id	sid	tid	token	lemma	pos
fuelectenerg-3080	1	1	facta	facta	PROPN
fuelectenerg-3080	1	2	universitatis	universitatis	PROPN
fuelectenerg-3080	1	3	series	series	NOUN
fuelectenerg-3080	1	4	:	:	PUNCT
fuelectenerg-3080	1	5	electronics	electronic	NOUN
fuelectenerg-3080	1	6	and	and	CCONJ
fuelectenerg-3080	1	7	energetics	energetics	NOUN
fuelectenerg-3080	1	8	vol	vol	NOUN
fuelectenerg-3080	1	9	.	.	PUNCT
fuelectenerg-3080	2	1	31	31	NUM
fuelectenerg-3080	2	2	,	,	PUNCT
fuelectenerg-3080	2	3	no	no	DET
fuelectenerg-3080	2	4	2	2	NUM
fuelectenerg-3080	2	5	,	,	PUNCT
fuelectenerg-3080	2	6	june	june	PROPN
fuelectenerg-3080	2	7	2018	2018	NUM
fuelectenerg-3080	2	8	,	,	PUNCT
fuelectenerg-3080	2	9	pp	pp	ADV
fuelectenerg-3080	2	10	.	.	PUNCT
fuelectenerg-3080	3	1	303	303	NUM
fuelectenerg-3080	3	2	311	311	NUM
fuelectenerg-3080	3	3	https://doi.org/10.2298/fuee1802303	https://doi.org/10.2298/fuee1802303	NOUN
fuelectenerg-3080	3	4	m	m	NOUN
fuelectenerg-3080	3	5	on	on	ADP
fuelectenerg-3080	3	6	a	a	DET
fuelectenerg-3080	3	7	property	property	NOUN
fuelectenerg-3080	3	8	of	of	ADP
fuelectenerg-3080	3	9	the	the	DET
fuelectenerg-3080	3	10	reed	reed	NOUN
fuelectenerg-3080	3	11	-	-	PUNCT
fuelectenerg-3080	3	12	muller	muller	NOUN
fuelectenerg-3080	3	13	-	-	PUNCT
fuelectenerg-3080	3	14	fourier	fourier	NOUN
fuelectenerg-3080	3	15	transform	transform	NOUN
fuelectenerg-3080	3	16			VERB
fuelectenerg-3080	3	17	claudio	claudio	PROPN
fuelectenerg-3080	3	18	moraga	moraga	PROPN
fuelectenerg-3080	3	19	faculty	faculty	NOUN
fuelectenerg-3080	3	20	of	of	ADP
fuelectenerg-3080	3	21	computer	computer	NOUN
fuelectenerg-3080	3	22	science	science	NOUN
fuelectenerg-3080	3	23	,	,	PUNCT
fuelectenerg-3080	3	24	technical	technical	ADJ
fuelectenerg-3080	3	25	university	university	PROPN
fuelectenerg-3080	3	26	of	of	ADP
fuelectenerg-3080	3	27	dortmund	dortmund	PROPN
fuelectenerg-3080	3	28	,	,	PUNCT
fuelectenerg-3080	3	29	germany	germany	PROPN
fuelectenerg-3080	3	30	abstract	abstract	NOUN
fuelectenerg-3080	3	31	.	.	PUNCT
fuelectenerg-3080	4	1	the	the	DET
fuelectenerg-3080	4	2	reed	reed	PROPN
fuelectenerg-3080	4	3	-	-	PUNCT
fuelectenerg-3080	4	4	muller	muller	NOUN
fuelectenerg-3080	4	5	-	-	PUNCT
fuelectenerg-3080	4	6	fourier	fourier	NOUN
fuelectenerg-3080	4	7	is	be	AUX
fuelectenerg-3080	4	8	reviewed	review	VERB
fuelectenerg-3080	4	9	and	and	CCONJ
fuelectenerg-3080	4	10	a	a	DET
fuelectenerg-3080	4	11	new	new	ADJ
fuelectenerg-3080	4	12	property	property	NOUN
fuelectenerg-3080	4	13	is	be	AUX
fuelectenerg-3080	4	14	presented	present	VERB
fuelectenerg-3080	4	15	:	:	PUNCT
fuelectenerg-3080	4	16	the	the	DET
fuelectenerg-3080	4	17	reed	reed	NOUN
fuelectenerg-3080	4	18	-	-	PUNCT
fuelectenerg-3080	4	19	muller	muller	NOUN
fuelectenerg-3080	4	20	-	-	PUNCT
fuelectenerg-3080	4	21	fourier	fourier	NOUN
fuelectenerg-3080	4	22	transform	transform	NOUN
fuelectenerg-3080	4	23	of	of	ADP
fuelectenerg-3080	4	24	an	an	DET
fuelectenerg-3080	4	25	n	n	CCONJ
fuelectenerg-3080	4	26	-	-	PUNCT
fuelectenerg-3080	4	27	place	place	NOUN
fuelectenerg-3080	4	28	p	p	NOUN
fuelectenerg-3080	4	29	-	-	PUNCT
fuelectenerg-3080	4	30	valued	value	VERB
fuelectenerg-3080	4	31	function	function	NOUN
fuelectenerg-3080	4	32	preserves	preserve	VERB
fuelectenerg-3080	4	33	any	any	DET
fuelectenerg-3080	4	34	permutation	permutation	NOUN
fuelectenerg-3080	4	35	of	of	ADP
fuelectenerg-3080	4	36	the	the	DET
fuelectenerg-3080	4	37	arguments	argument	NOUN
fuelectenerg-3080	4	38	.	.	PUNCT
fuelectenerg-3080	5	1	this	this	PRON
fuelectenerg-3080	5	2	leads	lead	VERB
fuelectenerg-3080	5	3	to	to	ADP
fuelectenerg-3080	5	4	the	the	DET
fuelectenerg-3080	5	5	additional	additional	ADJ
fuelectenerg-3080	5	6	result	result	NOUN
fuelectenerg-3080	5	7	that	that	SCONJ
fuelectenerg-3080	5	8	the	the	DET
fuelectenerg-3080	5	9	reed	reed	NOUN
fuelectenerg-3080	5	10	-	-	PUNCT
fuelectenerg-3080	5	11	mullerfourier	mullerfourier	NOUN
fuelectenerg-3080	5	12	spectrum	spectrum	NOUN
fuelectenerg-3080	5	13	of	of	ADP
fuelectenerg-3080	5	14	an	an	DET
fuelectenerg-3080	5	15	n	n	CCONJ
fuelectenerg-3080	5	16	-	-	PUNCT
fuelectenerg-3080	5	17	place	place	NOUN
fuelectenerg-3080	5	18	p	p	NOUN
fuelectenerg-3080	5	19	-	-	PUNCT
fuelectenerg-3080	5	20	valued	value	VERB
fuelectenerg-3080	5	21	symmetric	symmetric	ADJ
fuelectenerg-3080	5	22	function	function	NOUN
fuelectenerg-3080	5	23	is	be	AUX
fuelectenerg-3080	5	24	also	also	ADV
fuelectenerg-3080	5	25	symmetric	symmetric	ADJ
fuelectenerg-3080	5	26	.	.	PUNCT
fuelectenerg-3080	6	1	furthermore	furthermore	ADV
fuelectenerg-3080	6	2	,	,	PUNCT
fuelectenerg-3080	6	3	the	the	DET
fuelectenerg-3080	6	4	reed	reed	NOUN
fuelectenerg-3080	6	5	-	-	PUNCT
fuelectenerg-3080	6	6	muller	muller	NOUN
fuelectenerg-3080	6	7	and	and	CCONJ
fuelectenerg-3080	6	8	the	the	DET
fuelectenerg-3080	6	9	vilenkin	vilenkin	PROPN
fuelectenerg-3080	6	10	-	-	PUNCT
fuelectenerg-3080	6	11	chrestenson	chrestenson	NOUN
fuelectenerg-3080	6	12	spectra	spectra	NOUN
fuelectenerg-3080	6	13	of	of	ADP
fuelectenerg-3080	6	14	an	an	DET
fuelectenerg-3080	6	15	n	n	CCONJ
fuelectenerg-3080	6	16	-	-	PUNCT
fuelectenerg-3080	6	17	place	place	NOUN
fuelectenerg-3080	6	18	pvalued	pvalue	VERB
fuelectenerg-3080	6	19	symmetric	symmetric	ADJ
fuelectenerg-3080	6	20	function	function	NOUN
fuelectenerg-3080	6	21	are	be	AUX
fuelectenerg-3080	6	22	also	also	ADV
fuelectenerg-3080	6	23	symmetric	symmetric	ADJ
fuelectenerg-3080	6	24	.	.	PUNCT
fuelectenerg-3080	7	1	key	key	ADJ
fuelectenerg-3080	7	2	words	word	NOUN
fuelectenerg-3080	7	3	:	:	PUNCT
fuelectenerg-3080	7	4	multiple	multiple	ADJ
fuelectenerg-3080	7	5	-	-	PUNCT
fuelectenerg-3080	7	6	valued	value	VERB
fuelectenerg-3080	7	7	switching	switching	NOUN
fuelectenerg-3080	7	8	theory	theory	NOUN
fuelectenerg-3080	7	9	,	,	PUNCT
fuelectenerg-3080	7	10	symmetric	symmetric	ADJ
fuelectenerg-3080	7	11	functions	function	NOUN
fuelectenerg-3080	7	12	,	,	PUNCT
fuelectenerg-3080	7	13	reed	reed	NOUN
fuelectenerg-3080	7	14	-	-	PUNCT
fuelectenerg-3080	7	15	muller	muller	NOUN
fuelectenerg-3080	7	16	-	-	PUNCT
fuelectenerg-3080	7	17	fourier	fourier	NOUN
fuelectenerg-3080	7	18	transform	transform	NOUN
fuelectenerg-3080	7	19	.	.	PUNCT
fuelectenerg-3080	8	1	dedicated	dedicate	VERB
fuelectenerg-3080	8	2	to	to	PART
fuelectenerg-3080	8	3	prof	prof	PROPN
fuelectenerg-3080	8	4	.	.	PUNCT
fuelectenerg-3080	9	1	radomir	radomir	PROPN
fuelectenerg-3080	9	2	stanković	stanković	PROPN
fuelectenerg-3080	9	3	on	on	ADP
fuelectenerg-3080	9	4	the	the	DET
fuelectenerg-3080	9	5	occasion	occasion	NOUN
fuelectenerg-3080	9	6	of	of	ADP
fuelectenerg-3080	9	7	his	his	PRON
fuelectenerg-3080	9	8	65th	65th	ADJ
fuelectenerg-3080	9	9	birthday	birthday	NOUN
fuelectenerg-3080	9	10	1	1	NUM
fuelectenerg-3080	9	11	.	.	PUNCT
fuelectenerg-3080	10	1	introduction	introduction	NOUN
fuelectenerg-3080	10	2	the	the	DET
fuelectenerg-3080	10	3	fundamentals	fundamental	NOUN
fuelectenerg-3080	10	4	of	of	ADP
fuelectenerg-3080	10	5	the	the	DET
fuelectenerg-3080	10	6	reed	reed	NOUN
fuelectenerg-3080	10	7	-	-	PUNCT
fuelectenerg-3080	10	8	muller	muller	NOUN
fuelectenerg-3080	10	9	transform	transform	NOUN
fuelectenerg-3080	10	10	may	may	AUX
fuelectenerg-3080	10	11	be	be	AUX
fuelectenerg-3080	10	12	found	find	VERB
fuelectenerg-3080	10	13	in	in	ADP
fuelectenerg-3080	10	14	the	the	DET
fuelectenerg-3080	10	15	early	early	ADJ
fuelectenerg-3080	10	16	work	work	NOUN
fuelectenerg-3080	10	17	of	of	ADP
fuelectenerg-3080	10	18	i.	i.	PROPN
fuelectenerg-3080	10	19	zhegalkin	zhegalkin	PROPN
fuelectenerg-3080	11	1	[	[	X
fuelectenerg-3080	11	2	1	1	NUM
fuelectenerg-3080	11	3	]	]	PUNCT
fuelectenerg-3080	11	4	,	,	PUNCT
fuelectenerg-3080	11	5	[	[	X
fuelectenerg-3080	11	6	2	2	NUM
fuelectenerg-3080	11	7	]	]	PUNCT
fuelectenerg-3080	11	8	.	.	PUNCT
fuelectenerg-3080	12	1	however	however	ADV
fuelectenerg-3080	12	2	since	since	SCONJ
fuelectenerg-3080	12	3	his	his	PRON
fuelectenerg-3080	12	4	publications	publication	NOUN
fuelectenerg-3080	12	5	were	be	AUX
fuelectenerg-3080	12	6	in	in	ADP
fuelectenerg-3080	12	7	russian	russian	ADJ
fuelectenerg-3080	12	8	,	,	PUNCT
fuelectenerg-3080	12	9	they	they	PRON
fuelectenerg-3080	12	10	remained	remain	VERB
fuelectenerg-3080	12	11	practically	practically	ADV
fuelectenerg-3080	12	12	unknown	unknown	ADJ
fuelectenerg-3080	12	13	for	for	ADP
fuelectenerg-3080	12	14	scientists	scientist	NOUN
fuelectenerg-3080	12	15	not	not	PART
fuelectenerg-3080	12	16	proficient	proficient	ADJ
fuelectenerg-3080	12	17	in	in	ADP
fuelectenerg-3080	12	18	that	that	DET
fuelectenerg-3080	12	19	language	language	NOUN
fuelectenerg-3080	12	20	.	.	PUNCT
fuelectenerg-3080	13	1	the	the	DET
fuelectenerg-3080	13	2	transform	transform	NOUN
fuelectenerg-3080	13	3	was	be	AUX
fuelectenerg-3080	13	4	rediscovered	rediscover	VERB
fuelectenerg-3080	13	5	with	with	ADP
fuelectenerg-3080	13	6	the	the	DET
fuelectenerg-3080	13	7	works	work	NOUN
fuelectenerg-3080	13	8	of	of	ADP
fuelectenerg-3080	13	9	i.s	i.s	PROPN
fuelectenerg-3080	13	10	.	.	PUNCT
fuelectenerg-3080	14	1	reed	reed	PROPN
fuelectenerg-3080	15	1	[	[	X
fuelectenerg-3080	15	2	3	3	X
fuelectenerg-3080	15	3	]	]	PUNCT
fuelectenerg-3080	15	4	and	and	CCONJ
fuelectenerg-3080	15	5	d.e	d.e	PROPN
fuelectenerg-3080	15	6	.	.	PROPN
fuelectenerg-3080	15	7	muller	muller	NOUN
fuelectenerg-3080	16	1	[	[	X
fuelectenerg-3080	16	2	4	4	NUM
fuelectenerg-3080	16	3	]	]	PUNCT
fuelectenerg-3080	16	4	and	and	CCONJ
fuelectenerg-3080	16	5	since	since	SCONJ
fuelectenerg-3080	16	6	then	then	ADV
fuelectenerg-3080	16	7	,	,	PUNCT
fuelectenerg-3080	16	8	it	it	PRON
fuelectenerg-3080	16	9	carries	carry	VERB
fuelectenerg-3080	16	10	their	their	PRON
fuelectenerg-3080	16	11	names	name	NOUN
fuelectenerg-3080	16	12	.	.	PUNCT
fuelectenerg-3080	17	1	in	in	ADP
fuelectenerg-3080	17	2	the	the	DET
fuelectenerg-3080	17	3	literature	literature	NOUN
fuelectenerg-3080	17	4	frequently	frequently	ADV
fuelectenerg-3080	17	5	this	this	DET
fuelectenerg-3080	17	6	transform	transform	NOUN
fuelectenerg-3080	17	7	is	be	AUX
fuelectenerg-3080	17	8	mentioned	mention	VERB
fuelectenerg-3080	17	9	as	as	ADP
fuelectenerg-3080	17	10	the	the	DET
fuelectenerg-3080	17	11	rm	rm	NOUN
fuelectenerg-3080	17	12	transform	transform	NOUN
fuelectenerg-3080	17	13	.	.	PUNCT
fuelectenerg-3080	18	1	the	the	DET
fuelectenerg-3080	18	2	transform	transform	NOUN
fuelectenerg-3080	18	3	was	be	AUX
fuelectenerg-3080	18	4	developed	develop	VERB
fuelectenerg-3080	18	5	to	to	PART
fuelectenerg-3080	18	6	be	be	AUX
fuelectenerg-3080	18	7	applied	apply	VERB
fuelectenerg-3080	18	8	to	to	ADP
fuelectenerg-3080	18	9	boolean	boolean	ADJ
fuelectenerg-3080	18	10	functions	function	NOUN
fuelectenerg-3080	18	11	.	.	PUNCT
fuelectenerg-3080	19	1	the	the	DET
fuelectenerg-3080	19	2	later	later	ADJ
fuelectenerg-3080	19	3	extension	extension	NOUN
fuelectenerg-3080	19	4	of	of	ADP
fuelectenerg-3080	19	5	the	the	DET
fuelectenerg-3080	19	6	reed	reed	NOUN
fuelectenerg-3080	19	7	-	-	PUNCT
fuelectenerg-3080	19	8	muller	muller	NOUN
fuelectenerg-3080	19	9	transform	transform	NOUN
fuelectenerg-3080	19	10	to	to	ADP
fuelectenerg-3080	19	11	multiple	multiple	ADV
fuelectenerg-3080	19	12	-	-	PUNCT
fuelectenerg-3080	19	13	valued	value	VERB
fuelectenerg-3080	19	14	domains	domain	NOUN
fuelectenerg-3080	19	15	is	be	AUX
fuelectenerg-3080	19	16	due	due	ADJ
fuelectenerg-3080	19	17	to	to	ADP
fuelectenerg-3080	19	18	d.h	d.h	PROPN
fuelectenerg-3080	19	19	.	.	PROPN
fuelectenerg-3080	19	20	green	green	PROPN
fuelectenerg-3080	19	21	and	and	CCONJ
fuelectenerg-3080	19	22	i.s	i.s	PROPN
fuelectenerg-3080	19	23	.	.	PROPN
fuelectenerg-3080	19	24	taylor	taylor	PROPN
fuelectenerg-3080	20	1	[	[	X
fuelectenerg-3080	20	2	5	5	NUM
fuelectenerg-3080	20	3	]	]	PUNCT
fuelectenerg-3080	20	4	.	.	PUNCT
fuelectenerg-3080	21	1	the	the	DET
fuelectenerg-3080	21	2	reed	reed	PROPN
fuelectenerg-3080	21	3	-	-	PUNCT
fuelectenerg-3080	21	4	muller	muller	NOUN
fuelectenerg-3080	21	5	-	-	PUNCT
fuelectenerg-3080	21	6	fourier	fourier	NOUN
fuelectenerg-3080	21	7	transform	transform	NOUN
fuelectenerg-3080	21	8	(	(	PUNCT
fuelectenerg-3080	21	9	rmf	rmf	PROPN
fuelectenerg-3080	21	10	)	)	PUNCT
fuelectenerg-3080	21	11	was	be	AUX
fuelectenerg-3080	21	12	introduced	introduce	VERB
fuelectenerg-3080	21	13	by	by	ADP
fuelectenerg-3080	21	14	radomir	radomir	PROPN
fuelectenerg-3080	21	15	.	.	PUNCT
fuelectenerg-3080	22	1	s.	s.	PROPN
fuelectenerg-3080	22	2	stanković	stanković	PROPN
fuelectenerg-3080	23	1	[	[	X
fuelectenerg-3080	23	2	6	6	NUM
fuelectenerg-3080	23	3	]	]	PUNCT
fuelectenerg-3080	23	4	,	,	PUNCT
fuelectenerg-3080	23	5	[	[	X
fuelectenerg-3080	23	6	7	7	X
fuelectenerg-3080	23	7	]	]	PUNCT
fuelectenerg-3080	23	8	aiming	aim	VERB
fuelectenerg-3080	23	9	to	to	PART
fuelectenerg-3080	23	10	combine	combine	VERB
fuelectenerg-3080	23	11	relevant	relevant	ADJ
fuelectenerg-3080	23	12	properties	property	NOUN
fuelectenerg-3080	23	13	of	of	ADP
fuelectenerg-3080	23	14	the	the	DET
fuelectenerg-3080	23	15	reed	reed	NOUN
fuelectenerg-3080	23	16	-	-	PUNCT
fuelectenerg-3080	23	17	muller	muller	NOUN
fuelectenerg-3080	23	18	transform	transform	NOUN
fuelectenerg-3080	23	19	and	and	CCONJ
fuelectenerg-3080	23	20	the	the	DET
fuelectenerg-3080	23	21	discrete	discrete	ADJ
fuelectenerg-3080	23	22	fourier	fourier	NOUN
fuelectenerg-3080	23	23	transform	transform	NOUN
fuelectenerg-3080	23	24	.	.	PUNCT
fuelectenerg-3080	24	1	in	in	ADP
fuelectenerg-3080	24	2	a	a	DET
fuelectenerg-3080	24	3	way	way	NOUN
fuelectenerg-3080	24	4	,	,	PUNCT
fuelectenerg-3080	24	5	this	this	DET
fuelectenerg-3080	24	6	transform	transform	NOUN
fuelectenerg-3080	24	7	is	be	AUX
fuelectenerg-3080	24	8	another	another	DET
fuelectenerg-3080	24	9	extension	extension	NOUN
fuelectenerg-3080	24	10	of	of	ADP
fuelectenerg-3080	24	11	the	the	DET
fuelectenerg-3080	24	12	reedmuller	reedmuller	NOUN
fuelectenerg-3080	24	13	transform	transform	NOUN
fuelectenerg-3080	24	14	to	to	ADP
fuelectenerg-3080	24	15	the	the	DET
fuelectenerg-3080	24	16	multiple	multiple	ADV
fuelectenerg-3080	24	17	-	-	PUNCT
fuelectenerg-3080	24	18	valued	value	VERB
fuelectenerg-3080	24	19	domain	domain	NOUN
fuelectenerg-3080	24	20	.	.	PUNCT
fuelectenerg-3080	25	1	in	in	ADP
fuelectenerg-3080	25	2	the	the	DET
fuelectenerg-3080	25	3	binary	binary	ADJ
fuelectenerg-3080	25	4	case	case	NOUN
fuelectenerg-3080	25	5	,	,	PUNCT
fuelectenerg-3080	25	6	the	the	DET
fuelectenerg-3080	25	7	rmf	rmf	PROPN
fuelectenerg-3080	25	8	transform	transform	NOUN
fuelectenerg-3080	25	9	converges	converge	NOUN
fuelectenerg-3080	25	10	to	to	ADP
fuelectenerg-3080	25	11	the	the	DET
fuelectenerg-3080	25	12	reed	reed	NOUN
fuelectenerg-3080	25	13	-	-	PUNCT
fuelectenerg-3080	25	14	muller	muller	NOUN
fuelectenerg-3080	25	15	transform	transform	NOUN
fuelectenerg-3080	25	16	.	.	PUNCT
fuelectenerg-3080	26	1	received	receive	VERB
fuelectenerg-3080	26	2	august	august	PROPN
fuelectenerg-3080	26	3	3	3	NUM
fuelectenerg-3080	26	4	,	,	PUNCT
fuelectenerg-3080	26	5	2017	2017	NUM
fuelectenerg-3080	26	6	;	;	PUNCT
fuelectenerg-3080	26	7	received	receive	VERB
fuelectenerg-3080	26	8	in	in	ADP
fuelectenerg-3080	26	9	revised	revise	VERB
fuelectenerg-3080	26	10	form	form	NOUN
fuelectenerg-3080	26	11	september	september	PROPN
fuelectenerg-3080	26	12	8	8	NUM
fuelectenerg-3080	26	13	,	,	PUNCT
fuelectenerg-3080	26	14	2017	2017	NUM
fuelectenerg-3080	26	15	corresponding	correspond	VERB
fuelectenerg-3080	26	16	author	author	NOUN
fuelectenerg-3080	26	17	:	:	PUNCT
fuelectenerg-3080	26	18	claudio	claudio	PROPN
fuelectenerg-3080	26	19	moraga	moraga	PROPN
fuelectenerg-3080	26	20	faculty	faculty	NOUN
fuelectenerg-3080	26	21	of	of	ADP
fuelectenerg-3080	26	22	computer	computer	NOUN
fuelectenerg-3080	26	23	science	science	NOUN
fuelectenerg-3080	26	24	,	,	PUNCT
fuelectenerg-3080	26	25	technical	technical	ADJ
fuelectenerg-3080	26	26	university	university	PROPN
fuelectenerg-3080	26	27	of	of	ADP
fuelectenerg-3080	26	28	dortmund	dortmund	PROPN
fuelectenerg-3080	26	29	,	,	PUNCT
fuelectenerg-3080	26	30	germany	germany	PROPN
fuelectenerg-3080	26	31	(	(	PUNCT
fuelectenerg-3080	26	32	e	e	NOUN
fuelectenerg-3080	26	33	-	-	NOUN
fuelectenerg-3080	26	34	mail	mail	NOUN
fuelectenerg-3080	26	35	:	:	PUNCT
fuelectenerg-3080	26	36	claudio.moraga@tu-dortmund.de	claudio.moraga@tu-dortmund.de	NUM
fuelectenerg-3080	26	37	)	)	PUNCT
fuelectenerg-3080	26	38	304	304	NUM
fuelectenerg-3080	26	39	c.	c.	PROPN
fuelectenerg-3080	26	40	moraga	moraga	PROPN
fuelectenerg-3080	26	41	an	an	DET
fuelectenerg-3080	26	42	important	important	ADJ
fuelectenerg-3080	26	43	common	common	ADJ
fuelectenerg-3080	26	44	property	property	NOUN
fuelectenerg-3080	26	45	of	of	ADP
fuelectenerg-3080	26	46	both	both	CCONJ
fuelectenerg-3080	26	47	the	the	DET
fuelectenerg-3080	26	48	rm	rm	PROPN
fuelectenerg-3080	26	49	and	and	CCONJ
fuelectenerg-3080	26	50	rmf	rmf	PROPN
fuelectenerg-3080	26	51	transforms	transform	VERB
fuelectenerg-3080	26	52	is	be	AUX
fuelectenerg-3080	26	53	the	the	DET
fuelectenerg-3080	26	54	fact	fact	NOUN
fuelectenerg-3080	26	55	that	that	SCONJ
fuelectenerg-3080	26	56	they	they	PRON
fuelectenerg-3080	26	57	represent	represent	VERB
fuelectenerg-3080	26	58	bijections	bijection	NOUN
fuelectenerg-3080	26	59	in	in	ADP
fuelectenerg-3080	26	60	the	the	DET
fuelectenerg-3080	26	61	set	set	NOUN
fuelectenerg-3080	26	62	of	of	ADP
fuelectenerg-3080	26	63	p	p	PROPN
fuelectenerg-3080	26	64	–	–	PUNCT
fuelectenerg-3080	26	65	valued	value	VERB
fuelectenerg-3080	26	66	functions	function	NOUN
fuelectenerg-3080	26	67	.	.	PUNCT
fuelectenerg-3080	27	1	this	this	PRON
fuelectenerg-3080	27	2	means	mean	VERB
fuelectenerg-3080	27	3	that	that	SCONJ
fuelectenerg-3080	27	4	the	the	DET
fuelectenerg-3080	27	5	rm	rm	NOUN
fuelectenerg-3080	27	6	spectrum	spectrum	NOUN
fuelectenerg-3080	27	7	or	or	CCONJ
fuelectenerg-3080	27	8	the	the	DET
fuelectenerg-3080	27	9	rmf	rmf	PROPN
fuelectenerg-3080	27	10	spectrum	spectrum	NOUN
fuelectenerg-3080	27	11	of	of	ADP
fuelectenerg-3080	27	12	an	an	DET
fuelectenerg-3080	27	13	n	n	CCONJ
fuelectenerg-3080	27	14	–	–	PUNCT
fuelectenerg-3080	27	15	place	place	NOUN
fuelectenerg-3080	27	16	p	p	ADJ
fuelectenerg-3080	27	17	–	–	PUNCT
fuelectenerg-3080	27	18	valued	value	VERB
fuelectenerg-3080	27	19	functions	function	NOUN
fuelectenerg-3080	27	20	is	be	AUX
fuelectenerg-3080	27	21	again	again	ADV
fuelectenerg-3080	27	22	an	an	DET
fuelectenerg-3080	27	23	n	n	CCONJ
fuelectenerg-3080	27	24	–	–	PUNCT
fuelectenerg-3080	27	25	place	place	NOUN
fuelectenerg-3080	27	26	p	p	NOUN
fuelectenerg-3080	27	27	–	–	PUNCT
fuelectenerg-3080	27	28	valued	value	VERB
fuelectenerg-3080	27	29	function	function	NOUN
fuelectenerg-3080	27	30	,	,	PUNCT
fuelectenerg-3080	27	31	not	not	PART
fuelectenerg-3080	27	32	necessarily	necessarily	ADV
fuelectenerg-3080	27	33	different	different	ADJ
fuelectenerg-3080	27	34	from	from	ADP
fuelectenerg-3080	27	35	the	the	DET
fuelectenerg-3080	27	36	original	original	ADJ
fuelectenerg-3080	27	37	one	one	NUM
fuelectenerg-3080	27	38	.	.	PUNCT
fuelectenerg-3080	28	1	(	(	PUNCT
fuelectenerg-3080	28	2	it	it	PRON
fuelectenerg-3080	28	3	has	have	AUX
fuelectenerg-3080	28	4	been	be	AUX
fuelectenerg-3080	28	5	shown	show	VERB
fuelectenerg-3080	28	6	that	that	SCONJ
fuelectenerg-3080	28	7	both	both	DET
fuelectenerg-3080	28	8	transforms	transform	VERB
fuelectenerg-3080	28	9	have	have	AUX
fuelectenerg-3080	28	10	fixed	fix	VERB
fuelectenerg-3080	28	11	points	point	NOUN
fuelectenerg-3080	28	12	[	[	X
fuelectenerg-3080	28	13	8	8	NUM
fuelectenerg-3080	28	14	]	]	PUNCT
fuelectenerg-3080	28	15	,	,	PUNCT
fuelectenerg-3080	28	16	[	[	X
fuelectenerg-3080	28	17	9	9	NUM
fuelectenerg-3080	28	18	]	]	SYM
fuelectenerg-3080	28	19	)	)	PUNCT
fuelectenerg-3080	28	20	.	.	PUNCT
fuelectenerg-3080	29	1	moreover	moreover	ADV
fuelectenerg-3080	29	2	,	,	PUNCT
fuelectenerg-3080	29	3	both	both	CCONJ
fuelectenerg-3080	29	4	the	the	DET
fuelectenerg-3080	29	5	rm	rm	NOUN
fuelectenerg-3080	29	6	and	and	CCONJ
fuelectenerg-3080	29	7	the	the	DET
fuelectenerg-3080	29	8	rmf	rmf	PROPN
fuelectenerg-3080	29	9	transforms	transform	VERB
fuelectenerg-3080	29	10	have	have	VERB
fuelectenerg-3080	29	11	a	a	DET
fuelectenerg-3080	29	12	kronecker	kronecker	NOUN
fuelectenerg-3080	29	13	product	product	NOUN
fuelectenerg-3080	29	14	structure	structure	NOUN
fuelectenerg-3080	29	15	.	.	PUNCT
fuelectenerg-3080	30	1	(	(	PUNCT
fuelectenerg-3080	30	2	kronecker	kronecker	NOUN
fuelectenerg-3080	30	3	product	product	NOUN
fuelectenerg-3080	30	4	:	:	PUNCT
fuelectenerg-3080	30	5	see	see	VERB
fuelectenerg-3080	30	6	e.g.	e.g.	ADV
fuelectenerg-3080	30	7	[	[	X
fuelectenerg-3080	30	8	10	10	NUM
fuelectenerg-3080	30	9	]	]	PUNCT
fuelectenerg-3080	30	10	,	,	PUNCT
fuelectenerg-3080	30	11	[	[	X
fuelectenerg-3080	30	12	11	11	NUM
fuelectenerg-3080	30	13	]	]	NUM
fuelectenerg-3080	30	14	)	)	PUNCT
fuelectenerg-3080	30	15	.	.	PUNCT
fuelectenerg-3080	31	1	the	the	DET
fuelectenerg-3080	31	2	rmf	rmf	PROPN
fuelectenerg-3080	31	3	transform	transform	NOUN
fuelectenerg-3080	31	4	matrix	matrix	NOUN
fuelectenerg-3080	31	5	is	be	AUX
fuelectenerg-3080	31	6	lower	low	ADJ
fuelectenerg-3080	31	7	triangular	triangular	NOUN
fuelectenerg-3080	31	8	[	[	X
fuelectenerg-3080	31	9	12	12	NUM
fuelectenerg-3080	31	10	]	]	PUNCT
fuelectenerg-3080	31	11	and	and	CCONJ
fuelectenerg-3080	31	12	exhibits	exhibit	VERB
fuelectenerg-3080	31	13	special	special	ADJ
fuelectenerg-3080	31	14	similarities	similarity	NOUN
fuelectenerg-3080	31	15	with	with	ADP
fuelectenerg-3080	31	16	the	the	DET
fuelectenerg-3080	31	17	pascal	pascal	ADJ
fuelectenerg-3080	31	18	matrix	matrix	NOUN
fuelectenerg-3080	31	19	on	on	ADP
fuelectenerg-3080	31	20	finite	finite	ADJ
fuelectenerg-3080	31	21	fields	field	NOUN
fuelectenerg-3080	31	22	[	[	X
fuelectenerg-3080	31	23	13	13	NUM
fuelectenerg-3080	31	24	]	]	SYM
fuelectenerg-3080	31	25	.	.	PUNCT
fuelectenerg-3080	32	1	2	2	X
fuelectenerg-3080	32	2	.	.	X
fuelectenerg-3080	32	3	formalisms	formalism	NOUN
fuelectenerg-3080	32	4	notation	notation	NOUN
fuelectenerg-3080	32	5	:	:	PUNCT
fuelectenerg-3080	32	6	vectors	vector	NOUN
fuelectenerg-3080	32	7	and	and	CCONJ
fuelectenerg-3080	32	8	matrices	matrix	NOUN
fuelectenerg-3080	32	9	will	will	AUX
fuelectenerg-3080	32	10	be	be	AUX
fuelectenerg-3080	32	11	written	write	VERB
fuelectenerg-3080	32	12	with	with	ADP
fuelectenerg-3080	32	13	upper	upper	ADJ
fuelectenerg-3080	32	14	case	case	NOUN
fuelectenerg-3080	32	15	in	in	ADP
fuelectenerg-3080	32	16	bold	bold	ADJ
fuelectenerg-3080	32	17	.	.	PUNCT
fuelectenerg-3080	33	1	if	if	SCONJ
fuelectenerg-3080	33	2	m	m	NOUN
fuelectenerg-3080	33	3	is	be	AUX
fuelectenerg-3080	33	4	a	a	DET
fuelectenerg-3080	33	5	p	p	NOUN
fuelectenerg-3080	33	6	m	m	PRON
fuelectenerg-3080	33	7	p	p	PROPN
fuelectenerg-3080	33	8	n	n	PRON
fuelectenerg-3080	33	9	matrix	matrix	VERB
fuelectenerg-3080	33	10	,	,	PUNCT
fuelectenerg-3080	33	11	it	it	PRON
fuelectenerg-3080	33	12	will	will	AUX
fuelectenerg-3080	33	13	be	be	AUX
fuelectenerg-3080	33	14	denoted	denote	VERB
fuelectenerg-3080	33	15	simply	simply	ADV
fuelectenerg-3080	33	16	as	as	SCONJ
fuelectenerg-3080	33	17	mm	mm	PROPN
fuelectenerg-3080	33	18	,	,	PUNCT
fuelectenerg-3080	33	19	n.	n.	PROPN
fuelectenerg-3080	33	20	square	square	ADJ
fuelectenerg-3080	33	21	matrices	matrix	NOUN
fuelectenerg-3080	33	22	will	will	AUX
fuelectenerg-3080	33	23	be	be	AUX
fuelectenerg-3080	33	24	assigned	assign	VERB
fuelectenerg-3080	33	25	just	just	ADV
fuelectenerg-3080	33	26	one	one	NUM
fuelectenerg-3080	33	27	index	index	NOUN
fuelectenerg-3080	33	28	.	.	PUNCT
fuelectenerg-3080	34	1	if	if	SCONJ
fuelectenerg-3080	34	2	not	not	PART
fuelectenerg-3080	34	3	clear	clear	ADJ
fuelectenerg-3080	34	4	from	from	ADP
fuelectenerg-3080	34	5	the	the	DET
fuelectenerg-3080	34	6	context	context	NOUN
fuelectenerg-3080	34	7	,	,	PUNCT
fuelectenerg-3080	34	8	the	the	DET
fuelectenerg-3080	34	9	length	length	NOUN
fuelectenerg-3080	34	10	of	of	ADP
fuelectenerg-3080	34	11	vectors	vector	NOUN
fuelectenerg-3080	34	12	will	will	AUX
fuelectenerg-3080	34	13	be	be	AUX
fuelectenerg-3080	34	14	explicitly	explicitly	ADV
fuelectenerg-3080	34	15	given	give	VERB
fuelectenerg-3080	34	16	.	.	PUNCT
fuelectenerg-3080	35	1	an	an	DET
fuelectenerg-3080	35	2	exception	exception	NOUN
fuelectenerg-3080	35	3	to	to	ADP
fuelectenerg-3080	35	4	this	this	DET
fuelectenerg-3080	35	5	notation	notation	NOUN
fuelectenerg-3080	35	6	is	be	AUX
fuelectenerg-3080	35	7	“	"	PUNCT
fuelectenerg-3080	35	8	xprmf	xprmf	VERB
fuelectenerg-3080	35	9	”	"	PUNCT
fuelectenerg-3080	35	10	,	,	PUNCT
fuelectenerg-3080	35	11	which	which	PRON
fuelectenerg-3080	35	12	,	,	PUNCT
fuelectenerg-3080	35	13	for	for	ADP
fuelectenerg-3080	35	14	historical	historical	ADJ
fuelectenerg-3080	35	15	reasons	reason	NOUN
fuelectenerg-3080	35	16	[	[	X
fuelectenerg-3080	35	17	7	7	X
fuelectenerg-3080	35	18	]	]	PUNCT
fuelectenerg-3080	35	19	will	will	AUX
fuelectenerg-3080	35	20	be	be	AUX
fuelectenerg-3080	35	21	used	use	VERB
fuelectenerg-3080	35	22	to	to	PART
fuelectenerg-3080	35	23	denote	denote	VERB
fuelectenerg-3080	35	24	the	the	DET
fuelectenerg-3080	35	25	basis	basis	NOUN
fuelectenerg-3080	35	26	of	of	ADP
fuelectenerg-3080	35	27	the	the	DET
fuelectenerg-3080	35	28	rmf	rmf	PROPN
fuelectenerg-3080	35	29	transform	transform	NOUN
fuelectenerg-3080	35	30	.	.	PUNCT
fuelectenerg-3080	36	1	spectral	spectral	ADJ
fuelectenerg-3080	36	2	techniques	technique	NOUN
fuelectenerg-3080	36	3	in	in	ADP
fuelectenerg-3080	36	4	a	a	DET
fuelectenerg-3080	36	5	nut	nut	NOUN
fuelectenerg-3080	36	6	shell	shell	NOUN
fuelectenerg-3080	36	7	:	:	PUNCT
fuelectenerg-3080	36	8	let	let	VERB
fuelectenerg-3080	36	9	v	v	VERB
fuelectenerg-3080	36	10	=	=	SYM
fuelectenerg-3080	36	11	{	{	PUNCT
fuelectenerg-3080	36	12	0	0	NUM
fuelectenerg-3080	36	13	,	,	PUNCT
fuelectenerg-3080	36	14	1	1	NUM
fuelectenerg-3080	36	15	,	,	PUNCT
fuelectenerg-3080	36	16	…	…	PUNCT
fuelectenerg-3080	36	17	,	,	PUNCT
fuelectenerg-3080	36	18	p–1	p–1	NOUN
fuelectenerg-3080	36	19	}	}	PUNCT
fuelectenerg-3080	36	20	be	be	VERB
fuelectenerg-3080	36	21	the	the	DET
fuelectenerg-3080	36	22	domain	domain	NOUN
fuelectenerg-3080	36	23	of	of	ADP
fuelectenerg-3080	36	24	p	p	PROPN
fuelectenerg-3080	36	25	–	–	PUNCT
fuelectenerg-3080	36	26	valued	value	VERB
fuelectenerg-3080	36	27	functions	function	NOUN
fuelectenerg-3080	36	28	and	and	CCONJ
fuelectenerg-3080	36	29	let	let	VERB
fuelectenerg-3080	36	30	f	f	NOUN
fuelectenerg-3080	36	31	:	:	PUNCT
fuelectenerg-3080	36	32	v	v	NUM
fuelectenerg-3080	36	33	n	n	PRON
fuelectenerg-3080	36	34			NOUN
fuelectenerg-3080	36	35	v	v	NOUN
fuelectenerg-3080	36	36	,	,	PUNCT
fuelectenerg-3080	36	37	be	be	AUX
fuelectenerg-3080	36	38	an	an	DET
fuelectenerg-3080	36	39	nplace	nplace	NOUN
fuelectenerg-3080	36	40	p	p	NOUN
fuelectenerg-3080	36	41	–	–	PUNCT
fuelectenerg-3080	36	42	valued	value	VERB
fuelectenerg-3080	36	43	function	function	NOUN
fuelectenerg-3080	36	44	.	.	PUNCT
fuelectenerg-3080	37	1	to	to	ADP
fuelectenerg-3080	37	2	every	every	DET
fuelectenerg-3080	37	3	function	function	NOUN
fuelectenerg-3080	37	4	f	f	NOUN
fuelectenerg-3080	37	5	,	,	PUNCT
fuelectenerg-3080	37	6	a	a	DET
fuelectenerg-3080	37	7	value	value	NOUN
fuelectenerg-3080	37	8	column	column	NOUN
fuelectenerg-3080	37	9	vector	vector	NOUN
fuelectenerg-3080	37	10	f	f	PROPN
fuelectenerg-3080	37	11	of	of	ADP
fuelectenerg-3080	37	12	length	length	NOUN
fuelectenerg-3080	37	13	p	p	PROPN
fuelectenerg-3080	37	14	n	n	NUM
fuelectenerg-3080	37	15	is	be	AUX
fuelectenerg-3080	37	16	associated	associate	VERB
fuelectenerg-3080	37	17	.	.	PUNCT
fuelectenerg-3080	38	1	the	the	DET
fuelectenerg-3080	38	2	elements	element	NOUN
fuelectenerg-3080	38	3	of	of	ADP
fuelectenerg-3080	38	4	f	f	PROPN
fuelectenerg-3080	38	5	are	be	AUX
fuelectenerg-3080	38	6	the	the	DET
fuelectenerg-3080	38	7	values	value	NOUN
fuelectenerg-3080	38	8	of	of	ADP
fuelectenerg-3080	38	9	f	f	PROPN
fuelectenerg-3080	38	10	for	for	ADP
fuelectenerg-3080	38	11	all	all	DET
fuelectenerg-3080	38	12	the	the	DET
fuelectenerg-3080	38	13	different	different	ADJ
fuelectenerg-3080	38	14	value	value	NOUN
fuelectenerg-3080	38	15	assignments	assignment	NOUN
fuelectenerg-3080	38	16	to	to	ADP
fuelectenerg-3080	38	17	the	the	DET
fuelectenerg-3080	38	18	arguments	argument	NOUN
fuelectenerg-3080	38	19	.	.	PUNCT
fuelectenerg-3080	39	1	the	the	DET
fuelectenerg-3080	39	2	elements	element	NOUN
fuelectenerg-3080	39	3	of	of	ADP
fuelectenerg-3080	39	4	f	f	PRON
fuelectenerg-3080	39	5	follow	follow	VERB
fuelectenerg-3080	39	6	the	the	DET
fuelectenerg-3080	39	7	lexicographic	lexicographic	ADJ
fuelectenerg-3080	39	8	order	order	NOUN
fuelectenerg-3080	39	9	of	of	ADP
fuelectenerg-3080	39	10	the	the	DET
fuelectenerg-3080	39	11	value	value	NOUN
fuelectenerg-3080	39	12	assignments	assignment	NOUN
fuelectenerg-3080	39	13	to	to	ADP
fuelectenerg-3080	39	14	the	the	DET
fuelectenerg-3080	39	15	arguments	argument	NOUN
fuelectenerg-3080	39	16	of	of	ADP
fuelectenerg-3080	39	17	f.	f.	PROPN
fuelectenerg-3080	39	18	let	let	VERB
fuelectenerg-3080	39	19	f	f	PROPN
fuelectenerg-3080	39	20			PROPN
fuelectenerg-3080	39	21	f	f	PROPN
fuelectenerg-3080	39	22	denote	denote	VERB
fuelectenerg-3080	39	23	the	the	DET
fuelectenerg-3080	39	24	association	association	NOUN
fuelectenerg-3080	39	25	.	.	PUNCT
fuelectenerg-3080	40	1	it	it	PRON
fuelectenerg-3080	40	2	is	be	AUX
fuelectenerg-3080	40	3	obvious	obvious	ADJ
fuelectenerg-3080	40	4	that	that	SCONJ
fuelectenerg-3080	40	5	f	f	PROPN
fuelectenerg-3080	40	6			ADJ
fuelectenerg-3080	40	7	inf	inf	NOUN
fuelectenerg-3080	40	8	,	,	PUNCT
fuelectenerg-3080	40	9	where	where	SCONJ
fuelectenerg-3080	40	10	in	in	ADP
fuelectenerg-3080	40	11	denotes	denote	NOUN
fuelectenerg-3080	40	12	the	the	DET
fuelectenerg-3080	40	13	identity	identity	NOUN
fuelectenerg-3080	40	14	matrix	matrix	NOUN
fuelectenerg-3080	40	15	,	,	PUNCT
fuelectenerg-3080	40	16	represents	represent	VERB
fuelectenerg-3080	40	17	a	a	DET
fuelectenerg-3080	40	18	valid	valid	ADJ
fuelectenerg-3080	40	19	association	association	NOUN
fuelectenerg-3080	40	20	.	.	PUNCT
fuelectenerg-3080	41	1	if	if	SCONJ
fuelectenerg-3080	41	2	mn	mn	PROPN
fuelectenerg-3080	41	3	is	be	AUX
fuelectenerg-3080	41	4	a	a	DET
fuelectenerg-3080	41	5	non	non	ADJ
fuelectenerg-3080	41	6	-	-	ADJ
fuelectenerg-3080	41	7	singular	singular	ADJ
fuelectenerg-3080	41	8	matrix	matrix	NOUN
fuelectenerg-3080	41	9	,	,	PUNCT
fuelectenerg-3080	41	10	its	its	PRON
fuelectenerg-3080	41	11	inverse	inverse	NOUN
fuelectenerg-3080	41	12	is	be	AUX
fuelectenerg-3080	41	13	also	also	ADV
fuelectenerg-3080	41	14	non	non	ADJ
fuelectenerg-3080	41	15	-	-	ADJ
fuelectenerg-3080	41	16	singular	singular	ADJ
fuelectenerg-3080	41	17	and	and	CCONJ
fuelectenerg-3080	41	18	well	well	ADV
fuelectenerg-3080	41	19	defined	define	VERB
fuelectenerg-3080	41	20	.	.	PUNCT
fuelectenerg-3080	42	1	moreover	moreover	ADV
fuelectenerg-3080	42	2	since	since	SCONJ
fuelectenerg-3080	42	3	(	(	PUNCT
fuelectenerg-3080	42	4	mn	mn	NOUN
fuelectenerg-3080	42	5	)	)	PUNCT
fuelectenerg-3080	42	6	-1	-1	PUNCT
fuelectenerg-3080	42	7			NUM
fuelectenerg-3080	42	8	mn	mn	NOUN
fuelectenerg-3080	42	9	=	=	PUNCT
fuelectenerg-3080	42	10	in	in	ADP
fuelectenerg-3080	42	11	,	,	PUNCT
fuelectenerg-3080	42	12	then	then	ADV
fuelectenerg-3080	42	13	f	f	PROPN
fuelectenerg-3080	42	14			PROPN
fuelectenerg-3080	42	15	(	(	PUNCT
fuelectenerg-3080	42	16	mn	mn	PROPN
fuelectenerg-3080	42	17	)	)	PUNCT
fuelectenerg-3080	42	18	-1	-1	PUNCT
fuelectenerg-3080	42	19	mnf	mnf	PROPN
fuelectenerg-3080	42	20	is	be	AUX
fuelectenerg-3080	42	21	also	also	ADV
fuelectenerg-3080	42	22	a	a	DET
fuelectenerg-3080	42	23	valid	valid	ADJ
fuelectenerg-3080	42	24	association	association	NOUN
fuelectenerg-3080	42	25	and	and	CCONJ
fuelectenerg-3080	42	26	represents	represent	VERB
fuelectenerg-3080	42	27	the	the	DET
fuelectenerg-3080	42	28	basic	basic	ADJ
fuelectenerg-3080	42	29	concept	concept	NOUN
fuelectenerg-3080	42	30	of	of	ADP
fuelectenerg-3080	42	31	spectral	spectral	ADJ
fuelectenerg-3080	42	32	transformations	transformation	NOUN
fuelectenerg-3080	42	33	.	.	PUNCT
fuelectenerg-3080	43	1	since	since	SCONJ
fuelectenerg-3080	43	2	(	(	PUNCT
fuelectenerg-3080	43	3	mn	mn	PROPN
fuelectenerg-3080	43	4	)	)	PUNCT
fuelectenerg-3080	43	5	-1	-1	PUNCT
fuelectenerg-3080	43	6	is	be	AUX
fuelectenerg-3080	43	7	non	non	ADJ
fuelectenerg-3080	43	8	-	-	ADJ
fuelectenerg-3080	43	9	singular	singular	ADJ
fuelectenerg-3080	43	10	,	,	PUNCT
fuelectenerg-3080	43	11	its	its	PRON
fuelectenerg-3080	43	12	columns	column	NOUN
fuelectenerg-3080	43	13	form	form	VERB
fuelectenerg-3080	43	14	a	a	DET
fuelectenerg-3080	43	15	linearly	linearly	ADV
fuelectenerg-3080	43	16	independent	independent	ADJ
fuelectenerg-3080	43	17	set	set	NOUN
fuelectenerg-3080	43	18	.	.	PUNCT
fuelectenerg-3080	44	1	if	if	SCONJ
fuelectenerg-3080	44	2	the	the	DET
fuelectenerg-3080	44	3	columns	column	NOUN
fuelectenerg-3080	44	4	of	of	ADP
fuelectenerg-3080	44	5	(	(	PUNCT
fuelectenerg-3080	44	6	mn	mn	PROPN
fuelectenerg-3080	44	7	)	)	PUNCT
fuelectenerg-3080	44	8	-1	-1	PUNCT
fuelectenerg-3080	44	9	are	be	AUX
fuelectenerg-3080	44	10	considered	consider	VERB
fuelectenerg-3080	44	11	to	to	PART
fuelectenerg-3080	44	12	represent	represent	VERB
fuelectenerg-3080	44	13	value	value	NOUN
fuelectenerg-3080	44	14	vectors	vector	NOUN
fuelectenerg-3080	44	15	of	of	ADP
fuelectenerg-3080	44	16	auxiliary	auxiliary	ADJ
fuelectenerg-3080	44	17	functions	function	NOUN
fuelectenerg-3080	44	18	,	,	PUNCT
fuelectenerg-3080	44	19	then	then	ADV
fuelectenerg-3080	44	20	(	(	PUNCT
fuelectenerg-3080	44	21	mn	mn	NOUN
fuelectenerg-3080	44	22	)	)	PUNCT
fuelectenerg-3080	44	23	-1	-1	PUNCT
fuelectenerg-3080	44	24	constitutes	constitute	VERB
fuelectenerg-3080	44	25	a	a	DET
fuelectenerg-3080	44	26	basis	basis	NOUN
fuelectenerg-3080	44	27	.	.	PUNCT
fuelectenerg-3080	45	1	mn	mn	PROPN
fuelectenerg-3080	45	2	,	,	PUNCT
fuelectenerg-3080	45	3	the	the	DET
fuelectenerg-3080	45	4	inverse	inverse	NOUN
fuelectenerg-3080	45	5	of	of	ADP
fuelectenerg-3080	45	6	(	(	PUNCT
fuelectenerg-3080	45	7	mn	mn	PROPN
fuelectenerg-3080	45	8	)	)	PUNCT
fuelectenerg-3080	45	9	-1	-1	VERB
fuelectenerg-3080	45	10	,	,	PUNCT
fuelectenerg-3080	45	11	is	be	AUX
fuelectenerg-3080	45	12	called	call	VERB
fuelectenerg-3080	45	13	a	a	DET
fuelectenerg-3080	45	14	transform	transform	NOUN
fuelectenerg-3080	45	15	matrix	matrix	NOUN
fuelectenerg-3080	45	16	and	and	CCONJ
fuelectenerg-3080	45	17	the	the	DET
fuelectenerg-3080	45	18	product	product	NOUN
fuelectenerg-3080	45	19	mnf	mnf	NOUN
fuelectenerg-3080	45	20	is	be	AUX
fuelectenerg-3080	45	21	normally	normally	ADV
fuelectenerg-3080	45	22	called	call	VERB
fuelectenerg-3080	45	23	the	the	DET
fuelectenerg-3080	45	24	spectrum	spectrum	NOUN
fuelectenerg-3080	45	25	of	of	ADP
fuelectenerg-3080	45	26	f.	f.	PROPN
fuelectenerg-3080	45	27	the	the	DET
fuelectenerg-3080	45	28	inner	inner	ADJ
fuelectenerg-3080	45	29	product	product	NOUN
fuelectenerg-3080	45	30	of	of	ADP
fuelectenerg-3080	45	31	the	the	DET
fuelectenerg-3080	45	32	basis	basis	NOUN
fuelectenerg-3080	45	33	and	and	CCONJ
fuelectenerg-3080	45	34	the	the	DET
fuelectenerg-3080	45	35	spectrum	spectrum	NOUN
fuelectenerg-3080	45	36	leads	lead	VERB
fuelectenerg-3080	45	37	to	to	ADP
fuelectenerg-3080	45	38	a	a	DET
fuelectenerg-3080	45	39	polynomial	polynomial	ADJ
fuelectenerg-3080	45	40	expression	expression	NOUN
fuelectenerg-3080	45	41	of	of	ADP
fuelectenerg-3080	45	42	f.	f.	PROPN
fuelectenerg-3080	45	43	depending	depend	VERB
fuelectenerg-3080	45	44	on	on	ADP
fuelectenerg-3080	45	45	the	the	DET
fuelectenerg-3080	45	46	choice	choice	NOUN
fuelectenerg-3080	45	47	of	of	ADP
fuelectenerg-3080	45	48	(	(	PUNCT
fuelectenerg-3080	45	49	mn	mn	PROPN
fuelectenerg-3080	45	50	)	)	PUNCT
fuelectenerg-3080	45	51	-1	-1	ADV
fuelectenerg-3080	45	52	,	,	PUNCT
fuelectenerg-3080	45	53	different	different	ADJ
fuelectenerg-3080	45	54	polynomial	polynomial	ADJ
fuelectenerg-3080	45	55	expressions	expression	NOUN
fuelectenerg-3080	45	56	on	on	ADP
fuelectenerg-3080	45	57	elements	element	NOUN
fuelectenerg-3080	45	58	of	of	ADP
fuelectenerg-3080	45	59	the	the	DET
fuelectenerg-3080	45	60	basis	basis	NOUN
fuelectenerg-3080	45	61	will	will	AUX
fuelectenerg-3080	45	62	be	be	AUX
fuelectenerg-3080	45	63	obtained	obtain	VERB
fuelectenerg-3080	45	64	.	.	PUNCT
fuelectenerg-3080	46	1	definition	definition	NOUN
fuelectenerg-3080	46	2	1	1	NUM
fuelectenerg-3080	46	3	:	:	PUNCT
fuelectenerg-3080	46	4	let	let	VERB
fuelectenerg-3080	46	5	f	f	X
fuelectenerg-3080	46	6	,	,	PUNCT
fuelectenerg-3080	46	7	g	g	NOUN
fuelectenerg-3080	46	8	:	:	PUNCT
fuelectenerg-3080	46	9	zp	zp	PROPN
fuelectenerg-3080	46	10			PROPN
fuelectenerg-3080	47	1	zp	zp	X
fuelectenerg-3080	47	2	.	.	PUNCT
fuelectenerg-3080	48	1	the	the	DET
fuelectenerg-3080	48	2	gibbs	gibbs	PROPN
fuelectenerg-3080	48	3	convolution	convolution	NOUN
fuelectenerg-3080	48	4	product	product	NOUN
fuelectenerg-3080	48	5	(	(	PUNCT
fuelectenerg-3080	48	6			NOUN
fuelectenerg-3080	48	7	)	)	PUNCT
fuelectenerg-3080	48	8	of	of	ADP
fuelectenerg-3080	48	9	p	p	NOUN
fuelectenerg-3080	48	10	-	-	PUNCT
fuelectenerg-3080	48	11	valued	value	VERB
fuelectenerg-3080	48	12	functions	function	NOUN
fuelectenerg-3080	48	13	is	be	AUX
fuelectenerg-3080	48	14	calculated	calculate	VERB
fuelectenerg-3080	48	15	as	as	SCONJ
fuelectenerg-3080	48	16	follows	follow	VERB
fuelectenerg-3080	48	17	[	[	X
fuelectenerg-3080	48	18	6	6	NUM
fuelectenerg-3080	48	19	]	]	X
fuelectenerg-3080	48	20	:	:	PUNCT
fuelectenerg-3080	48	21	if	if	SCONJ
fuelectenerg-3080	48	22	x	x	SYM
fuelectenerg-3080	48	23	=	=	SYM
fuelectenerg-3080	48	24	0	0	NUM
fuelectenerg-3080	48	25	,	,	PUNCT
fuelectenerg-3080	48	26	then	then	ADV
fuelectenerg-3080	48	27	(	(	PUNCT
fuelectenerg-3080	48	28	f	f	PROPN
fuelectenerg-3080	48	29			PROPN
fuelectenerg-3080	48	30	g)(0	g)(0	PROPN
fuelectenerg-3080	48	31	)	)	PUNCT
fuelectenerg-3080	49	1	=	=	SYM
fuelectenerg-3080	49	2	0	0	X
fuelectenerg-3080	49	3	.	.	PUNCT
fuelectenerg-3080	50	1	if	if	SCONJ
fuelectenerg-3080	50	2	x	x	PROPN
fuelectenerg-3080	50	3			NOUN
fuelectenerg-3080	50	4	0	0	NUM
fuelectenerg-3080	50	5	,	,	PUNCT
fuelectenerg-3080	50	6	then	then	ADV
fuelectenerg-3080	50	7	(	(	PUNCT
fuelectenerg-3080	50	8	f	f	PROPN
fuelectenerg-3080	50	9			PROPN
fuelectenerg-3080	50	10	g)(x	g)(x	PROPN
fuelectenerg-3080	50	11	)	)	PUNCT
fuelectenerg-3080	50	12	=	=	PUNCT
fuelectenerg-3080	51	1	∑	∑	PROPN
fuelectenerg-3080	51	2	–	–	PUNCT
fuelectenerg-3080	51	3	–	–	PUNCT
fuelectenerg-3080	51	4	mod	mod	NOUN
fuelectenerg-3080	51	5	p	p	PROPN
fuelectenerg-3080	51	6	definition	definition	NOUN
fuelectenerg-3080	51	7	2	2	NUM
fuelectenerg-3080	51	8	:	:	PUNCT
fuelectenerg-3080	51	9	the	the	DET
fuelectenerg-3080	51	10	fundamental	fundamental	ADJ
fuelectenerg-3080	51	11	basis	basis	NOUN
fuelectenerg-3080	51	12	for	for	ADP
fuelectenerg-3080	51	13	the	the	DET
fuelectenerg-3080	51	14	rmf	rmf	PROPN
fuelectenerg-3080	51	15	transform	transform	NOUN
fuelectenerg-3080	51	16	,	,	PUNCT
fuelectenerg-3080	51	17	called	call	VERB
fuelectenerg-3080	51	18	xprmf	xprmf	VERB
fuelectenerg-3080	51	19	is	be	AUX
fuelectenerg-3080	51	20	the	the	DET
fuelectenerg-3080	51	21	following	following	NOUN
fuelectenerg-3080	51	22	[	[	X
fuelectenerg-3080	51	23	6	6	NUM
fuelectenerg-3080	51	24	]	]	PUNCT
fuelectenerg-3080	51	25	,	,	PUNCT
fuelectenerg-3080	51	26	[	[	X
fuelectenerg-3080	51	27	7	7	NUM
fuelectenerg-3080	51	28	]	]	PUNCT
fuelectenerg-3080	51	29	:	:	PUNCT
fuelectenerg-3080	51	30	xprmf	xprmf	VERB
fuelectenerg-3080	51	31	=	=	PUNCT
fuelectenerg-3080	52	1	[	[	X
fuelectenerg-3080	52	2	x	x	X
fuelectenerg-3080	52	3	*	*	NOUN
fuelectenerg-3080	52	4	0	0	PUNCT
fuelectenerg-3080	53	1	x	x	X
fuelectenerg-3080	53	2	*	*	PROPN
fuelectenerg-3080	53	3	1	1	NUM
fuelectenerg-3080	53	4	…	…	PUNCT
fuelectenerg-3080	53	5	x	x	SYM
fuelectenerg-3080	53	6	*	*	PUNCT
fuelectenerg-3080	53	7	(	(	PUNCT
fuelectenerg-3080	53	8	p–1	p–1	NOUN
fuelectenerg-3080	53	9	)	)	PUNCT
fuelectenerg-3080	53	10	]	]	PUNCT
fuelectenerg-3080	53	11	,	,	PUNCT
fuelectenerg-3080	53	12	where	where	SCONJ
fuelectenerg-3080	53	13	x	x	X
fuelectenerg-3080	53	14	*	*	NOUN
fuelectenerg-3080	53	15	0	0	PUNCT
fuelectenerg-3080	53	16	is	be	AUX
fuelectenerg-3080	53	17	defined	define	VERB
fuelectenerg-3080	53	18	to	to	PART
fuelectenerg-3080	53	19	be	be	AUX
fuelectenerg-3080	53	20	the	the	DET
fuelectenerg-3080	53	21	constant	constant	ADJ
fuelectenerg-3080	53	22	p	p	NOUN
fuelectenerg-3080	53	23	–	–	PUNCT
fuelectenerg-3080	53	24	1	1	NUM
fuelectenerg-3080	53	25	for	for	ADP
fuelectenerg-3080	53	26	all	all	DET
fuelectenerg-3080	53	27	x	x	NOUN
fuelectenerg-3080	53	28	,	,	PUNCT
fuelectenerg-3080	53	29	and	and	CCONJ
fuelectenerg-3080	53	30	for	for	ADP
fuelectenerg-3080	53	31	1	1	NUM
fuelectenerg-3080	53	32	≤	≤	NUM
fuelectenerg-3080	53	33	j	j	PROPN
fuelectenerg-3080	53	34	≤	≤	PROPN
fuelectenerg-3080	53	35	p	p	NOUN
fuelectenerg-3080	53	36	–	–	PUNCT
fuelectenerg-3080	53	37	1	1	NUM
fuelectenerg-3080	53	38	,	,	PUNCT
fuelectenerg-3080	53	39	the	the	DET
fuelectenerg-3080	53	40	powers	power	NOUN
fuelectenerg-3080	53	41	x	x	X
fuelectenerg-3080	53	42	*	*	PUNCT
fuelectenerg-3080	53	43	j	j	PROPN
fuelectenerg-3080	53	44	are	be	AUX
fuelectenerg-3080	53	45	calculated	calculate	VERB
fuelectenerg-3080	53	46	as	as	ADP
fuelectenerg-3080	53	47	the	the	DET
fuelectenerg-3080	53	48	j	j	PROPN
fuelectenerg-3080	53	49	–	–	PUNCT
fuelectenerg-3080	53	50	fold	fold	ADJ
fuelectenerg-3080	53	51	gibbs	gibbs	PROPN
fuelectenerg-3080	53	52	product	product	NOUN
fuelectenerg-3080	53	53	of	of	ADP
fuelectenerg-3080	53	54	x	x	X
fuelectenerg-3080	53	55	*	*	PROPN
fuelectenerg-3080	53	56	0	0	NUM
fuelectenerg-3080	53	57	with	with	ADP
fuelectenerg-3080	53	58	itself	itself	PRON
fuelectenerg-3080	53	59	.	.	PUNCT
fuelectenerg-3080	54	1	on	on	ADP
fuelectenerg-3080	54	2	a	a	DET
fuelectenerg-3080	54	3	property	property	NOUN
fuelectenerg-3080	54	4	of	of	ADP
fuelectenerg-3080	54	5	the	the	DET
fuelectenerg-3080	54	6	reed	reed	NOUN
fuelectenerg-3080	54	7	-	-	PUNCT
fuelectenerg-3080	54	8	muller	muller	NOUN
fuelectenerg-3080	54	9	-	-	PUNCT
fuelectenerg-3080	54	10	fourier	fourier	NOUN
fuelectenerg-3080	54	11	transform	transform	NOUN
fuelectenerg-3080	54	12	305	305	NUM
fuelectenerg-3080	54	13	it	it	PRON
fuelectenerg-3080	54	14	is	be	AUX
fuelectenerg-3080	54	15	simple	simple	ADJ
fuelectenerg-3080	54	16	to	to	PART
fuelectenerg-3080	54	17	show	show	VERB
fuelectenerg-3080	54	18	that	that	SCONJ
fuelectenerg-3080	54	19	xprmf	xprmf	VERB
fuelectenerg-3080	54	20	is	be	AUX
fuelectenerg-3080	54	21	its	its	PRON
fuelectenerg-3080	54	22	own	own	ADJ
fuelectenerg-3080	54	23	inverse	inverse	NOUN
fuelectenerg-3080	54	24	.	.	PUNCT
fuelectenerg-3080	55	1	therefore	therefore	ADV
fuelectenerg-3080	55	2	the	the	DET
fuelectenerg-3080	55	3	basic	basic	ADJ
fuelectenerg-3080	55	4	rmf	rmf	PROPN
fuelectenerg-3080	55	5	transform	transform	NOUN
fuelectenerg-3080	55	6	matrix	matrix	NOUN
fuelectenerg-3080	55	7	,	,	PUNCT
fuelectenerg-3080	55	8	called	call	VERB
fuelectenerg-3080	55	9	r1	r1	PROPN
fuelectenerg-3080	55	10	equals	equal	VERB
fuelectenerg-3080	55	11	xprmf	xprmf	VERB
fuelectenerg-3080	55	12	,	,	PUNCT
fuelectenerg-3080	55	13	and	and	CCONJ
fuelectenerg-3080	55	14	for	for	ADP
fuelectenerg-3080	55	15	all	all	DET
fuelectenerg-3080	55	16	n	n	DET
fuelectenerg-3080	55	17	>	>	SYM
fuelectenerg-3080	55	18	1	1	NUM
fuelectenerg-3080	55	19	holds	hold	NOUN
fuelectenerg-3080	55	20	:	:	PUNCT
fuelectenerg-3080	55	21	rn	rn	PROPN
fuelectenerg-3080	55	22	=	=	PUNCT
fuelectenerg-3080	55	23	(	(	PUNCT
fuelectenerg-3080	55	24	xprmf	xprmf	PROPN
fuelectenerg-3080	55	25	)	)	PUNCT
fuelectenerg-3080	55	26	n	n	NOUN
fuelectenerg-3080	55	27	,	,	PUNCT
fuelectenerg-3080	55	28	where	where	SCONJ
fuelectenerg-3080	55	29	the	the	DET
fuelectenerg-3080	55	30	exponent	exponent	NOUN
fuelectenerg-3080	55	31	“	"	PUNCT
fuelectenerg-3080	55	32	n	n	NOUN
fuelectenerg-3080	55	33	”	"	PUNCT
fuelectenerg-3080	55	34	denotes	denote	VERB
fuelectenerg-3080	55	35	the	the	DET
fuelectenerg-3080	55	36	n	n	ADV
fuelectenerg-3080	55	37	-	-	ADJ
fuelectenerg-3080	55	38	fold	fold	ADJ
fuelectenerg-3080	55	39	kronecker	kronecker	NOUN
fuelectenerg-3080	55	40	product	product	NOUN
fuelectenerg-3080	55	41	of	of	ADP
fuelectenerg-3080	55	42	xprmf	xprmf	VERB
fuelectenerg-3080	55	43	with	with	ADP
fuelectenerg-3080	55	44	itself	itself	PRON
fuelectenerg-3080	55	45	.	.	PUNCT
fuelectenerg-3080	56	1	since	since	SCONJ
fuelectenerg-3080	56	2	xprmf	xprmf	ADJ
fuelectenerg-3080	56	3	is	be	AUX
fuelectenerg-3080	56	4	its	its	PRON
fuelectenerg-3080	56	5	own	own	ADJ
fuelectenerg-3080	56	6	inverse	inverse	NOUN
fuelectenerg-3080	56	7	,	,	PUNCT
fuelectenerg-3080	56	8	it	it	PRON
fuelectenerg-3080	56	9	is	be	AUX
fuelectenerg-3080	56	10	easy	easy	ADJ
fuelectenerg-3080	56	11	to	to	PART
fuelectenerg-3080	56	12	see	see	VERB
fuelectenerg-3080	56	13	that	that	PRON
fuelectenerg-3080	56	14	rn	rn	PROPN
fuelectenerg-3080	56	15	will	will	AUX
fuelectenerg-3080	56	16	also	also	ADV
fuelectenerg-3080	56	17	be	be	AUX
fuelectenerg-3080	56	18	its	its	PRON
fuelectenerg-3080	56	19	own	own	ADJ
fuelectenerg-3080	56	20	inverse	inverse	NOUN
fuelectenerg-3080	56	21	.	.	PUNCT
fuelectenerg-3080	57	1	example	example	NOUN
fuelectenerg-3080	58	1	1	1	NUM
fuelectenerg-3080	58	2	:	:	PUNCT
fuelectenerg-3080	58	3	let	let	VERB
fuelectenerg-3080	58	4	n	n	NOUN
fuelectenerg-3080	58	5	=	=	SYM
fuelectenerg-3080	58	6	2	2	NUM
fuelectenerg-3080	58	7	and	and	CCONJ
fuelectenerg-3080	58	8	p	p	NOUN
fuelectenerg-3080	58	9	=	=	NOUN
fuelectenerg-3080	58	10	3	3	X
fuelectenerg-3080	58	11	.	.	PUNCT
fuelectenerg-3080	58	12	calculating	calculate	VERB
fuelectenerg-3080	58	13	mod	mod	PROPN
fuelectenerg-3080	58	14	3	3	NUM
fuelectenerg-3080	58	15	,	,	PUNCT
fuelectenerg-3080	58	16	notice	notice	VERB
fuelectenerg-3080	58	17	that	that	SCONJ
fuelectenerg-3080	58	18	the	the	DET
fuelectenerg-3080	58	19	borders	border	NOUN
fuelectenerg-3080	58	20	of	of	ADP
fuelectenerg-3080	58	21	r2	r2	PROPN
fuelectenerg-3080	58	22	look	look	VERB
fuelectenerg-3080	58	23	different	different	ADJ
fuelectenerg-3080	58	24	than	than	ADP
fuelectenerg-3080	58	25	those	those	PRON
fuelectenerg-3080	58	26	of	of	ADP
fuelectenerg-3080	58	27	r1	r1	PROPN
fuelectenerg-3080	58	28	.	.	PUNCT
fuelectenerg-3080	59	1	this	this	PRON
fuelectenerg-3080	59	2	will	will	AUX
fuelectenerg-3080	59	3	happen	happen	VERB
fuelectenerg-3080	59	4	whenever	whenever	SCONJ
fuelectenerg-3080	59	5	n	n	PRON
fuelectenerg-3080	59	6	is	be	AUX
fuelectenerg-3080	59	7	even	even	ADV
fuelectenerg-3080	59	8	,	,	PUNCT
fuelectenerg-3080	59	9	since	since	SCONJ
fuelectenerg-3080	59	10	for	for	ADP
fuelectenerg-3080	59	11	all	all	DET
fuelectenerg-3080	59	12	p	p	X
fuelectenerg-3080	59	13	,	,	PUNCT
fuelectenerg-3080	59	14	(	(	PUNCT
fuelectenerg-3080	59	15	p–1	p–1	NOUN
fuelectenerg-3080	59	16	)	)	PUNCT
fuelectenerg-3080	59	17	n	n	PROPN
fuelectenerg-3080	59	18			PROPN
fuelectenerg-3080	59	19	1	1	NUM
fuelectenerg-3080	59	20	mod	mod	NOUN
fuelectenerg-3080	60	1	p.	p.	NOUN
fuelectenerg-3080	60	2	if	if	SCONJ
fuelectenerg-3080	60	3	this	this	PRON
fuelectenerg-3080	60	4	is	be	AUX
fuelectenerg-3080	60	5	inconvenient	inconvenient	ADJ
fuelectenerg-3080	60	6	for	for	ADP
fuelectenerg-3080	60	7	some	some	DET
fuelectenerg-3080	60	8	application	application	NOUN
fuelectenerg-3080	60	9	,	,	PUNCT
fuelectenerg-3080	60	10	then	then	ADV
fuelectenerg-3080	60	11	a	a	DET
fuelectenerg-3080	60	12	normalized	normalize	VERB
fuelectenerg-3080	60	13	transform	transform	NOUN
fuelectenerg-3080	60	14	may	may	AUX
fuelectenerg-3080	60	15	be	be	AUX
fuelectenerg-3080	60	16	used	use	VERB
fuelectenerg-3080	60	17	.	.	PUNCT
fuelectenerg-3080	61	1	definition	definition	NOUN
fuelectenerg-3080	61	2	3	3	NUM
fuelectenerg-3080	61	3	:	:	PUNCT
fuelectenerg-3080	61	4	the	the	DET
fuelectenerg-3080	61	5	normalized	normalize	VERB
fuelectenerg-3080	61	6	rmf	rmf	PROPN
fuelectenerg-3080	61	7	transform	transform	NOUN
fuelectenerg-3080	61	8	is	be	AUX
fuelectenerg-3080	61	9	given	give	VERB
fuelectenerg-3080	61	10	by	by	ADP
fuelectenerg-3080	61	11	rn	rn	PROPN
fuelectenerg-3080	61	12	=	=	SYM
fuelectenerg-3080	61	13	(	(	PUNCT
fuelectenerg-3080	61	14	–	–	PUNCT
fuelectenerg-3080	61	15	1	1	NUM
fuelectenerg-3080	61	16	)	)	PUNCT
fuelectenerg-3080	61	17	n+1	n+1	PROPN
fuelectenerg-3080	61	18	xprmf(1)⨂	xprmf(1)⨂	PROPN
fuelectenerg-3080	61	19	n	n	PRON
fuelectenerg-3080	61	20	mod	mod	PROPN
fuelectenerg-3080	61	21	p.	p.	NOUN
fuelectenerg-3080	61	22	the	the	DET
fuelectenerg-3080	61	23	factor	factor	NOUN
fuelectenerg-3080	61	24	(	(	PUNCT
fuelectenerg-3080	61	25	–	–	PUNCT
fuelectenerg-3080	61	26	1	1	NUM
fuelectenerg-3080	61	27	)	)	PUNCT
fuelectenerg-3080	61	28	n+1	n+1	NUM
fuelectenerg-3080	61	29	is	be	AUX
fuelectenerg-3080	61	30	introduced	introduce	VERB
fuelectenerg-3080	61	31	to	to	PART
fuelectenerg-3080	61	32	preserve	preserve	VERB
fuelectenerg-3080	61	33	the	the	DET
fuelectenerg-3080	61	34	value	value	NOUN
fuelectenerg-3080	61	35	(	(	PUNCT
fuelectenerg-3080	61	36	p–1	p–1	NOUN
fuelectenerg-3080	61	37	)	)	PUNCT
fuelectenerg-3080	61	38	,	,	PUNCT
fuelectenerg-3080	61	39	in	in	ADP
fuelectenerg-3080	61	40	the	the	DET
fuelectenerg-3080	61	41	leftmost	leftmost	ADJ
fuelectenerg-3080	61	42	column	column	NOUN
fuelectenerg-3080	61	43	of	of	ADP
fuelectenerg-3080	61	44	the	the	DET
fuelectenerg-3080	61	45	matrix	matrix	NOUN
fuelectenerg-3080	61	46	when	when	SCONJ
fuelectenerg-3080	61	47	n	n	X
fuelectenerg-3080	61	48	is	be	AUX
fuelectenerg-3080	61	49	even	even	ADV
fuelectenerg-3080	61	50	,	,	PUNCT
fuelectenerg-3080	61	51	since	since	SCONJ
fuelectenerg-3080	61	52	(	(	PUNCT
fuelectenerg-3080	61	53	–	–	PUNCT
fuelectenerg-3080	61	54	1	1	NUM
fuelectenerg-3080	61	55	)	)	PUNCT
fuelectenerg-3080	61	56	n+1	n+1	PROPN
fuelectenerg-3080	61	57	(	(	PUNCT
fuelectenerg-3080	61	58	p–1	p–1	NOUN
fuelectenerg-3080	61	59	)	)	PUNCT
fuelectenerg-3080	62	1	n	n	PRON
fuelectenerg-3080	62	2	≡	≡	PROPN
fuelectenerg-3080	62	3	(	(	PUNCT
fuelectenerg-3080	62	4	p–1	p–1	NOUN
fuelectenerg-3080	62	5	)	)	PUNCT
fuelectenerg-3080	62	6	n+1	n+1	PROPN
fuelectenerg-3080	62	7	(	(	PUNCT
fuelectenerg-3080	62	8	p–1	p–1	NOUN
fuelectenerg-3080	62	9	)	)	PUNCT
fuelectenerg-3080	62	10	n	n	PRON
fuelectenerg-3080	62	11	≡	≡	PROPN
fuelectenerg-3080	62	12	(	(	PUNCT
fuelectenerg-3080	62	13	p–1	p–1	NOUN
fuelectenerg-3080	62	14	)	)	PUNCT
fuelectenerg-3080	62	15	2n+1	2n+1	PROPN
fuelectenerg-3080	62	16	mod	mod	PROPN
fuelectenerg-3080	63	1	p.	p.	NOUN
fuelectenerg-3080	63	2	2n	2n	NUM
fuelectenerg-3080	64	1	+	+	CCONJ
fuelectenerg-3080	64	2	1	1	NUM
fuelectenerg-3080	64	3	will	will	AUX
fuelectenerg-3080	64	4	be	be	AUX
fuelectenerg-3080	64	5	an	an	DET
fuelectenerg-3080	64	6	odd	odd	ADJ
fuelectenerg-3080	64	7	number	number	NOUN
fuelectenerg-3080	64	8	and	and	CCONJ
fuelectenerg-3080	64	9	an	an	DET
fuelectenerg-3080	64	10	odd	odd	ADJ
fuelectenerg-3080	64	11	power	power	NOUN
fuelectenerg-3080	64	12	of	of	ADP
fuelectenerg-3080	64	13	(	(	PUNCT
fuelectenerg-3080	64	14	p–1	p–1	NOUN
fuelectenerg-3080	64	15	)	)	PUNCT
fuelectenerg-3080	64	16	equals	equal	VERB
fuelectenerg-3080	64	17	(	(	PUNCT
fuelectenerg-3080	64	18	p–1	p–1	NOUN
fuelectenerg-3080	64	19	)	)	PUNCT
fuelectenerg-3080	64	20	mod	mod	PROPN
fuelectenerg-3080	65	1	p.	p.	NOUN
fuelectenerg-3080	65	2	it	it	PRON
fuelectenerg-3080	65	3	is	be	AUX
fuelectenerg-3080	65	4	simple	simple	ADJ
fuelectenerg-3080	65	5	to	to	PART
fuelectenerg-3080	65	6	see	see	VERB
fuelectenerg-3080	65	7	that	that	SCONJ
fuelectenerg-3080	65	8	in	in	ADP
fuelectenerg-3080	65	9	this	this	DET
fuelectenerg-3080	65	10	case	case	NOUN
fuelectenerg-3080	65	11	rn	rn	NOUN
fuelectenerg-3080	65	12	is	be	AUX
fuelectenerg-3080	65	13	also	also	ADV
fuelectenerg-3080	65	14	self	self	NOUN
fuelectenerg-3080	65	15	-	-	PUNCT
fuelectenerg-3080	65	16	inverse	inverse	ADJ
fuelectenerg-3080	65	17	.	.	PUNCT
fuelectenerg-3080	66	1	if	if	SCONJ
fuelectenerg-3080	66	2	for	for	ADP
fuelectenerg-3080	66	3	particular	particular	ADJ
fuelectenerg-3080	66	4	applications	application	NOUN
fuelectenerg-3080	66	5	a	a	DET
fuelectenerg-3080	66	6	“	"	PUNCT
fuelectenerg-3080	66	7	homogeneous	homogeneous	ADJ
fuelectenerg-3080	66	8	and	and	CCONJ
fuelectenerg-3080	66	9	dft	dft	ADJ
fuelectenerg-3080	66	10	-	-	PUNCT
fuelectenerg-3080	66	11	like	like	ADJ
fuelectenerg-3080	66	12	look	look	NOUN
fuelectenerg-3080	66	13	”	"	PUNCT
fuelectenerg-3080	66	14	is	be	AUX
fuelectenerg-3080	66	15	desirable	desirable	ADJ
fuelectenerg-3080	66	16	,	,	PUNCT
fuelectenerg-3080	66	17	then	then	ADV
fuelectenerg-3080	66	18	a	a	DET
fuelectenerg-3080	66	19	special	special	ADJ
fuelectenerg-3080	66	20	rmf	rmf	NOUN
fuelectenerg-3080	66	21	transform	transform	NOUN
fuelectenerg-3080	66	22	may	may	AUX
fuelectenerg-3080	66	23	be	be	AUX
fuelectenerg-3080	66	24	used	use	VERB
fuelectenerg-3080	66	25	.	.	PUNCT
fuelectenerg-3080	67	1	definition	definition	NOUN
fuelectenerg-3080	67	2	4	4	NUM
fuelectenerg-3080	67	3	:	:	PUNCT
fuelectenerg-3080	67	4	the	the	DET
fuelectenerg-3080	67	5	special	special	ADJ
fuelectenerg-3080	67	6	rmf	rmf	NOUN
fuelectenerg-3080	67	7	transform	transform	NOUN
fuelectenerg-3080	67	8	equals	equal	VERB
fuelectenerg-3080	68	1	(	(	PUNCT
fuelectenerg-3080	68	2	p-1)(xprmf	p-1)(xprmf	PROPN
fuelectenerg-3080	68	3	)	)	PUNCT
fuelectenerg-3080	68	4	n	n	NOUN
fuelectenerg-3080	68	5	mod	mod	PROPN
fuelectenerg-3080	68	6	p.	p.	PROPN
fuelectenerg-3080	68	7	see	see	VERB
fuelectenerg-3080	68	8	figure	figure	NOUN
fuelectenerg-3080	68	9	1	1	NUM
fuelectenerg-3080	68	10	.	.	PUNCT
fuelectenerg-3080	69	1	[	[	PUNCT
fuelectenerg-3080	69	2	]	]	X
fuelectenerg-3080	69	3	[	[	PUNCT
fuelectenerg-3080	69	4	]	]	X
fuelectenerg-3080	69	5	[	[	PUNCT
fuelectenerg-3080	69	6	]	]	X
fuelectenerg-3080	69	7	fig	fig	NOUN
fuelectenerg-3080	69	8	.	.	PUNCT
fuelectenerg-3080	69	9	1	1	NUM
fuelectenerg-3080	69	10	special	special	ADJ
fuelectenerg-3080	69	11	rmf	rmf	NOUN
fuelectenerg-3080	69	12	transform	transform	NOUN
fuelectenerg-3080	69	13	matrices	matrix	NOUN
fuelectenerg-3080	69	14	for	for	ADP
fuelectenerg-3080	69	15	p	p	NOUN
fuelectenerg-3080	69	16	=	=	SYM
fuelectenerg-3080	69	17	3	3	NUM
fuelectenerg-3080	69	18	,	,	PUNCT
fuelectenerg-3080	69	19	4	4	NUM
fuelectenerg-3080	69	20	,	,	PUNCT
fuelectenerg-3080	69	21	and	and	CCONJ
fuelectenerg-3080	69	22	5	5	NUM
fuelectenerg-3080	69	23	when	when	SCONJ
fuelectenerg-3080	69	24	n	n	X
fuelectenerg-3080	69	25	=	=	SYM
fuelectenerg-3080	69	26	1	1	NUM
fuelectenerg-3080	69	27	if	if	SCONJ
fuelectenerg-3080	69	28	for	for	ADP
fuelectenerg-3080	69	29	any	any	DET
fuelectenerg-3080	69	30	p	p	PROPN
fuelectenerg-3080	69	31	r1	r1	PROPN
fuelectenerg-3080	69	32	is	be	AUX
fuelectenerg-3080	69	33	expressed	express	VERB
fuelectenerg-3080	69	34	as	as	ADP
fuelectenerg-3080	69	35	[	[	X
fuelectenerg-3080	69	36	ri	ri	PROPN
fuelectenerg-3080	69	37	,	,	PUNCT
fuelectenerg-3080	69	38	j	j	PROPN
fuelectenerg-3080	69	39	]	]	X
fuelectenerg-3080	69	40	,	,	PUNCT
fuelectenerg-3080	69	41	i	i	PRON
fuelectenerg-3080	69	42	,	,	PUNCT
fuelectenerg-3080	69	43	j	j	PROPN
fuelectenerg-3080	69	44			PROPN
fuelectenerg-3080	69	45	ℤp	ℤp	PROPN
fuelectenerg-3080	69	46	,	,	PUNCT
fuelectenerg-3080	69	47	then	then	ADV
fuelectenerg-3080	69	48	(	(	PUNCT
fuelectenerg-3080	69	49	)	)	PUNCT
fuelectenerg-3080	69	50	mod	mod	PROPN
fuelectenerg-3080	70	1	p	p	X
fuelectenerg-3080	71	1	[	[	X
fuelectenerg-3080	71	2	12	12	NUM
fuelectenerg-3080	71	3	]	]	PUNCT
fuelectenerg-3080	71	4	.	.	PUNCT
fuelectenerg-3080	72	1	it	it	PRON
fuelectenerg-3080	72	2	may	may	AUX
fuelectenerg-3080	72	3	be	be	AUX
fuelectenerg-3080	72	4	observed	observe	VERB
fuelectenerg-3080	72	5	that	that	SCONJ
fuelectenerg-3080	72	6	in	in	ADP
fuelectenerg-3080	72	7	the	the	DET
fuelectenerg-3080	72	8	case	case	NOUN
fuelectenerg-3080	72	9	when	when	SCONJ
fuelectenerg-3080	72	10	p	p	NOUN
fuelectenerg-3080	72	11	is	be	AUX
fuelectenerg-3080	72	12	a	a	DET
fuelectenerg-3080	72	13	prime	prime	NOUN
fuelectenerg-3080	72	14	,	,	PUNCT
fuelectenerg-3080	72	15	the	the	DET
fuelectenerg-3080	72	16	matrices	matrix	NOUN
fuelectenerg-3080	72	17	are	be	AUX
fuelectenerg-3080	72	18	skewsymmetric	skewsymmetric	ADJ
fuelectenerg-3080	72	19	,	,	PUNCT
fuelectenerg-3080	72	20	i.e.	i.e.	X
fuelectenerg-3080	72	21	,	,	PUNCT
fuelectenerg-3080	72	22	symmetric	symmetric	ADJ
fuelectenerg-3080	72	23	with	with	ADP
fuelectenerg-3080	72	24	respect	respect	NOUN
fuelectenerg-3080	72	25	to	to	ADP
fuelectenerg-3080	72	26	the	the	DET
fuelectenerg-3080	72	27	diagonal	diagonal	ADJ
fuelectenerg-3080	72	28	with	with	ADP
fuelectenerg-3080	72	29	positive	positive	ADJ
fuelectenerg-3080	72	30	slope	slope	NOUN
fuelectenerg-3080	72	31	.	.	PUNCT
fuelectenerg-3080	73	1	furthermore	furthermore	ADV
fuelectenerg-3080	73	2	besides	besides	SCONJ
fuelectenerg-3080	73	3	being	be	AUX
fuelectenerg-3080	73	4	skew	skew	ADJ
fuelectenerg-3080	73	5	-	-	PUNCT
fuelectenerg-3080	73	6	symmetric	symmetric	ADJ
fuelectenerg-3080	73	7	and	and	CCONJ
fuelectenerg-3080	73	8	self	self	NOUN
fuelectenerg-3080	73	9	inverse	inverse	NOUN
fuelectenerg-3080	73	10	,	,	PUNCT
fuelectenerg-3080	73	11	starting	start	VERB
fuelectenerg-3080	73	12	at	at	ADP
fuelectenerg-3080	73	13	the	the	DET
fuelectenerg-3080	73	14	lower	low	ADJ
fuelectenerg-3080	73	15	left	left	ADJ
fuelectenerg-3080	73	16	corner	corner	NOUN
fuelectenerg-3080	73	17	and	and	CCONJ
fuelectenerg-3080	73	18	moving	move	VERB
fuelectenerg-3080	73	19	along	along	ADP
fuelectenerg-3080	73	20	the	the	DET
fuelectenerg-3080	73	21	diagonal	diagonal	ADJ
fuelectenerg-3080	73	22	with	with	ADP
fuelectenerg-3080	73	23	positive	positive	ADJ
fuelectenerg-3080	73	24	slope	slope	NOUN
fuelectenerg-3080	73	25	,	,	PUNCT
fuelectenerg-3080	73	26	a	a	DET
fuelectenerg-3080	73	27	pascal	pascal	ADJ
fuelectenerg-3080	73	28	triangle	triangle	NOUN
fuelectenerg-3080	73	29	mod	mod	PROPN
fuelectenerg-3080	73	30	p	p	PROPN
fuelectenerg-3080	73	31	is	be	AUX
fuelectenerg-3080	73	32	found	find	VERB
fuelectenerg-3080	73	33	.	.	PUNCT
fuelectenerg-3080	74	1	r2	r2	NOUN
fuelectenerg-3080	74	2	=	=	SYM
fuelectenerg-3080	74	3	306	306	NUM
fuelectenerg-3080	74	4	c.	c.	NOUN
fuelectenerg-3080	74	5	moraga	moraga	PROPN
fuelectenerg-3080	74	6	an	an	DET
fuelectenerg-3080	74	7	important	important	ADJ
fuelectenerg-3080	74	8	property	property	NOUN
fuelectenerg-3080	74	9	of	of	ADP
fuelectenerg-3080	74	10	the	the	DET
fuelectenerg-3080	74	11	rmf	rmf	PROPN
fuelectenerg-3080	74	12	transform	transform	NOUN
fuelectenerg-3080	74	13	is	be	AUX
fuelectenerg-3080	74	14	the	the	DET
fuelectenerg-3080	74	15	following	following	NOUN
fuelectenerg-3080	74	16	:	:	PUNCT
fuelectenerg-3080	74	17	the	the	DET
fuelectenerg-3080	74	18	rmf	rmf	PROPN
fuelectenerg-3080	74	19	transform	transform	NOUN
fuelectenerg-3080	74	20	of	of	ADP
fuelectenerg-3080	74	21	a	a	DET
fuelectenerg-3080	74	22	non	non	ADJ
fuelectenerg-3080	74	23	-	-	ADJ
fuelectenerg-3080	74	24	zero	zero	ADJ
fuelectenerg-3080	74	25	constant	constant	ADJ
fuelectenerg-3080	74	26	vector	vector	NOUN
fuelectenerg-3080	74	27	is	be	AUX
fuelectenerg-3080	74	28	an	an	DET
fuelectenerg-3080	74	29	“	"	PUNCT
fuelectenerg-3080	74	30	impulse	impulse	ADJ
fuelectenerg-3080	74	31	”	"	PUNCT
fuelectenerg-3080	74	32	vector	vector	NOUN
fuelectenerg-3080	74	33	,	,	PUNCT
fuelectenerg-3080	74	34	i.e.	i.e.	X
fuelectenerg-3080	74	35	a	a	DET
fuelectenerg-3080	74	36	vector	vector	NOUN
fuelectenerg-3080	74	37	with	with	ADP
fuelectenerg-3080	74	38	only	only	ADV
fuelectenerg-3080	74	39	one	one	NUM
fuelectenerg-3080	74	40	non	non	ADJ
fuelectenerg-3080	74	41	-	-	ADJ
fuelectenerg-3080	74	42	zero	zero	NUM
fuelectenerg-3080	74	43	entry	entry	NOUN
fuelectenerg-3080	74	44	,	,	PUNCT
fuelectenerg-3080	74	45	at	at	ADP
fuelectenerg-3080	74	46	the	the	DET
fuelectenerg-3080	74	47	0	0	NUM
fuelectenerg-3080	74	48	-	-	PUNCT
fuelectenerg-3080	74	49	th	th	VERB
fuelectenerg-3080	74	50	position	position	NOUN
fuelectenerg-3080	74	51	[	[	X
fuelectenerg-3080	74	52	12	12	NUM
fuelectenerg-3080	74	53	]	]	PUNCT
fuelectenerg-3080	74	54	.	.	PUNCT
fuelectenerg-3080	75	1	this	this	PRON
fuelectenerg-3080	75	2	is	be	AUX
fuelectenerg-3080	75	3	a	a	DET
fuelectenerg-3080	75	4	well	well	ADV
fuelectenerg-3080	75	5	known	know	VERB
fuelectenerg-3080	75	6	property	property	NOUN
fuelectenerg-3080	75	7	of	of	ADP
fuelectenerg-3080	75	8	the	the	DET
fuelectenerg-3080	75	9	dft	dft	PROPN
fuelectenerg-3080	75	10	,	,	PUNCT
fuelectenerg-3080	75	11	which	which	PRON
fuelectenerg-3080	75	12	is	be	AUX
fuelectenerg-3080	75	13	preserved	preserve	VERB
fuelectenerg-3080	75	14	by	by	ADP
fuelectenerg-3080	75	15	the	the	DET
fuelectenerg-3080	75	16	rmf	rmf	PROPN
fuelectenerg-3080	75	17	transform	transform	NOUN
fuelectenerg-3080	75	18	.	.	PUNCT
fuelectenerg-3080	76	1	3	3	X
fuelectenerg-3080	76	2	.	.	X
fuelectenerg-3080	76	3	theorems	theorem	NOUN
fuelectenerg-3080	76	4	theorem	theorem	VERB
fuelectenerg-3080	76	5	1	1	NUM
fuelectenerg-3080	76	6	.	.	PUNCT
fuelectenerg-3080	76	7	preliminaries	preliminary	NOUN
fuelectenerg-3080	76	8	:	:	PUNCT
fuelectenerg-3080	76	9	let	let	VERB
fuelectenerg-3080	76	10	v	v	VERB
fuelectenerg-3080	76	11	=	=	SYM
fuelectenerg-3080	76	12	{	{	PUNCT
fuelectenerg-3080	76	13	0	0	NUM
fuelectenerg-3080	76	14	,	,	PUNCT
fuelectenerg-3080	76	15	1	1	NUM
fuelectenerg-3080	76	16	,	,	PUNCT
fuelectenerg-3080	76	17	…	…	PUNCT
fuelectenerg-3080	76	18	,	,	PUNCT
fuelectenerg-3080	76	19	p–1	p–1	NOUN
fuelectenerg-3080	76	20	}	}	PUNCT
fuelectenerg-3080	76	21	be	be	VERB
fuelectenerg-3080	76	22	the	the	DET
fuelectenerg-3080	76	23	domain	domain	NOUN
fuelectenerg-3080	76	24	of	of	ADP
fuelectenerg-3080	76	25	p	p	PROPN
fuelectenerg-3080	76	26	–	–	PUNCT
fuelectenerg-3080	76	27	valued	value	VERB
fuelectenerg-3080	76	28	functions	function	NOUN
fuelectenerg-3080	76	29	and	and	CCONJ
fuelectenerg-3080	76	30	let	let	VERB
fuelectenerg-3080	76	31	f	f	NOUN
fuelectenerg-3080	76	32	:	:	PUNCT
fuelectenerg-3080	76	33	v	v	NUM
fuelectenerg-3080	76	34	2	2	NUM
fuelectenerg-3080	76	35			NOUN
fuelectenerg-3080	76	36	v	v	ADP
fuelectenerg-3080	76	37	,	,	PUNCT
fuelectenerg-3080	76	38	with	with	ADP
fuelectenerg-3080	76	39	value	value	NOUN
fuelectenerg-3080	76	40	vector	vector	NOUN
fuelectenerg-3080	76	41	f	f	PROPN
fuelectenerg-3080	76	42	of	of	ADP
fuelectenerg-3080	76	43	length	length	NOUN
fuelectenerg-3080	76	44	p	p	PROPN
fuelectenerg-3080	76	45	2	2	NUM
fuelectenerg-3080	76	46	.	.	PUNCT
fuelectenerg-3080	77	1	moreover	moreover	ADV
fuelectenerg-3080	77	2	let	let	VERB
fuelectenerg-3080	77	3	g	g	NOUN
fuelectenerg-3080	77	4	:	:	PUNCT
fuelectenerg-3080	77	5	v	v	NUM
fuelectenerg-3080	77	6	2	2	NUM
fuelectenerg-3080	77	7			NOUN
fuelectenerg-3080	77	8	v	v	ADP
fuelectenerg-3080	77	9	,	,	PUNCT
fuelectenerg-3080	77	10	such	such	ADJ
fuelectenerg-3080	77	11	that	that	DET
fuelectenerg-3080	77	12	g(x1	g(x1	NOUN
fuelectenerg-3080	77	13	,	,	PUNCT
fuelectenerg-3080	77	14	x2	x2	PROPN
fuelectenerg-3080	77	15	)	)	PUNCT
fuelectenerg-3080	78	1	=	=	SYM
fuelectenerg-3080	78	2	f	f	PROPN
fuelectenerg-3080	78	3	(	(	PUNCT
fuelectenerg-3080	78	4	x2	x2	PROPN
fuelectenerg-3080	78	5	,	,	PUNCT
fuelectenerg-3080	78	6	x1	x1	PROPN
fuelectenerg-3080	78	7	)	)	PUNCT
fuelectenerg-3080	78	8	.	.	PUNCT
fuelectenerg-3080	79	1	let	let	VERB
fuelectenerg-3080	79	2	the	the	DET
fuelectenerg-3080	79	3	value	value	NOUN
fuelectenerg-3080	79	4	vector	vector	NOUN
fuelectenerg-3080	79	5	of	of	ADP
fuelectenerg-3080	79	6	g	g	PROPN
fuelectenerg-3080	79	7	be	be	AUX
fuelectenerg-3080	79	8	g.	g.	PROPN
fuelectenerg-3080	79	9	furthermore	furthermore	ADV
fuelectenerg-3080	79	10	,	,	PUNCT
fuelectenerg-3080	79	11	let	let	VERB
fuelectenerg-3080	79	12	p2	p2	PROPN
fuelectenerg-3080	79	13	be	be	AUX
fuelectenerg-3080	79	14	a	a	DET
fuelectenerg-3080	79	15	permutation	permutation	NOUN
fuelectenerg-3080	79	16	matrix	matrix	NOUN
fuelectenerg-3080	79	17	such	such	ADJ
fuelectenerg-3080	79	18	that	that	SCONJ
fuelectenerg-3080	79	19	when	when	SCONJ
fuelectenerg-3080	79	20	applied	apply	VERB
fuelectenerg-3080	79	21	upon	upon	SCONJ
fuelectenerg-3080	79	22	f	f	PROPN
fuelectenerg-3080	79	23	induces	induces	AUX
fuelectenerg-3080	79	24	a	a	DET
fuelectenerg-3080	79	25	permutation	permutation	NOUN
fuelectenerg-3080	79	26	of	of	ADP
fuelectenerg-3080	79	27	its	its	PRON
fuelectenerg-3080	79	28	components	component	NOUN
fuelectenerg-3080	79	29	according	accord	VERB
fuelectenerg-3080	79	30	to	to	ADP
fuelectenerg-3080	79	31	the	the	DET
fuelectenerg-3080	79	32	reordering	reordering	NOUN
fuelectenerg-3080	79	33	of	of	ADP
fuelectenerg-3080	79	34	the	the	DET
fuelectenerg-3080	79	35	arguments	argument	NOUN
fuelectenerg-3080	79	36	of	of	ADP
fuelectenerg-3080	79	37	the	the	DET
fuelectenerg-3080	79	38	function	function	NOUN
fuelectenerg-3080	79	39	.	.	PUNCT
fuelectenerg-3080	80	1	hence	hence	ADV
fuelectenerg-3080	80	2	g	g	PROPN
fuelectenerg-3080	80	3	=	=	SYM
fuelectenerg-3080	80	4	p2f	p2f	PROPN
fuelectenerg-3080	80	5	.	.	PUNCT
fuelectenerg-3080	81	1	claim	claim	NOUN
fuelectenerg-3080	81	2	:	:	PUNCT
fuelectenerg-3080	81	3	the	the	DET
fuelectenerg-3080	81	4	rmf	rmf	PROPN
fuelectenerg-3080	81	5	transform	transform	NOUN
fuelectenerg-3080	81	6	of	of	ADP
fuelectenerg-3080	81	7	a	a	DET
fuelectenerg-3080	81	8	p	p	ADV
fuelectenerg-3080	81	9	-	-	PUNCT
fuelectenerg-3080	81	10	valued	value	VERB
fuelectenerg-3080	81	11	function	function	NOUN
fuelectenerg-3080	81	12	of	of	ADP
fuelectenerg-3080	81	13	two	two	NUM
fuelectenerg-3080	81	14	variables	variable	NOUN
fuelectenerg-3080	81	15	preserves	preserve	VERB
fuelectenerg-3080	81	16	the	the	DET
fuelectenerg-3080	81	17	order	order	NOUN
fuelectenerg-3080	81	18	of	of	ADP
fuelectenerg-3080	81	19	the	the	DET
fuelectenerg-3080	81	20	arguments	argument	NOUN
fuelectenerg-3080	81	21	.	.	PUNCT
fuelectenerg-3080	82	1	r2g	r2g	NOUN
fuelectenerg-3080	82	2	=	=	PUNCT
fuelectenerg-3080	83	1	r2p2f	r2p2f	NOUN
fuelectenerg-3080	84	1	=	=	PUNCT
fuelectenerg-3080	84	2	p2r2f	p2r2f	NOUN
fuelectenerg-3080	84	3	mod	mod	PROPN
fuelectenerg-3080	84	4	p.	p.	PROPN
fuelectenerg-3080	84	5	proof	proof	NOUN
fuelectenerg-3080	84	6	:	:	PUNCT
fuelectenerg-3080	84	7	let	let	VERB
fuelectenerg-3080	84	8	i	i	PRON
fuelectenerg-3080	84	9	,	,	PUNCT
fuelectenerg-3080	84	10	j	j	PROPN
fuelectenerg-3080	84	11			PROPN
fuelectenerg-3080	84	12	(	(	PUNCT
fuelectenerg-3080	84	13	ℤ	ℤ	PROPN
fuelectenerg-3080	84	14	)	)	PUNCT
fuelectenerg-3080	84	15	,	,	PUNCT
fuelectenerg-3080	84	16	with	with	ADP
fuelectenerg-3080	84	17	i	i	PRON
fuelectenerg-3080	84	18	=	=	PUNCT
fuelectenerg-3080	84	19	i1i0	i1i0	PROPN
fuelectenerg-3080	84	20	and	and	CCONJ
fuelectenerg-3080	84	21	j	j	PROPN
fuelectenerg-3080	84	22	=	=	SYM
fuelectenerg-3080	84	23	j1j0	j1j0	PROPN
fuelectenerg-3080	84	24	.	.	PUNCT
fuelectenerg-3080	85	1	since	since	SCONJ
fuelectenerg-3080	85	2	r	r	NOUN
fuelectenerg-3080	85	3	has	have	VERB
fuelectenerg-3080	85	4	a	a	DET
fuelectenerg-3080	85	5	kronecker	kronecker	NOUN
fuelectenerg-3080	85	6	product	product	NOUN
fuelectenerg-3080	85	7	structure	structure	NOUN
fuelectenerg-3080	85	8	,	,	PUNCT
fuelectenerg-3080	85	9	then	then	ADV
fuelectenerg-3080	85	10	r2	r2	PROPN
fuelectenerg-3080	85	11	=	=	PROPN
fuelectenerg-3080	85	12	r1	r1	PROPN
fuelectenerg-3080	85	13			PROPN
fuelectenerg-3080	85	14	r1	r1	PROPN
fuelectenerg-3080	86	1	mod	mod	PROPN
fuelectenerg-3080	86	2	p.	p.	PROPN
fuelectenerg-3080	86	3	if	if	SCONJ
fuelectenerg-3080	86	4	r2	r2	PROPN
fuelectenerg-3080	86	5	is	be	AUX
fuelectenerg-3080	86	6	expressed	express	VERB
fuelectenerg-3080	86	7	as	as	ADP
fuelectenerg-3080	86	8	[	[	X
fuelectenerg-3080	86	9	ri	ri	PROPN
fuelectenerg-3080	86	10	,	,	PUNCT
fuelectenerg-3080	86	11	j	j	PROPN
fuelectenerg-3080	86	12	]	]	X
fuelectenerg-3080	87	1	then	then	ADV
fuelectenerg-3080	87	2	ri	ri	PROPN
fuelectenerg-3080	87	3	,	,	PUNCT
fuelectenerg-3080	87	4	j	j	PROPN
fuelectenerg-3080	88	1	=	=	PRON
fuelectenerg-3080	88	2	(	(	PUNCT
fuelectenerg-3080	88	3	(	(	PUNCT
fuelectenerg-3080	88	4	)	)	PUNCT
fuelectenerg-3080	88	5	)	)	PUNCT
fuelectenerg-3080	88	6	(	(	PUNCT
fuelectenerg-3080	88	7	(	(	PUNCT
fuelectenerg-3080	88	8	)	)	PUNCT
fuelectenerg-3080	88	9	)	)	PUNCT
fuelectenerg-3080	89	1	mod	mod	PROPN
fuelectenerg-3080	89	2	p.	p.	NOUN
fuelectenerg-3080	89	3	if	if	SCONJ
fuelectenerg-3080	89	4	i1	i1	PROPN
fuelectenerg-3080	89	5	and	and	CCONJ
fuelectenerg-3080	89	6	i0	i0	PROPN
fuelectenerg-3080	89	7	are	be	AUX
fuelectenerg-3080	89	8	exchanged	exchange	VERB
fuelectenerg-3080	89	9	,	,	PUNCT
fuelectenerg-3080	89	10	then	then	ADV
fuelectenerg-3080	89	11	modified	modify	VERB
fuelectenerg-3080	89	12	ri	ri	PROPN
fuelectenerg-3080	89	13	,	,	PUNCT
fuelectenerg-3080	89	14	j	j	PROPN
fuelectenerg-3080	89	15	mod	mod	PROPN
fuelectenerg-3080	89	16	p.	p.	NOUN
fuelectenerg-3080	89	17	and	and	CCONJ
fuelectenerg-3080	89	18	if	if	SCONJ
fuelectenerg-3080	89	19	j1	j1	PROPN
fuelectenerg-3080	89	20	and	and	CCONJ
fuelectenerg-3080	89	21	j0	j0	PROPN
fuelectenerg-3080	89	22	are	be	AUX
fuelectenerg-3080	89	23	exchanged	exchange	VERB
fuelectenerg-3080	89	24	,	,	PUNCT
fuelectenerg-3080	89	25	then	then	ADV
fuelectenerg-3080	89	26	modified	modify	VERB
fuelectenerg-3080	89	27	ri	ri	PROPN
fuelectenerg-3080	89	28	,	,	PUNCT
fuelectenerg-3080	89	29	j	j	PROPN
fuelectenerg-3080	89	30	mod	mod	PROPN
fuelectenerg-3080	89	31	p.	p.	NOUN
fuelectenerg-3080	90	1	it	it	PRON
fuelectenerg-3080	90	2	is	be	AUX
fuelectenerg-3080	90	3	simple	simple	ADJ
fuelectenerg-3080	90	4	to	to	PART
fuelectenerg-3080	90	5	see	see	VERB
fuelectenerg-3080	90	6	that	that	SCONJ
fuelectenerg-3080	90	7	in	in	ADP
fuelectenerg-3080	90	8	both	both	DET
fuelectenerg-3080	90	9	cases	case	NOUN
fuelectenerg-3080	90	10	the	the	DET
fuelectenerg-3080	90	11	modified	modified	PROPN
fuelectenerg-3080	90	12	ri	ri	PROPN
fuelectenerg-3080	90	13	,	,	PUNCT
fuelectenerg-3080	90	14	j	j	PROPN
fuelectenerg-3080	90	15	takes	take	VERB
fuelectenerg-3080	90	16	the	the	DET
fuelectenerg-3080	90	17	same	same	ADJ
fuelectenerg-3080	90	18	value	value	NOUN
fuelectenerg-3080	90	19	.	.	PUNCT
fuelectenerg-3080	91	1	moreover	moreover	ADV
fuelectenerg-3080	91	2	,	,	PUNCT
fuelectenerg-3080	91	3	exchanging	exchange	VERB
fuelectenerg-3080	91	4	i1	i1	PROPN
fuelectenerg-3080	91	5	and	and	CCONJ
fuelectenerg-3080	91	6	i0	i0	PROPN
fuelectenerg-3080	91	7	has	have	VERB
fuelectenerg-3080	91	8	the	the	DET
fuelectenerg-3080	91	9	effect	effect	NOUN
fuelectenerg-3080	91	10	of	of	ADP
fuelectenerg-3080	91	11	exchanging	exchange	VERB
fuelectenerg-3080	91	12	(	(	PUNCT
fuelectenerg-3080	91	13	the	the	DET
fuelectenerg-3080	91	14	corresponding	corresponding	ADJ
fuelectenerg-3080	91	15	)	)	PUNCT
fuelectenerg-3080	91	16	two	two	NUM
fuelectenerg-3080	91	17	rows	row	NOUN
fuelectenerg-3080	91	18	of	of	ADP
fuelectenerg-3080	91	19	r2	r2	PROPN
fuelectenerg-3080	91	20	and	and	CCONJ
fuelectenerg-3080	91	21	,	,	PUNCT
fuelectenerg-3080	91	22	similarly	similarly	ADV
fuelectenerg-3080	91	23	,	,	PUNCT
fuelectenerg-3080	91	24	exchanging	exchange	VERB
fuelectenerg-3080	91	25	j1	j1	PROPN
fuelectenerg-3080	91	26	and	and	CCONJ
fuelectenerg-3080	91	27	j0	j0	PROPN
fuelectenerg-3080	91	28	has	have	VERB
fuelectenerg-3080	91	29	the	the	DET
fuelectenerg-3080	91	30	effect	effect	NOUN
fuelectenerg-3080	91	31	of	of	ADP
fuelectenerg-3080	91	32	exchanging	exchange	VERB
fuelectenerg-3080	91	33	(	(	PUNCT
fuelectenerg-3080	91	34	the	the	DET
fuelectenerg-3080	91	35	corresponding	corresponding	ADJ
fuelectenerg-3080	91	36	)	)	PUNCT
fuelectenerg-3080	91	37	two	two	NUM
fuelectenerg-3080	91	38	columns	column	NOUN
fuelectenerg-3080	91	39	of	of	ADP
fuelectenerg-3080	91	40	r2	r2	PROPN
fuelectenerg-3080	91	41	.	.	PUNCT
fuelectenerg-3080	92	1	exchanging	exchange	VERB
fuelectenerg-3080	92	2	i1	i1	PROPN
fuelectenerg-3080	92	3	and	and	CCONJ
fuelectenerg-3080	92	4	i0	i0	PROPN
fuelectenerg-3080	92	5	corresponds	correspond	VERB
fuelectenerg-3080	92	6	to	to	ADP
fuelectenerg-3080	92	7	p2r2	p2r2	NOUN
fuelectenerg-3080	92	8	,	,	PUNCT
fuelectenerg-3080	92	9	while	while	SCONJ
fuelectenerg-3080	92	10	exchanging	exchange	VERB
fuelectenerg-3080	92	11	j1	j1	PROPN
fuelectenerg-3080	92	12	and	and	CCONJ
fuelectenerg-3080	92	13	j0	j0	PROPN
fuelectenerg-3080	92	14	corresponds	correspond	VERB
fuelectenerg-3080	92	15	to	to	ADP
fuelectenerg-3080	92	16	r2p2	r2p2	PROPN
fuelectenerg-3080	92	17	.	.	PUNCT
fuelectenerg-3080	93	1	the	the	DET
fuelectenerg-3080	93	2	assertion	assertion	NOUN
fuelectenerg-3080	93	3	follows	follow	VERB
fuelectenerg-3080	93	4	.	.	PUNCT
fuelectenerg-3080	94	1	although	although	SCONJ
fuelectenerg-3080	94	2	not	not	PART
fuelectenerg-3080	94	3	explicitly	explicitly	ADV
fuelectenerg-3080	94	4	needed	need	VERB
fuelectenerg-3080	94	5	for	for	ADP
fuelectenerg-3080	94	6	theorem	theorem	NOUN
fuelectenerg-3080	94	7	1	1	NUM
fuelectenerg-3080	94	8	,	,	PUNCT
fuelectenerg-3080	94	9	it	it	PRON
fuelectenerg-3080	94	10	is	be	AUX
fuelectenerg-3080	94	11	not	not	PART
fuelectenerg-3080	94	12	difficult	difficult	ADJ
fuelectenerg-3080	94	13	to	to	PART
fuelectenerg-3080	94	14	construct	construct	VERB
fuelectenerg-3080	94	15	the	the	DET
fuelectenerg-3080	94	16	p2	p2	NOUN
fuelectenerg-3080	94	17	matrices	matrix	NOUN
fuelectenerg-3080	94	18	for	for	ADP
fuelectenerg-3080	94	19	different	different	ADJ
fuelectenerg-3080	94	20	values	value	NOUN
fuelectenerg-3080	94	21	of	of	ADP
fuelectenerg-3080	94	22	p	p	NOUN
fuelectenerg-3080	94	23	,	,	PUNCT
fuelectenerg-3080	94	24	because	because	SCONJ
fuelectenerg-3080	94	25	of	of	ADP
fuelectenerg-3080	94	26	the	the	DET
fuelectenerg-3080	94	27	strong	strong	ADJ
fuelectenerg-3080	94	28	regularity	regularity	NOUN
fuelectenerg-3080	94	29	of	of	ADP
fuelectenerg-3080	94	30	their	their	PRON
fuelectenerg-3080	94	31	structure	structure	NOUN
fuelectenerg-3080	94	32	.	.	PUNCT
fuelectenerg-3080	95	1	they	they	PRON
fuelectenerg-3080	95	2	are	be	AUX
fuelectenerg-3080	95	3	symmetric	symmetric	ADJ
fuelectenerg-3080	95	4	,	,	PUNCT
fuelectenerg-3080	95	5	skew	skew	ADJ
fuelectenerg-3080	95	6	-	-	PUNCT
fuelectenerg-3080	95	7	symmetric	symmetric	ADJ
fuelectenerg-3080	95	8	and	and	CCONJ
fuelectenerg-3080	95	9	self	self	NOUN
fuelectenerg-3080	95	10	inverse	inverse	NOUN
fuelectenerg-3080	95	11	.	.	PUNCT
fuelectenerg-3080	96	1	see	see	VERB
fuelectenerg-3080	96	2	figure	figure	NOUN
fuelectenerg-3080	96	3	2	2	NUM
fuelectenerg-3080	96	4	.	.	PUNCT
fuelectenerg-3080	97	1	on	on	ADP
fuelectenerg-3080	97	2	a	a	DET
fuelectenerg-3080	97	3	property	property	NOUN
fuelectenerg-3080	97	4	of	of	ADP
fuelectenerg-3080	97	5	the	the	DET
fuelectenerg-3080	97	6	reed	reed	NOUN
fuelectenerg-3080	97	7	-	-	PUNCT
fuelectenerg-3080	97	8	muller	muller	NOUN
fuelectenerg-3080	97	9	-	-	PUNCT
fuelectenerg-3080	97	10	fourier	fourier	NOUN
fuelectenerg-3080	97	11	transform	transform	NOUN
fuelectenerg-3080	97	12	307	307	NUM
fuelectenerg-3080	97	13	[	[	PUNCT
fuelectenerg-3080	97	14	]	]	X
fuelectenerg-3080	97	15	[	[	PUNCT
fuelectenerg-3080	97	16	]	]	X
fuelectenerg-3080	97	17	[	[	PUNCT
fuelectenerg-3080	97	18	]	]	X
fuelectenerg-3080	97	19	fig	fig	NOUN
fuelectenerg-3080	97	20	.	.	PUNCT
fuelectenerg-3080	97	21	2	2	NUM
fuelectenerg-3080	97	22	p2	p2	NOUN
fuelectenerg-3080	97	23	matrices	matrix	NOUN
fuelectenerg-3080	97	24	for	for	ADP
fuelectenerg-3080	97	25	p	p	NOUN
fuelectenerg-3080	97	26	=	=	SYM
fuelectenerg-3080	97	27	2	2	NUM
fuelectenerg-3080	97	28	,	,	PUNCT
fuelectenerg-3080	97	29	p	p	NOUN
fuelectenerg-3080	97	30	=	=	NOUN
fuelectenerg-3080	97	31	3	3	NUM
fuelectenerg-3080	97	32	,	,	PUNCT
fuelectenerg-3080	97	33	and	and	CCONJ
fuelectenerg-3080	97	34	p	p	NOUN
fuelectenerg-3080	97	35	=	=	SYM
fuelectenerg-3080	97	36	4	4	NUM
fuelectenerg-3080	97	37	corollary	corollary	NOUN
fuelectenerg-3080	97	38	1.1	1.1	NUM
fuelectenerg-3080	97	39	:	:	PUNCT
fuelectenerg-3080	97	40	from	from	ADP
fuelectenerg-3080	97	41	p2r2	p2r2	NOUN
fuelectenerg-3080	97	42	=	=	PUNCT
fuelectenerg-3080	97	43	r2p2	r2p2	PROPN
fuelectenerg-3080	97	44	and	and	CCONJ
fuelectenerg-3080	97	45	recalling	recall	VERB
fuelectenerg-3080	97	46	that	that	DET
fuelectenerg-3080	97	47	r2	r2	PROPN
fuelectenerg-3080	97	48	is	be	AUX
fuelectenerg-3080	97	49	self	self	NOUN
fuelectenerg-3080	97	50	inverse	inverse	NOUN
fuelectenerg-3080	97	51	follows	follow	VERB
fuelectenerg-3080	98	1	that	that	DET
fuelectenerg-3080	98	2	p2	p2	PROPN
fuelectenerg-3080	98	3	=	=	SYM
fuelectenerg-3080	98	4	r2p2r2	r2p2r2	PROPN
fuelectenerg-3080	98	5	.	.	PUNCT
fuelectenerg-3080	99	1	since	since	SCONJ
fuelectenerg-3080	99	2	p2	p2	PROPN
fuelectenerg-3080	99	3	is	be	AUX
fuelectenerg-3080	99	4	also	also	ADV
fuelectenerg-3080	99	5	self	self	NOUN
fuelectenerg-3080	99	6	inverse	inverse	NOUN
fuelectenerg-3080	99	7	,	,	PUNCT
fuelectenerg-3080	99	8	then	then	ADV
fuelectenerg-3080	99	9	p2p2	p2p2	PUNCT
fuelectenerg-3080	100	1	=	=	PUNCT
fuelectenerg-3080	101	1	r2p2r2p2	r2p2r2p2	NOUN
fuelectenerg-3080	101	2	=	=	SYM
fuelectenerg-3080	101	3	i2	i2	PROPN
fuelectenerg-3080	101	4	,	,	PUNCT
fuelectenerg-3080	101	5	meaning	mean	VERB
fuelectenerg-3080	101	6	that	that	SCONJ
fuelectenerg-3080	101	7	r2p2	r2p2	PROPN
fuelectenerg-3080	101	8	is	be	AUX
fuelectenerg-3080	101	9	also	also	ADV
fuelectenerg-3080	101	10	its	its	PRON
fuelectenerg-3080	101	11	own	own	ADJ
fuelectenerg-3080	101	12	inverse	inverse	NOUN
fuelectenerg-3080	101	13	.	.	PUNCT
fuelectenerg-3080	102	1	theorem	theorem	NOUN
fuelectenerg-3080	102	2	2	2	NUM
fuelectenerg-3080	102	3	.	.	PUNCT
fuelectenerg-3080	103	1	let	let	VERB
fuelectenerg-3080	103	2	n	n	PRON
fuelectenerg-3080	103	3			NUM
fuelectenerg-3080	103	4	2	2	NUM
fuelectenerg-3080	103	5	and	and	CCONJ
fuelectenerg-3080	103	6	k	k	X
fuelectenerg-3080	103	7	<	<	X
fuelectenerg-3080	103	8	n.	n.	X
fuelectenerg-3080	103	9	define	define	PROPN
fuelectenerg-3080	103	10	f	f	PROPN
fuelectenerg-3080	103	11	and	and	CCONJ
fuelectenerg-3080	103	12	g	g	PROPN
fuelectenerg-3080	103	13	to	to	PART
fuelectenerg-3080	103	14	be	be	AUX
fuelectenerg-3080	103	15	p	p	NOUN
fuelectenerg-3080	103	16	-	-	PUNCT
fuelectenerg-3080	103	17	valued	value	VERB
fuelectenerg-3080	103	18	functions	function	NOUN
fuelectenerg-3080	103	19	of	of	ADP
fuelectenerg-3080	103	20	n	n	PRON
fuelectenerg-3080	103	21	variables	variable	NOUN
fuelectenerg-3080	103	22	(	(	PUNCT
fuelectenerg-3080	103	23	i.e.	i.e.	X
fuelectenerg-3080	103	24	nplace	nplace	NOUN
fuelectenerg-3080	103	25	functions	function	NOUN
fuelectenerg-3080	103	26	)	)	PUNCT
fuelectenerg-3080	103	27	with	with	ADP
fuelectenerg-3080	103	28	value	value	NOUN
fuelectenerg-3080	103	29	vectors	vector	NOUN
fuelectenerg-3080	103	30	f	f	PROPN
fuelectenerg-3080	103	31	and	and	CCONJ
fuelectenerg-3080	103	32	g	g	PROPN
fuelectenerg-3080	103	33	,	,	PUNCT
fuelectenerg-3080	103	34	respectively	respectively	ADV
fuelectenerg-3080	103	35	,	,	PUNCT
fuelectenerg-3080	103	36	such	such	ADJ
fuelectenerg-3080	103	37	that	that	SCONJ
fuelectenerg-3080	103	38	for	for	ADP
fuelectenerg-3080	103	39	all	all	DET
fuelectenerg-3080	103	40	value	value	NOUN
fuelectenerg-3080	103	41	assignments	assignment	NOUN
fuelectenerg-3080	103	42	to	to	ADP
fuelectenerg-3080	103	43	the	the	DET
fuelectenerg-3080	103	44	arguments	argument	NOUN
fuelectenerg-3080	103	45	,	,	PUNCT
fuelectenerg-3080	103	46	g	g	PROPN
fuelectenerg-3080	103	47	equals	equal	VERB
fuelectenerg-3080	103	48	f	f	PROPN
fuelectenerg-3080	103	49	,	,	PUNCT
fuelectenerg-3080	103	50	but	but	CCONJ
fuelectenerg-3080	103	51	with	with	ADP
fuelectenerg-3080	103	52	transposed	transpose	VERB
fuelectenerg-3080	103	53	arguments	argument	NOUN
fuelectenerg-3080	103	54	xk	xk	PROPN
fuelectenerg-3080	103	55	and	and	CCONJ
fuelectenerg-3080	103	56	xk+1	xk+1	PROPN
fuelectenerg-3080	103	57	.	.	PUNCT
fuelectenerg-3080	104	1	let	let	VERB
fuelectenerg-3080	104	2	pn	pn	PART
fuelectenerg-3080	104	3	be	be	AUX
fuelectenerg-3080	104	4	a	a	DET
fuelectenerg-3080	104	5	permutation	permutation	NOUN
fuelectenerg-3080	104	6	which	which	PRON
fuelectenerg-3080	104	7	when	when	SCONJ
fuelectenerg-3080	104	8	applied	apply	VERB
fuelectenerg-3080	104	9	to	to	ADP
fuelectenerg-3080	104	10	f	f	PROPN
fuelectenerg-3080	104	11	has	have	VERB
fuelectenerg-3080	104	12	the	the	DET
fuelectenerg-3080	104	13	effect	effect	NOUN
fuelectenerg-3080	104	14	of	of	ADP
fuelectenerg-3080	104	15	transposing	transpose	VERB
fuelectenerg-3080	104	16	only	only	ADV
fuelectenerg-3080	104	17	the	the	DET
fuelectenerg-3080	104	18	two	two	NUM
fuelectenerg-3080	104	19	selected	select	VERB
fuelectenerg-3080	104	20	arguments	argument	NOUN
fuelectenerg-3080	104	21	,	,	PUNCT
fuelectenerg-3080	104	22	i.e.	i.e.	X
fuelectenerg-3080	104	23	,	,	PUNCT
fuelectenerg-3080	104	24	pn	pn	NOUN
fuelectenerg-3080	104	25	=	=	PUNCT
fuelectenerg-3080	104	26	(	(	PUNCT
fuelectenerg-3080	104	27	ik-1	ik-1	ADP
fuelectenerg-3080	104	28			ADJ
fuelectenerg-3080	104	29	p2	p2	X
fuelectenerg-3080	104	30			ADJ
fuelectenerg-3080	104	31	in	in	ADP
fuelectenerg-3080	104	32	-	-	PUNCT
fuelectenerg-3080	104	33	k-1	k-1	NOUN
fuelectenerg-3080	104	34	)	)	PUNCT
fuelectenerg-3080	104	35	.	.	PUNCT
fuelectenerg-3080	105	1	then	then	ADV
fuelectenerg-3080	105	2	rnpnf	rnpnf	VERB
fuelectenerg-3080	105	3	=	=	SYM
fuelectenerg-3080	105	4	pnrnf	pnrnf	PRON
fuelectenerg-3080	105	5	mod	mod	PROPN
fuelectenerg-3080	105	6	p.	p.	NOUN
fuelectenerg-3080	105	7	proof	proof	NOUN
fuelectenerg-3080	105	8	:	:	PUNCT
fuelectenerg-3080	105	9	decompose	decompose	VERB
fuelectenerg-3080	105	10	rn	rn	PROPN
fuelectenerg-3080	105	11	to	to	PART
fuelectenerg-3080	105	12	match	match	VERB
fuelectenerg-3080	105	13	the	the	DET
fuelectenerg-3080	105	14	structure	structure	NOUN
fuelectenerg-3080	105	15	of	of	ADP
fuelectenerg-3080	105	16	pn	pn	PROPN
fuelectenerg-3080	105	17	.	.	PUNCT
fuelectenerg-3080	105	18	i.e.	i.e.	X
fuelectenerg-3080	105	19	rn	rn	PROPN
fuelectenerg-3080	105	20	=	=	SYM
fuelectenerg-3080	105	21	rk-1	rk-1	NOUN
fuelectenerg-3080	105	22			PROPN
fuelectenerg-3080	105	23	r2	r2	PROPN
fuelectenerg-3080	105	24			PROPN
fuelectenerg-3080	105	25	rn	rn	PROPN
fuelectenerg-3080	105	26	-	-	PROPN
fuelectenerg-3080	105	27	k-1	k-1	PROPN
fuelectenerg-3080	105	28	,	,	PUNCT
fuelectenerg-3080	105	29	and	and	CCONJ
fuelectenerg-3080	105	30	apply	apply	VERB
fuelectenerg-3080	105	31	it	it	PRON
fuelectenerg-3080	105	32	to	to	ADP
fuelectenerg-3080	105	33	both	both	DET
fuelectenerg-3080	105	34	sides	side	NOUN
fuelectenerg-3080	105	35	of	of	ADP
fuelectenerg-3080	105	36	the	the	DET
fuelectenerg-3080	105	37	claim	claim	NOUN
fuelectenerg-3080	105	38	,	,	PUNCT
fuelectenerg-3080	105	39	taking	take	VERB
fuelectenerg-3080	105	40	advantage	advantage	NOUN
fuelectenerg-3080	105	41	of	of	ADP
fuelectenerg-3080	105	42	the	the	DET
fuelectenerg-3080	105	43	compatibility	compatibility	NOUN
fuelectenerg-3080	105	44	between	between	ADP
fuelectenerg-3080	105	45	kronecker	kronecker	NOUN
fuelectenerg-3080	105	46	and	and	CCONJ
fuelectenerg-3080	105	47	matrix	matrix	NOUN
fuelectenerg-3080	105	48	products	product	NOUN
fuelectenerg-3080	105	49	[	[	X
fuelectenerg-3080	105	50	11	11	NUM
fuelectenerg-3080	105	51	]	]	PUNCT
fuelectenerg-3080	105	52	:	:	PUNCT
fuelectenerg-3080	105	53	rnpnf	rnpnf	X
fuelectenerg-3080	105	54	=	=	SYM
fuelectenerg-3080	105	55	(	(	PUNCT
fuelectenerg-3080	105	56	rk-1	rk-1	NOUN
fuelectenerg-3080	105	57			PROPN
fuelectenerg-3080	105	58	r2	r2	PROPN
fuelectenerg-3080	105	59			PROPN
fuelectenerg-3080	105	60	rn	rn	PROPN
fuelectenerg-3080	105	61	-	-	PUNCT
fuelectenerg-3080	105	62	k-1)(ik-1	k-1)(ik-1	NOUN
fuelectenerg-3080	105	63			ADJ
fuelectenerg-3080	105	64	p2	p2	NOUN
fuelectenerg-3080	105	65			NOUN
fuelectenerg-3080	105	66	in	in	ADP
fuelectenerg-3080	105	67	-	-	PUNCT
fuelectenerg-3080	105	68	k-1)f	k-1)f	NOUN
fuelectenerg-3080	105	69	=	=	SYM
fuelectenerg-3080	105	70	(	(	PUNCT
fuelectenerg-3080	105	71	rk-1	rk-1	NOUN
fuelectenerg-3080	105	72			PRON
fuelectenerg-3080	105	73	r2p2	r2p2	PROPN
fuelectenerg-3080	105	74			ADJ
fuelectenerg-3080	105	75	rn	rn	NOUN
fuelectenerg-3080	105	76	-	-	ADJ
fuelectenerg-3080	105	77	k-1)f	k-1)f	ADJ
fuelectenerg-3080	105	78	mod	mod	PROPN
fuelectenerg-3080	105	79	p.	p.	NOUN
fuelectenerg-3080	105	80	pnrnf	pnrnf	PART
fuelectenerg-3080	106	1	=	=	PUNCT
fuelectenerg-3080	106	2	(	(	PUNCT
fuelectenerg-3080	106	3	ik-1	ik-1	ADP
fuelectenerg-3080	106	4			ADJ
fuelectenerg-3080	106	5	p2	p2	X
fuelectenerg-3080	106	6			ADJ
fuelectenerg-3080	106	7	in	in	ADP
fuelectenerg-3080	106	8	-	-	PUNCT
fuelectenerg-3080	106	9	k-1)(rk-1	k-1)(rk-1	NOUN
fuelectenerg-3080	106	10			PROPN
fuelectenerg-3080	106	11	r2	r2	PROPN
fuelectenerg-3080	106	12			PROPN
fuelectenerg-3080	106	13	rn	rn	PROPN
fuelectenerg-3080	106	14	-	-	PUNCT
fuelectenerg-3080	106	15	k-1)f	k-1)f	X
fuelectenerg-3080	106	16	=	=	SYM
fuelectenerg-3080	106	17	(	(	PUNCT
fuelectenerg-3080	106	18	rk-1	rk-1	AUX
fuelectenerg-3080	106	19			CCONJ
fuelectenerg-3080	106	20	p2r2	p2r2	X
fuelectenerg-3080	106	21			ADJ
fuelectenerg-3080	106	22	rn	rn	NOUN
fuelectenerg-3080	106	23	-	-	ADJ
fuelectenerg-3080	106	24	k-1)f	k-1)f	ADJ
fuelectenerg-3080	106	25	mod	mod	PROPN
fuelectenerg-3080	106	26	p.	p.	NOUN
fuelectenerg-3080	107	1	it	it	PRON
fuelectenerg-3080	107	2	is	be	AUX
fuelectenerg-3080	107	3	easy	easy	ADJ
fuelectenerg-3080	107	4	to	to	PART
fuelectenerg-3080	107	5	see	see	VERB
fuelectenerg-3080	107	6	that	that	SCONJ
fuelectenerg-3080	107	7	the	the	DET
fuelectenerg-3080	107	8	claim	claim	NOUN
fuelectenerg-3080	107	9	will	will	AUX
fuelectenerg-3080	107	10	be	be	AUX
fuelectenerg-3080	107	11	satisfied	satisfied	ADJ
fuelectenerg-3080	107	12	if	if	SCONJ
fuelectenerg-3080	107	13	and	and	CCONJ
fuelectenerg-3080	107	14	only	only	ADV
fuelectenerg-3080	107	15	if	if	SCONJ
fuelectenerg-3080	107	16	p2r2	p2r2	ADJ
fuelectenerg-3080	107	17	=	=	SYM
fuelectenerg-3080	107	18	r2p2	r2p2	ADJ
fuelectenerg-3080	107	19	.	.	PUNCT
fuelectenerg-3080	108	1	this	this	PRON
fuelectenerg-3080	108	2	was	be	AUX
fuelectenerg-3080	108	3	proven	prove	VERB
fuelectenerg-3080	108	4	in	in	ADP
fuelectenerg-3080	108	5	theorem	theorem	NOUN
fuelectenerg-3080	108	6	1	1	NUM
fuelectenerg-3080	108	7	.	.	PUNCT
fuelectenerg-3080	109	1	the	the	DET
fuelectenerg-3080	109	2	assertion	assertion	NOUN
fuelectenerg-3080	109	3	follows	follow	VERB
fuelectenerg-3080	109	4	.	.	PUNCT
fuelectenerg-3080	110	1	308	308	NUM
fuelectenerg-3080	110	2	c.	c.	PROPN
fuelectenerg-3080	110	3	moraga	moraga	PROPN
fuelectenerg-3080	110	4	example	example	NOUN
fuelectenerg-3080	110	5	2	2	X
fuelectenerg-3080	110	6	.	.	PUNCT
fuelectenerg-3080	111	1	let	let	VERB
fuelectenerg-3080	111	2	p	p	NOUN
fuelectenerg-3080	111	3	=	=	NOUN
fuelectenerg-3080	111	4	4	4	NUM
fuelectenerg-3080	111	5	and	and	CCONJ
fuelectenerg-3080	111	6	n	n	CCONJ
fuelectenerg-3080	111	7	=	=	SYM
fuelectenerg-3080	111	8	2	2	X
fuelectenerg-3080	111	9	.	.	NOUN
fuelectenerg-3080	111	10	calculate	calculate	NOUN
fuelectenerg-3080	111	11	p2r2	p2r2	NOUN
fuelectenerg-3080	111	12	operating	operate	VERB
fuelectenerg-3080	111	13	mod	mod	NOUN
fuelectenerg-3080	111	14	4	4	NUM
fuelectenerg-3080	111	15	.	.	PUNCT
fuelectenerg-3080	111	16	from	from	ADP
fuelectenerg-3080	111	17	corollary	corollary	ADJ
fuelectenerg-3080	111	18	1.1	1.1	NUM
fuelectenerg-3080	111	19	,	,	PUNCT
fuelectenerg-3080	111	20	(	(	PUNCT
fuelectenerg-3080	111	21	p2r2	p2r2	NOUN
fuelectenerg-3080	111	22	)	)	PUNCT
fuelectenerg-3080	111	23	-1	-1	PUNCT
fuelectenerg-3080	112	1	=	=	PUNCT
fuelectenerg-3080	112	2	p2r2	p2r2	NOUN
fuelectenerg-3080	112	3	=	=	PRON
fuelectenerg-3080	112	4	r2p2	r2p2	PROPN
fuelectenerg-3080	112	5	therefore	therefore	ADV
fuelectenerg-3080	112	6	commuting	commute	VERB
fuelectenerg-3080	112	7	the	the	DET
fuelectenerg-3080	112	8	factor	factor	NOUN
fuelectenerg-3080	112	9	matrices	matrix	NOUN
fuelectenerg-3080	112	10	will	will	AUX
fuelectenerg-3080	112	11	give	give	VERB
fuelectenerg-3080	112	12	the	the	DET
fuelectenerg-3080	112	13	same	same	ADJ
fuelectenerg-3080	112	14	result	result	NOUN
fuelectenerg-3080	112	15	.	.	PUNCT
fuelectenerg-3080	113	1	theorem	theorem	NOUN
fuelectenerg-3080	113	2	3	3	X
fuelectenerg-3080	113	3	.	.	PUNCT
fuelectenerg-3080	114	1	let	let	VERB
fuelectenerg-3080	114	2	f	f	PROPN
fuelectenerg-3080	114	3	and	and	CCONJ
fuelectenerg-3080	114	4	g	g	PROPN
fuelectenerg-3080	114	5	be	be	VERB
fuelectenerg-3080	114	6	n	n	X
fuelectenerg-3080	114	7	-	-	PUNCT
fuelectenerg-3080	114	8	place	place	NOUN
fuelectenerg-3080	114	9	p	p	NOUN
fuelectenerg-3080	114	10	-	-	PUNCT
fuelectenerg-3080	114	11	valued	value	VERB
fuelectenerg-3080	114	12	functions	function	NOUN
fuelectenerg-3080	114	13	with	with	ADP
fuelectenerg-3080	114	14	value	value	NOUN
fuelectenerg-3080	114	15	vectors	vector	NOUN
fuelectenerg-3080	114	16	f	f	PROPN
fuelectenerg-3080	114	17	and	and	CCONJ
fuelectenerg-3080	114	18	g	g	PROPN
fuelectenerg-3080	114	19	,	,	PUNCT
fuelectenerg-3080	114	20	respectively	respectively	ADV
fuelectenerg-3080	114	21	,	,	PUNCT
fuelectenerg-3080	114	22	such	such	ADJ
fuelectenerg-3080	114	23	that	that	SCONJ
fuelectenerg-3080	114	24	for	for	ADP
fuelectenerg-3080	114	25	all	all	DET
fuelectenerg-3080	114	26	value	value	NOUN
fuelectenerg-3080	114	27	assignments	assignment	NOUN
fuelectenerg-3080	114	28	to	to	ADP
fuelectenerg-3080	114	29	the	the	DET
fuelectenerg-3080	114	30	arguments	argument	NOUN
fuelectenerg-3080	114	31	,	,	PUNCT
fuelectenerg-3080	114	32	g	g	PROPN
fuelectenerg-3080	114	33	equals	equal	VERB
fuelectenerg-3080	114	34	f	f	PROPN
fuelectenerg-3080	114	35	,	,	PUNCT
fuelectenerg-3080	114	36	but	but	CCONJ
fuelectenerg-3080	114	37	with	with	ADP
fuelectenerg-3080	114	38	transposed	transpose	VERB
fuelectenerg-3080	114	39	arguments	argument	NOUN
fuelectenerg-3080	114	40	xk	xk	PROPN
fuelectenerg-3080	114	41	and	and	CCONJ
fuelectenerg-3080	114	42	xk+1	xk+1	PROPN
fuelectenerg-3080	114	43	and	and	CCONJ
fuelectenerg-3080	114	44	transposed	transpose	VERB
fuelectenerg-3080	114	45	arguments	argument	NOUN
fuelectenerg-3080	114	46	xh	xh	PROPN
fuelectenerg-3080	114	47	and	and	CCONJ
fuelectenerg-3080	114	48	xh+1	xh+1	PROPN
fuelectenerg-3080	114	49	.	.	PUNCT
fuelectenerg-3080	115	1	(	(	PUNCT
fuelectenerg-3080	115	2	n	n	X
fuelectenerg-3080	115	3	>	>	X
fuelectenerg-3080	115	4	k	k	X
fuelectenerg-3080	115	5	>	>	X
fuelectenerg-3080	115	6	h	h	PROPN
fuelectenerg-3080	115	7	>	>	X
fuelectenerg-3080	115	8	0	0	NUM
fuelectenerg-3080	115	9	)	)	PUNCT
fuelectenerg-3080	115	10	.	.	PUNCT
fuelectenerg-3080	116	1	if	if	SCONJ
fuelectenerg-3080	116	2	applied	apply	VERB
fuelectenerg-3080	116	3	independently	independently	ADV
fuelectenerg-3080	116	4	,	,	PUNCT
fuelectenerg-3080	116	5	let	let	VERB
fuelectenerg-3080	116	6	the	the	DET
fuelectenerg-3080	116	7	corresponding	correspond	VERB
fuelectenerg-3080	116	8	transposition	transposition	NOUN
fuelectenerg-3080	116	9	matrices	matrix	NOUN
fuelectenerg-3080	116	10	be	be	VERB
fuelectenerg-3080	116	11	and	and	CCONJ
fuelectenerg-3080	116	12	,	,	PUNCT
fuelectenerg-3080	116	13	respectively	respectively	ADV
fuelectenerg-3080	116	14	,	,	PUNCT
fuelectenerg-3080	116	15	leading	lead	VERB
fuelectenerg-3080	116	16	to	to	ADP
fuelectenerg-3080	116	17	g	g	NOUN
fuelectenerg-3080	116	18	=	=	SYM
fuelectenerg-3080	116	19			VERB
fuelectenerg-3080	116	20	f	f	NOUN
fuelectenerg-3080	116	21	.	.	PUNCT
fuelectenerg-3080	117	1	the	the	DET
fuelectenerg-3080	117	2	following	follow	VERB
fuelectenerg-3080	117	3	holds	hold	VERB
fuelectenerg-3080	117	4	:	:	PUNCT
fuelectenerg-3080	117	5	rng	rng	X
fuelectenerg-3080	117	6	=	=	SYM
fuelectenerg-3080	118	1			PROPN
fuelectenerg-3080	118	2	rnf	rnf	VERB
fuelectenerg-3080	118	3	mod	mod	ADJ
fuelectenerg-3080	118	4	p.	p.	NOUN
fuelectenerg-3080	118	5	proof	proof	NOUN
fuelectenerg-3080	118	6	:	:	PUNCT
fuelectenerg-3080	118	7	consider	consider	VERB
fuelectenerg-3080	118	8	first	first	ADJ
fuelectenerg-3080	118	9	one	one	NUM
fuelectenerg-3080	118	10	of	of	ADP
fuelectenerg-3080	118	11	the	the	DET
fuelectenerg-3080	118	12	transpositions	transposition	NOUN
fuelectenerg-3080	118	13	.	.	PUNCT
fuelectenerg-3080	119	1	let	let	VERB
fuelectenerg-3080	119	2	g	g	PRON
fuelectenerg-3080	119	3	’	'	PUNCT
fuelectenerg-3080	119	4	=	=	SYM
fuelectenerg-3080	119	5	f	f	ADJ
fuelectenerg-3080	120	1	mod	mod	PROPN
fuelectenerg-3080	120	2	p.	p.	NOUN
fuelectenerg-3080	120	3	then	then	ADV
fuelectenerg-3080	120	4	from	from	ADP
fuelectenerg-3080	120	5	theorem	theorem	ADJ
fuelectenerg-3080	120	6	1	1	NUM
fuelectenerg-3080	120	7	follows	follow	VERB
fuelectenerg-3080	120	8	that	that	DET
fuelectenerg-3080	120	9	rng	rng	NOUN
fuelectenerg-3080	120	10	’	'	PUNCT
fuelectenerg-3080	120	11	=	=	SYM
fuelectenerg-3080	120	12	rn	rn	NOUN
fuelectenerg-3080	120	13	f	f	NOUN
fuelectenerg-3080	120	14	=	=	PUNCT
fuelectenerg-3080	120	15	rnf	rnf	VERB
fuelectenerg-3080	120	16	mod	mod	PROPN
fuelectenerg-3080	120	17	p.	p.	PROPN
fuelectenerg-3080	120	18	now	now	ADV
fuelectenerg-3080	120	19	let	let	VERB
fuelectenerg-3080	120	20	the	the	DET
fuelectenerg-3080	120	21	second	second	ADJ
fuelectenerg-3080	120	22	transposition	transposition	NOUN
fuelectenerg-3080	120	23	be	be	AUX
fuelectenerg-3080	120	24	executed	execute	VERB
fuelectenerg-3080	120	25	.	.	PUNCT
fuelectenerg-3080	121	1	g	g	NOUN
fuelectenerg-3080	121	2	=	=	PUNCT
fuelectenerg-3080	121	3	g	g	PROPN
fuelectenerg-3080	121	4	’	'	PUNCT
fuelectenerg-3080	121	5	.	.	PUNCT
fuelectenerg-3080	122	1	then	then	ADV
fuelectenerg-3080	122	2	from	from	ADP
fuelectenerg-3080	122	3	theorem	theorem	ADJ
fuelectenerg-3080	122	4	1	1	NUM
fuelectenerg-3080	122	5	follows	follow	VERB
fuelectenerg-3080	122	6	that	that	SCONJ
fuelectenerg-3080	122	7	rng	rng	ADJ
fuelectenerg-3080	122	8	=	=	SYM
fuelectenerg-3080	122	9	rn	rn	NOUN
fuelectenerg-3080	122	10	g	g	NOUN
fuelectenerg-3080	122	11	’	'	PUNCT
fuelectenerg-3080	122	12	=	=	SYM
fuelectenerg-3080	122	13	rng	rng	NOUN
fuelectenerg-3080	122	14	’	'	PUNCT
fuelectenerg-3080	122	15	=	=	SYM
fuelectenerg-3080	122	16	=	=	SYM
fuelectenerg-3080	122	17			PROPN
fuelectenerg-3080	122	18	rnf	rnf	VERB
fuelectenerg-3080	122	19	mod	mod	PROPN
fuelectenerg-3080	122	20	p.	p.	PROPN
fuelectenerg-3080	122	21	p2r2	p2r2	NOUN
fuelectenerg-3080	122	22	=	=	PUNCT
fuelectenerg-3080	123	1	=	=	PUNCT
fuelectenerg-3080	123	2	=	=	PROPN
fuelectenerg-3080	123	3	on	on	ADP
fuelectenerg-3080	123	4	a	a	DET
fuelectenerg-3080	123	5	property	property	NOUN
fuelectenerg-3080	123	6	of	of	ADP
fuelectenerg-3080	123	7	the	the	DET
fuelectenerg-3080	123	8	reed	reed	NOUN
fuelectenerg-3080	123	9	-	-	PUNCT
fuelectenerg-3080	123	10	muller	muller	NOUN
fuelectenerg-3080	123	11	-	-	PUNCT
fuelectenerg-3080	123	12	fourier	fourier	NOUN
fuelectenerg-3080	123	13	transform	transform	VERB
fuelectenerg-3080	123	14	309	309	NUM
fuelectenerg-3080	123	15	theorem	theorem	NOUN
fuelectenerg-3080	123	16	4	4	NUM
fuelectenerg-3080	123	17	.	.	PUNCT
fuelectenerg-3080	124	1	let	let	VERB
fuelectenerg-3080	124	2	f	f	PROPN
fuelectenerg-3080	124	3	and	and	CCONJ
fuelectenerg-3080	124	4	g	g	PROPN
fuelectenerg-3080	124	5	be	be	VERB
fuelectenerg-3080	124	6	n	n	X
fuelectenerg-3080	124	7	-	-	PUNCT
fuelectenerg-3080	124	8	place	place	NOUN
fuelectenerg-3080	124	9	p	p	NOUN
fuelectenerg-3080	124	10	-	-	PUNCT
fuelectenerg-3080	124	11	valued	value	VERB
fuelectenerg-3080	124	12	functions	function	NOUN
fuelectenerg-3080	124	13	with	with	ADP
fuelectenerg-3080	124	14	value	value	NOUN
fuelectenerg-3080	124	15	vectors	vector	NOUN
fuelectenerg-3080	124	16	f	f	PROPN
fuelectenerg-3080	124	17	and	and	CCONJ
fuelectenerg-3080	124	18	g	g	PROPN
fuelectenerg-3080	124	19	,	,	PUNCT
fuelectenerg-3080	124	20	respectively	respectively	ADV
fuelectenerg-3080	124	21	,	,	PUNCT
fuelectenerg-3080	124	22	such	such	ADJ
fuelectenerg-3080	124	23	that	that	SCONJ
fuelectenerg-3080	124	24	for	for	ADP
fuelectenerg-3080	124	25	all	all	DET
fuelectenerg-3080	124	26	value	value	NOUN
fuelectenerg-3080	124	27	assignments	assignment	NOUN
fuelectenerg-3080	124	28	to	to	ADP
fuelectenerg-3080	124	29	the	the	DET
fuelectenerg-3080	124	30	arguments	argument	NOUN
fuelectenerg-3080	124	31	,	,	PUNCT
fuelectenerg-3080	124	32	g	g	PROPN
fuelectenerg-3080	124	33	equals	equal	VERB
fuelectenerg-3080	124	34	f	f	PROPN
fuelectenerg-3080	124	35	,	,	PUNCT
fuelectenerg-3080	124	36	but	but	CCONJ
fuelectenerg-3080	124	37	with	with	ADP
fuelectenerg-3080	124	38	permuted	permuted	ADJ
fuelectenerg-3080	124	39	arguments	argument	NOUN
fuelectenerg-3080	124	40	.	.	PUNCT
fuelectenerg-3080	125	1	let	let	VERB
fuelectenerg-3080	125	2	pn	pn	PART
fuelectenerg-3080	125	3	be	be	AUX
fuelectenerg-3080	125	4	a	a	DET
fuelectenerg-3080	125	5	permutation	permutation	NOUN
fuelectenerg-3080	125	6	matrix	matrix	NOUN
fuelectenerg-3080	125	7	,	,	PUNCT
fuelectenerg-3080	125	8	which	which	PRON
fuelectenerg-3080	125	9	when	when	SCONJ
fuelectenerg-3080	125	10	applied	apply	VERB
fuelectenerg-3080	125	11	to	to	ADP
fuelectenerg-3080	125	12	f	f	PROPN
fuelectenerg-3080	125	13	has	have	VERB
fuelectenerg-3080	125	14	the	the	DET
fuelectenerg-3080	125	15	same	same	ADJ
fuelectenerg-3080	125	16	effect	effect	NOUN
fuelectenerg-3080	125	17	as	as	ADP
fuelectenerg-3080	125	18	permuting	permute	VERB
fuelectenerg-3080	125	19	the	the	DET
fuelectenerg-3080	125	20	corresponding	corresponding	ADJ
fuelectenerg-3080	125	21	arguments	argument	NOUN
fuelectenerg-3080	125	22	.	.	PUNCT
fuelectenerg-3080	126	1	then	then	ADV
fuelectenerg-3080	126	2	rng	rng	NOUN
fuelectenerg-3080	126	3	=	=	PUNCT
fuelectenerg-3080	127	1	rnpnf	rnpnf	X
fuelectenerg-3080	127	2	=	=	SYM
fuelectenerg-3080	127	3	pnrnf	pnrnf	PRON
fuelectenerg-3080	127	4	mod	mod	PROPN
fuelectenerg-3080	127	5	p.	p.	PROPN
fuelectenerg-3080	127	6	proof	proof	NOUN
fuelectenerg-3080	127	7	:	:	PUNCT
fuelectenerg-3080	127	8	recall	recall	VERB
fuelectenerg-3080	127	9	that	that	SCONJ
fuelectenerg-3080	127	10	any	any	DET
fuelectenerg-3080	127	11	permutation	permutation	NOUN
fuelectenerg-3080	127	12	of	of	ADP
fuelectenerg-3080	127	13	an	an	DET
fuelectenerg-3080	127	14	ordered	order	VERB
fuelectenerg-3080	127	15	set	set	NOUN
fuelectenerg-3080	127	16	of	of	ADP
fuelectenerg-3080	127	17	arguments	argument	NOUN
fuelectenerg-3080	127	18	may	may	AUX
fuelectenerg-3080	127	19	be	be	AUX
fuelectenerg-3080	127	20	obtained	obtain	VERB
fuelectenerg-3080	127	21	with	with	ADP
fuelectenerg-3080	127	22	an	an	DET
fuelectenerg-3080	127	23	appropriate	appropriate	ADJ
fuelectenerg-3080	127	24	sequence	sequence	NOUN
fuelectenerg-3080	127	25	of	of	ADP
fuelectenerg-3080	127	26	transpositions	transposition	NOUN
fuelectenerg-3080	127	27	,	,	PUNCT
fuelectenerg-3080	127	28	and	and	CCONJ
fuelectenerg-3080	127	29	any	any	DET
fuelectenerg-3080	127	30	transposition	transposition	NOUN
fuelectenerg-3080	127	31	may	may	AUX
fuelectenerg-3080	127	32	be	be	AUX
fuelectenerg-3080	127	33	obtained	obtain	VERB
fuelectenerg-3080	127	34	with	with	ADP
fuelectenerg-3080	127	35	a	a	DET
fuelectenerg-3080	127	36	cascade	cascade	NOUN
fuelectenerg-3080	127	37	of	of	ADP
fuelectenerg-3080	127	38	transpositions	transposition	NOUN
fuelectenerg-3080	127	39	of	of	ADP
fuelectenerg-3080	127	40	neighbor	neighbor	NOUN
fuelectenerg-3080	127	41	arguments	argument	NOUN
fuelectenerg-3080	127	42	.	.	PUNCT
fuelectenerg-3080	128	1	apply	apply	VERB
fuelectenerg-3080	128	2	accordingly	accordingly	ADV
fuelectenerg-3080	128	3	theorems	theorem	NOUN
fuelectenerg-3080	128	4	2	2	NUM
fuelectenerg-3080	128	5	and	and	CCONJ
fuelectenerg-3080	128	6	3	3	NUM
fuelectenerg-3080	128	7	as	as	ADV
fuelectenerg-3080	128	8	many	many	ADJ
fuelectenerg-3080	128	9	times	time	NOUN
fuelectenerg-3080	128	10	as	as	SCONJ
fuelectenerg-3080	128	11	needed	need	VERB
fuelectenerg-3080	128	12	.	.	PUNCT
fuelectenerg-3080	129	1	theorem	theorem	NOUN
fuelectenerg-3080	129	2	5	5	NUM
fuelectenerg-3080	129	3	.	.	PUNCT
fuelectenerg-3080	130	1	the	the	DET
fuelectenerg-3080	130	2	rmf	rmf	PROPN
fuelectenerg-3080	130	3	spectrum	spectrum	NOUN
fuelectenerg-3080	130	4	of	of	ADP
fuelectenerg-3080	130	5	an	an	DET
fuelectenerg-3080	130	6	n	n	CCONJ
fuelectenerg-3080	130	7	-	-	PUNCT
fuelectenerg-3080	130	8	place	place	NOUN
fuelectenerg-3080	130	9	p	p	NOUN
fuelectenerg-3080	130	10	-	-	PUNCT
fuelectenerg-3080	130	11	valued	value	VERB
fuelectenerg-3080	130	12	symmetric	symmetric	ADJ
fuelectenerg-3080	130	13	function	function	NOUN
fuelectenerg-3080	130	14	is	be	AUX
fuelectenerg-3080	130	15	symmetric	symmetric	ADJ
fuelectenerg-3080	130	16	.	.	PUNCT
fuelectenerg-3080	131	1	proof	proof	NOUN
fuelectenerg-3080	131	2	:	:	PUNCT
fuelectenerg-3080	131	3	recall	recall	VERB
fuelectenerg-3080	131	4	that	that	SCONJ
fuelectenerg-3080	131	5	a	a	DET
fuelectenerg-3080	131	6	p	p	ADV
fuelectenerg-3080	131	7	-	-	PUNCT
fuelectenerg-3080	131	8	valued	value	VERB
fuelectenerg-3080	131	9	function	function	NOUN
fuelectenerg-3080	131	10	is	be	AUX
fuelectenerg-3080	131	11	symmetric	symmetric	ADJ
fuelectenerg-3080	131	12	iff	iff	PROPN
fuelectenerg-3080	131	13	it	it	PRON
fuelectenerg-3080	131	14	is	be	AUX
fuelectenerg-3080	131	15	invariant	invariant	ADJ
fuelectenerg-3080	131	16	with	with	ADP
fuelectenerg-3080	131	17	respect	respect	NOUN
fuelectenerg-3080	131	18	to	to	ADP
fuelectenerg-3080	131	19	any	any	DET
fuelectenerg-3080	131	20	permutation	permutation	NOUN
fuelectenerg-3080	131	21	of	of	ADP
fuelectenerg-3080	131	22	its	its	PRON
fuelectenerg-3080	131	23	arguments	argument	NOUN
fuelectenerg-3080	131	24	.	.	PUNCT
fuelectenerg-3080	132	1	(	(	PUNCT
fuelectenerg-3080	132	2	see	see	VERB
fuelectenerg-3080	132	3	e.g.	e.g.	ADV
fuelectenerg-3080	132	4	[	[	X
fuelectenerg-3080	132	5	14	14	NUM
fuelectenerg-3080	132	6	]	]	PUNCT
fuelectenerg-3080	132	7	,	,	PUNCT
fuelectenerg-3080	132	8	[	[	X
fuelectenerg-3080	132	9	15	15	NUM
fuelectenerg-3080	132	10	]	]	PUNCT
fuelectenerg-3080	132	11	,	,	PUNCT
fuelectenerg-3080	132	12	[	[	X
fuelectenerg-3080	132	13	16	16	NUM
fuelectenerg-3080	132	14	]	]	PUNCT
fuelectenerg-3080	132	15	,	,	PUNCT
fuelectenerg-3080	132	16	[	[	X
fuelectenerg-3080	132	17	17	17	NUM
fuelectenerg-3080	132	18	]	]	PUNCT
fuelectenerg-3080	132	19	)	)	PUNCT
fuelectenerg-3080	132	20	let	let	VERB
fuelectenerg-3080	132	21	f	f	PRON
fuelectenerg-3080	132	22	be	be	AUX
fuelectenerg-3080	132	23	the	the	DET
fuelectenerg-3080	132	24	value	value	NOUN
fuelectenerg-3080	132	25	vector	vector	NOUN
fuelectenerg-3080	132	26	of	of	ADP
fuelectenerg-3080	132	27	a	a	DET
fuelectenerg-3080	132	28	symmetric	symmetric	ADJ
fuelectenerg-3080	132	29	function	function	NOUN
fuelectenerg-3080	132	30	and	and	CCONJ
fuelectenerg-3080	132	31	let	let	VERB
fuelectenerg-3080	132	32	pn	pn	PART
fuelectenerg-3080	132	33	be	be	AUX
fuelectenerg-3080	132	34	equivalent	equivalent	ADJ
fuelectenerg-3080	132	35	to	to	ADP
fuelectenerg-3080	132	36	a	a	DET
fuelectenerg-3080	132	37	random	random	ADJ
fuelectenerg-3080	132	38	permutation	permutation	NOUN
fuelectenerg-3080	132	39	of	of	ADP
fuelectenerg-3080	132	40	its	its	PRON
fuelectenerg-3080	132	41	arguments	argument	NOUN
fuelectenerg-3080	132	42	.	.	PUNCT
fuelectenerg-3080	133	1	then	then	ADV
fuelectenerg-3080	133	2	f	f	X
fuelectenerg-3080	133	3	=	=	PUNCT
fuelectenerg-3080	133	4	pnf	pnf	VERB
fuelectenerg-3080	133	5	.	.	PUNCT
fuelectenerg-3080	134	1	from	from	ADP
fuelectenerg-3080	134	2	theorem	theorem	ADJ
fuelectenerg-3080	134	3	4	4	NUM
fuelectenerg-3080	134	4	,	,	PUNCT
fuelectenerg-3080	134	5	rnf	rnf	X
fuelectenerg-3080	134	6	=	=	NOUN
fuelectenerg-3080	134	7	rnpnf	rnpnf	NOUN
fuelectenerg-3080	134	8	=	=	SYM
fuelectenerg-3080	134	9	pnrnf	pnrnf	NOUN
fuelectenerg-3080	134	10	mod	mod	PROPN
fuelectenerg-3080	134	11	p.	p.	PROPN
fuelectenerg-3080	134	12	therefore	therefore	ADV
fuelectenerg-3080	134	13	rnf	rnf	VERB
fuelectenerg-3080	134	14	mod	mod	PROPN
fuelectenerg-3080	134	15	p	p	NOUN
fuelectenerg-3080	134	16	is	be	AUX
fuelectenerg-3080	134	17	symmetric	symmetric	ADJ
fuelectenerg-3080	134	18	.	.	PUNCT
fuelectenerg-3080	135	1	example	example	NOUN
fuelectenerg-3080	136	1	3	3	NUM
fuelectenerg-3080	136	2	:	:	PUNCT
fuelectenerg-3080	136	3	let	let	VERB
fuelectenerg-3080	136	4	p	p	NOUN
fuelectenerg-3080	136	5	=	=	NOUN
fuelectenerg-3080	136	6	4	4	NUM
fuelectenerg-3080	136	7	and	and	CCONJ
fuelectenerg-3080	136	8	f	f	NOUN
fuelectenerg-3080	136	9	:	:	PUNCT
fuelectenerg-3080	136	10	v	v	NUM
fuelectenerg-3080	136	11	2	2	NUM
fuelectenerg-3080	136	12			NOUN
fuelectenerg-3080	136	13	v	v	PART
fuelectenerg-3080	136	14	be	be	AUX
fuelectenerg-3080	136	15	symmetric	symmetric	ADJ
fuelectenerg-3080	136	16	,	,	PUNCT
fuelectenerg-3080	136	17	such	such	ADJ
fuelectenerg-3080	136	18	that	that	SCONJ
fuelectenerg-3080	136	19	f	f	PROPN
fuelectenerg-3080	136	20	=	=	PUNCT
fuelectenerg-3080	137	1	[	[	X
fuelectenerg-3080	137	2	1	1	NUM
fuelectenerg-3080	137	3	1	1	NUM
fuelectenerg-3080	137	4	0	0	NUM
fuelectenerg-3080	137	5	3	3	NUM
fuelectenerg-3080	137	6	1	1	NUM
fuelectenerg-3080	137	7	2	2	NUM
fuelectenerg-3080	137	8	3	3	NUM
fuelectenerg-3080	137	9	1	1	NUM
fuelectenerg-3080	137	10	0	0	NUM
fuelectenerg-3080	137	11	3	3	NUM
fuelectenerg-3080	137	12	3	3	NUM
fuelectenerg-3080	137	13	2	2	NUM
fuelectenerg-3080	137	14	3	3	NUM
fuelectenerg-3080	137	15	1	1	NUM
fuelectenerg-3080	137	16	2	2	NUM
fuelectenerg-3080	137	17	0	0	NUM
fuelectenerg-3080	137	18	]	]	PUNCT
fuelectenerg-3080	137	19	t	t	PROPN
fuelectenerg-3080	137	20	let	let	VERB
fuelectenerg-3080	137	21	s	s	NOUN
fuelectenerg-3080	137	22	=	=	PUNCT
fuelectenerg-3080	137	23	r2f	r2f	PROPN
fuelectenerg-3080	137	24	s	s	PART
fuelectenerg-3080	137	25	=	=	SYM
fuelectenerg-3080	137	26	310	310	NUM
fuelectenerg-3080	137	27	c.	c.	PROPN
fuelectenerg-3080	137	28	moraga	moraga	PROPN
fuelectenerg-3080	137	29	symmetry	symmetry	PROPN
fuelectenerg-3080	137	30	proof	proof	NOUN
fuelectenerg-3080	137	31	:	:	PUNCT
fuelectenerg-3080	138	1	x2	x2	PROPN
fuelectenerg-3080	138	2	x1	x1	PROPN
fuelectenerg-3080	138	3	ft	ft	X
fuelectenerg-3080	138	4	s	s	PROPN
fuelectenerg-3080	138	5	t	t	NOUN
fuelectenerg-3080	138	6	0	0	NUM
fuelectenerg-3080	138	7	1	1	NUM
fuelectenerg-3080	138	8	2	2	NUM
fuelectenerg-3080	138	9	3	3	NUM
fuelectenerg-3080	138	10	0	0	NUM
fuelectenerg-3080	138	11	1	1	NUM
fuelectenerg-3080	138	12	2	2	NUM
fuelectenerg-3080	138	13	3	3	NUM
fuelectenerg-3080	138	14	0	0	NUM
fuelectenerg-3080	138	15	1	1	NUM
fuelectenerg-3080	138	16	2	2	NUM
fuelectenerg-3080	138	17	3	3	NUM
fuelectenerg-3080	138	18	0	0	NUM
fuelectenerg-3080	138	19	1	1	NUM
fuelectenerg-3080	138	20	2	2	NUM
fuelectenerg-3080	138	21	3	3	NUM
fuelectenerg-3080	138	22	0	0	NUM
fuelectenerg-3080	138	23	0	0	NUM
fuelectenerg-3080	138	24	0	0	NUM
fuelectenerg-3080	138	25	0	0	NUM
fuelectenerg-3080	138	26	1	1	NUM
fuelectenerg-3080	138	27	1	1	NUM
fuelectenerg-3080	138	28	1	1	NUM
fuelectenerg-3080	138	29	1	1	NUM
fuelectenerg-3080	138	30	2	2	NUM
fuelectenerg-3080	138	31	2	2	NUM
fuelectenerg-3080	138	32	2	2	NUM
fuelectenerg-3080	138	33	2	2	NUM
fuelectenerg-3080	138	34	3	3	NUM
fuelectenerg-3080	138	35	3	3	NUM
fuelectenerg-3080	138	36	3	3	NUM
fuelectenerg-3080	138	37	3	3	NUM
fuelectenerg-3080	138	38	1	1	NUM
fuelectenerg-3080	138	39	1	1	NUM
fuelectenerg-3080	138	40	0	0	NUM
fuelectenerg-3080	138	41	3	3	NUM
fuelectenerg-3080	138	42	1	1	NUM
fuelectenerg-3080	138	43	2	2	NUM
fuelectenerg-3080	138	44	3	3	NUM
fuelectenerg-3080	138	45	1	1	NUM
fuelectenerg-3080	138	46	0	0	NUM
fuelectenerg-3080	138	47	3	3	NUM
fuelectenerg-3080	138	48	3	3	NUM
fuelectenerg-3080	138	49	2	2	NUM
fuelectenerg-3080	138	50	3	3	NUM
fuelectenerg-3080	138	51	1	1	NUM
fuelectenerg-3080	138	52	2	2	NUM
fuelectenerg-3080	138	53	0	0	NUM
fuelectenerg-3080	138	54	1	1	NUM
fuelectenerg-3080	138	55	0	0	NUM
fuelectenerg-3080	138	56	3	3	NUM
fuelectenerg-3080	138	57	3	3	NUM
fuelectenerg-3080	138	58	0	0	NUM
fuelectenerg-3080	138	59	1	1	NUM
fuelectenerg-3080	138	60	3	3	NUM
fuelectenerg-3080	138	61	0	0	NUM
fuelectenerg-3080	138	62	3	3	NUM
fuelectenerg-3080	138	63	3	3	NUM
fuelectenerg-3080	138	64	0	0	NUM
fuelectenerg-3080	138	65	3	3	NUM
fuelectenerg-3080	138	66	3	3	NUM
fuelectenerg-3080	138	67	0	0	NUM
fuelectenerg-3080	138	68	3	3	NUM
fuelectenerg-3080	138	69	2	2	NUM
fuelectenerg-3080	138	70	it	it	PRON
fuelectenerg-3080	138	71	is	be	AUX
fuelectenerg-3080	138	72	easy	easy	ADJ
fuelectenerg-3080	138	73	to	to	PART
fuelectenerg-3080	138	74	see	see	VERB
fuelectenerg-3080	138	75	that	that	PRON
fuelectenerg-3080	138	76	s	s	ADP
fuelectenerg-3080	138	77	,	,	PUNCT
fuelectenerg-3080	138	78	the	the	DET
fuelectenerg-3080	138	79	spectrum	spectrum	NOUN
fuelectenerg-3080	138	80	of	of	ADP
fuelectenerg-3080	138	81	f	f	PROPN
fuelectenerg-3080	138	82	,	,	PUNCT
fuelectenerg-3080	138	83	is	be	AUX
fuelectenerg-3080	138	84	also	also	ADV
fuelectenerg-3080	138	85	symmetric	symmetric	ADJ
fuelectenerg-3080	138	86	.	.	PUNCT
fuelectenerg-3080	139	1	remark	remark	NOUN
fuelectenerg-3080	139	2	:	:	PUNCT
fuelectenerg-3080	139	3	it	it	PRON
fuelectenerg-3080	139	4	was	be	AUX
fuelectenerg-3080	139	5	shown	show	VERB
fuelectenerg-3080	139	6	in	in	ADP
fuelectenerg-3080	139	7	[	[	X
fuelectenerg-3080	139	8	18	18	NUM
fuelectenerg-3080	139	9	]	]	PUNCT
fuelectenerg-3080	139	10	that	that	SCONJ
fuelectenerg-3080	139	11	an	an	DET
fuelectenerg-3080	139	12	analog	analog	NOUN
fuelectenerg-3080	139	13	to	to	PART
fuelectenerg-3080	139	14	theorem	theorem	VERB
fuelectenerg-3080	139	15	3	3	NUM
fuelectenerg-3080	139	16	holds	hold	NOUN
fuelectenerg-3080	139	17	for	for	ADP
fuelectenerg-3080	139	18	spectra	spectra	NOUN
fuelectenerg-3080	139	19	obtained	obtain	VERB
fuelectenerg-3080	139	20	with	with	ADP
fuelectenerg-3080	139	21	the	the	DET
fuelectenerg-3080	139	22	reed	reed	NOUN
fuelectenerg-3080	139	23	-	-	PUNCT
fuelectenerg-3080	139	24	muller	muller	NOUN
fuelectenerg-3080	139	25	or	or	CCONJ
fuelectenerg-3080	139	26	the	the	DET
fuelectenerg-3080	139	27	vilenkin	vilenkin	PROPN
fuelectenerg-3080	139	28	-	-	PUNCT
fuelectenerg-3080	139	29	chrestenson	chrestenson	NOUN
fuelectenerg-3080	139	30	transforms	transform	VERB
fuelectenerg-3080	139	31	.	.	PUNCT
fuelectenerg-3080	140	1	this	this	PRON
fuelectenerg-3080	140	2	also	also	ADV
fuelectenerg-3080	140	3	includes	include	VERB
fuelectenerg-3080	140	4	the	the	DET
fuelectenerg-3080	140	5	circular	circular	ADJ
fuelectenerg-3080	140	6	vilenkin	vilenkin	PROPN
fuelectenerg-3080	140	7	-	-	PUNCT
fuelectenerg-3080	140	8	chrestenson	chrestenson	NOUN
fuelectenerg-3080	140	9	spectrum	spectrum	NOUN
fuelectenerg-3080	140	10	.	.	PUNCT
fuelectenerg-3080	141	1	corollary	corollary	ADJ
fuelectenerg-3080	141	2	5.1	5.1	NUM
fuelectenerg-3080	141	3	.	.	PUNCT
fuelectenerg-3080	142	1	the	the	DET
fuelectenerg-3080	142	2	reed	reed	NOUN
fuelectenerg-3080	142	3	-	-	PUNCT
fuelectenerg-3080	142	4	muller	muller	NOUN
fuelectenerg-3080	142	5	and	and	CCONJ
fuelectenerg-3080	142	6	the	the	DET
fuelectenerg-3080	142	7	vilenkin	vilenkin	PROPN
fuelectenerg-3080	142	8	-	-	PUNCT
fuelectenerg-3080	142	9	chrestenson	chrestenson	NOUN
fuelectenerg-3080	142	10	spectra	spectra	NOUN
fuelectenerg-3080	142	11	of	of	ADP
fuelectenerg-3080	142	12	p	p	PROPN
fuelectenerg-3080	142	13	–	–	PUNCT
fuelectenerg-3080	142	14	valued	value	VERB
fuelectenerg-3080	142	15	symmetric	symmetric	ADJ
fuelectenerg-3080	142	16	functions	function	NOUN
fuelectenerg-3080	142	17	are	be	AUX
fuelectenerg-3080	142	18	symmetric	symmetric	ADJ
fuelectenerg-3080	142	19	.	.	PUNCT
fuelectenerg-3080	143	1	corollary	corollary	ADJ
fuelectenerg-3080	143	2	5.2	5.2	NUM
fuelectenerg-3080	143	3	.	.	PUNCT
fuelectenerg-3080	144	1	if	if	SCONJ
fuelectenerg-3080	144	2	f	f	PROPN
fuelectenerg-3080	144	3	is	be	AUX
fuelectenerg-3080	144	4	a	a	DET
fuelectenerg-3080	144	5	p	p	NOUN
fuelectenerg-3080	144	6	–	–	PUNCT
fuelectenerg-3080	144	7	valued	value	VERB
fuelectenerg-3080	144	8	bent	bent	ADJ
fuelectenerg-3080	144	9	function	function	NOUN
fuelectenerg-3080	144	10	[	[	X
fuelectenerg-3080	144	11	20	20	NUM
fuelectenerg-3080	144	12	]	]	PUNCT
fuelectenerg-3080	144	13	,	,	PUNCT
fuelectenerg-3080	144	14	[	[	X
fuelectenerg-3080	144	15	19	19	NUM
fuelectenerg-3080	144	16	]	]	PUNCT
fuelectenerg-3080	144	17	,	,	PUNCT
fuelectenerg-3080	144	18	then	then	ADV
fuelectenerg-3080	144	19	the	the	DET
fuelectenerg-3080	144	20	function	function	NOUN
fuelectenerg-3080	144	21	obtained	obtain	VERB
fuelectenerg-3080	144	22	after	after	ADP
fuelectenerg-3080	144	23	permuting	permute	VERB
fuelectenerg-3080	144	24	the	the	DET
fuelectenerg-3080	144	25	value	value	NOUN
fuelectenerg-3080	144	26	assignment	assignment	NOUN
fuelectenerg-3080	144	27	to	to	ADP
fuelectenerg-3080	144	28	the	the	DET
fuelectenerg-3080	144	29	arguments	argument	NOUN
fuelectenerg-3080	144	30	is	be	AUX
fuelectenerg-3080	144	31	also	also	ADV
fuelectenerg-3080	144	32	bent	bent	ADJ
fuelectenerg-3080	144	33	,	,	PUNCT
fuelectenerg-3080	144	34	since	since	SCONJ
fuelectenerg-3080	144	35	the	the	DET
fuelectenerg-3080	144	36	circular	circular	ADJ
fuelectenerg-3080	144	37	vilenkinchrestenson	vilenkinchrestenson	NOUN
fuelectenerg-3080	144	38	spectrum	spectrum	NOUN
fuelectenerg-3080	144	39	will	will	AUX
fuelectenerg-3080	144	40	remain	remain	VERB
fuelectenerg-3080	144	41	flat	flat	ADJ
fuelectenerg-3080	144	42	.	.	PUNCT
fuelectenerg-3080	145	1	,	,	PUNCT
fuelectenerg-3080	145	2	i.e.	i.e.	X
fuelectenerg-3080	145	3	all	all	DET
fuelectenerg-3080	145	4	its	its	PRON
fuelectenerg-3080	145	5	components	component	NOUN
fuelectenerg-3080	145	6	will	will	AUX
fuelectenerg-3080	145	7	have	have	VERB
fuelectenerg-3080	145	8	a	a	DET
fuelectenerg-3080	145	9	constant	constant	ADJ
fuelectenerg-3080	145	10	absolute	absolute	ADJ
fuelectenerg-3080	145	11	value	value	NOUN
fuelectenerg-3080	145	12	equal	equal	ADJ
fuelectenerg-3080	145	13	to	to	ADP
fuelectenerg-3080	145	14	p	p	NOUN
fuelectenerg-3080	145	15	n/2	n/2	NOUN
fuelectenerg-3080	145	16	.	.	PUNCT
fuelectenerg-3080	146	1	4	4	X
fuelectenerg-3080	146	2	.	.	X
fuelectenerg-3080	146	3	conclusions	conclusion	NOUN
fuelectenerg-3080	146	4	it	it	PRON
fuelectenerg-3080	146	5	has	have	AUX
fuelectenerg-3080	146	6	been	be	AUX
fuelectenerg-3080	146	7	shown	show	VERB
fuelectenerg-3080	146	8	that	that	SCONJ
fuelectenerg-3080	146	9	the	the	DET
fuelectenerg-3080	146	10	rmf	rmf	PROPN
fuelectenerg-3080	146	11	transform	transform	NOUN
fuelectenerg-3080	146	12	shares	share	NOUN
fuelectenerg-3080	146	13	with	with	ADP
fuelectenerg-3080	146	14	the	the	DET
fuelectenerg-3080	146	15	reed	reed	NOUN
fuelectenerg-3080	146	16	-	-	PUNCT
fuelectenerg-3080	146	17	muller	muller	NOUN
fuelectenerg-3080	146	18	and	and	CCONJ
fuelectenerg-3080	146	19	the	the	DET
fuelectenerg-3080	146	20	vilenkin	vilenkin	PROPN
fuelectenerg-3080	146	21	-	-	PUNCT
fuelectenerg-3080	146	22	chrestenson	chrestenson	NOUN
fuelectenerg-3080	146	23	transforms	transform	VERB
fuelectenerg-3080	146	24	the	the	DET
fuelectenerg-3080	146	25	property	property	NOUN
fuelectenerg-3080	146	26	of	of	ADP
fuelectenerg-3080	146	27	preserving	preserve	VERB
fuelectenerg-3080	146	28	any	any	DET
fuelectenerg-3080	146	29	permutation	permutation	NOUN
fuelectenerg-3080	146	30	of	of	ADP
fuelectenerg-3080	146	31	the	the	DET
fuelectenerg-3080	146	32	arguments	argument	NOUN
fuelectenerg-3080	146	33	,	,	PUNCT
fuelectenerg-3080	146	34	in	in	ADP
fuelectenerg-3080	146	35	spite	spite	NOUN
fuelectenerg-3080	146	36	of	of	ADP
fuelectenerg-3080	146	37	their	their	PRON
fuelectenerg-3080	146	38	different	different	ADJ
fuelectenerg-3080	146	39	structural	structural	ADJ
fuelectenerg-3080	146	40	attributes	attribute	NOUN
fuelectenerg-3080	146	41	.	.	PUNCT
fuelectenerg-3080	147	1	recall	recall	VERB
fuelectenerg-3080	147	2	that	that	SCONJ
fuelectenerg-3080	147	3	the	the	DET
fuelectenerg-3080	147	4	vilenkinchrestenson	vilenkinchrestenson	NOUN
fuelectenerg-3080	147	5	transform	transform	NOUN
fuelectenerg-3080	147	6	is	be	AUX
fuelectenerg-3080	147	7	complex	complex	ADV
fuelectenerg-3080	147	8	-	-	PUNCT
fuelectenerg-3080	147	9	valued	value	VERB
fuelectenerg-3080	147	10	,	,	PUNCT
fuelectenerg-3080	147	11	symmetric	symmetric	ADJ
fuelectenerg-3080	147	12	,	,	PUNCT
fuelectenerg-3080	147	13	and	and	CCONJ
fuelectenerg-3080	147	14	unitary	unitary	ADJ
fuelectenerg-3080	147	15	up	up	ADP
fuelectenerg-3080	147	16	to	to	ADP
fuelectenerg-3080	147	17	a	a	DET
fuelectenerg-3080	147	18	normalizing	normalizing	ADJ
fuelectenerg-3080	147	19	coefficient	coefficient	NOUN
fuelectenerg-3080	147	20	;	;	PUNCT
fuelectenerg-3080	147	21	the	the	DET
fuelectenerg-3080	147	22	reed	reed	NOUN
fuelectenerg-3080	147	23	-	-	PUNCT
fuelectenerg-3080	147	24	muller	muller	NOUN
fuelectenerg-3080	147	25	transform	transform	NOUN
fuelectenerg-3080	147	26	is	be	AUX
fuelectenerg-3080	147	27	integer	integer	NOUN
fuelectenerg-3080	147	28	-	-	PUNCT
fuelectenerg-3080	147	29	valued	value	VERB
fuelectenerg-3080	147	30	and	and	CCONJ
fuelectenerg-3080	147	31	neither	neither	CCONJ
fuelectenerg-3080	147	32	symmetric	symmetric	ADJ
fuelectenerg-3080	147	33	nor	nor	CCONJ
fuelectenerg-3080	147	34	orthogonal	orthogonal	ADJ
fuelectenerg-3080	147	35	;	;	PUNCT
fuelectenerg-3080	147	36	and	and	CCONJ
fuelectenerg-3080	147	37	the	the	DET
fuelectenerg-3080	147	38	reed	reed	NOUN
fuelectenerg-3080	147	39	-	-	PUNCT
fuelectenerg-3080	147	40	muller	muller	NOUN
fuelectenerg-3080	147	41	-	-	PUNCT
fuelectenerg-3080	147	42	fourier	fourier	NOUN
fuelectenerg-3080	147	43	transform	transform	NOUN
fuelectenerg-3080	147	44	is	be	AUX
fuelectenerg-3080	147	45	integer	integer	NOUN
fuelectenerg-3080	147	46	-	-	PUNCT
fuelectenerg-3080	147	47	valued	value	VERB
fuelectenerg-3080	147	48	,	,	PUNCT
fuelectenerg-3080	147	49	lower	low	ADJ
fuelectenerg-3080	147	50	triangular	triangular	NOUN
fuelectenerg-3080	147	51	,	,	PUNCT
fuelectenerg-3080	147	52	and	and	CCONJ
fuelectenerg-3080	147	53	self	self	NOUN
fuelectenerg-3080	147	54	inverse	inverse	NOUN
fuelectenerg-3080	147	55	.	.	PUNCT
fuelectenerg-3080	148	1	references	reference	NOUN
fuelectenerg-3080	148	2	[	[	X
fuelectenerg-3080	148	3	1	1	NUM
fuelectenerg-3080	148	4	]	]	X
fuelectenerg-3080	148	5	i.i	i.i	PROPN
fuelectenerg-3080	148	6	.	.	PROPN
fuelectenerg-3080	148	7	zhegalkin	zhegalkin	PROPN
fuelectenerg-3080	148	8	,	,	PUNCT
fuelectenerg-3080	148	9	“	"	PUNCT
fuelectenerg-3080	148	10	o	o	PROPN
fuelectenerg-3080	148	11	tekhnyke	tekhnyke	PROPN
fuelectenerg-3080	148	12	vychyslenyi	vychyslenyi	PROPN
fuelectenerg-3080	148	13	predlozhenyi	predlozhenyi	PROPN
fuelectenerg-3080	148	14	v	v	ADP
fuelectenerg-3080	148	15	symbolytscheskoi	symbolytscheskoi	NOUN
fuelectenerg-3080	148	16	logykye	logykye	NOUN
fuelectenerg-3080	148	17	,	,	PUNCT
fuelectenerg-3080	148	18	”	"	PUNCT
fuelectenerg-3080	148	19	math	math	NOUN
fuelectenerg-3080	148	20	.	.	PUNCT
fuelectenerg-3080	149	1	sb	sb	PROPN
fuelectenerg-3080	149	2	.	.	PROPN
fuelectenerg-3080	149	3	,	,	PUNCT
fuelectenerg-3080	149	4	vol	vol	NOUN
fuelectenerg-3080	149	5	.	.	PROPN
fuelectenerg-3080	150	1	34	34	NUM
fuelectenerg-3080	150	2	,	,	PUNCT
fuelectenerg-3080	150	3	pp	pp	ADJ
fuelectenerg-3080	150	4	.	.	PUNCT
fuelectenerg-3080	151	1	9	9	NUM
fuelectenerg-3080	151	2	-	-	SYM
fuelectenerg-3080	151	3	28	28	NUM
fuelectenerg-3080	151	4	,	,	PUNCT
fuelectenerg-3080	151	5	in	in	ADP
fuelectenerg-3080	151	6	russian	russian	NOUN
fuelectenerg-3080	151	7	,	,	PUNCT
fuelectenerg-3080	151	8	1927	1927	NUM
fuelectenerg-3080	151	9	.	.	PUNCT
fuelectenerg-3080	152	1	[	[	X
fuelectenerg-3080	152	2	2	2	NUM
fuelectenerg-3080	152	3	]	]	X
fuelectenerg-3080	152	4	i.i	i.i	PROPN
fuelectenerg-3080	152	5	.	.	PROPN
fuelectenerg-3080	152	6	zhegalkin	zhegalkin	PROPN
fuelectenerg-3080	152	7	,	,	PUNCT
fuelectenerg-3080	152	8	“	"	PUNCT
fuelectenerg-3080	152	9	aritmetizatiya	aritmetizatiya	VERB
fuelectenerg-3080	152	10	symbolytscheskoi	symbolytscheskoi	NOUN
fuelectenerg-3080	152	11	logyky	logyky	VERB
fuelectenerg-3080	152	12	,	,	PUNCT
fuelectenerg-3080	152	13	”	"	PUNCT
fuelectenerg-3080	152	14	math	math	NOUN
fuelectenerg-3080	152	15	.	.	PUNCT
fuelectenerg-3080	153	1	sb	sb	PROPN
fuelectenerg-3080	153	2	.	.	PROPN
fuelectenerg-3080	153	3	,	,	PUNCT
fuelectenerg-3080	153	4	vol	vol	NOUN
fuelectenerg-3080	153	5	.	.	PROPN
fuelectenerg-3080	153	6	35	35	NUM
fuelectenerg-3080	153	7	,	,	PUNCT
fuelectenerg-3080	154	1	pp	pp	ADJ
fuelectenerg-3080	154	2	.	.	PUNCT
fuelectenerg-3080	155	1	311	311	NUM
fuelectenerg-3080	155	2	-	-	SYM
fuelectenerg-3080	155	3	377	377	NUM
fuelectenerg-3080	155	4	,	,	PUNCT
fuelectenerg-3080	155	5	in	in	ADP
fuelectenerg-3080	155	6	russian	russian	ADJ
fuelectenerg-3080	155	7	,	,	PUNCT
fuelectenerg-3080	155	8	1928	1928	NUM
fuelectenerg-3080	155	9	.	.	PUNCT
fuelectenerg-3080	156	1	[	[	X
fuelectenerg-3080	156	2	3	3	X
fuelectenerg-3080	156	3	]	]	X
fuelectenerg-3080	156	4	i.s	i.s	PROPN
fuelectenerg-3080	156	5	.	.	PROPN
fuelectenerg-3080	156	6	reed	reed	PROPN
fuelectenerg-3080	156	7	,	,	PUNCT
fuelectenerg-3080	156	8	“	"	PUNCT
fuelectenerg-3080	156	9	a	a	DET
fuelectenerg-3080	156	10	class	class	NOUN
fuelectenerg-3080	156	11	of	of	ADP
fuelectenerg-3080	156	12	multiple	multiple	ADJ
fuelectenerg-3080	156	13	-	-	PUNCT
fuelectenerg-3080	156	14	error	error	NOUN
fuelectenerg-3080	156	15	-	-	PUNCT
fuelectenerg-3080	156	16	correcting	correct	VERB
fuelectenerg-3080	156	17	codes	code	NOUN
fuelectenerg-3080	156	18	and	and	CCONJ
fuelectenerg-3080	156	19	the	the	DET
fuelectenerg-3080	156	20	decoding	decode	VERB
fuelectenerg-3080	156	21	scheme	scheme	NOUN
fuelectenerg-3080	156	22	.	.	PUNCT
fuelectenerg-3080	156	23	”	"	PUNCT
fuelectenerg-3080	157	1	ire	ire	ADJ
fuelectenerg-3080	157	2	trans	tran	NOUN
fuelectenerg-3080	157	3	.	.	PUNCT
fuelectenerg-3080	158	1	on	on	ADP
fuelectenerg-3080	158	2	information	information	NOUN
fuelectenerg-3080	158	3	theory	theory	NOUN
fuelectenerg-3080	158	4	pgit-4	pgit-4	PROPN
fuelectenerg-3080	158	5	,	,	PUNCT
fuelectenerg-3080	158	6	pp	pp	ADJ
fuelectenerg-3080	158	7	.	.	PUNCT
fuelectenerg-3080	159	1	38	38	NUM
fuelectenerg-3080	159	2	-	-	SYM
fuelectenerg-3080	159	3	49	49	NUM
fuelectenerg-3080	159	4	,	,	PUNCT
fuelectenerg-3080	159	5	1954	1954	NUM
fuelectenerg-3080	159	6	.	.	PUNCT
fuelectenerg-3080	160	1	[	[	X
fuelectenerg-3080	160	2	4	4	X
fuelectenerg-3080	160	3	]	]	X
fuelectenerg-3080	160	4	d.e	d.e	PROPN
fuelectenerg-3080	160	5	.	.	PROPN
fuelectenerg-3080	160	6	muller	muller	PROPN
fuelectenerg-3080	160	7	,	,	PUNCT
fuelectenerg-3080	160	8	“	"	PUNCT
fuelectenerg-3080	160	9	application	application	NOUN
fuelectenerg-3080	160	10	of	of	ADP
fuelectenerg-3080	160	11	boolean	boolean	ADJ
fuelectenerg-3080	160	12	algebra	algebra	NOUN
fuelectenerg-3080	160	13	to	to	ADP
fuelectenerg-3080	160	14	switching	switch	VERB
fuelectenerg-3080	160	15	circuit	circuit	NOUN
fuelectenerg-3080	160	16	design	design	NOUN
fuelectenerg-3080	160	17	and	and	CCONJ
fuelectenerg-3080	160	18	to	to	ADP
fuelectenerg-3080	160	19	error	error	NOUN
fuelectenerg-3080	160	20	correction	correction	NOUN
fuelectenerg-3080	160	21	.	.	PUNCT
fuelectenerg-3080	160	22	”	"	PUNCT
fuelectenerg-3080	160	23	ire	ire	PROPN
fuelectenerg-3080	160	24	trans	tran	NOUN
fuelectenerg-3080	160	25	.	.	PUNCT
fuelectenerg-3080	161	1	on	on	ADP
fuelectenerg-3080	161	2	elec	elec	PROPN
fuelectenerg-3080	161	3	.	.	PUNCT
fuelectenerg-3080	161	4	computers	computer	NOUN
fuelectenerg-3080	161	5	ec-3	ec-3	ADP
fuelectenerg-3080	161	6	,	,	PUNCT
fuelectenerg-3080	161	7	vol	vol	NOUN
fuelectenerg-3080	161	8	.	.	PROPN
fuelectenerg-3080	162	1	3	3	NUM
fuelectenerg-3080	162	2	,	,	PUNCT
fuelectenerg-3080	162	3	pp	pp	ADJ
fuelectenerg-3080	162	4	.	.	PUNCT
fuelectenerg-3080	163	1	6	6	NUM
fuelectenerg-3080	163	2	-	-	SYM
fuelectenerg-3080	163	3	12	12	NUM
fuelectenerg-3080	163	4	,	,	PUNCT
fuelectenerg-3080	163	5	1954	1954	NUM
fuelectenerg-3080	163	6	.	.	PUNCT
fuelectenerg-3080	164	1	[	[	X
fuelectenerg-3080	164	2	5	5	X
fuelectenerg-3080	164	3	]	]	X
fuelectenerg-3080	164	4	d.h	d.h	PROPN
fuelectenerg-3080	164	5	.	.	PROPN
fuelectenerg-3080	164	6	green	green	PROPN
fuelectenerg-3080	164	7	and	and	CCONJ
fuelectenerg-3080	164	8	i.s	i.s	PROPN
fuelectenerg-3080	164	9	.	.	PROPN
fuelectenerg-3080	164	10	taylor	taylor	PROPN
fuelectenerg-3080	164	11	,	,	PUNCT
fuelectenerg-3080	164	12	“	"	PUNCT
fuelectenerg-3080	164	13	multiple	multiple	ADV
fuelectenerg-3080	164	14	-	-	PUNCT
fuelectenerg-3080	164	15	valued	value	VERB
fuelectenerg-3080	164	16	switching	switching	NOUN
fuelectenerg-3080	164	17	circuit	circuit	NOUN
fuelectenerg-3080	164	18	design	design	NOUN
fuelectenerg-3080	164	19	by	by	ADP
fuelectenerg-3080	164	20	means	mean	NOUN
fuelectenerg-3080	164	21	of	of	ADP
fuelectenerg-3080	164	22	generalized	generalized	ADJ
fuelectenerg-3080	164	23	reedmuller	reedmuller	NOUN
fuelectenerg-3080	164	24	expansions	expansion	NOUN
fuelectenerg-3080	164	25	.	.	PUNCT
fuelectenerg-3080	164	26	”	"	PUNCT
fuelectenerg-3080	165	1	digital	digital	ADJ
fuelectenerg-3080	165	2	processes	process	NOUN
fuelectenerg-3080	165	3	2	2	NUM
fuelectenerg-3080	165	4	,	,	PUNCT
fuelectenerg-3080	165	5	pp	pp	ADJ
fuelectenerg-3080	165	6	.	.	PUNCT
fuelectenerg-3080	166	1	63	63	NUM
fuelectenerg-3080	166	2	-	-	SYM
fuelectenerg-3080	166	3	81	81	NUM
fuelectenerg-3080	166	4	,	,	PUNCT
fuelectenerg-3080	166	5	1976	1976	NUM
fuelectenerg-3080	166	6	.	.	PUNCT
fuelectenerg-3080	167	1	[	[	X
fuelectenerg-3080	167	2	6	6	NUM
fuelectenerg-3080	167	3	]	]	X
fuelectenerg-3080	167	4	r.s	r.s	PROPN
fuelectenerg-3080	167	5	.	.	PROPN
fuelectenerg-3080	167	6	stanković	stanković	PROPN
fuelectenerg-3080	167	7	,	,	PUNCT
fuelectenerg-3080	167	8	“	"	PUNCT
fuelectenerg-3080	167	9	some	some	DET
fuelectenerg-3080	167	10	remarks	remark	NOUN
fuelectenerg-3080	167	11	on	on	ADP
fuelectenerg-3080	167	12	fourier	fourier	NOUN
fuelectenerg-3080	167	13	transforms	transform	NOUN
fuelectenerg-3080	167	14	and	and	CCONJ
fuelectenerg-3080	167	15	differential	differential	ADJ
fuelectenerg-3080	167	16	operators	operator	NOUN
fuelectenerg-3080	167	17	for	for	ADP
fuelectenerg-3080	167	18	digital	digital	ADJ
fuelectenerg-3080	167	19	functions	function	NOUN
fuelectenerg-3080	167	20	,	,	PUNCT
fuelectenerg-3080	167	21	”	"	PUNCT
fuelectenerg-3080	167	22	in	in	ADP
fuelectenerg-3080	167	23	proceedings	proceeding	NOUN
fuelectenerg-3080	167	24	of	of	ADP
fuelectenerg-3080	167	25	the	the	DET
fuelectenerg-3080	167	26	22nd	22nd	ADJ
fuelectenerg-3080	167	27	international	international	ADJ
fuelectenerg-3080	167	28	symposium	symposium	NOUN
fuelectenerg-3080	167	29	on	on	ADP
fuelectenerg-3080	167	30	multiple	multiple	ADV
fuelectenerg-3080	167	31	-	-	PUNCT
fuelectenerg-3080	167	32	valued	value	VERB
fuelectenerg-3080	167	33	logic	logic	NOUN
fuelectenerg-3080	167	34	,	,	PUNCT
fuelectenerg-3080	167	35	sendai	sendai	PROPN
fuelectenerg-3080	167	36	,	,	PUNCT
fuelectenerg-3080	167	37	japan	japan	PROPN
fuelectenerg-3080	167	38	,	,	PUNCT
fuelectenerg-3080	167	39	ieee	ieee	PROPN
fuelectenerg-3080	167	40	press	press	PROPN
fuelectenerg-3080	167	41	n.y	n.y	PROPN
fuelectenerg-3080	167	42	.	.	PROPN
fuelectenerg-3080	167	43	,	,	PUNCT
fuelectenerg-3080	167	44	1992	1992	NUM
fuelectenerg-3080	167	45	,	,	PUNCT
fuelectenerg-3080	167	46	pp	pp	ADJ
fuelectenerg-3080	167	47	.	.	PUNCT
fuelectenerg-3080	168	1	365	365	NUM
fuelectenerg-3080	168	2	-	-	SYM
fuelectenerg-3080	168	3	370	370	NUM
fuelectenerg-3080	168	4	.	.	PUNCT
fuelectenerg-3080	169	1	on	on	ADP
fuelectenerg-3080	169	2	a	a	DET
fuelectenerg-3080	169	3	property	property	NOUN
fuelectenerg-3080	169	4	of	of	ADP
fuelectenerg-3080	169	5	the	the	DET
fuelectenerg-3080	169	6	reed	reed	NOUN
fuelectenerg-3080	169	7	-	-	PUNCT
fuelectenerg-3080	169	8	muller	muller	NOUN
fuelectenerg-3080	169	9	-	-	PUNCT
fuelectenerg-3080	169	10	fourier	fourier	NOUN
fuelectenerg-3080	169	11	transform	transform	NOUN
fuelectenerg-3080	169	12	311	311	NUM
fuelectenerg-3080	169	13	[	[	X
fuelectenerg-3080	169	14	7	7	NUM
fuelectenerg-3080	169	15	]	]	X
fuelectenerg-3080	169	16	r.s	r.s	PROPN
fuelectenerg-3080	169	17	.	.	PROPN
fuelectenerg-3080	169	18	stanković	stanković	PROPN
fuelectenerg-3080	169	19	,	,	PUNCT
fuelectenerg-3080	169	20	“	"	PUNCT
fuelectenerg-3080	169	21	the	the	DET
fuelectenerg-3080	169	22	reed	reed	NOUN
fuelectenerg-3080	169	23	-	-	PUNCT
fuelectenerg-3080	169	24	muller	muller	NOUN
fuelectenerg-3080	169	25	-	-	PUNCT
fuelectenerg-3080	169	26	fourier	fourier	NOUN
fuelectenerg-3080	169	27	transform	transform	NOUN
fuelectenerg-3080	169	28	–	–	PUNCT
fuelectenerg-3080	169	29	computing	compute	VERB
fuelectenerg-3080	169	30	methods	method	NOUN
fuelectenerg-3080	169	31	and	and	CCONJ
fuelectenerg-3080	169	32	factorizations	factorization	NOUN
fuelectenerg-3080	169	33	”	"	PUNCT
fuelectenerg-3080	169	34	,	,	PUNCT
fuelectenerg-3080	169	35	claudio	claudio	PROPN
fuelectenerg-3080	169	36	moraga	moraga	NOUN
fuelectenerg-3080	169	37	:	:	PUNCT
fuelectenerg-3080	169	38	a	a	DET
fuelectenerg-3080	169	39	passion	passion	NOUN
fuelectenerg-3080	169	40	for	for	ADP
fuelectenerg-3080	169	41	multi	multi	ADJ
fuelectenerg-3080	169	42	-	-	ADJ
fuelectenerg-3080	169	43	valued	value	VERB
fuelectenerg-3080	169	44	logic	logic	NOUN
fuelectenerg-3080	169	45	and	and	CCONJ
fuelectenerg-3080	169	46	soft	soft	ADJ
fuelectenerg-3080	169	47	computing	computing	NOUN
fuelectenerg-3080	169	48	.	.	PUNCT
fuelectenerg-3080	170	1	(	(	PUNCT
fuelectenerg-3080	170	2	r.	r.	PROPN
fuelectenerg-3080	170	3	seising	seising	PROPN
fuelectenerg-3080	170	4	,	,	PUNCT
fuelectenerg-3080	170	5	h.	h.	PROPN
fuelectenerg-3080	170	6	allende	allende	PROPN
fuelectenerg-3080	170	7	-	-	PUNCT
fuelectenerg-3080	170	8	cid	cid	PROPN
fuelectenerg-3080	170	9	,	,	PUNCT
fuelectenerg-3080	170	10	eds	ed	NOUN
fuelectenerg-3080	170	11	.	.	PUNCT
fuelectenerg-3080	170	12	)	)	PUNCT
fuelectenerg-3080	170	13	,	,	PUNCT
fuelectenerg-3080	170	14	springer	springer	NOUN
fuelectenerg-3080	170	15	2017	2017	NUM
fuelectenerg-3080	170	16	,	,	PUNCT
fuelectenerg-3080	170	17	pp	pp	ADP
fuelectenerg-3080	170	18	.	.	PUNCT
fuelectenerg-3080	171	1	121	121	NUM
fuelectenerg-3080	171	2	-	-	SYM
fuelectenerg-3080	171	3	151	151	NUM
fuelectenerg-3080	171	4	.	.	PUNCT
fuelectenerg-3080	172	1	[	[	X
fuelectenerg-3080	172	2	8	8	NUM
fuelectenerg-3080	172	3	]	]	X
fuelectenerg-3080	172	4	c.	c.	PROPN
fuelectenerg-3080	172	5	moraga	moraga	PROPN
fuelectenerg-3080	172	6	,	,	PUNCT
fuelectenerg-3080	172	7	s.	s.	PROPN
fuelectenerg-3080	172	8	stojković	stojković	PROPN
fuelectenerg-3080	172	9	and	and	CCONJ
fuelectenerg-3080	172	10	r.s	r.s	PROPN
fuelectenerg-3080	172	11	.	.	PROPN
fuelectenerg-3080	172	12	stanković	stanković	PROPN
fuelectenerg-3080	172	13	,	,	PUNCT
fuelectenerg-3080	172	14	“	"	PUNCT
fuelectenerg-3080	172	15	on	on	ADP
fuelectenerg-3080	172	16	fixed	fix	VERB
fuelectenerg-3080	172	17	points	point	NOUN
fuelectenerg-3080	172	18	and	and	CCONJ
fuelectenerg-3080	172	19	cycles	cycle	NOUN
fuelectenerg-3080	172	20	in	in	ADP
fuelectenerg-3080	172	21	the	the	DET
fuelectenerg-3080	172	22	reed	reed	NOUN
fuelectenerg-3080	172	23	muller	muller	NOUN
fuelectenerg-3080	172	24	domain	domain	PROPN
fuelectenerg-3080	172	25	.	.	PUNCT
fuelectenerg-3080	172	26	”	"	PUNCT
fuelectenerg-3080	173	1	in	in	ADP
fuelectenerg-3080	173	2	proceedings	proceeding	NOUN
fuelectenerg-3080	173	3	of	of	ADP
fuelectenerg-3080	173	4	the	the	DET
fuelectenerg-3080	173	5	38th	38th	ADJ
fuelectenerg-3080	173	6	international	international	ADJ
fuelectenerg-3080	173	7	symposium	symposium	NOUN
fuelectenerg-3080	173	8	on	on	ADP
fuelectenerg-3080	173	9	multiple	multiple	ADV
fuelectenerg-3080	173	10	-	-	PUNCT
fuelectenerg-3080	173	11	valued	value	VERB
fuelectenerg-3080	173	12	logic	logic	NOUN
fuelectenerg-3080	173	13	,	,	PUNCT
fuelectenerg-3080	173	14	ieee	ieee	NOUN
fuelectenerg-3080	173	15	press	press	NOUN
fuelectenerg-3080	173	16	,	,	PUNCT
fuelectenerg-3080	173	17	2008	2008	NUM
fuelectenerg-3080	173	18	,	,	PUNCT
fuelectenerg-3080	173	19	pp	pp	ADJ
fuelectenerg-3080	173	20	.	.	PUNCT
fuelectenerg-3080	173	21	82	82	NUM
fuelectenerg-3080	173	22	-	-	SYM
fuelectenerg-3080	173	23	88	88	NUM
fuelectenerg-3080	173	24	.	.	PUNCT
fuelectenerg-3080	174	1	[	[	X
fuelectenerg-3080	174	2	9	9	NUM
fuelectenerg-3080	174	3	]	]	PUNCT
fuelectenerg-3080	174	4	c.	c.	PROPN
fuelectenerg-3080	174	5	moraga	moraga	PROPN
fuelectenerg-3080	174	6	,	,	PUNCT
fuelectenerg-3080	174	7	r.s	r.s	PROPN
fuelectenerg-3080	174	8	.	.	PROPN
fuelectenerg-3080	174	9	stanković	stanković	PROPN
fuelectenerg-3080	174	10	,	,	PUNCT
fuelectenerg-3080	174	11	m.	m.	NOUN
fuelectenerg-3080	174	12	stanković	stanković	PROPN
fuelectenerg-3080	174	13	and	and	CCONJ
fuelectenerg-3080	174	14	s.	s.	PROPN
fuelectenerg-3080	174	15	stojković	stojković	PROPN
fuelectenerg-3080	174	16	,	,	PUNCT
fuelectenerg-3080	174	17	“	"	PUNCT
fuelectenerg-3080	174	18	on	on	ADP
fuelectenerg-3080	174	19	fixed	fix	VERB
fuelectenerg-3080	174	20	points	point	NOUN
fuelectenerg-3080	174	21	of	of	ADP
fuelectenerg-3080	174	22	the	the	DET
fuelectenerg-3080	174	23	reed	reed	NOUN
fuelectenerg-3080	174	24	-	-	PUNCT
fuelectenerg-3080	174	25	muller	muller	NOUN
fuelectenerg-3080	174	26	-	-	PUNCT
fuelectenerg-3080	174	27	fourier	fourier	NOUN
fuelectenerg-3080	174	28	transform	transform	NOUN
fuelectenerg-3080	174	29	.	.	PUNCT
fuelectenerg-3080	174	30	”	"	PUNCT
fuelectenerg-3080	175	1	in	in	ADP
fuelectenerg-3080	175	2	proceedings	proceeding	NOUN
fuelectenerg-3080	175	3	of	of	ADP
fuelectenerg-3080	175	4	the	the	DET
fuelectenerg-3080	175	5	47th	47th	ADJ
fuelectenerg-3080	175	6	international	international	ADJ
fuelectenerg-3080	175	7	symposium	symposium	NOUN
fuelectenerg-3080	175	8	on	on	ADP
fuelectenerg-3080	175	9	multiple	multiple	ADV
fuelectenerg-3080	175	10	-	-	PUNCT
fuelectenerg-3080	175	11	valued	value	VERB
fuelectenerg-3080	175	12	logic	logic	NOUN
fuelectenerg-3080	175	13	,	,	PUNCT
fuelectenerg-3080	175	14	ieee	ieee	NOUN
fuelectenerg-3080	175	15	press	press	NOUN
fuelectenerg-3080	175	16	,	,	PUNCT
fuelectenerg-3080	175	17	2017	2017	NUM
fuelectenerg-3080	175	18	,	,	PUNCT
fuelectenerg-3080	175	19	pp	pp	ADJ
fuelectenerg-3080	175	20	.	.	PUNCT
fuelectenerg-3080	176	1	55	55	NUM
fuelectenerg-3080	176	2	-	-	SYM
fuelectenerg-3080	176	3	60	60	NUM
fuelectenerg-3080	176	4	.	.	PUNCT
fuelectenerg-3080	177	1	[	[	X
fuelectenerg-3080	177	2	10	10	NUM
fuelectenerg-3080	177	3	]	]	X
fuelectenerg-3080	177	4	a.	a.	NOUN
fuelectenerg-3080	177	5	graham	graham	PROPN
fuelectenerg-3080	177	6	,	,	PUNCT
fuelectenerg-3080	177	7	kronecker	kronecker	NOUN
fuelectenerg-3080	177	8	products	product	NOUN
fuelectenerg-3080	177	9	and	and	CCONJ
fuelectenerg-3080	177	10	matrix	matrix	NOUN
fuelectenerg-3080	177	11	calculus	calculus	NOUN
fuelectenerg-3080	177	12	with	with	ADP
fuelectenerg-3080	177	13	applications	application	NOUN
fuelectenerg-3080	177	14	.	.	PUNCT
fuelectenerg-3080	178	1	ellis	ellis	PROPN
fuelectenerg-3080	178	2	horwood	horwood	PROPN
fuelectenerg-3080	178	3	ltd	ltd	PROPN
fuelectenerg-3080	178	4	.	.	PROPN
fuelectenerg-3080	178	5	,	,	PUNCT
fuelectenerg-3080	178	6	chichester	chichester	PROPN
fuelectenerg-3080	178	7	uk	uk	PROPN
fuelectenerg-3080	178	8	,	,	PUNCT
fuelectenerg-3080	178	9	1981	1981	NUM
fuelectenerg-3080	178	10	.	.	PUNCT
fuelectenerg-3080	179	1	[	[	X
fuelectenerg-3080	179	2	11	11	NUM
fuelectenerg-3080	179	3	]	]	X
fuelectenerg-3080	179	4	r.a	r.a	PROPN
fuelectenerg-3080	179	5	.	.	PROPN
fuelectenerg-3080	179	6	horn	horn	NOUN
fuelectenerg-3080	179	7	and	and	CCONJ
fuelectenerg-3080	179	8	ch.r	ch.r	NOUN
fuelectenerg-3080	179	9	.	.	PUNCT
fuelectenerg-3080	180	1	johnson	johnson	PROPN
fuelectenerg-3080	180	2	,	,	PUNCT
fuelectenerg-3080	180	3	topics	topic	NOUN
fuelectenerg-3080	180	4	in	in	ADP
fuelectenerg-3080	180	5	matrix	matrix	NOUN
fuelectenerg-3080	180	6	analysis	analysis	NOUN
fuelectenerg-3080	180	7	.	.	PUNCT
fuelectenerg-3080	181	1	cambridge	cambridge	PROPN
fuelectenerg-3080	181	2	university	university	PROPN
fuelectenerg-3080	181	3	press	press	PROPN
fuelectenerg-3080	181	4	,	,	PUNCT
fuelectenerg-3080	181	5	new	new	PROPN
fuelectenerg-3080	181	6	york	york	PROPN
fuelectenerg-3080	181	7	,	,	PUNCT
fuelectenerg-3080	181	8	1991	1991	NUM
fuelectenerg-3080	181	9	.	.	PUNCT
fuelectenerg-3080	182	1	[	[	X
fuelectenerg-3080	182	2	12	12	NUM
fuelectenerg-3080	182	3	]	]	X
fuelectenerg-3080	182	4	c.	c.	PROPN
fuelectenerg-3080	182	5	moraga	moraga	PROPN
fuelectenerg-3080	182	6	,	,	PUNCT
fuelectenerg-3080	182	7	r.s	r.s	PROPN
fuelectenerg-3080	182	8	.	.	PROPN
fuelectenerg-3080	182	9	stanković	stanković	PROPN
fuelectenerg-3080	182	10	and	and	CCONJ
fuelectenerg-3080	182	11	m.	m.	PROPN
fuelectenerg-3080	182	12	stanković	stanković	PROPN
fuelectenerg-3080	182	13	,	,	PUNCT
fuelectenerg-3080	182	14	“	"	PUNCT
fuelectenerg-3080	182	15	a	a	DET
fuelectenerg-3080	182	16	comparative	comparative	ADJ
fuelectenerg-3080	182	17	study	study	NOUN
fuelectenerg-3080	182	18	of	of	ADP
fuelectenerg-3080	182	19	the	the	DET
fuelectenerg-3080	182	20	reed	reed	NOUN
fuelectenerg-3080	182	21	-	-	PUNCT
fuelectenerg-3080	182	22	muller	muller	NOUN
fuelectenerg-3080	182	23	-	-	PUNCT
fuelectenerg-3080	182	24	fourier	fourier	NOUN
fuelectenerg-3080	182	25	transform	transform	NOUN
fuelectenerg-3080	182	26	,	,	PUNCT
fuelectenerg-3080	182	27	the	the	DET
fuelectenerg-3080	182	28	pascal	pascal	ADJ
fuelectenerg-3080	182	29	matrix	matrix	NOUN
fuelectenerg-3080	182	30	,	,	PUNCT
fuelectenerg-3080	182	31	and	and	CCONJ
fuelectenerg-3080	182	32	the	the	DET
fuelectenerg-3080	182	33	discrete	discrete	ADJ
fuelectenerg-3080	182	34	pascal	pascal	ADJ
fuelectenerg-3080	182	35	transform	transform	NOUN
fuelectenerg-3080	182	36	.	.	PUNCT
fuelectenerg-3080	182	37	”	"	PUNCT
fuelectenerg-3080	182	38	research	research	NOUN
fuelectenerg-3080	182	39	report	report	NOUN
fuelectenerg-3080	182	40	fsc-2015	fsc-2015	ADV
fuelectenerg-3080	182	41	-	-	PUNCT
fuelectenerg-3080	182	42	02	02	NUM
fuelectenerg-3080	182	43	,	,	PUNCT
fuelectenerg-3080	182	44	european	european	ADJ
fuelectenerg-3080	182	45	centre	centre	NOUN
fuelectenerg-3080	182	46	for	for	ADP
fuelectenerg-3080	182	47	soft	soft	ADJ
fuelectenerg-3080	182	48	computing	computing	NOUN
fuelectenerg-3080	182	49	,	,	PUNCT
fuelectenerg-3080	182	50	mieres	miere	NOUN
fuelectenerg-3080	182	51	,	,	PUNCT
fuelectenerg-3080	182	52	asturias	asturias	PROPN
fuelectenerg-3080	182	53	,	,	PUNCT
fuelectenerg-3080	182	54	spain	spain	PROPN
fuelectenerg-3080	182	55	,	,	PUNCT
fuelectenerg-3080	182	56	2015	2015	NUM
fuelectenerg-3080	182	57	.	.	PUNCT
fuelectenerg-3080	183	1	[	[	X
fuelectenerg-3080	183	2	13	13	NUM
fuelectenerg-3080	183	3	]	]	X
fuelectenerg-3080	183	4	r.s	r.s	PROPN
fuelectenerg-3080	183	5	.	.	PROPN
fuelectenerg-3080	183	6	stanković	stanković	PROPN
fuelectenerg-3080	183	7	,	,	PUNCT
fuelectenerg-3080	183	8	j.t	j.t	PROPN
fuelectenerg-3080	183	9	.	.	PROPN
fuelectenerg-3080	183	10	astola	astola	PROPN
fuelectenerg-3080	183	11	and	and	CCONJ
fuelectenerg-3080	183	12	c.	c.	PROPN
fuelectenerg-3080	183	13	moraga	moraga	PROPN
fuelectenerg-3080	183	14	,	,	PUNCT
fuelectenerg-3080	183	15	“	"	PUNCT
fuelectenerg-3080	183	16	pascal	pascal	ADJ
fuelectenerg-3080	183	17	matrices	matrix	NOUN
fuelectenerg-3080	183	18	,	,	PUNCT
fuelectenerg-3080	183	19	reed	reed	NOUN
fuelectenerg-3080	183	20	-	-	PUNCT
fuelectenerg-3080	183	21	muller	muller	NOUN
fuelectenerg-3080	183	22	expressions	expression	NOUN
fuelectenerg-3080	183	23	,	,	PUNCT
fuelectenerg-3080	183	24	and	and	CCONJ
fuelectenerg-3080	183	25	reed	reed	NOUN
fuelectenerg-3080	183	26	-	-	PUNCT
fuelectenerg-3080	183	27	muller	muller	NOUN
fuelectenerg-3080	183	28	error	error	NOUN
fuelectenerg-3080	183	29	correcting	correct	VERB
fuelectenerg-3080	183	30	codes	code	NOUN
fuelectenerg-3080	183	31	.	.	PUNCT
fuelectenerg-3080	183	32	”	"	PUNCT
fuelectenerg-3080	184	1	in	in	ADP
fuelectenerg-3080	184	2	logic	logic	NOUN
fuelectenerg-3080	184	3	in	in	ADP
fuelectenerg-3080	184	4	computer	computer	PROPN
fuelectenerg-3080	184	5	science	science	PROPN
fuelectenerg-3080	184	6	ii	ii	PROPN
fuelectenerg-3080	184	7	,	,	PUNCT
fuelectenerg-3080	184	8	(	(	PUNCT
fuelectenerg-3080	184	9	s.	s.	PROPN
fuelectenerg-3080	184	10	ghilezan	ghilezan	PROPN
fuelectenerg-3080	184	11	,	,	PUNCT
fuelectenerg-3080	184	12	ed	ed	NOUN
fuelectenerg-3080	184	13	.	.	PUNCT
fuelectenerg-3080	184	14	)	)	PUNCT
fuelectenerg-3080	184	15	,	,	PUNCT
fuelectenerg-3080	184	16	press	press	PROPN
fuelectenerg-3080	184	17	mathematical	mathematical	PROPN
fuelectenerg-3080	184	18	institute	institute	PROPN
fuelectenerg-3080	184	19	of	of	ADP
fuelectenerg-3080	184	20	the	the	DET
fuelectenerg-3080	184	21	serbian	serbian	PROPN
fuelectenerg-3080	184	22	academy	academy	PROPN
fuelectenerg-3080	184	23	of	of	ADP
fuelectenerg-3080	184	24	science	science	PROPN
fuelectenerg-3080	184	25	,	,	PUNCT
fuelectenerg-3080	184	26	belgrade	belgrade	PROPN
fuelectenerg-3080	184	27	,	,	PUNCT
fuelectenerg-3080	184	28	serbia	serbia	PROPN
fuelectenerg-3080	184	29	,	,	PUNCT
fuelectenerg-3080	184	30	2015	2015	NUM
fuelectenerg-3080	184	31	.	.	PUNCT
fuelectenerg-3080	184	32	,	,	PUNCT
fuelectenerg-3080	184	33	zbornik	zbornik	X
fuelectenerg-3080	184	34	radova	radova	X
fuelectenerg-3080	184	35	18	18	NUM
fuelectenerg-3080	184	36	(	(	PUNCT
fuelectenerg-3080	184	37	26	26	NUM
fuelectenerg-3080	184	38	)	)	PUNCT
fuelectenerg-3080	184	39	,	,	PUNCT
fuelectenerg-3080	184	40	pp	pp	PROPN
fuelectenerg-3080	184	41	.	.	PUNCT
fuelectenerg-3080	184	42	145	145	NUM
fuelectenerg-3080	184	43	-	-	SYM
fuelectenerg-3080	184	44	172	172	NUM
fuelectenerg-3080	184	45	.	.	PUNCT
fuelectenerg-3080	185	1	[	[	X
fuelectenerg-3080	185	2	14	14	NUM
fuelectenerg-3080	185	3	]	]	X
fuelectenerg-3080	185	4	e.	e.	PROPN
fuelectenerg-3080	185	5	pogossova	pogossova	PROPN
fuelectenerg-3080	185	6	and	and	CCONJ
fuelectenerg-3080	185	7	k.	k.	PROPN
fuelectenerg-3080	185	8	egiazarian	egiazarian	PROPN
fuelectenerg-3080	185	9	,	,	PUNCT
fuelectenerg-3080	185	10	“	"	PUNCT
fuelectenerg-3080	185	11	reed	reed	NOUN
fuelectenerg-3080	185	12	-	-	PUNCT
fuelectenerg-3080	185	13	muller	muller	NOUN
fuelectenerg-3080	185	14	representation	representation	NOUN
fuelectenerg-3080	185	15	of	of	ADP
fuelectenerg-3080	185	16	symmetric	symmetric	ADJ
fuelectenerg-3080	185	17	functions	function	NOUN
fuelectenerg-3080	185	18	.	.	PUNCT
fuelectenerg-3080	185	19	”	"	PUNCT
fuelectenerg-3080	186	1	j.	j.	PROPN
fuelectenerg-3080	186	2	multiplevalued	multiplevalue	VERB
fuelectenerg-3080	186	3	logic	logic	NOUN
fuelectenerg-3080	186	4	and	and	CCONJ
fuelectenerg-3080	186	5	soft	soft	ADJ
fuelectenerg-3080	186	6	computing	computing	NOUN
fuelectenerg-3080	186	7	,	,	PUNCT
fuelectenerg-3080	186	8	vol	vol	NOUN
fuelectenerg-3080	186	9	.	.	PROPN
fuelectenerg-3080	186	10	10	10	NUM
fuelectenerg-3080	186	11	,	,	PUNCT
fuelectenerg-3080	186	12	no	no	INTJ
fuelectenerg-3080	186	13	.	.	NOUN
fuelectenerg-3080	186	14	1	1	NUM
fuelectenerg-3080	186	15	,	,	PUNCT
fuelectenerg-3080	186	16	pp	pp	ADJ
fuelectenerg-3080	186	17	.	.	PUNCT
fuelectenerg-3080	187	1	51	51	NUM
fuelectenerg-3080	187	2	-	-	SYM
fuelectenerg-3080	187	3	72	72	NUM
fuelectenerg-3080	187	4	,	,	PUNCT
fuelectenerg-3080	187	5	2004	2004	NUM
fuelectenerg-3080	187	6	.	.	PUNCT
fuelectenerg-3080	188	1	[	[	X
fuelectenerg-3080	188	2	15	15	NUM
fuelectenerg-3080	188	3	]	]	X
fuelectenerg-3080	188	4	r.s	r.s	PROPN
fuelectenerg-3080	188	5	.	.	PROPN
fuelectenerg-3080	188	6	stanković	stanković	PROPN
fuelectenerg-3080	188	7	,	,	PUNCT
fuelectenerg-3080	189	1	j.t	j.t	PROPN
fuelectenerg-3080	189	2	.	.	PROPN
fuelectenerg-3080	189	3	astola	astola	PROPN
fuelectenerg-3080	189	4	and	and	CCONJ
fuelectenerg-3080	189	5	k.	k.	PROPN
fuelectenerg-3080	189	6	egiazarian	egiazarian	PROPN
fuelectenerg-3080	189	7	,	,	PUNCT
fuelectenerg-3080	189	8	“	"	PUNCT
fuelectenerg-3080	189	9	remarks	remark	NOUN
fuelectenerg-3080	189	10	on	on	ADP
fuelectenerg-3080	189	11	symmetric	symmetric	ADJ
fuelectenerg-3080	189	12	binary	binary	ADJ
fuelectenerg-3080	189	13	and	and	CCONJ
fuelectenerg-3080	189	14	multiple	multiple	ADV
fuelectenerg-3080	189	15	-	-	PUNCT
fuelectenerg-3080	189	16	valued	value	VERB
fuelectenerg-3080	189	17	functions	function	NOUN
fuelectenerg-3080	189	18	.	.	PUNCT
fuelectenerg-3080	189	19	”	"	PUNCT
fuelectenerg-3080	190	1	in	in	ADP
fuelectenerg-3080	190	2	proceedings	proceeding	NOUN
fuelectenerg-3080	190	3	of	of	ADP
fuelectenerg-3080	190	4	the	the	DET
fuelectenerg-3080	190	5	6th	6th	ADJ
fuelectenerg-3080	190	6	international	international	ADJ
fuelectenerg-3080	190	7	workshop	workshop	NOUN
fuelectenerg-3080	190	8	boolean	boolean	ADJ
fuelectenerg-3080	190	9	problems	problem	NOUN
fuelectenerg-3080	190	10	,	,	PUNCT
fuelectenerg-3080	190	11	b.	b.	PROPN
fuelectenerg-3080	190	12	steinbach	steinbach	PROPN
fuelectenerg-3080	190	13	(	(	PUNCT
fuelectenerg-3080	190	14	ed	ed	NOUN
fuelectenerg-3080	190	15	.	.	PUNCT
fuelectenerg-3080	190	16	)	)	PUNCT
fuelectenerg-3080	190	17	,	,	PUNCT
fuelectenerg-3080	190	18	2004	2004	NUM
fuelectenerg-3080	190	19	,	,	PUNCT
fuelectenerg-3080	190	20	pp	pp	ADJ
fuelectenerg-3080	190	21	.	.	PUNCT
fuelectenerg-3080	191	1	83	83	NUM
fuelectenerg-3080	191	2	-	-	SYM
fuelectenerg-3080	191	3	87	87	NUM
fuelectenerg-3080	191	4	.	.	PUNCT
fuelectenerg-3080	192	1	[	[	X
fuelectenerg-3080	192	2	16	16	NUM
fuelectenerg-3080	192	3	]	]	X
fuelectenerg-3080	192	4	j.t	j.t	PROPN
fuelectenerg-3080	192	5	.	.	PROPN
fuelectenerg-3080	192	6	butler	butler	PROPN
fuelectenerg-3080	192	7	and	and	CCONJ
fuelectenerg-3080	192	8	k.	k.	PROPN
fuelectenerg-3080	192	9	a.	a.	PROPN
fuelectenerg-3080	192	10	schueller	schueller	PROPN
fuelectenerg-3080	192	11	,	,	PUNCT
fuelectenerg-3080	192	12	“	"	PUNCT
fuelectenerg-3080	192	13	worst	bad	ADJ
fuelectenerg-3080	192	14	case	case	NOUN
fuelectenerg-3080	192	15	number	number	NOUN
fuelectenerg-3080	192	16	of	of	ADP
fuelectenerg-3080	192	17	terms	term	NOUN
fuelectenerg-3080	192	18	in	in	ADP
fuelectenerg-3080	192	19	symmetric	symmetric	ADJ
fuelectenerg-3080	192	20	multiple	multiple	ADJ
fuelectenerg-3080	192	21	-	-	PUNCT
fuelectenerg-3080	192	22	valued	value	VERB
fuelectenerg-3080	192	23	functions	function	NOUN
fuelectenerg-3080	192	24	.	.	PUNCT
fuelectenerg-3080	192	25	”	"	PUNCT
fuelectenerg-3080	193	1	in	in	ADP
fuelectenerg-3080	193	2	proceedings	proceeding	NOUN
fuelectenerg-3080	193	3	of	of	ADP
fuelectenerg-3080	193	4	the	the	DET
fuelectenerg-3080	193	5	21st	21st	ADJ
fuelectenerg-3080	193	6	international	international	ADJ
fuelectenerg-3080	193	7	symposium	symposium	NOUN
fuelectenerg-3080	193	8	on	on	ADP
fuelectenerg-3080	193	9	multiple	multiple	ADV
fuelectenerg-3080	193	10	-	-	PUNCT
fuelectenerg-3080	193	11	valued	value	VERB
fuelectenerg-3080	193	12	logic	logic	NOUN
fuelectenerg-3080	193	13	.	.	PUNCT
fuelectenerg-3080	194	1	ieee	ieee	PROPN
fuelectenerg-3080	194	2	press	press	PROPN
fuelectenerg-3080	194	3	,	,	PUNCT
fuelectenerg-3080	194	4	1991	1991	NUM
fuelectenerg-3080	194	5	.	.	PUNCT
fuelectenerg-3080	195	1	[	[	X
fuelectenerg-3080	195	2	17	17	NUM
fuelectenerg-3080	195	3	]	]	X
fuelectenerg-3080	195	4	j.c	j.c	PROPN
fuelectenerg-3080	195	5	.	.	PROPN
fuelectenerg-3080	195	6	muzio	muzio	PROPN
fuelectenerg-3080	195	7	,	,	PUNCT
fuelectenerg-3080	195	8	“	"	PUNCT
fuelectenerg-3080	195	9	concerning	concern	VERB
fuelectenerg-3080	195	10	the	the	DET
fuelectenerg-3080	195	11	maximum	maximum	ADJ
fuelectenerg-3080	195	12	size	size	NOUN
fuelectenerg-3080	195	13	of	of	ADP
fuelectenerg-3080	195	14	the	the	DET
fuelectenerg-3080	195	15	terms	term	NOUN
fuelectenerg-3080	195	16	in	in	ADP
fuelectenerg-3080	195	17	the	the	DET
fuelectenerg-3080	195	18	realization	realization	NOUN
fuelectenerg-3080	195	19	of	of	ADP
fuelectenerg-3080	195	20	symmetric	symmetric	ADJ
fuelectenerg-3080	195	21	functions	function	NOUN
fuelectenerg-3080	195	22	.	.	PUNCT
fuelectenerg-3080	195	23	”	"	PUNCT
fuelectenerg-3080	196	1	in	in	ADP
fuelectenerg-3080	196	2	proceedings	proceeding	NOUN
fuelectenerg-3080	196	3	of	of	ADP
fuelectenerg-3080	196	4	the	the	DET
fuelectenerg-3080	196	5	20th	20th	ADJ
fuelectenerg-3080	196	6	international	international	ADJ
fuelectenerg-3080	196	7	symposium	symposium	NOUN
fuelectenerg-3080	196	8	on	on	ADP
fuelectenerg-3080	196	9	multiple	multiple	ADV
fuelectenerg-3080	196	10	-	-	PUNCT
fuelectenerg-3080	196	11	valued	value	VERB
fuelectenerg-3080	196	12	logic	logic	NOUN
fuelectenerg-3080	196	13	,	,	PUNCT
fuelectenerg-3080	196	14	1990	1990	NUM
fuelectenerg-3080	196	15	,	,	PUNCT
fuelectenerg-3080	196	16	pp	pp	ADJ
fuelectenerg-3080	196	17	.	.	PUNCT
fuelectenerg-3080	197	1	292	292	NUM
fuelectenerg-3080	197	2	-	-	SYM
fuelectenerg-3080	197	3	299	299	NUM
fuelectenerg-3080	197	4	.	.	PUNCT
fuelectenerg-3080	198	1	[	[	X
fuelectenerg-3080	198	2	18	18	NUM
fuelectenerg-3080	198	3	]	]	X
fuelectenerg-3080	198	4	c.	c.	PROPN
fuelectenerg-3080	198	5	moraga	moraga	PROPN
fuelectenerg-3080	198	6	,	,	PUNCT
fuelectenerg-3080	198	7	“	"	PUNCT
fuelectenerg-3080	198	8	permutations	permutation	NOUN
fuelectenerg-3080	198	9	under	under	ADP
fuelectenerg-3080	198	10	spectral	spectral	ADJ
fuelectenerg-3080	198	11	transforms	transform	NOUN
fuelectenerg-3080	198	12	.	.	PUNCT
fuelectenerg-3080	198	13	”	"	PUNCT
fuelectenerg-3080	198	14	in	in	ADP
fuelectenerg-3080	198	15	proceedings	proceeding	NOUN
fuelectenerg-3080	198	16	of	of	ADP
fuelectenerg-3080	198	17	the	the	DET
fuelectenerg-3080	198	18	38th	38th	ADJ
fuelectenerg-3080	198	19	international	international	ADJ
fuelectenerg-3080	198	20	symposium	symposium	NOUN
fuelectenerg-3080	198	21	on	on	ADP
fuelectenerg-3080	198	22	multiple	multiple	ADV
fuelectenerg-3080	198	23	-	-	PUNCT
fuelectenerg-3080	198	24	valued	value	VERB
fuelectenerg-3080	198	25	logic	logic	NOUN
fuelectenerg-3080	198	26	,	,	PUNCT
fuelectenerg-3080	198	27	ieee	ieee	NOUN
fuelectenerg-3080	198	28	press	press	NOUN
fuelectenerg-3080	198	29	,	,	PUNCT
fuelectenerg-3080	198	30	2008	2008	NUM
fuelectenerg-3080	198	31	,	,	PUNCT
fuelectenerg-3080	198	32	pp	pp	ADJ
fuelectenerg-3080	198	33	.	.	PUNCT
fuelectenerg-3080	199	1	76	76	NUM
fuelectenerg-3080	199	2	-	-	SYM
fuelectenerg-3080	199	3	81	81	NUM
fuelectenerg-3080	199	4	.	.	PUNCT
fuelectenerg-3080	200	1	[	[	X
fuelectenerg-3080	200	2	19	19	NUM
fuelectenerg-3080	200	3	]	]	X
fuelectenerg-3080	200	4	p.v	p.v	PROPN
fuelectenerg-3080	200	5	.	.	PROPN
fuelectenerg-3080	200	6	kumar	kumar	PROPN
fuelectenerg-3080	200	7	,	,	PUNCT
fuelectenerg-3080	200	8	r.a	r.a	PROPN
fuelectenerg-3080	200	9	.	.	PROPN
fuelectenerg-3080	200	10	scholz	scholz	NOUN
fuelectenerg-3080	200	11	and	and	CCONJ
fuelectenerg-3080	200	12	l.r	l.r	PROPN
fuelectenerg-3080	200	13	.	.	PROPN
fuelectenerg-3080	200	14	welch	welch	PROPN
fuelectenerg-3080	200	15	,	,	PUNCT
fuelectenerg-3080	200	16	“	"	PUNCT
fuelectenerg-3080	200	17	generalized	generalize	VERB
fuelectenerg-3080	200	18	bent	bent	ADJ
fuelectenerg-3080	200	19	functions	function	NOUN
fuelectenerg-3080	200	20	and	and	CCONJ
fuelectenerg-3080	200	21	their	their	PRON
fuelectenerg-3080	200	22	properties	property	NOUN
fuelectenerg-3080	200	23	.	.	PUNCT
fuelectenerg-3080	200	24	”	"	PUNCT
fuelectenerg-3080	201	1	jr	jr	PROPN
fuelectenerg-3080	201	2	.	.	PROPN
fuelectenerg-3080	201	3	combinatorial	combinatorial	PROPN
fuelectenerg-3080	201	4	theory	theory	PROPN
fuelectenerg-3080	201	5	series	series	PROPN
fuelectenerg-3080	201	6	a	a	PRON
fuelectenerg-3080	201	7	,	,	PUNCT
fuelectenerg-3080	201	8	vol	vol	NOUN
fuelectenerg-3080	201	9	.	.	PROPN
fuelectenerg-3080	201	10	40	40	NUM
fuelectenerg-3080	201	11	,	,	PUNCT
fuelectenerg-3080	201	12	no	no	INTJ
fuelectenerg-3080	201	13	.	.	NOUN
fuelectenerg-3080	201	14	1	1	NUM
fuelectenerg-3080	201	15	,	,	PUNCT
fuelectenerg-3080	201	16	90	90	NUM
fuelectenerg-3080	201	17	-	-	SYM
fuelectenerg-3080	201	18	107	107	NUM
fuelectenerg-3080	201	19	,	,	PUNCT
fuelectenerg-3080	201	20	1985	1985	NUM
fuelectenerg-3080	201	21	.	.	PUNCT
fuelectenerg-3080	202	1	[	[	X
fuelectenerg-3080	202	2	20	20	NUM
fuelectenerg-3080	202	3	]	]	X
fuelectenerg-3080	202	4	c.	c.	PROPN
fuelectenerg-3080	202	5	moraga	moraga	PROPN
fuelectenerg-3080	202	6	,	,	PUNCT
fuelectenerg-3080	202	7	m.	m.	NOUN
fuelectenerg-3080	202	8	stanković	stanković	PROPN
fuelectenerg-3080	202	9	,	,	PUNCT
fuelectenerg-3080	202	10	r.s	r.s	PROPN
fuelectenerg-3080	202	11	.	.	PROPN
fuelectenerg-3080	202	12	stanković	stanković	PROPN
fuelectenerg-3080	202	13	and	and	CCONJ
fuelectenerg-3080	202	14	s.	s.	PROPN
fuelectenerg-3080	202	15	stojković	stojković	PROPN
fuelectenerg-3080	202	16	,	,	PUNCT
fuelectenerg-3080	202	17	“	"	PUNCT
fuelectenerg-3080	202	18	contribution	contribution	NOUN
fuelectenerg-3080	202	19	to	to	ADP
fuelectenerg-3080	202	20	the	the	DET
fuelectenerg-3080	202	21	study	study	NOUN
fuelectenerg-3080	202	22	of	of	ADP
fuelectenerg-3080	202	23	multiplevalued	multiplevalue	VERB
fuelectenerg-3080	202	24	bent	bent	ADJ
fuelectenerg-3080	202	25	functions	function	NOUN
fuelectenerg-3080	202	26	.	.	PUNCT
fuelectenerg-3080	202	27	”	"	PUNCT
fuelectenerg-3080	203	1	in	in	ADP
fuelectenerg-3080	203	2	proceedings	proceeding	NOUN
fuelectenerg-3080	203	3	of	of	ADP
fuelectenerg-3080	203	4	the	the	DET
fuelectenerg-3080	203	5	33rd	33rd	ADJ
fuelectenerg-3080	203	6	international	international	ADJ
fuelectenerg-3080	203	7	symposium	symposium	NOUN
fuelectenerg-3080	203	8	on	on	ADP
fuelectenerg-3080	203	9	multiple	multiple	ADV
fuelectenerg-3080	203	10	-	-	PUNCT
fuelectenerg-3080	203	11	valued	value	VERB
fuelectenerg-3080	203	12	logic	logic	NOUN
fuelectenerg-3080	203	13	,	,	PUNCT
fuelectenerg-3080	203	14	ieee	ieee	NOUN
fuelectenerg-3080	203	15	press	press	NOUN
fuelectenerg-3080	203	16	,	,	PUNCT
fuelectenerg-3080	203	17	2013	2013	NUM
fuelectenerg-3080	203	18	,	,	PUNCT
fuelectenerg-3080	203	19	pp	pp	ADJ
fuelectenerg-3080	203	20	.	.	PUNCT
fuelectenerg-3080	203	21	340	340	NUM
fuelectenerg-3080	203	22	-	-	SYM
fuelectenerg-3080	203	23	345	345	NUM
fuelectenerg-3080	203	24	.	.	PUNCT