id	sid	tid	token	lemma	pos
ijassa-1077	1	1	microsoft	microsoft	PROPN
ijassa-1077	1	2	word	word	PROPN
ijassa-1077	1	3	1077	1077	NUM
ijassa-1077	1	4	article	article	NOUN
ijassa-1077	1	5	text	text	NOUN
ijassa-1077	1	6	,	,	PUNCT
ijassa-1077	1	7	copyedited.docx	copyedited.docx	VERB
ijassa-1077	1	8	adv	adv	PROPN
ijassa-1077	1	9	syst	syst	PROPN
ijassa-1077	1	10	sci	sci	PROPN
ijassa-1077	1	11	appl	appl	PROPN
ijassa-1077	1	12	2021	2021	NUM
ijassa-1077	1	13	;	;	PUNCT
ijassa-1077	1	14	02	02	NUM
ijassa-1077	1	15	;	;	PUNCT
ijassa-1077	1	16	117	117	NUM
ijassa-1077	1	17	-	-	SYM
ijassa-1077	1	18	132	132	NUM
ijassa-1077	1	19	published	publish	VERB
ijassa-1077	1	20	online	online	ADV
ijassa-1077	1	21	at	at	ADP
ijassa-1077	1	22	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1077	1	23	.	.	PUNCT
ijassa-1077	2	1	mathematical	mathematical	ADJ
ijassa-1077	2	2	modeling	modeling	NOUN
ijassa-1077	2	3	of	of	ADP
ijassa-1077	2	4	color	color	NOUN
ijassa-1077	2	5	printing	printing	NOUN
ijassa-1077	2	6	devices	device	NOUN
ijassa-1077	2	7	:	:	PUNCT
ijassa-1077	2	8	color	color	NOUN
ijassa-1077	2	9	gamut	gamut	NOUN
ijassa-1077	2	10	visualization	visualization	NOUN
ijassa-1077	2	11	and	and	CCONJ
ijassa-1077	2	12	colorimetric	colorimetric	ADJ
ijassa-1077	2	13	measurements	measurement	NOUN
ijassa-1077	2	14	regularization	regularization	NOUN
ijassa-1077	2	15	dmitry	dmitry	PROPN
ijassa-1077	2	16	v.	v.	ADP
ijassa-1077	2	17	tunitsky	tunitsky	PROPN
ijassa-1077	2	18	*	*	PUNCT
ijassa-1077	2	19	v.a	v.a	PROPN
ijassa-1077	2	20	.	.	PROPN
ijassa-1077	2	21	trapeznikov	trapeznikov	PROPN
ijassa-1077	2	22	institute	institute	PROPN
ijassa-1077	2	23	of	of	ADP
ijassa-1077	2	24	control	control	PROPN
ijassa-1077	2	25	sciences	sciences	PROPN
ijassa-1077	2	26	,	,	PUNCT
ijassa-1077	2	27	russian	russian	ADJ
ijassa-1077	2	28	academy	academy	PROPN
ijassa-1077	2	29	of	of	ADP
ijassa-1077	2	30	sciences	sciences	PROPN
ijassa-1077	2	31	,	,	PUNCT
ijassa-1077	2	32	moscow	moscow	PROPN
ijassa-1077	2	33	,	,	PUNCT
ijassa-1077	2	34	russia	russia	PROPN
ijassa-1077	2	35	e	e	NOUN
ijassa-1077	2	36	-	-	NOUN
ijassa-1077	2	37	mail	mail	NOUN
ijassa-1077	2	38	:	:	PUNCT
ijassa-1077	3	1	dtunitsky@yahoo.com	dtunitsky@yahoo.com	X
ijassa-1077	3	2	abstract	abstract	NOUN
ijassa-1077	3	3	:	:	PUNCT
ijassa-1077	3	4	the	the	DET
ijassa-1077	3	5	article	article	NOUN
ijassa-1077	3	6	concerns	concern	VERB
ijassa-1077	3	7	a	a	DET
ijassa-1077	3	8	piecewise	piecewise	NOUN
ijassa-1077	3	9	linear	linear	NOUN
ijassa-1077	3	10	modeling	modeling	NOUN
ijassa-1077	3	11	of	of	ADP
ijassa-1077	3	12	a	a	DET
ijassa-1077	3	13	vast	vast	ADJ
ijassa-1077	3	14	range	range	NOUN
ijassa-1077	3	15	of	of	ADP
ijassa-1077	3	16	color	color	NOUN
ijassa-1077	3	17	printing	printing	NOUN
ijassa-1077	3	18	devices	device	NOUN
ijassa-1077	3	19	:	:	PUNCT
ijassa-1077	3	20	various	various	ADJ
ijassa-1077	3	21	printers	printer	NOUN
ijassa-1077	3	22	of	of	ADP
ijassa-1077	3	23	different	different	ADJ
ijassa-1077	3	24	kind	kind	NOUN
ijassa-1077	3	25	and	and	CCONJ
ijassa-1077	3	26	nature	nature	NOUN
ijassa-1077	3	27	,	,	PUNCT
ijassa-1077	3	28	presses	press	NOUN
ijassa-1077	3	29	,	,	PUNCT
ijassa-1077	3	30	etc	etc	X
ijassa-1077	3	31	.	.	X
ijassa-1077	4	1	the	the	DET
ijassa-1077	4	2	central	central	ADJ
ijassa-1077	4	3	purpose	purpose	NOUN
ijassa-1077	4	4	is	be	AUX
ijassa-1077	4	5	not	not	PART
ijassa-1077	4	6	a	a	DET
ijassa-1077	4	7	presentation	presentation	NOUN
ijassa-1077	4	8	of	of	ADP
ijassa-1077	4	9	ready	ready	ADJ
ijassa-1077	4	10	to	to	PART
ijassa-1077	4	11	use	use	VERB
ijassa-1077	4	12	computational	computational	ADJ
ijassa-1077	4	13	algorithms	algorithm	NOUN
ijassa-1077	4	14	,	,	PUNCT
ijassa-1077	4	15	or	or	CCONJ
ijassa-1077	4	16	,	,	PUNCT
ijassa-1077	4	17	moreover	moreover	ADV
ijassa-1077	4	18	,	,	PUNCT
ijassa-1077	4	19	accomplished	accomplished	ADJ
ijassa-1077	4	20	software	software	NOUN
ijassa-1077	4	21	solutions	solution	NOUN
ijassa-1077	4	22	.	.	PUNCT
ijassa-1077	5	1	the	the	DET
ijassa-1077	5	2	point	point	NOUN
ijassa-1077	5	3	is	be	AUX
ijassa-1077	5	4	to	to	PART
ijassa-1077	5	5	reveal	reveal	VERB
ijassa-1077	5	6	some	some	DET
ijassa-1077	5	7	aspects	aspect	NOUN
ijassa-1077	5	8	of	of	ADP
ijassa-1077	5	9	mathematical	mathematical	ADJ
ijassa-1077	5	10	modeling	modeling	NOUN
ijassa-1077	5	11	,	,	PUNCT
ijassa-1077	5	12	which	which	PRON
ijassa-1077	5	13	could	could	AUX
ijassa-1077	5	14	serve	serve	VERB
ijassa-1077	5	15	as	as	ADP
ijassa-1077	5	16	both	both	CCONJ
ijassa-1077	5	17	a	a	DET
ijassa-1077	5	18	guideline	guideline	NOUN
ijassa-1077	5	19	for	for	ADP
ijassa-1077	5	20	creation	creation	NOUN
ijassa-1077	5	21	of	of	ADP
ijassa-1077	5	22	practical	practical	ADJ
ijassa-1077	5	23	and	and	CCONJ
ijassa-1077	5	24	robust	robust	ADJ
ijassa-1077	5	25	engineer	engineer	NOUN
ijassa-1077	5	26	solutions	solution	NOUN
ijassa-1077	5	27	and	and	CCONJ
ijassa-1077	5	28	an	an	DET
ijassa-1077	5	29	example	example	NOUN
ijassa-1077	5	30	of	of	ADP
ijassa-1077	5	31	nontrivial	nontrivial	ADJ
ijassa-1077	5	32	application	application	NOUN
ijassa-1077	5	33	of	of	ADP
ijassa-1077	5	34	piecewise	piecewise	NOUN
ijassa-1077	5	35	linear	linear	PROPN
ijassa-1077	5	36	topology	topology	NOUN
ijassa-1077	5	37	.	.	PUNCT
ijassa-1077	6	1	keywords	keyword	NOUN
ijassa-1077	6	2	:	:	PUNCT
ijassa-1077	6	3	colorant	colorant	ADJ
ijassa-1077	6	4	space	space	NOUN
ijassa-1077	6	5	,	,	PUNCT
ijassa-1077	6	6	reference	reference	NOUN
ijassa-1077	6	7	space	space	NOUN
ijassa-1077	6	8	,	,	PUNCT
ijassa-1077	6	9	piecewise	piecewise	PROPN
ijassa-1077	6	10	linear	linear	PROPN
ijassa-1077	6	11	model	model	NOUN
ijassa-1077	6	12	,	,	PUNCT
ijassa-1077	6	13	singular	singular	PROPN
ijassa-1077	6	14	faces	face	VERB
ijassa-1077	6	15	,	,	PUNCT
ijassa-1077	6	16	proper	proper	ADJ
ijassa-1077	6	17	printing	printing	NOUN
ijassa-1077	6	18	device	device	NOUN
ijassa-1077	6	19	,	,	PUNCT
ijassa-1077	6	20	non	non	ADJ
ijassa-1077	6	21	-	-	ADJ
ijassa-1077	6	22	degenerate	degenerate	ADJ
ijassa-1077	6	23	printing	printing	NOUN
ijassa-1077	6	24	device	device	NOUN
ijassa-1077	6	25	,	,	PUNCT
ijassa-1077	6	26	regular	regular	ADJ
ijassa-1077	6	27	printing	printing	NOUN
ijassa-1077	6	28	device	device	NOUN
ijassa-1077	6	29	1	1	NUM
ijassa-1077	6	30	.	.	PUNCT
ijassa-1077	7	1	preliminaries	preliminary	NOUN
ijassa-1077	7	2	consider	consider	VERB
ijassa-1077	7	3	a	a	DET
ijassa-1077	7	4	stimuli	stimulus	NOUN
ijassa-1077	7	5	space	space	NOUN
ijassa-1077	7	6	ℝ	ℝ	PROPN
ijassa-1077	7	7	!	!	PROPN
ijassa-1077	7	8	of	of	ADP
ijassa-1077	7	9	m	m	PROPN
ijassa-1077	7	10	colorants	colorant	NOUN
ijassa-1077	7	11	and	and	CCONJ
ijassa-1077	7	12	a	a	DET
ijassa-1077	7	13	reference	reference	NOUN
ijassa-1077	7	14	space	space	NOUN
ijassa-1077	7	15	ℝ	ℝ	PROPN
ijassa-1077	7	16	"	"	PUNCT
ijassa-1077	7	17	of	of	ADP
ijassa-1077	7	18	n	n	DET
ijassa-1077	7	19	colors	color	NOUN
ijassa-1077	7	20	.	.	PUNCT
ijassa-1077	8	1	in	in	ADP
ijassa-1077	8	2	color	color	NOUN
ijassa-1077	8	3	management	management	NOUN
ijassa-1077	8	4	practice	practice	NOUN
ijassa-1077	8	5	,	,	PUNCT
ijassa-1077	8	6	the	the	DET
ijassa-1077	8	7	dimension	dimension	NOUN
ijassa-1077	8	8	of	of	ADP
ijassa-1077	8	9	reference	reference	NOUN
ijassa-1077	8	10	space	space	NOUN
ijassa-1077	8	11	n	n	PRON
ijassa-1077	8	12	is	be	AUX
ijassa-1077	8	13	always	always	ADV
ijassa-1077	8	14	equal	equal	ADJ
ijassa-1077	8	15	to	to	ADP
ijassa-1077	8	16	three	three	NUM
ijassa-1077	8	17	,	,	PUNCT
ijassa-1077	8	18	n	n	NOUN
ijassa-1077	8	19	=	=	SYM
ijassa-1077	8	20	3	3	NUM
ijassa-1077	8	21	,	,	PUNCT
ijassa-1077	8	22	since	since	SCONJ
ijassa-1077	8	23	any	any	DET
ijassa-1077	8	24	color	color	NOUN
ijassa-1077	8	25	can	can	AUX
ijassa-1077	8	26	be	be	AUX
ijassa-1077	8	27	described	describe	VERB
ijassa-1077	8	28	exactly	exactly	ADV
ijassa-1077	8	29	by	by	ADP
ijassa-1077	8	30	three	three	NUM
ijassa-1077	8	31	real	real	ADJ
ijassa-1077	8	32	numbers	number	NOUN
ijassa-1077	8	33	who	who	PRON
ijassa-1077	8	34	are	be	AUX
ijassa-1077	8	35	the	the	DET
ijassa-1077	8	36	coordinates	coordinate	NOUN
ijassa-1077	8	37	of	of	ADP
ijassa-1077	8	38	this	this	DET
ijassa-1077	8	39	color	color	NOUN
ijassa-1077	8	40	in	in	ADP
ijassa-1077	8	41	some	some	DET
ijassa-1077	8	42	color	color	NOUN
ijassa-1077	8	43	space	space	NOUN
ijassa-1077	8	44	,	,	PUNCT
ijassa-1077	8	45	e.g.	e.g.	ADV
ijassa-1077	8	46	,	,	PUNCT
ijassa-1077	8	47	xyz	xyz	PROPN
ijassa-1077	8	48	,	,	PUNCT
ijassa-1077	8	49	lab	lab	NOUN
ijassa-1077	8	50	,	,	PUNCT
ijassa-1077	8	51	etc	etc	X
ijassa-1077	8	52	.	.	X
ijassa-1077	9	1	the	the	DET
ijassa-1077	9	2	dimension	dimension	NOUN
ijassa-1077	9	3	m	m	VERB
ijassa-1077	9	4	of	of	ADP
ijassa-1077	9	5	stimuli	stimulus	NOUN
ijassa-1077	9	6	space	space	NOUN
ijassa-1077	9	7	can	can	AUX
ijassa-1077	9	8	vary	vary	VERB
ijassa-1077	9	9	in	in	ADP
ijassa-1077	9	10	accordance	accordance	NOUN
ijassa-1077	9	11	with	with	ADP
ijassa-1077	9	12	the	the	DET
ijassa-1077	9	13	number	number	NOUN
ijassa-1077	9	14	of	of	ADP
ijassa-1077	9	15	colorants	colorant	NOUN
ijassa-1077	9	16	the	the	DET
ijassa-1077	9	17	considered	consider	VERB
ijassa-1077	9	18	printing	printing	NOUN
ijassa-1077	9	19	device	device	NOUN
ijassa-1077	9	20	uses	use	NOUN
ijassa-1077	9	21	.	.	PUNCT
ijassa-1077	10	1	this	this	DET
ijassa-1077	10	2	dimension	dimension	NOUN
ijassa-1077	10	3	is	be	AUX
ijassa-1077	10	4	called	call	VERB
ijassa-1077	10	5	a	a	DET
ijassa-1077	10	6	dimension	dimension	NOUN
ijassa-1077	10	7	of	of	ADP
ijassa-1077	10	8	a	a	DET
ijassa-1077	10	9	printing	printing	NOUN
ijassa-1077	10	10	device	device	NOUN
ijassa-1077	10	11	.	.	PUNCT
ijassa-1077	11	1	in	in	ADP
ijassa-1077	11	2	most	most	ADJ
ijassa-1077	11	3	practical	practical	ADJ
ijassa-1077	11	4	cases	case	NOUN
ijassa-1077	11	5	the	the	DET
ijassa-1077	11	6	dimension	dimension	NOUN
ijassa-1077	11	7	of	of	ADP
ijassa-1077	11	8	printing	printing	NOUN
ijassa-1077	11	9	device	device	NOUN
ijassa-1077	11	10	is	be	AUX
ijassa-1077	11	11	either	either	DET
ijassa-1077	11	12	three	three	NUM
ijassa-1077	11	13	,	,	PUNCT
ijassa-1077	11	14	m	m	VERB
ijassa-1077	11	15	=	=	NOUN
ijassa-1077	11	16	3	3	NUM
ijassa-1077	11	17	,	,	PUNCT
ijassa-1077	11	18	or	or	CCONJ
ijassa-1077	11	19	four	four	NUM
ijassa-1077	11	20	,	,	PUNCT
ijassa-1077	11	21	m	m	VERB
ijassa-1077	11	22	=	=	NOUN
ijassa-1077	11	23	4	4	X
ijassa-1077	11	24	.	.	PUNCT
ijassa-1077	12	1	in	in	ADP
ijassa-1077	12	2	the	the	DET
ijassa-1077	12	3	first	first	ADJ
ijassa-1077	12	4	case	case	NOUN
ijassa-1077	12	5	we	we	PRON
ijassa-1077	12	6	deal	deal	VERB
ijassa-1077	12	7	with	with	ADP
ijassa-1077	12	8	a	a	DET
ijassa-1077	12	9	three	three	NUM
ijassa-1077	12	10	-	-	PUNCT
ijassa-1077	12	11	dimensional	dimensional	ADJ
ijassa-1077	12	12	printing	printing	NOUN
ijassa-1077	12	13	device	device	NOUN
ijassa-1077	12	14	and	and	CCONJ
ijassa-1077	12	15	in	in	ADP
ijassa-1077	12	16	the	the	DET
ijassa-1077	12	17	second	second	ADJ
ijassa-1077	12	18	case	case	NOUN
ijassa-1077	12	19	we	we	PRON
ijassa-1077	12	20	deal	deal	VERB
ijassa-1077	12	21	with	with	ADP
ijassa-1077	12	22	a	a	DET
ijassa-1077	12	23	four	four	NUM
ijassa-1077	12	24	-	-	PUNCT
ijassa-1077	12	25	dimensional	dimensional	ADJ
ijassa-1077	12	26	printing	printing	NOUN
ijassa-1077	12	27	device	device	NOUN
ijassa-1077	12	28	.	.	PUNCT
ijassa-1077	13	1	not	not	PART
ijassa-1077	13	2	all	all	DET
ijassa-1077	13	3	the	the	DET
ijassa-1077	13	4	combinations	combination	NOUN
ijassa-1077	13	5	(	(	PUNCT
ijassa-1077	13	6	x1,	x1,	NOUN
ijassa-1077	13	7	…	…	X
ijassa-1077	13	8	,xm	,xm	X
ijassa-1077	13	9	)	)	PUNCT
ijassa-1077	13	10	of	of	ADP
ijassa-1077	13	11	real	real	ADJ
ijassa-1077	13	12	numbers	number	NOUN
ijassa-1077	13	13	represent	represent	VERB
ijassa-1077	13	14	combination	combination	NOUN
ijassa-1077	13	15	of	of	ADP
ijassa-1077	13	16	colorants	colorant	NOUN
ijassa-1077	13	17	,	,	PUNCT
ijassa-1077	13	18	because	because	SCONJ
ijassa-1077	13	19	the	the	DET
ijassa-1077	13	20	amount	amount	NOUN
ijassa-1077	13	21	xk	xk	PROPN
ijassa-1077	13	22	,	,	PUNCT
ijassa-1077	13	23	1£k£m	1£k£m	NUM
ijassa-1077	13	24	,	,	PUNCT
ijassa-1077	13	25	of	of	ADP
ijassa-1077	13	26	the	the	DET
ijassa-1077	13	27	k	k	PROPN
ijassa-1077	13	28	-	-	PUNCT
ijassa-1077	13	29	th	th	VERB
ijassa-1077	13	30	colorant	colorant	NOUN
ijassa-1077	13	31	is	be	AUX
ijassa-1077	13	32	measured	measure	VERB
ijassa-1077	13	33	in	in	ADP
ijassa-1077	13	34	percents	percent	NOUN
ijassa-1077	13	35	and	and	CCONJ
ijassa-1077	13	36	can	can	AUX
ijassa-1077	13	37	vary	vary	VERB
ijassa-1077	13	38	from	from	ADP
ijassa-1077	13	39	zero	zero	NUM
ijassa-1077	13	40	percents	percent	NOUN
ijassa-1077	13	41	(	(	PUNCT
ijassa-1077	13	42	do	do	AUX
ijassa-1077	13	43	not	not	PART
ijassa-1077	13	44	put	put	VERB
ijassa-1077	13	45	the	the	DET
ijassa-1077	13	46	colorant	colorant	NOUN
ijassa-1077	13	47	at	at	ADV
ijassa-1077	13	48	all	all	ADV
ijassa-1077	13	49	)	)	PUNCT
ijassa-1077	13	50	to	to	ADP
ijassa-1077	13	51	one	one	NUM
ijassa-1077	13	52	hundred	hundred	NUM
ijassa-1077	13	53	percents	percent	NOUN
ijassa-1077	13	54	(	(	PUNCT
ijassa-1077	13	55	put	put	VERB
ijassa-1077	13	56	as	as	ADV
ijassa-1077	13	57	much	much	ADJ
ijassa-1077	13	58	colorant	colorant	NOUN
ijassa-1077	13	59	as	as	ADP
ijassa-1077	13	60	possible	possible	ADJ
ijassa-1077	13	61	)	)	PUNCT
ijassa-1077	13	62	.	.	PUNCT
ijassa-1077	14	1	a	a	DET
ijassa-1077	14	2	printing	printing	NOUN
ijassa-1077	14	3	device	device	NOUN
ijassa-1077	14	4	renders	render	VERB
ijassa-1077	14	5	a	a	DET
ijassa-1077	14	6	combination	combination	NOUN
ijassa-1077	14	7	(	(	PUNCT
ijassa-1077	14	8	x1,	x1,	NOUN
ijassa-1077	14	9	…	…	X
ijassa-1077	14	10	,xm	,xm	X
ijassa-1077	14	11	)	)	PUNCT
ijassa-1077	14	12	of	of	ADP
ijassa-1077	14	13	colorants	colorant	NOUN
ijassa-1077	14	14	into	into	ADP
ijassa-1077	14	15	the	the	DET
ijassa-1077	14	16	corresponding	correspond	VERB
ijassa-1077	14	17	color	color	NOUN
ijassa-1077	14	18	(	(	PUNCT
ijassa-1077	14	19	y1	y1	NOUN
ijassa-1077	14	20	,	,	PUNCT
ijassa-1077	14	21	y2	y2	PROPN
ijassa-1077	14	22	,	,	PUNCT
ijassa-1077	14	23	y3	y3	PROPN
ijassa-1077	14	24	)	)	PUNCT
ijassa-1077	14	25	.	.	PUNCT
ijassa-1077	15	1	it	it	PRON
ijassa-1077	15	2	means	mean	VERB
ijassa-1077	15	3	that	that	SCONJ
ijassa-1077	15	4	a	a	DET
ijassa-1077	15	5	printing	printing	NOUN
ijassa-1077	15	6	device	device	NOUN
ijassa-1077	15	7	can	can	AUX
ijassa-1077	15	8	be	be	AUX
ijassa-1077	15	9	described	describe	VERB
ijassa-1077	15	10	by	by	ADP
ijassa-1077	15	11	a	a	DET
ijassa-1077	15	12	map	map	NOUN
ijassa-1077	15	13	f	f	X
ijassa-1077	15	14	:	:	PUNCT
ijassa-1077	15	15	wm	wm	PROPN
ijassa-1077	15	16	®	®	NOUN
ijassa-1077	15	17	ℝ	ℝ	NOUN
ijassa-1077	15	18	#	#	NOUN
ijassa-1077	15	19	,	,	PUNCT
ijassa-1077	15	20	where	where	SCONJ
ijassa-1077	15	21	wm	wm	PROPN
ijassa-1077	15	22	=	=	PRON
ijassa-1077	15	23	{	{	PUNCT
ijassa-1077	15	24	(	(	PUNCT
ijassa-1077	15	25	x1	x1	PROPN
ijassa-1077	15	26	,	,	PUNCT
ijassa-1077	15	27	…	…	PUNCT
ijassa-1077	15	28	,	,	PUNCT
ijassa-1077	15	29	xm	xm	PROPN
ijassa-1077	15	30	)	)	PUNCT
ijassa-1077	15	31	,	,	PUNCT
ijassa-1077	15	32	0	0	PUNCT
ijassa-1077	15	33	£	£	NUM
ijassa-1077	15	34	x1	x1	NUM
ijassa-1077	15	35	,	,	PUNCT
ijassa-1077	15	36	…	…	PUNCT
ijassa-1077	15	37	,	,	PUNCT
ijassa-1077	15	38	xm£100	xm£100	X
ijassa-1077	15	39	}	}	PUNCT
ijassa-1077	15	40	is	be	AUX
ijassa-1077	15	41	the	the	DET
ijassa-1077	15	42	m	m	ADJ
ijassa-1077	15	43	-	-	ADJ
ijassa-1077	15	44	dimensional	dimensional	ADJ
ijassa-1077	15	45	colorants	colorant	NOUN
ijassa-1077	15	46	cube	cube	NOUN
ijassa-1077	15	47	in	in	ADP
ijassa-1077	15	48	the	the	DET
ijassa-1077	15	49	stimuli	stimulus	NOUN
ijassa-1077	15	50	space	space	NOUN
ijassa-1077	15	51	ℝ	ℝ	PROPN
ijassa-1077	15	52	!	!	PROPN
ijassa-1077	15	53	and	and	CCONJ
ijassa-1077	15	54	f(x1	f(x1	ADJ
ijassa-1077	15	55	,	,	PUNCT
ijassa-1077	15	56	…	…	PUNCT
ijassa-1077	15	57	,	,	PUNCT
ijassa-1077	15	58	xm	xm	X
ijassa-1077	15	59	)	)	PUNCT
ijassa-1077	15	60	=	=	PRON
ijassa-1077	15	61	(	(	PUNCT
ijassa-1077	15	62	y1	y1	INTJ
ijassa-1077	15	63	,	,	PUNCT
ijassa-1077	15	64	y2	y2	PROPN
ijassa-1077	15	65	,	,	PUNCT
ijassa-1077	15	66	y3	y3	PROPN
ijassa-1077	15	67	)	)	PUNCT
ijassa-1077	15	68	is	be	AUX
ijassa-1077	15	69	the	the	DET
ijassa-1077	15	70	point	point	NOUN
ijassa-1077	15	71	,	,	PUNCT
ijassa-1077	15	72	whose	whose	DET
ijassa-1077	15	73	coordinates	coordinate	NOUN
ijassa-1077	15	74	correspond	correspond	VERB
ijassa-1077	15	75	to	to	ADP
ijassa-1077	15	76	the	the	DET
ijassa-1077	15	77	color	color	NOUN
ijassa-1077	15	78	rendered	render	VERB
ijassa-1077	15	79	by	by	ADP
ijassa-1077	15	80	mixture	mixture	NOUN
ijassa-1077	15	81	of	of	ADP
ijassa-1077	15	82	the	the	DET
ijassa-1077	15	83	colorants	colorant	NOUN
ijassa-1077	15	84	combination	combination	NOUN
ijassa-1077	15	85	.	.	PUNCT
ijassa-1077	16	1	we	we	PRON
ijassa-1077	16	2	will	will	AUX
ijassa-1077	16	3	call	call	VERB
ijassa-1077	16	4	such	such	DET
ijassa-1077	16	5	a	a	DET
ijassa-1077	16	6	map	map	NOUN
ijassa-1077	16	7	a	a	DET
ijassa-1077	16	8	printing	printing	NOUN
ijassa-1077	16	9	device	device	NOUN
ijassa-1077	16	10	.	.	PUNCT
ijassa-1077	17	1	to	to	PART
ijassa-1077	17	2	find	find	VERB
ijassa-1077	17	3	the	the	DET
ijassa-1077	17	4	value	value	NOUN
ijassa-1077	17	5	of	of	ADP
ijassa-1077	17	6	this	this	DET
ijassa-1077	17	7	function	function	NOUN
ijassa-1077	17	8	we	we	PRON
ijassa-1077	17	9	should	should	AUX
ijassa-1077	17	10	with	with	ADP
ijassa-1077	17	11	the	the	DET
ijassa-1077	17	12	printing	print	VERB
ijassa-1077	17	13	device	device	NOUN
ijassa-1077	17	14	under	under	ADP
ijassa-1077	17	15	consideration	consideration	NOUN
ijassa-1077	17	16	reproduce	reproduce	NOUN
ijassa-1077	17	17	on	on	ADP
ijassa-1077	17	18	a	a	DET
ijassa-1077	17	19	sheet	sheet	NOUN
ijassa-1077	17	20	of	of	ADP
ijassa-1077	17	21	paper	paper	NOUN
ijassa-1077	17	22	the	the	DET
ijassa-1077	17	23	patch	patch	NOUN
ijassa-1077	17	24	formed	form	VERB
ijassa-1077	17	25	by	by	ADP
ijassa-1077	17	26	the	the	DET
ijassa-1077	17	27	colorants	colorant	NOUN
ijassa-1077	17	28	combination	combination	NOUN
ijassa-1077	17	29	(	(	PUNCT
ijassa-1077	17	30	x1,	x1,	NOUN
ijassa-1077	17	31	…	…	X
ijassa-1077	17	32	,xm	,xm	X
ijassa-1077	17	33	)	)	PUNCT
ijassa-1077	17	34	and	and	CCONJ
ijassa-1077	17	35	measure	measure	VERB
ijassa-1077	17	36	the	the	DET
ijassa-1077	17	37	color	color	NOUN
ijassa-1077	17	38	coordinates	coordinate	NOUN
ijassa-1077	17	39	(	(	PUNCT
ijassa-1077	17	40	y1	y1	INTJ
ijassa-1077	17	41	,	,	PUNCT
ijassa-1077	17	42	y2	y2	PROPN
ijassa-1077	17	43	,	,	PUNCT
ijassa-1077	17	44	y3	y3	PROPN
ijassa-1077	17	45	)	)	PUNCT
ijassa-1077	17	46	of	of	ADP
ijassa-1077	17	47	this	this	DET
ijassa-1077	17	48	patch	patch	NOUN
ijassa-1077	17	49	by	by	ADP
ijassa-1077	17	50	a	a	DET
ijassa-1077	17	51	colorimetric	colorimetric	ADJ
ijassa-1077	17	52	measurement	measurement	NOUN
ijassa-1077	17	53	tool	tool	NOUN
ijassa-1077	17	54	.	.	PUNCT
ijassa-1077	18	1	the	the	DET
ijassa-1077	18	2	number	number	NOUN
ijassa-1077	18	3	of	of	ADP
ijassa-1077	18	4	colorants	colorant	NOUN
ijassa-1077	18	5	combinations	combination	NOUN
ijassa-1077	18	6	(	(	PUNCT
ijassa-1077	18	7	x1,	x1,	NOUN
ijassa-1077	18	8	…	…	X
ijassa-1077	18	9	,xm	,xm	PUNCT
ijassa-1077	18	10	)	)	PUNCT
ijassa-1077	18	11	in	in	ADP
ijassa-1077	18	12	the	the	DET
ijassa-1077	18	13	colorants	colorant	NOUN
ijassa-1077	18	14	cube	cube	NOUN
ijassa-1077	18	15	is	be	AUX
ijassa-1077	18	16	infinite	infinite	ADJ
ijassa-1077	18	17	and	and	CCONJ
ijassa-1077	18	18	of	of	ADP
ijassa-1077	18	19	cause	cause	SCONJ
ijassa-1077	18	20	it	it	PRON
ijassa-1077	18	21	’s	’	VERB
ijassa-1077	18	22	impossible	impossible	ADJ
ijassa-1077	18	23	to	to	PART
ijassa-1077	18	24	print	print	VERB
ijassa-1077	18	25	and	and	CCONJ
ijassa-1077	18	26	measure	measure	VERB
ijassa-1077	18	27	all	all	PRON
ijassa-1077	18	28	of	of	ADP
ijassa-1077	18	29	them	they	PRON
ijassa-1077	18	30	,	,	PUNCT
ijassa-1077	18	31	since	since	SCONJ
ijassa-1077	18	32	actually	actually	ADV
ijassa-1077	18	33	we	we	PRON
ijassa-1077	18	34	can	can	AUX
ijassa-1077	18	35	print	print	VERB
ijassa-1077	18	36	and	and	CCONJ
ijassa-1077	18	37	measure	measure	VERB
ijassa-1077	18	38	only	only	ADV
ijassa-1077	18	39	the	the	DET
ijassa-1077	18	40	finite	finite	NOUN
ijassa-1077	18	41	subset	subset	NOUN
ijassa-1077	18	42	of	of	ADP
ijassa-1077	18	43	such	such	ADJ
ijassa-1077	18	44	combinations	combination	NOUN
ijassa-1077	18	45	.	.	PUNCT
ijassa-1077	19	1	consider	consider	VERB
ijassa-1077	19	2	a	a	DET
ijassa-1077	19	3	finite	finite	ADJ
ijassa-1077	19	4	set	set	NOUN
ijassa-1077	19	5	{	{	PUNCT
ijassa-1077	19	6	wi	wi	PROPN
ijassa-1077	19	7	}	}	PUNCT
ijassa-1077	19	8	ì	ì	PROPN
ijassa-1077	19	9	wm	wm	PROPN
ijassa-1077	19	10	,	,	PUNCT
ijassa-1077	19	11	i.e.	i.e.	X
ijassa-1077	19	12	,	,	PUNCT
ijassa-1077	19	13	a	a	DET
ijassa-1077	19	14	*	*	PUNCT
ijassa-1077	19	15	corresponding	correspond	VERB
ijassa-1077	19	16	author	author	NOUN
ijassa-1077	19	17	:	:	PUNCT
ijassa-1077	19	18	dtunitsky@yahoo.com	dtunitsky@yahoo.com	X
ijassa-1077	19	19	mw	mw	PROPN
ijassa-1077	19	20	118	118	NUM
ijassa-1077	19	21	d.v	d.v	PROPN
ijassa-1077	19	22	.	.	PUNCT
ijassa-1077	20	1	tunitsky	tunitsky	NOUN
ijassa-1077	20	2	copyright	copyright	NOUN
ijassa-1077	21	1	©	©	PROPN
ijassa-1077	21	2	2021	2021	NUM
ijassa-1077	21	3	assa	assa	NOUN
ijassa-1077	21	4	.	.	PUNCT
ijassa-1077	22	1	adv	adv	PROPN
ijassa-1077	22	2	.	.	PUNCT
ijassa-1077	23	1	in	in	ADP
ijassa-1077	23	2	systems	system	NOUN
ijassa-1077	23	3	science	science	NOUN
ijassa-1077	23	4	and	and	CCONJ
ijassa-1077	23	5	appl	appl	NOUN
ijassa-1077	23	6	.	.	PUNCT
ijassa-1077	24	1	(	(	PUNCT
ijassa-1077	24	2	2021	2021	NUM
ijassa-1077	24	3	)	)	PUNCT
ijassa-1077	24	4	mesh	mesh	NOUN
ijassa-1077	24	5	of	of	ADP
ijassa-1077	24	6	fixed	fix	VERB
ijassa-1077	24	7	points	point	NOUN
ijassa-1077	24	8	wi	wi	PROPN
ijassa-1077	24	9	,	,	PUNCT
ijassa-1077	24	10	i=1,	i=1,	PROPN
ijassa-1077	24	11	…	…	SYM
ijassa-1077	24	12	,m	,m	ADJ
ijassa-1077	24	13	,	,	PUNCT
ijassa-1077	24	14	inside	inside	ADP
ijassa-1077	24	15	the	the	DET
ijassa-1077	24	16	colorants	colorant	NOUN
ijassa-1077	24	17	cube	cube	NOUN
ijassa-1077	24	18	and	and	CCONJ
ijassa-1077	24	19	a	a	DET
ijassa-1077	24	20	set	set	NOUN
ijassa-1077	24	21	{	{	PUNCT
ijassa-1077	24	22	pi	pi	NOUN
ijassa-1077	24	23	}	}	PUNCT
ijassa-1077	24	24	î	î	PROPN
ijassa-1077	24	25	ℝ	ℝ	PROPN
ijassa-1077	24	26	#	#	NOUN
ijassa-1077	24	27	=	=	SYM
ijassa-1077	24	28	{	{	PUNCT
ijassa-1077	24	29	(	(	PUNCT
ijassa-1077	24	30	y1	y1	INTJ
ijassa-1077	24	31	,	,	PUNCT
ijassa-1077	24	32	y2	y2	PROPN
ijassa-1077	24	33	,	,	PUNCT
ijassa-1077	24	34	y3	y3	PROPN
ijassa-1077	24	35	)	)	PUNCT
ijassa-1077	24	36	,	,	PUNCT
ijassa-1077	24	37	¥	¥	PRON
ijassa-1077	24	38	<	<	X
ijassa-1077	24	39	y1	y1	PROPN
ijassa-1077	24	40	,	,	PUNCT
ijassa-1077	24	41	y2	y2	PROPN
ijassa-1077	24	42	,	,	PUNCT
ijassa-1077	24	43	y3	y3	NOUN
ijassa-1077	24	44	<	<	X
ijassa-1077	24	45	+	+	NOUN
ijassa-1077	24	46	¥	¥	NOUN
ijassa-1077	24	47	}	}	PUNCT
ijassa-1077	24	48	of	of	ADP
ijassa-1077	24	49	the	the	DET
ijassa-1077	24	50	corresponding	correspond	VERB
ijassa-1077	24	51	values	value	NOUN
ijassa-1077	24	52	pi	pi	NOUN
ijassa-1077	24	53	,	,	PUNCT
ijassa-1077	24	54	f(wi	f(wi	NOUN
ijassa-1077	24	55	)	)	PUNCT
ijassa-1077	24	56	=	=	SYM
ijassa-1077	25	1	pi	pi	NOUN
ijassa-1077	25	2	,	,	PUNCT
ijassa-1077	25	3	i=1,	i=1,	PROPN
ijassa-1077	25	4	…	…	PUNCT
ijassa-1077	25	5	,m	,m	PUNCT
ijassa-1077	25	6	,	,	PUNCT
ijassa-1077	25	7	in	in	ADP
ijassa-1077	25	8	three	three	NUM
ijassa-1077	25	9	-	-	PUNCT
ijassa-1077	25	10	dimensional	dimensional	ADJ
ijassa-1077	25	11	color	color	NOUN
ijassa-1077	25	12	space	space	NOUN
ijassa-1077	25	13	.	.	PUNCT
ijassa-1077	26	1	call	call	VERB
ijassa-1077	26	2	this	this	DET
ijassa-1077	26	3	mesh	mesh	NOUN
ijassa-1077	26	4	function	function	NOUN
ijassa-1077	26	5	a	a	DET
ijassa-1077	26	6	measurement	measurement	NOUN
ijassa-1077	26	7	data	datum	NOUN
ijassa-1077	26	8	for	for	ADP
ijassa-1077	26	9	the	the	DET
ijassa-1077	26	10	printing	printing	NOUN
ijassa-1077	26	11	device	device	NOUN
ijassa-1077	26	12	under	under	ADP
ijassa-1077	26	13	consideration	consideration	NOUN
ijassa-1077	26	14	.	.	PUNCT
ijassa-1077	27	1	hence	hence	ADV
ijassa-1077	27	2	,	,	PUNCT
ijassa-1077	27	3	a	a	DET
ijassa-1077	27	4	measurement	measurement	NOUN
ijassa-1077	27	5	data	data	NOUN
ijassa-1077	27	6	is	be	AUX
ijassa-1077	27	7	a	a	DET
ijassa-1077	27	8	discrete	discrete	ADJ
ijassa-1077	27	9	map	map	NOUN
ijassa-1077	27	10	f	f	X
ijassa-1077	27	11	:	:	PUNCT
ijassa-1077	27	12	{	{	PUNCT
ijassa-1077	27	13	wi	wi	PROPN
ijassa-1077	27	14	}	}	PUNCT
ijassa-1077	27	15	®	®	NOUN
ijassa-1077	27	16	{	{	PUNCT
ijassa-1077	27	17	pi	pi	NOUN
ijassa-1077	27	18	}	}	PUNCT
ijassa-1077	27	19	such	such	ADJ
ijassa-1077	27	20	that	that	SCONJ
ijassa-1077	27	21	f(wi	f(wi	NOUN
ijassa-1077	27	22	)	)	PUNCT
ijassa-1077	27	23	=	=	SYM
ijassa-1077	27	24	pi	pi	NOUN
ijassa-1077	27	25	=	=	SYM
ijassa-1077	27	26	f(wi	f(wi	NOUN
ijassa-1077	27	27	)	)	PUNCT
ijassa-1077	27	28	for	for	ADP
ijassa-1077	27	29	i=1,	i=1,	NOUN
ijassa-1077	27	30	…	…	SYM
ijassa-1077	27	31	,m	,m	PUNCT
ijassa-1077	27	32	.	.	PUNCT
ijassa-1077	28	1	for	for	ADP
ijassa-1077	28	2	simplicity	simplicity	NOUN
ijassa-1077	28	3	,	,	PUNCT
ijassa-1077	28	4	we	we	PRON
ijassa-1077	28	5	will	will	AUX
ijassa-1077	28	6	restrict	restrict	VERB
ijassa-1077	28	7	ourselves	ourselves	PRON
ijassa-1077	28	8	to	to	ADP
ijassa-1077	28	9	the	the	DET
ijassa-1077	28	10	case	case	NOUN
ijassa-1077	28	11	of	of	ADP
ijassa-1077	28	12	a	a	DET
ijassa-1077	28	13	regular	regular	ADJ
ijassa-1077	28	14	mesh	mesh	NOUN
ijassa-1077	28	15	only	only	ADV
ijassa-1077	28	16	.	.	PUNCT
ijassa-1077	29	1	recall	recall	VERB
ijassa-1077	29	2	its	its	PRON
ijassa-1077	29	3	definition	definition	NOUN
ijassa-1077	29	4	.	.	PUNCT
ijassa-1077	30	1	definition	definition	NOUN
ijassa-1077	30	2	.	.	PUNCT
ijassa-1077	31	1	let	let	VERB
ijassa-1077	31	2	wm	wm	VERB
ijassa-1077	32	1	=	=	PUNCT
ijassa-1077	33	1	[	[	X
ijassa-1077	33	2	a1	a1	NOUN
ijassa-1077	33	3	,	,	PUNCT
ijassa-1077	33	4	b1	b1	NOUN
ijassa-1077	33	5	]	]	PUNCT
ijassa-1077	33	6	´	´	NOUN
ijassa-1077	33	7	…	…	PUNCT
ijassa-1077	33	8	´	´	NOUN
ijassa-1077	34	1	[	[	X
ijassa-1077	34	2	am	am	NOUN
ijassa-1077	34	3	,	,	PUNCT
ijassa-1077	34	4	bm	bm	PROPN
ijassa-1077	34	5	]	]	PUNCT
ijassa-1077	34	6	be	be	VERB
ijassa-1077	34	7	an	an	DET
ijassa-1077	34	8	m	m	ADV
ijassa-1077	34	9	-	-	ADJ
ijassa-1077	34	10	dimensional	dimensional	ADJ
ijassa-1077	34	11	rectangular	rectangular	ADJ
ijassa-1077	34	12	parallelepiped	parallelepipe	VERB
ijassa-1077	34	13	with	with	ADP
ijassa-1077	34	14	a1	a1	NOUN
ijassa-1077	34	15	<	<	X
ijassa-1077	34	16	b1	b1	PROPN
ijassa-1077	34	17	,	,	PUNCT
ijassa-1077	34	18	…	…	PUNCT
ijassa-1077	34	19	,	,	PUNCT
ijassa-1077	34	20	am	be	AUX
ijassa-1077	34	21	<	<	X
ijassa-1077	34	22	bm	bm	PROPN
ijassa-1077	34	23	.	.	PROPN
ijassa-1077	34	24	for	for	ADP
ijassa-1077	34	25	k	k	PROPN
ijassa-1077	34	26	=	=	SYM
ijassa-1077	34	27	1,	1,	NUM
ijassa-1077	34	28	…	…	NUM
ijassa-1077	34	29	,m	,m	PUNCT
ijassa-1077	34	30	consider	consider	VERB
ijassa-1077	34	31	finite	finite	ADJ
ijassa-1077	34	32	sets	set	NOUN
ijassa-1077	34	33	zk	zk	PROPN
ijassa-1077	34	34	=	=	SYM
ijassa-1077	34	35	{	{	PUNCT
ijassa-1077	34	36	xk0	xk0	PROPN
ijassa-1077	34	37	,	,	PUNCT
ijassa-1077	34	38	…	…	PUNCT
ijassa-1077	34	39	,	,	PUNCT
ijassa-1077	34	40	xkm(k	xkm(k	PROPN
ijassa-1077	34	41	)	)	PUNCT
ijassa-1077	34	42	}	}	PUNCT
ijassa-1077	34	43	,	,	PUNCT
ijassa-1077	34	44	ak	ak	PROPN
ijassa-1077	34	45	=	=	PUNCT
ijassa-1077	34	46	xk0	xk0	PROPN
ijassa-1077	34	47	<	<	X
ijassa-1077	34	48	…	…	PUNCT
ijassa-1077	34	49	<	<	X
ijassa-1077	34	50	xkm(k	xkm(k	PROPN
ijassa-1077	34	51	)	)	PUNCT
ijassa-1077	34	52	=	=	PUNCT
ijassa-1077	35	1	bk	bk	NOUN
ijassa-1077	35	2	,	,	PUNCT
ijassa-1077	35	3	of	of	ADP
ijassa-1077	35	4	m(k)+1	m(k)+1	NOUN
ijassa-1077	35	5	real	real	ADJ
ijassa-1077	35	6	numbers	number	NOUN
ijassa-1077	35	7	.	.	PUNCT
ijassa-1077	36	1	the	the	DET
ijassa-1077	36	2	product	product	NOUN
ijassa-1077	36	3	mesh	mesh	NOUN
ijassa-1077	36	4	{	{	PUNCT
ijassa-1077	36	5	wi	wi	PROPN
ijassa-1077	36	6	}	}	PUNCT
ijassa-1077	36	7	=	=	NOUN
ijassa-1077	36	8	z1	z1	VERB
ijassa-1077	36	9	´	´	NOUN
ijassa-1077	36	10	…	…	PUNCT
ijassa-1077	36	11	´	´	PROPN
ijassa-1077	36	12	zm	zm	PROPN
ijassa-1077	36	13	ì	ì	INTJ
ijassa-1077	36	14	wm	wm	PROPN
ijassa-1077	36	15	of	of	ADP
ijassa-1077	36	16	m	m	PROPN
ijassa-1077	36	17	points	point	NOUN
ijassa-1077	36	18	,	,	PUNCT
ijassa-1077	36	19	m	m	VERB
ijassa-1077	36	20	=	=	X
ijassa-1077	36	21	(	(	PUNCT
ijassa-1077	36	22	m(1)+1)	m(1)+1)	NOUN
ijassa-1077	36	23	…	…	SYM
ijassa-1077	36	24	(m(m)+1	(m(m)+1	NOUN
ijassa-1077	36	25	)	)	PUNCT
ijassa-1077	36	26	,	,	PUNCT
ijassa-1077	36	27	is	be	AUX
ijassa-1077	36	28	called	call	VERB
ijassa-1077	36	29	regular	regular	ADV
ijassa-1077	36	30	inside	inside	ADP
ijassa-1077	36	31	the	the	DET
ijassa-1077	36	32	m	m	ADV
ijassa-1077	36	33	-	-	ADJ
ijassa-1077	36	34	dimensional	dimensional	ADJ
ijassa-1077	36	35	parallelepiped	parallelepipe	VERB
ijassa-1077	36	36	.	.	PUNCT
ijassa-1077	37	1	there	there	PRON
ijassa-1077	37	2	are	be	VERB
ijassa-1077	37	3	two	two	NUM
ijassa-1077	37	4	principal	principal	ADJ
ijassa-1077	37	5	problems	problem	NOUN
ijassa-1077	37	6	of	of	ADP
ijassa-1077	37	7	mathematical	mathematical	ADJ
ijassa-1077	37	8	modeling	modeling	NOUN
ijassa-1077	37	9	of	of	ADP
ijassa-1077	37	10	a	a	DET
ijassa-1077	37	11	printing	printing	NOUN
ijassa-1077	37	12	device	device	NOUN
ijassa-1077	37	13	.	.	PUNCT
ijassa-1077	38	1	direct	direct	ADJ
ijassa-1077	38	2	problem	problem	NOUN
ijassa-1077	38	3	.	.	PUNCT
ijassa-1077	39	1	to	to	PART
ijassa-1077	39	2	find	find	VERB
ijassa-1077	39	3	a	a	DET
ijassa-1077	39	4	continuous	continuous	ADJ
ijassa-1077	39	5	map	map	NOUN
ijassa-1077	39	6	f	f	X
ijassa-1077	39	7	:	:	PUNCT
ijassa-1077	39	8	wm	wm	PROPN
ijassa-1077	39	9	®	®	NOUN
ijassa-1077	39	10	ℝ	ℝ	PROPN
ijassa-1077	39	11	#	#	NOUN
ijassa-1077	39	12	being	be	AUX
ijassa-1077	39	13	a	a	DET
ijassa-1077	39	14	satisfactory	satisfactory	ADJ
ijassa-1077	39	15	approximation	approximation	NOUN
ijassa-1077	39	16	to	to	ADP
ijassa-1077	39	17	a	a	DET
ijassa-1077	39	18	given	give	VERB
ijassa-1077	39	19	discrete	discrete	ADJ
ijassa-1077	39	20	function	function	NOUN
ijassa-1077	39	21	f	f	X
ijassa-1077	39	22	,	,	PUNCT
ijassa-1077	39	23	i.e.	i.e.	X
ijassa-1077	39	24	,	,	PUNCT
ijassa-1077	39	25	to	to	ADP
ijassa-1077	39	26	the	the	DET
ijassa-1077	39	27	measurement	measurement	NOUN
ijassa-1077	39	28	data	datum	NOUN
ijassa-1077	39	29	of	of	ADP
ijassa-1077	39	30	the	the	DET
ijassa-1077	39	31	printing	printing	NOUN
ijassa-1077	39	32	device	device	NOUN
ijassa-1077	39	33	under	under	ADP
ijassa-1077	39	34	consideration	consideration	NOUN
ijassa-1077	39	35	.	.	PUNCT
ijassa-1077	40	1	we	we	PRON
ijassa-1077	40	2	will	will	AUX
ijassa-1077	40	3	call	call	VERB
ijassa-1077	40	4	the	the	DET
ijassa-1077	40	5	solution	solution	NOUN
ijassa-1077	40	6	of	of	ADP
ijassa-1077	40	7	this	this	DET
ijassa-1077	40	8	problem	problem	NOUN
ijassa-1077	40	9	a	a	DET
ijassa-1077	40	10	model	model	NOUN
ijassa-1077	40	11	of	of	ADP
ijassa-1077	40	12	the	the	DET
ijassa-1077	40	13	printing	printing	NOUN
ijassa-1077	40	14	device	device	NOUN
ijassa-1077	40	15	or	or	CCONJ
ijassa-1077	40	16	for	for	ADP
ijassa-1077	40	17	conciseness	conciseness	NOUN
ijassa-1077	40	18	just	just	ADV
ijassa-1077	40	19	a	a	DET
ijassa-1077	40	20	printing	printing	NOUN
ijassa-1077	40	21	device	device	NOUN
ijassa-1077	40	22	described	describe	VERB
ijassa-1077	40	23	by	by	ADP
ijassa-1077	40	24	the	the	DET
ijassa-1077	40	25	corresponding	corresponding	ADJ
ijassa-1077	40	26	measurement	measurement	NOUN
ijassa-1077	40	27	data	datum	NOUN
ijassa-1077	40	28	(	(	PUNCT
ijassa-1077	40	29	see	see	VERB
ijassa-1077	40	30	section	section	NOUN
ijassa-1077	40	31	1	1	NUM
ijassa-1077	40	32	)	)	PUNCT
ijassa-1077	40	33	.	.	PUNCT
ijassa-1077	41	1	inverse	inverse	ADJ
ijassa-1077	41	2	problem	problem	NOUN
ijassa-1077	41	3	.	.	PUNCT
ijassa-1077	42	1	to	to	PART
ijassa-1077	42	2	find	find	VERB
ijassa-1077	42	3	a	a	DET
ijassa-1077	42	4	continuous	continuous	ADJ
ijassa-1077	42	5	map	map	NOUN
ijassa-1077	42	6	g	g	NOUN
ijassa-1077	42	7	:	:	PUNCT
ijassa-1077	42	8	f(wm	f(wm	NOUN
ijassa-1077	42	9	)	)	PUNCT
ijassa-1077	42	10	®	®	NOUN
ijassa-1077	42	11	wm	wm	PROPN
ijassa-1077	42	12	,	,	PUNCT
ijassa-1077	42	13	being	be	AUX
ijassa-1077	42	14	an	an	DET
ijassa-1077	42	15	inverse	inverse	NOUN
ijassa-1077	42	16	map	map	NOUN
ijassa-1077	42	17	to	to	ADP
ijassa-1077	42	18	f	f	PROPN
ijassa-1077	42	19	,	,	PUNCT
ijassa-1077	42	20	i.e.	i.e.	X
ijassa-1077	42	21	,	,	PUNCT
ijassa-1077	42	22	the	the	DET
ijassa-1077	42	23	composition	composition	NOUN
ijassa-1077	42	24	of	of	ADP
ijassa-1077	42	25	the	the	DET
ijassa-1077	42	26	maps	map	NOUN
ijassa-1077	42	27	g	g	PROPN
ijassa-1077	42	28	and	and	CCONJ
ijassa-1077	42	29	f	f	PROPN
ijassa-1077	42	30	should	should	AUX
ijassa-1077	42	31	be	be	AUX
ijassa-1077	42	32	the	the	DET
ijassa-1077	42	33	identical	identical	ADJ
ijassa-1077	42	34	map	map	NOUN
ijassa-1077	42	35	of	of	ADP
ijassa-1077	42	36	the	the	DET
ijassa-1077	42	37	set	set	NOUN
ijassa-1077	42	38	f(wm	f(wm	NOUN
ijassa-1077	42	39	)	)	PUNCT
ijassa-1077	42	40	,	,	PUNCT
ijassa-1077	42	41	.	.	PUNCT
ijassa-1077	43	1	the	the	DET
ijassa-1077	43	2	problem	problem	NOUN
ijassa-1077	43	3	,	,	PUNCT
ijassa-1077	43	4	naturally	naturally	ADV
ijassa-1077	43	5	,	,	PUNCT
ijassa-1077	43	6	involves	involve	VERB
ijassa-1077	43	7	description	description	NOUN
ijassa-1077	43	8	of	of	ADP
ijassa-1077	43	9	the	the	DET
ijassa-1077	43	10	gamut	gamut	NOUN
ijassa-1077	43	11	,	,	PUNCT
ijassa-1077	43	12	i.e.	i.e.	X
ijassa-1077	43	13	,	,	PUNCT
ijassa-1077	43	14	the	the	DET
ijassa-1077	43	15	image	image	NOUN
ijassa-1077	43	16	f(wm	f(wm	NOUN
ijassa-1077	43	17	)	)	PUNCT
ijassa-1077	43	18	to	to	ADP
ijassa-1077	43	19	the	the	DET
ijassa-1077	43	20	map	map	NOUN
ijassa-1077	43	21	f.	f.	PROPN
ijassa-1077	43	22	moreover	moreover	ADV
ijassa-1077	43	23	,	,	PUNCT
ijassa-1077	43	24	in	in	ADP
ijassa-1077	43	25	case	case	NOUN
ijassa-1077	43	26	m>3	m>3	ADP
ijassa-1077	43	27	an	an	DET
ijassa-1077	43	28	inverse	inverse	NOUN
ijassa-1077	43	29	map	map	NOUN
ijassa-1077	43	30	should	should	AUX
ijassa-1077	43	31	satisfy	satisfy	VERB
ijassa-1077	43	32	to	to	ADP
ijassa-1077	43	33	some	some	DET
ijassa-1077	43	34	additional	additional	ADJ
ijassa-1077	43	35	conditions	condition	NOUN
ijassa-1077	43	36	,	,	PUNCT
ijassa-1077	43	37	for	for	ADP
ijassa-1077	43	38	example	example	NOUN
ijassa-1077	43	39	,	,	PUNCT
ijassa-1077	43	40	the	the	DET
ijassa-1077	43	41	maximal	maximal	ADJ
ijassa-1077	43	42	(	(	PUNCT
ijassa-1077	43	43	minimal	minimal	ADJ
ijassa-1077	43	44	)	)	PUNCT
ijassa-1077	43	45	possible	possible	ADJ
ijassa-1077	43	46	amount	amount	NOUN
ijassa-1077	43	47	of	of	ADP
ijassa-1077	43	48	the	the	DET
ijassa-1077	43	49	m	m	PROPN
ijassa-1077	43	50	-	-	PUNCT
ijassa-1077	43	51	th	th	VERB
ijassa-1077	43	52	colorant	colorant	PROPN
ijassa-1077	43	53	component	component	NOUN
ijassa-1077	43	54	xm	xm	PROPN
ijassa-1077	43	55	.	.	PUNCT
ijassa-1077	44	1	we	we	PRON
ijassa-1077	44	2	will	will	AUX
ijassa-1077	44	3	restrict	restrict	VERB
ijassa-1077	44	4	our	our	PRON
ijassa-1077	44	5	examination	examination	NOUN
ijassa-1077	44	6	of	of	ADP
ijassa-1077	44	7	these	these	DET
ijassa-1077	44	8	problems	problem	NOUN
ijassa-1077	44	9	to	to	ADP
ijassa-1077	44	10	the	the	DET
ijassa-1077	44	11	class	class	NOUN
ijassa-1077	44	12	of	of	ADP
ijassa-1077	44	13	piecewise	piecewise	NOUN
ijassa-1077	44	14	linear	linear	NOUN
ijassa-1077	44	15	maps	map	NOUN
ijassa-1077	44	16	.	.	PUNCT
ijassa-1077	45	1	remind	remind	VERB
ijassa-1077	45	2	the	the	DET
ijassa-1077	45	3	necessary	necessary	ADJ
ijassa-1077	45	4	notions	notion	NOUN
ijassa-1077	45	5	.	.	PUNCT
ijassa-1077	46	1	a	a	DET
ijassa-1077	46	2	k	k	ADJ
ijassa-1077	46	3	-	-	ADJ
ijassa-1077	46	4	dimensional	dimensional	ADJ
ijassa-1077	46	5	simplex	simplex	NOUN
ijassa-1077	46	6	is	be	AUX
ijassa-1077	46	7	a	a	DET
ijassa-1077	46	8	convex	convex	ADJ
ijassa-1077	46	9	hull	hull	NOUN
ijassa-1077	46	10	of	of	ADP
ijassa-1077	46	11	k+1	k+1	X
ijassa-1077	46	12	affinely	affinely	ADV
ijassa-1077	46	13	independent	independent	ADJ
ijassa-1077	46	14	points	point	NOUN
ijassa-1077	46	15	of	of	ADP
ijassa-1077	46	16	an	an	DET
ijassa-1077	46	17	m	m	ADV
ijassa-1077	46	18	-	-	ADJ
ijassa-1077	46	19	dimensional	dimensional	ADJ
ijassa-1077	46	20	space	space	NOUN
ijassa-1077	46	21	ℝ	ℝ	PROPN
ijassa-1077	46	22	!	!	PROPN
ijassa-1077	46	23	,	,	PUNCT
ijassa-1077	46	24	where	where	SCONJ
ijassa-1077	46	25	0£k£m	0£k£m	X
ijassa-1077	46	26	.	.	PUNCT
ijassa-1077	47	1	the	the	DET
ijassa-1077	47	2	boundary	boundary	NOUN
ijassa-1077	47	3	of	of	ADP
ijassa-1077	47	4	a	a	DET
ijassa-1077	47	5	kdimensional	kdimensional	ADJ
ijassa-1077	47	6	simplex	simplex	NOUN
ijassa-1077	47	7	consists	consist	VERB
ijassa-1077	47	8	of	of	ADP
ijassa-1077	47	9	faces	face	NOUN
ijassa-1077	47	10	with	with	ADP
ijassa-1077	47	11	different	different	ADJ
ijassa-1077	47	12	dimensions	dimension	NOUN
ijassa-1077	47	13	:	:	PUNCT
ijassa-1077	47	14	k-1	k-1	PROPN
ijassa-1077	47	15	,	,	PUNCT
ijassa-1077	47	16	k-2	k-2	PROPN
ijassa-1077	47	17	,	,	PUNCT
ijassa-1077	47	18	…	…	PUNCT
ijassa-1077	47	19	,	,	PUNCT
ijassa-1077	47	20	0	0	X
ijassa-1077	47	21	.	.	X
ijassa-1077	47	22	onedimensional	onedimensional	ADJ
ijassa-1077	47	23	faces	face	NOUN
ijassa-1077	47	24	are	be	AUX
ijassa-1077	47	25	called	call	VERB
ijassa-1077	47	26	edges	edge	NOUN
ijassa-1077	47	27	,	,	PUNCT
ijassa-1077	47	28	and	and	CCONJ
ijassa-1077	47	29	zero	zero	NUM
ijassa-1077	47	30	-	-	PUNCT
ijassa-1077	47	31	dimensional	dimensional	ADJ
ijassa-1077	47	32	faces	face	NOUN
ijassa-1077	47	33	are	be	AUX
ijassa-1077	47	34	called	call	VERB
ijassa-1077	47	35	vertices	vertex	NOUN
ijassa-1077	47	36	.	.	PUNCT
ijassa-1077	48	1	definition	definition	NOUN
ijassa-1077	48	2	.	.	PUNCT
ijassa-1077	49	1	suppose	suppose	VERB
ijassa-1077	49	2	the	the	DET
ijassa-1077	49	3	colorants	colorant	NOUN
ijassa-1077	49	4	cube	cube	PROPN
ijassa-1077	49	5	wm	wm	PROPN
ijassa-1077	49	6	is	be	AUX
ijassa-1077	49	7	decomposed	decompose	VERB
ijassa-1077	49	8	into	into	ADP
ijassa-1077	49	9	a	a	DET
ijassa-1077	49	10	union	union	NOUN
ijassa-1077	49	11	of	of	ADP
ijassa-1077	49	12	n	n	CCONJ
ijassa-1077	49	13	,	,	PUNCT
ijassa-1077	49	14	n>0	n>0	NUM
ijassa-1077	49	15	,	,	PUNCT
ijassa-1077	49	16	sets	set	VERB
ijassa-1077	49	17	dj	dj	NOUN
ijassa-1077	49	18	,	,	PUNCT
ijassa-1077	49	19	.	.	PUNCT
ijassa-1077	50	1	this	this	DET
ijassa-1077	50	2	decomposition	decomposition	NOUN
ijassa-1077	50	3	is	be	AUX
ijassa-1077	50	4	called	call	VERB
ijassa-1077	50	5	simplex	simplex	NOUN
ijassa-1077	50	6	if	if	SCONJ
ijassa-1077	50	7	for	for	ADP
ijassa-1077	50	8	j=1	j=1	NOUN
ijassa-1077	50	9	,	,	PUNCT
ijassa-1077	50	10	…	…	PUNCT
ijassa-1077	50	11	,	,	PUNCT
ijassa-1077	50	12	n	n	CCONJ
ijassa-1077	50	13	the	the	DET
ijassa-1077	50	14	set	set	NOUN
ijassa-1077	50	15	dj	dj	NOUN
ijassa-1077	50	16	,	,	PUNCT
ijassa-1077	50	17	is	be	AUX
ijassa-1077	50	18	an	an	DET
ijassa-1077	50	19	m	m	ADJ
ijassa-1077	50	20	-	-	ADJ
ijassa-1077	50	21	dimensional	dimensional	ADJ
ijassa-1077	50	22	simplex	simplex	NOUN
ijassa-1077	50	23	and	and	CCONJ
ijassa-1077	50	24	the	the	DET
ijassa-1077	50	25	intersection	intersection	NOUN
ijassa-1077	50	26	of	of	ADP
ijassa-1077	50	27	any	any	DET
ijassa-1077	50	28	two	two	NUM
ijassa-1077	50	29	simplexes	simplexe	NOUN
ijassa-1077	50	30	dj	dj	NOUN
ijassa-1077	50	31	and	and	CCONJ
ijassa-1077	50	32	dk	dk	PROPN
ijassa-1077	50	33	is	be	AUX
ijassa-1077	50	34	either	either	CCONJ
ijassa-1077	50	35	empty	empty	ADJ
ijassa-1077	50	36	,	,	PUNCT
ijassa-1077	50	37	dj	dj	ADJ
ijassa-1077	50	38	ç	ç	NOUN
ijassa-1077	50	39	dk	dk	X
ijassa-1077	50	40	=	=	SYM
ijassa-1077	50	41	æ	æ	PROPN
ijassa-1077	50	42	,	,	PUNCT
ijassa-1077	50	43	or	or	CCONJ
ijassa-1077	50	44	is	be	AUX
ijassa-1077	50	45	a	a	DET
ijassa-1077	50	46	union	union	NOUN
ijassa-1077	50	47	of	of	ADP
ijassa-1077	50	48	whole	whole	ADJ
ijassa-1077	50	49	(	(	PUNCT
ijassa-1077	50	50	m–1)-	m–1)-	PROPN
ijassa-1077	50	51	,	,	PUNCT
ijassa-1077	50	52	(	(	PUNCT
ijassa-1077	50	53	m–2)-	m–2)-	NOUN
ijassa-1077	50	54	,	,	PUNCT
ijassa-1077	50	55	…	…	PUNCT
ijassa-1077	50	56	,	,	PUNCT
ijassa-1077	50	57	and	and	CCONJ
ijassa-1077	50	58	0	0	NUM
ijassa-1077	50	59	-	-	PUNCT
ijassa-1077	50	60	dimentional	dimentional	ADJ
ijassa-1077	50	61	faces	face	NOUN
ijassa-1077	50	62	to	to	ADP
ijassa-1077	50	63	these	these	DET
ijassa-1077	50	64	simplexes	simplexe	NOUN
ijassa-1077	50	65	.	.	PUNCT
ijassa-1077	51	1	definition	definition	NOUN
ijassa-1077	51	2	.	.	PUNCT
ijassa-1077	52	1	a	a	DET
ijassa-1077	52	2	continuous	continuous	ADJ
ijassa-1077	52	3	map	map	NOUN
ijassa-1077	52	4	f	f	X
ijassa-1077	52	5	:	:	PUNCT
ijassa-1077	52	6	wm	wm	PROPN
ijassa-1077	52	7	®	®	NOUN
ijassa-1077	52	8	ℝ	ℝ	NOUN
ijassa-1077	52	9	#	#	ADV
ijassa-1077	52	10	,	,	PUNCT
ijassa-1077	52	11	is	be	AUX
ijassa-1077	52	12	called	call	VERB
ijassa-1077	52	13	piecewise	piecewise	NOUN
ijassa-1077	52	14	linear	linear	NOUN
ijassa-1077	52	15	if	if	SCONJ
ijassa-1077	52	16	there	there	PRON
ijassa-1077	52	17	exists	exist	VERB
ijassa-1077	52	18	a	a	DET
ijassa-1077	52	19	simplex	simplex	NOUN
ijassa-1077	52	20	decomposition	decomposition	NOUN
ijassa-1077	52	21	of	of	ADP
ijassa-1077	52	22	the	the	DET
ijassa-1077	52	23	mdimensional	mdimensional	ADJ
ijassa-1077	52	24	colorant	colorant	NOUN
ijassa-1077	52	25	cube	cube	NOUN
ijassa-1077	52	26	such	such	ADJ
ijassa-1077	52	27	that	that	SCONJ
ijassa-1077	52	28	all	all	DET
ijassa-1077	52	29	the	the	DET
ijassa-1077	52	30	restrictions	restriction	NOUN
ijassa-1077	52	31	f½dj	f½dj	ADV
ijassa-1077	52	32	:	:	PUNCT
ijassa-1077	52	33	dj	dj	X
ijassa-1077	52	34	®	®	NOUN
ijassa-1077	52	35	ℝ	ℝ	NOUN
ijassa-1077	52	36	#	#	NOUN
ijassa-1077	52	37	of	of	ADP
ijassa-1077	52	38	the	the	DET
ijassa-1077	52	39	map	map	NOUN
ijassa-1077	52	40	f	f	X
ijassa-1077	52	41	to	to	ADP
ijassa-1077	52	42	tetrahedrons	tetrahedron	NOUN
ijassa-1077	52	43	dj	dj	NOUN
ijassa-1077	52	44	are	be	AUX
ijassa-1077	52	45	linear	linear	ADJ
ijassa-1077	52	46	maps	map	NOUN
ijassa-1077	52	47	.	.	PUNCT
ijassa-1077	53	1	in	in	ADP
ijassa-1077	53	2	other	other	ADJ
ijassa-1077	53	3	words	word	NOUN
ijassa-1077	53	4	,	,	PUNCT
ijassa-1077	53	5	f½dj	f½dj	PROPN
ijassa-1077	53	6	(	(	PUNCT
ijassa-1077	53	7	x	x	X
ijassa-1077	53	8	)	)	PUNCT
ijassa-1077	53	9	=	=	SYM
ijassa-1077	53	10	cj	cj	NOUN
ijassa-1077	54	1	+	+	CCONJ
ijassa-1077	54	2	bjx	bjx	ADV
ijassa-1077	54	3	,	,	PUNCT
ijassa-1077	54	4	where	where	SCONJ
ijassa-1077	54	5	x	x	PUNCT
ijassa-1077	54	6	=	=	PRON
ijassa-1077	54	7	(	(	PUNCT
ijassa-1077	54	8	x1	x1	PROPN
ijassa-1077	54	9	,	,	PUNCT
ijassa-1077	54	10	…	…	PUNCT
ijassa-1077	54	11	,	,	PUNCT
ijassa-1077	54	12	xm)t	xm)t	PROPN
ijassa-1077	54	13	mw	mw	X
ijassa-1077	54	14	mw	mw	PROPN
ijassa-1077	54	15	)	)	PUNCT
ijassa-1077	54	16	(	(	PUNCT
ijassa-1077	54	17	mwfidgf	mwfidgf	NOUN
ijassa-1077	54	18	=	=	NOUN
ijassa-1077	54	19	!	!	PUNCT
ijassa-1077	54	20	!	!	PUNCT
ijassa-1077	55	1	nj	nj	PROPN
ijassa-1077	56	1	j	j	PROPN
ijassa-1077	56	2	mw	mw	PROPN
ijassa-1077	56	3	,	,	PUNCT
ijassa-1077	56	4	...	...	PUNCT
ijassa-1077	56	5	,	,	PUNCT
ijassa-1077	56	6	1=	1=	X
ijassa-1077	56	7	d=	d=	NOUN
ijassa-1077	56	8	!	!	PUNCT
ijassa-1077	57	1	nj	nj	PROPN
ijassa-1077	58	1	j	j	PROPN
ijassa-1077	58	2	mw	mw	PROPN
ijassa-1077	58	3	,	,	PUNCT
ijassa-1077	58	4	...	...	PUNCT
ijassa-1077	58	5	,	,	PUNCT
ijassa-1077	58	6	1=	1=	X
ijassa-1077	58	7	d=	d=	NOUN
ijassa-1077	58	8	mw	mw	PROPN
ijassa-1077	58	9	mathematical	mathematical	ADJ
ijassa-1077	58	10	modeling	modeling	NOUN
ijassa-1077	58	11	of	of	ADP
ijassa-1077	58	12	color	color	NOUN
ijassa-1077	58	13	printing	printing	NOUN
ijassa-1077	58	14	devices	device	NOUN
ijassa-1077	58	15	:	:	PUNCT
ijassa-1077	58	16	color	color	NOUN
ijassa-1077	58	17	gamut	gamut	NOUN
ijassa-1077	58	18	visualization	visualization	NOUN
ijassa-1077	58	19	…	…	PUNCT
ijassa-1077	58	20	119	119	NUM
ijassa-1077	58	21	copyright	copyright	NOUN
ijassa-1077	58	22	©	©	PROPN
ijassa-1077	58	23	2021	2021	NUM
ijassa-1077	58	24	assa	assa	NOUN
ijassa-1077	58	25	.	.	PUNCT
ijassa-1077	59	1	adv	adv	PROPN
ijassa-1077	59	2	.	.	PUNCT
ijassa-1077	60	1	in	in	ADP
ijassa-1077	60	2	systems	system	NOUN
ijassa-1077	60	3	science	science	NOUN
ijassa-1077	60	4	and	and	CCONJ
ijassa-1077	60	5	appl	appl	NOUN
ijassa-1077	60	6	.	.	PUNCT
ijassa-1077	61	1	(	(	PUNCT
ijassa-1077	61	2	2021	2021	NUM
ijassa-1077	61	3	)	)	PUNCT
ijassa-1077	61	4	is	be	AUX
ijassa-1077	61	5	an	an	DET
ijassa-1077	61	6	m	m	ADV
ijassa-1077	61	7	-	-	ADJ
ijassa-1077	61	8	dimensional	dimensional	ADJ
ijassa-1077	61	9	vector	vector	NOUN
ijassa-1077	61	10	of	of	ADP
ijassa-1077	61	11	colorants	colorant	NOUN
ijassa-1077	61	12	combination	combination	NOUN
ijassa-1077	61	13	,	,	PUNCT
ijassa-1077	61	14	bj	bj	NOUN
ijassa-1077	61	15	is	be	AUX
ijassa-1077	61	16	a	a	DET
ijassa-1077	61	17	3´m	3´m	NUM
ijassa-1077	61	18	matrix	matrix	NOUN
ijassa-1077	61	19	,	,	PUNCT
ijassa-1077	61	20	and	and	CCONJ
ijassa-1077	61	21	cj	cj	PROPN
ijassa-1077	61	22	is	be	AUX
ijassa-1077	61	23	a	a	DET
ijassa-1077	61	24	threedimensional	threedimensional	ADJ
ijassa-1077	61	25	vector	vector	NOUN
ijassa-1077	61	26	,	,	PUNCT
ijassa-1077	61	27	cj	cj	PROPN
ijassa-1077	61	28	î	î	PROPN
ijassa-1077	61	29	ℝ	ℝ	PROPN
ijassa-1077	61	30	#	#	NOUN
ijassa-1077	61	31	,	,	PUNCT
ijassa-1077	61	32	for	for	ADP
ijassa-1077	61	33	j=1	j=1	PROPN
ijassa-1077	61	34	,	,	PUNCT
ijassa-1077	61	35	…	…	PUNCT
ijassa-1077	61	36	,	,	PUNCT
ijassa-1077	61	37	n	n	CCONJ
ijassa-1077	61	38	(	(	PUNCT
ijassa-1077	61	39	cf	cf	NOUN
ijassa-1077	61	40	.	.	PUNCT
ijassa-1077	62	1	[	[	X
ijassa-1077	62	2	1	1	NUM
ijassa-1077	62	3	,	,	PUNCT
ijassa-1077	62	4	sections	section	NOUN
ijassa-1077	62	5	1.4	1.4	NUM
ijassa-1077	62	6	and	and	CCONJ
ijassa-1077	62	7	2.3	2.3	NUM
ijassa-1077	62	8	]	]	PUNCT
ijassa-1077	62	9	.	.	PUNCT
ijassa-1077	63	1	remark	remark	PROPN
ijassa-1077	63	2	.	.	PUNCT
ijassa-1077	64	1	generally	generally	ADV
ijassa-1077	64	2	speaking	speak	VERB
ijassa-1077	64	3	,	,	PUNCT
ijassa-1077	64	4	for	for	ADP
ijassa-1077	64	5	real	real	ADJ
ijassa-1077	64	6	applications	application	NOUN
ijassa-1077	64	7	the	the	DET
ijassa-1077	64	8	formulated	formulate	VERB
ijassa-1077	64	9	above	above	ADP
ijassa-1077	64	10	notions	notion	NOUN
ijassa-1077	64	11	of	of	ADP
ijassa-1077	64	12	simplex	simplex	NOUN
ijassa-1077	64	13	decomposition	decomposition	NOUN
ijassa-1077	64	14	of	of	ADP
ijassa-1077	64	15	the	the	DET
ijassa-1077	64	16	colorants	colorant	NOUN
ijassa-1077	64	17	cube	cube	PROPN
ijassa-1077	64	18	wm	wm	PROPN
ijassa-1077	64	19	and	and	CCONJ
ijassa-1077	64	20	its	its	PRON
ijassa-1077	64	21	piecewise	piecewise	NOUN
ijassa-1077	64	22	linear	linear	NOUN
ijassa-1077	64	23	map	map	NOUN
ijassa-1077	64	24	is	be	AUX
ijassa-1077	64	25	not	not	PART
ijassa-1077	64	26	sufficient	sufficient	ADJ
ijassa-1077	64	27	.	.	PUNCT
ijassa-1077	65	1	indeed	indeed	ADV
ijassa-1077	65	2	,	,	PUNCT
ijassa-1077	65	3	rather	rather	ADV
ijassa-1077	65	4	often	often	ADV
ijassa-1077	65	5	a	a	DET
ijassa-1077	65	6	colorants	colorant	NOUN
ijassa-1077	65	7	limitations	limitation	NOUN
ijassa-1077	65	8	,	,	PUNCT
ijassa-1077	65	9	for	for	ADP
ijassa-1077	65	10	example	example	NOUN
ijassa-1077	65	11	,	,	PUNCT
ijassa-1077	65	12	,	,	PUNCT
ijassa-1077	65	13	where	where	SCONJ
ijassa-1077	65	14	,	,	PUNCT
ijassa-1077	65	15	should	should	AUX
ijassa-1077	65	16	be	be	AUX
ijassa-1077	65	17	applied	apply	VERB
ijassa-1077	65	18	to	to	ADP
ijassa-1077	65	19	the	the	DET
ijassa-1077	65	20	colorants	colorant	NOUN
ijassa-1077	65	21	cube	cube	NOUN
ijassa-1077	65	22	.	.	PUNCT
ijassa-1077	66	1	such	such	ADJ
ijassa-1077	66	2	limitations	limitation	NOUN
ijassa-1077	66	3	have	have	VERB
ijassa-1077	66	4	practical	practical	ADJ
ijassa-1077	66	5	sense	sense	NOUN
ijassa-1077	66	6	.	.	PUNCT
ijassa-1077	67	1	in	in	ADP
ijassa-1077	67	2	particular	particular	ADJ
ijassa-1077	67	3	,	,	PUNCT
ijassa-1077	67	4	they	they	PRON
ijassa-1077	67	5	allow	allow	VERB
ijassa-1077	67	6	to	to	PART
ijassa-1077	67	7	avoid	avoid	VERB
ijassa-1077	67	8	putting	put	VERB
ijassa-1077	67	9	too	too	ADV
ijassa-1077	67	10	much	much	ADJ
ijassa-1077	67	11	of	of	ADP
ijassa-1077	67	12	colorants	colorant	NOUN
ijassa-1077	67	13	to	to	ADP
ijassa-1077	67	14	a	a	DET
ijassa-1077	67	15	sheet	sheet	NOUN
ijassa-1077	67	16	of	of	ADP
ijassa-1077	67	17	paper	paper	NOUN
ijassa-1077	67	18	.	.	PUNCT
ijassa-1077	68	1	moreover	moreover	ADV
ijassa-1077	68	2	,	,	PUNCT
ijassa-1077	68	3	sometimes	sometimes	ADV
ijassa-1077	68	4	several	several	ADJ
ijassa-1077	68	5	color	color	NOUN
ijassa-1077	68	6	limitations	limitation	NOUN
ijassa-1077	68	7	should	should	AUX
ijassa-1077	68	8	be	be	AUX
ijassa-1077	68	9	applied	apply	VERB
ijassa-1077	68	10	to	to	ADP
ijassa-1077	68	11	the	the	DET
ijassa-1077	68	12	colorants	colorant	NOUN
ijassa-1077	68	13	cube	cube	NOUN
ijassa-1077	68	14	.	.	PUNCT
ijassa-1077	69	1	as	as	ADP
ijassa-1077	69	2	a	a	DET
ijassa-1077	69	3	result	result	NOUN
ijassa-1077	69	4	in	in	ADP
ijassa-1077	69	5	general	general	ADJ
ijassa-1077	69	6	case	case	NOUN
ijassa-1077	69	7	we	we	PRON
ijassa-1077	69	8	will	will	AUX
ijassa-1077	69	9	get	get	VERB
ijassa-1077	69	10	not	not	PART
ijassa-1077	69	11	a	a	DET
ijassa-1077	69	12	cube	cube	NOUN
ijassa-1077	69	13	decomposed	decompose	VERB
ijassa-1077	69	14	into	into	ADP
ijassa-1077	69	15	simplexes	simplexe	NOUN
ijassa-1077	69	16	but	but	CCONJ
ijassa-1077	69	17	a	a	DET
ijassa-1077	69	18	convex	convex	NOUN
ijassa-1077	69	19	polyhedron	polyhedron	NOUN
ijassa-1077	69	20	decomposed	decompose	VERB
ijassa-1077	69	21	into	into	ADP
ijassa-1077	69	22	intact	intact	ADJ
ijassa-1077	69	23	and	and	CCONJ
ijassa-1077	69	24	truncated	truncated	ADJ
ijassa-1077	69	25	simplexes	simplexe	NOUN
ijassa-1077	69	26	.	.	PUNCT
ijassa-1077	70	1	nevertheless	nevertheless	ADV
ijassa-1077	70	2	all	all	DET
ijassa-1077	70	3	the	the	DET
ijassa-1077	70	4	constructions	construction	NOUN
ijassa-1077	70	5	below	below	ADV
ijassa-1077	70	6	actually	actually	ADV
ijassa-1077	70	7	are	be	AUX
ijassa-1077	70	8	through	through	ADP
ijassa-1077	70	9	in	in	ADP
ijassa-1077	70	10	this	this	DET
ijassa-1077	70	11	general	general	ADJ
ijassa-1077	70	12	case	case	NOUN
ijassa-1077	70	13	.	.	PUNCT
ijassa-1077	71	1	therefore	therefore	ADV
ijassa-1077	71	2	the	the	DET
ijassa-1077	71	3	reader	reader	NOUN
ijassa-1077	71	4	,	,	PUNCT
ijassa-1077	71	5	especially	especially	ADV
ijassa-1077	71	6	the	the	DET
ijassa-1077	71	7	one	one	NOUN
ijassa-1077	71	8	who	who	PRON
ijassa-1077	71	9	is	be	AUX
ijassa-1077	71	10	mostly	mostly	ADV
ijassa-1077	71	11	interested	interested	ADJ
ijassa-1077	71	12	in	in	ADP
ijassa-1077	71	13	ideas	idea	NOUN
ijassa-1077	71	14	rather	rather	ADV
ijassa-1077	71	15	than	than	ADP
ijassa-1077	71	16	in	in	ADP
ijassa-1077	71	17	technical	technical	ADJ
ijassa-1077	71	18	details	detail	NOUN
ijassa-1077	71	19	,	,	PUNCT
ijassa-1077	71	20	can	can	AUX
ijassa-1077	71	21	easily	easily	ADV
ijassa-1077	71	22	content	content	VERB
ijassa-1077	71	23	himself	himself	PRON
ijassa-1077	71	24	with	with	ADP
ijassa-1077	71	25	the	the	DET
ijassa-1077	71	26	case	case	NOUN
ijassa-1077	71	27	of	of	ADP
ijassa-1077	71	28	cubes	cube	NOUN
ijassa-1077	71	29	and	and	CCONJ
ijassa-1077	71	30	simplexes	simplexe	NOUN
ijassa-1077	71	31	only	only	ADV
ijassa-1077	71	32	because	because	SCONJ
ijassa-1077	71	33	in	in	ADP
ijassa-1077	71	34	general	general	ADJ
ijassa-1077	71	35	case	case	NOUN
ijassa-1077	71	36	all	all	DET
ijassa-1077	71	37	the	the	DET
ijassa-1077	71	38	same	same	ADJ
ijassa-1077	71	39	ideas	idea	NOUN
ijassa-1077	71	40	and	and	CCONJ
ijassa-1077	71	41	methods	method	NOUN
ijassa-1077	71	42	are	be	AUX
ijassa-1077	71	43	practiced	practice	VERB
ijassa-1077	71	44	.	.	PUNCT
ijassa-1077	72	1	2	2	X
ijassa-1077	72	2	.	.	X
ijassa-1077	72	3	direct	direct	ADJ
ijassa-1077	72	4	problem	problem	NOUN
ijassa-1077	72	5	for	for	ADP
ijassa-1077	72	6	three	three	NUM
ijassa-1077	72	7	-	-	PUNCT
ijassa-1077	72	8	dimensional	dimensional	ADJ
ijassa-1077	72	9	printing	printing	NOUN
ijassa-1077	72	10	devices	device	NOUN
ijassa-1077	72	11	firstly	firstly	ADV
ijassa-1077	72	12	examine	examine	VERB
ijassa-1077	72	13	a	a	DET
ijassa-1077	72	14	problem	problem	NOUN
ijassa-1077	72	15	of	of	ADP
ijassa-1077	72	16	approximation	approximation	NOUN
ijassa-1077	72	17	for	for	ADP
ijassa-1077	72	18	a	a	DET
ijassa-1077	72	19	three	three	NUM
ijassa-1077	72	20	-	-	PUNCT
ijassa-1077	72	21	dimensional	dimensional	ADJ
ijassa-1077	72	22	printing	printing	NOUN
ijassa-1077	72	23	device	device	NOUN
ijassa-1077	72	24	.	.	PUNCT
ijassa-1077	73	1	let	let	VERB
ijassa-1077	73	2	a	a	DET
ijassa-1077	73	3	finite	finite	ADJ
ijassa-1077	73	4	set	set	NOUN
ijassa-1077	73	5	{	{	PUNCT
ijassa-1077	73	6	wi	wi	PROPN
ijassa-1077	73	7	}	}	PUNCT
ijassa-1077	73	8	ì	ì	PROPN
ijassa-1077	73	9	w3	w3	PROPN
ijassa-1077	73	10	of	of	ADP
ijassa-1077	73	11	points	point	NOUN
ijassa-1077	73	12	wi	wi	PROPN
ijassa-1077	73	13	,	,	PUNCT
ijassa-1077	73	14	i=1	i=1	X
ijassa-1077	73	15	,	,	PUNCT
ijassa-1077	73	16	…	…	PUNCT
ijassa-1077	73	17	,	,	PUNCT
ijassa-1077	73	18	m	m	PROPN
ijassa-1077	73	19	,	,	PUNCT
ijassa-1077	73	20	inside	inside	ADP
ijassa-1077	73	21	the	the	DET
ijassa-1077	73	22	colorants	colorant	NOUN
ijassa-1077	73	23	cube	cube	PROPN
ijassa-1077	73	24	w3	w3	PROPN
ijassa-1077	73	25	be	be	AUX
ijassa-1077	73	26	a	a	DET
ijassa-1077	73	27	regular	regular	ADJ
ijassa-1077	73	28	mesh	mesh	NOUN
ijassa-1077	73	29	.	.	PUNCT
ijassa-1077	74	1	consider	consider	VERB
ijassa-1077	74	2	a	a	DET
ijassa-1077	74	3	discrete	discrete	ADJ
ijassa-1077	74	4	map	map	NOUN
ijassa-1077	74	5	f	f	X
ijassa-1077	74	6	:	:	PUNCT
ijassa-1077	74	7	{	{	PUNCT
ijassa-1077	74	8	wi	wi	PROPN
ijassa-1077	74	9	}	}	PUNCT
ijassa-1077	74	10	®	®	NOUN
ijassa-1077	74	11	{	{	PUNCT
ijassa-1077	74	12	pi	pi	NOUN
ijassa-1077	74	13	}	}	PUNCT
ijassa-1077	74	14	,	,	PUNCT
ijassa-1077	74	15	of	of	ADP
ijassa-1077	74	16	measurement	measurement	NOUN
ijassa-1077	74	17	data	datum	NOUN
ijassa-1077	74	18	,	,	PUNCT
ijassa-1077	74	19	where	where	SCONJ
ijassa-1077	74	20	pi	pi	NOUN
ijassa-1077	74	21	=	=	SYM
ijassa-1077	74	22	f(wi	f(wi	NOUN
ijassa-1077	74	23	)	)	PUNCT
ijassa-1077	74	24	=	=	SYM
ijassa-1077	74	25	f(wi	f(wi	NOUN
ijassa-1077	74	26	)	)	PUNCT
ijassa-1077	74	27	for	for	ADP
ijassa-1077	74	28	i=1	i=1	PRON
ijassa-1077	74	29	,	,	PUNCT
ijassa-1077	74	30	…	…	PUNCT
ijassa-1077	74	31	,	,	PUNCT
ijassa-1077	74	32	n.	n.	NOUN
ijassa-1077	74	33	to	to	PART
ijassa-1077	74	34	approximate	approximate	VERB
ijassa-1077	74	35	the	the	DET
ijassa-1077	74	36	given	give	VERB
ijassa-1077	74	37	discrete	discrete	ADJ
ijassa-1077	74	38	map	map	NOUN
ijassa-1077	74	39	f	f	PROPN
ijassa-1077	74	40	by	by	ADP
ijassa-1077	74	41	a	a	DET
ijassa-1077	74	42	continuous	continuous	ADJ
ijassa-1077	74	43	one	one	NUM
ijassa-1077	74	44	f	f	NOUN
ijassa-1077	74	45	:	:	PUNCT
ijassa-1077	74	46	w3	w3	PROPN
ijassa-1077	74	47	®	®	NOUN
ijassa-1077	74	48	ℝ	ℝ	NOUN
ijassa-1077	74	49	#	#	ADV
ijassa-1077	74	50	,	,	PUNCT
ijassa-1077	74	51	use	use	VERB
ijassa-1077	74	52	a	a	DET
ijassa-1077	74	53	piecewise	piecewise	NOUN
ijassa-1077	74	54	linear	linear	NOUN
ijassa-1077	74	55	or	or	CCONJ
ijassa-1077	74	56	,	,	PUNCT
ijassa-1077	74	57	what	what	PRON
ijassa-1077	74	58	is	be	AUX
ijassa-1077	74	59	the	the	DET
ijassa-1077	74	60	same	same	ADJ
ijassa-1077	74	61	in	in	ADP
ijassa-1077	74	62	three	three	NUM
ijassa-1077	74	63	-	-	PUNCT
ijassa-1077	74	64	dimensional	dimensional	ADJ
ijassa-1077	74	65	case	case	NOUN
ijassa-1077	74	66	,	,	PUNCT
ijassa-1077	74	67	a	a	DET
ijassa-1077	74	68	tetrahedral	tetrahedral	ADJ
ijassa-1077	74	69	interpolation	interpolation	NOUN
ijassa-1077	74	70	.	.	PUNCT
ijassa-1077	75	1	we	we	PRON
ijassa-1077	75	2	will	will	AUX
ijassa-1077	75	3	mostly	mostly	ADV
ijassa-1077	75	4	follow	follow	VERB
ijassa-1077	75	5	the	the	DET
ijassa-1077	75	6	text	text	NOUN
ijassa-1077	75	7	-	-	PUNCT
ijassa-1077	75	8	book	book	NOUN
ijassa-1077	75	9	[	[	X
ijassa-1077	75	10	2	2	NUM
ijassa-1077	75	11	]	]	PUNCT
ijassa-1077	75	12	in	in	ADP
ijassa-1077	75	13	our	our	PRON
ijassa-1077	75	14	constructions	construction	NOUN
ijassa-1077	75	15	.	.	PUNCT
ijassa-1077	76	1	by	by	ADP
ijassa-1077	76	2	definition	definition	NOUN
ijassa-1077	76	3	of	of	ADP
ijassa-1077	76	4	a	a	DET
ijassa-1077	76	5	regular	regular	ADJ
ijassa-1077	76	6	mesh	mesh	NOUN
ijassa-1077	76	7	,	,	PUNCT
ijassa-1077	76	8	for	for	ADP
ijassa-1077	76	9	k=1,2,3	k=1,2,3	NUM
ijassa-1077	76	10	there	there	ADV
ijassa-1077	76	11	exist	exist	VERB
ijassa-1077	76	12	the	the	DET
ijassa-1077	76	13	one	one	NUM
ijassa-1077	76	14	-	-	PUNCT
ijassa-1077	76	15	dimensional	dimensional	ADJ
ijassa-1077	76	16	meshes	mesh	NOUN
ijassa-1077	76	17	zk	zk	X
ijassa-1077	76	18	=	=	SYM
ijassa-1077	76	19	{	{	PUNCT
ijassa-1077	76	20	xk0	xk0	PROPN
ijassa-1077	76	21	,	,	PUNCT
ijassa-1077	76	22	…	…	PUNCT
ijassa-1077	76	23	,	,	PUNCT
ijassa-1077	76	24	xkm(k	xkm(k	PROPN
ijassa-1077	76	25	)	)	PUNCT
ijassa-1077	76	26	}	}	PUNCT
ijassa-1077	76	27	,	,	PUNCT
ijassa-1077	76	28	ak	ak	PROPN
ijassa-1077	76	29	=	=	PUNCT
ijassa-1077	76	30	xk0	xk0	PROPN
ijassa-1077	76	31	<	<	X
ijassa-1077	76	32	…	…	PUNCT
ijassa-1077	76	33	<	<	X
ijassa-1077	76	34	xkm(k	xkm(k	PROPN
ijassa-1077	76	35	)	)	PUNCT
ijassa-1077	77	1	=	=	PUNCT
ijassa-1077	77	2	bk	bk	NOUN
ijassa-1077	77	3	,	,	PUNCT
ijassa-1077	77	4	of	of	ADP
ijassa-1077	77	5	m(k)+1	m(k)+1	NOUN
ijassa-1077	77	6	real	real	ADJ
ijassa-1077	77	7	numbers	number	NOUN
ijassa-1077	77	8	such	such	ADJ
ijassa-1077	77	9	that	that	SCONJ
ijassa-1077	77	10	{	{	PUNCT
ijassa-1077	77	11	wi	wi	PROPN
ijassa-1077	77	12	}	}	PUNCT
ijassa-1077	77	13	=	=	SYM
ijassa-1077	77	14	z1	z1	VERB
ijassa-1077	77	15	´	´	PROPN
ijassa-1077	77	16	z2	z2	PROPN
ijassa-1077	77	17	´	´	NOUN
ijassa-1077	77	18	z3	z3	PROPN
ijassa-1077	77	19	ì	ì	PROPN
ijassa-1077	77	20	w3	w3	PROPN
ijassa-1077	77	21	and	and	CCONJ
ijassa-1077	77	22	m	m	PROPN
ijassa-1077	77	23	=	=	PUNCT
ijassa-1077	77	24	(	(	PUNCT
ijassa-1077	77	25	m(1)+1)(m(2)+1)(m(3)+1	m(1)+1)(m(2)+1)(m(3)+1	NOUN
ijassa-1077	77	26	)	)	PUNCT
ijassa-1077	77	27	.	.	PUNCT
ijassa-1077	78	1	it	it	PRON
ijassa-1077	78	2	means	mean	VERB
ijassa-1077	78	3	that	that	SCONJ
ijassa-1077	78	4	the	the	DET
ijassa-1077	78	5	three	three	NUM
ijassa-1077	78	6	-	-	PUNCT
ijassa-1077	78	7	dimensional	dimensional	ADJ
ijassa-1077	78	8	colorants	colorant	NOUN
ijassa-1077	78	9	cube	cube	NOUN
ijassa-1077	78	10	w3	w3	PROPN
ijassa-1077	78	11	can	can	AUX
ijassa-1077	78	12	be	be	AUX
ijassa-1077	78	13	decomposed	decompose	VERB
ijassa-1077	78	14	into	into	ADP
ijassa-1077	78	15	the	the	DET
ijassa-1077	78	16	union	union	NOUN
ijassa-1077	78	17	of	of	ADP
ijassa-1077	78	18	the	the	DET
ijassa-1077	78	19	mesh	mesh	NOUN
ijassa-1077	78	20	parallelepiped	parallelepipe	VERB
ijassa-1077	78	21	cells	cell	NOUN
ijassa-1077	78	22	pi	pi	NOUN
ijassa-1077	78	23	,	,	PUNCT
ijassa-1077	78	24	j	j	PROPN
ijassa-1077	78	25	,	,	PUNCT
ijassa-1077	78	26	k	k	PROPN
ijassa-1077	79	1	=	=	PUNCT
ijassa-1077	80	1	[	[	X
ijassa-1077	80	2	x1i-1	x1i-1	PROPN
ijassa-1077	80	3	,	,	PUNCT
ijassa-1077	80	4	x1i	x1i	PROPN
ijassa-1077	80	5	]	]	PUNCT
ijassa-1077	80	6	´	´	VERB
ijassa-1077	81	1	[	[	X
ijassa-1077	81	2	x2j-1	x2j-1	X
ijassa-1077	81	3	,	,	PUNCT
ijassa-1077	81	4	x2j	x2j	PUNCT
ijassa-1077	81	5	]	]	PUNCT
ijassa-1077	81	6	´	´	VERB
ijassa-1077	82	1	[	[	X
ijassa-1077	82	2	x3k-1	x3k-1	PROPN
ijassa-1077	82	3	,	,	PUNCT
ijassa-1077	82	4	x3k	x3k	NOUN
ijassa-1077	82	5	]	]	X
ijassa-1077	82	6	,	,	PUNCT
ijassa-1077	82	7	i=1,	i=1,	NOUN
ijassa-1077	82	8	…	…	SYM
ijassa-1077	82	9	,m(1	,m(1	NUM
ijassa-1077	82	10	)	)	PUNCT
ijassa-1077	82	11	,	,	PUNCT
ijassa-1077	82	12	j=1,	j=1,	NOUN
ijassa-1077	82	13	…	…	PUNCT
ijassa-1077	82	14	,m(2	,m(2	NUM
ijassa-1077	82	15	)	)	PUNCT
ijassa-1077	82	16	,	,	PUNCT
ijassa-1077	82	17	k=1,	k=1,	NOUN
ijassa-1077	82	18	…	…	SYM
ijassa-1077	82	19	,m(3	,m(3	NUM
ijassa-1077	82	20	)	)	PUNCT
ijassa-1077	82	21	.	.	PUNCT
ijassa-1077	83	1	inside	inside	ADP
ijassa-1077	83	2	each	each	PRON
ijassa-1077	83	3	of	of	ADP
ijassa-1077	83	4	these	these	DET
ijassa-1077	83	5	parallelepiped	parallelepiped	ADJ
ijassa-1077	83	6	cells	cell	NOUN
ijassa-1077	83	7	the	the	DET
ijassa-1077	83	8	continuous	continuous	ADJ
ijassa-1077	83	9	approximation	approximation	NOUN
ijassa-1077	83	10	f	f	PROPN
ijassa-1077	83	11	of	of	ADP
ijassa-1077	83	12	the	the	DET
ijassa-1077	83	13	measurement	measurement	NOUN
ijassa-1077	83	14	discrete	discrete	NOUN
ijassa-1077	83	15	map	map	NOUN
ijassa-1077	83	16	f	f	PROPN
ijassa-1077	83	17	is	be	AUX
ijassa-1077	83	18	constructed	construct	VERB
ijassa-1077	83	19	by	by	ADP
ijassa-1077	83	20	the	the	DET
ijassa-1077	83	21	following	following	ADJ
ijassa-1077	83	22	way	way	NOUN
ijassa-1077	83	23	.	.	PUNCT
ijassa-1077	84	1	consider	consider	VERB
ijassa-1077	84	2	an	an	DET
ijassa-1077	84	3	arbitrary	arbitrary	ADJ
ijassa-1077	84	4	three	three	NUM
ijassa-1077	84	5	-	-	PUNCT
ijassa-1077	84	6	dimensional	dimensional	ADJ
ijassa-1077	84	7	rectangular	rectangular	ADJ
ijassa-1077	84	8	parallelepiped	parallelepiped	NOUN
ijassa-1077	84	9	p	p	NOUN
ijassa-1077	84	10	=	=	X
ijassa-1077	85	1	[	[	X
ijassa-1077	85	2	a1	a1	NOUN
ijassa-1077	85	3	,	,	PUNCT
ijassa-1077	85	4	b1	b1	NOUN
ijassa-1077	85	5	]	]	PUNCT
ijassa-1077	85	6	´	´	VERB
ijassa-1077	86	1	[	[	X
ijassa-1077	86	2	a2	a2	NOUN
ijassa-1077	86	3	,	,	PUNCT
ijassa-1077	86	4	b2	b2	NOUN
ijassa-1077	86	5	]	]	PUNCT
ijassa-1077	86	6	´	´	VERB
ijassa-1077	87	1	[	[	X
ijassa-1077	87	2	a3	a3	NOUN
ijassa-1077	87	3	,	,	PUNCT
ijassa-1077	87	4	b3	b3	PROPN
ijassa-1077	87	5	]	]	PUNCT
ijassa-1077	88	1	=	=	SYM
ijassa-1077	88	2	{	{	PUNCT
ijassa-1077	88	3	(	(	PUNCT
ijassa-1077	88	4	x1	x1	PROPN
ijassa-1077	88	5	,	,	PUNCT
ijassa-1077	88	6	x2	x2	PROPN
ijassa-1077	88	7	,	,	PUNCT
ijassa-1077	88	8	x3	x3	ADJ
ijassa-1077	88	9	)	)	PUNCT
ijassa-1077	88	10	,	,	PUNCT
ijassa-1077	88	11	a1	a1	VERB
ijassa-1077	88	12	£	£	PROPN
ijassa-1077	88	13	x1	x1	NUM
ijassa-1077	88	14	£	£	NOUN
ijassa-1077	88	15	b1	b1	NOUN
ijassa-1077	88	16	,	,	PUNCT
ijassa-1077	88	17	a2	a2	PROPN
ijassa-1077	88	18	£	£	PROPN
ijassa-1077	88	19	x2	x2	NOUN
ijassa-1077	88	20	£	£	NOUN
ijassa-1077	88	21	b2	b2	NOUN
ijassa-1077	88	22	,	,	PUNCT
ijassa-1077	88	23	a3	a3	VERB
ijassa-1077	88	24	£	£	SYM
ijassa-1077	88	25	x3	x3	ADJ
ijassa-1077	88	26	£	£	SYM
ijassa-1077	88	27	b3	b3	NOUN
ijassa-1077	88	28	}	}	PUNCT
ijassa-1077	88	29	,	,	PUNCT
ijassa-1077	88	30	where	where	SCONJ
ijassa-1077	88	31	a1	a1	NOUN
ijassa-1077	88	32	,	,	PUNCT
ijassa-1077	88	33	b1	b1	NOUN
ijassa-1077	88	34	,	,	PUNCT
ijassa-1077	88	35	a2	a2	PROPN
ijassa-1077	88	36	,	,	PUNCT
ijassa-1077	88	37	b2	b2	NOUN
ijassa-1077	88	38	,	,	PUNCT
ijassa-1077	88	39	a3	a3	NOUN
ijassa-1077	88	40	,	,	PUNCT
ijassa-1077	88	41	and	and	CCONJ
ijassa-1077	88	42	b3	b3	PROPN
ijassa-1077	88	43	are	be	AUX
ijassa-1077	88	44	fixed	fix	VERB
ijassa-1077	88	45	real	real	ADJ
ijassa-1077	88	46	numbers	number	NOUN
ijassa-1077	88	47	.	.	PUNCT
ijassa-1077	89	1	there	there	PRON
ijassa-1077	89	2	is	be	VERB
ijassa-1077	89	3	an	an	DET
ijassa-1077	89	4	obvious	obvious	ADJ
ijassa-1077	89	5	one	one	NUM
ijassa-1077	89	6	-	-	PUNCT
ijassa-1077	89	7	to	to	ADP
ijassa-1077	89	8	-	-	PUNCT
ijassa-1077	89	9	one	one	NUM
ijassa-1077	89	10	correspondence	correspondence	NOUN
ijassa-1077	89	11	of	of	ADP
ijassa-1077	89	12	the	the	DET
ijassa-1077	89	13	8	8	NUM
ijassa-1077	89	14	vertices	vertex	NOUN
ijassa-1077	89	15	to	to	ADP
ijassa-1077	89	16	the	the	DET
ijassa-1077	89	17	rectangular	rectangular	ADJ
ijassa-1077	89	18	parallelepiped	parallelepipe	VERB
ijassa-1077	89	19	p	p	NOUN
ijassa-1077	89	20	and	and	CCONJ
ijassa-1077	89	21	the	the	DET
ijassa-1077	89	22	8	8	NUM
ijassa-1077	89	23	vertices	vertex	NOUN
ijassa-1077	89	24	(	(	PUNCT
ijassa-1077	89	25	0,0,0	0,0,0	NOUN
ijassa-1077	89	26	)	)	PUNCT
ijassa-1077	89	27	,	,	PUNCT
ijassa-1077	89	28	(	(	PUNCT
ijassa-1077	89	29	0,0,1	0,0,1	NOUN
ijassa-1077	89	30	)	)	PUNCT
ijassa-1077	89	31	,	,	PUNCT
ijassa-1077	89	32	(	(	PUNCT
ijassa-1077	89	33	0,1,0	0,1,0	NUM
ijassa-1077	89	34	)	)	PUNCT
ijassa-1077	89	35	,	,	PUNCT
ijassa-1077	89	36	(	(	PUNCT
ijassa-1077	89	37	0,1,1	0,1,1	NOUN
ijassa-1077	89	38	)	)	PUNCT
ijassa-1077	89	39	,	,	PUNCT
ijassa-1077	89	40	(	(	PUNCT
ijassa-1077	89	41	1,0,0	1,0,0	NUM
ijassa-1077	89	42	)	)	PUNCT
ijassa-1077	89	43	,	,	PUNCT
ijassa-1077	89	44	(	(	PUNCT
ijassa-1077	89	45	1,0,1	1,0,1	NUM
ijassa-1077	89	46	)	)	PUNCT
ijassa-1077	89	47	,	,	PUNCT
ijassa-1077	89	48	(	(	PUNCT
ijassa-1077	89	49	1,1,0	1,1,0	NUM
ijassa-1077	89	50	)	)	PUNCT
ijassa-1077	89	51	,	,	PUNCT
ijassa-1077	89	52	(	(	PUNCT
ijassa-1077	89	53	1,1,1	1,1,1	NUM
ijassa-1077	89	54	)	)	PUNCT
ijassa-1077	89	55	to	to	ADP
ijassa-1077	89	56	the	the	DET
ijassa-1077	89	57	unit	unit	NOUN
ijassa-1077	89	58	three	three	NUM
ijassa-1077	89	59	-	-	PUNCT
ijassa-1077	89	60	dimensional	dimensional	ADJ
ijassa-1077	89	61	cube	cube	NOUN
ijassa-1077	89	62	p1	p1	NOUN
ijassa-1077	89	63	=	=	SYM
ijassa-1077	89	64	{	{	PUNCT
ijassa-1077	89	65	(	(	PUNCT
ijassa-1077	89	66	x1	x1	PROPN
ijassa-1077	89	67	,	,	PUNCT
ijassa-1077	89	68	x2	x2	PROPN
ijassa-1077	89	69	,	,	PUNCT
ijassa-1077	89	70	x3	x3	ADJ
ijassa-1077	89	71	)	)	PUNCT
ijassa-1077	89	72	,	,	PUNCT
ijassa-1077	89	73	0	0	PUNCT
ijassa-1077	89	74	£	£	SYM
ijassa-1077	89	75	x1	x1	NUM
ijassa-1077	89	76	£	£	SYM
ijassa-1077	89	77	1	1	NUM
ijassa-1077	89	78	,	,	PUNCT
ijassa-1077	89	79	0	0	NUM
ijassa-1077	89	80	£	£	NOUN
ijassa-1077	89	81	x2£1	x2£1	NOUN
ijassa-1077	89	82	,	,	PUNCT
ijassa-1077	89	83	0	0	NUM
ijassa-1077	89	84	£	£	NUM
ijassa-1077	89	85	x3	x3	ADJ
ijassa-1077	89	86	£	£	NOUN
ijassa-1077	89	87	1	1	NUM
ijassa-1077	89	88	}	}	PUNCT
ijassa-1077	89	89	.	.	PUNCT
ijassa-1077	90	1	cx	cx	NOUN
ijassa-1077	90	2	m	m	VERB
ijassa-1077	91	1	i	i	PRON
ijassa-1077	91	2	i	i	PRON
ijassa-1077	91	3	£	£	SYM
ijassa-1077	91	4	å	å	NOUN
ijassa-1077	91	5	=	=	NOUN
ijassa-1077	91	6	1	1	NUM
ijassa-1077	91	7	mc	mc	PROPN
ijassa-1077	91	8	100	100	NUM
ijassa-1077	91	9	<	<	X
ijassa-1077	91	10	mw	mw	X
ijassa-1077	91	11	!	!	PUNCT
ijassa-1077	91	12	)	)	PUNCT
ijassa-1077	92	1	3(,	3(,	NUM
ijassa-1077	92	2	...	...	PUNCT
ijassa-1077	92	3	,1	,1	PROPN
ijassa-1077	92	4	)	)	PUNCT
ijassa-1077	92	5	2(,	2(,	NUM
ijassa-1077	92	6	...	...	PUNCT
ijassa-1077	92	7	,1	,1	PUNCT
ijassa-1077	92	8	)	)	PUNCT
ijassa-1077	92	9	1(,	1(,	NUM
ijassa-1077	92	10	...	...	PUNCT
ijassa-1077	92	11	,1	,1	PUNCT
ijassa-1077	92	12	,	,	PUNCT
ijassa-1077	92	13	,	,	PUNCT
ijassa-1077	92	14	3	3	NUM
ijassa-1077	92	15	mk	mk	PROPN
ijassa-1077	92	16	mj	mj	PROPN
ijassa-1077	92	17	mi	mi	PROPN
ijassa-1077	92	18	kjiw	kjiw	PROPN
ijassa-1077	92	19	=	=	PUNCT
ijassa-1077	93	1	=	=	PUNCT
ijassa-1077	93	2	=	=	PUNCT
ijassa-1077	93	3	p=	p=	NOUN
ijassa-1077	93	4	120	120	NUM
ijassa-1077	93	5	d.v	d.v	PROPN
ijassa-1077	93	6	.	.	PUNCT
ijassa-1077	94	1	tunitsky	tunitsky	NOUN
ijassa-1077	94	2	copyright	copyright	NOUN
ijassa-1077	95	1	©	©	PROPN
ijassa-1077	95	2	2021	2021	NUM
ijassa-1077	95	3	assa	assa	NOUN
ijassa-1077	95	4	.	.	PUNCT
ijassa-1077	96	1	adv	adv	PROPN
ijassa-1077	96	2	.	.	PUNCT
ijassa-1077	97	1	in	in	ADP
ijassa-1077	97	2	systems	system	NOUN
ijassa-1077	97	3	science	science	NOUN
ijassa-1077	97	4	and	and	CCONJ
ijassa-1077	97	5	appl	appl	NOUN
ijassa-1077	97	6	.	.	PUNCT
ijassa-1077	98	1	(	(	PUNCT
ijassa-1077	98	2	2021	2021	NUM
ijassa-1077	98	3	)	)	PUNCT
ijassa-1077	98	4	numerate	numerate	VERB
ijassa-1077	98	5	all	all	DET
ijassa-1077	98	6	the	the	DET
ijassa-1077	98	7	8	8	NUM
ijassa-1077	98	8	vertices	vertex	NOUN
ijassa-1077	98	9	of	of	ADP
ijassa-1077	98	10	the	the	DET
ijassa-1077	98	11	rectangular	rectangular	ADJ
ijassa-1077	98	12	parallelepiped	parallelepiped	NOUN
ijassa-1077	98	13	p	p	NOUN
ijassa-1077	98	14	by	by	ADP
ijassa-1077	98	15	means	mean	NOUN
ijassa-1077	98	16	of	of	ADP
ijassa-1077	98	17	the	the	DET
ijassa-1077	98	18	corresponding	corresponding	ADJ
ijassa-1077	98	19	vertices	vertex	NOUN
ijassa-1077	98	20	of	of	ADP
ijassa-1077	98	21	the	the	DET
ijassa-1077	98	22	unit	unit	NOUN
ijassa-1077	98	23	cube	cube	PROPN
ijassa-1077	98	24	p1	p1	PROPN
ijassa-1077	98	25	,	,	PUNCT
ijassa-1077	98	26	x000	x000	PROPN
ijassa-1077	98	27	,	,	PUNCT
ijassa-1077	98	28	x001	x001	PROPN
ijassa-1077	98	29	,	,	PUNCT
ijassa-1077	98	30	x010	x010	PROPN
ijassa-1077	98	31	,	,	PUNCT
ijassa-1077	98	32	x011	x011	PROPN
ijassa-1077	98	33	,	,	PUNCT
ijassa-1077	98	34	x100	x100	PROPN
ijassa-1077	98	35	,	,	PUNCT
ijassa-1077	98	36	x101	x101	PROPN
ijassa-1077	98	37	,	,	PUNCT
ijassa-1077	98	38	x110	x110	PROPN
ijassa-1077	98	39	,	,	PUNCT
ijassa-1077	98	40	x111	x111	PROPN
ijassa-1077	98	41	.	.	PROPN
ijassa-1077	98	42	apply	apply	VERB
ijassa-1077	98	43	the	the	DET
ijassa-1077	98	44	same	same	ADJ
ijassa-1077	98	45	numeration	numeration	NOUN
ijassa-1077	98	46	to	to	ADP
ijassa-1077	98	47	the	the	DET
ijassa-1077	98	48	values	value	NOUN
ijassa-1077	98	49	of	of	ADP
ijassa-1077	98	50	the	the	DET
ijassa-1077	98	51	discrete	discrete	ADJ
ijassa-1077	98	52	map	map	NOUN
ijassa-1077	98	53	f	f	X
ijassa-1077	98	54	,	,	PUNCT
ijassa-1077	98	55	i.e.	i.e.	X
ijassa-1077	98	56	,	,	PUNCT
ijassa-1077	98	57	put	put	VERB
ijassa-1077	98	58	pijl	pijl	NOUN
ijassa-1077	98	59	=	=	SYM
ijassa-1077	98	60	f(xijl	f(xijl	NOUN
ijassa-1077	98	61	)	)	PUNCT
ijassa-1077	98	62	for	for	ADP
ijassa-1077	98	63	i	i	PROPN
ijassa-1077	98	64	,	,	PUNCT
ijassa-1077	98	65	j	j	PROPN
ijassa-1077	98	66	,	,	PUNCT
ijassa-1077	98	67	l=0,1	l=0,1	PROPN
ijassa-1077	98	68	.	.	PUNCT
ijassa-1077	99	1	define	define	VERB
ijassa-1077	99	2	the	the	DET
ijassa-1077	99	3	map	map	NOUN
ijassa-1077	99	4	f	f	PROPN
ijassa-1077	99	5	inside	inside	ADP
ijassa-1077	99	6	the	the	DET
ijassa-1077	99	7	rectangular	rectangular	ADJ
ijassa-1077	99	8	parallelepiped	parallelepipe	VERB
ijassa-1077	99	9	p	p	X
ijassa-1077	99	10	,	,	PUNCT
ijassa-1077	99	11	yn	yn	PROPN
ijassa-1077	99	12	=	=	SYM
ijassa-1077	99	13	fn(x1	fn(x1	PROPN
ijassa-1077	99	14	,	,	PUNCT
ijassa-1077	99	15	x2	x2	PROPN
ijassa-1077	99	16	,	,	PUNCT
ijassa-1077	99	17	x3	x3	ADJ
ijassa-1077	99	18	)	)	PUNCT
ijassa-1077	100	1	=	=	SYM
ijassa-1077	100	2	pn000	pn000	PROPN
ijassa-1077	100	3	+	+	CCONJ
ijassa-1077	100	4	rn1dx1	rn1dx1	NUM
ijassa-1077	100	5	+	+	CCONJ
ijassa-1077	100	6	rn2dx2	rn2dx2	NOUN
ijassa-1077	100	7	+	+	CCONJ
ijassa-1077	100	8	rn3dx3	rn3dx3	ADJ
ijassa-1077	100	9	,	,	PUNCT
ijassa-1077	100	10	where	where	SCONJ
ijassa-1077	100	11	n	n	CCONJ
ijassa-1077	100	12	,	,	PUNCT
ijassa-1077	100	13	n=1,2,3	n=1,2,3	NUM
ijassa-1077	100	14	,	,	PUNCT
ijassa-1077	100	15	is	be	AUX
ijassa-1077	100	16	the	the	DET
ijassa-1077	100	17	number	number	NOUN
ijassa-1077	100	18	of	of	ADP
ijassa-1077	100	19	component	component	NOUN
ijassa-1077	100	20	of	of	ADP
ijassa-1077	100	21	the	the	DET
ijassa-1077	100	22	map	map	NOUN
ijassa-1077	100	23	f	f	PROPN
ijassa-1077	100	24	in	in	ADP
ijassa-1077	100	25	three	three	NUM
ijassa-1077	100	26	-	-	PUNCT
ijassa-1077	100	27	dimensional	dimensional	ADJ
ijassa-1077	100	28	color	color	NOUN
ijassa-1077	100	29	space	space	NOUN
ijassa-1077	100	30	ℝ	ℝ	NOUN
ijassa-1077	100	31	#	#	NOUN
ijassa-1077	100	32	and	and	CCONJ
ijassa-1077	100	33	dxi	dxi	NOUN
ijassa-1077	100	34	=	=	SYM
ijassa-1077	100	35	(	(	PUNCT
ijassa-1077	100	36	xi	xi	X
ijassa-1077	100	37	xi0)/(xi1	xi0)/(xi1	PROPN
ijassa-1077	100	38	xi0	xi0	PROPN
ijassa-1077	100	39	)	)	PUNCT
ijassa-1077	100	40	for	for	ADP
ijassa-1077	100	41	i=1,2,3	i=1,2,3	NUM
ijassa-1077	100	42	.	.	PUNCT
ijassa-1077	101	1	the	the	DET
ijassa-1077	101	2	coefficients	coefficient	NOUN
ijassa-1077	101	3	rni	rni	PROPN
ijassa-1077	101	4	,	,	PUNCT
ijassa-1077	101	5	i=1,2,3	i=1,2,3	X
ijassa-1077	101	6	,	,	PUNCT
ijassa-1077	101	7	are	be	AUX
ijassa-1077	101	8	determined	determine	VERB
ijassa-1077	101	9	in	in	ADP
ijassa-1077	101	10	correspondence	correspondence	NOUN
ijassa-1077	101	11	with	with	ADP
ijassa-1077	101	12	the	the	DET
ijassa-1077	101	13	following	follow	VERB
ijassa-1077	101	14	table	table	NOUN
ijassa-1077	101	15	(	(	PUNCT
ijassa-1077	101	16	cf	cf	NOUN
ijassa-1077	101	17	.	.	PUNCT
ijassa-1077	102	1	[	[	X
ijassa-1077	102	2	2	2	NUM
ijassa-1077	102	3	,	,	PUNCT
ijassa-1077	102	4	p.	p.	NOUN
ijassa-1077	102	5	70–72	70–72	NUM
ijassa-1077	102	6	]	]	PUNCT
ijassa-1077	102	7	)	)	PUNCT
ijassa-1077	102	8	.	.	PUNCT
ijassa-1077	103	1	table	table	NOUN
ijassa-1077	103	2	1	1	NUM
ijassa-1077	103	3	.	.	PUNCT
ijassa-1077	103	4	coefficients	coefficients	PROPN
ijassa-1077	103	5	rni	rni	PROPN
ijassa-1077	103	6	,	,	PUNCT
ijassa-1077	103	7	i=1,2,3	i=1,2,3	VERB
ijassa-1077	103	8	the	the	DET
ijassa-1077	103	9	interpolation	interpolation	NOUN
ijassa-1077	103	10	under	under	ADP
ijassa-1077	103	11	consideration	consideration	NOUN
ijassa-1077	103	12	has	have	VERB
ijassa-1077	103	13	pure	pure	ADJ
ijassa-1077	103	14	geometrical	geometrical	ADJ
ijassa-1077	103	15	sense	sense	NOUN
ijassa-1077	103	16	.	.	PUNCT
ijassa-1077	104	1	we	we	PRON
ijassa-1077	104	2	decompose	decompose	VERB
ijassa-1077	104	3	a	a	DET
ijassa-1077	104	4	threedimensional	threedimensional	ADJ
ijassa-1077	104	5	rectangular	rectangular	ADJ
ijassa-1077	104	6	parallelepiped	parallelepipe	VERB
ijassa-1077	104	7	into	into	ADP
ijassa-1077	104	8	six	six	NUM
ijassa-1077	104	9	tetrahedrons	tetrahedron	NOUN
ijassa-1077	104	10	.	.	PUNCT
ijassa-1077	105	1	these	these	DET
ijassa-1077	105	2	tetrahedrons	tetrahedron	NOUN
ijassa-1077	105	3	are	be	AUX
ijassa-1077	105	4	defined	define	VERB
ijassa-1077	105	5	by	by	ADP
ijassa-1077	105	6	the	the	DET
ijassa-1077	105	7	conditions	condition	NOUN
ijassa-1077	105	8	in	in	ADP
ijassa-1077	105	9	the	the	DET
ijassa-1077	105	10	second	second	ADJ
ijassa-1077	105	11	column	column	NOUN
ijassa-1077	105	12	of	of	ADP
ijassa-1077	105	13	the	the	DET
ijassa-1077	105	14	table	table	NOUN
ijassa-1077	105	15	above	above	ADV
ijassa-1077	105	16	.	.	PUNCT
ijassa-1077	106	1	inside	inside	ADP
ijassa-1077	106	2	each	each	DET
ijassa-1077	106	3	tetrahedron	tetrahedron	NOUN
ijassa-1077	106	4	the	the	DET
ijassa-1077	106	5	map	map	NOUN
ijassa-1077	106	6	f	f	NOUN
ijassa-1077	106	7	is	be	AUX
ijassa-1077	106	8	constructed	construct	VERB
ijassa-1077	106	9	by	by	ADP
ijassa-1077	106	10	linear	linear	ADJ
ijassa-1077	106	11	interpolation	interpolation	NOUN
ijassa-1077	106	12	of	of	ADP
ijassa-1077	106	13	the	the	DET
ijassa-1077	106	14	values	value	NOUN
ijassa-1077	106	15	pijl	pijl	NOUN
ijassa-1077	106	16	,	,	PUNCT
ijassa-1077	106	17	i	i	PRON
ijassa-1077	106	18	,	,	PUNCT
ijassa-1077	106	19	j	j	PROPN
ijassa-1077	106	20	,	,	PUNCT
ijassa-1077	106	21	l=0,1	l=0,1	NOUN
ijassa-1077	106	22	,	,	PUNCT
ijassa-1077	106	23	of	of	ADP
ijassa-1077	106	24	the	the	DET
ijassa-1077	106	25	discrete	discrete	ADJ
ijassa-1077	106	26	map	map	NOUN
ijassa-1077	106	27	f	f	PROPN
ijassa-1077	106	28	at	at	ADP
ijassa-1077	106	29	the	the	DET
ijassa-1077	106	30	vertices	vertex	NOUN
ijassa-1077	106	31	to	to	ADP
ijassa-1077	106	32	the	the	DET
ijassa-1077	106	33	tetrahedrons	tetrahedron	NOUN
ijassa-1077	106	34	.	.	PUNCT
ijassa-1077	107	1	thus	thus	ADV
ijassa-1077	107	2	we	we	PRON
ijassa-1077	107	3	have	have	AUX
ijassa-1077	107	4	constructed	construct	VERB
ijassa-1077	107	5	the	the	DET
ijassa-1077	107	6	piecewise	piecewise	NOUN
ijassa-1077	107	7	linear	linear	NOUN
ijassa-1077	107	8	map	map	NOUN
ijassa-1077	107	9	f	f	NOUN
ijassa-1077	107	10	,	,	PUNCT
ijassa-1077	107	11	being	be	AUX
ijassa-1077	107	12	a	a	DET
ijassa-1077	107	13	solution	solution	NOUN
ijassa-1077	107	14	to	to	ADP
ijassa-1077	107	15	the	the	DET
ijassa-1077	107	16	direct	direct	ADJ
ijassa-1077	107	17	problem	problem	NOUN
ijassa-1077	107	18	of	of	ADP
ijassa-1077	107	19	mathematical	mathematical	ADJ
ijassa-1077	107	20	modeling	modeling	NOUN
ijassa-1077	107	21	for	for	ADP
ijassa-1077	107	22	a	a	DET
ijassa-1077	107	23	three	three	NUM
ijassa-1077	107	24	-	-	PUNCT
ijassa-1077	107	25	dimensional	dimensional	ADJ
ijassa-1077	107	26	printing	printing	NOUN
ijassa-1077	107	27	device	device	NOUN
ijassa-1077	107	28	.	.	PUNCT
ijassa-1077	108	1	in	in	ADP
ijassa-1077	108	2	other	other	ADJ
ijassa-1077	108	3	words	word	NOUN
ijassa-1077	108	4	,	,	PUNCT
ijassa-1077	108	5	we	we	PRON
ijassa-1077	108	6	have	have	AUX
ijassa-1077	108	7	constructed	construct	VERB
ijassa-1077	108	8	a	a	DET
ijassa-1077	108	9	piecewise	piecewise	NOUN
ijassa-1077	108	10	linear	linear	NOUN
ijassa-1077	108	11	model	model	NOUN
ijassa-1077	108	12	of	of	ADP
ijassa-1077	108	13	a	a	DET
ijassa-1077	108	14	three	three	NUM
ijassa-1077	108	15	-	-	PUNCT
ijassa-1077	108	16	dimensional	dimensional	ADJ
ijassa-1077	108	17	printing	printing	NOUN
ijassa-1077	108	18	device	device	NOUN
ijassa-1077	108	19	.	.	PUNCT
ijassa-1077	109	1	3	3	X
ijassa-1077	109	2	.	.	X
ijassa-1077	109	3	direct	direct	ADJ
ijassa-1077	109	4	problem	problem	NOUN
ijassa-1077	109	5	for	for	ADP
ijassa-1077	109	6	four	four	NUM
ijassa-1077	109	7	-	-	PUNCT
ijassa-1077	109	8	dimensional	dimensional	ADJ
ijassa-1077	109	9	printing	printing	NOUN
ijassa-1077	109	10	devices	device	NOUN
ijassa-1077	109	11	now	now	ADV
ijassa-1077	109	12	consider	consider	VERB
ijassa-1077	109	13	a	a	DET
ijassa-1077	109	14	four	four	NUM
ijassa-1077	109	15	-	-	PUNCT
ijassa-1077	109	16	dimensional	dimensional	ADJ
ijassa-1077	109	17	printing	printing	NOUN
ijassa-1077	109	18	device	device	NOUN
ijassa-1077	109	19	,	,	PUNCT
ijassa-1077	109	20	which	which	PRON
ijassa-1077	109	21	is	be	AUX
ijassa-1077	109	22	modelled	model	VERB
ijassa-1077	109	23	in	in	ADP
ijassa-1077	109	24	a	a	DET
ijassa-1077	109	25	way	way	NOUN
ijassa-1077	109	26	similar	similar	ADJ
ijassa-1077	109	27	to	to	ADP
ijassa-1077	109	28	the	the	DET
ijassa-1077	109	29	three	three	NUM
ijassa-1077	109	30	-	-	PUNCT
ijassa-1077	109	31	dimensional	dimensional	ADJ
ijassa-1077	109	32	case	case	NOUN
ijassa-1077	109	33	.	.	PUNCT
ijassa-1077	110	1	let	let	VERB
ijassa-1077	110	2	a	a	DET
ijassa-1077	110	3	finite	finite	ADJ
ijassa-1077	110	4	set	set	NOUN
ijassa-1077	110	5	{	{	PUNCT
ijassa-1077	110	6	wi	wi	PROPN
ijassa-1077	110	7	}	}	PUNCT
ijassa-1077	110	8	ì	ì	PROPN
ijassa-1077	110	9	w4	w4	NOUN
ijassa-1077	110	10	of	of	ADP
ijassa-1077	110	11	points	point	NOUN
ijassa-1077	110	12	wi	wi	PROPN
ijassa-1077	110	13	,	,	PUNCT
ijassa-1077	110	14	i=1,	i=1,	PROPN
ijassa-1077	110	15	…	…	SYM
ijassa-1077	110	16	,m	,m	NOUN
ijassa-1077	110	17	,	,	PUNCT
ijassa-1077	110	18	of	of	ADP
ijassa-1077	110	19	the	the	DET
ijassa-1077	110	20	colorants	colorant	NOUN
ijassa-1077	110	21	cube	cube	PROPN
ijassa-1077	110	22	w4	w4	PROPN
ijassa-1077	110	23	be	be	AUX
ijassa-1077	110	24	a	a	DET
ijassa-1077	110	25	regular	regular	ADJ
ijassa-1077	110	26	mesh	mesh	NOUN
ijassa-1077	110	27	.	.	PUNCT
ijassa-1077	111	1	the	the	DET
ijassa-1077	111	2	measurement	measurement	NOUN
ijassa-1077	111	3	data	datum	NOUN
ijassa-1077	111	4	pi	pi	NOUN
ijassa-1077	111	5	=	=	SYM
ijassa-1077	111	6	f(wi	f(wi	NOUN
ijassa-1077	111	7	)	)	PUNCT
ijassa-1077	111	8	=	=	SYM
ijassa-1077	111	9	f(wi	f(wi	NOUN
ijassa-1077	111	10	)	)	PUNCT
ijassa-1077	111	11	,	,	PUNCT
ijassa-1077	111	12	i=1	i=1	X
ijassa-1077	111	13	,	,	PUNCT
ijassa-1077	111	14	…	…	PUNCT
ijassa-1077	111	15	,	,	PUNCT
ijassa-1077	111	16	m	m	PRON
ijassa-1077	111	17	,	,	PUNCT
ijassa-1077	111	18	determines	determine	VERB
ijassa-1077	111	19	a	a	DET
ijassa-1077	111	20	discrete	discrete	ADJ
ijassa-1077	111	21	map	map	NOUN
ijassa-1077	111	22	f	f	X
ijassa-1077	111	23	:	:	PUNCT
ijassa-1077	111	24	{	{	PUNCT
ijassa-1077	111	25	wi	wi	PROPN
ijassa-1077	111	26	}	}	PUNCT
ijassa-1077	111	27	®	®	NOUN
ijassa-1077	111	28	{	{	PUNCT
ijassa-1077	111	29	pi	pi	NOUN
ijassa-1077	111	30	}	}	PUNCT
ijassa-1077	111	31	,	,	PUNCT
ijassa-1077	111	32	to	to	PART
ijassa-1077	111	33	approximate	approximate	VERB
ijassa-1077	111	34	the	the	DET
ijassa-1077	111	35	discrete	discrete	ADJ
ijassa-1077	111	36	map	map	NOUN
ijassa-1077	111	37	f	f	PROPN
ijassa-1077	111	38	by	by	ADP
ijassa-1077	111	39	a	a	DET
ijassa-1077	111	40	continuous	continuous	ADJ
ijassa-1077	111	41	map	map	NOUN
ijassa-1077	111	42	f	f	NOUN
ijassa-1077	111	43	:	:	PUNCT
ijassa-1077	111	44	w4	w4	NOUN
ijassa-1077	111	45	®	®	NOUN
ijassa-1077	111	46	ℝ	ℝ	NOUN
ijassa-1077	111	47	#	#	ADV
ijassa-1077	111	48	,	,	PUNCT
ijassa-1077	111	49	use	use	VERB
ijassa-1077	111	50	a	a	DET
ijassa-1077	111	51	piecewise	piecewise	NOUN
ijassa-1077	111	52	linear	linear	NOUN
ijassa-1077	111	53	or	or	CCONJ
ijassa-1077	111	54	,	,	PUNCT
ijassa-1077	111	55	which	which	PRON
ijassa-1077	111	56	in	in	ADP
ijassa-1077	111	57	four	four	NUM
ijassa-1077	111	58	-	-	PUNCT
ijassa-1077	111	59	dimensional	dimensional	ADJ
ijassa-1077	111	60	case	case	NOUN
ijassa-1077	111	61	is	be	AUX
ijassa-1077	111	62	the	the	DET
ijassa-1077	111	63	same	same	ADJ
ijassa-1077	111	64	,	,	PUNCT
ijassa-1077	111	65	pentahedral	pentahedral	ADJ
ijassa-1077	111	66	interpolation	interpolation	NOUN
ijassa-1077	111	67	.	.	PUNCT
ijassa-1077	112	1	by	by	ADP
ijassa-1077	112	2	definition	definition	NOUN
ijassa-1077	112	3	of	of	ADP
ijassa-1077	112	4	a	a	DET
ijassa-1077	112	5	regular	regular	ADJ
ijassa-1077	112	6	mesh	mesh	NOUN
ijassa-1077	112	7	,	,	PUNCT
ijassa-1077	112	8	for	for	ADP
ijassa-1077	112	9	k=1,2,3,4	k=1,2,3,4	PROPN
ijassa-1077	112	10	there	there	PRON
ijassa-1077	112	11	exist	exist	VERB
ijassa-1077	112	12	the	the	DET
ijassa-1077	112	13	one	one	NUM
ijassa-1077	112	14	-	-	PUNCT
ijassa-1077	112	15	dimensional	dimensional	ADJ
ijassa-1077	112	16	meshes	mesh	NOUN
ijassa-1077	112	17	zk	zk	X
ijassa-1077	112	18	=	=	PUNCT
ijassa-1077	112	19	{	{	PUNCT
ijassa-1077	112	20	xk0	xk0	PROPN
ijassa-1077	112	21	,	,	PUNCT
ijassa-1077	112	22	…	…	PUNCT
ijassa-1077	112	23	,	,	PUNCT
ijassa-1077	112	24	xkm(k	xkm(k	PROPN
ijassa-1077	112	25	)	)	PUNCT
ijassa-1077	112	26	}	}	PUNCT
ijassa-1077	112	27	,	,	PUNCT
ijassa-1077	112	28	ak	ak	PROPN
ijassa-1077	112	29	=	=	PUNCT
ijassa-1077	112	30	xk0	xk0	PROPN
ijassa-1077	112	31	<	<	X
ijassa-1077	112	32	…	…	PUNCT
ijassa-1077	112	33	<	<	X
ijassa-1077	112	34	xkm(k	xkm(k	PROPN
ijassa-1077	112	35	)	)	PUNCT
ijassa-1077	113	1	=	=	PUNCT
ijassa-1077	113	2	bk	bk	NOUN
ijassa-1077	113	3	,	,	PUNCT
ijassa-1077	113	4	of	of	ADP
ijassa-1077	113	5	m(k)+1	m(k)+1	NOUN
ijassa-1077	113	6	real	real	ADJ
ijassa-1077	113	7	numbers	number	NOUN
ijassa-1077	113	8	such	such	ADJ
ijassa-1077	113	9	that	that	SCONJ
ijassa-1077	113	10	{	{	PUNCT
ijassa-1077	113	11	wi	wi	PROPN
ijassa-1077	113	12	}	}	PUNCT
ijassa-1077	113	13	=	=	SYM
ijassa-1077	113	14	z1	z1	VERB
ijassa-1077	113	15	´	´	PROPN
ijassa-1077	113	16	z2	z2	PROPN
ijassa-1077	113	17	´	´	NOUN
ijassa-1077	113	18	z3	z3	PROPN
ijassa-1077	113	19	´	´	PROPN
ijassa-1077	113	20	z4	z4	PROPN
ijassa-1077	113	21	ì	ì	PROPN
ijassa-1077	113	22	w4	w4	PROPN
ijassa-1077	113	23	and	and	CCONJ
ijassa-1077	113	24	m	m	PROPN
ijassa-1077	113	25	=	=	SYM
ijassa-1077	113	26	(	(	PUNCT
ijassa-1077	113	27	m(1)+1)(m(2)+1)(m(3)+1)(m(4)+1	m(1)+1)(m(2)+1)(m(3)+1)(m(4)+1	NOUN
ijassa-1077	113	28	)	)	PUNCT
ijassa-1077	113	29	.	.	PUNCT
ijassa-1077	114	1	it	it	PRON
ijassa-1077	114	2	means	mean	VERB
ijassa-1077	114	3	that	that	SCONJ
ijassa-1077	114	4	the	the	DET
ijassa-1077	114	5	fourdimensional	fourdimensional	ADJ
ijassa-1077	114	6	colorants	colorant	NOUN
ijassa-1077	114	7	cube	cube	PROPN
ijassa-1077	114	8	w4	w4	NOUN
ijassa-1077	114	9	can	can	AUX
ijassa-1077	114	10	be	be	AUX
ijassa-1077	114	11	decomposed	decompose	VERB
ijassa-1077	114	12	into	into	ADP
ijassa-1077	114	13	the	the	DET
ijassa-1077	114	14	union	union	NOUN
ijassa-1077	114	15	of	of	ADP
ijassa-1077	114	16	the	the	DET
ijassa-1077	114	17	mesh	mesh	NOUN
ijassa-1077	114	18	of	of	ADP
ijassa-1077	114	19	parallelepiped	parallelepiped	ADJ
ijassa-1077	114	20	cells	cell	NOUN
ijassa-1077	114	21	:	:	PUNCT
ijassa-1077	114	22	,	,	PUNCT
ijassa-1077	114	23	pi	pi	PROPN
ijassa-1077	114	24	,	,	PUNCT
ijassa-1077	114	25	j	j	PROPN
ijassa-1077	114	26	,	,	PUNCT
ijassa-1077	114	27	k	k	PROPN
ijassa-1077	114	28	=	=	PUNCT
ijassa-1077	115	1	[	[	X
ijassa-1077	115	2	x1i-1	x1i-1	PROPN
ijassa-1077	115	3	,	,	PUNCT
ijassa-1077	115	4	x1i	x1i	PROPN
ijassa-1077	115	5	]	]	PUNCT
ijassa-1077	115	6	´	´	VERB
ijassa-1077	116	1	[	[	X
ijassa-1077	116	2	x2j-1	x2j-1	X
ijassa-1077	116	3	,	,	PUNCT
ijassa-1077	116	4	x2j	x2j	PUNCT
ijassa-1077	116	5	]	]	PUNCT
ijassa-1077	116	6	´	´	VERB
ijassa-1077	117	1	[	[	X
ijassa-1077	117	2	x3k-1	x3k-1	PROPN
ijassa-1077	117	3	,	,	PUNCT
ijassa-1077	117	4	x3k	x3k	PROPN
ijassa-1077	117	5	]	]	X
ijassa-1077	117	6	´	´	VERB
ijassa-1077	118	1	[	[	X
ijassa-1077	118	2	x4k-1	x4k-1	NOUN
ijassa-1077	118	3	,	,	PUNCT
ijassa-1077	118	4	x4k	x4k	NOUN
ijassa-1077	118	5	]	]	PUNCT
ijassa-1077	118	6	.	.	PUNCT
ijassa-1077	119	1	inside	inside	ADP
ijassa-1077	119	2	each	each	DET
ijassa-1077	119	3	parallelepiped	parallelepiped	ADJ
ijassa-1077	119	4	cell	cell	NOUN
ijassa-1077	119	5	pi	pi	NOUN
ijassa-1077	119	6	,	,	PUNCT
ijassa-1077	119	7	j	j	PROPN
ijassa-1077	119	8	,	,	PUNCT
ijassa-1077	119	9	k	k	PROPN
ijassa-1077	119	10	the	the	DET
ijassa-1077	119	11	continuous	continuous	ADJ
ijassa-1077	119	12	approximation	approximation	NOUN
ijassa-1077	119	13	f	f	PROPN
ijassa-1077	119	14	of	of	ADP
ijassa-1077	119	15	the	the	DET
ijassa-1077	119	16	discrete	discrete	ADJ
ijassa-1077	119	17	map	map	NOUN
ijassa-1077	119	18	f	f	NOUN
ijassa-1077	119	19	is	be	AUX
ijassa-1077	119	20	constructed	construct	VERB
ijassa-1077	119	21	by	by	ADP
ijassa-1077	119	22	the	the	DET
ijassa-1077	119	23	following	following	ADJ
ijassa-1077	119	24	way	way	NOUN
ijassa-1077	119	25	.	.	PUNCT
ijassa-1077	120	1	no	no	DET
ijassa-1077	120	2	conditions	condition	NOUN
ijassa-1077	120	3	rn1	rn1	PROPN
ijassa-1077	120	4	rn2	rn2	PROPN
ijassa-1077	120	5	rn3	rn3	PROPN
ijassa-1077	120	6	1	1	NUM
ijassa-1077	120	7	dx1	dx1	PROPN
ijassa-1077	120	8	³	³	X
ijassa-1077	120	9	dx2	dx2	PROPN
ijassa-1077	120	10	³	³	PROPN
ijassa-1077	120	11	dx3	dx3	PROPN
ijassa-1077	120	12	pn100pn000	pn100pn000	PROPN
ijassa-1077	120	13	pn110pn100	pn110pn100	NOUN
ijassa-1077	120	14	pn111pn110	pn111pn110	NOUN
ijassa-1077	120	15	2	2	NUM
ijassa-1077	120	16	dx1	dx1	PROPN
ijassa-1077	120	17	³	³	PROPN
ijassa-1077	120	18	d	d	PROPN
ijassa-1077	120	19	x3	x3	PROPN
ijassa-1077	120	20	³	³	X
ijassa-1077	120	21	dx2	dx2	PROPN
ijassa-1077	120	22	pn100pn000	pn100pn000	PROPN
ijassa-1077	120	23	pn111pn101	pn111pn101	PROPN
ijassa-1077	120	24	pn101pn100	pn101pn100	PROPN
ijassa-1077	120	25	3	3	NUM
ijassa-1077	120	26	dx3	dx3	PROPN
ijassa-1077	120	27	³	³	PROPN
ijassa-1077	120	28	dx1	dx1	PROPN
ijassa-1077	120	29	³	³	X
ijassa-1077	120	30	dx2	dx2	PROPN
ijassa-1077	120	31	pn101pn001	pn101pn001	NOUN
ijassa-1077	120	32	pn111pn101	pn111pn101	NOUN
ijassa-1077	120	33	pn001pn000	pn001pn000	NOUN
ijassa-1077	121	1	4	4	NUM
ijassa-1077	121	2	dx2	dx2	PROPN
ijassa-1077	121	3	³	³	PROPN
ijassa-1077	121	4	dx1	dx1	PROPN
ijassa-1077	121	5	³	³	PROPN
ijassa-1077	121	6	dx3	dx3	PROPN
ijassa-1077	121	7	pn110pn010	pn110pn010	PROPN
ijassa-1077	121	8	pn010pn000	pn010pn000	PROPN
ijassa-1077	121	9	pn111pn110	pn111pn110	NOUN
ijassa-1077	121	10	5	5	NUM
ijassa-1077	121	11	dx2	dx2	PROPN
ijassa-1077	121	12	³	³	PROPN
ijassa-1077	121	13	dx3	dx3	PROPN
ijassa-1077	121	14	³	³	PROPN
ijassa-1077	121	15	dx1	dx1	PROPN
ijassa-1077	121	16	pn111pn011	pn111pn011	PROPN
ijassa-1077	121	17	pn010pn000	pn010pn000	NUM
ijassa-1077	121	18	pn011pn010	pn011pn010	PROPN
ijassa-1077	121	19	6	6	NUM
ijassa-1077	121	20	dx3	dx3	PROPN
ijassa-1077	121	21	³	³	X
ijassa-1077	121	22	dx2	dx2	PROPN
ijassa-1077	121	23	³	³	PROPN
ijassa-1077	121	24	dx1	dx1	PROPN
ijassa-1077	121	25	pn111pn011	pn111pn011	X
ijassa-1077	121	26	pn011pn001	pn011pn001	PROPN
ijassa-1077	121	27	pn001pn000	pn001pn000	PROPN
ijassa-1077	121	28	!	!	PUNCT
ijassa-1077	121	29	)	)	PUNCT
ijassa-1077	122	1	4(,	4(,	NUM
ijassa-1077	122	2	...	...	PUNCT
ijassa-1077	122	3	,1	,1	NOUN
ijassa-1077	122	4	)	)	PUNCT
ijassa-1077	122	5	3(,	3(,	NUM
ijassa-1077	122	6	...	...	PUNCT
ijassa-1077	122	7	,1	,1	PROPN
ijassa-1077	122	8	)	)	PUNCT
ijassa-1077	122	9	2(,	2(,	NUM
ijassa-1077	122	10	...	...	PUNCT
ijassa-1077	122	11	,1	,1	PUNCT
ijassa-1077	122	12	)	)	PUNCT
ijassa-1077	122	13	1(,	1(,	NUM
ijassa-1077	122	14	...	...	PUNCT
ijassa-1077	122	15	,1	,1	ADJ
ijassa-1077	122	16	,	,	PUNCT
ijassa-1077	122	17	,	,	PUNCT
ijassa-1077	122	18	,	,	PUNCT
ijassa-1077	122	19	3	3	NUM
ijassa-1077	122	20	ml	ml	PROPN
ijassa-1077	122	21	mk	mk	PROPN
ijassa-1077	122	22	mj	mj	PROPN
ijassa-1077	122	23	mi	mi	PROPN
ijassa-1077	122	24	lkjiw	lkjiw	PROPN
ijassa-1077	122	25	=	=	PUNCT
ijassa-1077	123	1	=	=	PUNCT
ijassa-1077	123	2	=	=	PUNCT
ijassa-1077	123	3	=	=	PUNCT
ijassa-1077	123	4	p=	p=	PROPN
ijassa-1077	123	5	mathematical	mathematical	ADJ
ijassa-1077	123	6	modeling	modeling	NOUN
ijassa-1077	123	7	of	of	ADP
ijassa-1077	123	8	color	color	NOUN
ijassa-1077	123	9	printing	printing	NOUN
ijassa-1077	123	10	devices	device	NOUN
ijassa-1077	123	11	:	:	PUNCT
ijassa-1077	123	12	color	color	NOUN
ijassa-1077	123	13	gamut	gamut	NOUN
ijassa-1077	123	14	visualization	visualization	NOUN
ijassa-1077	123	15	…	…	PUNCT
ijassa-1077	123	16	121	121	NUM
ijassa-1077	123	17	copyright	copyright	NOUN
ijassa-1077	123	18	©	©	PROPN
ijassa-1077	123	19	2021	2021	NUM
ijassa-1077	123	20	assa	assa	NOUN
ijassa-1077	123	21	.	.	PUNCT
ijassa-1077	124	1	adv	adv	PROPN
ijassa-1077	124	2	.	.	PUNCT
ijassa-1077	125	1	in	in	ADP
ijassa-1077	125	2	systems	system	NOUN
ijassa-1077	125	3	science	science	NOUN
ijassa-1077	125	4	and	and	CCONJ
ijassa-1077	125	5	appl	appl	NOUN
ijassa-1077	125	6	.	.	PUNCT
ijassa-1077	126	1	(	(	PUNCT
ijassa-1077	126	2	2021	2021	NUM
ijassa-1077	126	3	)	)	PUNCT
ijassa-1077	126	4	consider	consider	VERB
ijassa-1077	126	5	an	an	DET
ijassa-1077	126	6	arbitrary	arbitrary	ADJ
ijassa-1077	126	7	four	four	NUM
ijassa-1077	126	8	-	-	PUNCT
ijassa-1077	126	9	dimensional	dimensional	ADJ
ijassa-1077	126	10	rectangular	rectangular	ADJ
ijassa-1077	126	11	parallelepiped	parallelepiped	NOUN
ijassa-1077	126	12	p	p	NOUN
ijassa-1077	126	13	=	=	X
ijassa-1077	126	14	{	{	PUNCT
ijassa-1077	126	15	(	(	PUNCT
ijassa-1077	126	16	x1	x1	PROPN
ijassa-1077	126	17	,	,	PUNCT
ijassa-1077	126	18	x2	x2	PROPN
ijassa-1077	126	19	,	,	PUNCT
ijassa-1077	126	20	x3	x3	PROPN
ijassa-1077	126	21	,	,	PUNCT
ijassa-1077	126	22	x4	x4	PROPN
ijassa-1077	126	23	)	)	PUNCT
ijassa-1077	126	24	,	,	PUNCT
ijassa-1077	126	25	a1	a1	VERB
ijassa-1077	126	26	£	£	PROPN
ijassa-1077	126	27	x1	x1	NUM
ijassa-1077	126	28	£	£	NOUN
ijassa-1077	126	29	b1	b1	NOUN
ijassa-1077	126	30	,	,	PUNCT
ijassa-1077	126	31	a2	a2	PROPN
ijassa-1077	126	32	£	£	PROPN
ijassa-1077	126	33	x2	x2	NOUN
ijassa-1077	126	34	£	£	NOUN
ijassa-1077	126	35	b2	b2	NOUN
ijassa-1077	126	36	,	,	PUNCT
ijassa-1077	126	37	a3	a3	VERB
ijassa-1077	126	38	£	£	SYM
ijassa-1077	126	39	x3	x3	ADJ
ijassa-1077	126	40	£	£	NOUN
ijassa-1077	126	41	b3	b3	NOUN
ijassa-1077	126	42	,	,	PUNCT
ijassa-1077	126	43	a4	a4	NOUN
ijassa-1077	126	44	£	£	NUM
ijassa-1077	126	45	x4	x4	ADV
ijassa-1077	126	46	£	£	NOUN
ijassa-1077	126	47	b4	b4	NOUN
ijassa-1077	126	48	}	}	PUNCT
ijassa-1077	126	49	.	.	PUNCT
ijassa-1077	127	1	there	there	PRON
ijassa-1077	127	2	is	be	VERB
ijassa-1077	127	3	an	an	DET
ijassa-1077	127	4	obvious	obvious	ADJ
ijassa-1077	127	5	one	one	NUM
ijassa-1077	127	6	-	-	PUNCT
ijassa-1077	127	7	to	to	ADP
ijassa-1077	127	8	-	-	PUNCT
ijassa-1077	127	9	one	one	NUM
ijassa-1077	127	10	correspondence	correspondence	NOUN
ijassa-1077	127	11	between	between	ADP
ijassa-1077	127	12	the	the	DET
ijassa-1077	127	13	vertices	vertex	NOUN
ijassa-1077	127	14	of	of	ADP
ijassa-1077	127	15	the	the	DET
ijassa-1077	127	16	parallelepiped	parallelepiped	ADJ
ijassa-1077	127	17	p	p	NOUN
ijassa-1077	127	18	and	and	CCONJ
ijassa-1077	127	19	the	the	DET
ijassa-1077	127	20	vertices	vertex	NOUN
ijassa-1077	127	21	(	(	PUNCT
ijassa-1077	127	22	0,0,0,0	0,0,0,0	NOUN
ijassa-1077	127	23	)	)	PUNCT
ijassa-1077	127	24	,	,	PUNCT
ijassa-1077	127	25	(	(	PUNCT
ijassa-1077	127	26	0,0,0,1	0,0,0,1	NOUN
ijassa-1077	127	27	)	)	PUNCT
ijassa-1077	127	28	,	,	PUNCT
ijassa-1077	127	29	(	(	PUNCT
ijassa-1077	127	30	0,0,1,0	0,0,1,0	NUM
ijassa-1077	127	31	)	)	PUNCT
ijassa-1077	127	32	,	,	PUNCT
ijassa-1077	127	33	(	(	PUNCT
ijassa-1077	127	34	0,0,1,1	0,0,1,1	NUM
ijassa-1077	127	35	)	)	PUNCT
ijassa-1077	127	36	,	,	PUNCT
ijassa-1077	127	37	(	(	PUNCT
ijassa-1077	127	38	0,1,0,0	0,1,0,0	NUM
ijassa-1077	127	39	)	)	PUNCT
ijassa-1077	127	40	,	,	PUNCT
ijassa-1077	127	41	(	(	PUNCT
ijassa-1077	127	42	0,1,0,1	0,1,0,1	NOUN
ijassa-1077	127	43	)	)	PUNCT
ijassa-1077	127	44	,	,	PUNCT
ijassa-1077	127	45	(	(	PUNCT
ijassa-1077	127	46	0,1,1,0	0,1,1,0	NUM
ijassa-1077	127	47	)	)	PUNCT
ijassa-1077	127	48	,	,	PUNCT
ijassa-1077	127	49	(	(	PUNCT
ijassa-1077	127	50	0,1,1,1	0,1,1,1	NUM
ijassa-1077	127	51	)	)	PUNCT
ijassa-1077	127	52	,	,	PUNCT
ijassa-1077	127	53	(	(	PUNCT
ijassa-1077	127	54	1,0,0,0	1,0,0,0	NUM
ijassa-1077	127	55	)	)	PUNCT
ijassa-1077	127	56	,	,	PUNCT
ijassa-1077	127	57	(	(	PUNCT
ijassa-1077	127	58	1,0,0,1	1,0,0,1	NUM
ijassa-1077	127	59	)	)	PUNCT
ijassa-1077	127	60	,	,	PUNCT
ijassa-1077	127	61	(	(	PUNCT
ijassa-1077	127	62	1,0,1,0	1,0,1,0	NUM
ijassa-1077	127	63	)	)	PUNCT
ijassa-1077	127	64	,	,	PUNCT
ijassa-1077	127	65	(	(	PUNCT
ijassa-1077	127	66	1,0,1,1	1,0,1,1	NUM
ijassa-1077	127	67	)	)	PUNCT
ijassa-1077	127	68	,	,	PUNCT
ijassa-1077	127	69	(	(	PUNCT
ijassa-1077	127	70	1,1,0,0	1,1,0,0	NUM
ijassa-1077	127	71	)	)	PUNCT
ijassa-1077	127	72	,	,	PUNCT
ijassa-1077	127	73	(	(	PUNCT
ijassa-1077	127	74	1,1,0,1	1,1,0,1	NUM
ijassa-1077	127	75	)	)	PUNCT
ijassa-1077	127	76	,	,	PUNCT
ijassa-1077	127	77	(	(	PUNCT
ijassa-1077	127	78	1,1,1,0	1,1,1,0	NUM
ijassa-1077	127	79	)	)	PUNCT
ijassa-1077	127	80	,	,	PUNCT
ijassa-1077	127	81	(	(	PUNCT
ijassa-1077	127	82	1,1,1,1	1,1,1,1	NUM
ijassa-1077	127	83	)	)	PUNCT
ijassa-1077	127	84	of	of	ADP
ijassa-1077	127	85	the	the	DET
ijassa-1077	127	86	unit	unit	NOUN
ijassa-1077	127	87	four	four	NUM
ijassa-1077	127	88	-	-	PUNCT
ijassa-1077	127	89	dimensional	dimensional	ADJ
ijassa-1077	127	90	cube	cube	NOUN
ijassa-1077	127	91	p1	p1	NOUN
ijassa-1077	127	92	=	=	SYM
ijassa-1077	127	93	{	{	PUNCT
ijassa-1077	127	94	(	(	PUNCT
ijassa-1077	127	95	x1	x1	PROPN
ijassa-1077	127	96	,	,	PUNCT
ijassa-1077	127	97	x2	x2	PROPN
ijassa-1077	127	98	,	,	PUNCT
ijassa-1077	127	99	x3	x3	PROPN
ijassa-1077	127	100	,	,	PUNCT
ijassa-1077	127	101	x4	x4	PROPN
ijassa-1077	127	102	)	)	PUNCT
ijassa-1077	127	103	,	,	PUNCT
ijassa-1077	127	104	0	0	NUM
ijassa-1077	127	105	£	£	NUM
ijassa-1077	127	106	x1£1	x1£1	NOUN
ijassa-1077	127	107	,	,	PUNCT
ijassa-1077	127	108	0	0	NUM
ijassa-1077	127	109	£	£	NUM
ijassa-1077	127	110	x2£1	x2£1	NOUN
ijassa-1077	127	111	,	,	PUNCT
ijassa-1077	127	112	0	0	NUM
ijassa-1077	127	113	£	£	SYM
ijassa-1077	127	114	x3£1	x3£1	ADJ
ijassa-1077	127	115	,	,	PUNCT
ijassa-1077	127	116	0	0	NUM
ijassa-1077	127	117	£	£	NUM
ijassa-1077	127	118	x4£1	x4£1	NUM
ijassa-1077	127	119	}	}	PUNCT
ijassa-1077	127	120	.	.	PUNCT
ijassa-1077	128	1	numerate	numerate	VERB
ijassa-1077	128	2	the	the	DET
ijassa-1077	128	3	vertices	vertex	NOUN
ijassa-1077	128	4	of	of	ADP
ijassa-1077	128	5	the	the	DET
ijassa-1077	128	6	rectangular	rectangular	ADJ
ijassa-1077	128	7	parallelepiped	parallelepipe	VERB
ijassa-1077	128	8	p	p	NOUN
ijassa-1077	128	9	by	by	ADP
ijassa-1077	128	10	the	the	DET
ijassa-1077	128	11	corresponding	corresponding	ADJ
ijassa-1077	128	12	vertices	vertex	NOUN
ijassa-1077	128	13	of	of	ADP
ijassa-1077	128	14	the	the	DET
ijassa-1077	128	15	cube	cube	NOUN
ijassa-1077	128	16	p1	p1	NOUN
ijassa-1077	128	17	:	:	PUNCT
ijassa-1077	128	18	x0000	x0000	PROPN
ijassa-1077	128	19	,	,	PUNCT
ijassa-1077	128	20	x0001	x0001	X
ijassa-1077	128	21	,	,	PUNCT
ijassa-1077	128	22	x0010	x0010	PROPN
ijassa-1077	128	23	,	,	PUNCT
ijassa-1077	128	24	x0011	x0011	PROPN
ijassa-1077	128	25	,	,	PUNCT
ijassa-1077	128	26	x0100	x0100	PROPN
ijassa-1077	128	27	,	,	PUNCT
ijassa-1077	128	28	x0101	x0101	PROPN
ijassa-1077	128	29	,	,	PUNCT
ijassa-1077	128	30	x0110	x0110	PROPN
ijassa-1077	128	31	,	,	PUNCT
ijassa-1077	128	32	x0111,x1000	x0111,x1000	PROPN
ijassa-1077	128	33	,	,	PUNCT
ijassa-1077	128	34	x1001	x1001	PROPN
ijassa-1077	128	35	,	,	PUNCT
ijassa-1077	128	36	x1010	x1010	PROPN
ijassa-1077	128	37	,	,	PUNCT
ijassa-1077	128	38	x1011	x1011	PROPN
ijassa-1077	128	39	,	,	PUNCT
ijassa-1077	128	40	x1100	x1100	PROPN
ijassa-1077	128	41	,	,	PUNCT
ijassa-1077	128	42	x1101	x1101	PROPN
ijassa-1077	128	43	,	,	PUNCT
ijassa-1077	128	44	x1110	x1110	PROPN
ijassa-1077	128	45	,	,	PUNCT
ijassa-1077	128	46	x1111	x1111	PROPN
ijassa-1077	128	47	.	.	PROPN
ijassa-1077	128	48	apply	apply	VERB
ijassa-1077	128	49	this	this	DET
ijassa-1077	128	50	numeration	numeration	NOUN
ijassa-1077	128	51	also	also	ADV
ijassa-1077	128	52	to	to	ADP
ijassa-1077	128	53	the	the	DET
ijassa-1077	128	54	values	value	NOUN
ijassa-1077	128	55	of	of	ADP
ijassa-1077	128	56	the	the	DET
ijassa-1077	128	57	map	map	NOUN
ijassa-1077	129	1	f	f	X
ijassa-1077	129	2	,	,	PUNCT
ijassa-1077	129	3	i.e.	i.e.	X
ijassa-1077	129	4	,	,	PUNCT
ijassa-1077	129	5	put	put	VERB
ijassa-1077	129	6	pijkl	pijkl	NOUN
ijassa-1077	129	7	=	=	SYM
ijassa-1077	129	8	f(xijkl	f(xijkl	NOUN
ijassa-1077	129	9	)	)	PUNCT
ijassa-1077	129	10	for	for	ADP
ijassa-1077	129	11	i	i	PROPN
ijassa-1077	129	12	,	,	PUNCT
ijassa-1077	129	13	j	j	PROPN
ijassa-1077	129	14	,	,	PUNCT
ijassa-1077	129	15	k	k	PROPN
ijassa-1077	129	16	,	,	PUNCT
ijassa-1077	129	17	l=0,1	l=0,1	NOUN
ijassa-1077	129	18	,	,	PUNCT
ijassa-1077	129	19	and	and	CCONJ
ijassa-1077	129	20	define	define	VERB
ijassa-1077	129	21	the	the	DET
ijassa-1077	129	22	components	component	NOUN
ijassa-1077	129	23	of	of	ADP
ijassa-1077	129	24	the	the	DET
ijassa-1077	129	25	map	map	NOUN
ijassa-1077	129	26	f	f	PROPN
ijassa-1077	129	27	on	on	ADP
ijassa-1077	129	28	the	the	DET
ijassa-1077	129	29	parallelepiped	parallelepiped	ADJ
ijassa-1077	129	30	p	p	X
ijassa-1077	129	31	:	:	PUNCT
ijassa-1077	129	32	yn	yn	PROPN
ijassa-1077	129	33	=	=	SYM
ijassa-1077	129	34	fn(x1	fn(x1	PROPN
ijassa-1077	129	35	,	,	PUNCT
ijassa-1077	129	36	x2	x2	PROPN
ijassa-1077	129	37	,	,	PUNCT
ijassa-1077	129	38	x3	x3	ADJ
ijassa-1077	129	39	,	,	PUNCT
ijassa-1077	129	40	x4	x4	PROPN
ijassa-1077	129	41	)	)	PUNCT
ijassa-1077	129	42	=	=	SYM
ijassa-1077	129	43	pn000	pn000	PROPN
ijassa-1077	129	44	+	+	CCONJ
ijassa-1077	129	45	rn1d	rn1d	PROPN
ijassa-1077	129	46	x1	x1	PROPN
ijassa-1077	129	47	+	+	CCONJ
ijassa-1077	129	48	rn2d	rn2d	ADJ
ijassa-1077	129	49	x2	x2	NOUN
ijassa-1077	129	50	+	+	PUNCT
ijassa-1077	129	51	rn3d	rn3d	X
ijassa-1077	129	52	x3	x3	VERB
ijassa-1077	129	53	+	+	CCONJ
ijassa-1077	129	54	rn4d	rn4d	PROPN
ijassa-1077	129	55	x4	x4	PROPN
ijassa-1077	129	56	,	,	PUNCT
ijassa-1077	129	57	where	where	SCONJ
ijassa-1077	129	58	n=1,2,3	n=1,2,3	NUM
ijassa-1077	129	59	,	,	PUNCT
ijassa-1077	129	60	dxi	dxi	NOUN
ijassa-1077	129	61	=	=	SYM
ijassa-1077	129	62	(	(	PUNCT
ijassa-1077	129	63	xi	xi	ADP
ijassa-1077	129	64	xi0)/	xi0)/	PROPN
ijassa-1077	129	65	(	(	PUNCT
ijassa-1077	129	66	xi1	xi1	PROPN
ijassa-1077	129	67	xi0	xi0	PROPN
ijassa-1077	129	68	)	)	PUNCT
ijassa-1077	129	69	for	for	ADP
ijassa-1077	129	70	i=1,2,3,4	i=1,2,3,4	PROPN
ijassa-1077	129	71	,	,	PUNCT
ijassa-1077	129	72	and	and	CCONJ
ijassa-1077	129	73	rni	rni	NOUN
ijassa-1077	129	74	are	be	AUX
ijassa-1077	129	75	determined	determine	VERB
ijassa-1077	129	76	by	by	ADP
ijassa-1077	129	77	the	the	DET
ijassa-1077	129	78	table	table	NOUN
ijassa-1077	129	79	:	:	PUNCT
ijassa-1077	130	1	table	table	NOUN
ijassa-1077	130	2	2	2	NUM
ijassa-1077	130	3	.	.	NOUN
ijassa-1077	130	4	coefficients	coefficients	PROPN
ijassa-1077	130	5	rni	rni	PROPN
ijassa-1077	130	6	,	,	PUNCT
ijassa-1077	130	7	i=1,2,3,4	i=1,2,3,4	ADJ
ijassa-1077	130	8	no	no	DET
ijassa-1077	130	9	conditions	condition	NOUN
ijassa-1077	130	10	rn1	rn1	PROPN
ijassa-1077	130	11	rn2	rn2	PROPN
ijassa-1077	130	12	rn3	rn3	PROPN
ijassa-1077	130	13	rn4	rn4	NOUN
ijassa-1077	130	14	1	1	NUM
ijassa-1077	130	15	dx1	dx1	PROPN
ijassa-1077	130	16	³	³	PROPN
ijassa-1077	130	17	dx2	dx2	PROPN
ijassa-1077	130	18	³	³	PROPN
ijassa-1077	130	19	dx3	dx3	PROPN
ijassa-1077	130	20	³	³	PROPN
ijassa-1077	130	21	dx4	dx4	PROPN
ijassa-1077	130	22	pn1000	pn1000	PROPN
ijassa-1077	130	23	-	-	PUNCT
ijassa-1077	130	24	pn0000	pn0000	NOUN
ijassa-1077	130	25	pn1100	pn1100	NOUN
ijassa-1077	130	26	-	-	PUNCT
ijassa-1077	130	27	pn1000	pn1000	PROPN
ijassa-1077	130	28	pn1110	pn1110	NOUN
ijassa-1077	130	29	-	-	PUNCT
ijassa-1077	130	30	pn1100	pn1100	NOUN
ijassa-1077	130	31	pn1111	pn1111	PROPN
ijassa-1077	130	32	-	-	PUNCT
ijassa-1077	130	33	pn1110	pn1110	NOUN
ijassa-1077	130	34	2	2	NUM
ijassa-1077	130	35	dx1	dx1	PROPN
ijassa-1077	130	36	³	³	X
ijassa-1077	130	37	dx2	dx2	PROPN
ijassa-1077	130	38	³	³	PROPN
ijassa-1077	130	39	dx4	dx4	PROPN
ijassa-1077	130	40	³	³	PROPN
ijassa-1077	130	41	dx3	dx3	PROPN
ijassa-1077	130	42	pn1000	pn1000	PROPN
ijassa-1077	130	43	-	-	PUNCT
ijassa-1077	130	44	pn0000	pn0000	PROPN
ijassa-1077	130	45	pn1100	pn1100	NOUN
ijassa-1077	130	46	-	-	PUNCT
ijassa-1077	130	47	pn1000	pn1000	NOUN
ijassa-1077	130	48	pn1111	pn1111	PROPN
ijassa-1077	130	49	-	-	PUNCT
ijassa-1077	130	50	pn1101	pn1101	PROPN
ijassa-1077	130	51	pn1101	pn1101	PROPN
ijassa-1077	130	52	-	-	PUNCT
ijassa-1077	130	53	pn1100	pn1100	PROPN
ijassa-1077	130	54	3	3	NUM
ijassa-1077	130	55	dx1	dx1	PROPN
ijassa-1077	130	56	³	³	PROPN
ijassa-1077	130	57	dx4	dx4	X
ijassa-1077	130	58	³	³	X
ijassa-1077	130	59	dx2	dx2	PROPN
ijassa-1077	130	60	³	³	PROPN
ijassa-1077	130	61	dx3	dx3	PROPN
ijassa-1077	130	62	pn1000	pn1000	PROPN
ijassa-1077	130	63	-	-	PUNCT
ijassa-1077	130	64	pn0000	pn0000	NOUN
ijassa-1077	130	65	pn1101	pn1101	PROPN
ijassa-1077	130	66	-	-	PUNCT
ijassa-1077	130	67	pn1001	pn1001	NOUN
ijassa-1077	130	68	pn1111	pn1111	PROPN
ijassa-1077	130	69	-	-	PUNCT
ijassa-1077	130	70	pn1101	pn1101	PROPN
ijassa-1077	130	71	pn1001	pn1001	NOUN
ijassa-1077	130	72	-	-	PUNCT
ijassa-1077	130	73	pn1000	pn1000	PROPN
ijassa-1077	130	74	4	4	NUM
ijassa-1077	130	75	dx4	dx4	NOUN
ijassa-1077	130	76	³	³	PROPN
ijassa-1077	130	77	dx1	dx1	PROPN
ijassa-1077	130	78	³	³	X
ijassa-1077	130	79	dx2	dx2	PROPN
ijassa-1077	130	80	³	³	PROPN
ijassa-1077	130	81	dx3	dx3	PROPN
ijassa-1077	130	82	pn1001	pn1001	PROPN
ijassa-1077	130	83	-	-	PUNCT
ijassa-1077	130	84	pn0001	pn0001	ADJ
ijassa-1077	130	85	pn1101	pn1101	PROPN
ijassa-1077	130	86	-	-	PUNCT
ijassa-1077	130	87	pn1001	pn1001	NOUN
ijassa-1077	130	88	pn1111	pn1111	PROPN
ijassa-1077	130	89	-	-	PUNCT
ijassa-1077	130	90	pn1101	pn1101	PROPN
ijassa-1077	130	91	pn0001	pn0001	NOUN
ijassa-1077	130	92	-	-	PUNCT
ijassa-1077	130	93	pn0000	pn0000	NOUN
ijassa-1077	130	94	5	5	NUM
ijassa-1077	130	95	dx1	dx1	PROPN
ijassa-1077	130	96	³	³	PROPN
ijassa-1077	130	97	dx3	dx3	PROPN
ijassa-1077	130	98	³	³	X
ijassa-1077	130	99	dx2	dx2	PROPN
ijassa-1077	130	100	³	³	PROPN
ijassa-1077	130	101	dx4	dx4	PROPN
ijassa-1077	130	102	pn1000	pn1000	PROPN
ijassa-1077	130	103	-	-	PUNCT
ijassa-1077	130	104	pn0000	pn0000	NOUN
ijassa-1077	130	105	pn1110	pn1110	PROPN
ijassa-1077	130	106	-	-	PUNCT
ijassa-1077	130	107	pn1010	pn1010	PROPN
ijassa-1077	130	108	pn1010	pn1010	PROPN
ijassa-1077	130	109	-	-	PUNCT
ijassa-1077	130	110	pn1000	pn1000	PROPN
ijassa-1077	130	111	pn1111	pn1111	PROPN
ijassa-1077	130	112	-	-	PUNCT
ijassa-1077	130	113	pn1110	pn1110	NOUN
ijassa-1077	130	114	6	6	NUM
ijassa-1077	130	115	dx1	dx1	PROPN
ijassa-1077	130	116	³	³	PROPN
ijassa-1077	130	117	dx3	dx3	PROPN
ijassa-1077	130	118	³	³	PROPN
ijassa-1077	130	119	dx4	dx4	PROPN
ijassa-1077	130	120	³	³	PROPN
ijassa-1077	130	121	dx2	dx2	PROPN
ijassa-1077	130	122	pn1000	pn1000	PROPN
ijassa-1077	130	123	-	-	PUNCT
ijassa-1077	130	124	pn0000	pn0000	NOUN
ijassa-1077	130	125	pn1111	pn1111	NOUN
ijassa-1077	130	126	-	-	PUNCT
ijassa-1077	130	127	pn1011	pn1011	NOUN
ijassa-1077	130	128	pn1010	pn1010	NOUN
ijassa-1077	130	129	-	-	PUNCT
ijassa-1077	130	130	pn1000	pn1000	PROPN
ijassa-1077	130	131	pn1011	pn1011	PROPN
ijassa-1077	130	132	-	-	PUNCT
ijassa-1077	130	133	pn1010	pn1010	PROPN
ijassa-1077	130	134	7	7	NUM
ijassa-1077	130	135	dx1	dx1	PROPN
ijassa-1077	130	136	³	³	PROPN
ijassa-1077	130	137	dx4	dx4	PROPN
ijassa-1077	130	138	³	³	PROPN
ijassa-1077	130	139	dx3	dx3	PROPN
ijassa-1077	130	140	³	³	PROPN
ijassa-1077	130	141	dx2	dx2	PROPN
ijassa-1077	130	142	pn1000	pn1000	PROPN
ijassa-1077	130	143	-	-	PUNCT
ijassa-1077	130	144	pn0000	pn0000	NOUN
ijassa-1077	130	145	pn1111	pn1111	NOUN
ijassa-1077	130	146	-	-	PUNCT
ijassa-1077	130	147	pn1011	pn1011	NOUN
ijassa-1077	130	148	pn1011	pn1011	NOUN
ijassa-1077	130	149	-	-	PUNCT
ijassa-1077	130	150	pn1001	pn1001	NOUN
ijassa-1077	130	151	pn1001	pn1001	NOUN
ijassa-1077	130	152	-	-	PUNCT
ijassa-1077	130	153	pn1000	pn1000	ADJ
ijassa-1077	130	154	8	8	NUM
ijassa-1077	130	155	dx4	dx4	NOUN
ijassa-1077	130	156	³	³	PROPN
ijassa-1077	130	157	dx1	dx1	PROPN
ijassa-1077	130	158	³	³	PROPN
ijassa-1077	130	159	dx3	dx3	PROPN
ijassa-1077	130	160	³	³	X
ijassa-1077	130	161	dx2	dx2	PROPN
ijassa-1077	130	162	pn1001	pn1001	NOUN
ijassa-1077	130	163	-	-	PUNCT
ijassa-1077	130	164	pn0001	pn0001	NOUN
ijassa-1077	130	165	pn1111	pn1111	NOUN
ijassa-1077	130	166	-	-	PUNCT
ijassa-1077	130	167	pn1011	pn1011	NOUN
ijassa-1077	130	168	pn1011	pn1011	NOUN
ijassa-1077	130	169	-	-	PUNCT
ijassa-1077	130	170	pn1001	pn1001	NOUN
ijassa-1077	130	171	pn0001	pn0001	NOUN
ijassa-1077	130	172	-	-	PUNCT
ijassa-1077	130	173	pn0000	pn0000	NOUN
ijassa-1077	130	174	9	9	NUM
ijassa-1077	130	175	dx3	dx3	PROPN
ijassa-1077	130	176	³	³	PROPN
ijassa-1077	130	177	dx1	dx1	PROPN
ijassa-1077	130	178	³	³	X
ijassa-1077	130	179	dx2	dx2	PROPN
ijassa-1077	130	180	³	³	PROPN
ijassa-1077	130	181	dx4	dx4	PROPN
ijassa-1077	130	182	pn1010	pn1010	PROPN
ijassa-1077	130	183	-	-	PUNCT
ijassa-1077	130	184	pn0010	pn0010	PROPN
ijassa-1077	130	185	pn1110	pn1110	NOUN
ijassa-1077	130	186	-	-	PUNCT
ijassa-1077	130	187	pn1010	pn1010	NOUN
ijassa-1077	130	188	pn0010	pn0010	ADJ
ijassa-1077	130	189	-	-	PUNCT
ijassa-1077	130	190	pn0000	pn0000	NOUN
ijassa-1077	130	191	pn1111	pn1111	PROPN
ijassa-1077	130	192	-	-	PUNCT
ijassa-1077	130	193	pn1110	pn1110	NOUN
ijassa-1077	130	194	10	10	NUM
ijassa-1077	130	195	dx3	dx3	PROPN
ijassa-1077	130	196	³	³	PROPN
ijassa-1077	130	197	dx1	dx1	PROPN
ijassa-1077	130	198	³	³	PROPN
ijassa-1077	130	199	dx4	dx4	PROPN
ijassa-1077	130	200	³	³	PROPN
ijassa-1077	130	201	dx2	dx2	PROPN
ijassa-1077	130	202	pn1010	pn1010	PROPN
ijassa-1077	130	203	-	-	PUNCT
ijassa-1077	130	204	pn0010	pn0010	ADJ
ijassa-1077	130	205	pn1111	pn1111	NOUN
ijassa-1077	130	206	-	-	PUNCT
ijassa-1077	130	207	pn1011	pn1011	NOUN
ijassa-1077	130	208	pn0010	pn0010	ADJ
ijassa-1077	130	209	-	-	PUNCT
ijassa-1077	130	210	pn0000	pn0000	NOUN
ijassa-1077	130	211	pn1011	pn1011	NOUN
ijassa-1077	130	212	-	-	PUNCT
ijassa-1077	130	213	pn1010	pn1010	PROPN
ijassa-1077	130	214	11	11	NUM
ijassa-1077	130	215	dx3	dx3	PROPN
ijassa-1077	130	216	³	³	PROPN
ijassa-1077	130	217	dx4	dx4	PROPN
ijassa-1077	130	218	³	³	PROPN
ijassa-1077	130	219	dx1	dx1	PROPN
ijassa-1077	130	220	³	³	PROPN
ijassa-1077	130	221	dx2	dx2	PROPN
ijassa-1077	130	222	pn1011	pn1011	PROPN
ijassa-1077	130	223	-	-	PUNCT
ijassa-1077	130	224	pn0011	pn0011	PROPN
ijassa-1077	130	225	pn1111	pn1111	NOUN
ijassa-1077	130	226	-	-	PUNCT
ijassa-1077	130	227	pn1011	pn1011	NOUN
ijassa-1077	130	228	pn0010	pn0010	ADJ
ijassa-1077	130	229	-	-	PUNCT
ijassa-1077	130	230	pn0000	pn0000	NOUN
ijassa-1077	130	231	pn0011	pn0011	PROPN
ijassa-1077	130	232	-	-	PUNCT
ijassa-1077	130	233	pn0010	pn0010	PROPN
ijassa-1077	130	234	12	12	NUM
ijassa-1077	130	235	dx4	dx4	PROPN
ijassa-1077	130	236	³	³	PROPN
ijassa-1077	130	237	dx3	dx3	PROPN
ijassa-1077	130	238	³	³	PROPN
ijassa-1077	130	239	dx1	dx1	PROPN
ijassa-1077	130	240	³	³	PROPN
ijassa-1077	130	241	dx2	dx2	PROPN
ijassa-1077	130	242	pn1011	pn1011	PROPN
ijassa-1077	130	243	-	-	PUNCT
ijassa-1077	130	244	pn0011	pn0011	PROPN
ijassa-1077	130	245	pn1111	pn1111	NOUN
ijassa-1077	130	246	-	-	PUNCT
ijassa-1077	130	247	pn1011	pn1011	NOUN
ijassa-1077	130	248	pn0011	pn0011	ADJ
ijassa-1077	130	249	-	-	PUNCT
ijassa-1077	130	250	pn0001	pn0001	NOUN
ijassa-1077	130	251	pn0001	pn0001	NOUN
ijassa-1077	130	252	-	-	PUNCT
ijassa-1077	130	253	pn0000	pn0000	NOUN
ijassa-1077	130	254	13	13	NUM
ijassa-1077	130	255	dx2	dx2	PROPN
ijassa-1077	130	256	³	³	PROPN
ijassa-1077	130	257	dx1	dx1	PROPN
ijassa-1077	130	258	³	³	PROPN
ijassa-1077	130	259	dx3	dx3	PROPN
ijassa-1077	130	260	³	³	PROPN
ijassa-1077	130	261	dx4	dx4	PROPN
ijassa-1077	130	262	pn1100	pn1100	NOUN
ijassa-1077	130	263	-	-	PUNCT
ijassa-1077	130	264	pn0100	pn0100	NOUN
ijassa-1077	130	265	pn0100	pn0100	NOUN
ijassa-1077	130	266	-	-	PUNCT
ijassa-1077	130	267	pn0000	pn0000	NOUN
ijassa-1077	130	268	pn1110	pn1110	NOUN
ijassa-1077	130	269	-	-	PUNCT
ijassa-1077	130	270	pn1100	pn1100	NOUN
ijassa-1077	130	271	pn1111	pn1111	PROPN
ijassa-1077	130	272	-	-	PUNCT
ijassa-1077	130	273	pn1110	pn1110	NOUN
ijassa-1077	130	274	14	14	NUM
ijassa-1077	130	275	dx2	dx2	PROPN
ijassa-1077	130	276	³	³	PROPN
ijassa-1077	130	277	dx1	dx1	PROPN
ijassa-1077	130	278	³dx4	³dx4	NUM
ijassa-1077	130	279	³	³	PROPN
ijassa-1077	130	280	dx3	dx3	PROPN
ijassa-1077	130	281	pn1100	pn1100	PROPN
ijassa-1077	130	282	-	-	PUNCT
ijassa-1077	130	283	pn0100	pn0100	NOUN
ijassa-1077	130	284	pn0100	pn0100	NOUN
ijassa-1077	130	285	-	-	PUNCT
ijassa-1077	130	286	pn0000	pn0000	NOUN
ijassa-1077	130	287	pn1111	pn1111	PROPN
ijassa-1077	130	288	-	-	PUNCT
ijassa-1077	130	289	pn1101	pn1101	PROPN
ijassa-1077	130	290	pn1101	pn1101	PROPN
ijassa-1077	130	291	-	-	PUNCT
ijassa-1077	130	292	pn1100	pn1100	PROPN
ijassa-1077	130	293	15	15	NUM
ijassa-1077	130	294	dx2	dx2	PROPN
ijassa-1077	130	295	³	³	PROPN
ijassa-1077	130	296	dx4	dx4	X
ijassa-1077	130	297	³	³	PROPN
ijassa-1077	130	298	dx1	dx1	PROPN
ijassa-1077	130	299	³	³	PROPN
ijassa-1077	130	300	dx3	dx3	PROPN
ijassa-1077	130	301	pn1101	pn1101	PROPN
ijassa-1077	130	302	-	-	PUNCT
ijassa-1077	130	303	pn0101	pn0101	PROPN
ijassa-1077	130	304	pn0100	pn0100	NOUN
ijassa-1077	130	305	-	-	PUNCT
ijassa-1077	130	306	pn0000	pn0000	NOUN
ijassa-1077	130	307	pn1111	pn1111	PROPN
ijassa-1077	130	308	-	-	PUNCT
ijassa-1077	130	309	pn1101	pn1101	PROPN
ijassa-1077	130	310	pn0101	pn0101	PROPN
ijassa-1077	130	311	-	-	PUNCT
ijassa-1077	130	312	pn0100	pn0100	PROPN
ijassa-1077	131	1	16	16	NUM
ijassa-1077	131	2	dx4	dx4	NOUN
ijassa-1077	131	3	³	³	X
ijassa-1077	131	4	dx2	dx2	PROPN
ijassa-1077	131	5	³	³	PROPN
ijassa-1077	131	6	dx1	dx1	PROPN
ijassa-1077	131	7	³	³	PROPN
ijassa-1077	131	8	dx3	dx3	PROPN
ijassa-1077	131	9	pn1101	pn1101	PROPN
ijassa-1077	131	10	-	-	PUNCT
ijassa-1077	131	11	pn0101	pn0101	PROPN
ijassa-1077	131	12	pn0101	pn0101	PROPN
ijassa-1077	131	13	-	-	PUNCT
ijassa-1077	131	14	pn0001	pn0001	NOUN
ijassa-1077	131	15	pn1111	pn1111	PROPN
ijassa-1077	131	16	-	-	PUNCT
ijassa-1077	131	17	pn1101	pn1101	PROPN
ijassa-1077	131	18	pn0001	pn0001	NOUN
ijassa-1077	131	19	-	-	PUNCT
ijassa-1077	131	20	pn0000	pn0000	NOUN
ijassa-1077	131	21	17	17	NUM
ijassa-1077	131	22	dx2	dx2	PROPN
ijassa-1077	131	23	³	³	PROPN
ijassa-1077	131	24	dx3	dx3	PROPN
ijassa-1077	131	25	³	³	PROPN
ijassa-1077	131	26	dx1	dx1	PROPN
ijassa-1077	131	27	³	³	PROPN
ijassa-1077	131	28	dx4	dx4	PROPN
ijassa-1077	131	29	pn1110	pn1110	PROPN
ijassa-1077	131	30	-	-	PUNCT
ijassa-1077	131	31	pn0110	pn0110	PROPN
ijassa-1077	131	32	pn0100	pn0100	NOUN
ijassa-1077	131	33	-	-	PUNCT
ijassa-1077	131	34	pn0000	pn0000	NOUN
ijassa-1077	131	35	pn0110	pn0110	NOUN
ijassa-1077	131	36	-	-	PUNCT
ijassa-1077	131	37	pn0100	pn0100	NOUN
ijassa-1077	131	38	pn1111	pn1111	PROPN
ijassa-1077	131	39	-	-	PUNCT
ijassa-1077	131	40	pn1110	pn1110	NOUN
ijassa-1077	131	41	18	18	NUM
ijassa-1077	131	42	dx2	dx2	PROPN
ijassa-1077	131	43	³	³	PROPN
ijassa-1077	131	44	dx3	dx3	PROPN
ijassa-1077	131	45	³	³	PROPN
ijassa-1077	131	46	dx4	dx4	PROPN
ijassa-1077	131	47	³	³	PROPN
ijassa-1077	131	48	dx1	dx1	PROPN
ijassa-1077	131	49	pn1111	pn1111	PROPN
ijassa-1077	131	50	-	-	PUNCT
ijassa-1077	131	51	pn0111	pn0111	PROPN
ijassa-1077	131	52	pn0100	pn0100	NOUN
ijassa-1077	131	53	-	-	PUNCT
ijassa-1077	131	54	pn0000	pn0000	NOUN
ijassa-1077	131	55	pn0110	pn0110	NOUN
ijassa-1077	131	56	-	-	PUNCT
ijassa-1077	131	57	pn0100	pn0100	NOUN
ijassa-1077	131	58	pn0111	pn0111	PROPN
ijassa-1077	131	59	-	-	PUNCT
ijassa-1077	131	60	pn0110	pn0110	PROPN
ijassa-1077	131	61	19	19	NUM
ijassa-1077	131	62	dx2	dx2	PROPN
ijassa-1077	131	63	³	³	PROPN
ijassa-1077	131	64	dx4	dx4	X
ijassa-1077	131	65	³	³	PROPN
ijassa-1077	131	66	dx3	dx3	PROPN
ijassa-1077	131	67	³	³	PROPN
ijassa-1077	131	68	dx1	dx1	PROPN
ijassa-1077	131	69	pn1111	pn1111	PROPN
ijassa-1077	131	70	-	-	PUNCT
ijassa-1077	131	71	pn0111	pn0111	PROPN
ijassa-1077	131	72	pn0100	pn0100	NOUN
ijassa-1077	131	73	-	-	PUNCT
ijassa-1077	131	74	pn0000	pn0000	NOUN
ijassa-1077	131	75	pn0111	pn0111	PROPN
ijassa-1077	131	76	-	-	PUNCT
ijassa-1077	131	77	pn0101	pn0101	PROPN
ijassa-1077	131	78	pn0101	pn0101	PROPN
ijassa-1077	131	79	-	-	PUNCT
ijassa-1077	131	80	pn0100	pn0100	PROPN
ijassa-1077	131	81	20	20	NUM
ijassa-1077	131	82	dx4	dx4	NOUN
ijassa-1077	131	83	³	³	X
ijassa-1077	131	84	dx2	dx2	PROPN
ijassa-1077	131	85	³	³	PROPN
ijassa-1077	131	86	dx3	dx3	PROPN
ijassa-1077	131	87	³	³	PROPN
ijassa-1077	131	88	dx1	dx1	PROPN
ijassa-1077	131	89	pn1111	pn1111	PROPN
ijassa-1077	131	90	-	-	PUNCT
ijassa-1077	131	91	pn0111	pn0111	PROPN
ijassa-1077	131	92	pn0101	pn0101	NOUN
ijassa-1077	131	93	-	-	PUNCT
ijassa-1077	131	94	pn0001	pn0001	NOUN
ijassa-1077	131	95	pn0111	pn0111	PROPN
ijassa-1077	131	96	-	-	PUNCT
ijassa-1077	131	97	pn0101	pn0101	PROPN
ijassa-1077	131	98	pn0001	pn0001	NOUN
ijassa-1077	131	99	-	-	PUNCT
ijassa-1077	131	100	pn0000	pn0000	NOUN
ijassa-1077	131	101	21	21	NUM
ijassa-1077	131	102	dx3	dx3	PROPN
ijassa-1077	131	103	³	³	X
ijassa-1077	131	104	dx2	dx2	PROPN
ijassa-1077	131	105	³	³	PROPN
ijassa-1077	131	106	dx1	dx1	PROPN
ijassa-1077	131	107	³	³	PROPN
ijassa-1077	131	108	dx4	dx4	PROPN
ijassa-1077	131	109	pn1110	pn1110	PROPN
ijassa-1077	131	110	-	-	PUNCT
ijassa-1077	131	111	pn0110	pn0110	NOUN
ijassa-1077	131	112	pn0110	pn0110	PROPN
ijassa-1077	131	113	-	-	PUNCT
ijassa-1077	131	114	pn0010	pn0010	ADJ
ijassa-1077	131	115	pn0010	pn0010	ADJ
ijassa-1077	131	116	-	-	PUNCT
ijassa-1077	131	117	pn0000	pn0000	NOUN
ijassa-1077	131	118	pn1111	pn1111	PROPN
ijassa-1077	131	119	-	-	PUNCT
ijassa-1077	131	120	pn1110	pn1110	NOUN
ijassa-1077	131	121	22	22	NUM
ijassa-1077	131	122	dx3	dx3	PROPN
ijassa-1077	131	123	³	³	X
ijassa-1077	131	124	dx2	dx2	PROPN
ijassa-1077	131	125	³	³	PROPN
ijassa-1077	131	126	dx4	dx4	PROPN
ijassa-1077	131	127	³	³	PROPN
ijassa-1077	131	128	dx1	dx1	PROPN
ijassa-1077	131	129	pn1111	pn1111	PROPN
ijassa-1077	131	130	-	-	PUNCT
ijassa-1077	131	131	pn0111	pn0111	NOUN
ijassa-1077	131	132	pn0110	pn0110	PROPN
ijassa-1077	131	133	-	-	PUNCT
ijassa-1077	131	134	pn0010	pn0010	ADJ
ijassa-1077	131	135	pn0010	pn0010	ADJ
ijassa-1077	131	136	-	-	PUNCT
ijassa-1077	131	137	pn0000	pn0000	NOUN
ijassa-1077	131	138	pn0111	pn0111	PROPN
ijassa-1077	131	139	-	-	PUNCT
ijassa-1077	131	140	pn0110	pn0110	PROPN
ijassa-1077	131	141	23	23	NUM
ijassa-1077	131	142	dx3	dx3	PROPN
ijassa-1077	131	143	³	³	PROPN
ijassa-1077	131	144	dx4	dx4	X
ijassa-1077	131	145	³	³	X
ijassa-1077	131	146	dx2	dx2	PROPN
ijassa-1077	131	147	³	³	PROPN
ijassa-1077	131	148	dx1	dx1	PROPN
ijassa-1077	131	149	pn1111	pn1111	PROPN
ijassa-1077	131	150	-	-	PUNCT
ijassa-1077	131	151	pn0111	pn0111	PROPN
ijassa-1077	131	152	pn0111	pn0111	PROPN
ijassa-1077	131	153	-	-	PUNCT
ijassa-1077	131	154	pn0011	pn0011	ADJ
ijassa-1077	131	155	pn0010	pn0010	ADJ
ijassa-1077	131	156	-	-	PUNCT
ijassa-1077	131	157	pn0000	pn0000	NOUN
ijassa-1077	131	158	pn0011	pn0011	PROPN
ijassa-1077	131	159	-	-	PUNCT
ijassa-1077	131	160	pn0010	pn0010	ADJ
ijassa-1077	131	161	24	24	NUM
ijassa-1077	131	162	dx4	dx4	PROPN
ijassa-1077	131	163	³	³	PROPN
ijassa-1077	131	164	dx3	dx3	PROPN
ijassa-1077	131	165	³	³	X
ijassa-1077	131	166	dx2	dx2	PROPN
ijassa-1077	131	167	³	³	PROPN
ijassa-1077	131	168	dx1	dx1	PROPN
ijassa-1077	131	169	pn1111	pn1111	PROPN
ijassa-1077	131	170	-	-	PUNCT
ijassa-1077	131	171	pn0111	pn0111	PROPN
ijassa-1077	131	172	pn0111	pn0111	PROPN
ijassa-1077	131	173	-	-	PUNCT
ijassa-1077	131	174	pn0011	pn0011	PROPN
ijassa-1077	131	175	pn0011	pn0011	PROPN
ijassa-1077	131	176	-	-	PUNCT
ijassa-1077	131	177	pn0001	pn0001	NOUN
ijassa-1077	131	178	pn0001	pn0001	NOUN
ijassa-1077	131	179	-	-	PUNCT
ijassa-1077	131	180	pn0000	pn0000	NOUN
ijassa-1077	131	181	the	the	DET
ijassa-1077	131	182	interpolation	interpolation	NOUN
ijassa-1077	131	183	under	under	ADP
ijassa-1077	131	184	consideration	consideration	NOUN
ijassa-1077	131	185	has	have	VERB
ijassa-1077	131	186	pure	pure	ADJ
ijassa-1077	131	187	geometrical	geometrical	ADJ
ijassa-1077	131	188	sense	sense	NOUN
ijassa-1077	131	189	.	.	PUNCT
ijassa-1077	132	1	we	we	PRON
ijassa-1077	132	2	decompose	decompose	VERB
ijassa-1077	132	3	a	a	DET
ijassa-1077	132	4	fourdimensional	fourdimensional	ADJ
ijassa-1077	132	5	rectangular	rectangular	ADJ
ijassa-1077	132	6	parallelepiped	parallelepipe	VERB
ijassa-1077	132	7	into	into	ADP
ijassa-1077	132	8	24	24	NUM
ijassa-1077	132	9	pentahedrons	pentahedron	NOUN
ijassa-1077	132	10	.	.	PUNCT
ijassa-1077	133	1	these	these	DET
ijassa-1077	133	2	pentahedrons	pentahedron	NOUN
ijassa-1077	133	3	are	be	AUX
ijassa-1077	133	4	defined	define	VERB
ijassa-1077	133	5	by	by	ADP
ijassa-1077	133	6	the	the	DET
ijassa-1077	133	7	conditions	condition	NOUN
ijassa-1077	133	8	in	in	ADP
ijassa-1077	133	9	the	the	DET
ijassa-1077	133	10	second	second	ADJ
ijassa-1077	133	11	column	column	NOUN
ijassa-1077	133	12	of	of	ADP
ijassa-1077	133	13	the	the	DET
ijassa-1077	133	14	table	table	NOUN
ijassa-1077	133	15	above	above	ADV
ijassa-1077	133	16	.	.	PUNCT
ijassa-1077	134	1	inside	inside	ADP
ijassa-1077	134	2	each	each	DET
ijassa-1077	134	3	tetrahedron	tetrahedron	NOUN
ijassa-1077	134	4	the	the	DET
ijassa-1077	134	5	map	map	NOUN
ijassa-1077	134	6	f	f	NOUN
ijassa-1077	134	7	is	be	AUX
ijassa-1077	134	8	constructed	construct	VERB
ijassa-1077	134	9	by	by	ADP
ijassa-1077	134	10	linear	linear	ADJ
ijassa-1077	134	11	interpolation	interpolation	NOUN
ijassa-1077	134	12	of	of	ADP
ijassa-1077	134	13	the	the	DET
ijassa-1077	134	14	values	value	NOUN
ijassa-1077	134	15	pikjl	pikjl	NOUN
ijassa-1077	134	16	,	,	PUNCT
ijassa-1077	134	17	i	i	PRON
ijassa-1077	134	18	,	,	PUNCT
ijassa-1077	134	19	j	j	PROPN
ijassa-1077	134	20	,	,	PUNCT
ijassa-1077	134	21	k	k	PROPN
ijassa-1077	134	22	,	,	PUNCT
ijassa-1077	134	23	l=0,1	l=0,1	NOUN
ijassa-1077	134	24	,	,	PUNCT
ijassa-1077	134	25	of	of	ADP
ijassa-1077	134	26	the	the	DET
ijassa-1077	134	27	discrete	discrete	ADJ
ijassa-1077	134	28	map	map	NOUN
ijassa-1077	134	29	f	f	PROPN
ijassa-1077	134	30	at	at	ADP
ijassa-1077	134	31	the	the	DET
ijassa-1077	134	32	vertices	vertex	NOUN
ijassa-1077	134	33	to	to	ADP
ijassa-1077	134	34	the	the	DET
ijassa-1077	134	35	pentahedrons	pentahedron	NOUN
ijassa-1077	134	36	.	.	PUNCT
ijassa-1077	135	1	122	122	NUM
ijassa-1077	135	2	d.v	d.v	PROPN
ijassa-1077	135	3	.	.	PUNCT
ijassa-1077	136	1	tunitsky	tunitsky	NOUN
ijassa-1077	136	2	copyright	copyright	NOUN
ijassa-1077	137	1	©	©	PROPN
ijassa-1077	137	2	2021	2021	NUM
ijassa-1077	137	3	assa	assa	NOUN
ijassa-1077	137	4	.	.	PUNCT
ijassa-1077	138	1	adv	adv	PROPN
ijassa-1077	138	2	.	.	PUNCT
ijassa-1077	139	1	in	in	ADP
ijassa-1077	139	2	systems	system	NOUN
ijassa-1077	139	3	science	science	NOUN
ijassa-1077	139	4	and	and	CCONJ
ijassa-1077	139	5	appl	appl	NOUN
ijassa-1077	139	6	.	.	PUNCT
ijassa-1077	140	1	(	(	PUNCT
ijassa-1077	140	2	2021	2021	NUM
ijassa-1077	140	3	)	)	PUNCT
ijassa-1077	140	4	thus	thus	ADV
ijassa-1077	140	5	we	we	PRON
ijassa-1077	140	6	have	have	AUX
ijassa-1077	140	7	constructed	construct	VERB
ijassa-1077	140	8	the	the	DET
ijassa-1077	140	9	piecewise	piecewise	NOUN
ijassa-1077	140	10	linear	linear	NOUN
ijassa-1077	140	11	map	map	NOUN
ijassa-1077	140	12	f	f	NOUN
ijassa-1077	140	13	,	,	PUNCT
ijassa-1077	140	14	being	be	AUX
ijassa-1077	140	15	a	a	DET
ijassa-1077	140	16	solution	solution	NOUN
ijassa-1077	140	17	to	to	ADP
ijassa-1077	140	18	the	the	DET
ijassa-1077	140	19	direct	direct	ADJ
ijassa-1077	140	20	problem	problem	NOUN
ijassa-1077	140	21	of	of	ADP
ijassa-1077	140	22	mathematical	mathematical	ADJ
ijassa-1077	140	23	modeling	modeling	NOUN
ijassa-1077	140	24	for	for	ADP
ijassa-1077	140	25	a	a	DET
ijassa-1077	140	26	four	four	NUM
ijassa-1077	140	27	-	-	PUNCT
ijassa-1077	140	28	dimensional	dimensional	ADJ
ijassa-1077	140	29	printing	printing	NOUN
ijassa-1077	140	30	device	device	NOUN
ijassa-1077	140	31	.	.	PUNCT
ijassa-1077	141	1	in	in	ADP
ijassa-1077	141	2	other	other	ADJ
ijassa-1077	141	3	words	word	NOUN
ijassa-1077	141	4	,	,	PUNCT
ijassa-1077	141	5	we	we	PRON
ijassa-1077	141	6	have	have	AUX
ijassa-1077	141	7	constructed	construct	VERB
ijassa-1077	141	8	a	a	DET
ijassa-1077	141	9	piecewise	piecewise	NOUN
ijassa-1077	141	10	linear	linear	NOUN
ijassa-1077	141	11	model	model	NOUN
ijassa-1077	141	12	of	of	ADP
ijassa-1077	141	13	a	a	DET
ijassa-1077	141	14	four	four	NUM
ijassa-1077	141	15	-	-	PUNCT
ijassa-1077	141	16	dimensional	dimensional	ADJ
ijassa-1077	141	17	printing	printing	NOUN
ijassa-1077	141	18	device	device	NOUN
ijassa-1077	141	19	.	.	PUNCT
ijassa-1077	142	1	4	4	X
ijassa-1077	142	2	.	.	X
ijassa-1077	142	3	gamut	gamut	NOUN
ijassa-1077	142	4	description	description	NOUN
ijassa-1077	142	5	for	for	ADP
ijassa-1077	142	6	three	three	NUM
ijassa-1077	142	7	-	-	PUNCT
ijassa-1077	142	8	dimensional	dimensional	ADJ
ijassa-1077	142	9	printing	printing	NOUN
ijassa-1077	142	10	devices	device	NOUN
ijassa-1077	142	11	consider	consider	VERB
ijassa-1077	142	12	a	a	DET
ijassa-1077	142	13	piecewise	piecewise	NOUN
ijassa-1077	142	14	linear	linear	NOUN
ijassa-1077	142	15	model	model	NOUN
ijassa-1077	142	16	f	f	X
ijassa-1077	142	17	:	:	PUNCT
ijassa-1077	142	18	w3	w3	PROPN
ijassa-1077	142	19	®	®	NOUN
ijassa-1077	142	20	ℝ	ℝ	PROPN
ijassa-1077	142	21	#	#	NOUN
ijassa-1077	142	22	of	of	ADP
ijassa-1077	142	23	a	a	DET
ijassa-1077	142	24	given	give	VERB
ijassa-1077	142	25	three	three	NUM
ijassa-1077	142	26	-	-	PUNCT
ijassa-1077	142	27	dimensional	dimensional	ADJ
ijassa-1077	142	28	printing	printing	NOUN
ijassa-1077	142	29	device	device	NOUN
ijassa-1077	142	30	.	.	PUNCT
ijassa-1077	143	1	for	for	ADP
ijassa-1077	143	2	practical	practical	ADJ
ijassa-1077	143	3	applications	application	NOUN
ijassa-1077	143	4	it	it	PRON
ijassa-1077	143	5	is	be	AUX
ijassa-1077	143	6	important	important	ADJ
ijassa-1077	143	7	to	to	PART
ijassa-1077	143	8	find	find	VERB
ijassa-1077	143	9	in	in	ADP
ijassa-1077	143	10	color	color	NOUN
ijassa-1077	143	11	space	space	NOUN
ijassa-1077	143	12	the	the	DET
ijassa-1077	143	13	gamut	gamut	NOUN
ijassa-1077	143	14	of	of	ADP
ijassa-1077	143	15	the	the	DET
ijassa-1077	143	16	printing	printing	NOUN
ijassa-1077	143	17	device	device	NOUN
ijassa-1077	143	18	,	,	PUNCT
ijassa-1077	143	19	i.e.	i.e.	X
ijassa-1077	143	20	,	,	PUNCT
ijassa-1077	143	21	the	the	DET
ijassa-1077	143	22	image	image	NOUN
ijassa-1077	143	23	f(w3	f(w3	NOUN
ijassa-1077	143	24	)	)	PUNCT
ijassa-1077	143	25	of	of	ADP
ijassa-1077	143	26	the	the	DET
ijassa-1077	143	27	piecewise	piecewise	NOUN
ijassa-1077	143	28	linear	linear	NOUN
ijassa-1077	143	29	map	map	NOUN
ijassa-1077	143	30	f.	f.	PROPN
ijassa-1077	143	31	in	in	ADP
ijassa-1077	143	32	particular	particular	ADJ
ijassa-1077	143	33	,	,	PUNCT
ijassa-1077	143	34	we	we	PRON
ijassa-1077	143	35	need	need	VERB
ijassa-1077	143	36	it	it	PRON
ijassa-1077	143	37	to	to	PART
ijassa-1077	143	38	go	go	VERB
ijassa-1077	143	39	on	on	ADP
ijassa-1077	143	40	with	with	ADP
ijassa-1077	143	41	the	the	DET
ijassa-1077	143	42	inverse	inverse	NOUN
ijassa-1077	143	43	problem	problem	NOUN
ijassa-1077	143	44	.	.	PUNCT
ijassa-1077	144	1	by	by	ADP
ijassa-1077	144	2	definition	definition	NOUN
ijassa-1077	144	3	of	of	ADP
ijassa-1077	144	4	a	a	DET
ijassa-1077	144	5	piecewise	piecewise	NOUN
ijassa-1077	144	6	linear	linear	NOUN
ijassa-1077	144	7	map	map	NOUN
ijassa-1077	144	8	f	f	X
ijassa-1077	144	9	,	,	PUNCT
ijassa-1077	144	10	we	we	PRON
ijassa-1077	144	11	have	have	VERB
ijassa-1077	144	12	the	the	DET
ijassa-1077	144	13	simplex	simplex	NOUN
ijassa-1077	144	14	decomposition	decomposition	NOUN
ijassa-1077	144	15	of	of	ADP
ijassa-1077	144	16	the	the	DET
ijassa-1077	144	17	three	three	NUM
ijassa-1077	144	18	-	-	PUNCT
ijassa-1077	144	19	dimensional	dimensional	ADJ
ijassa-1077	144	20	colorants	colorant	NOUN
ijassa-1077	144	21	cube	cube	NOUN
ijassa-1077	144	22	w3	w3	PROPN
ijassa-1077	144	23	into	into	ADP
ijassa-1077	144	24	the	the	DET
ijassa-1077	144	25	union	union	NOUN
ijassa-1077	144	26	of	of	ADP
ijassa-1077	144	27	n	n	CCONJ
ijassa-1077	144	28	,	,	PUNCT
ijassa-1077	144	29	n>0	n>0	PROPN
ijassa-1077	144	30	,	,	PUNCT
ijassa-1077	144	31	tetrahedrons	tetrahedron	NOUN
ijassa-1077	144	32	dj	dj	NOUN
ijassa-1077	144	33	:	:	PUNCT
ijassa-1077	144	34	.	.	PUNCT
ijassa-1077	145	1	each	each	DET
ijassa-1077	145	2	tetrahedron	tetrahedron	NOUN
ijassa-1077	145	3	has	have	VERB
ijassa-1077	145	4	four	four	NUM
ijassa-1077	145	5	two	two	NUM
ijassa-1077	145	6	-	-	PUNCT
ijassa-1077	145	7	dimensional	dimensional	ADJ
ijassa-1077	145	8	faces	face	NOUN
ijassa-1077	145	9	.	.	PUNCT
ijassa-1077	146	1	these	these	DET
ijassa-1077	146	2	faces	face	NOUN
ijassa-1077	146	3	are	be	AUX
ijassa-1077	146	4	triangles	triangle	NOUN
ijassa-1077	146	5	and	and	CCONJ
ijassa-1077	146	6	each	each	DET
ijassa-1077	146	7	triangle	triangle	NOUN
ijassa-1077	146	8	belongs	belong	VERB
ijassa-1077	146	9	either	either	CCONJ
ijassa-1077	146	10	to	to	ADP
ijassa-1077	146	11	one	one	NUM
ijassa-1077	146	12	or	or	CCONJ
ijassa-1077	146	13	several	several	ADJ
ijassa-1077	146	14	tetrahedrons	tetrahedron	NOUN
ijassa-1077	146	15	of	of	ADP
ijassa-1077	146	16	the	the	DET
ijassa-1077	146	17	set	set	NOUN
ijassa-1077	146	18	{	{	PUNCT
ijassa-1077	146	19	dj	dj	NOUN
ijassa-1077	146	20	}	}	PUNCT
ijassa-1077	146	21	.	.	PUNCT
ijassa-1077	147	1	in	in	ADP
ijassa-1077	147	2	a	a	DET
ijassa-1077	147	3	standard	standard	ADJ
ijassa-1077	147	4	way	way	NOUN
ijassa-1077	147	5	the	the	DET
ijassa-1077	147	6	faces	face	NOUN
ijassa-1077	147	7	of	of	ADP
ijassa-1077	147	8	these	these	DET
ijassa-1077	147	9	tetrahedrons	tetrahedron	NOUN
ijassa-1077	147	10	can	can	AUX
ijassa-1077	147	11	be	be	AUX
ijassa-1077	147	12	divided	divide	VERB
ijassa-1077	147	13	into	into	ADP
ijassa-1077	147	14	two	two	NUM
ijassa-1077	147	15	classes	class	NOUN
ijassa-1077	147	16	.	.	PUNCT
ijassa-1077	148	1	definition	definition	NOUN
ijassa-1077	148	2	.	.	PUNCT
ijassa-1077	149	1	fix	fix	VERB
ijassa-1077	149	2	a	a	DET
ijassa-1077	149	3	tetrahedron	tetrahedron	NOUN
ijassa-1077	149	4	dl	dl	PROPN
ijassa-1077	149	5	,	,	PUNCT
ijassa-1077	149	6	l=1,	l=1,	PROPN
ijassa-1077	149	7	…	…	X
ijassa-1077	149	8	,n	,n	NOUN
ijassa-1077	149	9	,	,	PUNCT
ijassa-1077	149	10	and	and	CCONJ
ijassa-1077	149	11	consider	consider	VERB
ijassa-1077	149	12	it	it	PRON
ijassa-1077	149	13	’s	’	VERB
ijassa-1077	149	14	two	two	NUM
ijassa-1077	149	15	-	-	PUNCT
ijassa-1077	149	16	dimensional	dimensional	ADJ
ijassa-1077	149	17	face	face	NOUN
ijassa-1077	149	18	d	d	NOUN
ijassa-1077	149	19	,	,	PUNCT
ijassa-1077	149	20	which	which	PRON
ijassa-1077	149	21	is	be	AUX
ijassa-1077	149	22	a	a	DET
ijassa-1077	149	23	triangle	triangle	NOUN
ijassa-1077	149	24	.	.	PUNCT
ijassa-1077	150	1	the	the	DET
ijassa-1077	150	2	face	face	NOUN
ijassa-1077	150	3	d	d	NOUN
ijassa-1077	150	4	is	be	AUX
ijassa-1077	150	5	called	call	VERB
ijassa-1077	150	6	boundary	boundary	ADJ
ijassa-1077	150	7	if	if	SCONJ
ijassa-1077	150	8	it	it	PRON
ijassa-1077	150	9	does	do	AUX
ijassa-1077	150	10	n’t	not	PART
ijassa-1077	150	11	belong	belong	VERB
ijassa-1077	150	12	to	to	ADP
ijassa-1077	150	13	any	any	DET
ijassa-1077	150	14	other	other	ADJ
ijassa-1077	150	15	tetrahedron	tetrahedron	NOUN
ijassa-1077	150	16	of	of	ADP
ijassa-1077	150	17	the	the	DET
ijassa-1077	150	18	set	set	NOUN
ijassa-1077	150	19	{	{	PUNCT
ijassa-1077	150	20	dj	dj	NOUN
ijassa-1077	150	21	}	}	PUNCT
ijassa-1077	150	22	.	.	PUNCT
ijassa-1077	151	1	in	in	ADP
ijassa-1077	151	2	other	other	ADJ
ijassa-1077	151	3	words	word	NOUN
ijassa-1077	151	4	,	,	PUNCT
ijassa-1077	151	5	d	d	PROPN
ijassa-1077	151	6	ì	ì	X
ijassa-1077	151	7	dl	dl	PROPN
ijassa-1077	151	8	,	,	PUNCT
ijassa-1077	151	9	and	and	CCONJ
ijassa-1077	151	10	d	d	X
ijassa-1077	151	11	ë	ë	PROPN
ijassa-1077	151	12	dk	dk	PROPN
ijassa-1077	151	13	for	for	ADP
ijassa-1077	151	14	k=1,	k=1,	PROPN
ijassa-1077	151	15	…	…	PUNCT
ijassa-1077	151	16	,l-1,l+1,	,l-1,l+1,	PUNCT
ijassa-1077	151	17	…	…	PUNCT
ijassa-1077	151	18	,n	,n	NOUN
ijassa-1077	151	19	.	.	PUNCT
ijassa-1077	152	1	the	the	DET
ijassa-1077	152	2	face	face	NOUN
ijassa-1077	152	3	d	d	NOUN
ijassa-1077	152	4	is	be	AUX
ijassa-1077	152	5	called	call	VERB
ijassa-1077	152	6	internal	internal	ADJ
ijassa-1077	152	7	if	if	SCONJ
ijassa-1077	152	8	there	there	PRON
ijassa-1077	152	9	is	be	VERB
ijassa-1077	152	10	a	a	DET
ijassa-1077	152	11	tetrahedron	tetrahedron	NOUN
ijassa-1077	152	12	dk	dk	NOUN
ijassa-1077	152	13	from	from	ADP
ijassa-1077	152	14	the	the	DET
ijassa-1077	152	15	set	set	NOUN
ijassa-1077	152	16	{	{	PUNCT
ijassa-1077	152	17	dj	dj	NOUN
ijassa-1077	152	18	}	}	PUNCT
ijassa-1077	152	19	such	such	ADJ
ijassa-1077	152	20	that	that	SCONJ
ijassa-1077	152	21	d	d	NOUN
ijassa-1077	152	22	belongs	belong	VERB
ijassa-1077	152	23	to	to	ADP
ijassa-1077	152	24	both	both	DET
ijassa-1077	152	25	dl	dl	PROPN
ijassa-1077	152	26	and	and	CCONJ
ijassa-1077	152	27	dk	dk	PROPN
ijassa-1077	152	28	,	,	PUNCT
ijassa-1077	153	1	i.e.	i.e.	X
ijassa-1077	153	2	,	,	PUNCT
ijassa-1077	153	3	d	d	X
ijassa-1077	153	4	í	í	PROPN
ijassa-1077	153	5	dl	dl	PROPN
ijassa-1077	153	6	ç	ç	X
ijassa-1077	153	7	dk	dk	PROPN
ijassa-1077	153	8	.	.	PROPN
ijassa-1077	153	9	denote	denote	VERB
ijassa-1077	153	10	the	the	DET
ijassa-1077	153	11	set	set	NOUN
ijassa-1077	153	12	of	of	ADP
ijassa-1077	153	13	all	all	DET
ijassa-1077	153	14	the	the	DET
ijassa-1077	153	15	boundary	boundary	ADJ
ijassa-1077	153	16	faces	face	NOUN
ijassa-1077	153	17	of	of	ADP
ijassa-1077	153	18	the	the	DET
ijassa-1077	153	19	colorants	colorant	NOUN
ijassa-1077	153	20	cube	cube	PROPN
ijassa-1077	153	21	w3	w3	PROPN
ijassa-1077	153	22	by	by	ADP
ijassa-1077	153	23	q.	q.	PROPN
ijassa-1077	153	24	remark	remark	PROPN
ijassa-1077	153	25	.	.	PUNCT
ijassa-1077	154	1	the	the	DET
ijassa-1077	154	2	set	set	NOUN
ijassa-1077	154	3	q	q	NOUN
ijassa-1077	154	4	of	of	ADP
ijassa-1077	154	5	all	all	DET
ijassa-1077	154	6	the	the	DET
ijassa-1077	154	7	boundary	boundary	ADJ
ijassa-1077	154	8	faces	face	NOUN
ijassa-1077	154	9	does	do	AUX
ijassa-1077	154	10	n’t	not	PART
ijassa-1077	154	11	depend	depend	VERB
ijassa-1077	154	12	on	on	ADP
ijassa-1077	154	13	the	the	DET
ijassa-1077	154	14	choice	choice	NOUN
ijassa-1077	154	15	of	of	ADP
ijassa-1077	154	16	the	the	DET
ijassa-1077	154	17	threedimensional	threedimensional	ADJ
ijassa-1077	154	18	printing	printing	NOUN
ijassa-1077	154	19	device	device	NOUN
ijassa-1077	154	20	,	,	PUNCT
ijassa-1077	154	21	i.e.	i.e.	X
ijassa-1077	154	22	,	,	PUNCT
ijassa-1077	154	23	on	on	ADP
ijassa-1077	154	24	the	the	DET
ijassa-1077	154	25	choice	choice	NOUN
ijassa-1077	154	26	of	of	ADP
ijassa-1077	154	27	the	the	DET
ijassa-1077	154	28	corresponding	corresponding	ADJ
ijassa-1077	154	29	piecewise	piecewise	NOUN
ijassa-1077	154	30	linear	linear	NOUN
ijassa-1077	154	31	map	map	NOUN
ijassa-1077	154	32	f.	f.	PROPN
ijassa-1077	154	33	indeed	indeed	ADV
ijassa-1077	154	34	,	,	PUNCT
ijassa-1077	154	35	the	the	DET
ijassa-1077	154	36	union	union	NOUN
ijassa-1077	154	37	of	of	ADP
ijassa-1077	154	38	all	all	DET
ijassa-1077	154	39	these	these	DET
ijassa-1077	154	40	faces	face	NOUN
ijassa-1077	154	41	always	always	ADV
ijassa-1077	154	42	coincides	coincide	VERB
ijassa-1077	154	43	with	with	ADP
ijassa-1077	154	44	the	the	DET
ijassa-1077	154	45	boundary	boundary	ADJ
ijassa-1077	154	46	¶w3	¶w3	PROPN
ijassa-1077	154	47	of	of	ADP
ijassa-1077	154	48	the	the	DET
ijassa-1077	154	49	threedimensional	threedimensional	ADJ
ijassa-1077	154	50	colorants	colorant	NOUN
ijassa-1077	154	51	cube	cube	NOUN
ijassa-1077	154	52	:	:	PUNCT
ijassa-1077	154	53	.	.	PUNCT
ijassa-1077	155	1	suppose	suppose	VERB
ijassa-1077	155	2	the	the	DET
ijassa-1077	155	3	printing	printing	NOUN
ijassa-1077	155	4	device	device	NOUN
ijassa-1077	155	5	under	under	ADP
ijassa-1077	155	6	consideration	consideration	NOUN
ijassa-1077	155	7	is	be	AUX
ijassa-1077	155	8	non	non	ADJ
ijassa-1077	155	9	-	-	ADJ
ijassa-1077	155	10	degenerate	degenerate	ADJ
ijassa-1077	155	11	,	,	PUNCT
ijassa-1077	155	12	i.e.	i.e.	X
ijassa-1077	155	13	,	,	PUNCT
ijassa-1077	155	14	the	the	DET
ijassa-1077	155	15	corresponding	corresponding	ADJ
ijassa-1077	155	16	piecewise	piecewise	NOUN
ijassa-1077	155	17	linear	linear	NOUN
ijassa-1077	155	18	map	map	NOUN
ijassa-1077	155	19	f	f	PROPN
ijassa-1077	155	20	is	be	AUX
ijassa-1077	155	21	non	non	ADJ
ijassa-1077	155	22	-	-	ADJ
ijassa-1077	155	23	degenerate	degenerate	ADJ
ijassa-1077	155	24	.	.	PUNCT
ijassa-1077	156	1	by	by	ADP
ijassa-1077	156	2	definition	definition	NOUN
ijassa-1077	156	3	,	,	PUNCT
ijassa-1077	156	4	it	it	PRON
ijassa-1077	156	5	means	mean	VERB
ijassa-1077	156	6	that	that	SCONJ
ijassa-1077	156	7	all	all	DET
ijassa-1077	156	8	the	the	DET
ijassa-1077	156	9	restrictions	restriction	NOUN
ijassa-1077	156	10	f½dj	f½dj	ADV
ijassa-1077	156	11	:	:	PUNCT
ijassa-1077	156	12	dj	dj	X
ijassa-1077	156	13	®	®	NOUN
ijassa-1077	156	14	ℝ	ℝ	NOUN
ijassa-1077	156	15	#	#	NOUN
ijassa-1077	156	16	,	,	PUNCT
ijassa-1077	156	17	of	of	ADP
ijassa-1077	156	18	the	the	DET
ijassa-1077	156	19	map	map	NOUN
ijassa-1077	156	20	f	f	X
ijassa-1077	156	21	to	to	ADP
ijassa-1077	156	22	tetrahedrons	tetrahedron	NOUN
ijassa-1077	156	23	dj	dj	NOUN
ijassa-1077	156	24	are	be	AUX
ijassa-1077	156	25	non	non	ADJ
ijassa-1077	156	26	-	-	ADJ
ijassa-1077	156	27	degenerate	degenerate	ADJ
ijassa-1077	156	28	linear	linear	NOUN
ijassa-1077	156	29	maps	map	NOUN
ijassa-1077	157	1	f½dj	f½dj	ADV
ijassa-1077	157	2	(	(	PUNCT
ijassa-1077	157	3	x	x	X
ijassa-1077	157	4	)	)	PUNCT
ijassa-1077	157	5	=	=	SYM
ijassa-1077	158	1	cj	cj	NOUN
ijassa-1077	159	1	+	+	CCONJ
ijassa-1077	159	2	bjx	bjx	INTJ
ijassa-1077	159	3	(	(	PUNCT
ijassa-1077	159	4	see	see	VERB
ijassa-1077	159	5	section	section	NOUN
ijassa-1077	159	6	1	1	NUM
ijassa-1077	159	7	)	)	PUNCT
ijassa-1077	159	8	.	.	PUNCT
ijassa-1077	160	1	in	in	ADP
ijassa-1077	160	2	other	other	ADJ
ijassa-1077	160	3	words	word	NOUN
ijassa-1077	160	4	,	,	PUNCT
ijassa-1077	160	5	the	the	DET
ijassa-1077	160	6	determinant	determinant	NOUN
ijassa-1077	160	7	of	of	ADP
ijassa-1077	160	8	the	the	DET
ijassa-1077	160	9	corresponding	correspond	VERB
ijassa-1077	160	10	matrix	matrix	NOUN
ijassa-1077	160	11	bj	bj	NOUN
ijassa-1077	160	12	is	be	AUX
ijassa-1077	160	13	either	either	CCONJ
ijassa-1077	160	14	positive	positive	ADJ
ijassa-1077	160	15	,	,	PUNCT
ijassa-1077	160	16	det	det	NOUN
ijassa-1077	160	17	bj	bj	VERB
ijassa-1077	160	18	>	>	X
ijassa-1077	160	19	0	0	NUM
ijassa-1077	160	20	,	,	PUNCT
ijassa-1077	160	21	or	or	CCONJ
ijassa-1077	160	22	negative	negative	ADJ
ijassa-1077	160	23	,	,	PUNCT
ijassa-1077	160	24	det	det	NOUN
ijassa-1077	160	25	bj	bj	VERB
ijassa-1077	160	26	<	<	X
ijassa-1077	160	27	0	0	NUM
ijassa-1077	160	28	.	.	PUNCT
ijassa-1077	161	1	definition	definition	NOUN
ijassa-1077	161	2	.	.	PUNCT
ijassa-1077	162	1	fix	fix	VERB
ijassa-1077	162	2	a	a	DET
ijassa-1077	162	3	number	number	NOUN
ijassa-1077	162	4	l	l	NOUN
ijassa-1077	162	5	,	,	PUNCT
ijassa-1077	162	6	l=1,	l=1,	NOUN
ijassa-1077	162	7	…	…	X
ijassa-1077	162	8	,n	,n	NOUN
ijassa-1077	162	9	,	,	PUNCT
ijassa-1077	162	10	and	and	CCONJ
ijassa-1077	162	11	consider	consider	VERB
ijassa-1077	162	12	two	two	NUM
ijassa-1077	162	13	-	-	PUNCT
ijassa-1077	162	14	dimensional	dimensional	ADJ
ijassa-1077	162	15	internal	internal	ADJ
ijassa-1077	162	16	face	face	NOUN
ijassa-1077	162	17	d	d	NOUN
ijassa-1077	162	18	of	of	ADP
ijassa-1077	162	19	the	the	DET
ijassa-1077	162	20	tetrahedron	tetrahedron	NOUN
ijassa-1077	162	21	dl	dl	PROPN
ijassa-1077	162	22	,	,	PUNCT
ijassa-1077	162	23	which	which	PRON
ijassa-1077	162	24	is	be	AUX
ijassa-1077	162	25	a	a	DET
ijassa-1077	162	26	triangle	triangle	NOUN
ijassa-1077	162	27	.	.	PUNCT
ijassa-1077	163	1	the	the	DET
ijassa-1077	163	2	internal	internal	ADJ
ijassa-1077	163	3	face	face	NOUN
ijassa-1077	163	4	d	d	NOUN
ijassa-1077	163	5	is	be	AUX
ijassa-1077	163	6	called	call	VERB
ijassa-1077	163	7	singular	singular	ADJ
ijassa-1077	163	8	if	if	SCONJ
ijassa-1077	163	9	there	there	PRON
ijassa-1077	163	10	exists	exist	VERB
ijassa-1077	163	11	a	a	DET
ijassa-1077	163	12	tetrahedron	tetrahedron	NOUN
ijassa-1077	163	13	dk	dk	NOUN
ijassa-1077	163	14	from	from	ADP
ijassa-1077	163	15	the	the	DET
ijassa-1077	163	16	set	set	NOUN
ijassa-1077	163	17	{	{	PUNCT
ijassa-1077	163	18	dj	dj	NOUN
ijassa-1077	163	19	}	}	PUNCT
ijassa-1077	163	20	such	such	ADJ
ijassa-1077	163	21	that	that	SCONJ
ijassa-1077	163	22	d	d	NOUN
ijassa-1077	163	23	belongs	belong	VERB
ijassa-1077	163	24	to	to	ADP
ijassa-1077	163	25	both	both	DET
ijassa-1077	163	26	dl	dl	PROPN
ijassa-1077	163	27	and	and	CCONJ
ijassa-1077	163	28	dk	dk	PROPN
ijassa-1077	163	29	,	,	PUNCT
ijassa-1077	163	30	d	d	X
ijassa-1077	163	31	í	í	PROPN
ijassa-1077	163	32	dl	dl	PROPN
ijassa-1077	163	33	ç	ç	X
ijassa-1077	163	34	dk	dk	PROPN
ijassa-1077	163	35	,	,	PUNCT
ijassa-1077	163	36	and	and	CCONJ
ijassa-1077	163	37	the	the	DET
ijassa-1077	163	38	determinants	determinant	NOUN
ijassa-1077	163	39	of	of	ADP
ijassa-1077	163	40	the	the	DET
ijassa-1077	163	41	corresponding	correspond	VERB
ijassa-1077	163	42	matrixes	matrix	NOUN
ijassa-1077	163	43	bl	bl	INTJ
ijassa-1077	163	44	and	and	CCONJ
ijassa-1077	163	45	bk	bk	VERB
ijassa-1077	163	46	have	have	VERB
ijassa-1077	163	47	different	different	ADJ
ijassa-1077	163	48	signs	sign	NOUN
ijassa-1077	163	49	,	,	PUNCT
ijassa-1077	163	50	i.e.	i.e.	X
ijassa-1077	163	51	,	,	PUNCT
ijassa-1077	163	52	det	det	PROPN
ijassa-1077	163	53	bl	bl	PROPN
ijassa-1077	163	54	×	×	PROPN
ijassa-1077	163	55	det	det	PROPN
ijassa-1077	163	56	bk	bk	ADP
ijassa-1077	163	57	<	<	X
ijassa-1077	163	58	0	0	NUM
ijassa-1077	163	59	.	.	PUNCT
ijassa-1077	163	60	denote	denote	VERB
ijassa-1077	163	61	the	the	DET
ijassa-1077	163	62	set	set	NOUN
ijassa-1077	163	63	of	of	ADP
ijassa-1077	163	64	all	all	DET
ijassa-1077	163	65	the	the	DET
ijassa-1077	163	66	singular	singular	ADJ
ijassa-1077	163	67	faces	face	NOUN
ijassa-1077	163	68	of	of	ADP
ijassa-1077	163	69	the	the	DET
ijassa-1077	163	70	given	give	VERB
ijassa-1077	163	71	three	three	NUM
ijassa-1077	163	72	-	-	PUNCT
ijassa-1077	163	73	dimensional	dimensional	ADJ
ijassa-1077	163	74	printing	printing	NOUN
ijassa-1077	163	75	device	device	NOUN
ijassa-1077	163	76	by	by	ADP
ijassa-1077	163	77	s.	s.	PROPN
ijassa-1077	163	78	remark	remark	PROPN
ijassa-1077	163	79	.	.	PUNCT
ijassa-1077	164	1	on	on	ADP
ijassa-1077	164	2	the	the	DET
ijassa-1077	164	3	contrary	contrary	NOUN
ijassa-1077	164	4	to	to	ADP
ijassa-1077	164	5	the	the	DET
ijassa-1077	164	6	set	set	NOUN
ijassa-1077	164	7	q	q	PROPN
ijassa-1077	164	8	of	of	ADP
ijassa-1077	164	9	all	all	DET
ijassa-1077	164	10	the	the	DET
ijassa-1077	164	11	boundary	boundary	ADJ
ijassa-1077	164	12	faces	face	NOUN
ijassa-1077	164	13	,	,	PUNCT
ijassa-1077	164	14	the	the	DET
ijassa-1077	164	15	set	set	NOUN
ijassa-1077	164	16	s	s	X
ijassa-1077	164	17	of	of	ADP
ijassa-1077	164	18	all	all	DET
ijassa-1077	164	19	the	the	DET
ijassa-1077	164	20	singular	singular	NOUN
ijassa-1077	164	21	faces	face	VERB
ijassa-1077	164	22	essentially	essentially	ADV
ijassa-1077	164	23	depends	depend	VERB
ijassa-1077	164	24	on	on	ADP
ijassa-1077	164	25	the	the	DET
ijassa-1077	164	26	choice	choice	NOUN
ijassa-1077	164	27	of	of	ADP
ijassa-1077	164	28	the	the	DET
ijassa-1077	164	29	three	three	NUM
ijassa-1077	164	30	-	-	PUNCT
ijassa-1077	164	31	dimensional	dimensional	ADJ
ijassa-1077	164	32	printing	printing	NOUN
ijassa-1077	164	33	device	device	NOUN
ijassa-1077	164	34	,	,	PUNCT
ijassa-1077	164	35	i.e.	i.e.	X
ijassa-1077	164	36	,	,	PUNCT
ijassa-1077	164	37	on	on	ADP
ijassa-1077	164	38	the	the	DET
ijassa-1077	164	39	choice	choice	NOUN
ijassa-1077	164	40	of	of	ADP
ijassa-1077	164	41	the	the	DET
ijassa-1077	164	42	corresponding	corresponding	ADJ
ijassa-1077	164	43	piecewise	piecewise	NOUN
ijassa-1077	164	44	linear	linear	NOUN
ijassa-1077	164	45	map	map	NOUN
ijassa-1077	164	46	f.	f.	PROPN
ijassa-1077	164	47	for	for	ADP
ijassa-1077	164	48	example	example	NOUN
ijassa-1077	164	49	,	,	PUNCT
ijassa-1077	164	50	for	for	ADP
ijassa-1077	164	51	some	some	DET
ijassa-1077	164	52	printing	printing	NOUN
ijassa-1077	164	53	devices	device	NOUN
ijassa-1077	164	54	this	this	DET
ijassa-1077	164	55	set	set	NOUN
ijassa-1077	164	56	is	be	AUX
ijassa-1077	164	57	empty	empty	ADJ
ijassa-1077	164	58	and	and	CCONJ
ijassa-1077	164	59	for	for	ADP
ijassa-1077	164	60	some	some	PRON
ijassa-1077	164	61	it	it	PRON
ijassa-1077	164	62	is	be	AUX
ijassa-1077	164	63	not	not	PART
ijassa-1077	164	64	(	(	PUNCT
ijassa-1077	164	65	see	see	VERB
ijassa-1077	164	66	section	section	NOUN
ijassa-1077	164	67	6	6	NUM
ijassa-1077	164	68	)	)	PUNCT
ijassa-1077	164	69	.	.	PUNCT
ijassa-1077	165	1	it	it	PRON
ijassa-1077	165	2	is	be	AUX
ijassa-1077	165	3	possible	possible	ADJ
ijassa-1077	165	4	to	to	PART
ijassa-1077	165	5	describe	describe	VERB
ijassa-1077	165	6	the	the	DET
ijassa-1077	165	7	gamut	gamut	NOUN
ijassa-1077	165	8	boundary	boundary	NOUN
ijassa-1077	165	9	of	of	ADP
ijassa-1077	165	10	a	a	DET
ijassa-1077	165	11	non	non	ADJ
ijassa-1077	165	12	-	-	ADJ
ijassa-1077	165	13	degenerate	degenerate	ADJ
ijassa-1077	165	14	printing	printing	NOUN
ijassa-1077	165	15	device	device	NOUN
ijassa-1077	165	16	in	in	ADP
ijassa-1077	165	17	terms	term	NOUN
ijassa-1077	165	18	of	of	ADP
ijassa-1077	165	19	boundary	boundary	ADJ
ijassa-1077	165	20	and	and	CCONJ
ijassa-1077	165	21	singular	singular	ADJ
ijassa-1077	165	22	faces	face	NOUN
ijassa-1077	165	23	.	.	PUNCT
ijassa-1077	166	1	the	the	DET
ijassa-1077	166	2	following	follow	VERB
ijassa-1077	166	3	theorem	theorem	NOUN
ijassa-1077	166	4	is	be	AUX
ijassa-1077	166	5	through	through	ADP
ijassa-1077	166	6	.	.	PUNCT
ijassa-1077	167	1	theorem	theorem	PROPN
ijassa-1077	167	2	.	.	PROPN
ijassa-1077	168	1	for	for	ADP
ijassa-1077	168	2	any	any	DET
ijassa-1077	168	3	non	non	ADJ
ijassa-1077	168	4	-	-	ADJ
ijassa-1077	168	5	degenerate	degenerate	ADJ
ijassa-1077	168	6	three	three	NUM
ijassa-1077	168	7	-	-	PUNCT
ijassa-1077	168	8	dimensional	dimensional	ADJ
ijassa-1077	168	9	printing	printing	NOUN
ijassa-1077	168	10	device	device	NOUN
ijassa-1077	168	11	the	the	DET
ijassa-1077	168	12	boundary	boundary	NOUN
ijassa-1077	168	13	of	of	ADP
ijassa-1077	168	14	the	the	DET
ijassa-1077	168	15	gamut	gamut	NOUN
ijassa-1077	168	16	is	be	AUX
ijassa-1077	168	17	a	a	DET
ijassa-1077	168	18	subset	subset	NOUN
ijassa-1077	168	19	of	of	ADP
ijassa-1077	168	20	the	the	DET
ijassa-1077	168	21	images	image	NOUN
ijassa-1077	168	22	of	of	ADP
ijassa-1077	168	23	all	all	DET
ijassa-1077	168	24	the	the	DET
ijassa-1077	168	25	boundary	boundary	ADJ
ijassa-1077	168	26	and	and	CCONJ
ijassa-1077	168	27	singular	singular	ADJ
ijassa-1077	168	28	faces	face	NOUN
ijassa-1077	168	29	,	,	PUNCT
ijassa-1077	168	30	i.e.	i.e.	X
ijassa-1077	168	31	,	,	PUNCT
ijassa-1077	168	32	!	!	PUNCT
ijassa-1077	169	1	nj	nj	PROPN
ijassa-1077	169	2	jw	jw	PROPN
ijassa-1077	169	3	,	,	PUNCT
ijassa-1077	169	4	...	...	PUNCT
ijassa-1077	169	5	,	,	PUNCT
ijassa-1077	169	6	1	1	NUM
ijassa-1077	169	7	3	3	NUM
ijassa-1077	169	8	=	=	SYM
ijassa-1077	169	9	d=	d=	NOUN
ijassa-1077	170	1	3w¶=	3w¶=	NUM
ijassa-1077	170	2	qî	qî	ADP
ijassa-1077	170	3	!	!	PUNCT
ijassa-1077	171	1	d	d	X
ijassa-1077	172	1	d	d	PROPN
ijassa-1077	172	2	mathematical	mathematical	ADJ
ijassa-1077	172	3	modeling	modeling	NOUN
ijassa-1077	172	4	of	of	ADP
ijassa-1077	172	5	color	color	NOUN
ijassa-1077	172	6	printing	printing	NOUN
ijassa-1077	172	7	devices	device	NOUN
ijassa-1077	172	8	:	:	PUNCT
ijassa-1077	172	9	color	color	NOUN
ijassa-1077	172	10	gamut	gamut	NOUN
ijassa-1077	172	11	visualization	visualization	NOUN
ijassa-1077	172	12	…	…	PUNCT
ijassa-1077	172	13	123	123	NUM
ijassa-1077	172	14	copyright	copyright	NOUN
ijassa-1077	172	15	©	©	PROPN
ijassa-1077	172	16	2021	2021	NUM
ijassa-1077	172	17	assa	assa	NOUN
ijassa-1077	172	18	.	.	PUNCT
ijassa-1077	173	1	adv	adv	PROPN
ijassa-1077	173	2	.	.	PUNCT
ijassa-1077	174	1	in	in	ADP
ijassa-1077	174	2	systems	system	NOUN
ijassa-1077	174	3	science	science	NOUN
ijassa-1077	174	4	and	and	CCONJ
ijassa-1077	174	5	appl	appl	NOUN
ijassa-1077	174	6	.	.	PUNCT
ijassa-1077	175	1	(	(	PUNCT
ijassa-1077	175	2	2021	2021	NUM
ijassa-1077	175	3	)	)	PUNCT
ijassa-1077	175	4	¶f(w3	¶f(w3	PROPN
ijassa-1077	175	5	)	)	PUNCT
ijassa-1077	175	6	í	í	PROPN
ijassa-1077	175	7	f(q	f(q	PROPN
ijassa-1077	175	8	)	)	PUNCT
ijassa-1077	176	1	è	è	PROPN
ijassa-1077	176	2	f(s	f(	NOUN
ijassa-1077	176	3	)	)	PUNCT
ijassa-1077	176	4	.	.	PUNCT
ijassa-1077	177	1	this	this	DET
ijassa-1077	177	2	theorem	theorem	NOUN
ijassa-1077	177	3	can	can	AUX
ijassa-1077	177	4	seem	seem	VERB
ijassa-1077	177	5	to	to	PART
ijassa-1077	177	6	be	be	AUX
ijassa-1077	177	7	a	a	DET
ijassa-1077	177	8	pure	pure	ADJ
ijassa-1077	177	9	abstract	abstract	ADJ
ijassa-1077	177	10	mathematical	mathematical	ADJ
ijassa-1077	177	11	proposition	proposition	NOUN
ijassa-1077	177	12	.	.	PUNCT
ijassa-1077	178	1	and	and	CCONJ
ijassa-1077	178	2	,	,	PUNCT
ijassa-1077	178	3	of	of	ADP
ijassa-1077	178	4	course	course	NOUN
ijassa-1077	178	5	,	,	PUNCT
ijassa-1077	178	6	it	it	PRON
ijassa-1077	178	7	really	really	ADV
ijassa-1077	178	8	is	be	AUX
ijassa-1077	178	9	.	.	PUNCT
ijassa-1077	179	1	but	but	CCONJ
ijassa-1077	179	2	nevertheless	nevertheless	ADV
ijassa-1077	179	3	,	,	PUNCT
ijassa-1077	179	4	it	it	PRON
ijassa-1077	179	5	does	do	VERB
ijassa-1077	179	6	significantly	significantly	ADV
ijassa-1077	179	7	more	more	ADV
ijassa-1077	179	8	because	because	SCONJ
ijassa-1077	179	9	it	it	PRON
ijassa-1077	179	10	gives	give	VERB
ijassa-1077	179	11	a	a	DET
ijassa-1077	179	12	strict	strict	ADJ
ijassa-1077	179	13	mathematical	mathematical	ADJ
ijassa-1077	179	14	ground	ground	NOUN
ijassa-1077	179	15	for	for	ADP
ijassa-1077	179	16	creation	creation	NOUN
ijassa-1077	179	17	of	of	ADP
ijassa-1077	179	18	a	a	DET
ijassa-1077	179	19	wide	wide	ADJ
ijassa-1077	179	20	range	range	NOUN
ijassa-1077	179	21	of	of	ADP
ijassa-1077	179	22	computational	computational	ADJ
ijassa-1077	179	23	algorithms	algorithm	NOUN
ijassa-1077	179	24	for	for	ADP
ijassa-1077	179	25	practical	practical	ADJ
ijassa-1077	179	26	approximation	approximation	NOUN
ijassa-1077	179	27	of	of	ADP
ijassa-1077	179	28	color	color	NOUN
ijassa-1077	179	29	gamut	gamut	NOUN
ijassa-1077	179	30	boundaries	boundary	NOUN
ijassa-1077	179	31	of	of	ADP
ijassa-1077	179	32	various	various	ADJ
ijassa-1077	179	33	three	three	NUM
ijassa-1077	179	34	-	-	PUNCT
ijassa-1077	179	35	dimensional	dimensional	ADJ
ijassa-1077	179	36	printing	printing	NOUN
ijassa-1077	179	37	devices	device	NOUN
ijassa-1077	179	38	.	.	PUNCT
ijassa-1077	180	1	in	in	ADP
ijassa-1077	180	2	particular	particular	ADJ
ijassa-1077	180	3	,	,	PUNCT
ijassa-1077	180	4	the	the	DET
ijassa-1077	180	5	author	author	NOUN
ijassa-1077	180	6	designed	design	VERB
ijassa-1077	180	7	a	a	DET
ijassa-1077	180	8	variant	variant	NOUN
ijassa-1077	180	9	of	of	ADP
ijassa-1077	180	10	such	such	DET
ijassa-1077	180	11	an	an	DET
ijassa-1077	180	12	algorithm	algorithm	NOUN
ijassa-1077	180	13	,	,	PUNCT
ijassa-1077	180	14	which	which	PRON
ijassa-1077	180	15	constructs	construct	VERB
ijassa-1077	180	16	a	a	DET
ijassa-1077	180	17	three	three	NUM
ijassa-1077	180	18	-	-	PUNCT
ijassa-1077	180	19	dimensional	dimensional	ADJ
ijassa-1077	180	20	gamut	gamut	NOUN
ijassa-1077	180	21	boundary	boundary	NOUN
ijassa-1077	180	22	for	for	ADP
ijassa-1077	180	23	any	any	DET
ijassa-1077	180	24	real	real	ADJ
ijassa-1077	180	25	color	color	NOUN
ijassa-1077	180	26	printing	printing	NOUN
ijassa-1077	180	27	device	device	NOUN
ijassa-1077	180	28	with	with	ADP
ijassa-1077	180	29	three	three	NUM
ijassa-1077	180	30	colorants	colorant	NOUN
ijassa-1077	180	31	.	.	PUNCT
ijassa-1077	181	1	as	as	ADP
ijassa-1077	181	2	an	an	DET
ijassa-1077	181	3	input	input	NOUN
ijassa-1077	181	4	it	it	PRON
ijassa-1077	181	5	takes	take	VERB
ijassa-1077	181	6	a	a	DET
ijassa-1077	181	7	file	file	NOUN
ijassa-1077	181	8	with	with	ADP
ijassa-1077	181	9	colorimetric	colorimetric	ADJ
ijassa-1077	181	10	measurements	measurement	NOUN
ijassa-1077	181	11	data	datum	NOUN
ijassa-1077	181	12	of	of	ADP
ijassa-1077	181	13	the	the	DET
ijassa-1077	181	14	printing	printing	NOUN
ijassa-1077	181	15	device	device	NOUN
ijassa-1077	181	16	under	under	ADP
ijassa-1077	181	17	consideration	consideration	NOUN
ijassa-1077	181	18	(	(	PUNCT
ijassa-1077	181	19	see	see	VERB
ijassa-1077	181	20	section	section	NOUN
ijassa-1077	181	21	1	1	NUM
ijassa-1077	181	22	)	)	PUNCT
ijassa-1077	181	23	,	,	PUNCT
ijassa-1077	181	24	and	and	CCONJ
ijassa-1077	181	25	as	as	ADP
ijassa-1077	181	26	an	an	DET
ijassa-1077	181	27	output	output	NOUN
ijassa-1077	181	28	it	it	PRON
ijassa-1077	181	29	constructs	construct	VERB
ijassa-1077	181	30	the	the	DET
ijassa-1077	181	31	color	color	NOUN
ijassa-1077	181	32	gamut	gamut	NOUN
ijassa-1077	181	33	boundary	boundary	NOUN
ijassa-1077	181	34	,	,	PUNCT
ijassa-1077	181	35	i.e.	i.e.	X
ijassa-1077	181	36	,	,	PUNCT
ijassa-1077	181	37	the	the	DET
ijassa-1077	181	38	corresponding	corresponding	ADJ
ijassa-1077	181	39	boundary	boundary	NOUN
ijassa-1077	181	40	of	of	ADP
ijassa-1077	181	41	the	the	DET
ijassa-1077	181	42	three	three	NUM
ijassa-1077	181	43	-	-	PUNCT
ijassa-1077	181	44	dimensional	dimensional	ADJ
ijassa-1077	181	45	body	body	NOUN
ijassa-1077	181	46	in	in	ADP
ijassa-1077	181	47	a	a	DET
ijassa-1077	181	48	reference	reference	NOUN
ijassa-1077	181	49	space	space	NOUN
ijassa-1077	181	50	of	of	ADP
ijassa-1077	181	51	three	three	NUM
ijassa-1077	181	52	colors	color	NOUN
ijassa-1077	181	53	.	.	PUNCT
ijassa-1077	182	1	as	as	SCONJ
ijassa-1077	182	2	it	it	PRON
ijassa-1077	182	3	was	be	AUX
ijassa-1077	182	4	said	say	VERB
ijassa-1077	182	5	in	in	ADP
ijassa-1077	182	6	the	the	DET
ijassa-1077	182	7	preface	preface	NOUN
ijassa-1077	182	8	,	,	PUNCT
ijassa-1077	182	9	the	the	DET
ijassa-1077	182	10	same	same	ADJ
ijassa-1077	182	11	details	detail	NOUN
ijassa-1077	182	12	of	of	ADP
ijassa-1077	182	13	computational	computational	ADJ
ijassa-1077	182	14	algorithms	algorithm	NOUN
ijassa-1077	182	15	are	be	AUX
ijassa-1077	182	16	not	not	PART
ijassa-1077	182	17	presented	present	VERB
ijassa-1077	182	18	in	in	ADP
ijassa-1077	182	19	this	this	DET
ijassa-1077	182	20	article	article	NOUN
ijassa-1077	182	21	.	.	PUNCT
ijassa-1077	183	1	therefore	therefore	ADV
ijassa-1077	183	2	,	,	PUNCT
ijassa-1077	183	3	we	we	PRON
ijassa-1077	183	4	will	will	AUX
ijassa-1077	183	5	just	just	ADV
ijassa-1077	183	6	give	give	VERB
ijassa-1077	183	7	an	an	DET
ijassa-1077	183	8	example	example	NOUN
ijassa-1077	183	9	of	of	ADP
ijassa-1077	183	10	what	what	PRON
ijassa-1077	183	11	the	the	DET
ijassa-1077	183	12	designed	design	VERB
ijassa-1077	183	13	algorithm	algorithm	NOUN
ijassa-1077	183	14	does	do	AUX
ijassa-1077	183	15	in	in	ADP
ijassa-1077	183	16	practice	practice	NOUN
ijassa-1077	183	17	.	.	PUNCT
ijassa-1077	184	1	the	the	DET
ijassa-1077	184	2	picture	picture	NOUN
ijassa-1077	184	3	below	below	ADV
ijassa-1077	184	4	visualizes	visualize	VERB
ijassa-1077	184	5	a	a	DET
ijassa-1077	184	6	piecewise	piecewise	NOUN
ijassa-1077	184	7	linear	linear	NOUN
ijassa-1077	184	8	approximation	approximation	NOUN
ijassa-1077	184	9	of	of	ADP
ijassa-1077	184	10	the	the	DET
ijassa-1077	184	11	gamut	gamut	NOUN
ijassa-1077	184	12	boundary	boundary	NOUN
ijassa-1077	184	13	of	of	ADP
ijassa-1077	184	14	a	a	DET
ijassa-1077	184	15	rather	rather	ADV
ijassa-1077	184	16	standard	standard	ADJ
ijassa-1077	184	17	printing	printing	NOUN
ijassa-1077	184	18	device	device	NOUN
ijassa-1077	184	19	with	with	ADP
ijassa-1077	184	20	three	three	NUM
ijassa-1077	184	21	colorants	colorant	NOUN
ijassa-1077	184	22	,	,	PUNCT
ijassa-1077	184	23	which	which	PRON
ijassa-1077	184	24	means	mean	VERB
ijassa-1077	184	25	that	that	SCONJ
ijassa-1077	184	26	the	the	DET
ijassa-1077	184	27	stimuli	stimulus	NOUN
ijassa-1077	184	28	space	space	NOUN
ijassa-1077	184	29	is	be	AUX
ijassa-1077	184	30	three	three	NUM
ijassa-1077	184	31	-	-	PUNCT
ijassa-1077	184	32	dimensional	dimensional	ADJ
ijassa-1077	184	33	in	in	ADP
ijassa-1077	184	34	this	this	DET
ijassa-1077	184	35	case	case	NOUN
ijassa-1077	184	36	.	.	PUNCT
ijassa-1077	185	1	in	in	ADP
ijassa-1077	185	2	reference	reference	NOUN
ijassa-1077	185	3	space	space	NOUN
ijassa-1077	185	4	the	the	DET
ijassa-1077	185	5	lab	lab	NOUN
ijassa-1077	185	6	coordinate	coordinate	NOUN
ijassa-1077	185	7	system	system	NOUN
ijassa-1077	185	8	is	be	AUX
ijassa-1077	185	9	chosen	choose	VERB
ijassa-1077	185	10	,	,	PUNCT
ijassa-1077	185	11	and	and	CCONJ
ijassa-1077	185	12	one	one	NUM
ijassa-1077	185	13	colorants	colorant	NOUN
ijassa-1077	185	14	limitation	limitation	NOUN
ijassa-1077	185	15	is	be	AUX
ijassa-1077	185	16	applied	apply	VERB
ijassa-1077	185	17	.	.	PUNCT
ijassa-1077	186	1	fig	fig	NOUN
ijassa-1077	186	2	.	.	PUNCT
ijassa-1077	187	1	1	1	X
ijassa-1077	187	2	.	.	X
ijassa-1077	187	3	a	a	DET
ijassa-1077	187	4	piecewise	piecewise	NOUN
ijassa-1077	187	5	linear	linear	NOUN
ijassa-1077	187	6	approximation	approximation	NOUN
ijassa-1077	187	7	of	of	ADP
ijassa-1077	187	8	the	the	DET
ijassa-1077	187	9	gamut	gamut	NOUN
ijassa-1077	187	10	boundary	boundary	NOUN
ijassa-1077	187	11	for	for	ADP
ijassa-1077	187	12	a	a	DET
ijassa-1077	187	13	three	three	NUM
ijassa-1077	187	14	-	-	PUNCT
ijassa-1077	187	15	dimensional	dimensional	ADJ
ijassa-1077	187	16	printing	printing	NOUN
ijassa-1077	187	17	device	device	NOUN
ijassa-1077	187	18	the	the	DET
ijassa-1077	187	19	next	next	ADJ
ijassa-1077	187	20	picture	picture	NOUN
ijassa-1077	187	21	gives	give	VERB
ijassa-1077	187	22	another	another	DET
ijassa-1077	187	23	example	example	NOUN
ijassa-1077	187	24	of	of	ADP
ijassa-1077	187	25	the	the	DET
ijassa-1077	187	26	output	output	NOUN
ijassa-1077	187	27	of	of	ADP
ijassa-1077	187	28	the	the	DET
ijassa-1077	187	29	same	same	ADJ
ijassa-1077	187	30	algorithm	algorithm	NOUN
ijassa-1077	187	31	,	,	PUNCT
ijassa-1077	187	32	which	which	PRON
ijassa-1077	187	33	is	be	AUX
ijassa-1077	187	34	a	a	DET
ijassa-1077	187	35	visualized	visualize	VERB
ijassa-1077	187	36	color	color	NOUN
ijassa-1077	187	37	gamut	gamut	NOUN
ijassa-1077	187	38	boundary	boundary	NOUN
ijassa-1077	187	39	.	.	PUNCT
ijassa-1077	188	1	here	here	ADV
ijassa-1077	188	2	we	we	PRON
ijassa-1077	188	3	handle	handle	VERB
ijassa-1077	188	4	exactly	exactly	ADV
ijassa-1077	188	5	the	the	DET
ijassa-1077	188	6	same	same	ADJ
ijassa-1077	188	7	printing	printing	NOUN
ijassa-1077	188	8	device	device	NOUN
ijassa-1077	188	9	as	as	ADP
ijassa-1077	188	10	in	in	ADP
ijassa-1077	188	11	the	the	DET
ijassa-1077	188	12	previous	previous	ADJ
ijassa-1077	188	13	case	case	NOUN
ijassa-1077	188	14	but	but	CCONJ
ijassa-1077	188	15	the	the	DET
ijassa-1077	188	16	colorants	colorant	NOUN
ijassa-1077	188	17	limitation	limitation	NOUN
ijassa-1077	188	18	is	be	AUX
ijassa-1077	188	19	changed	change	VERB
ijassa-1077	188	20	to	to	ADP
ijassa-1077	188	21	the	the	DET
ijassa-1077	188	22	tighter	tight	ADJ
ijassa-1077	188	23	one	one	NOUN
ijassa-1077	188	24	,	,	PUNCT
ijassa-1077	188	25	namely	namely	ADV
ijassa-1077	188	26	to	to	ADP
ijassa-1077	188	27	.	.	PUNCT
ijassa-1077	189	1	250	250	NUM
ijassa-1077	189	2	3	3	NUM
ijassa-1077	189	3	1	1	NUM
ijassa-1077	189	4	£	£	SYM
ijassa-1077	189	5	å	å	NOUN
ijassa-1077	189	6	=	=	NOUN
ijassa-1077	189	7	i	i	PRON
ijassa-1077	189	8	ix	ix	ADP
ijassa-1077	189	9	150	150	NUM
ijassa-1077	189	10	3	3	NUM
ijassa-1077	189	11	1	1	NUM
ijassa-1077	189	12	£	£	SYM
ijassa-1077	189	13	å	å	NOUN
ijassa-1077	189	14	=	=	NOUN
ijassa-1077	189	15	i	i	PRON
ijassa-1077	189	16	ix	ix	PROPN
ijassa-1077	189	17	124	124	NUM
ijassa-1077	189	18	d.v	d.v	PROPN
ijassa-1077	189	19	.	.	PUNCT
ijassa-1077	190	1	tunitsky	tunitsky	NOUN
ijassa-1077	190	2	copyright	copyright	NOUN
ijassa-1077	191	1	©	©	PROPN
ijassa-1077	191	2	2021	2021	NUM
ijassa-1077	191	3	assa	assa	NOUN
ijassa-1077	191	4	.	.	PUNCT
ijassa-1077	192	1	adv	adv	PROPN
ijassa-1077	192	2	.	.	PUNCT
ijassa-1077	193	1	in	in	ADP
ijassa-1077	193	2	systems	system	NOUN
ijassa-1077	193	3	science	science	NOUN
ijassa-1077	193	4	and	and	CCONJ
ijassa-1077	193	5	appl	appl	NOUN
ijassa-1077	193	6	.	.	PUNCT
ijassa-1077	194	1	(	(	PUNCT
ijassa-1077	194	2	2021	2021	NUM
ijassa-1077	194	3	)	)	PUNCT
ijassa-1077	194	4	the	the	DET
ijassa-1077	194	5	way	way	NOUN
ijassa-1077	194	6	of	of	ADP
ijassa-1077	194	7	visualization	visualization	NOUN
ijassa-1077	194	8	is	be	AUX
ijassa-1077	194	9	also	also	ADV
ijassa-1077	194	10	exactly	exactly	ADV
ijassa-1077	194	11	the	the	DET
ijassa-1077	194	12	same	same	ADJ
ijassa-1077	194	13	,	,	PUNCT
ijassa-1077	194	14	including	include	VERB
ijassa-1077	194	15	angle	angle	NOUN
ijassa-1077	194	16	of	of	ADP
ijassa-1077	194	17	view	view	NOUN
ijassa-1077	194	18	,	,	PUNCT
ijassa-1077	194	19	the	the	DET
ijassa-1077	194	20	scale	scale	NOUN
ijassa-1077	194	21	,	,	PUNCT
ijassa-1077	194	22	and	and	CCONJ
ijassa-1077	194	23	the	the	DET
ijassa-1077	194	24	coordinate	coordinate	NOUN
ijassa-1077	194	25	system	system	NOUN
ijassa-1077	194	26	.	.	PUNCT
ijassa-1077	195	1	fig	fig	NOUN
ijassa-1077	195	2	.	.	PUNCT
ijassa-1077	196	1	2	2	X
ijassa-1077	196	2	.	.	X
ijassa-1077	196	3	results	result	NOUN
ijassa-1077	196	4	of	of	ADP
ijassa-1077	196	5	the	the	DET
ijassa-1077	196	6	algorithm	algorithm	NOUN
ijassa-1077	196	7	for	for	ADP
ijassa-1077	196	8	the	the	DET
ijassa-1077	196	9	same	same	ADJ
ijassa-1077	196	10	printing	printing	NOUN
ijassa-1077	196	11	device	device	NOUN
ijassa-1077	196	12	with	with	ADP
ijassa-1077	196	13	tighter	tight	ADJ
ijassa-1077	196	14	colorants	colorant	NOUN
ijassa-1077	196	15	limitation	limitation	NOUN
ijassa-1077	196	16	5	5	NUM
ijassa-1077	196	17	.	.	PUNCT
ijassa-1077	196	18	gamut	gamut	NOUN
ijassa-1077	196	19	description	description	NOUN
ijassa-1077	196	20	for	for	ADP
ijassa-1077	196	21	four	four	NUM
ijassa-1077	196	22	-	-	PUNCT
ijassa-1077	196	23	dimensional	dimensional	ADJ
ijassa-1077	196	24	printing	printing	NOUN
ijassa-1077	196	25	devices	device	NOUN
ijassa-1077	196	26	consider	consider	VERB
ijassa-1077	196	27	a	a	DET
ijassa-1077	196	28	piecewise	piecewise	NOUN
ijassa-1077	196	29	linear	linear	NOUN
ijassa-1077	196	30	model	model	NOUN
ijassa-1077	196	31	f	f	NOUN
ijassa-1077	196	32	:	:	PUNCT
ijassa-1077	196	33	w4	w4	NOUN
ijassa-1077	196	34	®	®	NOUN
ijassa-1077	196	35	ℝ	ℝ	NOUN
ijassa-1077	196	36	#	#	NOUN
ijassa-1077	196	37	,	,	PUNCT
ijassa-1077	196	38	of	of	ADP
ijassa-1077	196	39	a	a	DET
ijassa-1077	196	40	four	four	NUM
ijassa-1077	196	41	-	-	PUNCT
ijassa-1077	196	42	dimensional	dimensional	ADJ
ijassa-1077	196	43	printing	printing	NOUN
ijassa-1077	196	44	device	device	NOUN
ijassa-1077	196	45	.	.	PUNCT
ijassa-1077	197	1	definition	definition	NOUN
ijassa-1077	197	2	.	.	PUNCT
ijassa-1077	198	1	if	if	SCONJ
ijassa-1077	198	2	the	the	DET
ijassa-1077	198	3	image	image	NOUN
ijassa-1077	198	4	of	of	ADP
ijassa-1077	198	5	the	the	DET
ijassa-1077	198	6	boundary	boundary	ADJ
ijassa-1077	198	7	¶w4	¶w4	PROPN
ijassa-1077	198	8	of	of	ADP
ijassa-1077	198	9	the	the	DET
ijassa-1077	198	10	four	four	NUM
ijassa-1077	198	11	-	-	PUNCT
ijassa-1077	198	12	dimensional	dimensional	ADJ
ijassa-1077	198	13	colorants	colorant	NOUN
ijassa-1077	198	14	cube	cube	NOUN
ijassa-1077	198	15	coincides	coincide	VERB
ijassa-1077	198	16	with	with	ADP
ijassa-1077	198	17	the	the	DET
ijassa-1077	198	18	image	image	NOUN
ijassa-1077	198	19	of	of	ADP
ijassa-1077	198	20	the	the	DET
ijassa-1077	198	21	whole	whole	ADJ
ijassa-1077	198	22	cube	cube	NOUN
ijassa-1077	198	23	w4	w4	NOUN
ijassa-1077	198	24	,	,	PUNCT
ijassa-1077	198	25	i.e.	i.e.	X
ijassa-1077	198	26	,	,	PUNCT
ijassa-1077	198	27	f(w4	f(w4	NOUN
ijassa-1077	198	28	)	)	PUNCT
ijassa-1077	198	29	=	=	SYM
ijassa-1077	199	1	f(¶w4	f(¶w4	PROPN
ijassa-1077	199	2	)	)	PUNCT
ijassa-1077	199	3	,	,	PUNCT
ijassa-1077	199	4	then	then	ADV
ijassa-1077	199	5	the	the	DET
ijassa-1077	199	6	fourdimensional	fourdimensional	ADJ
ijassa-1077	199	7	printing	printing	NOUN
ijassa-1077	199	8	device	device	NOUN
ijassa-1077	199	9	is	be	AUX
ijassa-1077	199	10	called	call	VERB
ijassa-1077	199	11	proper	proper	ADJ
ijassa-1077	199	12	.	.	PUNCT
ijassa-1077	200	1	remark	remark	PROPN
ijassa-1077	200	2	.	.	PUNCT
ijassa-1077	201	1	from	from	ADP
ijassa-1077	201	2	technological	technological	ADJ
ijassa-1077	201	3	point	point	NOUN
ijassa-1077	201	4	of	of	ADP
ijassa-1077	201	5	view	view	NOUN
ijassa-1077	201	6	,	,	PUNCT
ijassa-1077	201	7	the	the	DET
ijassa-1077	201	8	assumption	assumption	NOUN
ijassa-1077	201	9	of	of	ADP
ijassa-1077	201	10	a	a	DET
ijassa-1077	201	11	four	four	NUM
ijassa-1077	201	12	-	-	PUNCT
ijassa-1077	201	13	dimensional	dimensional	ADJ
ijassa-1077	201	14	printing	printing	NOUN
ijassa-1077	201	15	device	device	NOUN
ijassa-1077	201	16	to	to	PART
ijassa-1077	201	17	be	be	AUX
ijassa-1077	201	18	proper	proper	ADJ
ijassa-1077	201	19	is	be	AUX
ijassa-1077	201	20	reasonable	reasonable	ADJ
ijassa-1077	201	21	for	for	ADP
ijassa-1077	201	22	most	most	ADJ
ijassa-1077	201	23	real	real	ADJ
ijassa-1077	201	24	four	four	NUM
ijassa-1077	201	25	-	-	PUNCT
ijassa-1077	201	26	dimensional	dimensional	ADJ
ijassa-1077	201	27	printing	printing	NOUN
ijassa-1077	201	28	devices	device	NOUN
ijassa-1077	201	29	.	.	PUNCT
ijassa-1077	202	1	by	by	ADP
ijassa-1077	202	2	definition	definition	NOUN
ijassa-1077	202	3	of	of	ADP
ijassa-1077	202	4	the	the	DET
ijassa-1077	202	5	piecewise	piecewise	NOUN
ijassa-1077	202	6	linear	linear	NOUN
ijassa-1077	202	7	map	map	NOUN
ijassa-1077	202	8	f	f	NOUN
ijassa-1077	202	9	,	,	PUNCT
ijassa-1077	202	10	all	all	DET
ijassa-1077	202	11	the	the	DET
ijassa-1077	202	12	restrictions	restriction	NOUN
ijassa-1077	202	13	f½dj	f½dj	ADV
ijassa-1077	202	14	:	:	PUNCT
ijassa-1077	202	15	dj	dj	X
ijassa-1077	202	16	®	®	NOUN
ijassa-1077	202	17	ℝ	ℝ	NOUN
ijassa-1077	202	18	#	#	NOUN
ijassa-1077	202	19	,	,	PUNCT
ijassa-1077	202	20	of	of	ADP
ijassa-1077	202	21	the	the	DET
ijassa-1077	202	22	map	map	NOUN
ijassa-1077	202	23	f	f	X
ijassa-1077	202	24	to	to	ADP
ijassa-1077	202	25	pentahedrons	pentahedron	NOUN
ijassa-1077	202	26	dj	dj	NOUN
ijassa-1077	202	27	are	be	AUX
ijassa-1077	202	28	linear	linear	ADJ
ijassa-1077	202	29	maps	map	NOUN
ijassa-1077	202	30	,	,	PUNCT
ijassa-1077	202	31	i.e.	i.e.	X
ijassa-1077	202	32	,	,	PUNCT
ijassa-1077	202	33	f½dj	f½dj	PROPN
ijassa-1077	202	34	(	(	PUNCT
ijassa-1077	202	35	x	x	X
ijassa-1077	202	36	)	)	PUNCT
ijassa-1077	202	37	=	=	SYM
ijassa-1077	202	38	cj	cj	NOUN
ijassa-1077	203	1	+	+	CCONJ
ijassa-1077	203	2	bjx	bjx	ADV
ijassa-1077	203	3	,	,	PUNCT
ijassa-1077	203	4	where	where	SCONJ
ijassa-1077	203	5	bj	bj	NOUN
ijassa-1077	203	6	is	be	AUX
ijassa-1077	203	7	a	a	DET
ijassa-1077	203	8	3´4	3´4	NUM
ijassa-1077	203	9	matrix	matrix	NOUN
ijassa-1077	203	10	for	for	ADP
ijassa-1077	203	11	j=1,	j=1,	NOUN
ijassa-1077	203	12	…	…	PUNCT
ijassa-1077	203	13	,n	,n	PUNCT
ijassa-1077	203	14	.	.	PUNCT
ijassa-1077	204	1	let	let	VERB
ijassa-1077	204	2	bji	bji	PROPN
ijassa-1077	204	3	be	be	AUX
ijassa-1077	204	4	the	the	DET
ijassa-1077	204	5	3´3	3´3	NUM
ijassa-1077	204	6	matrix	matrix	NOUN
ijassa-1077	204	7	obtained	obtain	VERB
ijassa-1077	204	8	by	by	ADP
ijassa-1077	204	9	throwing	throw	VERB
ijassa-1077	204	10	away	away	ADP
ijassa-1077	204	11	the	the	DET
ijassa-1077	204	12	i	i	PROPN
ijassa-1077	204	13	-	-	PUNCT
ijassa-1077	204	14	th	th	VERB
ijassa-1077	204	15	column	column	NOUN
ijassa-1077	204	16	from	from	ADP
ijassa-1077	204	17	the	the	DET
ijassa-1077	204	18	3´4	3´4	NUM
ijassa-1077	204	19	matrix	matrix	NOUN
ijassa-1077	204	20	bj	bj	NOUN
ijassa-1077	204	21	and	and	CCONJ
ijassa-1077	204	22	put	put	VERB
ijassa-1077	204	23	cj	cj	NOUN
ijassa-1077	205	1	=	=	PUNCT
ijassa-1077	205	2	(	(	PUNCT
ijassa-1077	205	3	det	det	PROPN
ijassa-1077	205	4	bj1	bj1	PROPN
ijassa-1077	205	5	,	,	PUNCT
ijassa-1077	205	6	det	det	PROPN
ijassa-1077	205	7	bj2	bj2	PROPN
ijassa-1077	205	8	,	,	PUNCT
ijassa-1077	205	9	det	det	PROPN
ijassa-1077	205	10	bj3	bj3	PROPN
ijassa-1077	205	11	,	,	PUNCT
ijassa-1077	205	12	det	det	NOUN
ijassa-1077	205	13	bj4	bj4	NOUN
ijassa-1077	205	14	)	)	PUNCT
ijassa-1077	205	15	for	for	ADP
ijassa-1077	205	16	j=1	j=1	PROPN
ijassa-1077	205	17	,	,	PUNCT
ijassa-1077	205	18	…	…	NUM
ijassa-1077	205	19	,	,	PUNCT
ijassa-1077	205	20	n.	n.	NOUN
ijassa-1077	205	21	definition	definition	NOUN
ijassa-1077	205	22	.	.	PUNCT
ijassa-1077	206	1	consider	consider	VERB
ijassa-1077	206	2	the	the	DET
ijassa-1077	206	3	four	four	NUM
ijassa-1077	206	4	-	-	PUNCT
ijassa-1077	206	5	dimensional	dimensional	ADJ
ijassa-1077	206	6	printing	printing	NOUN
ijassa-1077	206	7	device	device	NOUN
ijassa-1077	206	8	corresponding	correspond	VERB
ijassa-1077	206	9	to	to	ADP
ijassa-1077	206	10	the	the	DET
ijassa-1077	206	11	piecewise	piecewise	NOUN
ijassa-1077	206	12	linear	linear	NOUN
ijassa-1077	206	13	map	map	NOUN
ijassa-1077	206	14	f.	f.	PROPN
ijassa-1077	206	15	a	a	DET
ijassa-1077	206	16	vector	vector	NOUN
ijassa-1077	206	17	field	field	NOUN
ijassa-1077	206	18	c	c	NOUN
ijassa-1077	206	19	on	on	ADP
ijassa-1077	206	20	the	the	DET
ijassa-1077	206	21	colorants	colorant	NOUN
ijassa-1077	206	22	cube	cube	PROPN
ijassa-1077	206	23	w4	w4	PROPN
ijassa-1077	206	24	is	be	AUX
ijassa-1077	206	25	called	call	VERB
ijassa-1077	206	26	the	the	DET
ijassa-1077	206	27	characteristic	characteristic	ADJ
ijassa-1077	206	28	vector	vector	NOUN
ijassa-1077	206	29	field	field	NOUN
ijassa-1077	206	30	of	of	ADP
ijassa-1077	206	31	the	the	DET
ijassa-1077	206	32	printing	printing	NOUN
ijassa-1077	206	33	device	device	NOUN
ijassa-1077	206	34	under	under	ADP
ijassa-1077	206	35	consideration	consideration	NOUN
ijassa-1077	206	36	if	if	SCONJ
ijassa-1077	206	37	c½dj	c½dj	PROPN
ijassa-1077	206	38	=	=	SYM
ijassa-1077	206	39	cj	cj	NOUN
ijassa-1077	206	40	for	for	ADP
ijassa-1077	206	41	j=1	j=1	PROPN
ijassa-1077	206	42	,	,	PUNCT
ijassa-1077	206	43	…	…	PUNCT
ijassa-1077	206	44	,	,	PUNCT
ijassa-1077	206	45	n	n	X
ijassa-1077	206	46	.	.	PUNCT
ijassa-1077	207	1	the	the	DET
ijassa-1077	207	2	four	four	NUM
ijassa-1077	207	3	-	-	PUNCT
ijassa-1077	207	4	dimensional	dimensional	ADJ
ijassa-1077	207	5	printing	printing	NOUN
ijassa-1077	207	6	device	device	NOUN
ijassa-1077	207	7	is	be	AUX
ijassa-1077	207	8	non	non	ADJ
ijassa-1077	207	9	-	-	ADJ
ijassa-1077	207	10	degenerate	degenerate	ADJ
ijassa-1077	207	11	if	if	SCONJ
ijassa-1077	207	12	the	the	DET
ijassa-1077	207	13	corresponding	corresponding	ADJ
ijassa-1077	207	14	characteristic	characteristic	ADJ
ijassa-1077	207	15	vector	vector	NOUN
ijassa-1077	207	16	field	field	NOUN
ijassa-1077	207	17	c	c	NOUN
ijassa-1077	207	18	is	be	AUX
ijassa-1077	207	19	nondegenerate	nondegenerate	ADJ
ijassa-1077	207	20	,	,	PUNCT
ijassa-1077	207	21	i.e.	i.e.	X
ijassa-1077	207	22	,	,	PUNCT
ijassa-1077	207	23	cj	cj	NOUN
ijassa-1077	207	24	¹	¹	PROPN
ijassa-1077	207	25	0	0	NUM
ijassa-1077	207	26	for	for	ADP
ijassa-1077	207	27	all	all	DET
ijassa-1077	207	28	j=1,	j=1,	NOUN
ijassa-1077	207	29	…	…	X
ijassa-1077	207	30	,n	,n	X
ijassa-1077	207	31	.	.	PUNCT
ijassa-1077	208	1	mathematical	mathematical	ADJ
ijassa-1077	208	2	modeling	modeling	NOUN
ijassa-1077	208	3	of	of	ADP
ijassa-1077	208	4	color	color	NOUN
ijassa-1077	208	5	printing	printing	NOUN
ijassa-1077	208	6	devices	device	NOUN
ijassa-1077	208	7	:	:	PUNCT
ijassa-1077	208	8	color	color	NOUN
ijassa-1077	208	9	gamut	gamut	NOUN
ijassa-1077	208	10	visualization	visualization	NOUN
ijassa-1077	208	11	…	…	PUNCT
ijassa-1077	208	12	125	125	NUM
ijassa-1077	208	13	copyright	copyright	NOUN
ijassa-1077	208	14	©	©	PROPN
ijassa-1077	208	15	2021	2021	NUM
ijassa-1077	208	16	assa	assa	NOUN
ijassa-1077	208	17	.	.	PUNCT
ijassa-1077	209	1	adv	adv	PROPN
ijassa-1077	209	2	.	.	PUNCT
ijassa-1077	210	1	in	in	ADP
ijassa-1077	210	2	systems	system	NOUN
ijassa-1077	210	3	science	science	NOUN
ijassa-1077	210	4	and	and	CCONJ
ijassa-1077	210	5	appl	appl	NOUN
ijassa-1077	210	6	.	.	PUNCT
ijassa-1077	211	1	(	(	PUNCT
ijassa-1077	211	2	2021	2021	NUM
ijassa-1077	211	3	)	)	PUNCT
ijassa-1077	211	4	remark	remark	NOUN
ijassa-1077	211	5	.	.	PUNCT
ijassa-1077	212	1	by	by	ADP
ijassa-1077	212	2	definition	definition	NOUN
ijassa-1077	212	3	,	,	PUNCT
ijassa-1077	212	4	the	the	DET
ijassa-1077	212	5	characteristic	characteristic	ADJ
ijassa-1077	212	6	vector	vector	NOUN
ijassa-1077	212	7	field	field	NOUN
ijassa-1077	212	8	of	of	ADP
ijassa-1077	212	9	any	any	DET
ijassa-1077	212	10	four	four	NUM
ijassa-1077	212	11	-	-	PUNCT
ijassa-1077	212	12	dimensional	dimensional	ADJ
ijassa-1077	212	13	printing	printing	NOUN
ijassa-1077	212	14	device	device	NOUN
ijassa-1077	212	15	is	be	AUX
ijassa-1077	212	16	a	a	DET
ijassa-1077	212	17	four	four	NUM
ijassa-1077	212	18	-	-	PUNCT
ijassa-1077	212	19	dimensional	dimensional	ADJ
ijassa-1077	212	20	piecewise	piecewise	NOUN
ijassa-1077	212	21	constant	constant	ADJ
ijassa-1077	212	22	vector	vector	NOUN
ijassa-1077	212	23	field	field	NOUN
ijassa-1077	212	24	on	on	ADP
ijassa-1077	212	25	the	the	DET
ijassa-1077	212	26	four	four	NUM
ijassa-1077	212	27	-	-	PUNCT
ijassa-1077	212	28	dimensional	dimensional	ADJ
ijassa-1077	212	29	colorants	colorant	NOUN
ijassa-1077	212	30	cube	cube	NOUN
ijassa-1077	212	31	w4	w4	NOUN
ijassa-1077	212	32	.	.	PUNCT
ijassa-1077	213	1	in	in	ADP
ijassa-1077	213	2	this	this	DET
ijassa-1077	213	3	section	section	NOUN
ijassa-1077	213	4	we	we	PRON
ijassa-1077	213	5	will	will	AUX
ijassa-1077	213	6	describe	describe	VERB
ijassa-1077	213	7	the	the	DET
ijassa-1077	213	8	gamut	gamut	NOUN
ijassa-1077	213	9	of	of	ADP
ijassa-1077	213	10	a	a	DET
ijassa-1077	213	11	proper	proper	ADJ
ijassa-1077	213	12	non	non	ADJ
ijassa-1077	213	13	-	-	ADJ
ijassa-1077	213	14	degenerate	degenerate	ADJ
ijassa-1077	213	15	four	four	NUM
ijassa-1077	213	16	-	-	PUNCT
ijassa-1077	213	17	dimensional	dimensional	ADJ
ijassa-1077	213	18	printing	printing	NOUN
ijassa-1077	213	19	device	device	NOUN
ijassa-1077	213	20	,	,	PUNCT
ijassa-1077	213	21	i.e.	i.e.	X
ijassa-1077	213	22	,	,	PUNCT
ijassa-1077	213	23	the	the	DET
ijassa-1077	213	24	image	image	NOUN
ijassa-1077	213	25	f(w4	f(w4	NOUN
ijassa-1077	213	26	)	)	PUNCT
ijassa-1077	213	27	of	of	ADP
ijassa-1077	213	28	the	the	DET
ijassa-1077	213	29	corresponding	corresponding	ADJ
ijassa-1077	213	30	piecewise	piecewise	NOUN
ijassa-1077	213	31	linear	linear	NOUN
ijassa-1077	213	32	map	map	NOUN
ijassa-1077	213	33	f	f	PROPN
ijassa-1077	213	34	in	in	ADP
ijassa-1077	213	35	color	color	NOUN
ijassa-1077	213	36	space	space	NOUN
ijassa-1077	213	37	.	.	PUNCT
ijassa-1077	214	1	by	by	ADP
ijassa-1077	214	2	definition	definition	NOUN
ijassa-1077	214	3	of	of	ADP
ijassa-1077	214	4	a	a	DET
ijassa-1077	214	5	piecewise	piecewise	NOUN
ijassa-1077	214	6	linear	linear	NOUN
ijassa-1077	214	7	map	map	NOUN
ijassa-1077	214	8	,	,	PUNCT
ijassa-1077	214	9	we	we	PRON
ijassa-1077	214	10	have	have	VERB
ijassa-1077	214	11	the	the	DET
ijassa-1077	214	12	simplex	simplex	NOUN
ijassa-1077	214	13	decomposition	decomposition	NOUN
ijassa-1077	214	14	of	of	ADP
ijassa-1077	214	15	the	the	DET
ijassa-1077	214	16	fourdimensional	fourdimensional	ADJ
ijassa-1077	214	17	colorants	colorant	NOUN
ijassa-1077	214	18	cube	cube	PROPN
ijassa-1077	214	19	w4	w4	NOUN
ijassa-1077	214	20	into	into	ADP
ijassa-1077	214	21	the	the	DET
ijassa-1077	214	22	union	union	NOUN
ijassa-1077	214	23	of	of	ADP
ijassa-1077	214	24	n	n	CCONJ
ijassa-1077	214	25	,	,	PUNCT
ijassa-1077	214	26	n>0	n>0	PROPN
ijassa-1077	214	27	,	,	PUNCT
ijassa-1077	214	28	pentahedrons	pentahedron	NOUN
ijassa-1077	214	29	dj	dj	NOUN
ijassa-1077	214	30	,	,	PUNCT
ijassa-1077	214	31	.	.	PUNCT
ijassa-1077	215	1	each	each	DET
ijassa-1077	215	2	pentahedron	pentahedron	NOUN
ijassa-1077	215	3	has	have	VERB
ijassa-1077	215	4	five	five	NUM
ijassa-1077	215	5	three	three	NUM
ijassa-1077	215	6	-	-	PUNCT
ijassa-1077	215	7	dimensional	dimensional	ADJ
ijassa-1077	215	8	faces	face	NOUN
ijassa-1077	215	9	.	.	PUNCT
ijassa-1077	216	1	these	these	DET
ijassa-1077	216	2	faces	face	NOUN
ijassa-1077	216	3	are	be	AUX
ijassa-1077	216	4	tetrahedrons	tetrahedron	NOUN
ijassa-1077	216	5	and	and	CCONJ
ijassa-1077	216	6	each	each	DET
ijassa-1077	216	7	tetrahedron	tetrahedron	NOUN
ijassa-1077	216	8	either	either	CCONJ
ijassa-1077	216	9	belongs	belong	VERB
ijassa-1077	216	10	to	to	ADP
ijassa-1077	216	11	one	one	NUM
ijassa-1077	216	12	or	or	CCONJ
ijassa-1077	216	13	several	several	ADJ
ijassa-1077	216	14	pentahedrons	pentahedron	NOUN
ijassa-1077	216	15	of	of	ADP
ijassa-1077	216	16	the	the	DET
ijassa-1077	216	17	set	set	NOUN
ijassa-1077	216	18	{	{	PUNCT
ijassa-1077	216	19	dj	dj	NOUN
ijassa-1077	216	20	}	}	PUNCT
ijassa-1077	216	21	.	.	PUNCT
ijassa-1077	217	1	definition	definition	NOUN
ijassa-1077	217	2	.	.	PUNCT
ijassa-1077	218	1	fix	fix	VERB
ijassa-1077	218	2	a	a	DET
ijassa-1077	218	3	pentahedron	pentahedron	PROPN
ijassa-1077	218	4	dl	dl	PROPN
ijassa-1077	218	5	,	,	PUNCT
ijassa-1077	218	6	l=1,	l=1,	PROPN
ijassa-1077	218	7	…	…	X
ijassa-1077	218	8	,n	,n	NOUN
ijassa-1077	218	9	,	,	PUNCT
ijassa-1077	218	10	and	and	CCONJ
ijassa-1077	218	11	consider	consider	VERB
ijassa-1077	218	12	it	it	PRON
ijassa-1077	218	13	’s	’	VERB
ijassa-1077	218	14	three	three	NUM
ijassa-1077	218	15	-	-	PUNCT
ijassa-1077	218	16	dimensional	dimensional	ADJ
ijassa-1077	218	17	face	face	NOUN
ijassa-1077	218	18	,	,	PUNCT
ijassa-1077	218	19	which	which	PRON
ijassa-1077	218	20	is	be	AUX
ijassa-1077	218	21	a	a	DET
ijassa-1077	218	22	tetrahedron	tetrahedron	NOUN
ijassa-1077	218	23	d.	d.	NOUN
ijassa-1077	218	24	the	the	DET
ijassa-1077	218	25	face	face	NOUN
ijassa-1077	219	1	d	d	NOUN
ijassa-1077	219	2	is	be	AUX
ijassa-1077	219	3	called	call	VERB
ijassa-1077	219	4	boundary	boundary	ADJ
ijassa-1077	219	5	if	if	SCONJ
ijassa-1077	219	6	it	it	PRON
ijassa-1077	219	7	does	do	AUX
ijassa-1077	219	8	n’t	not	PART
ijassa-1077	219	9	belong	belong	VERB
ijassa-1077	219	10	to	to	ADP
ijassa-1077	219	11	any	any	DET
ijassa-1077	219	12	other	other	ADJ
ijassa-1077	219	13	pentahedron	pentahedron	NOUN
ijassa-1077	219	14	of	of	ADP
ijassa-1077	219	15	the	the	DET
ijassa-1077	219	16	set	set	NOUN
ijassa-1077	219	17	{	{	PUNCT
ijassa-1077	219	18	dj	dj	NOUN
ijassa-1077	219	19	}	}	PUNCT
ijassa-1077	219	20	.	.	PUNCT
ijassa-1077	220	1	in	in	ADP
ijassa-1077	220	2	other	other	ADJ
ijassa-1077	220	3	words	word	NOUN
ijassa-1077	220	4	,	,	PUNCT
ijassa-1077	220	5	d	d	PROPN
ijassa-1077	220	6	ì	ì	X
ijassa-1077	220	7	dl	dl	PROPN
ijassa-1077	220	8	,	,	PUNCT
ijassa-1077	220	9	and	and	CCONJ
ijassa-1077	220	10	d	d	X
ijassa-1077	220	11	ë	ë	PROPN
ijassa-1077	220	12	dk	dk	PROPN
ijassa-1077	220	13	for	for	ADP
ijassa-1077	220	14	k=1,	k=1,	PROPN
ijassa-1077	220	15	…	…	PUNCT
ijassa-1077	220	16	,l-1,l+1,	,l-1,l+1,	PUNCT
ijassa-1077	220	17	…	…	PUNCT
ijassa-1077	220	18	,n	,n	SYM
ijassa-1077	220	19	.	.	PUNCT
ijassa-1077	220	20	denote	denote	VERB
ijassa-1077	220	21	the	the	DET
ijassa-1077	220	22	set	set	NOUN
ijassa-1077	220	23	of	of	ADP
ijassa-1077	220	24	all	all	DET
ijassa-1077	220	25	the	the	DET
ijassa-1077	220	26	boundary	boundary	ADJ
ijassa-1077	220	27	faces	face	NOUN
ijassa-1077	220	28	of	of	ADP
ijassa-1077	220	29	the	the	DET
ijassa-1077	220	30	colorants	colorant	NOUN
ijassa-1077	220	31	cube	cube	PROPN
ijassa-1077	220	32	w4	w4	PROPN
ijassa-1077	220	33	by	by	ADP
ijassa-1077	220	34	q.	q.	PROPN
ijassa-1077	220	35	remark	remark	PROPN
ijassa-1077	220	36	.	.	PUNCT
ijassa-1077	221	1	the	the	DET
ijassa-1077	221	2	set	set	NOUN
ijassa-1077	221	3	q	q	NOUN
ijassa-1077	221	4	of	of	ADP
ijassa-1077	221	5	all	all	DET
ijassa-1077	221	6	the	the	DET
ijassa-1077	221	7	boundary	boundary	ADJ
ijassa-1077	221	8	faces	face	NOUN
ijassa-1077	221	9	does	do	AUX
ijassa-1077	221	10	n’t	not	PART
ijassa-1077	221	11	depend	depend	VERB
ijassa-1077	221	12	on	on	ADP
ijassa-1077	221	13	the	the	DET
ijassa-1077	221	14	choice	choice	NOUN
ijassa-1077	221	15	of	of	ADP
ijassa-1077	221	16	the	the	DET
ijassa-1077	221	17	fourdimensional	fourdimensional	ADJ
ijassa-1077	221	18	printing	printing	NOUN
ijassa-1077	221	19	device	device	NOUN
ijassa-1077	221	20	,	,	PUNCT
ijassa-1077	221	21	i.e.	i.e.	X
ijassa-1077	221	22	,	,	PUNCT
ijassa-1077	221	23	on	on	ADP
ijassa-1077	221	24	the	the	DET
ijassa-1077	221	25	choice	choice	NOUN
ijassa-1077	221	26	of	of	ADP
ijassa-1077	221	27	the	the	DET
ijassa-1077	221	28	corresponding	corresponding	ADJ
ijassa-1077	221	29	piecewise	piecewise	NOUN
ijassa-1077	221	30	linear	linear	NOUN
ijassa-1077	221	31	map	map	NOUN
ijassa-1077	221	32	f.	f.	PROPN
ijassa-1077	221	33	the	the	DET
ijassa-1077	221	34	union	union	PROPN
ijassa-1077	221	35	of	of	ADP
ijassa-1077	221	36	all	all	DET
ijassa-1077	221	37	these	these	DET
ijassa-1077	221	38	faces	face	NOUN
ijassa-1077	221	39	always	always	ADV
ijassa-1077	221	40	coincides	coincide	VERB
ijassa-1077	221	41	with	with	ADP
ijassa-1077	221	42	the	the	DET
ijassa-1077	221	43	boundary	boundary	ADJ
ijassa-1077	221	44	¶w4	¶w4	PROPN
ijassa-1077	221	45	of	of	ADP
ijassa-1077	221	46	the	the	DET
ijassa-1077	221	47	four	four	NUM
ijassa-1077	221	48	-	-	PUNCT
ijassa-1077	221	49	dimensional	dimensional	ADJ
ijassa-1077	221	50	colorants	colorant	NOUN
ijassa-1077	221	51	cube	cube	NOUN
ijassa-1077	221	52	,	,	PUNCT
ijassa-1077	221	53	.	.	PUNCT
ijassa-1077	222	1	on	on	ADP
ijassa-1077	222	2	the	the	DET
ijassa-1077	222	3	boundary	boundary	ADJ
ijassa-1077	222	4	¶w4	¶w4	PROPN
ijassa-1077	222	5	of	of	ADP
ijassa-1077	222	6	the	the	DET
ijassa-1077	222	7	four	four	NUM
ijassa-1077	222	8	-	-	PUNCT
ijassa-1077	222	9	dimensional	dimensional	ADJ
ijassa-1077	222	10	colorants	colorant	NOUN
ijassa-1077	222	11	cube	cube	NOUN
ijassa-1077	222	12	w4	w4	PROPN
ijassa-1077	222	13	there	there	PRON
ijassa-1077	222	14	exists	exist	VERB
ijassa-1077	222	15	the	the	DET
ijassa-1077	222	16	normal	normal	ADJ
ijassa-1077	222	17	vector	vector	NOUN
ijassa-1077	222	18	field	field	NOUN
ijassa-1077	222	19	n	n	X
ijassa-1077	222	20	to	to	ADP
ijassa-1077	222	21	this	this	DET
ijassa-1077	222	22	cube	cube	NOUN
ijassa-1077	222	23	.	.	PUNCT
ijassa-1077	223	1	let	let	VERB
ijassa-1077	223	2	dj	dj	NOUN
ijassa-1077	223	3	,	,	PUNCT
ijassa-1077	223	4	j=1,	j=1,	NOUN
ijassa-1077	223	5	…	…	PUNCT
ijassa-1077	223	6	,n	,n	NOUN
ijassa-1077	223	7	,	,	PUNCT
ijassa-1077	223	8	be	be	AUX
ijassa-1077	223	9	a	a	DET
ijassa-1077	223	10	boundary	boundary	ADJ
ijassa-1077	223	11	face	face	NOUN
ijassa-1077	223	12	of	of	ADP
ijassa-1077	223	13	the	the	DET
ijassa-1077	223	14	four	four	NUM
ijassa-1077	223	15	-	-	PUNCT
ijassa-1077	223	16	dimensional	dimensional	ADJ
ijassa-1077	223	17	colorants	colorant	NOUN
ijassa-1077	223	18	cube	cube	NOUN
ijassa-1077	223	19	w4	w4	NOUN
ijassa-1077	223	20	belonging	belong	VERB
ijassa-1077	223	21	to	to	ADP
ijassa-1077	223	22	the	the	DET
ijassa-1077	223	23	pentahedron	pentahedron	PROPN
ijassa-1077	223	24	d	d	X
ijassa-1077	223	25	j.	j.	PROPN
ijassa-1077	223	26	denote	denote	VERB
ijassa-1077	223	27	by	by	ADP
ijassa-1077	223	28	nj	nj	PROPN
ijassa-1077	224	1	the	the	DET
ijassa-1077	224	2	restriction	restriction	NOUN
ijassa-1077	224	3	of	of	ADP
ijassa-1077	224	4	the	the	DET
ijassa-1077	224	5	normal	normal	ADJ
ijassa-1077	224	6	vector	vector	NOUN
ijassa-1077	224	7	field	field	NOUN
ijassa-1077	224	8	n	n	X
ijassa-1077	224	9	to	to	ADP
ijassa-1077	224	10	this	this	DET
ijassa-1077	224	11	face	face	NOUN
ijassa-1077	224	12	:	:	PUNCT
ijassa-1077	224	13	nj	nj	PROPN
ijassa-1077	224	14	=	=	PUNCT
ijassa-1077	225	1	n½dj	n½dj	ADV
ijassa-1077	225	2	.	.	PUNCT
ijassa-1077	226	1	let	let	VERB
ijassa-1077	226	2	dk	dk	PROPN
ijassa-1077	226	3	and	and	CCONJ
ijassa-1077	226	4	dl	dl	PROPN
ijassa-1077	226	5	be	be	AUX
ijassa-1077	226	6	boundary	boundary	ADJ
ijassa-1077	226	7	faces	face	NOUN
ijassa-1077	226	8	of	of	ADP
ijassa-1077	226	9	the	the	DET
ijassa-1077	226	10	four	four	NUM
ijassa-1077	226	11	-	-	PUNCT
ijassa-1077	226	12	dimensional	dimensional	ADJ
ijassa-1077	226	13	colorants	colorant	NOUN
ijassa-1077	226	14	cube	cube	NOUN
ijassa-1077	226	15	w4	w4	NOUN
ijassa-1077	226	16	such	such	ADJ
ijassa-1077	226	17	that	that	SCONJ
ijassa-1077	226	18	dk	dk	PROPN
ijassa-1077	226	19	ì	ì	PROPN
ijassa-1077	226	20	dk	dk	PROPN
ijassa-1077	226	21	,	,	PUNCT
ijassa-1077	226	22	dl	dl	PROPN
ijassa-1077	226	23	ì	ì	X
ijassa-1077	226	24	dl	dl	PROPN
ijassa-1077	226	25	for	for	ADP
ijassa-1077	226	26	some	some	DET
ijassa-1077	226	27	pentahedrons	pentahedron	NOUN
ijassa-1077	226	28	dk	dk	PROPN
ijassa-1077	226	29	and	and	CCONJ
ijassa-1077	226	30	dl	dl	PROPN
ijassa-1077	226	31	,	,	PUNCT
ijassa-1077	226	32	k	k	PROPN
ijassa-1077	226	33	,	,	PUNCT
ijassa-1077	226	34	l=1,	l=1,	NOUN
ijassa-1077	226	35	…	…	PUNCT
ijassa-1077	226	36	,n	,n	PUNCT
ijassa-1077	226	37	.	.	PUNCT
ijassa-1077	227	1	by	by	ADP
ijassa-1077	227	2	definition	definition	NOUN
ijassa-1077	227	3	,	,	PUNCT
ijassa-1077	227	4	these	these	DET
ijassa-1077	227	5	boundary	boundary	ADJ
ijassa-1077	227	6	faces	face	NOUN
ijassa-1077	227	7	are	be	AUX
ijassa-1077	227	8	tetrahedrons	tetrahedron	NOUN
ijassa-1077	227	9	.	.	PUNCT
ijassa-1077	228	1	suppose	suppose	VERB
ijassa-1077	228	2	they	they	PRON
ijassa-1077	228	3	have	have	VERB
ijassa-1077	228	4	a	a	DET
ijassa-1077	228	5	two	two	NUM
ijassa-1077	228	6	-	-	PUNCT
ijassa-1077	228	7	dimensional	dimensional	ADJ
ijassa-1077	228	8	face	face	NOUN
ijassa-1077	228	9	,	,	PUNCT
ijassa-1077	228	10	which	which	PRON
ijassa-1077	228	11	is	be	AUX
ijassa-1077	228	12	a	a	DET
ijassa-1077	228	13	triangle	triangle	NOUN
ijassa-1077	228	14	d	d	NOUN
ijassa-1077	228	15	,	,	PUNCT
ijassa-1077	228	16	in	in	ADP
ijassa-1077	228	17	common	common	ADJ
ijassa-1077	228	18	,	,	PUNCT
ijassa-1077	228	19	d	d	PROPN
ijassa-1077	228	20	=	=	PUNCT
ijassa-1077	228	21	dk	dk	PROPN
ijassa-1077	228	22	ç	ç	X
ijassa-1077	228	23	dl	dl	PROPN
ijassa-1077	228	24	.	.	PROPN
ijassa-1077	228	25	definition	definition	NOUN
ijassa-1077	228	26	.	.	PUNCT
ijassa-1077	229	1	the	the	DET
ijassa-1077	229	2	triangle	triangle	NOUN
ijassa-1077	229	3	d	d	NOUN
ijassa-1077	229	4	is	be	AUX
ijassa-1077	229	5	called	call	VERB
ijassa-1077	229	6	a	a	DET
ijassa-1077	229	7	singular	singular	ADJ
ijassa-1077	229	8	face	face	NOUN
ijassa-1077	229	9	of	of	ADP
ijassa-1077	229	10	a	a	DET
ijassa-1077	229	11	non	non	ADJ
ijassa-1077	229	12	-	-	ADJ
ijassa-1077	229	13	degenerate	degenerate	ADJ
ijassa-1077	229	14	four	four	NUM
ijassa-1077	229	15	-	-	PUNCT
ijassa-1077	229	16	dimensional	dimensional	ADJ
ijassa-1077	229	17	printing	printing	NOUN
ijassa-1077	229	18	device	device	NOUN
ijassa-1077	229	19	that	that	PRON
ijassa-1077	229	20	is	be	AUX
ijassa-1077	229	21	defined	define	VERB
ijassa-1077	229	22	by	by	ADP
ijassa-1077	229	23	the	the	DET
ijassa-1077	229	24	piecewise	piecewise	NOUN
ijassa-1077	229	25	linear	linear	NOUN
ijassa-1077	229	26	map	map	NOUN
ijassa-1077	229	27	f	f	PROPN
ijassa-1077	229	28	if	if	SCONJ
ijassa-1077	229	29	the	the	DET
ijassa-1077	229	30	inner	inner	ADJ
ijassa-1077	229	31	products	product	NOUN
ijassa-1077	229	32	(	(	PUNCT
ijassa-1077	229	33	nk	nk	PROPN
ijassa-1077	229	34	,	,	PUNCT
ijassa-1077	229	35	ck	ck	PROPN
ijassa-1077	229	36	)	)	PUNCT
ijassa-1077	229	37	and	and	CCONJ
ijassa-1077	229	38	(	(	PUNCT
ijassa-1077	229	39	nl	nl	NOUN
ijassa-1077	229	40	,	,	PUNCT
ijassa-1077	229	41	cl	cl	NOUN
ijassa-1077	229	42	)	)	PUNCT
ijassa-1077	229	43	of	of	ADP
ijassa-1077	229	44	the	the	DET
ijassa-1077	229	45	normal	normal	ADJ
ijassa-1077	229	46	vector	vector	NOUN
ijassa-1077	229	47	field	field	NOUN
ijassa-1077	229	48	n	n	CCONJ
ijassa-1077	229	49	and	and	CCONJ
ijassa-1077	229	50	the	the	DET
ijassa-1077	229	51	characteristic	characteristic	ADJ
ijassa-1077	229	52	vector	vector	NOUN
ijassa-1077	229	53	field	field	NOUN
ijassa-1077	229	54	c	c	AUX
ijassa-1077	229	55	have	have	VERB
ijassa-1077	229	56	different	different	ADJ
ijassa-1077	229	57	signs	sign	NOUN
ijassa-1077	229	58	:	:	PUNCT
ijassa-1077	229	59	(	(	PUNCT
ijassa-1077	229	60	nk	nk	PROPN
ijassa-1077	229	61	,	,	PUNCT
ijassa-1077	229	62	ck	ck	ADJ
ijassa-1077	229	63	)	)	PUNCT
ijassa-1077	229	64	×	×	NOUN
ijassa-1077	229	65	(	(	PUNCT
ijassa-1077	229	66	nl	nl	PROPN
ijassa-1077	229	67	,	,	PUNCT
ijassa-1077	229	68	cl	cl	NOUN
ijassa-1077	229	69	)	)	PUNCT
ijassa-1077	229	70	<	<	X
ijassa-1077	229	71	0	0	X
ijassa-1077	229	72	.	.	PUNCT
ijassa-1077	229	73	denote	denote	VERB
ijassa-1077	229	74	the	the	DET
ijassa-1077	229	75	set	set	NOUN
ijassa-1077	229	76	of	of	ADP
ijassa-1077	229	77	all	all	DET
ijassa-1077	229	78	the	the	DET
ijassa-1077	229	79	singular	singular	ADJ
ijassa-1077	229	80	faces	face	NOUN
ijassa-1077	229	81	of	of	ADP
ijassa-1077	229	82	the	the	DET
ijassa-1077	229	83	given	give	VERB
ijassa-1077	229	84	four	four	NUM
ijassa-1077	229	85	-	-	PUNCT
ijassa-1077	229	86	dimensional	dimensional	ADJ
ijassa-1077	229	87	printing	printing	NOUN
ijassa-1077	229	88	device	device	NOUN
ijassa-1077	229	89	by	by	ADP
ijassa-1077	229	90	s.	s.	PROPN
ijassa-1077	229	91	remark	remark	PROPN
ijassa-1077	229	92	.	.	PUNCT
ijassa-1077	230	1	the	the	DET
ijassa-1077	230	2	set	set	NOUN
ijassa-1077	230	3	q	q	NOUN
ijassa-1077	230	4	of	of	ADP
ijassa-1077	230	5	all	all	DET
ijassa-1077	230	6	the	the	DET
ijassa-1077	230	7	boundary	boundary	ADJ
ijassa-1077	230	8	faces	face	NOUN
ijassa-1077	230	9	does	do	AUX
ijassa-1077	230	10	n’t	not	PART
ijassa-1077	230	11	depend	depend	VERB
ijassa-1077	230	12	on	on	ADP
ijassa-1077	230	13	the	the	DET
ijassa-1077	230	14	choice	choice	NOUN
ijassa-1077	230	15	of	of	ADP
ijassa-1077	230	16	a	a	DET
ijassa-1077	230	17	printing	printing	NOUN
ijassa-1077	230	18	device	device	NOUN
ijassa-1077	230	19	.	.	PUNCT
ijassa-1077	231	1	on	on	ADP
ijassa-1077	231	2	the	the	DET
ijassa-1077	231	3	contrary	contrary	NOUN
ijassa-1077	231	4	,	,	PUNCT
ijassa-1077	231	5	the	the	DET
ijassa-1077	231	6	set	set	NOUN
ijassa-1077	231	7	s	s	X
ijassa-1077	231	8	of	of	ADP
ijassa-1077	231	9	all	all	DET
ijassa-1077	231	10	the	the	DET
ijassa-1077	231	11	singular	singular	NOUN
ijassa-1077	231	12	faces	face	VERB
ijassa-1077	231	13	essentially	essentially	ADV
ijassa-1077	231	14	depends	depend	VERB
ijassa-1077	231	15	on	on	ADP
ijassa-1077	231	16	the	the	DET
ijassa-1077	231	17	choice	choice	NOUN
ijassa-1077	231	18	of	of	ADP
ijassa-1077	231	19	a	a	DET
ijassa-1077	231	20	four	four	NUM
ijassa-1077	231	21	-	-	PUNCT
ijassa-1077	231	22	dimensional	dimensional	ADJ
ijassa-1077	231	23	printing	printing	NOUN
ijassa-1077	231	24	device	device	NOUN
ijassa-1077	231	25	,	,	PUNCT
ijassa-1077	231	26	i.e.	i.e.	X
ijassa-1077	231	27	,	,	PUNCT
ijassa-1077	231	28	on	on	ADP
ijassa-1077	231	29	the	the	DET
ijassa-1077	231	30	choice	choice	NOUN
ijassa-1077	231	31	of	of	ADP
ijassa-1077	231	32	the	the	DET
ijassa-1077	231	33	corresponding	corresponding	ADJ
ijassa-1077	231	34	piecewise	piecewise	NOUN
ijassa-1077	231	35	linear	linear	NOUN
ijassa-1077	231	36	map	map	NOUN
ijassa-1077	231	37	f.	f.	PROPN
ijassa-1077	231	38	moreover	moreover	ADV
ijassa-1077	231	39	,	,	PUNCT
ijassa-1077	231	40	a	a	DET
ijassa-1077	231	41	boundary	boundary	ADJ
ijassa-1077	231	42	face	face	NOUN
ijassa-1077	231	43	is	be	AUX
ijassa-1077	231	44	a	a	DET
ijassa-1077	231	45	three	three	NUM
ijassa-1077	231	46	-	-	PUNCT
ijassa-1077	231	47	dimensional	dimensional	ADJ
ijassa-1077	231	48	simplex	simplex	NOUN
ijassa-1077	231	49	,	,	PUNCT
ijassa-1077	231	50	i.e.	i.e.	X
ijassa-1077	231	51	,	,	PUNCT
ijassa-1077	231	52	a	a	DET
ijassa-1077	231	53	tetrahedron	tetrahedron	NOUN
ijassa-1077	231	54	,	,	PUNCT
ijassa-1077	231	55	whereas	whereas	SCONJ
ijassa-1077	231	56	a	a	DET
ijassa-1077	231	57	singular	singular	ADJ
ijassa-1077	231	58	face	face	NOUN
ijassa-1077	231	59	is	be	AUX
ijassa-1077	231	60	a	a	DET
ijassa-1077	231	61	two	two	NUM
ijassa-1077	231	62	-	-	PUNCT
ijassa-1077	231	63	dimensional	dimensional	ADJ
ijassa-1077	231	64	simplex	simplex	NOUN
ijassa-1077	231	65	,	,	PUNCT
ijassa-1077	231	66	i.e.	i.e.	X
ijassa-1077	231	67	,	,	PUNCT
ijassa-1077	231	68	a	a	DET
ijassa-1077	231	69	triangle	triangle	NOUN
ijassa-1077	231	70	.	.	PUNCT
ijassa-1077	232	1	there	there	PRON
ijassa-1077	232	2	is	be	VERB
ijassa-1077	232	3	also	also	ADV
ijassa-1077	232	4	a	a	DET
ijassa-1077	232	5	serious	serious	ADJ
ijassa-1077	232	6	difference	difference	NOUN
ijassa-1077	232	7	between	between	ADP
ijassa-1077	232	8	threeand	threeand	NOUN
ijassa-1077	232	9	four	four	NUM
ijassa-1077	232	10	-	-	PUNCT
ijassa-1077	232	11	dimensional	dimensional	ADJ
ijassa-1077	232	12	cases	case	NOUN
ijassa-1077	232	13	of	of	ADP
ijassa-1077	232	14	printing	printing	NOUN
ijassa-1077	232	15	devices	device	NOUN
ijassa-1077	232	16	.	.	PUNCT
ijassa-1077	233	1	indeed	indeed	ADV
ijassa-1077	233	2	,	,	PUNCT
ijassa-1077	233	3	in	in	ADP
ijassa-1077	233	4	three	three	NUM
ijassa-1077	233	5	-	-	PUNCT
ijassa-1077	233	6	dimensional	dimensional	ADJ
ijassa-1077	233	7	case	case	NOUN
ijassa-1077	233	8	the	the	DET
ijassa-1077	233	9	boundary	boundary	ADJ
ijassa-1077	233	10	faces	face	NOUN
ijassa-1077	233	11	are	be	AUX
ijassa-1077	233	12	two	two	NUM
ijassa-1077	233	13	-	-	PUNCT
ijassa-1077	233	14	dimensional	dimensional	ADJ
ijassa-1077	233	15	and	and	CCONJ
ijassa-1077	233	16	in	in	ADP
ijassa-1077	233	17	four	four	NUM
ijassa-1077	233	18	-	-	PUNCT
ijassa-1077	233	19	dimensional	dimensional	ADJ
ijassa-1077	233	20	case	case	NOUN
ijassa-1077	233	21	–	–	PUNCT
ijassa-1077	233	22	four	four	NUM
ijassa-1077	233	23	-	-	PUNCT
ijassa-1077	233	24	dimensional	dimensional	ADJ
ijassa-1077	233	25	.	.	PUNCT
ijassa-1077	234	1	an	an	DET
ijassa-1077	234	2	other	other	ADJ
ijassa-1077	234	3	important	important	ADJ
ijassa-1077	234	4	difference	difference	NOUN
ijassa-1077	234	5	is	be	AUX
ijassa-1077	234	6	the	the	DET
ijassa-1077	234	7	following	following	NOUN
ijassa-1077	234	8	:	:	PUNCT
ijassa-1077	234	9	for	for	ADP
ijassa-1077	234	10	most	most	ADJ
ijassa-1077	234	11	three	three	NUM
ijassa-1077	234	12	-	-	PUNCT
ijassa-1077	234	13	dimensional	dimensional	ADJ
ijassa-1077	234	14	printing	printing	NOUN
ijassa-1077	234	15	devices	device	NOUN
ijassa-1077	234	16	the	the	DET
ijassa-1077	234	17	set	set	NOUN
ijassa-1077	234	18	s	s	PRON
ijassa-1077	234	19	of	of	ADP
ijassa-1077	234	20	all	all	DET
ijassa-1077	234	21	the	the	DET
ijassa-1077	234	22	singular	singular	ADJ
ijassa-1077	234	23	faces	face	VERB
ijassa-1077	234	24	is	be	AUX
ijassa-1077	234	25	empty	empty	ADJ
ijassa-1077	234	26	,	,	PUNCT
ijassa-1077	234	27	while	while	SCONJ
ijassa-1077	234	28	for	for	ADP
ijassa-1077	234	29	any	any	DET
ijassa-1077	234	30	four	four	NUM
ijassa-1077	234	31	-	-	PUNCT
ijassa-1077	234	32	dimensional	dimensional	ADJ
ijassa-1077	234	33	printing	printing	NOUN
ijassa-1077	234	34	devices	device	NOUN
ijassa-1077	234	35	the	the	DET
ijassa-1077	234	36	set	set	NOUN
ijassa-1077	234	37	s	s	PRON
ijassa-1077	234	38	of	of	ADP
ijassa-1077	234	39	all	all	DET
ijassa-1077	234	40	the	the	DET
ijassa-1077	234	41	singular	singular	ADJ
ijassa-1077	234	42	faces	face	VERB
ijassa-1077	234	43	is	be	AUX
ijassa-1077	234	44	not	not	PART
ijassa-1077	234	45	empty	empty	ADJ
ijassa-1077	234	46	.	.	PUNCT
ijassa-1077	235	1	it	it	PRON
ijassa-1077	235	2	is	be	AUX
ijassa-1077	235	3	possible	possible	ADJ
ijassa-1077	235	4	to	to	PART
ijassa-1077	235	5	describe	describe	VERB
ijassa-1077	235	6	the	the	DET
ijassa-1077	235	7	gamut	gamut	NOUN
ijassa-1077	235	8	boundary	boundary	NOUN
ijassa-1077	235	9	of	of	ADP
ijassa-1077	235	10	a	a	DET
ijassa-1077	235	11	proper	proper	ADJ
ijassa-1077	235	12	non	non	ADJ
ijassa-1077	235	13	-	-	ADJ
ijassa-1077	235	14	degenerate	degenerate	ADJ
ijassa-1077	235	15	printing	printing	NOUN
ijassa-1077	235	16	device	device	NOUN
ijassa-1077	235	17	in	in	ADP
ijassa-1077	235	18	terms	term	NOUN
ijassa-1077	235	19	of	of	ADP
ijassa-1077	235	20	singular	singular	ADJ
ijassa-1077	235	21	faces	face	VERB
ijassa-1077	235	22	only	only	ADV
ijassa-1077	235	23	.	.	PUNCT
ijassa-1077	236	1	the	the	DET
ijassa-1077	236	2	following	follow	VERB
ijassa-1077	236	3	theorem	theorem	NOUN
ijassa-1077	236	4	is	be	AUX
ijassa-1077	236	5	through	through	ADP
ijassa-1077	236	6	.	.	PUNCT
ijassa-1077	237	1	theorem	theorem	PROPN
ijassa-1077	237	2	.	.	PROPN
ijassa-1077	238	1	for	for	ADP
ijassa-1077	238	2	any	any	DET
ijassa-1077	238	3	proper	proper	ADJ
ijassa-1077	238	4	non	non	ADJ
ijassa-1077	238	5	-	-	ADJ
ijassa-1077	238	6	degenerate	degenerate	ADJ
ijassa-1077	238	7	four	four	NUM
ijassa-1077	238	8	-	-	PUNCT
ijassa-1077	238	9	dimensional	dimensional	ADJ
ijassa-1077	238	10	printing	printing	NOUN
ijassa-1077	238	11	device	device	NOUN
ijassa-1077	238	12	the	the	DET
ijassa-1077	238	13	boundary	boundary	NOUN
ijassa-1077	238	14	of	of	ADP
ijassa-1077	238	15	the	the	DET
ijassa-1077	238	16	gamut	gamut	NOUN
ijassa-1077	238	17	is	be	AUX
ijassa-1077	238	18	a	a	DET
ijassa-1077	238	19	subset	subset	NOUN
ijassa-1077	238	20	of	of	ADP
ijassa-1077	238	21	the	the	DET
ijassa-1077	238	22	images	image	NOUN
ijassa-1077	238	23	of	of	ADP
ijassa-1077	238	24	all	all	DET
ijassa-1077	238	25	the	the	DET
ijassa-1077	238	26	singular	singular	NOUN
ijassa-1077	238	27	faces	face	VERB
ijassa-1077	238	28	,	,	PUNCT
ijassa-1077	238	29	i.e.	i.e.	X
ijassa-1077	238	30	,	,	PUNCT
ijassa-1077	238	31	¶f(w4	¶f(w4	NOUN
ijassa-1077	238	32	)	)	PUNCT
ijassa-1077	238	33	í	í	NOUN
ijassa-1077	238	34	f(s	f(	NOUN
ijassa-1077	238	35	)	)	PUNCT
ijassa-1077	238	36	.	.	PUNCT
ijassa-1077	239	1	all	all	DET
ijassa-1077	239	2	the	the	DET
ijassa-1077	239	3	remarks	remark	NOUN
ijassa-1077	239	4	that	that	PRON
ijassa-1077	239	5	were	be	AUX
ijassa-1077	239	6	made	make	VERB
ijassa-1077	239	7	in	in	ADP
ijassa-1077	239	8	the	the	DET
ijassa-1077	239	9	previous	previous	ADJ
ijassa-1077	239	10	section	section	NOUN
ijassa-1077	239	11	after	after	SCONJ
ijassa-1077	239	12	the	the	DET
ijassa-1077	239	13	theorem	theorem	NOUN
ijassa-1077	239	14	about	about	ADP
ijassa-1077	239	15	the	the	DET
ijassa-1077	239	16	gamut	gamut	NOUN
ijassa-1077	239	17	boundaries	boundary	NOUN
ijassa-1077	239	18	of	of	ADP
ijassa-1077	239	19	the	the	DET
ijassa-1077	239	20	three	three	NUM
ijassa-1077	239	21	-	-	PUNCT
ijassa-1077	239	22	dimensional	dimensional	ADJ
ijassa-1077	239	23	printing	printing	NOUN
ijassa-1077	239	24	devices	device	NOUN
ijassa-1077	239	25	are	be	AUX
ijassa-1077	239	26	entirely	entirely	ADV
ijassa-1077	239	27	correct	correct	ADJ
ijassa-1077	239	28	in	in	ADP
ijassa-1077	239	29	the	the	DET
ijassa-1077	239	30	case	case	NOUN
ijassa-1077	239	31	described	describe	VERB
ijassa-1077	239	32	by	by	ADP
ijassa-1077	239	33	the	the	DET
ijassa-1077	239	34	theorem	theorem	NOUN
ijassa-1077	239	35	under	under	ADP
ijassa-1077	239	36	consideration	consideration	NOUN
ijassa-1077	239	37	.	.	PUNCT
ijassa-1077	240	1	in	in	ADP
ijassa-1077	240	2	particular	particular	ADJ
ijassa-1077	240	3	,	,	PUNCT
ijassa-1077	240	4	a	a	DET
ijassa-1077	240	5	wide	wide	ADJ
ijassa-1077	240	6	range	range	NOUN
ijassa-1077	240	7	of	of	ADP
ijassa-1077	240	8	algorithms	algorithm	NOUN
ijassa-1077	240	9	that	that	PRON
ijassa-1077	240	10	approximate	approximate	VERB
ijassa-1077	240	11	!	!	PUNCT
ijassa-1077	241	1	nj	nj	PROPN
ijassa-1077	241	2	jw	jw	PROPN
ijassa-1077	241	3	,	,	PUNCT
ijassa-1077	241	4	...	...	PUNCT
ijassa-1077	241	5	,	,	PUNCT
ijassa-1077	241	6	1	1	NUM
ijassa-1077	241	7	4	4	NUM
ijassa-1077	241	8	=	=	SYM
ijassa-1077	241	9	d=	d=	NOUN
ijassa-1077	242	1	4w¶=	4w¶=	NUM
ijassa-1077	242	2	qî	qî	INTJ
ijassa-1077	242	3	!	!	PUNCT
ijassa-1077	243	1	d	d	X
ijassa-1077	243	2	d	d	NOUN
ijassa-1077	243	3	126	126	NUM
ijassa-1077	243	4	d.v	d.v	NOUN
ijassa-1077	243	5	.	.	PUNCT
ijassa-1077	244	1	tunitsky	tunitsky	NOUN
ijassa-1077	244	2	copyright	copyright	NOUN
ijassa-1077	245	1	©	©	PROPN
ijassa-1077	245	2	2021	2021	NUM
ijassa-1077	245	3	assa	assa	NOUN
ijassa-1077	245	4	.	.	PUNCT
ijassa-1077	246	1	adv	adv	PROPN
ijassa-1077	246	2	.	.	PUNCT
ijassa-1077	247	1	in	in	ADP
ijassa-1077	247	2	systems	system	NOUN
ijassa-1077	247	3	science	science	NOUN
ijassa-1077	247	4	and	and	CCONJ
ijassa-1077	247	5	appl	appl	NOUN
ijassa-1077	247	6	.	.	PUNCT
ijassa-1077	248	1	(	(	PUNCT
ijassa-1077	248	2	2021	2021	NUM
ijassa-1077	248	3	)	)	PUNCT
ijassa-1077	248	4	the	the	DET
ijassa-1077	248	5	color	color	NOUN
ijassa-1077	248	6	gamut	gamut	NOUN
ijassa-1077	248	7	boundary	boundary	NOUN
ijassa-1077	248	8	of	of	ADP
ijassa-1077	248	9	any	any	DET
ijassa-1077	248	10	real	real	ADJ
ijassa-1077	248	11	color	color	NOUN
ijassa-1077	248	12	printing	printing	NOUN
ijassa-1077	248	13	device	device	NOUN
ijassa-1077	248	14	with	with	ADP
ijassa-1077	248	15	four	four	NUM
ijassa-1077	248	16	colorants	colorant	NOUN
ijassa-1077	248	17	can	can	AUX
ijassa-1077	248	18	be	be	AUX
ijassa-1077	248	19	designed	design	VERB
ijassa-1077	248	20	grounded	ground	VERB
ijassa-1077	248	21	on	on	ADP
ijassa-1077	248	22	it	it	PRON
ijassa-1077	248	23	.	.	PUNCT
ijassa-1077	249	1	as	as	ADP
ijassa-1077	249	2	in	in	ADP
ijassa-1077	249	3	the	the	DET
ijassa-1077	249	4	case	case	NOUN
ijassa-1077	249	5	of	of	ADP
ijassa-1077	249	6	three	three	NUM
ijassa-1077	249	7	-	-	PUNCT
ijassa-1077	249	8	dimensional	dimensional	ADJ
ijassa-1077	249	9	stimuli	stimulus	NOUN
ijassa-1077	249	10	space	space	NOUN
ijassa-1077	249	11	an	an	DET
ijassa-1077	249	12	input	input	NOUN
ijassa-1077	249	13	for	for	ADP
ijassa-1077	249	14	this	this	DET
ijassa-1077	249	15	algorithm	algorithm	NOUN
ijassa-1077	249	16	is	be	AUX
ijassa-1077	249	17	a	a	DET
ijassa-1077	249	18	file	file	NOUN
ijassa-1077	249	19	with	with	ADP
ijassa-1077	249	20	colorimetric	colorimetric	ADJ
ijassa-1077	249	21	measurements	measurement	NOUN
ijassa-1077	249	22	data	datum	NOUN
ijassa-1077	249	23	of	of	ADP
ijassa-1077	249	24	the	the	DET
ijassa-1077	249	25	printing	printing	NOUN
ijassa-1077	249	26	device	device	NOUN
ijassa-1077	249	27	under	under	ADP
ijassa-1077	249	28	consideration	consideration	NOUN
ijassa-1077	249	29	(	(	PUNCT
ijassa-1077	249	30	see	see	VERB
ijassa-1077	249	31	the	the	DET
ijassa-1077	249	32	previous	previous	ADJ
ijassa-1077	249	33	section	section	NOUN
ijassa-1077	249	34	)	)	PUNCT
ijassa-1077	249	35	.	.	PUNCT
ijassa-1077	250	1	and	and	CCONJ
ijassa-1077	250	2	as	as	ADP
ijassa-1077	250	3	an	an	DET
ijassa-1077	250	4	output	output	NOUN
ijassa-1077	250	5	this	this	DET
ijassa-1077	250	6	algorithm	algorithm	NOUN
ijassa-1077	250	7	produces	produce	VERB
ijassa-1077	250	8	piecewise	piecewise	NOUN
ijassa-1077	250	9	linear	linear	ADJ
ijassa-1077	250	10	approximation	approximation	NOUN
ijassa-1077	250	11	of	of	ADP
ijassa-1077	250	12	the	the	DET
ijassa-1077	250	13	color	color	NOUN
ijassa-1077	250	14	gamut	gamut	NOUN
ijassa-1077	250	15	boundary	boundary	NOUN
ijassa-1077	250	16	,	,	PUNCT
ijassa-1077	250	17	i.e.	i.e.	X
ijassa-1077	250	18	,	,	PUNCT
ijassa-1077	250	19	the	the	DET
ijassa-1077	250	20	corresponding	corresponding	ADJ
ijassa-1077	250	21	three	three	NUM
ijassa-1077	250	22	-	-	PUNCT
ijassa-1077	250	23	dimensional	dimensional	ADJ
ijassa-1077	250	24	body	body	NOUN
ijassa-1077	250	25	boundary	boundary	ADJ
ijassa-1077	250	26	in	in	ADP
ijassa-1077	250	27	a	a	DET
ijassa-1077	250	28	reference	reference	NOUN
ijassa-1077	250	29	space	space	NOUN
ijassa-1077	250	30	of	of	ADP
ijassa-1077	250	31	three	three	NUM
ijassa-1077	250	32	colors	color	NOUN
ijassa-1077	250	33	.	.	PUNCT
ijassa-1077	251	1	the	the	DET
ijassa-1077	251	2	following	follow	VERB
ijassa-1077	251	3	picture	picture	NOUN
ijassa-1077	251	4	gives	give	VERB
ijassa-1077	251	5	an	an	DET
ijassa-1077	251	6	example	example	NOUN
ijassa-1077	251	7	of	of	ADP
ijassa-1077	251	8	such	such	ADJ
ijassa-1077	251	9	approximation	approximation	NOUN
ijassa-1077	251	10	.	.	PUNCT
ijassa-1077	252	1	it	it	PRON
ijassa-1077	252	2	shows	show	VERB
ijassa-1077	252	3	the	the	DET
ijassa-1077	252	4	color	color	NOUN
ijassa-1077	252	5	gamut	gamut	NOUN
ijassa-1077	252	6	boundary	boundary	ADJ
ijassa-1077	252	7	in	in	ADP
ijassa-1077	252	8	reference	reference	NOUN
ijassa-1077	252	9	space	space	NOUN
ijassa-1077	252	10	of	of	ADP
ijassa-1077	252	11	a	a	DET
ijassa-1077	252	12	rather	rather	ADV
ijassa-1077	252	13	standard	standard	ADJ
ijassa-1077	252	14	printing	printing	NOUN
ijassa-1077	252	15	device	device	NOUN
ijassa-1077	252	16	with	with	ADP
ijassa-1077	252	17	four	four	NUM
ijassa-1077	252	18	colorants	colorant	NOUN
ijassa-1077	252	19	(	(	PUNCT
ijassa-1077	252	20	cyan	cyan	NOUN
ijassa-1077	252	21	,	,	PUNCT
ijassa-1077	252	22	magenta	magenta	NOUN
ijassa-1077	252	23	,	,	PUNCT
ijassa-1077	252	24	yellow	yellow	ADJ
ijassa-1077	252	25	,	,	PUNCT
ijassa-1077	252	26	and	and	CCONJ
ijassa-1077	252	27	black	black	ADJ
ijassa-1077	252	28	)	)	PUNCT
ijassa-1077	252	29	,	,	PUNCT
ijassa-1077	252	30	which	which	PRON
ijassa-1077	252	31	means	mean	VERB
ijassa-1077	252	32	that	that	SCONJ
ijassa-1077	252	33	the	the	DET
ijassa-1077	252	34	stimuli	stimulus	NOUN
ijassa-1077	252	35	space	space	NOUN
ijassa-1077	252	36	is	be	AUX
ijassa-1077	252	37	four	four	NUM
ijassa-1077	252	38	-	-	PUNCT
ijassa-1077	252	39	dimensional	dimensional	ADJ
ijassa-1077	252	40	.	.	PUNCT
ijassa-1077	253	1	to	to	PART
ijassa-1077	253	2	be	be	AUX
ijassa-1077	253	3	definite	definite	ADJ
ijassa-1077	253	4	,	,	PUNCT
ijassa-1077	253	5	call	call	VERB
ijassa-1077	253	6	the	the	DET
ijassa-1077	253	7	measurement	measurement	NOUN
ijassa-1077	253	8	file	file	NOUN
ijassa-1077	253	9	of	of	ADP
ijassa-1077	253	10	this	this	DET
ijassa-1077	253	11	device	device	NOUN
ijassa-1077	253	12	cmyk.dat	cmyk.dat	NOUN
ijassa-1077	253	13	.	.	PUNCT
ijassa-1077	254	1	in	in	ADP
ijassa-1077	254	2	reference	reference	NOUN
ijassa-1077	254	3	space	space	NOUN
ijassa-1077	254	4	the	the	DET
ijassa-1077	254	5	lab	lab	NOUN
ijassa-1077	254	6	coordinate	coordinate	NOUN
ijassa-1077	254	7	system	system	NOUN
ijassa-1077	254	8	chosen	choose	VERB
ijassa-1077	254	9	,	,	PUNCT
ijassa-1077	254	10	and	and	CCONJ
ijassa-1077	254	11	one	one	NUM
ijassa-1077	254	12	colorants	colorant	NOUN
ijassa-1077	254	13	limitation	limitation	NOUN
ijassa-1077	254	14	is	be	AUX
ijassa-1077	254	15	applied	apply	VERB
ijassa-1077	254	16	.	.	PUNCT
ijassa-1077	255	1	fig	fig	NOUN
ijassa-1077	255	2	.	.	PUNCT
ijassa-1077	256	1	3	3	X
ijassa-1077	256	2	.	.	X
ijassa-1077	257	1	the	the	DET
ijassa-1077	257	2	color	color	NOUN
ijassa-1077	257	3	gamut	gamut	NOUN
ijassa-1077	257	4	boundary	boundary	NOUN
ijassa-1077	257	5	for	for	ADP
ijassa-1077	257	6	a	a	DET
ijassa-1077	257	7	four	four	NUM
ijassa-1077	257	8	-	-	PUNCT
ijassa-1077	257	9	dimensional	dimensional	ADJ
ijassa-1077	257	10	printing	printing	NOUN
ijassa-1077	257	11	device	device	NOUN
ijassa-1077	257	12	the	the	DET
ijassa-1077	257	13	next	next	ADJ
ijassa-1077	257	14	picture	picture	NOUN
ijassa-1077	257	15	gives	give	VERB
ijassa-1077	257	16	another	another	DET
ijassa-1077	257	17	example	example	NOUN
ijassa-1077	257	18	of	of	ADP
ijassa-1077	257	19	the	the	DET
ijassa-1077	257	20	algorithm	algorithm	NOUN
ijassa-1077	257	21	output	output	NOUN
ijassa-1077	257	22	.	.	PUNCT
ijassa-1077	258	1	here	here	ADV
ijassa-1077	258	2	we	we	PRON
ijassa-1077	258	3	have	have	VERB
ijassa-1077	258	4	exactly	exactly	ADV
ijassa-1077	258	5	the	the	DET
ijassa-1077	258	6	same	same	ADJ
ijassa-1077	258	7	printing	printing	NOUN
ijassa-1077	258	8	device	device	NOUN
ijassa-1077	258	9	as	as	ADP
ijassa-1077	258	10	in	in	ADP
ijassa-1077	258	11	the	the	DET
ijassa-1077	258	12	previous	previous	ADJ
ijassa-1077	258	13	picture	picture	NOUN
ijassa-1077	258	14	,	,	PUNCT
ijassa-1077	258	15	which	which	PRON
ijassa-1077	258	16	is	be	AUX
ijassa-1077	258	17	described	describe	VERB
ijassa-1077	258	18	by	by	ADP
ijassa-1077	258	19	measurement	measurement	NOUN
ijassa-1077	258	20	data	datum	NOUN
ijassa-1077	258	21	from	from	ADP
ijassa-1077	258	22	cmyk.dat	cmyk.dat	NOUN
ijassa-1077	258	23	file	file	NOUN
ijassa-1077	258	24	,	,	PUNCT
ijassa-1077	258	25	but	but	CCONJ
ijassa-1077	258	26	the	the	DET
ijassa-1077	258	27	colorants	colorant	NOUN
ijassa-1077	258	28	limitation	limitation	NOUN
ijassa-1077	258	29	is	be	AUX
ijassa-1077	258	30	changed	change	VERB
ijassa-1077	258	31	to	to	ADP
ijassa-1077	258	32	a	a	DET
ijassa-1077	258	33	tighter	tight	ADJ
ijassa-1077	258	34	one	one	NOUN
ijassa-1077	258	35	,	,	PUNCT
ijassa-1077	258	36	namely	namely	ADV
ijassa-1077	258	37	to	to	ADP
ijassa-1077	258	38	.	.	PUNCT
ijassa-1077	259	1	the	the	DET
ijassa-1077	259	2	way	way	NOUN
ijassa-1077	259	3	of	of	ADP
ijassa-1077	259	4	rendering	rendering	NOUN
ijassa-1077	259	5	is	be	AUX
ijassa-1077	259	6	exactly	exactly	ADV
ijassa-1077	259	7	the	the	DET
ijassa-1077	259	8	same	same	ADJ
ijassa-1077	259	9	,	,	PUNCT
ijassa-1077	259	10	including	include	VERB
ijassa-1077	259	11	angle	angle	NOUN
ijassa-1077	259	12	of	of	ADP
ijassa-1077	259	13	view	view	NOUN
ijassa-1077	259	14	,	,	PUNCT
ijassa-1077	259	15	the	the	DET
ijassa-1077	259	16	scale	scale	NOUN
ijassa-1077	259	17	,	,	PUNCT
ijassa-1077	259	18	and	and	CCONJ
ijassa-1077	259	19	the	the	DET
ijassa-1077	259	20	coordinate	coordinate	NOUN
ijassa-1077	259	21	system	system	NOUN
ijassa-1077	259	22	.	.	PUNCT
ijassa-1077	260	1	250	250	NUM
ijassa-1077	260	2	4	4	NUM
ijassa-1077	260	3	1	1	NUM
ijassa-1077	260	4	£	£	SYM
ijassa-1077	260	5	å	å	NOUN
ijassa-1077	260	6	=	=	NOUN
ijassa-1077	260	7	i	i	PRON
ijassa-1077	260	8	ix	ix	ADP
ijassa-1077	260	9	150	150	NUM
ijassa-1077	260	10	4	4	NUM
ijassa-1077	260	11	1	1	NUM
ijassa-1077	260	12	£	£	SYM
ijassa-1077	260	13	å	å	NOUN
ijassa-1077	260	14	=	=	NOUN
ijassa-1077	260	15	i	i	PRON
ijassa-1077	260	16	ix	ix	PROPN
ijassa-1077	260	17	mathematical	mathematical	ADJ
ijassa-1077	260	18	modeling	modeling	NOUN
ijassa-1077	260	19	of	of	ADP
ijassa-1077	260	20	color	color	NOUN
ijassa-1077	260	21	printing	printing	NOUN
ijassa-1077	260	22	devices	device	NOUN
ijassa-1077	260	23	:	:	PUNCT
ijassa-1077	260	24	color	color	NOUN
ijassa-1077	260	25	gamut	gamut	NOUN
ijassa-1077	260	26	visualization	visualization	NOUN
ijassa-1077	260	27	…	…	PUNCT
ijassa-1077	260	28	127	127	NUM
ijassa-1077	260	29	copyright	copyright	NOUN
ijassa-1077	260	30	©	©	PROPN
ijassa-1077	260	31	2021	2021	NUM
ijassa-1077	260	32	assa	assa	NOUN
ijassa-1077	260	33	.	.	PUNCT
ijassa-1077	261	1	adv	adv	PROPN
ijassa-1077	261	2	.	.	PUNCT
ijassa-1077	262	1	in	in	ADP
ijassa-1077	262	2	systems	system	NOUN
ijassa-1077	262	3	science	science	NOUN
ijassa-1077	262	4	and	and	CCONJ
ijassa-1077	262	5	appl	appl	NOUN
ijassa-1077	262	6	.	.	PUNCT
ijassa-1077	263	1	(	(	PUNCT
ijassa-1077	263	2	2021	2021	NUM
ijassa-1077	263	3	)	)	PUNCT
ijassa-1077	263	4	fig	fig	NOUN
ijassa-1077	263	5	.	.	PUNCT
ijassa-1077	264	1	4	4	X
ijassa-1077	264	2	.	.	X
ijassa-1077	264	3	results	result	NOUN
ijassa-1077	264	4	of	of	ADP
ijassa-1077	264	5	the	the	DET
ijassa-1077	264	6	algorithm	algorithm	NOUN
ijassa-1077	264	7	for	for	ADP
ijassa-1077	264	8	the	the	DET
ijassa-1077	264	9	same	same	ADJ
ijassa-1077	264	10	printing	printing	NOUN
ijassa-1077	264	11	device	device	NOUN
ijassa-1077	264	12	with	with	ADP
ijassa-1077	264	13	tighter	tight	ADJ
ijassa-1077	264	14	colorants	colorant	NOUN
ijassa-1077	264	15	limitation	limitation	NOUN
ijassa-1077	264	16	6	6	NUM
ijassa-1077	264	17	.	.	PUNCT
ijassa-1077	264	18	three	three	NUM
ijassa-1077	264	19	-	-	PUNCT
ijassa-1077	264	20	dimensional	dimensional	ADJ
ijassa-1077	264	21	regular	regular	ADJ
ijassa-1077	264	22	printing	printing	NOUN
ijassa-1077	264	23	devices	device	NOUN
ijassa-1077	264	24	consider	consider	VERB
ijassa-1077	264	25	a	a	DET
ijassa-1077	264	26	piecewise	piecewise	NOUN
ijassa-1077	264	27	linear	linear	NOUN
ijassa-1077	264	28	model	model	NOUN
ijassa-1077	264	29	f	f	X
ijassa-1077	264	30	:	:	PUNCT
ijassa-1077	264	31	w3	w3	PROPN
ijassa-1077	264	32	®	®	NOUN
ijassa-1077	264	33	ℝ	ℝ	PROPN
ijassa-1077	264	34	#	#	NOUN
ijassa-1077	264	35	of	of	ADP
ijassa-1077	264	36	a	a	DET
ijassa-1077	264	37	three	three	NUM
ijassa-1077	264	38	-	-	PUNCT
ijassa-1077	264	39	dimensional	dimensional	ADJ
ijassa-1077	264	40	printing	printing	NOUN
ijassa-1077	264	41	device	device	NOUN
ijassa-1077	264	42	.	.	PUNCT
ijassa-1077	265	1	definition	definition	NOUN
ijassa-1077	265	2	.	.	PUNCT
ijassa-1077	266	1	the	the	DET
ijassa-1077	266	2	three	three	NUM
ijassa-1077	266	3	-	-	PUNCT
ijassa-1077	266	4	dimensional	dimensional	ADJ
ijassa-1077	266	5	printing	printing	NOUN
ijassa-1077	266	6	device	device	NOUN
ijassa-1077	266	7	is	be	AUX
ijassa-1077	266	8	called	call	VERB
ijassa-1077	266	9	regular	regular	ADJ
ijassa-1077	266	10	if	if	SCONJ
ijassa-1077	266	11	the	the	DET
ijassa-1077	266	12	piecewise	piecewise	NOUN
ijassa-1077	266	13	linear	linear	NOUN
ijassa-1077	266	14	map	map	NOUN
ijassa-1077	266	15	f	f	PROPN
ijassa-1077	266	16	is	be	AUX
ijassa-1077	266	17	an	an	DET
ijassa-1077	266	18	injection	injection	NOUN
ijassa-1077	266	19	.	.	PUNCT
ijassa-1077	267	1	lemma	lemma	PROPN
ijassa-1077	267	2	.	.	PUNCT
ijassa-1077	268	1	let	let	VERB
ijassa-1077	268	2	a	a	DET
ijassa-1077	268	3	topological	topological	ADJ
ijassa-1077	268	4	space	space	NOUN
ijassa-1077	268	5	w	w	NOUN
ijassa-1077	268	6	be	be	AUX
ijassa-1077	268	7	compact	compact	ADJ
ijassa-1077	268	8	and	and	CCONJ
ijassa-1077	268	9	a	a	DET
ijassa-1077	268	10	map	map	NOUN
ijassa-1077	269	1	f	f	X
ijassa-1077	269	2	,	,	PUNCT
ijassa-1077	269	3	f	f	X
ijassa-1077	269	4	:	:	PUNCT
ijassa-1077	269	5	w	w	PROPN
ijassa-1077	269	6	®	®	NOUN
ijassa-1077	269	7	f(w	f(w	PROPN
ijassa-1077	269	8	)	)	PUNCT
ijassa-1077	269	9	,	,	PUNCT
ijassa-1077	269	10	be	be	AUX
ijassa-1077	269	11	a	a	DET
ijassa-1077	269	12	continuous	continuous	ADJ
ijassa-1077	269	13	injection	injection	NOUN
ijassa-1077	269	14	.	.	PUNCT
ijassa-1077	270	1	then	then	ADV
ijassa-1077	270	2	there	there	PRON
ijassa-1077	270	3	exists	exist	VERB
ijassa-1077	270	4	the	the	DET
ijassa-1077	270	5	unique	unique	ADJ
ijassa-1077	270	6	continuous	continuous	ADJ
ijassa-1077	270	7	inverse	inverse	NOUN
ijassa-1077	270	8	map	map	NOUN
ijassa-1077	270	9	g	g	NOUN
ijassa-1077	270	10	=	=	SYM
ijassa-1077	270	11	f-1	f-1	NOUN
ijassa-1077	270	12	:	:	PUNCT
ijassa-1077	270	13	f(w	f(w	PROPN
ijassa-1077	270	14	)	)	PUNCT
ijassa-1077	270	15	®	®	NOUN
ijassa-1077	270	16	w.	w.	NOUN
ijassa-1077	270	17	in	in	ADP
ijassa-1077	270	18	other	other	ADJ
ijassa-1077	270	19	words	word	NOUN
ijassa-1077	270	20	,	,	PUNCT
ijassa-1077	270	21	then	then	ADV
ijassa-1077	270	22	the	the	DET
ijassa-1077	270	23	map	map	NOUN
ijassa-1077	270	24	f	f	PROPN
ijassa-1077	270	25	is	be	AUX
ijassa-1077	270	26	a	a	DET
ijassa-1077	270	27	homeomorphism	homeomorphism	NOUN
ijassa-1077	270	28	.	.	PUNCT
ijassa-1077	271	1	proof	proof	NOUN
ijassa-1077	271	2	.	.	PUNCT
ijassa-1077	272	1	see	see	VERB
ijassa-1077	272	2	[	[	X
ijassa-1077	272	3	3	3	NUM
ijassa-1077	272	4	,	,	PUNCT
ijassa-1077	272	5	ch	ch	NOUN
ijassa-1077	272	6	.	.	PROPN
ijassa-1077	272	7	2	2	NUM
ijassa-1077	272	8	,	,	PUNCT
ijassa-1077	272	9	§	§	NOUN
ijassa-1077	272	10	8	8	NUM
ijassa-1077	272	11	]	]	PUNCT
ijassa-1077	272	12	.	.	PUNCT
ijassa-1077	273	1	remark	remark	PROPN
ijassa-1077	273	2	.	.	PUNCT
ijassa-1077	274	1	since	since	SCONJ
ijassa-1077	274	2	the	the	DET
ijassa-1077	274	3	three	three	NUM
ijassa-1077	274	4	-	-	PUNCT
ijassa-1077	274	5	dimensional	dimensional	ADJ
ijassa-1077	274	6	cube	cube	NOUN
ijassa-1077	274	7	w3	w3	NOUN
ijassa-1077	274	8	is	be	AUX
ijassa-1077	274	9	a	a	DET
ijassa-1077	274	10	compact	compact	ADJ
ijassa-1077	274	11	topological	topological	ADJ
ijassa-1077	274	12	space	space	NOUN
ijassa-1077	274	13	the	the	DET
ijassa-1077	274	14	lemma	lemma	PROPN
ijassa-1077	274	15	under	under	ADP
ijassa-1077	274	16	consideration	consideration	NOUN
ijassa-1077	274	17	gives	give	VERB
ijassa-1077	274	18	a	a	DET
ijassa-1077	274	19	satisfactory	satisfactory	ADJ
ijassa-1077	274	20	approach	approach	NOUN
ijassa-1077	274	21	to	to	ADP
ijassa-1077	274	22	solution	solution	NOUN
ijassa-1077	274	23	of	of	ADP
ijassa-1077	274	24	the	the	DET
ijassa-1077	274	25	inverse	inverse	NOUN
ijassa-1077	274	26	problem	problem	NOUN
ijassa-1077	274	27	of	of	ADP
ijassa-1077	274	28	modeling	modeling	NOUN
ijassa-1077	274	29	of	of	ADP
ijassa-1077	274	30	three	three	NUM
ijassa-1077	274	31	-	-	PUNCT
ijassa-1077	274	32	dimensional	dimensional	ADJ
ijassa-1077	274	33	regular	regular	ADJ
ijassa-1077	274	34	printing	printing	NOUN
ijassa-1077	274	35	devices	device	NOUN
ijassa-1077	274	36	(	(	PUNCT
ijassa-1077	274	37	see	see	VERB
ijassa-1077	274	38	section	section	NOUN
ijassa-1077	274	39	1	1	NUM
ijassa-1077	274	40	)	)	PUNCT
ijassa-1077	274	41	.	.	PUNCT
ijassa-1077	275	1	important	important	ADJ
ijassa-1077	275	2	to	to	PART
ijassa-1077	275	3	note	note	VERB
ijassa-1077	275	4	,	,	PUNCT
ijassa-1077	275	5	that	that	SCONJ
ijassa-1077	275	6	most	most	ADJ
ijassa-1077	275	7	of	of	ADP
ijassa-1077	275	8	the	the	DET
ijassa-1077	275	9	three	three	NUM
ijassa-1077	275	10	-	-	PUNCT
ijassa-1077	275	11	dimensional	dimensional	ADJ
ijassa-1077	275	12	printing	printing	NOUN
ijassa-1077	275	13	devices	device	NOUN
ijassa-1077	275	14	are	be	AUX
ijassa-1077	275	15	regular	regular	ADJ
ijassa-1077	275	16	though	though	SCONJ
ijassa-1077	275	17	sometimes	sometimes	ADV
ijassa-1077	275	18	singular	singular	ADJ
ijassa-1077	275	19	printers	printer	NOUN
ijassa-1077	275	20	are	be	AUX
ijassa-1077	275	21	met	meet	VERB
ijassa-1077	275	22	.	.	PUNCT
ijassa-1077	276	1	128	128	NUM
ijassa-1077	276	2	d.v	d.v	NOUN
ijassa-1077	276	3	.	.	PUNCT
ijassa-1077	277	1	tunitsky	tunitsky	NOUN
ijassa-1077	277	2	copyright	copyright	NOUN
ijassa-1077	278	1	©	©	PROPN
ijassa-1077	278	2	2021	2021	NUM
ijassa-1077	278	3	assa	assa	NOUN
ijassa-1077	278	4	.	.	PUNCT
ijassa-1077	279	1	adv	adv	PROPN
ijassa-1077	279	2	.	.	PUNCT
ijassa-1077	280	1	in	in	ADP
ijassa-1077	280	2	systems	system	NOUN
ijassa-1077	280	3	science	science	NOUN
ijassa-1077	280	4	and	and	CCONJ
ijassa-1077	280	5	appl	appl	NOUN
ijassa-1077	280	6	.	.	PUNCT
ijassa-1077	281	1	(	(	PUNCT
ijassa-1077	281	2	2021	2021	NUM
ijassa-1077	281	3	)	)	PUNCT
ijassa-1077	281	4	by	by	ADP
ijassa-1077	281	5	definition	definition	NOUN
ijassa-1077	281	6	of	of	ADP
ijassa-1077	281	7	a	a	DET
ijassa-1077	281	8	piecewise	piecewise	NOUN
ijassa-1077	281	9	linear	linear	NOUN
ijassa-1077	281	10	map	map	NOUN
ijassa-1077	281	11	,	,	PUNCT
ijassa-1077	281	12	we	we	PRON
ijassa-1077	281	13	have	have	VERB
ijassa-1077	281	14	the	the	DET
ijassa-1077	281	15	simplex	simplex	NOUN
ijassa-1077	281	16	decomposition	decomposition	NOUN
ijassa-1077	281	17	of	of	ADP
ijassa-1077	281	18	the	the	DET
ijassa-1077	281	19	threedimensional	threedimensional	ADJ
ijassa-1077	281	20	colorants	colorant	NOUN
ijassa-1077	281	21	cube	cube	PROPN
ijassa-1077	281	22	w3	w3	PROPN
ijassa-1077	281	23	into	into	ADP
ijassa-1077	281	24	the	the	DET
ijassa-1077	281	25	set	set	NOUN
ijassa-1077	281	26	of	of	ADP
ijassa-1077	281	27	n	n	CCONJ
ijassa-1077	281	28	,	,	PUNCT
ijassa-1077	281	29	n>0	n>0	PROPN
ijassa-1077	281	30	,	,	PUNCT
ijassa-1077	281	31	tetrahedrons	tetrahedron	NOUN
ijassa-1077	281	32	dj	dj	NOUN
ijassa-1077	281	33	,	,	PUNCT
ijassa-1077	281	34	,	,	PUNCT
ijassa-1077	281	35	such	such	ADJ
ijassa-1077	281	36	that	that	SCONJ
ijassa-1077	281	37	all	all	DET
ijassa-1077	281	38	the	the	DET
ijassa-1077	281	39	restrictions	restriction	NOUN
ijassa-1077	281	40	f½dj	f½dj	ADV
ijassa-1077	281	41	:	:	PUNCT
ijassa-1077	281	42	dj	dj	X
ijassa-1077	281	43	®	®	NOUN
ijassa-1077	281	44	ℝ	ℝ	NOUN
ijassa-1077	281	45	#	#	NOUN
ijassa-1077	281	46	,	,	PUNCT
ijassa-1077	281	47	of	of	ADP
ijassa-1077	281	48	the	the	DET
ijassa-1077	281	49	map	map	NOUN
ijassa-1077	281	50	f	f	X
ijassa-1077	281	51	to	to	ADP
ijassa-1077	281	52	tetrahedrons	tetrahedron	NOUN
ijassa-1077	281	53	dj	dj	NOUN
ijassa-1077	281	54	are	be	AUX
ijassa-1077	281	55	linear	linear	ADJ
ijassa-1077	281	56	maps	map	NOUN
ijassa-1077	281	57	,	,	PUNCT
ijassa-1077	281	58	i.e.	i.e.	X
ijassa-1077	281	59	,	,	PUNCT
ijassa-1077	281	60	f½dj	f½dj	PROPN
ijassa-1077	281	61	(	(	PUNCT
ijassa-1077	281	62	x	x	X
ijassa-1077	281	63	)	)	PUNCT
ijassa-1077	282	1	=	=	SYM
ijassa-1077	282	2	cj	cj	NOUN
ijassa-1077	283	1	+	+	CCONJ
ijassa-1077	283	2	bjx	bjx	ADV
ijassa-1077	283	3	,	,	PUNCT
ijassa-1077	283	4	where	where	SCONJ
ijassa-1077	283	5	bj	bj	NOUN
ijassa-1077	283	6	is	be	AUX
ijassa-1077	283	7	a	a	DET
ijassa-1077	283	8	3´3	3´3	NUM
ijassa-1077	283	9	matrix	matrix	NOUN
ijassa-1077	283	10	,	,	PUNCT
ijassa-1077	283	11	and	and	CCONJ
ijassa-1077	283	12	x	x	X
ijassa-1077	283	13	,	,	PUNCT
ijassa-1077	283	14	cj	cj	PROPN
ijassa-1077	283	15	are	be	AUX
ijassa-1077	283	16	three	three	NUM
ijassa-1077	283	17	-	-	PUNCT
ijassa-1077	283	18	dimensional	dimensional	ADJ
ijassa-1077	283	19	vectors	vector	NOUN
ijassa-1077	283	20	for	for	ADP
ijassa-1077	283	21	j=1	j=1	PROPN
ijassa-1077	283	22	,	,	PUNCT
ijassa-1077	283	23	…	…	NUM
ijassa-1077	283	24	,	,	PUNCT
ijassa-1077	283	25	n.	n.	NOUN
ijassa-1077	283	26	definition	definition	NOUN
ijassa-1077	283	27	.	.	PUNCT
ijassa-1077	284	1	a	a	DET
ijassa-1077	284	2	three	three	NUM
ijassa-1077	284	3	-	-	PUNCT
ijassa-1077	284	4	dimensional	dimensional	ADJ
ijassa-1077	284	5	printing	printing	NOUN
ijassa-1077	284	6	device	device	NOUN
ijassa-1077	284	7	is	be	AUX
ijassa-1077	284	8	called	call	VERB
ijassa-1077	284	9	strictly	strictly	ADV
ijassa-1077	284	10	non	non	ADJ
ijassa-1077	284	11	-	-	ADJ
ijassa-1077	284	12	degenerate	degenerate	ADJ
ijassa-1077	284	13	if	if	SCONJ
ijassa-1077	284	14	all	all	DET
ijassa-1077	284	15	the	the	DET
ijassa-1077	284	16	determinates	determinate	NOUN
ijassa-1077	284	17	of	of	ADP
ijassa-1077	284	18	the	the	DET
ijassa-1077	284	19	matrixes	matrix	NOUN
ijassa-1077	284	20	bj	bj	VERB
ijassa-1077	284	21	are	be	AUX
ijassa-1077	284	22	of	of	ADP
ijassa-1077	284	23	the	the	DET
ijassa-1077	284	24	same	same	ADJ
ijassa-1077	284	25	sign	sign	NOUN
ijassa-1077	284	26	,	,	PUNCT
ijassa-1077	284	27	i.e.	i.e.	X
ijassa-1077	284	28	,	,	PUNCT
ijassa-1077	284	29	det	det	NOUN
ijassa-1077	284	30	bj	bj	ADP
ijassa-1077	284	31	×	×	PROPN
ijassa-1077	284	32	det	det	NOUN
ijassa-1077	284	33	bj	bj	ADP
ijassa-1077	284	34	>	>	X
ijassa-1077	284	35	0	0	PUNCT
ijassa-1077	285	1	for	for	ADP
ijassa-1077	285	2	all	all	DET
ijassa-1077	285	3	the	the	DET
ijassa-1077	285	4	indexes	index	NOUN
ijassa-1077	285	5	i	i	PRON
ijassa-1077	285	6	,	,	PUNCT
ijassa-1077	285	7	j=1,	j=1,	NOUN
ijassa-1077	285	8	…	…	SYM
ijassa-1077	285	9	,n	,n	SYM
ijassa-1077	285	10	.	.	PUNCT
ijassa-1077	285	11	remark	remark	PROPN
ijassa-1077	285	12	.	.	PUNCT
ijassa-1077	286	1	by	by	ADP
ijassa-1077	286	2	definition	definition	NOUN
ijassa-1077	286	3	of	of	ADP
ijassa-1077	286	4	a	a	DET
ijassa-1077	286	5	singular	singular	ADJ
ijassa-1077	286	6	face	face	NOUN
ijassa-1077	286	7	(	(	PUNCT
ijassa-1077	286	8	see	see	VERB
ijassa-1077	286	9	section	section	NOUN
ijassa-1077	286	10	4	4	NUM
ijassa-1077	286	11	)	)	PUNCT
ijassa-1077	286	12	,	,	PUNCT
ijassa-1077	286	13	a	a	DET
ijassa-1077	286	14	three	three	NUM
ijassa-1077	286	15	-	-	PUNCT
ijassa-1077	286	16	dimensional	dimensional	ADJ
ijassa-1077	286	17	printing	printing	NOUN
ijassa-1077	286	18	device	device	NOUN
ijassa-1077	286	19	is	be	AUX
ijassa-1077	286	20	strongly	strongly	ADV
ijassa-1077	286	21	non	non	ADJ
ijassa-1077	286	22	-	-	ADJ
ijassa-1077	286	23	degenerate	degenerate	ADJ
ijassa-1077	286	24	if	if	SCONJ
ijassa-1077	287	1	and	and	CCONJ
ijassa-1077	287	2	only	only	ADV
ijassa-1077	287	3	if	if	SCONJ
ijassa-1077	287	4	the	the	DET
ijassa-1077	287	5	set	set	NOUN
ijassa-1077	287	6	s	s	X
ijassa-1077	287	7	of	of	ADP
ijassa-1077	287	8	all	all	PRON
ijassa-1077	287	9	its	its	PRON
ijassa-1077	287	10	singular	singular	ADJ
ijassa-1077	287	11	faces	face	NOUN
ijassa-1077	287	12	is	be	AUX
ijassa-1077	287	13	empty	empty	ADJ
ijassa-1077	287	14	,	,	PUNCT
ijassa-1077	287	15	s	s	NOUN
ijassa-1077	287	16	=	=	SYM
ijassa-1077	287	17	æ	æ	PROPN
ijassa-1077	287	18	.	.	PUNCT
ijassa-1077	288	1	any	any	DET
ijassa-1077	288	2	three	three	NUM
ijassa-1077	288	3	-	-	PUNCT
ijassa-1077	288	4	dimensional	dimensional	ADJ
ijassa-1077	288	5	strongly	strongly	ADV
ijassa-1077	288	6	non	non	ADJ
ijassa-1077	288	7	-	-	ADJ
ijassa-1077	288	8	degenerate	degenerate	ADJ
ijassa-1077	288	9	printing	printing	NOUN
ijassa-1077	288	10	device	device	NOUN
ijassa-1077	288	11	is	be	AUX
ijassa-1077	288	12	non	non	ADJ
ijassa-1077	288	13	-	-	ADJ
ijassa-1077	288	14	degenerate	degenerate	ADJ
ijassa-1077	288	15	.	.	PUNCT
ijassa-1077	289	1	the	the	DET
ijassa-1077	289	2	inverse	inverse	ADJ
ijassa-1077	289	3	statement	statement	NOUN
ijassa-1077	289	4	is	be	AUX
ijassa-1077	289	5	false	false	ADJ
ijassa-1077	289	6	because	because	SCONJ
ijassa-1077	289	7	there	there	PRON
ijassa-1077	289	8	exist	exist	VERB
ijassa-1077	289	9	three	three	NUM
ijassa-1077	289	10	-	-	PUNCT
ijassa-1077	289	11	dimensional	dimensional	ADJ
ijassa-1077	289	12	non	non	ADJ
ijassa-1077	289	13	-	-	ADJ
ijassa-1077	289	14	degenerate	degenerate	ADJ
ijassa-1077	289	15	printing	printing	NOUN
ijassa-1077	289	16	devices	device	NOUN
ijassa-1077	289	17	that	that	PRON
ijassa-1077	289	18	are	be	AUX
ijassa-1077	289	19	not	not	PART
ijassa-1077	289	20	strongly	strongly	ADV
ijassa-1077	289	21	non	non	ADJ
ijassa-1077	289	22	-	-	ADJ
ijassa-1077	289	23	degenerate	degenerate	ADJ
ijassa-1077	289	24	.	.	PUNCT
ijassa-1077	290	1	there	there	PRON
ijassa-1077	290	2	is	be	VERB
ijassa-1077	290	3	an	an	DET
ijassa-1077	290	4	effective	effective	ADJ
ijassa-1077	290	5	criterion	criterion	NOUN
ijassa-1077	290	6	of	of	ADP
ijassa-1077	290	7	a	a	DET
ijassa-1077	290	8	three	three	NUM
ijassa-1077	290	9	-	-	PUNCT
ijassa-1077	290	10	dimensional	dimensional	ADJ
ijassa-1077	290	11	printing	printing	NOUN
ijassa-1077	290	12	device	device	NOUN
ijassa-1077	290	13	to	to	PART
ijassa-1077	290	14	be	be	AUX
ijassa-1077	290	15	regular	regular	ADJ
ijassa-1077	290	16	.	.	PUNCT
ijassa-1077	291	1	theorem	theorem	VERB
ijassa-1077	291	2	.	.	PUNCT
ijassa-1077	292	1	let	let	VERB
ijassa-1077	292	2	f	f	X
ijassa-1077	292	3	:	:	PUNCT
ijassa-1077	292	4	w3	w3	PROPN
ijassa-1077	292	5	®	®	NOUN
ijassa-1077	292	6	ℝ	ℝ	PROPN
ijassa-1077	292	7	#	#	NOUN
ijassa-1077	292	8	be	be	VERB
ijassa-1077	292	9	a	a	DET
ijassa-1077	292	10	piecewise	piecewise	NOUN
ijassa-1077	292	11	linear	linear	NOUN
ijassa-1077	292	12	model	model	NOUN
ijassa-1077	292	13	of	of	ADP
ijassa-1077	292	14	a	a	DET
ijassa-1077	292	15	three	three	NUM
ijassa-1077	292	16	-	-	PUNCT
ijassa-1077	292	17	dimensional	dimensional	ADJ
ijassa-1077	292	18	printing	printing	NOUN
ijassa-1077	292	19	device	device	NOUN
ijassa-1077	292	20	.	.	PUNCT
ijassa-1077	293	1	this	this	DET
ijassa-1077	293	2	printing	printing	NOUN
ijassa-1077	293	3	device	device	NOUN
ijassa-1077	293	4	is	be	AUX
ijassa-1077	293	5	regular	regular	ADJ
ijassa-1077	293	6	if	if	SCONJ
ijassa-1077	293	7	and	and	CCONJ
ijassa-1077	293	8	only	only	ADV
ijassa-1077	293	9	if	if	SCONJ
ijassa-1077	293	10	it	it	PRON
ijassa-1077	293	11	is	be	AUX
ijassa-1077	293	12	strongly	strongly	ADV
ijassa-1077	293	13	non	non	ADJ
ijassa-1077	293	14	-	-	ADJ
ijassa-1077	293	15	degenerate	degenerate	ADJ
ijassa-1077	293	16	and	and	CCONJ
ijassa-1077	293	17	the	the	DET
ijassa-1077	293	18	restriction	restriction	NOUN
ijassa-1077	293	19	f½¶w3	f½¶w3	NUM
ijassa-1077	293	20	:	:	PUNCT
ijassa-1077	293	21	¶w3	¶w3	PROPN
ijassa-1077	293	22	®	®	VERB
ijassa-1077	293	23	ℝ	ℝ	NOUN
ijassa-1077	293	24	#	#	NOUN
ijassa-1077	293	25	of	of	ADP
ijassa-1077	293	26	the	the	DET
ijassa-1077	293	27	map	map	NOUN
ijassa-1077	293	28	f	f	X
ijassa-1077	293	29	to	to	ADP
ijassa-1077	293	30	the	the	DET
ijassa-1077	293	31	boundary	boundary	ADJ
ijassa-1077	293	32	¶w3	¶w3	PROPN
ijassa-1077	293	33	of	of	ADP
ijassa-1077	293	34	the	the	DET
ijassa-1077	293	35	three	three	NUM
ijassa-1077	293	36	-	-	PUNCT
ijassa-1077	293	37	dimensional	dimensional	ADJ
ijassa-1077	293	38	colorants	colorant	NOUN
ijassa-1077	293	39	cube	cube	NOUN
ijassa-1077	293	40	w3	w3	PROPN
ijassa-1077	293	41	is	be	AUX
ijassa-1077	293	42	an	an	DET
ijassa-1077	293	43	injection	injection	NOUN
ijassa-1077	293	44	.	.	PUNCT
ijassa-1077	294	1	by	by	ADP
ijassa-1077	294	2	this	this	DET
ijassa-1077	294	3	theorem	theorem	NOUN
ijassa-1077	294	4	,	,	PUNCT
ijassa-1077	294	5	the	the	DET
ijassa-1077	294	6	necessary	necessary	ADJ
ijassa-1077	294	7	condition	condition	NOUN
ijassa-1077	294	8	of	of	ADP
ijassa-1077	294	9	a	a	DET
ijassa-1077	294	10	three	three	NUM
ijassa-1077	294	11	-	-	PUNCT
ijassa-1077	294	12	dimensional	dimensional	ADJ
ijassa-1077	294	13	printing	printing	NOUN
ijassa-1077	294	14	device	device	NOUN
ijassa-1077	294	15	to	to	PART
ijassa-1077	294	16	be	be	AUX
ijassa-1077	294	17	regular	regular	ADJ
ijassa-1077	294	18	is	be	AUX
ijassa-1077	294	19	its	its	PRON
ijassa-1077	294	20	strong	strong	ADJ
ijassa-1077	294	21	non	non	NOUN
ijassa-1077	294	22	-	-	NOUN
ijassa-1077	294	23	degeneracy	degeneracy	NOUN
ijassa-1077	294	24	.	.	PUNCT
ijassa-1077	295	1	by	by	ADP
ijassa-1077	295	2	definition	definition	NOUN
ijassa-1077	295	3	,	,	PUNCT
ijassa-1077	295	4	it	it	PRON
ijassa-1077	295	5	means	mean	VERB
ijassa-1077	295	6	that	that	SCONJ
ijassa-1077	295	7	all	all	DET
ijassa-1077	295	8	the	the	DET
ijassa-1077	295	9	determinates	determinate	NOUN
ijassa-1077	295	10	of	of	ADP
ijassa-1077	295	11	the	the	DET
ijassa-1077	295	12	matrixes	matrix	NOUN
ijassa-1077	295	13	bj	bj	NOUN
ijassa-1077	295	14	of	of	ADP
ijassa-1077	295	15	the	the	DET
ijassa-1077	295	16	piecewise	piecewise	NOUN
ijassa-1077	295	17	linear	linear	NOUN
ijassa-1077	295	18	map	map	NOUN
ijassa-1077	295	19	f	f	PROPN
ijassa-1077	295	20	have	have	VERB
ijassa-1077	295	21	the	the	DET
ijassa-1077	295	22	same	same	ADJ
ijassa-1077	295	23	sign	sign	NOUN
ijassa-1077	295	24	.	.	PUNCT
ijassa-1077	296	1	describe	describe	VERB
ijassa-1077	296	2	the	the	DET
ijassa-1077	296	3	scheme	scheme	NOUN
ijassa-1077	296	4	of	of	ADP
ijassa-1077	296	5	an	an	DET
ijassa-1077	296	6	algorithmic	algorithmic	ADJ
ijassa-1077	296	7	approach	approach	NOUN
ijassa-1077	296	8	to	to	ADP
ijassa-1077	296	9	forcing	force	VERB
ijassa-1077	296	10	a	a	DET
ijassa-1077	296	11	three	three	NUM
ijassa-1077	296	12	-	-	PUNCT
ijassa-1077	296	13	dimensional	dimensional	ADJ
ijassa-1077	296	14	printing	printing	NOUN
ijassa-1077	296	15	device	device	NOUN
ijassa-1077	296	16	to	to	PART
ijassa-1077	296	17	become	become	VERB
ijassa-1077	296	18	strictly	strictly	ADV
ijassa-1077	296	19	nondegenerate	nondegenerate	ADJ
ijassa-1077	296	20	.	.	PUNCT
ijassa-1077	297	1	at	at	ADP
ijassa-1077	297	2	the	the	DET
ijassa-1077	297	3	first	first	ADJ
ijassa-1077	297	4	step	step	NOUN
ijassa-1077	297	5	count	count	VERB
ijassa-1077	297	6	the	the	DET
ijassa-1077	297	7	number	number	NOUN
ijassa-1077	297	8	n+	n+	NUM
ijassa-1077	297	9	of	of	ADP
ijassa-1077	297	10	positive	positive	ADJ
ijassa-1077	297	11	determinants	determinant	NOUN
ijassa-1077	297	12	and	and	CCONJ
ijassa-1077	297	13	the	the	DET
ijassa-1077	297	14	number	number	NOUN
ijassa-1077	297	15	nof	nof	NOUN
ijassa-1077	297	16	negative	negative	ADJ
ijassa-1077	297	17	determinants	determinant	NOUN
ijassa-1077	297	18	.	.	PUNCT
ijassa-1077	298	1	for	for	ADP
ijassa-1077	298	2	clarity	clarity	NOUN
ijassa-1077	298	3	,	,	PUNCT
ijassa-1077	298	4	assume	assume	VERB
ijassa-1077	298	5	that	that	SCONJ
ijassa-1077	298	6	n+	n+	ADP
ijassa-1077	298	7	>	>	X
ijassa-1077	298	8	n-	n-	X
ijassa-1077	298	9	.	.	PUNCT
ijassa-1077	299	1	at	at	ADP
ijassa-1077	299	2	the	the	DET
ijassa-1077	299	3	second	second	ADJ
ijassa-1077	299	4	step	step	NOUN
ijassa-1077	299	5	define	define	VERB
ijassa-1077	299	6	a	a	DET
ijassa-1077	299	7	positive	positive	ADJ
ijassa-1077	299	8	threshold	threshold	NOUN
ijassa-1077	299	9	e	e	NOUN
ijassa-1077	299	10	,	,	PUNCT
ijassa-1077	299	11	e	e	X
ijassa-1077	299	12	>	>	X
ijassa-1077	299	13	0	0	PROPN
ijassa-1077	299	14	,	,	PUNCT
ijassa-1077	299	15	which	which	PRON
ijassa-1077	299	16	is	be	AUX
ijassa-1077	299	17	usually	usually	ADV
ijassa-1077	299	18	a	a	DET
ijassa-1077	299	19	small	small	ADJ
ijassa-1077	299	20	real	real	ADJ
ijassa-1077	299	21	number	number	NOUN
ijassa-1077	299	22	,	,	PUNCT
ijassa-1077	299	23	and	and	CCONJ
ijassa-1077	299	24	construct	construct	VERB
ijassa-1077	299	25	the	the	DET
ijassa-1077	299	26	error	error	NOUN
ijassa-1077	299	27	functional	functional	ADJ
ijassa-1077	299	28	r	r	NOUN
ijassa-1077	299	29	,	,	PUNCT
ijassa-1077	299	30	,	,	PUNCT
ijassa-1077	299	31	where	where	SCONJ
ijassa-1077	299	32	rj	rj	PROPN
ijassa-1077	299	33	=	=	PUNCT
ijassa-1077	299	34	rj(p1	rj(p1	NOUN
ijassa-1077	299	35	,	,	PUNCT
ijassa-1077	299	36	…	…	PUNCT
ijassa-1077	299	37	,	,	PUNCT
ijassa-1077	299	38	pm	pm	NOUN
ijassa-1077	299	39	)	)	PUNCT
ijassa-1077	299	40	=	=	SYM
ijassa-1077	299	41	0	0	PUNCT
ijassa-1077	300	1	if	if	SCONJ
ijassa-1077	300	2	det	det	NOUN
ijassa-1077	300	3	bj	bj	VERB
ijassa-1077	300	4	≥	≥	NOUN
ijassa-1077	300	5	e	e	NOUN
ijassa-1077	300	6	,	,	PUNCT
ijassa-1077	300	7	and	and	CCONJ
ijassa-1077	300	8	rj	rj	PROPN
ijassa-1077	300	9	=	=	PUNCT
ijassa-1077	300	10	rj(p1	rj(p1	NOUN
ijassa-1077	300	11	,	,	PUNCT
ijassa-1077	300	12	…	…	PUNCT
ijassa-1077	300	13	,	,	PUNCT
ijassa-1077	300	14	pm	pm	NOUN
ijassa-1077	300	15	)	)	PUNCT
ijassa-1077	300	16	=	=	SYM
ijassa-1077	300	17	(	(	PUNCT
ijassa-1077	300	18	e	e	X
ijassa-1077	300	19	det	det	PROPN
ijassa-1077	300	20	bj)2	bj)2	VERB
ijassa-1077	300	21	if	if	SCONJ
ijassa-1077	300	22	det	det	NOUN
ijassa-1077	300	23	bj	bj	VERB
ijassa-1077	300	24	<	<	X
ijassa-1077	300	25	e	e	NOUN
ijassa-1077	300	26	,	,	PUNCT
ijassa-1077	300	27	j=1	j=1	NOUN
ijassa-1077	300	28	,	,	PUNCT
ijassa-1077	300	29	…	…	PUNCT
ijassa-1077	300	30	,	,	PUNCT
ijassa-1077	300	31	n.	n.	PROPN
ijassa-1077	300	32	here	here	ADV
ijassa-1077	300	33	p1	p1	PROPN
ijassa-1077	300	34	,	,	PUNCT
ijassa-1077	300	35	…	…	PUNCT
ijassa-1077	300	36	,	,	PUNCT
ijassa-1077	300	37	pm	pm	NOUN
ijassa-1077	300	38	are	be	AUX
ijassa-1077	300	39	the	the	DET
ijassa-1077	300	40	three	three	NUM
ijassa-1077	300	41	-	-	PUNCT
ijassa-1077	300	42	dimensional	dimensional	ADJ
ijassa-1077	300	43	vectors	vector	NOUN
ijassa-1077	300	44	in	in	ADP
ijassa-1077	300	45	color	color	NOUN
ijassa-1077	300	46	space	space	NOUN
ijassa-1077	300	47	,	,	PUNCT
ijassa-1077	300	48	forming	form	VERB
ijassa-1077	300	49	the	the	DET
ijassa-1077	300	50	measurement	measurement	NOUN
ijassa-1077	300	51	data	datum	NOUN
ijassa-1077	300	52	of	of	ADP
ijassa-1077	300	53	the	the	DET
ijassa-1077	300	54	three	three	NUM
ijassa-1077	300	55	-	-	PUNCT
ijassa-1077	300	56	dimensional	dimensional	ADJ
ijassa-1077	300	57	printing	printing	NOUN
ijassa-1077	300	58	device	device	NOUN
ijassa-1077	300	59	under	under	ADP
ijassa-1077	300	60	consideration	consideration	NOUN
ijassa-1077	300	61	(	(	PUNCT
ijassa-1077	300	62	see	see	VERB
ijassa-1077	300	63	section	section	NOUN
ijassa-1077	300	64	1	1	NUM
ijassa-1077	300	65	)	)	PUNCT
ijassa-1077	300	66	.	.	PUNCT
ijassa-1077	301	1	by	by	ADP
ijassa-1077	301	2	construction	construction	NOUN
ijassa-1077	301	3	of	of	ADP
ijassa-1077	301	4	the	the	DET
ijassa-1077	301	5	direct	direct	ADJ
ijassa-1077	301	6	problem	problem	NOUN
ijassa-1077	301	7	solution	solution	NOUN
ijassa-1077	301	8	,	,	PUNCT
ijassa-1077	301	9	all	all	DET
ijassa-1077	301	10	the	the	DET
ijassa-1077	301	11	determinants	determinant	NOUN
ijassa-1077	301	12	det	det	NOUN
ijassa-1077	301	13	bj	bj	NOUN
ijassa-1077	301	14	of	of	ADP
ijassa-1077	301	15	the	the	DET
ijassa-1077	301	16	piecewise	piecewise	NOUN
ijassa-1077	301	17	linear	linear	NOUN
ijassa-1077	301	18	map	map	NOUN
ijassa-1077	301	19	f	f	PROPN
ijassa-1077	301	20	are	be	AUX
ijassa-1077	301	21	third	third	ADJ
ijassa-1077	301	22	order	order	NOUN
ijassa-1077	301	23	polynomials	polynomial	NOUN
ijassa-1077	301	24	with	with	ADP
ijassa-1077	301	25	respect	respect	NOUN
ijassa-1077	301	26	to	to	ADP
ijassa-1077	301	27	measurement	measurement	NOUN
ijassa-1077	301	28	data	datum	NOUN
ijassa-1077	301	29	p1	p1	PROPN
ijassa-1077	301	30	,	,	PUNCT
ijassa-1077	301	31	…	…	PUNCT
ijassa-1077	301	32	,	,	PUNCT
ijassa-1077	301	33	pm	pm	NOUN
ijassa-1077	301	34	for	for	ADP
ijassa-1077	301	35	j=1,	j=1,	NOUN
ijassa-1077	301	36	…	…	PUNCT
ijassa-1077	301	37	,n	,n	PUNCT
ijassa-1077	301	38	(	(	PUNCT
ijassa-1077	301	39	see	see	VERB
ijassa-1077	301	40	section	section	NOUN
ijassa-1077	301	41	2	2	NUM
ijassa-1077	301	42	)	)	PUNCT
ijassa-1077	301	43	.	.	PUNCT
ijassa-1077	302	1	hence	hence	ADV
ijassa-1077	302	2	,	,	PUNCT
ijassa-1077	302	3	all	all	DET
ijassa-1077	302	4	the	the	DET
ijassa-1077	302	5	functions	function	NOUN
ijassa-1077	302	6	rj	rj	PROPN
ijassa-1077	302	7	are	be	AUX
ijassa-1077	302	8	smooth	smooth	ADJ
ijassa-1077	302	9	for	for	ADP
ijassa-1077	302	10	j=1,	j=1,	NOUN
ijassa-1077	302	11	…	…	PUNCT
ijassa-1077	302	12	,n	,n	PUNCT
ijassa-1077	302	13	and	and	CCONJ
ijassa-1077	302	14	the	the	DET
ijassa-1077	302	15	error	error	NOUN
ijassa-1077	302	16	functional	functional	ADJ
ijassa-1077	302	17	r	r	NOUN
ijassa-1077	302	18	=	=	NOUN
ijassa-1077	302	19	r(p1	r(p1	NOUN
ijassa-1077	302	20	,	,	PUNCT
ijassa-1077	302	21	…	…	PUNCT
ijassa-1077	302	22	,	,	PUNCT
ijassa-1077	302	23	pm	pm	NOUN
ijassa-1077	302	24	)	)	PUNCT
ijassa-1077	302	25	is	be	AUX
ijassa-1077	302	26	smooth	smooth	ADJ
ijassa-1077	302	27	with	with	ADP
ijassa-1077	302	28	respect	respect	NOUN
ijassa-1077	302	29	to	to	ADP
ijassa-1077	302	30	measurement	measurement	NOUN
ijassa-1077	302	31	data	datum	NOUN
ijassa-1077	302	32	p1,	p1,	ADJ
ijassa-1077	302	33	…	…	PUNCT
ijassa-1077	302	34	,pm	,pm	PUNCT
ijassa-1077	302	35	too	too	ADV
ijassa-1077	302	36	.	.	PUNCT
ijassa-1077	303	1	at	at	ADP
ijassa-1077	303	2	the	the	DET
ijassa-1077	303	3	third	third	ADJ
ijassa-1077	303	4	step	step	NOUN
ijassa-1077	303	5	minimize	minimize	VERB
ijassa-1077	303	6	the	the	DET
ijassa-1077	303	7	error	error	NOUN
ijassa-1077	303	8	functional	functional	ADJ
ijassa-1077	303	9	r	r	NOUN
ijassa-1077	303	10	with	with	ADP
ijassa-1077	303	11	respect	respect	NOUN
ijassa-1077	303	12	to	to	ADP
ijassa-1077	303	13	measurement	measurement	NOUN
ijassa-1077	303	14	data	datum	NOUN
ijassa-1077	303	15	p1,	p1,	ADP
ijassa-1077	303	16	…	…	PUNCT
ijassa-1077	303	17	,pm	,pm	PUNCT
ijassa-1077	303	18	,	,	PUNCT
ijassa-1077	303	19	i.e.	i.e.	X
ijassa-1077	303	20	,	,	PUNCT
ijassa-1077	303	21	r(p1	r(p1	NOUN
ijassa-1077	303	22	,	,	PUNCT
ijassa-1077	303	23	…	…	PUNCT
ijassa-1077	303	24	,	,	PUNCT
ijassa-1077	303	25	pm	pm	NOUN
ijassa-1077	303	26	)	)	PUNCT
ijassa-1077	303	27	®	®	NOUN
ijassa-1077	303	28	min	min	NOUN
ijassa-1077	303	29	,	,	PUNCT
ijassa-1077	303	30	by	by	ADP
ijassa-1077	303	31	some	some	DET
ijassa-1077	303	32	minimization	minimization	NOUN
ijassa-1077	303	33	method	method	NOUN
ijassa-1077	303	34	.	.	PUNCT
ijassa-1077	304	1	the	the	DET
ijassa-1077	304	2	resulting	result	VERB
ijassa-1077	304	3	argument	argument	NOUN
ijassa-1077	304	4	(	(	PUNCT
ijassa-1077	304	5	p10	p10	NOUN
ijassa-1077	304	6	,	,	PUNCT
ijassa-1077	304	7	…	…	PUNCT
ijassa-1077	304	8	,	,	PUNCT
ijassa-1077	304	9	pm0	pm0	PROPN
ijassa-1077	304	10	)	)	PUNCT
ijassa-1077	304	11	of	of	ADP
ijassa-1077	304	12	the	the	DET
ijassa-1077	304	13	minimal	minimal	ADJ
ijassa-1077	304	14	value	value	NOUN
ijassa-1077	304	15	is	be	AUX
ijassa-1077	304	16	the	the	DET
ijassa-1077	304	17	measurement	measurement	NOUN
ijassa-1077	304	18	data	datum	NOUN
ijassa-1077	304	19	for	for	ADP
ijassa-1077	304	20	regularized	regularize	VERB
ijassa-1077	304	21	three	three	NUM
ijassa-1077	304	22	-	-	PUNCT
ijassa-1077	304	23	dimensional	dimensional	ADJ
ijassa-1077	304	24	printing	printing	NOUN
ijassa-1077	304	25	device	device	NOUN
ijassa-1077	304	26	.	.	PUNCT
ijassa-1077	305	1	remark	remark	NOUN
ijassa-1077	305	2	.	.	PUNCT
ijassa-1077	306	1	there	there	PRON
ijassa-1077	306	2	are	be	VERB
ijassa-1077	306	3	m	m	PROPN
ijassa-1077	306	4	three	three	NUM
ijassa-1077	306	5	-	-	PUNCT
ijassa-1077	306	6	dimensional	dimensional	ADJ
ijassa-1077	306	7	vectors	vector	NOUN
ijassa-1077	306	8	in	in	ADP
ijassa-1077	306	9	measurement	measurement	NOUN
ijassa-1077	306	10	data	datum	NOUN
ijassa-1077	306	11	.	.	PUNCT
ijassa-1077	307	1	therefore	therefore	ADV
ijassa-1077	307	2	the	the	DET
ijassa-1077	307	3	total	total	ADJ
ijassa-1077	307	4	dimension	dimension	NOUN
ijassa-1077	307	5	of	of	ADP
ijassa-1077	307	6	the	the	DET
ijassa-1077	307	7	space	space	NOUN
ijassa-1077	307	8	is	be	AUX
ijassa-1077	307	9	3	3	NUM
ijassa-1077	307	10	m.	m.	NOUN
ijassa-1077	307	11	thus	thus	ADV
ijassa-1077	307	12	we	we	PRON
ijassa-1077	307	13	have	have	VERB
ijassa-1077	307	14	a	a	DET
ijassa-1077	307	15	3m	3m	NUM
ijassa-1077	307	16	-	-	PUNCT
ijassa-1077	307	17	dimensional	dimensional	ADJ
ijassa-1077	307	18	non	non	ADJ
ijassa-1077	307	19	-	-	ADJ
ijassa-1077	307	20	convex	convex	ADJ
ijassa-1077	307	21	minimization	minimization	NOUN
ijassa-1077	307	22	problem	problem	NOUN
ijassa-1077	307	23	.	.	PUNCT
ijassa-1077	308	1	by	by	ADP
ijassa-1077	308	2	construction	construction	NOUN
ijassa-1077	308	3	,	,	PUNCT
ijassa-1077	308	4	the	the	DET
ijassa-1077	308	5	error	error	NOUN
ijassa-1077	308	6	functional	functional	ADJ
ijassa-1077	308	7	r	r	NOUN
ijassa-1077	308	8	is	be	AUX
ijassa-1077	308	9	not	not	PART
ijassa-1077	308	10	convex	convex	ADJ
ijassa-1077	308	11	and	and	CCONJ
ijassa-1077	308	12	can	can	AUX
ijassa-1077	308	13	have	have	VERB
ijassa-1077	308	14	more	more	ADJ
ijassa-1077	308	15	than	than	ADP
ijassa-1077	308	16	one	one	NUM
ijassa-1077	308	17	minimal	minimal	ADJ
ijassa-1077	308	18	point	point	NOUN
ijassa-1077	308	19	.	.	PUNCT
ijassa-1077	308	20	!	!	PUNCT
ijassa-1077	309	1	nj	nj	PROPN
ijassa-1077	309	2	jw	jw	PROPN
ijassa-1077	309	3	,	,	PUNCT
ijassa-1077	309	4	...	...	PUNCT
ijassa-1077	309	5	,	,	PUNCT
ijassa-1077	309	6	1	1	NUM
ijassa-1077	309	7	3	3	NUM
ijassa-1077	309	8	=	=	SYM
ijassa-1077	309	9	d=	d=	NOUN
ijassa-1077	310	1	å	å	X
ijassa-1077	310	2	=	=	SYM
ijassa-1077	310	3	=	=	SYM
ijassa-1077	310	4	=	=	SYM
ijassa-1077	310	5	n	n	PROPN
ijassa-1077	310	6	j	j	PROPN
ijassa-1077	310	7	mjm	mjm	PROPN
ijassa-1077	310	8	pprpprr	pprpprr	PROPN
ijassa-1077	310	9	1	1	NUM
ijassa-1077	310	10	11	11	NUM
ijassa-1077	310	11	)	)	PUNCT
ijassa-1077	310	12	,	,	PUNCT
ijassa-1077	310	13	...	...	PUNCT
ijassa-1077	310	14	,	,	PUNCT
ijassa-1077	310	15	(	(	PUNCT
ijassa-1077	310	16	)	)	PUNCT
ijassa-1077	310	17	,	,	PUNCT
ijassa-1077	310	18	...	...	PUNCT
ijassa-1077	310	19	,	,	PUNCT
ijassa-1077	310	20	(	(	PUNCT
ijassa-1077	310	21	mathematical	mathematical	ADJ
ijassa-1077	310	22	modeling	modeling	NOUN
ijassa-1077	310	23	of	of	ADP
ijassa-1077	310	24	color	color	NOUN
ijassa-1077	310	25	printing	printing	NOUN
ijassa-1077	310	26	devices	device	NOUN
ijassa-1077	310	27	:	:	PUNCT
ijassa-1077	310	28	color	color	NOUN
ijassa-1077	310	29	gamut	gamut	NOUN
ijassa-1077	310	30	visualization	visualization	NOUN
ijassa-1077	310	31	…	…	PUNCT
ijassa-1077	310	32	129	129	NUM
ijassa-1077	310	33	copyright	copyright	NOUN
ijassa-1077	310	34	©	©	PROPN
ijassa-1077	310	35	2021	2021	NUM
ijassa-1077	310	36	assa	assa	NOUN
ijassa-1077	310	37	.	.	PUNCT
ijassa-1077	311	1	adv	adv	PROPN
ijassa-1077	311	2	.	.	PUNCT
ijassa-1077	312	1	in	in	ADP
ijassa-1077	312	2	systems	system	NOUN
ijassa-1077	312	3	science	science	NOUN
ijassa-1077	312	4	and	and	CCONJ
ijassa-1077	312	5	appl	appl	NOUN
ijassa-1077	312	6	.	.	PUNCT
ijassa-1077	313	1	(	(	PUNCT
ijassa-1077	313	2	2021	2021	NUM
ijassa-1077	313	3	)	)	PUNCT
ijassa-1077	313	4	7	7	NUM
ijassa-1077	313	5	.	.	X
ijassa-1077	313	6	four	four	NUM
ijassa-1077	313	7	-	-	PUNCT
ijassa-1077	313	8	dimensional	dimensional	ADJ
ijassa-1077	313	9	regular	regular	ADJ
ijassa-1077	313	10	printing	printing	NOUN
ijassa-1077	313	11	devices	device	NOUN
ijassa-1077	313	12	consider	consider	VERB
ijassa-1077	313	13	a	a	DET
ijassa-1077	313	14	piecewise	piecewise	NOUN
ijassa-1077	313	15	linear	linear	NOUN
ijassa-1077	313	16	model	model	NOUN
ijassa-1077	313	17	f	f	NOUN
ijassa-1077	313	18	:	:	PUNCT
ijassa-1077	313	19	w4	w4	NOUN
ijassa-1077	313	20	®	®	NOUN
ijassa-1077	313	21	ℝ	ℝ	NOUN
ijassa-1077	313	22	#	#	NOUN
ijassa-1077	313	23	of	of	ADP
ijassa-1077	313	24	a	a	DET
ijassa-1077	313	25	four	four	NUM
ijassa-1077	313	26	-	-	PUNCT
ijassa-1077	313	27	dimensional	dimensional	ADJ
ijassa-1077	313	28	printing	printing	NOUN
ijassa-1077	313	29	device	device	NOUN
ijassa-1077	313	30	.	.	PUNCT
ijassa-1077	314	1	definition	definition	NOUN
ijassa-1077	314	2	.	.	PUNCT
ijassa-1077	315	1	the	the	DET
ijassa-1077	315	2	four	four	NUM
ijassa-1077	315	3	-	-	PUNCT
ijassa-1077	315	4	dimensional	dimensional	ADJ
ijassa-1077	315	5	printing	printing	NOUN
ijassa-1077	315	6	device	device	NOUN
ijassa-1077	315	7	is	be	AUX
ijassa-1077	315	8	called	call	VERB
ijassa-1077	315	9	regular	regular	ADJ
ijassa-1077	315	10	if	if	SCONJ
ijassa-1077	315	11	the	the	DET
ijassa-1077	315	12	following	follow	VERB
ijassa-1077	315	13	three	three	NUM
ijassa-1077	315	14	conditions	condition	NOUN
ijassa-1077	315	15	hold	hold	VERB
ijassa-1077	315	16	for	for	ADP
ijassa-1077	315	17	the	the	DET
ijassa-1077	315	18	piecewise	piecewise	NOUN
ijassa-1077	315	19	linear	linear	NOUN
ijassa-1077	315	20	map	map	NOUN
ijassa-1077	315	21	f.	f.	PROPN
ijassa-1077	315	22	(	(	PUNCT
ijassa-1077	315	23	1	1	X
ijassa-1077	315	24	)	)	PUNCT
ijassa-1077	315	25	the	the	DET
ijassa-1077	315	26	color	color	NOUN
ijassa-1077	315	27	gamut	gamut	NOUN
ijassa-1077	315	28	f(w4	f(w4	NOUN
ijassa-1077	315	29	)	)	PUNCT
ijassa-1077	315	30	is	be	AUX
ijassa-1077	315	31	homeomorphic	homeomorphic	ADJ
ijassa-1077	315	32	to	to	PART
ijassa-1077	315	33	closed	closed	VERB
ijassa-1077	315	34	three	three	NUM
ijassa-1077	315	35	-	-	PUNCT
ijassa-1077	315	36	dimensional	dimensional	ADJ
ijassa-1077	315	37	disk	disk	NOUN
ijassa-1077	315	38	d3	d3	NOUN
ijassa-1077	315	39	.	.	PUNCT
ijassa-1077	316	1	(	(	PUNCT
ijassa-1077	316	2	2	2	X
ijassa-1077	316	3	)	)	PUNCT
ijassa-1077	316	4	for	for	ADP
ijassa-1077	316	5	any	any	DET
ijassa-1077	316	6	internal	internal	ADJ
ijassa-1077	316	7	point	point	NOUN
ijassa-1077	316	8	p	p	NOUN
ijassa-1077	316	9	of	of	ADP
ijassa-1077	316	10	the	the	DET
ijassa-1077	316	11	color	color	NOUN
ijassa-1077	316	12	gamut	gamut	NOUN
ijassa-1077	316	13	f(w4	f(w4	NOUN
ijassa-1077	316	14	)	)	PUNCT
ijassa-1077	316	15	,	,	PUNCT
ijassa-1077	316	16	p	p	PROPN
ijassa-1077	316	17	î	î	PROPN
ijassa-1077	316	18	int	int	NOUN
ijassa-1077	316	19	f(w4	f(w4	NOUN
ijassa-1077	316	20	)	)	PUNCT
ijassa-1077	316	21	,	,	PUNCT
ijassa-1077	316	22	the	the	DET
ijassa-1077	316	23	pre	pre	ADJ
ijassa-1077	316	24	-	-	ADJ
ijassa-1077	316	25	image	image	ADJ
ijassa-1077	316	26	f-1(p	f-1(p	NOUN
ijassa-1077	316	27	)	)	PUNCT
ijassa-1077	316	28	is	be	AUX
ijassa-1077	316	29	homeomorphic	homeomorphic	ADJ
ijassa-1077	316	30	to	to	ADP
ijassa-1077	316	31	a	a	DET
ijassa-1077	316	32	segment	segment	NOUN
ijassa-1077	316	33	[	[	X
ijassa-1077	316	34	a	a	X
ijassa-1077	316	35	,	,	PUNCT
ijassa-1077	316	36	b	b	NOUN
ijassa-1077	316	37	]	]	X
ijassa-1077	316	38	,	,	PUNCT
ijassa-1077	316	39	a	a	DET
ijassa-1077	316	40	<	<	X
ijassa-1077	316	41	b	b	NOUN
ijassa-1077	316	42	,	,	PUNCT
ijassa-1077	316	43	and	and	CCONJ
ijassa-1077	316	44	the	the	DET
ijassa-1077	316	45	intersection	intersection	NOUN
ijassa-1077	316	46	f-1(p	f-1(p	PROPN
ijassa-1077	316	47	)	)	PUNCT
ijassa-1077	316	48	ç	ç	SYM
ijassa-1077	316	49	¶w4	¶w4	NOUN
ijassa-1077	316	50	of	of	ADP
ijassa-1077	316	51	this	this	DET
ijassa-1077	316	52	pre	pre	NOUN
ijassa-1077	316	53	-	-	NOUN
ijassa-1077	316	54	image	image	NOUN
ijassa-1077	316	55	and	and	CCONJ
ijassa-1077	316	56	the	the	DET
ijassa-1077	316	57	boundary	boundary	ADJ
ijassa-1077	316	58	¶w4	¶w4	PROPN
ijassa-1077	316	59	of	of	ADP
ijassa-1077	316	60	the	the	DET
ijassa-1077	316	61	colorants	colorant	NOUN
ijassa-1077	316	62	cube	cube	PROPN
ijassa-1077	316	63	w4	w4	PROPN
ijassa-1077	316	64	consists	consist	VERB
ijassa-1077	316	65	exactly	exactly	ADV
ijassa-1077	316	66	of	of	ADP
ijassa-1077	316	67	the	the	DET
ijassa-1077	316	68	two	two	NUM
ijassa-1077	316	69	boundary	boundary	ADJ
ijassa-1077	316	70	points	point	NOUN
ijassa-1077	316	71	of	of	ADP
ijassa-1077	316	72	the	the	DET
ijassa-1077	316	73	pre	pre	ADJ
ijassa-1077	316	74	-	-	ADJ
ijassa-1077	316	75	image	image	ADJ
ijassa-1077	316	76	f-1(p	f-1(p	NOUN
ijassa-1077	316	77	)	)	PUNCT
ijassa-1077	316	78	.	.	PUNCT
ijassa-1077	317	1	(	(	PUNCT
ijassa-1077	317	2	3	3	X
ijassa-1077	317	3	)	)	PUNCT
ijassa-1077	317	4	for	for	ADP
ijassa-1077	317	5	any	any	DET
ijassa-1077	317	6	boundary	boundary	ADJ
ijassa-1077	317	7	point	point	NOUN
ijassa-1077	317	8	p	p	NOUN
ijassa-1077	317	9	of	of	ADP
ijassa-1077	317	10	the	the	DET
ijassa-1077	317	11	gamut	gamut	NOUN
ijassa-1077	317	12	f(w4	f(w4	NOUN
ijassa-1077	317	13	)	)	PUNCT
ijassa-1077	317	14	,	,	PUNCT
ijassa-1077	317	15	p	p	PROPN
ijassa-1077	317	16	î	î	PROPN
ijassa-1077	317	17	¶f(w4	¶f(w4	NOUN
ijassa-1077	317	18	)	)	PUNCT
ijassa-1077	317	19	,	,	PUNCT
ijassa-1077	317	20	the	the	DET
ijassa-1077	317	21	pre	pre	ADJ
ijassa-1077	317	22	-	-	ADJ
ijassa-1077	317	23	image	image	ADJ
ijassa-1077	317	24	f-1(p	f-1(p	NOUN
ijassa-1077	317	25	)	)	PUNCT
ijassa-1077	317	26	consists	consist	VERB
ijassa-1077	317	27	of	of	ADP
ijassa-1077	317	28	exactly	exactly	ADV
ijassa-1077	317	29	one	one	NUM
ijassa-1077	317	30	point	point	NOUN
ijassa-1077	317	31	.	.	PUNCT
ijassa-1077	318	1	remark	remark	NOUN
ijassa-1077	318	2	.	.	PUNCT
ijassa-1077	319	1	if	if	SCONJ
ijassa-1077	319	2	a	a	DET
ijassa-1077	319	3	four	four	NUM
ijassa-1077	319	4	-	-	PUNCT
ijassa-1077	319	5	dimensional	dimensional	ADJ
ijassa-1077	319	6	printing	printing	NOUN
ijassa-1077	319	7	device	device	NOUN
ijassa-1077	319	8	is	be	AUX
ijassa-1077	319	9	regular	regular	ADJ
ijassa-1077	319	10	then	then	ADV
ijassa-1077	319	11	it	it	PRON
ijassa-1077	319	12	is	be	AUX
ijassa-1077	319	13	non	non	ADJ
ijassa-1077	319	14	-	-	ADJ
ijassa-1077	319	15	degenerate	degenerate	ADJ
ijassa-1077	319	16	and	and	CCONJ
ijassa-1077	319	17	proper	proper	ADJ
ijassa-1077	319	18	.	.	PUNCT
ijassa-1077	320	1	of	of	ADP
ijassa-1077	320	2	cause	cause	NOUN
ijassa-1077	320	3	,	,	PUNCT
ijassa-1077	320	4	the	the	DET
ijassa-1077	320	5	inverse	inverse	ADJ
ijassa-1077	320	6	statement	statement	NOUN
ijassa-1077	320	7	is	be	AUX
ijassa-1077	320	8	false	false	ADJ
ijassa-1077	320	9	because	because	SCONJ
ijassa-1077	320	10	there	there	PRON
ijassa-1077	320	11	exist	exist	VERB
ijassa-1077	320	12	four	four	NUM
ijassa-1077	320	13	-	-	PUNCT
ijassa-1077	320	14	dimensional	dimensional	ADJ
ijassa-1077	320	15	nondegenerate	nondegenerate	ADJ
ijassa-1077	320	16	proper	proper	ADJ
ijassa-1077	320	17	printing	printing	NOUN
ijassa-1077	320	18	devices	device	NOUN
ijassa-1077	320	19	that	that	PRON
ijassa-1077	320	20	are	be	AUX
ijassa-1077	320	21	not	not	PART
ijassa-1077	320	22	regular	regular	ADJ
ijassa-1077	320	23	.	.	PUNCT
ijassa-1077	321	1	let	let	VERB
ijassa-1077	321	2	c	c	PRON
ijassa-1077	321	3	be	be	AUX
ijassa-1077	321	4	the	the	DET
ijassa-1077	321	5	characteristic	characteristic	ADJ
ijassa-1077	321	6	vector	vector	NOUN
ijassa-1077	321	7	field	field	NOUN
ijassa-1077	321	8	of	of	ADP
ijassa-1077	321	9	the	the	DET
ijassa-1077	321	10	four	four	NUM
ijassa-1077	321	11	-	-	PUNCT
ijassa-1077	321	12	dimensional	dimensional	ADJ
ijassa-1077	321	13	printing	printing	NOUN
ijassa-1077	321	14	device	device	NOUN
ijassa-1077	321	15	under	under	ADP
ijassa-1077	321	16	consideration	consideration	NOUN
ijassa-1077	321	17	.	.	PUNCT
ijassa-1077	322	1	by	by	ADP
ijassa-1077	322	2	definition	definition	NOUN
ijassa-1077	322	3	,	,	PUNCT
ijassa-1077	322	4	it	it	PRON
ijassa-1077	322	5	is	be	AUX
ijassa-1077	322	6	a	a	DET
ijassa-1077	322	7	piecewise	piecewise	NOUN
ijassa-1077	322	8	constant	constant	ADJ
ijassa-1077	322	9	vector	vector	NOUN
ijassa-1077	322	10	field	field	NOUN
ijassa-1077	322	11	such	such	ADJ
ijassa-1077	322	12	that	that	DET
ijassa-1077	322	13	c½dj	c½dj	PROPN
ijassa-1077	322	14	=	=	PUNCT
ijassa-1077	322	15	cj	cj	PROPN
ijassa-1077	322	16	,	,	PUNCT
ijassa-1077	322	17	where	where	SCONJ
ijassa-1077	322	18	cj	cj	VERB
ijassa-1077	322	19	=	=	SYM
ijassa-1077	322	20	(	(	PUNCT
ijassa-1077	322	21	det	det	PROPN
ijassa-1077	322	22	bj1	bj1	PROPN
ijassa-1077	322	23	,	,	PUNCT
ijassa-1077	322	24	det	det	PROPN
ijassa-1077	322	25	bj2	bj2	PROPN
ijassa-1077	322	26	,	,	PUNCT
ijassa-1077	322	27	det	det	PROPN
ijassa-1077	322	28	bj3	bj3	PROPN
ijassa-1077	322	29	,	,	PUNCT
ijassa-1077	322	30	det	det	NOUN
ijassa-1077	322	31	bj4	bj4	NOUN
ijassa-1077	322	32	)	)	PUNCT
ijassa-1077	322	33	for	for	ADP
ijassa-1077	322	34	j=1,	j=1,	NOUN
ijassa-1077	322	35	…	…	PUNCT
ijassa-1077	322	36	,n	,n	PUNCT
ijassa-1077	322	37	(	(	PUNCT
ijassa-1077	322	38	see	see	VERB
ijassa-1077	322	39	section	section	NOUN
ijassa-1077	322	40	5	5	NUM
ijassa-1077	322	41	)	)	PUNCT
ijassa-1077	322	42	.	.	PUNCT
ijassa-1077	323	1	definition	definition	NOUN
ijassa-1077	323	2	.	.	PUNCT
ijassa-1077	324	1	a	a	DET
ijassa-1077	324	2	four	four	NUM
ijassa-1077	324	3	-	-	PUNCT
ijassa-1077	324	4	dimensional	dimensional	ADJ
ijassa-1077	324	5	printing	printing	NOUN
ijassa-1077	324	6	device	device	NOUN
ijassa-1077	324	7	is	be	AUX
ijassa-1077	324	8	called	call	VERB
ijassa-1077	324	9	strictly	strictly	ADV
ijassa-1077	324	10	non	non	ADJ
ijassa-1077	324	11	-	-	ADJ
ijassa-1077	324	12	degenerate	degenerate	ADJ
ijassa-1077	324	13	if	if	SCONJ
ijassa-1077	324	14	it	it	PRON
ijassa-1077	324	15	is	be	AUX
ijassa-1077	324	16	non	non	ADJ
ijassa-1077	324	17	-	-	ADJ
ijassa-1077	324	18	degenerate	degenerate	ADJ
ijassa-1077	324	19	and	and	CCONJ
ijassa-1077	324	20	at	at	ADP
ijassa-1077	324	21	any	any	DET
ijassa-1077	324	22	point	point	NOUN
ijassa-1077	324	23	x	x	PUNCT
ijassa-1077	324	24	of	of	ADP
ijassa-1077	324	25	the	the	DET
ijassa-1077	324	26	four	four	NUM
ijassa-1077	324	27	-	-	PUNCT
ijassa-1077	324	28	dimensional	dimensional	ADJ
ijassa-1077	324	29	colorants	colorant	NOUN
ijassa-1077	324	30	cube	cube	NOUN
ijassa-1077	324	31	w4	w4	NOUN
ijassa-1077	324	32	all	all	DET
ijassa-1077	324	33	the	the	DET
ijassa-1077	324	34	four	four	NUM
ijassa-1077	324	35	coordinates	coordinate	NOUN
ijassa-1077	324	36	of	of	ADP
ijassa-1077	324	37	the	the	DET
ijassa-1077	324	38	characteristic	characteristic	ADJ
ijassa-1077	324	39	vector	vector	NOUN
ijassa-1077	324	40	field	field	NOUN
ijassa-1077	324	41	c	c	AUX
ijassa-1077	324	42	have	have	VERB
ijassa-1077	324	43	the	the	DET
ijassa-1077	324	44	same	same	ADJ
ijassa-1077	324	45	sign	sign	NOUN
ijassa-1077	324	46	.	.	PUNCT
ijassa-1077	325	1	in	in	ADP
ijassa-1077	325	2	other	other	ADJ
ijassa-1077	325	3	words	word	NOUN
ijassa-1077	325	4	,	,	PUNCT
ijassa-1077	325	5	for	for	ADP
ijassa-1077	325	6	all	all	DET
ijassa-1077	325	7	j=2,	j=2,	PROPN
ijassa-1077	325	8	…	…	PUNCT
ijassa-1077	325	9	,n	,n	PUNCT
ijassa-1077	325	10	the	the	DET
ijassa-1077	325	11	i	i	NOUN
ijassa-1077	325	12	-	-	PUNCT
ijassa-1077	325	13	th	th	X
ijassa-1077	325	14	coordinate	coordinate	NOUN
ijassa-1077	325	15	cji	cji	NOUN
ijassa-1077	325	16	=	=	SYM
ijassa-1077	325	17	(	(	PUNCT
ijassa-1077	325	18	-1)i+1det	-1)i+1det	X
ijassa-1077	325	19	bji	bji	NOUN
ijassa-1077	325	20	of	of	ADP
ijassa-1077	325	21	the	the	DET
ijassa-1077	325	22	characteristic	characteristic	ADJ
ijassa-1077	325	23	vector	vector	NOUN
ijassa-1077	325	24	field	field	NOUN
ijassa-1077	325	25	c	c	NOUN
ijassa-1077	325	26	at	at	ADP
ijassa-1077	325	27	the	the	DET
ijassa-1077	325	28	j	j	PROPN
ijassa-1077	325	29	-	-	PUNCT
ijassa-1077	325	30	th	th	VERB
ijassa-1077	325	31	simplex	simplex	NOUN
ijassa-1077	325	32	has	have	VERB
ijassa-1077	325	33	the	the	DET
ijassa-1077	325	34	same	same	ADJ
ijassa-1077	325	35	sign	sign	NOUN
ijassa-1077	325	36	as	as	SCONJ
ijassa-1077	325	37	the	the	DET
ijassa-1077	325	38	i	i	PROPN
ijassa-1077	325	39	-	-	PUNCT
ijassa-1077	325	40	th	th	X
ijassa-1077	325	41	coordinate	coordinate	NOUN
ijassa-1077	325	42	c1i	c1i	NOUN
ijassa-1077	325	43	=	=	SYM
ijassa-1077	325	44	(	(	PUNCT
ijassa-1077	325	45	-1)i+1det	-1)i+1det	X
ijassa-1077	325	46	b1i	b1i	NOUN
ijassa-1077	325	47	of	of	ADP
ijassa-1077	325	48	the	the	DET
ijassa-1077	325	49	characteristic	characteristic	ADJ
ijassa-1077	325	50	vector	vector	NOUN
ijassa-1077	325	51	field	field	NOUN
ijassa-1077	325	52	c	c	NOUN
ijassa-1077	325	53	at	at	ADP
ijassa-1077	325	54	the	the	DET
ijassa-1077	325	55	first	first	ADJ
ijassa-1077	325	56	simplex	simplex	NOUN
ijassa-1077	325	57	for	for	ADP
ijassa-1077	325	58	i=1,2,3,4	i=1,2,3,4	PROPN
ijassa-1077	325	59	.	.	PROPN
ijassa-1077	325	60	remark	remark	PROPN
ijassa-1077	325	61	.	.	PUNCT
ijassa-1077	326	1	it	it	PRON
ijassa-1077	326	2	is	be	AUX
ijassa-1077	326	3	possible	possible	ADJ
ijassa-1077	326	4	to	to	PART
ijassa-1077	326	5	show	show	VERB
ijassa-1077	326	6	that	that	SCONJ
ijassa-1077	326	7	for	for	ADP
ijassa-1077	326	8	a	a	DET
ijassa-1077	326	9	strictly	strictly	ADV
ijassa-1077	326	10	non	non	ADJ
ijassa-1077	326	11	-	-	ADJ
ijassa-1077	326	12	degenerate	degenerate	ADJ
ijassa-1077	326	13	four	four	NUM
ijassa-1077	326	14	-	-	PUNCT
ijassa-1077	326	15	dimensional	dimensional	ADJ
ijassa-1077	326	16	printing	printing	NOUN
ijassa-1077	326	17	device	device	NOUN
ijassa-1077	326	18	the	the	DET
ijassa-1077	326	19	set	set	NOUN
ijassa-1077	326	20	s	s	X
ijassa-1077	326	21	of	of	ADP
ijassa-1077	326	22	all	all	PRON
ijassa-1077	326	23	its	its	PRON
ijassa-1077	326	24	singular	singular	ADJ
ijassa-1077	326	25	faces	face	NOUN
ijassa-1077	326	26	is	be	AUX
ijassa-1077	326	27	homeomorphic	homeomorphic	ADJ
ijassa-1077	326	28	to	to	ADP
ijassa-1077	326	29	two	two	NUM
ijassa-1077	326	30	-	-	PUNCT
ijassa-1077	326	31	dimensional	dimensional	ADJ
ijassa-1077	326	32	sphere	sphere	NOUN
ijassa-1077	326	33	s2	s2	NOUN
ijassa-1077	326	34	.	.	PUNCT
ijassa-1077	327	1	there	there	PRON
ijassa-1077	327	2	is	be	VERB
ijassa-1077	327	3	a	a	DET
ijassa-1077	327	4	sufficient	sufficient	ADJ
ijassa-1077	327	5	condition	condition	NOUN
ijassa-1077	327	6	of	of	ADP
ijassa-1077	327	7	a	a	DET
ijassa-1077	327	8	four	four	NUM
ijassa-1077	327	9	-	-	PUNCT
ijassa-1077	327	10	dimensional	dimensional	ADJ
ijassa-1077	327	11	printing	printing	NOUN
ijassa-1077	327	12	device	device	NOUN
ijassa-1077	327	13	to	to	PART
ijassa-1077	327	14	be	be	AUX
ijassa-1077	327	15	regular	regular	ADJ
ijassa-1077	327	16	.	.	PUNCT
ijassa-1077	328	1	theorem	theorem	VERB
ijassa-1077	328	2	.	.	PROPN
ijassa-1077	328	3	suppose	suppose	VERB
ijassa-1077	328	4	the	the	DET
ijassa-1077	328	5	four	four	NUM
ijassa-1077	328	6	-	-	PUNCT
ijassa-1077	328	7	dimensional	dimensional	ADJ
ijassa-1077	328	8	printing	printing	NOUN
ijassa-1077	328	9	device	device	NOUN
ijassa-1077	328	10	under	under	ADP
ijassa-1077	328	11	consideration	consideration	NOUN
ijassa-1077	328	12	is	be	AUX
ijassa-1077	328	13	strictly	strictly	ADV
ijassa-1077	328	14	non	non	ADJ
ijassa-1077	328	15	-	-	ADJ
ijassa-1077	328	16	degenerate	degenerate	ADJ
ijassa-1077	328	17	and	and	CCONJ
ijassa-1077	328	18	the	the	DET
ijassa-1077	328	19	restriction	restriction	NOUN
ijassa-1077	328	20	f½s	f½s	PROPN
ijassa-1077	328	21	of	of	ADP
ijassa-1077	328	22	the	the	DET
ijassa-1077	328	23	piecewise	piecewise	NOUN
ijassa-1077	328	24	linear	linear	NOUN
ijassa-1077	328	25	map	map	NOUN
ijassa-1077	328	26	f	f	X
ijassa-1077	328	27	to	to	ADP
ijassa-1077	328	28	the	the	DET
ijassa-1077	328	29	set	set	NOUN
ijassa-1077	328	30	s	s	X
ijassa-1077	328	31	of	of	ADP
ijassa-1077	328	32	all	all	PRON
ijassa-1077	328	33	its	its	PRON
ijassa-1077	328	34	singular	singular	ADJ
ijassa-1077	328	35	faces	face	NOUN
ijassa-1077	328	36	is	be	AUX
ijassa-1077	328	37	an	an	DET
ijassa-1077	328	38	injection	injection	NOUN
ijassa-1077	328	39	.	.	PUNCT
ijassa-1077	329	1	then	then	ADV
ijassa-1077	329	2	this	this	DET
ijassa-1077	329	3	printing	printing	NOUN
ijassa-1077	329	4	device	device	NOUN
ijassa-1077	329	5	is	be	AUX
ijassa-1077	329	6	regular	regular	ADJ
ijassa-1077	329	7	.	.	PUNCT
ijassa-1077	330	1	describe	describe	VERB
ijassa-1077	330	2	the	the	DET
ijassa-1077	330	3	scheme	scheme	NOUN
ijassa-1077	330	4	of	of	ADP
ijassa-1077	330	5	an	an	DET
ijassa-1077	330	6	algorithmic	algorithmic	ADJ
ijassa-1077	330	7	approach	approach	NOUN
ijassa-1077	330	8	that	that	PRON
ijassa-1077	330	9	allows	allow	VERB
ijassa-1077	330	10	forcing	force	VERB
ijassa-1077	330	11	a	a	DET
ijassa-1077	330	12	four	four	NUM
ijassa-1077	330	13	-	-	PUNCT
ijassa-1077	330	14	dimensional	dimensional	ADJ
ijassa-1077	330	15	printing	printing	NOUN
ijassa-1077	330	16	device	device	NOUN
ijassa-1077	330	17	to	to	PART
ijassa-1077	330	18	become	become	VERB
ijassa-1077	330	19	strictly	strictly	ADV
ijassa-1077	330	20	non	non	ADJ
ijassa-1077	330	21	-	-	ADJ
ijassa-1077	330	22	degenerate	degenerate	ADJ
ijassa-1077	330	23	.	.	PUNCT
ijassa-1077	331	1	at	at	ADP
ijassa-1077	331	2	the	the	DET
ijassa-1077	331	3	first	first	ADJ
ijassa-1077	331	4	step	step	NOUN
ijassa-1077	331	5	count	count	NOUN
ijassa-1077	331	6	the	the	DET
ijassa-1077	331	7	number	number	NOUN
ijassa-1077	331	8	ni+	ni+	NOUN
ijassa-1077	331	9	of	of	ADP
ijassa-1077	331	10	positive	positive	ADJ
ijassa-1077	331	11	i	i	PROPN
ijassa-1077	331	12	-	-	PUNCT
ijassa-1077	331	13	th	th	X
ijassa-1077	331	14	coordinates	coordinate	NOUN
ijassa-1077	331	15	and	and	CCONJ
ijassa-1077	331	16	the	the	DET
ijassa-1077	331	17	number	number	NOUN
ijassa-1077	331	18	niof	niof	PART
ijassa-1077	331	19	negative	negative	ADJ
ijassa-1077	331	20	i	i	PRON
ijassa-1077	331	21	-	-	PUNCT
ijassa-1077	331	22	th	th	X
ijassa-1077	331	23	coordinates	coordinate	NOUN
ijassa-1077	331	24	of	of	ADP
ijassa-1077	331	25	the	the	DET
ijassa-1077	331	26	characteristic	characteristic	ADJ
ijassa-1077	331	27	vector	vector	NOUN
ijassa-1077	331	28	field	field	NOUN
ijassa-1077	331	29	c	c	NOUN
ijassa-1077	331	30	,	,	PUNCT
ijassa-1077	331	31	i=1,2,3,4	i=1,2,3,4	PROPN
ijassa-1077	331	32	.	.	PROPN
ijassa-1077	331	33	for	for	ADP
ijassa-1077	331	34	clarity	clarity	NOUN
ijassa-1077	331	35	,	,	PUNCT
ijassa-1077	331	36	assume	assume	VERB
ijassa-1077	331	37	that	that	SCONJ
ijassa-1077	331	38	ni+	ni+	NOUN
ijassa-1077	331	39	>	>	X
ijassa-1077	331	40	nifor	nifor	PROPN
ijassa-1077	331	41	i=1,2,3	i=1,2,3	PROPN
ijassa-1077	331	42	and	and	CCONJ
ijassa-1077	331	43	n4	n4	PROPN
ijassa-1077	332	1	+	+	PROPN
ijassa-1077	332	2	<	<	X
ijassa-1077	332	3	n4	n4	PROPN
ijassa-1077	332	4	.	.	PUNCT
ijassa-1077	333	1	at	at	ADP
ijassa-1077	333	2	the	the	DET
ijassa-1077	333	3	second	second	ADJ
ijassa-1077	333	4	step	step	NOUN
ijassa-1077	333	5	define	define	VERB
ijassa-1077	333	6	a	a	DET
ijassa-1077	333	7	positive	positive	ADJ
ijassa-1077	333	8	threshold	threshold	NOUN
ijassa-1077	333	9	e	e	NOUN
ijassa-1077	333	10	,	,	PUNCT
ijassa-1077	333	11	e	e	X
ijassa-1077	333	12	>	>	X
ijassa-1077	333	13	0	0	PROPN
ijassa-1077	333	14	,	,	PUNCT
ijassa-1077	333	15	which	which	PRON
ijassa-1077	333	16	is	be	AUX
ijassa-1077	333	17	usually	usually	ADV
ijassa-1077	333	18	a	a	DET
ijassa-1077	333	19	small	small	ADJ
ijassa-1077	333	20	real	real	ADJ
ijassa-1077	333	21	number	number	NOUN
ijassa-1077	333	22	,	,	PUNCT
ijassa-1077	333	23	and	and	CCONJ
ijassa-1077	333	24	construct	construct	VERB
ijassa-1077	333	25	the	the	DET
ijassa-1077	333	26	error	error	NOUN
ijassa-1077	333	27	functional	functional	ADJ
ijassa-1077	333	28	r	r	NOUN
ijassa-1077	333	29	,	,	PUNCT
ijassa-1077	333	30	.	.	PUNCT
ijassa-1077	334	1	here	here	ADV
ijassa-1077	334	2	rji	rji	VERB
ijassa-1077	334	3	=	=	SYM
ijassa-1077	334	4	rji(p1	rji(p1	PROPN
ijassa-1077	334	5	,	,	PUNCT
ijassa-1077	334	6	…	…	PUNCT
ijassa-1077	334	7	,	,	PUNCT
ijassa-1077	334	8	pm	pm	NOUN
ijassa-1077	334	9	)	)	PUNCT
ijassa-1077	334	10	=	=	SYM
ijassa-1077	334	11	0	0	PUNCT
ijassa-1077	335	1	if	if	SCONJ
ijassa-1077	335	2	(	(	PUNCT
ijassa-1077	335	3	-1)i+1det	-1)i+1det	NOUN
ijassa-1077	335	4	bji	bji	PROPN
ijassa-1077	335	5	≥	≥	PROPN
ijassa-1077	335	6	e	e	NOUN
ijassa-1077	335	7	and	and	CCONJ
ijassa-1077	335	8	rj	rj	PROPN
ijassa-1077	335	9	=	=	SYM
ijassa-1077	335	10	rj(p1	rj(p1	NOUN
ijassa-1077	335	11	,	,	PUNCT
ijassa-1077	335	12	…	…	PUNCT
ijassa-1077	335	13	,	,	PUNCT
ijassa-1077	335	14	pm	pm	NOUN
ijassa-1077	335	15	)	)	PUNCT
ijassa-1077	335	16	=	=	SYM
ijassa-1077	335	17	(	(	PUNCT
ijassa-1077	335	18	e	e	X
ijassa-1077	335	19	det	det	PROPN
ijassa-1077	335	20	bj)2	bj)2	VERB
ijassa-1077	335	21	if	if	SCONJ
ijassa-1077	335	22	(	(	PUNCT
ijassa-1077	335	23	-1)i+1det	-1)i+1det	X
ijassa-1077	335	24	bji	bji	PROPN
ijassa-1077	335	25	<	<	X
ijassa-1077	335	26	e	e	NOUN
ijassa-1077	335	27	for	for	ADP
ijassa-1077	335	28	i=1,2,3	i=1,2,3	NUM
ijassa-1077	335	29	.	.	PUNCT
ijassa-1077	336	1	for	for	ADP
ijassa-1077	336	2	i=4	i=4	ADJ
ijassa-1077	336	3	rj4	rj4	NOUN
ijassa-1077	336	4	=	=	PUNCT
ijassa-1077	336	5	rj4(p1	rj4(p1	NOUN
ijassa-1077	336	6	,	,	PUNCT
ijassa-1077	336	7	…	…	PUNCT
ijassa-1077	336	8	,	,	PUNCT
ijassa-1077	336	9	pm	pm	NOUN
ijassa-1077	336	10	)	)	PUNCT
ijassa-1077	336	11	=	=	SYM
ijassa-1077	336	12	0	0	PUNCT
ijassa-1077	336	13	if	if	SCONJ
ijassa-1077	336	14	det	det	PROPN
ijassa-1077	336	15	bji	bji	VERB
ijassa-1077	336	16	≥	≥	PROPN
ijassa-1077	336	17	e	e	NOUN
ijassa-1077	336	18	and	and	CCONJ
ijassa-1077	336	19	rj	rj	PROPN
ijassa-1077	336	20	=	=	SYM
ijassa-1077	336	21	rj(p1	rj(p1	NOUN
ijassa-1077	336	22	,	,	PUNCT
ijassa-1077	336	23	…	…	PUNCT
ijassa-1077	336	24	,	,	PUNCT
ijassa-1077	336	25	pm	pm	NOUN
ijassa-1077	336	26	)	)	PUNCT
ijassa-1077	336	27	=	=	SYM
ijassa-1077	336	28	(	(	PUNCT
ijassa-1077	336	29	e	e	X
ijassa-1077	336	30	det	det	PROPN
ijassa-1077	336	31	bj)2	bj)2	VERB
ijassa-1077	336	32	if	if	SCONJ
ijassa-1077	336	33	det	det	PROPN
ijassa-1077	336	34	bji	bji	VERB
ijassa-1077	336	35	<	<	X
ijassa-1077	336	36	e	e	PROPN
ijassa-1077	336	37	for	for	ADP
ijassa-1077	336	38	j=1,	j=1,	NOUN
ijassa-1077	336	39	…	…	PUNCT
ijassa-1077	336	40	,n	,n	PUNCT
ijassa-1077	336	41	.	.	PUNCT
ijassa-1077	337	1	in	in	ADP
ijassa-1077	337	2	both	both	DET
ijassa-1077	337	3	cases	case	NOUN
ijassa-1077	337	4	p1	p1	PROPN
ijassa-1077	337	5	,	,	PUNCT
ijassa-1077	337	6	…	…	PUNCT
ijassa-1077	337	7	,	,	PUNCT
ijassa-1077	337	8	pm	pm	NOUN
ijassa-1077	337	9	are	be	AUX
ijassa-1077	337	10	the	the	DET
ijassa-1077	337	11	three	three	NUM
ijassa-1077	337	12	-	-	PUNCT
ijassa-1077	337	13	dimensional	dimensional	ADJ
ijassa-1077	337	14	vectors	vector	NOUN
ijassa-1077	337	15	in	in	ADP
ijassa-1077	337	16	color	color	NOUN
ijassa-1077	337	17	space	space	NOUN
ijassa-1077	337	18	that	that	PRON
ijassa-1077	337	19	form	form	VERB
ijassa-1077	337	20	the	the	DET
ijassa-1077	337	21	measurement	measurement	NOUN
ijassa-1077	337	22	data	datum	NOUN
ijassa-1077	337	23	of	of	ADP
ijassa-1077	337	24	the	the	DET
ijassa-1077	337	25	four	four	NUM
ijassa-1077	337	26	-	-	PUNCT
ijassa-1077	337	27	dimensional	dimensional	ADJ
ijassa-1077	337	28	printing	printing	NOUN
ijassa-1077	337	29	device	device	NOUN
ijassa-1077	337	30	under	under	ADP
ijassa-1077	337	31	consideration	consideration	NOUN
ijassa-1077	337	32	(	(	PUNCT
ijassa-1077	337	33	see	see	VERB
ijassa-1077	337	34	section	section	NOUN
ijassa-1077	337	35	1	1	NUM
ijassa-1077	337	36	)	)	PUNCT
ijassa-1077	337	37	.	.	PUNCT
ijassa-1077	338	1	by	by	ADP
ijassa-1077	338	2	construction	construction	NOUN
ijassa-1077	338	3	of	of	ADP
ijassa-1077	338	4	the	the	DET
ijassa-1077	338	5	piecewise	piecewise	NOUN
ijassa-1077	338	6	linear	linear	NOUN
ijassa-1077	338	7	map	map	NOUN
ijassa-1077	338	8	f	f	NOUN
ijassa-1077	338	9	,	,	PUNCT
ijassa-1077	338	10	all	all	DET
ijassa-1077	338	11	the	the	DET
ijassa-1077	338	12	determinants	determinant	NOUN
ijassa-1077	338	13	det	det	PROPN
ijassa-1077	338	14	bji	bji	PROPN
ijassa-1077	338	15	are	be	AUX
ijassa-1077	338	16	the	the	DET
ijassa-1077	338	17	third	third	ADJ
ijassa-1077	338	18	order	order	NOUN
ijassa-1077	338	19	polynomials	polynomial	NOUN
ijassa-1077	338	20	with	with	ADP
ijassa-1077	338	21	respect	respect	NOUN
ijassa-1077	338	22	to	to	ADP
ijassa-1077	338	23	measurement	measurement	NOUN
ijassa-1077	338	24	data	datum	NOUN
ijassa-1077	338	25	vectors	vector	NOUN
ijassa-1077	338	26	åå	åå	ADP
ijassa-1077	339	1	=	=	SYM
ijassa-1077	339	2	=	=	PUNCT
ijassa-1077	340	1	=	=	SYM
ijassa-1077	340	2	=	=	SYM
ijassa-1077	340	3	4	4	NUM
ijassa-1077	340	4	1	1	NUM
ijassa-1077	340	5	1	1	NUM
ijassa-1077	340	6	11	11	NUM
ijassa-1077	340	7	)	)	PUNCT
ijassa-1077	340	8	,	,	PUNCT
ijassa-1077	340	9	...	...	PUNCT
ijassa-1077	340	10	,	,	PUNCT
ijassa-1077	340	11	(	(	PUNCT
ijassa-1077	340	12	)	)	PUNCT
ijassa-1077	340	13	,	,	PUNCT
ijassa-1077	340	14	...	...	PUNCT
ijassa-1077	340	15	,	,	PUNCT
ijassa-1077	340	16	(	(	PUNCT
ijassa-1077	340	17	i	i	PRON
ijassa-1077	340	18	n	n	VERB
ijassa-1077	340	19	j	j	NOUN
ijassa-1077	340	20	m	m	VERB
ijassa-1077	340	21	i	i	NOUN
ijassa-1077	340	22	jm	jm	PROPN
ijassa-1077	340	23	pprpprr	pprpprr	PROPN
ijassa-1077	340	24	130	130	NUM
ijassa-1077	340	25	d.v	d.v	PROPN
ijassa-1077	340	26	.	.	PUNCT
ijassa-1077	341	1	tunitsky	tunitsky	NOUN
ijassa-1077	341	2	copyright	copyright	NOUN
ijassa-1077	342	1	©	©	PROPN
ijassa-1077	342	2	2021	2021	NUM
ijassa-1077	342	3	assa	assa	NOUN
ijassa-1077	342	4	.	.	PUNCT
ijassa-1077	343	1	adv	adv	PROPN
ijassa-1077	343	2	.	.	PUNCT
ijassa-1077	344	1	in	in	ADP
ijassa-1077	344	2	systems	system	NOUN
ijassa-1077	344	3	science	science	NOUN
ijassa-1077	344	4	and	and	CCONJ
ijassa-1077	344	5	appl	appl	NOUN
ijassa-1077	344	6	.	.	PUNCT
ijassa-1077	345	1	(	(	PUNCT
ijassa-1077	345	2	2021	2021	NUM
ijassa-1077	345	3	)	)	PUNCT
ijassa-1077	346	1	p1,	p1,	ADJ
ijassa-1077	346	2	…	…	PUNCT
ijassa-1077	346	3	,pm	,pm	PUNCT
ijassa-1077	346	4	for	for	ADP
ijassa-1077	346	5	j=1,	j=1,	NOUN
ijassa-1077	346	6	…	…	PUNCT
ijassa-1077	346	7	,n	,n	PUNCT
ijassa-1077	346	8	and	and	CCONJ
ijassa-1077	346	9	i=1,2,3,4	i=1,2,3,4	ADJ
ijassa-1077	346	10	(	(	PUNCT
ijassa-1077	346	11	see	see	VERB
ijassa-1077	346	12	section	section	NOUN
ijassa-1077	346	13	3	3	NUM
ijassa-1077	346	14	)	)	PUNCT
ijassa-1077	346	15	.	.	PUNCT
ijassa-1077	347	1	thence	thence	NOUN
ijassa-1077	347	2	all	all	DET
ijassa-1077	347	3	the	the	DET
ijassa-1077	347	4	functions	function	NOUN
ijassa-1077	347	5	rji	rji	VERB
ijassa-1077	347	6	are	be	AUX
ijassa-1077	347	7	smooth	smooth	ADJ
ijassa-1077	347	8	for	for	ADP
ijassa-1077	347	9	j=1,	j=1,	NOUN
ijassa-1077	347	10	…	…	PUNCT
ijassa-1077	347	11	,n	,n	NOUN
ijassa-1077	347	12	,	,	PUNCT
ijassa-1077	347	13	i=1,2,3,4	i=1,2,3,4	ADJ
ijassa-1077	347	14	,	,	PUNCT
ijassa-1077	347	15	and	and	CCONJ
ijassa-1077	347	16	the	the	DET
ijassa-1077	347	17	error	error	NOUN
ijassa-1077	347	18	functional	functional	ADJ
ijassa-1077	347	19	r	r	NOUN
ijassa-1077	347	20	=	=	NOUN
ijassa-1077	347	21	r(p1	r(p1	NOUN
ijassa-1077	347	22	,	,	PUNCT
ijassa-1077	347	23	…	…	PUNCT
ijassa-1077	347	24	,	,	PUNCT
ijassa-1077	347	25	pm	pm	NOUN
ijassa-1077	347	26	)	)	PUNCT
ijassa-1077	347	27	is	be	AUX
ijassa-1077	347	28	smooth	smooth	ADJ
ijassa-1077	347	29	with	with	ADP
ijassa-1077	347	30	respect	respect	NOUN
ijassa-1077	347	31	to	to	ADP
ijassa-1077	347	32	measurement	measurement	NOUN
ijassa-1077	347	33	data	datum	NOUN
ijassa-1077	347	34	vectors	vector	NOUN
ijassa-1077	347	35	p1,	p1,	ADP
ijassa-1077	347	36	…	…	PUNCT
ijassa-1077	347	37	,pm	,pm	PUNCT
ijassa-1077	347	38	too	too	ADV
ijassa-1077	347	39	.	.	PUNCT
ijassa-1077	348	1	at	at	ADP
ijassa-1077	348	2	the	the	DET
ijassa-1077	348	3	third	third	ADJ
ijassa-1077	348	4	step	step	NOUN
ijassa-1077	348	5	minimize	minimize	VERB
ijassa-1077	348	6	the	the	DET
ijassa-1077	348	7	error	error	NOUN
ijassa-1077	348	8	functional	functional	ADJ
ijassa-1077	348	9	r	r	NOUN
ijassa-1077	348	10	with	with	ADP
ijassa-1077	348	11	respect	respect	NOUN
ijassa-1077	348	12	to	to	ADP
ijassa-1077	348	13	measurement	measurement	NOUN
ijassa-1077	348	14	data	datum	NOUN
ijassa-1077	348	15	p1,	p1,	ADP
ijassa-1077	348	16	…	…	PUNCT
ijassa-1077	348	17	,pm	,pm	PUNCT
ijassa-1077	348	18	,	,	PUNCT
ijassa-1077	348	19	i.e.	i.e.	X
ijassa-1077	348	20	,	,	PUNCT
ijassa-1077	348	21	r(p1	r(p1	NOUN
ijassa-1077	348	22	,	,	PUNCT
ijassa-1077	348	23	…	…	PUNCT
ijassa-1077	348	24	,	,	PUNCT
ijassa-1077	348	25	pm	pm	NOUN
ijassa-1077	348	26	)	)	PUNCT
ijassa-1077	348	27	®	®	NOUN
ijassa-1077	348	28	min	min	NOUN
ijassa-1077	348	29	,	,	PUNCT
ijassa-1077	348	30	by	by	ADP
ijassa-1077	348	31	some	some	DET
ijassa-1077	348	32	minimization	minimization	NOUN
ijassa-1077	348	33	method	method	NOUN
ijassa-1077	348	34	.	.	PUNCT
ijassa-1077	349	1	the	the	DET
ijassa-1077	349	2	resulting	result	VERB
ijassa-1077	349	3	argument	argument	NOUN
ijassa-1077	349	4	(	(	PUNCT
ijassa-1077	349	5	p10	p10	NOUN
ijassa-1077	349	6	,	,	PUNCT
ijassa-1077	349	7	…	…	PUNCT
ijassa-1077	349	8	,	,	PUNCT
ijassa-1077	349	9	pm0	pm0	PROPN
ijassa-1077	349	10	)	)	PUNCT
ijassa-1077	349	11	of	of	ADP
ijassa-1077	349	12	the	the	DET
ijassa-1077	349	13	minimal	minimal	ADJ
ijassa-1077	349	14	value	value	NOUN
ijassa-1077	349	15	is	be	AUX
ijassa-1077	349	16	the	the	DET
ijassa-1077	349	17	measurement	measurement	NOUN
ijassa-1077	349	18	data	datum	NOUN
ijassa-1077	349	19	for	for	ADP
ijassa-1077	349	20	regularized	regularize	VERB
ijassa-1077	349	21	four	four	NUM
ijassa-1077	349	22	-	-	PUNCT
ijassa-1077	349	23	dimensional	dimensional	ADJ
ijassa-1077	349	24	printing	printing	NOUN
ijassa-1077	349	25	device	device	NOUN
ijassa-1077	349	26	.	.	PUNCT
ijassa-1077	350	1	remark	remark	NOUN
ijassa-1077	350	2	.	.	PUNCT
ijassa-1077	351	1	the	the	DET
ijassa-1077	351	2	dimension	dimension	NOUN
ijassa-1077	351	3	of	of	ADP
ijassa-1077	351	4	the	the	DET
ijassa-1077	351	5	space	space	NOUN
ijassa-1077	351	6	of	of	ADP
ijassa-1077	351	7	measurement	measurement	NOUN
ijassa-1077	351	8	data	datum	NOUN
ijassa-1077	351	9	is	be	AUX
ijassa-1077	351	10	3	3	NUM
ijassa-1077	351	11	m.	m.	NOUN
ijassa-1077	351	12	thus	thus	ADV
ijassa-1077	351	13	we	we	PRON
ijassa-1077	351	14	obtain	obtain	VERB
ijassa-1077	351	15	a	a	DET
ijassa-1077	351	16	3mdimensional	3mdimensional	ADJ
ijassa-1077	351	17	non	non	ADJ
ijassa-1077	351	18	-	-	ADJ
ijassa-1077	351	19	convex	convex	ADJ
ijassa-1077	351	20	minimization	minimization	NOUN
ijassa-1077	351	21	problem	problem	NOUN
ijassa-1077	351	22	.	.	PUNCT
ijassa-1077	352	1	by	by	ADP
ijassa-1077	352	2	construction	construction	NOUN
ijassa-1077	352	3	,	,	PUNCT
ijassa-1077	352	4	the	the	DET
ijassa-1077	352	5	error	error	NOUN
ijassa-1077	352	6	functional	functional	ADJ
ijassa-1077	352	7	r	r	NOUN
ijassa-1077	352	8	is	be	AUX
ijassa-1077	352	9	not	not	PART
ijassa-1077	352	10	convex	convex	ADJ
ijassa-1077	352	11	and	and	CCONJ
ijassa-1077	352	12	can	can	AUX
ijassa-1077	352	13	have	have	VERB
ijassa-1077	352	14	more	more	ADJ
ijassa-1077	352	15	than	than	ADP
ijassa-1077	352	16	one	one	NUM
ijassa-1077	352	17	minimal	minimal	ADJ
ijassa-1077	352	18	point	point	NOUN
ijassa-1077	352	19	.	.	PUNCT
ijassa-1077	353	1	consider	consider	VERB
ijassa-1077	353	2	the	the	DET
ijassa-1077	353	3	measurement	measurement	NOUN
ijassa-1077	353	4	file	file	VERB
ijassa-1077	353	5	cmyk.dat	cmyk.dat	NOUN
ijassa-1077	353	6	that	that	PRON
ijassa-1077	353	7	we	we	PRON
ijassa-1077	353	8	have	have	AUX
ijassa-1077	353	9	used	use	VERB
ijassa-1077	353	10	in	in	ADP
ijassa-1077	353	11	the	the	DET
ijassa-1077	353	12	example	example	NOUN
ijassa-1077	353	13	of	of	ADP
ijassa-1077	353	14	section	section	NOUN
ijassa-1077	353	15	5	5	NUM
ijassa-1077	353	16	.	.	PUNCT
ijassa-1077	354	1	direct	direct	ADJ
ijassa-1077	354	2	calculations	calculation	NOUN
ijassa-1077	354	3	show	show	VERB
ijassa-1077	354	4	that	that	SCONJ
ijassa-1077	354	5	this	this	DET
ijassa-1077	354	6	printing	printing	NOUN
ijassa-1077	354	7	device	device	NOUN
ijassa-1077	354	8	is	be	AUX
ijassa-1077	354	9	not	not	PART
ijassa-1077	354	10	strictly	strictly	ADV
ijassa-1077	354	11	non	non	ADJ
ijassa-1077	354	12	-	-	ADJ
ijassa-1077	354	13	degenerate	degenerate	ADJ
ijassa-1077	354	14	.	.	PUNCT
ijassa-1077	355	1	indeed	indeed	ADV
ijassa-1077	355	2	,	,	PUNCT
ijassa-1077	355	3	the	the	DET
ijassa-1077	355	4	table	table	NOUN
ijassa-1077	355	5	below	below	ADV
ijassa-1077	355	6	indicates	indicate	VERB
ijassa-1077	355	7	that	that	SCONJ
ijassa-1077	355	8	some	some	DET
ijassa-1077	355	9	coordinates	coordinate	NOUN
ijassa-1077	355	10	of	of	ADP
ijassa-1077	355	11	the	the	DET
ijassa-1077	355	12	characteristic	characteristic	ADJ
ijassa-1077	355	13	vector	vector	NOUN
ijassa-1077	355	14	field	field	NOUN
ijassa-1077	355	15	are	be	AUX
ijassa-1077	355	16	positive	positive	ADJ
ijassa-1077	355	17	whereas	whereas	SCONJ
ijassa-1077	355	18	some	some	PRON
ijassa-1077	355	19	are	be	AUX
ijassa-1077	355	20	negative	negative	ADJ
ijassa-1077	355	21	:	:	PUNCT
ijassa-1077	355	22	fig	fig	NOUN
ijassa-1077	355	23	.	.	PUNCT
ijassa-1077	356	1	5	5	X
ijassa-1077	356	2	.	.	X
ijassa-1077	356	3	distribution	distribution	NOUN
ijassa-1077	356	4	for	for	ADP
ijassa-1077	356	5	coordinates	coordinate	NOUN
ijassa-1077	356	6	of	of	ADP
ijassa-1077	356	7	the	the	DET
ijassa-1077	356	8	characteristic	characteristic	ADJ
ijassa-1077	356	9	vector	vector	NOUN
ijassa-1077	356	10	field	field	NOUN
ijassa-1077	356	11	from	from	ADP
ijassa-1077	356	12	geometrical	geometrical	ADJ
ijassa-1077	356	13	point	point	NOUN
ijassa-1077	356	14	of	of	ADP
ijassa-1077	356	15	view	view	NOUN
ijassa-1077	356	16	,	,	PUNCT
ijassa-1077	356	17	it	it	PRON
ijassa-1077	356	18	means	mean	VERB
ijassa-1077	356	19	that	that	SCONJ
ijassa-1077	356	20	we	we	PRON
ijassa-1077	356	21	have	have	VERB
ijassa-1077	356	22	too	too	ADV
ijassa-1077	356	23	many	many	ADJ
ijassa-1077	356	24	singular	singular	ADJ
ijassa-1077	356	25	faces	face	NOUN
ijassa-1077	356	26	that	that	PRON
ijassa-1077	356	27	lead	lead	VERB
ijassa-1077	356	28	to	to	ADP
ijassa-1077	356	29	formation	formation	NOUN
ijassa-1077	356	30	of	of	ADP
ijassa-1077	356	31	redundant	redundant	ADJ
ijassa-1077	356	32	faces	face	NOUN
ijassa-1077	356	33	or	or	CCONJ
ijassa-1077	356	34	singularities	singularity	NOUN
ijassa-1077	356	35	inside	inside	ADP
ijassa-1077	356	36	the	the	DET
ijassa-1077	356	37	color	color	NOUN
ijassa-1077	356	38	gamut	gamut	NOUN
ijassa-1077	356	39	.	.	PUNCT
ijassa-1077	357	1	visualization	visualization	NOUN
ijassa-1077	357	2	of	of	ADP
ijassa-1077	357	3	these	these	DET
ijassa-1077	357	4	singularities	singularity	NOUN
ijassa-1077	357	5	can	can	AUX
ijassa-1077	357	6	be	be	AUX
ijassa-1077	357	7	seen	see	VERB
ijassa-1077	357	8	in	in	ADP
ijassa-1077	357	9	the	the	DET
ijassa-1077	357	10	picture	picture	NOUN
ijassa-1077	357	11	below	below	ADV
ijassa-1077	357	12	:	:	PUNCT
ijassa-1077	357	13	fig	fig	NOUN
ijassa-1077	357	14	.	.	PUNCT
ijassa-1077	358	1	6	6	NUM
ijassa-1077	358	2	.	.	X
ijassa-1077	358	3	singularities	singularity	NOUN
ijassa-1077	358	4	inside	inside	ADP
ijassa-1077	358	5	the	the	DET
ijassa-1077	358	6	color	color	NOUN
ijassa-1077	358	7	gamut	gamut	NOUN
ijassa-1077	358	8	mathematical	mathematical	ADJ
ijassa-1077	358	9	modeling	modeling	NOUN
ijassa-1077	358	10	of	of	ADP
ijassa-1077	358	11	color	color	NOUN
ijassa-1077	358	12	printing	printing	NOUN
ijassa-1077	358	13	devices	device	NOUN
ijassa-1077	358	14	:	:	PUNCT
ijassa-1077	358	15	color	color	NOUN
ijassa-1077	358	16	gamut	gamut	NOUN
ijassa-1077	358	17	visualization	visualization	NOUN
ijassa-1077	358	18	…	…	PUNCT
ijassa-1077	358	19	131	131	NUM
ijassa-1077	358	20	copyright	copyright	NOUN
ijassa-1077	358	21	©	©	PROPN
ijassa-1077	358	22	2021	2021	NUM
ijassa-1077	358	23	assa	assa	NOUN
ijassa-1077	358	24	.	.	PUNCT
ijassa-1077	359	1	adv	adv	PROPN
ijassa-1077	359	2	.	.	PUNCT
ijassa-1077	360	1	in	in	ADP
ijassa-1077	360	2	systems	system	NOUN
ijassa-1077	360	3	science	science	NOUN
ijassa-1077	360	4	and	and	CCONJ
ijassa-1077	360	5	appl	appl	NOUN
ijassa-1077	360	6	.	.	PUNCT
ijassa-1077	361	1	(	(	PUNCT
ijassa-1077	361	2	2021	2021	NUM
ijassa-1077	361	3	)	)	PUNCT
ijassa-1077	361	4	in	in	ADP
ijassa-1077	361	5	particular	particular	ADJ
ijassa-1077	361	6	,	,	PUNCT
ijassa-1077	361	7	the	the	DET
ijassa-1077	361	8	singularities	singularity	NOUN
ijassa-1077	361	9	are	be	AUX
ijassa-1077	361	10	the	the	DET
ijassa-1077	361	11	polyhedrons	polyhedron	NOUN
ijassa-1077	361	12	in	in	ADP
ijassa-1077	361	13	white	white	ADJ
ijassa-1077	361	14	,	,	PUNCT
ijassa-1077	361	15	magenta	magenta	NOUN
ijassa-1077	361	16	,	,	PUNCT
ijassa-1077	361	17	yellow	yellow	ADJ
ijassa-1077	361	18	,	,	PUNCT
ijassa-1077	361	19	and	and	CCONJ
ijassa-1077	361	20	red	red	ADJ
ijassa-1077	361	21	.	.	PUNCT
ijassa-1077	362	1	therefore	therefore	ADV
ijassa-1077	362	2	,	,	PUNCT
ijassa-1077	362	3	it	it	PRON
ijassa-1077	362	4	makes	make	VERB
ijassa-1077	362	5	sense	sense	NOUN
ijassa-1077	362	6	to	to	PART
ijassa-1077	362	7	implement	implement	VERB
ijassa-1077	362	8	the	the	DET
ijassa-1077	362	9	described	describe	VERB
ijassa-1077	362	10	above	above	ADP
ijassa-1077	362	11	algorithmic	algorithmic	ADJ
ijassa-1077	362	12	scheme	scheme	NOUN
ijassa-1077	362	13	and	and	CCONJ
ijassa-1077	362	14	apply	apply	VERB
ijassa-1077	362	15	the	the	DET
ijassa-1077	362	16	resulting	result	VERB
ijassa-1077	362	17	tool	tool	NOUN
ijassa-1077	362	18	to	to	ADP
ijassa-1077	362	19	the	the	DET
ijassa-1077	362	20	measurement	measurement	NOUN
ijassa-1077	362	21	data	datum	NOUN
ijassa-1077	362	22	from	from	ADP
ijassa-1077	362	23	cmyk.dat	cmyk.dat	NOUN
ijassa-1077	362	24	file	file	NOUN
ijassa-1077	362	25	.	.	PUNCT
ijassa-1077	363	1	the	the	DET
ijassa-1077	363	2	author	author	NOUN
ijassa-1077	363	3	have	have	AUX
ijassa-1077	363	4	implemented	implement	VERB
ijassa-1077	363	5	such	such	DET
ijassa-1077	363	6	a	a	DET
ijassa-1077	363	7	tool	tool	NOUN
ijassa-1077	363	8	and	and	CCONJ
ijassa-1077	363	9	successfully	successfully	ADV
ijassa-1077	363	10	applied	apply	VERB
ijassa-1077	363	11	it	it	PRON
ijassa-1077	363	12	to	to	PART
ijassa-1077	363	13	force	force	VERB
ijassa-1077	363	14	the	the	DET
ijassa-1077	363	15	data	datum	NOUN
ijassa-1077	363	16	to	to	PART
ijassa-1077	363	17	become	become	VERB
ijassa-1077	363	18	strictly	strictly	ADV
ijassa-1077	363	19	non	non	ADJ
ijassa-1077	363	20	-	-	ADJ
ijassa-1077	363	21	degenerate	degenerate	ADJ
ijassa-1077	363	22	.	.	PUNCT
ijassa-1077	364	1	the	the	DET
ijassa-1077	364	2	table	table	NOUN
ijassa-1077	364	3	below	below	ADV
ijassa-1077	364	4	shows	show	VERB
ijassa-1077	364	5	that	that	SCONJ
ijassa-1077	364	6	after	after	ADP
ijassa-1077	364	7	the	the	DET
ijassa-1077	364	8	work	work	NOUN
ijassa-1077	364	9	of	of	ADP
ijassa-1077	364	10	this	this	DET
ijassa-1077	364	11	tool	tool	NOUN
ijassa-1077	364	12	the	the	DET
ijassa-1077	364	13	data	datum	NOUN
ijassa-1077	364	14	became	become	VERB
ijassa-1077	364	15	really	really	ADV
ijassa-1077	364	16	strictly	strictly	ADV
ijassa-1077	364	17	non	non	ADJ
ijassa-1077	364	18	-	-	ADJ
ijassa-1077	364	19	degenerate	degenerate	ADJ
ijassa-1077	364	20	:	:	PUNCT
ijassa-1077	364	21	fig	fig	NOUN
ijassa-1077	364	22	.	.	PUNCT
ijassa-1077	365	1	7	7	X
ijassa-1077	365	2	.	.	X
ijassa-1077	365	3	distribution	distribution	NOUN
ijassa-1077	365	4	for	for	ADP
ijassa-1077	365	5	coordinates	coordinate	NOUN
ijassa-1077	365	6	after	after	ADP
ijassa-1077	365	7	applying	apply	VERB
ijassa-1077	365	8	the	the	DET
ijassa-1077	365	9	algorithm	algorithm	NOUN
ijassa-1077	365	10	from	from	ADP
ijassa-1077	365	11	geometrical	geometrical	ADJ
ijassa-1077	365	12	point	point	NOUN
ijassa-1077	365	13	of	of	ADP
ijassa-1077	365	14	view	view	NOUN
ijassa-1077	365	15	,	,	PUNCT
ijassa-1077	365	16	it	it	PRON
ijassa-1077	365	17	means	mean	VERB
ijassa-1077	365	18	that	that	SCONJ
ijassa-1077	365	19	all	all	DET
ijassa-1077	365	20	the	the	DET
ijassa-1077	365	21	redundant	redundant	ADJ
ijassa-1077	365	22	singular	singular	NOUN
ijassa-1077	365	23	faces	face	NOUN
ijassa-1077	365	24	have	have	AUX
ijassa-1077	365	25	been	be	AUX
ijassa-1077	365	26	removed	remove	VERB
ijassa-1077	365	27	and	and	CCONJ
ijassa-1077	365	28	,	,	PUNCT
ijassa-1077	365	29	therefore	therefore	ADV
ijassa-1077	365	30	,	,	PUNCT
ijassa-1077	365	31	no	no	DET
ijassa-1077	365	32	singularities	singularity	NOUN
ijassa-1077	365	33	exist	exist	VERB
ijassa-1077	365	34	anymore	anymore	ADV
ijassa-1077	365	35	.	.	PUNCT
ijassa-1077	366	1	visualization	visualization	NOUN
ijassa-1077	366	2	of	of	ADP
ijassa-1077	366	3	color	color	NOUN
ijassa-1077	366	4	gamut	gamut	NOUN
ijassa-1077	366	5	of	of	ADP
ijassa-1077	366	6	the	the	DET
ijassa-1077	366	7	printing	printing	NOUN
ijassa-1077	366	8	device	device	NOUN
ijassa-1077	366	9	after	after	ADP
ijassa-1077	366	10	forcing	force	VERB
ijassa-1077	366	11	it	it	PRON
ijassa-1077	366	12	to	to	PART
ijassa-1077	366	13	become	become	VERB
ijassa-1077	366	14	strictly	strictly	ADV
ijassa-1077	366	15	non	non	ADJ
ijassa-1077	366	16	-	-	ADJ
ijassa-1077	366	17	degenerated	degenerated	ADJ
ijassa-1077	366	18	is	be	AUX
ijassa-1077	366	19	given	give	VERB
ijassa-1077	366	20	in	in	ADP
ijassa-1077	366	21	the	the	DET
ijassa-1077	366	22	picture	picture	NOUN
ijassa-1077	366	23	below	below	ADV
ijassa-1077	366	24	:	:	PUNCT
ijassa-1077	366	25	fig	fig	NOUN
ijassa-1077	366	26	.	.	PUNCT
ijassa-1077	367	1	8	8	X
ijassa-1077	367	2	.	.	PUNCT
ijassa-1077	368	1	the	the	DET
ijassa-1077	368	2	color	color	NOUN
ijassa-1077	368	3	gamut	gamut	NOUN
ijassa-1077	368	4	without	without	ADP
ijassa-1077	368	5	singularities	singularity	NOUN
ijassa-1077	368	6	after	after	ADP
ijassa-1077	368	7	applying	apply	VERB
ijassa-1077	368	8	the	the	DET
ijassa-1077	368	9	algorithm	algorithm	NOUN
ijassa-1077	368	10	indeed	indeed	ADV
ijassa-1077	368	11	,	,	PUNCT
ijassa-1077	368	12	no	no	DET
ijassa-1077	368	13	singularities	singularity	NOUN
ijassa-1077	368	14	are	be	AUX
ijassa-1077	368	15	present	present	ADJ
ijassa-1077	368	16	anymore	anymore	ADV
ijassa-1077	368	17	.	.	PUNCT
ijassa-1077	369	1	132	132	NUM
ijassa-1077	369	2	d.v	d.v	NOUN
ijassa-1077	369	3	.	.	PUNCT
ijassa-1077	370	1	tunitsky	tunitsky	NOUN
ijassa-1077	370	2	copyright	copyright	NOUN
ijassa-1077	371	1	©	©	PROPN
ijassa-1077	371	2	2021	2021	NUM
ijassa-1077	371	3	assa	assa	NOUN
ijassa-1077	371	4	.	.	PUNCT
ijassa-1077	372	1	adv	adv	PROPN
ijassa-1077	372	2	.	.	PUNCT
ijassa-1077	373	1	in	in	ADP
ijassa-1077	373	2	systems	system	NOUN
ijassa-1077	373	3	science	science	NOUN
ijassa-1077	373	4	and	and	CCONJ
ijassa-1077	373	5	appl	appl	NOUN
ijassa-1077	373	6	.	.	PUNCT
ijassa-1077	374	1	(	(	PUNCT
ijassa-1077	374	2	2021	2021	NUM
ijassa-1077	374	3	)	)	PUNCT
ijassa-1077	374	4	acknowledgements	acknowledgement	NOUN
ijassa-1077	374	5	this	this	DET
ijassa-1077	374	6	research	research	NOUN
ijassa-1077	374	7	was	be	AUX
ijassa-1077	374	8	carried	carry	VERB
ijassa-1077	374	9	out	out	ADP
ijassa-1077	374	10	with	with	ADP
ijassa-1077	374	11	the	the	DET
ijassa-1077	374	12	support	support	NOUN
ijassa-1077	374	13	of	of	ADP
ijassa-1077	374	14	the	the	DET
ijassa-1077	374	15	russian	russian	ADJ
ijassa-1077	374	16	foundation	foundation	NOUN
ijassa-1077	374	17	for	for	ADP
ijassa-1077	374	18	basic	basic	ADJ
ijassa-1077	374	19	research	research	NOUN
ijassa-1077	374	20	under	under	ADP
ijassa-1077	374	21	grant	grant	NOUN
ijassa-1077	374	22	no	no	NOUN
ijassa-1077	374	23	.	.	NOUN
ijassa-1077	374	24	20	20	NUM
ijassa-1077	374	25	-	-	PUNCT
ijassa-1077	374	26	01	01	NUM
ijassa-1077	374	27	-	-	PUNCT
ijassa-1077	374	28	00610	00610	NUM
ijassa-1077	374	29	a	a	PRON
ijassa-1077	374	30	and	and	CCONJ
ijassa-1077	374	31	the	the	DET
ijassa-1077	374	32	russian	russian	ADJ
ijassa-1077	374	33	scientific	scientific	ADJ
ijassa-1077	374	34	foundation	foundation	NOUN
ijassa-1077	374	35	under	under	ADP
ijassa-1077	374	36	grant	grant	PROPN
ijassa-1077	374	37	no	no	PROPN
ijassa-1077	374	38	.	.	NOUN
ijassa-1077	374	39	19	19	NUM
ijassa-1077	374	40	-	-	SYM
ijassa-1077	374	41	1100223	1100223	NUM
ijassa-1077	374	42	.	.	PUNCT
ijassa-1077	375	1	references	reference	NOUN
ijassa-1077	375	2	1	1	NUM
ijassa-1077	375	3	.	.	PUNCT
ijassa-1077	375	4	rurk	rurk	PROPN
ijassa-1077	376	1	c.p	c.p	PROPN
ijassa-1077	376	2	.	.	PROPN
ijassa-1077	376	3	,	,	PUNCT
ijassa-1077	376	4	sanderson	sanderson	PROPN
ijassa-1077	376	5	b.j	b.j	PROPN
ijassa-1077	376	6	.	.	PUNCT
ijassa-1077	377	1	(	(	PUNCT
ijassa-1077	377	2	1982	1982	NUM
ijassa-1077	377	3	)	)	PUNCT
ijassa-1077	377	4	an	an	DET
ijassa-1077	377	5	introduction	introduction	NOUN
ijassa-1077	377	6	to	to	PART
ijassa-1077	377	7	piecewise	piecewise	VERB
ijassa-1077	377	8	linear	linear	PROPN
ijassa-1077	377	9	topology	topology	NOUN
ijassa-1077	377	10	.	.	PUNCT
ijassa-1077	378	1	springer	springer	NOUN
ijassa-1077	378	2	–	–	PUNCT
ijassa-1077	378	3	verlag	verlag	PROPN
ijassa-1077	378	4	,	,	PUNCT
ijassa-1077	378	5	berlin	berlin	PROPN
ijassa-1077	378	6	–	–	PUNCT
ijassa-1077	378	7	new	new	PROPN
ijassa-1077	378	8	york	york	PROPN
ijassa-1077	378	9	.	.	PUNCT
ijassa-1077	379	1	2	2	X
ijassa-1077	379	2	.	.	X
ijassa-1077	379	3	kang	kang	PROPN
ijassa-1077	379	4	h.	h.	PROPN
ijassa-1077	379	5	(	(	PUNCT
ijassa-1077	379	6	1997	1997	NUM
ijassa-1077	379	7	)	)	PUNCT
ijassa-1077	379	8	color	color	NOUN
ijassa-1077	379	9	technology	technology	NOUN
ijassa-1077	379	10	for	for	ADP
ijassa-1077	379	11	electronic	electronic	ADJ
ijassa-1077	379	12	imaging	imaging	NOUN
ijassa-1077	379	13	devices	device	NOUN
ijassa-1077	379	14	.	.	PUNCT
ijassa-1077	380	1	spie	spie	NOUN
ijassa-1077	380	2	:	:	PUNCT
ijassa-1077	380	3	bellingham	bellingham	PROPN
ijassa-1077	380	4	,	,	PUNCT
ijassa-1077	380	5	washington	washington	PROPN
ijassa-1077	380	6	.	.	PUNCT
ijassa-1077	381	1	3	3	X
ijassa-1077	381	2	.	.	X
ijassa-1077	381	3	seifert	seifert	PROPN
ijassa-1077	381	4	h.	h.	PROPN
ijassa-1077	381	5	,	,	PUNCT
ijassa-1077	381	6	trelfall	trelfall	PROPN
ijassa-1077	381	7	w.	w.	PROPN
ijassa-1077	381	8	(	(	PUNCT
ijassa-1077	381	9	1980	1980	NUM
ijassa-1077	381	10	)	)	PUNCT
ijassa-1077	381	11	a	a	DET
ijassa-1077	381	12	textbook	textbook	NOUN
ijassa-1077	381	13	in	in	ADP
ijassa-1077	381	14	topology	topology	NOUN
ijassa-1077	381	15	.	.	PUNCT
ijassa-1077	382	1	algebraic	algebraic	PROPN
ijassa-1077	382	2	press	press	PROPN
ijassa-1077	382	3	,	,	PUNCT
ijassa-1077	382	4	new	new	PROPN
ijassa-1077	382	5	york	york	PROPN
ijassa-1077	382	6	.	.	PUNCT