444	586	14	chen	chen	PROPN
ejpam-4444	586	15	.	.	PUNCT
ejpam-4444	587	1	monotonicity	monotonicity	NOUN
ejpam-4444	587	2	of	of	ADP
ejpam-4444	587	3	the	the	DET
ejpam-4444	587	4	ratio	ratio	NOUN
ejpam-4444	587	5	between	between	ADP
ejpam-4444	587	6	the	the	DET
ejpam-4444	587	7	generalized	generalize	VERB
ejpam-4444	587	8	logarithmic	logarithmic	ADJ
ejpam-4444	587	9	means	mean	NOUN
ejpam-4444	587	10	.	.	PUNCT
ejpam-4444	588	1	math	math	NOUN
ejpam-4444	588	2	.	.	PUNCT
ejpam-4444	589	1	inequalities	inequalities	PROPN
ejpam-4444	589	2	appl	appl	PROPN
ejpam-4444	589	3	.	.	PROPN
ejpam-4444	589	4	,	,	PUNCT
ejpam-4444	589	5	10:559–564	10:559–564	NUM
ejpam-4444	589	6	,	,	PUNCT
ejpam-4444	589	7	2007	2007	NUM
ejpam-4444	589	8	.	.	PUNCT
ejpam-4444	590	1	[	[	X
ejpam-4444	590	2	14	14	NUM
ejpam-4444	590	3	]	]	X
ejpam-4444	590	4	w	w	PROPN
ejpam-4444	590	5	m	m	PROPN
ejpam-4444	590	6	qian	qian	ADJ
ejpam-4444	590	7	and	and	CCONJ
ejpam-4444	590	8	y	y	PROPN
ejpam-4444	590	9	m	m	PROPN
ejpam-4444	590	10	chu	chu	PROPN
ejpam-4444	590	11	.	.	PUNCT
ejpam-4444	591	1	best	good	ADJ
ejpam-4444	591	2	possible	possible	ADJ
ejpam-4444	591	3	bounds	bound	NOUN
ejpam-4444	591	4	for	for	ADP
ejpam-4444	591	5	yang	yang	PROPN
ejpam-4444	591	6	mean	mean	VERB
ejpam-4444	591	7	using	use	VERB
ejpam-4444	591	8	generalized	generalized	ADJ
ejpam-4444	591	9	logarithmic	logarithmic	ADJ
ejpam-4444	591	10	mean	mean	NOUN
ejpam-4444	591	11	.	.	PUNCT
ejpam-4444	592	1	math	math	NOUN
ejpam-4444	592	2	.	.	PUNCT
ejpam-4444	593	1	probl	probl	PROPN
ejpam-4444	593	2	.	.	PUNCT
ejpam-4444	594	1	eng	eng	PROPN
ejpam-4444	594	2	.	.	PROPN
ejpam-4444	594	3	,	,	PUNCT
ejpam-4444	594	4	article	article	NOUN
ejpam-4444	594	5	i	i	PROPN
ejpam-4444	594	6	d	d	PROPN
ejpam-4444	594	7	8901258:7	8901258:7	NUM
ejpam-4444	594	8	pages	page	NOUN
ejpam-4444	594	9	,	,	PUNCT
ejpam-4444	594	10	2016	2016	NUM
ejpam-4444	594	11	.	.	PUNCT
ejpam-4444	595	1	[	[	X
ejpam-4444	595	2	15	15	NUM
ejpam-4444	595	3	]	]	X
ejpam-4444	595	4	w	w	PROPN
ejpam-4444	595	5	m	m	VERB
ejpam-4444	595	6	qian	qian	ADJ
ejpam-4444	595	7	,	,	PUNCT
ejpam-4444	595	8	z	z	PROPN
ejpam-4444	595	9	y	y	PROPN
ejpam-4444	595	10	he	he	PRON
ejpam-4444	595	11	,	,	PUNCT
ejpam-4444	595	12	h	h	PROPN
ejpam-4444	595	13	w	w	PROPN
ejpam-4444	595	14	zhang	zhang	PROPN
ejpam-4444	595	15	,	,	PUNCT
ejpam-4444	595	16	and	and	CCONJ
ejpam-4444	595	17	y	y	PROPN
ejpam-4444	595	18	m	m	PROPN
ejpam-4444	595	19	chu	chu	PROPN
ejpam-4444	595	20	.	.	PUNCT
ejpam-4444	596	1	sharp	sharp	ADJ
ejpam-4444	596	2	bounds	bound	NOUN
ejpam-4444	596	3	for	for	ADP
ejpam-4444	596	4	neuman	neuman	NOUN
ejpam-4444	596	5	means	mean	NOUN
ejpam-4444	596	6	in	in	ADP
ejpam-4444	596	7	terms	term	NOUN
ejpam-4444	596	8	of	of	ADP
ejpam-4444	596	9	two	two	NUM
ejpam-4444	596	10	-	-	PUNCT
ejpam-4444	596	11	parameter	parameter	NOUN
ejpam-4444	596	12	contraharmonic	contraharmonic	NOUN
ejpam-4444	596	13	and	and	CCONJ
ejpam-4444	596	14	arithmetic	arithmetic	ADJ
ejpam-4444	596	15	mean	mean	NOUN
ejpam-4444	596	16	.	.	PUNCT
ejpam-4444	597	1	j.	j.	PROPN
ejpam-4444	597	2	inequal	inequal	PROPN
ejpam-4444	597	3	.	.	PUNCT
ejpam-4444	598	1	appl	appl	PROPN
ejpam-4444	598	2	.	.	PROPN
ejpam-4444	598	3	,	,	PUNCT
ejpam-4444	598	4	168:13	168:13	NUM
ejpam-4444	598	5	pages	page	NOUN
ejpam-4444	598	6	,	,	PUNCT
ejpam-4444	598	7	2019	2019	NUM
ejpam-4444	598	8	.	.	PUNCT
ejpam-4444	599	1	[	[	X
ejpam-4444	599	2	16	16	NUM
ejpam-4444	599	3	]	]	X
ejpam-4444	599	4	w	w	PROPN
ejpam-4444	599	5	m	m	PROPN
ejpam-4444	599	6	qian	qian	ADJ
ejpam-4444	599	7	and	and	CCONJ
ejpam-4444	599	8	b	b	SYM
ejpam-4444	599	9	y	y	PROPN
ejpam-4444	599	10	long	long	ADV
ejpam-4444	599	11	.	.	PUNCT
ejpam-4444	600	1	sharp	sharp	ADJ
ejpam-4444	600	2	bounds	bound	NOUN
ejpam-4444	600	3	by	by	ADP
ejpam-4444	600	4	the	the	DET
ejpam-4444	600	5	generalized	generalize	VERB
ejpam-4444	600	6	logarithmic	logarithmic	ADJ
ejpam-4444	600	7	mean	mean	NOUN
ejpam-4444	600	8	for	for	ADP
ejpam-4444	600	9	the	the	DET
ejpam-4444	600	10	geometric	geometric	ADJ
ejpam-4444	600	11	weighted	weight	VERB
ejpam-4444	600	12	mean	mean	NOUN
ejpam-4444	600	13	of	of	ADP
ejpam-4444	600	14	the	the	DET
ejpam-4444	600	15	geometric	geometric	ADJ
ejpam-4444	600	16	and	and	CCONJ
ejpam-4444	600	17	harmonic	harmonic	ADJ
ejpam-4444	600	18	means	mean	NOUN
ejpam-4444	600	19	.	.	PUNCT
ejpam-4444	601	1	j.	j.	PROPN
ejpam-4444	601	2	appl	appl	PROPN
ejpam-4444	601	3	.	.	PROPN
ejpam-4444	601	4	math	math	PROPN
ejpam-4444	601	5	.	.	PUNCT
ejpam-4444	602	1	,	,	PUNCT
ejpam-4444	602	2	article	article	NOUN
ejpam-4444	602	3	i	i	PROPN
ejpam-4444	602	4	d	d	PROPN
ejpam-4444	602	5	480689:8	480689:8	NUM
ejpam-4444	602	6	pages	page	NOUN
ejpam-4444	602	7	,	,	PUNCT
ejpam-4444	602	8	2012	2012	NUM
ejpam-4444	602	9	.	.	PUNCT
ejpam-4444	603	1	[	[	X
ejpam-4444	603	2	17	17	NUM
ejpam-4444	603	3	]	]	X
ejpam-4444	603	4	w	w	PROPN
ejpam-4444	603	5	m	m	VERB
ejpam-4444	603	6	qian	qian	ADJ
ejpam-4444	603	7	,	,	PUNCT
ejpam-4444	603	8	x	x	PROPN
ejpam-4444	603	9	h	h	PROPN
ejpam-4444	603	10	zhang	zhang	PROPN
ejpam-4444	603	11	,	,	PUNCT
ejpam-4444	603	12	and	and	CCONJ
ejpam-4444	603	13	y	y	PROPN
ejpam-4444	603	14	m	m	PROPN
ejpam-4444	603	15	chu	chu	PROPN
ejpam-4444	603	16	.	.	PUNCT
ejpam-4444	604	1	sharp	sharp	ADJ
ejpam-4444	604	2	bounds	bound	NOUN
ejpam-4444	604	3	for	for	ADP
ejpam-4444	604	4	the	the	DET
ejpam-4444	604	5	toader	toader	NOUN
ejpam-4444	604	6	-	-	PUNCT
ejpam-4444	604	7	qi	qi	NOUN
ejpam-4444	604	8	mean	mean	NOUN
ejpam-4444	604	9	in	in	ADP
ejpam-4444	604	10	terms	term	NOUN
ejpam-4444	604	11	of	of	ADP
ejpam-4444	604	12	harmonic	harmonic	ADJ
ejpam-4444	604	13	and	and	CCONJ
ejpam-4444	604	14	geometric	geometric	ADJ
ejpam-4444	604	15	means	mean	NOUN
ejpam-4444	604	16	.	.	PUNCT
ejpam-4444	605	1	j.	j.	PROPN
ejpam-4444	605	2	math	math	PROPN
ejpam-4444	605	3	.	.	PUNCT
ejpam-4444	606	1	inequal	inequal	ADJ
ejpam-4444	606	2	.	.	PUNCT
ejpam-4444	606	3	,	,	PUNCT
ejpam-4444	606	4	11:121–127	11:121–127	NUM
ejpam-4444	606	5	,	,	PUNCT
ejpam-4444	606	6	2017	2017	NUM
ejpam-4444	606	7	.	.	PUNCT
ejpam-4444	607	1	[	[	X
ejpam-4444	607	2	18	18	NUM
ejpam-4444	607	3	]	]	X
ejpam-4444	607	4	h	h	NOUN
ejpam-4444	607	5	n	n	PROPN
ejpam-4444	607	6	shi	shi	PROPN
ejpam-4444	607	7	.	.	PUNCT
ejpam-4444	607	8	schur	schur	VERB
ejpam-4444	607	9	-	-	PUNCT
ejpam-4444	607	10	convex	convex	NOUN
ejpam-4444	607	11	functions	function	NOUN
ejpam-4444	607	12	related	relate	VERB
ejpam-4444	607	13	to	to	ADP
ejpam-4444	607	14	hadamard	hadamard	ADJ
ejpam-4444	607	15	-	-	PUNCT
ejpam-4444	607	16	type	type	NOUN
ejpam-4444	607	17	inequalities	inequality	NOUN
ejpam-4444	607	18	.	.	PUNCT
ejpam-4444	608	1	j.	j.	PROPN
ejpam-4444	608	2	math	math	PROPN
ejpam-4444	608	3	.	.	PUNCT
ejpam-4444	609	1	inequal	inequal	ADJ
ejpam-4444	609	2	.	.	PUNCT
ejpam-4444	609	3	,	,	PUNCT
ejpam-4444	609	4	1:127–136	1:127–136	NUM
ejpam-4444	609	5	,	,	PUNCT
ejpam-4444	609	6	2007	2007	NUM
ejpam-4444	609	7	.	.	PUNCT
ejpam-4444	610	1	[	[	X
ejpam-4444	610	2	19	19	NUM
ejpam-4444	610	3	]	]	X
ejpam-4444	610	4	k	k	PROPN
ejpam-4444	610	5	b	b	PROPN
ejpam-4444	610	6	stolarsky	stolarsky	PROPN
ejpam-4444	610	7	.	.	PUNCT
ejpam-4444	611	1	the	the	DET
ejpam-4444	611	2	power	power	NOUN
ejpam-4444	611	3	and	and	CCONJ
ejpam-4444	611	4	generalized	generalized	ADJ
ejpam-4444	611	5	logarithmic	logarithmic	ADJ
ejpam-4444	611	6	means	mean	NOUN
ejpam-4444	611	7	.	.	PUNCT
ejpam-4444	612	1	am	be	AUX
ejpam-4444	612	2	.	.	PUNCT
ejpam-4444	613	1	math	math	NOUN
ejpam-4444	613	2	.	.	PUNCT
ejpam-4444	614	1	mon	mon	PROPN
ejpam-4444	614	2	.	.	PROPN
ejpam-4444	614	3	,	,	PUNCT
ejpam-4444	614	4	87:545–548	87:545–548	NUM
ejpam-4444	614	5	,	,	PUNCT
ejpam-4444	614	6	1980	1980	NUM
ejpam-4444	614	7	.	.	PUNCT
ejpam-4444	615	1	references	reference	NOUN
ejpam-4444	615	2	1143	1143	NUM
ejpam-4444	615	3	[	[	X
ejpam-4444	615	4	20	20	NUM
ejpam-4444	615	5	]	]	X
ejpam-4444	615	6	h	h	NOUN
ejpam-4444	615	7	z	z	PROPN
ejpam-4444	615	8	xu	xu	PROPN
ejpam-4444	615	9	,	,	PUNCT
ejpam-4444	615	10	y	y	PROPN
ejpam-4444	615	11	m	m	PROPN
ejpam-4444	615	12	chu	chu	PROPN
ejpam-4444	615	13	,	,	PUNCT
ejpam-4444	615	14	and	and	CCONJ
ejpam-4444	615	15	w	w	PROPN
ejpam-4444	615	16	m	m	PROPN
ejpam-4444	615	17	qian	qian	PROPN
ejpam-4444	615	18	.	.	PUNCT
ejpam-4444	616	1	sharp	sharp	ADJ
ejpam-4444	616	2	bounds	bound	NOUN
ejpam-4444	616	3	for	for	ADP
ejpam-4444	616	4	the	the	DET
ejpam-4444	616	5	sándor	sándor	PROPN
ejpam-4444	616	6	–	–	PUNCT
ejpam-4444	616	7	yang	yang	PROPN
ejpam-4444	616	8	means	mean	VERB
ejpam-4444	616	9	in	in	ADP
ejpam-4444	616	10	terms	term	NOUN
ejpam-4444	616	11	of	of	ADP
ejpam-4444	616	12	arithmetic	arithmetic	ADJ
ejpam-4444	616	13	and	and	CCONJ
ejpam-4444	616	14	contra	contra	ADJ
ejpam-4444	616	15	-	-	ADJ
ejpam-4444	616	16	harmonic	harmonic	ADJ
ejpam-4444	616	17	means	mean	NOUN
ejpam-4444	616	18	.	.	PUNCT
ejpam-4444	617	1	j.	j.	PROPN
ejpam-4444	617	2	inequal	inequal	PROPN
ejpam-4444	617	3	.	.	PUNCT
ejpam-4444	618	1	appl	appl	PROPN
ejpam-4444	618	2	.	.	PROPN
ejpam-4444	618	3	,	,	PUNCT
ejpam-4444	618	4	127:13	127:13	NUM
ejpam-4444	618	5	pages	page	NOUN
ejpam-4444	618	6	,	,	PUNCT
ejpam-4444	618	7	2018	2018	NUM
ejpam-4444	618	8	.	.	PUNCT