id	sid	tid	token	lemma	pos
ejpam-3165	1	1	european	european	PROPN
ejpam-3165	1	2	journal	journal	PROPN
ejpam-3165	1	3	of	of	ADP
ejpam-3165	1	4	pure	pure	ADJ
ejpam-3165	1	5	and	and	CCONJ
ejpam-3165	1	6	applied	apply	VERB
ejpam-3165	1	7	mathematics	mathematic	NOUN
ejpam-3165	1	8	vol	vol	NOUN
ejpam-3165	1	9	.	.	PUNCT
ejpam-3165	2	1	11	11	NUM
ejpam-3165	2	2	,	,	PUNCT
ejpam-3165	2	3	no	no	INTJ
ejpam-3165	2	4	.	.	NOUN
ejpam-3165	2	5	1	1	NUM
ejpam-3165	2	6	,	,	PUNCT
ejpam-3165	2	7	2018	2018	NUM
ejpam-3165	2	8	,	,	PUNCT
ejpam-3165	2	9	352	352	NUM
ejpam-3165	2	10	-	-	SYM
ejpam-3165	2	11	361	361	NUM
ejpam-3165	2	12	issn	issn	PROPN
ejpam-3165	2	13	1307	1307	NUM
ejpam-3165	2	14	-	-	SYM
ejpam-3165	2	15	5543	5543	NUM
ejpam-3165	2	16	–	–	PUNCT
ejpam-3165	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3165	2	18	published	publish	VERB
ejpam-3165	2	19	by	by	ADP
ejpam-3165	2	20	new	new	PROPN
ejpam-3165	2	21	york	york	PROPN
ejpam-3165	2	22	business	business	PROPN
ejpam-3165	2	23	global	global	PROPN
ejpam-3165	2	24	the	the	DET
ejpam-3165	2	25	proofs	proof	NOUN
ejpam-3165	2	26	of	of	ADP
ejpam-3165	2	27	triangle	triangle	NOUN
ejpam-3165	2	28	inequality	inequality	NOUN
ejpam-3165	2	29	using	use	VERB
ejpam-3165	2	30	binomial	binomial	ADJ
ejpam-3165	2	31	inequalities	inequality	NOUN
ejpam-3165	2	32	benedict	benedict	PROPN
ejpam-3165	2	33	barnes1,∗	barnes1,∗	PROPN
ejpam-3165	2	34	,	,	PUNCT
ejpam-3165	2	35	e.	e.	PROPN
ejpam-3165	2	36	d.	d.	PROPN
ejpam-3165	2	37	j.	j.	PROPN
ejpam-3165	2	38	owusu	owusu	PROPN
ejpam-3165	2	39	-	-	PROPN
ejpam-3165	2	40	ansah1	ansah1	PROPN
ejpam-3165	2	41	,	,	PUNCT
ejpam-3165	2	42	s.	s.	PROPN
ejpam-3165	2	43	k.	k.	PROPN
ejpam-3165	2	44	amponsah1	amponsah1	PROPN
ejpam-3165	2	45	,	,	PUNCT
ejpam-3165	2	46	i.	i.	PROPN
ejpam-3165	2	47	a.	a.	PROPN
ejpam-3165	2	48	adjei1	adjei1	PROPN
ejpam-3165	3	1	1	1	NUM
ejpam-3165	3	2	department	department	NOUN
ejpam-3165	3	3	of	of	ADP
ejpam-3165	3	4	mathematics	mathematics	PROPN
ejpam-3165	3	5	,	,	PUNCT
ejpam-3165	3	6	kwame	kwame	PROPN
ejpam-3165	3	7	nkrumah	nkrumah	PROPN
ejpam-3165	3	8	university	university	PROPN
ejpam-3165	3	9	of	of	ADP
ejpam-3165	3	10	science	science	NOUN
ejpam-3165	3	11	and	and	CCONJ
ejpam-3165	3	12	technology	technology	NOUN
ejpam-3165	3	13	,	,	PUNCT
ejpam-3165	3	14	kumasi	kumasi	PROPN
ejpam-3165	3	15	,	,	PUNCT
ejpam-3165	3	16	ghana	ghana	PROPN
ejpam-3165	3	17	abstract	abstract	NOUN
ejpam-3165	3	18	.	.	PUNCT
ejpam-3165	4	1	in	in	ADP
ejpam-3165	4	2	this	this	DET
ejpam-3165	4	3	paper	paper	NOUN
ejpam-3165	4	4	,	,	PUNCT
ejpam-3165	4	5	we	we	PRON
ejpam-3165	4	6	introduce	introduce	VERB
ejpam-3165	4	7	the	the	DET
ejpam-3165	4	8	different	different	ADJ
ejpam-3165	4	9	ways	way	NOUN
ejpam-3165	4	10	of	of	ADP
ejpam-3165	4	11	proving	prove	VERB
ejpam-3165	4	12	the	the	DET
ejpam-3165	4	13	triangle	triangle	NOUN
ejpam-3165	4	14	inequality	inequality	NOUN
ejpam-3165	4	15	‖u	‖u	NOUN
ejpam-3165	4	16	−	−	PROPN
ejpam-3165	4	17	v‖	v‖	NOUN
ejpam-3165	4	18	≤	≤	NOUN
ejpam-3165	4	19	‖u‖+	‖u‖+	X
ejpam-3165	4	20	‖v‖	‖v‖	PROPN
ejpam-3165	4	21	,	,	PUNCT
ejpam-3165	4	22	in	in	ADP
ejpam-3165	4	23	the	the	DET
ejpam-3165	4	24	hilbert	hilbert	NOUN
ejpam-3165	4	25	space	space	NOUN
ejpam-3165	4	26	.	.	PUNCT
ejpam-3165	5	1	thus	thus	ADV
ejpam-3165	5	2	,	,	PUNCT
ejpam-3165	5	3	we	we	PRON
ejpam-3165	5	4	prove	prove	VERB
ejpam-3165	5	5	this	this	DET
ejpam-3165	5	6	triangle	triangle	NOUN
ejpam-3165	5	7	inequality	inequality	NOUN
ejpam-3165	5	8	through	through	ADP
ejpam-3165	5	9	the	the	DET
ejpam-3165	5	10	binomial	binomial	ADJ
ejpam-3165	5	11	inequality	inequality	NOUN
ejpam-3165	5	12	and	and	CCONJ
ejpam-3165	5	13	also	also	ADV
ejpam-3165	5	14	,	,	PUNCT
ejpam-3165	5	15	prove	prove	VERB
ejpam-3165	5	16	it	it	PRON
ejpam-3165	5	17	through	through	ADP
ejpam-3165	5	18	the	the	DET
ejpam-3165	5	19	euclidean	euclidean	ADJ
ejpam-3165	5	20	norm	norm	NOUN
ejpam-3165	5	21	.	.	PUNCT
ejpam-3165	6	1	the	the	DET
ejpam-3165	6	2	first	first	ADJ
ejpam-3165	6	3	generalized	generalized	ADJ
ejpam-3165	6	4	procedure	procedure	NOUN
ejpam-3165	6	5	for	for	ADP
ejpam-3165	6	6	proving	prove	VERB
ejpam-3165	6	7	the	the	DET
ejpam-3165	6	8	triangle	triangle	NOUN
ejpam-3165	6	9	inequality	inequality	NOUN
ejpam-3165	6	10	is	be	AUX
ejpam-3165	6	11	feasible	feasible	ADJ
ejpam-3165	6	12	for	for	ADP
ejpam-3165	6	13	any	any	DET
ejpam-3165	6	14	even	even	ADV
ejpam-3165	6	15	positive	positive	ADJ
ejpam-3165	6	16	integer	integer	NOUN
ejpam-3165	6	17	n.	n.	NOUN
ejpam-3165	6	18	the	the	DET
ejpam-3165	6	19	second	second	ADJ
ejpam-3165	6	20	alternative	alternative	ADJ
ejpam-3165	6	21	proof	proof	NOUN
ejpam-3165	6	22	of	of	ADP
ejpam-3165	6	23	the	the	DET
ejpam-3165	6	24	triangle	triangle	NOUN
ejpam-3165	6	25	inequality	inequality	NOUN
ejpam-3165	6	26	establishes	establish	VERB
ejpam-3165	6	27	the	the	DET
ejpam-3165	6	28	euclidean	euclidean	ADJ
ejpam-3165	6	29	norm	norm	NOUN
ejpam-3165	6	30	of	of	ADP
ejpam-3165	6	31	any	any	DET
ejpam-3165	6	32	two	two	NUM
ejpam-3165	6	33	vectors	vector	NOUN
ejpam-3165	6	34	in	in	ADP
ejpam-3165	6	35	the	the	DET
ejpam-3165	6	36	hilbert	hilbert	NOUN
ejpam-3165	6	37	space	space	NOUN
ejpam-3165	6	38	.	.	PUNCT
ejpam-3165	7	1	2010	2010	NUM
ejpam-3165	7	2	mathematics	mathematic	NOUN
ejpam-3165	7	3	subject	subject	NOUN
ejpam-3165	7	4	classifications	classification	NOUN
ejpam-3165	7	5	:	:	PUNCT
ejpam-3165	7	6	44b43	44b43	NUM
ejpam-3165	7	7	,	,	PUNCT
ejpam-3165	7	8	44b44	44b44	X
ejpam-3165	7	9	key	key	ADJ
ejpam-3165	7	10	words	word	NOUN
ejpam-3165	7	11	and	and	CCONJ
ejpam-3165	7	12	phrases	phrase	NOUN
ejpam-3165	7	13	:	:	PUNCT
ejpam-3165	7	14	triangle	triangle	NOUN
ejpam-3165	7	15	inequality	inequality	NOUN
ejpam-3165	7	16	,	,	PUNCT
ejpam-3165	7	17	triangle	triangle	VERB
ejpam-3165	7	18	through	through	ADP
ejpam-3165	7	19	binomial	binomial	ADJ
ejpam-3165	7	20	inequality	inequality	NOUN
ejpam-3165	7	21	,	,	PUNCT
ejpam-3165	7	22	triangle	triangle	NOUN
ejpam-3165	7	23	inequality	inequality	NOUN
ejpam-3165	7	24	through	through	ADP
ejpam-3165	7	25	euclidean	euclidean	ADJ
ejpam-3165	7	26	norm	norm	NOUN
ejpam-3165	7	27	,	,	PUNCT
ejpam-3165	7	28	hilbert	hilbert	NOUN
ejpam-3165	7	29	space	space	NOUN
ejpam-3165	7	30	1	1	NUM
ejpam-3165	7	31	.	.	PUNCT
ejpam-3165	8	1	introduction	introduction	NOUN
ejpam-3165	8	2	the	the	DET
ejpam-3165	8	3	importance	importance	NOUN
ejpam-3165	8	4	of	of	ADP
ejpam-3165	8	5	estimating	estimate	VERB
ejpam-3165	8	6	norms	norm	NOUN
ejpam-3165	8	7	can	can	AUX
ejpam-3165	8	8	not	not	PART
ejpam-3165	8	9	be	be	AUX
ejpam-3165	8	10	overemphasized	overemphasize	VERB
ejpam-3165	8	11	on	on	ADP
ejpam-3165	8	12	the	the	DET
ejpam-3165	8	13	grounds	ground	NOUN
ejpam-3165	8	14	that	that	SCONJ
ejpam-3165	8	15	,	,	PUNCT
ejpam-3165	8	16	in	in	ADP
ejpam-3165	8	17	most	most	ADJ
ejpam-3165	8	18	practices	practice	NOUN
ejpam-3165	8	19	,	,	PUNCT
ejpam-3165	8	20	the	the	DET
ejpam-3165	8	21	quantification	quantification	NOUN
ejpam-3165	8	22	of	of	ADP
ejpam-3165	8	23	exact	exact	ADJ
ejpam-3165	8	24	norm	norm	NOUN
ejpam-3165	8	25	of	of	ADP
ejpam-3165	8	26	the	the	DET
ejpam-3165	8	27	two	two	NUM
ejpam-3165	8	28	vector	vector	NOUN
ejpam-3165	8	29	points	point	NOUN
ejpam-3165	8	30	in	in	ADP
ejpam-3165	8	31	a	a	DET
ejpam-3165	8	32	complete	complete	ADJ
ejpam-3165	8	33	normed	normed	ADJ
ejpam-3165	8	34	space	space	NOUN
ejpam-3165	8	35	is	be	AUX
ejpam-3165	8	36	tedious	tedious	ADJ
ejpam-3165	8	37	and	and	CCONJ
ejpam-3165	8	38	sometimes	sometimes	ADV
ejpam-3165	8	39	the	the	DET
ejpam-3165	8	40	procedure	procedure	NOUN
ejpam-3165	8	41	is	be	AUX
ejpam-3165	8	42	cumbersome	cumbersome	ADJ
ejpam-3165	8	43	.	.	PUNCT
ejpam-3165	9	1	in	in	ADP
ejpam-3165	9	2	this	this	DET
ejpam-3165	9	3	regard	regard	NOUN
ejpam-3165	9	4	,	,	PUNCT
ejpam-3165	9	5	we	we	PRON
ejpam-3165	9	6	fall	fall	VERB
ejpam-3165	9	7	on	on	ADP
ejpam-3165	9	8	the	the	DET
ejpam-3165	9	9	estimation	estimation	NOUN
ejpam-3165	9	10	of	of	ADP
ejpam-3165	9	11	norms	norm	NOUN
ejpam-3165	9	12	of	of	ADP
ejpam-3165	9	13	vector	vector	NOUN
ejpam-3165	9	14	points	point	NOUN
ejpam-3165	9	15	.	.	PUNCT
ejpam-3165	10	1	inequalities	inequality	NOUN
ejpam-3165	10	2	are	be	AUX
ejpam-3165	10	3	used	use	VERB
ejpam-3165	10	4	to	to	PART
ejpam-3165	10	5	describe	describe	VERB
ejpam-3165	10	6	the	the	DET
ejpam-3165	10	7	geometric	geometric	ADJ
ejpam-3165	10	8	structures	structure	NOUN
ejpam-3165	10	9	such	such	ADJ
ejpam-3165	10	10	as	as	ADP
ejpam-3165	10	11	boundedness	boundedness	NOUN
ejpam-3165	10	12	,	,	PUNCT
ejpam-3165	10	13	continuity	continuity	NOUN
ejpam-3165	10	14	,	,	PUNCT
ejpam-3165	10	15	uniform	uniform	ADJ
ejpam-3165	10	16	non	non	NOUN
ejpam-3165	10	17	-	-	NOUN
ejpam-3165	10	18	ln1−ness	ln1−ness	NOUN
ejpam-3165	10	19	of	of	ADP
ejpam-3165	10	20	mappings	mapping	NOUN
ejpam-3165	10	21	or	or	CCONJ
ejpam-3165	10	22	operators	operator	NOUN
ejpam-3165	10	23	of	of	ADP
ejpam-3165	10	24	the	the	DET
ejpam-3165	10	25	linear	linear	ADJ
ejpam-3165	10	26	spaces	space	NOUN
ejpam-3165	10	27	and	and	CCONJ
ejpam-3165	10	28	also	also	ADV
ejpam-3165	10	29	,	,	PUNCT
ejpam-3165	10	30	the	the	DET
ejpam-3165	10	31	embeddings	embedding	NOUN
ejpam-3165	10	32	of	of	ADP
ejpam-3165	10	33	one	one	NUM
ejpam-3165	10	34	vector	vector	NOUN
ejpam-3165	10	35	space	space	NOUN
ejpam-3165	10	36	into	into	ADP
ejpam-3165	10	37	another	another	DET
ejpam-3165	10	38	vector	vector	NOUN
ejpam-3165	10	39	space	space	NOUN
ejpam-3165	10	40	.	.	PUNCT
ejpam-3165	11	1	recently	recently	ADV
ejpam-3165	11	2	,	,	PUNCT
ejpam-3165	11	3	some	some	DET
ejpam-3165	11	4	applications	application	NOUN
ejpam-3165	11	5	of	of	ADP
ejpam-3165	11	6	the	the	DET
ejpam-3165	11	7	triangle	triangle	NOUN
ejpam-3165	11	8	inequality	inequality	NOUN
ejpam-3165	11	9	in	in	ADP
ejpam-3165	11	10	the	the	DET
ejpam-3165	11	11	operations	operation	NOUN
ejpam-3165	11	12	research	research	NOUN
ejpam-3165	11	13	have	have	AUX
ejpam-3165	11	14	been	be	AUX
ejpam-3165	11	15	found	find	VERB
ejpam-3165	11	16	,	,	PUNCT
ejpam-3165	11	17	see	see	VERB
ejpam-3165	11	18	research	research	NOUN
ejpam-3165	11	19	papers	paper	NOUN
ejpam-3165	11	20	by	by	ADP
ejpam-3165	11	21	[	[	X
ejpam-3165	11	22	1	1	NUM
ejpam-3165	11	23	,	,	PUNCT
ejpam-3165	11	24	2	2	NUM
ejpam-3165	11	25	]	]	PUNCT
ejpam-3165	11	26	.	.	PUNCT
ejpam-3165	12	1	the	the	DET
ejpam-3165	12	2	proof	proof	NOUN
ejpam-3165	12	3	of	of	ADP
ejpam-3165	12	4	the	the	DET
ejpam-3165	12	5	triangle	triangle	NOUN
ejpam-3165	12	6	inequality	inequality	NOUN
ejpam-3165	12	7	of	of	ADP
ejpam-3165	12	8	the	the	DET
ejpam-3165	12	9	form	form	NOUN
ejpam-3165	12	10	‖u+	‖u+	PROPN
ejpam-3165	12	11	v‖	v‖	NOUN
ejpam-3165	12	12	≤	≤	NOUN
ejpam-3165	12	13	‖u‖+	‖u‖+	X
ejpam-3165	12	14	‖v‖	‖v‖	PROPN
ejpam-3165	12	15	,	,	PUNCT
ejpam-3165	12	16	is	be	AUX
ejpam-3165	12	17	well	well	ADV
ejpam-3165	12	18	-	-	PUNCT
ejpam-3165	12	19	known	know	VERB
ejpam-3165	12	20	and	and	CCONJ
ejpam-3165	12	21	many	many	ADJ
ejpam-3165	12	22	researchers	researcher	NOUN
ejpam-3165	12	23	across	across	ADP
ejpam-3165	12	24	the	the	DET
ejpam-3165	12	25	globe	globe	NOUN
ejpam-3165	12	26	have	have	AUX
ejpam-3165	12	27	shown	show	VERB
ejpam-3165	12	28	different	different	ADJ
ejpam-3165	12	29	ways	way	NOUN
ejpam-3165	12	30	for	for	ADP
ejpam-3165	12	31	obtaining	obtain	VERB
ejpam-3165	12	32	this	this	DET
ejpam-3165	12	33	result	result	NOUN
ejpam-3165	12	34	.	.	PUNCT
ejpam-3165	13	1	a	a	DET
ejpam-3165	13	2	lot	lot	NOUN
ejpam-3165	13	3	of	of	ADP
ejpam-3165	13	4	studies	study	NOUN
ejpam-3165	13	5	delineate	delineate	VERB
ejpam-3165	13	6	the	the	DET
ejpam-3165	13	7	origin	origin	NOUN
ejpam-3165	13	8	of	of	ADP
ejpam-3165	13	9	inequalities	inequality	NOUN
ejpam-3165	13	10	.	.	PUNCT
ejpam-3165	14	1	for	for	ADP
ejpam-3165	14	2	example	example	NOUN
ejpam-3165	14	3	,	,	PUNCT
ejpam-3165	14	4	see	see	VERB
ejpam-3165	14	5	∗corresponding	∗corresponde	VERB
ejpam-3165	14	6	author	author	NOUN
ejpam-3165	14	7	.	.	PUNCT
ejpam-3165	15	1	email	email	NOUN
ejpam-3165	15	2	addresses	address	NOUN
ejpam-3165	15	3	:	:	PUNCT
ejpam-3165	15	4	bbarnes.cos@knust.edu.gh	bbarnes.cos@knust.edu.gh	NOUN
ejpam-3165	15	5	(	(	PUNCT
ejpam-3165	15	6	b.	b.	PROPN
ejpam-3165	15	7	barnes	barnes	PROPN
ejpam-3165	15	8	)	)	PUNCT
ejpam-3165	15	9	,	,	PUNCT
ejpam-3165	15	10	degraftt@gmail.com	degraftt@gmail.com	X
ejpam-3165	15	11	(	(	PUNCT
ejpam-3165	15	12	e.	e.	PROPN
ejpam-3165	15	13	d.	d.	PROPN
ejpam-3165	15	14	j.	j.	PROPN
ejpam-3165	15	15	owusu	owusu	PROPN
ejpam-3165	15	16	-	-	PROPN
ejpam-3165	15	17	ansah	ansah	PROPN
ejpam-3165	15	18	)	)	PUNCT
ejpam-3165	15	19	,	,	PUNCT
ejpam-3165	15	20	skamponsah@knust.edu.gh	skamponsah@knust.edu.gh	NOUN
ejpam-3165	15	21	(	(	PUNCT
ejpam-3165	15	22	s.	s.	PROPN
ejpam-3165	15	23	k.	k.	PROPN
ejpam-3165	15	24	amponsah	amponsah	PROPN
ejpam-3165	15	25	)	)	PUNCT
ejpam-3165	15	26	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3165	16	1	352	352	NUM
ejpam-3165	16	2	c	c	AUX
ejpam-3165	16	3	©	©	PROPN
ejpam-3165	16	4	2018	2018	NUM
ejpam-3165	16	5	ejpam	ejpam	VERB
ejpam-3165	16	6	all	all	DET
ejpam-3165	16	7	rights	right	NOUN
ejpam-3165	16	8	reserved	reserve	VERB
ejpam-3165	16	9	.	.	PUNCT
ejpam-3165	17	1	barnes	barnes	PROPN
ejpam-3165	17	2	et	et	PROPN
ejpam-3165	17	3	al	al	PROPN
ejpam-3165	17	4	.	.	PUNCT
ejpam-3165	17	5	/	/	SYM
ejpam-3165	17	6	eur	eur	PROPN
ejpam-3165	17	7	.	.	PUNCT
ejpam-3165	18	1	j.	j.	PROPN
ejpam-3165	18	2	pure	pure	PROPN
ejpam-3165	18	3	appl	appl	PROPN
ejpam-3165	18	4	.	.	PROPN
ejpam-3165	18	5	math	math	PROPN
ejpam-3165	18	6	,	,	PUNCT
ejpam-3165	18	7	11	11	NUM
ejpam-3165	18	8	(	(	PUNCT
ejpam-3165	18	9	1	1	NUM
ejpam-3165	18	10	)	)	PUNCT
ejpam-3165	18	11	(	(	PUNCT
ejpam-3165	18	12	2018	2018	NUM
ejpam-3165	18	13	)	)	PUNCT
ejpam-3165	18	14	,	,	PUNCT
ejpam-3165	18	15	352	352	NUM
ejpam-3165	18	16	-	-	SYM
ejpam-3165	18	17	361	361	NUM
ejpam-3165	18	18	353	353	NUM
ejpam-3165	18	19	a	a	DET
ejpam-3165	18	20	research	research	NOUN
ejpam-3165	18	21	paper	paper	NOUN
ejpam-3165	18	22	by	by	ADP
ejpam-3165	18	23	author	author	NOUN
ejpam-3165	18	24	in	in	ADP
ejpam-3165	18	25	[	[	X
ejpam-3165	18	26	3	3	NUM
ejpam-3165	18	27	]	]	PUNCT
ejpam-3165	18	28	.	.	PUNCT
ejpam-3165	19	1	in	in	ADP
ejpam-3165	19	2	[	[	X
ejpam-3165	19	3	4	4	NUM
ejpam-3165	19	4	]	]	PUNCT
ejpam-3165	19	5	,	,	PUNCT
ejpam-3165	19	6	the	the	DET
ejpam-3165	19	7	author	author	NOUN
ejpam-3165	19	8	applied	apply	VERB
ejpam-3165	19	9	generalized	generalize	VERB
ejpam-3165	19	10	minkowski	minkowski	PROPN
ejpam-3165	19	11	’s	’s	PART
ejpam-3165	19	12	inequality	inequality	NOUN
ejpam-3165	19	13	in	in	ADP
ejpam-3165	19	14	a	a	DET
ejpam-3165	19	15	generalized	generalized	ADJ
ejpam-3165	19	16	vector	vector	NOUN
ejpam-3165	19	17	space	space	NOUN
ejpam-3165	19	18	to	to	PART
ejpam-3165	19	19	obtain	obtain	VERB
ejpam-3165	19	20	the	the	DET
ejpam-3165	19	21	triangle	triangle	NOUN
ejpam-3165	19	22	inequality	inequality	NOUN
ejpam-3165	19	23	.	.	PUNCT
ejpam-3165	20	1	the	the	DET
ejpam-3165	20	2	authors	author	NOUN
ejpam-3165	20	3	in	in	ADP
ejpam-3165	20	4	[	[	X
ejpam-3165	20	5	5	5	NUM
ejpam-3165	20	6	]	]	PUNCT
ejpam-3165	20	7	,	,	PUNCT
ejpam-3165	20	8	used	use	VERB
ejpam-3165	20	9	both	both	PRON
ejpam-3165	20	10	the	the	DET
ejpam-3165	20	11	notion	notion	NOUN
ejpam-3165	20	12	of	of	ADP
ejpam-3165	20	13	q−norm	q−norm	NOUN
ejpam-3165	20	14	and	and	CCONJ
ejpam-3165	20	15	-	-	PUNCT
ejpam-3165	20	16	ψ	ψ	NOUN
ejpam-3165	20	17	norm	norm	NOUN
ejpam-3165	20	18	to	to	PART
ejpam-3165	20	19	construct	construct	VERB
ejpam-3165	20	20	the	the	DET
ejpam-3165	20	21	triangle	triangle	NOUN
ejpam-3165	20	22	inequality	inequality	NOUN
ejpam-3165	20	23	.	.	PUNCT
ejpam-3165	21	1	another	another	DET
ejpam-3165	21	2	version	version	NOUN
ejpam-3165	21	3	for	for	ADP
ejpam-3165	21	4	obtaining	obtain	VERB
ejpam-3165	21	5	this	this	DET
ejpam-3165	21	6	kind	kind	NOUN
ejpam-3165	21	7	of	of	ADP
ejpam-3165	21	8	triangle	triangle	NOUN
ejpam-3165	21	9	inequality	inequality	NOUN
ejpam-3165	21	10	in	in	ADP
ejpam-3165	21	11	banach	banach	NOUN
ejpam-3165	21	12	space	space	NOUN
ejpam-3165	21	13	was	be	AUX
ejpam-3165	21	14	obtained	obtain	VERB
ejpam-3165	21	15	by	by	ADP
ejpam-3165	21	16	authors	author	NOUN
ejpam-3165	21	17	in	in	ADP
ejpam-3165	21	18	[	[	X
ejpam-3165	21	19	6	6	NUM
ejpam-3165	21	20	]	]	PUNCT
ejpam-3165	21	21	.	.	PUNCT
ejpam-3165	22	1	the	the	DET
ejpam-3165	22	2	author	author	NOUN
ejpam-3165	22	3	in	in	ADP
ejpam-3165	22	4	[	[	X
ejpam-3165	22	5	7	7	NUM
ejpam-3165	22	6	]	]	PUNCT
ejpam-3165	22	7	,	,	PUNCT
ejpam-3165	22	8	obtained	obtain	VERB
ejpam-3165	22	9	an	an	DET
ejpam-3165	22	10	alternative	alternative	ADJ
ejpam-3165	22	11	way	way	NOUN
ejpam-3165	22	12	of	of	ADP
ejpam-3165	22	13	proving	prove	VERB
ejpam-3165	22	14	triangle	triangle	NOUN
ejpam-3165	22	15	inequality	inequality	NOUN
ejpam-3165	22	16	in	in	ADP
ejpam-3165	22	17	banach	banach	NOUN
ejpam-3165	22	18	space	space	NOUN
ejpam-3165	22	19	.	.	PUNCT
ejpam-3165	23	1	in	in	ADP
ejpam-3165	23	2	[	[	X
ejpam-3165	23	3	8	8	NUM
ejpam-3165	23	4	]	]	PUNCT
ejpam-3165	23	5	,	,	PUNCT
ejpam-3165	23	6	the	the	DET
ejpam-3165	23	7	authors	author	NOUN
ejpam-3165	23	8	applied	apply	VERB
ejpam-3165	23	9	the	the	DET
ejpam-3165	23	10	ψ−	ψ−	ADJ
ejpam-3165	23	11	sum	sum	NOUN
ejpam-3165	23	12	of	of	ADP
ejpam-3165	23	13	the	the	DET
ejpam-3165	23	14	vector	vector	NOUN
ejpam-3165	23	15	points	point	NOUN
ejpam-3165	23	16	in	in	ADP
ejpam-3165	23	17	the	the	DET
ejpam-3165	23	18	banach	banach	NOUN
ejpam-3165	23	19	space	space	NOUN
ejpam-3165	23	20	to	to	PART
ejpam-3165	23	21	construct	construct	VERB
ejpam-3165	23	22	the	the	DET
ejpam-3165	23	23	triangle	triangle	NOUN
ejpam-3165	23	24	inequality	inequality	NOUN
ejpam-3165	23	25	.	.	PUNCT
ejpam-3165	24	1	the	the	DET
ejpam-3165	24	2	authors	author	NOUN
ejpam-3165	24	3	in	in	ADP
ejpam-3165	24	4	[	[	X
ejpam-3165	24	5	9	9	NUM
ejpam-3165	24	6	]	]	PUNCT
ejpam-3165	24	7	,	,	PUNCT
ejpam-3165	24	8	observed	observe	VERB
ejpam-3165	24	9	that	that	SCONJ
ejpam-3165	24	10	for	for	ADP
ejpam-3165	24	11	any	any	DET
ejpam-3165	24	12	vectors	vector	NOUN
ejpam-3165	24	13	(	(	PUNCT
ejpam-3165	24	14	µ1	µ1	PROPN
ejpam-3165	24	15	,	,	PUNCT
ejpam-3165	24	16	µ2	µ2	PROPN
ejpam-3165	24	17	,	,	PUNCT
ejpam-3165	24	18	.	.	PUNCT
ejpam-3165	24	19	.	.	PUNCT
ejpam-3165	25	1	.	.	PUNCT
ejpam-3165	26	1	,	,	PUNCT
ejpam-3165	26	2	µn	µn	PROPN
ejpam-3165	26	3	)	)	PUNCT
ejpam-3165	26	4	,	,	PUNCT
ejpam-3165	26	5	in	in	ADP
ejpam-3165	26	6	the	the	DET
ejpam-3165	26	7	euclidean	euclidean	ADJ
ejpam-3165	26	8	space	space	NOUN
ejpam-3165	26	9	the	the	DET
ejpam-3165	26	10	following	follow	VERB
ejpam-3165	26	11	inequality	inequality	NOUN
ejpam-3165	26	12	holds	hold	VERB
ejpam-3165	26	13	:	:	PUNCT
ejpam-3165	26	14	‖x1	‖x1	NOUN
ejpam-3165	27	1	+	+	X
ejpam-3165	27	2	.	.	PUNCT
ejpam-3165	27	3	.	.	PUNCT
ejpam-3165	28	1	.	.	PUNCT
ejpam-3165	29	1	,	,	PUNCT
ejpam-3165	29	2	xn‖p	xn‖p	PROPN
ejpam-3165	29	3	≤	≤	PROPN
ejpam-3165	29	4	‖x1‖p	‖x1‖p	PUNCT
ejpam-3165	29	5	µ1	µ1	PROPN
ejpam-3165	29	6	+	+	X
ejpam-3165	29	7	.	.	PUNCT
ejpam-3165	29	8	.	.	PUNCT
ejpam-3165	30	1	.+	.+	NOUN
ejpam-3165	31	1	‖xn‖p	‖xn‖p	PROPN
ejpam-3165	31	2	µn	µn	PROPN
ejpam-3165	31	3	.	.	PUNCT
ejpam-3165	32	1	the	the	DET
ejpam-3165	32	2	triangle	triangle	NOUN
ejpam-3165	32	3	inequality	inequality	NOUN
ejpam-3165	32	4	has	have	VERB
ejpam-3165	32	5	different	different	ADJ
ejpam-3165	32	6	versions	version	NOUN
ejpam-3165	32	7	.	.	PUNCT
ejpam-3165	33	1	one	one	NUM
ejpam-3165	33	2	of	of	ADP
ejpam-3165	33	3	the	the	DET
ejpam-3165	33	4	particular	particular	ADJ
ejpam-3165	33	5	version	version	NOUN
ejpam-3165	33	6	which	which	PRON
ejpam-3165	33	7	is	be	AUX
ejpam-3165	33	8	recent	recent	ADJ
ejpam-3165	33	9	and	and	CCONJ
ejpam-3165	33	10	has	have	AUX
ejpam-3165	33	11	attracted	attract	VERB
ejpam-3165	33	12	much	much	ADJ
ejpam-3165	33	13	attention	attention	NOUN
ejpam-3165	33	14	of	of	ADP
ejpam-3165	33	15	scientists	scientist	NOUN
ejpam-3165	33	16	in	in	ADP
ejpam-3165	33	17	the	the	DET
ejpam-3165	33	18	21st	21st	ADJ
ejpam-3165	33	19	century	century	NOUN
ejpam-3165	33	20	is	be	AUX
ejpam-3165	33	21	the	the	DET
ejpam-3165	33	22	triangle	triangle	NOUN
ejpam-3165	33	23	inequality	inequality	NOUN
ejpam-3165	33	24	of	of	ADP
ejpam-3165	33	25	the	the	DET
ejpam-3165	33	26	form	form	NOUN
ejpam-3165	33	27	:	:	PUNCT
ejpam-3165	33	28	‖u−	‖u−	NUM
ejpam-3165	33	29	v‖	v‖	NOUN
ejpam-3165	33	30	≤	≤	NOUN
ejpam-3165	33	31	‖u‖+	‖u‖+	PRON
ejpam-3165	33	32	‖v‖	‖v‖	PROPN
ejpam-3165	33	33	,	,	PUNCT
ejpam-3165	33	34	(	(	PUNCT
ejpam-3165	33	35	1	1	X
ejpam-3165	33	36	)	)	PUNCT
ejpam-3165	33	37	for	for	ADP
ejpam-3165	33	38	any	any	DET
ejpam-3165	33	39	two	two	NUM
ejpam-3165	33	40	vectors	vector	NOUN
ejpam-3165	33	41	in	in	ADP
ejpam-3165	33	42	a	a	DET
ejpam-3165	33	43	normed	normed	ADJ
ejpam-3165	33	44	linear	linear	ADJ
ejpam-3165	33	45	space	space	NOUN
ejpam-3165	33	46	v	v	NOUN
ejpam-3165	34	1	[	[	X
ejpam-3165	34	2	see	see	VERB
ejpam-3165	34	3	10	10	NUM
ejpam-3165	34	4	]	]	PUNCT
ejpam-3165	34	5	.	.	PUNCT
ejpam-3165	35	1	this	this	DET
ejpam-3165	35	2	inequality	inequality	NOUN
ejpam-3165	35	3	has	have	VERB
ejpam-3165	35	4	alternative	alternative	ADJ
ejpam-3165	35	5	ways	way	NOUN
ejpam-3165	35	6	of	of	ADP
ejpam-3165	35	7	proving	prove	VERB
ejpam-3165	35	8	it	it	PRON
ejpam-3165	35	9	.	.	PUNCT
ejpam-3165	36	1	for	for	ADP
ejpam-3165	36	2	example	example	NOUN
ejpam-3165	36	3	,	,	PUNCT
ejpam-3165	36	4	see	see	VERB
ejpam-3165	36	5	a	a	DET
ejpam-3165	36	6	research	research	NOUN
ejpam-3165	36	7	paper	paper	NOUN
ejpam-3165	36	8	by	by	ADP
ejpam-3165	36	9	authors	author	NOUN
ejpam-3165	36	10	[	[	X
ejpam-3165	36	11	11	11	NUM
ejpam-3165	36	12	]	]	PUNCT
ejpam-3165	36	13	.	.	PUNCT
ejpam-3165	37	1	in	in	ADP
ejpam-3165	37	2	this	this	DET
ejpam-3165	37	3	paper	paper	NOUN
ejpam-3165	37	4	,	,	PUNCT
ejpam-3165	37	5	we	we	PRON
ejpam-3165	37	6	present	present	VERB
ejpam-3165	37	7	alternative	alternative	ADJ
ejpam-3165	37	8	ways	way	NOUN
ejpam-3165	37	9	of	of	ADP
ejpam-3165	37	10	proving	prove	VERB
ejpam-3165	37	11	triangle	triangle	NOUN
ejpam-3165	37	12	inequality	inequality	NOUN
ejpam-3165	37	13	in	in	ADP
ejpam-3165	37	14	(	(	PUNCT
ejpam-3165	37	15	1	1	NUM
ejpam-3165	37	16	)	)	PUNCT
ejpam-3165	37	17	;	;	PUNCT
ejpam-3165	37	18	by	by	ADP
ejpam-3165	37	19	the	the	DET
ejpam-3165	37	20	use	use	NOUN
ejpam-3165	37	21	of	of	ADP
ejpam-3165	37	22	concept	concept	NOUN
ejpam-3165	37	23	of	of	ADP
ejpam-3165	37	24	binomial	binomial	NOUN
ejpam-3165	37	25	of	of	ADP
ejpam-3165	37	26	two	two	NUM
ejpam-3165	37	27	vector	vector	NOUN
ejpam-3165	37	28	points	point	NOUN
ejpam-3165	37	29	in	in	ADP
ejpam-3165	37	30	the	the	DET
ejpam-3165	37	31	hilbert	hilbert	NOUN
ejpam-3165	37	32	space	space	NOUN
ejpam-3165	37	33	.	.	PUNCT
ejpam-3165	38	1	this	this	DET
ejpam-3165	38	2	result	result	NOUN
ejpam-3165	38	3	generalizes	generalize	VERB
ejpam-3165	38	4	the	the	DET
ejpam-3165	38	5	proof	proof	NOUN
ejpam-3165	38	6	of	of	ADP
ejpam-3165	38	7	the	the	DET
ejpam-3165	38	8	triangle	triangle	NOUN
ejpam-3165	38	9	inequality	inequality	NOUN
ejpam-3165	38	10	.	.	PUNCT
ejpam-3165	39	1	also	also	ADV
ejpam-3165	39	2	,	,	PUNCT
ejpam-3165	39	3	the	the	DET
ejpam-3165	39	4	proof	proof	NOUN
ejpam-3165	39	5	of	of	ADP
ejpam-3165	39	6	the	the	DET
ejpam-3165	39	7	triangle	triangle	NOUN
ejpam-3165	39	8	inequality	inequality	NOUN
ejpam-3165	39	9	is	be	AUX
ejpam-3165	39	10	proved	prove	VERB
ejpam-3165	39	11	through	through	ADP
ejpam-3165	39	12	the	the	DET
ejpam-3165	39	13	euclidean	euclidean	ADJ
ejpam-3165	39	14	norm	norm	NOUN
ejpam-3165	39	15	.	.	PUNCT
ejpam-3165	40	1	the	the	DET
ejpam-3165	40	2	paper	paper	NOUN
ejpam-3165	40	3	is	be	AUX
ejpam-3165	40	4	organized	organize	VERB
ejpam-3165	40	5	as	as	SCONJ
ejpam-3165	40	6	follows	follow	VERB
ejpam-3165	40	7	.	.	PUNCT
ejpam-3165	41	1	section	section	NOUN
ejpam-3165	41	2	1	1	NUM
ejpam-3165	41	3	contains	contain	VERB
ejpam-3165	41	4	the	the	DET
ejpam-3165	41	5	introduction	introduction	NOUN
ejpam-3165	41	6	,	,	PUNCT
ejpam-3165	41	7	the	the	DET
ejpam-3165	41	8	new	new	ADJ
ejpam-3165	41	9	methods	method	NOUN
ejpam-3165	41	10	for	for	ADP
ejpam-3165	41	11	proving	prove	VERB
ejpam-3165	41	12	the	the	DET
ejpam-3165	41	13	triangle	triangle	NOUN
ejpam-3165	41	14	inequality	inequality	NOUN
ejpam-3165	41	15	in	in	ADP
ejpam-3165	41	16	(	(	PUNCT
ejpam-3165	41	17	1	1	X
ejpam-3165	41	18	)	)	PUNCT
ejpam-3165	41	19	is	be	AUX
ejpam-3165	41	20	seen	see	VERB
ejpam-3165	41	21	in	in	ADP
ejpam-3165	41	22	section	section	NOUN
ejpam-3165	41	23	2	2	NUM
ejpam-3165	41	24	and	and	CCONJ
ejpam-3165	41	25	section	section	NOUN
ejpam-3165	41	26	(	(	PUNCT
ejpam-3165	41	27	3	3	NUM
ejpam-3165	41	28	)	)	PUNCT
ejpam-3165	41	29	contains	contain	VERB
ejpam-3165	41	30	the	the	DET
ejpam-3165	41	31	summary	summary	NOUN
ejpam-3165	41	32	of	of	ADP
ejpam-3165	41	33	this	this	DET
ejpam-3165	41	34	paper	paper	NOUN
ejpam-3165	41	35	.	.	PUNCT
ejpam-3165	42	1	2	2	X
ejpam-3165	42	2	.	.	X
ejpam-3165	42	3	main	main	ADJ
ejpam-3165	42	4	result	result	NOUN
ejpam-3165	42	5	in	in	ADP
ejpam-3165	42	6	this	this	DET
ejpam-3165	42	7	section	section	NOUN
ejpam-3165	42	8	,	,	PUNCT
ejpam-3165	42	9	we	we	PRON
ejpam-3165	42	10	introduce	introduce	VERB
ejpam-3165	42	11	a	a	DET
ejpam-3165	42	12	general	general	ADJ
ejpam-3165	42	13	procedures	procedure	NOUN
ejpam-3165	42	14	for	for	ADP
ejpam-3165	42	15	proving	prove	VERB
ejpam-3165	42	16	the	the	DET
ejpam-3165	42	17	inequality	inequality	NOUN
ejpam-3165	42	18	in	in	ADP
ejpam-3165	42	19	(	(	PUNCT
ejpam-3165	42	20	1	1	NUM
ejpam-3165	42	21	)	)	PUNCT
ejpam-3165	42	22	.	.	PUNCT
ejpam-3165	43	1	firstly	firstly	ADV
ejpam-3165	43	2	,	,	PUNCT
ejpam-3165	43	3	we	we	PRON
ejpam-3165	43	4	make	make	VERB
ejpam-3165	43	5	use	use	NOUN
ejpam-3165	43	6	of	of	ADP
ejpam-3165	43	7	binomial	binomial	NOUN
ejpam-3165	43	8	of	of	ADP
ejpam-3165	43	9	two	two	NUM
ejpam-3165	43	10	vector	vector	NOUN
ejpam-3165	43	11	points	point	NOUN
ejpam-3165	43	12	to	to	PART
ejpam-3165	43	13	establish	establish	VERB
ejpam-3165	43	14	the	the	DET
ejpam-3165	43	15	triangle	triangle	NOUN
ejpam-3165	43	16	inequality	inequality	NOUN
ejpam-3165	43	17	in	in	ADP
ejpam-3165	43	18	the	the	DET
ejpam-3165	43	19	hilbert	hilbert	NOUN
ejpam-3165	43	20	space	space	NOUN
ejpam-3165	43	21	for	for	ADP
ejpam-3165	43	22	any	any	DET
ejpam-3165	43	23	positive	positive	ADJ
ejpam-3165	43	24	integer	integer	NOUN
ejpam-3165	43	25	n.	n.	NOUN
ejpam-3165	43	26	in	in	ADP
ejpam-3165	43	27	addition	addition	NOUN
ejpam-3165	43	28	,	,	PUNCT
ejpam-3165	43	29	we	we	PRON
ejpam-3165	43	30	obtain	obtain	VERB
ejpam-3165	43	31	the	the	DET
ejpam-3165	43	32	same	same	ADJ
ejpam-3165	43	33	result	result	NOUN
ejpam-3165	43	34	by	by	ADP
ejpam-3165	43	35	applying	apply	VERB
ejpam-3165	43	36	the	the	DET
ejpam-3165	43	37	young	young	ADJ
ejpam-3165	43	38	’s	’s	PART
ejpam-3165	43	39	inequality	inequality	NOUN
ejpam-3165	43	40	of	of	ADP
ejpam-3165	43	41	the	the	DET
ejpam-3165	43	42	two	two	NUM
ejpam-3165	43	43	vector	vector	NOUN
ejpam-3165	43	44	points	point	NOUN
ejpam-3165	43	45	through	through	ADP
ejpam-3165	43	46	the	the	DET
ejpam-3165	43	47	euclidean	euclidean	ADJ
ejpam-3165	43	48	norm	norm	NOUN
ejpam-3165	43	49	.	.	PUNCT
ejpam-3165	44	1	these	these	DET
ejpam-3165	44	2	approaches	approach	NOUN
ejpam-3165	44	3	are	be	AUX
ejpam-3165	44	4	easier	easy	ADJ
ejpam-3165	44	5	and	and	CCONJ
ejpam-3165	44	6	give	give	VERB
ejpam-3165	44	7	better	well	ADJ
ejpam-3165	44	8	understanding	understanding	NOUN
ejpam-3165	44	9	of	of	ADP
ejpam-3165	44	10	the	the	DET
ejpam-3165	44	11	triangle	triangle	NOUN
ejpam-3165	44	12	inequality	inequality	NOUN
ejpam-3165	44	13	.	.	PUNCT
ejpam-3165	45	1	definition	definition	NOUN
ejpam-3165	45	2	1	1	NUM
ejpam-3165	45	3	(	(	PUNCT
ejpam-3165	45	4	inner	inner	ADJ
ejpam-3165	45	5	product	product	NOUN
ejpam-3165	45	6	space	space	NOUN
ejpam-3165	45	7	)	)	PUNCT
ejpam-3165	45	8	.	.	PUNCT
ejpam-3165	46	1	let	let	VERB
ejpam-3165	46	2	x	x	PRON
ejpam-3165	46	3	be	be	AUX
ejpam-3165	46	4	a	a	DET
ejpam-3165	46	5	vector	vector	NOUN
ejpam-3165	46	6	space	space	NOUN
ejpam-3165	46	7	of	of	ADP
ejpam-3165	46	8	over	over	ADP
ejpam-3165	46	9	k.	k.	PROPN
ejpam-3165	46	10	a	a	DET
ejpam-3165	46	11	function	function	NOUN
ejpam-3165	46	12	(	(	PUNCT
ejpam-3165	46	13	.	.	PUNCT
ejpam-3165	46	14	,	,	PUNCT
ejpam-3165	46	15	.	.	PUNCT
ejpam-3165	46	16	)	)	PUNCT
ejpam-3165	47	1	:	:	PUNCT
ejpam-3165	47	2	x	x	X
ejpam-3165	47	3	×x	×x	NUM
ejpam-3165	47	4	→	→	SYM
ejpam-3165	47	5	k	k	X
ejpam-3165	47	6	is	be	AUX
ejpam-3165	47	7	called	call	VERB
ejpam-3165	47	8	an	an	DET
ejpam-3165	47	9	inner	inner	ADJ
ejpam-3165	47	10	product	product	NOUN
ejpam-3165	47	11	space	space	NOUN
ejpam-3165	47	12	on	on	ADP
ejpam-3165	47	13	the	the	DET
ejpam-3165	47	14	vector	vector	NOUN
ejpam-3165	47	15	space	space	NOUN
ejpam-3165	47	16	x	x	NOUN
ejpam-3165	47	17	over	over	ADP
ejpam-3165	47	18	k	k	PROPN
ejpam-3165	47	19	if	if	SCONJ
ejpam-3165	47	20	:	:	PUNCT
ejpam-3165	47	21	p1	p1	NOUN
ejpam-3165	47	22	:	:	PUNCT
ejpam-3165	47	23	for	for	ADP
ejpam-3165	47	24	all	all	PRON
ejpam-3165	47	25	x	x	SYM
ejpam-3165	47	26	∈	∈	PROPN
ejpam-3165	47	27	x	x	X
ejpam-3165	47	28	,	,	PUNCT
ejpam-3165	47	29	(	(	PUNCT
ejpam-3165	47	30	x	x	NOUN
ejpam-3165	47	31	,	,	PUNCT
ejpam-3165	47	32	x	x	X
ejpam-3165	47	33	)	)	PUNCT
ejpam-3165	47	34	≥	≥	NOUN
ejpam-3165	47	35	0	0	NUM
ejpam-3165	47	36	,	,	PUNCT
ejpam-3165	47	37	and	and	CCONJ
ejpam-3165	47	38	(	(	PUNCT
ejpam-3165	47	39	x	x	NOUN
ejpam-3165	47	40	,	,	PUNCT
ejpam-3165	47	41	x	x	X
ejpam-3165	47	42	)	)	PUNCT
ejpam-3165	47	43	=	=	SYM
ejpam-3165	47	44	0	0	PUNCT
ejpam-3165	48	1	if	if	SCONJ
ejpam-3165	48	2	and	and	CCONJ
ejpam-3165	48	3	only	only	ADV
ejpam-3165	48	4	if	if	SCONJ
ejpam-3165	48	5	x	x	SYM
ejpam-3165	48	6	=	=	SYM
ejpam-3165	48	7	0	0	NUM
ejpam-3165	48	8	p2	p2	NOUN
ejpam-3165	48	9	:	:	PUNCT
ejpam-3165	48	10	(	(	PUNCT
ejpam-3165	48	11	x1	x1	PROPN
ejpam-3165	48	12	+	+	CCONJ
ejpam-3165	48	13	x2	x2	PROPN
ejpam-3165	48	14	,	,	PUNCT
ejpam-3165	48	15	y	y	NOUN
ejpam-3165	48	16	)	)	PUNCT
ejpam-3165	48	17	=	=	SYM
ejpam-3165	48	18	(	(	PUNCT
ejpam-3165	48	19	x1	x1	PROPN
ejpam-3165	48	20	,	,	PUNCT
ejpam-3165	48	21	y	y	PROPN
ejpam-3165	48	22	)	)	PUNCT
ejpam-3165	49	1	+	+	CCONJ
ejpam-3165	49	2	(	(	PUNCT
ejpam-3165	49	3	x2	x2	PROPN
ejpam-3165	49	4	,	,	PUNCT
ejpam-3165	49	5	y	y	PROPN
ejpam-3165	49	6	)	)	PUNCT
ejpam-3165	49	7	and	and	CCONJ
ejpam-3165	49	8	(	(	PUNCT
ejpam-3165	49	9	αx	αx	NOUN
ejpam-3165	49	10	,	,	PUNCT
ejpam-3165	49	11	y	y	NOUN
ejpam-3165	49	12	)	)	PUNCT
ejpam-3165	49	13	=	=	SYM
ejpam-3165	49	14	α(x	α(x	PROPN
ejpam-3165	49	15	,	,	PUNCT
ejpam-3165	49	16	y	y	PROPN
ejpam-3165	49	17	)	)	PUNCT
ejpam-3165	49	18	,	,	PUNCT
ejpam-3165	49	19	for	for	ADP
ejpam-3165	49	20	all	all	DET
ejpam-3165	49	21	x1	x1	PROPN
ejpam-3165	49	22	,	,	PUNCT
ejpam-3165	49	23	x2	x2	PROPN
ejpam-3165	49	24	,	,	PUNCT
ejpam-3165	49	25	y	y	PROPN
ejpam-3165	49	26	∈	∈	PROPN
ejpam-3165	49	27	x	x	X
ejpam-3165	49	28	and	and	CCONJ
ejpam-3165	49	29	α	α	PROPN
ejpam-3165	49	30	∈	∈	PROPN
ejpam-3165	49	31	k	k	PROPN
ejpam-3165	49	32	p3	p3	PROPN
ejpam-3165	49	33	:	:	PUNCT
ejpam-3165	49	34	(	(	PUNCT
ejpam-3165	49	35	x	x	X
ejpam-3165	49	36	,	,	PUNCT
ejpam-3165	49	37	y	y	NOUN
ejpam-3165	49	38	)	)	PUNCT
ejpam-3165	49	39	=	=	SYM
ejpam-3165	49	40	¯(y	¯(y	NOUN
ejpam-3165	49	41	,	,	PUNCT
ejpam-3165	49	42	x	x	NOUN
ejpam-3165	49	43	)	)	PUNCT
ejpam-3165	49	44	,	,	PUNCT
ejpam-3165	49	45	for	for	ADP
ejpam-3165	49	46	all	all	DET
ejpam-3165	49	47	x	x	NOUN
ejpam-3165	49	48	,	,	PUNCT
ejpam-3165	49	49	y	y	PROPN
ejpam-3165	49	50	∈	∈	PROPN
ejpam-3165	49	51	x.	x.	NOUN
ejpam-3165	50	1	the	the	DET
ejpam-3165	50	2	bar	bar	NOUN
ejpam-3165	50	3	denotes	denote	VERB
ejpam-3165	50	4	complex	complex	ADJ
ejpam-3165	50	5	conjugate	conjugate	NOUN
ejpam-3165	50	6	of	of	ADP
ejpam-3165	50	7	two	two	NUM
ejpam-3165	50	8	vector	vector	NOUN
ejpam-3165	50	9	points	point	NOUN
ejpam-3165	50	10	in	in	ADP
ejpam-3165	50	11	x	x	X
ejpam-3165	50	12	(	(	PUNCT
ejpam-3165	50	13	see	see	VERB
ejpam-3165	50	14	,	,	PUNCT
ejpam-3165	50	15	12	12	NUM
ejpam-3165	50	16	)	)	PUNCT
ejpam-3165	50	17	thus	thus	ADV
ejpam-3165	50	18	,	,	PUNCT
ejpam-3165	50	19	an	an	DET
ejpam-3165	50	20	inner	inner	ADJ
ejpam-3165	50	21	product	product	NOUN
ejpam-3165	50	22	space	space	NOUN
ejpam-3165	50	23	is	be	AUX
ejpam-3165	50	24	a	a	DET
ejpam-3165	50	25	vector	vector	NOUN
ejpam-3165	50	26	space	space	NOUN
ejpam-3165	50	27	endowed	endow	VERB
ejpam-3165	50	28	with	with	ADP
ejpam-3165	50	29	an	an	DET
ejpam-3165	50	30	inner	inner	ADJ
ejpam-3165	50	31	product	product	NOUN
ejpam-3165	50	32	.	.	PUNCT
ejpam-3165	51	1	barnes	barnes	PROPN
ejpam-3165	51	2	et	et	PROPN
ejpam-3165	51	3	al	al	PROPN
ejpam-3165	51	4	.	.	PUNCT
ejpam-3165	51	5	/	/	SYM
ejpam-3165	51	6	eur	eur	PROPN
ejpam-3165	51	7	.	.	PUNCT
ejpam-3165	52	1	j.	j.	PROPN
ejpam-3165	52	2	pure	pure	PROPN
ejpam-3165	52	3	appl	appl	PROPN
ejpam-3165	52	4	.	.	PROPN
ejpam-3165	52	5	math	math	PROPN
ejpam-3165	52	6	,	,	PUNCT
ejpam-3165	52	7	11	11	NUM
ejpam-3165	52	8	(	(	PUNCT
ejpam-3165	52	9	1	1	NUM
ejpam-3165	52	10	)	)	PUNCT
ejpam-3165	52	11	(	(	PUNCT
ejpam-3165	52	12	2018	2018	NUM
ejpam-3165	52	13	)	)	PUNCT
ejpam-3165	52	14	,	,	PUNCT
ejpam-3165	52	15	352	352	NUM
ejpam-3165	52	16	-	-	SYM
ejpam-3165	52	17	361	361	NUM
ejpam-3165	52	18	354	354	NUM
ejpam-3165	52	19	theorem	theorem	NOUN
ejpam-3165	52	20	1	1	NUM
ejpam-3165	52	21	(	(	PUNCT
ejpam-3165	52	22	cauchy	cauchy	NOUN
ejpam-3165	52	23	-	-	PUNCT
ejpam-3165	52	24	schwarz	schwarz	PROPN
ejpam-3165	52	25	inequality	inequality	NOUN
ejpam-3165	52	26	)	)	PUNCT
ejpam-3165	52	27	.	.	PUNCT
ejpam-3165	53	1	if	if	SCONJ
ejpam-3165	53	2	u	u	PROPN
ejpam-3165	53	3	and	and	CCONJ
ejpam-3165	53	4	v	v	NOUN
ejpam-3165	53	5	are	be	AUX
ejpam-3165	53	6	any	any	DET
ejpam-3165	53	7	two	two	NUM
ejpam-3165	53	8	vectors	vector	NOUN
ejpam-3165	53	9	in	in	ADP
ejpam-3165	53	10	an	an	DET
ejpam-3165	53	11	inner	inner	ADJ
ejpam-3165	53	12	product	product	NOUN
ejpam-3165	53	13	space	space	NOUN
ejpam-3165	53	14	v	v	NOUN
ejpam-3165	53	15	,	,	PUNCT
ejpam-3165	53	16	then	then	ADV
ejpam-3165	53	17	|(u	|(u	NUM
ejpam-3165	53	18	,	,	PUNCT
ejpam-3165	53	19	v)|	v)|	VERB
ejpam-3165	53	20	≤	≤	ADJ
ejpam-3165	53	21	‖u‖‖v‖	‖u‖‖v‖	PROPN
ejpam-3165	53	22	(	(	PUNCT
ejpam-3165	53	23	see	see	PROPN
ejpam-3165	53	24	,	,	PUNCT
ejpam-3165	53	25	13	13	NUM
ejpam-3165	53	26	)	)	PUNCT
ejpam-3165	53	27	.	.	PUNCT
ejpam-3165	54	1	2.1	2.1	NUM
ejpam-3165	54	2	.	.	PUNCT
ejpam-3165	55	1	a	a	DET
ejpam-3165	55	2	proof	proof	NOUN
ejpam-3165	55	3	of	of	ADP
ejpam-3165	55	4	triangle	triangle	NOUN
ejpam-3165	55	5	inequality	inequality	NOUN
ejpam-3165	55	6	through	through	ADP
ejpam-3165	55	7	binomial	binomial	ADJ
ejpam-3165	55	8	inequality	inequality	NOUN
ejpam-3165	55	9	in	in	ADP
ejpam-3165	55	10	this	this	DET
ejpam-3165	55	11	section	section	NOUN
ejpam-3165	55	12	,	,	PUNCT
ejpam-3165	55	13	we	we	PRON
ejpam-3165	55	14	introduce	introduce	VERB
ejpam-3165	55	15	an	an	DET
ejpam-3165	55	16	alternative	alternative	ADJ
ejpam-3165	55	17	way	way	NOUN
ejpam-3165	55	18	of	of	ADP
ejpam-3165	55	19	proving	prove	VERB
ejpam-3165	55	20	the	the	DET
ejpam-3165	55	21	triangle	triangle	NOUN
ejpam-3165	55	22	inequality	inequality	NOUN
ejpam-3165	55	23	through	through	ADP
ejpam-3165	55	24	binomial	binomial	ADJ
ejpam-3165	55	25	inequality	inequality	NOUN
ejpam-3165	55	26	.	.	PUNCT
ejpam-3165	56	1	by	by	ADP
ejpam-3165	56	2	induction	induction	NOUN
ejpam-3165	56	3	,	,	PUNCT
ejpam-3165	56	4	we	we	PRON
ejpam-3165	56	5	prove	prove	VERB
ejpam-3165	56	6	the	the	DET
ejpam-3165	56	7	triangle	triangle	NOUN
ejpam-3165	56	8	inequality	inequality	NOUN
ejpam-3165	56	9	in	in	ADP
ejpam-3165	56	10	(	(	PUNCT
ejpam-3165	56	11	1	1	NUM
ejpam-3165	56	12	)	)	PUNCT
ejpam-3165	56	13	as	as	SCONJ
ejpam-3165	56	14	follows	follow	VERB
ejpam-3165	56	15	.	.	PUNCT
ejpam-3165	57	1	firstly	firstly	ADV
ejpam-3165	57	2	,	,	PUNCT
ejpam-3165	57	3	we	we	PRON
ejpam-3165	57	4	consider	consider	VERB
ejpam-3165	57	5	an	an	DET
ejpam-3165	57	6	integer	integer	NOUN
ejpam-3165	57	7	n	n	NOUN
ejpam-3165	57	8	=	=	SYM
ejpam-3165	57	9	2	2	NUM
ejpam-3165	57	10	,	,	PUNCT
ejpam-3165	57	11	we	we	PRON
ejpam-3165	57	12	observe	observe	VERB
ejpam-3165	57	13	the	the	DET
ejpam-3165	57	14	following	following	NOUN
ejpam-3165	57	15	:	:	PUNCT
ejpam-3165	57	16	(	(	PUNCT
ejpam-3165	57	17	u+	u+	NUM
ejpam-3165	57	18	v)2	v)2	PROPN
ejpam-3165	57	19	≥	≥	NOUN
ejpam-3165	57	20	0	0	NUM
ejpam-3165	57	21	(	(	PUNCT
ejpam-3165	57	22	u	u	NOUN
ejpam-3165	57	23	,	,	PUNCT
ejpam-3165	57	24	u	u	NOUN
ejpam-3165	57	25	)	)	PUNCT
ejpam-3165	57	26	+	+	CCONJ
ejpam-3165	57	27	2(u	2(u	NUM
ejpam-3165	57	28	,	,	PUNCT
ejpam-3165	57	29	v	v	NOUN
ejpam-3165	57	30	)	)	PUNCT
ejpam-3165	57	31	+	+	CCONJ
ejpam-3165	57	32	(	(	PUNCT
ejpam-3165	57	33	v	v	NOUN
ejpam-3165	57	34	,	,	PUNCT
ejpam-3165	57	35	v	v	NOUN
ejpam-3165	57	36	)	)	PUNCT
ejpam-3165	57	37	≥	≥	NOUN
ejpam-3165	57	38	0	0	NUM
ejpam-3165	57	39	{	{	PUNCT
ejpam-3165	57	40	(	(	PUNCT
ejpam-3165	57	41	u	u	NOUN
ejpam-3165	57	42	,	,	PUNCT
ejpam-3165	57	43	u	u	NOUN
ejpam-3165	57	44	)	)	PUNCT
ejpam-3165	57	45	+	+	CCONJ
ejpam-3165	57	46	(	(	PUNCT
ejpam-3165	57	47	v	v	NOUN
ejpam-3165	57	48	,	,	PUNCT
ejpam-3165	57	49	v	v	NOUN
ejpam-3165	57	50	)	)	PUNCT
ejpam-3165	57	51	}	}	PUNCT
ejpam-3165	57	52	≥	≥	PROPN
ejpam-3165	57	53	−2(u	−2(u	NUM
ejpam-3165	57	54	,	,	PUNCT
ejpam-3165	57	55	v	v	NOUN
ejpam-3165	57	56	)	)	PUNCT
ejpam-3165	57	57	−{(u	−{(u	NOUN
ejpam-3165	57	58	,	,	PUNCT
ejpam-3165	57	59	u	u	NOUN
ejpam-3165	57	60	)	)	PUNCT
ejpam-3165	58	1	+	+	CCONJ
ejpam-3165	58	2	(	(	PUNCT
ejpam-3165	58	3	v	v	NOUN
ejpam-3165	58	4	,	,	PUNCT
ejpam-3165	58	5	v	v	NOUN
ejpam-3165	58	6	)	)	PUNCT
ejpam-3165	58	7	}	}	PUNCT
ejpam-3165	58	8	≤	≤	NUM
ejpam-3165	58	9	2(u	2(u	NUM
ejpam-3165	58	10	,	,	PUNCT
ejpam-3165	58	11	v	v	NOUN
ejpam-3165	58	12	)	)	PUNCT
ejpam-3165	58	13	−{(u	−{(u	NOUN
ejpam-3165	58	14	,	,	PUNCT
ejpam-3165	58	15	u	u	NOUN
ejpam-3165	58	16	)	)	PUNCT
ejpam-3165	58	17	+	+	CCONJ
ejpam-3165	58	18	(	(	PUNCT
ejpam-3165	58	19	v	v	NOUN
ejpam-3165	58	20	,	,	PUNCT
ejpam-3165	58	21	v)−	v)−	PROPN
ejpam-3165	58	22	2(u	2(u	NUM
ejpam-3165	58	23	,	,	PUNCT
ejpam-3165	58	24	v	v	NOUN
ejpam-3165	58	25	)	)	PUNCT
ejpam-3165	58	26	}	}	PUNCT
ejpam-3165	58	27	=	=	SYM
ejpam-3165	58	28	4(u	4(u	NUM
ejpam-3165	58	29	,	,	PUNCT
ejpam-3165	58	30	v	v	NOUN
ejpam-3165	58	31	)	)	PUNCT
ejpam-3165	58	32	−(u−	−(u−	ADV
ejpam-3165	58	33	v)2	v)2	PROPN
ejpam-3165	58	34	=	=	SYM
ejpam-3165	58	35	4(u	4(u	NUM
ejpam-3165	58	36	,	,	PUNCT
ejpam-3165	58	37	v	v	NOUN
ejpam-3165	58	38	)	)	PUNCT
ejpam-3165	58	39	‖	‖	PROPN
ejpam-3165	58	40	−	−	PROPN
ejpam-3165	58	41	(	(	PUNCT
ejpam-3165	58	42	u−	u−	NOUN
ejpam-3165	58	43	v)2‖	v)2‖	NOUN
ejpam-3165	58	44	=	=	SYM
ejpam-3165	58	45	‖4(u	‖4(u	PROPN
ejpam-3165	58	46	,	,	PUNCT
ejpam-3165	58	47	v)‖	v)‖	NOUN
ejpam-3165	58	48	‖(u−	‖(u−	PUNCT
ejpam-3165	58	49	v)‖2	v)‖2	NOUN
ejpam-3165	58	50	≤	≤	NUM
ejpam-3165	58	51	4‖u‖‖v‖	4‖u‖‖v‖	NOUN
ejpam-3165	58	52	(	(	PUNCT
ejpam-3165	58	53	2	2	NUM
ejpam-3165	58	54	)	)	PUNCT
ejpam-3165	58	55	on	on	ADP
ejpam-3165	58	56	other	other	ADJ
ejpam-3165	58	57	hand	hand	NOUN
ejpam-3165	58	58	,	,	PUNCT
ejpam-3165	58	59	we	we	PRON
ejpam-3165	58	60	see	see	VERB
ejpam-3165	58	61	that	that	PRON
ejpam-3165	58	62	:	:	PUNCT
ejpam-3165	58	63	(	(	PUNCT
ejpam-3165	58	64	u−	u−	PROPN
ejpam-3165	58	65	v)2	v)2	ADJ
ejpam-3165	58	66	≥	≥	NOUN
ejpam-3165	58	67	0	0	NUM
ejpam-3165	58	68	(	(	PUNCT
ejpam-3165	58	69	u	u	NOUN
ejpam-3165	58	70	,	,	PUNCT
ejpam-3165	58	71	u)−	u)−	PROPN
ejpam-3165	58	72	2(u	2(u	NUM
ejpam-3165	58	73	,	,	PUNCT
ejpam-3165	58	74	v	v	NOUN
ejpam-3165	58	75	)	)	PUNCT
ejpam-3165	58	76	+	+	CCONJ
ejpam-3165	58	77	(	(	PUNCT
ejpam-3165	58	78	v	v	NOUN
ejpam-3165	58	79	,	,	PUNCT
ejpam-3165	58	80	v	v	NOUN
ejpam-3165	58	81	)	)	PUNCT
ejpam-3165	58	82	≥	≥	NOUN
ejpam-3165	58	83	0	0	NUM
ejpam-3165	58	84	−2(u	−2(u	NUM
ejpam-3165	58	85	,	,	PUNCT
ejpam-3165	58	86	v	v	NOUN
ejpam-3165	58	87	)	)	PUNCT
ejpam-3165	58	88	=	=	SYM
ejpam-3165	58	89	−{(u	−{(u	NOUN
ejpam-3165	58	90	,	,	PUNCT
ejpam-3165	58	91	u	u	NOUN
ejpam-3165	58	92	)	)	PUNCT
ejpam-3165	58	93	+	+	CCONJ
ejpam-3165	58	94	(	(	PUNCT
ejpam-3165	58	95	v	v	NOUN
ejpam-3165	58	96	,	,	PUNCT
ejpam-3165	58	97	v	v	NOUN
ejpam-3165	58	98	)	)	PUNCT
ejpam-3165	58	99	}	}	PUNCT
ejpam-3165	58	100	2(u	2(u	NUM
ejpam-3165	58	101	,	,	PUNCT
ejpam-3165	58	102	v	v	NOUN
ejpam-3165	58	103	)	)	PUNCT
ejpam-3165	58	104	≤	≤	NOUN
ejpam-3165	58	105	{	{	PUNCT
ejpam-3165	58	106	(	(	PUNCT
ejpam-3165	58	107	u	u	NOUN
ejpam-3165	58	108	,	,	PUNCT
ejpam-3165	58	109	u	u	NOUN
ejpam-3165	58	110	)	)	PUNCT
ejpam-3165	58	111	+	+	CCONJ
ejpam-3165	58	112	(	(	PUNCT
ejpam-3165	58	113	v	v	NOUN
ejpam-3165	58	114	,	,	PUNCT
ejpam-3165	58	115	v	v	NOUN
ejpam-3165	58	116	)	)	PUNCT
ejpam-3165	58	117	}	}	PUNCT
ejpam-3165	58	118	4(u	4(u	NUM
ejpam-3165	58	119	,	,	PUNCT
ejpam-3165	58	120	v	v	NOUN
ejpam-3165	58	121	)	)	PUNCT
ejpam-3165	58	122	=	=	SYM
ejpam-3165	58	123	{	{	PUNCT
ejpam-3165	58	124	(	(	PUNCT
ejpam-3165	58	125	u	u	NOUN
ejpam-3165	58	126	,	,	PUNCT
ejpam-3165	58	127	u	u	NOUN
ejpam-3165	58	128	)	)	PUNCT
ejpam-3165	58	129	+	+	CCONJ
ejpam-3165	58	130	(	(	PUNCT
ejpam-3165	58	131	v	v	NOUN
ejpam-3165	58	132	,	,	PUNCT
ejpam-3165	58	133	v	v	NOUN
ejpam-3165	58	134	)	)	PUNCT
ejpam-3165	58	135	+	+	CCONJ
ejpam-3165	58	136	2(u	2(u	NUM
ejpam-3165	58	137	,	,	PUNCT
ejpam-3165	58	138	v	v	NOUN
ejpam-3165	58	139	)	)	PUNCT
ejpam-3165	58	140	}	}	PUNCT
ejpam-3165	58	141	4(u	4(u	NUM
ejpam-3165	58	142	,	,	PUNCT
ejpam-3165	58	143	v	v	NOUN
ejpam-3165	58	144	)	)	PUNCT
ejpam-3165	58	145	=	=	PUNCT
ejpam-3165	58	146	(	(	PUNCT
ejpam-3165	58	147	u+	u+	NUM
ejpam-3165	58	148	v)2	v)2	PROPN
ejpam-3165	58	149	‖4(u	‖4(u	PROPN
ejpam-3165	58	150	,	,	PUNCT
ejpam-3165	58	151	v)‖	v)‖	NOUN
ejpam-3165	58	152	=	=	PUNCT
ejpam-3165	58	153	‖(u+	‖(u+	NUM
ejpam-3165	58	154	v)2‖	v)2‖	NOUN
ejpam-3165	58	155	4‖u‖‖v‖	4‖u‖‖v‖	NOUN
ejpam-3165	58	156	≤	≤	PROPN
ejpam-3165	58	157	‖u+	‖u+	NOUN
ejpam-3165	58	158	v‖2	v‖2	PROPN
ejpam-3165	58	159	(	(	PUNCT
ejpam-3165	58	160	3	3	X
ejpam-3165	58	161	)	)	PUNCT
ejpam-3165	58	162	applying	apply	VERB
ejpam-3165	58	163	the	the	DET
ejpam-3165	58	164	transitive	transitive	ADJ
ejpam-3165	58	165	law	law	NOUN
ejpam-3165	58	166	to	to	ADP
ejpam-3165	58	167	(	(	PUNCT
ejpam-3165	58	168	2	2	NUM
ejpam-3165	58	169	)	)	PUNCT
ejpam-3165	58	170	and	and	CCONJ
ejpam-3165	58	171	(	(	PUNCT
ejpam-3165	58	172	3	3	NUM
ejpam-3165	58	173	)	)	PUNCT
ejpam-3165	58	174	,	,	PUNCT
ejpam-3165	58	175	we	we	PRON
ejpam-3165	58	176	obtain	obtain	VERB
ejpam-3165	58	177	‖u−	‖u−	ADJ
ejpam-3165	58	178	v‖2	v‖2	NOUN
ejpam-3165	58	179	≤	≤	NUM
ejpam-3165	58	180	‖u+	‖u+	NOUN
ejpam-3165	58	181	v‖2	v‖2	PROPN
ejpam-3165	58	182	(	(	PUNCT
ejpam-3165	58	183	‖u−	‖u−	PROPN
ejpam-3165	58	184	v‖2	v‖2	NOUN
ejpam-3165	58	185	)	)	PUNCT
ejpam-3165	58	186	1	1	NUM
ejpam-3165	58	187	2	2	NUM
ejpam-3165	58	188	=	=	SYM
ejpam-3165	58	189	(	(	PUNCT
ejpam-3165	58	190	‖u+	‖u+	NOUN
ejpam-3165	58	191	v‖2	v‖2	NOUN
ejpam-3165	58	192	)	)	PUNCT
ejpam-3165	58	193	1	1	NUM
ejpam-3165	58	194	2	2	NUM
ejpam-3165	58	195	⇒	⇒	NOUN
ejpam-3165	58	196	‖u−	‖u−	PROPN
ejpam-3165	58	197	v‖	v‖	NOUN
ejpam-3165	58	198	=	=	PUNCT
ejpam-3165	59	1	‖u+	‖u+	NOUN
ejpam-3165	59	2	v‖	v‖	NOUN
ejpam-3165	59	3	⇒	⇒	VERB
ejpam-3165	59	4	‖u−	‖u−	DET
ejpam-3165	59	5	v‖	v‖	NOUN
ejpam-3165	59	6	≤	≤	NOUN
ejpam-3165	59	7	‖u‖+	‖u‖+	PRON
ejpam-3165	59	8	‖v‖	‖v‖	PROPN
ejpam-3165	59	9	for	for	ADP
ejpam-3165	59	10	n	n	NOUN
ejpam-3165	59	11	=	=	SYM
ejpam-3165	59	12	4	4	NUM
ejpam-3165	59	13	,	,	PUNCT
ejpam-3165	59	14	we	we	PRON
ejpam-3165	59	15	observe	observe	VERB
ejpam-3165	59	16	that	that	SCONJ
ejpam-3165	59	17	:	:	PUNCT
ejpam-3165	59	18	(	(	PUNCT
ejpam-3165	59	19	u+	u+	NUM
ejpam-3165	59	20	v)4	v)4	PROPN
ejpam-3165	59	21	≥	≥	X
ejpam-3165	59	22	0	0	NUM
ejpam-3165	59	23	barnes	barnes	PROPN
ejpam-3165	59	24	et	et	PROPN
ejpam-3165	59	25	al	al	PROPN
ejpam-3165	59	26	.	.	PUNCT
ejpam-3165	59	27	/	/	SYM
ejpam-3165	59	28	eur	eur	PROPN
ejpam-3165	59	29	.	.	PUNCT
ejpam-3165	60	1	j.	j.	PROPN
ejpam-3165	60	2	pure	pure	PROPN
ejpam-3165	60	3	appl	appl	PROPN
ejpam-3165	60	4	.	.	PROPN
ejpam-3165	60	5	math	math	PROPN
ejpam-3165	60	6	,	,	PUNCT
ejpam-3165	60	7	11	11	NUM
ejpam-3165	60	8	(	(	PUNCT
ejpam-3165	60	9	1	1	NUM
ejpam-3165	60	10	)	)	PUNCT
ejpam-3165	60	11	(	(	PUNCT
ejpam-3165	60	12	2018	2018	NUM
ejpam-3165	60	13	)	)	PUNCT
ejpam-3165	60	14	,	,	PUNCT
ejpam-3165	60	15	352	352	NUM
ejpam-3165	60	16	-	-	SYM
ejpam-3165	60	17	361	361	NUM
ejpam-3165	60	18	355	355	NUM
ejpam-3165	60	19	(	(	PUNCT
ejpam-3165	60	20	u	u	NOUN
ejpam-3165	60	21	,	,	PUNCT
ejpam-3165	60	22	u)2	u)2	PROPN
ejpam-3165	60	23	+	+	CCONJ
ejpam-3165	60	24	4(u	4(u	NOUN
ejpam-3165	60	25	,	,	PUNCT
ejpam-3165	60	26	u)(u	u)(u	ADJ
ejpam-3165	60	27	,	,	PUNCT
ejpam-3165	60	28	v	v	NOUN
ejpam-3165	60	29	)	)	PUNCT
ejpam-3165	60	30	+	+	CCONJ
ejpam-3165	60	31	6(u	6(u	NUM
ejpam-3165	60	32	,	,	PUNCT
ejpam-3165	60	33	u)(v	u)(v	PROPN
ejpam-3165	60	34	,	,	PUNCT
ejpam-3165	60	35	v	v	NOUN
ejpam-3165	60	36	)	)	PUNCT
ejpam-3165	61	1	+	+	CCONJ
ejpam-3165	61	2	4(u	4(u	NOUN
ejpam-3165	61	3	,	,	PUNCT
ejpam-3165	61	4	v)(v	v)(v	NOUN
ejpam-3165	61	5	,	,	PUNCT
ejpam-3165	61	6	v	v	NOUN
ejpam-3165	61	7	)	)	PUNCT
ejpam-3165	62	1	+	+	CCONJ
ejpam-3165	62	2	(	(	PUNCT
ejpam-3165	62	3	v	v	NOUN
ejpam-3165	62	4	,	,	PUNCT
ejpam-3165	62	5	v)2	v)2	X
ejpam-3165	62	6	≥	≥	NOUN
ejpam-3165	62	7	0	0	NUM
ejpam-3165	62	8	{	{	PUNCT
ejpam-3165	62	9	(	(	PUNCT
ejpam-3165	62	10	u	u	NOUN
ejpam-3165	62	11	,	,	PUNCT
ejpam-3165	62	12	u)2	u)2	ADV
ejpam-3165	62	13	+	+	CCONJ
ejpam-3165	62	14	(	(	PUNCT
ejpam-3165	62	15	v	v	NOUN
ejpam-3165	62	16	,	,	PUNCT
ejpam-3165	62	17	v)2	v)2	ADJ
ejpam-3165	62	18	+	+	CCONJ
ejpam-3165	62	19	6(u	6(u	NUM
ejpam-3165	62	20	,	,	PUNCT
ejpam-3165	62	21	u)(v	u)(v	PROPN
ejpam-3165	62	22	,	,	PUNCT
ejpam-3165	62	23	v	v	NOUN
ejpam-3165	62	24	)	)	PUNCT
ejpam-3165	62	25	}	}	PUNCT
ejpam-3165	62	26	≥	≥	X
ejpam-3165	62	27	−4(u	−4(u	NOUN
ejpam-3165	62	28	,	,	PUNCT
ejpam-3165	62	29	v){(u	v){(u	PROPN
ejpam-3165	62	30	,	,	PUNCT
ejpam-3165	62	31	u	u	NOUN
ejpam-3165	62	32	)	)	PUNCT
ejpam-3165	62	33	+	+	CCONJ
ejpam-3165	62	34	(	(	PUNCT
ejpam-3165	62	35	v	v	NOUN
ejpam-3165	62	36	,	,	PUNCT
ejpam-3165	62	37	v	v	NOUN
ejpam-3165	62	38	)	)	PUNCT
ejpam-3165	62	39	}	}	PUNCT
ejpam-3165	62	40	−{(u	−{(u	NOUN
ejpam-3165	62	41	,	,	PUNCT
ejpam-3165	62	42	u)2	u)2	ADV
ejpam-3165	62	43	+	+	CCONJ
ejpam-3165	62	44	(	(	PUNCT
ejpam-3165	62	45	v	v	NOUN
ejpam-3165	62	46	,	,	PUNCT
ejpam-3165	62	47	v)2	v)2	ADJ
ejpam-3165	62	48	+	+	CCONJ
ejpam-3165	62	49	6(u	6(u	NUM
ejpam-3165	62	50	,	,	PUNCT
ejpam-3165	62	51	u)(v	u)(v	PROPN
ejpam-3165	62	52	,	,	PUNCT
ejpam-3165	62	53	v	v	NOUN
ejpam-3165	62	54	)	)	PUNCT
ejpam-3165	62	55	}	}	PUNCT
ejpam-3165	62	56	≤	≤	ADV
ejpam-3165	62	57	4(u	4(u	NUM
ejpam-3165	62	58	,	,	PUNCT
ejpam-3165	62	59	v){(u	v){(u	PROPN
ejpam-3165	62	60	,	,	PUNCT
ejpam-3165	62	61	u	u	NOUN
ejpam-3165	62	62	)	)	PUNCT
ejpam-3165	62	63	+	+	CCONJ
ejpam-3165	62	64	(	(	PUNCT
ejpam-3165	62	65	v	v	NOUN
ejpam-3165	62	66	,	,	PUNCT
ejpam-3165	62	67	v	v	NOUN
ejpam-3165	62	68	)	)	PUNCT
ejpam-3165	62	69	}	}	PUNCT
ejpam-3165	62	70	{	{	PUNCT
ejpam-3165	62	71	(	(	PUNCT
ejpam-3165	62	72	u	u	NOUN
ejpam-3165	62	73	,	,	PUNCT
ejpam-3165	62	74	u)2	u)2	ADV
ejpam-3165	62	75	+	+	CCONJ
ejpam-3165	62	76	(	(	PUNCT
ejpam-3165	62	77	v	v	NOUN
ejpam-3165	62	78	,	,	PUNCT
ejpam-3165	62	79	v)2	v)2	ADJ
ejpam-3165	62	80	+	+	CCONJ
ejpam-3165	62	81	6(u	6(u	NUM
ejpam-3165	62	82	,	,	PUNCT
ejpam-3165	62	83	u)(v	u)(v	PROPN
ejpam-3165	62	84	,	,	PUNCT
ejpam-3165	62	85	v)−	v)−	PROPN
ejpam-3165	62	86	4(u	4(u	NOUN
ejpam-3165	62	87	,	,	PUNCT
ejpam-3165	62	88	u)(u	u)(u	PROPN
ejpam-3165	62	89	,	,	PUNCT
ejpam-3165	62	90	v)−	v)−	PROPN
ejpam-3165	62	91	4(u	4(u	NUM
ejpam-3165	62	92	,	,	PUNCT
ejpam-3165	62	93	v)(v	v)(v	PROPN
ejpam-3165	62	94	,	,	PUNCT
ejpam-3165	62	95	v	v	NOUN
ejpam-3165	62	96	)	)	PUNCT
ejpam-3165	62	97	}	}	PUNCT
ejpam-3165	62	98	=	=	SYM
ejpam-3165	62	99	8(u	8(u	NUM
ejpam-3165	62	100	,	,	PUNCT
ejpam-3165	62	101	v){(u	v){(u	ADP
ejpam-3165	62	102	,	,	PUNCT
ejpam-3165	62	103	u	u	NOUN
ejpam-3165	62	104	)	)	PUNCT
ejpam-3165	62	105	+	+	CCONJ
ejpam-3165	62	106	(	(	PUNCT
ejpam-3165	62	107	v	v	NOUN
ejpam-3165	62	108	,	,	PUNCT
ejpam-3165	62	109	v	v	NOUN
ejpam-3165	62	110	)	)	PUNCT
ejpam-3165	62	111	}	}	PUNCT
ejpam-3165	62	112	−(u−	−(u−	ADV
ejpam-3165	62	113	v)4	v)4	PROPN
ejpam-3165	62	114	=	=	PUNCT
ejpam-3165	62	115	8(u	8(u	NUM
ejpam-3165	62	116	,	,	PUNCT
ejpam-3165	62	117	v){(u	v){(u	ADP
ejpam-3165	62	118	,	,	PUNCT
ejpam-3165	62	119	u	u	NOUN
ejpam-3165	62	120	)	)	PUNCT
ejpam-3165	62	121	+	+	CCONJ
ejpam-3165	62	122	(	(	PUNCT
ejpam-3165	62	123	v	v	NOUN
ejpam-3165	62	124	,	,	PUNCT
ejpam-3165	62	125	v	v	NOUN
ejpam-3165	62	126	)	)	PUNCT
ejpam-3165	62	127	}	}	PUNCT
ejpam-3165	62	128	‖	‖	PROPN
ejpam-3165	62	129	−	−	PROPN
ejpam-3165	62	130	(	(	PUNCT
ejpam-3165	62	131	u−	u−	NOUN
ejpam-3165	62	132	v)‖4	v)‖4	PROPN
ejpam-3165	62	133	=	=	SYM
ejpam-3165	62	134	‖8(u	‖8(u	PROPN
ejpam-3165	62	135	,	,	PUNCT
ejpam-3165	62	136	v){(u	v){(u	ADP
ejpam-3165	62	137	,	,	PUNCT
ejpam-3165	62	138	u	u	NOUN
ejpam-3165	62	139	)	)	PUNCT
ejpam-3165	62	140	+	+	CCONJ
ejpam-3165	62	141	(	(	PUNCT
ejpam-3165	62	142	v	v	NOUN
ejpam-3165	62	143	,	,	PUNCT
ejpam-3165	62	144	v)}‖	v)}‖	PROPN
ejpam-3165	62	145	‖u−	‖u−	PROPN
ejpam-3165	62	146	v‖4	v‖4	PROPN
ejpam-3165	62	147	≤	≤	NUM
ejpam-3165	62	148	8‖u‖‖v‖{‖u‖2	8‖u‖‖v‖{‖u‖2	PROPN
ejpam-3165	62	149	+	+	CCONJ
ejpam-3165	62	150	‖v‖2	‖v‖2	NOUN
ejpam-3165	62	151	}	}	PUNCT
ejpam-3165	62	152	(	(	PUNCT
ejpam-3165	62	153	4	4	X
ejpam-3165	62	154	)	)	PUNCT
ejpam-3165	62	155	also	also	ADV
ejpam-3165	62	156	,	,	PUNCT
ejpam-3165	62	157	we	we	PRON
ejpam-3165	62	158	see	see	VERB
ejpam-3165	62	159	that	that	PRON
ejpam-3165	62	160	:	:	PUNCT
ejpam-3165	62	161	(	(	PUNCT
ejpam-3165	62	162	u−	u−	PROPN
ejpam-3165	62	163	v)4	v)4	PROPN
ejpam-3165	62	164	≥	≥	NOUN
ejpam-3165	62	165	0	0	NUM
ejpam-3165	62	166	(	(	PUNCT
ejpam-3165	62	167	u	u	NOUN
ejpam-3165	62	168	,	,	PUNCT
ejpam-3165	62	169	u)2	u)2	ADV
ejpam-3165	62	170	−	−	PROPN
ejpam-3165	62	171	4(u	4(u	NOUN
ejpam-3165	62	172	,	,	PUNCT
ejpam-3165	62	173	u)(u	u)(u	ADJ
ejpam-3165	62	174	,	,	PUNCT
ejpam-3165	62	175	v	v	NOUN
ejpam-3165	62	176	)	)	PUNCT
ejpam-3165	62	177	+	+	CCONJ
ejpam-3165	62	178	6(u	6(u	NUM
ejpam-3165	62	179	,	,	PUNCT
ejpam-3165	62	180	u)(v	u)(v	PROPN
ejpam-3165	62	181	,	,	PUNCT
ejpam-3165	62	182	v)−	v)−	PROPN
ejpam-3165	62	183	4(u	4(u	NUM
ejpam-3165	62	184	,	,	PUNCT
ejpam-3165	62	185	v)(v	v)(v	NOUN
ejpam-3165	62	186	,	,	PUNCT
ejpam-3165	62	187	v	v	NOUN
ejpam-3165	62	188	)	)	PUNCT
ejpam-3165	62	189	+	+	CCONJ
ejpam-3165	62	190	(	(	PUNCT
ejpam-3165	62	191	v	v	NOUN
ejpam-3165	62	192	,	,	PUNCT
ejpam-3165	62	193	v)2	v)2	X
ejpam-3165	62	194	≥	≥	NOUN
ejpam-3165	62	195	0	0	NUM
ejpam-3165	62	196	−4(u	−4(u	NOUN
ejpam-3165	62	197	,	,	PUNCT
ejpam-3165	62	198	v){(u	v){(u	PROPN
ejpam-3165	62	199	,	,	PUNCT
ejpam-3165	62	200	u	u	NOUN
ejpam-3165	62	201	)	)	PUNCT
ejpam-3165	63	1	+	+	CCONJ
ejpam-3165	63	2	(	(	PUNCT
ejpam-3165	63	3	v	v	NOUN
ejpam-3165	63	4	,	,	PUNCT
ejpam-3165	63	5	v	v	NOUN
ejpam-3165	63	6	)	)	PUNCT
ejpam-3165	63	7	}	}	PUNCT
ejpam-3165	63	8	=	=	SYM
ejpam-3165	63	9	−{(u	−{(u	NOUN
ejpam-3165	63	10	,	,	PUNCT
ejpam-3165	63	11	u)2	u)2	ADV
ejpam-3165	63	12	+	+	CCONJ
ejpam-3165	63	13	(	(	PUNCT
ejpam-3165	63	14	v	v	NOUN
ejpam-3165	63	15	,	,	PUNCT
ejpam-3165	63	16	v)2	v)2	ADJ
ejpam-3165	63	17	+	+	CCONJ
ejpam-3165	63	18	6(u	6(u	NUM
ejpam-3165	63	19	,	,	PUNCT
ejpam-3165	63	20	u)(v	u)(v	PROPN
ejpam-3165	63	21	,	,	PUNCT
ejpam-3165	63	22	v	v	NOUN
ejpam-3165	63	23	)	)	PUNCT
ejpam-3165	63	24	}	}	PUNCT
ejpam-3165	63	25	4(u	4(u	NUM
ejpam-3165	63	26	,	,	PUNCT
ejpam-3165	63	27	v){(u	v){(u	PROPN
ejpam-3165	63	28	,	,	PUNCT
ejpam-3165	63	29	u	u	NOUN
ejpam-3165	63	30	)	)	PUNCT
ejpam-3165	63	31	+	+	CCONJ
ejpam-3165	63	32	(	(	PUNCT
ejpam-3165	63	33	v	v	NOUN
ejpam-3165	63	34	,	,	PUNCT
ejpam-3165	63	35	v	v	NOUN
ejpam-3165	63	36	)	)	PUNCT
ejpam-3165	63	37	}	}	PUNCT
ejpam-3165	63	38	≤	≤	NOUN
ejpam-3165	63	39	{	{	PUNCT
ejpam-3165	63	40	(	(	PUNCT
ejpam-3165	63	41	u	u	NOUN
ejpam-3165	63	42	,	,	PUNCT
ejpam-3165	63	43	u)2	u)2	ADV
ejpam-3165	63	44	+	+	CCONJ
ejpam-3165	63	45	(	(	PUNCT
ejpam-3165	63	46	v	v	NOUN
ejpam-3165	63	47	,	,	PUNCT
ejpam-3165	63	48	v)2	v)2	ADJ
ejpam-3165	63	49	+	+	CCONJ
ejpam-3165	63	50	6(u	6(u	NUM
ejpam-3165	63	51	,	,	PUNCT
ejpam-3165	63	52	u)(v	u)(v	PROPN
ejpam-3165	63	53	,	,	PUNCT
ejpam-3165	63	54	v	v	NOUN
ejpam-3165	63	55	)	)	PUNCT
ejpam-3165	63	56	}	}	PUNCT
ejpam-3165	63	57	8(u	8(u	NUM
ejpam-3165	63	58	,	,	PUNCT
ejpam-3165	63	59	v){(u	v){(u	ADP
ejpam-3165	63	60	,	,	PUNCT
ejpam-3165	63	61	u	u	NOUN
ejpam-3165	63	62	)	)	PUNCT
ejpam-3165	63	63	+	+	CCONJ
ejpam-3165	63	64	(	(	PUNCT
ejpam-3165	63	65	v	v	NOUN
ejpam-3165	63	66	,	,	PUNCT
ejpam-3165	63	67	v	v	NOUN
ejpam-3165	63	68	)	)	PUNCT
ejpam-3165	63	69	}	}	PUNCT
ejpam-3165	63	70	=	=	SYM
ejpam-3165	63	71	(	(	PUNCT
ejpam-3165	63	72	u+	u+	NUM
ejpam-3165	63	73	v)4	v)4	PROPN
ejpam-3165	63	74	‖8(u	‖8(u	NOUN
ejpam-3165	63	75	,	,	PUNCT
ejpam-3165	63	76	v){(u	v){(u	ADP
ejpam-3165	63	77	,	,	PUNCT
ejpam-3165	63	78	u	u	NOUN
ejpam-3165	63	79	)	)	PUNCT
ejpam-3165	63	80	+	+	CCONJ
ejpam-3165	63	81	(	(	PUNCT
ejpam-3165	63	82	v	v	NOUN
ejpam-3165	63	83	,	,	PUNCT
ejpam-3165	63	84	v)}‖	v)}‖	PROPN
ejpam-3165	63	85	=	=	PUNCT
ejpam-3165	64	1	‖(u+	‖(u+	NUM
ejpam-3165	64	2	v)‖4	v)‖4	PROPN
ejpam-3165	64	3	8‖u‖‖v‖{‖u‖2	8‖u‖‖v‖{‖u‖2	PROPN
ejpam-3165	64	4	+	+	CCONJ
ejpam-3165	64	5	‖v‖2	‖v‖2	NOUN
ejpam-3165	64	6	}	}	PUNCT
ejpam-3165	64	7	≤	≤	NUM
ejpam-3165	64	8	‖u+	‖u+	PROPN
ejpam-3165	64	9	v‖4	v‖4	PROPN
ejpam-3165	64	10	(	(	PUNCT
ejpam-3165	64	11	5	5	NUM
ejpam-3165	64	12	)	)	PUNCT
ejpam-3165	64	13	we	we	PRON
ejpam-3165	64	14	see	see	VERB
ejpam-3165	64	15	from	from	ADP
ejpam-3165	64	16	(	(	PUNCT
ejpam-3165	64	17	4	4	NUM
ejpam-3165	64	18	)	)	PUNCT
ejpam-3165	64	19	and	and	CCONJ
ejpam-3165	64	20	(	(	PUNCT
ejpam-3165	64	21	5	5	NUM
ejpam-3165	64	22	)	)	PUNCT
ejpam-3165	64	23	that	that	SCONJ
ejpam-3165	64	24	:	:	PUNCT
ejpam-3165	64	25	‖u−	‖u−	PROPN
ejpam-3165	64	26	v‖4	v‖4	PROPN
ejpam-3165	64	27	≤	≤	PROPN
ejpam-3165	64	28	‖u+	‖u+	PROPN
ejpam-3165	64	29	v‖4	v‖4	PROPN
ejpam-3165	64	30	(	(	PUNCT
ejpam-3165	64	31	‖u−	‖u−	PROPN
ejpam-3165	64	32	v‖4	v‖4	NOUN
ejpam-3165	64	33	)	)	PUNCT
ejpam-3165	64	34	1	1	NUM
ejpam-3165	64	35	4	4	NUM
ejpam-3165	64	36	=	=	SYM
ejpam-3165	64	37	(	(	PUNCT
ejpam-3165	64	38	‖u+	‖u+	NOUN
ejpam-3165	64	39	v‖4	v‖4	NOUN
ejpam-3165	64	40	)	)	PUNCT
ejpam-3165	64	41	1	1	NUM
ejpam-3165	64	42	4	4	NUM
ejpam-3165	64	43	⇒	⇒	NOUN
ejpam-3165	64	44	‖u−	‖u−	PROPN
ejpam-3165	64	45	v‖	v‖	NOUN
ejpam-3165	64	46	=	=	PUNCT
ejpam-3165	64	47	‖u+	‖u+	NOUN
ejpam-3165	64	48	v‖	v‖	NOUN
ejpam-3165	64	49	⇒	⇒	VERB
ejpam-3165	64	50	‖u−	‖u−	PRON
ejpam-3165	64	51	v‖	v‖	NOUN
ejpam-3165	64	52	≤	≤	NUM
ejpam-3165	64	53	‖u‖+	‖u‖+	PRON
ejpam-3165	64	54	‖v‖	‖v‖	PROPN
ejpam-3165	64	55	again	again	ADV
ejpam-3165	64	56	,	,	PUNCT
ejpam-3165	64	57	when	when	SCONJ
ejpam-3165	64	58	n	n	X
ejpam-3165	64	59	=	=	SYM
ejpam-3165	64	60	6	6	NUM
ejpam-3165	64	61	,	,	PUNCT
ejpam-3165	64	62	we	we	PRON
ejpam-3165	64	63	observe	observe	VERB
ejpam-3165	64	64	the	the	DET
ejpam-3165	64	65	following	following	NOUN
ejpam-3165	64	66	:	:	PUNCT
ejpam-3165	64	67	⇒	⇒	NOUN
ejpam-3165	64	68	(	(	PUNCT
ejpam-3165	64	69	u+	u+	NUM
ejpam-3165	64	70	v)6	v)6	NOUN
ejpam-3165	64	71	≥	≥	NOUN
ejpam-3165	64	72	0	0	NUM
ejpam-3165	64	73	⇒	⇒	PROPN
ejpam-3165	64	74	(	(	PUNCT
ejpam-3165	64	75	u	u	NOUN
ejpam-3165	64	76	,	,	PUNCT
ejpam-3165	64	77	u)3	u)3	ADJ
ejpam-3165	64	78	+	+	CCONJ
ejpam-3165	64	79	6(u	6(u	NUM
ejpam-3165	64	80	,	,	PUNCT
ejpam-3165	64	81	u)2(u	u)2(u	NOUN
ejpam-3165	64	82	,	,	PUNCT
ejpam-3165	64	83	v	v	NOUN
ejpam-3165	64	84	)	)	PUNCT
ejpam-3165	64	85	+	+	NOUN
ejpam-3165	64	86	15(u	15(u	NUM
ejpam-3165	64	87	,	,	PUNCT
ejpam-3165	64	88	u)2(v	u)2(v	NOUN
ejpam-3165	64	89	,	,	PUNCT
ejpam-3165	64	90	v	v	NOUN
ejpam-3165	64	91	)	)	PUNCT
ejpam-3165	64	92	+	+	NUM
ejpam-3165	64	93	20(u	20(u	NUM
ejpam-3165	64	94	,	,	PUNCT
ejpam-3165	64	95	v)(u	v)(u	NUM
ejpam-3165	64	96	,	,	PUNCT
ejpam-3165	64	97	u)(v	u)(v	PROPN
ejpam-3165	64	98	,	,	PUNCT
ejpam-3165	64	99	v	v	NOUN
ejpam-3165	64	100	)	)	PUNCT
ejpam-3165	64	101	+	+	NOUN
ejpam-3165	64	102	15(u	15(u	NUM
ejpam-3165	64	103	,	,	PUNCT
ejpam-3165	64	104	u)(v	u)(v	PROPN
ejpam-3165	64	105	,	,	PUNCT
ejpam-3165	64	106	v)2	v)2	ADJ
ejpam-3165	64	107	+	+	CCONJ
ejpam-3165	64	108	6(u	6(u	NUM
ejpam-3165	64	109	,	,	PUNCT
ejpam-3165	64	110	v)(v	v)(v	NOUN
ejpam-3165	64	111	,	,	PUNCT
ejpam-3165	64	112	v)2	v)2	ADJ
ejpam-3165	64	113	+	+	CCONJ
ejpam-3165	64	114	(	(	PUNCT
ejpam-3165	64	115	v	v	NOUN
ejpam-3165	64	116	,	,	PUNCT
ejpam-3165	64	117	v)3	v)3	PROPN
ejpam-3165	64	118	≥	≥	NOUN
ejpam-3165	64	119	0	0	NUM
ejpam-3165	64	120	⇒	⇒	NOUN
ejpam-3165	64	121	6(u	6(u	NUM
ejpam-3165	64	122	,	,	PUNCT
ejpam-3165	64	123	v){(u	v){(u	NOUN
ejpam-3165	64	124	,	,	PUNCT
ejpam-3165	64	125	u)2	u)2	PROPN
ejpam-3165	64	126	+	+	CCONJ
ejpam-3165	64	127	(	(	PUNCT
ejpam-3165	64	128	v	v	NOUN
ejpam-3165	64	129	,	,	PUNCT
ejpam-3165	64	130	v)2	v)2	ADJ
ejpam-3165	65	1	+	+	CCONJ
ejpam-3165	65	2	20	20	NUM
ejpam-3165	65	3	6	6	NUM
ejpam-3165	65	4	(	(	PUNCT
ejpam-3165	65	5	u	u	NOUN
ejpam-3165	65	6	,	,	PUNCT
ejpam-3165	65	7	u)(v	u)(v	PROPN
ejpam-3165	65	8	,	,	PUNCT
ejpam-3165	65	9	v	v	NOUN
ejpam-3165	65	10	)	)	PUNCT
ejpam-3165	65	11	}	}	PUNCT
ejpam-3165	65	12	≥	≥	NOUN
ejpam-3165	65	13	−{(u	−{(u	NOUN
ejpam-3165	65	14	,	,	PUNCT
ejpam-3165	65	15	u)3	u)3	NOUN
ejpam-3165	65	16	+	+	CCONJ
ejpam-3165	65	17	15(u	15(u	NUM
ejpam-3165	65	18	,	,	PUNCT
ejpam-3165	65	19	u)2(v	u)2(v	NOUN
ejpam-3165	65	20	,	,	PUNCT
ejpam-3165	65	21	v	v	NOUN
ejpam-3165	65	22	)	)	PUNCT
ejpam-3165	65	23	+	+	NOUN
ejpam-3165	65	24	15(u	15(u	NUM
ejpam-3165	65	25	,	,	PUNCT
ejpam-3165	65	26	u)(v	u)(v	PROPN
ejpam-3165	65	27	,	,	PUNCT
ejpam-3165	65	28	v)2	v)2	X
ejpam-3165	65	29	+	+	CCONJ
ejpam-3165	65	30	(	(	PUNCT
ejpam-3165	65	31	v	v	NOUN
ejpam-3165	65	32	,	,	PUNCT
ejpam-3165	65	33	v)3	v)3	NOUN
ejpam-3165	65	34	}	}	PUNCT
ejpam-3165	65	35	⇒	⇒	VERB
ejpam-3165	65	36	−{(u	−{(u	NOUN
ejpam-3165	65	37	,	,	PUNCT
ejpam-3165	65	38	u)3	u)3	NOUN
ejpam-3165	65	39	+	+	CCONJ
ejpam-3165	65	40	15(u	15(u	NUM
ejpam-3165	65	41	,	,	PUNCT
ejpam-3165	65	42	u)2(v	u)2(v	NOUN
ejpam-3165	65	43	,	,	PUNCT
ejpam-3165	65	44	v	v	NOUN
ejpam-3165	65	45	)	)	PUNCT
ejpam-3165	65	46	+	+	NOUN
ejpam-3165	65	47	15(u	15(u	NUM
ejpam-3165	65	48	,	,	PUNCT
ejpam-3165	65	49	u)(v	u)(v	PROPN
ejpam-3165	65	50	,	,	PUNCT
ejpam-3165	65	51	v)2	v)2	X
ejpam-3165	65	52	+	+	CCONJ
ejpam-3165	65	53	(	(	PUNCT
ejpam-3165	65	54	v	v	NOUN
ejpam-3165	65	55	,	,	PUNCT
ejpam-3165	65	56	v)3	v)3	NOUN
ejpam-3165	65	57	}	}	PUNCT
ejpam-3165	65	58	≤	≤	NUM
ejpam-3165	65	59	6(u	6(u	NUM
ejpam-3165	65	60	,	,	PUNCT
ejpam-3165	65	61	v){(u	v){(u	NOUN
ejpam-3165	65	62	,	,	PUNCT
ejpam-3165	65	63	u)2	u)2	PROPN
ejpam-3165	65	64	+	+	CCONJ
ejpam-3165	65	65	(	(	PUNCT
ejpam-3165	65	66	v	v	NOUN
ejpam-3165	65	67	,	,	PUNCT
ejpam-3165	65	68	v)2	v)2	ADJ
ejpam-3165	65	69	+	+	CCONJ
ejpam-3165	65	70	20	20	NUM
ejpam-3165	65	71	6	6	NUM
ejpam-3165	65	72	(	(	PUNCT
ejpam-3165	65	73	u	u	NOUN
ejpam-3165	65	74	,	,	PUNCT
ejpam-3165	65	75	u)(v	u)(v	PROPN
ejpam-3165	65	76	,	,	PUNCT
ejpam-3165	65	77	v	v	NOUN
ejpam-3165	65	78	)	)	PUNCT
ejpam-3165	65	79	}	}	PUNCT
ejpam-3165	65	80	⇒	⇒	VERB
ejpam-3165	65	81	−(u−	−(u−	DET
ejpam-3165	65	82	v)6	v)6	NOUN
ejpam-3165	65	83	=	=	PUNCT
ejpam-3165	65	84	12(u	12(u	NUM
ejpam-3165	65	85	,	,	PUNCT
ejpam-3165	65	86	v){(u	v){(u	ADP
ejpam-3165	65	87	,	,	PUNCT
ejpam-3165	65	88	u)2	u)2	PROPN
ejpam-3165	65	89	+	+	CCONJ
ejpam-3165	65	90	(	(	PUNCT
ejpam-3165	65	91	v	v	NOUN
ejpam-3165	65	92	,	,	PUNCT
ejpam-3165	65	93	v)2	v)2	ADJ
ejpam-3165	66	1	+	+	CCONJ
ejpam-3165	66	2	20	20	NUM
ejpam-3165	66	3	6	6	NUM
ejpam-3165	66	4	(	(	PUNCT
ejpam-3165	66	5	u	u	NOUN
ejpam-3165	66	6	,	,	PUNCT
ejpam-3165	66	7	u)(v	u)(v	PROPN
ejpam-3165	66	8	,	,	PUNCT
ejpam-3165	66	9	v	v	NOUN
ejpam-3165	66	10	)	)	PUNCT
ejpam-3165	66	11	}	}	PUNCT
ejpam-3165	66	12	⇒	⇒	NOUN
ejpam-3165	66	13	‖	‖	ADJ
ejpam-3165	66	14	−	−	PROPN
ejpam-3165	66	15	(	(	PUNCT
ejpam-3165	66	16	u−	u−	PROPN
ejpam-3165	66	17	v)6‖	v)6‖	NOUN
ejpam-3165	66	18	=	=	NOUN
ejpam-3165	66	19	‖12(u	‖12(u	NOUN
ejpam-3165	66	20	,	,	PUNCT
ejpam-3165	66	21	v){(u	v){(u	NOUN
ejpam-3165	66	22	,	,	PUNCT
ejpam-3165	66	23	u)2	u)2	PROPN
ejpam-3165	66	24	+	+	CCONJ
ejpam-3165	66	25	(	(	PUNCT
ejpam-3165	66	26	v	v	NOUN
ejpam-3165	66	27	,	,	PUNCT
ejpam-3165	66	28	v)2	v)2	ADJ
ejpam-3165	66	29	+	+	CCONJ
ejpam-3165	66	30	20	20	NUM
ejpam-3165	66	31	6	6	NUM
ejpam-3165	66	32	(	(	PUNCT
ejpam-3165	66	33	u	u	NOUN
ejpam-3165	66	34	,	,	PUNCT
ejpam-3165	66	35	u)(v	u)(v	PROPN
ejpam-3165	66	36	,	,	PUNCT
ejpam-3165	66	37	v)}‖	v)}‖	PROPN
ejpam-3165	66	38	⇒	⇒	VERB
ejpam-3165	66	39	‖(u−	‖(u−	NUM
ejpam-3165	66	40	v)‖6	v)‖6	PROPN
ejpam-3165	66	41	≤	≤	PROPN
ejpam-3165	66	42	12‖u‖‖v‖{‖u‖4	12‖u‖‖v‖{‖u‖4	NUM
ejpam-3165	66	43	+	+	CCONJ
ejpam-3165	66	44	‖v‖4	‖v‖4	X
ejpam-3165	67	1	+	+	CCONJ
ejpam-3165	67	2	20	20	NUM
ejpam-3165	67	3	6	6	NUM
ejpam-3165	67	4	‖u‖2‖v‖2	‖u‖2‖v‖2	NOUN
ejpam-3165	67	5	}	}	PUNCT
ejpam-3165	67	6	.	.	PUNCT
ejpam-3165	68	1	(	(	PUNCT
ejpam-3165	68	2	6	6	X
ejpam-3165	68	3	)	)	PUNCT
ejpam-3165	68	4	barnes	barne	NOUN
ejpam-3165	68	5	et	et	PROPN
ejpam-3165	68	6	al	al	PROPN
ejpam-3165	68	7	.	.	PUNCT
ejpam-3165	68	8	/	/	SYM
ejpam-3165	68	9	eur	eur	PROPN
ejpam-3165	68	10	.	.	PUNCT
ejpam-3165	69	1	j.	j.	PROPN
ejpam-3165	69	2	pure	pure	PROPN
ejpam-3165	69	3	appl	appl	PROPN
ejpam-3165	69	4	.	.	PROPN
ejpam-3165	69	5	math	math	PROPN
ejpam-3165	69	6	,	,	PUNCT
ejpam-3165	69	7	11	11	NUM
ejpam-3165	69	8	(	(	PUNCT
ejpam-3165	69	9	1	1	NUM
ejpam-3165	69	10	)	)	PUNCT
ejpam-3165	69	11	(	(	PUNCT
ejpam-3165	69	12	2018	2018	NUM
ejpam-3165	69	13	)	)	PUNCT
ejpam-3165	69	14	,	,	PUNCT
ejpam-3165	69	15	352	352	NUM
ejpam-3165	69	16	-	-	SYM
ejpam-3165	69	17	361	361	NUM
ejpam-3165	69	18	356	356	NUM
ejpam-3165	69	19	also	also	ADV
ejpam-3165	69	20	,	,	PUNCT
ejpam-3165	69	21	we	we	PRON
ejpam-3165	69	22	observe	observe	VERB
ejpam-3165	69	23	that	that	SCONJ
ejpam-3165	69	24	:	:	PUNCT
ejpam-3165	69	25	(	(	PUNCT
ejpam-3165	69	26	u−	u−	ADJ
ejpam-3165	69	27	v)6	v)6	NOUN
ejpam-3165	69	28	≥	≥	NOUN
ejpam-3165	69	29	0	0	NUM
ejpam-3165	69	30	⇒	⇒	PROPN
ejpam-3165	69	31	(	(	PUNCT
ejpam-3165	69	32	u	u	NOUN
ejpam-3165	69	33	,	,	PUNCT
ejpam-3165	69	34	u)3	u)3	ADJ
ejpam-3165	69	35	−	−	PROPN
ejpam-3165	69	36	6(u	6(u	NUM
ejpam-3165	69	37	,	,	PUNCT
ejpam-3165	69	38	u)2(u	u)2(u	NOUN
ejpam-3165	69	39	,	,	PUNCT
ejpam-3165	69	40	v	v	NOUN
ejpam-3165	69	41	)	)	PUNCT
ejpam-3165	69	42	+	+	NOUN
ejpam-3165	69	43	15(u	15(u	NUM
ejpam-3165	69	44	,	,	PUNCT
ejpam-3165	69	45	u)2(v	u)2(v	PRON
ejpam-3165	69	46	,	,	PUNCT
ejpam-3165	69	47	v)−	v)−	PROPN
ejpam-3165	69	48	20(u	20(u	NUM
ejpam-3165	69	49	,	,	PUNCT
ejpam-3165	69	50	v)(u	v)(u	NUM
ejpam-3165	69	51	,	,	PUNCT
ejpam-3165	69	52	u)(v	u)(v	PROPN
ejpam-3165	69	53	,	,	PUNCT
ejpam-3165	69	54	v	v	NOUN
ejpam-3165	69	55	)	)	PUNCT
ejpam-3165	69	56	+	+	NOUN
ejpam-3165	69	57	15(u	15(u	NUM
ejpam-3165	69	58	,	,	PUNCT
ejpam-3165	69	59	u)(v	u)(v	PROPN
ejpam-3165	69	60	,	,	PUNCT
ejpam-3165	69	61	v)2	v)2	ADJ
ejpam-3165	69	62	−	−	NOUN
ejpam-3165	69	63	6(u	6(u	NUM
ejpam-3165	69	64	,	,	PUNCT
ejpam-3165	69	65	v)(v	v)(v	NOUN
ejpam-3165	69	66	,	,	PUNCT
ejpam-3165	69	67	v)2	v)2	ADJ
ejpam-3165	69	68	+	+	CCONJ
ejpam-3165	69	69	(	(	PUNCT
ejpam-3165	69	70	v	v	NOUN
ejpam-3165	69	71	,	,	PUNCT
ejpam-3165	69	72	v)3	v)3	PROPN
ejpam-3165	69	73	≥	≥	NOUN
ejpam-3165	69	74	0	0	NUM
ejpam-3165	69	75	⇒	⇒	PROPN
ejpam-3165	69	76	−6(u	−6(u	NOUN
ejpam-3165	69	77	,	,	PUNCT
ejpam-3165	69	78	v){(u	v){(u	NOUN
ejpam-3165	69	79	,	,	PUNCT
ejpam-3165	69	80	u)2	u)2	PROPN
ejpam-3165	69	81	+	+	CCONJ
ejpam-3165	69	82	(	(	PUNCT
ejpam-3165	69	83	v	v	NOUN
ejpam-3165	69	84	,	,	PUNCT
ejpam-3165	69	85	v)2	v)2	ADJ
ejpam-3165	69	86	+	+	CCONJ
ejpam-3165	69	87	20	20	NUM
ejpam-3165	69	88	6	6	NUM
ejpam-3165	69	89	(	(	PUNCT
ejpam-3165	69	90	u	u	NOUN
ejpam-3165	69	91	,	,	PUNCT
ejpam-3165	69	92	u)(v	u)(v	PROPN
ejpam-3165	69	93	,	,	PUNCT
ejpam-3165	69	94	v	v	NOUN
ejpam-3165	69	95	)	)	PUNCT
ejpam-3165	69	96	}	}	PUNCT
ejpam-3165	69	97	=	=	SYM
ejpam-3165	69	98	−{(u	−{(u	NOUN
ejpam-3165	69	99	,	,	PUNCT
ejpam-3165	69	100	u)3	u)3	NOUN
ejpam-3165	69	101	+	+	CCONJ
ejpam-3165	69	102	15(u	15(u	NUM
ejpam-3165	69	103	,	,	PUNCT
ejpam-3165	69	104	u)2(v	u)2(v	NOUN
ejpam-3165	69	105	,	,	PUNCT
ejpam-3165	69	106	v	v	NOUN
ejpam-3165	69	107	)	)	PUNCT
ejpam-3165	69	108	+	+	NOUN
ejpam-3165	69	109	15(u	15(u	NUM
ejpam-3165	69	110	,	,	PUNCT
ejpam-3165	69	111	u)(v	u)(v	PROPN
ejpam-3165	69	112	,	,	PUNCT
ejpam-3165	69	113	v)2	v)2	X
ejpam-3165	69	114	+	+	CCONJ
ejpam-3165	69	115	(	(	PUNCT
ejpam-3165	69	116	v	v	NOUN
ejpam-3165	69	117	,	,	PUNCT
ejpam-3165	69	118	v)3	v)3	NOUN
ejpam-3165	69	119	}	}	PUNCT
ejpam-3165	69	120	⇒	⇒	VERB
ejpam-3165	69	121	6(u	6(u	NUM
ejpam-3165	69	122	,	,	PUNCT
ejpam-3165	69	123	v){(u	v){(u	NOUN
ejpam-3165	69	124	,	,	PUNCT
ejpam-3165	69	125	u)2	u)2	PROPN
ejpam-3165	69	126	+	+	CCONJ
ejpam-3165	69	127	(	(	PUNCT
ejpam-3165	69	128	v	v	NOUN
ejpam-3165	69	129	,	,	PUNCT
ejpam-3165	69	130	v)2	v)2	ADJ
ejpam-3165	70	1	+	+	CCONJ
ejpam-3165	70	2	20	20	NUM
ejpam-3165	70	3	6	6	NUM
ejpam-3165	70	4	(	(	PUNCT
ejpam-3165	70	5	u	u	NOUN
ejpam-3165	70	6	,	,	PUNCT
ejpam-3165	70	7	u)(v	u)(v	PROPN
ejpam-3165	70	8	,	,	PUNCT
ejpam-3165	70	9	v	v	NOUN
ejpam-3165	70	10	)	)	PUNCT
ejpam-3165	70	11	}	}	PUNCT
ejpam-3165	70	12	≤	≤	NOUN
ejpam-3165	70	13	{	{	PUNCT
ejpam-3165	70	14	(	(	PUNCT
ejpam-3165	70	15	u	u	NOUN
ejpam-3165	70	16	,	,	PUNCT
ejpam-3165	70	17	u)3	u)3	NOUN
ejpam-3165	70	18	+	+	CCONJ
ejpam-3165	70	19	15(u	15(u	NUM
ejpam-3165	70	20	,	,	PUNCT
ejpam-3165	70	21	u)2(v	u)2(v	NOUN
ejpam-3165	70	22	,	,	PUNCT
ejpam-3165	70	23	v	v	NOUN
ejpam-3165	70	24	)	)	PUNCT
ejpam-3165	70	25	+	+	NOUN
ejpam-3165	70	26	15(u	15(u	NUM
ejpam-3165	70	27	,	,	PUNCT
ejpam-3165	70	28	u)(v	u)(v	PROPN
ejpam-3165	70	29	,	,	PUNCT
ejpam-3165	70	30	v)2	v)2	X
ejpam-3165	70	31	+	+	CCONJ
ejpam-3165	70	32	(	(	PUNCT
ejpam-3165	70	33	v	v	NOUN
ejpam-3165	70	34	,	,	PUNCT
ejpam-3165	70	35	v)3	v)3	NOUN
ejpam-3165	70	36	}	}	PUNCT
ejpam-3165	70	37	⇒	⇒	NOUN
ejpam-3165	70	38	12(u	12(u	NUM
ejpam-3165	70	39	,	,	PUNCT
ejpam-3165	70	40	v){(u	v){(u	ADP
ejpam-3165	70	41	,	,	PUNCT
ejpam-3165	70	42	u)2	u)2	PROPN
ejpam-3165	70	43	+	+	CCONJ
ejpam-3165	70	44	(	(	PUNCT
ejpam-3165	70	45	v	v	NOUN
ejpam-3165	70	46	,	,	PUNCT
ejpam-3165	70	47	v)2	v)2	ADJ
ejpam-3165	70	48	+	+	CCONJ
ejpam-3165	70	49	20	20	NUM
ejpam-3165	70	50	6	6	NUM
ejpam-3165	70	51	(	(	PUNCT
ejpam-3165	70	52	u	u	NOUN
ejpam-3165	70	53	,	,	PUNCT
ejpam-3165	70	54	u)(v	u)(v	PROPN
ejpam-3165	70	55	,	,	PUNCT
ejpam-3165	70	56	v	v	NOUN
ejpam-3165	70	57	)	)	PUNCT
ejpam-3165	70	58	}	}	PUNCT
ejpam-3165	70	59	=	=	SYM
ejpam-3165	70	60	(	(	PUNCT
ejpam-3165	70	61	u+	u+	NOUN
ejpam-3165	70	62	v)6	v)6	NOUN
ejpam-3165	70	63	⇒	⇒	NOUN
ejpam-3165	70	64	‖12(u	‖12(u	NOUN
ejpam-3165	70	65	,	,	PUNCT
ejpam-3165	70	66	v){(u	v){(u	NOUN
ejpam-3165	70	67	,	,	PUNCT
ejpam-3165	70	68	u)2	u)2	PROPN
ejpam-3165	70	69	+	+	CCONJ
ejpam-3165	70	70	(	(	PUNCT
ejpam-3165	70	71	v	v	NOUN
ejpam-3165	70	72	,	,	PUNCT
ejpam-3165	70	73	v)2	v)2	ADJ
ejpam-3165	71	1	+	+	CCONJ
ejpam-3165	71	2	20	20	NUM
ejpam-3165	71	3	6	6	NUM
ejpam-3165	71	4	(	(	PUNCT
ejpam-3165	71	5	u	u	NOUN
ejpam-3165	71	6	,	,	PUNCT
ejpam-3165	71	7	u)(v	u)(v	PROPN
ejpam-3165	71	8	,	,	PUNCT
ejpam-3165	71	9	v)}‖	v)}‖	PROPN
ejpam-3165	71	10	=	=	SYM
ejpam-3165	72	1	‖(u+	‖(u+	NUM
ejpam-3165	72	2	v)6‖	v)6‖	NOUN
ejpam-3165	72	3	⇒	⇒	NOUN
ejpam-3165	72	4	12‖u‖‖v‖{‖u‖4	12‖u‖‖v‖{‖u‖4	NUM
ejpam-3165	72	5	+	+	CCONJ
ejpam-3165	72	6	‖v‖4	‖v‖4	X
ejpam-3165	72	7	+	+	CCONJ
ejpam-3165	72	8	20	20	NUM
ejpam-3165	72	9	6	6	NUM
ejpam-3165	72	10	‖u‖2‖v‖2	‖u‖2‖v‖2	NOUN
ejpam-3165	72	11	}	}	PUNCT
ejpam-3165	72	12	≤	≤	NOUN
ejpam-3165	73	1	‖(u+	‖(u+	NUM
ejpam-3165	73	2	v)‖6	v)‖6	NOUN
ejpam-3165	73	3	(	(	PUNCT
ejpam-3165	73	4	7	7	X
ejpam-3165	73	5	)	)	PUNCT
ejpam-3165	73	6	we	we	PRON
ejpam-3165	73	7	see	see	VERB
ejpam-3165	73	8	from	from	ADP
ejpam-3165	73	9	inequalities	inequality	NOUN
ejpam-3165	73	10	(	(	PUNCT
ejpam-3165	73	11	6	6	NUM
ejpam-3165	73	12	)	)	PUNCT
ejpam-3165	73	13	and	and	CCONJ
ejpam-3165	73	14	(	(	PUNCT
ejpam-3165	73	15	7	7	X
ejpam-3165	73	16	)	)	PUNCT
ejpam-3165	73	17	that	that	PRON
ejpam-3165	73	18	:	:	PUNCT
ejpam-3165	73	19	‖u−	‖u−	NUM
ejpam-3165	73	20	v‖6	v‖6	VERB
ejpam-3165	73	21	≤	≤	NUM
ejpam-3165	73	22	‖u+	‖u+	PROPN
ejpam-3165	73	23	v‖6	v‖6	X
ejpam-3165	73	24	(	(	PUNCT
ejpam-3165	73	25	‖u−	‖u−	PROPN
ejpam-3165	73	26	v‖6	v‖6	PROPN
ejpam-3165	73	27	)	)	PUNCT
ejpam-3165	73	28	1	1	NUM
ejpam-3165	73	29	6	6	NUM
ejpam-3165	73	30	=	=	SYM
ejpam-3165	73	31	(	(	PUNCT
ejpam-3165	73	32	‖u+	‖u+	NOUN
ejpam-3165	73	33	v‖6	v‖6	PROPN
ejpam-3165	73	34	)	)	PUNCT
ejpam-3165	73	35	1	1	NUM
ejpam-3165	73	36	6	6	NUM
ejpam-3165	73	37	⇒	⇒	NOUN
ejpam-3165	73	38	‖u−	‖u−	PROPN
ejpam-3165	73	39	v‖	v‖	NOUN
ejpam-3165	73	40	=	=	PUNCT
ejpam-3165	73	41	‖u+	‖u+	NOUN
ejpam-3165	73	42	v‖	v‖	NOUN
ejpam-3165	73	43	⇒	⇒	VERB
ejpam-3165	73	44	‖u−	‖u−	DET
ejpam-3165	73	45	v‖	v‖	NOUN
ejpam-3165	73	46	≤	≤	NOUN
ejpam-3165	73	47	‖u‖+	‖u‖+	PRON
ejpam-3165	73	48	‖v‖	‖v‖	PROPN
ejpam-3165	73	49	for	for	ADP
ejpam-3165	73	50	any	any	DET
ejpam-3165	73	51	even	even	ADV
ejpam-3165	73	52	positive	positive	ADJ
ejpam-3165	73	53	integer	integer	NOUN
ejpam-3165	73	54	n	n	CCONJ
ejpam-3165	73	55	,	,	PUNCT
ejpam-3165	73	56	we	we	PRON
ejpam-3165	73	57	observe	observe	VERB
ejpam-3165	73	58	the	the	DET
ejpam-3165	73	59	following	follow	VERB
ejpam-3165	73	60	binomial	binomial	ADJ
ejpam-3165	73	61	inequality	inequality	NOUN
ejpam-3165	73	62	:	:	PUNCT
ejpam-3165	73	63	(	(	PUNCT
ejpam-3165	73	64	u+	u+	NUM
ejpam-3165	73	65	v)n	v)n	ADJ
ejpam-3165	73	66	≥	≥	NOUN
ejpam-3165	73	67	0	0	NUM
ejpam-3165	73	68	⇒	⇒	NOUN
ejpam-3165	73	69	(	(	PUNCT
ejpam-3165	73	70	u	u	NOUN
ejpam-3165	73	71	,	,	PUNCT
ejpam-3165	73	72	u	u	NOUN
ejpam-3165	73	73	)	)	PUNCT
ejpam-3165	73	74	n	n	ADV
ejpam-3165	73	75	2	2	NUM
ejpam-3165	73	76	+	+	NOUN
ejpam-3165	73	77	n	n	PRON
ejpam-3165	73	78	c1(u	c1(u	NOUN
ejpam-3165	73	79	,	,	PUNCT
ejpam-3165	73	80	v)(u	v)(u	NUM
ejpam-3165	73	81	,	,	PUNCT
ejpam-3165	73	82	u	u	NOUN
ejpam-3165	73	83	)	)	PUNCT
ejpam-3165	73	84	n−2	n−2	PROPN
ejpam-3165	73	85	2	2	NUM
ejpam-3165	73	86	+	+	NOUN
ejpam-3165	73	87	n	n	PROPN
ejpam-3165	73	88	c2(u	c2(u	PROPN
ejpam-3165	73	89	,	,	PUNCT
ejpam-3165	73	90	u	u	NOUN
ejpam-3165	73	91	)	)	PUNCT
ejpam-3165	73	92	n−2	n−2	PROPN
ejpam-3165	73	93	2	2	NUM
ejpam-3165	73	94	(	(	PUNCT
ejpam-3165	73	95	v	v	NOUN
ejpam-3165	73	96	,	,	PUNCT
ejpam-3165	73	97	v	v	NOUN
ejpam-3165	73	98	)	)	PUNCT
ejpam-3165	74	1	+	+	NOUN
ejpam-3165	74	2	n	n	SYM
ejpam-3165	74	3	c3(u	c3(u	PROPN
ejpam-3165	74	4	,	,	PUNCT
ejpam-3165	74	5	u	u	NOUN
ejpam-3165	74	6	)	)	PUNCT
ejpam-3165	74	7	n−4	n−4	PROPN
ejpam-3165	74	8	2	2	NUM
ejpam-3165	74	9	(	(	PUNCT
ejpam-3165	74	10	v	v	NOUN
ejpam-3165	74	11	,	,	PUNCT
ejpam-3165	74	12	v)(u	v)(u	ADJ
ejpam-3165	74	13	,	,	PUNCT
ejpam-3165	74	14	v	v	NOUN
ejpam-3165	74	15	)	)	PUNCT
ejpam-3165	75	1	+	+	CCONJ
ejpam-3165	75	2	nc4(u	nc4(u	PROPN
ejpam-3165	75	3	,	,	PUNCT
ejpam-3165	75	4	u	u	NOUN
ejpam-3165	75	5	)	)	PUNCT
ejpam-3165	75	6	n−4	n−4	PROPN
ejpam-3165	75	7	2	2	NUM
ejpam-3165	75	8	(	(	PUNCT
ejpam-3165	75	9	v	v	NOUN
ejpam-3165	75	10	,	,	PUNCT
ejpam-3165	75	11	v)2	v)2	ADJ
ejpam-3165	75	12	+	+	NOUN
ejpam-3165	75	13	n	n	PROPN
ejpam-3165	75	14	c5(u	c5(u	PROPN
ejpam-3165	75	15	,	,	PUNCT
ejpam-3165	75	16	u	u	NOUN
ejpam-3165	75	17	)	)	PUNCT
ejpam-3165	75	18	n−6	n−6	PROPN
ejpam-3165	75	19	2	2	NUM
ejpam-3165	75	20	(	(	PUNCT
ejpam-3165	75	21	v	v	NOUN
ejpam-3165	75	22	,	,	PUNCT
ejpam-3165	75	23	v)2(u	v)2(u	NUM
ejpam-3165	75	24	,	,	PUNCT
ejpam-3165	75	25	v	v	NOUN
ejpam-3165	75	26	)	)	PUNCT
ejpam-3165	75	27	+	+	NOUN
ejpam-3165	75	28	n	n	PRON
ejpam-3165	75	29	c6(u	c6(u	PROPN
ejpam-3165	75	30	,	,	PUNCT
ejpam-3165	75	31	u	u	NOUN
ejpam-3165	75	32	)	)	PUNCT
ejpam-3165	75	33	n−6	n−6	PROPN
ejpam-3165	75	34	2	2	NUM
ejpam-3165	75	35	(	(	PUNCT
ejpam-3165	75	36	v	v	NOUN
ejpam-3165	75	37	,	,	PUNCT
ejpam-3165	75	38	v)3	v)3	PROPN
ejpam-3165	75	39	+	+	CCONJ
ejpam-3165	75	40	nc7(u	nc7(u	PROPN
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ejpam-3165	75	49	v)3(u	v)3(u	NOUN
ejpam-3165	75	50	,	,	PUNCT
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ejpam-3165	75	53	+	+	CCONJ
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ejpam-3165	76	13	,	,	PUNCT
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ejpam-3165	76	17	(	(	PUNCT
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ejpam-3165	76	19	,	,	PUNCT
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ejpam-3165	76	24	+	+	CCONJ
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ejpam-3165	77	3	1)(n−	1)(n−	PROPN
ejpam-3165	77	4	2)(u	2)(u	NUM
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ejpam-3165	77	6	u	u	NOUN
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ejpam-3165	77	9	2	2	NUM
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ejpam-3165	77	12	,	,	PUNCT
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ejpam-3165	77	15	+	+	CCONJ
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ejpam-3165	78	1	(	(	PUNCT
ejpam-3165	78	2	n−	n−	NOUN
ejpam-3165	78	3	1)(n−	1)(n−	NUM
ejpam-3165	78	4	2)(n−	2)(n−	NUM
ejpam-3165	78	5	3)(n−	3)(n−	NUM
ejpam-3165	78	6	4)(u	4)(u	NUM
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ejpam-3165	78	9	)	)	PUNCT
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ejpam-3165	79	2	n−	n−	NOUN
ejpam-3165	79	3	1)(n−	1)(n−	NUM
ejpam-3165	79	4	2)(n−	2)(n−	NUM
ejpam-3165	79	5	3)(n−	3)(n−	NUM
ejpam-3165	79	6	4)(n−	4)(n−	PROPN
ejpam-3165	79	7	5)(n−	5)(n−	NUM
ejpam-3165	79	8	6)(u	6)(u	NUM
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ejpam-3165	79	12	n−8	n−8	PROPN
ejpam-3165	79	13	2	2	NUM
ejpam-3165	79	14	(	(	PUNCT
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ejpam-3165	79	17	v)3	v)3	PROPN
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ejpam-3165	80	5	v	v	NOUN
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ejpam-3165	80	8	2	2	NUM
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ejpam-3165	80	15	u	u	NOUN
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ejpam-3165	80	18	2	2	NUM
ejpam-3165	80	19	+	+	NOUN
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ejpam-3165	80	22	,	,	PUNCT
ejpam-3165	80	23	u	u	NOUN
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ejpam-3165	80	25	n−2	n−2	PROPN
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ejpam-3165	80	30	v	v	NOUN
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ejpam-3165	80	39	2	2	NUM
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ejpam-3165	80	47	,	,	PUNCT
ejpam-3165	80	48	u	u	NOUN
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ejpam-3165	80	50	n−6	n−6	PROPN
ejpam-3165	80	51	2	2	NUM
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ejpam-3165	80	54	,	,	PUNCT
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ejpam-3165	81	8	2	2	X
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ejpam-3165	81	10	⇒	⇒	VERB
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ejpam-3165	84	6	,	,	PUNCT
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ejpam-3165	84	21	,	,	PUNCT
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ejpam-3165	84	25	(	(	PUNCT
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ejpam-3165	84	30	n−2	n−2	PROPN
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ejpam-3165	85	3	1)(n−	1)(n−	PROPN
ejpam-3165	85	4	2)(u	2)(u	NUM
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ejpam-3165	85	15	+	+	CCONJ
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ejpam-3165	86	1	(	(	PUNCT
ejpam-3165	86	2	n−	n−	NOUN
ejpam-3165	86	3	1)(n−	1)(n−	NUM
ejpam-3165	86	4	2)(n−	2)(n−	NUM
ejpam-3165	86	5	3)(n−	3)(n−	NUM
ejpam-3165	86	6	4)(u	4)(u	NUM
ejpam-3165	86	7	,	,	PUNCT
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ejpam-3165	86	9	)	)	PUNCT
ejpam-3165	86	10	n−6	n−6	PROPN
ejpam-3165	86	11	2	2	NUM
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ejpam-3165	86	14	,	,	PUNCT
ejpam-3165	86	15	v)2	v)2	ADJ
ejpam-3165	86	16	+	+	CCONJ
ejpam-3165	86	17	1	1	NUM
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ejpam-3165	87	1	(	(	PUNCT
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ejpam-3165	87	3	1)(n−	1)(n−	NUM
ejpam-3165	87	4	2)(n−	2)(n−	NUM
ejpam-3165	87	5	3)(n−	3)(n−	NUM
ejpam-3165	87	6	4)(n−	4)(n−	PROPN
ejpam-3165	87	7	5)(n−	5)(n−	NUM
ejpam-3165	87	8	6)(u	6)(u	NUM
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ejpam-3165	87	11	)	)	PUNCT
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ejpam-3165	88	8	2	2	NUM
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ejpam-3165	88	10	⇒	⇒	VERB
ejpam-3165	88	11	−(u−	−(u−	PRON
ejpam-3165	88	12	v)n	v)n	PUNCT
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ejpam-3165	89	3	,	,	PUNCT
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ejpam-3165	89	5	)	)	PUNCT
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ejpam-3165	89	7	(	(	PUNCT
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ejpam-3165	89	9	,	,	PUNCT
ejpam-3165	89	10	u	u	NOUN
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ejpam-3165	89	12	n−2	n−2	PROPN
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ejpam-3165	89	14	+	+	CCONJ
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ejpam-3165	90	1	(	(	PUNCT
ejpam-3165	90	2	n−	n−	NOUN
ejpam-3165	90	3	1)(n−	1)(n−	PROPN
ejpam-3165	90	4	2)(u	2)(u	NUM
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ejpam-3165	90	9	2	2	NUM
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ejpam-3165	90	15	+	+	CCONJ
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ejpam-3165	91	1	(	(	PUNCT
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ejpam-3165	91	3	1)(n−	1)(n−	NUM
ejpam-3165	91	4	2)(n−	2)(n−	NUM
ejpam-3165	91	5	3)(n−	3)(n−	NUM
ejpam-3165	91	6	4)(u	4)(u	NUM
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ejpam-3165	91	9	)	)	PUNCT
ejpam-3165	91	10	n−6	n−6	PROPN
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ejpam-3165	92	3	1)(n−	1)(n−	NUM
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ejpam-3165	92	6	4)(n−	4)(n−	PROPN
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ejpam-3165	92	15	v	v	NOUN
ejpam-3165	92	16	,	,	PUNCT
ejpam-3165	92	17	v)3	v)3	PROPN
ejpam-3165	92	18	+	+	X
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ejpam-3165	92	20	.	.	PUNCT
ejpam-3165	93	1	.+	.+	NOUN
ejpam-3165	93	2	(	(	PUNCT
ejpam-3165	93	3	v	v	NOUN
ejpam-3165	93	4	,	,	PUNCT
ejpam-3165	93	5	v	v	NOUN
ejpam-3165	93	6	)	)	PUNCT
ejpam-3165	93	7	n−2	n−2	PROPN
ejpam-3165	93	8	2	2	NUM
ejpam-3165	93	9	}	}	PUNCT
ejpam-3165	93	10	⇒	⇒	NOUN
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ejpam-3165	93	12	(	(	PUNCT
ejpam-3165	93	13	u−	u−	NUM
ejpam-3165	93	14	v)n	v)n	ADJ
ejpam-3165	93	15	∥∥∥	∥∥∥	PROPN
ejpam-3165	93	16	=	=	SYM
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ejpam-3165	93	18	,	,	PUNCT
ejpam-3165	93	19	v	v	NOUN
ejpam-3165	93	20	)	)	PUNCT
ejpam-3165	93	21	{	{	PUNCT
ejpam-3165	93	22	(	(	PUNCT
ejpam-3165	93	23	u	u	NOUN
ejpam-3165	93	24	,	,	PUNCT
ejpam-3165	93	25	u	u	NOUN
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ejpam-3165	93	27	n−2	n−2	PROPN
ejpam-3165	93	28	2	2	NUM
ejpam-3165	93	29	+	+	CCONJ
ejpam-3165	93	30	1	1	NUM
ejpam-3165	93	31	3	3	NUM
ejpam-3165	93	32	!	!	PUNCT
ejpam-3165	94	1	(	(	PUNCT
ejpam-3165	94	2	n−	n−	NOUN
ejpam-3165	94	3	1)(n−	1)(n−	PROPN
ejpam-3165	94	4	2)(u	2)(u	NUM
ejpam-3165	94	5	,	,	PUNCT
ejpam-3165	94	6	u	u	NOUN
ejpam-3165	94	7	)	)	PUNCT
ejpam-3165	94	8	n−4	n−4	PROPN
ejpam-3165	94	9	2	2	NUM
ejpam-3165	94	10	(	(	PUNCT
ejpam-3165	94	11	v	v	NOUN
ejpam-3165	94	12	,	,	PUNCT
ejpam-3165	94	13	v	v	NOUN
ejpam-3165	94	14	)	)	PUNCT
ejpam-3165	94	15	+	+	CCONJ
ejpam-3165	94	16	1	1	NUM
ejpam-3165	94	17	5	5	NUM
ejpam-3165	94	18	!	!	PUNCT
ejpam-3165	95	1	(	(	PUNCT
ejpam-3165	95	2	n−	n−	NOUN
ejpam-3165	95	3	1)(n−	1)(n−	NUM
ejpam-3165	95	4	2)(n−	2)(n−	NUM
ejpam-3165	95	5	3)(n−	3)(n−	NUM
ejpam-3165	95	6	4)(u	4)(u	NUM
ejpam-3165	95	7	,	,	PUNCT
ejpam-3165	95	8	u	u	NOUN
ejpam-3165	95	9	)	)	PUNCT
ejpam-3165	95	10	n−6	n−6	PROPN
ejpam-3165	95	11	2	2	NUM
ejpam-3165	95	12	(	(	PUNCT
ejpam-3165	95	13	v	v	NOUN
ejpam-3165	95	14	,	,	PUNCT
ejpam-3165	95	15	v)2	v)2	ADJ
ejpam-3165	95	16	+	+	CCONJ
ejpam-3165	95	17	1	1	NUM
ejpam-3165	95	18	7	7	NUM
ejpam-3165	95	19	!	!	PUNCT
ejpam-3165	96	1	(	(	PUNCT
ejpam-3165	96	2	n−	n−	NOUN
ejpam-3165	96	3	1)(n−	1)(n−	NUM
ejpam-3165	96	4	2)(n−	2)(n−	NUM
ejpam-3165	96	5	3)(n−	3)(n−	NUM
ejpam-3165	96	6	4)(n−	4)(n−	PROPN
ejpam-3165	96	7	5)(n−	5)(n−	NUM
ejpam-3165	96	8	6)(u	6)(u	NUM
ejpam-3165	96	9	,	,	PUNCT
ejpam-3165	96	10	u	u	NOUN
ejpam-3165	96	11	)	)	PUNCT
ejpam-3165	96	12	n−8	n−8	PROPN
ejpam-3165	96	13	2	2	NUM
ejpam-3165	96	14	(	(	PUNCT
ejpam-3165	96	15	v	v	NOUN
ejpam-3165	96	16	,	,	PUNCT
ejpam-3165	96	17	v)3	v)3	PROPN
ejpam-3165	96	18	+	+	X
ejpam-3165	96	19	.	.	PUNCT
ejpam-3165	96	20	.	.	PUNCT
ejpam-3165	97	1	.+	.+	NOUN
ejpam-3165	97	2	(	(	PUNCT
ejpam-3165	97	3	v	v	NOUN
ejpam-3165	97	4	,	,	PUNCT
ejpam-3165	97	5	v	v	NOUN
ejpam-3165	97	6	)	)	PUNCT
ejpam-3165	97	7	n−2	n−2	PROPN
ejpam-3165	97	8	2	2	NUM
ejpam-3165	97	9	}	}	PUNCT
ejpam-3165	97	10	∥∥∥	∥∥∥	PROPN
ejpam-3165	97	11	⇒	⇒	NOUN
ejpam-3165	97	12	∥∥∥(u−	∥∥∥(u−	VERB
ejpam-3165	97	13	v	v	NOUN
ejpam-3165	97	14	)	)	PUNCT
ejpam-3165	97	15	∥∥∥n	∥∥∥n	NOUN
ejpam-3165	97	16	≤	≤	NOUN
ejpam-3165	97	17	2n‖u‖‖v‖	2n‖u‖‖v‖	NUM
ejpam-3165	97	18	∥∥∥{(u	∥∥∥{(u	ADJ
ejpam-3165	97	19	,	,	PUNCT
ejpam-3165	97	20	u	u	NOUN
ejpam-3165	97	21	)	)	PUNCT
ejpam-3165	97	22	n−2	n−2	PROPN
ejpam-3165	97	23	2	2	NUM
ejpam-3165	97	24	+	+	CCONJ
ejpam-3165	97	25	1	1	NUM
ejpam-3165	97	26	3	3	NUM
ejpam-3165	97	27	!	!	PUNCT
ejpam-3165	98	1	(	(	PUNCT
ejpam-3165	98	2	n−	n−	NOUN
ejpam-3165	98	3	1)(n−	1)(n−	PROPN
ejpam-3165	98	4	2)(u	2)(u	NUM
ejpam-3165	98	5	,	,	PUNCT
ejpam-3165	98	6	u	u	NOUN
ejpam-3165	98	7	)	)	PUNCT
ejpam-3165	98	8	n−4	n−4	PROPN
ejpam-3165	98	9	2	2	NUM
ejpam-3165	98	10	(	(	PUNCT
ejpam-3165	98	11	v	v	NOUN
ejpam-3165	98	12	,	,	PUNCT
ejpam-3165	98	13	v	v	NOUN
ejpam-3165	98	14	)	)	PUNCT
ejpam-3165	98	15	+	+	CCONJ
ejpam-3165	98	16	1	1	NUM
ejpam-3165	98	17	5	5	NUM
ejpam-3165	98	18	!	!	PUNCT
ejpam-3165	99	1	(	(	PUNCT
ejpam-3165	99	2	n−	n−	NOUN
ejpam-3165	99	3	1)(n−	1)(n−	NUM
ejpam-3165	99	4	2)(n−	2)(n−	NUM
ejpam-3165	99	5	3)(n−	3)(n−	NUM
ejpam-3165	99	6	4)(u	4)(u	NUM
ejpam-3165	99	7	,	,	PUNCT
ejpam-3165	99	8	u	u	NOUN
ejpam-3165	99	9	)	)	PUNCT
ejpam-3165	99	10	n−6	n−6	PROPN
ejpam-3165	99	11	2	2	NUM
ejpam-3165	99	12	(	(	PUNCT
ejpam-3165	99	13	v	v	NOUN
ejpam-3165	99	14	,	,	PUNCT
ejpam-3165	99	15	v)2	v)2	ADJ
ejpam-3165	99	16	+	+	CCONJ
ejpam-3165	99	17	1	1	NUM
ejpam-3165	99	18	7	7	NUM
ejpam-3165	99	19	!	!	PUNCT
ejpam-3165	100	1	(	(	PUNCT
ejpam-3165	100	2	n−	n−	NOUN
ejpam-3165	100	3	1)(n−	1)(n−	NUM
ejpam-3165	100	4	2)(n−	2)(n−	NUM
ejpam-3165	100	5	3)(n−	3)(n−	NUM
ejpam-3165	100	6	4)(n−	4)(n−	PROPN
ejpam-3165	100	7	5)(n−	5)(n−	NUM
ejpam-3165	100	8	6)(u	6)(u	NUM
ejpam-3165	100	9	,	,	PUNCT
ejpam-3165	100	10	u	u	NOUN
ejpam-3165	100	11	)	)	PUNCT
ejpam-3165	100	12	n−8	n−8	PROPN
ejpam-3165	100	13	2	2	NUM
ejpam-3165	100	14	(	(	PUNCT
ejpam-3165	100	15	v	v	NOUN
ejpam-3165	100	16	,	,	PUNCT
ejpam-3165	100	17	v)3	v)3	PROPN
ejpam-3165	100	18	+	+	X
ejpam-3165	100	19	.	.	PUNCT
ejpam-3165	100	20	.	.	PUNCT
ejpam-3165	101	1	.+	.+	NOUN
ejpam-3165	101	2	(	(	PUNCT
ejpam-3165	101	3	v	v	NOUN
ejpam-3165	101	4	,	,	PUNCT
ejpam-3165	101	5	v	v	NOUN
ejpam-3165	101	6	)	)	PUNCT
ejpam-3165	101	7	n−2	n−2	PROPN
ejpam-3165	101	8	2	2	NUM
ejpam-3165	101	9	}	}	PUNCT
ejpam-3165	101	10	∥∥∥	∥∥∥	PROPN
ejpam-3165	101	11	(	(	PUNCT
ejpam-3165	101	12	8)	8)	NUM
ejpam-3165	101	13	on	on	ADP
ejpam-3165	101	14	the	the	DET
ejpam-3165	101	15	other	other	ADJ
ejpam-3165	101	16	hand	hand	NOUN
ejpam-3165	101	17	,	,	PUNCT
ejpam-3165	101	18	we	we	PRON
ejpam-3165	101	19	see	see	VERB
ejpam-3165	101	20	that	that	PRON
ejpam-3165	101	21	:	:	PUNCT
ejpam-3165	101	22	(	(	PUNCT
ejpam-3165	101	23	u−	u−	NUM
ejpam-3165	101	24	v)n	v)n	ADJ
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ejpam-3165	101	26	0	0	NUM
ejpam-3165	101	27	⇒	⇒	NOUN
ejpam-3165	101	28	(	(	PUNCT
ejpam-3165	101	29	u	u	NOUN
ejpam-3165	101	30	,	,	PUNCT
ejpam-3165	101	31	u	u	NOUN
ejpam-3165	101	32	)	)	PUNCT
ejpam-3165	101	33	n	n	PRON
ejpam-3165	101	34	2	2	NUM
ejpam-3165	101	35	−n	−n	NUM
ejpam-3165	101	36	c1(u	c1(u	NOUN
ejpam-3165	101	37	,	,	PUNCT
ejpam-3165	101	38	v)(u	v)(u	NUM
ejpam-3165	101	39	,	,	PUNCT
ejpam-3165	101	40	u	u	NOUN
ejpam-3165	101	41	)	)	PUNCT
ejpam-3165	101	42	n−2	n−2	PROPN
ejpam-3165	101	43	2	2	NUM
ejpam-3165	101	44	+	+	NOUN
ejpam-3165	101	45	n	n	PROPN
ejpam-3165	101	46	c2(u	c2(u	PROPN
ejpam-3165	101	47	,	,	PUNCT
ejpam-3165	101	48	u	u	NOUN
ejpam-3165	101	49	)	)	PUNCT
ejpam-3165	101	50	n−2	n−2	PROPN
ejpam-3165	101	51	2	2	NUM
ejpam-3165	101	52	(	(	PUNCT
ejpam-3165	101	53	v	v	NOUN
ejpam-3165	101	54	,	,	PUNCT
ejpam-3165	101	55	v)−n	v)−n	PROPN
ejpam-3165	101	56	c3(u	c3(u	PROPN
ejpam-3165	101	57	,	,	PUNCT
ejpam-3165	101	58	u	u	NOUN
ejpam-3165	101	59	)	)	PUNCT
ejpam-3165	101	60	n−4	n−4	PROPN
ejpam-3165	101	61	2	2	NUM
ejpam-3165	101	62	(	(	PUNCT
ejpam-3165	101	63	v	v	NOUN
ejpam-3165	101	64	,	,	PUNCT
ejpam-3165	101	65	v)(u	v)(u	ADJ
ejpam-3165	101	66	,	,	PUNCT
ejpam-3165	101	67	v	v	NOUN
ejpam-3165	101	68	)	)	PUNCT
ejpam-3165	101	69	+	+	PROPN
ejpam-3165	101	70	n	n	PRON
ejpam-3165	101	71	c4(u	c4(u	PROPN
ejpam-3165	101	72	,	,	PUNCT
ejpam-3165	101	73	u	u	NOUN
ejpam-3165	101	74	)	)	PUNCT
ejpam-3165	101	75	n−4	n−4	PROPN
ejpam-3165	101	76	2	2	NUM
ejpam-3165	101	77	(	(	PUNCT
ejpam-3165	101	78	v	v	NOUN
ejpam-3165	101	79	,	,	PUNCT
ejpam-3165	101	80	v)2	v)2	ADJ
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ejpam-3165	101	82	nc5(u	nc5(u	PROPN
ejpam-3165	101	83	,	,	PUNCT
ejpam-3165	101	84	u	u	NOUN
ejpam-3165	101	85	)	)	PUNCT
ejpam-3165	101	86	n−6	n−6	PROPN
ejpam-3165	101	87	2	2	NUM
ejpam-3165	101	88	(	(	PUNCT
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ejpam-3165	101	90	,	,	PUNCT
ejpam-3165	101	91	v)2(u	v)2(u	NUM
ejpam-3165	101	92	,	,	PUNCT
ejpam-3165	101	93	v	v	NOUN
ejpam-3165	101	94	)	)	PUNCT
ejpam-3165	101	95	+	+	NOUN
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ejpam-3165	101	97	c6(u	c6(u	PROPN
ejpam-3165	101	98	,	,	PUNCT
ejpam-3165	101	99	u	u	NOUN
ejpam-3165	101	100	)	)	PUNCT
ejpam-3165	101	101	n−6	n−6	PROPN
ejpam-3165	101	102	2	2	NUM
ejpam-3165	101	103	(	(	PUNCT
ejpam-3165	101	104	v	v	NOUN
ejpam-3165	101	105	,	,	PUNCT
ejpam-3165	101	106	v)3	v)3	PROPN
ejpam-3165	101	107	−n	−n	PROPN
ejpam-3165	101	108	c7(u	c7(u	PROPN
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ejpam-3165	101	110	u	u	NOUN
ejpam-3165	101	111	)	)	PUNCT
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ejpam-3165	101	118	,	,	PUNCT
ejpam-3165	101	119	v	v	NOUN
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ejpam-3165	101	121	+	+	CCONJ
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ejpam-3165	102	1	.+	.+	NOUN
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ejpam-3165	102	5	u	u	NOUN
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ejpam-3165	102	8	2	2	NUM
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ejpam-3165	102	10	0	0	NUM
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ejpam-3165	102	12	−n(u	−n(u	NOUN
ejpam-3165	102	13	,	,	PUNCT
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ejpam-3165	102	15	)	)	PUNCT
ejpam-3165	102	16	{	{	PUNCT
ejpam-3165	102	17	(	(	PUNCT
ejpam-3165	102	18	u	u	NOUN
ejpam-3165	102	19	,	,	PUNCT
ejpam-3165	102	20	u	u	NOUN
ejpam-3165	102	21	)	)	PUNCT
ejpam-3165	102	22	n−2	n−2	PROPN
ejpam-3165	102	23	2	2	NUM
ejpam-3165	102	24	+	+	CCONJ
ejpam-3165	102	25	1	1	NUM
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ejpam-3165	102	27	!	!	PUNCT
ejpam-3165	103	1	(	(	PUNCT
ejpam-3165	103	2	n−	n−	NOUN
ejpam-3165	103	3	1)(n−	1)(n−	PROPN
ejpam-3165	103	4	2)(u	2)(u	NUM
ejpam-3165	103	5	,	,	PUNCT
ejpam-3165	103	6	u	u	NOUN
ejpam-3165	103	7	)	)	PUNCT
ejpam-3165	103	8	n−4	n−4	PROPN
ejpam-3165	103	9	2	2	NUM
ejpam-3165	103	10	(	(	PUNCT
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ejpam-3165	103	12	,	,	PUNCT
ejpam-3165	103	13	v	v	NOUN
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ejpam-3165	103	15	+	+	CCONJ
ejpam-3165	103	16	1	1	NUM
ejpam-3165	103	17	5	5	NUM
ejpam-3165	103	18	!	!	PUNCT
ejpam-3165	104	1	(	(	PUNCT
ejpam-3165	104	2	n−	n−	NOUN
ejpam-3165	104	3	1)(n−	1)(n−	NUM
ejpam-3165	104	4	2)(n−	2)(n−	NUM
ejpam-3165	104	5	3)(n−	3)(n−	NUM
ejpam-3165	104	6	4)(u	4)(u	NUM
ejpam-3165	104	7	,	,	PUNCT
ejpam-3165	104	8	u	u	NOUN
ejpam-3165	104	9	)	)	PUNCT
ejpam-3165	104	10	n−6	n−6	PROPN
ejpam-3165	104	11	2	2	NUM
ejpam-3165	104	12	(	(	PUNCT
ejpam-3165	104	13	v	v	NOUN
ejpam-3165	104	14	,	,	PUNCT
ejpam-3165	104	15	v)2	v)2	ADJ
ejpam-3165	104	16	+	+	CCONJ
ejpam-3165	104	17	1	1	NUM
ejpam-3165	104	18	7	7	NUM
ejpam-3165	104	19	!	!	PUNCT
ejpam-3165	105	1	(	(	PUNCT
ejpam-3165	105	2	n−	n−	NOUN
ejpam-3165	105	3	1)(n−	1)(n−	NUM
ejpam-3165	105	4	2)(n−	2)(n−	NUM
ejpam-3165	105	5	3)(n−	3)(n−	NUM
ejpam-3165	105	6	4)(n−	4)(n−	PROPN
ejpam-3165	105	7	5)(n−	5)(n−	NUM
ejpam-3165	105	8	6)(u	6)(u	NUM
ejpam-3165	105	9	,	,	PUNCT
ejpam-3165	105	10	u	u	NOUN
ejpam-3165	105	11	)	)	PUNCT
ejpam-3165	105	12	n−8	n−8	PROPN
ejpam-3165	105	13	2	2	NUM
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ejpam-3165	105	18	+	+	X
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ejpam-3165	106	4	,	,	PUNCT
ejpam-3165	106	5	v	v	NOUN
ejpam-3165	106	6	)	)	PUNCT
ejpam-3165	106	7	n−2	n−2	PROPN
ejpam-3165	106	8	2	2	NUM
ejpam-3165	106	9	}	}	PUNCT
ejpam-3165	106	10	=	=	PUNCT
ejpam-3165	106	11	−	−	PROPN
ejpam-3165	106	12	−	−	PROPN
ejpam-3165	106	13	{	{	PUNCT
ejpam-3165	106	14	(	(	PUNCT
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ejpam-3165	106	16	,	,	PUNCT
ejpam-3165	106	17	u	u	NOUN
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ejpam-3165	106	19	n	n	ADV
ejpam-3165	106	20	2	2	NUM
ejpam-3165	106	21	+	+	NOUN
ejpam-3165	106	22	n	n	PROPN
ejpam-3165	106	23	c2(u	c2(u	PROPN
ejpam-3165	106	24	,	,	PUNCT
ejpam-3165	106	25	u	u	NOUN
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ejpam-3165	106	27	n−2	n−2	PROPN
ejpam-3165	106	28	2	2	NUM
ejpam-3165	106	29	(	(	PUNCT
ejpam-3165	106	30	v	v	NOUN
ejpam-3165	106	31	,	,	PUNCT
ejpam-3165	106	32	v	v	NOUN
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ejpam-3165	106	34	+	+	NOUN
ejpam-3165	106	35	n	n	PROPN
ejpam-3165	106	36	c2(u	c2(u	PROPN
ejpam-3165	106	37	,	,	PUNCT
ejpam-3165	106	38	u	u	NOUN
ejpam-3165	106	39	)	)	PUNCT
ejpam-3165	106	40	n−4	n−4	PROPN
ejpam-3165	106	41	2	2	NUM
ejpam-3165	106	42	(	(	PUNCT
ejpam-3165	106	43	v	v	NOUN
ejpam-3165	106	44	,	,	PUNCT
ejpam-3165	106	45	v)2	v)2	ADJ
ejpam-3165	106	46	+	+	PROPN
ejpam-3165	106	47	n	n	PROPN
ejpam-3165	106	48	c2(u	c2(u	PROPN
ejpam-3165	106	49	,	,	PUNCT
ejpam-3165	106	50	u	u	NOUN
ejpam-3165	106	51	)	)	PUNCT
ejpam-3165	106	52	n−6	n−6	PROPN
ejpam-3165	106	53	2	2	NUM
ejpam-3165	106	54	(	(	PUNCT
ejpam-3165	106	55	v	v	NOUN
ejpam-3165	106	56	,	,	PUNCT
ejpam-3165	106	57	v)3	v)3	PROPN
ejpam-3165	106	58	+	+	X
ejpam-3165	106	59	.	.	PUNCT
ejpam-3165	106	60	.	.	PUNCT
ejpam-3165	107	1	.+	.+	NOUN
ejpam-3165	107	2	(	(	PUNCT
ejpam-3165	107	3	v	v	NOUN
ejpam-3165	107	4	,	,	PUNCT
ejpam-3165	107	5	v	v	NOUN
ejpam-3165	107	6	)	)	PUNCT
ejpam-3165	107	7	n	n	PRON
ejpam-3165	107	8	2	2	X
ejpam-3165	107	9	}	}	PUNCT
ejpam-3165	107	10	⇒	⇒	VERB
ejpam-3165	107	11	n(u	n(u	PROPN
ejpam-3165	107	12	,	,	PUNCT
ejpam-3165	107	13	v	v	NOUN
ejpam-3165	107	14	)	)	PUNCT
ejpam-3165	107	15	{	{	PUNCT
ejpam-3165	107	16	(	(	PUNCT
ejpam-3165	107	17	u	u	NOUN
ejpam-3165	107	18	,	,	PUNCT
ejpam-3165	107	19	u	u	NOUN
ejpam-3165	107	20	)	)	PUNCT
ejpam-3165	107	21	n−2	n−2	PROPN
ejpam-3165	107	22	2	2	NUM
ejpam-3165	107	23	+	+	CCONJ
ejpam-3165	107	24	1	1	NUM
ejpam-3165	107	25	3	3	NUM
ejpam-3165	107	26	!	!	PUNCT
ejpam-3165	108	1	(	(	PUNCT
ejpam-3165	108	2	n−	n−	NOUN
ejpam-3165	108	3	1)(n−	1)(n−	PROPN
ejpam-3165	108	4	2)(u	2)(u	NUM
ejpam-3165	108	5	,	,	PUNCT
ejpam-3165	108	6	u	u	NOUN
ejpam-3165	108	7	)	)	PUNCT
ejpam-3165	108	8	n−4	n−4	PROPN
ejpam-3165	108	9	2	2	NUM
ejpam-3165	108	10	(	(	PUNCT
ejpam-3165	108	11	v	v	NOUN
ejpam-3165	108	12	,	,	PUNCT
ejpam-3165	108	13	v	v	NOUN
ejpam-3165	108	14	)	)	PUNCT
ejpam-3165	108	15	+	+	CCONJ
ejpam-3165	108	16	1	1	NUM
ejpam-3165	108	17	5	5	NUM
ejpam-3165	108	18	!	!	PUNCT
ejpam-3165	109	1	(	(	PUNCT
ejpam-3165	109	2	n−	n−	NOUN
ejpam-3165	109	3	1)(n−	1)(n−	NUM
ejpam-3165	109	4	2)(n−	2)(n−	NUM
ejpam-3165	109	5	3)(n−	3)(n−	NUM
ejpam-3165	109	6	4)(u	4)(u	NUM
ejpam-3165	109	7	,	,	PUNCT
ejpam-3165	109	8	u	u	NOUN
ejpam-3165	109	9	)	)	PUNCT
ejpam-3165	109	10	n−6	n−6	PROPN
ejpam-3165	109	11	2	2	NUM
ejpam-3165	109	12	(	(	PUNCT
ejpam-3165	109	13	v	v	NOUN
ejpam-3165	109	14	,	,	PUNCT
ejpam-3165	109	15	v)2	v)2	ADJ
ejpam-3165	109	16	+	+	CCONJ
ejpam-3165	109	17	1	1	NUM
ejpam-3165	109	18	7	7	NUM
ejpam-3165	109	19	!	!	PUNCT
ejpam-3165	110	1	(	(	PUNCT
ejpam-3165	110	2	n−	n−	NOUN
ejpam-3165	110	3	1)(n−	1)(n−	NUM
ejpam-3165	110	4	2)(n−	2)(n−	NUM
ejpam-3165	110	5	3)(n−	3)(n−	NUM
ejpam-3165	110	6	4)(n−	4)(n−	PROPN
ejpam-3165	110	7	5)(n−	5)(n−	NUM
ejpam-3165	110	8	6)(u	6)(u	NUM
ejpam-3165	110	9	,	,	PUNCT
ejpam-3165	110	10	u	u	NOUN
ejpam-3165	110	11	)	)	PUNCT
ejpam-3165	110	12	n−8	n−8	PROPN
ejpam-3165	110	13	2	2	NUM
ejpam-3165	110	14	(	(	PUNCT
ejpam-3165	110	15	v	v	NOUN
ejpam-3165	110	16	,	,	PUNCT
ejpam-3165	110	17	v)3	v)3	PROPN
ejpam-3165	110	18	+	+	X
ejpam-3165	110	19	.	.	PUNCT
ejpam-3165	110	20	.	.	PUNCT
ejpam-3165	111	1	.+	.+	NOUN
ejpam-3165	111	2	(	(	PUNCT
ejpam-3165	111	3	v	v	NOUN
ejpam-3165	111	4	,	,	PUNCT
ejpam-3165	111	5	v	v	NOUN
ejpam-3165	111	6	)	)	PUNCT
ejpam-3165	111	7	n−2	n−2	PROPN
ejpam-3165	111	8	2	2	NUM
ejpam-3165	111	9	}	}	PUNCT
ejpam-3165	111	10	≤	≤	NOUN
ejpam-3165	111	11	{	{	PUNCT
ejpam-3165	111	12	(	(	PUNCT
ejpam-3165	111	13	u	u	NOUN
ejpam-3165	111	14	,	,	PUNCT
ejpam-3165	111	15	u	u	NOUN
ejpam-3165	111	16	)	)	PUNCT
ejpam-3165	111	17	n	n	ADV
ejpam-3165	111	18	2	2	NUM
ejpam-3165	111	19	+	+	NOUN
ejpam-3165	111	20	n	n	PROPN
ejpam-3165	111	21	c2(u	c2(u	PROPN
ejpam-3165	111	22	,	,	PUNCT
ejpam-3165	111	23	u	u	NOUN
ejpam-3165	111	24	)	)	PUNCT
ejpam-3165	111	25	n−2	n−2	PROPN
ejpam-3165	111	26	2	2	NUM
ejpam-3165	111	27	(	(	PUNCT
ejpam-3165	111	28	v	v	NOUN
ejpam-3165	111	29	,	,	PUNCT
ejpam-3165	111	30	v	v	NOUN
ejpam-3165	111	31	)	)	PUNCT
ejpam-3165	111	32	+	+	NOUN
ejpam-3165	111	33	n	n	PROPN
ejpam-3165	111	34	c2(u	c2(u	PROPN
ejpam-3165	111	35	,	,	PUNCT
ejpam-3165	111	36	u	u	NOUN
ejpam-3165	111	37	)	)	PUNCT
ejpam-3165	111	38	n−4	n−4	PROPN
ejpam-3165	111	39	2	2	NUM
ejpam-3165	111	40	(	(	PUNCT
ejpam-3165	111	41	v	v	NOUN
ejpam-3165	111	42	,	,	PUNCT
ejpam-3165	111	43	v)2	v)2	ADJ
ejpam-3165	111	44	+	+	PROPN
ejpam-3165	111	45	n	n	PROPN
ejpam-3165	111	46	c2(u	c2(u	PROPN
ejpam-3165	111	47	,	,	PUNCT
ejpam-3165	111	48	u	u	NOUN
ejpam-3165	111	49	)	)	PUNCT
ejpam-3165	111	50	n−6	n−6	PROPN
ejpam-3165	111	51	2	2	NUM
ejpam-3165	111	52	(	(	PUNCT
ejpam-3165	111	53	v	v	NOUN
ejpam-3165	111	54	,	,	PUNCT
ejpam-3165	111	55	v)3	v)3	PROPN
ejpam-3165	111	56	+	+	X
ejpam-3165	111	57	.	.	PUNCT
ejpam-3165	111	58	.	.	PUNCT
ejpam-3165	112	1	.+	.+	NOUN
ejpam-3165	112	2	(	(	PUNCT
ejpam-3165	112	3	v	v	NOUN
ejpam-3165	112	4	,	,	PUNCT
ejpam-3165	112	5	v	v	NOUN
ejpam-3165	112	6	)	)	PUNCT
ejpam-3165	112	7	n	n	PRON
ejpam-3165	112	8	2	2	X
ejpam-3165	112	9	}	}	PUNCT
ejpam-3165	112	10	barnes	barne	VERB
ejpam-3165	112	11	et	et	PROPN
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ejpam-3165	112	13	.	.	PUNCT
ejpam-3165	112	14	/	/	SYM
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ejpam-3165	112	16	.	.	PUNCT
ejpam-3165	113	1	j.	j.	PROPN
ejpam-3165	113	2	pure	pure	PROPN
ejpam-3165	113	3	appl	appl	PROPN
ejpam-3165	113	4	.	.	PROPN
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ejpam-3165	113	6	,	,	PUNCT
ejpam-3165	113	7	11	11	NUM
ejpam-3165	113	8	(	(	PUNCT
ejpam-3165	113	9	1	1	NUM
ejpam-3165	113	10	)	)	PUNCT
ejpam-3165	113	11	(	(	PUNCT
ejpam-3165	113	12	2018	2018	NUM
ejpam-3165	113	13	)	)	PUNCT
ejpam-3165	113	14	,	,	PUNCT
ejpam-3165	113	15	352	352	NUM
ejpam-3165	113	16	-	-	SYM
ejpam-3165	113	17	361	361	NUM
ejpam-3165	113	18	358	358	NUM
ejpam-3165	113	19	⇒	⇒	NOUN
ejpam-3165	113	20	2n(u	2n(u	NUM
ejpam-3165	113	21	,	,	PUNCT
ejpam-3165	113	22	v	v	NOUN
ejpam-3165	113	23	)	)	PUNCT
ejpam-3165	113	24	{	{	PUNCT
ejpam-3165	113	25	(	(	PUNCT
ejpam-3165	113	26	u	u	NOUN
ejpam-3165	113	27	,	,	PUNCT
ejpam-3165	113	28	u	u	NOUN
ejpam-3165	113	29	)	)	PUNCT
ejpam-3165	113	30	n−2	n−2	PROPN
ejpam-3165	113	31	2	2	NUM
ejpam-3165	113	32	+	+	CCONJ
ejpam-3165	113	33	1	1	NUM
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ejpam-3165	113	35	!	!	PUNCT
ejpam-3165	114	1	(	(	PUNCT
ejpam-3165	114	2	n−	n−	NOUN
ejpam-3165	114	3	1)(n−	1)(n−	PROPN
ejpam-3165	114	4	2)(u	2)(u	NUM
ejpam-3165	114	5	,	,	PUNCT
ejpam-3165	114	6	u	u	NOUN
ejpam-3165	114	7	)	)	PUNCT
ejpam-3165	114	8	n−4	n−4	PROPN
ejpam-3165	114	9	2	2	NUM
ejpam-3165	114	10	(	(	PUNCT
ejpam-3165	114	11	v	v	NOUN
ejpam-3165	114	12	,	,	PUNCT
ejpam-3165	114	13	v	v	NOUN
ejpam-3165	114	14	)	)	PUNCT
ejpam-3165	114	15	+	+	CCONJ
ejpam-3165	114	16	1	1	NUM
ejpam-3165	114	17	5	5	NUM
ejpam-3165	114	18	!	!	PUNCT
ejpam-3165	115	1	(	(	PUNCT
ejpam-3165	115	2	n−	n−	NOUN
ejpam-3165	115	3	1)(n−	1)(n−	NUM
ejpam-3165	115	4	2)(n−	2)(n−	NUM
ejpam-3165	115	5	3)(n−	3)(n−	NUM
ejpam-3165	115	6	4)(u	4)(u	NUM
ejpam-3165	115	7	,	,	PUNCT
ejpam-3165	115	8	u	u	NOUN
ejpam-3165	115	9	)	)	PUNCT
ejpam-3165	115	10	n−6	n−6	PROPN
ejpam-3165	115	11	2	2	NUM
ejpam-3165	115	12	(	(	PUNCT
ejpam-3165	115	13	v	v	NOUN
ejpam-3165	115	14	,	,	PUNCT
ejpam-3165	115	15	v)2	v)2	ADJ
ejpam-3165	115	16	+	+	CCONJ
ejpam-3165	115	17	1	1	NUM
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ejpam-3165	115	19	!	!	PUNCT
ejpam-3165	116	1	(	(	PUNCT
ejpam-3165	116	2	n−	n−	NOUN
ejpam-3165	116	3	1)(n−	1)(n−	NUM
ejpam-3165	116	4	2)(n−	2)(n−	NUM
ejpam-3165	116	5	3)(n−	3)(n−	NUM
ejpam-3165	116	6	4)(n−	4)(n−	PROPN
ejpam-3165	116	7	5)(n−	5)(n−	NUM
ejpam-3165	116	8	6)(u	6)(u	NUM
ejpam-3165	116	9	,	,	PUNCT
ejpam-3165	116	10	u	u	NOUN
ejpam-3165	116	11	)	)	PUNCT
ejpam-3165	116	12	n−8	n−8	PROPN
ejpam-3165	116	13	2	2	NUM
ejpam-3165	116	14	(	(	PUNCT
ejpam-3165	116	15	v	v	NOUN
ejpam-3165	116	16	,	,	PUNCT
ejpam-3165	116	17	v)3	v)3	PROPN
ejpam-3165	116	18	+	+	X
ejpam-3165	116	19	.	.	PUNCT
ejpam-3165	116	20	.	.	PUNCT
ejpam-3165	117	1	.+	.+	NOUN
ejpam-3165	117	2	(	(	PUNCT
ejpam-3165	117	3	v	v	NOUN
ejpam-3165	117	4	,	,	PUNCT
ejpam-3165	117	5	v	v	NOUN
ejpam-3165	117	6	)	)	PUNCT
ejpam-3165	117	7	n−2	n−2	PROPN
ejpam-3165	117	8	2	2	NUM
ejpam-3165	117	9	}	}	PUNCT
ejpam-3165	117	10	=	=	SYM
ejpam-3165	117	11	(	(	PUNCT
ejpam-3165	117	12	u+	u+	NUM
ejpam-3165	117	13	v)n	v)n	NOUN
ejpam-3165	117	14	⇒	⇒	PROPN
ejpam-3165	117	15	∥∥∥2n(u	∥∥∥2n(u	PROPN
ejpam-3165	117	16	,	,	PUNCT
ejpam-3165	117	17	v	v	NOUN
ejpam-3165	117	18	)	)	PUNCT
ejpam-3165	117	19	{	{	PUNCT
ejpam-3165	117	20	(	(	PUNCT
ejpam-3165	117	21	u	u	NOUN
ejpam-3165	117	22	,	,	PUNCT
ejpam-3165	117	23	u	u	NOUN
ejpam-3165	117	24	)	)	PUNCT
ejpam-3165	117	25	n−2	n−2	PROPN
ejpam-3165	117	26	2	2	NUM
ejpam-3165	117	27	+	+	CCONJ
ejpam-3165	117	28	1	1	NUM
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ejpam-3165	117	30	!	!	PUNCT
ejpam-3165	118	1	(	(	PUNCT
ejpam-3165	118	2	n−	n−	NOUN
ejpam-3165	118	3	1)(n−	1)(n−	PROPN
ejpam-3165	118	4	2)(u	2)(u	NUM
ejpam-3165	118	5	,	,	PUNCT
ejpam-3165	118	6	u	u	NOUN
ejpam-3165	118	7	)	)	PUNCT
ejpam-3165	118	8	n−4	n−4	PROPN
ejpam-3165	118	9	2	2	NUM
ejpam-3165	118	10	(	(	PUNCT
ejpam-3165	118	11	v	v	NOUN
ejpam-3165	118	12	,	,	PUNCT
ejpam-3165	118	13	v	v	NOUN
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ejpam-3165	118	15	+	+	CCONJ
ejpam-3165	118	16	1	1	NUM
ejpam-3165	118	17	5	5	NUM
ejpam-3165	118	18	!	!	PUNCT
ejpam-3165	119	1	(	(	PUNCT
ejpam-3165	119	2	n−	n−	NOUN
ejpam-3165	119	3	1)(n−	1)(n−	NUM
ejpam-3165	119	4	2)(n−	2)(n−	NUM
ejpam-3165	119	5	3)(n−	3)(n−	NUM
ejpam-3165	119	6	4)(u	4)(u	NUM
ejpam-3165	119	7	,	,	PUNCT
ejpam-3165	119	8	u	u	NOUN
ejpam-3165	119	9	)	)	PUNCT
ejpam-3165	119	10	n−6	n−6	PROPN
ejpam-3165	119	11	2	2	NUM
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ejpam-3165	119	14	,	,	PUNCT
ejpam-3165	119	15	v)2	v)2	ADJ
ejpam-3165	119	16	+	+	CCONJ
ejpam-3165	119	17	1	1	NUM
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ejpam-3165	119	19	!	!	PUNCT
ejpam-3165	120	1	(	(	PUNCT
ejpam-3165	120	2	n−	n−	NOUN
ejpam-3165	120	3	1)(n−	1)(n−	NUM
ejpam-3165	120	4	2)(n−	2)(n−	NUM
ejpam-3165	120	5	3)(n−	3)(n−	NUM
ejpam-3165	120	6	4)(n−	4)(n−	PROPN
ejpam-3165	120	7	5)(n−	5)(n−	NUM
ejpam-3165	120	8	6)(u	6)(u	NUM
ejpam-3165	120	9	,	,	PUNCT
ejpam-3165	120	10	u	u	NOUN
ejpam-3165	120	11	)	)	PUNCT
ejpam-3165	120	12	n−8	n−8	PROPN
ejpam-3165	120	13	2	2	NUM
ejpam-3165	120	14	(	(	PUNCT
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ejpam-3165	120	16	,	,	PUNCT
ejpam-3165	120	17	v)3	v)3	PROPN
ejpam-3165	120	18	+	+	X
ejpam-3165	120	19	.	.	PUNCT
ejpam-3165	120	20	.	.	PUNCT
ejpam-3165	121	1	.+	.+	NOUN
ejpam-3165	121	2	(	(	PUNCT
ejpam-3165	121	3	v	v	NOUN
ejpam-3165	121	4	,	,	PUNCT
ejpam-3165	121	5	v	v	NOUN
ejpam-3165	121	6	)	)	PUNCT
ejpam-3165	121	7	n−2	n−2	PROPN
ejpam-3165	121	8	2	2	NUM
ejpam-3165	121	9	}	}	PUNCT
ejpam-3165	121	10	∥∥∥	∥∥∥	NOUN
ejpam-3165	121	11	=	=	SYM
ejpam-3165	121	12	∥∥∥(u+	∥∥∥(u+	PROPN
ejpam-3165	121	13	v)n	v)n	NOUN
ejpam-3165	121	14	∥∥∥	∥∥∥	NOUN
ejpam-3165	121	15	⇒	⇒	NOUN
ejpam-3165	121	16	2n‖u‖‖v‖	2n‖u‖‖v‖	PROPN
ejpam-3165	121	17	∥∥∥{(u	∥∥∥{(u	ADJ
ejpam-3165	121	18	,	,	PUNCT
ejpam-3165	121	19	u	u	NOUN
ejpam-3165	121	20	)	)	PUNCT
ejpam-3165	121	21	n−2	n−2	PROPN
ejpam-3165	121	22	2	2	NUM
ejpam-3165	121	23	+	+	CCONJ
ejpam-3165	121	24	1	1	NUM
ejpam-3165	121	25	3	3	NUM
ejpam-3165	121	26	!	!	PUNCT
ejpam-3165	122	1	(	(	PUNCT
ejpam-3165	122	2	n−	n−	NOUN
ejpam-3165	122	3	1)(n−	1)(n−	NUM
ejpam-3165	122	4	2)(u.u	2)(u.u	NOUN
ejpam-3165	122	5	)	)	PUNCT
ejpam-3165	122	6	n−4	n−4	PROPN
ejpam-3165	122	7	2	2	NUM
ejpam-3165	122	8	(	(	PUNCT
ejpam-3165	122	9	v	v	NOUN
ejpam-3165	122	10	,	,	PUNCT
ejpam-3165	122	11	v	v	NOUN
ejpam-3165	122	12	)	)	PUNCT
ejpam-3165	122	13	+	+	CCONJ
ejpam-3165	122	14	1	1	NUM
ejpam-3165	122	15	5	5	NUM
ejpam-3165	122	16	!	!	PUNCT
ejpam-3165	123	1	(	(	PUNCT
ejpam-3165	123	2	n−	n−	NOUN
ejpam-3165	123	3	1)(n−	1)(n−	NUM
ejpam-3165	123	4	2)(n−	2)(n−	NUM
ejpam-3165	123	5	3)(n−	3)(n−	NUM
ejpam-3165	123	6	4)(u	4)(u	NUM
ejpam-3165	123	7	,	,	PUNCT
ejpam-3165	123	8	u	u	NOUN
ejpam-3165	123	9	)	)	PUNCT
ejpam-3165	123	10	n−6	n−6	PROPN
ejpam-3165	123	11	2	2	NUM
ejpam-3165	123	12	(	(	PUNCT
ejpam-3165	123	13	v	v	NOUN
ejpam-3165	123	14	,	,	PUNCT
ejpam-3165	123	15	v)2	v)2	ADJ
ejpam-3165	123	16	+	+	CCONJ
ejpam-3165	123	17	1	1	NUM
ejpam-3165	123	18	7	7	NUM
ejpam-3165	123	19	!	!	PUNCT
ejpam-3165	124	1	(	(	PUNCT
ejpam-3165	124	2	n−	n−	NOUN
ejpam-3165	124	3	1)(n−	1)(n−	NUM
ejpam-3165	124	4	2)(n−	2)(n−	NUM
ejpam-3165	124	5	3)(n−	3)(n−	NUM
ejpam-3165	124	6	4)(n−	4)(n−	PROPN
ejpam-3165	124	7	5)(n−	5)(n−	NUM
ejpam-3165	124	8	6)(u	6)(u	NUM
ejpam-3165	124	9	,	,	PUNCT
ejpam-3165	124	10	u	u	NOUN
ejpam-3165	124	11	)	)	PUNCT
ejpam-3165	124	12	n−8	n−8	PROPN
ejpam-3165	124	13	2	2	NUM
ejpam-3165	124	14	(	(	PUNCT
ejpam-3165	124	15	v	v	NOUN
ejpam-3165	124	16	,	,	PUNCT
ejpam-3165	124	17	v)3	v)3	PROPN
ejpam-3165	124	18	+	+	X
ejpam-3165	124	19	.	.	PUNCT
ejpam-3165	124	20	.	.	PUNCT
ejpam-3165	125	1	.+	.+	NOUN
ejpam-3165	125	2	(	(	PUNCT
ejpam-3165	125	3	v	v	NOUN
ejpam-3165	125	4	,	,	PUNCT
ejpam-3165	125	5	v	v	NOUN
ejpam-3165	125	6	)	)	PUNCT
ejpam-3165	125	7	n−2	n−2	PROPN
ejpam-3165	125	8	2	2	NUM
ejpam-3165	125	9	}	}	PUNCT
ejpam-3165	125	10	∥∥∥	∥∥∥	PROPN
ejpam-3165	125	11	≤	≤	NUM
ejpam-3165	125	12	∥∥∥(u+	∥∥∥(u+	PROPN
ejpam-3165	125	13	v	v	NOUN
ejpam-3165	125	14	)	)	PUNCT
ejpam-3165	125	15	∥∥∥n	∥∥∥n	NOUN
ejpam-3165	125	16	(	(	PUNCT
ejpam-3165	125	17	9	9	NUM
ejpam-3165	125	18	)	)	PUNCT
ejpam-3165	125	19	by	by	ADP
ejpam-3165	125	20	transitivity	transitivity	NOUN
ejpam-3165	125	21	,	,	PUNCT
ejpam-3165	125	22	inequalities	inequality	NOUN
ejpam-3165	125	23	(	(	PUNCT
ejpam-3165	125	24	8)	8)	NUM
ejpam-3165	125	25	and	and	CCONJ
ejpam-3165	125	26	(	(	PUNCT
ejpam-3165	125	27	9	9	X
ejpam-3165	125	28	)	)	PUNCT
ejpam-3165	125	29	yields	yield	NOUN
ejpam-3165	125	30	‖u−	‖u−	PROPN
ejpam-3165	125	31	v‖n	v‖n	PROPN
ejpam-3165	125	32	≤	≤	PROPN
ejpam-3165	126	1	‖u+	‖u+	PROPN
ejpam-3165	126	2	v‖n	v‖n	X
ejpam-3165	126	3	(	(	PUNCT
ejpam-3165	126	4	‖u−	‖u−	PROPN
ejpam-3165	126	5	v‖n	v‖n	NOUN
ejpam-3165	126	6	)	)	PUNCT
ejpam-3165	126	7	1	1	NUM
ejpam-3165	126	8	n	n	NOUN
ejpam-3165	126	9	=	=	SYM
ejpam-3165	126	10	(	(	PUNCT
ejpam-3165	126	11	‖u+	‖u+	NOUN
ejpam-3165	126	12	v‖n	v‖n	ADJ
ejpam-3165	126	13	)	)	PUNCT
ejpam-3165	126	14	1	1	NUM
ejpam-3165	126	15	n	n	NOUN
ejpam-3165	126	16	⇒	⇒	VERB
ejpam-3165	126	17	‖u−	‖u−	PRON
ejpam-3165	126	18	v‖	v‖	NOUN
ejpam-3165	126	19	=	=	PUNCT
ejpam-3165	127	1	‖u+	‖u+	NOUN
ejpam-3165	127	2	v‖	v‖	NOUN
ejpam-3165	127	3	⇒	⇒	VERB
ejpam-3165	127	4	‖u−	‖u−	DET
ejpam-3165	127	5	v‖	v‖	NOUN
ejpam-3165	127	6	≤	≤	NOUN
ejpam-3165	127	7	‖u‖+	‖u‖+	PRON
ejpam-3165	127	8	‖v‖	‖v‖	PROPN
ejpam-3165	127	9	(	(	PUNCT
ejpam-3165	127	10	10	10	NUM
ejpam-3165	127	11	)	)	PUNCT
ejpam-3165	127	12	2.2	2.2	NUM
ejpam-3165	127	13	.	.	PUNCT
ejpam-3165	128	1	the	the	DET
ejpam-3165	128	2	proof	proof	NOUN
ejpam-3165	128	3	of	of	ADP
ejpam-3165	128	4	the	the	DET
ejpam-3165	128	5	triangle	triangle	NOUN
ejpam-3165	128	6	inequality	inequality	NOUN
ejpam-3165	128	7	through	through	ADP
ejpam-3165	128	8	euclidean	euclidean	ADJ
ejpam-3165	128	9	norm	norm	NOUN
ejpam-3165	128	10	in	in	ADP
ejpam-3165	128	11	this	this	DET
ejpam-3165	128	12	subsection	subsection	NOUN
ejpam-3165	128	13	,	,	PUNCT
ejpam-3165	128	14	we	we	PRON
ejpam-3165	128	15	will	will	AUX
ejpam-3165	128	16	establish	establish	VERB
ejpam-3165	128	17	the	the	DET
ejpam-3165	128	18	same	same	ADJ
ejpam-3165	128	19	result	result	NOUN
ejpam-3165	128	20	as	as	ADP
ejpam-3165	128	21	in	in	ADP
ejpam-3165	128	22	(	(	PUNCT
ejpam-3165	128	23	10	10	NUM
ejpam-3165	128	24	)	)	PUNCT
ejpam-3165	128	25	,	,	PUNCT
ejpam-3165	128	26	by	by	ADP
ejpam-3165	128	27	making	make	VERB
ejpam-3165	128	28	use	use	NOUN
ejpam-3165	128	29	of	of	ADP
ejpam-3165	128	30	both	both	CCONJ
ejpam-3165	128	31	the	the	DET
ejpam-3165	128	32	binomial	binomial	ADJ
ejpam-3165	128	33	inequality	inequality	NOUN
ejpam-3165	128	34	of	of	ADP
ejpam-3165	128	35	two	two	NUM
ejpam-3165	128	36	vector	vector	NOUN
ejpam-3165	128	37	points	point	NOUN
ejpam-3165	128	38	and	and	CCONJ
ejpam-3165	128	39	the	the	DET
ejpam-3165	128	40	young	young	PROPN
ejpam-3165	128	41	’s	’s	PART
ejpam-3165	128	42	inequality	inequality	NOUN
ejpam-3165	128	43	.	.	PUNCT
ejpam-3165	129	1	definition	definition	NOUN
ejpam-3165	129	2	2	2	NUM
ejpam-3165	129	3	(	(	PUNCT
ejpam-3165	129	4	young	young	PROPN
ejpam-3165	129	5	’s	’s	PART
ejpam-3165	129	6	inequality	inequality	NOUN
ejpam-3165	129	7	)	)	PUNCT
ejpam-3165	129	8	.	.	PUNCT
ejpam-3165	130	1	let	let	VERB
ejpam-3165	130	2	1	1	NUM
ejpam-3165	130	3	<	<	X
ejpam-3165	130	4	p	p	X
ejpam-3165	130	5	<	<	X
ejpam-3165	130	6	∞	∞	PROPN
ejpam-3165	130	7	,	,	PUNCT
ejpam-3165	130	8	q	q	X
ejpam-3165	130	9	the	the	DET
ejpam-3165	130	10	conjugate	conjugate	NOUN
ejpam-3165	130	11	of	of	ADP
ejpam-3165	130	12	p	p	NOUN
ejpam-3165	130	13	,	,	PUNCT
ejpam-3165	130	14	and	and	CCONJ
ejpam-3165	130	15	any	any	DET
ejpam-3165	130	16	two	two	NUM
ejpam-3165	130	17	vectors	vector	NOUN
ejpam-3165	130	18	u	u	NOUN
ejpam-3165	130	19	and	and	CCONJ
ejpam-3165	130	20	v	v	NOUN
ejpam-3165	130	21	,	,	PUNCT
ejpam-3165	130	22	then	then	ADV
ejpam-3165	130	23	(	(	PUNCT
ejpam-3165	130	24	u	u	NOUN
ejpam-3165	130	25	,	,	PUNCT
ejpam-3165	130	26	v	v	NOUN
ejpam-3165	130	27	)	)	PUNCT
ejpam-3165	130	28	≤	≤	NOUN
ejpam-3165	130	29	up	up	ADP
ejpam-3165	130	30	p	p	NOUN
ejpam-3165	130	31	+	+	PROPN
ejpam-3165	130	32	vq	vq	PROPN
ejpam-3165	130	33	q	q	X
ejpam-3165	130	34	,	,	PUNCT
ejpam-3165	130	35	where	where	SCONJ
ejpam-3165	130	36	1	1	NUM
ejpam-3165	130	37	p	p	NOUN
ejpam-3165	130	38	+	+	NOUN
ejpam-3165	130	39	1	1	NUM
ejpam-3165	130	40	q	q	NOUN
ejpam-3165	130	41	=	=	SYM
ejpam-3165	130	42	1	1	NUM
ejpam-3165	130	43	see	see	VERB
ejpam-3165	130	44	[	[	X
ejpam-3165	130	45	14	14	NUM
ejpam-3165	130	46	]	]	PUNCT
ejpam-3165	130	47	.	.	PUNCT
ejpam-3165	131	1	barnes	barnes	PROPN
ejpam-3165	131	2	et	et	PROPN
ejpam-3165	131	3	al	al	PROPN
ejpam-3165	131	4	.	.	PUNCT
ejpam-3165	131	5	/	/	SYM
ejpam-3165	131	6	eur	eur	PROPN
ejpam-3165	131	7	.	.	PUNCT
ejpam-3165	132	1	j.	j.	PROPN
ejpam-3165	132	2	pure	pure	PROPN
ejpam-3165	132	3	appl	appl	PROPN
ejpam-3165	132	4	.	.	PROPN
ejpam-3165	132	5	math	math	PROPN
ejpam-3165	132	6	,	,	PUNCT
ejpam-3165	132	7	11	11	NUM
ejpam-3165	132	8	(	(	PUNCT
ejpam-3165	132	9	1	1	NUM
ejpam-3165	132	10	)	)	PUNCT
ejpam-3165	132	11	(	(	PUNCT
ejpam-3165	132	12	2018	2018	NUM
ejpam-3165	132	13	)	)	PUNCT
ejpam-3165	132	14	,	,	PUNCT
ejpam-3165	132	15	352	352	NUM
ejpam-3165	132	16	-	-	SYM
ejpam-3165	132	17	361	361	NUM
ejpam-3165	132	18	359	359	NUM
ejpam-3165	132	19	firstly	firstly	ADV
ejpam-3165	132	20	,	,	PUNCT
ejpam-3165	132	21	we	we	PRON
ejpam-3165	132	22	observe	observe	VERB
ejpam-3165	132	23	the	the	DET
ejpam-3165	132	24	two	two	NUM
ejpam-3165	132	25	vectors	vector	NOUN
ejpam-3165	132	26	in	in	ADP
ejpam-3165	132	27	the	the	DET
ejpam-3165	132	28	hilbert	hilbert	NOUN
ejpam-3165	132	29	space	space	NOUN
ejpam-3165	132	30	as	as	ADP
ejpam-3165	132	31	:	:	PUNCT
ejpam-3165	132	32	(	(	PUNCT
ejpam-3165	132	33	u+	u+	NUM
ejpam-3165	132	34	v)2	v)2	PROPN
ejpam-3165	132	35	≥	≥	NOUN
ejpam-3165	132	36	0	0	NUM
ejpam-3165	132	37	(	(	PUNCT
ejpam-3165	132	38	u	u	NOUN
ejpam-3165	132	39	,	,	PUNCT
ejpam-3165	132	40	u	u	NOUN
ejpam-3165	132	41	)	)	PUNCT
ejpam-3165	132	42	+	+	CCONJ
ejpam-3165	132	43	2(u	2(u	NUM
ejpam-3165	132	44	,	,	PUNCT
ejpam-3165	132	45	v	v	NOUN
ejpam-3165	132	46	)	)	PUNCT
ejpam-3165	132	47	+	+	CCONJ
ejpam-3165	132	48	(	(	PUNCT
ejpam-3165	132	49	v	v	NOUN
ejpam-3165	132	50	,	,	PUNCT
ejpam-3165	132	51	v	v	NOUN
ejpam-3165	132	52	)	)	PUNCT
ejpam-3165	132	53	≥	≥	NOUN
ejpam-3165	132	54	0	0	NUM
ejpam-3165	133	1	−{(u	−{(u	NOUN
ejpam-3165	133	2	,	,	PUNCT
ejpam-3165	133	3	u	u	NOUN
ejpam-3165	133	4	)	)	PUNCT
ejpam-3165	133	5	+	+	CCONJ
ejpam-3165	133	6	(	(	PUNCT
ejpam-3165	133	7	v	v	NOUN
ejpam-3165	133	8	,	,	PUNCT
ejpam-3165	133	9	v	v	NOUN
ejpam-3165	133	10	)	)	PUNCT
ejpam-3165	133	11	}	}	PUNCT
ejpam-3165	133	12	≤	≤	NUM
ejpam-3165	133	13	2(u	2(u	NUM
ejpam-3165	133	14	,	,	PUNCT
ejpam-3165	133	15	v	v	NOUN
ejpam-3165	133	16	)	)	PUNCT
ejpam-3165	133	17	−{(u	−{(u	NOUN
ejpam-3165	133	18	,	,	PUNCT
ejpam-3165	133	19	u	u	NOUN
ejpam-3165	133	20	)	)	PUNCT
ejpam-3165	133	21	+	+	CCONJ
ejpam-3165	133	22	(	(	PUNCT
ejpam-3165	133	23	v	v	NOUN
ejpam-3165	133	24	,	,	PUNCT
ejpam-3165	133	25	v)−	v)−	PROPN
ejpam-3165	133	26	2(u	2(u	NUM
ejpam-3165	133	27	,	,	PUNCT
ejpam-3165	133	28	v	v	NOUN
ejpam-3165	133	29	)	)	PUNCT
ejpam-3165	133	30	}	}	PUNCT
ejpam-3165	133	31	≤	≤	NUM
ejpam-3165	133	32	2(u	2(u	NUM
ejpam-3165	133	33	,	,	PUNCT
ejpam-3165	133	34	v	v	NOUN
ejpam-3165	133	35	)	)	PUNCT
ejpam-3165	133	36	−(u−	−(u−	ADV
ejpam-3165	133	37	v)2	v)2	X
ejpam-3165	133	38	=	=	SYM
ejpam-3165	133	39	2(u	2(u	NUM
ejpam-3165	133	40	,	,	PUNCT
ejpam-3165	133	41	v	v	NOUN
ejpam-3165	133	42	)	)	PUNCT
ejpam-3165	133	43	‖	‖	PROPN
ejpam-3165	133	44	−	−	PROPN
ejpam-3165	133	45	(	(	PUNCT
ejpam-3165	133	46	u−	u−	NOUN
ejpam-3165	133	47	v)2‖	v)2‖	NOUN
ejpam-3165	133	48	=	=	SYM
ejpam-3165	133	49	‖2(u	‖2(u	ADJ
ejpam-3165	133	50	,	,	PUNCT
ejpam-3165	133	51	v)‖	v)‖	NOUN
ejpam-3165	133	52	‖(u−	‖(u−	PUNCT
ejpam-3165	133	53	v)‖2	v)‖2	NOUN
ejpam-3165	133	54	=	=	SYM
ejpam-3165	133	55	|2||(u	|2||(u	NOUN
ejpam-3165	133	56	,	,	PUNCT
ejpam-3165	133	57	v)|	v)|	NOUN
ejpam-3165	133	58	⇒	⇒	PROPN
ejpam-3165	133	59	‖(u−	‖(u−	PUNCT
ejpam-3165	133	60	v)‖2	v)‖2	NOUN
ejpam-3165	133	61	≤	≤	NOUN
ejpam-3165	133	62	2|(u	2|(u	NUM
ejpam-3165	133	63	,	,	PUNCT
ejpam-3165	133	64	v)|	v)|	NOUN
ejpam-3165	133	65	(	(	PUNCT
ejpam-3165	133	66	11	11	NUM
ejpam-3165	133	67	)	)	PUNCT
ejpam-3165	133	68	applying	apply	VERB
ejpam-3165	133	69	the	the	DET
ejpam-3165	133	70	young	young	ADJ
ejpam-3165	133	71	’s	’s	PART
ejpam-3165	133	72	inequality	inequality	NOUN
ejpam-3165	133	73	of	of	ADP
ejpam-3165	133	74	two	two	NUM
ejpam-3165	133	75	vectors	vector	NOUN
ejpam-3165	133	76	|(u	|(u	NUM
ejpam-3165	133	77	,	,	PUNCT
ejpam-3165	133	78	v)|	v)|	VERB
ejpam-3165	133	79	≤	≤	PUNCT
ejpam-3165	133	80	∣∣∣u2	∣∣∣u2	PROPN
ejpam-3165	133	81	2	2	NUM
ejpam-3165	133	82	+	+	CCONJ
ejpam-3165	133	83	v2	v2	PROPN
ejpam-3165	133	84	2	2	NUM
ejpam-3165	133	85	∣∣∣	∣∣∣	NOUN
ejpam-3165	133	86	‖(u	‖(u	NOUN
ejpam-3165	133	87	,	,	PUNCT
ejpam-3165	133	88	v)‖	v)‖	ADJ
ejpam-3165	133	89	≤	≤	X
ejpam-3165	133	90	|u|2	|u|2	PROPN
ejpam-3165	133	91	2	2	NUM
ejpam-3165	133	92	+	+	NUM
ejpam-3165	133	93	|v|2	|v|2	PROPN
ejpam-3165	133	94	2	2	NUM
ejpam-3165	133	95	,	,	PUNCT
ejpam-3165	133	96	(	(	PUNCT
ejpam-3165	133	97	12	12	NUM
ejpam-3165	133	98	)	)	PUNCT
ejpam-3165	133	99	where	where	SCONJ
ejpam-3165	133	100	p	p	NOUN
ejpam-3165	133	101	=	=	X
ejpam-3165	133	102	q	q	NOUN
ejpam-3165	133	103	=	=	NOUN
ejpam-3165	133	104	2	2	X
ejpam-3165	133	105	.	.	PUNCT
ejpam-3165	133	106	substituting	substitute	VERB
ejpam-3165	133	107	the	the	DET
ejpam-3165	133	108	inequality	inequality	NOUN
ejpam-3165	133	109	in	in	ADP
ejpam-3165	133	110	(	(	PUNCT
ejpam-3165	133	111	12	12	NUM
ejpam-3165	133	112	)	)	PUNCT
ejpam-3165	133	113	into	into	ADP
ejpam-3165	133	114	left	left	ADJ
ejpam-3165	133	115	hand	hand	NOUN
ejpam-3165	133	116	side	side	NOUN
ejpam-3165	133	117	of	of	ADP
ejpam-3165	133	118	inequality	inequality	NOUN
ejpam-3165	133	119	(	(	PUNCT
ejpam-3165	133	120	11	11	NUM
ejpam-3165	133	121	)	)	PUNCT
ejpam-3165	133	122	yields	yield	NOUN
ejpam-3165	133	123	:	:	PUNCT
ejpam-3165	133	124	‖(u−	‖(u−	PUNCT
ejpam-3165	133	125	v)‖2	v)‖2	NOUN
ejpam-3165	133	126	≤	≤	NUM
ejpam-3165	133	127	2{|u|	2{|u|	NUM
ejpam-3165	133	128	2	2	NUM
ejpam-3165	133	129	2	2	NUM
ejpam-3165	133	130	+	+	CCONJ
ejpam-3165	133	131	|v|2	|v|2	PROPN
ejpam-3165	133	132	2	2	NUM
ejpam-3165	133	133	}	}	PUNCT
ejpam-3165	133	134	⇒	⇒	VERB
ejpam-3165	133	135	‖(u−	‖(u−	PUNCT
ejpam-3165	133	136	v)‖2	v)‖2	NOUN
ejpam-3165	133	137	=	=	SYM
ejpam-3165	133	138	|u|2	|u|2	PROPN
ejpam-3165	133	139	+	+	NUM
ejpam-3165	133	140	|v|2	|v|2	PROPN
ejpam-3165	133	141	⇒	⇒	VERB
ejpam-3165	133	142	‖(u−	‖(u−	PUNCT
ejpam-3165	133	143	v)‖	v)‖	NOUN
ejpam-3165	133	144	≤	≤	PROPN
ejpam-3165	133	145	√	√	ADP
ejpam-3165	133	146	|u|2	|u|2	PROPN
ejpam-3165	133	147	+	+	PROPN
ejpam-3165	133	148	|v|2	|v|2	PROPN
ejpam-3165	133	149	.	.	PUNCT
ejpam-3165	134	1	(	(	PUNCT
ejpam-3165	134	2	13	13	NUM
ejpam-3165	134	3	)	)	PUNCT
ejpam-3165	134	4	on	on	ADP
ejpam-3165	134	5	the	the	DET
ejpam-3165	134	6	other	other	ADJ
ejpam-3165	134	7	hand	hand	NOUN
ejpam-3165	134	8	,	,	PUNCT
ejpam-3165	134	9	the	the	DET
ejpam-3165	134	10	norm	norm	NOUN
ejpam-3165	134	11	of	of	ADP
ejpam-3165	134	12	sum	sum	NOUN
ejpam-3165	134	13	of	of	ADP
ejpam-3165	134	14	two	two	NUM
ejpam-3165	134	15	vectors	vector	NOUN
ejpam-3165	134	16	in	in	ADP
ejpam-3165	134	17	hilbert	hilbert	NOUN
ejpam-3165	134	18	space	space	NOUN
ejpam-3165	134	19	was	be	AUX
ejpam-3165	134	20	observed	observe	VERB
ejpam-3165	134	21	as	as	ADP
ejpam-3165	134	22	:	:	PUNCT
ejpam-3165	134	23	(	(	PUNCT
ejpam-3165	134	24	u+	u+	NUM
ejpam-3165	134	25	v)2	v)2	PROPN
ejpam-3165	134	26	≥	≥	NUM
ejpam-3165	134	27	0	0	NUM
ejpam-3165	134	28	⇒	⇒	PROPN
ejpam-3165	134	29	−{(u	−{(u	NOUN
ejpam-3165	134	30	,	,	PUNCT
ejpam-3165	134	31	u	u	NOUN
ejpam-3165	134	32	)	)	PUNCT
ejpam-3165	135	1	+	+	CCONJ
ejpam-3165	135	2	(	(	PUNCT
ejpam-3165	135	3	v	v	NOUN
ejpam-3165	135	4	,	,	PUNCT
ejpam-3165	135	5	v	v	NOUN
ejpam-3165	135	6	)	)	PUNCT
ejpam-3165	135	7	}	}	PUNCT
ejpam-3165	135	8	≤	≤	NUM
ejpam-3165	135	9	2(u	2(u	NUM
ejpam-3165	135	10	,	,	PUNCT
ejpam-3165	135	11	v	v	NOUN
ejpam-3165	135	12	)	)	PUNCT
ejpam-3165	135	13	⇒	⇒	NOUN
ejpam-3165	135	14	−2(u	−2(u	NUM
ejpam-3165	135	15	,	,	PUNCT
ejpam-3165	135	16	v	v	NOUN
ejpam-3165	135	17	)	)	PUNCT
ejpam-3165	135	18	≤	≤	NOUN
ejpam-3165	135	19	{	{	PUNCT
ejpam-3165	135	20	(	(	PUNCT
ejpam-3165	135	21	u	u	NOUN
ejpam-3165	135	22	,	,	PUNCT
ejpam-3165	135	23	u	u	NOUN
ejpam-3165	135	24	)	)	PUNCT
ejpam-3165	135	25	+	+	CCONJ
ejpam-3165	135	26	(	(	PUNCT
ejpam-3165	135	27	v	v	NOUN
ejpam-3165	135	28	,	,	PUNCT
ejpam-3165	135	29	v	v	NOUN
ejpam-3165	135	30	)	)	PUNCT
ejpam-3165	135	31	+	+	CCONJ
ejpam-3165	135	32	2(u	2(u	NUM
ejpam-3165	135	33	,	,	PUNCT
ejpam-3165	135	34	v	v	NOUN
ejpam-3165	135	35	)	)	PUNCT
ejpam-3165	135	36	}	}	PUNCT
ejpam-3165	135	37	⇒	⇒	PROPN
ejpam-3165	135	38	−2(u	−2(u	NUM
ejpam-3165	135	39	,	,	PUNCT
ejpam-3165	135	40	v	v	NOUN
ejpam-3165	135	41	)	)	PUNCT
ejpam-3165	135	42	=	=	PUNCT
ejpam-3165	135	43	(	(	PUNCT
ejpam-3165	135	44	u+	u+	NUM
ejpam-3165	135	45	v)2	v)2	PROPN
ejpam-3165	135	46	⇒	⇒	NOUN
ejpam-3165	135	47	‖−	‖−	PROPN
ejpam-3165	135	48	2(u	2(u	NUM
ejpam-3165	135	49	,	,	PUNCT
ejpam-3165	135	50	v)‖	v)‖	NOUN
ejpam-3165	135	51	=	=	SYM
ejpam-3165	135	52	‖(u+	‖(u+	NUM
ejpam-3165	135	53	v)2‖	v)2‖	NOUN
ejpam-3165	135	54	⇒	⇒	NOUN
ejpam-3165	135	55	2|(u	2|(u	NUM
ejpam-3165	135	56	,	,	PUNCT
ejpam-3165	135	57	v)|	v)|	VERB
ejpam-3165	135	58	≤	≤	NUM
ejpam-3165	135	59	‖u+	‖u+	PROPN
ejpam-3165	135	60	v‖2	v‖2	PROPN
ejpam-3165	135	61	⇒	⇒	NOUN
ejpam-3165	135	62	2{|u|	2{|u|	NUM
ejpam-3165	135	63	2	2	NUM
ejpam-3165	135	64	2	2	NUM
ejpam-3165	135	65	+	+	CCONJ
ejpam-3165	135	66	|v|2	|v|2	PROPN
ejpam-3165	135	67	2	2	NUM
ejpam-3165	135	68	}	}	PUNCT
ejpam-3165	135	69	≤	≤	NUM
ejpam-3165	135	70	‖u+	‖u+	NOUN
ejpam-3165	135	71	v‖2	v‖2	PROPN
ejpam-3165	135	72	⇒	⇒	VERB
ejpam-3165	135	73	|u|2	|u|2	PROPN
ejpam-3165	135	74	+	+	NUM
ejpam-3165	135	75	|v|2	|v|2	PROPN
ejpam-3165	135	76	=	=	PUNCT
ejpam-3165	135	77	‖u+	‖u+	PROPN
ejpam-3165	135	78	v‖2	v‖2	PROPN
ejpam-3165	135	79	⇒	⇒	NOUN
ejpam-3165	135	80	√	√	NUM
ejpam-3165	135	81	|u|2	|u|2	PROPN
ejpam-3165	135	82	+	+	NUM
ejpam-3165	135	83	|v|2	|v|2	PROPN
ejpam-3165	135	84	≤	≤	PROPN
ejpam-3165	135	85	‖u+	‖u+	PROPN
ejpam-3165	135	86	v‖	v‖	NOUN
ejpam-3165	135	87	(	(	PUNCT
ejpam-3165	135	88	14	14	NUM
ejpam-3165	135	89	)	)	PUNCT
ejpam-3165	135	90	by	by	ADP
ejpam-3165	135	91	transitivity	transitivity	NOUN
ejpam-3165	135	92	,	,	PUNCT
ejpam-3165	135	93	the	the	DET
ejpam-3165	135	94	inequalities	inequality	NOUN
ejpam-3165	135	95	(	(	PUNCT
ejpam-3165	135	96	13	13	NUM
ejpam-3165	135	97	)	)	PUNCT
ejpam-3165	135	98	and	and	CCONJ
ejpam-3165	135	99	(	(	PUNCT
ejpam-3165	135	100	14	14	NUM
ejpam-3165	135	101	)	)	PUNCT
ejpam-3165	135	102	yields	yield	NOUN
ejpam-3165	135	103	‖u−	‖u−	PROPN
ejpam-3165	135	104	v‖	v‖	NOUN
ejpam-3165	135	105	≤	≤	NOUN
ejpam-3165	135	106	‖u‖+	‖u‖+	PRON
ejpam-3165	135	107	‖v‖	‖v‖	PROPN
ejpam-3165	135	108	(	(	PUNCT
ejpam-3165	135	109	15	15	NUM
ejpam-3165	135	110	)	)	PUNCT
ejpam-3165	135	111	references	reference	NOUN
ejpam-3165	135	112	360	360	NUM
ejpam-3165	135	113	3	3	NUM
ejpam-3165	135	114	.	.	PUNCT
ejpam-3165	136	1	discussion	discussion	NOUN
ejpam-3165	136	2	we	we	PRON
ejpam-3165	136	3	have	have	AUX
ejpam-3165	136	4	obtained	obtain	VERB
ejpam-3165	136	5	the	the	DET
ejpam-3165	136	6	generalized	generalized	ADJ
ejpam-3165	136	7	alternative	alternative	ADJ
ejpam-3165	136	8	way	way	NOUN
ejpam-3165	136	9	of	of	ADP
ejpam-3165	136	10	proving	prove	VERB
ejpam-3165	136	11	the	the	DET
ejpam-3165	136	12	triangle	triangle	NOUN
ejpam-3165	136	13	inequality	inequality	NOUN
ejpam-3165	136	14	in	in	ADP
ejpam-3165	136	15	(	(	PUNCT
ejpam-3165	136	16	1	1	NUM
ejpam-3165	136	17	)	)	PUNCT
ejpam-3165	136	18	for	for	ADP
ejpam-3165	136	19	any	any	DET
ejpam-3165	136	20	positive	positive	ADJ
ejpam-3165	136	21	integer	integer	NOUN
ejpam-3165	136	22	n	n	CCONJ
ejpam-3165	136	23	,	,	PUNCT
ejpam-3165	136	24	unlike	unlike	ADP
ejpam-3165	136	25	the	the	DET
ejpam-3165	136	26	results	result	NOUN
ejpam-3165	136	27	obtained	obtain	VERB
ejpam-3165	136	28	by	by	ADP
ejpam-3165	136	29	other	other	ADJ
ejpam-3165	136	30	researchers	researcher	NOUN
ejpam-3165	136	31	.	.	PUNCT
ejpam-3165	137	1	also	also	ADV
ejpam-3165	137	2	,	,	PUNCT
ejpam-3165	137	3	the	the	DET
ejpam-3165	137	4	second	second	ADJ
ejpam-3165	137	5	alternative	alternative	ADJ
ejpam-3165	137	6	proof	proof	NOUN
ejpam-3165	137	7	of	of	ADP
ejpam-3165	137	8	the	the	DET
ejpam-3165	137	9	triangle	triangle	NOUN
ejpam-3165	137	10	inequality	inequality	NOUN
ejpam-3165	137	11	establishes	establish	VERB
ejpam-3165	137	12	2−	2−	NUM
ejpam-3165	137	13	norm	norm	NOUN
ejpam-3165	137	14	of	of	ADP
ejpam-3165	137	15	any	any	DET
ejpam-3165	137	16	two	two	NUM
ejpam-3165	137	17	vector	vector	NOUN
ejpam-3165	137	18	points	point	NOUN
ejpam-3165	137	19	in	in	ADP
ejpam-3165	137	20	the	the	DET
ejpam-3165	137	21	hilbert	hilbert	NOUN
ejpam-3165	137	22	space	space	NOUN
ejpam-3165	137	23	.	.	PUNCT
ejpam-3165	138	1	4	4	X
ejpam-3165	138	2	.	.	X
ejpam-3165	138	3	conclusion	conclusion	NOUN
ejpam-3165	138	4	we	we	PRON
ejpam-3165	138	5	have	have	AUX
ejpam-3165	138	6	shown	show	VERB
ejpam-3165	138	7	the	the	DET
ejpam-3165	138	8	general	general	ADJ
ejpam-3165	138	9	alternative	alternative	ADJ
ejpam-3165	138	10	ways	way	NOUN
ejpam-3165	138	11	of	of	ADP
ejpam-3165	138	12	proving	prove	VERB
ejpam-3165	138	13	the	the	DET
ejpam-3165	138	14	triangle	triangle	NOUN
ejpam-3165	138	15	inequality	inequality	NOUN
ejpam-3165	138	16	‖u−v‖	‖u−v‖	PROPN
ejpam-3165	138	17	≤	≤	NOUN
ejpam-3165	138	18	‖u‖+‖v‖	‖u‖+‖v‖	ADV
ejpam-3165	138	19	,	,	PUNCT
ejpam-3165	138	20	through	through	ADP
ejpam-3165	138	21	the	the	DET
ejpam-3165	138	22	binomial	binomial	ADJ
ejpam-3165	138	23	inequality	inequality	NOUN
ejpam-3165	138	24	and	and	CCONJ
ejpam-3165	138	25	also	also	ADV
ejpam-3165	138	26	,	,	PUNCT
ejpam-3165	138	27	through	through	ADP
ejpam-3165	138	28	the	the	DET
ejpam-3165	138	29	euclidean	euclidean	ADJ
ejpam-3165	138	30	norm	norm	NOUN
ejpam-3165	138	31	in	in	ADP
ejpam-3165	138	32	hilbert	hilbert	NOUN
ejpam-3165	138	33	space	space	NOUN
ejpam-3165	138	34	.	.	PUNCT
ejpam-3165	139	1	references	reference	NOUN
ejpam-3165	139	2	[	[	X
ejpam-3165	139	3	1	1	NUM
ejpam-3165	139	4	]	]	PUNCT
ejpam-3165	139	5	c.	c.	PROPN
ejpam-3165	139	6	l.	l.	PROPN
ejpam-3165	139	7	fleming	fleming	PROPN
ejpam-3165	139	8	,	,	PUNCT
ejpam-3165	139	9	s.	s.	PROPN
ejpam-3165	139	10	e.	e.	PROPN
ejpam-3165	139	11	griffis	griffis	PROPN
ejpam-3165	139	12	and	and	CCONJ
ejpam-3165	139	13	j.	j.	PROPN
ejpam-3165	139	14	e.	e.	PROPN
ejpam-3165	139	15	bell	bell	PROPN
ejpam-3165	139	16	,	,	PUNCT
ejpam-3165	139	17	the	the	DET
ejpam-3165	139	18	effects	effect	NOUN
ejpam-3165	139	19	of	of	ADP
ejpam-3165	139	20	triangle	triangle	NOUN
ejpam-3165	139	21	inequality	inequality	NOUN
ejpam-3165	139	22	on	on	ADP
ejpam-3165	139	23	the	the	DET
ejpam-3165	139	24	vehicle	vehicle	NOUN
ejpam-3165	139	25	routing	routing	NOUN
ejpam-3165	139	26	problem	problem	NOUN
ejpam-3165	139	27	,	,	PUNCT
ejpam-3165	139	28	european	european	PROPN
ejpam-3165	139	29	journal	journal	PROPN
ejpam-3165	139	30	of	of	ADP
ejpam-3165	139	31	operational	operational	ADJ
ejpam-3165	139	32	research	research	NOUN
ejpam-3165	139	33	224	224	NUM
ejpam-3165	139	34	,	,	PUNCT
ejpam-3165	139	35	1	1	NUM
ejpam-3165	139	36	,	,	PUNCT
ejpam-3165	139	37	(	(	PUNCT
ejpam-3165	139	38	2013).pp	2013).pp	NOUN
ejpam-3165	139	39	.	.	NOUN
ejpam-3165	140	1	1	1	NUM
ejpam-3165	140	2	-	-	SYM
ejpam-3165	140	3	7	7	NUM
ejpam-3165	140	4	[	[	X
ejpam-3165	140	5	2	2	NUM
ejpam-3165	140	6	]	]	X
ejpam-3165	140	7	b.	b.	PROPN
ejpam-3165	140	8	kr	kr	PROPN
ejpam-3165	140	9	.	.	PROPN
ejpam-3165	140	10	patra	patra	PROPN
ejpam-3165	140	11	,	,	PUNCT
ejpam-3165	140	12	international	international	ADJ
ejpam-3165	140	13	conference	conference	NOUN
ejpam-3165	140	14	on	on	ADP
ejpam-3165	140	15	communication	communication	NOUN
ejpam-3165	140	16	computing	computing	NOUN
ejpam-3165	140	17	and	and	CCONJ
ejpam-3165	140	18	security	security	NOUN
ejpam-3165	140	19	:	:	PUNCT
ejpam-3165	140	20	using	use	VERB
ejpam-3165	140	21	the	the	DET
ejpam-3165	140	22	triangle	triangle	NOUN
ejpam-3165	140	23	inequality	inequality	NOUN
ejpam-3165	140	24	to	to	PART
ejpam-3165	140	25	accelerate	accelerate	VERB
ejpam-3165	140	26	density	density	NOUN
ejpam-3165	140	27	based	base	VERB
ejpam-3165	140	28	outlier	outlier	NOUN
ejpam-3165	140	29	detection	detection	NOUN
ejpam-3165	140	30	method	method	NOUN
ejpam-3165	140	31	,	,	PUNCT
ejpam-3165	140	32	procedia	procedia	NOUN
ejpam-3165	140	33	technology	technology	NOUN
ejpam-3165	140	34	6	6	NUM
ejpam-3165	140	35	,	,	PUNCT
ejpam-3165	140	36	(	(	PUNCT
ejpam-3165	140	37	2012).pp	2012).pp	NUM
ejpam-3165	140	38	.	.	PUNCT
ejpam-3165	141	1	469	469	NUM
ejpam-3165	141	2	-	-	NUM
ejpam-3165	141	3	474	474	NUM
ejpam-3165	141	4	[	[	X
ejpam-3165	141	5	3	3	NUM
ejpam-3165	141	6	]	]	PUNCT
ejpam-3165	141	7	a.	a.	NOUN
ejpam-3165	141	8	m.	m.	PROPN
ejpam-3165	141	9	fink	fink	PROPN
ejpam-3165	141	10	,	,	PUNCT
ejpam-3165	141	11	an	an	DET
ejpam-3165	141	12	essay	essay	NOUN
ejpam-3165	141	13	on	on	ADP
ejpam-3165	141	14	the	the	DET
ejpam-3165	141	15	history	history	NOUN
ejpam-3165	141	16	of	of	ADP
ejpam-3165	141	17	inequalities	inequality	NOUN
ejpam-3165	141	18	,	,	PUNCT
ejpam-3165	141	19	journal	journal	NOUN
ejpam-3165	141	20	of	of	ADP
ejpam-3165	141	21	mathematical	mathematical	ADJ
ejpam-3165	141	22	analysis	analysis	NOUN
ejpam-3165	141	23	and	and	CCONJ
ejpam-3165	141	24	applications	application	NOUN
ejpam-3165	141	25	,	,	PUNCT
ejpam-3165	141	26	249	249	NUM
ejpam-3165	141	27	,	,	PUNCT
ejpam-3165	141	28	(	(	PUNCT
ejpam-3165	141	29	2000).pp	2000).pp	NUM
ejpam-3165	141	30	.	.	NOUN
ejpam-3165	141	31	118	118	NUM
ejpam-3165	141	32	-	-	SYM
ejpam-3165	141	33	134	134	NUM
ejpam-3165	141	34	.	.	PUNCT
ejpam-3165	142	1	[	[	X
ejpam-3165	142	2	4	4	X
ejpam-3165	142	3	]	]	PUNCT
ejpam-3165	142	4	h.	h.	PROPN
ejpam-3165	142	5	p.	p.	PROPN
ejpam-3165	142	6	mulholland	mulholland	PROPN
ejpam-3165	142	7	,	,	PUNCT
ejpam-3165	142	8	on	on	ADP
ejpam-3165	142	9	generalizations	generalization	NOUN
ejpam-3165	142	10	of	of	ADP
ejpam-3165	142	11	minkowski	minkowski	PROPN
ejpam-3165	142	12	’s	’s	PART
ejpam-3165	142	13	inequality	inequality	NOUN
ejpam-3165	142	14	in	in	ADP
ejpam-3165	142	15	the	the	DET
ejpam-3165	142	16	form	form	NOUN
ejpam-3165	142	17	of	of	ADP
ejpam-3165	142	18	a	a	DET
ejpam-3165	142	19	triangle	triangle	NOUN
ejpam-3165	142	20	inequality	inequality	NOUN
ejpam-3165	142	21	,	,	PUNCT
ejpam-3165	142	22	proceedings	proceeding	NOUN
ejpam-3165	142	23	of	of	ADP
ejpam-3165	142	24	the	the	DET
ejpam-3165	142	25	london	london	PROPN
ejpam-3165	142	26	mathematical	mathematical	ADJ
ejpam-3165	142	27	society	society	NOUN
ejpam-3165	142	28	vol	vol	NOUN
ejpam-3165	142	29	.	.	PROPN
ejpam-3165	143	1	2	2	NUM
ejpam-3165	143	2	-	-	SYM
ejpam-3165	143	3	51	51	NUM
ejpam-3165	143	4	,	,	PUNCT
ejpam-3165	143	5	no	no	INTJ
ejpam-3165	143	6	.	.	NOUN
ejpam-3165	143	7	1	1	NUM
ejpam-3165	143	8	,	,	PUNCT
ejpam-3165	143	9	(	(	PUNCT
ejpam-3165	143	10	1949	1949	NUM
ejpam-3165	143	11	)	)	PUNCT
ejpam-3165	143	12	.	.	PUNCT
ejpam-3165	144	1	pp	pp	ADV
ejpam-3165	144	2	.	.	PUNCT
ejpam-3165	145	1	294	294	NUM
ejpam-3165	145	2	-	-	SYM
ejpam-3165	145	3	307	307	NUM
ejpam-3165	145	4	.	.	PUNCT
ejpam-3165	146	1	[	[	X
ejpam-3165	146	2	5	5	NUM
ejpam-3165	146	3	]	]	X
ejpam-3165	146	4	k	k	PROPN
ejpam-3165	146	5	-	-	PUNCT
ejpam-3165	146	6	s.	s.	PROPN
ejpam-3165	146	7	saito	saito	PROPN
ejpam-3165	146	8	,	,	PUNCT
ejpam-3165	146	9	r.	r.	PROPN
ejpam-3165	146	10	an	an	PROPN
ejpam-3165	146	11	,	,	PUNCT
ejpam-3165	146	12	h.	h.	PROPN
ejpam-3165	146	13	mizuguchi	mizuguchi	PROPN
ejpam-3165	146	14	and	and	CCONJ
ejpam-3165	146	15	k	k	PROPN
ejpam-3165	146	16	-	-	PROPN
ejpam-3165	146	17	i.	i.	PROPN
ejpam-3165	146	18	mitani	mitani	PROPN
ejpam-3165	146	19	,	,	PUNCT
ejpam-3165	146	20	another	another	DET
ejpam-3165	146	21	aspect	aspect	NOUN
ejpam-3165	146	22	of	of	ADP
ejpam-3165	146	23	triangle	triangle	NOUN
ejpam-3165	146	24	inequality	inequality	NOUN
ejpam-3165	146	25	,	,	PUNCT
ejpam-3165	146	26	international	international	ADJ
ejpam-3165	146	27	scholarly	scholarly	ADJ
ejpam-3165	146	28	research	research	NOUN
ejpam-3165	146	29	network(2011	network(2011	NOUN
ejpam-3165	146	30	)	)	PUNCT
ejpam-3165	146	31	.	.	PUNCT
ejpam-3165	147	1	pp	pp	ADV
ejpam-3165	147	2	.	.	PUNCT
ejpam-3165	148	1	5	5	NUM
ejpam-3165	148	2	doi	doi	NOUN
ejpam-3165	148	3	:	:	PUNCT
ejpam-3165	148	4	10.5402/2011/514184	10.5402/2011/514184	X
ejpam-3165	148	5	.	.	PUNCT
ejpam-3165	149	1	[	[	X
ejpam-3165	149	2	6	6	NUM
ejpam-3165	149	3	]	]	X
ejpam-3165	149	4	k	k	PROPN
ejpam-3165	149	5	-	-	PUNCT
ejpam-3165	149	6	i.	i.	PROPN
ejpam-3165	149	7	mitani	mitani	PROPN
ejpam-3165	149	8	and	and	CCONJ
ejpam-3165	149	9	k	k	PROPN
ejpam-3165	149	10	-	-	PUNCT
ejpam-3165	149	11	s	s	VERB
ejpam-3165	149	12	saito	saito	ADJ
ejpam-3165	149	13	,	,	PUNCT
ejpam-3165	149	14	on	on	ADP
ejpam-3165	149	15	sharp	sharp	ADJ
ejpam-3165	149	16	triangle	triangle	NOUN
ejpam-3165	149	17	inequalities	inequality	NOUN
ejpam-3165	149	18	in	in	ADP
ejpam-3165	149	19	banach	banach	NOUN
ejpam-3165	149	20	spaces	space	NOUN
ejpam-3165	149	21	ii	ii	PROPN
ejpam-3165	149	22	,	,	PUNCT
ejpam-3165	149	23	journal	journal	NOUN
ejpam-3165	149	24	of	of	ADP
ejpam-3165	149	25	inequalities	inequality	NOUN
ejpam-3165	149	26	and	and	CCONJ
ejpam-3165	149	27	applications	application	NOUN
ejpam-3165	149	28	,	,	PUNCT
ejpam-3165	149	29	(	(	PUNCT
ejpam-3165	149	30	2010	2010	NUM
ejpam-3165	149	31	)	)	PUNCT
ejpam-3165	149	32	.	.	PUNCT
ejpam-3165	150	1	pp	pp	ADV
ejpam-3165	150	2	.	.	PUNCT
ejpam-3165	151	1	17	17	NUM
ejpam-3165	151	2	doi	doi	NOUN
ejpam-3165	151	3	:	:	PUNCT
ejpam-3165	151	4	10.1155/2010/323609	10.1155/2010/323609	NUM
ejpam-3165	151	5	[	[	X
ejpam-3165	151	6	7	7	NUM
ejpam-3165	151	7	]	]	X
ejpam-3165	151	8	s.	s.	PROPN
ejpam-3165	151	9	saitoh	saitoh	PROPN
ejpam-3165	151	10	,	,	PUNCT
ejpam-3165	151	11	generalizations	generalization	NOUN
ejpam-3165	151	12	of	of	ADP
ejpam-3165	151	13	the	the	DET
ejpam-3165	151	14	triangle	triangle	NOUN
ejpam-3165	151	15	inequality	inequality	NOUN
ejpam-3165	151	16	,	,	PUNCT
ejpam-3165	151	17	journal	journal	NOUN
ejpam-3165	151	18	of	of	ADP
ejpam-3165	151	19	inequalities	inequality	NOUN
ejpam-3165	151	20	in	in	ADP
ejpam-3165	151	21	pure	pure	ADJ
ejpam-3165	151	22	and	and	CCONJ
ejpam-3165	151	23	applied	apply	VERB
ejpam-3165	151	24	mathematics	mathematic	NOUN
ejpam-3165	151	25	vol	vol	NOUN
ejpam-3165	151	26	.	.	PROPN
ejpam-3165	152	1	4	4	NUM
ejpam-3165	152	2	,	,	PUNCT
ejpam-3165	152	3	no	no	INTJ
ejpam-3165	152	4	.	.	NOUN
ejpam-3165	152	5	3	3	NUM
ejpam-3165	152	6	,	,	PUNCT
ejpam-3165	152	7	(	(	PUNCT
ejpam-3165	152	8	2003	2003	NUM
ejpam-3165	152	9	)	)	PUNCT
ejpam-3165	153	1	[	[	X
ejpam-3165	153	2	8	8	X
ejpam-3165	153	3	]	]	X
ejpam-3165	153	4	t.	t.	PROPN
ejpam-3165	153	5	izumida	izumida	PROPN
ejpam-3165	153	6	,	,	PUNCT
ejpam-3165	153	7	k	k	PROPN
ejpam-3165	153	8	-	-	PUNCT
ejpam-3165	153	9	i.	i.	PROPN
ejpam-3165	153	10	mitani	mitani	PROPN
ejpam-3165	153	11	and	and	CCONJ
ejpam-3165	153	12	k	k	PROPN
ejpam-3165	153	13	-	-	PUNCT
ejpam-3165	153	14	s	s	VERB
ejpam-3165	153	15	saito	saito	ADJ
ejpam-3165	153	16	,	,	PUNCT
ejpam-3165	153	17	another	another	DET
ejpam-3165	153	18	approach	approach	NOUN
ejpam-3165	153	19	to	to	ADP
ejpam-3165	153	20	characterization	characterization	NOUN
ejpam-3165	153	21	of	of	ADP
ejpam-3165	153	22	generalized	generalized	ADJ
ejpam-3165	153	23	triangle	triangle	NOUN
ejpam-3165	153	24	inequality	inequality	NOUN
ejpam-3165	153	25	in	in	ADP
ejpam-3165	153	26	normed	normed	ADJ
ejpam-3165	153	27	space	space	NOUN
ejpam-3165	153	28	,	,	PUNCT
ejpam-3165	153	29	central	central	ADJ
ejpam-3165	153	30	european	european	ADJ
ejpam-3165	153	31	journal	journal	NOUN
ejpam-3165	153	32	of	of	ADP
ejpam-3165	153	33	mathematics	mathematics	PROPN
ejpam-3165	153	34	12	12	NUM
ejpam-3165	153	35	,	,	PUNCT
ejpam-3165	153	36	11	11	NUM
ejpam-3165	153	37	,	,	PUNCT
ejpam-3165	153	38	(	(	PUNCT
ejpam-3165	153	39	2014).pp	2014).pp	NOUN
ejpam-3165	153	40	.	.	NOUN
ejpam-3165	153	41	1615	1615	NUM
ejpam-3165	153	42	-	-	SYM
ejpam-3165	153	43	1623	1623	NUM
ejpam-3165	153	44	[	[	X
ejpam-3165	153	45	9	9	NUM
ejpam-3165	153	46	]	]	X
ejpam-3165	153	47	f.	f.	PROPN
ejpam-3165	153	48	dadipour	dadipour	PROPN
ejpam-3165	153	49	,	,	PUNCT
ejpam-3165	153	50	m.s	m.s	PROPN
ejpam-3165	153	51	.	.	PROPN
ejpam-3165	153	52	moslehian	moslehian	PROPN
ejpam-3165	153	53	,	,	PUNCT
ejpam-3165	153	54	j.	j.	PROPN
ejpam-3165	153	55	m.	m.	PROPN
ejpam-3165	153	56	rassias	rassias	PROPN
ejpam-3165	153	57	and	and	CCONJ
ejpam-3165	153	58	s	s	PROPN
ejpam-3165	153	59	-	-	PROPN
ejpam-3165	153	60	e.	e.	PROPN
ejpam-3165	153	61	takahasi	takahasi	PROPN
ejpam-3165	153	62	,	,	PUNCT
ejpam-3165	153	63	characterization	characterization	NOUN
ejpam-3165	153	64	of	of	ADP
ejpam-3165	153	65	a	a	DET
ejpam-3165	153	66	generalized	generalized	ADJ
ejpam-3165	153	67	triangle	triangle	NOUN
ejpam-3165	153	68	inequality	inequality	NOUN
ejpam-3165	153	69	in	in	ADP
ejpam-3165	153	70	normed	normed	ADJ
ejpam-3165	153	71	spaces	space	NOUN
ejpam-3165	153	72	,	,	PUNCT
ejpam-3165	153	73	nonlinear	nonlinear	ADJ
ejpam-3165	153	74	analysis	analysis	NOUN
ejpam-3165	153	75	vol	vol	NOUN
ejpam-3165	153	76	.	.	PUNCT
ejpam-3165	154	1	75	75	NUM
ejpam-3165	154	2	,	,	PUNCT
ejpam-3165	154	3	no	no	INTJ
ejpam-3165	154	4	.	.	NOUN
ejpam-3165	154	5	2	2	NUM
ejpam-3165	154	6	,	,	PUNCT
ejpam-3165	154	7	(	(	PUNCT
ejpam-3165	154	8	2012	2012	NUM
ejpam-3165	154	9	)	)	PUNCT
ejpam-3165	154	10	.	.	PUNCT
ejpam-3165	155	1	pp	pp	ADV
ejpam-3165	155	2	.	.	PUNCT
ejpam-3165	156	1	735	735	NUM
ejpam-3165	156	2	-	-	SYM
ejpam-3165	156	3	741	741	NUM
ejpam-3165	156	4	references	reference	NOUN
ejpam-3165	156	5	361	361	NUM
ejpam-3165	156	6	[	[	X
ejpam-3165	156	7	10	10	NUM
ejpam-3165	156	8	]	]	PUNCT
ejpam-3165	156	9	j.	j.	PROPN
ejpam-3165	156	10	t.	t.	PROPN
ejpam-3165	156	11	scheick	scheick	PROPN
ejpam-3165	156	12	,	,	PUNCT
ejpam-3165	156	13	linear	linear	ADJ
ejpam-3165	156	14	algebra	algebra	NOUN
ejpam-3165	156	15	with	with	ADP
ejpam-3165	156	16	applications	application	NOUN
ejpam-3165	156	17	,	,	PUNCT
ejpam-3165	156	18	prentice	prentice	NOUN
ejpam-3165	156	19	-	-	PUNCT
ejpam-3165	156	20	hall	hall	NOUN
ejpam-3165	156	21	,	,	PUNCT
ejpam-3165	156	22	inc	inc	PROPN
ejpam-3165	156	23	,	,	PUNCT
ejpam-3165	156	24	new	new	PROPN
ejpam-3165	156	25	york	york	PROPN
ejpam-3165	156	26	;	;	PUNCT
ejpam-3165	156	27	1997	1997	NUM
ejpam-3165	156	28	.	.	PUNCT
ejpam-3165	157	1	[	[	X
ejpam-3165	157	2	11	11	NUM
ejpam-3165	157	3	]	]	X
ejpam-3165	157	4	n.	n.	NOUN
ejpam-3165	157	5	minculete	minculete	NOUN
ejpam-3165	157	6	and	and	CCONJ
ejpam-3165	157	7	r.	r.	PROPN
ejpam-3165	157	8	pãltãnea	pãltãnea	PROPN
ejpam-3165	157	9	,	,	PUNCT
ejpam-3165	157	10	improved	improve	VERB
ejpam-3165	157	11	estimates	estimate	NOUN
ejpam-3165	157	12	for	for	ADP
ejpam-3165	157	13	the	the	DET
ejpam-3165	157	14	triangle	triangle	NOUN
ejpam-3165	157	15	inequality	inequality	NOUN
ejpam-3165	157	16	,	,	PUNCT
ejpam-3165	157	17	journal	journal	NOUN
ejpam-3165	157	18	of	of	ADP
ejpam-3165	157	19	inequality	inequality	NOUN
ejpam-3165	157	20	and	and	CCONJ
ejpam-3165	157	21	applications	application	NOUN
ejpam-3165	157	22	,	,	PUNCT
ejpam-3165	157	23	(	(	PUNCT
ejpam-3165	157	24	2017	2017	NUM
ejpam-3165	157	25	)	)	PUNCT
ejpam-3165	157	26	.	.	PUNCT
ejpam-3165	158	1	doi	doi	PROPN
ejpam-3165	158	2	.	.	PUNCT
ejpam-3165	158	3	10.1186	10.1186	NUM
ejpam-3165	158	4	/	/	SYM
ejpam-3165	158	5	s13660−	s13660−	NOUN
ejpam-3165	158	6	016−	016−	NOUN
ejpam-3165	158	7	1281−	1281−	NUM
ejpam-3165	158	8	z	z	X
ejpam-3165	159	1	[	[	X
ejpam-3165	159	2	12	12	NUM
ejpam-3165	159	3	]	]	X
ejpam-3165	159	4	j.	j.	PROPN
ejpam-3165	159	5	t.	t.	PROPN
ejpam-3165	159	6	oden	oden	PROPN
ejpam-3165	159	7	,	,	PUNCT
ejpam-3165	159	8	applied	apply	VERB
ejpam-3165	159	9	function	function	NOUN
ejpam-3165	159	10	analysis	analysis	NOUN
ejpam-3165	159	11	;	;	PUNCT
ejpam-3165	159	12	a	a	DET
ejpam-3165	159	13	first	first	ADJ
ejpam-3165	159	14	course	course	NOUN
ejpam-3165	159	15	for	for	ADP
ejpam-3165	159	16	students	student	NOUN
ejpam-3165	159	17	of	of	ADP
ejpam-3165	159	18	mechanics	mechanic	NOUN
ejpam-3165	159	19	and	and	CCONJ
ejpam-3165	159	20	engineering	engineering	NOUN
ejpam-3165	159	21	science	science	NOUN
ejpam-3165	159	22	,	,	PUNCT
ejpam-3165	159	23	englewood	englewood	PROPN
ejpam-3165	159	24	cliffs	cliffs	PROPN
ejpam-3165	159	25	,	,	PUNCT
ejpam-3165	159	26	n.j	n.j	PROPN
ejpam-3165	159	27	.	.	PROPN
ejpam-3165	159	28	prentice	prentice	PROPN
ejpam-3165	159	29	-	-	PUNCT
ejpam-3165	159	30	hall	hall	NOUN
ejpam-3165	159	31	,	,	PUNCT
ejpam-3165	159	32	1979	1979	NUM
ejpam-3165	159	33	.	.	PUNCT
ejpam-3165	160	1	[	[	X
ejpam-3165	160	2	13	13	NUM
ejpam-3165	160	3	]	]	X
ejpam-3165	160	4	b.	b.	PROPN
ejpam-3165	160	5	kolman	kolman	PROPN
ejpam-3165	160	6	and	and	CCONJ
ejpam-3165	160	7	d.	d.	PROPN
ejpam-3165	160	8	r.	r.	PROPN
ejpam-3165	160	9	hill	hill	PROPN
ejpam-3165	160	10	,	,	PUNCT
ejpam-3165	160	11	elementary	elementary	ADJ
ejpam-3165	160	12	linear	linear	PROPN
ejpam-3165	160	13	algebra	algebra	PROPN
ejpam-3165	160	14	,	,	PUNCT
ejpam-3165	160	15	prentice	prentice	NOUN
ejpam-3165	160	16	-	-	PUNCT
ejpam-3165	160	17	hall	hall	NOUN
ejpam-3165	160	18	,	,	PUNCT
ejpam-3165	160	19	inc	inc	PROPN
ejpam-3165	160	20	,	,	PUNCT
ejpam-3165	160	21	new	new	PROPN
ejpam-3165	160	22	jersey	jersey	PROPN
ejpam-3165	160	23	;	;	PUNCT
ejpam-3165	160	24	2000	2000	NUM
ejpam-3165	160	25	.	.	PUNCT
ejpam-3165	161	1	[	[	X
ejpam-3165	161	2	14	14	NUM
ejpam-3165	161	3	]	]	X
ejpam-3165	161	4	h.	h.	PROPN
ejpam-3165	161	5	royden	royden	PROPN
ejpam-3165	161	6	and	and	CCONJ
ejpam-3165	161	7	p.	p.	PROPN
ejpam-3165	161	8	fitxpatrick	fitxpatrick	PROPN
ejpam-3165	161	9	,	,	PUNCT
ejpam-3165	161	10	real	real	ADJ
ejpam-3165	161	11	analysis	analysis	NOUN
ejpam-3165	161	12	.	.	PUNCT
ejpam-3165	162	1	pearson	pearson	PROPN
ejpam-3165	162	2	education	education	PROPN
ejpam-3165	162	3	,	,	PUNCT
ejpam-3165	162	4	inc	inc	PROPN
ejpam-3165	162	5	,	,	PUNCT
ejpam-3165	162	6	4th	4th	ADJ
ejpam-3165	162	7	ed	ed	NOUN
ejpam-3165	162	8	.	.	PROPN
ejpam-3165	162	9	,	,	PUNCT
ejpam-3165	162	10	upper	upper	ADJ
ejpam-3165	162	11	saddle	saddle	NOUN
ejpam-3165	162	12	river	river	NOUN
ejpam-3165	162	13	;	;	PUNCT
ejpam-3165	162	14	2010	2010	NUM
ejpam-3165	162	15	.	.	PUNCT