id	sid	tid	token	lemma	pos
ejpam-3517	1	1	european	european	PROPN
ejpam-3517	1	2	journal	journal	PROPN
ejpam-3517	1	3	of	of	ADP
ejpam-3517	1	4	pure	pure	ADJ
ejpam-3517	1	5	and	and	CCONJ
ejpam-3517	1	6	applied	apply	VERB
ejpam-3517	1	7	mathematics	mathematic	NOUN
ejpam-3517	1	8	vol	vol	NOUN
ejpam-3517	1	9	.	.	PROPN
ejpam-3517	2	1	12	12	NUM
ejpam-3517	2	2	,	,	PUNCT
ejpam-3517	2	3	no	no	INTJ
ejpam-3517	2	4	.	.	NOUN
ejpam-3517	2	5	4	4	NUM
ejpam-3517	2	6	,	,	PUNCT
ejpam-3517	2	7	2019	2019	NUM
ejpam-3517	2	8	,	,	PUNCT
ejpam-3517	2	9	1360	1360	NUM
ejpam-3517	2	10	-	-	SYM
ejpam-3517	2	11	1370	1370	NUM
ejpam-3517	2	12	issn	issn	PROPN
ejpam-3517	2	13	1307	1307	NUM
ejpam-3517	2	14	-	-	SYM
ejpam-3517	2	15	5543	5543	NUM
ejpam-3517	2	16	–	–	PUNCT
ejpam-3517	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3517	2	18	published	publish	VERB
ejpam-3517	2	19	by	by	ADP
ejpam-3517	2	20	new	new	PROPN
ejpam-3517	2	21	york	york	PROPN
ejpam-3517	2	22	business	business	PROPN
ejpam-3517	2	23	global	global	ADJ
ejpam-3517	2	24	optimal	optimal	ADJ
ejpam-3517	2	25	solution	solution	NOUN
ejpam-3517	2	26	properties	property	NOUN
ejpam-3517	2	27	of	of	ADP
ejpam-3517	2	28	an	an	DET
ejpam-3517	2	29	overdetermined	overdetermine	VERB
ejpam-3517	2	30	system	system	NOUN
ejpam-3517	2	31	of	of	ADP
ejpam-3517	2	32	linear	linear	PROPN
ejpam-3517	2	33	equations	equation	NOUN
ejpam-3517	2	34	vedran	vedran	NOUN
ejpam-3517	2	35	novoselac1,∗	novoselac1,∗	PROPN
ejpam-3517	2	36	,	,	PUNCT
ejpam-3517	2	37	zlatko	zlatko	PROPN
ejpam-3517	2	38	pavić	pavić	VERB
ejpam-3517	2	39	1	1	NUM
ejpam-3517	2	40	1	1	NUM
ejpam-3517	2	41	mechanical	mechanical	ADJ
ejpam-3517	2	42	engineering	engineering	NOUN
ejpam-3517	2	43	faculty	faculty	NOUN
ejpam-3517	2	44	in	in	ADP
ejpam-3517	2	45	slavonski	slavonski	PROPN
ejpam-3517	2	46	brod	brod	NOUN
ejpam-3517	2	47	,	,	PUNCT
ejpam-3517	2	48	university	university	NOUN
ejpam-3517	2	49	of	of	ADP
ejpam-3517	2	50	osijek	osijek	PROPN
ejpam-3517	2	51	,	,	PUNCT
ejpam-3517	2	52	trg	trg	PROPN
ejpam-3517	2	53	ivane	ivane	NOUN
ejpam-3517	2	54	brlić	brlić	PROPN
ejpam-3517	3	1	mažuranić	mažuranić	VERB
ejpam-3517	3	2	2	2	NUM
ejpam-3517	3	3	,	,	PUNCT
ejpam-3517	3	4	35000	35000	NUM
ejpam-3517	3	5	slavonski	slavonski	NOUN
ejpam-3517	3	6	brod	brod	NOUN
ejpam-3517	3	7	,	,	PUNCT
ejpam-3517	3	8	croatia	croatia	PROPN
ejpam-3517	3	9	abstract	abstract	NOUN
ejpam-3517	3	10	.	.	PUNCT
ejpam-3517	4	1	the	the	DET
ejpam-3517	4	2	paper	paper	NOUN
ejpam-3517	4	3	considers	consider	VERB
ejpam-3517	4	4	the	the	DET
ejpam-3517	4	5	solution	solution	NOUN
ejpam-3517	4	6	properties	property	NOUN
ejpam-3517	4	7	of	of	ADP
ejpam-3517	4	8	an	an	DET
ejpam-3517	4	9	overdetermined	overdetermine	VERB
ejpam-3517	4	10	system	system	NOUN
ejpam-3517	4	11	of	of	ADP
ejpam-3517	4	12	linear	linear	PROPN
ejpam-3517	4	13	equations	equation	NOUN
ejpam-3517	4	14	in	in	ADP
ejpam-3517	4	15	a	a	DET
ejpam-3517	4	16	given	give	VERB
ejpam-3517	4	17	norm	norm	NOUN
ejpam-3517	4	18	.	.	PUNCT
ejpam-3517	5	1	the	the	DET
ejpam-3517	5	2	problem	problem	NOUN
ejpam-3517	5	3	is	be	AUX
ejpam-3517	5	4	observed	observe	VERB
ejpam-3517	5	5	as	as	ADP
ejpam-3517	5	6	a	a	DET
ejpam-3517	5	7	minimization	minimization	NOUN
ejpam-3517	5	8	of	of	ADP
ejpam-3517	5	9	the	the	DET
ejpam-3517	5	10	corresponding	corresponding	ADJ
ejpam-3517	5	11	functional	functional	NOUN
ejpam-3517	5	12	of	of	ADP
ejpam-3517	5	13	the	the	DET
ejpam-3517	5	14	errors	error	NOUN
ejpam-3517	5	15	.	.	PUNCT
ejpam-3517	6	1	presenting	present	VERB
ejpam-3517	6	2	the	the	DET
ejpam-3517	6	3	main	main	ADJ
ejpam-3517	6	4	results	result	NOUN
ejpam-3517	6	5	of	of	ADP
ejpam-3517	6	6	p	p	NOUN
ejpam-3517	6	7	norm	norm	NOUN
ejpam-3517	6	8	it	it	PRON
ejpam-3517	6	9	is	be	AUX
ejpam-3517	6	10	shown	show	VERB
ejpam-3517	6	11	that	that	SCONJ
ejpam-3517	6	12	the	the	DET
ejpam-3517	6	13	functional	functional	ADJ
ejpam-3517	6	14	is	be	AUX
ejpam-3517	6	15	convex	convex	ADJ
ejpam-3517	6	16	.	.	PUNCT
ejpam-3517	7	1	following	follow	VERB
ejpam-3517	7	2	the	the	DET
ejpam-3517	7	3	convex	convex	NOUN
ejpam-3517	7	4	properties	property	NOUN
ejpam-3517	7	5	we	we	PRON
ejpam-3517	7	6	examine	examine	VERB
ejpam-3517	7	7	minimization	minimization	NOUN
ejpam-3517	7	8	properties	property	NOUN
ejpam-3517	7	9	showing	show	VERB
ejpam-3517	7	10	that	that	SCONJ
ejpam-3517	7	11	the	the	DET
ejpam-3517	7	12	problem	problem	NOUN
ejpam-3517	7	13	possesses	possess	VERB
ejpam-3517	7	14	regression	regression	NOUN
ejpam-3517	7	15	,	,	PUNCT
ejpam-3517	7	16	scale	scale	NOUN
ejpam-3517	7	17	,	,	PUNCT
ejpam-3517	7	18	and	and	CCONJ
ejpam-3517	7	19	affine	affine	VERB
ejpam-3517	7	20	equivariant	equivariant	ADJ
ejpam-3517	7	21	properties	property	NOUN
ejpam-3517	7	22	.	.	PUNCT
ejpam-3517	8	1	as	as	ADP
ejpam-3517	8	2	an	an	DET
ejpam-3517	8	3	example	example	NOUN
ejpam-3517	8	4	we	we	PRON
ejpam-3517	8	5	illustrated	illustrate	VERB
ejpam-3517	8	6	the	the	DET
ejpam-3517	8	7	problem	problem	NOUN
ejpam-3517	8	8	of	of	ADP
ejpam-3517	8	9	finding	find	VERB
ejpam-3517	8	10	the	the	DET
ejpam-3517	8	11	weighted	weight	VERB
ejpam-3517	8	12	mean	mean	NOUN
ejpam-3517	8	13	and	and	CCONJ
ejpam-3517	8	14	weighted	weight	VERB
ejpam-3517	8	15	median	median	NOUN
ejpam-3517	8	16	of	of	ADP
ejpam-3517	8	17	the	the	DET
ejpam-3517	8	18	data	datum	NOUN
ejpam-3517	8	19	.	.	PUNCT
ejpam-3517	9	1	2010	2010	NUM
ejpam-3517	9	2	mathematics	mathematic	NOUN
ejpam-3517	9	3	subject	subject	NOUN
ejpam-3517	9	4	classifications	classification	NOUN
ejpam-3517	9	5	:	:	PUNCT
ejpam-3517	9	6	15a06	15a06	NUM
ejpam-3517	9	7	,	,	PUNCT
ejpam-3517	9	8	65f20	65f20	NOUN
ejpam-3517	9	9	,	,	PUNCT
ejpam-3517	9	10	58k70	58k70	NUM
ejpam-3517	9	11	key	key	ADJ
ejpam-3517	9	12	words	word	NOUN
ejpam-3517	9	13	and	and	CCONJ
ejpam-3517	9	14	phrases	phrase	NOUN
ejpam-3517	9	15	:	:	PUNCT
ejpam-3517	9	16	linear	linear	ADJ
ejpam-3517	9	17	equations	equation	NOUN
ejpam-3517	9	18	,	,	PUNCT
ejpam-3517	9	19	overdetermined	overdetermine	VERB
ejpam-3517	9	20	systems	system	NOUN
ejpam-3517	9	21	,	,	PUNCT
ejpam-3517	9	22	equivariance	equivariance	NOUN
ejpam-3517	9	23	1	1	NUM
ejpam-3517	9	24	.	.	PUNCT
ejpam-3517	9	25	introduction	introduction	NOUN
ejpam-3517	9	26	a	a	DET
ejpam-3517	9	27	system	system	NOUN
ejpam-3517	9	28	of	of	ADP
ejpam-3517	9	29	linear	linear	ADJ
ejpam-3517	9	30	equations	equation	NOUN
ejpam-3517	9	31	denoted	denote	VERB
ejpam-3517	9	32	as	as	ADP
ejpam-3517	9	33	ax	ax	NOUN
ejpam-3517	9	34	=	=	SYM
ejpam-3517	9	35	b	b	PROPN
ejpam-3517	9	36	where	where	SCONJ
ejpam-3517	9	37	a	a	DET
ejpam-3517	9	38	=	=	NOUN
ejpam-3517	9	39			NUM
ejpam-3517	9	40	a11	a11	PROPN
ejpam-3517	9	41	.	.	PUNCT
ejpam-3517	9	42	.	.	PUNCT
ejpam-3517	9	43	.	.	PUNCT
ejpam-3517	10	1	a1n	a1n	NOUN
ejpam-3517	10	2	...	...	PUNCT
ejpam-3517	10	3	...	...	PUNCT
ejpam-3517	10	4	...	...	PUNCT
ejpam-3517	11	1	am1	am1	INTJ
ejpam-3517	11	2	.	.	PUNCT
ejpam-3517	11	3	.	.	PUNCT
ejpam-3517	11	4	.	.	PUNCT
ejpam-3517	12	1	amn	amn	PROPN
ejpam-3517	12	2			NUM
ejpam-3517	12	3	∈	∈	PROPN
ejpam-3517	12	4	rm×n	rm×n	NOUN
ejpam-3517	12	5	,	,	PUNCT
ejpam-3517	12	6	x	x	SYM
ejpam-3517	12	7	=	=	PUNCT
ejpam-3517	12	8			NOUN
ejpam-3517	13	1	x1	x1	PRON
ejpam-3517	13	2	...	...	PUNCT
ejpam-3517	13	3	xn	xn	PROPN
ejpam-3517	14	1			NUM
ejpam-3517	14	2	∈	∈	PROPN
ejpam-3517	14	3	rn	rn	PROPN
ejpam-3517	14	4	,	,	PUNCT
ejpam-3517	14	5	b	b	X
ejpam-3517	14	6	=	=	SYM
ejpam-3517	14	7			NUM
ejpam-3517	14	8	b1	b1	NOUN
ejpam-3517	14	9	...	...	PUNCT
ejpam-3517	15	1	bm	bm	PROPN
ejpam-3517	15	2			PROPN
ejpam-3517	15	3	∈	∈	PROPN
ejpam-3517	15	4	rm	rm	NOUN
ejpam-3517	15	5	.	.	PUNCT
ejpam-3517	16	1	(	(	PUNCT
ejpam-3517	16	2	1	1	X
ejpam-3517	16	3	)	)	PUNCT
ejpam-3517	16	4	if	if	SCONJ
ejpam-3517	16	5	a	a	PRON
ejpam-3517	16	6	is	be	AUX
ejpam-3517	16	7	m	m	PROPN
ejpam-3517	16	8	×	×	NOUN
ejpam-3517	16	9	n	n	PRON
ejpam-3517	16	10	matrix	matrix	NOUN
ejpam-3517	16	11	,	,	PUNCT
ejpam-3517	16	12	with	with	ADP
ejpam-3517	16	13	m	m	PROPN
ejpam-3517	16	14	>	>	X
ejpam-3517	16	15	n	n	CCONJ
ejpam-3517	16	16	,	,	PUNCT
ejpam-3517	16	17	then	then	ADV
ejpam-3517	16	18	it	it	PRON
ejpam-3517	16	19	is	be	AUX
ejpam-3517	16	20	said	say	VERB
ejpam-3517	16	21	that	that	SCONJ
ejpam-3517	16	22	the	the	DET
ejpam-3517	16	23	linear	linear	ADJ
ejpam-3517	16	24	system	system	NOUN
ejpam-3517	16	25	of	of	ADP
ejpam-3517	16	26	equations	equation	NOUN
ejpam-3517	16	27	is	be	AUX
ejpam-3517	16	28	overdetermined	overdetermine	VERB
ejpam-3517	16	29	.	.	PUNCT
ejpam-3517	17	1	in	in	ADP
ejpam-3517	17	2	general	general	ADJ
ejpam-3517	17	3	,	,	PUNCT
ejpam-3517	17	4	such	such	DET
ejpam-3517	17	5	a	a	DET
ejpam-3517	17	6	system	system	NOUN
ejpam-3517	17	7	will	will	AUX
ejpam-3517	17	8	have	have	VERB
ejpam-3517	17	9	no	no	DET
ejpam-3517	17	10	solution	solution	NOUN
ejpam-3517	17	11	,	,	PUNCT
ejpam-3517	17	12	i.e.	i.e.	X
ejpam-3517	17	13	it	it	PRON
ejpam-3517	17	14	is	be	AUX
ejpam-3517	17	15	inconsistent	inconsistent	ADJ
ejpam-3517	17	16	,	,	PUNCT
ejpam-3517	17	17	i.e.	i.e.	X
ejpam-3517	17	18	b	b	X
ejpam-3517	17	19	/∈	/∈	PUNCT
ejpam-3517	17	20	r(a	r(a	NUM
ejpam-3517	17	21	)	)	PUNCT
ejpam-3517	17	22	.	.	PUNCT
ejpam-3517	18	1	instead	instead	ADV
ejpam-3517	18	2	the	the	DET
ejpam-3517	18	3	solution	solution	NOUN
ejpam-3517	18	4	with	with	ADP
ejpam-3517	18	5	the	the	DET
ejpam-3517	18	6	smallest	small	ADJ
ejpam-3517	18	7	error	error	NOUN
ejpam-3517	18	8	‖b−	‖b−	ADP
ejpam-3517	18	9	ax‖p	ax‖p	PROPN
ejpam-3517	18	10	is	be	AUX
ejpam-3517	18	11	observed	observe	VERB
ejpam-3517	18	12	using	use	VERB
ejpam-3517	18	13	some	some	DET
ejpam-3517	18	14	p	p	NOUN
ejpam-3517	18	15	∈	∈	PROPN
ejpam-3517	18	16	[	[	X
ejpam-3517	18	17	1,∞	1,∞	NUM
ejpam-3517	18	18	〉	〉	NUM
ejpam-3517	18	19	norme	norme	NOUN
ejpam-3517	18	20	,	,	PUNCT
ejpam-3517	18	21	where	where	SCONJ
ejpam-3517	18	22	the	the	DET
ejpam-3517	18	23	problem	problem	NOUN
ejpam-3517	18	24	is	be	AUX
ejpam-3517	18	25	to	to	PART
ejpam-3517	18	26	find	find	VERB
ejpam-3517	18	27	a	a	DET
ejpam-3517	18	28	vector	vector	NOUN
ejpam-3517	18	29	x	x	SYM
ejpam-3517	18	30	∈	∈	PROPN
ejpam-3517	18	31	rn	rn	NOUN
ejpam-3517	18	32	such	such	ADJ
ejpam-3517	18	33	that	that	DET
ejpam-3517	18	34	min	min	PROPN
ejpam-3517	18	35	x∈rn	x∈rn	PROPN
ejpam-3517	18	36	‖b−ax‖p	‖b−ax‖p	PROPN
ejpam-3517	18	37	,	,	PUNCT
ejpam-3517	18	38	p	p	NOUN
ejpam-3517	18	39	∈	∈	PROPN
ejpam-3517	19	1	[	[	X
ejpam-3517	19	2	1,∞	1,∞	NUM
ejpam-3517	19	3	〉	〉	NUM
ejpam-3517	19	4	.	.	PUNCT
ejpam-3517	20	1	(	(	PUNCT
ejpam-3517	20	2	2	2	X
ejpam-3517	20	3	)	)	PUNCT
ejpam-3517	20	4	figure	figure	NOUN
ejpam-3517	20	5	1	1	NUM
ejpam-3517	20	6	presents	present	VERB
ejpam-3517	20	7	the	the	DET
ejpam-3517	20	8	problem	problem	NOUN
ejpam-3517	20	9	of	of	ADP
ejpam-3517	20	10	an	an	DET
ejpam-3517	20	11	overdetermined	overdetermine	VERB
ejpam-3517	20	12	system	system	NOUN
ejpam-3517	20	13	of	of	ADP
ejpam-3517	20	14	linear	linear	PROPN
ejpam-3517	20	15	equations	equation	NOUN
ejpam-3517	20	16	.	.	PUNCT
ejpam-3517	21	1	∗corresponding	∗corresponde	VERB
ejpam-3517	21	2	author	author	NOUN
ejpam-3517	21	3	.	.	PUNCT
ejpam-3517	22	1	doi	doi	NOUN
ejpam-3517	22	2	:	:	PUNCT
ejpam-3517	22	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3517	https://doi.org/10.29020/nybg.ejpam.v12i4.3517	PROPN
ejpam-3517	22	4	email	email	NOUN
ejpam-3517	22	5	addresses	address	NOUN
ejpam-3517	22	6	:	:	PUNCT
ejpam-3517	22	7	vedran.novoselac@sfsb.hr	vedran.novoselac@sfsb.hr	NOUN
ejpam-3517	22	8	(	(	PUNCT
ejpam-3517	22	9	v.	v.	X
ejpam-3517	22	10	novoselac	novoselac	PROPN
ejpam-3517	22	11	)	)	PUNCT
ejpam-3517	22	12	,	,	PUNCT
ejpam-3517	22	13	zlatko.pavic@sfsb.hr	zlatko.pavic@sfsb.hr	PROPN
ejpam-3517	22	14	(	(	PUNCT
ejpam-3517	22	15	z.	z.	PROPN
ejpam-3517	22	16	pavić	pavić	PROPN
ejpam-3517	22	17	)	)	PUNCT
ejpam-3517	22	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3517	23	1	1360	1360	NUM
ejpam-3517	23	2	c	c	X
ejpam-3517	23	3	©	©	PROPN
ejpam-3517	23	4	2019	2019	NUM
ejpam-3517	23	5	ejpam	ejpam	NOUN
ejpam-3517	23	6	all	all	DET
ejpam-3517	23	7	rights	right	NOUN
ejpam-3517	23	8	reserved	reserve	VERB
ejpam-3517	23	9	.	.	PUNCT
ejpam-3517	24	1	v.	v.	CCONJ
ejpam-3517	24	2	novoselac	novoselac	PROPN
ejpam-3517	24	3	,	,	PUNCT
ejpam-3517	24	4	z.	z.	PROPN
ejpam-3517	24	5	pavić	pavić	PROPN
ejpam-3517	24	6	/	/	SYM
ejpam-3517	24	7	eur	eur	PROPN
ejpam-3517	24	8	.	.	PUNCT
ejpam-3517	25	1	j.	j.	PROPN
ejpam-3517	25	2	pure	pure	PROPN
ejpam-3517	25	3	appl	appl	PROPN
ejpam-3517	25	4	.	.	PROPN
ejpam-3517	25	5	math	math	PROPN
ejpam-3517	25	6	,	,	PUNCT
ejpam-3517	25	7	12	12	NUM
ejpam-3517	25	8	(	(	PUNCT
ejpam-3517	25	9	4	4	NUM
ejpam-3517	25	10	)	)	PUNCT
ejpam-3517	25	11	(	(	PUNCT
ejpam-3517	25	12	2019	2019	NUM
ejpam-3517	25	13	)	)	PUNCT
ejpam-3517	25	14	,	,	PUNCT
ejpam-3517	25	15	1360	1360	NUM
ejpam-3517	25	16	-	-	SYM
ejpam-3517	25	17	1370	1370	NUM
ejpam-3517	25	18	1361	1361	NUM
ejpam-3517	25	19	figure	figure	NOUN
ejpam-3517	25	20	1	1	NUM
ejpam-3517	25	21	:	:	PUNCT
ejpam-3517	25	22	graphic	graphic	ADJ
ejpam-3517	25	23	illustration	illustration	NOUN
ejpam-3517	25	24	of	of	ADP
ejpam-3517	25	25	an	an	DET
ejpam-3517	25	26	overdetermined	overdetermine	VERB
ejpam-3517	25	27	system	system	NOUN
ejpam-3517	25	28	ax	ax	NOUN
ejpam-3517	25	29	=	=	PROPN
ejpam-3517	25	30	b.	b.	PROPN
ejpam-3517	25	31	problem	problem	NOUN
ejpam-3517	25	32	(	(	PUNCT
ejpam-3517	25	33	2	2	X
ejpam-3517	25	34	)	)	PUNCT
ejpam-3517	25	35	can	can	AUX
ejpam-3517	25	36	be	be	AUX
ejpam-3517	25	37	observed	observe	VERB
ejpam-3517	25	38	as	as	ADP
ejpam-3517	25	39	a	a	DET
ejpam-3517	25	40	minimization	minimization	NOUN
ejpam-3517	25	41	problem	problem	NOUN
ejpam-3517	25	42	of	of	ADP
ejpam-3517	25	43	a	a	DET
ejpam-3517	25	44	functional	functional	ADJ
ejpam-3517	25	45	fp(x	fp(x	NOUN
ejpam-3517	25	46	)	)	PUNCT
ejpam-3517	25	47	=	=	PUNCT
ejpam-3517	26	1	‖b−ax‖p	‖b−ax‖p	NOUN
ejpam-3517	26	2	=	=	SYM
ejpam-3517	26	3			PROPN
ejpam-3517	26	4	m∑	m∑	VERB
ejpam-3517	26	5	i=1	i=1	PROPN
ejpam-3517	26	6	|bi	|bi	NUM
ejpam-3517	26	7	−	−	PROPN
ejpam-3517	26	8	n∑	n∑	NOUN
ejpam-3517	26	9	j=1	j=1	ADJ
ejpam-3517	26	10	aijxj	aijxj	NOUN
ejpam-3517	26	11	|p	|p	NOUN
ejpam-3517	26	12			PROPN
ejpam-3517	26	13	1	1	NUM
ejpam-3517	26	14	p	p	NOUN
ejpam-3517	26	15	,	,	PUNCT
ejpam-3517	26	16	p	p	NOUN
ejpam-3517	26	17	∈	∈	PROPN
ejpam-3517	27	1	[	[	X
ejpam-3517	27	2	1,∞	1,∞	NUM
ejpam-3517	27	3	〉	〉	NUM
ejpam-3517	27	4	.	.	PUNCT
ejpam-3517	28	1	(	(	PUNCT
ejpam-3517	28	2	3	3	X
ejpam-3517	28	3	)	)	PUNCT
ejpam-3517	28	4	many	many	ADJ
ejpam-3517	28	5	problems	problem	NOUN
ejpam-3517	28	6	can	can	AUX
ejpam-3517	28	7	be	be	AUX
ejpam-3517	28	8	presented	present	VERB
ejpam-3517	28	9	as	as	ADP
ejpam-3517	28	10	an	an	DET
ejpam-3517	28	11	overdetermined	overdetermined	ADJ
ejpam-3517	28	12	system	system	NOUN
ejpam-3517	28	13	of	of	ADP
ejpam-3517	28	14	linear	linear	ADJ
ejpam-3517	28	15	equations	equation	NOUN
ejpam-3517	28	16	such	such	ADJ
ejpam-3517	28	17	as	as	ADP
ejpam-3517	28	18	the	the	DET
ejpam-3517	28	19	problem	problem	NOUN
ejpam-3517	28	20	of	of	ADP
ejpam-3517	28	21	determinating	determinate	VERB
ejpam-3517	28	22	linear	linear	NOUN
ejpam-3517	28	23	models	model	NOUN
ejpam-3517	28	24	for	for	ADP
ejpam-3517	28	25	fitting	fitting	ADJ
ejpam-3517	28	26	experimental	experimental	ADJ
ejpam-3517	28	27	data	datum	NOUN
ejpam-3517	28	28	.	.	PUNCT
ejpam-3517	29	1	it	it	PRON
ejpam-3517	29	2	is	be	AUX
ejpam-3517	29	3	intended	intend	VERB
ejpam-3517	29	4	to	to	PART
ejpam-3517	29	5	help	help	VERB
ejpam-3517	29	6	researchers	researcher	NOUN
ejpam-3517	29	7	fit	fit	VERB
ejpam-3517	29	8	appropriate	appropriate	ADJ
ejpam-3517	29	9	curves	curve	NOUN
ejpam-3517	29	10	to	to	ADP
ejpam-3517	29	11	their	their	PRON
ejpam-3517	29	12	data	datum	NOUN
ejpam-3517	29	13	.	.	PUNCT
ejpam-3517	30	1	curve	curve	VERB
ejpam-3517	30	2	fitting	fitting	ADJ
ejpam-3517	30	3	,	,	PUNCT
ejpam-3517	30	4	also	also	ADV
ejpam-3517	30	5	known	know	VERB
ejpam-3517	30	6	as	as	ADP
ejpam-3517	30	7	regression	regression	NOUN
ejpam-3517	30	8	analysis	analysis	NOUN
ejpam-3517	30	9	,	,	PUNCT
ejpam-3517	30	10	is	be	AUX
ejpam-3517	30	11	a	a	DET
ejpam-3517	30	12	common	common	ADJ
ejpam-3517	30	13	technique	technique	NOUN
ejpam-3517	30	14	for	for	ADP
ejpam-3517	30	15	modelling	model	VERB
ejpam-3517	30	16	data	datum	NOUN
ejpam-3517	30	17	[	[	X
ejpam-3517	30	18	13	13	NUM
ejpam-3517	30	19	]	]	PUNCT
ejpam-3517	30	20	.	.	PUNCT
ejpam-3517	31	1	the	the	DET
ejpam-3517	31	2	problem	problem	NOUN
ejpam-3517	31	3	of	of	ADP
ejpam-3517	31	4	determining	determine	VERB
ejpam-3517	31	5	ndimensional	ndimensional	ADJ
ejpam-3517	31	6	hyperplane	hyperplane	NOUN
ejpam-3517	31	7	,	,	PUNCT
ejpam-3517	31	8	in	in	ADP
ejpam-3517	31	9	order	order	NOUN
ejpam-3517	31	10	to	to	PART
ejpam-3517	31	11	have	have	AUX
ejpam-3517	31	12	its	its	PRON
ejpam-3517	31	13	graph	graph	NOUN
ejpam-3517	31	14	pass	pass	VERB
ejpam-3517	31	15	as	as	ADV
ejpam-3517	31	16	close	close	ADJ
ejpam-3517	31	17	as	as	ADP
ejpam-3517	31	18	possible	possible	ADJ
ejpam-3517	31	19	to	to	AUX
ejpam-3517	31	20	given	give	VERB
ejpam-3517	31	21	points	point	NOUN
ejpam-3517	31	22	in	in	ADP
ejpam-3517	31	23	sense	sense	NOUN
ejpam-3517	31	24	of	of	ADP
ejpam-3517	31	25	p	p	PROPN
ejpam-3517	31	26	norme	norme	NOUN
ejpam-3517	31	27	,	,	PUNCT
ejpam-3517	31	28	can	can	AUX
ejpam-3517	31	29	be	be	AUX
ejpam-3517	31	30	presented	present	VERB
ejpam-3517	31	31	as	as	ADP
ejpam-3517	31	32	an	an	DET
ejpam-3517	31	33	overdetermined	overdetermined	ADJ
ejpam-3517	31	34	system	system	NOUN
ejpam-3517	31	35	of	of	ADP
ejpam-3517	31	36	linear	linear	PROPN
ejpam-3517	31	37	equations	equation	NOUN
ejpam-3517	31	38	[	[	X
ejpam-3517	31	39	2	2	NUM
ejpam-3517	31	40	]	]	PUNCT
ejpam-3517	31	41	.	.	PUNCT
ejpam-3517	32	1	in	in	ADP
ejpam-3517	32	2	linear	linear	PROPN
ejpam-3517	32	3	regression	regression	NOUN
ejpam-3517	32	4	analysis	analysis	NOUN
ejpam-3517	32	5	it	it	PRON
ejpam-3517	32	6	is	be	AUX
ejpam-3517	32	7	most	most	ADV
ejpam-3517	32	8	frequently	frequently	ADV
ejpam-3517	32	9	assumed	assume	VERB
ejpam-3517	32	10	that	that	SCONJ
ejpam-3517	32	11	errors	error	NOUN
ejpam-3517	32	12	,	,	PUNCT
ejpam-3517	32	13	i.e.	i.e.	X
ejpam-3517	32	14	so	so	ADV
ejpam-3517	32	15	called	call	VERB
ejpam-3517	32	16	’	'	PUNCT
ejpam-3517	32	17	outliers	outlier	NOUN
ejpam-3517	32	18	’	'	PUNCT
ejpam-3517	32	19	,	,	PUNCT
ejpam-3517	32	20	can	can	AUX
ejpam-3517	32	21	occur	occur	VERB
ejpam-3517	32	22	in	in	ADP
ejpam-3517	32	23	measured	measured	ADJ
ejpam-3517	32	24	values	value	NOUN
ejpam-3517	32	25	of	of	ADP
ejpam-3517	32	26	the	the	DET
ejpam-3517	32	27	independent	independent	ADJ
ejpam-3517	32	28	variable	variable	NOUN
ejpam-3517	32	29	.	.	PUNCT
ejpam-3517	33	1	in	in	ADP
ejpam-3517	33	2	this	this	DET
ejpam-3517	33	3	case	case	NOUN
ejpam-3517	33	4	,	,	PUNCT
ejpam-3517	33	5	if	if	SCONJ
ejpam-3517	33	6	euclidian	euclidian	ADJ
ejpam-3517	33	7	norm	norm	NOUN
ejpam-3517	33	8	(	(	PUNCT
ejpam-3517	33	9	p	p	NOUN
ejpam-3517	33	10	=	=	NOUN
ejpam-3517	33	11	2	2	NUM
ejpam-3517	33	12	)	)	PUNCT
ejpam-3517	33	13	is	be	AUX
ejpam-3517	33	14	used	use	VERB
ejpam-3517	33	15	,	,	PUNCT
ejpam-3517	33	16	vector	vector	NOUN
ejpam-3517	33	17	x	x	SYM
ejpam-3517	33	18	∈	∈	PROPN
ejpam-3517	33	19	rn	rn	PROPN
ejpam-3517	33	20	is	be	AUX
ejpam-3517	33	21	obtained	obtain	VERB
ejpam-3517	33	22	in	in	ADP
ejpam-3517	33	23	the	the	DET
ejpam-3517	33	24	sense	sense	NOUN
ejpam-3517	33	25	of	of	ADP
ejpam-3517	33	26	least	least	ADJ
ejpam-3517	33	27	squares	square	NOUN
ejpam-3517	33	28	(	(	PUNCT
ejpam-3517	33	29	ls	ls	ADJ
ejpam-3517	33	30	)	)	PUNCT
ejpam-3517	33	31	problem	problem	NOUN
ejpam-3517	33	32	by	by	ADP
ejpam-3517	33	33	minimizing	minimize	VERB
ejpam-3517	33	34	(	(	PUNCT
ejpam-3517	33	35	3	3	NUM
ejpam-3517	33	36	)	)	PUNCT
ejpam-3517	33	37	.	.	PUNCT
ejpam-3517	34	1	in	in	ADP
ejpam-3517	34	2	many	many	ADJ
ejpam-3517	34	3	technical	technical	ADJ
ejpam-3517	34	4	and	and	CCONJ
ejpam-3517	34	5	other	other	ADJ
ejpam-3517	34	6	applications	application	NOUN
ejpam-3517	34	7	using	use	VERB
ejpam-3517	34	8	the	the	DET
ejpam-3517	34	9	p	p	NOUN
ejpam-3517	34	10	=	=	SYM
ejpam-3517	34	11	1	1	NUM
ejpam-3517	34	12	norm	norm	NOUN
ejpam-3517	34	13	is	be	AUX
ejpam-3517	34	14	much	much	ADV
ejpam-3517	34	15	more	more	ADV
ejpam-3517	34	16	interesting	interesting	ADJ
ejpam-3517	34	17	.	.	PUNCT
ejpam-3517	35	1	because	because	SCONJ
ejpam-3517	35	2	of	of	ADP
ejpam-3517	35	3	robust	robust	ADJ
ejpam-3517	35	4	properties	property	NOUN
ejpam-3517	35	5	of	of	ADP
ejpam-3517	35	6	p	p	NOUN
ejpam-3517	35	7	=	=	SYM
ejpam-3517	35	8	1	1	NUM
ejpam-3517	35	9	norm	norm	VERB
ejpam-3517	35	10	the	the	DET
ejpam-3517	35	11	outliers	outlier	NOUN
ejpam-3517	35	12	in	in	ADP
ejpam-3517	35	13	data	datum	NOUN
ejpam-3517	35	14	should	should	AUX
ejpam-3517	35	15	not	not	PART
ejpam-3517	35	16	affect	affect	VERB
ejpam-3517	35	17	the	the	DET
ejpam-3517	35	18	obtained	obtain	VERB
ejpam-3517	35	19	results	result	NOUN
ejpam-3517	35	20	.	.	PUNCT
ejpam-3517	36	1	in	in	ADP
ejpam-3517	36	2	literature	literature	NOUN
ejpam-3517	36	3	this	this	DET
ejpam-3517	36	4	problem	problem	NOUN
ejpam-3517	36	5	is	be	AUX
ejpam-3517	36	6	known	know	VERB
ejpam-3517	36	7	as	as	ADP
ejpam-3517	36	8	the	the	DET
ejpam-3517	36	9	least	least	ADJ
ejpam-3517	36	10	absolute	absolute	ADJ
ejpam-3517	36	11	deviation	deviation	NOUN
ejpam-3517	36	12	(	(	PUNCT
ejpam-3517	36	13	lad	lad	NOUN
ejpam-3517	36	14	)	)	PUNCT
ejpam-3517	36	15	problem	problem	NOUN
ejpam-3517	36	16	,	,	PUNCT
ejpam-3517	36	17	and	and	CCONJ
ejpam-3517	36	18	is	be	AUX
ejpam-3517	36	19	an	an	DET
ejpam-3517	36	20	efficient	efficient	ADJ
ejpam-3517	36	21	method	method	NOUN
ejpam-3517	36	22	for	for	ADP
ejpam-3517	36	23	outlier	outlier	ADJ
ejpam-3517	36	24	detection	detection	NOUN
ejpam-3517	37	1	[	[	X
ejpam-3517	37	2	11	11	NUM
ejpam-3517	37	3	,	,	PUNCT
ejpam-3517	37	4	14	14	NUM
ejpam-3517	37	5	]	]	PUNCT
ejpam-3517	37	6	.	.	PUNCT
ejpam-3517	38	1	for	for	ADP
ejpam-3517	38	2	that	that	DET
ejpam-3517	38	3	purpose	purpose	NOUN
ejpam-3517	38	4	some	some	DET
ejpam-3517	38	5	properties	property	NOUN
ejpam-3517	38	6	of	of	ADP
ejpam-3517	38	7	functional	functional	ADJ
ejpam-3517	38	8	fp	fp	X
ejpam-3517	38	9	:	:	PUNCT
ejpam-3517	38	10	rn	rn	PROPN
ejpam-3517	38	11	→	→	SYM
ejpam-3517	38	12	r	r	NOUN
ejpam-3517	38	13	are	be	AUX
ejpam-3517	38	14	shown	show	VERB
ejpam-3517	38	15	in	in	ADP
ejpam-3517	38	16	section	section	NOUN
ejpam-3517	38	17	2	2	NUM
ejpam-3517	38	18	,	,	PUNCT
ejpam-3517	38	19	especially	especially	ADV
ejpam-3517	38	20	taking	take	VERB
ejpam-3517	38	21	into	into	ADP
ejpam-3517	38	22	account	account	NOUN
ejpam-3517	38	23	the	the	DET
ejpam-3517	38	24	equivariant	equivariant	ADJ
ejpam-3517	38	25	properties	property	NOUN
ejpam-3517	38	26	of	of	ADP
ejpam-3517	38	27	a	a	DET
ejpam-3517	38	28	solution	solution	NOUN
ejpam-3517	38	29	of	of	ADP
ejpam-3517	38	30	an	an	DET
ejpam-3517	38	31	overdetermined	overdetermine	VERB
ejpam-3517	38	32	system	system	NOUN
ejpam-3517	38	33	of	of	ADP
ejpam-3517	38	34	linear	linear	PROPN
ejpam-3517	38	35	equations	equation	NOUN
ejpam-3517	38	36	.	.	PUNCT
ejpam-3517	39	1	in	in	ADP
ejpam-3517	39	2	section	section	NOUN
ejpam-3517	39	3	3	3	NUM
ejpam-3517	39	4	,	,	PUNCT
ejpam-3517	39	5	we	we	PRON
ejpam-3517	39	6	analyzed	analyze	VERB
ejpam-3517	39	7	equivariant	equivariant	ADJ
ejpam-3517	39	8	properties	property	NOUN
ejpam-3517	39	9	of	of	ADP
ejpam-3517	39	10	the	the	DET
ejpam-3517	39	11	weighted	weight	VERB
ejpam-3517	39	12	mean	mean	NOUN
ejpam-3517	39	13	and	and	CCONJ
ejpam-3517	39	14	weighted	weight	VERB
ejpam-3517	39	15	median	median	NOUN
ejpam-3517	39	16	of	of	ADP
ejpam-3517	39	17	the	the	DET
ejpam-3517	39	18	data	datum	NOUN
ejpam-3517	39	19	,	,	PUNCT
ejpam-3517	39	20	which	which	PRON
ejpam-3517	39	21	are	be	AUX
ejpam-3517	39	22	a	a	DET
ejpam-3517	39	23	reduced	reduce	VERB
ejpam-3517	39	24	case	case	NOUN
ejpam-3517	39	25	of	of	ADP
ejpam-3517	39	26	an	an	DET
ejpam-3517	39	27	overdetermined	overdetermine	VERB
ejpam-3517	39	28	system	system	NOUN
ejpam-3517	39	29	of	of	ADP
ejpam-3517	39	30	linear	linear	PROPN
ejpam-3517	39	31	equations	equation	NOUN
ejpam-3517	39	32	,	,	PUNCT
ejpam-3517	39	33	where	where	SCONJ
ejpam-3517	39	34	p	p	NOUN
ejpam-3517	39	35	=	=	NOUN
ejpam-3517	39	36	1	1	NUM
ejpam-3517	39	37	,	,	PUNCT
ejpam-3517	39	38	p	p	NOUN
ejpam-3517	39	39	=	=	SYM
ejpam-3517	39	40	2	2	NUM
ejpam-3517	39	41	is	be	AUX
ejpam-3517	39	42	observed	observe	VERB
ejpam-3517	39	43	,	,	PUNCT
ejpam-3517	39	44	and	and	CCONJ
ejpam-3517	39	45	n	n	CCONJ
ejpam-3517	39	46	=	=	SYM
ejpam-3517	39	47	1	1	NUM
ejpam-3517	39	48	respectively	respectively	ADV
ejpam-3517	39	49	.	.	PUNCT
ejpam-3517	40	1	2	2	X
ejpam-3517	40	2	.	.	X
ejpam-3517	40	3	properties	property	NOUN
ejpam-3517	40	4	of	of	ADP
ejpam-3517	40	5	the	the	DET
ejpam-3517	40	6	functional	functional	ADJ
ejpam-3517	40	7	fp	fp	NOUN
ejpam-3517	40	8	in	in	ADP
ejpam-3517	40	9	this	this	DET
ejpam-3517	40	10	section	section	NOUN
ejpam-3517	40	11	we	we	PRON
ejpam-3517	40	12	present	present	VERB
ejpam-3517	40	13	some	some	DET
ejpam-3517	40	14	properties	property	NOUN
ejpam-3517	40	15	of	of	ADP
ejpam-3517	40	16	functional	functional	ADJ
ejpam-3517	40	17	fp	fp	X
ejpam-3517	40	18	:	:	PUNCT
ejpam-3517	40	19	rn	rn	PROPN
ejpam-3517	40	20	→	→	SYM
ejpam-3517	40	21	r	r	NOUN
ejpam-3517	40	22	in	in	ADP
ejpam-3517	40	23	order	order	NOUN
ejpam-3517	40	24	to	to	PART
ejpam-3517	40	25	prove	prove	VERB
ejpam-3517	40	26	equivariant	equivariant	ADJ
ejpam-3517	40	27	properties	property	NOUN
ejpam-3517	40	28	.	.	PUNCT
ejpam-3517	41	1	following	follow	VERB
ejpam-3517	41	2	the	the	DET
ejpam-3517	41	3	minkowski	minkowski	PROPN
ejpam-3517	41	4	inequality	inequality	NOUN
ejpam-3517	41	5	presented	present	VERB
ejpam-3517	41	6	in	in	ADP
ejpam-3517	41	7	theorem	theorem	NOUN
ejpam-3517	41	8	9	9	NUM
ejpam-3517	41	9	,	,	PUNCT
ejpam-3517	41	10	which	which	PRON
ejpam-3517	41	11	is	be	AUX
ejpam-3517	41	12	proven	prove	VERB
ejpam-3517	41	13	in	in	ADP
ejpam-3517	41	14	section	section	NOUN
ejpam-3517	41	15	5	5	NUM
ejpam-3517	41	16	,	,	PUNCT
ejpam-3517	41	17	presented	present	VERB
ejpam-3517	41	18	in	in	ADP
ejpam-3517	41	19	appendix	appendix	NOUN
ejpam-3517	41	20	,	,	PUNCT
ejpam-3517	41	21	we	we	PRON
ejpam-3517	41	22	give	give	VERB
ejpam-3517	41	23	directly	directly	ADV
ejpam-3517	41	24	the	the	DET
ejpam-3517	41	25	next	next	ADJ
ejpam-3517	41	26	theorem	theorem	PROPN
ejpam-3517	41	27	.	.	PUNCT
ejpam-3517	41	28	theorem	theorem	NOUN
ejpam-3517	41	29	1	1	NUM
ejpam-3517	41	30	.	.	PUNCT
ejpam-3517	41	31	functional	functional	ADJ
ejpam-3517	41	32	fp	fp	X
ejpam-3517	41	33	:	:	PUNCT
ejpam-3517	41	34	rn	rn	PROPN
ejpam-3517	41	35	→	→	SYM
ejpam-3517	41	36	r	r	NOUN
ejpam-3517	41	37	is	be	AUX
ejpam-3517	41	38	convex	convex	ADJ
ejpam-3517	41	39	on	on	ADP
ejpam-3517	41	40	rn	rn	PROPN
ejpam-3517	41	41	.	.	PUNCT
ejpam-3517	42	1	the	the	DET
ejpam-3517	42	2	importance	importance	NOUN
ejpam-3517	42	3	of	of	ADP
ejpam-3517	42	4	the	the	DET
ejpam-3517	42	5	extremum	extremum	ADJ
ejpam-3517	42	6	problems	problem	NOUN
ejpam-3517	42	7	in	in	ADP
ejpam-3517	42	8	applied	applied	ADJ
ejpam-3517	42	9	mathematics	mathematic	NOUN
ejpam-3517	42	10	leads	lead	VERB
ejpam-3517	42	11	us	we	PRON
ejpam-3517	42	12	to	to	ADP
ejpam-3517	42	13	the	the	DET
ejpam-3517	42	14	general	general	ADJ
ejpam-3517	42	15	study	study	NOUN
ejpam-3517	42	16	of	of	ADP
ejpam-3517	42	17	extremum	extremum	ADJ
ejpam-3517	42	18	of	of	ADP
ejpam-3517	42	19	functional	functional	ADJ
ejpam-3517	42	20	.	.	PUNCT
ejpam-3517	43	1	it	it	PRON
ejpam-3517	43	2	is	be	AUX
ejpam-3517	43	3	not	not	PART
ejpam-3517	43	4	easy	easy	ADJ
ejpam-3517	43	5	to	to	PART
ejpam-3517	43	6	know	know	VERB
ejpam-3517	43	7	the	the	DET
ejpam-3517	43	8	extremum	extremum	ADJ
ejpam-3517	43	9	points	point	NOUN
ejpam-3517	43	10	v.	v.	ADP
ejpam-3517	43	11	novoselac	novoselac	PROPN
ejpam-3517	43	12	,	,	PUNCT
ejpam-3517	44	1	z.	z.	PROPN
ejpam-3517	44	2	pavić	pavić	PROPN
ejpam-3517	44	3	/	/	SYM
ejpam-3517	44	4	eur	eur	PROPN
ejpam-3517	44	5	.	.	PUNCT
ejpam-3517	45	1	j.	j.	PROPN
ejpam-3517	45	2	pure	pure	PROPN
ejpam-3517	45	3	appl	appl	PROPN
ejpam-3517	45	4	.	.	PROPN
ejpam-3517	45	5	math	math	PROPN
ejpam-3517	45	6	,	,	PUNCT
ejpam-3517	45	7	12	12	NUM
ejpam-3517	45	8	(	(	PUNCT
ejpam-3517	45	9	4	4	NUM
ejpam-3517	45	10	)	)	PUNCT
ejpam-3517	45	11	(	(	PUNCT
ejpam-3517	45	12	2019	2019	NUM
ejpam-3517	45	13	)	)	PUNCT
ejpam-3517	45	14	,	,	PUNCT
ejpam-3517	45	15	1360	1360	NUM
ejpam-3517	45	16	-	-	SYM
ejpam-3517	45	17	1370	1370	NUM
ejpam-3517	45	18	1362	1362	NUM
ejpam-3517	45	19	for	for	ADP
ejpam-3517	45	20	differentiable	differentiable	ADJ
ejpam-3517	45	21	functions	function	NOUN
ejpam-3517	45	22	,	,	PUNCT
ejpam-3517	45	23	because	because	SCONJ
ejpam-3517	45	24	it	it	PRON
ejpam-3517	45	25	is	be	AUX
ejpam-3517	45	26	not	not	PART
ejpam-3517	45	27	always	always	ADV
ejpam-3517	45	28	possible	possible	ADJ
ejpam-3517	45	29	to	to	PART
ejpam-3517	45	30	solve	solve	VERB
ejpam-3517	45	31	∇fp(x	∇fp(x	PROPN
ejpam-3517	45	32	)	)	PUNCT
ejpam-3517	45	33	=	=	SYM
ejpam-3517	45	34	0	0	PUNCT
ejpam-3517	45	35	to	to	PART
ejpam-3517	45	36	calculate	calculate	VERB
ejpam-3517	45	37	critical	critical	ADJ
ejpam-3517	45	38	points	point	NOUN
ejpam-3517	45	39	.	.	PUNCT
ejpam-3517	46	1	in	in	ADP
ejpam-3517	46	2	the	the	DET
ejpam-3517	46	3	situation	situation	NOUN
ejpam-3517	46	4	when	when	SCONJ
ejpam-3517	46	5	p	p	PROPN
ejpam-3517	46	6	=	=	NOUN
ejpam-3517	46	7	2	2	NUM
ejpam-3517	46	8	,	,	PUNCT
ejpam-3517	46	9	the	the	DET
ejpam-3517	46	10	problem	problem	NOUN
ejpam-3517	46	11	is	be	AUX
ejpam-3517	46	12	known	know	VERB
ejpam-3517	46	13	as	as	ADP
ejpam-3517	46	14	the	the	DET
ejpam-3517	46	15	ls	ls	ADJ
ejpam-3517	46	16	problem	problem	NOUN
ejpam-3517	46	17	and	and	CCONJ
ejpam-3517	46	18	it	it	PRON
ejpam-3517	46	19	always	always	ADV
ejpam-3517	46	20	has	have	VERB
ejpam-3517	46	21	a	a	DET
ejpam-3517	46	22	solution	solution	NOUN
ejpam-3517	46	23	.	.	PUNCT
ejpam-3517	47	1	in	in	ADP
ejpam-3517	47	2	this	this	DET
ejpam-3517	47	3	case	case	NOUN
ejpam-3517	47	4	x∗	x∗	PROPN
ejpam-3517	47	5	minimizes	minimize	VERB
ejpam-3517	47	6	f2	f2	PROPN
ejpam-3517	47	7	if	if	SCONJ
ejpam-3517	47	8	and	and	CCONJ
ejpam-3517	47	9	only	only	ADV
ejpam-3517	47	10	if	if	SCONJ
ejpam-3517	47	11	x∗	x∗	PROPN
ejpam-3517	47	12	solves	solve	VERB
ejpam-3517	47	13	normal	normal	ADJ
ejpam-3517	47	14	equation	equation	NOUN
ejpam-3517	47	15	system	system	NOUN
ejpam-3517	47	16	atax	atax	NOUN
ejpam-3517	47	17	=	=	PUNCT
ejpam-3517	47	18	at	at	ADP
ejpam-3517	47	19	b.	b.	PROPN
ejpam-3517	47	20	it	it	PRON
ejpam-3517	47	21	can	can	AUX
ejpam-3517	47	22	be	be	AUX
ejpam-3517	47	23	shown	show	VERB
ejpam-3517	47	24	that	that	SCONJ
ejpam-3517	47	25	if	if	SCONJ
ejpam-3517	47	26	a	a	DET
ejpam-3517	47	27	∈	∈	NOUN
ejpam-3517	47	28	rm×n	rm×n	NOUN
ejpam-3517	47	29	has	have	VERB
ejpam-3517	47	30	full	full	ADJ
ejpam-3517	47	31	rank	rank	NOUN
ejpam-3517	47	32	n	n	CCONJ
ejpam-3517	47	33	,	,	PUNCT
ejpam-3517	47	34	then	then	ADV
ejpam-3517	47	35	the	the	DET
ejpam-3517	47	36	ls	ls	ADJ
ejpam-3517	47	37	problem	problem	NOUN
ejpam-3517	47	38	has	have	VERB
ejpam-3517	47	39	a	a	DET
ejpam-3517	47	40	unique	unique	ADJ
ejpam-3517	47	41	minimizer	minimizer	NOUN
ejpam-3517	47	42	.	.	PUNCT
ejpam-3517	48	1	in	in	ADP
ejpam-3517	48	2	that	that	DET
ejpam-3517	48	3	case	case	NOUN
ejpam-3517	48	4	global	global	ADJ
ejpam-3517	48	5	extremum	extremum	NOUN
ejpam-3517	48	6	can	can	AUX
ejpam-3517	48	7	be	be	AUX
ejpam-3517	48	8	presented	present	VERB
ejpam-3517	48	9	as	as	ADP
ejpam-3517	48	10	x∗	x∗	PROPN
ejpam-3517	48	11	=	=	SYM
ejpam-3517	48	12	a+b	a+b	PROPN
ejpam-3517	48	13	,	,	PUNCT
ejpam-3517	48	14	where	where	SCONJ
ejpam-3517	48	15	matrix	matrix	NOUN
ejpam-3517	48	16	a+	a+	PUNCT
ejpam-3517	49	1	=	=	X
ejpam-3517	49	2	(	(	PUNCT
ejpam-3517	49	3	ata)−1at	ata)−1at	PROPN
ejpam-3517	49	4	is	be	AUX
ejpam-3517	49	5	usually	usually	ADV
ejpam-3517	49	6	called	call	VERB
ejpam-3517	49	7	the	the	DET
ejpam-3517	49	8	moorepenrose	moorepenrose	ADJ
ejpam-3517	49	9	inverse	inverse	NOUN
ejpam-3517	49	10	[	[	X
ejpam-3517	49	11	3	3	NUM
ejpam-3517	49	12	]	]	PUNCT
ejpam-3517	49	13	.	.	PUNCT
ejpam-3517	50	1	in	in	ADP
ejpam-3517	50	2	most	most	ADJ
ejpam-3517	50	3	general	general	ADJ
ejpam-3517	50	4	cases	case	NOUN
ejpam-3517	50	5	,	,	PUNCT
ejpam-3517	50	6	convex	convex	VERB
ejpam-3517	50	7	functional	functional	ADJ
ejpam-3517	50	8	fp	fp	AUX
ejpam-3517	50	9	has	have	VERB
ejpam-3517	50	10	a	a	DET
ejpam-3517	50	11	particularly	particularly	ADV
ejpam-3517	50	12	simple	simple	ADJ
ejpam-3517	50	13	extremal	extremal	ADJ
ejpam-3517	50	14	structure	structure	NOUN
ejpam-3517	50	15	,	,	PUNCT
ejpam-3517	50	16	and	and	CCONJ
ejpam-3517	50	17	there	there	PRON
ejpam-3517	50	18	are	be	VERB
ejpam-3517	50	19	algorithms	algorithm	NOUN
ejpam-3517	50	20	to	to	PART
ejpam-3517	50	21	calculate	calculate	VERB
ejpam-3517	50	22	extremum	extremum	ADJ
ejpam-3517	50	23	points	point	NOUN
ejpam-3517	50	24	,	,	PUNCT
ejpam-3517	50	25	supposing	suppose	VERB
ejpam-3517	50	26	its	its	PRON
ejpam-3517	50	27	existance	existance	NOUN
ejpam-3517	50	28	[	[	X
ejpam-3517	50	29	15	15	NUM
ejpam-3517	50	30	]	]	PUNCT
ejpam-3517	50	31	.	.	PUNCT
ejpam-3517	51	1	knowing	know	VERB
ejpam-3517	51	2	whether	whether	SCONJ
ejpam-3517	51	3	or	or	CCONJ
ejpam-3517	51	4	not	not	PART
ejpam-3517	51	5	a	a	DET
ejpam-3517	51	6	local	local	ADJ
ejpam-3517	51	7	minimum	minimum	NOUN
ejpam-3517	51	8	is	be	AUX
ejpam-3517	51	9	also	also	ADV
ejpam-3517	51	10	global	global	ADJ
ejpam-3517	51	11	,	,	PUNCT
ejpam-3517	51	12	is	be	AUX
ejpam-3517	51	13	one	one	NUM
ejpam-3517	51	14	of	of	ADP
ejpam-3517	51	15	the	the	DET
ejpam-3517	51	16	most	most	ADV
ejpam-3517	51	17	important	important	ADJ
ejpam-3517	51	18	questions	question	NOUN
ejpam-3517	51	19	in	in	ADP
ejpam-3517	51	20	optimization	optimization	NOUN
ejpam-3517	51	21	[	[	X
ejpam-3517	51	22	7	7	NUM
ejpam-3517	51	23	]	]	PUNCT
ejpam-3517	51	24	.	.	PUNCT
ejpam-3517	52	1	the	the	DET
ejpam-3517	52	2	assumption	assumption	NOUN
ejpam-3517	52	3	of	of	ADP
ejpam-3517	52	4	convexity	convexity	NOUN
ejpam-3517	52	5	gives	give	VERB
ejpam-3517	52	6	a	a	DET
ejpam-3517	52	7	positive	positive	ADJ
ejpam-3517	52	8	answer	answer	NOUN
ejpam-3517	52	9	to	to	ADP
ejpam-3517	52	10	this	this	DET
ejpam-3517	52	11	question	question	NOUN
ejpam-3517	52	12	as	as	SCONJ
ejpam-3517	52	13	it	it	PRON
ejpam-3517	52	14	is	be	AUX
ejpam-3517	52	15	stated	state	VERB
ejpam-3517	52	16	in	in	ADP
ejpam-3517	52	17	the	the	DET
ejpam-3517	52	18	following	follow	VERB
ejpam-3517	52	19	theorem	theorem	PROPN
ejpam-3517	52	20	.	.	PUNCT
ejpam-3517	52	21	theorem	theorem	NOUN
ejpam-3517	52	22	2	2	NUM
ejpam-3517	52	23	.	.	PUNCT
ejpam-3517	53	1	a	a	DET
ejpam-3517	53	2	local	local	ADJ
ejpam-3517	53	3	minimum	minimum	ADJ
ejpam-3517	53	4	x∗	x∗	NOUN
ejpam-3517	53	5	of	of	ADP
ejpam-3517	53	6	a	a	DET
ejpam-3517	53	7	functional	functional	ADJ
ejpam-3517	53	8	fp	fp	X
ejpam-3517	53	9	:	:	PUNCT
ejpam-3517	53	10	rn	rn	PROPN
ejpam-3517	53	11	→	→	SYM
ejpam-3517	53	12	r	r	NOUN
ejpam-3517	53	13	is	be	AUX
ejpam-3517	53	14	always	always	ADV
ejpam-3517	53	15	a	a	DET
ejpam-3517	53	16	global	global	ADJ
ejpam-3517	53	17	extremum	extremum	NOUN
ejpam-3517	53	18	.	.	PUNCT
ejpam-3517	54	1	proof	proof	NOUN
ejpam-3517	54	2	.	.	PUNCT
ejpam-3517	55	1	suppose	suppose	VERB
ejpam-3517	55	2	that	that	SCONJ
ejpam-3517	55	3	x∗	x∗	PROPN
ejpam-3517	55	4	is	be	AUX
ejpam-3517	55	5	a	a	DET
ejpam-3517	55	6	local	local	ADJ
ejpam-3517	55	7	minimum	minimum	NOUN
ejpam-3517	55	8	of	of	ADP
ejpam-3517	55	9	fp	fp	NOUN
ejpam-3517	55	10	,	,	PUNCT
ejpam-3517	55	11	that	that	ADV
ejpam-3517	55	12	is	is	ADV
ejpam-3517	55	13	,	,	PUNCT
ejpam-3517	55	14	there	there	PRON
ejpam-3517	55	15	is	be	VERB
ejpam-3517	55	16	an	an	DET
ejpam-3517	55	17	open	open	ADJ
ejpam-3517	55	18	neighborhood	neighborhood	NOUN
ejpam-3517	55	19	u	u	NOUN
ejpam-3517	55	20	of	of	ADP
ejpam-3517	55	21	x∗	x∗	PROPN
ejpam-3517	55	22	where	where	SCONJ
ejpam-3517	55	23	fp(x	fp(x	PUNCT
ejpam-3517	55	24	∗	∗	NOUN
ejpam-3517	55	25	)	)	PUNCT
ejpam-3517	55	26	≤	≤	NOUN
ejpam-3517	55	27	fp(x	fp(x	NUM
ejpam-3517	55	28	)	)	PUNCT
ejpam-3517	55	29	,	,	PUNCT
ejpam-3517	55	30	∀x	∀x	VERB
ejpam-3517	55	31	∈	∈	PROPN
ejpam-3517	55	32	u.we	u.we	NOUN
ejpam-3517	55	33	prove	prove	VERB
ejpam-3517	55	34	that	that	SCONJ
ejpam-3517	55	35	fp(x	fp(x	PUNCT
ejpam-3517	55	36	∗	∗	NOUN
ejpam-3517	55	37	)	)	PUNCT
ejpam-3517	55	38	≤	≤	NOUN
ejpam-3517	55	39	fp(y∗	fp(y∗	NUM
ejpam-3517	55	40	)	)	PUNCT
ejpam-3517	55	41	for	for	ADP
ejpam-3517	55	42	arbitrary	arbitrary	ADJ
ejpam-3517	55	43	y∗	y∗	PROPN
ejpam-3517	55	44	∈	∈	PROPN
ejpam-3517	55	45	rn	rn	PROPN
ejpam-3517	55	46	.	.	PROPN
ejpam-3517	55	47	consider	consider	VERB
ejpam-3517	55	48	the	the	DET
ejpam-3517	55	49	convex	convex	NOUN
ejpam-3517	55	50	combination	combination	NOUN
ejpam-3517	55	51	(	(	PUNCT
ejpam-3517	55	52	1	1	NUM
ejpam-3517	55	53	−	−	NOUN
ejpam-3517	55	54	λ)x∗	λ)x∗	X
ejpam-3517	55	55	+	+	CCONJ
ejpam-3517	55	56	λy∗	λy∗	ADJ
ejpam-3517	55	57	,	,	PUNCT
ejpam-3517	55	58	for	for	ADP
ejpam-3517	55	59	λ	λ	PROPN
ejpam-3517	55	60	∈	∈	PROPN
ejpam-3517	56	1	[	[	X
ejpam-3517	56	2	0	0	NUM
ejpam-3517	56	3	,	,	PUNCT
ejpam-3517	56	4	1	1	NUM
ejpam-3517	56	5	]	]	PUNCT
ejpam-3517	56	6	,	,	PUNCT
ejpam-3517	56	7	the	the	DET
ejpam-3517	56	8	convex	convex	NOUN
ejpam-3517	56	9	combination	combination	NOUN
ejpam-3517	56	10	approaches	approach	NOUN
ejpam-3517	56	11	to	to	ADP
ejpam-3517	56	12	x∗	x∗	PROPN
ejpam-3517	56	13	as	as	ADP
ejpam-3517	56	14	λ	λ	PROPN
ejpam-3517	56	15	→	→	SYM
ejpam-3517	56	16	0	0	NUM
ejpam-3517	56	17	.	.	PUNCT
ejpam-3517	57	1	therefore	therefore	ADV
ejpam-3517	57	2	for	for	ADP
ejpam-3517	57	3	small	small	ADJ
ejpam-3517	57	4	enough	enough	ADJ
ejpam-3517	57	5	λ	λ	NOUN
ejpam-3517	57	6	,	,	PUNCT
ejpam-3517	57	7	(	(	PUNCT
ejpam-3517	57	8	1	1	NUM
ejpam-3517	57	9	−	−	NOUN
ejpam-3517	57	10	λ)x∗	λ)x∗	PRON
ejpam-3517	57	11	+	+	CCONJ
ejpam-3517	57	12	λy∗	λy∗	ADJ
ejpam-3517	57	13	is	be	AUX
ejpam-3517	57	14	in	in	ADP
ejpam-3517	57	15	the	the	DET
ejpam-3517	57	16	neighborhood	neighborhood	NOUN
ejpam-3517	57	17	u	u	NOUN
ejpam-3517	57	18	.	.	PUNCT
ejpam-3517	58	1	then	then	ADV
ejpam-3517	58	2	fp(x	fp(x	PUNCT
ejpam-3517	58	3	∗	∗	NOUN
ejpam-3517	58	4	)	)	PUNCT
ejpam-3517	58	5	≤	≤	NOUN
ejpam-3517	59	1	fp((1−	fp((1−	PROPN
ejpam-3517	59	2	λ)x∗	λ)x∗	X
ejpam-3517	59	3	+	+	CCONJ
ejpam-3517	59	4	λy∗	λy∗	ADJ
ejpam-3517	59	5	)	)	PUNCT
ejpam-3517	59	6	≤	≤	NOUN
ejpam-3517	59	7	(	(	PUNCT
ejpam-3517	59	8	1−	1−	NUM
ejpam-3517	59	9	λ)fp(x	λ)fp(x	PROPN
ejpam-3517	59	10	∗	∗	NOUN
ejpam-3517	59	11	)	)	PUNCT
ejpam-3517	60	1	+	+	CCONJ
ejpam-3517	60	2	λfp(y	λfp(y	PROPN
ejpam-3517	60	3	∗	∗	NOUN
ejpam-3517	60	4	)	)	PUNCT
ejpam-3517	60	5	.	.	PUNCT
ejpam-3517	61	1	(	(	PUNCT
ejpam-3517	61	2	4	4	X
ejpam-3517	61	3	)	)	PUNCT
ejpam-3517	61	4	rearranging	rearrange	VERB
ejpam-3517	61	5	terms	term	NOUN
ejpam-3517	61	6	,	,	PUNCT
ejpam-3517	61	7	we	we	PRON
ejpam-3517	61	8	have	have	AUX
ejpam-3517	61	9	fp(x	fp(x	VERB
ejpam-3517	61	10	∗	∗	NOUN
ejpam-3517	61	11	)	)	PUNCT
ejpam-3517	61	12	≤	≤	NOUN
ejpam-3517	61	13	fp(y∗	fp(y∗	NUM
ejpam-3517	61	14	)	)	PUNCT
ejpam-3517	61	15	.	.	PUNCT
ejpam-3517	62	1	from	from	ADP
ejpam-3517	62	2	the	the	DET
ejpam-3517	62	3	theorem	theorem	NOUN
ejpam-3517	62	4	2	2	NUM
ejpam-3517	62	5	,	,	PUNCT
ejpam-3517	62	6	it	it	PRON
ejpam-3517	62	7	directly	directly	ADV
ejpam-3517	62	8	follows	follow	VERB
ejpam-3517	62	9	that	that	SCONJ
ejpam-3517	62	10	the	the	DET
ejpam-3517	62	11	local	local	ADJ
ejpam-3517	62	12	minimum	minimum	NOUN
ejpam-3517	62	13	of	of	ADP
ejpam-3517	62	14	a	a	DET
ejpam-3517	62	15	convex	convex	ADJ
ejpam-3517	62	16	functional	functional	NOUN
ejpam-3517	62	17	is	be	AUX
ejpam-3517	62	18	necessarily	necessarily	ADV
ejpam-3517	62	19	the	the	DET
ejpam-3517	62	20	global	global	ADJ
ejpam-3517	62	21	minimum	minimum	NOUN
ejpam-3517	62	22	.	.	PUNCT
ejpam-3517	63	1	however	however	ADV
ejpam-3517	63	2	,	,	PUNCT
ejpam-3517	63	3	this	this	DET
ejpam-3517	63	4	minimum	minimum	NOUN
ejpam-3517	63	5	is	be	AUX
ejpam-3517	63	6	not	not	PART
ejpam-3517	63	7	necessarily	necessarily	ADV
ejpam-3517	63	8	unique	unique	ADJ
ejpam-3517	63	9	,	,	PUNCT
ejpam-3517	63	10	a	a	DET
ejpam-3517	63	11	sufficient	sufficient	ADJ
ejpam-3517	63	12	condition	condition	NOUN
ejpam-3517	63	13	is	be	AUX
ejpam-3517	63	14	strict	strict	ADJ
ejpam-3517	63	15	convexity	convexity	NOUN
ejpam-3517	63	16	.	.	PUNCT
ejpam-3517	64	1	let	let	VERB
ejpam-3517	64	2	us	we	PRON
ejpam-3517	64	3	now	now	ADV
ejpam-3517	64	4	discuss	discuss	VERB
ejpam-3517	64	5	some	some	DET
ejpam-3517	64	6	equivariant	equivariant	ADJ
ejpam-3517	64	7	properties	property	NOUN
ejpam-3517	64	8	of	of	ADP
ejpam-3517	64	9	functional	functional	ADJ
ejpam-3517	64	10	fp	fp	NOUN
ejpam-3517	64	11	.	.	PUNCT
ejpam-3517	65	1	we	we	PRON
ejpam-3517	65	2	considered	consider	VERB
ejpam-3517	65	3	three	three	NUM
ejpam-3517	65	4	types	type	NOUN
ejpam-3517	65	5	of	of	ADP
ejpam-3517	65	6	equivariance	equivariance	NOUN
ejpam-3517	65	7	:	:	PUNCT
ejpam-3517	65	8	regression	regression	NOUN
ejpam-3517	65	9	,	,	PUNCT
ejpam-3517	65	10	scale	scale	NOUN
ejpam-3517	65	11	,	,	PUNCT
ejpam-3517	65	12	and	and	CCONJ
ejpam-3517	65	13	affine	affine	VERB
ejpam-3517	65	14	equivariance	equivariance	NOUN
ejpam-3517	65	15	[	[	X
ejpam-3517	65	16	11	11	NUM
ejpam-3517	65	17	]	]	PUNCT
ejpam-3517	65	18	.	.	PUNCT
ejpam-3517	66	1	the	the	DET
ejpam-3517	66	2	next	next	ADJ
ejpam-3517	66	3	theorem	theorem	NOUN
ejpam-3517	66	4	shows	show	VERB
ejpam-3517	66	5	that	that	SCONJ
ejpam-3517	66	6	functional	functional	ADJ
ejpam-3517	66	7	fp	fp	X
ejpam-3517	66	8	possesses	possess	VERB
ejpam-3517	66	9	these	these	DET
ejpam-3517	66	10	three	three	NUM
ejpam-3517	66	11	types	type	NOUN
ejpam-3517	66	12	of	of	ADP
ejpam-3517	66	13	equvivarance	equvivarance	NOUN
ejpam-3517	66	14	.	.	PUNCT
ejpam-3517	67	1	theorem	theorem	NOUN
ejpam-3517	67	2	3	3	X
ejpam-3517	67	3	.	.	PUNCT
ejpam-3517	68	1	let	let	VERB
ejpam-3517	68	2	a	a	DET
ejpam-3517	68	3	∈	∈	PROPN
ejpam-3517	68	4	rm×n	rm×n	NOUN
ejpam-3517	68	5	,	,	PUNCT
ejpam-3517	68	6	m	m	VERB
ejpam-3517	68	7	>	>	X
ejpam-3517	68	8	n	n	CCONJ
ejpam-3517	68	9	,	,	PUNCT
ejpam-3517	68	10	b	b	PROPN
ejpam-3517	68	11	∈	∈	PROPN
ejpam-3517	68	12	rm	rm	NOUN
ejpam-3517	68	13	,	,	PUNCT
ejpam-3517	68	14	and	and	CCONJ
ejpam-3517	68	15	x∗	x∗	PROPN
ejpam-3517	68	16	∈	∈	PROPN
ejpam-3517	69	1	rn	rn	PROPN
ejpam-3517	69	2	such	such	ADJ
ejpam-3517	69	3	that	that	SCONJ
ejpam-3517	69	4	fp(x	fp(x	PUNCT
ejpam-3517	69	5	∗	∗	NOUN
ejpam-3517	69	6	)	)	PUNCT
ejpam-3517	70	1	=	=	SYM
ejpam-3517	70	2	min	min	NOUN
ejpam-3517	70	3	x∈rn	x∈rn	PROPN
ejpam-3517	70	4	‖b−ax‖p	‖b−ax‖p	PROPN
ejpam-3517	70	5	,	,	PUNCT
ejpam-3517	70	6	p	p	NOUN
ejpam-3517	70	7	∈	∈	PROPN
ejpam-3517	71	1	[	[	X
ejpam-3517	71	2	1,∞	1,∞	NUM
ejpam-3517	71	3	〉	〉	NUM
ejpam-3517	71	4	.	.	PUNCT
ejpam-3517	72	1	(	(	PUNCT
ejpam-3517	72	2	5	5	NUM
ejpam-3517	72	3	)	)	PUNCT
ejpam-3517	72	4	then	then	ADV
ejpam-3517	72	5	(	(	PUNCT
ejpam-3517	72	6	a	a	X
ejpam-3517	72	7	)	)	PUNCT
ejpam-3517	72	8	for	for	ADP
ejpam-3517	72	9	an	an	DET
ejpam-3517	72	10	arbitrary	arbitrary	ADJ
ejpam-3517	72	11	v	v	ADP
ejpam-3517	72	12	∈	∈	PROPN
ejpam-3517	72	13	rn	rn	PROPN
ejpam-3517	72	14	,	,	PUNCT
ejpam-3517	72	15	vector	vector	NOUN
ejpam-3517	72	16	x∗	x∗	NOUN
ejpam-3517	73	1	+	+	CCONJ
ejpam-3517	73	2	v	v	NOUN
ejpam-3517	73	3	is	be	AUX
ejpam-3517	73	4	a	a	DET
ejpam-3517	73	5	solution	solution	NOUN
ejpam-3517	73	6	of	of	ADP
ejpam-3517	73	7	min	min	NOUN
ejpam-3517	73	8	x∈rn	x∈rn	PROPN
ejpam-3517	73	9	‖b+av	‖b+av	PROPN
ejpam-3517	73	10	−ax‖p	−ax‖p	PROPN
ejpam-3517	73	11	.	.	PUNCT
ejpam-3517	74	1	(	(	PUNCT
ejpam-3517	74	2	6	6	NUM
ejpam-3517	74	3	)	)	PUNCT
ejpam-3517	74	4	(	(	PUNCT
ejpam-3517	74	5	b	b	NOUN
ejpam-3517	74	6	)	)	PUNCT
ejpam-3517	74	7	for	for	ADP
ejpam-3517	74	8	any	any	DET
ejpam-3517	74	9	c	c	PROPN
ejpam-3517	74	10	∈	∈	PROPN
ejpam-3517	74	11	r	r	NOUN
ejpam-3517	74	12	,	,	PUNCT
ejpam-3517	74	13	vector	vector	NOUN
ejpam-3517	74	14	c	c	NOUN
ejpam-3517	74	15	x∗	x∗	PROPN
ejpam-3517	74	16	is	be	AUX
ejpam-3517	74	17	a	a	DET
ejpam-3517	74	18	solution	solution	NOUN
ejpam-3517	74	19	of	of	ADP
ejpam-3517	74	20	min	min	NOUN
ejpam-3517	74	21	x∈rn	x∈rn	PROPN
ejpam-3517	74	22	‖c	‖c	PROPN
ejpam-3517	74	23	b−ax‖p	b−ax‖p	PROPN
ejpam-3517	74	24	.	.	PUNCT
ejpam-3517	75	1	(	(	PUNCT
ejpam-3517	75	2	7	7	X
ejpam-3517	75	3	)	)	PUNCT
ejpam-3517	75	4	v.	v.	CCONJ
ejpam-3517	75	5	novoselac	novoselac	PROPN
ejpam-3517	75	6	,	,	PUNCT
ejpam-3517	75	7	z.	z.	PROPN
ejpam-3517	75	8	pavić	pavić	PROPN
ejpam-3517	75	9	/	/	SYM
ejpam-3517	75	10	eur	eur	PROPN
ejpam-3517	75	11	.	.	PUNCT
ejpam-3517	76	1	j.	j.	PROPN
ejpam-3517	76	2	pure	pure	PROPN
ejpam-3517	76	3	appl	appl	PROPN
ejpam-3517	76	4	.	.	PROPN
ejpam-3517	76	5	math	math	PROPN
ejpam-3517	76	6	,	,	PUNCT
ejpam-3517	76	7	12	12	NUM
ejpam-3517	76	8	(	(	PUNCT
ejpam-3517	76	9	4	4	NUM
ejpam-3517	76	10	)	)	PUNCT
ejpam-3517	76	11	(	(	PUNCT
ejpam-3517	76	12	2019	2019	NUM
ejpam-3517	76	13	)	)	PUNCT
ejpam-3517	76	14	,	,	PUNCT
ejpam-3517	76	15	1360	1360	NUM
ejpam-3517	76	16	-	-	SYM
ejpam-3517	76	17	1370	1370	NUM
ejpam-3517	76	18	1363	1363	NUM
ejpam-3517	76	19	(	(	PUNCT
ejpam-3517	76	20	c	c	NOUN
ejpam-3517	76	21	)	)	PUNCT
ejpam-3517	76	22	for	for	ADP
ejpam-3517	76	23	a	a	DET
ejpam-3517	76	24	nonsingular	nonsingular	ADJ
ejpam-3517	76	25	matrix	matrix	NOUN
ejpam-3517	76	26	b	b	PROPN
ejpam-3517	76	27	∈	∈	PROPN
ejpam-3517	76	28	rn×n	rn×n	NOUN
ejpam-3517	76	29	,	,	PUNCT
ejpam-3517	76	30	vector	vector	NOUN
ejpam-3517	76	31	b−1x∗	b−1x∗	PROPN
ejpam-3517	76	32	is	be	AUX
ejpam-3517	76	33	a	a	DET
ejpam-3517	76	34	solution	solution	NOUN
ejpam-3517	76	35	of	of	ADP
ejpam-3517	76	36	min	min	PROPN
ejpam-3517	76	37	x∈rn	x∈rn	PROPN
ejpam-3517	76	38	‖b−abx‖p	‖b−abx‖p	PROPN
ejpam-3517	76	39	.	.	PROPN
ejpam-3517	77	1	(	(	PUNCT
ejpam-3517	77	2	8)	8)	NUM
ejpam-3517	77	3	proof	proof	NOUN
ejpam-3517	77	4	.	.	PUNCT
ejpam-3517	78	1	let	let	VERB
ejpam-3517	78	2	us	we	PRON
ejpam-3517	78	3	discuss	discuss	VERB
ejpam-3517	78	4	:	:	PUNCT
ejpam-3517	78	5	(	(	PUNCT
ejpam-3517	78	6	a	a	X
ejpam-3517	78	7	)	)	PUNCT
ejpam-3517	78	8	let	let	VERB
ejpam-3517	78	9	y∗	y∗	ADV
ejpam-3517	78	10	be	be	AUX
ejpam-3517	78	11	a	a	DET
ejpam-3517	78	12	solution	solution	NOUN
ejpam-3517	78	13	of	of	ADP
ejpam-3517	78	14	(	(	PUNCT
ejpam-3517	78	15	6	6	NUM
ejpam-3517	78	16	)	)	PUNCT
ejpam-3517	78	17	.	.	PUNCT
ejpam-3517	79	1	then	then	ADV
ejpam-3517	79	2	‖b+av	‖b+av	VERB
ejpam-3517	79	3	−ay∗‖p	−ay∗‖p	SYM
ejpam-3517	79	4	=	=	SYM
ejpam-3517	79	5	‖b−a(y∗	‖b−a(y∗	PROPN
ejpam-3517	80	1	−	−	PROPN
ejpam-3517	81	1	v)‖p	v)‖p	VERB
ejpam-3517	81	2	≥	≥	PRON
ejpam-3517	81	3	‖b−ax∗‖p	‖b−ax∗‖p	NOUN
ejpam-3517	81	4	,	,	PUNCT
ejpam-3517	81	5	(	(	PUNCT
ejpam-3517	81	6	9	9	X
ejpam-3517	81	7	)	)	PUNCT
ejpam-3517	81	8	whereby	whereby	SCONJ
ejpam-3517	81	9	the	the	DET
ejpam-3517	81	10	equation	equation	NOUN
ejpam-3517	81	11	is	be	AUX
ejpam-3517	81	12	only	only	ADV
ejpam-3517	81	13	if	if	SCONJ
ejpam-3517	81	14	y∗	y∗	PROPN
ejpam-3517	81	15	−	−	NOUN
ejpam-3517	81	16	v	v	NOUN
ejpam-3517	81	17	=	=	SYM
ejpam-3517	81	18	x∗.	x∗.	PROPN
ejpam-3517	82	1	(	(	PUNCT
ejpam-3517	82	2	b	b	NOUN
ejpam-3517	82	3	)	)	PUNCT
ejpam-3517	82	4	for	for	ADP
ejpam-3517	82	5	c	c	NOUN
ejpam-3517	82	6	=	=	SYM
ejpam-3517	82	7	0	0	NOUN
ejpam-3517	83	1	the	the	DET
ejpam-3517	83	2	assertion	assertion	NOUN
ejpam-3517	83	3	is	be	AUX
ejpam-3517	83	4	obvious	obvious	ADJ
ejpam-3517	83	5	.	.	PUNCT
ejpam-3517	84	1	let	let	VERB
ejpam-3517	84	2	c	c	NOUN
ejpam-3517	84	3	6=	6=	ADP
ejpam-3517	84	4	0	0	NUM
ejpam-3517	84	5	,	,	PUNCT
ejpam-3517	84	6	and	and	CCONJ
ejpam-3517	84	7	y∗	y∗	ADV
ejpam-3517	84	8	such	such	ADJ
ejpam-3517	84	9	that	that	PRON
ejpam-3517	84	10	is	be	AUX
ejpam-3517	84	11	a	a	DET
ejpam-3517	84	12	solution	solution	NOUN
ejpam-3517	84	13	of	of	ADP
ejpam-3517	84	14	(	(	PUNCT
ejpam-3517	84	15	7	7	NUM
ejpam-3517	84	16	)	)	PUNCT
ejpam-3517	84	17	.	.	PUNCT
ejpam-3517	85	1	then	then	ADV
ejpam-3517	85	2	‖cb−ay∗‖p	‖cb−ay∗‖p	PROPN
ejpam-3517	85	3	=	=	PROPN
ejpam-3517	85	4	|c|	|c|	PROPN
ejpam-3517	85	5	∥∥∥∥b−a(y∗c	∥∥∥∥b−a(y∗c	NUM
ejpam-3517	85	6	)	)	PUNCT
ejpam-3517	85	7	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3517	86	1	p	p	X
ejpam-3517	86	2	≥	≥	X
ejpam-3517	86	3	|c|‖b−ax∗‖p	|c|‖b−ax∗‖p	NOUN
ejpam-3517	86	4	,	,	PUNCT
ejpam-3517	86	5	(	(	PUNCT
ejpam-3517	86	6	10	10	NUM
ejpam-3517	86	7	)	)	PUNCT
ejpam-3517	86	8	whereby	whereby	SCONJ
ejpam-3517	86	9	the	the	DET
ejpam-3517	86	10	equation	equation	NOUN
ejpam-3517	86	11	is	be	AUX
ejpam-3517	86	12	only	only	ADV
ejpam-3517	86	13	if	if	SCONJ
ejpam-3517	86	14	y∗	y∗	PROPN
ejpam-3517	86	15	c	c	NOUN
ejpam-3517	86	16	=	=	SYM
ejpam-3517	86	17	x∗.	x∗.	PROPN
ejpam-3517	87	1	(	(	PUNCT
ejpam-3517	87	2	c	c	X
ejpam-3517	87	3	)	)	PUNCT
ejpam-3517	87	4	let	let	VERB
ejpam-3517	87	5	y∗	y∗	ADV
ejpam-3517	87	6	be	be	AUX
ejpam-3517	87	7	a	a	DET
ejpam-3517	87	8	solution	solution	NOUN
ejpam-3517	87	9	of	of	ADP
ejpam-3517	87	10	(	(	PUNCT
ejpam-3517	87	11	8)	8)	NUM
ejpam-3517	87	12	.	.	PUNCT
ejpam-3517	88	1	then	then	ADV
ejpam-3517	88	2	‖b−aby∗‖p	‖b−aby∗‖p	PROPN
ejpam-3517	88	3	≥	≥	NOUN
ejpam-3517	88	4	‖b−ax∗‖p	‖b−ax∗‖p	NOUN
ejpam-3517	88	5	,	,	PUNCT
ejpam-3517	88	6	(	(	PUNCT
ejpam-3517	88	7	11	11	NUM
ejpam-3517	88	8	)	)	PUNCT
ejpam-3517	88	9	whereby	whereby	SCONJ
ejpam-3517	88	10	the	the	DET
ejpam-3517	88	11	equation	equation	NOUN
ejpam-3517	88	12	is	be	AUX
ejpam-3517	88	13	only	only	ADV
ejpam-3517	88	14	if	if	SCONJ
ejpam-3517	88	15	by∗	by∗	NOUN
ejpam-3517	88	16	=	=	SYM
ejpam-3517	88	17	x∗.	x∗.	NOUN
ejpam-3517	88	18	corollary	corollary	ADJ
ejpam-3517	88	19	1	1	X
ejpam-3517	88	20	.	.	PUNCT
ejpam-3517	89	1	let	let	VERB
ejpam-3517	89	2	a	a	DET
ejpam-3517	89	3	∈	∈	PROPN
ejpam-3517	89	4	rm×n	rm×n	NOUN
ejpam-3517	89	5	,	,	PUNCT
ejpam-3517	89	6	m	m	VERB
ejpam-3517	89	7	>	>	X
ejpam-3517	89	8	n	n	CCONJ
ejpam-3517	89	9	,	,	PUNCT
ejpam-3517	89	10	b	b	PROPN
ejpam-3517	89	11	∈	∈	PROPN
ejpam-3517	89	12	rm	rm	NOUN
ejpam-3517	89	13	,	,	PUNCT
ejpam-3517	89	14	and	and	CCONJ
ejpam-3517	89	15	x∗	x∗	PROPN
ejpam-3517	89	16	∈	∈	PROPN
ejpam-3517	90	1	rn	rn	PROPN
ejpam-3517	90	2	such	such	ADJ
ejpam-3517	90	3	that	that	SCONJ
ejpam-3517	90	4	fp(x	fp(x	PUNCT
ejpam-3517	90	5	∗	∗	NOUN
ejpam-3517	90	6	)	)	PUNCT
ejpam-3517	91	1	=	=	SYM
ejpam-3517	91	2	min	min	NOUN
ejpam-3517	91	3	x∈rn	x∈rn	PROPN
ejpam-3517	91	4	‖b−ax‖p	‖b−ax‖p	PROPN
ejpam-3517	91	5	,	,	PUNCT
ejpam-3517	91	6	p	p	NOUN
ejpam-3517	91	7	∈	∈	PROPN
ejpam-3517	92	1	[	[	X
ejpam-3517	92	2	1,∞	1,∞	NUM
ejpam-3517	92	3	〉	〉	NUM
ejpam-3517	92	4	.	.	PUNCT
ejpam-3517	93	1	(	(	PUNCT
ejpam-3517	93	2	12	12	NUM
ejpam-3517	93	3	)	)	PUNCT
ejpam-3517	93	4	then	then	ADV
ejpam-3517	93	5	for	for	ADP
ejpam-3517	93	6	an	an	DET
ejpam-3517	93	7	arbitrary	arbitrary	ADJ
ejpam-3517	93	8	v	v	ADP
ejpam-3517	93	9	∈	∈	PROPN
ejpam-3517	93	10	rn	rn	PROPN
ejpam-3517	93	11	,	,	PUNCT
ejpam-3517	93	12	c	c	PROPN
ejpam-3517	93	13	∈	∈	PROPN
ejpam-3517	93	14	r	r	NOUN
ejpam-3517	93	15	,	,	PUNCT
ejpam-3517	93	16	and	and	CCONJ
ejpam-3517	93	17	nonsingular	nonsingular	ADJ
ejpam-3517	93	18	matrix	matrix	NOUN
ejpam-3517	93	19	b	b	PROPN
ejpam-3517	93	20	∈	∈	PROPN
ejpam-3517	93	21	rn×n	rn×n	NOUN
ejpam-3517	93	22	,	,	PUNCT
ejpam-3517	93	23	vector	vector	NOUN
ejpam-3517	93	24	cb−1(x∗	cb−1(x∗	NOUN
ejpam-3517	93	25	+	+	CCONJ
ejpam-3517	93	26	v	v	NOUN
ejpam-3517	93	27	)	)	PUNCT
ejpam-3517	93	28	is	be	AUX
ejpam-3517	93	29	a	a	DET
ejpam-3517	93	30	solution	solution	NOUN
ejpam-3517	93	31	of	of	ADP
ejpam-3517	93	32	min	min	NOUN
ejpam-3517	93	33	x∈rn	x∈rn	PROPN
ejpam-3517	93	34	‖c(b+av)−abx‖p	‖c(b+av)−abx‖p	PROPN
ejpam-3517	93	35	.	.	PUNCT
ejpam-3517	94	1	(	(	PUNCT
ejpam-3517	94	2	13	13	NUM
ejpam-3517	94	3	)	)	PUNCT
ejpam-3517	94	4	3	3	NUM
ejpam-3517	94	5	.	.	PUNCT
ejpam-3517	94	6	weighted	weight	VERB
ejpam-3517	94	7	mean	mean	ADV
ejpam-3517	94	8	and	and	CCONJ
ejpam-3517	94	9	weighted	weight	VERB
ejpam-3517	94	10	median	median	NOUN
ejpam-3517	94	11	of	of	ADP
ejpam-3517	94	12	the	the	DET
ejpam-3517	94	13	data	datum	NOUN
ejpam-3517	94	14	in	in	ADP
ejpam-3517	94	15	this	this	DET
ejpam-3517	94	16	section	section	NOUN
ejpam-3517	94	17	we	we	PRON
ejpam-3517	94	18	will	will	AUX
ejpam-3517	94	19	illustrate	illustrate	VERB
ejpam-3517	94	20	the	the	DET
ejpam-3517	94	21	equivariant	equivariant	ADJ
ejpam-3517	94	22	properties	property	NOUN
ejpam-3517	94	23	of	of	ADP
ejpam-3517	94	24	the	the	DET
ejpam-3517	94	25	weighted	weight	VERB
ejpam-3517	94	26	mean	mean	NOUN
ejpam-3517	94	27	and	and	CCONJ
ejpam-3517	94	28	weighted	weight	VERB
ejpam-3517	94	29	median	median	NOUN
ejpam-3517	94	30	of	of	ADP
ejpam-3517	94	31	the	the	DET
ejpam-3517	94	32	data	datum	NOUN
ejpam-3517	94	33	.	.	PUNCT
ejpam-3517	95	1	as	as	SCONJ
ejpam-3517	95	2	we	we	PRON
ejpam-3517	95	3	mentioned	mention	VERB
ejpam-3517	95	4	,	,	PUNCT
ejpam-3517	95	5	the	the	DET
ejpam-3517	95	6	problem	problem	NOUN
ejpam-3517	95	7	of	of	ADP
ejpam-3517	95	8	the	the	DET
ejpam-3517	95	9	weighted	weight	VERB
ejpam-3517	95	10	mean	mean	NOUN
ejpam-3517	95	11	and	and	CCONJ
ejpam-3517	95	12	weighted	weight	VERB
ejpam-3517	95	13	median	median	NOUN
ejpam-3517	95	14	are	be	AUX
ejpam-3517	95	15	essentially	essentially	ADV
ejpam-3517	95	16	reduced	reduce	VERB
ejpam-3517	95	17	to	to	ADP
ejpam-3517	95	18	solving	solve	VERB
ejpam-3517	95	19	an	an	DET
ejpam-3517	95	20	overdetermined	overdetermine	VERB
ejpam-3517	95	21	system	system	NOUN
ejpam-3517	95	22	of	of	ADP
ejpam-3517	95	23	linear	linear	PROPN
ejpam-3517	95	24	equations	equation	NOUN
ejpam-3517	95	25	.	.	PUNCT
ejpam-3517	96	1	numerous	numerous	ADJ
ejpam-3517	96	2	applications	application	NOUN
ejpam-3517	96	3	of	of	ADP
ejpam-3517	96	4	this	this	DET
ejpam-3517	96	5	problem	problem	NOUN
ejpam-3517	96	6	can	can	AUX
ejpam-3517	96	7	be	be	AUX
ejpam-3517	96	8	found	find	VERB
ejpam-3517	96	9	in	in	ADP
ejpam-3517	96	10	various	various	ADJ
ejpam-3517	96	11	branches	branch	NOUN
ejpam-3517	96	12	of	of	ADP
ejpam-3517	96	13	applied	apply	VERB
ejpam-3517	96	14	research	research	NOUN
ejpam-3517	96	15	,	,	PUNCT
ejpam-3517	96	16	like	like	ADP
ejpam-3517	96	17	image	image	NOUN
ejpam-3517	96	18	processing	processing	NOUN
ejpam-3517	96	19	[	[	X
ejpam-3517	96	20	10	10	NUM
ejpam-3517	96	21	]	]	PUNCT
ejpam-3517	96	22	,	,	PUNCT
ejpam-3517	96	23	or	or	CCONJ
ejpam-3517	96	24	methods	method	NOUN
ejpam-3517	96	25	for	for	ADP
ejpam-3517	96	26	outlier	outlier	ADJ
ejpam-3517	96	27	detection	detection	NOUN
ejpam-3517	96	28	[	[	X
ejpam-3517	96	29	11	11	NUM
ejpam-3517	96	30	]	]	PUNCT
ejpam-3517	96	31	.	.	PUNCT
ejpam-3517	97	1	let	let	VERB
ejpam-3517	97	2	a	a	DET
ejpam-3517	97	3	∈	∈	PROPN
ejpam-3517	97	4	rm	rm	NOUN
ejpam-3517	97	5	be	be	AUX
ejpam-3517	97	6	the	the	DET
ejpam-3517	97	7	vector	vector	NOUN
ejpam-3517	97	8	data	datum	NOUN
ejpam-3517	97	9	with	with	ADP
ejpam-3517	97	10	corresponding	correspond	VERB
ejpam-3517	97	11	positive	positive	ADJ
ejpam-3517	97	12	vector	vector	NOUN
ejpam-3517	97	13	data	datum	NOUN
ejpam-3517	97	14	weights	weight	VERB
ejpam-3517	97	15	w	w	PROPN
ejpam-3517	97	16	∈	∈	PROPN
ejpam-3517	97	17	rm	rm	NOUN
ejpam-3517	98	1	+	+	X
ejpam-3517	98	2	.	.	PUNCT
ejpam-3517	99	1	if	if	SCONJ
ejpam-3517	99	2	we	we	PRON
ejpam-3517	99	3	denote	denote	VERB
ejpam-3517	99	4	by	by	ADP
ejpam-3517	99	5	a	a	DET
ejpam-3517	99	6	=	=	X
ejpam-3517	99	7	[	[	PUNCT
ejpam-3517	99	8	p	p	NOUN
ejpam-3517	99	9	√	√	PROPN
ejpam-3517	99	10	w1	w1	NOUN
ejpam-3517	99	11	,	,	PUNCT
ejpam-3517	99	12	.	.	PUNCT
ejpam-3517	99	13	.	.	PUNCT
ejpam-3517	100	1	.	.	PUNCT
ejpam-3517	101	1	,	,	PUNCT
ejpam-3517	101	2	p	p	NOUN
ejpam-3517	101	3	√	√	PROPN
ejpam-3517	101	4	wm]t	wm]t	PROPN
ejpam-3517	101	5	and	and	CCONJ
ejpam-3517	101	6	b	b	NOUN
ejpam-3517	102	1	=	=	PUNCT
ejpam-3517	102	2	[	[	PUNCT
ejpam-3517	102	3	p	p	NOUN
ejpam-3517	102	4	√	√	NUM
ejpam-3517	102	5	w1a1	w1a1	NOUN
ejpam-3517	102	6	,	,	PUNCT
ejpam-3517	102	7	.	.	PUNCT
ejpam-3517	102	8	.	.	PUNCT
ejpam-3517	103	1	.	.	PUNCT
ejpam-3517	104	1	,	,	PUNCT
ejpam-3517	105	1	p	p	NOUN
ejpam-3517	105	2	√	√	PROPN
ejpam-3517	105	3	wmam]t	wmam]t	PROPN
ejpam-3517	105	4	in	in	ADP
ejpam-3517	105	5	function	function	NOUN
ejpam-3517	105	6	fp	fp	X
ejpam-3517	105	7	:	:	PUNCT
ejpam-3517	105	8	r→	r→	PROPN
ejpam-3517	105	9	r	r	NOUN
ejpam-3517	105	10	,	,	PUNCT
ejpam-3517	105	11	where	where	SCONJ
ejpam-3517	105	12	n	n	NOUN
ejpam-3517	105	13	=	=	SYM
ejpam-3517	105	14	1	1	NUM
ejpam-3517	105	15	,	,	PUNCT
ejpam-3517	105	16	then	then	ADV
ejpam-3517	105	17	follows	follow	VERB
ejpam-3517	105	18	that	that	SCONJ
ejpam-3517	105	19	f2(x	f2(x	PROPN
ejpam-3517	105	20	)	)	PUNCT
ejpam-3517	105	21	=	=	PUNCT
ejpam-3517	106	1	‖b−ax‖2	‖b−ax‖2	PUNCT
ejpam-3517	106	2	=	=	PUNCT
ejpam-3517	106	3	√√√√	√√√√	PRON
ejpam-3517	106	4	m∑	m∑	NOUN
ejpam-3517	106	5	i=1	i=1	NOUN
ejpam-3517	106	6	wi(ai	wi(ai	ADJ
ejpam-3517	106	7	−	−	ADP
ejpam-3517	106	8	x)2	x)2	NOUN
ejpam-3517	106	9	,	,	PUNCT
ejpam-3517	106	10	(	(	PUNCT
ejpam-3517	106	11	14	14	NUM
ejpam-3517	106	12	)	)	PUNCT
ejpam-3517	106	13	v.	v.	CCONJ
ejpam-3517	106	14	novoselac	novoselac	PROPN
ejpam-3517	106	15	,	,	PUNCT
ejpam-3517	106	16	z.	z.	PROPN
ejpam-3517	106	17	pavić	pavić	PROPN
ejpam-3517	106	18	/	/	SYM
ejpam-3517	106	19	eur	eur	PROPN
ejpam-3517	106	20	.	.	PUNCT
ejpam-3517	107	1	j.	j.	PROPN
ejpam-3517	107	2	pure	pure	PROPN
ejpam-3517	107	3	appl	appl	PROPN
ejpam-3517	107	4	.	.	PROPN
ejpam-3517	107	5	math	math	PROPN
ejpam-3517	107	6	,	,	PUNCT
ejpam-3517	107	7	12	12	NUM
ejpam-3517	107	8	(	(	PUNCT
ejpam-3517	107	9	4	4	NUM
ejpam-3517	107	10	)	)	PUNCT
ejpam-3517	107	11	(	(	PUNCT
ejpam-3517	107	12	2019	2019	NUM
ejpam-3517	107	13	)	)	PUNCT
ejpam-3517	107	14	,	,	PUNCT
ejpam-3517	107	15	1360	1360	NUM
ejpam-3517	107	16	-	-	SYM
ejpam-3517	107	17	1370	1370	NUM
ejpam-3517	107	18	1364	1364	NUM
ejpam-3517	107	19	is	be	AUX
ejpam-3517	107	20	convex	convex	ADJ
ejpam-3517	107	21	and	and	CCONJ
ejpam-3517	107	22	attains	attain	VERB
ejpam-3517	107	23	its	its	PRON
ejpam-3517	107	24	global	global	ADJ
ejpam-3517	107	25	minimum	minimum	NOUN
ejpam-3517	107	26	on	on	ADP
ejpam-3517	107	27	the	the	DET
ejpam-3517	107	28	set	set	NOUN
ejpam-3517	107	29	r	r	NOUN
ejpam-3517	107	30	,	,	PUNCT
ejpam-3517	107	31	which	which	PRON
ejpam-3517	107	32	is	be	AUX
ejpam-3517	107	33	denoted	denote	VERB
ejpam-3517	107	34	by	by	ADP
ejpam-3517	107	35	x∗	x∗	PROPN
ejpam-3517	107	36	=	=	SYM
ejpam-3517	107	37	mean(w	mean(w	PROPN
ejpam-3517	107	38	,	,	PUNCT
ejpam-3517	107	39	a	a	PRON
ejpam-3517	107	40	)	)	PUNCT
ejpam-3517	107	41	and	and	CCONJ
ejpam-3517	107	42	called	call	VERB
ejpam-3517	107	43	the	the	DET
ejpam-3517	107	44	weighted	weight	VERB
ejpam-3517	107	45	mean	mean	NOUN
ejpam-3517	107	46	of	of	ADP
ejpam-3517	107	47	the	the	DET
ejpam-3517	107	48	data	datum	NOUN
ejpam-3517	107	49	.	.	PUNCT
ejpam-3517	108	1	if	if	SCONJ
ejpam-3517	108	2	w1	w1	NOUN
ejpam-3517	108	3	=	=	SYM
ejpam-3517	108	4	·	·	PUNCT
ejpam-3517	108	5	·	·	PUNCT
ejpam-3517	108	6	·	·	PUNCT
ejpam-3517	109	1	=	=	PUNCT
ejpam-3517	109	2	wm	wm	PROPN
ejpam-3517	109	3	=	=	SYM
ejpam-3517	109	4	1	1	NUM
ejpam-3517	109	5	,	,	PUNCT
ejpam-3517	109	6	the	the	DET
ejpam-3517	109	7	global	global	ADJ
ejpam-3517	109	8	minimum	minimum	NOUN
ejpam-3517	109	9	of	of	ADP
ejpam-3517	109	10	the	the	DET
ejpam-3517	109	11	corresponding	corresponding	ADJ
ejpam-3517	109	12	functional	functional	ADJ
ejpam-3517	109	13	(	(	PUNCT
ejpam-3517	109	14	14	14	NUM
ejpam-3517	109	15	)	)	PUNCT
ejpam-3517	109	16	is	be	AUX
ejpam-3517	109	17	denoted	denote	VERB
ejpam-3517	109	18	by	by	ADP
ejpam-3517	109	19	x∗	x∗	PROPN
ejpam-3517	109	20	=	=	SYM
ejpam-3517	109	21	mean(a	mean(a	PROPN
ejpam-3517	109	22	)	)	PUNCT
ejpam-3517	109	23	and	and	CCONJ
ejpam-3517	109	24	called	call	VERB
ejpam-3517	109	25	the	the	DET
ejpam-3517	109	26	mean	mean	NOUN
ejpam-3517	109	27	of	of	ADP
ejpam-3517	109	28	the	the	DET
ejpam-3517	109	29	data	datum	NOUN
ejpam-3517	109	30	.	.	PUNCT
ejpam-3517	110	1	analogously	analogously	ADV
ejpam-3517	110	2	,	,	PUNCT
ejpam-3517	110	3	a	a	DET
ejpam-3517	110	4	real	real	ADJ
ejpam-3517	110	5	number	number	NOUN
ejpam-3517	110	6	which	which	PRON
ejpam-3517	110	7	minimizes	minimize	VERB
ejpam-3517	110	8	function	function	NOUN
ejpam-3517	110	9	f1(x	f1(x	NOUN
ejpam-3517	110	10	)	)	PUNCT
ejpam-3517	110	11	=	=	PUNCT
ejpam-3517	111	1	‖b−ax‖1	‖b−ax‖1	NOUN
ejpam-3517	111	2	=	=	PUNCT
ejpam-3517	111	3	m∑	m∑	NOUN
ejpam-3517	111	4	i=1	i=1	PROPN
ejpam-3517	111	5	wi|ai	wi|ai	PROPN
ejpam-3517	111	6	−	−	PROPN
ejpam-3517	111	7	x|	x|	PROPN
ejpam-3517	111	8	,	,	PUNCT
ejpam-3517	111	9	(	(	PUNCT
ejpam-3517	111	10	15	15	NUM
ejpam-3517	111	11	)	)	PUNCT
ejpam-3517	111	12	is	be	AUX
ejpam-3517	111	13	called	call	VERB
ejpam-3517	111	14	the	the	DET
ejpam-3517	111	15	weighted	weight	VERB
ejpam-3517	111	16	median	median	NOUN
ejpam-3517	111	17	of	of	ADP
ejpam-3517	111	18	the	the	DET
ejpam-3517	111	19	data	datum	NOUN
ejpam-3517	111	20	and	and	CCONJ
ejpam-3517	111	21	is	be	AUX
ejpam-3517	111	22	denoted	denote	VERB
ejpam-3517	111	23	by	by	ADP
ejpam-3517	111	24	x∗	x∗	PROPN
ejpam-3517	111	25	=	=	SYM
ejpam-3517	111	26	med(w	med(w	PROPN
ejpam-3517	111	27	,	,	PUNCT
ejpam-3517	111	28	a	a	PRON
ejpam-3517	111	29	)	)	PUNCT
ejpam-3517	111	30	.	.	PUNCT
ejpam-3517	112	1	if	if	SCONJ
ejpam-3517	112	2	w1	w1	NOUN
ejpam-3517	112	3	=	=	SYM
ejpam-3517	112	4	·	·	PUNCT
ejpam-3517	112	5	·	·	PUNCT
ejpam-3517	112	6	·	·	PUNCT
ejpam-3517	113	1	=	=	PUNCT
ejpam-3517	113	2	wm	wm	PROPN
ejpam-3517	113	3	=	=	SYM
ejpam-3517	113	4	1	1	NUM
ejpam-3517	113	5	,	,	PUNCT
ejpam-3517	113	6	the	the	DET
ejpam-3517	113	7	global	global	ADJ
ejpam-3517	113	8	minimum	minimum	NOUN
ejpam-3517	113	9	of	of	ADP
ejpam-3517	113	10	the	the	DET
ejpam-3517	113	11	corresponding	correspond	VERB
ejpam-3517	113	12	function	function	NOUN
ejpam-3517	113	13	(	(	PUNCT
ejpam-3517	113	14	15	15	NUM
ejpam-3517	113	15	)	)	PUNCT
ejpam-3517	113	16	is	be	AUX
ejpam-3517	113	17	denoted	denote	VERB
ejpam-3517	113	18	by	by	ADP
ejpam-3517	113	19	x∗	x∗	PROPN
ejpam-3517	113	20	=	=	SYM
ejpam-3517	113	21	med(a	med(a	PROPN
ejpam-3517	113	22	)	)	PUNCT
ejpam-3517	113	23	and	and	CCONJ
ejpam-3517	113	24	called	call	VERB
ejpam-3517	113	25	the	the	DET
ejpam-3517	113	26	median	median	NOUN
ejpam-3517	113	27	of	of	ADP
ejpam-3517	113	28	the	the	DET
ejpam-3517	113	29	data	datum	NOUN
ejpam-3517	113	30	.	.	PUNCT
ejpam-3517	114	1	in	in	ADP
ejpam-3517	114	2	the	the	DET
ejpam-3517	114	3	figure	figure	NOUN
ejpam-3517	114	4	2	2	NUM
ejpam-3517	114	5	we	we	PRON
ejpam-3517	114	6	present	present	VERB
ejpam-3517	114	7	the	the	DET
ejpam-3517	114	8	example	example	NOUN
ejpam-3517	114	9	of	of	ADP
ejpam-3517	114	10	function	function	NOUN
ejpam-3517	114	11	fp	fp	PROPN
ejpam-3517	114	12	,	,	PUNCT
ejpam-3517	114	13	for	for	ADP
ejpam-3517	114	14	p	p	NOUN
ejpam-3517	114	15	=	=	SYM
ejpam-3517	114	16	2	2	NUM
ejpam-3517	114	17	and	and	CCONJ
ejpam-3517	114	18	p	p	NOUN
ejpam-3517	114	19	=	=	SYM
ejpam-3517	114	20	1	1	NUM
ejpam-3517	114	21	norm	norm	NOUN
ejpam-3517	114	22	.	.	PUNCT
ejpam-3517	115	1	functions	function	NOUN
ejpam-3517	115	2	are	be	AUX
ejpam-3517	115	3	generated	generate	VERB
ejpam-3517	115	4	with	with	ADP
ejpam-3517	115	5	data	datum	NOUN
ejpam-3517	115	6	vector	vector	NOUN
ejpam-3517	115	7	a	a	PRON
ejpam-3517	115	8	=	=	SYM
ejpam-3517	116	1	[	[	X
ejpam-3517	116	2	1	1	NUM
ejpam-3517	116	3	,	,	PUNCT
ejpam-3517	116	4	2	2	NUM
ejpam-3517	116	5	,	,	PUNCT
ejpam-3517	116	6	3	3	NUM
ejpam-3517	116	7	,	,	PUNCT
ejpam-3517	116	8	4	4	NUM
ejpam-3517	116	9	,	,	PUNCT
ejpam-3517	116	10	5]t	5]t	NUM
ejpam-3517	116	11	and	and	CCONJ
ejpam-3517	116	12	corresponding	correspond	VERB
ejpam-3517	116	13	weights	weight	NOUN
ejpam-3517	116	14	vector	vector	NOUN
ejpam-3517	117	1	w	w	NOUN
ejpam-3517	117	2	=	=	PUNCT
ejpam-3517	118	1	[	[	X
ejpam-3517	118	2	1	1	NUM
ejpam-3517	118	3	,	,	PUNCT
ejpam-3517	118	4	1	1	NUM
ejpam-3517	118	5	,	,	PUNCT
ejpam-3517	118	6	2	2	NUM
ejpam-3517	118	7	,	,	PUNCT
ejpam-3517	118	8	1	1	NUM
ejpam-3517	118	9	,	,	PUNCT
ejpam-3517	118	10	1]t	1]t	NUM
ejpam-3517	118	11	presented	present	VERB
ejpam-3517	118	12	in	in	ADP
ejpam-3517	118	13	figure	figure	NOUN
ejpam-3517	118	14	2(a	2(a	NUM
ejpam-3517	118	15	)	)	PUNCT
ejpam-3517	118	16	for	for	ADP
ejpam-3517	118	17	p	p	NOUN
ejpam-3517	118	18	=	=	SYM
ejpam-3517	118	19	2	2	NUM
ejpam-3517	118	20	,	,	PUNCT
ejpam-3517	118	21	and	and	CCONJ
ejpam-3517	118	22	for	for	ADP
ejpam-3517	118	23	p=1	p=1	PROPN
ejpam-3517	118	24	in	in	ADP
ejpam-3517	118	25	figure	figure	NOUN
ejpam-3517	118	26	2(b	2(b	NUM
ejpam-3517	118	27	)	)	PUNCT
ejpam-3517	118	28	.	.	PUNCT
ejpam-3517	119	1	in	in	ADP
ejpam-3517	119	2	theorem	theorem	NOUN
ejpam-3517	119	3	4	4	NUM
ejpam-3517	119	4	it	it	PRON
ejpam-3517	119	5	is	be	AUX
ejpam-3517	119	6	shown	show	VERB
ejpam-3517	119	7	that	that	SCONJ
ejpam-3517	119	8	the	the	DET
ejpam-3517	119	9	minimum	minimum	NOUN
ejpam-3517	119	10	of	of	ADP
ejpam-3517	119	11	the	the	DET
ejpam-3517	119	12	function	function	NOUN
ejpam-3517	119	13	f2	f2	PROPN
ejpam-3517	119	14	,	,	PUNCT
ejpam-3517	119	15	i.e.	i.e.	X
ejpam-3517	119	16	weighted	weight	VERB
ejpam-3517	119	17	mean	mean	ADJ
ejpam-3517	119	18	,	,	PUNCT
ejpam-3517	119	19	always	always	ADV
ejpam-3517	119	20	achieved	achieve	VERB
ejpam-3517	119	21	unique	unique	ADJ
ejpam-3517	119	22	minimum	minimum	NOUN
ejpam-3517	119	23	.	.	PUNCT
ejpam-3517	120	1	considering	consider	VERB
ejpam-3517	120	2	the	the	DET
ejpam-3517	120	3	different	different	ADJ
ejpam-3517	120	4	data	datum	NOUN
ejpam-3517	120	5	weights	weight	VERB
ejpam-3517	120	6	w	w	NOUN
ejpam-3517	120	7	=	=	PUNCT
ejpam-3517	121	1	[	[	X
ejpam-3517	121	2	1	1	NUM
ejpam-3517	121	3	,	,	PUNCT
ejpam-3517	121	4	3	3	NUM
ejpam-3517	121	5	,	,	PUNCT
ejpam-3517	121	6	2	2	NUM
ejpam-3517	121	7	,	,	PUNCT
ejpam-3517	121	8	1	1	NUM
ejpam-3517	121	9	,	,	PUNCT
ejpam-3517	121	10	1]t	1]t	NUM
ejpam-3517	121	11	,	,	PUNCT
ejpam-3517	121	12	presented	present	VERB
ejpam-3517	121	13	in	in	ADP
ejpam-3517	121	14	figure	figure	NOUN
ejpam-3517	121	15	2(c	2(c	NUM
ejpam-3517	121	16	)	)	PUNCT
ejpam-3517	121	17	,	,	PUNCT
ejpam-3517	121	18	it	it	PRON
ejpam-3517	121	19	can	can	AUX
ejpam-3517	121	20	be	be	AUX
ejpam-3517	121	21	seen	see	VERB
ejpam-3517	121	22	that	that	SCONJ
ejpam-3517	121	23	the	the	DET
ejpam-3517	121	24	construction	construction	NOUN
ejpam-3517	121	25	of	of	ADP
ejpam-3517	121	26	the	the	DET
ejpam-3517	121	27	minimum	minimum	NOUN
ejpam-3517	121	28	of	of	ADP
ejpam-3517	121	29	f1	f1	NOUN
ejpam-3517	121	30	,	,	PUNCT
ejpam-3517	121	31	i.e.	i.e.	X
ejpam-3517	121	32	weighted	weighted	ADJ
ejpam-3517	121	33	median	median	NOUN
ejpam-3517	121	34	,	,	PUNCT
ejpam-3517	121	35	directly	directly	ADV
ejpam-3517	121	36	depends	depend	VERB
ejpam-3517	121	37	on	on	ADP
ejpam-3517	121	38	it	it	PRON
ejpam-3517	121	39	,	,	PUNCT
ejpam-3517	121	40	and	and	CCONJ
ejpam-3517	121	41	achieved	achieve	VERB
ejpam-3517	121	42	its	its	PRON
ejpam-3517	121	43	minimum	minimum	NOUN
ejpam-3517	121	44	on	on	ADP
ejpam-3517	121	45	interval	interval	NOUN
ejpam-3517	121	46	[	[	X
ejpam-3517	121	47	a(2	a(2	NOUN
ejpam-3517	121	48	)	)	PUNCT
ejpam-3517	121	49	,	,	PUNCT
ejpam-3517	121	50	a(3	a(3	PROPN
ejpam-3517	121	51	)	)	PUNCT
ejpam-3517	121	52	]	]	PUNCT
ejpam-3517	121	53	,	,	PUNCT
ejpam-3517	121	54	in	in	ADP
ejpam-3517	121	55	contrast	contrast	NOUN
ejpam-3517	121	56	to	to	ADP
ejpam-3517	121	57	the	the	DET
ejpam-3517	121	58	situation	situation	NOUN
ejpam-3517	121	59	in	in	ADP
ejpam-3517	121	60	figure	figure	NOUN
ejpam-3517	121	61	2(b	2(b	NUM
ejpam-3517	121	62	)	)	PUNCT
ejpam-3517	121	63	where	where	SCONJ
ejpam-3517	121	64	the	the	DET
ejpam-3517	121	65	minimum	minimum	NOUN
ejpam-3517	121	66	is	be	AUX
ejpam-3517	121	67	unique	unique	ADJ
ejpam-3517	121	68	.	.	PUNCT
ejpam-3517	122	1	also	also	ADV
ejpam-3517	122	2	,	,	PUNCT
ejpam-3517	122	3	it	it	PRON
ejpam-3517	122	4	can	can	AUX
ejpam-3517	122	5	be	be	AUX
ejpam-3517	122	6	seen	see	VERB
ejpam-3517	122	7	that	that	SCONJ
ejpam-3517	122	8	function	function	NOUN
ejpam-3517	122	9	f1	f1	NOUN
ejpam-3517	122	10	is	be	AUX
ejpam-3517	122	11	a	a	DET
ejpam-3517	122	12	piecewise	piecewise	NOUN
ejpam-3517	122	13	linear	linear	NOUN
ejpam-3517	122	14	function	function	NOUN
ejpam-3517	122	15	.	.	PUNCT
ejpam-3517	123	1	this	this	DET
ejpam-3517	123	2	property	property	NOUN
ejpam-3517	123	3	of	of	ADP
ejpam-3517	123	4	functional	functional	ADJ
ejpam-3517	123	5	f1	f1	NOUN
ejpam-3517	123	6	is	be	AUX
ejpam-3517	123	7	considered	consider	VERB
ejpam-3517	123	8	for	for	ADP
ejpam-3517	123	9	finding	find	VERB
ejpam-3517	123	10	a	a	DET
ejpam-3517	123	11	minimum	minimum	NOUN
ejpam-3517	123	12	,	,	PUNCT
ejpam-3517	123	13	where	where	SCONJ
ejpam-3517	123	14	details	detail	NOUN
ejpam-3517	123	15	are	be	AUX
ejpam-3517	123	16	presented	present	VERB
ejpam-3517	123	17	in	in	ADP
ejpam-3517	123	18	theorem	theorem	NOUN
ejpam-3517	123	19	5	5	NUM
ejpam-3517	123	20	.	.	PUNCT
ejpam-3517	124	1	in	in	ADP
ejpam-3517	124	2	the	the	DET
ejpam-3517	124	3	sequel	sequel	NOUN
ejpam-3517	124	4	we	we	PRON
ejpam-3517	124	5	give	give	VERB
ejpam-3517	124	6	solutions	solution	NOUN
ejpam-3517	124	7	for	for	ADP
ejpam-3517	124	8	minimizing	minimize	VERB
ejpam-3517	124	9	problems	problem	NOUN
ejpam-3517	124	10	(	(	PUNCT
ejpam-3517	124	11	14	14	NUM
ejpam-3517	124	12	)	)	PUNCT
ejpam-3517	124	13	and	and	CCONJ
ejpam-3517	124	14	(	(	PUNCT
ejpam-3517	124	15	15	15	NUM
ejpam-3517	124	16	)	)	PUNCT
ejpam-3517	124	17	,	,	PUNCT
ejpam-3517	124	18	i.e.	i.e.	X
ejpam-3517	124	19	for	for	ADP
ejpam-3517	124	20	the	the	DET
ejpam-3517	124	21	weighted	weight	VERB
ejpam-3517	124	22	mean	mean	NOUN
ejpam-3517	124	23	and	and	CCONJ
ejpam-3517	124	24	weighted	weight	VERB
ejpam-3517	124	25	median	median	NOUN
ejpam-3517	124	26	of	of	ADP
ejpam-3517	124	27	the	the	DET
ejpam-3517	124	28	data	datum	NOUN
ejpam-3517	124	29	.	.	PUNCT
ejpam-3517	125	1	2	2	NUM
ejpam-3517	125	2	4	4	NUM
ejpam-3517	125	3	6	6	NUM
ejpam-3517	125	4	8	8	NUM
ejpam-3517	125	5	y	y	NOUN
ejpam-3517	125	6	x	x	NOUN
ejpam-3517	125	7	f2	f2	NOUN
ejpam-3517	125	8	x∗	x∗	PROPN
ejpam-3517	125	9	=	=	SYM
ejpam-3517	125	10	mean(w	mean(w	PROPN
ejpam-3517	125	11	,	,	PUNCT
ejpam-3517	125	12	a	a	PRON
ejpam-3517	125	13	)	)	PUNCT
ejpam-3517	125	14	5	5	NUM
ejpam-3517	125	15	10	10	NUM
ejpam-3517	125	16	15	15	NUM
ejpam-3517	125	17	20	20	NUM
ejpam-3517	125	18	y	y	NOUN
ejpam-3517	125	19	x	x	PROPN
ejpam-3517	125	20	f1	f1	PROPN
ejpam-3517	125	21	a(1	a(1	NOUN
ejpam-3517	125	22	)	)	PUNCT
ejpam-3517	125	23	a(2	a(2	PROPN
ejpam-3517	125	24	)	)	PUNCT
ejpam-3517	125	25	a(3	a(3	PROPN
ejpam-3517	125	26	)	)	PUNCT
ejpam-3517	125	27	a(4	a(4	PROPN
ejpam-3517	125	28	)	)	PUNCT
ejpam-3517	125	29	a(5	a(5	NOUN
ejpam-3517	125	30	)	)	PUNCT
ejpam-3517	125	31	5	5	NUM
ejpam-3517	125	32	10	10	NUM
ejpam-3517	125	33	15	15	NUM
ejpam-3517	125	34	20	20	NUM
ejpam-3517	125	35	25	25	NUM
ejpam-3517	125	36	y	y	PROPN
ejpam-3517	125	37	x	x	PROPN
ejpam-3517	125	38	f1	f1	PROPN
ejpam-3517	125	39	a(1	a(1	NOUN
ejpam-3517	125	40	)	)	PUNCT
ejpam-3517	125	41	a(2	a(2	PROPN
ejpam-3517	125	42	)	)	PUNCT
ejpam-3517	125	43	a(3	a(3	PROPN
ejpam-3517	125	44	)	)	PUNCT
ejpam-3517	125	45	a(4	a(4	PROPN
ejpam-3517	125	46	)	)	PUNCT
ejpam-3517	125	47	a(5	a(5	PROPN
ejpam-3517	125	48	)	)	PUNCT
ejpam-3517	125	49	(	(	PUNCT
ejpam-3517	125	50	a	a	X
ejpam-3517	125	51	)	)	PUNCT
ejpam-3517	125	52	(	(	PUNCT
ejpam-3517	125	53	b	b	X
ejpam-3517	125	54	)	)	PUNCT
ejpam-3517	125	55	(	(	PUNCT
ejpam-3517	125	56	c	c	X
ejpam-3517	125	57	)	)	PUNCT
ejpam-3517	125	58	figure	figure	NOUN
ejpam-3517	125	59	2	2	NUM
ejpam-3517	125	60	:	:	PUNCT
ejpam-3517	125	61	function	function	VERB
ejpam-3517	125	62	fp	fp	X
ejpam-3517	125	63	:	:	PUNCT
ejpam-3517	125	64	r→	r→	PROPN
ejpam-3517	125	65	r.	r.	PROPN
ejpam-3517	125	66	theorem	theorem	VERB
ejpam-3517	125	67	4	4	X
ejpam-3517	125	68	.	.	PUNCT
ejpam-3517	126	1	let	let	VERB
ejpam-3517	126	2	a	a	DET
ejpam-3517	126	3	∈	∈	PROPN
ejpam-3517	126	4	rm	rm	NOUN
ejpam-3517	126	5	,	,	PUNCT
ejpam-3517	126	6	m	m	VERB
ejpam-3517	126	7	≥	≥	NOUN
ejpam-3517	126	8	2	2	NUM
ejpam-3517	126	9	,	,	PUNCT
ejpam-3517	126	10	be	be	AUX
ejpam-3517	126	11	the	the	DET
ejpam-3517	126	12	data	data	NOUN
ejpam-3517	126	13	vector	vector	NOUN
ejpam-3517	126	14	with	with	ADP
ejpam-3517	126	15	corresponding	corresponding	ADJ
ejpam-3517	126	16	data	datum	NOUN
ejpam-3517	126	17	weights	weight	NOUN
ejpam-3517	126	18	w	w	PROPN
ejpam-3517	126	19	∈	∈	PROPN
ejpam-3517	126	20	rm	rm	NOUN
ejpam-3517	127	1	+	+	X
ejpam-3517	127	2	.	.	PUNCT
ejpam-3517	128	1	then	then	ADV
ejpam-3517	128	2	mean(w	mean(w	PRON
ejpam-3517	128	3	,	,	PUNCT
ejpam-3517	128	4	a	a	PRON
ejpam-3517	128	5	)	)	PUNCT
ejpam-3517	128	6	=	=	SYM
ejpam-3517	128	7	1	1	NUM
ejpam-3517	128	8	w	w	NOUN
ejpam-3517	128	9	m∑	m∑	NOUN
ejpam-3517	128	10	i=1	i=1	PROPN
ejpam-3517	128	11	wiai	wiai	PROPN
ejpam-3517	128	12	,	,	PUNCT
ejpam-3517	128	13	w	w	NOUN
ejpam-3517	128	14	=	=	PUNCT
ejpam-3517	128	15	m∑	m∑	PROPN
ejpam-3517	128	16	i=1	i=1	PROPN
ejpam-3517	128	17	wi	wi	PROPN
ejpam-3517	128	18	.	.	PUNCT
ejpam-3517	129	1	(	(	PUNCT
ejpam-3517	129	2	16	16	NUM
ejpam-3517	129	3	)	)	PUNCT
ejpam-3517	129	4	proof	proof	NOUN
ejpam-3517	129	5	.	.	PUNCT
ejpam-3517	130	1	because	because	SCONJ
ejpam-3517	130	2	the	the	DET
ejpam-3517	130	3	functional	functional	ADJ
ejpam-3517	130	4	defined	define	VERB
ejpam-3517	130	5	by	by	ADP
ejpam-3517	130	6	(	(	PUNCT
ejpam-3517	130	7	14	14	NUM
ejpam-3517	130	8	)	)	PUNCT
ejpam-3517	130	9	is	be	AUX
ejpam-3517	130	10	derivable	derivable	ADJ
ejpam-3517	130	11	,	,	PUNCT
ejpam-3517	130	12	the	the	DET
ejpam-3517	130	13	minimum	minimum	NOUN
ejpam-3517	130	14	is	be	AUX
ejpam-3517	130	15	attained	attain	VERB
ejpam-3517	130	16	by	by	ADP
ejpam-3517	130	17	finding	find	VERB
ejpam-3517	130	18	a	a	DET
ejpam-3517	130	19	solution	solution	NOUN
ejpam-3517	130	20	of	of	ADP
ejpam-3517	130	21	∂f2(x	∂f2(x	NOUN
ejpam-3517	130	22	)	)	PUNCT
ejpam-3517	130	23	∂x	∂x	PROPN
ejpam-3517	130	24	=	=	SYM
ejpam-3517	131	1	0	0	PROPN
ejpam-3517	131	2	.	.	PUNCT
ejpam-3517	132	1	v.	v.	CCONJ
ejpam-3517	132	2	novoselac	novoselac	PROPN
ejpam-3517	132	3	,	,	PUNCT
ejpam-3517	132	4	z.	z.	PROPN
ejpam-3517	132	5	pavić	pavić	PROPN
ejpam-3517	132	6	/	/	SYM
ejpam-3517	132	7	eur	eur	PROPN
ejpam-3517	132	8	.	.	PUNCT
ejpam-3517	133	1	j.	j.	PROPN
ejpam-3517	133	2	pure	pure	PROPN
ejpam-3517	133	3	appl	appl	PROPN
ejpam-3517	133	4	.	.	PROPN
ejpam-3517	133	5	math	math	PROPN
ejpam-3517	133	6	,	,	PUNCT
ejpam-3517	133	7	12	12	NUM
ejpam-3517	133	8	(	(	PUNCT
ejpam-3517	133	9	4	4	NUM
ejpam-3517	133	10	)	)	PUNCT
ejpam-3517	133	11	(	(	PUNCT
ejpam-3517	133	12	2019	2019	NUM
ejpam-3517	133	13	)	)	PUNCT
ejpam-3517	133	14	,	,	PUNCT
ejpam-3517	133	15	1360	1360	NUM
ejpam-3517	133	16	-	-	SYM
ejpam-3517	133	17	1370	1370	NUM
ejpam-3517	133	18	1365	1365	NUM
ejpam-3517	133	19	corollary	corollary	NOUN
ejpam-3517	133	20	2	2	NUM
ejpam-3517	133	21	.	.	PUNCT
ejpam-3517	134	1	let	let	VERB
ejpam-3517	134	2	a	a	DET
ejpam-3517	134	3	∈	∈	PROPN
ejpam-3517	134	4	rm	rm	NOUN
ejpam-3517	134	5	,	,	PUNCT
ejpam-3517	134	6	m	m	VERB
ejpam-3517	134	7	≥	≥	NOUN
ejpam-3517	134	8	2	2	NUM
ejpam-3517	134	9	,	,	PUNCT
ejpam-3517	134	10	be	be	AUX
ejpam-3517	134	11	the	the	DET
ejpam-3517	134	12	data	data	NOUN
ejpam-3517	134	13	vector	vector	NOUN
ejpam-3517	134	14	,	,	PUNCT
ejpam-3517	134	15	then	then	ADV
ejpam-3517	134	16	mean(a	mean(a	NUM
ejpam-3517	134	17	)	)	PUNCT
ejpam-3517	134	18	=	=	SYM
ejpam-3517	134	19	1	1	NUM
ejpam-3517	134	20	m	m	VERB
ejpam-3517	134	21	m∑	m∑	NOUN
ejpam-3517	134	22	i=1	i=1	PROPN
ejpam-3517	134	23	ai	ai	VERB
ejpam-3517	134	24	.	.	PUNCT
ejpam-3517	135	1	(	(	PUNCT
ejpam-3517	135	2	17	17	NUM
ejpam-3517	135	3	)	)	PUNCT
ejpam-3517	135	4	theorem	theorem	NOUN
ejpam-3517	135	5	5	5	NUM
ejpam-3517	135	6	.	.	PUNCT
ejpam-3517	136	1	let	let	VERB
ejpam-3517	136	2	a	a	DET
ejpam-3517	136	3	∈	∈	PROPN
ejpam-3517	136	4	rm	rm	NOUN
ejpam-3517	136	5	,	,	PUNCT
ejpam-3517	136	6	m	m	VERB
ejpam-3517	136	7	≥	≥	NOUN
ejpam-3517	136	8	2	2	NUM
ejpam-3517	136	9	,	,	PUNCT
ejpam-3517	136	10	be	be	AUX
ejpam-3517	136	11	the	the	DET
ejpam-3517	136	12	data	data	NOUN
ejpam-3517	136	13	vector	vector	NOUN
ejpam-3517	136	14	with	with	ADP
ejpam-3517	136	15	corresponding	corresponding	ADJ
ejpam-3517	136	16	data	datum	NOUN
ejpam-3517	136	17	weights	weight	NOUN
ejpam-3517	136	18	w	w	PROPN
ejpam-3517	136	19	∈	∈	PROPN
ejpam-3517	136	20	rm	rm	NOUN
ejpam-3517	137	1	+	+	X
ejpam-3517	137	2	.	.	PUNCT
ejpam-3517	138	1	let	let	VERB
ejpam-3517	138	2	a(1	a(1	NOUN
ejpam-3517	138	3	)	)	PUNCT
ejpam-3517	138	4	≤	≤	PUNCT
ejpam-3517	139	1	a(2	a(2	PROPN
ejpam-3517	139	2	)	)	PUNCT
ejpam-3517	139	3	≤	≤	NOUN
ejpam-3517	139	4	.	.	PUNCT
ejpam-3517	139	5	.	.	PUNCT
ejpam-3517	139	6	.	.	PUNCT
ejpam-3517	140	1	≤	≤	NUM
ejpam-3517	140	2	a(m	a(m	NOUN
ejpam-3517	140	3	)	)	PUNCT
ejpam-3517	140	4	denote	denote	NOUN
ejpam-3517	140	5	ordered	order	VERB
ejpam-3517	140	6	observation	observation	NOUN
ejpam-3517	140	7	and	and	CCONJ
ejpam-3517	140	8	0	0	NUM
ejpam-3517	140	9	<	<	X
ejpam-3517	140	10	w(1	w(1	PROPN
ejpam-3517	140	11	)	)	PUNCT
ejpam-3517	140	12	≤	≤	NOUN
ejpam-3517	140	13	w(2	w(2	NOUN
ejpam-3517	140	14	)	)	PUNCT
ejpam-3517	140	15	≤	≤	NOUN
ejpam-3517	140	16	.	.	PUNCT
ejpam-3517	140	17	.	.	PUNCT
ejpam-3517	140	18	.	.	PUNCT
ejpam-3517	141	1	≤	≤	NUM
ejpam-3517	141	2	w(m	w(m	PROPN
ejpam-3517	141	3	)	)	PUNCT
ejpam-3517	141	4	corresponding	correspond	VERB
ejpam-3517	141	5	weights	weight	NOUN
ejpam-3517	141	6	.	.	PUNCT
ejpam-3517	142	1	thereby	thereby	ADV
ejpam-3517	142	2	with	with	ADP
ejpam-3517	142	3	the	the	DET
ejpam-3517	142	4	denotation	denotation	NOUN
ejpam-3517	142	5	l	l	NOUN
ejpam-3517	142	6	:	:	PUNCT
ejpam-3517	142	7	=	=	SYM
ejpam-3517	142	8	{	{	PUNCT
ejpam-3517	142	9	l	l	NOUN
ejpam-3517	142	10	:	:	PUNCT
ejpam-3517	142	11	l∑	l∑	PROPN
ejpam-3517	142	12	i=1	i=1	PROPN
ejpam-3517	142	13	w(i	w(i	PROPN
ejpam-3517	142	14	)	)	PUNCT
ejpam-3517	142	15	≤	≤	PROPN
ejpam-3517	143	1	w	w	ADP
ejpam-3517	143	2	2	2	NUM
ejpam-3517	143	3	}	}	PUNCT
ejpam-3517	143	4	,	,	PUNCT
ejpam-3517	143	5	l	l	PROPN
ejpam-3517	143	6	∈	∈	PROPN
ejpam-3517	143	7	{	{	PUNCT
ejpam-3517	143	8	1	1	NUM
ejpam-3517	143	9	,	,	PUNCT
ejpam-3517	143	10	.	.	PUNCT
ejpam-3517	143	11	.	.	PUNCT
ejpam-3517	143	12	.	.	PUNCT
ejpam-3517	144	1	,	,	PUNCT
ejpam-3517	144	2	m	m	VERB
ejpam-3517	144	3	}	}	PUNCT
ejpam-3517	144	4	,	,	PUNCT
ejpam-3517	144	5	w	w	NOUN
ejpam-3517	144	6	=	=	PUNCT
ejpam-3517	144	7	m∑	m∑	PROPN
ejpam-3517	144	8	i=1	i=1	PROPN
ejpam-3517	144	9	wi	wi	PROPN
ejpam-3517	144	10	,	,	PUNCT
ejpam-3517	144	11	(	(	PUNCT
ejpam-3517	144	12	18	18	NUM
ejpam-3517	144	13	)	)	PUNCT
ejpam-3517	144	14	(	(	PUNCT
ejpam-3517	144	15	a	a	X
ejpam-3517	144	16	)	)	PUNCT
ejpam-3517	144	17	if	if	SCONJ
ejpam-3517	144	18	l	l	NOUN
ejpam-3517	144	19	=	=	SYM
ejpam-3517	144	20	∅	∅	NOUN
ejpam-3517	144	21	,	,	PUNCT
ejpam-3517	144	22	then	then	ADV
ejpam-3517	144	23	med(w	med(w	PROPN
ejpam-3517	144	24	,	,	PUNCT
ejpam-3517	144	25	a	a	PRON
ejpam-3517	144	26	)	)	PUNCT
ejpam-3517	144	27	=	=	PUNCT
ejpam-3517	145	1	a(1	a(1	PROPN
ejpam-3517	145	2	)	)	PUNCT
ejpam-3517	145	3	;	;	PUNCT
ejpam-3517	145	4	(	(	PUNCT
ejpam-3517	145	5	b	b	X
ejpam-3517	145	6	)	)	PUNCT
ejpam-3517	145	7	if	if	SCONJ
ejpam-3517	145	8	l	l	NOUN
ejpam-3517	145	9	6=	6=	ADP
ejpam-3517	145	10	∅	∅	NOUN
ejpam-3517	145	11	,	,	PUNCT
ejpam-3517	145	12	then	then	ADV
ejpam-3517	145	13	with	with	ADP
ejpam-3517	145	14	the	the	DET
ejpam-3517	145	15	denotation	denotation	NOUN
ejpam-3517	145	16	l0	l0	NOUN
ejpam-3517	145	17	=	=	PUNCT
ejpam-3517	146	1	maxl	maxl	VERB
ejpam-3517	146	2	there	there	ADV
ejpam-3517	146	3	holds	hold	VERB
ejpam-3517	146	4	:	:	PUNCT
ejpam-3517	146	5	(	(	PUNCT
ejpam-3517	147	1	i	i	NOUN
ejpam-3517	147	2	)	)	PUNCT
ejpam-3517	147	3	if	if	SCONJ
ejpam-3517	147	4	l0∑	l0∑	PROPN
ejpam-3517	147	5	i=1	i=1	PROPN
ejpam-3517	147	6	w(i	w(i	PROPN
ejpam-3517	147	7	)	)	PUNCT
ejpam-3517	147	8	<	<	X
ejpam-3517	147	9	w	w	PROPN
ejpam-3517	147	10	2	2	NUM
ejpam-3517	147	11	,	,	PUNCT
ejpam-3517	147	12	then	then	ADV
ejpam-3517	147	13	med(w	med(w	PROPN
ejpam-3517	147	14	,	,	PUNCT
ejpam-3517	147	15	a	a	PRON
ejpam-3517	147	16	)	)	PUNCT
ejpam-3517	147	17	=	=	PUNCT
ejpam-3517	148	1	a(l0	a(l0	PROPN
ejpam-3517	149	1	+	+	NOUN
ejpam-3517	149	2	1	1	NUM
ejpam-3517	149	3	)	)	PUNCT
ejpam-3517	150	1	;	;	PUNCT
ejpam-3517	150	2	(	(	PUNCT
ejpam-3517	150	3	ii	ii	NOUN
ejpam-3517	150	4	)	)	PUNCT
ejpam-3517	150	5	if	if	SCONJ
ejpam-3517	150	6	l0∑	l0∑	PROPN
ejpam-3517	150	7	i=1	i=1	PROPN
ejpam-3517	150	8	w(i	w(i	PROPN
ejpam-3517	150	9	)	)	PUNCT
ejpam-3517	151	1	=	=	PUNCT
ejpam-3517	151	2	w	w	PROPN
ejpam-3517	151	3	2	2	NUM
ejpam-3517	151	4	,	,	PUNCT
ejpam-3517	151	5	then	then	ADV
ejpam-3517	151	6	med(w	med(w	PROPN
ejpam-3517	151	7	,	,	PUNCT
ejpam-3517	151	8	a	a	PRON
ejpam-3517	151	9	)	)	PUNCT
ejpam-3517	151	10	∈	∈	PROPN
ejpam-3517	152	1	[	[	X
ejpam-3517	152	2	a(l0	a(l0	NOUN
ejpam-3517	152	3	)	)	PUNCT
ejpam-3517	152	4	,	,	PUNCT
ejpam-3517	152	5	a(l0	a(l0	PROPN
ejpam-3517	153	1	+	+	NOUN
ejpam-3517	153	2	1	1	NUM
ejpam-3517	153	3	)	)	PUNCT
ejpam-3517	153	4	]	]	PUNCT
ejpam-3517	153	5	.	.	PUNCT
ejpam-3517	154	1	proof	proof	NOUN
ejpam-3517	154	2	.	.	PUNCT
ejpam-3517	155	1	notice	notice	VERB
ejpam-3517	155	2	that	that	SCONJ
ejpam-3517	155	3	on	on	ADP
ejpam-3517	155	4	each	each	DET
ejpam-3517	155	5	interval	interval	NOUN
ejpam-3517	155	6	〈	〈	PROPN
ejpam-3517	155	7	−∞	−∞	NOUN
ejpam-3517	155	8	,	,	PUNCT
ejpam-3517	155	9	a(1	a(1	ADJ
ejpam-3517	155	10	)	)	PUNCT
ejpam-3517	155	11	〉	〉	PROPN
ejpam-3517	155	12	,	,	PUNCT
ejpam-3517	155	13	〈	〈	PROPN
ejpam-3517	155	14	a(1	a(1	NOUN
ejpam-3517	155	15	)	)	PUNCT
ejpam-3517	155	16	,	,	PUNCT
ejpam-3517	155	17	a(2	a(2	PROPN
ejpam-3517	155	18	)	)	PUNCT
ejpam-3517	155	19	〉	〉	PROPN
ejpam-3517	155	20	,	,	PUNCT
ejpam-3517	155	21	.	.	PUNCT
ejpam-3517	155	22	.	.	PUNCT
ejpam-3517	155	23	.	.	PUNCT
ejpam-3517	156	1	,	,	PUNCT
ejpam-3517	156	2	〈	〈	PROPN
ejpam-3517	156	3	a(m−1	a(m−1	PROPN
ejpam-3517	156	4	)	)	PUNCT
ejpam-3517	156	5	,	,	PUNCT
ejpam-3517	156	6	a(m	a(m	PROPN
ejpam-3517	156	7	)	)	PUNCT
ejpam-3517	156	8	〉	〉	PROPN
ejpam-3517	156	9	,	,	PUNCT
ejpam-3517	156	10	〈	〈	PROPN
ejpam-3517	156	11	a(m),∞	a(m),∞	PROPN
ejpam-3517	156	12	〉	〉	PROPN
ejpam-3517	156	13	,	,	PUNCT
ejpam-3517	156	14	function	function	NOUN
ejpam-3517	156	15	f1	f1	NOUN
ejpam-3517	156	16	:	:	PUNCT
ejpam-3517	156	17	r	r	NOUN
ejpam-3517	156	18	→	→	SYM
ejpam-3517	156	19	r	r	NOUN
ejpam-3517	156	20	defined	define	VERB
ejpam-3517	156	21	by	by	ADP
ejpam-3517	156	22	(	(	PUNCT
ejpam-3517	156	23	15	15	NUM
ejpam-3517	156	24	)	)	PUNCT
ejpam-3517	156	25	is	be	AUX
ejpam-3517	156	26	linear	linear	ADJ
ejpam-3517	156	27	,	,	PUNCT
ejpam-3517	156	28	and	and	CCONJ
ejpam-3517	156	29	thereby	thereby	ADV
ejpam-3517	156	30	derivable	derivable	ADJ
ejpam-3517	156	31	.	.	PUNCT
ejpam-3517	157	1	the	the	DET
ejpam-3517	157	2	slopes	slope	NOUN
ejpam-3517	157	3	of	of	ADP
ejpam-3517	157	4	those	those	DET
ejpam-3517	157	5	linear	linear	ADJ
ejpam-3517	157	6	functions	function	NOUN
ejpam-3517	157	7	are	be	AUX
ejpam-3517	157	8	consecutively	consecutively	ADV
ejpam-3517	157	9	kl	kl	NOUN
ejpam-3517	157	10	,	,	PUNCT
ejpam-3517	157	11	l	l	PROPN
ejpam-3517	157	12	=	=	SYM
ejpam-3517	157	13	0	0	NUM
ejpam-3517	157	14	,	,	PUNCT
ejpam-3517	157	15	.	.	PUNCT
ejpam-3517	157	16	.	.	PUNCT
ejpam-3517	157	17	.	.	PUNCT
ejpam-3517	158	1	,	,	PUNCT
ejpam-3517	158	2	m	m	PROPN
ejpam-3517	158	3	,	,	PUNCT
ejpam-3517	158	4	where	where	SCONJ
ejpam-3517	158	5	k0	k0	PROPN
ejpam-3517	158	6	=	=	PUNCT
ejpam-3517	158	7	−	−	PROPN
ejpam-3517	158	8	m∑	m∑	INTJ
ejpam-3517	158	9	i=1	i=1	PROPN
ejpam-3517	158	10	wi	wi	PROPN
ejpam-3517	158	11	,	,	PUNCT
ejpam-3517	158	12	km	km	PROPN
ejpam-3517	158	13	=	=	PUNCT
ejpam-3517	158	14	m∑	m∑	CCONJ
ejpam-3517	158	15	i=1	i=1	PROPN
ejpam-3517	158	16	wi	wi	PROPN
ejpam-3517	158	17	(	(	PUNCT
ejpam-3517	158	18	19	19	NUM
ejpam-3517	158	19	)	)	PUNCT
ejpam-3517	158	20	and	and	CCONJ
ejpam-3517	158	21	for	for	ADP
ejpam-3517	158	22	l	l	NOUN
ejpam-3517	158	23	=	=	SYM
ejpam-3517	158	24	1	1	NUM
ejpam-3517	158	25	,	,	PUNCT
ejpam-3517	158	26	.	.	PUNCT
ejpam-3517	158	27	.	.	PUNCT
ejpam-3517	158	28	.	.	PUNCT
ejpam-3517	159	1	,	,	PUNCT
ejpam-3517	159	2	m−	m−	PROPN
ejpam-3517	159	3	1	1	NUM
ejpam-3517	159	4	kl	kl	NOUN
ejpam-3517	159	5	=	=	SYM
ejpam-3517	159	6	2	2	NUM
ejpam-3517	159	7	l∑	l∑	NUM
ejpam-3517	159	8	i=1	i=1	PROPN
ejpam-3517	159	9	w(i	w(i	PROPN
ejpam-3517	159	10	)	)	PUNCT
ejpam-3517	159	11	−	−	PROPN
ejpam-3517	160	1	m∑	m∑	ADP
ejpam-3517	160	2	i=1	i=1	PROPN
ejpam-3517	160	3	wi	wi	PROPN
ejpam-3517	160	4	=	=	PUNCT
ejpam-3517	160	5	kl−1	kl−1	PROPN
ejpam-3517	160	6	+	+	CCONJ
ejpam-3517	160	7	2w(l	2w(l	NUM
ejpam-3517	160	8	)	)	PUNCT
ejpam-3517	160	9	.	.	PUNCT
ejpam-3517	161	1	(	(	PUNCT
ejpam-3517	161	2	20	20	NUM
ejpam-3517	161	3	)	)	PUNCT
ejpam-3517	161	4	if	if	SCONJ
ejpam-3517	161	5	l	l	NOUN
ejpam-3517	161	6	=	=	SYM
ejpam-3517	161	7	∅	∅	NOUN
ejpam-3517	161	8	,	,	PUNCT
ejpam-3517	161	9	then	then	ADV
ejpam-3517	161	10	for	for	ADP
ejpam-3517	161	11	every	every	DET
ejpam-3517	161	12	l	l	NOUN
ejpam-3517	161	13	=	=	SYM
ejpam-3517	161	14	1	1	NUM
ejpam-3517	161	15	,	,	PUNCT
ejpam-3517	161	16	.	.	PUNCT
ejpam-3517	161	17	.	.	PUNCT
ejpam-3517	161	18	.	.	PUNCT
ejpam-3517	162	1	,	,	PUNCT
ejpam-3517	162	2	m−	m−	PROPN
ejpam-3517	162	3	1	1	NUM
ejpam-3517	162	4	,	,	PUNCT
ejpam-3517	162	5	is	be	AUX
ejpam-3517	162	6	k0	k0	PROPN
ejpam-3517	162	7	<	<	X
ejpam-3517	162	8	0	0	PUNCT
ejpam-3517	162	9	<	<	X
ejpam-3517	162	10	kl	kl	X
ejpam-3517	162	11	.	.	PUNCT
ejpam-3517	163	1	it	it	PRON
ejpam-3517	163	2	follows	follow	VERB
ejpam-3517	163	3	that	that	SCONJ
ejpam-3517	163	4	f1	f1	NOUN
ejpam-3517	163	5	is	be	AUX
ejpam-3517	163	6	strongly	strongly	ADV
ejpam-3517	163	7	decreasing	decrease	VERB
ejpam-3517	163	8	on	on	ADP
ejpam-3517	163	9	〈	〈	PROPN
ejpam-3517	163	10	−∞	−∞	NOUN
ejpam-3517	163	11	,	,	PUNCT
ejpam-3517	163	12	a(1	a(1	ADJ
ejpam-3517	163	13	)	)	PUNCT
ejpam-3517	163	14	〉	〉	NOUN
ejpam-3517	163	15	and	and	CCONJ
ejpam-3517	163	16	strongly	strongly	ADV
ejpam-3517	163	17	increasing	increase	VERB
ejpam-3517	163	18	on	on	ADP
ejpam-3517	163	19	〈	〈	PROPN
ejpam-3517	163	20	a(1),∞	a(1),∞	PROPN
ejpam-3517	163	21	〉	〉	PROPN
ejpam-3517	163	22	,	,	PUNCT
ejpam-3517	163	23	therefore	therefore	ADV
ejpam-3517	163	24	the	the	DET
ejpam-3517	163	25	minimum	minimum	NOUN
ejpam-3517	163	26	of	of	ADP
ejpam-3517	163	27	f1	f1	NOUN
ejpam-3517	163	28	is	be	AUX
ejpam-3517	163	29	attained	attain	VERB
ejpam-3517	163	30	for	for	ADP
ejpam-3517	163	31	x∗	x∗	PROPN
ejpam-3517	163	32	=	=	PUNCT
ejpam-3517	163	33	a(1	a(1	PROPN
ejpam-3517	163	34	)	)	PUNCT
ejpam-3517	163	35	.	.	PUNCT
ejpam-3517	164	1	if	if	SCONJ
ejpam-3517	164	2	l	l	PROPN
ejpam-3517	164	3	6=	6=	ADP
ejpam-3517	164	4	∅	∅	NOUN
ejpam-3517	164	5	,	,	PUNCT
ejpam-3517	164	6	then	then	ADV
ejpam-3517	164	7	kl+1	kl+1	PROPN
ejpam-3517	164	8	−	−	PROPN
ejpam-3517	164	9	kl	kl	PROPN
ejpam-3517	165	1	=	=	SYM
ejpam-3517	165	2	2w(l+1	2w(l+1	PROPN
ejpam-3517	165	3	)	)	PUNCT
ejpam-3517	165	4	>	>	X
ejpam-3517	165	5	0	0	NUM
ejpam-3517	165	6	,	,	PUNCT
ejpam-3517	165	7	and	and	CCONJ
ejpam-3517	165	8	the	the	DET
ejpam-3517	165	9	sequence	sequence	NOUN
ejpam-3517	165	10	(	(	PUNCT
ejpam-3517	165	11	kl	kl	PROPN
ejpam-3517	165	12	)	)	PUNCT
ejpam-3517	165	13	is	be	AUX
ejpam-3517	165	14	increasing	increase	VERB
ejpam-3517	165	15	and	and	CCONJ
ejpam-3517	165	16	k0	k0	PROPN
ejpam-3517	165	17	<	<	X
ejpam-3517	165	18	k1	k1	X
ejpam-3517	165	19	<	<	X
ejpam-3517	165	20	·	·	PUNCT
ejpam-3517	165	21	·	·	PUNCT
ejpam-3517	165	22	·	·	PUNCT
ejpam-3517	166	1	<	<	X
ejpam-3517	166	2	kl0	kl0	VERB
ejpam-3517	166	3	≤	≤	ADV
ejpam-3517	166	4	0	0	NUM
ejpam-3517	166	5	<	<	X
ejpam-3517	166	6	kl0	kl0	PROPN
ejpam-3517	166	7	+	+	PROPN
ejpam-3517	166	8	1	1	NUM
ejpam-3517	166	9	<	<	X
ejpam-3517	166	10	·	·	PUNCT
ejpam-3517	166	11	·	·	PUNCT
ejpam-3517	166	12	·	·	PUNCT
ejpam-3517	167	1	<	<	X
ejpam-3517	167	2	km	km	PROPN
ejpam-3517	167	3	.	.	PUNCT
ejpam-3517	168	1	(	(	PUNCT
ejpam-3517	168	2	21	21	NUM
ejpam-3517	168	3	)	)	PUNCT
ejpam-3517	168	4	if	if	SCONJ
ejpam-3517	168	5	k(l0	k(l0	NOUN
ejpam-3517	168	6	)	)	PUNCT
ejpam-3517	168	7	<	<	X
ejpam-3517	168	8	0	0	NUM
ejpam-3517	168	9	,	,	PUNCT
ejpam-3517	168	10	it	it	PRON
ejpam-3517	168	11	follows	follow	VERB
ejpam-3517	168	12	from	from	ADP
ejpam-3517	168	13	(	(	PUNCT
ejpam-3517	168	14	21	21	NUM
ejpam-3517	168	15	)	)	PUNCT
ejpam-3517	168	16	that	that	DET
ejpam-3517	168	17	f1	f1	NOUN
ejpam-3517	168	18	is	be	AUX
ejpam-3517	168	19	decreasing	decrease	VERB
ejpam-3517	168	20	on	on	ADP
ejpam-3517	168	21	〈	〈	PROPN
ejpam-3517	168	22	−∞	−∞	NOUN
ejpam-3517	168	23	,	,	PUNCT
ejpam-3517	168	24	a(l0	a(l0	PROPN
ejpam-3517	168	25	+	+	ADJ
ejpam-3517	168	26	1	1	NUM
ejpam-3517	168	27	)	)	PUNCT
ejpam-3517	168	28	〉	〉	NOUN
ejpam-3517	168	29	and	and	CCONJ
ejpam-3517	168	30	increasing	increase	VERB
ejpam-3517	168	31	on	on	ADP
ejpam-3517	168	32	〈	〈	PROPN
ejpam-3517	168	33	a(l0	a(l0	NOUN
ejpam-3517	168	34	+	+	NOUN
ejpam-3517	168	35	1),∞	1),∞	PROPN
ejpam-3517	168	36	〉	〉	NUM
ejpam-3517	168	37	,	,	PUNCT
ejpam-3517	168	38	therefore	therefore	ADV
ejpam-3517	168	39	the	the	DET
ejpam-3517	168	40	minimum	minimum	NOUN
ejpam-3517	168	41	of	of	ADP
ejpam-3517	168	42	f1	f1	NOUN
ejpam-3517	168	43	is	be	AUX
ejpam-3517	168	44	attained	attain	VERB
ejpam-3517	168	45	for	for	ADP
ejpam-3517	168	46	x∗	x∗	PROPN
ejpam-3517	168	47	=	=	SYM
ejpam-3517	169	1	a(l0	a(l0	PROPN
ejpam-3517	170	1	+	+	ADJ
ejpam-3517	170	2	1	1	NUM
ejpam-3517	170	3	)	)	PUNCT
ejpam-3517	170	4	v.	v.	CCONJ
ejpam-3517	170	5	novoselac	novoselac	PROPN
ejpam-3517	170	6	,	,	PUNCT
ejpam-3517	170	7	z.	z.	PROPN
ejpam-3517	170	8	pavić	pavić	PROPN
ejpam-3517	170	9	/	/	SYM
ejpam-3517	170	10	eur	eur	PROPN
ejpam-3517	170	11	.	.	PUNCT
ejpam-3517	171	1	j.	j.	PROPN
ejpam-3517	171	2	pure	pure	PROPN
ejpam-3517	171	3	appl	appl	PROPN
ejpam-3517	171	4	.	.	PROPN
ejpam-3517	171	5	math	math	PROPN
ejpam-3517	171	6	,	,	PUNCT
ejpam-3517	171	7	12	12	NUM
ejpam-3517	171	8	(	(	PUNCT
ejpam-3517	171	9	4	4	NUM
ejpam-3517	171	10	)	)	PUNCT
ejpam-3517	171	11	(	(	PUNCT
ejpam-3517	171	12	2019	2019	NUM
ejpam-3517	171	13	)	)	PUNCT
ejpam-3517	171	14	,	,	PUNCT
ejpam-3517	171	15	1360	1360	NUM
ejpam-3517	171	16	-	-	SYM
ejpam-3517	171	17	1370	1370	NUM
ejpam-3517	171	18	1366	1366	NUM
ejpam-3517	171	19	if	if	SCONJ
ejpam-3517	171	20	k(l0	k(l0	NOUN
ejpam-3517	171	21	)	)	PUNCT
ejpam-3517	172	1	=	=	SYM
ejpam-3517	172	2	0	0	NUM
ejpam-3517	172	3	,	,	PUNCT
ejpam-3517	172	4	it	it	PRON
ejpam-3517	172	5	follows	follow	VERB
ejpam-3517	172	6	from	from	ADP
ejpam-3517	172	7	(	(	PUNCT
ejpam-3517	172	8	21	21	NUM
ejpam-3517	172	9	)	)	PUNCT
ejpam-3517	172	10	that	that	DET
ejpam-3517	172	11	f1	f1	NOUN
ejpam-3517	172	12	is	be	AUX
ejpam-3517	172	13	decreasing	decrease	VERB
ejpam-3517	172	14	on	on	ADP
ejpam-3517	172	15	〈	〈	PROPN
ejpam-3517	172	16	−∞	−∞	NOUN
ejpam-3517	172	17	,	,	PUNCT
ejpam-3517	172	18	a(l0	a(l0	NOUN
ejpam-3517	172	19	)	)	PUNCT
ejpam-3517	172	20	〉	〉	PROPN
ejpam-3517	172	21	,	,	PUNCT
ejpam-3517	172	22	is	be	AUX
ejpam-3517	172	23	constant	constant	ADJ
ejpam-3517	172	24	on	on	ADP
ejpam-3517	172	25	[	[	X
ejpam-3517	172	26	a(l0	a(l0	NOUN
ejpam-3517	172	27	)	)	PUNCT
ejpam-3517	172	28	,	,	PUNCT
ejpam-3517	172	29	a(l0)+1	a(l0)+1	PROPN
ejpam-3517	172	30	]	]	PUNCT
ejpam-3517	172	31	and	and	CCONJ
ejpam-3517	172	32	increasing	increase	VERB
ejpam-3517	172	33	on	on	ADP
ejpam-3517	172	34	〈	〈	PROPN
ejpam-3517	172	35	a(l0	a(l0	NOUN
ejpam-3517	172	36	+	+	NOUN
ejpam-3517	172	37	1),∞	1),∞	PROPN
ejpam-3517	172	38	〉	〉	NUM
ejpam-3517	172	39	,	,	PUNCT
ejpam-3517	172	40	therefore	therefore	ADV
ejpam-3517	172	41	the	the	DET
ejpam-3517	172	42	minimum	minimum	NOUN
ejpam-3517	172	43	of	of	ADP
ejpam-3517	172	44	f1	f1	NOUN
ejpam-3517	172	45	is	be	AUX
ejpam-3517	172	46	attained	attain	VERB
ejpam-3517	172	47	at	at	ADP
ejpam-3517	172	48	every	every	DET
ejpam-3517	172	49	point	point	NOUN
ejpam-3517	172	50	x∗	x∗	PROPN
ejpam-3517	172	51	∈	∈	PROPN
ejpam-3517	173	1	[	[	X
ejpam-3517	173	2	a(l0	a(l0	NOUN
ejpam-3517	173	3	)	)	PUNCT
ejpam-3517	173	4	,	,	PUNCT
ejpam-3517	174	1	a(l0	a(l0	PROPN
ejpam-3517	175	1	+	+	NOUN
ejpam-3517	175	2	1	1	NUM
ejpam-3517	175	3	)	)	PUNCT
ejpam-3517	175	4	]	]	PUNCT
ejpam-3517	175	5	.	.	PUNCT
ejpam-3517	176	1	figure	figure	NOUN
ejpam-3517	176	2	3(a	3(a	NUM
ejpam-3517	176	3	)	)	PUNCT
ejpam-3517	177	1	present	present	VERB
ejpam-3517	177	2	the	the	DET
ejpam-3517	177	3	value	value	NOUN
ejpam-3517	177	4	of	of	ADP
ejpam-3517	177	5	data	datum	NOUN
ejpam-3517	177	6	vector	vector	NOUN
ejpam-3517	177	7	a	a	NOUN
ejpam-3517	177	8	=	=	SYM
ejpam-3517	178	1	[	[	X
ejpam-3517	178	2	1	1	NUM
ejpam-3517	178	3	,	,	PUNCT
ejpam-3517	178	4	2	2	NUM
ejpam-3517	178	5	,	,	PUNCT
ejpam-3517	178	6	3	3	NUM
ejpam-3517	178	7	,	,	PUNCT
ejpam-3517	178	8	4	4	NUM
ejpam-3517	178	9	,	,	PUNCT
ejpam-3517	178	10	5]t	5]t	NUM
ejpam-3517	178	11	.	.	PUNCT
ejpam-3517	179	1	in	in	ADP
ejpam-3517	179	2	this	this	DET
ejpam-3517	179	3	situation	situation	NOUN
ejpam-3517	179	4	it	it	PRON
ejpam-3517	179	5	is	be	AUX
ejpam-3517	179	6	obvious	obvious	ADJ
ejpam-3517	179	7	that	that	SCONJ
ejpam-3517	179	8	the	the	DET
ejpam-3517	179	9	weighted	weight	VERB
ejpam-3517	179	10	mean	mean	NOUN
ejpam-3517	179	11	and	and	CCONJ
ejpam-3517	179	12	weighted	weight	VERB
ejpam-3517	179	13	median	median	PROPN
ejpam-3517	179	14	with	with	ADP
ejpam-3517	179	15	corresponding	correspond	VERB
ejpam-3517	179	16	data	datum	NOUN
ejpam-3517	179	17	weights	weight	NOUN
ejpam-3517	179	18	w	w	NOUN
ejpam-3517	180	1	=	=	PUNCT
ejpam-3517	181	1	[	[	X
ejpam-3517	181	2	1	1	NUM
ejpam-3517	181	3	,	,	PUNCT
ejpam-3517	181	4	1	1	NUM
ejpam-3517	181	5	,	,	PUNCT
ejpam-3517	181	6	2	2	NUM
ejpam-3517	181	7	,	,	PUNCT
ejpam-3517	181	8	1	1	NUM
ejpam-3517	181	9	,	,	PUNCT
ejpam-3517	181	10	1]t	1]t	NUM
ejpam-3517	181	11	of	of	ADP
ejpam-3517	181	12	the	the	DET
ejpam-3517	181	13	observed	observe	VERB
ejpam-3517	181	14	data	datum	NOUN
ejpam-3517	181	15	are	be	AUX
ejpam-3517	181	16	equal	equal	ADJ
ejpam-3517	181	17	.	.	PUNCT
ejpam-3517	182	1	suppose	suppose	VERB
ejpam-3517	182	2	that	that	SCONJ
ejpam-3517	182	3	in	in	ADP
ejpam-3517	182	4	some	some	DET
ejpam-3517	182	5	situation	situation	NOUN
ejpam-3517	182	6	two	two	NUM
ejpam-3517	182	7	outliers	outlier	NOUN
ejpam-3517	182	8	are	be	AUX
ejpam-3517	182	9	added	add	VERB
ejpam-3517	182	10	,	,	PUNCT
ejpam-3517	182	11	e.g.	e.g.	ADV
ejpam-3517	182	12	because	because	SCONJ
ejpam-3517	182	13	of	of	ADP
ejpam-3517	182	14	a	a	DET
ejpam-3517	182	15	copying	copying	NOUN
ejpam-3517	182	16	or	or	CCONJ
ejpam-3517	182	17	transmission	transmission	NOUN
ejpam-3517	182	18	error	error	NOUN
ejpam-3517	182	19	.	.	PUNCT
ejpam-3517	183	1	figure	figure	NOUN
ejpam-3517	183	2	3(b	3(b	NUM
ejpam-3517	183	3	)	)	PUNCT
ejpam-3517	183	4	displays	display	VERB
ejpam-3517	183	5	such	such	DET
ejpam-3517	183	6	a	a	DET
ejpam-3517	183	7	situation	situation	NOUN
ejpam-3517	183	8	,	,	PUNCT
ejpam-3517	183	9	where	where	SCONJ
ejpam-3517	183	10	the	the	DET
ejpam-3517	183	11	two	two	NUM
ejpam-3517	183	12	last	last	ADJ
ejpam-3517	183	13	data	datum	NOUN
ejpam-3517	183	14	have	have	AUX
ejpam-3517	183	15	moved	move	VERB
ejpam-3517	183	16	up	up	ADV
ejpam-3517	183	17	and	and	CCONJ
ejpam-3517	183	18	away	away	ADV
ejpam-3517	183	19	from	from	ADP
ejpam-3517	183	20	its	its	PRON
ejpam-3517	183	21	original	original	ADJ
ejpam-3517	183	22	position	position	NOUN
ejpam-3517	183	23	.	.	PUNCT
ejpam-3517	184	1	these	these	PRON
ejpam-3517	184	2	are	be	AUX
ejpam-3517	184	3	so	so	ADV
ejpam-3517	184	4	called	call	VERB
ejpam-3517	184	5	outliers	outlier	NOUN
ejpam-3517	184	6	,	,	PUNCT
ejpam-3517	184	7	and	and	CCONJ
ejpam-3517	184	8	they	they	PRON
ejpam-3517	184	9	have	have	VERB
ejpam-3517	184	10	a	a	DET
ejpam-3517	184	11	large	large	ADJ
ejpam-3517	184	12	influence	influence	NOUN
ejpam-3517	184	13	on	on	ADP
ejpam-3517	184	14	the	the	DET
ejpam-3517	184	15	weighted	weight	VERB
ejpam-3517	184	16	mean	mean	NOUN
ejpam-3517	184	17	,	,	PUNCT
ejpam-3517	184	18	i.e.	i.e.	X
ejpam-3517	184	19	ls	ls	ADJ
ejpam-3517	184	20	problem	problem	NOUN
ejpam-3517	184	21	,	,	PUNCT
ejpam-3517	184	22	which	which	PRON
ejpam-3517	184	23	is	be	AUX
ejpam-3517	184	24	quite	quite	ADV
ejpam-3517	184	25	different	different	ADJ
ejpam-3517	184	26	from	from	ADP
ejpam-3517	184	27	the	the	DET
ejpam-3517	184	28	weighted	weight	VERB
ejpam-3517	184	29	mean	mean	NOUN
ejpam-3517	184	30	in	in	ADP
ejpam-3517	184	31	figure	figure	NOUN
ejpam-3517	184	32	3(a	3(a	NUM
ejpam-3517	184	33	)	)	PUNCT
ejpam-3517	184	34	.	.	PUNCT
ejpam-3517	185	1	1	1	NUM
ejpam-3517	185	2	2	2	NUM
ejpam-3517	185	3	3	3	NUM
ejpam-3517	185	4	4	4	NUM
ejpam-3517	185	5	5	5	NUM
ejpam-3517	185	6	1	1	NUM
ejpam-3517	185	7	2	2	NUM
ejpam-3517	185	8	3	3	NUM
ejpam-3517	185	9	4	4	NUM
ejpam-3517	185	10	5	5	NUM
ejpam-3517	185	11	1	1	NUM
ejpam-3517	185	12	2	2	NUM
ejpam-3517	185	13	3	3	NUM
ejpam-3517	185	14	4	4	NUM
ejpam-3517	185	15	1	1	NUM
ejpam-3517	185	16	2	2	NUM
ejpam-3517	185	17	3	3	NUM
ejpam-3517	185	18	4	4	NUM
ejpam-3517	185	19	5	5	NUM
ejpam-3517	185	20	1	1	NUM
ejpam-3517	185	21	2	2	NUM
ejpam-3517	185	22	3	3	NUM
ejpam-3517	185	23	4	4	NUM
ejpam-3517	185	24	5	5	NUM
ejpam-3517	185	25	1	1	NUM
ejpam-3517	185	26	2	2	NUM
ejpam-3517	185	27	3	3	NUM
ejpam-3517	185	28	8	8	NUM
ejpam-3517	185	29	ai	ai	NOUN
ejpam-3517	185	30	ai	ai	VERB
ejpam-3517	185	31	i	i	PRON
ejpam-3517	185	32	i	i	PRON
ejpam-3517	185	33	mean(w	mean(w	PROPN
ejpam-3517	185	34	,	,	PUNCT
ejpam-3517	185	35	a	a	PRON
ejpam-3517	185	36	)	)	PUNCT
ejpam-3517	185	37	med(w	med(w	NOUN
ejpam-3517	185	38	,	,	PUNCT
ejpam-3517	185	39	a	a	PRON
ejpam-3517	185	40	)	)	PUNCT
ejpam-3517	185	41	mean(w	mean(w	PROPN
ejpam-3517	185	42	,	,	PUNCT
ejpam-3517	185	43	a	a	PRON
ejpam-3517	185	44	)	)	PUNCT
ejpam-3517	185	45	med(w	med(w	NOUN
ejpam-3517	185	46	,	,	PUNCT
ejpam-3517	185	47	a	a	PRON
ejpam-3517	185	48	)	)	PUNCT
ejpam-3517	185	49	outliers	outlier	NOUN
ejpam-3517	185	50	(	(	PUNCT
ejpam-3517	185	51	a	a	X
ejpam-3517	185	52	)	)	PUNCT
ejpam-3517	185	53	(	(	PUNCT
ejpam-3517	185	54	b	b	X
ejpam-3517	185	55	)	)	PUNCT
ejpam-3517	185	56	figure	figure	NOUN
ejpam-3517	185	57	3	3	NUM
ejpam-3517	185	58	:	:	PUNCT
ejpam-3517	185	59	weighted	weight	VERB
ejpam-3517	185	60	mean	mean	NOUN
ejpam-3517	185	61	and	and	CCONJ
ejpam-3517	185	62	weighted	weight	VERB
ejpam-3517	185	63	median	median	NOUN
ejpam-3517	185	64	:	:	PUNCT
ejpam-3517	185	65	(	(	PUNCT
ejpam-3517	185	66	a	a	X
ejpam-3517	185	67	)	)	PUNCT
ejpam-3517	185	68	original	original	ADJ
ejpam-3517	185	69	data	datum	NOUN
ejpam-3517	185	70	;	;	PUNCT
ejpam-3517	185	71	(	(	PUNCT
ejpam-3517	185	72	b	b	X
ejpam-3517	185	73	)	)	PUNCT
ejpam-3517	185	74	same	same	ADJ
ejpam-3517	185	75	data	datum	NOUN
ejpam-3517	185	76	as	as	ADP
ejpam-3517	185	77	in	in	ADP
ejpam-3517	185	78	part	part	NOUN
ejpam-3517	185	79	(	(	PUNCT
ejpam-3517	185	80	a	a	NOUN
ejpam-3517	185	81	)	)	PUNCT
ejpam-3517	185	82	,	,	PUNCT
ejpam-3517	185	83	but	but	CCONJ
ejpam-3517	185	84	with	with	ADP
ejpam-3517	185	85	two	two	NUM
ejpam-3517	185	86	outliers	outlier	NOUN
ejpam-3517	185	87	.	.	PUNCT
ejpam-3517	186	1	in	in	ADP
ejpam-3517	186	2	the	the	DET
ejpam-3517	186	3	sequel	sequel	NOUN
ejpam-3517	186	4	,	,	PUNCT
ejpam-3517	186	5	the	the	DET
ejpam-3517	186	6	corollary	corollary	NOUN
ejpam-3517	186	7	is	be	AUX
ejpam-3517	186	8	mentioned	mention	VERB
ejpam-3517	186	9	,	,	PUNCT
ejpam-3517	186	10	which	which	PRON
ejpam-3517	186	11	specializes	specialize	VERB
ejpam-3517	186	12	the	the	DET
ejpam-3517	186	13	situation	situation	NOUN
ejpam-3517	186	14	for	for	ADP
ejpam-3517	186	15	the	the	DET
ejpam-3517	186	16	case	case	NOUN
ejpam-3517	186	17	if	if	SCONJ
ejpam-3517	186	18	the	the	DET
ejpam-3517	186	19	weights	weight	NOUN
ejpam-3517	186	20	of	of	ADP
ejpam-3517	186	21	the	the	DET
ejpam-3517	186	22	data	datum	NOUN
ejpam-3517	186	23	are	be	AUX
ejpam-3517	186	24	not	not	PART
ejpam-3517	186	25	assigned	assign	VERB
ejpam-3517	186	26	,	,	PUNCT
ejpam-3517	186	27	or	or	CCONJ
ejpam-3517	186	28	if	if	SCONJ
ejpam-3517	186	29	all	all	DET
ejpam-3517	186	30	weights	weight	NOUN
ejpam-3517	186	31	are	be	AUX
ejpam-3517	186	32	mutually	mutually	ADV
ejpam-3517	186	33	equal	equal	ADJ
ejpam-3517	186	34	.	.	PUNCT
ejpam-3517	187	1	also	also	ADV
ejpam-3517	187	2	,	,	PUNCT
ejpam-3517	187	3	a	a	DET
ejpam-3517	187	4	description	description	NOUN
ejpam-3517	187	5	of	of	ADP
ejpam-3517	187	6	the	the	DET
ejpam-3517	187	7	pseudo	pseudo	NOUN
ejpam-3517	187	8	-	-	PUNCT
ejpam-3517	187	9	halving	halve	VERB
ejpam-3517	187	10	property	property	NOUN
ejpam-3517	187	11	is	be	AUX
ejpam-3517	187	12	mentioned	mention	VERB
ejpam-3517	187	13	[	[	X
ejpam-3517	187	14	1	1	NUM
ejpam-3517	187	15	]	]	PUNCT
ejpam-3517	187	16	,	,	PUNCT
ejpam-3517	187	17	which	which	PRON
ejpam-3517	187	18	follows	follow	VERB
ejpam-3517	187	19	directly	directly	ADV
ejpam-3517	187	20	from	from	ADP
ejpam-3517	187	21	theorem	theorem	ADJ
ejpam-3517	187	22	5	5	NUM
ejpam-3517	187	23	.	.	PUNCT
ejpam-3517	187	24	corollary	corollary	ADJ
ejpam-3517	187	25	3	3	X
ejpam-3517	187	26	.	.	PUNCT
ejpam-3517	188	1	let	let	VERB
ejpam-3517	188	2	a	a	DET
ejpam-3517	188	3	∈	∈	PROPN
ejpam-3517	188	4	rm	rm	NOUN
ejpam-3517	188	5	,	,	PUNCT
ejpam-3517	188	6	m	m	VERB
ejpam-3517	188	7	≥	≥	NOUN
ejpam-3517	188	8	2	2	NUM
ejpam-3517	188	9	,	,	PUNCT
ejpam-3517	188	10	be	be	AUX
ejpam-3517	188	11	the	the	DET
ejpam-3517	188	12	data	data	NOUN
ejpam-3517	188	13	vector	vector	NOUN
ejpam-3517	188	14	and	and	CCONJ
ejpam-3517	188	15	y(1	y(1	PROPN
ejpam-3517	188	16	)	)	PUNCT
ejpam-3517	188	17	≤	≤	NOUN
ejpam-3517	188	18	y(2	y(2	NOUN
ejpam-3517	188	19	)	)	PUNCT
ejpam-3517	188	20	≤	≤	NOUN
ejpam-3517	188	21	.	.	PUNCT
ejpam-3517	188	22	.	.	PUNCT
ejpam-3517	188	23	.	.	PUNCT
ejpam-3517	189	1	≤	≤	NUM
ejpam-3517	189	2	y(m	y(m	ADV
ejpam-3517	189	3	)	)	PUNCT
ejpam-3517	189	4	denoted	denote	VERB
ejpam-3517	189	5	ordered	order	VERB
ejpam-3517	189	6	observation	observation	NOUN
ejpam-3517	189	7	.	.	PUNCT
ejpam-3517	190	1	then	then	ADV
ejpam-3517	190	2	follows	follow	VERB
ejpam-3517	190	3	(	(	PUNCT
ejpam-3517	190	4	a	a	X
ejpam-3517	190	5	)	)	PUNCT
ejpam-3517	190	6	if	if	SCONJ
ejpam-3517	190	7	m	m	PROPN
ejpam-3517	190	8	is	be	AUX
ejpam-3517	190	9	odd	odd	ADJ
ejpam-3517	190	10	(	(	PUNCT
ejpam-3517	190	11	m	m	PROPN
ejpam-3517	190	12	=	=	SYM
ejpam-3517	190	13	2l0	2l0	NUM
ejpam-3517	190	14	+	+	CCONJ
ejpam-3517	190	15	1	1	NUM
ejpam-3517	190	16	)	)	PUNCT
ejpam-3517	190	17	,	,	PUNCT
ejpam-3517	190	18	med(a	med(a	PROPN
ejpam-3517	190	19	)	)	PUNCT
ejpam-3517	190	20	=	=	PUNCT
ejpam-3517	191	1	a(l0	a(l0	PROPN
ejpam-3517	192	1	+	+	NOUN
ejpam-3517	192	2	1	1	NUM
ejpam-3517	192	3	)	)	PUNCT
ejpam-3517	192	4	;	;	PUNCT
ejpam-3517	192	5	(	(	PUNCT
ejpam-3517	192	6	b	b	X
ejpam-3517	192	7	)	)	PUNCT
ejpam-3517	192	8	if	if	SCONJ
ejpam-3517	192	9	m	m	NOUN
ejpam-3517	192	10	is	be	AUX
ejpam-3517	192	11	even	even	ADV
ejpam-3517	192	12	(	(	PUNCT
ejpam-3517	192	13	m	m	VERB
ejpam-3517	192	14	=	=	NOUN
ejpam-3517	192	15	2l0	2l0	NUM
ejpam-3517	192	16	)	)	PUNCT
ejpam-3517	192	17	,	,	PUNCT
ejpam-3517	192	18	med(a	med(a	PROPN
ejpam-3517	192	19	)	)	PUNCT
ejpam-3517	192	20	is	be	AUX
ejpam-3517	192	21	every	every	DET
ejpam-3517	192	22	number	number	NOUN
ejpam-3517	192	23	from	from	ADP
ejpam-3517	192	24	the	the	DET
ejpam-3517	192	25	segment	segment	NOUN
ejpam-3517	192	26	[	[	X
ejpam-3517	192	27	a(l0	a(l0	NOUN
ejpam-3517	192	28	)	)	PUNCT
ejpam-3517	192	29	,	,	PUNCT
ejpam-3517	192	30	a(l0	a(l0	PROPN
ejpam-3517	192	31	+	+	NOUN
ejpam-3517	192	32	1	1	NUM
ejpam-3517	192	33	)	)	PUNCT
ejpam-3517	192	34	]	]	PUNCT
ejpam-3517	192	35	.	.	PUNCT
ejpam-3517	193	1	corollary	corollary	ADJ
ejpam-3517	193	2	4	4	NUM
ejpam-3517	193	3	.	.	PUNCT
ejpam-3517	194	1	let	let	VERB
ejpam-3517	194	2	a	a	DET
ejpam-3517	194	3	∈	∈	PROPN
ejpam-3517	194	4	rm	rm	NOUN
ejpam-3517	194	5	,	,	PUNCT
ejpam-3517	194	6	m	m	VERB
ejpam-3517	194	7	≥	≥	NOUN
ejpam-3517	194	8	2	2	NUM
ejpam-3517	194	9	,	,	PUNCT
ejpam-3517	194	10	be	be	AUX
ejpam-3517	194	11	the	the	DET
ejpam-3517	194	12	data	data	NOUN
ejpam-3517	194	13	vector	vector	NOUN
ejpam-3517	194	14	with	with	ADP
ejpam-3517	194	15	corresponding	corresponding	ADJ
ejpam-3517	194	16	data	datum	NOUN
ejpam-3517	194	17	weights	weight	NOUN
ejpam-3517	194	18	w	w	PROPN
ejpam-3517	194	19	∈	∈	PROPN
ejpam-3517	194	20	rm	rm	NOUN
ejpam-3517	195	1	+	+	X
ejpam-3517	195	2	.	.	PUNCT
ejpam-3517	196	1	let	let	VERB
ejpam-3517	196	2	a(1	a(1	NOUN
ejpam-3517	196	3	)	)	PUNCT
ejpam-3517	196	4	≤	≤	PUNCT
ejpam-3517	197	1	a(2	a(2	PROPN
ejpam-3517	197	2	)	)	PUNCT
ejpam-3517	197	3	≤	≤	NOUN
ejpam-3517	197	4	.	.	PUNCT
ejpam-3517	197	5	.	.	PUNCT
ejpam-3517	197	6	.	.	PUNCT
ejpam-3517	198	1	≤	≤	NUM
ejpam-3517	198	2	a(m	a(m	NOUN
ejpam-3517	198	3	)	)	PUNCT
ejpam-3517	198	4	denote	denote	NOUN
ejpam-3517	198	5	ordered	order	VERB
ejpam-3517	198	6	observation	observation	NOUN
ejpam-3517	198	7	and	and	CCONJ
ejpam-3517	198	8	0	0	NUM
ejpam-3517	198	9	<	<	X
ejpam-3517	198	10	w(1	w(1	PROPN
ejpam-3517	198	11	)	)	PUNCT
ejpam-3517	198	12	≤	≤	NOUN
ejpam-3517	198	13	w(2	w(2	NOUN
ejpam-3517	198	14	)	)	PUNCT
ejpam-3517	198	15	≤	≤	NOUN
ejpam-3517	198	16	.	.	PUNCT
ejpam-3517	198	17	.	.	PUNCT
ejpam-3517	198	18	.	.	PUNCT
ejpam-3517	199	1	≤	≤	NUM
ejpam-3517	199	2	w(m	w(m	PROPN
ejpam-3517	199	3	)	)	PUNCT
ejpam-3517	199	4	corresponding	correspond	VERB
ejpam-3517	199	5	weights	weight	NOUN
ejpam-3517	199	6	.	.	PUNCT
ejpam-3517	200	1	then	then	ADV
ejpam-3517	200	2	there	there	PRON
ejpam-3517	200	3	holds	hold	VERB
ejpam-3517	200	4	that	that	SCONJ
ejpam-3517	200	5	the	the	DET
ejpam-3517	200	6	pseudo	pseudo	NOUN
ejpam-3517	200	7	-	-	PUNCT
ejpam-3517	200	8	halving	halve	VERB
ejpam-3517	200	9	property	property	NOUN
ejpam-3517	200	10	∑	∑	PROPN
ejpam-3517	200	11	a(i)<x∗	a(i)<x∗	PROPN
ejpam-3517	200	12	w(i	w(i	PROPN
ejpam-3517	200	13	)	)	PUNCT
ejpam-3517	200	14	≤	≤	PROPN
ejpam-3517	200	15	w	w	ADP
ejpam-3517	200	16	2	2	NUM
ejpam-3517	200	17	and	and	CCONJ
ejpam-3517	200	18	∑	∑	PUNCT
ejpam-3517	200	19	a(i)>x∗	a(i)>x∗	NOUN
ejpam-3517	200	20	w(i	w(i	NOUN
ejpam-3517	200	21	)	)	PUNCT
ejpam-3517	200	22	≤	≤	NOUN
ejpam-3517	200	23	w	w	ADP
ejpam-3517	200	24	2	2	NUM
ejpam-3517	200	25	,	,	PUNCT
ejpam-3517	200	26	w	w	NOUN
ejpam-3517	200	27	=	=	PUNCT
ejpam-3517	200	28	m∑	m∑	PROPN
ejpam-3517	200	29	i=1	i=1	PROPN
ejpam-3517	200	30	wi	wi	PROPN
ejpam-3517	200	31	.	.	PUNCT
ejpam-3517	201	1	(	(	PUNCT
ejpam-3517	201	2	22	22	NUM
ejpam-3517	201	3	)	)	PUNCT
ejpam-3517	201	4	v.	v.	CCONJ
ejpam-3517	201	5	novoselac	novoselac	PROPN
ejpam-3517	201	6	,	,	PUNCT
ejpam-3517	201	7	z.	z.	PROPN
ejpam-3517	201	8	pavić	pavić	PROPN
ejpam-3517	201	9	/	/	SYM
ejpam-3517	201	10	eur	eur	PROPN
ejpam-3517	201	11	.	.	PUNCT
ejpam-3517	202	1	j.	j.	PROPN
ejpam-3517	202	2	pure	pure	PROPN
ejpam-3517	202	3	appl	appl	PROPN
ejpam-3517	202	4	.	.	PROPN
ejpam-3517	202	5	math	math	PROPN
ejpam-3517	202	6	,	,	PUNCT
ejpam-3517	202	7	12	12	NUM
ejpam-3517	202	8	(	(	PUNCT
ejpam-3517	202	9	4	4	NUM
ejpam-3517	202	10	)	)	PUNCT
ejpam-3517	202	11	(	(	PUNCT
ejpam-3517	202	12	2019	2019	NUM
ejpam-3517	202	13	)	)	PUNCT
ejpam-3517	202	14	,	,	PUNCT
ejpam-3517	202	15	1360	1360	NUM
ejpam-3517	202	16	-	-	SYM
ejpam-3517	202	17	1370	1370	NUM
ejpam-3517	202	18	1367	1367	NUM
ejpam-3517	202	19	theorem	theorem	NOUN
ejpam-3517	202	20	6	6	NUM
ejpam-3517	202	21	.	.	PUNCT
ejpam-3517	203	1	let	let	VERB
ejpam-3517	203	2	a	a	DET
ejpam-3517	203	3	∈	∈	PROPN
ejpam-3517	203	4	rm	rm	NOUN
ejpam-3517	203	5	,	,	PUNCT
ejpam-3517	203	6	m	m	VERB
ejpam-3517	203	7	≥	≥	NOUN
ejpam-3517	203	8	2	2	NUM
ejpam-3517	203	9	,	,	PUNCT
ejpam-3517	203	10	be	be	AUX
ejpam-3517	203	11	the	the	DET
ejpam-3517	203	12	data	data	NOUN
ejpam-3517	203	13	vector	vector	NOUN
ejpam-3517	203	14	with	with	ADP
ejpam-3517	203	15	corresponding	corresponding	ADJ
ejpam-3517	203	16	data	datum	NOUN
ejpam-3517	203	17	weights	weight	NOUN
ejpam-3517	203	18	w	w	PROPN
ejpam-3517	203	19	∈	∈	PROPN
ejpam-3517	203	20	rm	rm	NOUN
ejpam-3517	204	1	+	+	CCONJ
ejpam-3517	204	2	.	.	PUNCT
ejpam-3517	205	1	then	then	ADV
ejpam-3517	205	2	for	for	ADP
ejpam-3517	205	3	α	α	PROPN
ejpam-3517	205	4	,	,	PUNCT
ejpam-3517	205	5	β	β	X
ejpam-3517	205	6	,	,	PUNCT
ejpam-3517	205	7	γ	γ	PROPN
ejpam-3517	205	8	∈	∈	PROPN
ejpam-3517	205	9	r	r	PROPN
ejpam-3517	205	10	,	,	PUNCT
ejpam-3517	205	11	α	α	NOUN
ejpam-3517	205	12	>	>	X
ejpam-3517	205	13	0	0	NUM
ejpam-3517	205	14	,	,	PUNCT
ejpam-3517	205	15	there	there	PRON
ejpam-3517	205	16	holds	hold	VERB
ejpam-3517	205	17	that	that	SCONJ
ejpam-3517	205	18	(	(	PUNCT
ejpam-3517	205	19	a	a	X
ejpam-3517	205	20	)	)	PUNCT
ejpam-3517	205	21	mean(αw	mean(αw	NOUN
ejpam-3517	205	22	,	,	PUNCT
ejpam-3517	205	23	βa+	βa+	NOUN
ejpam-3517	205	24	γe	γe	NOUN
ejpam-3517	205	25	)	)	PUNCT
ejpam-3517	205	26	=	=	SYM
ejpam-3517	206	1	βmean(w	βmean(w	ADV
ejpam-3517	206	2	,	,	PUNCT
ejpam-3517	206	3	a	a	PRON
ejpam-3517	206	4	)	)	PUNCT
ejpam-3517	206	5	+	+	CCONJ
ejpam-3517	206	6	γ	γ	X
ejpam-3517	206	7	;	;	PUNCT
ejpam-3517	206	8	(	(	PUNCT
ejpam-3517	206	9	b	b	NOUN
ejpam-3517	206	10	)	)	PUNCT
ejpam-3517	206	11	med(αw	med(αw	NOUN
ejpam-3517	206	12	,	,	PUNCT
ejpam-3517	206	13	βa+	βa+	NOUN
ejpam-3517	206	14	γe	γe	NOUN
ejpam-3517	206	15	)	)	PUNCT
ejpam-3517	206	16	=	=	SYM
ejpam-3517	206	17	βmed(w	βmed(w	PROPN
ejpam-3517	206	18	,	,	PUNCT
ejpam-3517	206	19	a	a	PRON
ejpam-3517	206	20	)	)	PUNCT
ejpam-3517	206	21	+	+	CCONJ
ejpam-3517	206	22	γ	γ	X
ejpam-3517	206	23	,	,	PUNCT
ejpam-3517	206	24	where	where	SCONJ
ejpam-3517	206	25	e	e	NOUN
ejpam-3517	206	26	=	=	PUNCT
ejpam-3517	207	1	[	[	X
ejpam-3517	207	2	1	1	NUM
ejpam-3517	207	3	,	,	PUNCT
ejpam-3517	207	4	.	.	PUNCT
ejpam-3517	207	5	.	.	PUNCT
ejpam-3517	208	1	.	.	PUNCT
ejpam-3517	209	1	,	,	PUNCT
ejpam-3517	209	2	1]t	1]t	NUM
ejpam-3517	209	3	∈	∈	PROPN
ejpam-3517	209	4	rm	rm	NOUN
ejpam-3517	209	5	.	.	PUNCT
ejpam-3517	210	1	proof	proof	NOUN
ejpam-3517	210	2	.	.	PUNCT
ejpam-3517	211	1	first	first	ADV
ejpam-3517	211	2	we	we	PRON
ejpam-3517	211	3	prove	prove	VERB
ejpam-3517	211	4	(	(	PUNCT
ejpam-3517	211	5	a	a	X
ejpam-3517	211	6	)	)	PUNCT
ejpam-3517	211	7	,	,	PUNCT
ejpam-3517	211	8	while	while	SCONJ
ejpam-3517	211	9	the	the	DET
ejpam-3517	211	10	proof	proof	NOUN
ejpam-3517	211	11	of	of	ADP
ejpam-3517	211	12	(	(	PUNCT
ejpam-3517	211	13	b	b	NOUN
ejpam-3517	211	14	)	)	PUNCT
ejpam-3517	211	15	is	be	AUX
ejpam-3517	211	16	going	go	VERB
ejpam-3517	211	17	analogue	analogue	NOUN
ejpam-3517	211	18	of	of	ADP
ejpam-3517	211	19	(	(	PUNCT
ejpam-3517	211	20	a	a	NOUN
ejpam-3517	211	21	)	)	PUNCT
ejpam-3517	211	22	.	.	PUNCT
ejpam-3517	212	1	notice	notice	VERB
ejpam-3517	212	2	that	that	SCONJ
ejpam-3517	212	3	equality	equality	NOUN
ejpam-3517	212	4	(	(	PUNCT
ejpam-3517	212	5	a	a	NOUN
ejpam-3517	212	6	)	)	PUNCT
ejpam-3517	212	7	holds	hold	VERB
ejpam-3517	212	8	if	if	SCONJ
ejpam-3517	212	9	and	and	CCONJ
ejpam-3517	212	10	only	only	ADV
ejpam-3517	212	11	if	if	SCONJ
ejpam-3517	212	12	mean(αw	mean(αw	NOUN
ejpam-3517	212	13	,	,	PUNCT
ejpam-3517	212	14	a	a	PRON
ejpam-3517	212	15	)	)	PUNCT
ejpam-3517	212	16	=	=	SYM
ejpam-3517	212	17	mean(w	mean(w	PROPN
ejpam-3517	212	18	,	,	PUNCT
ejpam-3517	212	19	a	a	PRON
ejpam-3517	212	20	)	)	PUNCT
ejpam-3517	212	21	,	,	PUNCT
ejpam-3517	212	22	and	and	CCONJ
ejpam-3517	212	23	(	(	PUNCT
ejpam-3517	212	24	23	23	X
ejpam-3517	212	25	)	)	PUNCT
ejpam-3517	212	26	mean(αw	mean(αw	NOUN
ejpam-3517	212	27	,	,	PUNCT
ejpam-3517	212	28	βa+	βa+	NOUN
ejpam-3517	212	29	γe	γe	NOUN
ejpam-3517	212	30	)	)	PUNCT
ejpam-3517	212	31	=	=	SYM
ejpam-3517	213	1	βmean(w	βmean(w	ADV
ejpam-3517	213	2	,	,	PUNCT
ejpam-3517	213	3	a	a	PRON
ejpam-3517	213	4	)	)	PUNCT
ejpam-3517	213	5	+	+	CCONJ
ejpam-3517	213	6	γ	γ	X
ejpam-3517	213	7	.	.	PROPN
ejpam-3517	213	8	(	(	PUNCT
ejpam-3517	213	9	24	24	NUM
ejpam-3517	213	10	)	)	PUNCT
ejpam-3517	213	11	property	property	NOUN
ejpam-3517	213	12	(	(	PUNCT
ejpam-3517	213	13	23	23	NUM
ejpam-3517	213	14	)	)	PUNCT
ejpam-3517	213	15	is	be	AUX
ejpam-3517	213	16	trivial	trivial	ADJ
ejpam-3517	213	17	to	to	PART
ejpam-3517	213	18	prove	prove	VERB
ejpam-3517	213	19	.	.	PUNCT
ejpam-3517	214	1	property	property	NOUN
ejpam-3517	214	2	(	(	PUNCT
ejpam-3517	214	3	24	24	NUM
ejpam-3517	214	4	)	)	PUNCT
ejpam-3517	214	5	follows	follow	VERB
ejpam-3517	214	6	immediately	immediately	ADV
ejpam-3517	214	7	from	from	ADP
ejpam-3517	214	8	theorem	theorem	ADJ
ejpam-3517	214	9	3	3	NUM
ejpam-3517	214	10	,	,	PUNCT
ejpam-3517	214	11	i.e.	i.e.	X
ejpam-3517	214	12	from	from	ADP
ejpam-3517	214	13	regression	regression	NOUN
ejpam-3517	214	14	and	and	CCONJ
ejpam-3517	214	15	scale	scale	NOUN
ejpam-3517	214	16	equivariant	equivariant	ADJ
ejpam-3517	214	17	property	property	NOUN
ejpam-3517	214	18	.	.	PUNCT
ejpam-3517	215	1	the	the	DET
ejpam-3517	215	2	next	next	ADJ
ejpam-3517	215	3	figure	figure	NOUN
ejpam-3517	215	4	presents	present	VERB
ejpam-3517	215	5	the	the	DET
ejpam-3517	215	6	weighted	weight	VERB
ejpam-3517	215	7	mean	mean	NOUN
ejpam-3517	215	8	and	and	CCONJ
ejpam-3517	215	9	weighted	weight	VERB
ejpam-3517	215	10	median	median	ADJ
ejpam-3517	215	11	equivariance	equivariance	NOUN
ejpam-3517	215	12	properties	property	NOUN
ejpam-3517	215	13	presented	present	VERB
ejpam-3517	215	14	in	in	ADP
ejpam-3517	215	15	theorem	theorem	ADJ
ejpam-3517	215	16	6	6	NUM
ejpam-3517	215	17	.	.	X
ejpam-3517	216	1	for	for	ADP
ejpam-3517	216	2	example	example	NOUN
ejpam-3517	216	3	we	we	PRON
ejpam-3517	216	4	observed	observe	VERB
ejpam-3517	216	5	data	datum	NOUN
ejpam-3517	216	6	vector	vector	NOUN
ejpam-3517	216	7	a	a	PRON
ejpam-3517	216	8	and	and	CCONJ
ejpam-3517	216	9	weight	weight	NOUN
ejpam-3517	216	10	vector	vector	NOUN
ejpam-3517	216	11	w	w	NOUN
ejpam-3517	216	12	from	from	ADP
ejpam-3517	216	13	figure	figure	NOUN
ejpam-3517	216	14	3(a	3(a	NUM
ejpam-3517	216	15	)	)	PUNCT
ejpam-3517	216	16	.	.	PUNCT
ejpam-3517	217	1	parameter	parameter	PROPN
ejpam-3517	217	2	α	α	PROPN
ejpam-3517	217	3	>	>	X
ejpam-3517	217	4	0	0	NUM
ejpam-3517	217	5	do	do	AUX
ejpam-3517	217	6	not	not	PART
ejpam-3517	217	7	have	have	VERB
ejpam-3517	217	8	influence	influence	NOUN
ejpam-3517	217	9	on	on	ADP
ejpam-3517	217	10	results	result	NOUN
ejpam-3517	217	11	of	of	ADP
ejpam-3517	217	12	the	the	DET
ejpam-3517	217	13	weighted	weight	VERB
ejpam-3517	217	14	mean	mean	NOUN
ejpam-3517	217	15	and	and	CCONJ
ejpam-3517	217	16	median	median	ADJ
ejpam-3517	217	17	.	.	PUNCT
ejpam-3517	218	1	for	for	ADP
ejpam-3517	218	2	other	other	ADJ
ejpam-3517	218	3	parameters	parameter	NOUN
ejpam-3517	218	4	we	we	PRON
ejpam-3517	218	5	observed	observe	VERB
ejpam-3517	218	6	case	case	NOUN
ejpam-3517	218	7	β	β	X
ejpam-3517	218	8	=	=	SYM
ejpam-3517	218	9	−2	−2	NOUN
ejpam-3517	218	10	,	,	PUNCT
ejpam-3517	218	11	and	and	CCONJ
ejpam-3517	218	12	γ	γ	X
ejpam-3517	218	13	=	=	SYM
ejpam-3517	218	14	25	25	NUM
ejpam-3517	218	15	.	.	NOUN
ejpam-3517	218	16	1	1	NUM
ejpam-3517	218	17	2	2	NUM
ejpam-3517	218	18	3	3	NUM
ejpam-3517	218	19	4	4	NUM
ejpam-3517	218	20	5	5	NUM
ejpam-3517	218	21	1	1	NUM
ejpam-3517	218	22	2	2	NUM
ejpam-3517	218	23	3	3	NUM
ejpam-3517	218	24	4	4	NUM
ejpam-3517	218	25	5	5	NUM
ejpam-3517	218	26	23	23	NUM
ejpam-3517	218	27	21	21	NUM
ejpam-3517	218	28	19	19	NUM
ejpam-3517	218	29	17	17	NUM
ejpam-3517	218	30	15	15	NUM
ejpam-3517	218	31	1	1	NUM
ejpam-3517	218	32	2	2	NUM
ejpam-3517	218	33	3	3	NUM
ejpam-3517	218	34	4	4	NUM
ejpam-3517	218	35	5	5	NUM
ejpam-3517	218	36	1	1	NUM
ejpam-3517	218	37	2	2	NUM
ejpam-3517	218	38	3	3	NUM
ejpam-3517	218	39	4	4	NUM
ejpam-3517	218	40	5	5	NUM
ejpam-3517	218	41	23	23	NUM
ejpam-3517	218	42	21	21	NUM
ejpam-3517	218	43	19	19	NUM
ejpam-3517	218	44	17	17	NUM
ejpam-3517	218	45	15	15	NUM
ejpam-3517	218	46	βai	βai	NOUN
ejpam-3517	219	1	+	+	CCONJ
ejpam-3517	219	2	γ	γ	X
ejpam-3517	219	3	ai	ai	VERB
ejpam-3517	219	4	i	i	PRON
ejpam-3517	219	5	i	i	PRON
ejpam-3517	219	6	mean(αw	mean(αw	VERB
ejpam-3517	219	7	,	,	PUNCT
ejpam-3517	219	8	βa+	βa+	NOUN
ejpam-3517	219	9	γe	γe	NOUN
ejpam-3517	219	10	)	)	PUNCT
ejpam-3517	219	11	mean(αw	mean(αw	NOUN
ejpam-3517	219	12	,	,	PUNCT
ejpam-3517	219	13	a	a	PRON
ejpam-3517	219	14	)	)	PUNCT
ejpam-3517	219	15	med(αw	med(αw	NOUN
ejpam-3517	219	16	,	,	PUNCT
ejpam-3517	219	17	βa+	βa+	NOUN
ejpam-3517	219	18	γe	γe	NOUN
ejpam-3517	219	19	)	)	PUNCT
ejpam-3517	219	20	med(αw	med(αw	PROPN
ejpam-3517	219	21	,	,	PUNCT
ejpam-3517	219	22	a	a	NOUN
ejpam-3517	219	23	)	)	PUNCT
ejpam-3517	219	24	(	(	PUNCT
ejpam-3517	219	25	a	a	X
ejpam-3517	219	26	)	)	PUNCT
ejpam-3517	219	27	(	(	PUNCT
ejpam-3517	219	28	b	b	X
ejpam-3517	219	29	)	)	PUNCT
ejpam-3517	219	30	figure	figure	NOUN
ejpam-3517	219	31	4	4	NUM
ejpam-3517	219	32	:	:	PUNCT
ejpam-3517	219	33	equivariance	equivariance	NOUN
ejpam-3517	219	34	properties	property	NOUN
ejpam-3517	219	35	:	:	PUNCT
ejpam-3517	219	36	(	(	PUNCT
ejpam-3517	219	37	a	a	X
ejpam-3517	219	38	)	)	PUNCT
ejpam-3517	219	39	weighted	weight	VERB
ejpam-3517	219	40	mean	mean	NOUN
ejpam-3517	219	41	;	;	PUNCT
ejpam-3517	219	42	(	(	PUNCT
ejpam-3517	219	43	b	b	X
ejpam-3517	219	44	)	)	PUNCT
ejpam-3517	219	45	weighted	weight	VERB
ejpam-3517	219	46	median	median	NOUN
ejpam-3517	219	47	.	.	PUNCT
ejpam-3517	220	1	4	4	X
ejpam-3517	220	2	.	.	X
ejpam-3517	220	3	conclusion	conclusion	NOUN
ejpam-3517	220	4	considering	consider	VERB
ejpam-3517	220	5	the	the	DET
ejpam-3517	220	6	properties	property	NOUN
ejpam-3517	220	7	of	of	ADP
ejpam-3517	220	8	an	an	DET
ejpam-3517	220	9	overdetermined	overdetermine	VERB
ejpam-3517	220	10	system	system	NOUN
ejpam-3517	220	11	of	of	ADP
ejpam-3517	220	12	linear	linear	PROPN
ejpam-3517	220	13	equations	equation	NOUN
ejpam-3517	220	14	it	it	PRON
ejpam-3517	220	15	is	be	AUX
ejpam-3517	220	16	established	establish	VERB
ejpam-3517	220	17	that	that	SCONJ
ejpam-3517	220	18	the	the	DET
ejpam-3517	220	19	solution	solution	NOUN
ejpam-3517	220	20	of	of	ADP
ejpam-3517	220	21	the	the	DET
ejpam-3517	220	22	system	system	NOUN
ejpam-3517	220	23	possesses	possess	VERB
ejpam-3517	220	24	regression	regression	NOUN
ejpam-3517	220	25	,	,	PUNCT
ejpam-3517	220	26	scale	scale	NOUN
ejpam-3517	220	27	,	,	PUNCT
ejpam-3517	220	28	and	and	CCONJ
ejpam-3517	220	29	affine	affine	VERB
ejpam-3517	220	30	equivariant	equivariant	ADJ
ejpam-3517	220	31	properties	property	NOUN
ejpam-3517	220	32	in	in	ADP
ejpam-3517	220	33	observed	observed	ADJ
ejpam-3517	220	34	norm	norm	NOUN
ejpam-3517	220	35	p	p	X
ejpam-3517	220	36	∈	∈	PROPN
ejpam-3517	221	1	[	[	X
ejpam-3517	221	2	1,∞	1,∞	NUM
ejpam-3517	221	3	〉	〉	NUM
ejpam-3517	221	4	.	.	PUNCT
ejpam-3517	222	1	as	as	ADP
ejpam-3517	222	2	an	an	DET
ejpam-3517	222	3	example	example	NOUN
ejpam-3517	222	4	we	we	PRON
ejpam-3517	222	5	observed	observe	VERB
ejpam-3517	222	6	the	the	DET
ejpam-3517	222	7	problem	problem	NOUN
ejpam-3517	222	8	of	of	ADP
ejpam-3517	222	9	finding	find	VERB
ejpam-3517	222	10	the	the	DET
ejpam-3517	222	11	weighted	weight	VERB
ejpam-3517	222	12	mean	mean	NOUN
ejpam-3517	222	13	and	and	CCONJ
ejpam-3517	222	14	weighted	weight	VERB
ejpam-3517	222	15	median	median	NOUN
ejpam-3517	222	16	of	of	ADP
ejpam-3517	222	17	the	the	DET
ejpam-3517	222	18	data	datum	NOUN
ejpam-3517	222	19	.	.	PUNCT
ejpam-3517	223	1	v.	v.	ADP
ejpam-3517	223	2	novoselac	novoselac	PROPN
ejpam-3517	223	3	,	,	PUNCT
ejpam-3517	223	4	z.	z.	PROPN
ejpam-3517	223	5	pavić	pavić	PROPN
ejpam-3517	223	6	/	/	SYM
ejpam-3517	223	7	eur	eur	PROPN
ejpam-3517	223	8	.	.	PUNCT
ejpam-3517	224	1	j.	j.	PROPN
ejpam-3517	224	2	pure	pure	PROPN
ejpam-3517	224	3	appl	appl	PROPN
ejpam-3517	224	4	.	.	PROPN
ejpam-3517	224	5	math	math	PROPN
ejpam-3517	224	6	,	,	PUNCT
ejpam-3517	224	7	12	12	NUM
ejpam-3517	224	8	(	(	PUNCT
ejpam-3517	224	9	4	4	NUM
ejpam-3517	224	10	)	)	PUNCT
ejpam-3517	224	11	(	(	PUNCT
ejpam-3517	224	12	2019	2019	NUM
ejpam-3517	224	13	)	)	PUNCT
ejpam-3517	224	14	,	,	PUNCT
ejpam-3517	224	15	1360	1360	NUM
ejpam-3517	224	16	-	-	SYM
ejpam-3517	224	17	1370	1370	NUM
ejpam-3517	224	18	1368	1368	NUM
ejpam-3517	224	19	5	5	NUM
ejpam-3517	224	20	.	.	PUNCT
ejpam-3517	224	21	appendix	appendix	VERB
ejpam-3517	224	22	discrete	discrete	ADJ
ejpam-3517	224	23	forms	form	NOUN
ejpam-3517	224	24	of	of	ADP
ejpam-3517	224	25	inequalities	inequality	NOUN
ejpam-3517	224	26	a	a	DET
ejpam-3517	224	27	set	set	NOUN
ejpam-3517	224	28	s	s	NOUN
ejpam-3517	224	29	⊆	⊆	NUM
ejpam-3517	224	30	rn	rn	NOUN
ejpam-3517	224	31	is	be	AUX
ejpam-3517	224	32	said	say	VERB
ejpam-3517	224	33	to	to	PART
ejpam-3517	224	34	be	be	AUX
ejpam-3517	224	35	convex	convex	ADJ
ejpam-3517	224	36	if	if	SCONJ
ejpam-3517	224	37	,	,	PUNCT
ejpam-3517	224	38	for	for	ADP
ejpam-3517	224	39	all	all	DET
ejpam-3517	224	40	x	x	NOUN
ejpam-3517	224	41	,	,	PUNCT
ejpam-3517	224	42	y	y	PROPN
ejpam-3517	224	43	∈	∈	PROPN
ejpam-3517	224	44	s	s	X
ejpam-3517	224	45	and	and	CCONJ
ejpam-3517	224	46	all	all	DET
ejpam-3517	224	47	λ	λ	X
ejpam-3517	224	48	∈	∈	PROPN
ejpam-3517	225	1	[	[	X
ejpam-3517	225	2	0	0	NUM
ejpam-3517	225	3	,	,	PUNCT
ejpam-3517	225	4	1	1	NUM
ejpam-3517	225	5	]	]	PUNCT
ejpam-3517	225	6	,	,	PUNCT
ejpam-3517	225	7	the	the	DET
ejpam-3517	225	8	point	point	NOUN
ejpam-3517	225	9	(	(	PUNCT
ejpam-3517	225	10	1	1	NUM
ejpam-3517	225	11	−	−	NOUN
ejpam-3517	225	12	λ)x	λ)x	NOUN
ejpam-3517	225	13	+	+	CCONJ
ejpam-3517	225	14	λy	λy	PROPN
ejpam-3517	225	15	also	also	ADV
ejpam-3517	225	16	belongs	belong	VERB
ejpam-3517	225	17	to	to	ADP
ejpam-3517	225	18	s	s	PRON
ejpam-3517	225	19	,	,	PUNCT
ejpam-3517	225	20	i.e.	i.e.	X
ejpam-3517	225	21	(	(	PUNCT
ejpam-3517	225	22	1	1	NUM
ejpam-3517	225	23	−	−	NOUN
ejpam-3517	225	24	λ)x	λ)x	NOUN
ejpam-3517	225	25	+	+	CCONJ
ejpam-3517	225	26	λy	λy	PROPN
ejpam-3517	225	27	∈	∈	PROPN
ejpam-3517	225	28	s.	s.	PROPN
ejpam-3517	225	29	the	the	DET
ejpam-3517	225	30	sum	sum	NOUN
ejpam-3517	225	31	(	(	PUNCT
ejpam-3517	225	32	1	1	NUM
ejpam-3517	225	33	−	−	NOUN
ejpam-3517	225	34	λ)x	λ)x	NOUN
ejpam-3517	225	35	+	+	CCONJ
ejpam-3517	225	36	λy	λy	PROPN
ejpam-3517	225	37	is	be	AUX
ejpam-3517	225	38	called	call	VERB
ejpam-3517	225	39	binomial	binomial	ADJ
ejpam-3517	225	40	convex	convex	NOUN
ejpam-3517	225	41	combination	combination	NOUN
ejpam-3517	225	42	.	.	PUNCT
ejpam-3517	226	1	it	it	PRON
ejpam-3517	226	2	can	can	AUX
ejpam-3517	226	3	be	be	AUX
ejpam-3517	226	4	easily	easily	ADV
ejpam-3517	226	5	seen	see	VERB
ejpam-3517	226	6	that	that	SCONJ
ejpam-3517	226	7	if	if	SCONJ
ejpam-3517	226	8	we	we	PRON
ejpam-3517	226	9	have	have	VERB
ejpam-3517	226	10	m	m	NOUN
ejpam-3517	226	11	observations	observation	NOUN
ejpam-3517	226	12	x1	x1	NUM
ejpam-3517	226	13	,	,	PUNCT
ejpam-3517	226	14	.	.	PUNCT
ejpam-3517	226	15	.	.	PUNCT
ejpam-3517	227	1	.	.	PUNCT
ejpam-3517	228	1	,	,	PUNCT
ejpam-3517	228	2	xm	xm	PROPN
ejpam-3517	228	3	∈	∈	PROPN
ejpam-3517	228	4	s	s	AUX
ejpam-3517	228	5	in	in	ADP
ejpam-3517	228	6	convex	convex	NOUN
ejpam-3517	228	7	set	set	VERB
ejpam-3517	228	8	s	s	PROPN
ejpam-3517	228	9	,	,	PUNCT
ejpam-3517	228	10	and	and	CCONJ
ejpam-3517	228	11	λ1	λ1	ADJ
ejpam-3517	228	12	,	,	PUNCT
ejpam-3517	228	13	.	.	PUNCT
ejpam-3517	228	14	.	.	PUNCT
ejpam-3517	229	1	.	.	PUNCT
ejpam-3517	230	1	,	,	PUNCT
ejpam-3517	230	2	λm	λm	ADP
ejpam-3517	230	3	nonnegative	nonnegative	ADJ
ejpam-3517	230	4	number	number	NOUN
ejpam-3517	230	5	such	such	ADJ
ejpam-3517	230	6	that	that	DET
ejpam-3517	230	7	∑m	∑m	PROPN
ejpam-3517	230	8	i=1	i=1	X
ejpam-3517	230	9	λi	λi	NOUN
ejpam-3517	231	1	=	=	ADJ
ejpam-3517	232	1	1	1	NUM
ejpam-3517	232	2	,	,	PUNCT
ejpam-3517	232	3	then	then	ADV
ejpam-3517	232	4	∑m	∑m	PROPN
ejpam-3517	232	5	i=1	i=1	PROPN
ejpam-3517	232	6	λixi	λixi	PROPN
ejpam-3517	232	7	∈	∈	PROPN
ejpam-3517	232	8	s.	s.	PROPN
ejpam-3517	232	9	a	a	DET
ejpam-3517	232	10	point	point	NOUN
ejpam-3517	232	11	of	of	ADP
ejpam-3517	232	12	this	this	DET
ejpam-3517	232	13	type	type	NOUN
ejpam-3517	232	14	is	be	AUX
ejpam-3517	232	15	known	know	VERB
ejpam-3517	232	16	as	as	ADP
ejpam-3517	232	17	a	a	DET
ejpam-3517	232	18	m	m	NOUN
ejpam-3517	232	19	-	-	PUNCT
ejpam-3517	232	20	member	member	NOUN
ejpam-3517	232	21	convex	convex	NOUN
ejpam-3517	232	22	combination	combination	NOUN
ejpam-3517	232	23	of	of	ADP
ejpam-3517	232	24	x1	x1	PROPN
ejpam-3517	232	25	,	,	PUNCT
ejpam-3517	232	26	.	.	PUNCT
ejpam-3517	232	27	.	.	PUNCT
ejpam-3517	233	1	.	.	PUNCT
ejpam-3517	234	1	,	,	PUNCT
ejpam-3517	234	2	xm	xm	PROPN
ejpam-3517	234	3	.	.	PUNCT
ejpam-3517	235	1	let	let	VERB
ejpam-3517	235	2	s	s	PRON
ejpam-3517	235	3	⊆	⊆	NUM
ejpam-3517	235	4	rn	rn	NOUN
ejpam-3517	235	5	be	be	AUX
ejpam-3517	235	6	convex	convex	PROPN
ejpam-3517	235	7	,	,	PUNCT
ejpam-3517	235	8	a	a	DET
ejpam-3517	235	9	functional	functional	ADJ
ejpam-3517	235	10	f	f	NOUN
ejpam-3517	235	11	:	:	PUNCT
ejpam-3517	235	12	s	s	X
ejpam-3517	235	13	→	→	SYM
ejpam-3517	235	14	r	r	NOUN
ejpam-3517	235	15	is	be	AUX
ejpam-3517	235	16	said	say	VERB
ejpam-3517	235	17	to	to	PART
ejpam-3517	235	18	be	be	AUX
ejpam-3517	235	19	convex	convex	ADJ
ejpam-3517	235	20	if	if	SCONJ
ejpam-3517	235	21	the	the	DET
ejpam-3517	235	22	inequality	inequality	NOUN
ejpam-3517	235	23	f((1−	f((1−	PROPN
ejpam-3517	235	24	λ)x+	λ)x+	X
ejpam-3517	235	25	λy	λy	NOUN
ejpam-3517	235	26	)	)	PUNCT
ejpam-3517	235	27	≤	≤	NOUN
ejpam-3517	235	28	(	(	PUNCT
ejpam-3517	235	29	1−	1−	NUM
ejpam-3517	235	30	λ)f(x	λ)f(x	NOUN
ejpam-3517	235	31	)	)	PUNCT
ejpam-3517	235	32	+	+	NUM
ejpam-3517	235	33	λf(y	λf(y	NUM
ejpam-3517	235	34	)	)	PUNCT
ejpam-3517	235	35	(	(	PUNCT
ejpam-3517	235	36	25	25	NUM
ejpam-3517	235	37	)	)	PUNCT
ejpam-3517	235	38	holds	hold	VERB
ejpam-3517	235	39	for	for	ADP
ejpam-3517	235	40	all	all	DET
ejpam-3517	235	41	points	point	NOUN
ejpam-3517	235	42	x	x	PRON
ejpam-3517	235	43	,	,	PUNCT
ejpam-3517	235	44	y	y	PROPN
ejpam-3517	235	45	∈	∈	PROPN
ejpam-3517	235	46	s	s	PART
ejpam-3517	235	47	and	and	CCONJ
ejpam-3517	235	48	coefficient	coefficient	NOUN
ejpam-3517	235	49	λ	λ	X
ejpam-3517	235	50	∈	∈	PROPN
ejpam-3517	236	1	[	[	X
ejpam-3517	236	2	0	0	NUM
ejpam-3517	236	3	,	,	PUNCT
ejpam-3517	236	4	1	1	NUM
ejpam-3517	236	5	]	]	PUNCT
ejpam-3517	236	6	.	.	PUNCT
ejpam-3517	237	1	if	if	SCONJ
ejpam-3517	237	2	the	the	DET
ejpam-3517	237	3	inequality	inequality	NOUN
ejpam-3517	237	4	(	(	PUNCT
ejpam-3517	237	5	25	25	NUM
ejpam-3517	237	6	)	)	PUNCT
ejpam-3517	237	7	is	be	AUX
ejpam-3517	237	8	strict	strict	ADJ
ejpam-3517	237	9	for	for	SCONJ
ejpam-3517	237	10	all	all	DET
ejpam-3517	237	11	x	x	NOUN
ejpam-3517	237	12	,	,	PUNCT
ejpam-3517	237	13	y	y	PROPN
ejpam-3517	237	14	∈	∈	PROPN
ejpam-3517	237	15	s	s	PROPN
ejpam-3517	237	16	,	,	PUNCT
ejpam-3517	237	17	then	then	ADV
ejpam-3517	237	18	f(x	f(x	PROPN
ejpam-3517	237	19	)	)	PUNCT
ejpam-3517	237	20	is	be	AUX
ejpam-3517	237	21	called	call	VERB
ejpam-3517	237	22	strictly	strictly	ADV
ejpam-3517	237	23	convex	convex	ADJ
ejpam-3517	237	24	.	.	PUNCT
ejpam-3517	238	1	using	use	VERB
ejpam-3517	238	2	mathematical	mathematical	ADJ
ejpam-3517	238	3	induction	induction	NOUN
ejpam-3517	238	4	,	,	PUNCT
ejpam-3517	238	5	the	the	DET
ejpam-3517	238	6	inequality	inequality	NOUN
ejpam-3517	238	7	in	in	ADP
ejpam-3517	238	8	formula	formula	NOUN
ejpam-3517	238	9	(	(	PUNCT
ejpam-3517	238	10	25	25	NUM
ejpam-3517	238	11	)	)	PUNCT
ejpam-3517	238	12	can	can	AUX
ejpam-3517	238	13	be	be	AUX
ejpam-3517	238	14	extended	extend	VERB
ejpam-3517	238	15	to	to	PART
ejpam-3517	238	16	mmembered	mmembered	VERB
ejpam-3517	238	17	convex	convex	NOUN
ejpam-3517	238	18	combinations	combination	NOUN
ejpam-3517	238	19	.	.	PUNCT
ejpam-3517	239	1	theorem	theorem	VERB
ejpam-3517	239	2	7	7	NUM
ejpam-3517	239	3	.	.	PUNCT
ejpam-3517	240	1	(	(	PUNCT
ejpam-3517	240	2	discrete	discrete	ADJ
ejpam-3517	240	3	form	form	NOUN
ejpam-3517	240	4	of	of	ADP
ejpam-3517	240	5	jensen	jensen	PROPN
ejpam-3517	240	6	’s	’s	PART
ejpam-3517	240	7	inequality	inequality	NOUN
ejpam-3517	240	8	)	)	PUNCT
ejpam-3517	240	9	let	let	VERB
ejpam-3517	240	10	s	s	PRON
ejpam-3517	240	11	⊆	⊆	NUM
ejpam-3517	240	12	rn	rn	NOUN
ejpam-3517	240	13	be	be	AUX
ejpam-3517	240	14	a	a	DET
ejpam-3517	240	15	convex	convex	NOUN
ejpam-3517	240	16	set	set	NOUN
ejpam-3517	240	17	,	,	PUNCT
ejpam-3517	240	18	let	let	VERB
ejpam-3517	240	19	xi	xi	PRON
ejpam-3517	240	20	∈	∈	PROPN
ejpam-3517	240	21	s	s	AUX
ejpam-3517	240	22	be	be	AUX
ejpam-3517	240	23	points	point	NOUN
ejpam-3517	240	24	,	,	PUNCT
ejpam-3517	240	25	and	and	CCONJ
ejpam-3517	240	26	let	let	VERB
ejpam-3517	240	27	λi	λi	PRON
ejpam-3517	240	28	∈	∈	PRON
ejpam-3517	241	1	[	[	X
ejpam-3517	241	2	0	0	NUM
ejpam-3517	241	3	,	,	PUNCT
ejpam-3517	241	4	1	1	NUM
ejpam-3517	241	5	]	]	PUNCT
ejpam-3517	241	6	be	be	AUX
ejpam-3517	241	7	coefficients	coefficient	NOUN
ejpam-3517	242	1	such	such	ADJ
ejpam-3517	242	2	that	that	SCONJ
ejpam-3517	242	3	m∑	m∑	VERB
ejpam-3517	242	4	i=1	i=1	PROPN
ejpam-3517	242	5	λi	λi	NOUN
ejpam-3517	242	6	=	=	ADJ
ejpam-3517	242	7	1	1	X
ejpam-3517	242	8	.	.	PUNCT
ejpam-3517	243	1	then	then	ADV
ejpam-3517	243	2	each	each	DET
ejpam-3517	243	3	convex	convex	NOUN
ejpam-3517	243	4	function	function	NOUN
ejpam-3517	243	5	f	f	NOUN
ejpam-3517	243	6	:	:	PUNCT
ejpam-3517	243	7	s	s	X
ejpam-3517	243	8	→	→	SYM
ejpam-3517	243	9	r	r	NOUN
ejpam-3517	243	10	satisfies	satisfy	VERB
ejpam-3517	243	11	the	the	DET
ejpam-3517	243	12	inequality	inequality	NOUN
ejpam-3517	243	13	f	f	PROPN
ejpam-3517	243	14	(	(	PUNCT
ejpam-3517	243	15	m∑	m∑	CCONJ
ejpam-3517	243	16	i=1	i=1	PROPN
ejpam-3517	243	17	λixi	λixi	ADJ
ejpam-3517	243	18	)	)	PUNCT
ejpam-3517	243	19	≤	≤	NOUN
ejpam-3517	244	1	m∑	m∑	CCONJ
ejpam-3517	244	2	i=1	i=1	PROPN
ejpam-3517	244	3	λif(xi	λif(xi	PROPN
ejpam-3517	244	4	)	)	PUNCT
ejpam-3517	244	5	.	.	PUNCT
ejpam-3517	245	1	(	(	PUNCT
ejpam-3517	245	2	26	26	NUM
ejpam-3517	245	3	)	)	PUNCT
ejpam-3517	245	4	theorem	theorem	NOUN
ejpam-3517	245	5	8	8	NUM
ejpam-3517	245	6	.	.	PUNCT
ejpam-3517	246	1	(	(	PUNCT
ejpam-3517	246	2	discrete	discrete	ADJ
ejpam-3517	246	3	form	form	NOUN
ejpam-3517	246	4	of	of	ADP
ejpam-3517	246	5	hölder	hölder	NOUN
ejpam-3517	246	6	’s	’s	PART
ejpam-3517	246	7	inequality	inequality	NOUN
ejpam-3517	246	8	)	)	PUNCT
ejpam-3517	246	9	let	let	VERB
ejpam-3517	246	10	x	x	PRON
ejpam-3517	246	11	,	,	PUNCT
ejpam-3517	246	12	y	y	PROPN
ejpam-3517	246	13	∈	∈	PROPN
ejpam-3517	246	14	rn	rn	PROPN
ejpam-3517	246	15	be	be	AUX
ejpam-3517	246	16	points	point	NOUN
ejpam-3517	246	17	,	,	PUNCT
ejpam-3517	246	18	and	and	CCONJ
ejpam-3517	246	19	let	let	VERB
ejpam-3517	246	20	p	p	PRON
ejpam-3517	246	21	,	,	PUNCT
ejpam-3517	246	22	q	q	PROPN
ejpam-3517	246	23	∈	∈	PROPN
ejpam-3517	246	24	〈	〈	PROPN
ejpam-3517	246	25	0,∞	0,∞	PROPN
ejpam-3517	246	26	〉	〉	PROPN
ejpam-3517	246	27	be	be	AUX
ejpam-3517	246	28	numbers	number	NOUN
ejpam-3517	246	29	such	such	ADJ
ejpam-3517	246	30	that	that	DET
ejpam-3517	246	31	1	1	NUM
ejpam-3517	246	32	/	/	SYM
ejpam-3517	246	33	p+	p+	NOUN
ejpam-3517	247	1	1	1	NUM
ejpam-3517	247	2	/	/	SYM
ejpam-3517	247	3	q	q	NOUN
ejpam-3517	247	4	=	=	ADJ
ejpam-3517	247	5	1	1	X
ejpam-3517	247	6	.	.	PUNCT
ejpam-3517	248	1	then	then	ADV
ejpam-3517	248	2	we	we	PRON
ejpam-3517	248	3	have	have	VERB
ejpam-3517	248	4	the	the	DET
ejpam-3517	248	5	inequality	inequality	NOUN
ejpam-3517	248	6	m∑	m∑	SCONJ
ejpam-3517	248	7	i=1	i=1	PROPN
ejpam-3517	248	8	|xiyi|	|xiyi|	PROPN
ejpam-3517	248	9	≤	≤	PROPN
ejpam-3517	248	10	(	(	PUNCT
ejpam-3517	248	11	m∑	m∑	INTJ
ejpam-3517	248	12	i=1	i=1	PROPN
ejpam-3517	248	13	|xi|p	|xi|p	ADJ
ejpam-3517	248	14	)	)	PUNCT
ejpam-3517	248	15	1	1	NUM
ejpam-3517	248	16	p	p	NOUN
ejpam-3517	248	17	(	(	PUNCT
ejpam-3517	248	18	m∑	m∑	NOUN
ejpam-3517	248	19	i=1	i=1	PROPN
ejpam-3517	248	20	|yi|q	|yi|q	NOUN
ejpam-3517	248	21	)	)	PUNCT
ejpam-3517	248	22	1	1	NUM
ejpam-3517	248	23	q	q	NOUN
ejpam-3517	248	24	.	.	PUNCT
ejpam-3517	249	1	(	(	PUNCT
ejpam-3517	249	2	27	27	NUM
ejpam-3517	249	3	)	)	PUNCT
ejpam-3517	249	4	proof	proof	NOUN
ejpam-3517	249	5	.	.	PUNCT
ejpam-3517	250	1	assuming	assume	VERB
ejpam-3517	250	2	that	that	SCONJ
ejpam-3517	250	3	all	all	DET
ejpam-3517	250	4	points	point	NOUN
ejpam-3517	250	5	yi	yi	PROPN
ejpam-3517	250	6	are	be	AUX
ejpam-3517	250	7	different	different	ADJ
ejpam-3517	250	8	from	from	ADP
ejpam-3517	250	9	zero	zero	NUM
ejpam-3517	250	10	,	,	PUNCT
ejpam-3517	250	11	formula	formula	NOUN
ejpam-3517	250	12	(	(	PUNCT
ejpam-3517	250	13	27	27	NUM
ejpam-3517	250	14	)	)	PUNCT
ejpam-3517	250	15	can	can	AUX
ejpam-3517	250	16	be	be	AUX
ejpam-3517	250	17	obtained	obtain	VERB
ejpam-3517	250	18	from	from	ADP
ejpam-3517	250	19	formula	formula	NOUN
ejpam-3517	250	20	(	(	PUNCT
ejpam-3517	250	21	26	26	NUM
ejpam-3517	250	22	)	)	PUNCT
ejpam-3517	250	23	as	as	SCONJ
ejpam-3517	250	24	follows	follow	VERB
ejpam-3517	250	25	.	.	PUNCT
ejpam-3517	251	1	using	use	VERB
ejpam-3517	251	2	the	the	DET
ejpam-3517	251	3	points	point	NOUN
ejpam-3517	251	4	|xi||yi|−	|xi||yi|−	PROPN
ejpam-3517	251	5	q	q	NOUN
ejpam-3517	251	6	p	p	NOUN
ejpam-3517	251	7	as	as	ADP
ejpam-3517	251	8	xi	xi	PROPN
ejpam-3517	251	9	,	,	PUNCT
ejpam-3517	251	10	the	the	DET
ejpam-3517	251	11	coefficients	coefficient	NOUN
ejpam-3517	251	12	λi	λi	ADP
ejpam-3517	251	13	=	=	NOUN
ejpam-3517	251	14	|yi|q	|yi|q	NOUN
ejpam-3517	251	15	m∑	m∑	PUNCT
ejpam-3517	251	16	i=1	i=1	PROPN
ejpam-3517	251	17	|yi|q	|yi|q	NOUN
ejpam-3517	251	18	,	,	PUNCT
ejpam-3517	251	19	and	and	CCONJ
ejpam-3517	251	20	the	the	DET
ejpam-3517	251	21	convex	convex	PROPN
ejpam-3517	251	22	function	function	NOUN
ejpam-3517	251	23	xp	xp	INTJ
ejpam-3517	251	24	,	,	PUNCT
ejpam-3517	251	25	we	we	PRON
ejpam-3517	251	26	get	get	VERB
ejpam-3517	251	27	1	1	NUM
ejpam-3517	251	28	m∑	m∑	NOUN
ejpam-3517	251	29	i=1	i=1	PROPN
ejpam-3517	251	30	|yi|q	|yi|q	NOUN
ejpam-3517	251	31	m∑	m∑	NOUN
ejpam-3517	251	32	i=1	i=1	NOUN
ejpam-3517	251	33	|yi|q|xi||yi|−	|yi|q|xi||yi|−	PUNCT
ejpam-3517	251	34	q	q	PUNCT
ejpam-3517	251	35	p	p	NOUN
ejpam-3517	251	36			NOUN
ejpam-3517	251	37	p	p	NOUN
ejpam-3517	251	38	≤	≤	NUM
ejpam-3517	251	39	1	1	NUM
ejpam-3517	251	40	m∑	m∑	NOUN
ejpam-3517	251	41	i=1	i=1	PROPN
ejpam-3517	251	42	|yi|q	|yi|q	NOUN
ejpam-3517	251	43	m∑	m∑	PUNCT
ejpam-3517	251	44	i=1	i=1	PROPN
ejpam-3517	251	45	|yi|q	|yi|q	PROPN
ejpam-3517	251	46	(	(	PUNCT
ejpam-3517	251	47	|xi||yi|−	|xi||yi|−	PROPN
ejpam-3517	251	48	q	q	PROPN
ejpam-3517	251	49	p	p	NOUN
ejpam-3517	251	50	)	)	PUNCT
ejpam-3517	251	51	p	p	NOUN
ejpam-3517	251	52	.	.	PUNCT
ejpam-3517	252	1	v.	v.	CCONJ
ejpam-3517	252	2	novoselac	novoselac	PROPN
ejpam-3517	252	3	,	,	PUNCT
ejpam-3517	252	4	z.	z.	PROPN
ejpam-3517	252	5	pavić	pavić	PROPN
ejpam-3517	252	6	/	/	SYM
ejpam-3517	252	7	eur	eur	PROPN
ejpam-3517	252	8	.	.	PUNCT
ejpam-3517	253	1	j.	j.	PROPN
ejpam-3517	253	2	pure	pure	PROPN
ejpam-3517	253	3	appl	appl	PROPN
ejpam-3517	253	4	.	.	PROPN
ejpam-3517	253	5	math	math	PROPN
ejpam-3517	253	6	,	,	PUNCT
ejpam-3517	253	7	12	12	NUM
ejpam-3517	253	8	(	(	PUNCT
ejpam-3517	253	9	4	4	NUM
ejpam-3517	253	10	)	)	PUNCT
ejpam-3517	253	11	(	(	PUNCT
ejpam-3517	253	12	2019	2019	NUM
ejpam-3517	253	13	)	)	PUNCT
ejpam-3517	253	14	,	,	PUNCT
ejpam-3517	253	15	1360	1360	NUM
ejpam-3517	253	16	-	-	SYM
ejpam-3517	253	17	1370	1370	NUM
ejpam-3517	253	18	1369	1369	NUM
ejpam-3517	253	19	since	since	SCONJ
ejpam-3517	253	20	q	q	PROPN
ejpam-3517	253	21	−	−	PROPN
ejpam-3517	253	22	q	q	NOUN
ejpam-3517	253	23	/	/	SYM
ejpam-3517	253	24	p	p	NOUN
ejpam-3517	253	25	=	=	NOUN
ejpam-3517	253	26	1	1	NUM
ejpam-3517	253	27	,	,	PUNCT
ejpam-3517	253	28	it	it	PRON
ejpam-3517	253	29	follows	follow	VERB
ejpam-3517	253	30	that	that	PROPN
ejpam-3517	253	31	1	1	NUM
ejpam-3517	253	32	m∑	m∑	NOUN
ejpam-3517	254	1	i=1	i=1	PROPN
ejpam-3517	255	1	|yi|q	|yi|q	NOUN
ejpam-3517	255	2	m∑	m∑	CCONJ
ejpam-3517	255	3	i=1	i=1	PROPN
ejpam-3517	255	4	|xiyi|	|xiyi|	PROPN
ejpam-3517	255	5			NOUN
ejpam-3517	255	6	p	p	NOUN
ejpam-3517	255	7	≤	≤	NUM
ejpam-3517	255	8	1	1	NUM
ejpam-3517	255	9	m∑	m∑	NOUN
ejpam-3517	255	10	i=1	i=1	PROPN
ejpam-3517	255	11	|yi|q	|yi|q	NOUN
ejpam-3517	255	12	m∑	m∑	X
ejpam-3517	255	13	i=1	i=1	PROPN
ejpam-3517	255	14	|xi|p	|xi|p	PROPN
ejpam-3517	255	15	.	.	PUNCT
ejpam-3517	256	1	taking	take	VERB
ejpam-3517	256	2	the	the	DET
ejpam-3517	256	3	p	p	NOUN
ejpam-3517	256	4	-	-	PUNCT
ejpam-3517	256	5	th	th	VERB
ejpam-3517	256	6	root	root	NOUN
ejpam-3517	256	7	,	,	PUNCT
ejpam-3517	256	8	multiplying	multiply	VERB
ejpam-3517	256	9	by	by	ADP
ejpam-3517	256	10	∑m	∑m	PROPN
ejpam-3517	256	11	i=1	i=1	PROPN
ejpam-3517	256	12	|yi|q	|yi|q	PROPN
ejpam-3517	256	13	,	,	PUNCT
ejpam-3517	256	14	and	and	CCONJ
ejpam-3517	256	15	using	use	VERB
ejpam-3517	256	16	the	the	DET
ejpam-3517	256	17	exponent	exponent	NOUN
ejpam-3517	256	18	1	1	NUM
ejpam-3517	256	19	/	/	SYM
ejpam-3517	256	20	q	q	NOUN
ejpam-3517	256	21	instead	instead	ADV
ejpam-3517	256	22	of	of	ADP
ejpam-3517	256	23	1−	1−	NUM
ejpam-3517	256	24	1	1	NUM
ejpam-3517	256	25	/	/	SYM
ejpam-3517	256	26	p	p	NOUN
ejpam-3517	256	27	,	,	PUNCT
ejpam-3517	256	28	we	we	PRON
ejpam-3517	256	29	achieve	achieve	VERB
ejpam-3517	256	30	the	the	DET
ejpam-3517	256	31	inequality	inequality	NOUN
ejpam-3517	256	32	in	in	ADP
ejpam-3517	256	33	formula	formula	NOUN
ejpam-3517	256	34	(	(	PUNCT
ejpam-3517	256	35	27	27	NUM
ejpam-3517	256	36	)	)	PUNCT
ejpam-3517	256	37	.	.	PUNCT
ejpam-3517	257	1	if	if	SCONJ
ejpam-3517	257	2	some	some	DET
ejpam-3517	257	3	yj	yj	PROPN
ejpam-3517	257	4	is	be	AUX
ejpam-3517	257	5	equal	equal	ADJ
ejpam-3517	257	6	to	to	ADP
ejpam-3517	257	7	zero	zero	NUM
ejpam-3517	257	8	,	,	PUNCT
ejpam-3517	257	9	then	then	ADV
ejpam-3517	257	10	xjyj	xjyj	PUNCT
ejpam-3517	257	11	=	=	SYM
ejpam-3517	257	12	0	0	PUNCT
ejpam-3517	257	13	does	do	AUX
ejpam-3517	257	14	not	not	PART
ejpam-3517	257	15	increase	increase	VERB
ejpam-3517	257	16	the	the	DET
ejpam-3517	257	17	left	left	ADJ
ejpam-3517	257	18	side	side	NOUN
ejpam-3517	257	19	of	of	ADP
ejpam-3517	257	20	formula	formula	NOUN
ejpam-3517	257	21	(	(	PUNCT
ejpam-3517	257	22	27	27	NUM
ejpam-3517	257	23	)	)	PUNCT
ejpam-3517	257	24	,	,	PUNCT
ejpam-3517	257	25	but	but	CCONJ
ejpam-3517	257	26	xj	xj	PROPN
ejpam-3517	257	27	6=	6=	ADP
ejpam-3517	257	28	0	0	NUM
ejpam-3517	257	29	increases	increase	VERB
ejpam-3517	257	30	the	the	DET
ejpam-3517	257	31	right	right	ADJ
ejpam-3517	257	32	side	side	NOUN
ejpam-3517	257	33	.	.	PUNCT
ejpam-3517	258	1	utilizing	utilize	VERB
ejpam-3517	258	2	the	the	DET
ejpam-3517	258	3	vectors	vector	NOUN
ejpam-3517	258	4	x	x	PUNCT
ejpam-3517	259	1	=	=	PUNCT
ejpam-3517	260	1	[	[	X
ejpam-3517	260	2	x1	x1	PROPN
ejpam-3517	260	3	,	,	PUNCT
ejpam-3517	260	4	.	.	PUNCT
ejpam-3517	260	5	.	.	PUNCT
ejpam-3517	261	1	.	.	PUNCT
ejpam-3517	262	1	,	,	PUNCT
ejpam-3517	263	1	xn]t	xn]t	PROPN
ejpam-3517	263	2	,	,	PUNCT
ejpam-3517	263	3	y	y	PROPN
ejpam-3517	263	4	=	=	PUNCT
ejpam-3517	264	1	[	[	X
ejpam-3517	264	2	y1	y1	X
ejpam-3517	264	3	,	,	PUNCT
ejpam-3517	264	4	.	.	PUNCT
ejpam-3517	264	5	.	.	PUNCT
ejpam-3517	265	1	.	.	PUNCT
ejpam-3517	266	1	,	,	PUNCT
ejpam-3517	266	2	yn]t	yn]t	PROPN
ejpam-3517	266	3	and	and	CCONJ
ejpam-3517	266	4	z	z	NOUN
ejpam-3517	266	5	=	=	PUNCT
ejpam-3517	267	1	[	[	X
ejpam-3517	267	2	x1y1	x1y1	X
ejpam-3517	267	3	,	,	PUNCT
ejpam-3517	267	4	.	.	PUNCT
ejpam-3517	267	5	.	.	PUNCT
ejpam-3517	268	1	.	.	PUNCT
ejpam-3517	269	1	,	,	PUNCT
ejpam-3517	269	2	xnyn]t	xnyn]t	NOUN
ejpam-3517	269	3	,	,	PUNCT
ejpam-3517	269	4	formula	formula	NOUN
ejpam-3517	269	5	(	(	PUNCT
ejpam-3517	269	6	27	27	NUM
ejpam-3517	269	7	)	)	PUNCT
ejpam-3517	269	8	can	can	AUX
ejpam-3517	269	9	be	be	AUX
ejpam-3517	269	10	expressed	express	VERB
ejpam-3517	269	11	by	by	ADP
ejpam-3517	269	12	the	the	DET
ejpam-3517	269	13	norms	norm	NOUN
ejpam-3517	269	14	,	,	PUNCT
ejpam-3517	269	15	‖z‖1	‖z‖1	PROPN
ejpam-3517	269	16	≤	≤	PUNCT
ejpam-3517	269	17	‖x‖p‖y‖q	‖x‖p‖y‖q	NOUN
ejpam-3517	269	18	.	.	PUNCT
ejpam-3517	270	1	(	(	PUNCT
ejpam-3517	270	2	28	28	NUM
ejpam-3517	270	3	)	)	PUNCT
ejpam-3517	270	4	theorem	theorem	NOUN
ejpam-3517	270	5	9	9	NUM
ejpam-3517	270	6	.	.	PUNCT
ejpam-3517	271	1	(	(	PUNCT
ejpam-3517	271	2	discrete	discrete	ADJ
ejpam-3517	271	3	form	form	NOUN
ejpam-3517	271	4	of	of	ADP
ejpam-3517	271	5	minkowski	minkowski	PROPN
ejpam-3517	271	6	’s	’s	PART
ejpam-3517	271	7	inequality	inequality	NOUN
ejpam-3517	271	8	)	)	PUNCT
ejpam-3517	271	9	let	let	VERB
ejpam-3517	271	10	x	x	PRON
ejpam-3517	271	11	,	,	PUNCT
ejpam-3517	271	12	y	y	PROPN
ejpam-3517	271	13	∈	∈	PROPN
ejpam-3517	271	14	rn	rn	PROPN
ejpam-3517	271	15	be	be	AUX
ejpam-3517	271	16	points	point	NOUN
ejpam-3517	271	17	,	,	PUNCT
ejpam-3517	271	18	and	and	CCONJ
ejpam-3517	271	19	let	let	VERB
ejpam-3517	271	20	p	p	X
ejpam-3517	271	21	∈	∈	PROPN
ejpam-3517	272	1	[	[	X
ejpam-3517	272	2	1,∞	1,∞	NUM
ejpam-3517	272	3	)	)	PUNCT
ejpam-3517	272	4	be	be	VERB
ejpam-3517	272	5	a	a	DET
ejpam-3517	272	6	number	number	NOUN
ejpam-3517	272	7	.	.	PUNCT
ejpam-3517	273	1	then	then	ADV
ejpam-3517	273	2	we	we	PRON
ejpam-3517	273	3	have	have	VERB
ejpam-3517	273	4	the	the	DET
ejpam-3517	273	5	inequality	inequality	NOUN
ejpam-3517	273	6	(	(	PUNCT
ejpam-3517	273	7	m∑	m∑	ADV
ejpam-3517	273	8	i=1	i=1	PROPN
ejpam-3517	273	9	|xi	|xi	X
ejpam-3517	274	1	+	+	CCONJ
ejpam-3517	274	2	yi|p	yi|p	ADJ
ejpam-3517	274	3	)	)	PUNCT
ejpam-3517	274	4	1	1	NUM
ejpam-3517	274	5	p	p	NOUN
ejpam-3517	274	6	≤	≤	NOUN
ejpam-3517	274	7	(	(	PUNCT
ejpam-3517	274	8	m∑	m∑	INTJ
ejpam-3517	274	9	i=1	i=1	PROPN
ejpam-3517	274	10	|xi|p	|xi|p	ADJ
ejpam-3517	274	11	)	)	PUNCT
ejpam-3517	274	12	1	1	NUM
ejpam-3517	274	13	p	p	NOUN
ejpam-3517	275	1	+	+	X
ejpam-3517	275	2	(	(	PUNCT
ejpam-3517	275	3	m∑	m∑	INTJ
ejpam-3517	275	4	i=1	i=1	PROPN
ejpam-3517	275	5	|yi|p	|yi|p	NOUN
ejpam-3517	275	6	)	)	PUNCT
ejpam-3517	275	7	1	1	NUM
ejpam-3517	275	8	p	p	NOUN
ejpam-3517	275	9	.	.	PUNCT
ejpam-3517	276	1	(	(	PUNCT
ejpam-3517	276	2	29	29	NUM
ejpam-3517	276	3	)	)	PUNCT
ejpam-3517	276	4	proof	proof	NOUN
ejpam-3517	276	5	.	.	PUNCT
ejpam-3517	277	1	if	if	SCONJ
ejpam-3517	277	2	all	all	DET
ejpam-3517	277	3	xi	xi	X
ejpam-3517	277	4	and	and	CCONJ
ejpam-3517	277	5	yi	yi	PROPN
ejpam-3517	277	6	are	be	AUX
ejpam-3517	277	7	equal	equal	ADJ
ejpam-3517	277	8	to	to	ADP
ejpam-3517	277	9	zero	zero	NUM
ejpam-3517	277	10	,	,	PUNCT
ejpam-3517	277	11	then	then	ADV
ejpam-3517	277	12	formula	formula	NOUN
ejpam-3517	277	13	(	(	PUNCT
ejpam-3517	277	14	29	29	NUM
ejpam-3517	277	15	)	)	PUNCT
ejpam-3517	277	16	trivially	trivially	ADV
ejpam-3517	277	17	holds	hold	VERB
ejpam-3517	277	18	.	.	PUNCT
ejpam-3517	278	1	if	if	SCONJ
ejpam-3517	278	2	p	p	NOUN
ejpam-3517	278	3	=	=	NOUN
ejpam-3517	278	4	1	1	NUM
ejpam-3517	278	5	,	,	PUNCT
ejpam-3517	278	6	then	then	ADV
ejpam-3517	278	7	the	the	DET
ejpam-3517	278	8	inequality	inequality	NOUN
ejpam-3517	278	9	in	in	ADP
ejpam-3517	278	10	formula	formula	NOUN
ejpam-3517	278	11	(	(	PUNCT
ejpam-3517	278	12	29	29	NUM
ejpam-3517	278	13	)	)	PUNCT
ejpam-3517	278	14	follows	follow	VERB
ejpam-3517	278	15	from	from	ADP
ejpam-3517	278	16	the	the	DET
ejpam-3517	278	17	simple	simple	ADJ
ejpam-3517	278	18	triangle	triangle	NOUN
ejpam-3517	278	19	inequality	inequality	NOUN
ejpam-3517	278	20	|xi	|xi	X
ejpam-3517	279	1	+	+	NUM
ejpam-3517	279	2	yi|	yi|	PROPN
ejpam-3517	279	3	≤	≤	NOUN
ejpam-3517	279	4	|xi|+	|xi|+	VERB
ejpam-3517	279	5	|yi|	|yi|	PROPN
ejpam-3517	279	6	.	.	PUNCT
ejpam-3517	280	1	if	if	SCONJ
ejpam-3517	280	2	some	some	PRON
ejpam-3517	280	3	of	of	ADP
ejpam-3517	280	4	the	the	DET
ejpam-3517	280	5	points	point	NOUN
ejpam-3517	280	6	are	be	AUX
ejpam-3517	280	7	different	different	ADJ
ejpam-3517	280	8	from	from	ADP
ejpam-3517	280	9	zero	zero	NUM
ejpam-3517	280	10	,	,	PUNCT
ejpam-3517	280	11	and	and	CCONJ
ejpam-3517	280	12	if	if	SCONJ
ejpam-3517	280	13	p	p	X
ejpam-3517	280	14	>	>	X
ejpam-3517	280	15	1	1	NUM
ejpam-3517	280	16	,	,	PUNCT
ejpam-3517	280	17	the	the	DET
ejpam-3517	280	18	inequality	inequality	NOUN
ejpam-3517	280	19	in	in	ADP
ejpam-3517	280	20	formula	formula	NOUN
ejpam-3517	280	21	(	(	PUNCT
ejpam-3517	280	22	29	29	NUM
ejpam-3517	280	23	)	)	PUNCT
ejpam-3517	280	24	can	can	AUX
ejpam-3517	280	25	be	be	AUX
ejpam-3517	280	26	derived	derive	VERB
ejpam-3517	280	27	by	by	ADP
ejpam-3517	280	28	using	use	VERB
ejpam-3517	280	29	the	the	DET
ejpam-3517	280	30	simple	simple	ADJ
ejpam-3517	280	31	triangle	triangle	NOUN
ejpam-3517	280	32	inequality	inequality	NOUN
ejpam-3517	280	33	,	,	PUNCT
ejpam-3517	280	34	and	and	CCONJ
ejpam-3517	280	35	the	the	DET
ejpam-3517	280	36	inequality	inequality	NOUN
ejpam-3517	280	37	in	in	ADP
ejpam-3517	280	38	formula	formula	NOUN
ejpam-3517	280	39	(	(	PUNCT
ejpam-3517	280	40	27	27	NUM
ejpam-3517	280	41	)	)	PUNCT
ejpam-3517	280	42	.	.	PUNCT
ejpam-3517	281	1	in	in	ADP
ejpam-3517	281	2	this	this	DET
ejpam-3517	281	3	intention	intention	NOUN
ejpam-3517	281	4	,	,	PUNCT
ejpam-3517	281	5	we	we	PRON
ejpam-3517	281	6	have	have	VERB
ejpam-3517	281	7	m∑	m∑	NOUN
ejpam-3517	281	8	i=1	i=1	PROPN
ejpam-3517	281	9	|xi	|xi	X
ejpam-3517	282	1	+	+	PUNCT
ejpam-3517	282	2	yi|p	yi|p	ADJ
ejpam-3517	282	3	≤	≤	NOUN
ejpam-3517	282	4	m∑	m∑	CCONJ
ejpam-3517	282	5	i=1	i=1	PROPN
ejpam-3517	282	6	|xi||xi	|xi||xi	PROPN
ejpam-3517	283	1	+	+	NUM
ejpam-3517	284	1	yi|p−1	yi|p−1	PROPN
ejpam-3517	284	2	+	+	CCONJ
ejpam-3517	284	3	m∑	m∑	CCONJ
ejpam-3517	284	4	i=1	i=1	PROPN
ejpam-3517	284	5	|yi||xi	|yi||xi	PROPN
ejpam-3517	284	6	+	+	CCONJ
ejpam-3517	284	7	yi|p−1	yi|p−1	PROPN
ejpam-3517	284	8	≤	≤	NOUN
ejpam-3517	284	9	(	(	PUNCT
ejpam-3517	284	10	m∑	m∑	INTJ
ejpam-3517	284	11	i=1	i=1	PROPN
ejpam-3517	284	12	|xi|p	|xi|p	ADV
ejpam-3517	284	13	)	)	PUNCT
ejpam-3517	284	14	1	1	NUM
ejpam-3517	284	15	p	p	NOUN
ejpam-3517	284	16	(	(	PUNCT
ejpam-3517	284	17	m∑	m∑	INTJ
ejpam-3517	284	18	i=1	i=1	PROPN
ejpam-3517	284	19	|xi	|xi	X
ejpam-3517	285	1	+	+	NUM
ejpam-3517	285	2	yi|(p−1)q	yi|(p−1)q	NOUN
ejpam-3517	285	3	)	)	PUNCT
ejpam-3517	285	4	1	1	NUM
ejpam-3517	285	5	q	q	NOUN
ejpam-3517	285	6	+	+	CCONJ
ejpam-3517	285	7	(	(	PUNCT
ejpam-3517	285	8	m∑	m∑	INTJ
ejpam-3517	285	9	i=1	i=1	PROPN
ejpam-3517	285	10	|yi|p	|yi|p	NOUN
ejpam-3517	285	11	)	)	PUNCT
ejpam-3517	285	12	1	1	NUM
ejpam-3517	285	13	p	p	NOUN
ejpam-3517	285	14	(	(	PUNCT
ejpam-3517	285	15	m∑	m∑	INTJ
ejpam-3517	285	16	i=1	i=1	PROPN
ejpam-3517	285	17	|xi	|xi	X
ejpam-3517	286	1	+	+	NUM
ejpam-3517	286	2	yi|(p−1)q	yi|(p−1)q	NOUN
ejpam-3517	286	3	)	)	PUNCT
ejpam-3517	286	4	1	1	NUM
ejpam-3517	286	5	q	q	NOUN
ejpam-3517	286	6	=	=	SYM
ejpam-3517	286	7			PROPN
ejpam-3517	286	8	(	(	PUNCT
ejpam-3517	286	9	m∑	m∑	ADV
ejpam-3517	286	10	i=1	i=1	PROPN
ejpam-3517	286	11	|xi|p	|xi|p	ADJ
ejpam-3517	286	12	)	)	PUNCT
ejpam-3517	286	13	1	1	NUM
ejpam-3517	286	14	p	p	NOUN
ejpam-3517	286	15	+	+	X
ejpam-3517	286	16	(	(	PUNCT
ejpam-3517	286	17	m∑	m∑	INTJ
ejpam-3517	286	18	i=1	i=1	PROPN
ejpam-3517	286	19	|yi|p	|yi|p	NOUN
ejpam-3517	286	20	)	)	PUNCT
ejpam-3517	286	21	1	1	NUM
ejpam-3517	286	22	p	p	PRON
ejpam-3517	286	23			PROPN
ejpam-3517	286	24	(	(	PUNCT
ejpam-3517	286	25	m∑	m∑	ADV
ejpam-3517	286	26	i=1	i=1	PROPN
ejpam-3517	286	27	|xi	|xi	X
ejpam-3517	287	1	+	+	CCONJ
ejpam-3517	287	2	yi|p	yi|p	ADJ
ejpam-3517	287	3	)	)	PUNCT
ejpam-3517	287	4	1	1	NUM
ejpam-3517	287	5	q	q	NOUN
ejpam-3517	287	6	because	because	SCONJ
ejpam-3517	287	7	(	(	PUNCT
ejpam-3517	287	8	p−1)q	p−1)q	NOUN
ejpam-3517	287	9	=	=	SYM
ejpam-3517	287	10	p.	p.	NOUN
ejpam-3517	287	11	dividing	dividing	NOUN
ejpam-3517	287	12	by	by	ADP
ejpam-3517	287	13	(	(	PUNCT
ejpam-3517	287	14	∑n	∑n	PROPN
ejpam-3517	287	15	i=1	i=1	PROPN
ejpam-3517	287	16	|xi	|xi	X
ejpam-3517	287	17	+	+	NOUN
ejpam-3517	287	18	yi|p	yi|p	ADJ
ejpam-3517	287	19	)	)	PUNCT
ejpam-3517	287	20	1	1	NUM
ejpam-3517	287	21	/	/	SYM
ejpam-3517	287	22	q	q	NOUN
ejpam-3517	287	23	,	,	PUNCT
ejpam-3517	287	24	and	and	CCONJ
ejpam-3517	287	25	putting	put	VERB
ejpam-3517	287	26	1	1	NUM
ejpam-3517	287	27	/	/	SYM
ejpam-3517	287	28	p	p	NOUN
ejpam-3517	287	29	instead	instead	ADV
ejpam-3517	287	30	of	of	ADP
ejpam-3517	287	31	1−1	1−1	NUM
ejpam-3517	287	32	/	/	SYM
ejpam-3517	287	33	q	q	NOUN
ejpam-3517	287	34	,	,	PUNCT
ejpam-3517	287	35	we	we	PRON
ejpam-3517	287	36	obtain	obtain	VERB
ejpam-3517	287	37	the	the	DET
ejpam-3517	287	38	inequality	inequality	NOUN
ejpam-3517	287	39	in	in	ADP
ejpam-3517	287	40	formula	formula	NOUN
ejpam-3517	287	41	(	(	PUNCT
ejpam-3517	287	42	29	29	NUM
ejpam-3517	287	43	)	)	PUNCT
ejpam-3517	287	44	.	.	PUNCT
ejpam-3517	288	1	using	use	VERB
ejpam-3517	288	2	p	p	NOUN
ejpam-3517	288	3	norms	norm	NOUN
ejpam-3517	288	4	of	of	ADP
ejpam-3517	288	5	the	the	DET
ejpam-3517	288	6	vectors	vector	NOUN
ejpam-3517	288	7	x	x	SYM
ejpam-3517	288	8	,	,	PUNCT
ejpam-3517	288	9	y	y	PROPN
ejpam-3517	288	10	and	and	CCONJ
ejpam-3517	288	11	x	x	PROPN
ejpam-3517	289	1	+	+	CCONJ
ejpam-3517	289	2	y	y	PROPN
ejpam-3517	289	3	,	,	PUNCT
ejpam-3517	289	4	the	the	DET
ejpam-3517	289	5	inequality	inequality	NOUN
ejpam-3517	289	6	in	in	ADP
ejpam-3517	289	7	formula	formula	NOUN
ejpam-3517	289	8	(	(	PUNCT
ejpam-3517	289	9	29	29	NUM
ejpam-3517	289	10	)	)	PUNCT
ejpam-3517	289	11	takes	take	VERB
ejpam-3517	289	12	the	the	DET
ejpam-3517	289	13	form	form	NOUN
ejpam-3517	289	14	‖x+	‖x+	PROPN
ejpam-3517	289	15	y‖p	y‖p	NOUN
ejpam-3517	289	16	≤	≤	NUM
ejpam-3517	289	17	‖x‖p	‖x‖p	PROPN
ejpam-3517	289	18	+	+	CCONJ
ejpam-3517	289	19	‖y‖p	‖y‖p	NOUN
ejpam-3517	289	20	.	.	PUNCT
ejpam-3517	290	1	(	(	PUNCT
ejpam-3517	290	2	30	30	NUM
ejpam-3517	290	3	)	)	PUNCT
ejpam-3517	290	4	references	reference	NOUN
ejpam-3517	290	5	1370	1370	NUM
ejpam-3517	290	6	references	reference	NOUN
ejpam-3517	290	7	[	[	X
ejpam-3517	290	8	1	1	NUM
ejpam-3517	290	9	]	]	PUNCT
ejpam-3517	290	10	p.	p.	PROPN
ejpam-3517	290	11	bloomfield	bloomfield	PROPN
ejpam-3517	290	12	,	,	PUNCT
ejpam-3517	290	13	and	and	CCONJ
ejpam-3517	290	14	w.	w.	PROPN
ejpam-3517	290	15	steiger	steiger	PROPN
ejpam-3517	290	16	.	.	PUNCT
ejpam-3517	291	1	least	least	ADJ
ejpam-3517	291	2	absolute	absolute	ADJ
ejpam-3517	291	3	deviations	deviation	NOUN
ejpam-3517	291	4	:	:	PUNCT
ejpam-3517	291	5	theory	theory	NOUN
ejpam-3517	291	6	,	,	PUNCT
ejpam-3517	291	7	applications	application	NOUN
ejpam-3517	291	8	and	and	CCONJ
ejpam-3517	291	9	algorithms	algorithm	NOUN
ejpam-3517	291	10	.	.	PUNCT
ejpam-3517	292	1	birkhauser	birkhauser	PROPN
ejpam-3517	292	2	,	,	PUNCT
ejpam-3517	292	3	boston	boston	PROPN
ejpam-3517	292	4	,	,	PUNCT
ejpam-3517	292	5	1983	1983	NUM
ejpam-3517	292	6	.	.	PUNCT
ejpam-3517	293	1	[	[	X
ejpam-3517	293	2	2	2	X
ejpam-3517	293	3	]	]	PUNCT
ejpam-3517	293	4	j.	j.	PROPN
ejpam-3517	293	5	a.	a.	PROPN
ejpam-3517	293	6	cadzow	cadzow	PROPN
ejpam-3517	293	7	.	.	PUNCT
ejpam-3517	294	1	minimum	minimum	ADJ
ejpam-3517	294	2	`	`	PUNCT
ejpam-3517	294	3	1	1	NUM
ejpam-3517	294	4	,	,	PUNCT
ejpam-3517	294	5	`	`	PUNCT
ejpam-3517	294	6	2	2	NUM
ejpam-3517	294	7	,	,	PUNCT
ejpam-3517	294	8	and	and	CCONJ
ejpam-3517	294	9	`	`	PUNCT
ejpam-3517	294	10	∞	∞	NUM
ejpam-3517	294	11	norm	norm	NOUN
ejpam-3517	294	12	approximate	approximate	ADJ
ejpam-3517	294	13	solutions	solution	NOUN
ejpam-3517	294	14	to	to	ADP
ejpam-3517	294	15	an	an	DET
ejpam-3517	294	16	overdetermined	overdetermine	VERB
ejpam-3517	294	17	system	system	NOUN
ejpam-3517	294	18	of	of	ADP
ejpam-3517	294	19	linear	linear	PROPN
ejpam-3517	294	20	equations	equation	NOUN
ejpam-3517	294	21	.	.	PUNCT
ejpam-3517	295	1	digital	digital	ADJ
ejpam-3517	295	2	signal	signal	NOUN
ejpam-3517	295	3	processing	processing	NOUN
ejpam-3517	295	4	,	,	PUNCT
ejpam-3517	295	5	12(4	12(4	NUM
ejpam-3517	295	6	):	):	PUNCT
ejpam-3517	295	7	524	524	NUM
ejpam-3517	295	8	-	-	SYM
ejpam-3517	295	9	560	560	NUM
ejpam-3517	295	10	,	,	PUNCT
ejpam-3517	295	11	2002	2002	NUM
ejpam-3517	295	12	.	.	PUNCT
ejpam-3517	296	1	[	[	X
ejpam-3517	296	2	3	3	X
ejpam-3517	296	3	]	]	PUNCT
ejpam-3517	296	4	m.	m.	NOUN
ejpam-3517	296	5	fiedler	fiedler	PROPN
ejpam-3517	296	6	,	,	PUNCT
ejpam-3517	296	7	j.	j.	PROPN
ejpam-3517	296	8	nedoma	nedoma	PROPN
ejpam-3517	296	9	,	,	PUNCT
ejpam-3517	296	10	j.	j.	PROPN
ejpam-3517	296	11	ramik	ramik	PROPN
ejpam-3517	296	12	,	,	PUNCT
ejpam-3517	296	13	j.	j.	PROPN
ejpam-3517	296	14	rohn	rohn	PROPN
ejpam-3517	296	15	,	,	PUNCT
ejpam-3517	296	16	and	and	CCONJ
ejpam-3517	296	17	k.	k.	PROPN
ejpam-3517	296	18	zimmermann	zimmermann	PROPN
ejpam-3517	296	19	.	.	PUNCT
ejpam-3517	297	1	linear	linear	ADJ
ejpam-3517	297	2	optimization	optimization	NOUN
ejpam-3517	297	3	problems	problem	NOUN
ejpam-3517	297	4	with	with	ADP
ejpam-3517	297	5	inexact	inexact	ADJ
ejpam-3517	297	6	data	datum	NOUN
ejpam-3517	297	7	.	.	PUNCT
ejpam-3517	298	1	springer	springer	NOUN
ejpam-3517	298	2	,	,	PUNCT
ejpam-3517	298	3	2006	2006	NUM
ejpam-3517	298	4	.	.	PUNCT
ejpam-3517	299	1	[	[	X
ejpam-3517	299	2	4	4	X
ejpam-3517	299	3	]	]	PUNCT
ejpam-3517	299	4	j.	j.	PROPN
ejpam-3517	299	5	mićić	mićić	PROPN
ejpam-3517	299	6	,	,	PUNCT
ejpam-3517	299	7	z.	z.	PROPN
ejpam-3517	299	8	pavić	pavić	PROPN
ejpam-3517	299	9	,	,	PUNCT
ejpam-3517	299	10	and	and	CCONJ
ejpam-3517	299	11	j.	j.	PROPN
ejpam-3517	299	12	pečarić.	pečarić.	PROPN
ejpam-3517	299	13	the	the	DET
ejpam-3517	299	14	inequalities	inequality	NOUN
ejpam-3517	299	15	for	for	ADP
ejpam-3517	299	16	quasiarithmetic	quasiarithmetic	ADJ
ejpam-3517	299	17	means	mean	NOUN
ejpam-3517	299	18	.	.	PUNCT
ejpam-3517	300	1	abstract	abstract	ADJ
ejpam-3517	300	2	and	and	CCONJ
ejpam-3517	300	3	applied	apply	VERB
ejpam-3517	300	4	analysis	analysis	NOUN
ejpam-3517	300	5	,	,	PUNCT
ejpam-3517	300	6	2012	2012	NUM
ejpam-3517	300	7	:	:	PUNCT
ejpam-3517	300	8	1	1	NUM
ejpam-3517	300	9	-	-	SYM
ejpam-3517	300	10	25	25	NUM
ejpam-3517	300	11	,	,	PUNCT
ejpam-3517	300	12	2012	2012	NUM
ejpam-3517	300	13	.	.	PUNCT
ejpam-3517	301	1	[	[	X
ejpam-3517	301	2	5	5	X
ejpam-3517	301	3	]	]	PUNCT
ejpam-3517	301	4	t.	t.	PROPN
ejpam-3517	301	5	needham	needham	PROPN
ejpam-3517	301	6	.	.	PUNCT
ejpam-3517	302	1	a	a	DET
ejpam-3517	302	2	visual	visual	ADJ
ejpam-3517	302	3	explanation	explanation	NOUN
ejpam-3517	302	4	of	of	ADP
ejpam-3517	302	5	jensen	jensen	PROPN
ejpam-3517	302	6	’s	’s	PART
ejpam-3517	302	7	inequality	inequality	NOUN
ejpam-3517	302	8	.	.	PUNCT
ejpam-3517	303	1	american	american	PROPN
ejpam-3517	303	2	mathematical	mathematical	PROPN
ejpam-3517	303	3	monthly	monthly	ADV
ejpam-3517	303	4	,	,	PUNCT
ejpam-3517	303	5	100(8	100(8	NUM
ejpam-3517	303	6	):	):	PUNCT
ejpam-3517	303	7	768	768	NUM
ejpam-3517	303	8	-	-	SYM
ejpam-3517	303	9	771	771	NUM
ejpam-3517	303	10	,	,	PUNCT
ejpam-3517	303	11	1993	1993	NUM
ejpam-3517	303	12	.	.	PUNCT
ejpam-3517	304	1	[	[	X
ejpam-3517	304	2	6	6	NUM
ejpam-3517	304	3	]	]	PUNCT
ejpam-3517	304	4	c.	c.	PROPN
ejpam-3517	304	5	p.	p.	PROPN
ejpam-3517	304	6	niculescu	niculescu	PROPN
ejpam-3517	304	7	,	,	PUNCT
ejpam-3517	304	8	and	and	CCONJ
ejpam-3517	304	9	l.	l.	PROPN
ejpam-3517	304	10	e.	e.	PROPN
ejpam-3517	304	11	persson	persson	PROPN
ejpam-3517	304	12	.	.	PUNCT
ejpam-3517	304	13	convex	convex	NOUN
ejpam-3517	304	14	functions	function	NOUN
ejpam-3517	304	15	and	and	CCONJ
ejpam-3517	304	16	their	their	PRON
ejpam-3517	304	17	applications	application	NOUN
ejpam-3517	304	18	.	.	PUNCT
ejpam-3517	305	1	canadian	canadian	ADJ
ejpam-3517	305	2	mathematical	mathematical	ADJ
ejpam-3517	305	3	society	society	NOUN
ejpam-3517	305	4	,	,	PUNCT
ejpam-3517	305	5	springer	springer	NOUN
ejpam-3517	305	6	,	,	PUNCT
ejpam-3517	305	7	new	new	PROPN
ejpam-3517	305	8	york	york	PROPN
ejpam-3517	305	9	,	,	PUNCT
ejpam-3517	305	10	usa	usa	PROPN
ejpam-3517	305	11	,	,	PUNCT
ejpam-3517	305	12	2006	2006	NUM
ejpam-3517	305	13	.	.	PUNCT
ejpam-3517	306	1	[	[	X
ejpam-3517	306	2	7	7	X
ejpam-3517	306	3	]	]	PUNCT
ejpam-3517	306	4	m.	m.	PROPN
ejpam-3517	306	5	r.	r.	PROPN
ejpam-3517	306	6	osborne	osborne	PROPN
ejpam-3517	306	7	.	.	PUNCT
ejpam-3517	307	1	finite	finite	PROPN
ejpam-3517	307	2	algorithms	algorithm	NOUN
ejpam-3517	307	3	in	in	ADP
ejpam-3517	307	4	optimization	optimization	NOUN
ejpam-3517	307	5	and	and	CCONJ
ejpam-3517	307	6	data	datum	NOUN
ejpam-3517	307	7	analysis	analysis	NOUN
ejpam-3517	307	8	.	.	PUNCT
ejpam-3517	308	1	departmant	departmant	ADJ
ejpam-3517	308	2	of	of	ADP
ejpam-3517	308	3	statistics	statistic	NOUN
ejpam-3517	308	4	,	,	PUNCT
ejpam-3517	308	5	australian	australian	ADJ
ejpam-3517	308	6	national	national	ADJ
ejpam-3517	308	7	university	university	PROPN
ejpam-3517	308	8	,	,	PUNCT
ejpam-3517	308	9	camberra	camberra	PROPN
ejpam-3517	308	10	,	,	PUNCT
ejpam-3517	308	11	john	john	PROPN
ejpam-3517	308	12	wiley	wiley	PROPN
ejpam-3517	308	13	,	,	PUNCT
ejpam-3517	308	14	1985	1985	NUM
ejpam-3517	308	15	.	.	PUNCT
ejpam-3517	309	1	[	[	X
ejpam-3517	309	2	8	8	NUM
ejpam-3517	309	3	]	]	PUNCT
ejpam-3517	309	4	z.	z.	PROPN
ejpam-3517	309	5	pavić	pavić	PROPN
ejpam-3517	309	6	,	,	PUNCT
ejpam-3517	309	7	j.	j.	PROPN
ejpam-3517	309	8	pečarić	pečarić	PROPN
ejpam-3517	309	9	,	,	PUNCT
ejpam-3517	309	10	and	and	CCONJ
ejpam-3517	309	11	i.	i.	PROPN
ejpam-3517	309	12	perić.	perić.	PROPN
ejpam-3517	309	13	integral	integral	ADJ
ejpam-3517	309	14	,	,	PUNCT
ejpam-3517	309	15	discrete	discrete	ADJ
ejpam-3517	309	16	and	and	CCONJ
ejpam-3517	309	17	functional	functional	ADJ
ejpam-3517	309	18	variants	variant	NOUN
ejpam-3517	309	19	of	of	ADP
ejpam-3517	309	20	jensen	jensen	PROPN
ejpam-3517	309	21	’s	’s	PART
ejpam-3517	309	22	inequality	inequality	NOUN
ejpam-3517	309	23	.	.	PUNCT
ejpam-3517	310	1	journal	journal	PROPN
ejpam-3517	310	2	of	of	ADP
ejpam-3517	310	3	mathematical	mathematical	ADJ
ejpam-3517	310	4	inequalities	inequality	NOUN
ejpam-3517	310	5	,	,	PUNCT
ejpam-3517	310	6	5(2	5(2	NUM
ejpam-3517	310	7	):	):	PUNCT
ejpam-3517	310	8	253	253	NUM
ejpam-3517	310	9	-	-	SYM
ejpam-3517	310	10	264	264	NUM
ejpam-3517	310	11	,	,	PUNCT
ejpam-3517	310	12	2011	2011	NUM
ejpam-3517	310	13	.	.	PUNCT
ejpam-3517	311	1	[	[	X
ejpam-3517	311	2	9	9	NUM
ejpam-3517	311	3	]	]	PUNCT
ejpam-3517	311	4	j.	j.	PROPN
ejpam-3517	311	5	e.	e.	PROPN
ejpam-3517	311	6	pečarić	pečarić	PROPN
ejpam-3517	311	7	,	,	PUNCT
ejpam-3517	311	8	f.	f.	PROPN
ejpam-3517	311	9	proschan	proschan	PROPN
ejpam-3517	311	10	,	,	PUNCT
ejpam-3517	311	11	and	and	CCONJ
ejpam-3517	311	12	y.	y.	PROPN
ejpam-3517	311	13	l.	l.	PROPN
ejpam-3517	311	14	tong	tong	PROPN
ejpam-3517	311	15	.	.	PUNCT
ejpam-3517	312	1	convex	convex	PROPN
ejpam-3517	312	2	functions	function	NOUN
ejpam-3517	312	3	,	,	PUNCT
ejpam-3517	312	4	partial	partial	ADJ
ejpam-3517	312	5	orderings	ordering	NOUN
ejpam-3517	312	6	,	,	PUNCT
ejpam-3517	312	7	and	and	CCONJ
ejpam-3517	312	8	statistical	statistical	ADJ
ejpam-3517	312	9	applications	application	NOUN
ejpam-3517	312	10	.	.	PUNCT
ejpam-3517	313	1	academic	academic	ADJ
ejpam-3517	313	2	press	press	NOUN
ejpam-3517	313	3	,	,	PUNCT
ejpam-3517	313	4	new	new	PROPN
ejpam-3517	313	5	york	york	PROPN
ejpam-3517	313	6	,	,	PUNCT
ejpam-3517	313	7	usa	usa	PROPN
ejpam-3517	313	8	,	,	PUNCT
ejpam-3517	313	9	1992	1992	NUM
ejpam-3517	313	10	.	.	PUNCT
ejpam-3517	314	1	[	[	X
ejpam-3517	314	2	10	10	NUM
ejpam-3517	314	3	]	]	X
ejpam-3517	314	4	i.	i.	NOUN
ejpam-3517	314	5	pitas	pitas	PROPN
ejpam-3517	314	6	.	.	PUNCT
ejpam-3517	315	1	digital	digital	ADJ
ejpam-3517	315	2	image	image	NOUN
ejpam-3517	315	3	processing	processing	NOUN
ejpam-3517	315	4	algorithms	algorithm	NOUN
ejpam-3517	315	5	and	and	CCONJ
ejpam-3517	315	6	applications	application	NOUN
ejpam-3517	315	7	.	.	PUNCT
ejpam-3517	316	1	john	john	PROPN
ejpam-3517	316	2	wiley	wiley	PROPN
ejpam-3517	316	3	&	&	CCONJ
ejpam-3517	316	4	sons	son	NOUN
ejpam-3517	316	5	,	,	PUNCT
ejpam-3517	316	6	2000	2000	NUM
ejpam-3517	316	7	.	.	PUNCT
ejpam-3517	317	1	[	[	X
ejpam-3517	317	2	11	11	NUM
ejpam-3517	317	3	]	]	PUNCT
ejpam-3517	317	4	p.	p.	PROPN
ejpam-3517	317	5	j.	j.	PROPN
ejpam-3517	317	6	rousseeuw	rousseeuw	PROPN
ejpam-3517	317	7	,	,	PUNCT
ejpam-3517	317	8	and	and	CCONJ
ejpam-3517	317	9	a.	a.	NOUN
ejpam-3517	317	10	m.	m.	PROPN
ejpam-3517	317	11	leroy	leroy	PROPN
ejpam-3517	317	12	.	.	PUNCT
ejpam-3517	318	1	robust	robust	ADJ
ejpam-3517	318	2	regression	regression	NOUN
ejpam-3517	318	3	and	and	CCONJ
ejpam-3517	318	4	outlier	outlier	NOUN
ejpam-3517	318	5	detection	detection	NOUN
ejpam-3517	318	6	.	.	PUNCT
ejpam-3517	319	1	wiley	wiley	PROPN
ejpam-3517	319	2	,	,	PUNCT
ejpam-3517	319	3	new	new	PROPN
ejpam-3517	319	4	york	york	PROPN
ejpam-3517	319	5	,	,	PUNCT
ejpam-3517	319	6	2003	2003	NUM
ejpam-3517	319	7	.	.	PUNCT
ejpam-3517	320	1	[	[	X
ejpam-3517	320	2	12	12	NUM
ejpam-3517	320	3	]	]	X
ejpam-3517	320	4	w.	w.	PROPN
ejpam-3517	320	5	rudin	rudin	PROPN
ejpam-3517	320	6	.	.	PUNCT
ejpam-3517	321	1	real	real	ADJ
ejpam-3517	321	2	and	and	CCONJ
ejpam-3517	321	3	complex	complex	ADJ
ejpam-3517	321	4	analysis	analysis	NOUN
ejpam-3517	321	5	.	.	PUNCT
ejpam-3517	322	1	mcgraw	mcgraw	PROPN
ejpam-3517	322	2	-	-	PUNCT
ejpam-3517	322	3	hill	hill	PROPN
ejpam-3517	322	4	,	,	PUNCT
ejpam-3517	322	5	new	new	PROPN
ejpam-3517	322	6	york	york	PROPN
ejpam-3517	322	7	,	,	PUNCT
ejpam-3517	322	8	usa	usa	PROPN
ejpam-3517	322	9	,	,	PUNCT
ejpam-3517	322	10	1987	1987	NUM
ejpam-3517	322	11	.	.	PUNCT
ejpam-3517	323	1	[	[	X
ejpam-3517	323	2	13	13	NUM
ejpam-3517	323	3	]	]	X
ejpam-3517	323	4	v.	v.	ADP
ejpam-3517	323	5	sit	sit	VERB
ejpam-3517	323	6	,	,	PUNCT
ejpam-3517	323	7	and	and	CCONJ
ejpam-3517	323	8	m.	m.	PROPN
ejpam-3517	323	9	poulin	poulin	PROPN
ejpam-3517	323	10	-	-	PUNCT
ejpam-3517	323	11	costello	costello	PROPN
ejpam-3517	323	12	.	.	PUNCT
ejpam-3517	324	1	catalogue	catalogue	NOUN
ejpam-3517	324	2	of	of	ADP
ejpam-3517	324	3	curves	curve	NOUN
ejpam-3517	324	4	for	for	ADP
ejpam-3517	324	5	curve	curve	NOUN
ejpam-3517	324	6	fitting	fitting	ADJ
ejpam-3517	324	7	.	.	PUNCT
ejpam-3517	325	1	biometrics	biometric	NOUN
ejpam-3517	325	2	information	information	PROPN
ejpam-3517	325	3	handbook	handbook	NOUN
ejpam-3517	325	4	series	series	PROPN
ejpam-3517	325	5	,	,	PUNCT
ejpam-3517	325	6	no	no	INTJ
ejpam-3517	325	7	.	.	NOUN
ejpam-3517	325	8	4	4	NUM
ejpam-3517	325	9	,	,	PUNCT
ejpam-3517	325	10	1994	1994	NUM
ejpam-3517	325	11	.	.	PUNCT
ejpam-3517	326	1	[	[	X
ejpam-3517	326	2	14	14	NUM
ejpam-3517	326	3	]	]	X
ejpam-3517	326	4	i.	i.	NOUN
ejpam-3517	326	5	vazler	vazler	PROPN
ejpam-3517	326	6	,	,	PUNCT
ejpam-3517	326	7	k.	k.	PROPN
ejpam-3517	326	8	sabo	sabo	PROPN
ejpam-3517	326	9	,	,	PUNCT
ejpam-3517	326	10	and	and	CCONJ
ejpam-3517	326	11	r.	r.	PROPN
ejpam-3517	326	12	scitovski	scitovski	PROPN
ejpam-3517	326	13	.	.	PUNCT
ejpam-3517	327	1	weighted	weight	VERB
ejpam-3517	327	2	median	median	NOUN
ejpam-3517	327	3	of	of	ADP
ejpam-3517	327	4	the	the	DET
ejpam-3517	327	5	data	datum	NOUN
ejpam-3517	327	6	in	in	ADP
ejpam-3517	327	7	solving	solve	VERB
ejpam-3517	327	8	least	least	ADJ
ejpam-3517	327	9	absolute	absolute	ADJ
ejpam-3517	327	10	deviations	deviation	NOUN
ejpam-3517	327	11	problems	problem	NOUN
ejpam-3517	327	12	.	.	PUNCT
ejpam-3517	328	1	communications	communication	NOUN
ejpam-3517	328	2	in	in	ADP
ejpam-3517	328	3	statistics	statistic	NOUN
ejpam-3517	328	4	-	-	PUNCT
ejpam-3517	328	5	theory	theory	NOUN
ejpam-3517	328	6	and	and	CCONJ
ejpam-3517	328	7	methods	method	NOUN
ejpam-3517	328	8	,	,	PUNCT
ejpam-3517	328	9	41(8	41(8	NUM
ejpam-3517	328	10	):	):	PUNCT
ejpam-3517	328	11	1455	1455	NUM
ejpam-3517	328	12	-	-	SYM
ejpam-3517	328	13	1465	1465	NUM
ejpam-3517	328	14	,	,	PUNCT
ejpam-3517	328	15	2012	2012	NUM
ejpam-3517	328	16	.	.	PUNCT
ejpam-3517	329	1	[	[	X
ejpam-3517	329	2	15	15	NUM
ejpam-3517	329	3	]	]	X
ejpam-3517	329	4	g.	g.	PROPN
ejpam-3517	329	5	a.	a.	PROPN
ejpam-3517	329	6	watson	watson	PROPN
ejpam-3517	329	7	.	.	PUNCT
ejpam-3517	330	1	aproximation	aproximation	NOUN
ejpam-3517	330	2	theory	theory	NOUN
ejpam-3517	330	3	and	and	CCONJ
ejpam-3517	330	4	numerical	numerical	ADJ
ejpam-3517	330	5	methods	method	NOUN
ejpam-3517	330	6	.	.	PUNCT
ejpam-3517	331	1	john	john	PROPN
ejpam-3517	331	2	wiley	wiley	PROPN
ejpam-3517	331	3	&	&	CCONJ
ejpam-3517	331	4	sons	son	NOUN
ejpam-3517	331	5	,	,	PUNCT
ejpam-3517	331	6	1980	1980	NUM
ejpam-3517	331	7	.	.	PUNCT