id	sid	tid	token	lemma	pos
ejpam-3300	1	1	the	the	DET
ejpam-3300	1	2	proofs	proof	NOUN
ejpam-3300	1	3	of	of	ADP
ejpam-3300	1	4	the	the	DET
ejpam-3300	1	5	arithmetic	arithmetic	ADJ
ejpam-3300	1	6	-	-	PUNCT
ejpam-3300	1	7	geometric	geometric	ADJ
ejpam-3300	1	8	mean	mean	NOUN
ejpam-3300	1	9	inequality	inequality	NOUN
ejpam-3300	1	10	through	through	ADP
ejpam-3300	1	11	both	both	CCONJ
ejpam-3300	1	12	the	the	DET
ejpam-3300	1	13	product	product	NOUN
ejpam-3300	1	14	and	and	CCONJ
ejpam-3300	1	15	binomial	binomial	ADJ
ejpam-3300	1	16	inequalities	inequality	NOUN
ejpam-3300	1	17	european	european	PROPN
ejpam-3300	1	18	journal	journal	PROPN
ejpam-3300	1	19	of	of	ADP
ejpam-3300	1	20	pure	pure	ADJ
ejpam-3300	1	21	and	and	CCONJ
ejpam-3300	1	22	applied	apply	VERB
ejpam-3300	1	23	mathematics	mathematic	NOUN
ejpam-3300	1	24	vol	vol	NOUN
ejpam-3300	1	25	.	.	PUNCT
ejpam-3300	1	26	11	11	NUM
ejpam-3300	1	27	,	,	PUNCT
ejpam-3300	1	28	no	no	INTJ
ejpam-3300	1	29	.	.	NOUN
ejpam-3300	1	30	4	4	NUM
ejpam-3300	1	31	,	,	PUNCT
ejpam-3300	1	32	2018	2018	NUM
ejpam-3300	1	33	,	,	PUNCT
ejpam-3300	1	34	1100	1100	NUM
ejpam-3300	1	35	-	-	SYM
ejpam-3300	1	36	1107	1107	NUM
ejpam-3300	1	37	issn	issn	PROPN
ejpam-3300	1	38	1307	1307	NUM
ejpam-3300	1	39	-	-	SYM
ejpam-3300	1	40	5543	5543	NUM
ejpam-3300	1	41	–	–	PUNCT
ejpam-3300	1	42	www.ejpam.com	www.ejpam.com	X
ejpam-3300	1	43	published	publish	VERB
ejpam-3300	1	44	by	by	ADP
ejpam-3300	1	45	new	new	PROPN
ejpam-3300	1	46	york	york	PROPN
ejpam-3300	1	47	business	business	PROPN
ejpam-3300	1	48	global	global	PROPN
ejpam-3300	1	49	the	the	DET
ejpam-3300	1	50	proofs	proof	NOUN
ejpam-3300	1	51	of	of	ADP
ejpam-3300	1	52	the	the	DET
ejpam-3300	1	53	arithmetic	arithmetic	ADJ
ejpam-3300	1	54	-	-	PUNCT
ejpam-3300	1	55	geometric	geometric	ADJ
ejpam-3300	1	56	mean	mean	NOUN
ejpam-3300	1	57	inequality	inequality	NOUN
ejpam-3300	1	58	through	through	ADP
ejpam-3300	1	59	both	both	CCONJ
ejpam-3300	1	60	the	the	DET
ejpam-3300	1	61	product	product	NOUN
ejpam-3300	1	62	and	and	CCONJ
ejpam-3300	1	63	binomial	binomial	ADJ
ejpam-3300	1	64	inequalities	inequality	NOUN
ejpam-3300	1	65	benedict	benedict	PROPN
ejpam-3300	1	66	barnes1,∗	barnes1,∗	PROPN
ejpam-3300	1	67	,	,	PUNCT
ejpam-3300	1	68	e.	e.	PROPN
ejpam-3300	1	69	harris1	harris1	PROPN
ejpam-3300	1	70	,	,	PUNCT
ejpam-3300	1	71	n.	n.	PROPN
ejpam-3300	1	72	f.	f.	PROPN
ejpam-3300	1	73	darquah2	darquah2	PROPN
ejpam-3300	1	74	,	,	PUNCT
ejpam-3300	1	75	g.	g.	PROPN
ejpam-3300	1	76	hughes3	hughes3	PROPN
ejpam-3300	2	1	1	1	NUM
ejpam-3300	2	2	department	department	NOUN
ejpam-3300	2	3	of	of	ADP
ejpam-3300	2	4	mathematics	mathematics	PROPN
ejpam-3300	2	5	,	,	PUNCT
ejpam-3300	2	6	kwame	kwame	PROPN
ejpam-3300	2	7	nkrumah	nkrumah	PROPN
ejpam-3300	2	8	university	university	PROPN
ejpam-3300	2	9	of	of	ADP
ejpam-3300	2	10	science	science	NOUN
ejpam-3300	2	11	and	and	CCONJ
ejpam-3300	2	12	technology	technology	NOUN
ejpam-3300	2	13	,	,	PUNCT
ejpam-3300	2	14	kumasi	kumasi	PROPN
ejpam-3300	2	15	,	,	PUNCT
ejpam-3300	2	16	ghana	ghana	PROPN
ejpam-3300	2	17	2	2	NUM
ejpam-3300	2	18	department	department	NOUN
ejpam-3300	2	19	of	of	ADP
ejpam-3300	2	20	computer	computer	NOUN
ejpam-3300	2	21	science	science	NOUN
ejpam-3300	2	22	,	,	PUNCT
ejpam-3300	2	23	kwame	kwame	PROPN
ejpam-3300	2	24	nkrumah	nkrumah	PROPN
ejpam-3300	2	25	university	university	PROPN
ejpam-3300	2	26	of	of	ADP
ejpam-3300	2	27	science	science	NOUN
ejpam-3300	2	28	and	and	CCONJ
ejpam-3300	2	29	technology	technology	NOUN
ejpam-3300	2	30	,	,	PUNCT
ejpam-3300	2	31	kumasi	kumasi	PROPN
ejpam-3300	2	32	,	,	PUNCT
ejpam-3300	2	33	ghana	ghana	PROPN
ejpam-3300	2	34	3	3	NUM
ejpam-3300	2	35	department	department	PROPN
ejpam-3300	2	36	of	of	ADP
ejpam-3300	2	37	economics	economic	NOUN
ejpam-3300	2	38	,	,	PUNCT
ejpam-3300	2	39	central	central	ADJ
ejpam-3300	2	40	university	university	NOUN
ejpam-3300	2	41	,	,	PUNCT
ejpam-3300	2	42	accra	accra	PROPN
ejpam-3300	2	43	,	,	PUNCT
ejpam-3300	2	44	ghana	ghana	PROPN
ejpam-3300	2	45	abstract	abstract	NOUN
ejpam-3300	2	46	.	.	PUNCT
ejpam-3300	3	1	in	in	ADP
ejpam-3300	3	2	this	this	DET
ejpam-3300	3	3	paper	paper	NOUN
ejpam-3300	3	4	,	,	PUNCT
ejpam-3300	3	5	we	we	PRON
ejpam-3300	3	6	show	show	VERB
ejpam-3300	3	7	new	new	ADJ
ejpam-3300	3	8	ways	way	NOUN
ejpam-3300	3	9	of	of	ADP
ejpam-3300	3	10	proving	prove	VERB
ejpam-3300	3	11	the	the	DET
ejpam-3300	3	12	arithmetic	arithmetic	ADJ
ejpam-3300	3	13	-	-	PUNCT
ejpam-3300	3	14	geometric	geometric	ADJ
ejpam-3300	3	15	mean	mean	NOUN
ejpam-3300	3	16	agm	agm	PROPN
ejpam-3300	3	17	inequality	inequality	NOUN
ejpam-3300	3	18	through	through	ADP
ejpam-3300	3	19	the	the	DET
ejpam-3300	3	20	first	first	ADJ
ejpam-3300	3	21	product	product	NOUN
ejpam-3300	3	22	and	and	CCONJ
ejpam-3300	3	23	the	the	DET
ejpam-3300	3	24	second	second	ADJ
ejpam-3300	3	25	product	product	NOUN
ejpam-3300	3	26	inequalities	inequality	NOUN
ejpam-3300	3	27	.	.	PUNCT
ejpam-3300	4	1	in	in	ADP
ejpam-3300	4	2	addition	addition	NOUN
ejpam-3300	4	3	,	,	PUNCT
ejpam-3300	4	4	we	we	PRON
ejpam-3300	4	5	prove	prove	VERB
ejpam-3300	4	6	the	the	DET
ejpam-3300	4	7	agm	agm	PROPN
ejpam-3300	4	8	inequality	inequality	NOUN
ejpam-3300	4	9	through	through	ADP
ejpam-3300	4	10	the	the	DET
ejpam-3300	4	11	binomial	binomial	ADJ
ejpam-3300	4	12	inequalities	inequality	NOUN
ejpam-3300	4	13	.	.	PUNCT
ejpam-3300	5	1	these	these	DET
ejpam-3300	5	2	methods	method	NOUN
ejpam-3300	5	3	are	be	AUX
ejpam-3300	5	4	alternative	alternative	ADJ
ejpam-3300	5	5	ways	way	NOUN
ejpam-3300	5	6	of	of	ADP
ejpam-3300	5	7	proving	prove	VERB
ejpam-3300	5	8	agm	agm	PROPN
ejpam-3300	5	9	inequalities	inequality	NOUN
ejpam-3300	5	10	.	.	PUNCT
ejpam-3300	6	1	2010	2010	NUM
ejpam-3300	6	2	mathematics	mathematic	NOUN
ejpam-3300	6	3	subject	subject	NOUN
ejpam-3300	6	4	classifications	classification	NOUN
ejpam-3300	6	5	:	:	PUNCT
ejpam-3300	6	6	44b51	44b51	NUM
ejpam-3300	6	7	44b52	44b52	NUM
ejpam-3300	6	8	key	key	ADJ
ejpam-3300	6	9	words	word	NOUN
ejpam-3300	6	10	and	and	CCONJ
ejpam-3300	6	11	phrases	phrase	NOUN
ejpam-3300	6	12	:	:	PUNCT
ejpam-3300	6	13	arithmetic	arithmetic	ADJ
ejpam-3300	6	14	-	-	PUNCT
ejpam-3300	6	15	geometric	geometric	ADJ
ejpam-3300	6	16	inequality	inequality	NOUN
ejpam-3300	6	17	,	,	PUNCT
ejpam-3300	6	18	first	first	ADJ
ejpam-3300	6	19	product	product	NOUN
ejpam-3300	6	20	inequality	inequality	NOUN
ejpam-3300	6	21	,	,	PUNCT
ejpam-3300	6	22	second	second	ADJ
ejpam-3300	6	23	product	product	NOUN
ejpam-3300	6	24	inequality	inequality	NOUN
ejpam-3300	6	25	and	and	CCONJ
ejpam-3300	6	26	binomial	binomial	ADJ
ejpam-3300	6	27	inequalities	inequality	NOUN
ejpam-3300	6	28	1	1	NUM
ejpam-3300	6	29	.	.	PUNCT
ejpam-3300	6	30	introduction	introduction	VERB
ejpam-3300	6	31	the	the	DET
ejpam-3300	6	32	importance	importance	NOUN
ejpam-3300	6	33	of	of	ADP
ejpam-3300	6	34	inequalities	inequality	NOUN
ejpam-3300	6	35	can	can	AUX
ejpam-3300	6	36	not	not	PART
ejpam-3300	6	37	be	be	AUX
ejpam-3300	6	38	underestimated	underestimate	VERB
ejpam-3300	6	39	as	as	SCONJ
ejpam-3300	6	40	they	they	PRON
ejpam-3300	6	41	play	play	VERB
ejpam-3300	6	42	central	central	ADJ
ejpam-3300	6	43	role	role	NOUN
ejpam-3300	6	44	in	in	ADP
ejpam-3300	6	45	mathematical	mathematical	ADJ
ejpam-3300	6	46	analysis	analysis	NOUN
ejpam-3300	6	47	.	.	PUNCT
ejpam-3300	7	1	in	in	ADP
ejpam-3300	7	2	the	the	DET
ejpam-3300	7	3	21st	21st	ADJ
ejpam-3300	7	4	century	century	NOUN
ejpam-3300	7	5	,	,	PUNCT
ejpam-3300	7	6	the	the	DET
ejpam-3300	7	7	agm	agm	PROPN
ejpam-3300	7	8	inequality	inequality	NOUN
ejpam-3300	7	9	has	have	AUX
ejpam-3300	7	10	received	receive	VERB
ejpam-3300	7	11	much	much	ADJ
ejpam-3300	7	12	attention	attention	NOUN
ejpam-3300	7	13	and	and	CCONJ
ejpam-3300	7	14	has	have	AUX
ejpam-3300	7	15	been	be	AUX
ejpam-3300	7	16	applied	apply	VERB
ejpam-3300	7	17	in	in	ADP
ejpam-3300	7	18	the	the	DET
ejpam-3300	7	19	areas	area	NOUN
ejpam-3300	7	20	of	of	ADP
ejpam-3300	7	21	statistics	statistic	NOUN
ejpam-3300	7	22	and	and	CCONJ
ejpam-3300	7	23	engineering	engineering	NOUN
ejpam-3300	7	24	.	.	PUNCT
ejpam-3300	8	1	the	the	DET
ejpam-3300	8	2	agm	agm	PROPN
ejpam-3300	8	3	inequality	inequality	NOUN
ejpam-3300	8	4	was	be	AUX
ejpam-3300	8	5	first	first	ADV
ejpam-3300	8	6	introduced	introduce	VERB
ejpam-3300	8	7	by	by	ADP
ejpam-3300	8	8	lagrange	lagrange	PROPN
ejpam-3300	8	9	(	(	PUNCT
ejpam-3300	8	10	as	as	SCONJ
ejpam-3300	8	11	cited	cite	VERB
ejpam-3300	8	12	in	in	ADP
ejpam-3300	8	13	[	[	X
ejpam-3300	8	14	1	1	NUM
ejpam-3300	8	15	]	]	PUNCT
ejpam-3300	8	16	)	)	PUNCT
ejpam-3300	8	17	.	.	PUNCT
ejpam-3300	9	1	since	since	SCONJ
ejpam-3300	9	2	then	then	ADV
ejpam-3300	9	3	the	the	DET
ejpam-3300	9	4	agm	agm	PROPN
ejpam-3300	9	5	inequality	inequality	NOUN
ejpam-3300	9	6	has	have	AUX
ejpam-3300	9	7	used	use	VERB
ejpam-3300	9	8	to	to	PART
ejpam-3300	9	9	establish	establish	VERB
ejpam-3300	9	10	the	the	DET
ejpam-3300	9	11	relationships	relationship	NOUN
ejpam-3300	9	12	between	between	ADP
ejpam-3300	9	13	the	the	DET
ejpam-3300	9	14	areas	area	NOUN
ejpam-3300	9	15	and	and	CCONJ
ejpam-3300	9	16	perimeters	perimeter	NOUN
ejpam-3300	9	17	of	of	ADP
ejpam-3300	9	18	geometrical	geometrical	ADJ
ejpam-3300	9	19	plane	plane	NOUN
ejpam-3300	9	20	figures	figure	NOUN
ejpam-3300	9	21	,	,	PUNCT
ejpam-3300	9	22	the	the	DET
ejpam-3300	9	23	so	so	ADV
ejpam-3300	9	24	-	-	PUNCT
ejpam-3300	9	25	called	call	VERB
ejpam-3300	9	26	isoperimetric	isoperimetric	ADJ
ejpam-3300	9	27	inequalities	inequality	NOUN
ejpam-3300	9	28	,	,	PUNCT
ejpam-3300	9	29	for	for	ADP
ejpam-3300	9	30	example	example	NOUN
ejpam-3300	9	31	,	,	PUNCT
ejpam-3300	9	32	see	see	VERB
ejpam-3300	9	33	authors	author	NOUN
ejpam-3300	9	34	in	in	ADP
ejpam-3300	9	35	[	[	X
ejpam-3300	9	36	2	2	NUM
ejpam-3300	9	37	,	,	PUNCT
ejpam-3300	9	38	3	3	NUM
ejpam-3300	9	39	]	]	PUNCT
ejpam-3300	9	40	.	.	PUNCT
ejpam-3300	10	1	however	however	ADV
ejpam-3300	10	2	,	,	PUNCT
ejpam-3300	10	3	a	a	DET
ejpam-3300	10	4	substantial	substantial	ADJ
ejpam-3300	10	5	progress	progress	NOUN
ejpam-3300	10	6	has	have	AUX
ejpam-3300	10	7	been	be	AUX
ejpam-3300	10	8	made	make	VERB
ejpam-3300	10	9	to	to	PART
ejpam-3300	10	10	increase	increase	VERB
ejpam-3300	10	11	the	the	DET
ejpam-3300	10	12	understanding	understanding	NOUN
ejpam-3300	10	13	of	of	ADP
ejpam-3300	10	14	the	the	DET
ejpam-3300	10	15	agm	agm	PROPN
ejpam-3300	10	16	inequality	inequality	NOUN
ejpam-3300	10	17	by	by	ADP
ejpam-3300	10	18	the	the	DET
ejpam-3300	10	19	researchers	researcher	NOUN
ejpam-3300	10	20	across	across	ADP
ejpam-3300	10	21	the	the	DET
ejpam-3300	10	22	globe	globe	NOUN
ejpam-3300	10	23	.	.	PUNCT
ejpam-3300	11	1	in	in	ADP
ejpam-3300	11	2	[	[	X
ejpam-3300	11	3	4	4	NUM
ejpam-3300	11	4	]	]	PUNCT
ejpam-3300	11	5	,	,	PUNCT
ejpam-3300	11	6	the	the	DET
ejpam-3300	11	7	author	author	NOUN
ejpam-3300	11	8	proved	prove	VERB
ejpam-3300	11	9	the	the	DET
ejpam-3300	11	10	agm	agm	PROPN
ejpam-3300	11	11	inequality	inequality	NOUN
ejpam-3300	11	12	using	use	VERB
ejpam-3300	11	13	the	the	DET
ejpam-3300	11	14	heuristic	heuristic	ADJ
ejpam-3300	11	15	method	method	NOUN
ejpam-3300	11	16	.	.	PUNCT
ejpam-3300	12	1	the	the	DET
ejpam-3300	12	2	author	author	NOUN
ejpam-3300	12	3	in	in	ADP
ejpam-3300	12	4	[	[	X
ejpam-3300	12	5	5	5	NUM
ejpam-3300	12	6	]	]	PUNCT
ejpam-3300	12	7	observed	observe	VERB
ejpam-3300	12	8	that	that	SCONJ
ejpam-3300	12	9	the	the	DET
ejpam-3300	12	10	mutatis	mutatis	NOUN
ejpam-3300	12	11	mutandis	mutandis	NOUN
ejpam-3300	12	12	’	'	PUNCT
ejpam-3300	12	13	method	method	NOUN
ejpam-3300	12	14	for	for	ADP
ejpam-3300	12	15	proving	prove	VERB
ejpam-3300	12	16	the	the	DET
ejpam-3300	12	17	agm	agm	PROPN
ejpam-3300	12	18	inequality	inequality	NOUN
ejpam-3300	12	19	was	be	AUX
ejpam-3300	12	20	similar	similar	ADJ
ejpam-3300	12	21	to	to	ADP
ejpam-3300	12	22	the	the	DET
ejpam-3300	12	23	result	result	NOUN
ejpam-3300	12	24	obtained	obtain	VERB
ejpam-3300	12	25	by	by	ADP
ejpam-3300	12	26	jacobsthal	jacobsthal	ADJ
ejpam-3300	12	27	and	and	CCONJ
ejpam-3300	12	28	rado	rado	PROPN
ejpam-3300	12	29	,	,	PUNCT
ejpam-3300	12	30	for	for	ADP
ejpam-3300	12	31	∗corresponding	∗corresponde	VERB
ejpam-3300	12	32	author	author	NOUN
ejpam-3300	12	33	.	.	PUNCT
ejpam-3300	13	1	doi	doi	NOUN
ejpam-3300	13	2	:	:	PUNCT
ejpam-3300	13	3	https://doi.org/10.29020/nybg.ejpam.v11i4.3300	https://doi.org/10.29020/nybg.ejpam.v11i4.3300	DET
ejpam-3300	13	4	email	email	NOUN
ejpam-3300	13	5	addresses	address	VERB
ejpam-3300	13	6	:	:	PUNCT
ejpam-3300	14	1	ewiekwamina@gmail.com	ewiekwamina@gmail.com	X
ejpam-3300	14	2	bbarnes.cos@knust.edu.gh	bbarnes.cos@knust.edu.gh	PROPN
ejpam-3300	14	3	(	(	PUNCT
ejpam-3300	14	4	b.	b.	PROPN
ejpam-3300	14	5	barnes	barnes	PROPN
ejpam-3300	14	6	)	)	PUNCT
ejpam-3300	14	7	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3300	15	1	1100	1100	NUM
ejpam-3300	15	2	c	c	X
ejpam-3300	15	3	©	©	PROPN
ejpam-3300	15	4	2018	2018	NUM
ejpam-3300	15	5	ejpam	ejpam	VERB
ejpam-3300	15	6	all	all	DET
ejpam-3300	15	7	rights	right	NOUN
ejpam-3300	15	8	reserved	reserve	VERB
ejpam-3300	15	9	.	.	PUNCT
ejpam-3300	16	1	b.	b.	PROPN
ejpam-3300	16	2	barnes	barnes	PROPN
ejpam-3300	16	3	et	et	PROPN
ejpam-3300	16	4	al	al	PROPN
ejpam-3300	16	5	.	.	PUNCT
ejpam-3300	16	6	/	/	SYM
ejpam-3300	16	7	eur	eur	PROPN
ejpam-3300	16	8	.	.	PUNCT
ejpam-3300	17	1	j.	j.	PROPN
ejpam-3300	17	2	pure	pure	PROPN
ejpam-3300	17	3	appl	appl	PROPN
ejpam-3300	17	4	.	.	PROPN
ejpam-3300	17	5	math	math	PROPN
ejpam-3300	17	6	,	,	PUNCT
ejpam-3300	17	7	11	11	NUM
ejpam-3300	17	8	(	(	PUNCT
ejpam-3300	17	9	4	4	NUM
ejpam-3300	17	10	)	)	PUNCT
ejpam-3300	17	11	(	(	PUNCT
ejpam-3300	17	12	2018	2018	NUM
ejpam-3300	17	13	)	)	PUNCT
ejpam-3300	17	14	,	,	PUNCT
ejpam-3300	17	15	1100	1100	NUM
ejpam-3300	17	16	-	-	SYM
ejpam-3300	17	17	1107	1107	NUM
ejpam-3300	17	18	1101	1101	NUM
ejpam-3300	17	19	example	example	NOUN
ejpam-3300	17	20	,	,	PUNCT
ejpam-3300	17	21	see	see	VERB
ejpam-3300	17	22	[	[	X
ejpam-3300	17	23	6	6	NUM
ejpam-3300	17	24	]	]	PUNCT
ejpam-3300	17	25	.	.	PUNCT
ejpam-3300	18	1	in	in	ADP
ejpam-3300	18	2	[	[	X
ejpam-3300	18	3	7	7	NUM
ejpam-3300	18	4	]	]	PUNCT
ejpam-3300	18	5	,	,	PUNCT
ejpam-3300	18	6	the	the	DET
ejpam-3300	18	7	author	author	NOUN
ejpam-3300	18	8	proved	prove	VERB
ejpam-3300	18	9	the	the	DET
ejpam-3300	18	10	agm	agm	PROPN
ejpam-3300	18	11	inequality	inequality	NOUN
ejpam-3300	18	12	through	through	ADP
ejpam-3300	18	13	taylor	taylor	PROPN
ejpam-3300	18	14	’s	’s	PART
ejpam-3300	18	15	theorem	theorem	VERB
ejpam-3300	18	16	about	about	ADP
ejpam-3300	18	17	x	x	SYM
ejpam-3300	18	18	=	=	SYM
ejpam-3300	18	19	1	1	NUM
ejpam-3300	18	20	2	2	NUM
ejpam-3300	18	21	by	by	ADP
ejpam-3300	18	22	setting	set	VERB
ejpam-3300	18	23	the	the	DET
ejpam-3300	18	24	function	function	NOUN
ejpam-3300	18	25	f(x	f(x	PROPN
ejpam-3300	18	26	)	)	PUNCT
ejpam-3300	18	27	equals	equal	VERB
ejpam-3300	18	28	to	to	ADP
ejpam-3300	18	29	the	the	DET
ejpam-3300	18	30	heinz	heinz	ADJ
ejpam-3300	18	31	mean	mean	NOUN
ejpam-3300	18	32	.	.	PUNCT
ejpam-3300	19	1	thus	thus	ADV
ejpam-3300	19	2	,	,	PUNCT
ejpam-3300	19	3	f(x	f(x	PROPN
ejpam-3300	19	4	)	)	PUNCT
ejpam-3300	19	5	=	=	PUNCT
ejpam-3300	20	1	axb1−x	axb1−x	PROPN
ejpam-3300	21	1	+	+	CCONJ
ejpam-3300	21	2	a1−xbx	a1−xbx	ADP
ejpam-3300	21	3	2	2	NUM
ejpam-3300	21	4	,	,	PUNCT
ejpam-3300	21	5	∀	∀	X
ejpam-3300	21	6	0	0	NUM
ejpam-3300	21	7	≤	≤	NUM
ejpam-3300	21	8	x	x	SYM
ejpam-3300	21	9	≤	≤	NUM
ejpam-3300	21	10	1	1	NUM
ejpam-3300	21	11	and	and	CCONJ
ejpam-3300	21	12	f	f	PROPN
ejpam-3300	21	13	∈	∈	PROPN
ejpam-3300	21	14	c2[0	c2[0	PROPN
ejpam-3300	21	15	,	,	PUNCT
ejpam-3300	21	16	1	1	NUM
ejpam-3300	21	17	]	]	PUNCT
ejpam-3300	21	18	.	.	PUNCT
ejpam-3300	22	1	in	in	ADP
ejpam-3300	22	2	a	a	DET
ejpam-3300	22	3	similar	similar	ADJ
ejpam-3300	22	4	development	development	NOUN
ejpam-3300	22	5	,	,	PUNCT
ejpam-3300	22	6	another	another	DET
ejpam-3300	22	7	refinement	refinement	NOUN
ejpam-3300	22	8	of	of	ADP
ejpam-3300	22	9	the	the	DET
ejpam-3300	22	10	agm	agm	PROPN
ejpam-3300	22	11	inequality	inequality	NOUN
ejpam-3300	22	12	was	be	AUX
ejpam-3300	22	13	given	give	VERB
ejpam-3300	22	14	by	by	ADP
ejpam-3300	22	15	the	the	DET
ejpam-3300	22	16	authors	author	NOUN
ejpam-3300	22	17	in	in	ADP
ejpam-3300	22	18	[	[	X
ejpam-3300	22	19	8	8	NUM
ejpam-3300	22	20	]	]	PUNCT
ejpam-3300	22	21	.	.	PUNCT
ejpam-3300	23	1	they	they	PRON
ejpam-3300	23	2	obtained	obtain	VERB
ejpam-3300	23	3	their	their	PRON
ejpam-3300	23	4	result	result	NOUN
ejpam-3300	23	5	through	through	ADP
ejpam-3300	23	6	taylor	taylor	PROPN
ejpam-3300	23	7	’s	’s	PART
ejpam-3300	23	8	theorem	theorem	VERB
ejpam-3300	23	9	about	about	ADP
ejpam-3300	23	10	x	x	SYM
ejpam-3300	23	11	=	=	SYM
ejpam-3300	23	12	1	1	NUM
ejpam-3300	23	13	2	2	NUM
ejpam-3300	23	14	,	,	PUNCT
ejpam-3300	23	15	by	by	ADP
ejpam-3300	23	16	setting	set	VERB
ejpam-3300	23	17	f(x	f(x	PROPN
ejpam-3300	23	18	)	)	PUNCT
ejpam-3300	24	1	=	=	NOUN
ejpam-3300	24	2	ax	ax	NOUN
ejpam-3300	24	3	+	+	CCONJ
ejpam-3300	24	4	a1−x	a1−x	PROPN
ejpam-3300	24	5	2	2	NUM
ejpam-3300	24	6	,	,	PUNCT
ejpam-3300	24	7	∀	∀	X
ejpam-3300	24	8	0	0	NUM
ejpam-3300	24	9	≤	≤	NUM
ejpam-3300	24	10	x	x	SYM
ejpam-3300	24	11	≤	≤	NUM
ejpam-3300	24	12	1	1	NUM
ejpam-3300	24	13	and	and	CCONJ
ejpam-3300	24	14	f	f	PROPN
ejpam-3300	24	15	∈	∈	PROPN
ejpam-3300	24	16	ck(0,∞	ck(0,∞	NOUN
ejpam-3300	24	17	)	)	PUNCT
ejpam-3300	24	18	.	.	PUNCT
ejpam-3300	25	1	notwithstanding	notwithstanding	ADP
ejpam-3300	25	2	,	,	PUNCT
ejpam-3300	25	3	in	in	ADP
ejpam-3300	25	4	[	[	PUNCT
ejpam-3300	25	5	9	9	NUM
ejpam-3300	25	6	]	]	PUNCT
ejpam-3300	25	7	,	,	PUNCT
ejpam-3300	25	8	the	the	DET
ejpam-3300	25	9	authors	author	NOUN
ejpam-3300	25	10	proved	prove	VERB
ejpam-3300	25	11	the	the	DET
ejpam-3300	25	12	agm	agm	PROPN
ejpam-3300	25	13	inequality	inequality	NOUN
ejpam-3300	25	14	with	with	ADP
ejpam-3300	25	15	the	the	DET
ejpam-3300	25	16	use	use	NOUN
ejpam-3300	25	17	of	of	ADP
ejpam-3300	25	18	second	second	ADJ
ejpam-3300	25	19	derivative	derivative	ADJ
ejpam-3300	25	20	test	test	NOUN
ejpam-3300	25	21	by	by	ADP
ejpam-3300	25	22	setting	set	VERB
ejpam-3300	25	23	f(x	f(x	PROPN
ejpam-3300	25	24	)	)	PUNCT
ejpam-3300	25	25	=	=	PUNCT
ejpam-3300	26	1	(	(	PUNCT
ejpam-3300	26	2	x−	x−	PROPN
ejpam-3300	26	3	a)2	a)2	PROPN
ejpam-3300	26	4	a(x+	a(x+	PROPN
ejpam-3300	26	5	max{x	max{x	PROPN
ejpam-3300	26	6	,	,	PUNCT
ejpam-3300	26	7	a	a	PRON
ejpam-3300	26	8	}	}	PUNCT
ejpam-3300	26	9	)	)	PUNCT
ejpam-3300	27	1	+	+	CCONJ
ejpam-3300	27	2	lnx	lnx	PROPN
ejpam-3300	27	3	,	,	PUNCT
ejpam-3300	27	4	∀	∀	X
ejpam-3300	27	5	a	a	DET
ejpam-3300	27	6	>	>	X
ejpam-3300	27	7	0	0	NUM
ejpam-3300	27	8	and	and	CCONJ
ejpam-3300	27	9	f	f	PROPN
ejpam-3300	27	10	∈	∈	PROPN
ejpam-3300	27	11	c2(0,∞	c2(0,∞	NOUN
ejpam-3300	27	12	)	)	PUNCT
ejpam-3300	27	13	.	.	PUNCT
ejpam-3300	28	1	some	some	DET
ejpam-3300	28	2	researchers	researcher	NOUN
ejpam-3300	28	3	have	have	AUX
ejpam-3300	28	4	applied	apply	VERB
ejpam-3300	28	5	agm	agm	PROPN
ejpam-3300	28	6	inequality	inequality	NOUN
ejpam-3300	28	7	to	to	PART
ejpam-3300	28	8	solve	solve	VERB
ejpam-3300	28	9	matrix	matrix	NOUN
ejpam-3300	28	10	algebra	algebra	NOUN
ejpam-3300	28	11	.	.	PUNCT
ejpam-3300	29	1	for	for	ADP
ejpam-3300	29	2	example	example	NOUN
ejpam-3300	29	3	,	,	PUNCT
ejpam-3300	29	4	see	see	VERB
ejpam-3300	29	5	authors	author	NOUN
ejpam-3300	29	6	in	in	ADP
ejpam-3300	29	7	[	[	X
ejpam-3300	29	8	10	10	NUM
ejpam-3300	29	9	,	,	PUNCT
ejpam-3300	29	10	11	11	NUM
ejpam-3300	29	11	]	]	PUNCT
ejpam-3300	29	12	.	.	PUNCT
ejpam-3300	30	1	the	the	DET
ejpam-3300	30	2	author	author	NOUN
ejpam-3300	30	3	in	in	ADP
ejpam-3300	30	4	[	[	X
ejpam-3300	30	5	12	12	NUM
ejpam-3300	30	6	]	]	PUNCT
ejpam-3300	30	7	extended	extend	VERB
ejpam-3300	30	8	the	the	DET
ejpam-3300	30	9	agm	agm	PROPN
ejpam-3300	30	10	inequality	inequality	NOUN
ejpam-3300	30	11	to	to	PART
ejpam-3300	30	12	include	include	VERB
ejpam-3300	30	13	the	the	DET
ejpam-3300	30	14	harmonic	harmonic	ADJ
ejpam-3300	30	15	mean	mean	NOUN
ejpam-3300	30	16	called	call	VERB
ejpam-3300	30	17	aghm	aghm	ADJ
ejpam-3300	30	18	inequality	inequality	NOUN
ejpam-3300	30	19	.	.	PUNCT
ejpam-3300	31	1	in	in	ADP
ejpam-3300	31	2	this	this	DET
ejpam-3300	31	3	paper	paper	NOUN
ejpam-3300	31	4	,	,	PUNCT
ejpam-3300	31	5	the	the	DET
ejpam-3300	31	6	agm	agm	PROPN
ejpam-3300	31	7	inequality	inequality	NOUN
ejpam-3300	31	8	is	be	AUX
ejpam-3300	31	9	proved	prove	VERB
ejpam-3300	31	10	through	through	ADP
ejpam-3300	31	11	the	the	DET
ejpam-3300	31	12	first	first	ADJ
ejpam-3300	31	13	product	product	NOUN
ejpam-3300	31	14	inequality	inequality	NOUN
ejpam-3300	31	15	in	in	ADP
ejpam-3300	31	16	a	a	DET
ejpam-3300	31	17	closed	closed	ADJ
ejpam-3300	31	18	interval	interval	NOUN
ejpam-3300	31	19	[	[	X
ejpam-3300	31	20	0	0	NUM
ejpam-3300	31	21	,	,	PUNCT
ejpam-3300	31	22	2	2	NUM
ejpam-3300	31	23	]	]	PUNCT
ejpam-3300	31	24	,	,	PUNCT
ejpam-3300	31	25	then	then	ADV
ejpam-3300	31	26	through	through	ADP
ejpam-3300	31	27	the	the	DET
ejpam-3300	31	28	second	second	ADJ
ejpam-3300	31	29	product	product	NOUN
ejpam-3300	31	30	inequality	inequality	NOUN
ejpam-3300	31	31	in	in	ADP
ejpam-3300	31	32	a	a	DET
ejpam-3300	31	33	half	half	ADJ
ejpam-3300	31	34	open	open	ADJ
ejpam-3300	31	35	ended	end	VERB
ejpam-3300	31	36	interval	interval	NOUN
ejpam-3300	31	37	[	[	X
ejpam-3300	31	38	2,∞	2,∞	NUM
ejpam-3300	31	39	)	)	PUNCT
ejpam-3300	31	40	and	and	CCONJ
ejpam-3300	31	41	finally	finally	ADV
ejpam-3300	31	42	,	,	PUNCT
ejpam-3300	31	43	through	through	ADP
ejpam-3300	31	44	the	the	DET
ejpam-3300	31	45	binomial	binomial	ADJ
ejpam-3300	31	46	inequalities	inequality	NOUN
ejpam-3300	31	47	of	of	ADP
ejpam-3300	31	48	rational	rational	ADJ
ejpam-3300	31	49	numbers	number	NOUN
ejpam-3300	31	50	.	.	PUNCT
ejpam-3300	32	1	definition	definition	NOUN
ejpam-3300	32	2	1	1	NUM
ejpam-3300	32	3	.	.	PUNCT
ejpam-3300	33	1	let	let	VERB
ejpam-3300	33	2	a	a	PRON
ejpam-3300	33	3	be	be	AUX
ejpam-3300	33	4	a	a	DET
ejpam-3300	33	5	linear	linear	ADJ
ejpam-3300	33	6	vector	vector	NOUN
ejpam-3300	33	7	space	space	NOUN
ejpam-3300	33	8	defined	define	VERB
ejpam-3300	33	9	over	over	ADP
ejpam-3300	33	10	the	the	DET
ejpam-3300	33	11	real	real	ADJ
ejpam-3300	33	12	number	number	NOUN
ejpam-3300	33	13	field	field	NOUN
ejpam-3300	33	14	r.	r.	VERB
ejpam-3300	33	15	a	a	DET
ejpam-3300	33	16	scalar	scalar	ADV
ejpam-3300	33	17	-	-	PUNCT
ejpam-3300	33	18	valued	value	VERB
ejpam-3300	33	19	function	function	NOUN
ejpam-3300	33	20	p	p	NOUN
ejpam-3300	33	21	:	:	PUNCT
ejpam-3300	33	22	a×a→	a×a→	PROPN
ejpam-3300	33	23	r	r	NOUN
ejpam-3300	33	24	that	that	PRON
ejpam-3300	33	25	associates	associate	NOUN
ejpam-3300	33	26	with	with	ADP
ejpam-3300	33	27	each	each	DET
ejpam-3300	33	28	pair	pair	NOUN
ejpam-3300	33	29	a1	a1	NOUN
ejpam-3300	33	30	,	,	PUNCT
ejpam-3300	33	31	a2	a2	PROPN
ejpam-3300	33	32	of	of	ADP
ejpam-3300	33	33	vectors	vector	NOUN
ejpam-3300	33	34	in	in	ADP
ejpam-3300	33	35	a	a	DET
ejpam-3300	33	36	a	a	DET
ejpam-3300	33	37	scalar	scalar	ADJ
ejpam-3300	33	38	,	,	PUNCT
ejpam-3300	33	39	denoted	denote	VERB
ejpam-3300	33	40	(	(	PUNCT
ejpam-3300	33	41	a1	a1	NOUN
ejpam-3300	33	42	,	,	PUNCT
ejpam-3300	33	43	a2	a2	PROPN
ejpam-3300	33	44	)	)	PUNCT
ejpam-3300	33	45	,	,	PUNCT
ejpam-3300	33	46	is	be	AUX
ejpam-3300	33	47	called	call	VERB
ejpam-3300	33	48	an	an	DET
ejpam-3300	33	49	inner	inner	ADJ
ejpam-3300	33	50	product	product	NOUN
ejpam-3300	33	51	on	on	ADP
ejpam-3300	33	52	a	a	DET
ejpam-3300	33	53	if	if	NOUN
ejpam-3300	33	54	and	and	CCONJ
ejpam-3300	33	55	only	only	ADV
ejpam-3300	33	56	if	if	SCONJ
ejpam-3300	33	57	(	(	PUNCT
ejpam-3300	33	58	i	i	NOUN
ejpam-3300	33	59	)	)	PUNCT
ejpam-3300	33	60	(	(	PUNCT
ejpam-3300	33	61	a1	a1	PROPN
ejpam-3300	33	62	,	,	PUNCT
ejpam-3300	33	63	a2	a2	PROPN
ejpam-3300	33	64	)	)	PUNCT
ejpam-3300	33	65	>	>	X
ejpam-3300	33	66	0	0	PUNCT
ejpam-3300	34	1	whenever	whenever	SCONJ
ejpam-3300	34	2	a	a	DET
ejpam-3300	34	3	6=	6=	NUM
ejpam-3300	34	4	0	0	NUM
ejpam-3300	34	5	,	,	PUNCT
ejpam-3300	34	6	and	and	CCONJ
ejpam-3300	34	7	(	(	PUNCT
ejpam-3300	34	8	a1	a1	NOUN
ejpam-3300	34	9	,	,	PUNCT
ejpam-3300	34	10	a1	a1	NOUN
ejpam-3300	34	11	)	)	PUNCT
ejpam-3300	34	12	=	=	SYM
ejpam-3300	34	13	0	0	PUNCT
ejpam-3300	34	14	if	if	SCONJ
ejpam-3300	34	15	and	and	CCONJ
ejpam-3300	34	16	only	only	ADV
ejpam-3300	34	17	if	if	SCONJ
ejpam-3300	34	18	a1	a1	NOUN
ejpam-3300	34	19	=	=	SYM
ejpam-3300	34	20	0	0	NUM
ejpam-3300	34	21	(	(	PUNCT
ejpam-3300	34	22	ii	ii	NOUN
ejpam-3300	34	23	)	)	PUNCT
ejpam-3300	34	24	(	(	PUNCT
ejpam-3300	34	25	a1	a1	PROPN
ejpam-3300	34	26	,	,	PUNCT
ejpam-3300	34	27	a2	a2	NOUN
ejpam-3300	34	28	)	)	PUNCT
ejpam-3300	34	29	=	=	SYM
ejpam-3300	34	30	(	(	PUNCT
ejpam-3300	34	31	a2	a2	PROPN
ejpam-3300	34	32	,	,	PUNCT
ejpam-3300	34	33	a1	a1	NOUN
ejpam-3300	34	34	)	)	PUNCT
ejpam-3300	34	35	,	,	PUNCT
ejpam-3300	34	36	∀	∀	X
ejpam-3300	34	37	a1	a1	NOUN
ejpam-3300	34	38	,	,	PUNCT
ejpam-3300	34	39	a2	a2	PROPN
ejpam-3300	34	40	∈	∈	PROPN
ejpam-3300	34	41	a	a	DET
ejpam-3300	34	42	(	(	PUNCT
ejpam-3300	34	43	iii	iii	NOUN
ejpam-3300	34	44	)	)	PUNCT
ejpam-3300	34	45	(	(	PUNCT
ejpam-3300	34	46	αa1	αa1	PROPN
ejpam-3300	34	47	+	+	CCONJ
ejpam-3300	34	48	βa2	βa2	PROPN
ejpam-3300	34	49	,	,	PUNCT
ejpam-3300	34	50	a3	a3	NOUN
ejpam-3300	34	51	)	)	PUNCT
ejpam-3300	34	52	=	=	SYM
ejpam-3300	34	53	α(a1	α(a1	NOUN
ejpam-3300	34	54	,	,	PUNCT
ejpam-3300	34	55	a3	a3	NOUN
ejpam-3300	34	56	)	)	PUNCT
ejpam-3300	34	57	+	+	CCONJ
ejpam-3300	34	58	β(a2	β(a2	ADJ
ejpam-3300	34	59	,	,	PUNCT
ejpam-3300	34	60	a3	a3	NOUN
ejpam-3300	34	61	)	)	PUNCT
ejpam-3300	34	62	,	,	PUNCT
ejpam-3300	34	63	∀	∀	X
ejpam-3300	34	64	α	α	NOUN
ejpam-3300	34	65	,	,	PUNCT
ejpam-3300	34	66	β	β	X
ejpam-3300	34	67	∈	∈	NOUN
ejpam-3300	34	68	r	r	NOUN
ejpam-3300	34	69	,	,	PUNCT
ejpam-3300	34	70	and	and	CCONJ
ejpam-3300	34	71	a1	a1	NOUN
ejpam-3300	34	72	,	,	PUNCT
ejpam-3300	34	73	a2	a2	PROPN
ejpam-3300	34	74	,	,	PUNCT
ejpam-3300	34	75	a3	a3	NOUN
ejpam-3300	34	76	∈	∈	PROPN
ejpam-3300	34	77	v	v	NOUN
ejpam-3300	34	78	.	.	PUNCT
ejpam-3300	35	1	see	see	VERB
ejpam-3300	35	2	[	[	X
ejpam-3300	35	3	13	13	NUM
ejpam-3300	35	4	]	]	PUNCT
ejpam-3300	35	5	definition	definition	NOUN
ejpam-3300	35	6	2	2	NUM
ejpam-3300	35	7	.	.	PUNCT
ejpam-3300	36	1	let	let	VERB
ejpam-3300	36	2	a	a	PRON
ejpam-3300	36	3	be	be	AUX
ejpam-3300	36	4	a	a	DET
ejpam-3300	36	5	linear	linear	ADJ
ejpam-3300	36	6	space	space	NOUN
ejpam-3300	36	7	over	over	ADP
ejpam-3300	36	8	r.	r.	PROPN
ejpam-3300	36	9	a	a	DET
ejpam-3300	36	10	norm	norm	NOUN
ejpam-3300	36	11	on	on	ADP
ejpam-3300	36	12	a	a	PRON
ejpam-3300	36	13	is	be	AUX
ejpam-3300	36	14	a	a	DET
ejpam-3300	36	15	real	real	ADV
ejpam-3300	36	16	-	-	PUNCT
ejpam-3300	36	17	valued	value	VERB
ejpam-3300	36	18	function	function	NOUN
ejpam-3300	36	19	‖	‖	PROPN
ejpam-3300	36	20	·	·	PROPN
ejpam-3300	36	21	‖	‖	ADJ
ejpam-3300	36	22	:	:	PUNCT
ejpam-3300	36	23	a→	a→	X
ejpam-3300	36	24	[	[	X
ejpam-3300	36	25	0,∞	0,∞	X
ejpam-3300	36	26	)	)	PUNCT
ejpam-3300	36	27	such	such	ADJ
ejpam-3300	36	28	that	that	PRON
ejpam-3300	36	29	for	for	ADP
ejpam-3300	36	30	any	any	DET
ejpam-3300	36	31	a1	a1	NOUN
ejpam-3300	36	32	,	,	PUNCT
ejpam-3300	36	33	a2	a2	PROPN
ejpam-3300	36	34	∈	∈	PROPN
ejpam-3300	36	35	a	a	PRON
ejpam-3300	36	36	and	and	CCONJ
ejpam-3300	36	37	α	α	NOUN
ejpam-3300	36	38	∈	∈	NOUN
ejpam-3300	36	39	r	r	NOUN
ejpam-3300	36	40	the	the	DET
ejpam-3300	36	41	following	follow	VERB
ejpam-3300	36	42	conditions	condition	NOUN
ejpam-3300	36	43	are	be	AUX
ejpam-3300	36	44	met	meet	VERB
ejpam-3300	36	45	:	:	PUNCT
ejpam-3300	37	1	‖a‖	‖a‖	X
ejpam-3300	37	2	≥	≥	NOUN
ejpam-3300	37	3	0	0	NUM
ejpam-3300	37	4	,	,	PUNCT
ejpam-3300	37	5	and	and	CCONJ
ejpam-3300	37	6	‖a‖	‖a‖	PROPN
ejpam-3300	37	7	=	=	SYM
ejpam-3300	37	8	0	0	NUM
ejpam-3300	37	9	,	,	PUNCT
ejpam-3300	37	10	iff	iff	VERB
ejpam-3300	37	11	a	a	PRON
ejpam-3300	37	12	=	=	NOUN
ejpam-3300	37	13	0	0	NUM
ejpam-3300	37	14	‖αa‖	‖αa‖	X
ejpam-3300	37	15	=	=	SYM
ejpam-3300	37	16	|α|‖ua‖	|α|‖ua‖	PROPN
ejpam-3300	37	17	,	,	PUNCT
ejpam-3300	37	18	∀	∀	X
ejpam-3300	37	19	a	a	DET
ejpam-3300	37	20	∈	∈	PROPN
ejpam-3300	37	21	a	a	PRON
ejpam-3300	37	22	and	and	CCONJ
ejpam-3300	37	23	α	α	NOUN
ejpam-3300	37	24	∈	∈	NOUN
ejpam-3300	37	25	r	r	NOUN
ejpam-3300	37	26	‖a1	‖a1	NOUN
ejpam-3300	37	27	±	±	NUM
ejpam-3300	37	28	a2‖	a2‖	PROPN
ejpam-3300	37	29	≤	≤	NOUN
ejpam-3300	38	1	‖a1‖+	‖a1‖+	NOUN
ejpam-3300	38	2	‖a2‖	‖a2‖	PROPN
ejpam-3300	38	3	,	,	PUNCT
ejpam-3300	38	4	∀	∀	X
ejpam-3300	38	5	a1	a1	NOUN
ejpam-3300	38	6	,	,	PUNCT
ejpam-3300	38	7	a2	a2	PROPN
ejpam-3300	38	8	∈	∈	PROPN
ejpam-3300	38	9	a	a	PRON
ejpam-3300	38	10	,	,	PUNCT
ejpam-3300	38	11	see	see	VERB
ejpam-3300	38	12	[	[	X
ejpam-3300	38	13	14	14	NUM
ejpam-3300	38	14	]	]	PUNCT
ejpam-3300	38	15	.	.	PUNCT
ejpam-3300	39	1	b.	b.	PROPN
ejpam-3300	39	2	barnes	barnes	PROPN
ejpam-3300	39	3	et	et	PROPN
ejpam-3300	39	4	al	al	PROPN
ejpam-3300	39	5	.	.	PUNCT
ejpam-3300	39	6	/	/	SYM
ejpam-3300	39	7	eur	eur	PROPN
ejpam-3300	39	8	.	.	PUNCT
ejpam-3300	40	1	j.	j.	PROPN
ejpam-3300	40	2	pure	pure	PROPN
ejpam-3300	40	3	appl	appl	PROPN
ejpam-3300	40	4	.	.	PROPN
ejpam-3300	40	5	math	math	PROPN
ejpam-3300	40	6	,	,	PUNCT
ejpam-3300	40	7	11	11	NUM
ejpam-3300	40	8	(	(	PUNCT
ejpam-3300	40	9	4	4	NUM
ejpam-3300	40	10	)	)	PUNCT
ejpam-3300	40	11	(	(	PUNCT
ejpam-3300	40	12	2018	2018	NUM
ejpam-3300	40	13	)	)	PUNCT
ejpam-3300	40	14	,	,	PUNCT
ejpam-3300	40	15	1100	1100	NUM
ejpam-3300	40	16	-	-	SYM
ejpam-3300	40	17	1107	1107	NUM
ejpam-3300	40	18	1102	1102	NUM
ejpam-3300	40	19	definition	definition	NOUN
ejpam-3300	40	20	3	3	NUM
ejpam-3300	40	21	(	(	PUNCT
ejpam-3300	40	22	first	first	ADJ
ejpam-3300	40	23	and	and	CCONJ
ejpam-3300	40	24	second	second	ADJ
ejpam-3300	40	25	product	product	NOUN
ejpam-3300	40	26	inequalities	inequality	NOUN
ejpam-3300	40	27	)	)	PUNCT
ejpam-3300	40	28	.	.	PUNCT
ejpam-3300	41	1	let	let	VERB
ejpam-3300	41	2	a1	a1	NOUN
ejpam-3300	41	3	and	and	CCONJ
ejpam-3300	41	4	a2	a2	PROPN
ejpam-3300	41	5	be	be	VERB
ejpam-3300	41	6	any	any	DET
ejpam-3300	41	7	two	two	NUM
ejpam-3300	41	8	positive	positive	ADJ
ejpam-3300	41	9	real	real	ADJ
ejpam-3300	41	10	numbers	number	NOUN
ejpam-3300	41	11	,	,	PUNCT
ejpam-3300	41	12	then	then	ADV
ejpam-3300	41	13	(	(	PUNCT
ejpam-3300	41	14	i)‖a1‖‖a2‖	i)‖a1‖‖a2‖	NOUN
ejpam-3300	41	15	≤	≤	ADJ
ejpam-3300	41	16	‖a1‖+	‖a1‖+	NUM
ejpam-3300	41	17	‖a2‖	‖a2‖	PROPN
ejpam-3300	41	18	,	,	PUNCT
ejpam-3300	41	19	∀a1	∀a1	PROPN
ejpam-3300	41	20	,	,	PUNCT
ejpam-3300	41	21	a2	a2	PROPN
ejpam-3300	41	22	∈	∈	PROPN
ejpam-3300	42	1	[	[	X
ejpam-3300	42	2	0	0	NUM
ejpam-3300	42	3	,	,	PUNCT
ejpam-3300	42	4	2	2	NUM
ejpam-3300	42	5	]	]	PUNCT
ejpam-3300	42	6	.	.	PUNCT
ejpam-3300	43	1	(	(	PUNCT
ejpam-3300	43	2	1	1	X
ejpam-3300	43	3	)	)	PUNCT
ejpam-3300	43	4	(	(	PUNCT
ejpam-3300	43	5	ii)‖a1‖+	ii)‖a1‖+	NOUN
ejpam-3300	43	6	‖a2‖	‖a2‖	PROPN
ejpam-3300	43	7	≤	≤	PROPN
ejpam-3300	43	8	‖a1‖‖a2‖	‖a1‖‖a2‖	NUM
ejpam-3300	43	9	,	,	PUNCT
ejpam-3300	43	10	∀a1	∀a1	PROPN
ejpam-3300	43	11	,	,	PUNCT
ejpam-3300	43	12	a2	a2	PROPN
ejpam-3300	43	13	∈	∈	PROPN
ejpam-3300	44	1	[	[	X
ejpam-3300	44	2	2,∞	2,∞	NUM
ejpam-3300	44	3	)	)	PUNCT
ejpam-3300	44	4	.	.	PUNCT
ejpam-3300	45	1	(	(	PUNCT
ejpam-3300	45	2	2	2	X
ejpam-3300	45	3	)	)	PUNCT
ejpam-3300	45	4	see	see	VERB
ejpam-3300	45	5	[	[	X
ejpam-3300	45	6	15	15	NUM
ejpam-3300	45	7	]	]	SYM
ejpam-3300	45	8	.	.	PUNCT
ejpam-3300	46	1	1.1	1.1	NUM
ejpam-3300	46	2	.	.	PUNCT
ejpam-3300	47	1	the	the	DET
ejpam-3300	47	2	proof	proof	NOUN
ejpam-3300	47	3	of	of	ADP
ejpam-3300	47	4	the	the	DET
ejpam-3300	47	5	agm	agm	PROPN
ejpam-3300	47	6	inequality	inequality	NOUN
ejpam-3300	47	7	through	through	ADP
ejpam-3300	47	8	the	the	DET
ejpam-3300	47	9	first	first	ADJ
ejpam-3300	47	10	product	product	NOUN
ejpam-3300	47	11	inequality	inequality	NOUN
ejpam-3300	47	12	in	in	ADP
ejpam-3300	47	13	this	this	DET
ejpam-3300	47	14	section	section	NOUN
ejpam-3300	47	15	,	,	PUNCT
ejpam-3300	47	16	we	we	PRON
ejpam-3300	47	17	obtain	obtain	VERB
ejpam-3300	47	18	the	the	DET
ejpam-3300	47	19	agm	agm	PROPN
ejpam-3300	47	20	inequality	inequality	NOUN
ejpam-3300	47	21	through	through	ADP
ejpam-3300	47	22	both	both	CCONJ
ejpam-3300	47	23	the	the	DET
ejpam-3300	47	24	first	first	ADJ
ejpam-3300	47	25	and	and	CCONJ
ejpam-3300	47	26	second	second	ADJ
ejpam-3300	47	27	product	product	NOUN
ejpam-3300	47	28	inequalities	inequality	NOUN
ejpam-3300	47	29	by	by	ADP
ejpam-3300	47	30	induction	induction	NOUN
ejpam-3300	47	31	as	as	SCONJ
ejpam-3300	47	32	follows	follow	VERB
ejpam-3300	47	33	.	.	PUNCT
ejpam-3300	48	1	multiplying	multiply	VERB
ejpam-3300	48	2	both	both	DET
ejpam-3300	48	3	sides	side	NOUN
ejpam-3300	48	4	of	of	ADP
ejpam-3300	48	5	inequality	inequality	NOUN
ejpam-3300	48	6	(	(	PUNCT
ejpam-3300	48	7	1	1	NUM
ejpam-3300	48	8	)	)	PUNCT
ejpam-3300	48	9	by	by	ADP
ejpam-3300	48	10	(	(	PUNCT
ejpam-3300	48	11	1−	1−	NUM
ejpam-3300	48	12	p	p	NOUN
ejpam-3300	48	13	)	)	PUNCT
ejpam-3300	48	14	yields	yield	NOUN
ejpam-3300	48	15	(	(	PUNCT
ejpam-3300	48	16	1−	1−	NUM
ejpam-3300	48	17	p	p	NOUN
ejpam-3300	48	18	)	)	PUNCT
ejpam-3300	48	19	(	(	PUNCT
ejpam-3300	48	20	‖a1‖‖a2‖	‖a1‖‖a2‖	CCONJ
ejpam-3300	48	21	)	)	PUNCT
ejpam-3300	48	22	≤	≤	NOUN
ejpam-3300	48	23	(	(	PUNCT
ejpam-3300	48	24	1−	1−	NUM
ejpam-3300	48	25	p	p	NOUN
ejpam-3300	48	26	)	)	PUNCT
ejpam-3300	48	27	{	{	PUNCT
ejpam-3300	48	28	‖a1‖+	‖a1‖+	NOUN
ejpam-3300	48	29	‖a2‖	‖a2‖	PROPN
ejpam-3300	48	30	}	}	PUNCT
ejpam-3300	48	31	,	,	PUNCT
ejpam-3300	48	32	∀	∀	PUNCT
ejpam-3300	48	33	p	p	NOUN
ejpam-3300	48	34	∈	∈	PROPN
ejpam-3300	49	1	[	[	X
ejpam-3300	49	2	0	0	NUM
ejpam-3300	49	3	,	,	PUNCT
ejpam-3300	49	4	1	1	NUM
ejpam-3300	49	5	]	]	PUNCT
ejpam-3300	49	6	.	.	PUNCT
ejpam-3300	50	1	(	(	PUNCT
ejpam-3300	50	2	3	3	NUM
ejpam-3300	50	3	)	)	PUNCT
ejpam-3300	50	4	but	but	CCONJ
ejpam-3300	50	5	,	,	PUNCT
ejpam-3300	50	6	we	we	PRON
ejpam-3300	50	7	see	see	VERB
ejpam-3300	50	8	that	that	PRON
ejpam-3300	50	9	:(	:(	PUNCT
ejpam-3300	50	10	‖a1‖‖a2‖	‖a1‖‖a2‖	NUM
ejpam-3300	50	11	)	)	PUNCT
ejpam-3300	50	12	(	(	PUNCT
ejpam-3300	50	13	1−p	1−p	NUM
ejpam-3300	50	14	)	)	PUNCT
ejpam-3300	50	15	≤	≤	NOUN
ejpam-3300	50	16	(	(	PUNCT
ejpam-3300	50	17	1−	1−	NUM
ejpam-3300	50	18	p	p	NOUN
ejpam-3300	50	19	)	)	PUNCT
ejpam-3300	50	20	(	(	PUNCT
ejpam-3300	50	21	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	50	22	)	)	PUNCT
ejpam-3300	50	23	.	.	PUNCT
ejpam-3300	51	1	(	(	PUNCT
ejpam-3300	51	2	4	4	X
ejpam-3300	51	3	)	)	PUNCT
ejpam-3300	51	4	substituting	substitute	VERB
ejpam-3300	51	5	inequality	inequality	NOUN
ejpam-3300	51	6	(	(	PUNCT
ejpam-3300	51	7	4	4	NUM
ejpam-3300	51	8	)	)	PUNCT
ejpam-3300	51	9	into	into	ADP
ejpam-3300	51	10	inequality	inequality	NOUN
ejpam-3300	51	11	(	(	PUNCT
ejpam-3300	51	12	3	3	NUM
ejpam-3300	51	13	)	)	PUNCT
ejpam-3300	51	14	yields	yield	NOUN
ejpam-3300	51	15	(	(	PUNCT
ejpam-3300	51	16	‖a1‖‖a2‖	‖a1‖‖a2‖	NUM
ejpam-3300	51	17	)	)	PUNCT
ejpam-3300	51	18	(	(	PUNCT
ejpam-3300	51	19	1−p	1−p	NUM
ejpam-3300	51	20	)	)	PUNCT
ejpam-3300	51	21	≤	≤	NOUN
ejpam-3300	51	22	(	(	PUNCT
ejpam-3300	51	23	1−	1−	NUM
ejpam-3300	51	24	p	p	NOUN
ejpam-3300	51	25	)	)	PUNCT
ejpam-3300	51	26	(	(	PUNCT
ejpam-3300	51	27	‖a1‖+	‖a1‖+	NOUN
ejpam-3300	51	28	‖a2‖	‖a2‖	PROPN
ejpam-3300	51	29	)	)	PUNCT
ejpam-3300	51	30	.	.	PUNCT
ejpam-3300	52	1	(	(	PUNCT
ejpam-3300	52	2	5	5	X
ejpam-3300	52	3	)	)	PUNCT
ejpam-3300	52	4	setting	set	VERB
ejpam-3300	52	5	p	p	NOUN
ejpam-3300	52	6	=	=	NOUN
ejpam-3300	52	7	1	1	NUM
ejpam-3300	52	8	2	2	NUM
ejpam-3300	52	9	into	into	ADP
ejpam-3300	52	10	inequality	inequality	NOUN
ejpam-3300	52	11	(	(	PUNCT
ejpam-3300	52	12	5	5	NUM
ejpam-3300	52	13	)	)	PUNCT
ejpam-3300	52	14	yields	yield	NOUN
ejpam-3300	52	15	(	(	PUNCT
ejpam-3300	52	16	‖a1‖‖a2‖	‖a1‖‖a2‖	NUM
ejpam-3300	52	17	)	)	PUNCT
ejpam-3300	52	18	1	1	NUM
ejpam-3300	52	19	2	2	NUM
ejpam-3300	52	20	≤	≤	NUM
ejpam-3300	52	21	1	1	NUM
ejpam-3300	52	22	2	2	NUM
ejpam-3300	52	23	(	(	PUNCT
ejpam-3300	52	24	‖a1‖+	‖a1‖+	NOUN
ejpam-3300	52	25	‖a2‖	‖a2‖	ADJ
ejpam-3300	52	26	)	)	PUNCT
ejpam-3300	52	27	⇒	⇒	NOUN
ejpam-3300	52	28	(	(	PUNCT
ejpam-3300	52	29	2∏	2∏	NUM
ejpam-3300	52	30	i=1	i=1	INTJ
ejpam-3300	53	1	ai	ai	VERB
ejpam-3300	53	2	)	)	PUNCT
ejpam-3300	53	3	1	1	NUM
ejpam-3300	53	4	2	2	NUM
ejpam-3300	53	5	≤	≤	NUM
ejpam-3300	53	6	1	1	NUM
ejpam-3300	53	7	2	2	NUM
ejpam-3300	53	8	2∑	2∑	NOUN
ejpam-3300	54	1	i=1	i=1	X
ejpam-3300	54	2	ai	ai	VERB
ejpam-3300	54	3	.	.	PUNCT
ejpam-3300	55	1	we	we	PRON
ejpam-3300	55	2	can	can	AUX
ejpam-3300	55	3	see	see	VERB
ejpam-3300	55	4	that	that	PRON
ejpam-3300	55	5	for	for	ADP
ejpam-3300	55	6	any	any	DET
ejpam-3300	55	7	three	three	NUM
ejpam-3300	55	8	positive	positive	ADJ
ejpam-3300	55	9	real	real	ADJ
ejpam-3300	55	10	numbers	number	NOUN
ejpam-3300	55	11	n	n	X
ejpam-3300	55	12	=	=	SYM
ejpam-3300	55	13	3	3	NUM
ejpam-3300	55	14	,	,	PUNCT
ejpam-3300	55	15	the	the	DET
ejpam-3300	55	16	following	follow	VERB
ejpam-3300	55	17	inequality	inequality	NOUN
ejpam-3300	55	18	holds	hold	VERB
ejpam-3300	55	19	.	.	PUNCT
ejpam-3300	56	1	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	VERB
ejpam-3300	56	2	≤	≤	NUM
ejpam-3300	56	3	‖a1‖+	‖a1‖+	NUM
ejpam-3300	56	4	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	56	5	‖a3‖	‖a3‖	NOUN
ejpam-3300	56	6	,	,	PUNCT
ejpam-3300	56	7	∀a1	∀a1	PROPN
ejpam-3300	56	8	,	,	PUNCT
ejpam-3300	56	9	a2	a2	PROPN
ejpam-3300	56	10	,	,	PUNCT
ejpam-3300	56	11	a3	a3	NOUN
ejpam-3300	56	12	∈	∈	PROPN
ejpam-3300	57	1	[	[	X
ejpam-3300	57	2	0	0	NUM
ejpam-3300	57	3	,	,	PUNCT
ejpam-3300	57	4	2	2	NUM
ejpam-3300	57	5	]	]	PUNCT
ejpam-3300	57	6	⇒	⇒	NOUN
ejpam-3300	57	7	(	(	PUNCT
ejpam-3300	57	8	1−	1−	NUM
ejpam-3300	57	9	p	p	NOUN
ejpam-3300	57	10	)	)	PUNCT
ejpam-3300	57	11	(	(	PUNCT
ejpam-3300	57	12	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	57	13	)	)	PUNCT
ejpam-3300	57	14	=	=	PUNCT
ejpam-3300	57	15	(	(	PUNCT
ejpam-3300	57	16	1−	1−	NUM
ejpam-3300	57	17	p	p	NOUN
ejpam-3300	57	18	)	)	PUNCT
ejpam-3300	57	19	(	(	PUNCT
ejpam-3300	57	20	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	57	21	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	57	22	‖a3‖	‖a3‖	NOUN
ejpam-3300	57	23	)	)	PUNCT
ejpam-3300	57	24	⇒	⇒	NOUN
ejpam-3300	57	25	(	(	PUNCT
ejpam-3300	57	26	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	57	27	)	)	PUNCT
ejpam-3300	57	28	(	(	PUNCT
ejpam-3300	57	29	1−p	1−p	NUM
ejpam-3300	57	30	)	)	PUNCT
ejpam-3300	57	31	≤	≤	NOUN
ejpam-3300	57	32	(	(	PUNCT
ejpam-3300	57	33	1−	1−	NUM
ejpam-3300	57	34	p	p	NOUN
ejpam-3300	57	35	)	)	PUNCT
ejpam-3300	57	36	(	(	PUNCT
ejpam-3300	57	37	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	57	38	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	57	39	‖a3‖	‖a3‖	NOUN
ejpam-3300	57	40	)	)	PUNCT
ejpam-3300	57	41	.	.	PUNCT
ejpam-3300	58	1	setting	set	VERB
ejpam-3300	58	2	p	p	NOUN
ejpam-3300	58	3	=	=	NOUN
ejpam-3300	58	4	2	2	NUM
ejpam-3300	58	5	3	3	NUM
ejpam-3300	58	6	into	into	ADP
ejpam-3300	58	7	the	the	DET
ejpam-3300	58	8	above	above	ADJ
ejpam-3300	58	9	inequality	inequality	NOUN
ejpam-3300	58	10	,	,	PUNCT
ejpam-3300	58	11	we	we	PRON
ejpam-3300	58	12	obtain	obtain	VERB
ejpam-3300	58	13	(	(	PUNCT
ejpam-3300	58	14	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	58	15	)	)	PUNCT
ejpam-3300	58	16	1	1	NUM
ejpam-3300	59	1	3	3	NUM
ejpam-3300	59	2	≤	≤	NUM
ejpam-3300	59	3	1	1	NUM
ejpam-3300	59	4	3	3	NUM
ejpam-3300	59	5	(	(	PUNCT
ejpam-3300	59	6	‖a1‖+	‖a1‖+	NUM
ejpam-3300	59	7	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	59	8	‖a3‖	‖a3‖	NOUN
ejpam-3300	59	9	)	)	PUNCT
ejpam-3300	59	10	b.	b.	PROPN
ejpam-3300	59	11	barnes	barnes	PROPN
ejpam-3300	59	12	et	et	PROPN
ejpam-3300	59	13	al	al	PROPN
ejpam-3300	59	14	.	.	PUNCT
ejpam-3300	59	15	/	/	SYM
ejpam-3300	59	16	eur	eur	PROPN
ejpam-3300	59	17	.	.	PUNCT
ejpam-3300	60	1	j.	j.	PROPN
ejpam-3300	60	2	pure	pure	PROPN
ejpam-3300	60	3	appl	appl	PROPN
ejpam-3300	60	4	.	.	PROPN
ejpam-3300	60	5	math	math	PROPN
ejpam-3300	60	6	,	,	PUNCT
ejpam-3300	60	7	11	11	NUM
ejpam-3300	60	8	(	(	PUNCT
ejpam-3300	60	9	4	4	NUM
ejpam-3300	60	10	)	)	PUNCT
ejpam-3300	60	11	(	(	PUNCT
ejpam-3300	60	12	2018	2018	NUM
ejpam-3300	60	13	)	)	PUNCT
ejpam-3300	60	14	,	,	PUNCT
ejpam-3300	60	15	1100	1100	NUM
ejpam-3300	60	16	-	-	SYM
ejpam-3300	60	17	1107	1107	NUM
ejpam-3300	60	18	1103	1103	NUM
ejpam-3300	60	19	⇒	⇒	NOUN
ejpam-3300	60	20	(	(	PUNCT
ejpam-3300	60	21	3∏	3∏	X
ejpam-3300	60	22	i=1	i=1	PROPN
ejpam-3300	60	23	ai	ai	VERB
ejpam-3300	60	24	)	)	PUNCT
ejpam-3300	60	25	1	1	NUM
ejpam-3300	60	26	3	3	NUM
ejpam-3300	60	27	≤	≤	NUM
ejpam-3300	60	28	1	1	NUM
ejpam-3300	60	29	3	3	NUM
ejpam-3300	60	30	3∑	3∑	NUM
ejpam-3300	60	31	i=1	i=1	PRON
ejpam-3300	60	32	ai	ai	VERB
ejpam-3300	60	33	.	.	PUNCT
ejpam-3300	61	1	for	for	ADP
ejpam-3300	61	2	any	any	DET
ejpam-3300	61	3	number	number	NOUN
ejpam-3300	61	4	of	of	ADP
ejpam-3300	61	5	positive	positive	ADJ
ejpam-3300	61	6	real	real	ADJ
ejpam-3300	61	7	numbers	number	NOUN
ejpam-3300	61	8	n	n	CCONJ
ejpam-3300	61	9	,	,	PUNCT
ejpam-3300	61	10	the	the	DET
ejpam-3300	61	11	following	follow	VERB
ejpam-3300	61	12	inequalities	inequality	NOUN
ejpam-3300	61	13	are	be	AUX
ejpam-3300	61	14	observed	observe	VERB
ejpam-3300	61	15	:	:	PUNCT
ejpam-3300	61	16	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	61	17	.	.	PUNCT
ejpam-3300	61	18	.	.	PUNCT
ejpam-3300	61	19	.	.	PUNCT
ejpam-3300	62	1	‖an‖	‖an‖	PROPN
ejpam-3300	62	2	≤	≤	NUM
ejpam-3300	63	1	‖a1‖+	‖a1‖+	NUM
ejpam-3300	63	2	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	63	3	.	.	PUNCT
ejpam-3300	63	4	.	.	PUNCT
ejpam-3300	64	1	.+	.+	PROPN
ejpam-3300	64	2	‖an‖	‖an‖	PROPN
ejpam-3300	64	3	∀a1	∀a1	PROPN
ejpam-3300	64	4	,	,	PUNCT
ejpam-3300	64	5	a2	a2	PROPN
ejpam-3300	64	6	,	,	PUNCT
ejpam-3300	64	7	.	.	PUNCT
ejpam-3300	64	8	.	.	PUNCT
ejpam-3300	65	1	.	.	PUNCT
ejpam-3300	66	1	,	,	PUNCT
ejpam-3300	66	2	an	an	DET
ejpam-3300	66	3	∈	∈	PROPN
ejpam-3300	67	1	[	[	X
ejpam-3300	67	2	0	0	NUM
ejpam-3300	67	3	,	,	PUNCT
ejpam-3300	67	4	2	2	NUM
ejpam-3300	67	5	]	]	PUNCT
ejpam-3300	67	6	⇒	⇒	NOUN
ejpam-3300	67	7	(	(	PUNCT
ejpam-3300	67	8	1−	1−	NUM
ejpam-3300	67	9	p	p	NOUN
ejpam-3300	67	10	)	)	PUNCT
ejpam-3300	67	11	(	(	PUNCT
ejpam-3300	67	12	‖a1‖‖a2‖	‖a1‖‖a2‖	X
ejpam-3300	67	13	,	,	PUNCT
ejpam-3300	67	14	.	.	PUNCT
ejpam-3300	67	15	.	.	PUNCT
ejpam-3300	68	1	.	.	PUNCT
ejpam-3300	69	1	,	,	PUNCT
ejpam-3300	69	2	‖an‖	‖an‖	PROPN
ejpam-3300	69	3	)	)	PUNCT
ejpam-3300	69	4	≤	≤	NOUN
ejpam-3300	69	5	(	(	PUNCT
ejpam-3300	69	6	1−	1−	NUM
ejpam-3300	69	7	p	p	NOUN
ejpam-3300	69	8	)	)	PUNCT
ejpam-3300	69	9	(	(	PUNCT
ejpam-3300	69	10	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	69	11	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	69	12	.	.	PUNCT
ejpam-3300	69	13	.	.	PUNCT
ejpam-3300	70	1	.+	.+	NOUN
ejpam-3300	70	2	‖an‖	‖an‖	PROPN
ejpam-3300	70	3	)	)	PUNCT
ejpam-3300	70	4	⇒	⇒	NOUN
ejpam-3300	70	5	(	(	PUNCT
ejpam-3300	70	6	‖a1‖‖a2‖	‖a1‖‖a2‖	NUM
ejpam-3300	70	7	,	,	PUNCT
ejpam-3300	70	8	.	.	PUNCT
ejpam-3300	70	9	.	.	PUNCT
ejpam-3300	70	10	.	.	PUNCT
ejpam-3300	71	1	,	,	PUNCT
ejpam-3300	71	2	‖an‖	‖an‖	PROPN
ejpam-3300	71	3	)	)	PUNCT
ejpam-3300	71	4	(	(	PUNCT
ejpam-3300	71	5	1−p	1−p	NUM
ejpam-3300	71	6	)	)	PUNCT
ejpam-3300	71	7	≤	≤	NOUN
ejpam-3300	71	8	(	(	PUNCT
ejpam-3300	71	9	1−	1−	NUM
ejpam-3300	71	10	p	p	NOUN
ejpam-3300	71	11	)	)	PUNCT
ejpam-3300	71	12	(	(	PUNCT
ejpam-3300	71	13	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	71	14	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	71	15	.	.	PUNCT
ejpam-3300	71	16	.	.	PUNCT
ejpam-3300	72	1	.+	.+	NOUN
ejpam-3300	72	2	‖an‖	‖an‖	PROPN
ejpam-3300	72	3	)	)	PUNCT
ejpam-3300	72	4	.	.	PUNCT
ejpam-3300	73	1	setting	set	VERB
ejpam-3300	73	2	p	p	X
ejpam-3300	73	3	=	=	X
ejpam-3300	73	4	(	(	PUNCT
ejpam-3300	73	5	n−1	n−1	PROPN
ejpam-3300	73	6	)	)	PUNCT
ejpam-3300	73	7	n	n	NOUN
ejpam-3300	73	8	into	into	ADP
ejpam-3300	73	9	the	the	DET
ejpam-3300	73	10	above	above	ADJ
ejpam-3300	73	11	inequality	inequality	NOUN
ejpam-3300	73	12	yields	yield	NOUN
ejpam-3300	73	13	(	(	PUNCT
ejpam-3300	73	14	‖a1‖‖a2‖	‖a1‖‖a2‖	NUM
ejpam-3300	73	15	,	,	PUNCT
ejpam-3300	73	16	.	.	PUNCT
ejpam-3300	73	17	.	.	PUNCT
ejpam-3300	74	1	.	.	PUNCT
ejpam-3300	75	1	,	,	PUNCT
ejpam-3300	75	2	‖an‖	‖an‖	PROPN
ejpam-3300	75	3	)	)	PUNCT
ejpam-3300	75	4	1	1	NUM
ejpam-3300	75	5	n	n	NOUN
ejpam-3300	75	6	≤	≤	NUM
ejpam-3300	75	7	1	1	NUM
ejpam-3300	75	8	n	n	NOUN
ejpam-3300	75	9	(	(	PUNCT
ejpam-3300	75	10	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	75	11	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	75	12	.	.	PUNCT
ejpam-3300	75	13	.	.	PUNCT
ejpam-3300	76	1	.+	.+	NOUN
ejpam-3300	76	2	‖an‖	‖an‖	PROPN
ejpam-3300	76	3	)	)	PUNCT
ejpam-3300	76	4	⇒	⇒	NOUN
ejpam-3300	76	5	(	(	PUNCT
ejpam-3300	76	6	n∏	n∏	PROPN
ejpam-3300	76	7	i=1	i=1	PROPN
ejpam-3300	76	8	ai	ai	VERB
ejpam-3300	76	9	)	)	PUNCT
ejpam-3300	76	10	1	1	NUM
ejpam-3300	76	11	n	n	DET
ejpam-3300	76	12	≤	≤	NUM
ejpam-3300	76	13	1	1	NUM
ejpam-3300	76	14	n	n	NUM
ejpam-3300	76	15	n∑	n∑	NOUN
ejpam-3300	76	16	i=1	i=1	PROPN
ejpam-3300	76	17	ai	ai	VERB
ejpam-3300	76	18	∀	∀	NOUN
ejpam-3300	76	19	a1	a1	NOUN
ejpam-3300	76	20	,	,	PUNCT
ejpam-3300	76	21	a2	a2	PROPN
ejpam-3300	76	22	,	,	PUNCT
ejpam-3300	76	23	.	.	PUNCT
ejpam-3300	76	24	.	.	PUNCT
ejpam-3300	77	1	.	.	PUNCT
ejpam-3300	78	1	,	,	PUNCT
ejpam-3300	78	2	an	an	DET
ejpam-3300	78	3	∈	∈	PROPN
ejpam-3300	79	1	[	[	X
ejpam-3300	79	2	0	0	NUM
ejpam-3300	79	3	,	,	PUNCT
ejpam-3300	79	4	2	2	NUM
ejpam-3300	79	5	]	]	PUNCT
ejpam-3300	79	6	.	.	PUNCT
ejpam-3300	80	1	1.2	1.2	NUM
ejpam-3300	80	2	.	.	PUNCT
ejpam-3300	81	1	the	the	DET
ejpam-3300	81	2	proof	proof	NOUN
ejpam-3300	81	3	of	of	ADP
ejpam-3300	81	4	the	the	DET
ejpam-3300	81	5	agm	agm	PROPN
ejpam-3300	81	6	inequality	inequality	NOUN
ejpam-3300	81	7	through	through	ADP
ejpam-3300	81	8	the	the	DET
ejpam-3300	81	9	second	second	ADJ
ejpam-3300	81	10	product	product	NOUN
ejpam-3300	81	11	inequality	inequality	NOUN
ejpam-3300	81	12	in	in	ADP
ejpam-3300	81	13	a	a	DET
ejpam-3300	81	14	similar	similar	ADJ
ejpam-3300	81	15	development	development	NOUN
ejpam-3300	81	16	,	,	PUNCT
ejpam-3300	81	17	we	we	PRON
ejpam-3300	81	18	prove	prove	VERB
ejpam-3300	81	19	the	the	DET
ejpam-3300	81	20	agm	agm	PROPN
ejpam-3300	81	21	inequality	inequality	NOUN
ejpam-3300	81	22	through	through	ADP
ejpam-3300	81	23	the	the	DET
ejpam-3300	81	24	second	second	ADJ
ejpam-3300	81	25	product	product	NOUN
ejpam-3300	81	26	inequality	inequality	NOUN
ejpam-3300	81	27	.	.	PUNCT
ejpam-3300	82	1	the	the	DET
ejpam-3300	82	2	agm	agm	PROPN
ejpam-3300	82	3	inequality	inequality	NOUN
ejpam-3300	82	4	is	be	AUX
ejpam-3300	82	5	obtained	obtain	VERB
ejpam-3300	82	6	by	by	ADP
ejpam-3300	82	7	induction	induction	NOUN
ejpam-3300	82	8	.	.	PUNCT
ejpam-3300	83	1	multiplying	multiply	VERB
ejpam-3300	83	2	both	both	DET
ejpam-3300	83	3	sides	side	NOUN
ejpam-3300	83	4	of	of	ADP
ejpam-3300	83	5	inequality	inequality	NOUN
ejpam-3300	83	6	(	(	PUNCT
ejpam-3300	83	7	2	2	NUM
ejpam-3300	83	8	)	)	PUNCT
ejpam-3300	83	9	by	by	ADP
ejpam-3300	83	10	p	p	NOUN
ejpam-3300	83	11	yields	yield	NOUN
ejpam-3300	83	12	p	p	NOUN
ejpam-3300	84	1	(	(	PUNCT
ejpam-3300	84	2	‖a1‖+	‖a1‖+	X
ejpam-3300	84	3	‖a2‖	‖a2‖	PROPN
ejpam-3300	84	4	)	)	PUNCT
ejpam-3300	84	5	≤	≤	NOUN
ejpam-3300	84	6	p	p	NOUN
ejpam-3300	84	7	{	{	PUNCT
ejpam-3300	84	8	‖a1‖‖a2‖	‖a1‖‖a2‖	NUM
ejpam-3300	84	9	}	}	PUNCT
ejpam-3300	84	10	,	,	PUNCT
ejpam-3300	84	11	∀	∀	PUNCT
ejpam-3300	84	12	p	p	NOUN
ejpam-3300	84	13	∈	∈	PROPN
ejpam-3300	85	1	[	[	X
ejpam-3300	85	2	0	0	NUM
ejpam-3300	85	3	,	,	PUNCT
ejpam-3300	85	4	1	1	NUM
ejpam-3300	85	5	]	]	PUNCT
ejpam-3300	85	6	.	.	PUNCT
ejpam-3300	86	1	(	(	PUNCT
ejpam-3300	86	2	6	6	NUM
ejpam-3300	86	3	)	)	PUNCT
ejpam-3300	86	4	but	but	CCONJ
ejpam-3300	86	5	,	,	PUNCT
ejpam-3300	86	6	we	we	PRON
ejpam-3300	86	7	see	see	VERB
ejpam-3300	86	8	that	that	PRON
ejpam-3300	86	9	:(	:(	PUNCT
ejpam-3300	86	10	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	86	11	)	)	PUNCT
ejpam-3300	86	12	p	p	NOUN
ejpam-3300	86	13	≤	≤	ADJ
ejpam-3300	86	14	p	p	NOUN
ejpam-3300	86	15	(	(	PUNCT
ejpam-3300	86	16	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	86	17	)	)	PUNCT
ejpam-3300	86	18	.	.	PUNCT
ejpam-3300	87	1	(	(	PUNCT
ejpam-3300	87	2	7	7	X
ejpam-3300	87	3	)	)	PUNCT
ejpam-3300	87	4	substituting	substitute	VERB
ejpam-3300	87	5	inequality	inequality	NOUN
ejpam-3300	87	6	(	(	PUNCT
ejpam-3300	87	7	7	7	NUM
ejpam-3300	87	8	)	)	PUNCT
ejpam-3300	87	9	into	into	ADP
ejpam-3300	87	10	inequality	inequality	NOUN
ejpam-3300	87	11	(	(	PUNCT
ejpam-3300	87	12	6	6	NUM
ejpam-3300	87	13	)	)	PUNCT
ejpam-3300	87	14	,	,	PUNCT
ejpam-3300	87	15	we	we	PRON
ejpam-3300	87	16	get	get	VERB
ejpam-3300	87	17	(	(	PUNCT
ejpam-3300	87	18	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	87	19	)	)	PUNCT
ejpam-3300	88	1	p	p	NOUN
ejpam-3300	88	2	≤	≤	ADJ
ejpam-3300	88	3	p	p	NOUN
ejpam-3300	88	4	(	(	PUNCT
ejpam-3300	88	5	‖a1‖+	‖a1‖+	NOUN
ejpam-3300	88	6	‖a2‖	‖a2‖	PROPN
ejpam-3300	88	7	)	)	PUNCT
ejpam-3300	88	8	.	.	PUNCT
ejpam-3300	89	1	(	(	PUNCT
ejpam-3300	89	2	8)	8)	NUM
ejpam-3300	89	3	setting	set	VERB
ejpam-3300	89	4	p	p	NOUN
ejpam-3300	89	5	=	=	NOUN
ejpam-3300	89	6	1	1	NUM
ejpam-3300	89	7	2	2	NUM
ejpam-3300	89	8	into	into	ADP
ejpam-3300	89	9	inequality	inequality	NOUN
ejpam-3300	89	10	(	(	PUNCT
ejpam-3300	89	11	8)	8)	NUM
ejpam-3300	89	12	yields	yield	NOUN
ejpam-3300	89	13	(	(	PUNCT
ejpam-3300	89	14	‖a1‖‖a2‖	‖a1‖‖a2‖	NUM
ejpam-3300	89	15	)	)	PUNCT
ejpam-3300	89	16	1	1	NUM
ejpam-3300	89	17	2	2	NUM
ejpam-3300	89	18	≤	≤	NUM
ejpam-3300	89	19	1	1	NUM
ejpam-3300	89	20	2	2	NUM
ejpam-3300	89	21	(	(	PUNCT
ejpam-3300	89	22	‖a1‖+	‖a1‖+	NOUN
ejpam-3300	89	23	‖a2‖	‖a2‖	ADJ
ejpam-3300	89	24	)	)	PUNCT
ejpam-3300	89	25	⇒	⇒	NOUN
ejpam-3300	89	26	(	(	PUNCT
ejpam-3300	89	27	2∏	2∏	NUM
ejpam-3300	89	28	i=1	i=1	INTJ
ejpam-3300	89	29	ai	ai	VERB
ejpam-3300	89	30	)	)	PUNCT
ejpam-3300	89	31	1	1	NUM
ejpam-3300	89	32	2	2	NUM
ejpam-3300	89	33	≤	≤	NUM
ejpam-3300	89	34	1	1	NUM
ejpam-3300	89	35	2	2	NUM
ejpam-3300	89	36	2∑	2∑	NOUN
ejpam-3300	89	37	i=1	i=1	X
ejpam-3300	89	38	ai	ai	VERB
ejpam-3300	89	39	.	.	PUNCT
ejpam-3300	90	1	again	again	ADV
ejpam-3300	90	2	,	,	PUNCT
ejpam-3300	90	3	we	we	PRON
ejpam-3300	90	4	observed	observe	VERB
ejpam-3300	90	5	that	that	SCONJ
ejpam-3300	90	6	:	:	PUNCT
ejpam-3300	90	7	‖a1‖+	‖a1‖+	NUM
ejpam-3300	90	8	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	90	9	‖a3‖	‖a3‖	NOUN
ejpam-3300	90	10	≤	≤	X
ejpam-3300	90	11	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	90	12	∀a1	∀a1	PROPN
ejpam-3300	90	13	,	,	PUNCT
ejpam-3300	90	14	a2	a2	PROPN
ejpam-3300	90	15	,	,	PUNCT
ejpam-3300	90	16	a3	a3	NOUN
ejpam-3300	90	17	∈	∈	PROPN
ejpam-3300	91	1	[	[	X
ejpam-3300	91	2	2,∞	2,∞	NUM
ejpam-3300	91	3	)	)	PUNCT
ejpam-3300	91	4	b.	b.	PROPN
ejpam-3300	91	5	barnes	barnes	PROPN
ejpam-3300	91	6	et	et	PROPN
ejpam-3300	91	7	al	al	PROPN
ejpam-3300	91	8	.	.	PUNCT
ejpam-3300	91	9	/	/	SYM
ejpam-3300	91	10	eur	eur	PROPN
ejpam-3300	91	11	.	.	PUNCT
ejpam-3300	92	1	j.	j.	PROPN
ejpam-3300	92	2	pure	pure	PROPN
ejpam-3300	92	3	appl	appl	PROPN
ejpam-3300	92	4	.	.	PROPN
ejpam-3300	92	5	math	math	PROPN
ejpam-3300	92	6	,	,	PUNCT
ejpam-3300	92	7	11	11	NUM
ejpam-3300	92	8	(	(	PUNCT
ejpam-3300	92	9	4	4	NUM
ejpam-3300	92	10	)	)	PUNCT
ejpam-3300	92	11	(	(	PUNCT
ejpam-3300	92	12	2018	2018	NUM
ejpam-3300	92	13	)	)	PUNCT
ejpam-3300	92	14	,	,	PUNCT
ejpam-3300	92	15	1100	1100	NUM
ejpam-3300	92	16	-	-	SYM
ejpam-3300	92	17	1107	1107	NUM
ejpam-3300	92	18	1104	1104	NUM
ejpam-3300	92	19	⇒	⇒	NOUN
ejpam-3300	92	20	p	p	X
ejpam-3300	92	21	(	(	PUNCT
ejpam-3300	92	22	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	92	23	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	92	24	‖a3‖	‖a3‖	NOUN
ejpam-3300	92	25	)	)	PUNCT
ejpam-3300	92	26	≤	≤	NOUN
ejpam-3300	93	1	p	p	NOUN
ejpam-3300	93	2	(	(	PUNCT
ejpam-3300	93	3	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	93	4	)	)	PUNCT
ejpam-3300	93	5	.	.	PUNCT
ejpam-3300	94	1	(	(	PUNCT
ejpam-3300	94	2	9	9	X
ejpam-3300	94	3	)	)	PUNCT
ejpam-3300	94	4	we	we	PRON
ejpam-3300	94	5	observed	observe	VERB
ejpam-3300	94	6	that	that	SCONJ
ejpam-3300	94	7	:(	:(	PUNCT
ejpam-3300	94	8	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	VERB
ejpam-3300	94	9	)	)	PUNCT
ejpam-3300	94	10	p	p	NOUN
ejpam-3300	94	11	≤	≤	ADJ
ejpam-3300	94	12	p	p	NOUN
ejpam-3300	94	13	(	(	PUNCT
ejpam-3300	94	14	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	94	15	)	)	PUNCT
ejpam-3300	94	16	.	.	PUNCT
ejpam-3300	95	1	(	(	PUNCT
ejpam-3300	95	2	10	10	NUM
ejpam-3300	95	3	)	)	PUNCT
ejpam-3300	95	4	substituting	substitute	VERB
ejpam-3300	95	5	inequality	inequality	NOUN
ejpam-3300	95	6	(	(	PUNCT
ejpam-3300	95	7	10	10	NUM
ejpam-3300	95	8	)	)	PUNCT
ejpam-3300	95	9	into	into	ADP
ejpam-3300	95	10	inequality	inequality	NOUN
ejpam-3300	95	11	(	(	PUNCT
ejpam-3300	95	12	9	9	NUM
ejpam-3300	95	13	)	)	PUNCT
ejpam-3300	95	14	yields	yield	NOUN
ejpam-3300	95	15	(	(	PUNCT
ejpam-3300	95	16	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	NOUN
ejpam-3300	95	17	)	)	PUNCT
ejpam-3300	95	18	p	p	NOUN
ejpam-3300	95	19	≤	≤	ADJ
ejpam-3300	95	20	p	p	NOUN
ejpam-3300	95	21	(	(	PUNCT
ejpam-3300	95	22	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	95	23	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	95	24	‖a3‖	‖a3‖	NOUN
ejpam-3300	95	25	)	)	PUNCT
ejpam-3300	95	26	.	.	PUNCT
ejpam-3300	96	1	setting	set	VERB
ejpam-3300	96	2	p	p	NOUN
ejpam-3300	96	3	=	=	NOUN
ejpam-3300	96	4	1	1	NUM
ejpam-3300	96	5	3	3	NUM
ejpam-3300	96	6	into	into	ADP
ejpam-3300	96	7	the	the	DET
ejpam-3300	96	8	above	above	ADJ
ejpam-3300	96	9	inequality	inequality	NOUN
ejpam-3300	96	10	,	,	PUNCT
ejpam-3300	96	11	we	we	PRON
ejpam-3300	96	12	obtain	obtain	VERB
ejpam-3300	96	13	(	(	PUNCT
ejpam-3300	96	14	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	96	15	)	)	PUNCT
ejpam-3300	96	16	1	1	NUM
ejpam-3300	97	1	3	3	NUM
ejpam-3300	97	2	≤	≤	NUM
ejpam-3300	97	3	1	1	NUM
ejpam-3300	97	4	3	3	NUM
ejpam-3300	97	5	(	(	PUNCT
ejpam-3300	97	6	‖a1‖+	‖a1‖+	NUM
ejpam-3300	97	7	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	97	8	‖a3‖	‖a3‖	NOUN
ejpam-3300	97	9	)	)	PUNCT
ejpam-3300	97	10	⇒	⇒	NOUN
ejpam-3300	97	11	(	(	PUNCT
ejpam-3300	97	12	3∏	3∏	X
ejpam-3300	97	13	i=1	i=1	PROPN
ejpam-3300	97	14	ai	ai	VERB
ejpam-3300	97	15	)	)	PUNCT
ejpam-3300	97	16	1	1	NUM
ejpam-3300	97	17	3	3	NUM
ejpam-3300	97	18	≤	≤	NUM
ejpam-3300	97	19	1	1	NUM
ejpam-3300	97	20	3	3	NUM
ejpam-3300	97	21	3∑	3∑	NUM
ejpam-3300	97	22	i=1	i=1	PRON
ejpam-3300	97	23	ai	ai	VERB
ejpam-3300	97	24	.	.	PUNCT
ejpam-3300	98	1	we	we	PRON
ejpam-3300	98	2	observed	observe	VERB
ejpam-3300	98	3	for	for	ADP
ejpam-3300	98	4	any	any	DET
ejpam-3300	98	5	number	number	NOUN
ejpam-3300	98	6	of	of	ADP
ejpam-3300	98	7	positive	positive	ADJ
ejpam-3300	98	8	real	real	ADJ
ejpam-3300	98	9	numbers	number	NOUN
ejpam-3300	98	10	n	n	CCONJ
ejpam-3300	98	11	,	,	PUNCT
ejpam-3300	98	12	we	we	PRON
ejpam-3300	98	13	have	have	VERB
ejpam-3300	98	14	:	:	PUNCT
ejpam-3300	98	15	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	98	16	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	98	17	.	.	PUNCT
ejpam-3300	98	18	.	.	PUNCT
ejpam-3300	99	1	.+	.+	NOUN
ejpam-3300	99	2	‖an‖	‖an‖	PROPN
ejpam-3300	99	3	≤	≤	PROPN
ejpam-3300	99	4	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	99	5	.	.	PUNCT
ejpam-3300	99	6	.	.	PUNCT
ejpam-3300	99	7	.	.	PUNCT
ejpam-3300	100	1	‖an‖	‖an‖	PROPN
ejpam-3300	100	2	∀a1	∀a1	PROPN
ejpam-3300	100	3	,	,	PUNCT
ejpam-3300	100	4	a2	a2	PROPN
ejpam-3300	100	5	,	,	PUNCT
ejpam-3300	100	6	.	.	PUNCT
ejpam-3300	100	7	.	.	PUNCT
ejpam-3300	100	8	.	.	PUNCT
ejpam-3300	101	1	,	,	PUNCT
ejpam-3300	101	2	an	an	DET
ejpam-3300	101	3	∈	∈	PROPN
ejpam-3300	102	1	[	[	X
ejpam-3300	102	2	2,∞	2,∞	NUM
ejpam-3300	102	3	)	)	PUNCT
ejpam-3300	102	4	⇒	⇒	VERB
ejpam-3300	102	5	p	p	NOUN
ejpam-3300	102	6	(	(	PUNCT
ejpam-3300	102	7	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	102	8	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	102	9	.	.	PUNCT
ejpam-3300	102	10	.	.	PUNCT
ejpam-3300	103	1	.+	.+	NOUN
ejpam-3300	103	2	‖an‖	‖an‖	PROPN
ejpam-3300	103	3	)	)	PUNCT
ejpam-3300	103	4	≤	≤	NOUN
ejpam-3300	103	5	p	p	NOUN
ejpam-3300	103	6	(	(	PUNCT
ejpam-3300	103	7	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	103	8	.	.	PUNCT
ejpam-3300	103	9	.	.	PUNCT
ejpam-3300	103	10	.	.	PUNCT
ejpam-3300	104	1	‖an‖	‖an‖	PROPN
ejpam-3300	104	2	)	)	PUNCT
ejpam-3300	104	3	.	.	PUNCT
ejpam-3300	105	1	(	(	PUNCT
ejpam-3300	105	2	11	11	NUM
ejpam-3300	105	3	)	)	PUNCT
ejpam-3300	105	4	but	but	CCONJ
ejpam-3300	105	5	we	we	PRON
ejpam-3300	105	6	see	see	VERB
ejpam-3300	105	7	that	that	PRON
ejpam-3300	105	8	:(	:(	PUNCT
ejpam-3300	105	9	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	105	10	.	.	PUNCT
ejpam-3300	105	11	.	.	PUNCT
ejpam-3300	105	12	.	.	PUNCT
ejpam-3300	106	1	‖an‖	‖an‖	PROPN
ejpam-3300	106	2	)	)	PUNCT
ejpam-3300	107	1	p	p	NOUN
ejpam-3300	107	2	≤	≤	NOUN
ejpam-3300	107	3	p	p	NOUN
ejpam-3300	107	4	(	(	PUNCT
ejpam-3300	107	5	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	107	6	.	.	PUNCT
ejpam-3300	107	7	.	.	PUNCT
ejpam-3300	107	8	.	.	PUNCT
ejpam-3300	108	1	‖an‖	‖an‖	PROPN
ejpam-3300	108	2	)	)	PUNCT
ejpam-3300	108	3	.	.	PUNCT
ejpam-3300	109	1	(	(	PUNCT
ejpam-3300	109	2	12	12	X
ejpam-3300	109	3	)	)	PUNCT
ejpam-3300	109	4	substituting	substitute	VERB
ejpam-3300	109	5	inequality	inequality	NOUN
ejpam-3300	109	6	(	(	PUNCT
ejpam-3300	109	7	12	12	NUM
ejpam-3300	109	8	)	)	PUNCT
ejpam-3300	109	9	into	into	ADP
ejpam-3300	109	10	inequality	inequality	NOUN
ejpam-3300	109	11	(	(	PUNCT
ejpam-3300	109	12	11	11	NUM
ejpam-3300	109	13	)	)	PUNCT
ejpam-3300	109	14	yields	yield	NOUN
ejpam-3300	109	15	(	(	PUNCT
ejpam-3300	109	16	‖a1‖‖a2‖	‖a1‖‖a2‖	PUNCT
ejpam-3300	109	17	.	.	PUNCT
ejpam-3300	109	18	.	.	PUNCT
ejpam-3300	109	19	.	.	PUNCT
ejpam-3300	110	1	‖an‖	‖an‖	PROPN
ejpam-3300	110	2	)	)	PUNCT
ejpam-3300	111	1	p	p	NOUN
ejpam-3300	111	2	≤	≤	NOUN
ejpam-3300	111	3	p	p	NOUN
ejpam-3300	111	4	(	(	PUNCT
ejpam-3300	111	5	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	111	6	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	111	7	.	.	PUNCT
ejpam-3300	111	8	.	.	PUNCT
ejpam-3300	112	1	.+	.+	NOUN
ejpam-3300	112	2	‖an‖	‖an‖	PROPN
ejpam-3300	112	3	)	)	PUNCT
ejpam-3300	112	4	.	.	PUNCT
ejpam-3300	113	1	setting	set	VERB
ejpam-3300	113	2	p	p	NOUN
ejpam-3300	113	3	=	=	SYM
ejpam-3300	113	4	1	1	NUM
ejpam-3300	113	5	n	n	NOUN
ejpam-3300	113	6	in	in	ADP
ejpam-3300	113	7	the	the	DET
ejpam-3300	113	8	above	above	ADJ
ejpam-3300	113	9	equation	equation	NOUN
ejpam-3300	113	10	yields	yield	NOUN
ejpam-3300	113	11	(	(	PUNCT
ejpam-3300	113	12	n∏	n∏	NOUN
ejpam-3300	113	13	i=1	i=1	PROPN
ejpam-3300	113	14	ai	ai	VERB
ejpam-3300	113	15	)	)	PUNCT
ejpam-3300	113	16	1	1	NUM
ejpam-3300	113	17	n	n	PRON
ejpam-3300	113	18	≤	≤	NUM
ejpam-3300	113	19	1	1	NUM
ejpam-3300	113	20	n	n	NUM
ejpam-3300	114	1	n∑	n∑	NOUN
ejpam-3300	114	2	i=1	i=1	PROPN
ejpam-3300	114	3	ai	ai	VERB
ejpam-3300	114	4	∀	∀	NOUN
ejpam-3300	114	5	a1	a1	NOUN
ejpam-3300	114	6	,	,	PUNCT
ejpam-3300	114	7	a2	a2	PROPN
ejpam-3300	114	8	,	,	PUNCT
ejpam-3300	114	9	.	.	PUNCT
ejpam-3300	114	10	.	.	PUNCT
ejpam-3300	115	1	.	.	PUNCT
ejpam-3300	116	1	,	,	PUNCT
ejpam-3300	116	2	an	an	DET
ejpam-3300	116	3	∈	∈	NOUN
ejpam-3300	116	4	[	[	X
ejpam-3300	116	5	2,∞	2,∞	NUM
ejpam-3300	116	6	)	)	PUNCT
ejpam-3300	116	7	.	.	PUNCT
ejpam-3300	117	1	1.3	1.3	NUM
ejpam-3300	117	2	.	.	PUNCT
ejpam-3300	118	1	the	the	DET
ejpam-3300	118	2	proof	proof	NOUN
ejpam-3300	118	3	of	of	ADP
ejpam-3300	118	4	the	the	DET
ejpam-3300	118	5	agm	agm	PROPN
ejpam-3300	118	6	inequality	inequality	NOUN
ejpam-3300	118	7	through	through	ADP
ejpam-3300	118	8	the	the	DET
ejpam-3300	118	9	binomial	binomial	ADJ
ejpam-3300	118	10	inequalities	inequality	NOUN
ejpam-3300	118	11	in	in	ADP
ejpam-3300	118	12	this	this	DET
ejpam-3300	118	13	section	section	NOUN
ejpam-3300	118	14	,	,	PUNCT
ejpam-3300	118	15	the	the	DET
ejpam-3300	118	16	agm	agm	PROPN
ejpam-3300	118	17	inequality	inequality	NOUN
ejpam-3300	118	18	is	be	AUX
ejpam-3300	118	19	proved	prove	VERB
ejpam-3300	118	20	through	through	ADP
ejpam-3300	118	21	new	new	ADJ
ejpam-3300	118	22	binomial	binomial	ADJ
ejpam-3300	118	23	inequalities	inequality	NOUN
ejpam-3300	118	24	of	of	ADP
ejpam-3300	118	25	rational	rational	ADJ
ejpam-3300	118	26	numbers	number	NOUN
ejpam-3300	118	27	.	.	PUNCT
ejpam-3300	119	1	we	we	PRON
ejpam-3300	119	2	can	can	AUX
ejpam-3300	119	3	see	see	VERB
ejpam-3300	119	4	that	that	DET
ejpam-3300	119	5	n	n	NOUN
ejpam-3300	119	6	=	=	SYM
ejpam-3300	119	7	2	2	NUM
ejpam-3300	119	8	,	,	PUNCT
ejpam-3300	119	9	the	the	DET
ejpam-3300	119	10	following	follow	VERB
ejpam-3300	119	11	inequality	inequality	NOUN
ejpam-3300	119	12	holds	hold	VERB
ejpam-3300	119	13	.	.	PUNCT
ejpam-3300	120	1	(	(	PUNCT
ejpam-3300	120	2	√	√	PUNCT
ejpam-3300	120	3	a1	a1	NOUN
ejpam-3300	120	4	+	+	CCONJ
ejpam-3300	120	5	√	√	NOUN
ejpam-3300	120	6	a2	a2	NOUN
ejpam-3300	120	7	)	)	PUNCT
ejpam-3300	120	8	2	2	NUM
ejpam-3300	120	9	≥	≥	NOUN
ejpam-3300	120	10	0	0	NUM
ejpam-3300	120	11	⇒	⇒	NOUN
ejpam-3300	120	12	(	(	PUNCT
ejpam-3300	120	13	‖a1a2‖	‖a1a2‖	NUM
ejpam-3300	120	14	)	)	PUNCT
ejpam-3300	120	15	1	1	NUM
ejpam-3300	120	16	2	2	NUM
ejpam-3300	120	17	≤	≤	NUM
ejpam-3300	120	18	1	1	NUM
ejpam-3300	120	19	2	2	NUM
ejpam-3300	120	20	(	(	PUNCT
ejpam-3300	120	21	‖a1‖+	‖a1‖+	PROPN
ejpam-3300	120	22	‖a2‖	‖a2‖	PROPN
ejpam-3300	120	23	)	)	PUNCT
ejpam-3300	121	1	b.	b.	PROPN
ejpam-3300	121	2	barnes	barnes	PROPN
ejpam-3300	121	3	et	et	PROPN
ejpam-3300	121	4	al	al	PROPN
ejpam-3300	121	5	.	.	PUNCT
ejpam-3300	121	6	/	/	SYM
ejpam-3300	121	7	eur	eur	PROPN
ejpam-3300	121	8	.	.	PUNCT
ejpam-3300	122	1	j.	j.	PROPN
ejpam-3300	122	2	pure	pure	PROPN
ejpam-3300	122	3	appl	appl	PROPN
ejpam-3300	122	4	.	.	PROPN
ejpam-3300	122	5	math	math	PROPN
ejpam-3300	122	6	,	,	PUNCT
ejpam-3300	122	7	11	11	NUM
ejpam-3300	122	8	(	(	PUNCT
ejpam-3300	122	9	4	4	NUM
ejpam-3300	122	10	)	)	PUNCT
ejpam-3300	122	11	(	(	PUNCT
ejpam-3300	122	12	2018	2018	NUM
ejpam-3300	122	13	)	)	PUNCT
ejpam-3300	122	14	,	,	PUNCT
ejpam-3300	122	15	1100	1100	NUM
ejpam-3300	122	16	-	-	SYM
ejpam-3300	122	17	1107	1107	NUM
ejpam-3300	122	18	1105	1105	NUM
ejpam-3300	122	19	⇒	⇒	NOUN
ejpam-3300	122	20	‖a1‖	‖a1‖	NOUN
ejpam-3300	122	21	1	1	NUM
ejpam-3300	122	22	2	2	NUM
ejpam-3300	122	23	‖a2‖	‖a2‖	PROPN
ejpam-3300	122	24	1	1	NUM
ejpam-3300	122	25	2	2	NUM
ejpam-3300	122	26	≤	≤	NUM
ejpam-3300	122	27	1	1	NUM
ejpam-3300	122	28	2	2	NUM
ejpam-3300	122	29	(	(	PUNCT
ejpam-3300	122	30	‖a1‖+	‖a1‖+	NOUN
ejpam-3300	122	31	‖a2‖	‖a2‖	ADJ
ejpam-3300	122	32	)	)	PUNCT
ejpam-3300	122	33	⇒	⇒	NOUN
ejpam-3300	122	34	(	(	PUNCT
ejpam-3300	122	35	2∏	2∏	NUM
ejpam-3300	122	36	i=1	i=1	INTJ
ejpam-3300	122	37	ai	ai	VERB
ejpam-3300	122	38	)	)	PUNCT
ejpam-3300	122	39	1	1	NUM
ejpam-3300	122	40	2	2	NUM
ejpam-3300	122	41	≤	≤	NUM
ejpam-3300	122	42	1	1	NUM
ejpam-3300	122	43	2	2	NUM
ejpam-3300	122	44	2∑	2∑	NOUN
ejpam-3300	122	45	i=1	i=1	X
ejpam-3300	122	46	ai	ai	VERB
ejpam-3300	122	47	.	.	PUNCT
ejpam-3300	123	1	also	also	ADV
ejpam-3300	123	2	,	,	PUNCT
ejpam-3300	123	3	let	let	VERB
ejpam-3300	123	4	a1	a1	NOUN
ejpam-3300	123	5	,	,	PUNCT
ejpam-3300	123	6	a2	a2	PROPN
ejpam-3300	123	7	and	and	CCONJ
ejpam-3300	123	8	a3	a3	NOUN
ejpam-3300	123	9	be	be	VERB
ejpam-3300	123	10	three	three	NUM
ejpam-3300	123	11	positive	positive	ADJ
ejpam-3300	123	12	real	real	ADJ
ejpam-3300	123	13	numbers	number	NOUN
ejpam-3300	123	14	,	,	PUNCT
ejpam-3300	123	15	then	then	ADV
ejpam-3300	123	16	(	(	PUNCT
ejpam-3300	123	17	√	√	ADV
ejpam-3300	123	18	a1	a1	NOUN
ejpam-3300	123	19	+	+	CCONJ
ejpam-3300	123	20	√	√	NOUN
ejpam-3300	123	21	a2	a2	PROPN
ejpam-3300	123	22	+	+	CCONJ
ejpam-3300	123	23	√	√	PROPN
ejpam-3300	123	24	a3	a3	NOUN
ejpam-3300	123	25	)	)	PUNCT
ejpam-3300	123	26	2	2	NUM
ejpam-3300	123	27	≥	≥	NOUN
ejpam-3300	123	28	0	0	NUM
ejpam-3300	123	29	⇒	⇒	PROPN
ejpam-3300	123	30	−2	−2	NOUN
ejpam-3300	123	31	(	(	PUNCT
ejpam-3300	123	32	√	√	INTJ
ejpam-3300	124	1	a1a2	a1a2	INTJ
ejpam-3300	124	2	+	+	NOUN
ejpam-3300	124	3	√	√	ADJ
ejpam-3300	124	4	a1a3	a1a3	ADP
ejpam-3300	124	5	+	+	CCONJ
ejpam-3300	124	6	√	√	NUM
ejpam-3300	124	7	a2a3	a2a3	PROPN
ejpam-3300	124	8	)	)	PUNCT
ejpam-3300	124	9	≤	≤	NOUN
ejpam-3300	124	10	(	(	PUNCT
ejpam-3300	124	11	a1	a1	NOUN
ejpam-3300	124	12	+	+	CCONJ
ejpam-3300	124	13	a2	a2	PROPN
ejpam-3300	124	14	+	+	CCONJ
ejpam-3300	124	15	a3	a3	NOUN
ejpam-3300	124	16	)	)	PUNCT
ejpam-3300	124	17	⇒	⇒	PROPN
ejpam-3300	124	18	−2	−2	PROPN
ejpam-3300	124	19	3	3	NUM
ejpam-3300	124	20	(	(	PUNCT
ejpam-3300	124	21	√	√	NUM
ejpam-3300	125	1	a1a2	a1a2	INTJ
ejpam-3300	125	2	+	+	NOUN
ejpam-3300	125	3	√	√	ADJ
ejpam-3300	125	4	a1a3	a1a3	ADP
ejpam-3300	125	5	+	+	CCONJ
ejpam-3300	125	6	√	√	NUM
ejpam-3300	125	7	a2a3	a2a3	NOUN
ejpam-3300	125	8	)	)	PUNCT
ejpam-3300	125	9	=	=	SYM
ejpam-3300	126	1	(	(	PUNCT
ejpam-3300	126	2	a1	a1	NOUN
ejpam-3300	126	3	+	+	CCONJ
ejpam-3300	126	4	a2	a2	PROPN
ejpam-3300	126	5	+	+	CCONJ
ejpam-3300	126	6	a3	a3	NOUN
ejpam-3300	126	7	)	)	PUNCT
ejpam-3300	126	8	3	3	NUM
ejpam-3300	126	9	⇒	⇒	NOUN
ejpam-3300	126	10	−4	−4	X
ejpam-3300	126	11	3	3	NUM
ejpam-3300	126	12	{	{	PUNCT
ejpam-3300	126	13	1	1	NUM
ejpam-3300	126	14	2	2	NUM
ejpam-3300	126	15	(	(	PUNCT
ejpam-3300	126	16	√	√	NUM
ejpam-3300	126	17	a1a2	a1a2	INTJ
ejpam-3300	126	18	+	+	CCONJ
ejpam-3300	126	19	√	√	NOUN
ejpam-3300	126	20	a3	a3	NOUN
ejpam-3300	126	21	)	)	PUNCT
ejpam-3300	126	22	}	}	PUNCT
ejpam-3300	126	23	≤	≤	NOUN
ejpam-3300	126	24	(	(	PUNCT
ejpam-3300	126	25	a1	a1	NOUN
ejpam-3300	126	26	+	+	CCONJ
ejpam-3300	126	27	a2	a2	PROPN
ejpam-3300	126	28	+	+	CCONJ
ejpam-3300	126	29	a3	a3	NOUN
ejpam-3300	126	30	)	)	PUNCT
ejpam-3300	126	31	3	3	NUM
ejpam-3300	126	32	⇒	⇒	NOUN
ejpam-3300	127	1	‖−4	‖−4	NOUN
ejpam-3300	127	2	3	3	NUM
ejpam-3300	127	3	{	{	PUNCT
ejpam-3300	127	4	1	1	NUM
ejpam-3300	127	5	2	2	NUM
ejpam-3300	127	6	(	(	PUNCT
ejpam-3300	127	7	√	√	NUM
ejpam-3300	127	8	a1a2	a1a2	INTJ
ejpam-3300	127	9	+	+	CCONJ
ejpam-3300	127	10	√	√	NOUN
ejpam-3300	127	11	a3	a3	NOUN
ejpam-3300	127	12	)	)	PUNCT
ejpam-3300	127	13	}	}	PUNCT
ejpam-3300	128	1	‖	‖	PROPN
ejpam-3300	128	2	≤	≤	PUNCT
ejpam-3300	128	3	‖(a1	‖(a1	NUM
ejpam-3300	128	4	+	+	NUM
ejpam-3300	128	5	a2	a2	PROPN
ejpam-3300	128	6	+	+	CCONJ
ejpam-3300	128	7	a3	a3	NOUN
ejpam-3300	128	8	)	)	PUNCT
ejpam-3300	128	9	3	3	NUM
ejpam-3300	128	10	‖	‖	PROPN
ejpam-3300	128	11	⇒	⇒	NOUN
ejpam-3300	128	12	4	4	NUM
ejpam-3300	128	13	3	3	NUM
ejpam-3300	128	14	∥∥∥{1	∥∥∥{1	NOUN
ejpam-3300	128	15	2	2	NUM
ejpam-3300	128	16	(	(	PUNCT
ejpam-3300	128	17	√	√	INTJ
ejpam-3300	128	18	a1a2	a1a2	INTJ
ejpam-3300	128	19	+	+	CCONJ
ejpam-3300	128	20	√	√	NOUN
ejpam-3300	128	21	a3	a3	NOUN
ejpam-3300	128	22	)	)	PUNCT
ejpam-3300	128	23	}	}	PUNCT
ejpam-3300	128	24	∥∥∥	∥∥∥	NUM
ejpam-3300	128	25	≤	≤	NUM
ejpam-3300	128	26	1	1	NUM
ejpam-3300	128	27	3	3	NUM
ejpam-3300	128	28	(	(	PUNCT
ejpam-3300	128	29	‖a1‖+	‖a1‖+	NUM
ejpam-3300	128	30	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	128	31	‖a3‖	‖a3‖	NOUN
ejpam-3300	128	32	)	)	PUNCT
ejpam-3300	128	33	⇒	⇒	VERB
ejpam-3300	128	34	4	4	NUM
ejpam-3300	128	35	3	3	NUM
ejpam-3300	128	36	(	(	PUNCT
ejpam-3300	128	37	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	128	38	)	)	PUNCT
ejpam-3300	128	39	1	1	NUM
ejpam-3300	128	40	4	4	NUM
ejpam-3300	128	41	≤	≤	NUM
ejpam-3300	128	42	1	1	NUM
ejpam-3300	128	43	3	3	NUM
ejpam-3300	128	44	(	(	PUNCT
ejpam-3300	128	45	‖a1‖+	‖a1‖+	NUM
ejpam-3300	128	46	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	128	47	‖a3‖	‖a3‖	NOUN
ejpam-3300	128	48	)	)	PUNCT
ejpam-3300	128	49	.	.	PUNCT
ejpam-3300	129	1	(	(	PUNCT
ejpam-3300	129	2	13	13	X
ejpam-3300	129	3	)	)	PUNCT
ejpam-3300	129	4	we	we	PRON
ejpam-3300	129	5	see	see	VERB
ejpam-3300	129	6	that	that	SCONJ
ejpam-3300	129	7	:(	:(	PUNCT
ejpam-3300	129	8	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	VERB
ejpam-3300	129	9	)	)	PUNCT
ejpam-3300	130	1	1	1	NUM
ejpam-3300	130	2	3	3	NUM
ejpam-3300	130	3	≤	≤	NUM
ejpam-3300	130	4	4	4	NUM
ejpam-3300	130	5	3	3	NUM
ejpam-3300	130	6	(	(	PUNCT
ejpam-3300	130	7	‖a1‖‖a2‖‖a3‖	‖a1‖‖a2‖‖a3‖	PROPN
ejpam-3300	130	8	)	)	PUNCT
ejpam-3300	130	9	1	1	NUM
ejpam-3300	130	10	4	4	NUM
ejpam-3300	130	11	.	.	PUNCT
ejpam-3300	131	1	(	(	PUNCT
ejpam-3300	131	2	14	14	NUM
ejpam-3300	131	3	)	)	PUNCT
ejpam-3300	131	4	substituting	substitute	VERB
ejpam-3300	131	5	inequality	inequality	NOUN
ejpam-3300	131	6	(	(	PUNCT
ejpam-3300	131	7	13	13	NUM
ejpam-3300	131	8	)	)	PUNCT
ejpam-3300	131	9	into	into	ADP
ejpam-3300	131	10	inequality	inequality	NOUN
ejpam-3300	131	11	(	(	PUNCT
ejpam-3300	131	12	14	14	NUM
ejpam-3300	131	13	)	)	PUNCT
ejpam-3300	131	14	yields	yield	VERB
ejpam-3300	131	15	⇒	⇒	NOUN
ejpam-3300	131	16	(	(	PUNCT
ejpam-3300	131	17	3∏	3∏	X
ejpam-3300	131	18	i=1	i=1	PROPN
ejpam-3300	131	19	ai	ai	VERB
ejpam-3300	131	20	)	)	PUNCT
ejpam-3300	131	21	1	1	NUM
ejpam-3300	131	22	3	3	NUM
ejpam-3300	131	23	≤	≤	NUM
ejpam-3300	131	24	1	1	NUM
ejpam-3300	131	25	3	3	NUM
ejpam-3300	131	26	3∑	3∑	NUM
ejpam-3300	131	27	i=1	i=1	PRON
ejpam-3300	131	28	ai	ai	VERB
ejpam-3300	131	29	.	.	PUNCT
ejpam-3300	132	1	similarly	similarly	ADV
ejpam-3300	132	2	,	,	PUNCT
ejpam-3300	132	3	we	we	PRON
ejpam-3300	132	4	can	can	AUX
ejpam-3300	132	5	see	see	VERB
ejpam-3300	132	6	that	that	PRON
ejpam-3300	132	7	:	:	PUNCT
ejpam-3300	132	8	(	(	PUNCT
ejpam-3300	132	9	√	√	ADV
ejpam-3300	132	10	a1	a1	NOUN
ejpam-3300	132	11	+	+	CCONJ
ejpam-3300	132	12	√	√	NOUN
ejpam-3300	132	13	a2	a2	PROPN
ejpam-3300	132	14	+	+	CCONJ
ejpam-3300	132	15	√	√	PROPN
ejpam-3300	132	16	a3	a3	NOUN
ejpam-3300	132	17	+	+	CCONJ
ejpam-3300	132	18	√	√	NUM
ejpam-3300	132	19	a4	a4	NUM
ejpam-3300	132	20	)	)	PUNCT
ejpam-3300	132	21	2	2	NUM
ejpam-3300	132	22	≥	≥	NOUN
ejpam-3300	132	23	0	0	NUM
ejpam-3300	132	24	⇒	⇒	NOUN
ejpam-3300	132	25	(	(	PUNCT
ejpam-3300	132	26	a1	a1	NOUN
ejpam-3300	132	27	+	+	CCONJ
ejpam-3300	132	28	a2	a2	PROPN
ejpam-3300	132	29	+	+	CCONJ
ejpam-3300	132	30	a3	a3	NOUN
ejpam-3300	132	31	+	+	CCONJ
ejpam-3300	132	32	a4	a4	NOUN
ejpam-3300	132	33	)	)	PUNCT
ejpam-3300	132	34	≥	≥	NOUN
ejpam-3300	132	35	−2	−2	NOUN
ejpam-3300	132	36	(	(	PUNCT
ejpam-3300	132	37	√	√	INTJ
ejpam-3300	132	38	a1a2	a1a2	INTJ
ejpam-3300	132	39	+	+	NOUN
ejpam-3300	132	40	√	√	PRON
ejpam-3300	132	41	a3a4	a3a4	VERB
ejpam-3300	132	42	+	+	CCONJ
ejpam-3300	132	43	√	√	NUM
ejpam-3300	132	44	a1a3	a1a3	PUNCT
ejpam-3300	133	1	+	+	CCONJ
ejpam-3300	133	2	√	√	PROPN
ejpam-3300	133	3	a1a4	a1a4	NOUN
ejpam-3300	133	4	+	+	CCONJ
ejpam-3300	133	5	√	√	ADJ
ejpam-3300	133	6	a2a3	a2a3	VERB
ejpam-3300	133	7	+	+	CCONJ
ejpam-3300	133	8	√	√	ADP
ejpam-3300	133	9	a2a4	a2a4	NOUN
ejpam-3300	133	10	)	)	PUNCT
ejpam-3300	133	11	⇒	⇒	NOUN
ejpam-3300	133	12	−1	−1	NOUN
ejpam-3300	133	13	2	2	NUM
ejpam-3300	133	14	(	(	PUNCT
ejpam-3300	133	15	√	√	INTJ
ejpam-3300	134	1	a1a2	a1a2	INTJ
ejpam-3300	134	2	+	+	NOUN
ejpam-3300	134	3	√	√	PRON
ejpam-3300	134	4	a3a4	a3a4	VERB
ejpam-3300	134	5	+	+	CCONJ
ejpam-3300	134	6	√	√	NUM
ejpam-3300	134	7	a1a3	a1a3	PUNCT
ejpam-3300	135	1	+	+	CCONJ
ejpam-3300	135	2	√	√	PROPN
ejpam-3300	135	3	a1a4	a1a4	NOUN
ejpam-3300	135	4	+	+	CCONJ
ejpam-3300	135	5	√	√	ADJ
ejpam-3300	135	6	a2a3	a2a3	VERB
ejpam-3300	135	7	+	+	CCONJ
ejpam-3300	135	8	√	√	NUM
ejpam-3300	135	9	a2a4	a2a4	SYM
ejpam-3300	135	10	)	)	PUNCT
ejpam-3300	135	11	≤	≤	NOUN
ejpam-3300	135	12	(	(	PUNCT
ejpam-3300	135	13	a1	a1	NOUN
ejpam-3300	135	14	+	+	CCONJ
ejpam-3300	135	15	a2	a2	PROPN
ejpam-3300	135	16	+	+	CCONJ
ejpam-3300	135	17	a3	a3	NOUN
ejpam-3300	135	18	+	+	CCONJ
ejpam-3300	135	19	a4	a4	NOUN
ejpam-3300	135	20	)	)	PUNCT
ejpam-3300	135	21	4	4	NUM
ejpam-3300	135	22	⇒	⇒	NOUN
ejpam-3300	135	23	−1	−1	NOUN
ejpam-3300	135	24	2	2	NUM
ejpam-3300	135	25	(	(	PUNCT
ejpam-3300	135	26	√	√	INTJ
ejpam-3300	136	1	a1a2	a1a2	INTJ
ejpam-3300	136	2	+	+	CCONJ
ejpam-3300	136	3	√	√	ADJ
ejpam-3300	136	4	a3a4	a3a4	VERB
ejpam-3300	136	5	)	)	PUNCT
ejpam-3300	136	6	≤	≤	NOUN
ejpam-3300	136	7	(	(	PUNCT
ejpam-3300	136	8	a1	a1	NOUN
ejpam-3300	136	9	+	+	CCONJ
ejpam-3300	136	10	a2	a2	PROPN
ejpam-3300	136	11	+	+	CCONJ
ejpam-3300	136	12	a3	a3	NOUN
ejpam-3300	136	13	+	+	CCONJ
ejpam-3300	136	14	a4	a4	NOUN
ejpam-3300	136	15	)	)	PUNCT
ejpam-3300	136	16	4	4	NUM
ejpam-3300	136	17	⇒	⇒	NOUN
ejpam-3300	136	18	‖−	‖−	NOUN
ejpam-3300	136	19	1	1	NUM
ejpam-3300	136	20	2	2	NUM
ejpam-3300	136	21	(	(	PUNCT
ejpam-3300	136	22	√	√	INTJ
ejpam-3300	136	23	a1a2	a1a2	INTJ
ejpam-3300	136	24	+	+	CCONJ
ejpam-3300	136	25	√	√	ADJ
ejpam-3300	136	26	a3a4	a3a4	VERB
ejpam-3300	136	27	)	)	PUNCT
ejpam-3300	136	28	‖	‖	PROPN
ejpam-3300	136	29	=	=	SYM
ejpam-3300	136	30	‖(a1	‖(a1	PROPN
ejpam-3300	136	31	+	+	NUM
ejpam-3300	136	32	a2	a2	PROPN
ejpam-3300	136	33	+	+	CCONJ
ejpam-3300	136	34	a3	a3	NOUN
ejpam-3300	136	35	+	+	CCONJ
ejpam-3300	136	36	a4	a4	NOUN
ejpam-3300	136	37	)	)	PUNCT
ejpam-3300	136	38	4	4	NUM
ejpam-3300	137	1	‖	‖	ADJ
ejpam-3300	137	2	⇒	⇒	NOUN
ejpam-3300	137	3	1	1	NUM
ejpam-3300	137	4	2	2	NUM
ejpam-3300	137	5	‖	‖	PROPN
ejpam-3300	137	6	(	(	PUNCT
ejpam-3300	137	7	√	√	INTJ
ejpam-3300	137	8	a1a2	a1a2	INTJ
ejpam-3300	137	9	+	+	CCONJ
ejpam-3300	137	10	√	√	ADJ
ejpam-3300	137	11	a3a4	a3a4	VERB
ejpam-3300	137	12	)	)	PUNCT
ejpam-3300	137	13	‖	‖	PROPN
ejpam-3300	137	14	≤	≤	NUM
ejpam-3300	137	15	1	1	NUM
ejpam-3300	137	16	4	4	NUM
ejpam-3300	137	17	(	(	PUNCT
ejpam-3300	137	18	‖a1‖+	‖a1‖+	NUM
ejpam-3300	137	19	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	137	20	‖a3‖+	‖a3‖+	NUM
ejpam-3300	137	21	‖a4‖	‖a4‖	NOUN
ejpam-3300	137	22	)	)	PUNCT
ejpam-3300	137	23	⇒	⇒	NOUN
ejpam-3300	137	24	(	(	PUNCT
ejpam-3300	137	25	‖a1‖‖a2‖‖a3‖‖a4‖	‖a1‖‖a2‖‖a3‖‖a4‖	PROPN
ejpam-3300	137	26	)	)	PUNCT
ejpam-3300	137	27	1	1	NUM
ejpam-3300	137	28	4	4	NUM
ejpam-3300	137	29	≤	≤	NUM
ejpam-3300	137	30	1	1	NUM
ejpam-3300	137	31	4	4	NUM
ejpam-3300	137	32	(	(	PUNCT
ejpam-3300	137	33	‖a1‖+	‖a1‖+	NUM
ejpam-3300	137	34	‖a2‖+	‖a2‖+	PROPN
ejpam-3300	137	35	‖a3‖+	‖a3‖+	NUM
ejpam-3300	137	36	‖a4‖	‖a4‖	NOUN
ejpam-3300	137	37	)	)	PUNCT
ejpam-3300	137	38	references	reference	NOUN
ejpam-3300	137	39	1106	1106	NUM
ejpam-3300	137	40	⇒	⇒	NOUN
ejpam-3300	137	41	(	(	PUNCT
ejpam-3300	137	42	4∏	4∏	X
ejpam-3300	137	43	i=1	i=1	PROPN
ejpam-3300	137	44	ai	ai	VERB
ejpam-3300	137	45	)	)	PUNCT
ejpam-3300	138	1	1	1	NUM
ejpam-3300	138	2	4	4	NUM
ejpam-3300	138	3	≤	≤	NUM
ejpam-3300	138	4	1	1	NUM
ejpam-3300	138	5	4	4	NUM
ejpam-3300	138	6	4∑	4∑	NOUN
ejpam-3300	138	7	i=1	i=1	PRON
ejpam-3300	138	8	ai	ai	VERB
ejpam-3300	138	9	.	.	PUNCT
ejpam-3300	139	1	by	by	ADP
ejpam-3300	139	2	the	the	DET
ejpam-3300	139	3	principle	principle	NOUN
ejpam-3300	139	4	of	of	ADP
ejpam-3300	139	5	induction	induction	NOUN
ejpam-3300	139	6	,	,	PUNCT
ejpam-3300	139	7	we	we	PRON
ejpam-3300	139	8	see	see	VERB
ejpam-3300	139	9	that	that	SCONJ
ejpam-3300	139	10	for	for	ADP
ejpam-3300	139	11	any	any	PRON
ejpam-3300	139	12	n	n	DET
ejpam-3300	139	13	number	number	NOUN
ejpam-3300	139	14	of	of	ADP
ejpam-3300	139	15	real	real	ADJ
ejpam-3300	139	16	numbers	number	NOUN
ejpam-3300	139	17	,	,	PUNCT
ejpam-3300	139	18	we	we	PRON
ejpam-3300	139	19	have	have	VERB
ejpam-3300	139	20	:(	:(	PROPN
ejpam-3300	139	21	n∏	n∏	PROPN
ejpam-3300	139	22	i=1	i=1	PROPN
ejpam-3300	139	23	ai	ai	VERB
ejpam-3300	139	24	)	)	PUNCT
ejpam-3300	139	25	1	1	NUM
ejpam-3300	139	26	n	n	DET
ejpam-3300	139	27	≤	≤	NUM
ejpam-3300	139	28	1	1	NUM
ejpam-3300	139	29	n	n	NUM
ejpam-3300	139	30	n∑	n∑	NOUN
ejpam-3300	139	31	i=1	i=1	PROPN
ejpam-3300	139	32	ai	ai	VERB
ejpam-3300	139	33	.	.	PUNCT
ejpam-3300	140	1	this	this	PRON
ejpam-3300	140	2	completes	complete	VERB
ejpam-3300	140	3	the	the	DET
ejpam-3300	140	4	prove	prove	NOUN
ejpam-3300	140	5	.	.	PUNCT
ejpam-3300	141	1	2	2	X
ejpam-3300	141	2	.	.	X
ejpam-3300	141	3	conclusion	conclusion	NOUN
ejpam-3300	141	4	in	in	ADP
ejpam-3300	141	5	a	a	DET
ejpam-3300	141	6	nutsell	nutsell	NOUN
ejpam-3300	141	7	,	,	PUNCT
ejpam-3300	141	8	we	we	PRON
ejpam-3300	141	9	have	have	AUX
ejpam-3300	141	10	provided	provide	VERB
ejpam-3300	141	11	the	the	DET
ejpam-3300	141	12	new	new	ADJ
ejpam-3300	141	13	ways	way	NOUN
ejpam-3300	141	14	of	of	ADP
ejpam-3300	141	15	proving	prove	VERB
ejpam-3300	141	16	the	the	DET
ejpam-3300	141	17	agm	agm	PROPN
ejpam-3300	141	18	inequality	inequality	NOUN
ejpam-3300	141	19	through	through	ADP
ejpam-3300	141	20	the	the	DET
ejpam-3300	141	21	product	product	NOUN
ejpam-3300	141	22	and	and	CCONJ
ejpam-3300	141	23	binomial	binomial	ADJ
ejpam-3300	141	24	inequalities	inequality	NOUN
ejpam-3300	141	25	.	.	PUNCT
ejpam-3300	142	1	references	reference	NOUN
ejpam-3300	142	2	[	[	X
ejpam-3300	142	3	1	1	NUM
ejpam-3300	142	4	]	]	PUNCT
ejpam-3300	142	5	bracken	bracken	NOUN
ejpam-3300	142	6	p.(2001	p.(2001	PROPN
ejpam-3300	142	7	)	)	PUNCT
ejpam-3300	142	8	.	.	PUNCT
ejpam-3300	143	1	an	an	DET
ejpam-3300	143	2	arithmetic	arithmetic	ADJ
ejpam-3300	143	3	-	-	PUNCT
ejpam-3300	143	4	geometric	geometric	ADJ
ejpam-3300	143	5	mean	mean	NOUN
ejpam-3300	143	6	inequality	inequality	NOUN
ejpam-3300	143	7	.	.	PUNCT
ejpam-3300	144	1	expositiones	expositione	NOUN
ejpam-3300	144	2	mathematicae	mathematicae	VERB
ejpam-3300	144	3	19	19	NUM
ejpam-3300	144	4	:	:	PUNCT
ejpam-3300	144	5	273	273	NUM
ejpam-3300	144	6	-	-	SYM
ejpam-3300	144	7	279	279	NUM
ejpam-3300	144	8	.	.	PUNCT
ejpam-3300	145	1	[	[	X
ejpam-3300	145	2	2	2	NUM
ejpam-3300	145	3	]	]	PUNCT
ejpam-3300	145	4	grabiner	grabiner	NOUN
ejpam-3300	145	5	j.	j.	PROPN
ejpam-3300	145	6	v.	v.	PROPN
ejpam-3300	145	7	(	(	PUNCT
ejpam-3300	145	8	1997	1997	NUM
ejpam-3300	145	9	)	)	PUNCT
ejpam-3300	145	10	.	.	PUNCT
ejpam-3300	146	1	was	be	AUX
ejpam-3300	146	2	newton	newton	PROPN
ejpam-3300	146	3	’s	’s	PART
ejpam-3300	146	4	calculus	calculus	NOUN
ejpam-3300	146	5	a	a	DET
ejpam-3300	146	6	dead	dead	ADJ
ejpam-3300	146	7	end	end	NOUN
ejpam-3300	146	8	?	?	PUNCT
ejpam-3300	147	1	the	the	DET
ejpam-3300	147	2	continental	continental	ADJ
ejpam-3300	147	3	influence	influence	NOUN
ejpam-3300	147	4	of	of	ADP
ejpam-3300	147	5	maclaurin	maclaurin	NOUN
ejpam-3300	147	6	’s	’s	PART
ejpam-3300	147	7	treatise	treatise	NOUN
ejpam-3300	147	8	of	of	ADP
ejpam-3300	147	9	fluxions	fluxion	NOUN
ejpam-3300	147	10	.	.	PUNCT
ejpam-3300	148	1	american	american	ADJ
ejpam-3300	148	2	mathematics	mathematics	PROPN
ejpam-3300	148	3	monthly	monthly	ADV
ejpam-3300	148	4	,	,	PUNCT
ejpam-3300	148	5	104	104	NUM
ejpam-3300	148	6	:	:	PUNCT
ejpam-3300	148	7	393	393	NUM
ejpam-3300	148	8	-	-	SYM
ejpam-3300	148	9	410	410	NUM
ejpam-3300	148	10	.	.	PUNCT
ejpam-3300	149	1	[	[	X
ejpam-3300	149	2	3	3	NUM
ejpam-3300	149	3	]	]	X
ejpam-3300	149	4	mitrinović	mitrinović	PROPN
ejpam-3300	149	5	d.	d.	PROPN
ejpam-3300	149	6	s.	s.	PROPN
ejpam-3300	149	7	,	,	PUNCT
ejpam-3300	149	8	pec̆arić	pec̆arić	PROPN
ejpam-3300	149	9	j.	j.	PROPN
ejpam-3300	149	10	e.	e.	PROPN
ejpam-3300	149	11	,	,	PUNCT
ejpam-3300	149	12	and	and	CCONJ
ejpam-3300	149	13	fink	fink	PROPN
ejpam-3300	149	14	a.	a.	PROPN
ejpam-3300	149	15	m.	m.	PROPN
ejpam-3300	149	16	(	(	PUNCT
ejpam-3300	149	17	1993	1993	NUM
ejpam-3300	149	18	)	)	PUNCT
ejpam-3300	149	19	.	.	PUNCT
ejpam-3300	150	1	classical	classical	ADJ
ejpam-3300	150	2	and	and	CCONJ
ejpam-3300	150	3	new	new	ADJ
ejpam-3300	150	4	inequalities	inequality	NOUN
ejpam-3300	150	5	in	in	ADP
ejpam-3300	150	6	analysis	analysis	NOUN
ejpam-3300	150	7	.	.	PUNCT
ejpam-3300	151	1	kluwer	kluwer	NOUN
ejpam-3300	151	2	academic	academic	PROPN
ejpam-3300	151	3	,	,	PUNCT
ejpam-3300	151	4	dordrecht	dordrecht	X
ejpam-3300	151	5	(	(	PUNCT
ejpam-3300	151	6	1993	1993	NUM
ejpam-3300	151	7	):	):	PUNCT
ejpam-3300	151	8	69	69	NUM
ejpam-3300	151	9	-	-	SYM
ejpam-3300	151	10	72	72	NUM
ejpam-3300	151	11	.	.	PUNCT
ejpam-3300	152	1	[	[	X
ejpam-3300	152	2	4	4	NUM
ejpam-3300	152	3	]	]	X
ejpam-3300	152	4	alzer	alzer	NOUN
ejpam-3300	152	5	h.	h.	PROPN
ejpam-3300	152	6	(	(	PUNCT
ejpam-3300	152	7	1997	1997	NUM
ejpam-3300	152	8	)	)	PUNCT
ejpam-3300	152	9	.	.	PUNCT
ejpam-3300	153	1	a	a	DET
ejpam-3300	153	2	new	new	ADJ
ejpam-3300	153	3	refinement	refinement	NOUN
ejpam-3300	153	4	of	of	ADP
ejpam-3300	153	5	the	the	DET
ejpam-3300	153	6	arithmetic	arithmetic	ADJ
ejpam-3300	153	7	mean	mean	ADJ
ejpam-3300	153	8	-	-	PUNCT
ejpam-3300	153	9	geometric	geometric	ADJ
ejpam-3300	153	10	mean	mean	NOUN
ejpam-3300	153	11	inequality	inequality	NOUN
ejpam-3300	153	12	.	.	PUNCT
ejpam-3300	154	1	rocky	rocky	ADJ
ejpam-3300	154	2	mountain	mountain	PROPN
ejpam-3300	154	3	journal	journal	NOUN
ejpam-3300	154	4	of	of	ADP
ejpam-3300	154	5	mathematics	mathematic	NOUN
ejpam-3300	154	6	,	,	PUNCT
ejpam-3300	154	7	27	27	NUM
ejpam-3300	154	8	:	:	PUNCT
ejpam-3300	154	9	663	663	NUM
ejpam-3300	154	10	-	-	SYM
ejpam-3300	154	11	667	667	NUM
ejpam-3300	154	12	.	.	PUNCT
ejpam-3300	155	1	[	[	X
ejpam-3300	155	2	5	5	X
ejpam-3300	155	3	]	]	PUNCT
ejpam-3300	155	4	rüthing	rüthe	VERB
ejpam-3300	155	5	d.	d.	PROPN
ejpam-3300	155	6	(	(	PUNCT
ejpam-3300	155	7	1982	1982	NUM
ejpam-3300	155	8	)	)	PUNCT
ejpam-3300	155	9	.	.	PUNCT
ejpam-3300	156	1	proofs	proof	NOUN
ejpam-3300	156	2	of	of	ADP
ejpam-3300	156	3	the	the	DET
ejpam-3300	156	4	arithmetic	arithmetic	ADJ
ejpam-3300	156	5	mean	mean	ADJ
ejpam-3300	156	6	-	-	PUNCT
ejpam-3300	156	7	geometric	geometric	ADJ
ejpam-3300	156	8	mean	mean	NOUN
ejpam-3300	156	9	inequality	inequality	NOUN
ejpam-3300	156	10	.	.	PUNCT
ejpam-3300	157	1	international	international	ADJ
ejpam-3300	157	2	journal	journal	PROPN
ejpam-3300	157	3	of	of	ADP
ejpam-3300	157	4	mathematical	mathematical	ADJ
ejpam-3300	157	5	education	education	NOUN
ejpam-3300	157	6	in	in	ADP
ejpam-3300	157	7	science	science	NOUN
ejpam-3300	157	8	and	and	CCONJ
ejpam-3300	157	9	technology	technology	NOUN
ejpam-3300	157	10	,	,	PUNCT
ejpam-3300	157	11	13(1	13(1	NUM
ejpam-3300	157	12	):	):	PUNCT
ejpam-3300	157	13	49	49	NUM
ejpam-3300	157	14	-	-	SYM
ejpam-3300	157	15	54	54	NUM
ejpam-3300	157	16	.	.	PUNCT
ejpam-3300	158	1	[	[	X
ejpam-3300	158	2	6	6	NUM
ejpam-3300	158	3	]	]	X
ejpam-3300	158	4	hardy	hardy	PROPN
ejpam-3300	158	5	g.	g.	PROPN
ejpam-3300	158	6	h.	h.	PROPN
ejpam-3300	158	7	,	,	PUNCT
ejpam-3300	158	8	littlewood	littlewood	PROPN
ejpam-3300	158	9	j.	j.	PROPN
ejpam-3300	158	10	e.	e.	PROPN
ejpam-3300	158	11	and	and	CCONJ
ejpam-3300	158	12	polya	polya	PROPN
ejpam-3300	158	13	g.	g.	PROPN
ejpam-3300	158	14	(	(	PUNCT
ejpam-3300	158	15	1978	1978	NUM
ejpam-3300	158	16	)	)	PUNCT
ejpam-3300	158	17	.	.	PUNCT
ejpam-3300	159	1	inequalities	inequality	NOUN
ejpam-3300	159	2	.	.	PUNCT
ejpam-3300	160	1	london	london	PROPN
ejpam-3300	160	2	,	,	PUNCT
ejpam-3300	160	3	new	new	PROPN
ejpam-3300	160	4	york	york	PROPN
ejpam-3300	160	5	;	;	PUNCT
ejpam-3300	160	6	cambridge	cambridge	PROPN
ejpam-3300	160	7	university	university	PROPN
ejpam-3300	160	8	press	press	NOUN
ejpam-3300	160	9	,	,	PUNCT
ejpam-3300	160	10	1978	1978	NUM
ejpam-3300	160	11	.	.	PUNCT
ejpam-3300	161	1	[	[	X
ejpam-3300	161	2	7	7	X
ejpam-3300	161	3	]	]	X
ejpam-3300	161	4	bhatia	bhatia	PROPN
ejpam-3300	161	5	r	r	PROPN
ejpam-3300	161	6	(	(	PUNCT
ejpam-3300	161	7	2006	2006	NUM
ejpam-3300	161	8	)	)	PUNCT
ejpam-3300	161	9	.	.	PUNCT
ejpam-3300	162	1	interpolating	interpolate	VERB
ejpam-3300	162	2	the	the	DET
ejpam-3300	162	3	arithmetic	arithmetic	ADJ
ejpam-3300	162	4	-	-	PUNCT
ejpam-3300	162	5	geometric	geometric	ADJ
ejpam-3300	162	6	mean	mean	NOUN
ejpam-3300	162	7	inequality	inequality	NOUN
ejpam-3300	162	8	and	and	CCONJ
ejpam-3300	162	9	its	its	PRON
ejpam-3300	162	10	operator	operator	NOUN
ejpam-3300	162	11	version	version	NOUN
ejpam-3300	162	12	.	.	PUNCT
ejpam-3300	163	1	linear	linear	ADJ
ejpam-3300	163	2	algebra	algebra	NOUN
ejpam-3300	163	3	and	and	CCONJ
ejpam-3300	163	4	its	its	PRON
ejpam-3300	163	5	applications	application	NOUN
ejpam-3300	163	6	,	,	PUNCT
ejpam-3300	163	7	413	413	NUM
ejpam-3300	163	8	:	:	PUNCT
ejpam-3300	163	9	355	355	NUM
ejpam-3300	163	10	-	-	SYM
ejpam-3300	163	11	363	363	NUM
ejpam-3300	163	12	.	.	PUNCT
ejpam-3300	164	1	[	[	X
ejpam-3300	164	2	8	8	NUM
ejpam-3300	164	3	]	]	X
ejpam-3300	164	4	zou	zou	PROPN
ejpam-3300	164	5	l.	l.	PROPN
ejpam-3300	164	6	and	and	CCONJ
ejpam-3300	164	7	huang	huang	PROPN
ejpam-3300	164	8	y.	y.	PROPN
ejpam-3300	164	9	(	(	PUNCT
ejpam-3300	164	10	2014	2014	NUM
ejpam-3300	164	11	)	)	PUNCT
ejpam-3300	164	12	.	.	PUNCT
ejpam-3300	165	1	a	a	DET
ejpam-3300	165	2	refinement	refinement	NOUN
ejpam-3300	165	3	of	of	ADP
ejpam-3300	165	4	the	the	DET
ejpam-3300	165	5	arithmetic	arithmetic	ADJ
ejpam-3300	165	6	-	-	PUNCT
ejpam-3300	165	7	geometric	geometric	ADJ
ejpam-3300	165	8	mean	mean	NOUN
ejpam-3300	165	9	inequality	inequality	NOUN
ejpam-3300	165	10	.	.	PUNCT
ejpam-3300	166	1	international	international	ADJ
ejpam-3300	166	2	journal	journal	PROPN
ejpam-3300	166	3	of	of	ADP
ejpam-3300	166	4	mathematical	mathematical	ADJ
ejpam-3300	166	5	education	education	NOUN
ejpam-3300	166	6	in	in	ADP
ejpam-3300	166	7	science	science	NOUN
ejpam-3300	166	8	and	and	CCONJ
ejpam-3300	166	9	technology	technology	NOUN
ejpam-3300	166	10	,	,	PUNCT
ejpam-3300	166	11	46(1	46(1	PROPN
ejpam-3300	166	12	)	)	PUNCT
ejpam-3300	166	13	:	:	PUNCT
ejpam-3300	167	1	158	158	NUM
ejpam-3300	167	2	-	-	SYM
ejpam-3300	167	3	160	160	NUM
ejpam-3300	167	4	.	.	PUNCT
ejpam-3300	168	1	[	[	X
ejpam-3300	168	2	9	9	NUM
ejpam-3300	168	3	]	]	X
ejpam-3300	168	4	adiyasuren	adiyasuren	PROPN
ejpam-3300	168	5	v.	v.	PROPN
ejpam-3300	168	6	,	,	PUNCT
ejpam-3300	168	7	batbold	batbold	PROPN
ejpam-3300	168	8	t.	t.	PROPN
ejpam-3300	168	9	and	and	CCONJ
ejpam-3300	168	10	khan	khan	PROPN
ejpam-3300	168	11	m.	m.	PROPN
ejpam-3300	168	12	a.	a.	PROPN
ejpam-3300	168	13	(	(	PUNCT
ejpam-3300	168	14	2016	2016	NUM
ejpam-3300	168	15	)	)	PUNCT
ejpam-3300	168	16	.	.	PUNCT
ejpam-3300	169	1	refined	refined	ADJ
ejpam-3300	169	2	arithmetic	arithmetic	ADJ
ejpam-3300	169	3	-	-	PUNCT
ejpam-3300	169	4	geometric	geometric	ADJ
ejpam-3300	169	5	mean	mean	NOUN
ejpam-3300	169	6	inequality	inequality	NOUN
ejpam-3300	169	7	and	and	CCONJ
ejpam-3300	169	8	new	new	ADJ
ejpam-3300	169	9	entropy	entropy	NOUN
ejpam-3300	169	10	upper	upper	PROPN
ejpam-3300	169	11	bound	bind	VERB
ejpam-3300	169	12	.	.	PUNCT
ejpam-3300	170	1	commun	commun	PROPN
ejpam-3300	170	2	.	.	PUNCT
ejpam-3300	171	1	korean	korean	PROPN
ejpam-3300	171	2	.	.	PUNCT
ejpam-3300	171	3	math	math	PROPN
ejpam-3300	171	4	.	.	PUNCT
ejpam-3300	172	1	soc	soc	PROPN
ejpam-3300	172	2	.	.	PROPN
ejpam-3300	172	3	,	,	PUNCT
ejpam-3300	172	4	31(1	31(1	NUM
ejpam-3300	172	5	)	)	PUNCT
ejpam-3300	172	6	:	:	PUNCT
ejpam-3300	172	7	95	95	NUM
ejpam-3300	172	8	-	-	SYM
ejpam-3300	172	9	100	100	NUM
ejpam-3300	172	10	.	.	PUNCT
ejpam-3300	173	1	references	reference	NOUN
ejpam-3300	173	2	1107	1107	NUM
ejpam-3300	173	3	[	[	X
ejpam-3300	173	4	10	10	NUM
ejpam-3300	173	5	]	]	X
ejpam-3300	173	6	zou	zou	PROPN
ejpam-3300	173	7	l.	l.	PROPN
ejpam-3300	173	8	(	(	PUNCT
ejpam-3300	173	9	2017	2017	NUM
ejpam-3300	173	10	)	)	PUNCT
ejpam-3300	173	11	.	.	PUNCT
ejpam-3300	174	1	an	an	DET
ejpam-3300	174	2	arithmetic	arithmetic	ADJ
ejpam-3300	174	3	-	-	PUNCT
ejpam-3300	174	4	geometric	geometric	ADJ
ejpam-3300	174	5	mean	mean	NOUN
ejpam-3300	174	6	inequality	inequality	NOUN
ejpam-3300	174	7	for	for	ADP
ejpam-3300	174	8	singular	singular	ADJ
ejpam-3300	174	9	values	value	NOUN
ejpam-3300	174	10	and	and	CCONJ
ejpam-3300	174	11	its	its	PRON
ejpam-3300	174	12	applications	application	NOUN
ejpam-3300	174	13	.	.	PUNCT
ejpam-3300	175	1	linear	linear	ADJ
ejpam-3300	175	2	algebra	algebra	NOUN
ejpam-3300	175	3	and	and	CCONJ
ejpam-3300	175	4	its	its	PRON
ejpam-3300	175	5	applications	application	NOUN
ejpam-3300	175	6	,	,	PUNCT
ejpam-3300	175	7	528	528	NUM
ejpam-3300	175	8	:	:	PUNCT
ejpam-3300	175	9	25	25	NUM
ejpam-3300	175	10	-	-	SYM
ejpam-3300	175	11	32	32	NUM
ejpam-3300	175	12	.	.	PUNCT
ejpam-3300	176	1	[	[	X
ejpam-3300	176	2	11	11	NUM
ejpam-3300	176	3	]	]	X
ejpam-3300	176	4	sheikhhosseini	sheikhhosseini	ADJ
ejpam-3300	176	5	a.	a.	NOUN
ejpam-3300	176	6	(	(	PUNCT
ejpam-3300	176	7	2017	2017	NUM
ejpam-3300	176	8	)	)	PUNCT
ejpam-3300	176	9	.	.	PUNCT
ejpam-3300	177	1	an	an	DET
ejpam-3300	177	2	arithmetic	arithmetic	ADJ
ejpam-3300	177	3	-	-	PUNCT
ejpam-3300	177	4	geometric	geometric	ADJ
ejpam-3300	177	5	mean	mean	NOUN
ejpam-3300	177	6	inequality	inequality	NOUN
ejpam-3300	177	7	related	relate	VERB
ejpam-3300	177	8	to	to	ADP
ejpam-3300	177	9	numerical	numerical	ADJ
ejpam-3300	177	10	radius	radius	NOUN
ejpam-3300	177	11	of	of	ADP
ejpam-3300	177	12	matrices	matrix	NOUN
ejpam-3300	177	13	.	.	PUNCT
ejpam-3300	178	1	konuralp	konuralp	PROPN
ejpam-3300	178	2	journal	journal	PROPN
ejpam-3300	178	3	of	of	ADP
ejpam-3300	178	4	mathematics	mathematic	NOUN
ejpam-3300	178	5	,	,	PUNCT
ejpam-3300	178	6	5(1	5(1	NUM
ejpam-3300	178	7	)	)	PUNCT
ejpam-3300	178	8	:	:	PUNCT
ejpam-3300	178	9	85	85	NUM
ejpam-3300	178	10	-	-	SYM
ejpam-3300	178	11	91	91	NUM
ejpam-3300	178	12	.	.	PUNCT
ejpam-3300	179	1	[	[	X
ejpam-3300	179	2	12	12	NUM
ejpam-3300	179	3	]	]	X
ejpam-3300	179	4	raüssouli	raüssouli	PROPN
ejpam-3300	179	5	m.	m.	NOUN
ejpam-3300	179	6	,	,	PUNCT
ejpam-3300	179	7	leazizi	leazizi	PROPN
ejpam-3300	179	8	f.	f.	PROPN
ejpam-3300	179	9	and	and	CCONJ
ejpam-3300	179	10	chergui	chergui	PROPN
ejpam-3300	179	11	m.	m.	NOUN
ejpam-3300	179	12	(	(	PUNCT
ejpam-3300	179	13	2009	2009	NUM
ejpam-3300	179	14	)	)	PUNCT
ejpam-3300	179	15	.	.	PUNCT
ejpam-3300	180	1	arithmetic	arithmetic	ADJ
ejpam-3300	180	2	-	-	PUNCT
ejpam-3300	180	3	geometric	geometric	ADJ
ejpam-3300	180	4	-	-	ADJ
ejpam-3300	180	5	harmonic	harmonic	ADJ
ejpam-3300	180	6	mean	mean	NOUN
ejpam-3300	180	7	of	of	ADP
ejpam-3300	180	8	three	three	NUM
ejpam-3300	180	9	positive	positive	ADJ
ejpam-3300	180	10	operators	operator	NOUN
ejpam-3300	180	11	.	.	PUNCT
ejpam-3300	181	1	journal	journal	PROPN
ejpam-3300	181	2	of	of	ADP
ejpam-3300	181	3	inequalities	inequality	NOUN
ejpam-3300	181	4	in	in	ADP
ejpam-3300	181	5	pure	pure	ADJ
ejpam-3300	181	6	and	and	CCONJ
ejpam-3300	181	7	applied	applied	ADJ
ejpam-3300	181	8	mathematics	mathematic	NOUN
ejpam-3300	181	9	,	,	PUNCT
ejpam-3300	181	10	10(4	10(4	NUM
ejpam-3300	181	11	)	)	PUNCT
ejpam-3300	182	1	[	[	X
ejpam-3300	182	2	13	13	NUM
ejpam-3300	182	3	]	]	PUNCT
ejpam-3300	182	4	chidume	chidume	PROPN
ejpam-3300	182	5	c.	c.	PROPN
ejpam-3300	182	6	e.	e.	PROPN
ejpam-3300	182	7	(	(	PUNCT
ejpam-3300	182	8	1989	1989	NUM
ejpam-3300	182	9	)	)	PUNCT
ejpam-3300	182	10	.	.	PUNCT
ejpam-3300	183	1	functional	functional	ADJ
ejpam-3300	183	2	analysis	analysis	NOUN
ejpam-3300	183	3	:	:	PUNCT
ejpam-3300	183	4	an	an	DET
ejpam-3300	183	5	introduction	introduction	NOUN
ejpam-3300	183	6	to	to	ADP
ejpam-3300	183	7	metric	metric	ADJ
ejpam-3300	183	8	spaces	space	NOUN
ejpam-3300	183	9	.	.	PUNCT
ejpam-3300	184	1	longman	longman	PROPN
ejpam-3300	184	2	,	,	PUNCT
ejpam-3300	184	3	nigeria	nigeria	PROPN
ejpam-3300	184	4	.	.	PUNCT
ejpam-3300	185	1	[	[	X
ejpam-3300	185	2	14	14	NUM
ejpam-3300	185	3	]	]	X
ejpam-3300	185	4	royden	royden	PROPN
ejpam-3300	185	5	h.	h.	PROPN
ejpam-3300	185	6	and	and	CCONJ
ejpam-3300	185	7	fitxpatrick	fitxpatrick	PROPN
ejpam-3300	185	8	p.	p.	NOUN
ejpam-3300	185	9	(	(	PUNCT
ejpam-3300	185	10	2010	2010	NUM
ejpam-3300	185	11	)	)	PUNCT
ejpam-3300	185	12	.	.	PUNCT
ejpam-3300	186	1	real	real	ADJ
ejpam-3300	186	2	analysis	analysis	NOUN
ejpam-3300	186	3	.	.	PUNCT
ejpam-3300	187	1	pearson	pearson	PROPN
ejpam-3300	187	2	education	education	PROPN
ejpam-3300	187	3	,	,	PUNCT
ejpam-3300	187	4	inc	inc	PROPN
ejpam-3300	187	5	,	,	PUNCT
ejpam-3300	187	6	4th	4th	ADJ
ejpam-3300	187	7	ed	ed	NOUN
ejpam-3300	187	8	.	.	PROPN
ejpam-3300	187	9	,	,	PUNCT
ejpam-3300	187	10	upper	upper	ADJ
ejpam-3300	187	11	saddle	saddle	NOUN
ejpam-3300	187	12	river	river	NOUN
ejpam-3300	187	13	.	.	PUNCT
ejpam-3300	188	1	[	[	X
ejpam-3300	188	2	15	15	NUM
ejpam-3300	188	3	]	]	X
ejpam-3300	188	4	barnes	barnes	PROPN
ejpam-3300	188	5	b.	b.	PROPN
ejpam-3300	188	6	,	,	PUNCT
ejpam-3300	188	7	owusu	owusu	PROPN
ejpam-3300	188	8	-	-	PROPN
ejpam-3300	188	9	ansah	ansah	PROPN
ejpam-3300	188	10	e.	e.	PROPN
ejpam-3300	188	11	d.	d.	PROPN
ejpam-3300	188	12	j.	j.	PROPN
ejpam-3300	188	13	,	,	PUNCT
ejpam-3300	188	14	amponsah	amponsah	PROPN
ejpam-3300	188	15	s.	s.	PROPN
ejpam-3300	188	16	k.	k.	PROPN
ejpam-3300	188	17	and	and	CCONJ
ejpam-3300	188	18	sebil	sebil	PROPN
ejpam-3300	188	19	c.	c.	PROPN
ejpam-3300	188	20	(	(	PUNCT
ejpam-3300	188	21	2018	2018	NUM
ejpam-3300	188	22	)	)	PUNCT
ejpam-3300	188	23	.	.	PUNCT
ejpam-3300	189	1	the	the	DET
ejpam-3300	189	2	proofs	proof	NOUN
ejpam-3300	189	3	of	of	ADP
ejpam-3300	189	4	product	product	NOUN
ejpam-3300	189	5	inequalities	inequality	NOUN
ejpam-3300	189	6	in	in	ADP
ejpam-3300	189	7	a	a	DET
ejpam-3300	189	8	generalized	generalized	ADJ
ejpam-3300	189	9	vector	vector	NOUN
ejpam-3300	189	10	space	space	NOUN
ejpam-3300	189	11	.	.	PUNCT
ejpam-3300	190	1	european	european	ADJ
ejpam-3300	190	2	journal	journal	PROPN
ejpam-3300	190	3	of	of	ADP
ejpam-3300	190	4	pure	pure	ADJ
ejpam-3300	190	5	and	and	CCONJ
ejpam-3300	190	6	applied	applied	ADJ
ejpam-3300	190	7	mathematics	mathematic	NOUN
ejpam-3300	190	8	,	,	PUNCT
ejpam-3300	190	9	11(2	11(2	NUM
ejpam-3300	190	10	):	):	PUNCT
ejpam-3300	190	11	375	375	NUM
ejpam-3300	190	12	-	-	SYM
ejpam-3300	190	13	389	389	NUM
ejpam-3300	190	14	.	.	PUNCT