id	sid	tid	token	lemma	pos
uiug.30112106882779	1	1	629	629	NUM
uiug.30112106882779	1	2	.	.	PUNCT
uiug.30112106882779	2	1	13	13	NUM
uiug.30112106882779	2	2	12	12	NUM
uiug.30112106882779	2	3	325th	325th	NOUN
uiug.30112106882779	2	4	and	and	CCONJ
uiug.30112106882779	2	5	space	space	NOUN
uiug.30112106882779	2	6	aeronautics	aeronautics	PROPN
uiug.30112106882779	2	7	nasa	nasa	PROPN
uiug.30112106882779	2	8	technical	technical	PROPN
uiug.30112106882779	2	9	note	note	PROPN
uiug.30112106882779	2	10	nasa	nasa	PROPN
uiug.30112106882779	2	11	tn	tn	PROPN
uiug.30112106882779	2	12	d-6677	d-6677	PROPN
uiug.30112106882779	3	1	tvnotinn	tvnotinn	NOUN
uiug.30112106882779	3	2	stration	stration	PROPN
uiug.30112106882779	3	3	u.s.a	u.s.a	PROPN
uiug.30112106882779	3	4	.	.	PROPN
uiug.30112106882779	3	5	nasa	nasa	PROPN
uiug.30112106882779	3	6	tn	tn	PROPN
uiug.30112106882779	3	7	d-6677	d-6677	PROPN
uiug.30112106882779	4	1	the	the	DET
uiug.30112106882779	4	2	library	library	NOUN
uiug.30112106882779	4	3	of	of	ADP
uiug.30112106882779	4	4	the	the	DET
uiug.30112106882779	4	5	apr	apr	PROPN
uiug.30112106882779	4	6	2	2	NUM
uiug.30112106882779	4	7	4	4	NUM
uiug.30112106882779	4	8	1972	1972	NUM
uiug.30112106882779	4	9	university	university	PROPN
uiug.30112106882779	4	10	of	of	ADP
uiug.30112106882779	4	11	illinois	illinois	PROPN
uiug.30112106882779	4	12	at	at	ADP
uiug.30112106882779	4	13	urbana	urbana	ADJ
uiug.30112106882779	4	14	-	-	PUNCT
uiug.30112106882779	4	15	champaign	champaign	NOUN
uiug.30112106882779	4	16	vlasov	vlasov	NOUN
uiug.30112106882779	4	17	equation	equation	NOUN
uiug.30112106882779	4	18	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	4	19	and	and	CCONJ
uiug.30112106882779	4	20	eigenvectors	eigenvector	NOUN
uiug.30112106882779	4	21	for	for	ADP
uiug.30112106882779	4	22	fourier	fourier	NOUN
uiug.30112106882779	4	23	-	-	PUNCT
uiug.30112106882779	4	24	hermite	hermite	NOUN
uiug.30112106882779	4	25	dispersion	dispersion	NOUN
uiug.30112106882779	4	26	matrices	matrix	NOUN
uiug.30112106882779	4	27	of	of	ADP
uiug.30112106882779	4	28	order	order	NOUN
uiug.30112106882779	4	29	greater	great	ADJ
uiug.30112106882779	4	30	than	than	ADP
uiug.30112106882779	4	31	1000	1000	NUM
uiug.30112106882779	4	32	by	by	ADP
uiug.30112106882779	4	33	frederick	frederick	PROPN
uiug.30112106882779	4	34	c.	c.	PROPN
uiug.30112106882779	4	35	grant	grant	PROPN
uiug.30112106882779	4	36	langley	langley	PROPN
uiug.30112106882779	4	37	research	research	PROPN
uiug.30112106882779	4	38	center	center	PROPN
uiug.30112106882779	4	39	hampton	hampton	PROPN
uiug.30112106882779	4	40	,	,	PUNCT
uiug.30112106882779	4	41	va	va	PROPN
uiug.30112106882779	4	42	.	.	PROPN
uiug.30112106882779	5	1	23365	23365	NUM
uiug.30112106882779	5	2	national	national	ADJ
uiug.30112106882779	5	3	aeronautics	aeronautic	NOUN
uiug.30112106882779	5	4	and	and	CCONJ
uiug.30112106882779	5	5	space	space	PROPN
uiug.30112106882779	5	6	administration	administration	PROPN
uiug.30112106882779	5	7	•	•	CCONJ
uiug.30112106882779	5	8	washington	washington	PROPN
uiug.30112106882779	5	9	,	,	PUNCT
uiug.30112106882779	5	10	d.	d.	PROPN
uiug.30112106882779	5	11	c	c	PROPN
uiug.30112106882779	5	12	..	..	PUNCT
uiug.30112106882779	5	13	april	april	PROPN
uiug.30112106882779	5	14	1972	1972	NUM
uiug.30112106882779	5	15	university	university	PROPN
uiug.30112106882779	5	16	of	of	ADP
uiug.30112106882779	5	17	illinois	illinois	PROPN
uiug.30112106882779	5	18	-	-	PUNCT
uiug.30112106882779	5	19	urbana	urbana	ADJ
uiug.30112106882779	5	20	30112	30112	NUM
uiug.30112106882779	5	21	106882779	106882779	NUM
uiug.30112106882779	5	22	3	3	NUM
uiug.30112106882779	5	23	.	.	PROPN
uiug.30112106882779	5	24	recipient	recipient	NOUN
uiug.30112106882779	5	25	's	's	PART
uiug.30112106882779	5	26	catalog	catalog	NOUN
uiug.30112106882779	5	27	no	no	NOUN
uiug.30112106882779	5	28	.	.	NOUN
uiug.30112106882779	6	1	1	1	NUM
uiug.30112106882779	6	2	.	.	X
uiug.30112106882779	6	3	report	report	VERB
uiug.30112106882779	6	4	no	no	INTJ
uiug.30112106882779	6	5	.	.	NOUN
uiug.30112106882779	6	6	2	2	NUM
uiug.30112106882779	6	7	.	.	X
uiug.30112106882779	7	1	government	government	NOUN
uiug.30112106882779	7	2	accession	accession	NOUN
uiug.30112106882779	7	3	no	no	PRON
uiug.30112106882779	7	4	.	.	PUNCT
uiug.30112106882779	8	1	nasa	nasa	PROPN
uiug.30112106882779	8	2	tn	tn	PROPN
uiug.30112106882779	8	3	d-6677	d-6677	PROPN
uiug.30112106882779	8	4	4	4	NUM
uiug.30112106882779	8	5	.	.	X
uiug.30112106882779	9	1	title	title	NOUN
uiug.30112106882779	9	2	and	and	CCONJ
uiug.30112106882779	9	3	subtitle	subtitle	NOUN
uiug.30112106882779	9	4	vlasov	vlasov	NOUN
uiug.30112106882779	9	5	equation	equation	NOUN
uiug.30112106882779	9	6	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	9	7	and	and	CCONJ
uiug.30112106882779	9	8	eigenvectors	eigenvector	NOUN
uiug.30112106882779	9	9	for	for	ADP
uiug.30112106882779	9	10	fourier	fourier	NOUN
uiug.30112106882779	9	11	-	-	PUNCT
uiug.30112106882779	9	12	hermite	hermite	NOUN
uiug.30112106882779	9	13	dispersion	dispersion	NOUN
uiug.30112106882779	9	14	matrices	matrix	NOUN
uiug.30112106882779	9	15	of	of	ADP
uiug.30112106882779	9	16	order	order	NOUN
uiug.30112106882779	9	17	greater	great	ADJ
uiug.30112106882779	9	18	than	than	ADP
uiug.30112106882779	9	19	1000	1000	NUM
uiug.30112106882779	9	20	5	5	NUM
uiug.30112106882779	9	21	.	.	PUNCT
uiug.30112106882779	10	1	report	report	NOUN
uiug.30112106882779	10	2	date	date	NOUN
uiug.30112106882779	10	3	april	april	PROPN
uiug.30112106882779	10	4	1972	1972	NUM
uiug.30112106882779	10	5	6	6	NUM
uiug.30112106882779	10	6	.	.	PUNCT
uiug.30112106882779	11	1	performing	perform	VERB
uiug.30112106882779	11	2	organization	organization	NOUN
uiug.30112106882779	11	3	code	code	PROPN
uiug.30112106882779	11	4	7	7	NUM
uiug.30112106882779	11	5	.	.	PUNCT
uiug.30112106882779	12	1	author(s	author(s	PROPN
uiug.30112106882779	12	2	)	)	PUNCT
uiug.30112106882779	12	3	frederick	frederick	PROPN
uiug.30112106882779	12	4	c.	c.	PROPN
uiug.30112106882779	12	5	grant	grant	PROPN
uiug.30112106882779	12	6	8	8	NUM
uiug.30112106882779	12	7	.	.	PUNCT
uiug.30112106882779	12	8	performing	perform	VERB
uiug.30112106882779	12	9	organization	organization	NOUN
uiug.30112106882779	12	10	report	report	NOUN
uiug.30112106882779	12	11	no	no	INTJ
uiug.30112106882779	12	12	.	.	PUNCT
uiug.30112106882779	12	13	l-8141	l-8141	VERB
uiug.30112106882779	12	14	10	10	NUM
uiug.30112106882779	12	15	.	.	PUNCT
uiug.30112106882779	13	1	work	work	NOUN
uiug.30112106882779	13	2	unit	unit	NOUN
uiug.30112106882779	13	3	no	no	NOUN
uiug.30112106882779	13	4	.	.	NOUN
uiug.30112106882779	13	5	188	188	NUM
uiug.30112106882779	13	6	-	-	SYM
uiug.30112106882779	13	7	36	36	NUM
uiug.30112106882779	13	8	-	-	PUNCT
uiug.30112106882779	13	9	56	56	NUM
uiug.30112106882779	13	10	-	-	SYM
uiug.30112106882779	13	11	02	02	NUM
uiug.30112106882779	13	12	9	9	NUM
uiug.30112106882779	13	13	.	.	PUNCT
uiug.30112106882779	14	1	performing	perform	VERB
uiug.30112106882779	14	2	organization	organization	NOUN
uiug.30112106882779	14	3	name	name	NOUN
uiug.30112106882779	14	4	and	and	CCONJ
uiug.30112106882779	14	5	address	address	VERB
uiug.30112106882779	14	6	nasa	nasa	PROPN
uiug.30112106882779	14	7	langley	langley	PROPN
uiug.30112106882779	14	8	research	research	PROPN
uiug.30112106882779	14	9	center	center	PROPN
uiug.30112106882779	14	10	hampton	hampton	PROPN
uiug.30112106882779	14	11	,	,	PUNCT
uiug.30112106882779	14	12	va	va	PROPN
uiug.30112106882779	14	13	.	.	PROPN
uiug.30112106882779	15	1	23365	23365	NUM
uiug.30112106882779	15	2	11	11	NUM
uiug.30112106882779	15	3	.	.	PUNCT
uiug.30112106882779	16	1	contract	contract	NOUN
uiug.30112106882779	16	2	or	or	CCONJ
uiug.30112106882779	16	3	grant	grant	VERB
uiug.30112106882779	16	4	no	no	NOUN
uiug.30112106882779	16	5	.	.	PROPN
uiug.30112106882779	16	6	13	13	NUM
uiug.30112106882779	16	7	.	.	PUNCT
uiug.30112106882779	17	1	type	type	NOUN
uiug.30112106882779	17	2	of	of	ADP
uiug.30112106882779	17	3	report	report	NOUN
uiug.30112106882779	17	4	and	and	CCONJ
uiug.30112106882779	17	5	period	period	NOUN
uiug.30112106882779	17	6	covered	cover	VERB
uiug.30112106882779	17	7	technical	technical	ADJ
uiug.30112106882779	17	8	note	note	NOUN
uiug.30112106882779	17	9	12	12	NUM
uiug.30112106882779	17	10	.	.	PUNCT
uiug.30112106882779	18	1	sponsoring	sponsor	VERB
uiug.30112106882779	18	2	agency	agency	NOUN
uiug.30112106882779	18	3	name	name	NOUN
uiug.30112106882779	18	4	and	and	CCONJ
uiug.30112106882779	18	5	address	address	VERB
uiug.30112106882779	18	6	national	national	ADJ
uiug.30112106882779	18	7	aeronautics	aeronautic	NOUN
uiug.30112106882779	18	8	and	and	CCONJ
uiug.30112106882779	18	9	space	space	PROPN
uiug.30112106882779	18	10	administration	administration	PROPN
uiug.30112106882779	18	11	washington	washington	PROPN
uiug.30112106882779	18	12	,	,	PUNCT
uiug.30112106882779	18	13	d.c	d.c	PROPN
uiug.30112106882779	18	14	.	.	PROPN
uiug.30112106882779	19	1	20546	20546	NUM
uiug.30112106882779	19	2	14	14	NUM
uiug.30112106882779	19	3	.	.	PUNCT
uiug.30112106882779	20	1	sponsoring	sponsor	VERB
uiug.30112106882779	20	2	agency	agency	PROPN
uiug.30112106882779	20	3	code	code	PROPN
uiug.30112106882779	20	4	15	15	NUM
uiug.30112106882779	20	5	.	.	PUNCT
uiug.30112106882779	21	1	supplementary	supplementary	ADJ
uiug.30112106882779	21	2	notes	note	NOUN
uiug.30112106882779	21	3	16	16	NUM
uiug.30112106882779	21	4	.	.	PUNCT
uiug.30112106882779	22	1	abstract	abstract	ADJ
uiug.30112106882779	22	2	the	the	DET
uiug.30112106882779	22	3	connection	connection	NOUN
uiug.30112106882779	22	4	between	between	ADP
uiug.30112106882779	22	5	the	the	DET
uiug.30112106882779	22	6	van	van	PROPN
uiug.30112106882779	22	7	kampen	kampen	PROPN
uiug.30112106882779	22	8	and	and	CCONJ
uiug.30112106882779	22	9	landau	landau	NOUN
uiug.30112106882779	22	10	representations	representation	NOUN
uiug.30112106882779	22	11	of	of	ADP
uiug.30112106882779	22	12	the	the	DET
uiug.30112106882779	22	13	vlasov	vlasov	NOUN
uiug.30112106882779	22	14	equations	equation	NOUN
uiug.30112106882779	22	15	has	have	AUX
uiug.30112106882779	22	16	been	be	AUX
uiug.30112106882779	22	17	extended	extend	VERB
uiug.30112106882779	22	18	to	to	ADP
uiug.30112106882779	22	19	fourier	fourier	NOUN
uiug.30112106882779	22	20	-	-	PUNCT
uiug.30112106882779	22	21	hermite	hermite	NOUN
uiug.30112106882779	22	22	expansions	expansion	NOUN
uiug.30112106882779	22	23	containing	contain	VERB
uiug.30112106882779	22	24	more	more	ADJ
uiug.30112106882779	22	25	than	than	ADP
uiug.30112106882779	22	26	1000	1000	NUM
uiug.30112106882779	22	27	terms	term	NOUN
uiug.30112106882779	22	28	by	by	ADP
uiug.30112106882779	22	29	taking	take	VERB
uiug.30112106882779	22	30	advantage	advantage	NOUN
uiug.30112106882779	22	31	of	of	ADP
uiug.30112106882779	22	32	the	the	DET
uiug.30112106882779	22	33	properties	property	NOUN
uiug.30112106882779	22	34	of	of	ADP
uiug.30112106882779	22	35	tridiagonal	tridiagonal	ADJ
uiug.30112106882779	22	36	matrices	matrix	NOUN
uiug.30112106882779	22	37	.	.	PUNCT
uiug.30112106882779	23	1	these	these	DET
uiug.30112106882779	23	2	numerical	numerical	ADJ
uiug.30112106882779	23	3	results	result	NOUN
uiug.30112106882779	23	4	are	be	AUX
uiug.30112106882779	23	5	regarded	regard	VERB
uiug.30112106882779	23	6	as	as	ADP
uiug.30112106882779	23	7	conclusive	conclusive	ADJ
uiug.30112106882779	23	8	indications	indication	NOUN
uiug.30112106882779	23	9	of	of	ADP
uiug.30112106882779	23	10	the	the	DET
uiug.30112106882779	23	11	nonuniformly	nonuniformly	ADV
uiug.30112106882779	23	12	convergent	convergent	ADJ
uiug.30112106882779	23	13	behavior	behavior	NOUN
uiug.30112106882779	23	14	of	of	ADP
uiug.30112106882779	23	15	the	the	DET
uiug.30112106882779	23	16	approximation	approximation	NOUN
uiug.30112106882779	23	17	curve	curve	NOUN
uiug.30112106882779	23	18	in	in	ADP
uiug.30112106882779	23	19	the	the	DET
uiug.30112106882779	23	20	limit	limit	NOUN
uiug.30112106882779	23	21	of	of	ADP
uiug.30112106882779	23	22	an	an	DET
uiug.30112106882779	23	23	infinite	infinite	ADJ
uiug.30112106882779	23	24	number	number	NOUN
uiug.30112106882779	23	25	of	of	ADP
uiug.30112106882779	23	26	terms	term	NOUN
uiug.30112106882779	23	27	and	and	CCONJ
uiug.30112106882779	23	28	represent	represent	VERB
uiug.30112106882779	23	29	an	an	DET
uiug.30112106882779	23	30	extension	extension	NOUN
uiug.30112106882779	23	31	of	of	ADP
uiug.30112106882779	23	32	work	work	NOUN
uiug.30112106882779	23	33	begun	begin	VERB
uiug.30112106882779	23	34	by	by	ADP
uiug.30112106882779	23	35	grant	grant	NOUN
uiug.30112106882779	23	36	(	(	PUNCT
uiug.30112106882779	23	37	1967	1967	NUM
uiug.30112106882779	23	38	)	)	PUNCT
uiug.30112106882779	23	39	and	and	CCONJ
uiug.30112106882779	23	40	by	by	ADP
uiug.30112106882779	23	41	grant	grant	NOUN
uiug.30112106882779	23	42	and	and	CCONJ
uiug.30112106882779	23	43	feix	feix	PRON
uiug.30112106882779	23	44	(	(	PUNCT
uiug.30112106882779	23	45	1967	1967	NUM
uiug.30112106882779	23	46	)	)	PUNCT
uiug.30112106882779	23	47	.	.	PUNCT
uiug.30112106882779	24	1	18	18	NUM
uiug.30112106882779	24	2	.	.	X
uiug.30112106882779	24	3	distribution	distribution	NOUN
uiug.30112106882779	24	4	statement	statement	NOUN
uiug.30112106882779	24	5	unclassified	unclassifie	VERB
uiug.30112106882779	24	6	unlimited	unlimited	ADJ
uiug.30112106882779	24	7	17	17	NUM
uiug.30112106882779	24	8	.	.	PUNCT
uiug.30112106882779	25	1	key	key	ADJ
uiug.30112106882779	25	2	words	word	NOUN
uiug.30112106882779	25	3	(	(	PUNCT
uiug.30112106882779	25	4	suggested	suggest	VERB
uiug.30112106882779	25	5	by	by	ADP
uiug.30112106882779	25	6	author(s	author(s	PROPN
uiug.30112106882779	25	7	)	)	PUNCT
uiug.30112106882779	25	8	)	)	PUNCT
uiug.30112106882779	25	9	plasma	plasma	NOUN
uiug.30112106882779	25	10	oscillations	oscillation	NOUN
uiug.30112106882779	25	11	transform	transform	VERB
uiug.30112106882779	25	12	methods	method	NOUN
uiug.30112106882779	25	13	in	in	ADP
uiug.30112106882779	25	14	plasma	plasma	NOUN
uiug.30112106882779	25	15	physics	physics	NOUN
uiug.30112106882779	25	16	fourier	fourier	NOUN
uiug.30112106882779	25	17	-	-	PUNCT
uiug.30112106882779	25	18	hermite	hermite	NOUN
uiug.30112106882779	25	19	transform	transform	NOUN
uiug.30112106882779	25	20	*	*	PUNCT
uiug.30112106882779	25	21	22	22	NUM
uiug.30112106882779	25	22	.	.	PUNCT
uiug.30112106882779	26	1	price	price	NOUN
uiug.30112106882779	26	2	*	*	SYM
uiug.30112106882779	26	3	19	19	NUM
uiug.30112106882779	26	4	.	.	PUNCT
uiug.30112106882779	27	1	security	security	NOUN
uiug.30112106882779	27	2	classif	classif	NOUN
uiug.30112106882779	27	3	.	.	PUNCT
uiug.30112106882779	28	1	(	(	PUNCT
uiug.30112106882779	28	2	of	of	ADP
uiug.30112106882779	28	3	this	this	DET
uiug.30112106882779	28	4	report	report	NOUN
uiug.30112106882779	28	5	)	)	PUNCT
uiug.30112106882779	28	6	unclassified	unclassified	ADJ
uiug.30112106882779	28	7	20	20	NUM
uiug.30112106882779	28	8	.	.	PUNCT
uiug.30112106882779	29	1	security	security	NOUN
uiug.30112106882779	29	2	classif	classif	NOUN
uiug.30112106882779	29	3	.	.	PUNCT
uiug.30112106882779	30	1	(	(	PUNCT
uiug.30112106882779	30	2	of	of	ADP
uiug.30112106882779	30	3	this	this	DET
uiug.30112106882779	30	4	page	page	NOUN
uiug.30112106882779	30	5	)	)	PUNCT
uiug.30112106882779	30	6	unclassified	unclassified	ADJ
uiug.30112106882779	30	7	21	21	NUM
uiug.30112106882779	30	8	.	.	PUNCT
uiug.30112106882779	31	1	no	no	INTJ
uiug.30112106882779	31	2	.	.	NOUN
uiug.30112106882779	31	3	of	of	ADP
uiug.30112106882779	31	4	pages	page	NOUN
uiug.30112106882779	31	5	21	21	NUM
uiug.30112106882779	31	6	$	$	SYM
uiug.30112106882779	31	7	3.00	3.00	NUM
uiug.30112106882779	31	8	for	for	ADP
uiug.30112106882779	31	9	sale	sale	NOUN
uiug.30112106882779	31	10	by	by	ADP
uiug.30112106882779	31	11	the	the	DET
uiug.30112106882779	31	12	national	national	ADJ
uiug.30112106882779	31	13	technical	technical	ADJ
uiug.30112106882779	31	14	information	information	NOUN
uiug.30112106882779	31	15	service	service	NOUN
uiug.30112106882779	31	16	,	,	PUNCT
uiug.30112106882779	31	17	springfield	springfield	PROPN
uiug.30112106882779	31	18	,	,	PUNCT
uiug.30112106882779	31	19	virginia	virginia	PROPN
uiug.30112106882779	31	20	22151	22151	NUM
uiug.30112106882779	32	1	i	i	PRON
uiug.30112106882779	32	2	vlasov	vlasov	VERB
uiug.30112106882779	32	3	equation	equation	NOUN
uiug.30112106882779	32	4	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	32	5	and	and	CCONJ
uiug.30112106882779	32	6	eigenvectors	eigenvector	NOUN
uiug.30112106882779	32	7	for	for	ADP
uiug.30112106882779	32	8	fourier	fourier	NOUN
uiug.30112106882779	32	9	-	-	PUNCT
uiug.30112106882779	32	10	hermite	hermite	NOUN
uiug.30112106882779	32	11	dispersion	dispersion	NOUN
uiug.30112106882779	32	12	matrices	matrix	NOUN
uiug.30112106882779	32	13	of	of	ADP
uiug.30112106882779	32	14	order	order	NOUN
uiug.30112106882779	32	15	greater	great	ADJ
uiug.30112106882779	32	16	than	than	ADP
uiug.30112106882779	32	17	1000	1000	NUM
uiug.30112106882779	32	18	by	by	ADP
uiug.30112106882779	32	19	frederick	frederick	PROPN
uiug.30112106882779	32	20	c.	c.	PROPN
uiug.30112106882779	32	21	grant	grant	PROPN
uiug.30112106882779	32	22	langley	langley	PROPN
uiug.30112106882779	32	23	research	research	NOUN
uiug.30112106882779	32	24	center	center	NOUN
uiug.30112106882779	32	25	summary	summary	VERB
uiug.30112106882779	32	26	the	the	DET
uiug.30112106882779	32	27	connection	connection	NOUN
uiug.30112106882779	32	28	between	between	ADP
uiug.30112106882779	32	29	the	the	DET
uiug.30112106882779	32	30	van	van	PROPN
uiug.30112106882779	32	31	kampen	kampen	PROPN
uiug.30112106882779	32	32	and	and	CCONJ
uiug.30112106882779	32	33	landau	landau	NOUN
uiug.30112106882779	32	34	representations	representation	NOUN
uiug.30112106882779	32	35	of	of	ADP
uiug.30112106882779	32	36	the	the	DET
uiug.30112106882779	32	37	vlasov	vlasov	NOUN
uiug.30112106882779	32	38	equations	equation	NOUN
uiug.30112106882779	32	39	has	have	AUX
uiug.30112106882779	32	40	been	be	AUX
uiug.30112106882779	32	41	extended	extend	VERB
uiug.30112106882779	32	42	to	to	ADP
uiug.30112106882779	32	43	fourier	fourier	NOUN
uiug.30112106882779	32	44	-	-	PUNCT
uiug.30112106882779	32	45	hermite	hermite	NOUN
uiug.30112106882779	32	46	expansions	expansion	NOUN
uiug.30112106882779	32	47	containing	contain	VERB
uiug.30112106882779	32	48	more	more	ADJ
uiug.30112106882779	32	49	than	than	ADP
uiug.30112106882779	32	50	1000	1000	NUM
uiug.30112106882779	32	51	terms	term	NOUN
uiug.30112106882779	32	52	by	by	ADP
uiug.30112106882779	32	53	taking	take	VERB
uiug.30112106882779	32	54	advantage	advantage	NOUN
uiug.30112106882779	32	55	of	of	ADP
uiug.30112106882779	32	56	the	the	DET
uiug.30112106882779	32	57	properties	property	NOUN
uiug.30112106882779	32	58	of	of	ADP
uiug.30112106882779	32	59	tridiagonal	tridiagonal	ADJ
uiug.30112106882779	32	60	matrices	matrix	NOUN
uiug.30112106882779	32	61	.	.	PUNCT
uiug.30112106882779	33	1	these	these	DET
uiug.30112106882779	33	2	numerical	numerical	ADJ
uiug.30112106882779	33	3	results	result	NOUN
uiug.30112106882779	33	4	are	be	AUX
uiug.30112106882779	33	5	regarded	regard	VERB
uiug.30112106882779	33	6	as	as	ADP
uiug.30112106882779	33	7	conclusive	conclusive	ADJ
uiug.30112106882779	33	8	indications	indication	NOUN
uiug.30112106882779	33	9	of	of	ADP
uiug.30112106882779	33	10	the	the	DET
uiug.30112106882779	33	11	nonuniformly	nonuniformly	ADV
uiug.30112106882779	33	12	convergent	convergent	ADJ
uiug.30112106882779	33	13	behavior	behavior	NOUN
uiug.30112106882779	33	14	of	of	ADP
uiug.30112106882779	33	15	the	the	DET
uiug.30112106882779	33	16	approximation	approximation	NOUN
uiug.30112106882779	33	17	curve	curve	NOUN
uiug.30112106882779	33	18	in	in	ADP
uiug.30112106882779	33	19	the	the	DET
uiug.30112106882779	33	20	limit	limit	NOUN
uiug.30112106882779	33	21	of	of	ADP
uiug.30112106882779	33	22	an	an	DET
uiug.30112106882779	33	23	infinite	infinite	ADJ
uiug.30112106882779	33	24	number	number	NOUN
uiug.30112106882779	33	25	of	of	ADP
uiug.30112106882779	33	26	terms	term	NOUN
uiug.30112106882779	33	27	and	and	CCONJ
uiug.30112106882779	33	28	represent	represent	VERB
uiug.30112106882779	33	29	an	an	DET
uiug.30112106882779	33	30	extension	extension	NOUN
uiug.30112106882779	33	31	of	of	ADP
uiug.30112106882779	33	32	work	work	NOUN
uiug.30112106882779	33	33	begun	begin	VERB
uiug.30112106882779	33	34	by	by	ADP
uiug.30112106882779	33	35	grant	grant	NOUN
uiug.30112106882779	33	36	(	(	PUNCT
uiug.30112106882779	33	37	1967	1967	NUM
uiug.30112106882779	33	38	)	)	PUNCT
uiug.30112106882779	33	39	and	and	CCONJ
uiug.30112106882779	33	40	by	by	ADP
uiug.30112106882779	33	41	grant	grant	NOUN
uiug.30112106882779	33	42	and	and	CCONJ
uiug.30112106882779	33	43	feix	feix	PRON
uiug.30112106882779	33	44	(	(	PUNCT
uiug.30112106882779	33	45	1967	1967	NUM
uiug.30112106882779	33	46	)	)	PUNCT
uiug.30112106882779	33	47	.	.	PUNCT
uiug.30112106882779	34	1	introduction	introduction	NOUN
uiug.30112106882779	34	2	in	in	ADP
uiug.30112106882779	34	3	a	a	DET
uiug.30112106882779	34	4	fully	fully	ADV
uiug.30112106882779	34	5	ionized	ionized	ADJ
uiug.30112106882779	34	6	plasma	plasma	NOUN
uiug.30112106882779	34	7	such	such	ADJ
uiug.30112106882779	34	8	as	as	ADP
uiug.30112106882779	34	9	the	the	DET
uiug.30112106882779	34	10	solar	solar	ADJ
uiug.30112106882779	34	11	corona	corona	PROPN
uiug.30112106882779	34	12	,	,	PUNCT
uiug.30112106882779	34	13	which	which	PRON
uiug.30112106882779	34	14	has	have	VERB
uiug.30112106882779	34	15	a	a	DET
uiug.30112106882779	34	16	large	large	ADJ
uiug.30112106882779	34	17	number	number	NOUN
uiug.30112106882779	34	18	of	of	ADP
uiug.30112106882779	34	19	electrons	electron	NOUN
uiug.30112106882779	34	20	in	in	ADP
uiug.30112106882779	34	21	a	a	DET
uiug.30112106882779	34	22	debye	debye	ADJ
uiug.30112106882779	34	23	cube	cube	NOUN
uiug.30112106882779	34	24	(	(	PUNCT
uiug.30112106882779	34	25	the	the	DET
uiug.30112106882779	34	26	edge	edge	NOUN
uiug.30112106882779	34	27	of	of	ADP
uiug.30112106882779	34	28	which	which	PRON
uiug.30112106882779	34	29	measures	measure	VERB
uiug.30112106882779	34	30	the	the	DET
uiug.30112106882779	34	31	screening	screening	NOUN
uiug.30112106882779	34	32	distance	distance	NOUN
uiug.30112106882779	34	33	about	about	ADP
uiug.30112106882779	34	34	an	an	DET
uiug.30112106882779	34	35	introduced	introduce	VERB
uiug.30112106882779	34	36	charge	charge	NOUN
uiug.30112106882779	34	37	)	)	PUNCT
uiug.30112106882779	34	38	,	,	PUNCT
uiug.30112106882779	34	39	the	the	DET
uiug.30112106882779	34	40	effect	effect	NOUN
uiug.30112106882779	34	41	of	of	ADP
uiug.30112106882779	34	42	collisions	collision	NOUN
uiug.30112106882779	34	43	is	be	AUX
uiug.30112106882779	34	44	negligible	negligible	ADJ
uiug.30112106882779	34	45	and	and	CCONJ
uiug.30112106882779	34	46	the	the	DET
uiug.30112106882779	34	47	vlasov	vlasov	NOUN
uiug.30112106882779	34	48	equations	equation	NOUN
uiug.30112106882779	34	49	describe	describe	VERB
uiug.30112106882779	34	50	the	the	DET
uiug.30112106882779	34	51	space	space	NOUN
uiug.30112106882779	34	52	-	-	PUNCT
uiug.30112106882779	34	53	time	time	NOUN
uiug.30112106882779	34	54	evolution	evolution	NOUN
uiug.30112106882779	34	55	of	of	ADP
uiug.30112106882779	34	56	the	the	DET
uiug.30112106882779	34	57	single	single	ADJ
uiug.30112106882779	34	58	-	-	PUNCT
uiug.30112106882779	34	59	particle	particle	NOUN
uiug.30112106882779	34	60	distribution	distribution	NOUN
uiug.30112106882779	34	61	function	function	NOUN
uiug.30112106882779	34	62	.	.	PUNCT
uiug.30112106882779	35	1	the	the	DET
uiug.30112106882779	35	2	nonlinear	nonlinear	ADJ
uiug.30112106882779	35	3	vlasov	vlasov	NOUN
uiug.30112106882779	35	4	equations	equation	NOUN
uiug.30112106882779	35	5	have	have	AUX
uiug.30112106882779	35	6	been	be	AUX
uiug.30112106882779	35	7	studied	study	VERB
uiug.30112106882779	35	8	only	only	ADV
uiug.30112106882779	35	9	for	for	ADP
uiug.30112106882779	35	10	special	special	ADJ
uiug.30112106882779	35	11	cases	case	NOUN
uiug.30112106882779	35	12	,	,	PUNCT
uiug.30112106882779	35	13	a	a	DET
uiug.30112106882779	35	14	common	common	ADJ
uiug.30112106882779	35	15	one	one	NUM
uiug.30112106882779	35	16	of	of	ADP
uiug.30112106882779	35	17	which	which	PRON
uiug.30112106882779	35	18	is	be	AUX
uiug.30112106882779	35	19	assumed	assume	VERB
uiug.30112106882779	35	20	herein	herein	ADV
uiug.30112106882779	35	21	:	:	PUNCT
uiug.30112106882779	35	22	a	a	DET
uiug.30112106882779	35	23	single	single	ADJ
uiug.30112106882779	35	24	space	space	NOUN
uiug.30112106882779	35	25	and	and	CCONJ
uiug.30112106882779	35	26	velocity	velocity	NOUN
uiug.30112106882779	35	27	variable	variable	NOUN
uiug.30112106882779	35	28	,	,	PUNCT
uiug.30112106882779	35	29	periodic	periodic	ADJ
uiug.30112106882779	35	30	spatial	spatial	ADJ
uiug.30112106882779	35	31	boundary	boundary	ADJ
uiug.30112106882779	35	32	conditions	condition	NOUN
uiug.30112106882779	35	33	,	,	PUNCT
uiug.30112106882779	35	34	a	a	DET
uiug.30112106882779	35	35	uniform	uniform	ADJ
uiug.30112106882779	35	36	steady	steady	ADJ
uiug.30112106882779	35	37	ion	ion	NOUN
uiug.30112106882779	35	38	background	background	NOUN
uiug.30112106882779	35	39	against	against	ADP
uiug.30112106882779	35	40	which	which	PRON
uiug.30112106882779	35	41	the	the	DET
uiug.30112106882779	35	42	electrons	electron	NOUN
uiug.30112106882779	35	43	move	move	VERB
uiug.30112106882779	35	44	,	,	PUNCT
uiug.30112106882779	35	45	and	and	CCONJ
uiug.30112106882779	35	46	an	an	DET
uiug.30112106882779	35	47	initial	initial	ADJ
uiug.30112106882779	35	48	maxwellian	maxwellian	ADJ
uiug.30112106882779	35	49	electronic	electronic	ADJ
uiug.30112106882779	35	50	distribution	distribution	NOUN
uiug.30112106882779	35	51	function	function	NOUN
uiug.30112106882779	35	52	.	.	PUNCT
uiug.30112106882779	36	1	because	because	SCONJ
uiug.30112106882779	36	2	of	of	ADP
uiug.30112106882779	36	3	their	their	PRON
uiug.30112106882779	36	4	formidable	formidable	ADJ
uiug.30112106882779	36	5	nature	nature	NOUN
uiug.30112106882779	36	6	,	,	PUNCT
uiug.30112106882779	36	7	the	the	DET
uiug.30112106882779	36	8	vlasov	vlasov	NOUN
uiug.30112106882779	36	9	équations	équation	NOUN
uiug.30112106882779	36	10	have	have	AUX
uiug.30112106882779	36	11	been	be	AUX
uiug.30112106882779	36	12	treated	treat	VERB
uiug.30112106882779	36	13	mostly	mostly	ADV
uiug.30112106882779	36	14	by	by	ADP
uiug.30112106882779	36	15	numerical	numerical	ADJ
uiug.30112106882779	36	16	techniques	technique	NOUN
uiug.30112106882779	36	17	.	.	PUNCT
uiug.30112106882779	37	1	however	however	ADV
uiug.30112106882779	37	2	,	,	PUNCT
uiug.30112106882779	37	3	when	when	SCONJ
uiug.30112106882779	37	4	ordinary	ordinary	ADJ
uiug.30112106882779	37	5	x	x	NOUN
uiug.30112106882779	37	6	-	-	NOUN
uiug.30112106882779	37	7	v	v	ADJ
uiug.30112106882779	37	8	-	-	PUNCT
uiug.30112106882779	37	9	t	t	NOUN
uiug.30112106882779	37	10	space	space	NOUN
uiug.30112106882779	37	11	is	be	AUX
uiug.30112106882779	37	12	used	use	VERB
uiug.30112106882779	37	13	,	,	PUNCT
uiug.30112106882779	37	14	an	an	DET
uiug.30112106882779	37	15	insuperable	insuperable	ADJ
uiug.30112106882779	37	16	difficulty	difficulty	NOUN
uiug.30112106882779	37	17	arises	arise	VERB
uiug.30112106882779	37	18	in	in	ADP
uiug.30112106882779	37	19	the	the	DET
uiug.30112106882779	37	20	velocity	velocity	NOUN
uiug.30112106882779	37	21	space	space	NOUN
uiug.30112106882779	37	22	.	.	PUNCT
uiug.30112106882779	38	1	increasingly	increasingly	ADV
uiug.30112106882779	38	2	steep	steep	ADJ
uiug.30112106882779	38	3	oscillatory	oscillatory	ADJ
uiug.30112106882779	38	4	gradients	gradient	NOUN
uiug.30112106882779	38	5	with	with	ADP
uiug.30112106882779	38	6	evershorter	evershorter	ADJ
uiug.30112106882779	38	7	wavelengths	wavelength	NOUN
uiug.30112106882779	38	8	develop	develop	VERB
uiug.30112106882779	38	9	in	in	ADP
uiug.30112106882779	38	10	the	the	DET
uiug.30112106882779	38	11	distribution	distribution	NOUN
uiug.30112106882779	38	12	function	function	NOUN
uiug.30112106882779	38	13	.	.	PUNCT
uiug.30112106882779	39	1	to	to	PART
uiug.30112106882779	39	2	circumvent	circumvent	VERB
uiug.30112106882779	39	3	the	the	DET
uiug.30112106882779	39	4	difficulty	difficulty	NOUN
uiug.30112106882779	39	5	,	,	PUNCT
uiug.30112106882779	39	6	transform	transform	NOUN
uiug.30112106882779	39	7	methods	method	NOUN
uiug.30112106882779	39	8	have	have	AUX
uiug.30112106882779	39	9	been	be	AUX
uiug.30112106882779	39	10	introduced	introduce	VERB
uiug.30112106882779	39	11	,	,	PUNCT
uiug.30112106882779	39	12	and	and	CCONJ
uiug.30112106882779	39	13	among	among	ADP
uiug.30112106882779	39	14	these	these	PRON
uiug.30112106882779	39	15	is	be	AUX
uiug.30112106882779	39	16	the	the	DET
uiug.30112106882779	39	17	fourier	fourier	NOUN
uiug.30112106882779	39	18	expansion	expansion	NOUN
uiug.30112106882779	39	19	on	on	ADP
uiug.30112106882779	39	20	space	space	NOUN
uiug.30112106882779	39	21	and	and	CCONJ
uiug.30112106882779	39	22	the	the	DET
uiug.30112106882779	39	23	hermite	hermite	ADJ
uiug.30112106882779	39	24	expansion	expansion	NOUN
uiug.30112106882779	39	25	on	on	ADP
uiug.30112106882779	39	26	velocity	velocity	NOUN
uiug.30112106882779	39	27	which	which	PRON
uiug.30112106882779	39	28	lead	lead	VERB
uiug.30112106882779	39	29	,	,	PUNCT
uiug.30112106882779	39	30	in	in	ADP
uiug.30112106882779	39	31	the	the	DET
uiug.30112106882779	39	32	nonlinear	nonlinear	ADJ
uiug.30112106882779	39	33	case	case	NOUN
uiug.30112106882779	39	34	,	,	PUNCT
uiug.30112106882779	39	35	to	to	ADP
uiug.30112106882779	39	36	a	a	DET
uiug.30112106882779	39	37	set	set	NOUN
uiug.30112106882779	39	38	of	of	ADP
uiug.30112106882779	39	39	coupled	couple	VERB
uiug.30112106882779	39	40	ordinary	ordinary	ADJ
uiug.30112106882779	39	41	differential	differential	ADJ
uiug.30112106882779	39	42	equations	equation	NOUN
uiug.30112106882779	39	43	for	for	ADP
uiug.30112106882779	39	44	the	the	DET
uiug.30112106882779	39	45	elements	element	NOUN
uiug.30112106882779	39	46	of	of	ADP
uiug.30112106882779	39	47	a	a	DET
uiug.30112106882779	39	48	matrix	matrix	NOUN
uiug.30112106882779	39	49	,	,	PUNCT
uiug.30112106882779	39	50	the	the	DET
uiug.30112106882779	39	51	fourierhermite	fourierhermite	NOUN
uiug.30112106882779	39	52	expansion	expansion	NOUN
uiug.30112106882779	39	53	coefficients	coefficient	NOUN
uiug.30112106882779	39	54	of	of	ADP
uiug.30112106882779	39	55	the	the	DET
uiug.30112106882779	39	56	fourier	fourier	ADJ
uiug.30112106882779	39	57	-	-	PUNCT
uiug.30112106882779	39	58	hermite	hermite	NOUN
uiug.30112106882779	39	59	representation	representation	NOUN
uiug.30112106882779	39	60	.	.	PUNCT
uiug.30112106882779	40	1	(	(	PUNCT
uiug.30112106882779	40	2	each	each	DET
uiug.30112106882779	40	3	transformed	transform	VERB
uiug.30112106882779	40	4	set	set	NOUN
uiug.30112106882779	40	5	of	of	ADP
uiug.30112106882779	40	6	equations	equation	NOUN
uiug.30112106882779	40	7	is	be	AUX
uiug.30112106882779	40	8	called	call	VERB
uiug.30112106882779	40	9	a	a	DET
uiug.30112106882779	40	10	representation	representation	NOUN
uiug.30112106882779	40	11	of	of	ADP
uiug.30112106882779	40	12	the	the	DET
uiug.30112106882779	40	13	original	original	ADJ
uiug.30112106882779	40	14	x	x	NOUN
uiug.30112106882779	40	15	-	-	NOUN
uiug.30112106882779	40	16	v	v	ADJ
uiug.30112106882779	40	17	-	-	PUNCT
uiug.30112106882779	40	18	t	t	NOUN
uiug.30112106882779	40	19	equations	equation	NOUN
uiug.30112106882779	40	20	.	.	PUNCT
uiug.30112106882779	40	21	)	)	PUNCT
uiug.30112106882779	41	1	when	when	SCONJ
uiug.30112106882779	41	2	the	the	DET
uiug.30112106882779	41	3	nonlinear	nonlinear	ADJ
uiug.30112106882779	41	4	fourier	fourier	ADJ
uiug.30112106882779	41	5	-	-	PUNCT
uiug.30112106882779	41	6	hermite	hermite	NOUN
uiug.30112106882779	41	7	equations	equation	NOUN
uiug.30112106882779	41	8	are	be	AUX
uiug.30112106882779	41	9	linearized	linearize	VERB
uiug.30112106882779	41	10	and	and	CCONJ
uiug.30112106882779	41	11	an	an	DET
uiug.30112106882779	41	12	eigenvalueeigenvector	eigenvalueeigenvector	NOUN
uiug.30112106882779	41	13	solution	solution	NOUN
uiug.30112106882779	41	14	is	be	AUX
uiug.30112106882779	41	15	sought	seek	VERB
uiug.30112106882779	41	16	,	,	PUNCT
uiug.30112106882779	41	17	another	another	DET
uiug.30112106882779	41	18	matrix	matrix	NOUN
uiug.30112106882779	41	19	appears	appear	VERB
uiug.30112106882779	41	20	,	,	PUNCT
uiug.30112106882779	41	21	the	the	DET
uiug.30112106882779	41	22	fourier	fourier	ADJ
uiug.30112106882779	41	23	-	-	PUNCT
uiug.30112106882779	41	24	hermite	hermite	NOUN
uiug.30112106882779	41	25	dispersion	dispersion	NOUN
uiug.30112106882779	41	26	matrix	matrix	NOUN
uiug.30112106882779	41	27	.	.	PUNCT
uiug.30112106882779	42	1	at	at	ADP
uiug.30112106882779	42	2	this	this	DET
uiug.30112106882779	42	3	point	point	NOUN
uiug.30112106882779	42	4	contact	contact	NOUN
uiug.30112106882779	42	5	is	be	AUX
uiug.30112106882779	42	6	made	make	VERB
uiug.30112106882779	42	7	with	with	ADP
uiug.30112106882779	42	8	two	two	NUM
uiug.30112106882779	42	9	classical	classical	ADJ
uiug.30112106882779	42	10	linearized	linearize	VERB
uiug.30112106882779	42	11	representations	representation	NOUN
uiug.30112106882779	42	12	:	:	PUNCT
uiug.30112106882779	42	13	that	that	PRON
uiug.30112106882779	42	14	of	of	ADP
uiug.30112106882779	42	15	landau	landau	NOUN
uiug.30112106882779	42	16	(	(	PUNCT
uiug.30112106882779	42	17	ref	ref	PROPN
uiug.30112106882779	42	18	.	.	PUNCT
uiug.30112106882779	43	1	1	1	X
uiug.30112106882779	43	2	)	)	PUNCT
uiug.30112106882779	43	3	and	and	CCONJ
uiug.30112106882779	43	4	that	that	PRON
uiug.30112106882779	43	5	of	of	ADP
uiug.30112106882779	43	6	van	van	PROPN
uiug.30112106882779	43	7	kampen	kampen	PROPN
uiug.30112106882779	43	8	(	(	PUNCT
uiug.30112106882779	43	9	ref	ref	PROPN
uiug.30112106882779	43	10	.	.	PUNCT
uiug.30112106882779	44	1	2	2	X
uiug.30112106882779	44	2	)	)	PUNCT
uiug.30112106882779	44	3	.	.	PUNCT
uiug.30112106882779	45	1	landau	landau	NOUN
uiug.30112106882779	45	2	uses	use	VERB
uiug.30112106882779	45	3	a	a	DET
uiug.30112106882779	45	4	fourier	fourier	NOUN
uiug.30112106882779	45	5	-	-	PUNCT
uiug.30112106882779	45	6	laplace	laplace	NOUN
uiug.30112106882779	45	7	transform	transform	NOUN
uiug.30112106882779	45	8	on	on	ADP
uiug.30112106882779	45	9	space	space	NOUN
uiug.30112106882779	45	10	and	and	CCONJ
uiug.30112106882779	45	11	time	time	NOUN
uiug.30112106882779	45	12	,	,	PUNCT
uiug.30112106882779	45	13	while	while	SCONJ
uiug.30112106882779	45	14	van	van	PROPN
uiug.30112106882779	45	15	kampen	kampen	PROPN
uiug.30112106882779	45	16	performs	perform	VERB
uiug.30112106882779	45	17	essentially	essentially	ADV
uiug.30112106882779	45	18	a	a	DET
uiug.30112106882779	45	19	fourier	fourier	NOUN
uiug.30112106882779	45	20	transform	transform	NOUN
uiug.30112106882779	45	21	on	on	ADP
uiug.30112106882779	45	22	both	both	DET
uiug.30112106882779	45	23	space	space	NOUN
uiug.30112106882779	45	24	and	and	CCONJ
uiug.30112106882779	45	25	time	time	NOUN
uiug.30112106882779	45	26	.	.	PUNCT
uiug.30112106882779	46	1	as	as	SCONJ
uiug.30112106882779	46	2	it	it	PRON
uiug.30112106882779	46	3	happens	happen	VERB
uiug.30112106882779	46	4	,	,	PUNCT
uiug.30112106882779	46	5	the	the	DET
uiug.30112106882779	46	6	continuum	continuum	PROPN
uiug.30112106882779	46	7	of	of	ADP
uiug.30112106882779	46	8	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	46	9	in	in	ADP
uiug.30112106882779	46	10	van	van	PROPN
uiug.30112106882779	46	11	kampen	kampen	PROPN
uiug.30112106882779	46	12	's	's	PART
uiug.30112106882779	46	13	representation	representation	NOUN
uiug.30112106882779	46	14	are	be	AUX
uiug.30112106882779	46	15	all	all	ADV
uiug.30112106882779	46	16	undamped	undamped	ADJ
uiug.30112106882779	46	17	(	(	PUNCT
uiug.30112106882779	46	18	real	real	ADJ
uiug.30112106882779	46	19	)	)	PUNCT
uiug.30112106882779	46	20	while	while	SCONJ
uiug.30112106882779	46	21	the	the	DET
uiug.30112106882779	46	22	discrete	discrete	ADJ
uiug.30112106882779	46	23	poles	pole	NOUN
uiug.30112106882779	46	24	of	of	ADP
uiug.30112106882779	46	25	landau	landau	NOUN
uiug.30112106882779	46	26	are	be	AUX
uiug.30112106882779	46	27	all	all	PRON
uiug.30112106882779	46	28	damped	damp	VERB
uiug.30112106882779	46	29	(	(	PUNCT
uiug.30112106882779	46	30	complex	complex	NOUN
uiug.30112106882779	46	31	)	)	PUNCT
uiug.30112106882779	46	32	.	.	PUNCT
uiug.30112106882779	47	1	in	in	ADP
uiug.30112106882779	47	2	particular	particular	ADJ
uiug.30112106882779	47	3	,	,	PUNCT
uiug.30112106882779	47	4	a	a	DET
uiug.30112106882779	47	5	pair	pair	NOUN
uiug.30112106882779	47	6	of	of	ADP
uiug.30112106882779	47	7	highly	highly	ADV
uiug.30112106882779	47	8	excited	excited	ADJ
uiug.30112106882779	47	9	poles	pole	NOUN
uiug.30112106882779	47	10	,	,	PUNCT
uiug.30112106882779	47	11	called	call	VERB
uiug.30112106882779	47	12	landau	landau	NOUN
uiug.30112106882779	47	13	poles	pole	NOUN
uiug.30112106882779	47	14	,	,	PUNCT
uiug.30112106882779	47	15	dominates	dominate	VERB
uiug.30112106882779	47	16	the	the	DET
uiug.30112106882779	47	17	motion	motion	NOUN
uiug.30112106882779	47	18	for	for	ADP
uiug.30112106882779	47	19	long	long	ADJ
uiug.30112106882779	47	20	times	time	NOUN
uiug.30112106882779	47	21	when	when	SCONJ
uiug.30112106882779	47	22	the	the	DET
uiug.30112106882779	47	23	initial	initial	ADJ
uiug.30112106882779	47	24	conditions	condition	NOUN
uiug.30112106882779	47	25	are	be	AUX
uiug.30112106882779	47	26	stable	stable	ADJ
uiug.30112106882779	47	27	.	.	PUNCT
uiug.30112106882779	48	1	the	the	DET
uiug.30112106882779	48	2	fourier	fourier	ADJ
uiug.30112106882779	48	3	-	-	PUNCT
uiug.30112106882779	48	4	hermite	hermite	NOUN
uiug.30112106882779	48	5	representation	representation	NOUN
uiug.30112106882779	48	6	has	have	VERB
uiug.30112106882779	48	7	discrete	discrete	ADJ
uiug.30112106882779	48	8	,	,	PUNCT
uiug.30112106882779	48	9	real	real	ADJ
uiug.30112106882779	48	10	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	48	11	,	,	PUNCT
uiug.30112106882779	48	12	and	and	CCONJ
uiug.30112106882779	48	13	hence	hence	ADV
uiug.30112106882779	48	14	it	it	PRON
uiug.30112106882779	48	15	seems	seem	VERB
uiug.30112106882779	48	16	clearly	clearly	ADV
uiug.30112106882779	48	17	akin	akin	ADJ
uiug.30112106882779	48	18	to	to	ADP
uiug.30112106882779	48	19	van	van	PROPN
uiug.30112106882779	48	20	kampen	kampen	PROPN
uiug.30112106882779	48	21	's	's	PART
uiug.30112106882779	48	22	representation	representation	NOUN
uiug.30112106882779	48	23	.	.	PUNCT
uiug.30112106882779	49	1	when	when	SCONJ
uiug.30112106882779	49	2	numerical	numerical	ADJ
uiug.30112106882779	49	3	integration	integration	NOUN
uiug.30112106882779	49	4	of	of	ADP
uiug.30112106882779	49	5	the	the	DET
uiug.30112106882779	49	6	fourier	fourier	NOUN
uiug.30112106882779	49	7	-	-	PUNCT
uiug.30112106882779	49	8	hermite	hermite	NOUN
uiug.30112106882779	49	9	equations	equation	NOUN
uiug.30112106882779	49	10	is	be	AUX
uiug.30112106882779	49	11	performed	perform	VERB
uiug.30112106882779	49	12	,	,	PUNCT
uiug.30112106882779	49	13	a	a	DET
uiug.30112106882779	49	14	numerical	numerical	ADJ
uiug.30112106882779	49	15	instability	instability	NOUN
uiug.30112106882779	49	16	appears	appear	VERB
uiug.30112106882779	49	17	at	at	ADP
uiug.30112106882779	49	18	the	the	DET
uiug.30112106882779	49	19	highest	high	ADJ
uiug.30112106882779	49	20	order	order	NOUN
uiug.30112106882779	49	21	hermite	hermite	NOUN
uiug.30112106882779	49	22	index	index	NOUN
uiug.30112106882779	49	23	and	and	CCONJ
uiug.30112106882779	49	24	spreads	spread	VERB
uiug.30112106882779	49	25	toward	toward	ADP
uiug.30112106882779	49	26	the	the	DET
uiug.30112106882779	49	27	lower	low	ADJ
uiug.30112106882779	49	28	.	.	PUNCT
uiug.30112106882779	50	1	if	if	SCONJ
uiug.30112106882779	50	2	a	a	DET
uiug.30112106882779	50	3	fokker	fokker	NOUN
uiug.30112106882779	50	4	-	-	PUNCT
uiug.30112106882779	50	5	planck	planck	NOUN
uiug.30112106882779	50	6	(	(	PUNCT
uiug.30112106882779	50	7	weak	weak	ADJ
uiug.30112106882779	50	8	-	-	PUNCT
uiug.30112106882779	50	9	collision	collision	NOUN
uiug.30112106882779	50	10	or	or	CCONJ
uiug.30112106882779	50	11	distant	distant	ADJ
uiug.30112106882779	50	12	-	-	PUNCT
uiug.30112106882779	50	13	encounter	encounter	NOUN
uiug.30112106882779	50	14	)	)	PUNCT
uiug.30112106882779	50	15	term	term	NOUN
uiug.30112106882779	50	16	is	be	AUX
uiug.30112106882779	50	17	introduced	introduce	VERB
uiug.30112106882779	50	18	into	into	ADP
uiug.30112106882779	50	19	the	the	DET
uiug.30112106882779	50	20	fourier	fourier	NOUN
uiug.30112106882779	50	21	-	-	PUNCT
uiug.30112106882779	50	22	hermite	hermite	NOUN
uiug.30112106882779	50	23	representation	representation	NOUN
uiug.30112106882779	50	24	,	,	PUNCT
uiug.30112106882779	50	25	it	it	PRON
uiug.30112106882779	50	26	damps	damp	VERB
uiug.30112106882779	50	27	most	most	ADV
uiug.30112106882779	50	28	strongly	strongly	ADV
uiug.30112106882779	50	29	the	the	DET
uiug.30112106882779	50	30	coefficients	coefficient	NOUN
uiug.30112106882779	50	31	of	of	ADP
uiug.30112106882779	50	32	highest	high	ADJ
uiug.30112106882779	50	33	hermite	hermite	ADJ
uiug.30112106882779	50	34	order	order	NOUN
uiug.30112106882779	50	35	.	.	PUNCT
uiug.30112106882779	51	1	macroscopic	macroscopic	ADJ
uiug.30112106882779	51	2	physical	physical	ADJ
uiug.30112106882779	51	3	entities	entity	NOUN
uiug.30112106882779	51	4	such	such	ADJ
uiug.30112106882779	51	5	as	as	ADP
uiug.30112106882779	51	6	the	the	DET
uiug.30112106882779	51	7	electric	electric	ADJ
uiug.30112106882779	51	8	field	field	NOUN
uiug.30112106882779	51	9	depend	depend	VERB
uiug.30112106882779	51	10	on	on	ADP
uiug.30112106882779	51	11	coefficients	coefficient	NOUN
uiug.30112106882779	51	12	of	of	ADP
uiug.30112106882779	51	13	the	the	DET
uiug.30112106882779	51	14	lowest	low	ADJ
uiug.30112106882779	51	15	orders	order	NOUN
uiug.30112106882779	51	16	,	,	PUNCT
uiug.30112106882779	51	17	and	and	CCONJ
uiug.30112106882779	51	18	thus	thus	ADV
uiug.30112106882779	51	19	the	the	DET
uiug.30112106882779	51	20	selective	selective	ADJ
uiug.30112106882779	51	21	character	character	NOUN
uiug.30112106882779	51	22	of	of	ADP
uiug.30112106882779	51	23	the	the	DET
uiug.30112106882779	51	24	fokker	fokker	PROPN
uiug.30112106882779	51	25	-	-	PUNCT
uiug.30112106882779	51	26	planck	planck	NOUN
uiug.30112106882779	51	27	term	term	NOUN
uiug.30112106882779	51	28	makes	make	VERB
uiug.30112106882779	51	29	it	it	PRON
uiug.30112106882779	51	30	possible	possible	ADJ
uiug.30112106882779	51	31	,	,	PUNCT
uiug.30112106882779	51	32	with	with	ADP
uiug.30112106882779	51	33	many	many	ADJ
uiug.30112106882779	51	34	fourier	fourier	NOUN
uiug.30112106882779	51	35	-	-	PUNCT
uiug.30112106882779	51	36	hermite	hermite	NOUN
uiug.30112106882779	51	37	coefficients	coefficient	NOUN
uiug.30112106882779	51	38	,	,	PUNCT
uiug.30112106882779	51	39	to	to	PART
uiug.30112106882779	51	40	quench	quench	VERB
uiug.30112106882779	51	41	the	the	DET
uiug.30112106882779	51	42	instability	instability	NOUN
uiug.30112106882779	51	43	with	with	ADP
uiug.30112106882779	51	44	few	few	ADJ
uiug.30112106882779	51	45	collisions	collision	NOUN
uiug.30112106882779	51	46	and	and	CCONJ
uiug.30112106882779	51	47	little	little	ADJ
uiug.30112106882779	51	48	degradation	degradation	NOUN
uiug.30112106882779	51	49	of	of	ADP
uiug.30112106882779	51	50	the	the	DET
uiug.30112106882779	51	51	results	result	NOUN
uiug.30112106882779	51	52	.	.	PUNCT
uiug.30112106882779	52	1	at	at	ADP
uiug.30112106882779	52	2	this	this	DET
uiug.30112106882779	52	3	point	point	NOUN
uiug.30112106882779	52	4	the	the	DET
uiug.30112106882779	52	5	fact	fact	NOUN
uiug.30112106882779	52	6	that	that	SCONJ
uiug.30112106882779	52	7	the	the	DET
uiug.30112106882779	52	8	fourier	fourier	ADJ
uiug.30112106882779	52	9	-	-	PUNCT
uiug.30112106882779	52	10	hermite	hermite	NOUN
uiug.30112106882779	52	11	representation	representation	NOUN
uiug.30112106882779	52	12	bridges	bridge	VERB
uiug.30112106882779	52	13	the	the	DET
uiug.30112106882779	52	14	gap	gap	NOUN
uiug.30112106882779	52	15	between	between	ADP
uiug.30112106882779	52	16	landau	landau	NOUN
uiug.30112106882779	52	17	and	and	CCONJ
uiug.30112106882779	52	18	van	van	PROPN
uiug.30112106882779	52	19	kampen	kampen	PROPN
uiug.30112106882779	52	20	representations	representation	NOUN
uiug.30112106882779	52	21	was	be	AUX
uiug.30112106882779	52	22	discovered	discover	VERB
uiug.30112106882779	52	23	(	(	PUNCT
uiug.30112106882779	52	24	ref	ref	NOUN
uiug.30112106882779	52	25	.	.	PUNCT
uiug.30112106882779	52	26	3	3	X
uiug.30112106882779	52	27	)	)	PUNCT
uiug.30112106882779	52	28	.	.	PUNCT
uiug.30112106882779	53	1	in	in	ADP
uiug.30112106882779	53	2	reference	reference	NOUN
uiug.30112106882779	53	3	3	3	NUM
uiug.30112106882779	53	4	the	the	DET
uiug.30112106882779	53	5	transition	transition	NOUN
uiug.30112106882779	53	6	between	between	ADP
uiug.30112106882779	53	7	van	van	PROPN
uiug.30112106882779	53	8	kampen	kampen	PROPN
uiug.30112106882779	53	9	and	and	CCONJ
uiug.30112106882779	53	10	landau	landau	NOUN
uiug.30112106882779	53	11	representations	representation	NOUN
uiug.30112106882779	53	12	of	of	ADP
uiug.30112106882779	53	13	the	the	DET
uiug.30112106882779	53	14	vlasov	vlasov	NOUN
uiug.30112106882779	53	15	equations	equation	NOUN
uiug.30112106882779	53	16	is	be	AUX
uiug.30112106882779	53	17	shown	show	VERB
uiug.30112106882779	53	18	in	in	ADP
uiug.30112106882779	53	19	terms	term	NOUN
uiug.30112106882779	53	20	of	of	ADP
uiug.30112106882779	53	21	a	a	DET
uiug.30112106882779	53	22	delicate	delicate	ADJ
uiug.30112106882779	53	23	limiting	limit	VERB
uiug.30112106882779	53	24	process	process	NOUN
uiug.30112106882779	53	25	that	that	PRON
uiug.30112106882779	53	26	requires	require	VERB
uiug.30112106882779	53	27	an	an	DET
uiug.30112106882779	53	28	indefinite	indefinite	ADJ
uiug.30112106882779	53	29	increase	increase	NOUN
uiug.30112106882779	53	30	in	in	ADP
uiug.30112106882779	53	31	the	the	DET
uiug.30112106882779	53	32	number	number	NOUN
uiug.30112106882779	53	33	of	of	ADP
uiug.30112106882779	53	34	terms	term	NOUN
uiug.30112106882779	53	35	kept	keep	VERB
uiug.30112106882779	53	36	in	in	ADP
uiug.30112106882779	53	37	the	the	DET
uiug.30112106882779	53	38	approximate	approximate	ADJ
uiug.30112106882779	53	39	fourier	fourier	ADJ
uiug.30112106882779	53	40	-	-	PUNCT
uiug.30112106882779	53	41	hermite	hermite	NOUN
uiug.30112106882779	53	42	distribution	distribution	NOUN
uiug.30112106882779	53	43	function	function	NOUN
uiug.30112106882779	53	44	and	and	CCONJ
uiug.30112106882779	53	45	,	,	PUNCT
uiug.30112106882779	53	46	simultaneously	simultaneously	ADV
uiug.30112106882779	53	47	,	,	PUNCT
uiug.30112106882779	53	48	an	an	DET
uiug.30112106882779	53	49	indefinite	indefinite	ADJ
uiug.30112106882779	53	50	decrease	decrease	NOUN
uiug.30112106882779	53	51	in	in	ADP
uiug.30112106882779	53	52	the	the	DET
uiug.30112106882779	53	53	strength	strength	NOUN
uiug.30112106882779	53	54	of	of	ADP
uiug.30112106882779	53	55	the	the	DET
uiug.30112106882779	53	56	introduced	introduce	VERB
uiug.30112106882779	53	57	fokker	fokker	PROPN
uiug.30112106882779	53	58	-	-	PUNCT
uiug.30112106882779	53	59	planck	planck	NOUN
uiug.30112106882779	53	60	collision	collision	NOUN
uiug.30112106882779	53	61	term	term	NOUN
uiug.30112106882779	53	62	.	.	PUNCT
uiug.30112106882779	54	1	a	a	DET
uiug.30112106882779	54	2	full	full	ADJ
uiug.30112106882779	54	3	account	account	NOUN
uiug.30112106882779	54	4	of	of	ADP
uiug.30112106882779	54	5	the	the	DET
uiug.30112106882779	54	6	fourier	fourier	NOUN
uiug.30112106882779	54	7	-	-	PUNCT
uiug.30112106882779	54	8	hermite	hermite	NOUN
uiug.30112106882779	54	9	representation	representation	NOUN
uiug.30112106882779	54	10	may	may	AUX
uiug.30112106882779	54	11	be	be	AUX
uiug.30112106882779	54	12	found	find	VERB
uiug.30112106882779	54	13	in	in	ADP
uiug.30112106882779	54	14	reference	reference	NOUN
uiug.30112106882779	54	15	4	4	NUM
uiug.30112106882779	54	16	.	.	PUNCT
uiug.30112106882779	55	1	the	the	DET
uiug.30112106882779	55	2	full	full	ADJ
uiug.30112106882779	55	3	matrix	matrix	NOUN
uiug.30112106882779	55	4	techniques	technique	NOUN
uiug.30112106882779	55	5	used	use	VERB
uiug.30112106882779	55	6	in	in	ADP
uiug.30112106882779	55	7	reference	reference	NOUN
uiug.30112106882779	55	8	3	3	NUM
uiug.30112106882779	55	9	allowed	allow	VERB
uiug.30112106882779	55	10	only	only	ADV
uiug.30112106882779	55	11	about	about	ADV
uiug.30112106882779	55	12	60	60	NUM
uiug.30112106882779	55	13	terms	term	NOUN
uiug.30112106882779	55	14	to	to	PART
uiug.30112106882779	55	15	be	be	AUX
uiug.30112106882779	55	16	kept	keep	VERB
uiug.30112106882779	55	17	because	because	SCONJ
uiug.30112106882779	55	18	of	of	ADP
uiug.30112106882779	55	19	computer	computer	NOUN
uiug.30112106882779	55	20	storage	storage	NOUN
uiug.30112106882779	55	21	limitations	limitation	NOUN
uiug.30112106882779	55	22	.	.	PUNCT
uiug.30112106882779	56	1	when	when	SCONJ
uiug.30112106882779	56	2	recursion	recursion	NOUN
uiug.30112106882779	56	3	techniques	technique	NOUN
uiug.30112106882779	56	4	are	be	AUX
uiug.30112106882779	56	5	used	use	VERB
uiug.30112106882779	56	6	in	in	ADP
uiug.30112106882779	56	7	the	the	DET
uiug.30112106882779	56	8	tridiagonal	tridiagonal	ADJ
uiug.30112106882779	56	9	dispersion	dispersion	NOUN
uiug.30112106882779	56	10	matrices	matrix	NOUN
uiug.30112106882779	56	11	,	,	PUNCT
uiug.30112106882779	56	12	the	the	DET
uiug.30112106882779	56	13	storage	storage	NOUN
uiug.30112106882779	56	14	required	require	VERB
uiug.30112106882779	56	15	is	be	AUX
uiug.30112106882779	56	16	proportional	proportional	ADJ
uiug.30112106882779	56	17	to	to	ADP
uiug.30112106882779	56	18	the	the	DET
uiug.30112106882779	56	19	matrix	matrix	NOUN
uiug.30112106882779	56	20	order	order	NOUN
uiug.30112106882779	56	21	rather	rather	ADV
uiug.30112106882779	56	22	than	than	ADP
uiug.30112106882779	56	23	to	to	ADP
uiug.30112106882779	56	24	the	the	DET
uiug.30112106882779	56	25	order	order	NOUN
uiug.30112106882779	56	26	squared	square	VERB
uiug.30112106882779	56	27	.	.	PUNCT
uiug.30112106882779	57	1	the	the	DET
uiug.30112106882779	57	2	economy	economy	NOUN
uiug.30112106882779	57	3	of	of	ADP
uiug.30112106882779	57	4	recursive	recursive	ADJ
uiug.30112106882779	57	5	methods	method	NOUN
uiug.30112106882779	57	6	has	have	AUX
uiug.30112106882779	57	7	allowed	allow	VERB
uiug.30112106882779	57	8	the	the	DET
uiug.30112106882779	57	9	calculation	calculation	NOUN
uiug.30112106882779	57	10	of	of	ADP
uiug.30112106882779	57	11	the	the	DET
uiug.30112106882779	57	12	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	57	13	and	and	CCONJ
uiug.30112106882779	57	14	eigenvectors	eigenvector	NOUN
uiug.30112106882779	57	15	for	for	ADP
uiug.30112106882779	57	16	dispersion	dispersion	NOUN
uiug.30112106882779	57	17	matrices	matrix	NOUN
uiug.30112106882779	57	18	larger	large	ADJ
uiug.30112106882779	57	19	than	than	ADP
uiug.30112106882779	57	20	1000	1000	NUM
uiug.30112106882779	57	21	x	x	SYM
uiug.30112106882779	57	22	1000	1000	NUM
uiug.30112106882779	57	23	.	.	PUNCT
uiug.30112106882779	58	1	the	the	DET
uiug.30112106882779	58	2	ability	ability	NOUN
uiug.30112106882779	58	3	to	to	PART
uiug.30112106882779	58	4	treat	treat	VERB
uiug.30112106882779	58	5	fourier	fourier	NOUN
uiug.30112106882779	58	6	-	-	PUNCT
uiug.30112106882779	58	7	hermite	hermite	NOUN
uiug.30112106882779	58	8	matrices	matrix	NOUN
uiug.30112106882779	58	9	of	of	ADP
uiug.30112106882779	58	10	orders	order	NOUN
uiug.30112106882779	58	11	as	as	ADV
uiug.30112106882779	58	12	great	great	ADJ
uiug.30112106882779	58	13	as	as	ADP
uiug.30112106882779	58	14	1000	1000	NUM
uiug.30112106882779	58	15	carries	carry	VERB
uiug.30112106882779	58	16	the	the	DET
uiug.30112106882779	58	17	number	number	NOUN
uiug.30112106882779	58	18	of	of	ADP
uiug.30112106882779	58	19	fourier	fourier	NOUN
uiug.30112106882779	58	20	-	-	PUNCT
uiug.30112106882779	58	21	hermite	hermite	NOUN
uiug.30112106882779	58	22	coefficients	coefficient	VERB
uiug.30112106882779	58	23	far	far	ADV
uiug.30112106882779	58	24	enough	enough	ADV
uiug.30112106882779	58	25	to	to	PART
uiug.30112106882779	58	26	make	make	VERB
uiug.30112106882779	58	27	available	available	ADJ
uiug.30112106882779	58	28	the	the	DET
uiug.30112106882779	58	29	appropriate	appropriate	ADJ
uiug.30112106882779	58	30	value	value	NOUN
uiug.30112106882779	58	31	of	of	ADP
uiug.30112106882779	58	32	fokker	fokker	PROPN
uiug.30112106882779	58	33	-	-	PUNCT
uiug.30112106882779	58	34	planck	planck	NOUN
uiug.30112106882779	58	35	damping	damp	VERB
uiug.30112106882779	58	36	for	for	ADP
uiug.30112106882779	58	37	best	good	ADJ
uiug.30112106882779	58	38	plasma	plasma	NOUN
uiug.30112106882779	58	39	simulation	simulation	NOUN
uiug.30112106882779	58	40	over	over	ADP
uiug.30112106882779	58	41	the	the	DET
uiug.30112106882779	58	42	entire	entire	ADJ
uiug.30112106882779	58	43	practical	practical	ADJ
uiug.30112106882779	58	44	range	range	NOUN
uiug.30112106882779	58	45	of	of	ADP
uiug.30112106882779	58	46	expansion	expansion	NOUN
uiug.30112106882779	58	47	coefficient	coefficient	NOUN
uiug.30112106882779	58	48	order	order	NOUN
uiug.30112106882779	58	49	(	(	PUNCT
uiug.30112106882779	58	50	several	several	ADJ
uiug.30112106882779	58	51	hundred	hundred	NUM
uiug.30112106882779	58	52	)	)	PUNCT
uiug.30112106882779	58	53	for	for	ADP
uiug.30112106882779	58	54	the	the	DET
uiug.30112106882779	58	55	nonlinear	nonlinear	ADJ
uiug.30112106882779	58	56	problem	problem	NOUN
uiug.30112106882779	58	57	.	.	PUNCT
uiug.30112106882779	59	1	in	in	ADP
uiug.30112106882779	59	2	the	the	DET
uiug.30112106882779	59	3	general	general	ADJ
uiug.30112106882779	59	4	,	,	PUNCT
uiug.30112106882779	59	5	nonlinear	nonlinear	ADJ
uiug.30112106882779	59	6	problem	problem	NOUN
uiug.30112106882779	59	7	,	,	PUNCT
uiug.30112106882779	59	8	as	as	ADP
uiug.30112106882779	59	9	in	in	ADP
uiug.30112106882779	59	10	the	the	DET
uiug.30112106882779	59	11	linear	linear	ADJ
uiug.30112106882779	59	12	problem	problem	NOUN
uiug.30112106882779	59	13	,	,	PUNCT
uiug.30112106882779	59	14	addition	addition	NOUN
uiug.30112106882779	59	15	of	of	ADP
uiug.30112106882779	59	16	a	a	DET
uiug.30112106882779	59	17	small	small	ADJ
uiug.30112106882779	59	18	damping	damp	VERB
uiug.30112106882779	59	19	term	term	NOUN
uiug.30112106882779	59	20	of	of	ADP
uiug.30112106882779	59	21	proper	proper	ADJ
uiug.30112106882779	59	22	strength	strength	NOUN
uiug.30112106882779	59	23	extends	extend	VERB
uiug.30112106882779	59	24	the	the	DET
uiug.30112106882779	59	25	time	time	NOUN
uiug.30112106882779	59	26	of	of	ADP
uiug.30112106882779	59	27	good	good	ADJ
uiug.30112106882779	59	28	simulation	simulation	NOUN
uiug.30112106882779	59	29	at	at	ADP
uiug.30112106882779	59	30	the	the	DET
uiug.30112106882779	59	31	cost	cost	NOUN
uiug.30112106882779	59	32	of	of	ADP
uiug.30112106882779	59	33	slightly	slightly	ADV
uiug.30112106882779	59	34	degraded	degrade	VERB
uiug.30112106882779	59	35	results	result	NOUN
uiug.30112106882779	59	36	.	.	PUNCT
uiug.30112106882779	60	1	2	2	NUM
uiug.30112106882779	60	2	symbols	symbol	NOUN
uiug.30112106882779	60	3	aaß	aaß	PROPN
uiug.30112106882779	60	4	fourier	fourier	NOUN
uiug.30112106882779	60	5	-	-	PUNCT
uiug.30112106882779	60	6	hermite	hermite	NOUN
uiug.30112106882779	60	7	expansion	expansion	NOUN
uiug.30112106882779	60	8	coefficient	coefficient	NOUN
uiug.30112106882779	60	9	b	b	PROPN
uiug.30112106882779	60	10	strength	strength	PROPN
uiug.30112106882779	60	11	parameter	parameter	NOUN
uiug.30112106882779	60	12	of	of	ADP
uiug.30112106882779	60	13	fokker	fokker	PROPN
uiug.30112106882779	60	14	-	-	PUNCT
uiug.30112106882779	60	15	planck	planck	NOUN
uiug.30112106882779	60	16	collision	collision	NOUN
uiug.30112106882779	60	17	term	term	NOUN
uiug.30112106882779	60	18	c(f	c(f	PROPN
uiug.30112106882779	60	19	)	)	PUNCT
uiug.30112106882779	60	20	collision	collision	NOUN
uiug.30112106882779	60	21	term	term	NOUN
uiug.30112106882779	60	22	dn	dn	NOUN
uiug.30112106882779	60	23	determinant	determinant	NOUN
uiug.30112106882779	60	24	of	of	ADP
uiug.30112106882779	60	25	fourier	fourier	NOUN
uiug.30112106882779	60	26	-	-	PUNCT
uiug.30112106882779	60	27	hermite	hermite	NOUN
uiug.30112106882779	60	28	dispersion	dispersion	NOUN
uiug.30112106882779	60	29	matrix	matrix	NOUN
uiug.30112106882779	60	30	e	e	PROPN
uiug.30112106882779	60	31	electric	electric	PROPN
uiug.30112106882779	60	32	field	field	PROPN
uiug.30112106882779	60	33	e	e	NOUN
uiug.30112106882779	60	34	magnitude	magnitude	NOUN
uiug.30112106882779	60	35	of	of	ADP
uiug.30112106882779	60	36	electronic	electronic	ADJ
uiug.30112106882779	60	37	charge	charge	NOUN
uiug.30112106882779	60	38	f	f	PROPN
uiug.30112106882779	60	39	maxwellian	maxwellian	PROPN
uiug.30112106882779	60	40	velocity	velocity	NOUN
uiug.30112106882779	60	41	distribution	distribution	NOUN
uiug.30112106882779	60	42	,	,	PUNCT
uiug.30112106882779	60	43	exp(-v2/2	exp(-v2/2	PROPN
uiug.30112106882779	60	44	)	)	PUNCT
uiug.30112106882779	60	45	v21	v21	NOUN
uiug.30112106882779	60	46	27	27	NUM
uiug.30112106882779	60	47	f	f	PROPN
uiug.30112106882779	60	48	'	'	PUNCT
uiug.30112106882779	60	49	df	df	NOUN
uiug.30112106882779	60	50	=	=	X
uiug.30112106882779	60	51	dv	dv	PROPN
uiug.30112106882779	60	52	f	f	X
uiug.30112106882779	60	53	{	{	PUNCT
uiug.30112106882779	60	54	}	}	PUNCT
uiug.30112106882779	60	55	fourier	fourier	NOUN
uiug.30112106882779	60	56	-	-	PUNCT
uiug.30112106882779	60	57	transform	transform	NOUN
uiug.30112106882779	60	58	operator	operator	NOUN
uiug.30112106882779	60	59	f	f	PROPN
uiug.30112106882779	60	60	distribution	distribution	NOUN
uiug.30112106882779	60	61	function	function	NOUN
uiug.30112106882779	60	62	of	of	ADP
uiug.30112106882779	60	63	electrons	electron	NOUN
uiug.30112106882779	60	64	fo	fo	ADP
uiug.30112106882779	60	65	fourier	fourier	NOUN
uiug.30112106882779	60	66	transform	transform	NOUN
uiug.30112106882779	60	67	of	of	ADP
uiug.30112106882779	60	68	initial	initial	ADJ
uiug.30112106882779	60	69	perturbation	perturbation	NOUN
uiug.30112106882779	60	70	in	in	ADP
uiug.30112106882779	60	71	f	f	PROPN
uiug.30112106882779	60	72	ft	ft	PROPN
uiug.30112106882779	60	73	fokker	fokker	PROPN
uiug.30112106882779	60	74	-	-	PUNCT
uiug.30112106882779	60	75	planck	planck	NOUN
uiug.30112106882779	60	76	collision	collision	NOUN
uiug.30112106882779	60	77	term	term	NOUN
uiug.30112106882779	60	78	#	#	SYM
uiug.30112106882779	60	79	g	g	NOUN
uiug.30112106882779	60	80	h	h	NOUN
uiug.30112106882779	60	81	в	в	PROPN
uiug.30112106882779	60	82	hermite	hermite	PROPN
uiug.30112106882779	60	83	polynomial	polynomial	NOUN
uiug.30112106882779	60	84	of	of	ADP
uiug.30112106882779	60	85	order	order	NOUN
uiug.30112106882779	61	1	b	b	NOUN
uiug.30112106882779	61	2	i	i	PRON
uiug.30112106882779	61	3	=	=	VERB
uiug.30112106882779	61	4	v-1	v-1	X
uiug.30112106882779	61	5	=	=	PRON
uiug.30112106882779	61	6	211	211	NUM
uiug.30112106882779	61	7	k	k	PROPN
uiug.30112106882779	61	8	wave	wave	NOUN
uiug.30112106882779	61	9	number	number	NOUN
uiug.30112106882779	61	10	,	,	PUNCT
uiug.30112106882779	61	11	boltzmann	boltzmann	PROPN
uiug.30112106882779	61	12	constant	constant	ADJ
uiug.30112106882779	61	13	wavelength	wavelength	PROPN
uiug.30112106882779	61	14	l	l	PROPN
uiug.30112106882779	61	15	laplace	laplace	NOUN
uiug.30112106882779	61	16	-	-	PUNCT
uiug.30112106882779	61	17	transform	transform	NOUN
uiug.30112106882779	61	18	operator	operator	NOUN
uiug.30112106882779	61	19	m	m	NOUN
uiug.30112106882779	61	20	electronic	electronic	ADJ
uiug.30112106882779	61	21	mass	mass	NOUN
uiug.30112106882779	61	22	n	n	ADP
uiug.30112106882779	61	23	order	order	NOUN
uiug.30112106882779	61	24	of	of	ADP
uiug.30112106882779	61	25	highest	high	ADJ
uiug.30112106882779	61	26	term	term	NOUN
uiug.30112106882779	61	27	kept	keep	VERB
uiug.30112106882779	61	28	in	in	ADP
uiug.30112106882779	61	29	fourier	fourier	NOUN
uiug.30112106882779	61	30	-	-	PUNCT
uiug.30112106882779	61	31	hermite	hermite	NOUN
uiug.30112106882779	61	32	expansion	expansion	NOUN
uiug.30112106882779	61	33	of	of	ADP
uiug.30112106882779	61	34	f	f	PROPN
uiug.30112106882779	61	35	n	n	CCONJ
uiug.30112106882779	61	36	electron	electron	NOUN
uiug.30112106882779	61	37	density	density	NOUN
uiug.30112106882779	61	38	;	;	PUNCT
uiug.30112106882779	61	39	fourier	fourier	NOUN
uiug.30112106882779	61	40	-	-	PUNCT
uiug.30112106882779	61	41	laplace	laplace	NOUN
uiug.30112106882779	61	42	transform	transform	NOUN
uiug.30112106882779	61	43	of	of	ADP
uiug.30112106882779	61	44	electron	electron	NOUN
uiug.30112106882779	61	45	density	density	NOUN
uiug.30112106882779	61	46	3	3	NUM
uiug.30112106882779	62	1	no	no	DET
uiug.30112106882779	62	2	mean	mean	ADJ
uiug.30112106882779	62	3	electron	electron	NOUN
uiug.30112106882779	62	4	density	density	NOUN
uiug.30112106882779	62	5	s	s	PART
uiug.30112106882779	62	6	complex	complex	ADJ
uiug.30112106882779	62	7	argument	argument	NOUN
uiug.30112106882779	62	8	of	of	ADP
uiug.30112106882779	62	9	laplace	laplace	NOUN
uiug.30112106882779	62	10	transform	transform	VERB
uiug.30112106882779	62	11	t	t	PROPN
uiug.30112106882779	62	12	absolute	absolute	ADJ
uiug.30112106882779	62	13	temperature	temperature	NOUN
uiug.30112106882779	62	14	t	t	PROPN
uiug.30112106882779	62	15	time	time	PROPN
uiug.30112106882779	62	16	v	v	PROPN
uiug.30112106882779	62	17	electron	electron	NOUN
uiug.30112106882779	62	18	velocity	velocity	NOUN
uiug.30112106882779	62	19	v3,0	v3,0	DET
uiug.30112106882779	62	20	first	first	ADJ
uiug.30112106882779	62	21	component	component	NOUN
uiug.30112106882779	62	22	of	of	ADP
uiug.30112106882779	62	23	normalized	normalized	ADJ
uiug.30112106882779	62	24	eigenvector	eigenvector	NOUN
uiug.30112106882779	62	25	corresponding	correspond	VERB
uiug.30112106882779	62	26	to	to	ADP
uiug.30112106882779	62	27	jth	jth	PROPN
uiug.30112106882779	62	28	eigenvelocity	eigenvelocity	PROPN
uiug.30112106882779	62	29	w	w	PROPN
uiug.30112106882779	62	30	w	w	PROPN
uiug.30112106882779	62	31	;	;	PUNCT
uiug.30112106882779	62	32	w	w	ADJ
uiug.30112106882779	62	33	phase	phase	NOUN
uiug.30112106882779	62	34	velocity	velocity	NOUN
uiug.30112106882779	62	35	,	,	PUNCT
uiug.30112106882779	62	36	w	w	PROPN
uiug.30112106882779	62	37	/	/	SYM
uiug.30112106882779	62	38	k	k	PROPN
uiug.30112106882779	62	39	wn	wn	PROPN
uiug.30112106882779	62	40	nth	nth	PROPN
uiug.30112106882779	62	41	eigenvelocity	eigenvelocity	PROPN
uiug.30112106882779	62	42	x	x	SYM
uiug.30112106882779	62	43	spatial	spatial	ADJ
uiug.30112106882779	62	44	coordinate	coordinate	NOUN
uiug.30112106882779	62	45	a	a	DET
uiug.30112106882779	62	46	,	,	PUNCT
uiug.30112106882779	62	47	ß	ß	NUM
uiug.30112106882779	62	48	fourier	fourier	NOUN
uiug.30112106882779	62	49	and	and	CCONJ
uiug.30112106882779	62	50	hermite	hermite	NOUN
uiug.30112106882779	62	51	indices	index	NOUN
uiug.30112106882779	62	52	,	,	PUNCT
uiug.30112106882779	62	53	respectively	respectively	ADV
uiug.30112106882779	62	54	-γ	-γ	PUNCT
uiug.30112106882779	62	55	imaginary	imaginary	ADJ
uiug.30112106882779	62	56	part	part	NOUN
uiug.30112106882779	62	57	of	of	ADP
uiug.30112106882779	62	58	w	w	X
uiug.30112106882779	62	59	(	(	PUNCT
uiug.30112106882779	62	60	y	y	PROPN
uiug.30112106882779	62	61	is	be	AUX
uiug.30112106882779	62	62	negative	negative	ADJ
uiug.30112106882779	62	63	for	for	ADP
uiug.30112106882779	62	64	stability	stability	NOUN
uiug.30112106882779	62	65	)	)	PUNCT
uiug.30112106882779	62	66	ab	ab	PROPN
uiug.30112106882779	62	67	arbitrary	arbitrary	ADJ
uiug.30112106882779	62	68	small	small	ADJ
uiug.30112106882779	62	69	increment	increment	NOUN
uiug.30112106882779	62	70	in	in	ADP
uiug.30112106882779	62	71	b	b	NOUN
uiug.30112106882779	62	72	ad	ad	NOUN
uiug.30112106882779	62	73	change	change	NOUN
uiug.30112106882779	62	74	in	in	ADP
uiug.30112106882779	62	75	dn	dn	NOUN
uiug.30112106882779	62	76	when	when	SCONJ
uiug.30112106882779	62	77	w	w	PROPN
uiug.30112106882779	62	78	becomes	become	VERB
uiug.30112106882779	62	79	w	w	ADJ
uiug.30112106882779	63	1	+	+	ADJ
uiug.30112106882779	63	2	aw	aw	INTJ
uiug.30112106882779	63	3	n	n	CCONJ
uiug.30112106882779	63	4	δω	δω	X
uiug.30112106882779	63	5	arbitrary	arbitrary	ADJ
uiug.30112106882779	63	6	small	small	ADJ
uiug.30112106882779	63	7	change	change	NOUN
uiug.30112106882779	63	8	in	in	ADP
uiug.30112106882779	63	9	3	3	NUM
uiug.30112106882779	63	10	8	8	NUM
uiug.30112106882779	63	11	small	small	ADJ
uiug.30112106882779	63	12	positive	positive	ADJ
uiug.30112106882779	63	13	quantity	quantity	NOUN
uiug.30112106882779	63	14	δαβ	δαβ	NOUN
uiug.30112106882779	63	15	kronecker	kronecker	PROPN
uiug.30112106882779	63	16	delta	delta	PROPN
uiug.30112106882779	63	17	e	e	PROPN
uiug.30112106882779	63	18	plasma	plasma	NOUN
uiug.30112106882779	63	19	dielectric	dielectric	NOUN
uiug.30112106882779	63	20	constant	constant	ADJ
uiug.30112106882779	63	21	fo	fo	ADP
uiug.30112106882779	63	22	€	€	SYM
uiug.30112106882779	63	23	(	(	PUNCT
uiug.30112106882779	63	24	k	k	PROPN
uiug.30112106882779	63	25	,	,	PUNCT
uiug.30112106882779	63	26	w=0	w=0	PROPN
uiug.30112106882779	63	27	)	)	PUNCT
uiug.30112106882779	63	28	;	;	PUNCT
uiug.30112106882779	63	29	permittivity	permittivity	ADJ
uiug.30112106882779	63	30	of	of	ADP
uiug.30112106882779	63	31	vacuum	vacuum	NOUN
uiug.30112106882779	63	32	a	a	DET
uiug.30112106882779	63	33	eigenvelocity	eigenvelocity	NOUN
uiug.30112106882779	63	34	3	3	NUM
uiug.30112106882779	63	35	complex	complex	ADJ
uiug.30112106882779	63	36	argument	argument	NOUN
uiug.30112106882779	63	37	,	,	PUNCT
uiug.30112106882779	63	38	w	w	PROPN
uiug.30112106882779	63	39	/	/	SYM
uiug.30112106882779	63	40	k/2	k/2	PROPN
uiug.30112106882779	63	41	4	4	NUM
uiug.30112106882779	63	42	w	w	PROPN
uiug.30112106882779	63	43	n(k	n(k	PROPN
uiug.30112106882779	63	44	,	,	PUNCT
uiug.30112106882779	63	45	s	s	PART
uiug.30112106882779	63	46	)	)	PUNCT
uiug.30112106882779	63	47	9	9	NUM
uiug.30112106882779	63	48	ik2	ik2	PROPN
uiug.30112106882779	63	49	&	&	CCONJ
uiug.30112106882779	63	50	fourier	fourier	NOUN
uiug.30112106882779	63	51	transform	transform	NOUN
uiug.30112106882779	63	52	of	of	ADP
uiug.30112106882779	63	53	time	time	NOUN
uiug.30112106882779	63	54	variation	variation	NOUN
uiug.30112106882779	63	55	of	of	ADP
uiug.30112106882779	63	56	n	n	NOUN
uiug.30112106882779	63	57	4j	4j	NOUN
uiug.30112106882779	63	58	,	,	PUNCT
uiug.30112106882779	63	59	j+1	j+1	X
uiug.30112106882779	63	60	ordinate	ordinate	NOUN
uiug.30112106882779	63	61	of	of	ADP
uiug.30112106882779	63	62	histogram	histogram	NOUN
uiug.30112106882779	63	63	between	between	ADP
uiug.30112106882779	63	64	w	w	PROPN
uiug.30112106882779	63	65	;	;	PUNCT
uiug.30112106882779	63	66	and	and	CCONJ
uiug.30112106882779	63	67	w	w	PROPN
uiug.30112106882779	63	68	,	,	PUNCT
uiug.30112106882779	63	69	w	w	ADP
uiug.30112106882779	63	70	j+1	j+1	X
uiug.30112106882779	63	71	3	3	NUM
uiug.30112106882779	63	72	argument	argument	NOUN
uiug.30112106882779	63	73	of	of	ADP
uiug.30112106882779	63	74	dn	dn	NOUN
uiug.30112106882779	63	75	;	;	PUNCT
uiug.30112106882779	63	76	complex	complex	ADJ
uiug.30112106882779	63	77	eigenvalue	eigenvalue	NOUN
uiug.30112106882779	63	78	(	(	PUNCT
uiug.30112106882779	63	79	root	root	NOUN
uiug.30112106882779	63	80	,	,	PUNCT
uiug.30112106882779	63	81	pole	pole	NOUN
uiug.30112106882779	63	82	,	,	PUNCT
uiug.30112106882779	63	83	eigenfrequency	eigenfrequency	NOUN
uiug.30112106882779	63	84	)	)	PUNCT
uiug.30112106882779	63	85	;	;	PUNCT
uiug.30112106882779	63	86	s	s	VERB
uiug.30112106882779	63	87	/	/	PUNCT
uiug.30112106882779	63	88	i	i	PRON
uiug.30112106882779	63	89	'	'	VERB
uiug.30112106882779	63	90	36	36	NUM
uiug.30112106882779	63	91	nth	nth	NOUN
uiug.30112106882779	63	92	order	order	NOUN
uiug.30112106882779	63	93	approximation	approximation	NOUN
uiug.30112106882779	63	94	to	to	PART
uiug.30112106882779	63	95	eigenvalue	eigenvalue	NOUN
uiug.30112106882779	63	96	average	average	NOUN
uiug.30112106882779	63	97	over	over	ADP
uiug.30112106882779	63	98	velocity	velocity	NOUN
uiug.30112106882779	63	99	space	space	NOUN
uiug.30112106882779	63	100	subscripts	subscript	NOUN
uiug.30112106882779	63	101	:	:	PUNCT
uiug.30112106882779	63	102	i	i	PRON
uiug.30112106882779	63	103	imaginary	imaginary	ADJ
uiug.30112106882779	63	104	part	part	NOUN
uiug.30112106882779	63	105	r	r	NOUN
uiug.30112106882779	63	106	real	real	ADJ
uiug.30112106882779	63	107	part	part	NOUN
uiug.30112106882779	63	108	superscript	superscript	NOUN
uiug.30112106882779	63	109	:	:	PUNCT
uiug.30112106882779	63	110	*	*	PUNCT
uiug.30112106882779	63	111	complex	complex	ADJ
uiug.30112106882779	63	112	conjugate	conjugate	NOUN
uiug.30112106882779	63	113	analysis	analysis	NOUN
uiug.30112106882779	63	114	fourier	fourier	NOUN
uiug.30112106882779	63	115	-	-	PUNCT
uiug.30112106882779	63	116	hermite	hermite	NOUN
uiug.30112106882779	63	117	representation	representation	NOUN
uiug.30112106882779	63	118	consider	consider	VERB
uiug.30112106882779	63	119	the	the	DET
uiug.30112106882779	63	120	ordinary	ordinary	ADJ
uiug.30112106882779	63	121	one	one	NUM
uiug.30112106882779	63	122	-	-	PUNCT
uiug.30112106882779	63	123	dimensional	dimensional	ADJ
uiug.30112106882779	63	124	boltzmann	boltzmann	PROPN
uiug.30112106882779	63	125	equation	equation	NOUN
uiug.30112106882779	63	126	(	(	PUNCT
uiug.30112106882779	63	127	in	in	ADP
uiug.30112106882779	63	128	natural	natural	ADJ
uiug.30112106882779	63	129	units	unit	NOUN
uiug.30112106882779	63	130	)	)	PUNCT
uiug.30112106882779	63	131	for	for	ADP
uiug.30112106882779	63	132	the	the	DET
uiug.30112106882779	63	133	single	single	ADJ
uiug.30112106882779	63	134	-	-	PUNCT
uiug.30112106882779	63	135	particle	particle	NOUN
uiug.30112106882779	63	136	distribution	distribution	NOUN
uiug.30112106882779	63	137	function	function	NOUN
uiug.30112106882779	63	138	f	f	PROPN
uiug.30112106882779	63	139	of	of	ADP
uiug.30112106882779	63	140	the	the	DET
uiug.30112106882779	63	141	electrons	electron	NOUN
uiug.30112106882779	63	142	:	:	PUNCT
uiug.30112106882779	63	143	if	if	SCONJ
uiug.30112106882779	63	144	+	+	CCONJ
uiug.30112106882779	63	145	v	v	NOUN
uiug.30112106882779	63	146	e	e	X
uiug.30112106882779	63	147	o	o	X
uiug.30112106882779	63	148	=	=	PUNCT
uiug.30112106882779	63	149	c(1	c(1	PROPN
uiug.30112106882779	63	150	)	)	PUNCT
uiug.30112106882779	64	1	af	af	PROPN
uiug.30112106882779	65	1	+	+	INTJ
uiug.30112106882779	65	2	af	af	INTJ
uiug.30112106882779	65	3	af	af	INTJ
uiug.30112106882779	65	4	ax	ax	PROPN
uiug.30112106882779	65	5	e	e	X
uiug.30112106882779	65	6	f	f	X
uiug.30112106882779	65	7	(	(	PUNCT
uiug.30112106882779	65	8	1	1	X
uiug.30112106882779	65	9	)	)	PUNCT
uiug.30112106882779	65	10	ду	ду	X
uiug.30112106882779	65	11	where	where	SCONJ
uiug.30112106882779	65	12	the	the	DET
uiug.30112106882779	65	13	right	right	ADJ
uiug.30112106882779	65	14	-	-	PUNCT
uiug.30112106882779	65	15	hand	hand	NOUN
uiug.30112106882779	65	16	side	side	NOUN
uiug.30112106882779	65	17	denotes	denote	VERB
uiug.30112106882779	65	18	a	a	DET
uiug.30112106882779	65	19	collision	collision	NOUN
uiug.30112106882779	65	20	term	term	NOUN
uiug.30112106882779	65	21	that	that	PRON
uiug.30112106882779	65	22	is	be	AUX
uiug.30112106882779	65	23	a	a	DET
uiug.30112106882779	65	24	functional	functional	ADJ
uiug.30112106882779	65	25	off	off	ADP
uiug.30112106882779	65	26	.	.	PUNCT
uiug.30112106882779	66	1	the	the	DET
uiug.30112106882779	66	2	natural	natural	ADJ
uiug.30112106882779	66	3	units	unit	NOUN
uiug.30112106882779	66	4	of	of	ADP
uiug.30112106882779	66	5	equation	equation	NOUN
uiug.30112106882779	66	6	(	(	PUNCT
uiug.30112106882779	66	7	1	1	X
uiug.30112106882779	66	8	)	)	PUNCT
uiug.30112106882779	66	9	are	be	AUX
uiug.30112106882779	66	10	lekt	lekt	NOUN
uiug.30112106882779	67	1	debye	debye	ADJ
uiug.30112106882779	67	2	length	length	NOUN
uiug.30112106882779	67	3	noe2	noe2	PROPN
uiug.30112106882779	67	4	監	監	ADV
uiug.30112106882779	67	5	​ikt	​ikt	ADJ
uiug.30112106882779	67	6	thermal	thermal	ADJ
uiug.30112106882779	67	7	speed	speed	NOUN
uiug.30112106882779	67	8	ut	ut	PROPN
uiug.30112106882779	67	9	5	5	NUM
uiug.30112106882779	67	10	com	com	NOUN
uiug.30112106882779	67	11	inverse	inverse	NOUN
uiug.30112106882779	67	12	plasma	plasma	NOUN
uiug.30112106882779	67	13	frequency	frequency	NOUN
uiug.30112106882779	67	14	ne2	ne2	PROPN
uiug.30112106882779	68	1	the	the	DET
uiug.30112106882779	68	2	debye	debye	ADJ
uiug.30112106882779	68	3	length	length	NOUN
uiug.30112106882779	68	4	is	be	AUX
uiug.30112106882779	68	5	a	a	DET
uiug.30112106882779	68	6	measure	measure	NOUN
uiug.30112106882779	68	7	of	of	ADP
uiug.30112106882779	68	8	the	the	DET
uiug.30112106882779	68	9	distance	distance	NOUN
uiug.30112106882779	68	10	at	at	ADP
uiug.30112106882779	68	11	which	which	PRON
uiug.30112106882779	68	12	an	an	DET
uiug.30112106882779	68	13	introduced	introduce	VERB
uiug.30112106882779	68	14	charge	charge	NOUN
uiug.30112106882779	68	15	is	be	AUX
uiug.30112106882779	68	16	screened	screen	VERB
uiug.30112106882779	68	17	,	,	PUNCT
uiug.30112106882779	68	18	and	and	CCONJ
uiug.30112106882779	68	19	the	the	DET
uiug.30112106882779	68	20	plasma	plasma	NOUN
uiug.30112106882779	68	21	frequency	frequency	NOUN
uiug.30112106882779	68	22	measures	measure	VERB
uiug.30112106882779	68	23	the	the	DET
uiug.30112106882779	68	24	rapidity	rapidity	NOUN
uiug.30112106882779	68	25	of	of	ADP
uiug.30112106882779	68	26	oscillations	oscillation	NOUN
uiug.30112106882779	68	27	in	in	ADP
uiug.30112106882779	68	28	electron	electron	NOUN
uiug.30112106882779	68	29	density	density	NOUN
uiug.30112106882779	68	30	.	.	PUNCT
uiug.30112106882779	69	1	a	a	DET
uiug.30112106882779	69	2	neutralizing	neutralize	VERB
uiug.30112106882779	69	3	uniform	uniform	ADJ
uiug.30112106882779	69	4	positive	positive	ADJ
uiug.30112106882779	69	5	background	background	NOUN
uiug.30112106882779	69	6	is	be	AUX
uiug.30112106882779	69	7	assumed	assume	VERB
uiug.30112106882779	69	8	.	.	PUNCT
uiug.30112106882779	70	1	the	the	DET
uiug.30112106882779	70	2	external	external	ADJ
uiug.30112106882779	70	3	field	field	NOUN
uiug.30112106882779	70	4	e	e	NOUN
uiug.30112106882779	70	5	acting	act	VERB
uiug.30112106882779	70	6	on	on	ADP
uiug.30112106882779	70	7	the	the	DET
uiug.30112106882779	70	8	electrons	electron	NOUN
uiug.30112106882779	70	9	is	be	AUX
uiug.30112106882779	70	10	the	the	DET
uiug.30112106882779	70	11	self	self	NOUN
uiug.30112106882779	70	12	-	-	PUNCT
uiug.30112106882779	70	13	field	field	NOUN
uiug.30112106882779	70	14	of	of	ADP
uiug.30112106882779	70	15	the	the	DET
uiug.30112106882779	70	16	electrons	electron	NOUN
uiug.30112106882779	70	17	themselves	themselves	PRON
uiug.30112106882779	70	18	given	give	VERB
uiug.30112106882779	70	19	by	by	ADP
uiug.30112106882779	70	20	poisson	poisson	PROPN
uiug.30112106882779	70	21	's	's	PART
uiug.30112106882779	70	22	equation	equation	NOUN
uiug.30112106882779	70	23	:	:	PUNCT
uiug.30112106882779	70	24	ae	ae	PROPN
uiug.30112106882779	70	25	ax	ax	PROPN
uiug.30112106882779	70	26	sand	sand	NOUN
uiug.30112106882779	70	27	1	1	NUM
uiug.30112106882779	70	28	(	(	PUNCT
uiug.30112106882779	70	29	2	2	NUM
uiug.30112106882779	70	30	)	)	PUNCT
uiug.30112106882779	70	31	if	if	SCONJ
uiug.30112106882779	70	32	the	the	DET
uiug.30112106882779	70	33	number	number	NOUN
uiug.30112106882779	70	34	of	of	ADP
uiug.30112106882779	70	35	particles	particle	NOUN
uiug.30112106882779	70	36	in	in	ADP
uiug.30112106882779	70	37	a	a	DET
uiug.30112106882779	70	38	debye	debye	ADJ
uiug.30112106882779	70	39	cube	cube	NOUN
uiug.30112106882779	70	40	is	be	AUX
uiug.30112106882779	70	41	large	large	ADJ
uiug.30112106882779	70	42	,	,	PUNCT
uiug.30112106882779	70	43	as	as	ADP
uiug.30112106882779	70	44	in	in	ADP
uiug.30112106882779	70	45	a	a	DET
uiug.30112106882779	70	46	thermonuclear	thermonuclear	ADJ
uiug.30112106882779	70	47	plasma	plasma	NOUN
uiug.30112106882779	70	48	,	,	PUNCT
uiug.30112106882779	70	49	the	the	DET
uiug.30112106882779	70	50	collision	collision	NOUN
uiug.30112106882779	70	51	term	term	NOUN
uiug.30112106882779	70	52	c	c	NOUN
uiug.30112106882779	70	53	may	may	AUX
uiug.30112106882779	70	54	be	be	AUX
uiug.30112106882779	70	55	neglected	neglect	VERB
uiug.30112106882779	70	56	.	.	PUNCT
uiug.30112106882779	71	1	in	in	ADP
uiug.30112106882779	71	2	the	the	DET
uiug.30112106882779	71	3	case	case	NOUN
uiug.30112106882779	71	4	of	of	ADP
uiug.30112106882779	71	5	identically	identically	ADV
uiug.30112106882779	71	6	vanishing	vanish	VERB
uiug.30112106882779	71	7	c	c	PROPN
uiug.30112106882779	71	8	,	,	PUNCT
uiug.30112106882779	71	9	equations	equation	NOUN
uiug.30112106882779	71	10	(	(	PUNCT
uiug.30112106882779	71	11	1	1	NUM
uiug.30112106882779	71	12	)	)	PUNCT
uiug.30112106882779	71	13	and	and	CCONJ
uiug.30112106882779	71	14	(	(	PUNCT
uiug.30112106882779	71	15	2	2	X
uiug.30112106882779	71	16	)	)	PUNCT
uiug.30112106882779	71	17	are	be	AUX
uiug.30112106882779	71	18	known	know	VERB
uiug.30112106882779	71	19	as	as	ADP
uiug.30112106882779	71	20	vlasov	vlasov	NOUN
uiug.30112106882779	71	21	equations	equation	NOUN
uiug.30112106882779	71	22	.	.	PUNCT
uiug.30112106882779	72	1	the	the	DET
uiug.30112106882779	72	2	fourier	fourier	ADJ
uiug.30112106882779	72	3	-	-	PUNCT
uiug.30112106882779	72	4	hermite	hermite	NOUN
uiug.30112106882779	72	5	expansion	expansion	NOUN
uiug.30112106882779	72	6	of	of	ADP
uiug.30112106882779	72	7	f	f	PROPN
uiug.30112106882779	72	8	is	be	AUX
uiug.30112106882779	72	9	v27	v27	NOUN
uiug.30112106882779	72	10	f	f	X
uiug.30112106882779	72	11	=	=	X
uiug.30112106882779	72	12	a=-b=0	a=-b=0	X
uiug.30112106882779	72	13	[	[	PUNCT
uiug.30112106882779	72	14	acp	acp	PROPN
uiug.30112106882779	72	15	exp(iakx)āg(v)exp(-v2/2	exp(iakx)āg(v)exp(-v2/2	PROPN
uiug.30112106882779	72	16	)	)	PUNCT
uiug.30112106882779	73	1	(	(	PUNCT
uiug.30112106882779	73	2	3	3	X
uiug.30112106882779	73	3	)	)	PUNCT
uiug.30112106882779	73	4	where	where	SCONJ
uiug.30112106882779	73	5	#	#	SYM
uiug.30112106882779	73	6	g(x	g(x	NOUN
uiug.30112106882779	73	7	)	)	PUNCT
uiug.30112106882779	73	8	=	=	PROPN
uiug.30112106882779	73	9	(	(	PUNCT
uiug.30112106882779	73	10	-1*exp(v2/2)(a)*exp(-v2/2	-1*exp(v2/2)(a)*exp(-v2/2	PROPN
uiug.30112106882779	73	11	)	)	PUNCT
uiug.30112106882779	73	12	dv	dv	PRON
uiug.30112106882779	73	13	is	be	AUX
uiug.30112106882779	73	14	rodrigues	rodrigue	NOUN
uiug.30112106882779	73	15	'	'	PART
uiug.30112106882779	73	16	formula	formula	NOUN
uiug.30112106882779	73	17	and	and	CCONJ
uiug.30112106882779	73	18	s	s	NUM
uiug.30112106882779	73	19	®	®	NOUN
uiug.30112106882779	73	20	(	(	PUNCT
uiug.30112106882779	73	21	v)ęg(v)exp(-v2/2)dv	v)ęg(v)exp(-v2/2)dv	PROPN
uiug.30112106882779	73	22	=	=	SYM
uiug.30112106882779	73	23	8qpv21	8qpv21	NUM
uiug.30112106882779	73	24	n	n	NOUN
uiug.30112106882779	73	25	!	!	PUNCT
uiug.30112106882779	74	1	2πη	2πη	PROPN
uiug.30112106882779	75	1	α	α	PROPN
uiug.30112106882779	75	2	substitution	substitution	NOUN
uiug.30112106882779	75	3	of	of	ADP
uiug.30112106882779	75	4	equation	equation	NOUN
uiug.30112106882779	75	5	(	(	PUNCT
uiug.30112106882779	75	6	3	3	NUM
uiug.30112106882779	75	7	)	)	PUNCT
uiug.30112106882779	75	8	into	into	ADP
uiug.30112106882779	75	9	equations	equation	NOUN
uiug.30112106882779	75	10	(	(	PUNCT
uiug.30112106882779	75	11	1	1	NUM
uiug.30112106882779	75	12	)	)	PUNCT
uiug.30112106882779	75	13	and	and	CCONJ
uiug.30112106882779	75	14	(	(	PUNCT
uiug.30112106882779	75	15	2	2	X
uiug.30112106882779	75	16	)	)	PUNCT
uiug.30112106882779	75	17	yields	yield	NOUN
uiug.30112106882779	75	18	,	,	PUNCT
uiug.30112106882779	75	19	after	after	ADP
uiug.30112106882779	75	20	multiplication	multiplication	NOUN
uiug.30112106882779	75	21	by	by	ADP
uiug.30112106882779	75	22	exp(-ia	exp(-ia	NOUN
uiug.30112106882779	75	23	kx)āg(v	kx)āg(v	PROPN
uiug.30112106882779	75	24	)	)	PUNCT
uiug.30112106882779	75	25	and	and	CCONJ
uiug.30112106882779	75	26	integration	integration	NOUN
uiug.30112106882779	75	27	over	over	ADP
uiug.30112106882779	75	28	x	x	NOUN
uiug.30112106882779	75	29	-	-	NOUN
uiug.30112106882779	75	30	v	v	NOUN
uiug.30112106882779	75	31	space	space	NOUN
uiug.30112106882779	75	32	,	,	PUNCT
uiug.30112106882779	75	33	an	an	DET
uiug.30112106882779	75	34	infinite	infinite	ADJ
uiug.30112106882779	75	35	set	set	NOUN
uiug.30112106882779	75	36	of	of	ADP
uiug.30112106882779	75	37	ordinary	ordinary	ADJ
uiug.30112106882779	75	38	differen	differen	ADJ
uiug.30112106882779	75	39	,	,	PUNCT
uiug.30112106882779	75	40	tial	tial	ADJ
uiug.30112106882779	75	41	equations	equation	NOUN
uiug.30112106882779	75	42	for	for	ADP
uiug.30112106882779	75	43	the	the	DET
uiug.30112106882779	75	44	coefficients	coefficient	NOUN
uiug.30112106882779	75	45	auß	auß	PROPN
uiug.30112106882779	75	46	of	of	ADP
uiug.30112106882779	75	47	the	the	DET
uiug.30112106882779	75	48	fourier	fourier	ADJ
uiug.30112106882779	75	49	-	-	PUNCT
uiug.30112106882779	75	50	hermite	hermite	NOUN
uiug.30112106882779	75	51	expansion	expansion	NOUN
uiug.30112106882779	75	52	.	.	PUNCT
uiug.30112106882779	76	1	this	this	DET
uiug.30112106882779	76	2	set	set	NOUN
uiug.30112106882779	76	3	of	of	ADP
uiug.30112106882779	76	4	equations	equation	NOUN
uiug.30112106882779	76	5	for	for	ADP
uiug.30112106882779	76	6	the	the	DET
uiug.30112106882779	76	7	matrix	matrix	NOUN
uiug.30112106882779	76	8	elements	element	NOUN
uiug.30112106882779	76	9	a	a	DET
uiug.30112106882779	76	10	aß	aß	NOUN
uiug.30112106882779	76	11	is	be	AUX
uiug.30112106882779	76	12	the	the	DET
uiug.30112106882779	76	13	fourier	fourier	ADJ
uiug.30112106882779	76	14	-	-	PUNCT
uiug.30112106882779	76	15	hermite	hermite	NOUN
uiug.30112106882779	76	16	representation	representation	NOUN
uiug.30112106882779	76	17	of	of	ADP
uiug.30112106882779	76	18	the	the	DET
uiug.30112106882779	76	19	vlasov	vlasov	NOUN
uiug.30112106882779	76	20	equations	equation	NOUN
uiug.30112106882779	76	21	(	(	PUNCT
uiug.30112106882779	76	22	1	1	NUM
uiug.30112106882779	76	23	)	)	PUNCT
uiug.30112106882779	76	24	and	and	CCONJ
uiug.30112106882779	76	25	(	(	PUNCT
uiug.30112106882779	76	26	2	2	NUM
uiug.30112106882779	76	27	)	)	PUNCT
uiug.30112106882779	76	28	.	.	PUNCT
uiug.30112106882779	77	1	truncation	truncation	NOUN
uiug.30112106882779	77	2	after	after	SCONJ
uiug.30112106882779	77	3	the	the	DET
uiug.30112106882779	77	4	second	second	ADJ
uiug.30112106882779	77	5	row	row	NOUN
uiug.30112106882779	77	6	yields	yield	VERB
uiug.30112106882779	77	7	the	the	DET
uiug.30112106882779	77	8	fourier	fourier	ADJ
uiug.30112106882779	77	9	-	-	PUNCT
uiug.30112106882779	77	10	hermite	hermite	NOUN
uiug.30112106882779	77	11	linearization	linearization	NOUN
uiug.30112106882779	77	12	.	.	PUNCT
uiug.30112106882779	78	1	further	further	ADJ
uiug.30112106882779	78	2	truncation	truncation	NOUN
uiug.30112106882779	78	3	at	at	ADP
uiug.30112106882779	78	4	b	b	NOUN
uiug.30112106882779	78	5	=	=	NOUN
uiug.30112106882779	78	6	n	n	CCONJ
uiug.30112106882779	78	7	yields	yield	VERB
uiug.30112106882779	78	8	the	the	DET
uiug.30112106882779	78	9	finite	finite	ADJ
uiug.30112106882779	78	10	approximation	approximation	NOUN
uiug.30112106882779	78	11	to	to	ADP
uiug.30112106882779	78	12	the	the	DET
uiug.30112106882779	78	13	linearized	linearized	ADJ
uiug.30112106882779	78	14	case	case	NOUN
uiug.30112106882779	78	15	.	.	PUNCT
uiug.30112106882779	79	1	finally	finally	ADV
uiug.30112106882779	79	2	,	,	PUNCT
uiug.30112106882779	79	3	assumption	assumption	NOUN
uiug.30112106882779	79	4	of	of	ADP
uiug.30112106882779	79	5	an	an	DET
uiug.30112106882779	79	6	expliwt	expliwt	ADJ
uiug.30112106882779	79	7	)	)	PUNCT
uiug.30112106882779	79	8	variation	variation	NOUN
uiug.30112106882779	79	9	of	of	ADP
uiug.30112106882779	79	10	the	the	DET
uiug.30112106882779	79	11	elements	element	NOUN
uiug.30112106882779	79	12	leads	lead	VERB
uiug.30112106882779	79	13	to	to	ADP
uiug.30112106882779	79	14	a	a	DET
uiug.30112106882779	79	15	dispersion	dispersion	NOUN
uiug.30112106882779	79	16	relation	relation	NOUN
uiug.30112106882779	79	17	of	of	ADP
uiug.30112106882779	79	18	order	order	NOUN
uiug.30112106882779	79	19	(	(	PUNCT
uiug.30112106882779	79	20	n	n	CCONJ
uiug.30112106882779	79	21	+	+	CCONJ
uiug.30112106882779	79	22	1	1	NUM
uiug.30112106882779	79	23	)	)	PUNCT
uiug.30112106882779	79	24	.	.	PUNCT
uiug.30112106882779	80	1	aaß	aaß	NOUN
uiug.30112106882779	80	2	with	with	ADP
uiug.30112106882779	80	3	maxwell	maxwell	PROPN
uiug.30112106882779	80	4	's	's	PART
uiug.30112106882779	80	5	distribution	distribution	NOUN
uiug.30112106882779	80	6	as	as	ADP
uiug.30112106882779	80	7	background	background	NOUN
uiug.30112106882779	80	8	,	,	PUNCT
uiug.30112106882779	80	9	the	the	DET
uiug.30112106882779	80	10	fourier	fourier	NOUN
uiug.30112106882779	80	11	-	-	PUNCT
uiug.30112106882779	80	12	hermite	hermite	NOUN
uiug.30112106882779	80	13	dispersion	dispersion	NOUN
uiug.30112106882779	80	14	relation	relation	NOUN
uiug.30112106882779	80	15	(	(	PUNCT
uiug.30112106882779	80	16	from	from	ADP
uiug.30112106882779	80	17	ref	ref	PROPN
uiug.30112106882779	80	18	.	.	PUNCT
uiug.30112106882779	81	1	5	5	NUM
uiug.30112106882779	81	2	with	with	ADP
uiug.30112106882779	81	3	a	a	DET
uiug.30112106882779	81	4	sign	sign	NOUN
uiug.30112106882779	81	5	change	change	NOUN
uiug.30112106882779	81	6	on	on	ADP
uiug.30112106882779	81	7	b	b	PROPN
uiug.30112106882779	81	8	)	)	PUNCT
uiug.30112106882779	81	9	for	for	ADP
uiug.30112106882779	81	10	cutoff	cutoff	NOUN
uiug.30112106882779	81	11	of	of	ADP
uiug.30112106882779	81	12	the	the	DET
uiug.30112106882779	81	13	expansion	expansion	NOUN
uiug.30112106882779	81	14	at	at	ADP
uiug.30112106882779	81	15	order	order	NOUN
uiug.30112106882779	81	16	nis	nis	PROPN
uiug.30112106882779	81	17	6	6	NUM
uiug.30112106882779	81	18	w	w	PROPN
uiug.30112106882779	81	19	(	(	PUNCT
uiug.30112106882779	81	20	1	1	NUM
uiug.30112106882779	81	21	+	+	NUM
uiug.30112106882779	81	22	k2)1/2	k2)1/2	VERB
uiug.30112106882779	81	23	0	0	NUM
uiug.30112106882779	81	24	0	0	NUM
uiug.30112106882779	81	25	0	0	NUM
uiug.30112106882779	81	26	(	(	PUNCT
uiug.30112106882779	81	27	1	1	NUM
uiug.30112106882779	81	28	+	+	NUM
uiug.30112106882779	81	29	k2)1/2	k2)1/2	VERB
uiug.30112106882779	82	1	w	w	X
uiug.30112106882779	82	2	+	+	NOUN
uiug.30112106882779	82	3	ib	ib	INTJ
uiug.30112106882779	82	4	kv2	kv2	NOUN
uiug.30112106882779	82	5	0	0	NUM
uiug.30112106882779	82	6	0	0	NUM
uiug.30112106882779	82	7	det	det	PROPN
uiug.30112106882779	82	8	0	0	PUNCT
uiug.30112106882779	83	1	kv2	kv2	PROPN
uiug.30112106882779	83	2	w	w	NOUN
uiug.30112106882779	83	3	+	+	NOUN
uiug.30112106882779	83	4	2ib	2ib	NOUN
uiug.30112106882779	83	5	0	0	PUNCT
uiug.30112106882779	83	6	=	=	SYM
uiug.30112106882779	83	7	0	0	NUM
uiug.30112106882779	83	8	(	(	PUNCT
uiug.30112106882779	83	9	4	4	NUM
uiug.30112106882779	83	10	)	)	PUNCT
uiug.30112106882779	83	11	0	0	NUM
uiug.30112106882779	83	12	0	0	NUM
uiug.30112106882779	84	1	kn1/2	kn1/2	PROPN
uiug.30112106882779	84	2	0	0	NUM
uiug.30112106882779	84	3	0	0	NUM
uiug.30112106882779	84	4	0	0	NUM
uiug.30112106882779	85	1	knl/2	knl/2	PROPN
uiug.30112106882779	85	2	w	w	X
uiug.30112106882779	85	3	+	+	CCONJ
uiug.30112106882779	85	4	nib	nib	PROPN
uiug.30112106882779	85	5	w	w	PROPN
uiug.30112106882779	85	6	in	in	ADP
uiug.30112106882779	85	7	equation	equation	NOUN
uiug.30112106882779	85	8	(	(	PUNCT
uiug.30112106882779	85	9	4	4	NUM
uiug.30112106882779	85	10	)	)	PUNCT
uiug.30112106882779	85	11	,	,	PUNCT
uiug.30112106882779	85	12	w	w	PROPN
uiug.30112106882779	85	13	is	be	AUX
uiug.30112106882779	85	14	an	an	DET
uiug.30112106882779	85	15	eigenfrequency	eigenfrequency	NOUN
uiug.30112106882779	85	16	(	(	PUNCT
uiug.30112106882779	85	17	eigenvalue	eigenvalue	NOUN
uiug.30112106882779	85	18	)	)	PUNCT
uiug.30112106882779	85	19	and	and	CCONJ
uiug.30112106882779	85	20	k	k	PROPN
uiug.30112106882779	85	21	is	be	AUX
uiug.30112106882779	85	22	the	the	DET
uiug.30112106882779	85	23	wave	wave	NOUN
uiug.30112106882779	85	24	number	number	NOUN
uiug.30112106882779	85	25	of	of	ADP
uiug.30112106882779	85	26	an	an	DET
uiug.30112106882779	85	27	assumed	assume	VERB
uiug.30112106882779	85	28	small	small	ADJ
uiug.30112106882779	85	29	cos(kx	cos(kx	NOUN
uiug.30112106882779	85	30	)	)	PUNCT
uiug.30112106882779	85	31	disturbance	disturbance	NOUN
uiug.30112106882779	85	32	in	in	ADP
uiug.30112106882779	85	33	electron	electron	NOUN
uiug.30112106882779	85	34	density	density	NOUN
uiug.30112106882779	85	35	.	.	PUNCT
uiug.30112106882779	86	1	if	if	SCONJ
uiug.30112106882779	86	2	is	be	AUX
uiug.30112106882779	86	3	a	a	DET
uiug.30112106882779	86	4	root	root	NOUN
uiug.30112106882779	86	5	of	of	ADP
uiug.30112106882779	86	6	equation	equation	NOUN
uiug.30112106882779	86	7	(	(	PUNCT
uiug.30112106882779	86	8	4	4	NUM
uiug.30112106882779	86	9	)	)	PUNCT
uiug.30112106882779	86	10	,	,	PUNCT
uiug.30112106882779	86	11	then	then	ADV
uiug.30112106882779	86	12	so	so	ADV
uiug.30112106882779	86	13	is	be	AUX
uiug.30112106882779	86	14	-w	-w	PROPN
uiug.30112106882779	86	15	*	*	NOUN
uiug.30112106882779	86	16	.	.	PUNCT
uiug.30112106882779	87	1	the	the	DET
uiug.30112106882779	87	2	parameter	parameter	NOUN
uiug.30112106882779	87	3	b20	b20	NUM
uiug.30112106882779	87	4	is	be	AUX
uiug.30112106882779	87	5	a	a	DET
uiug.30112106882779	87	6	measure	measure	NOUN
uiug.30112106882779	87	7	of	of	ADP
uiug.30112106882779	87	8	the	the	DET
uiug.30112106882779	87	9	strength	strength	NOUN
uiug.30112106882779	87	10	of	of	ADP
uiug.30112106882779	87	11	the	the	DET
uiug.30112106882779	87	12	fokkerplanck	fokkerplanck	ADJ
uiug.30112106882779	87	13	collision	collision	NOUN
uiug.30112106882779	87	14	term	term	NOUN
uiug.30112106882779	87	15	(	(	PUNCT
uiug.30112106882779	87	16	ref	ref	VERB
uiug.30112106882779	87	17	.	.	PUNCT
uiug.30112106882779	88	1	6	6	X
uiug.30112106882779	88	2	)	)	PUNCT
uiug.30112106882779	88	3	,	,	PUNCT
uiug.30112106882779	88	4	a	a	DET
uiug.30112106882779	88	5	1	1	NUM
uiug.30112106882779	88	6	=	=	SYM
uiug.30112106882779	88	7	b	b	NOUN
uiug.30112106882779	88	8	)	)	PUNCT
uiug.30112106882779	88	9	and	and	CCONJ
uiug.30112106882779	88	10	ft	ft	PROPN
uiug.30112106882779	88	11	b	b	PROPN
uiug.30112106882779	88	12	22f	22f	NOUN
uiug.30112106882779	88	13	(	(	PUNCT
uiug.30112106882779	88	14	vf	vf	NOUN
uiug.30112106882779	88	15	)	)	PUNCT
uiug.30112106882779	88	16	+	+	CCONJ
uiug.30112106882779	88	17	(	(	PUNCT
uiug.30112106882779	88	18	v2	v2	NOUN
uiug.30112106882779	88	19	)	)	PUNCT
uiug.30112106882779	88	20	ay2	ay2	NOUN
uiug.30112106882779	88	21	ду	ду	X
uiug.30112106882779	88	22	which	which	PRON
uiug.30112106882779	88	23	modifies	modify	VERB
uiug.30112106882779	88	24	the	the	DET
uiug.30112106882779	88	25	one	one	NUM
uiug.30112106882779	88	26	-	-	PUNCT
uiug.30112106882779	88	27	dimensional	dimensional	ADJ
uiug.30112106882779	88	28	vlasov	vlasov	NOUN
uiug.30112106882779	88	29	equations	equation	NOUN
uiug.30112106882779	88	30	(	(	PUNCT
uiug.30112106882779	88	31	1	1	NUM
uiug.30112106882779	88	32	)	)	PUNCT
uiug.30112106882779	88	33	and	and	CCONJ
uiug.30112106882779	88	34	(	(	PUNCT
uiug.30112106882779	88	35	2	2	X
uiug.30112106882779	88	36	)	)	PUNCT
uiug.30112106882779	88	37	into	into	ADP
uiug.30112106882779	88	38	af	af	INTJ
uiug.30112106882779	88	39	af	af	PROPN
uiug.30112106882779	88	40	+	+	ADP
uiug.30112106882779	88	41	v	v	NOUN
uiug.30112106882779	88	42	at	at	ADP
uiug.30112106882779	88	43	ax	ax	NOUN
uiug.30112106882779	88	44	of	of	ADP
uiug.30112106882779	88	45	+	+	NOUN
uiug.30112106882779	88	46	v	v	NOUN
uiug.30112106882779	88	47	e	e	X
uiug.30112106882779	88	48	=	=	NOUN
uiug.30112106882779	88	49	fi	fi	X
uiug.30112106882779	88	50	af	af	PROPN
uiug.30112106882779	88	51	ε	ε	PROPN
uiug.30112106882779	88	52	ay	ay	PROPN
uiug.30112106882779	88	53	ft	ft	PROPN
uiug.30112106882779	88	54	ae	ae	PROPN
uiug.30112106882779	88	55	ax	ax	PROPN
uiug.30112106882779	88	56	be	be	AUX
uiug.30112106882779	88	57	se	se	PROPN
uiug.30112106882779	88	58	=	=	PROPN
uiug.30112106882779	88	59	f	f	X
uiug.30112106882779	88	60	dy	dy	X
uiug.30112106882779	88	61	1	1	NUM
uiug.30112106882779	88	62	=	=	SYM
uiug.30112106882779	88	63	b	b	NOUN
uiug.30112106882779	88	64	=	=	PUNCT
uiug.30112106882779	88	65	the	the	DET
uiug.30112106882779	88	66	vlasov	vlasov	NOUN
uiug.30112106882779	88	67	case	case	NOUN
uiug.30112106882779	88	68	occurs	occur	VERB
uiug.30112106882779	88	69	at	at	ADP
uiug.30112106882779	88	70	b	b	PROPN
uiug.30112106882779	88	71	=	=	SYM
uiug.30112106882779	88	72	0	0	NUM
uiug.30112106882779	88	73	.	.	PUNCT
uiug.30112106882779	89	1	when	when	SCONJ
uiug.30112106882779	89	2	b	b	NOUN
uiug.30112106882779	89	3	=	=	SYM
uiug.30112106882779	89	4	0	0	NUM
uiug.30112106882779	90	1	the	the	DET
uiug.30112106882779	90	2	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	90	3	of	of	ADP
uiug.30112106882779	90	4	equation	equation	NOUN
uiug.30112106882779	90	5	(	(	PUNCT
uiug.30112106882779	90	6	4	4	X
uiug.30112106882779	90	7	)	)	PUNCT
uiug.30112106882779	90	8	are	be	AUX
uiug.30112106882779	90	9	all	all	ADV
uiug.30112106882779	90	10	real	real	ADJ
uiug.30112106882779	90	11	,	,	PUNCT
uiug.30112106882779	90	12	which	which	PRON
uiug.30112106882779	90	13	suggests	suggest	VERB
uiug.30112106882779	90	14	the	the	DET
uiug.30112106882779	90	15	equivalence	equivalence	NOUN
uiug.30112106882779	90	16	of	of	ADP
uiug.30112106882779	90	17	the	the	DET
uiug.30112106882779	90	18	fourier	fourier	ADJ
uiug.30112106882779	90	19	-	-	PUNCT
uiug.30112106882779	90	20	hermite	hermite	NOUN
uiug.30112106882779	90	21	representation	representation	NOUN
uiug.30112106882779	90	22	(	(	PUNCT
uiug.30112106882779	90	23	ref	ref	PROPN
uiug.30112106882779	90	24	.	.	PUNCT
uiug.30112106882779	90	25	5	5	X
uiug.30112106882779	90	26	)	)	PUNCT
uiug.30112106882779	90	27	to	to	ADP
uiug.30112106882779	90	28	that	that	PRON
uiug.30112106882779	90	29	of	of	ADP
uiug.30112106882779	90	30	van	van	PROPN
uiug.30112106882779	90	31	kampen	kampen	PROPN
uiug.30112106882779	90	32	(	(	PUNCT
uiug.30112106882779	90	33	ref	ref	PROPN
uiug.30112106882779	90	34	.	.	PUNCT
uiug.30112106882779	91	1	2	2	X
uiug.30112106882779	91	2	)	)	PUNCT
uiug.30112106882779	91	3	rather	rather	ADV
uiug.30112106882779	91	4	than	than	ADP
uiug.30112106882779	91	5	to	to	ADP
uiug.30112106882779	91	6	that	that	PRON
uiug.30112106882779	91	7	of	of	ADP
uiug.30112106882779	91	8	landau	landau	NOUN
uiug.30112106882779	91	9	(	(	PUNCT
uiug.30112106882779	91	10	ref	ref	PROPN
uiug.30112106882779	91	11	.	.	PUNCT
uiug.30112106882779	92	1	1	1	X
uiug.30112106882779	92	2	)	)	PUNCT
uiug.30112106882779	92	3	.	.	PUNCT
uiug.30112106882779	93	1	however	however	ADV
uiug.30112106882779	93	2	,	,	PUNCT
uiug.30112106882779	93	3	as	as	ADP
uiug.30112106882779	93	4	increases	increase	NOUN
uiug.30112106882779	93	5	from	from	ADP
uiug.30112106882779	93	6	zero	zero	NUM
uiug.30112106882779	93	7	,	,	PUNCT
uiug.30112106882779	93	8	the	the	DET
uiug.30112106882779	93	9	surprising	surprising	ADJ
uiug.30112106882779	93	10	behavior	behavior	NOUN
uiug.30112106882779	93	11	first	first	ADV
uiug.30112106882779	93	12	reported	report	VERB
uiug.30112106882779	93	13	in	in	ADP
uiug.30112106882779	93	14	reference	reference	NOUN
uiug.30112106882779	93	15	3	3	NUM
uiug.30112106882779	93	16	and	and	CCONJ
uiug.30112106882779	93	17	shown	show	VERB
uiug.30112106882779	93	18	in	in	ADP
uiug.30112106882779	93	19	figure	figure	NOUN
uiug.30112106882779	93	20	1	1	NUM
uiug.30112106882779	93	21	occurs	occur	VERB
uiug.30112106882779	93	22	.	.	PUNCT
uiug.30112106882779	94	1	all	all	PRON
uiug.30112106882779	94	2	but	but	SCONJ
uiug.30112106882779	94	3	one	one	NUM
uiug.30112106882779	94	4	of	of	ADP
uiug.30112106882779	94	5	the	the	DET
uiug.30112106882779	94	6	poles	pole	NOUN
uiug.30112106882779	94	7	(	(	PUNCT
uiug.30112106882779	94	8	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	94	9	)	)	PUNCT
uiug.30112106882779	94	10	move	move	VERB
uiug.30112106882779	94	11	rapidly	rapidly	ADV
uiug.30112106882779	94	12	into	into	ADP
uiug.30112106882779	94	13	the	the	DET
uiug.30112106882779	94	14	ywr	ywr	ADJ
uiug.30112106882779	94	15	-	-	PUNCT
uiug.30112106882779	94	16	plane	plane	NOUN
uiug.30112106882779	94	17	where	where	SCONJ
uiug.30112106882779	94	18	w	w	NOUN
uiug.30112106882779	94	19	=	=	X
uiug.30112106882779	94	20	wr	wr	PROPN
uiug.30112106882779	94	21	iy	iy	PROPN
uiug.30112106882779	94	22	and	and	CCONJ
uiug.30112106882779	94	23	f	f	PROPN
uiug.30112106882779	94	24	o	o	PROPN
uiug.30112106882779	94	25	exp(iwt	exp(iwt	PROPN
uiug.30112106882779	94	26	)	)	PUNCT
uiug.30112106882779	94	27	.	.	PUNCT
uiug.30112106882779	95	1	the	the	DET
uiug.30112106882779	95	2	anomalous	anomalous	ADJ
uiug.30112106882779	95	3	pole	pole	NOUN
uiug.30112106882779	95	4	is	be	AUX
uiug.30112106882779	95	5	detained	detain	VERB
uiug.30112106882779	95	6	in	in	ADP
uiug.30112106882779	95	7	the	the	DET
uiug.30112106882779	95	8	region	region	NOUN
uiug.30112106882779	95	9	of	of	ADP
uiug.30112106882779	95	10	the	the	DET
uiug.30112106882779	95	11	landau	landau	PROPN
uiug.30112106882779	95	12	pole	pole	NOUN
uiug.30112106882779	95	13	.	.	PUNCT
uiug.30112106882779	96	1	detailed	detailed	ADJ
uiug.30112106882779	96	2	investigation	investigation	NOUN
uiug.30112106882779	96	3	of	of	ADP
uiug.30112106882779	96	4	the	the	DET
uiug.30112106882779	96	5	behavior	behavior	NOUN
uiug.30112106882779	96	6	of	of	ADP
uiug.30112106882779	96	7	the	the	DET
uiug.30112106882779	96	8	anomalous	anomalous	ADJ
uiug.30112106882779	96	9	pole	pole	NOUN
uiug.30112106882779	96	10	for	for	ADP
uiug.30112106882779	96	11	fourierhermite	fourierhermite	NOUN
uiug.30112106882779	96	12	expansions	expansion	NOUN
uiug.30112106882779	96	13	up	up	ADV
uiug.30112106882779	96	14	to	to	PART
uiug.30112106882779	96	15	order	order	NOUN
uiug.30112106882779	96	16	63	63	NUM
uiug.30112106882779	96	17	suggested	suggest	VERB
uiug.30112106882779	96	18	that	that	SCONJ
uiug.30112106882779	96	19	the	the	DET
uiug.30112106882779	96	20	equivalence	equivalence	NOUN
uiug.30112106882779	96	21	of	of	ADP
uiug.30112106882779	96	22	van	van	PROPN
uiug.30112106882779	96	23	kampen	kampen	PROPN
uiug.30112106882779	96	24	and	and	CCONJ
uiug.30112106882779	96	25	landau	landau	NOUN
uiug.30112106882779	96	26	treatments	treatment	NOUN
uiug.30112106882779	96	27	was	be	AUX
uiug.30112106882779	96	28	being	be	AUX
uiug.30112106882779	96	29	observed	observe	VERB
uiug.30112106882779	96	30	within	within	ADP
uiug.30112106882779	96	31	the	the	DET
uiug.30112106882779	96	32	fourier	fourier	NOUN
uiug.30112106882779	96	33	-	-	PUNCT
uiug.30112106882779	96	34	hermite	hermite	NOUN
uiug.30112106882779	96	35	representation	representation	NOUN
uiug.30112106882779	96	36	.	.	PUNCT
uiug.30112106882779	97	1	a	a	DET
uiug.30112106882779	97	2	more	more	ADV
uiug.30112106882779	97	3	powerful	powerful	ADJ
uiug.30112106882779	97	4	numerical	numerical	ADJ
uiug.30112106882779	97	5	technique	technique	NOUN
uiug.30112106882779	97	6	has	have	AUX
uiug.30112106882779	97	7	verified	verify	VERB
uiug.30112106882779	97	8	the	the	DET
uiug.30112106882779	97	9	behavior	behavior	NOUN
uiug.30112106882779	97	10	to	to	ADP
uiug.30112106882779	97	11	orders	order	NOUN
uiug.30112106882779	97	12	over	over	ADP
uiug.30112106882779	97	13	1000	1000	NUM
uiug.30112106882779	97	14	,	,	PUNCT
uiug.30112106882779	97	15	which	which	PRON
uiug.30112106882779	97	16	is	be	AUX
uiug.30112106882779	97	17	sufficiently	sufficiently	ADV
uiug.30112106882779	97	18	near	near	ADP
uiug.30112106882779	97	19	infinity	infinity	NOUN
uiug.30112106882779	97	20	to	to	PART
uiug.30112106882779	97	21	establish	establish	VERB
uiug.30112106882779	97	22	the	the	DET
uiug.30112106882779	97	23	nonuniformity	nonuniformity	NOUN
uiug.30112106882779	97	24	convergent	convergent	ADJ
uiug.30112106882779	97	25	behavior	behavior	NOUN
uiug.30112106882779	97	26	of	of	ADP
uiug.30112106882779	97	27	the	the	DET
uiug.30112106882779	97	28	approximation	approximation	NOUN
uiug.30112106882779	97	29	curve	curve	NOUN
uiug.30112106882779	97	30	as	as	ADP
uiug.30112106882779	97	31	nand	nand	PROPN
uiug.30112106882779	97	32	b-0	b-0	PROPN
uiug.30112106882779	97	33	.	.	PUNCT
uiug.30112106882779	98	1	numerical	numerical	PROPN
uiug.30112106882779	98	2	algorithm	algorithm	PROPN
uiug.30112106882779	98	3	the	the	DET
uiug.30112106882779	98	4	improved	improve	VERB
uiug.30112106882779	98	5	technique	technique	NOUN
uiug.30112106882779	98	6	is	be	AUX
uiug.30112106882779	98	7	based	base	VERB
uiug.30112106882779	98	8	on	on	ADP
uiug.30112106882779	98	9	recursion	recursion	NOUN
uiug.30112106882779	98	10	(	(	PUNCT
uiug.30112106882779	98	11	ref	ref	NOUN
uiug.30112106882779	98	12	.	.	PUNCT
uiug.30112106882779	98	13	7	7	X
uiug.30112106882779	98	14	)	)	PUNCT
uiug.30112106882779	98	15	.	.	PUNCT
uiug.30112106882779	99	1	if	if	SCONJ
uiug.30112106882779	99	2	the	the	DET
uiug.30112106882779	99	3	determinant	determinant	NOUN
uiug.30112106882779	99	4	of	of	ADP
uiug.30112106882779	99	5	order	order	NOUN
uiug.30112106882779	99	6	(	(	PUNCT
uiug.30112106882779	99	7	n	n	CCONJ
uiug.30112106882779	99	8	+	+	ADP
uiug.30112106882779	99	9	1	1	X
uiug.30112106882779	99	10	)	)	PUNCT
uiug.30112106882779	99	11	in	in	ADP
uiug.30112106882779	99	12	equation	equation	NOUN
uiug.30112106882779	99	13	(	(	PUNCT
uiug.30112106882779	99	14	4	4	NUM
uiug.30112106882779	99	15	)	)	PUNCT
uiug.30112106882779	99	16	is	be	AUX
uiug.30112106882779	99	17	denoted	denote	VERB
uiug.30112106882779	99	18	as	as	ADP
uiug.30112106882779	99	19	dn+1	dn+1	ADV
uiug.30112106882779	99	20	,	,	PUNCT
uiug.30112106882779	99	21	expansion	expansion	NOUN
uiug.30112106882779	99	22	on	on	ADP
uiug.30112106882779	99	23	the	the	DET
uiug.30112106882779	99	24	last	last	ADJ
uiug.30112106882779	99	25	column	column	NOUN
uiug.30112106882779	99	26	yields	yield	VERB
uiug.30112106882779	99	27	7	7	NUM
uiug.30112106882779	99	28	dn+1	dn+1	NOUN
uiug.30112106882779	99	29	=	=	VERB
uiug.30112106882779	99	30	(	(	PUNCT
uiug.30112106882779	99	31	w	w	X
uiug.30112106882779	99	32	+	+	CCONJ
uiug.30112106882779	99	33	inb)dn	inb)dn	ADV
uiug.30112106882779	99	34	nkadn-1	nkadn-1	PROPN
uiug.30112106882779	99	35	(	(	PUNCT
uiug.30112106882779	99	36	5	5	NUM
uiug.30112106882779	99	37	)	)	PUNCT
uiug.30112106882779	99	38	in	in	ADP
uiug.30112106882779	99	39	particular	particular	ADJ
uiug.30112106882779	99	40	,	,	PUNCT
uiug.30112106882779	99	41	d1	d1	X
uiug.30112106882779	99	42	=	=	X
uiug.30112106882779	99	43	w	w	PROPN
uiug.30112106882779	99	44	d2	d2	PROPN
uiug.30112106882779	99	45	=	=	NOUN
uiug.30112106882779	99	46	www	www	PROPN
uiug.30112106882779	99	47	+	+	PROPN
uiug.30112106882779	99	48	ib	ib	PROPN
uiug.30112106882779	99	49	)	)	PUNCT
uiug.30112106882779	99	50	(	(	PUNCT
uiug.30112106882779	99	51	i	i	NOUN
uiug.30112106882779	99	52	+	+	CCONJ
uiug.30112106882779	99	53	k2	k2	ADJ
uiug.30112106882779	99	54	)	)	PUNCT
uiug.30112106882779	99	55	in	in	ADP
uiug.30112106882779	99	56	principle	principle	NOUN
uiug.30112106882779	99	57	,	,	PUNCT
uiug.30112106882779	99	58	the	the	DET
uiug.30112106882779	99	59	value	value	NOUN
uiug.30112106882779	99	60	of	of	ADP
uiug.30112106882779	99	61	dn+1	dn+1	NOUN
uiug.30112106882779	99	62	for	for	ADP
uiug.30112106882779	99	63	arbitrary	arbitrary	ADJ
uiug.30112106882779	99	64	large	large	ADJ
uiug.30112106882779	99	65	n	n	NOUN
uiug.30112106882779	99	66	is	be	AUX
uiug.30112106882779	99	67	obtained	obtain	VERB
uiug.30112106882779	99	68	in	in	ADP
uiug.30112106882779	99	69	about	about	ADP
uiug.30112106882779	99	70	n	n	CCONJ
uiug.30112106882779	99	71	steps	step	NOUN
uiug.30112106882779	99	72	,	,	PUNCT
uiug.30112106882779	99	73	each	each	PRON
uiug.30112106882779	99	74	of	of	ADP
uiug.30112106882779	99	75	simple	simple	ADJ
uiug.30112106882779	99	76	multiplication	multiplication	NOUN
uiug.30112106882779	99	77	and	and	CCONJ
uiug.30112106882779	99	78	addition	addition	NOUN
uiug.30112106882779	99	79	.	.	PUNCT
uiug.30112106882779	100	1	in	in	ADP
uiug.30112106882779	100	2	contrast	contrast	NOUN
uiug.30112106882779	100	3	,	,	PUNCT
uiug.30112106882779	100	4	the	the	DET
uiug.30112106882779	100	5	full	full	ADJ
uiug.30112106882779	100	6	matrix	matrix	NOUN
uiug.30112106882779	100	7	treatment	treatment	NOUN
uiug.30112106882779	100	8	of	of	ADP
uiug.30112106882779	100	9	reference	reference	NOUN
uiug.30112106882779	100	10	3	3	NUM
uiug.30112106882779	100	11	requires	require	VERB
uiug.30112106882779	100	12	n2	n2	PROPN
uiug.30112106882779	100	13	words	word	NOUN
uiug.30112106882779	100	14	just	just	ADV
uiug.30112106882779	100	15	to	to	PART
uiug.30112106882779	100	16	record	record	VERB
uiug.30112106882779	100	17	the	the	DET
uiug.30112106882779	100	18	elements	element	NOUN
uiug.30112106882779	100	19	of	of	ADP
uiug.30112106882779	100	20	the	the	DET
uiug.30112106882779	100	21	matrix	matrix	NOUN
uiug.30112106882779	100	22	.	.	PUNCT
uiug.30112106882779	101	1	to	to	PART
uiug.30112106882779	101	2	apply	apply	VERB
uiug.30112106882779	101	3	recursion	recursion	NOUN
uiug.30112106882779	101	4	equation	equation	NOUN
uiug.30112106882779	101	5	(	(	PUNCT
uiug.30112106882779	101	6	5	5	NUM
uiug.30112106882779	101	7	)	)	PUNCT
uiug.30112106882779	101	8	to	to	ADP
uiug.30112106882779	101	9	the	the	DET
uiug.30112106882779	101	10	eigenvalue	eigenvalue	NOUN
uiug.30112106882779	101	11	problem	problem	NOUN
uiug.30112106882779	101	12	,	,	PUNCT
uiug.30112106882779	101	13	the	the	DET
uiug.30112106882779	101	14	fourier	fourier	NOUN
uiug.30112106882779	101	15	-	-	PUNCT
uiug.30112106882779	101	16	hermite	hermite	NOUN
uiug.30112106882779	101	17	root	root	NOUN
uiug.30112106882779	101	18	(	(	PUNCT
uiug.30112106882779	101	19	eigenvalue	eigenvalue	NOUN
uiug.30112106882779	101	20	)	)	PUNCT
uiug.30112106882779	101	21	nearest	near	ADJ
uiug.30112106882779	101	22	in	in	ADP
uiug.30112106882779	101	23	value	value	NOUN
uiug.30112106882779	101	24	to	to	ADP
uiug.30112106882779	101	25	the	the	DET
uiug.30112106882779	101	26	real	real	ADJ
uiug.30112106882779	101	27	part	part	NOUN
uiug.30112106882779	101	28	of	of	ADP
uiug.30112106882779	101	29	the	the	DET
uiug.30112106882779	101	30	landau	landau	NOUN
uiug.30112106882779	101	31	pole	pole	NOUN
uiug.30112106882779	101	32	is	be	AUX
uiug.30112106882779	101	33	identified	identify	VERB
uiug.30112106882779	101	34	for	for	ADP
uiug.30112106882779	101	35	b	b	PROPN
uiug.30112106882779	101	36	=	=	SYM
uiug.30112106882779	101	37	0	0	NUM
uiug.30112106882779	101	38	.	.	PUNCT
uiug.30112106882779	102	1	a	a	DET
uiug.30112106882779	102	2	small	small	ADJ
uiug.30112106882779	102	3	positive	positive	ADJ
uiug.30112106882779	102	4	increment	increment	NOUN
uiug.30112106882779	102	5	in	in	ADP
uiug.30112106882779	102	6	b	b	PROPN
uiug.30112106882779	102	7	,	,	PUNCT
uiug.30112106882779	102	8	ab	ab	PROPN
uiug.30112106882779	102	9	,	,	PUNCT
uiug.30112106882779	102	10	and	and	CCONJ
uiug.30112106882779	102	11	a	a	DET
uiug.30112106882779	102	12	small	small	ADJ
uiug.30112106882779	102	13	increment	increment	NOUN
uiug.30112106882779	102	14	in	in	ADP
uiug.30112106882779	102	15	w	w	PROPN
uiug.30112106882779	102	16	,	,	PUNCT
uiug.30112106882779	102	17	aw	aw	INTJ
uiug.30112106882779	102	18	,	,	PUNCT
uiug.30112106882779	102	19	are	be	AUX
uiug.30112106882779	102	20	introduced	introduce	VERB
uiug.30112106882779	102	21	and	and	CCONJ
uiug.30112106882779	102	22	the	the	DET
uiug.30112106882779	102	23	approximate	approximate	ADJ
uiug.30112106882779	102	24	derivative	derivative	PROPN
uiug.30112106882779	102	25	adn+1/4w	adn+1/4w	PROPN
uiug.30112106882779	102	26	is	be	AUX
uiug.30112106882779	102	27	computed	compute	VERB
uiug.30112106882779	102	28	.	.	PUNCT
uiug.30112106882779	103	1	use	use	NOUN
uiug.30112106882779	103	2	of	of	ADP
uiug.30112106882779	103	3	the	the	DET
uiug.30112106882779	103	4	approximate	approximate	ADJ
uiug.30112106882779	103	5	derivative	derivative	NOUN
uiug.30112106882779	103	6	in	in	ADP
uiug.30112106882779	103	7	the	the	DET
uiug.30112106882779	103	8	newton	newton	PROPN
uiug.30112106882779	103	9	-	-	PUNCT
uiug.30112106882779	103	10	raphson	raphson	PROPN
uiug.30112106882779	103	11	method	method	NOUN
uiug.30112106882779	103	12	gives	give	VERB
uiug.30112106882779	103	13	a	a	DET
uiug.30112106882779	103	14	first	first	ADJ
uiug.30112106882779	103	15	approximation	approximation	NOUN
uiug.30112106882779	103	16	to	to	ADP
uiug.30112106882779	103	17	the	the	DET
uiug.30112106882779	103	18	shifted	shifted	ADJ
uiug.30112106882779	103	19	eigenvalue	eigenvalue	NOUN
uiug.30112106882779	103	20	.	.	PUNCT
uiug.30112106882779	104	1	in	in	ADP
uiug.30112106882779	104	2	general	general	ADJ
uiug.30112106882779	104	3	,	,	PUNCT
uiug.30112106882779	104	4	δω	δω	PROPN
uiug.30112106882779	104	5	n+1	n+1	X
uiug.30112106882779	104	6	=	=	PUNCT
uiug.30112106882779	104	7	wn	wn	PROPN
uiug.30112106882779	104	8	dn+1(b+ab	dn+1(b+ab	PROPN
uiug.30112106882779	104	9	,	,	PUNCT
uiug.30112106882779	104	10	wn	wn	PROPN
uiug.30112106882779	104	11	)	)	PUNCT
uiug.30112106882779	104	12	adn-1	adn-1	ADP
uiug.30112106882779	104	13	+	+	PROPN
uiug.30112106882779	104	14	(	(	PUNCT
uiug.30112106882779	104	15	6	6	X
uiug.30112106882779	104	16	)	)	PUNCT
uiug.30112106882779	104	17	adn+1	adn+1	ADJ
uiug.30112106882779	104	18	=	=	NOUN
uiug.30112106882779	104	19	dn+1(b+ab	dn+1(b+ab	PROPN
uiug.30112106882779	104	20	,	,	PUNCT
uiug.30112106882779	104	21	wn+aw	wn+aw	PROPN
uiug.30112106882779	104	22	)	)	PUNCT
uiug.30112106882779	104	23	dn+1(b+ab	dn+1(b+ab	NOUN
uiug.30112106882779	104	24	,	,	PUNCT
uiug.30112106882779	104	25	wn	wn	PROPN
uiug.30112106882779	104	26	)	)	PUNCT
uiug.30112106882779	104	27	after	after	ADP
uiug.30112106882779	104	28	the	the	DET
uiug.30112106882779	104	29	first	first	ADJ
uiug.30112106882779	104	30	step	step	NOUN
uiug.30112106882779	104	31	,	,	PUNCT
uiug.30112106882779	104	32	iteration	iteration	NOUN
uiug.30112106882779	104	33	on	on	ADP
uiug.30112106882779	104	34	the	the	DET
uiug.30112106882779	104	35	quasi	quasi	PROPN
uiug.30112106882779	104	36	-	-	PROPN
uiug.30112106882779	104	37	newton	newton	PROPN
uiug.30112106882779	104	38	-	-	PUNCT
uiug.30112106882779	104	39	raphson	raphson	PROPN
uiug.30112106882779	104	40	equations	equation	NOUN
uiug.30112106882779	104	41	(	(	PUNCT
uiug.30112106882779	104	42	6	6	NUM
uiug.30112106882779	104	43	)	)	PUNCT
uiug.30112106882779	104	44	yields	yield	VERB
uiug.30112106882779	104	45	a	a	DET
uiug.30112106882779	104	46	sharp	sharp	ADJ
uiug.30112106882779	104	47	value	value	NOUN
uiug.30112106882779	104	48	of	of	ADP
uiug.30112106882779	104	49	w(ab	w(ab	PROPN
uiug.30112106882779	104	50	)	)	PUNCT
uiug.30112106882779	104	51	.	.	PUNCT
uiug.30112106882779	105	1	a	a	DET
uiug.30112106882779	105	2	second	second	ADJ
uiug.30112106882779	105	3	increment	increment	NOUN
uiug.30112106882779	105	4	of	of	ADP
uiug.30112106882779	105	5	ab	ab	PROPN
uiug.30112106882779	105	6	leads	lead	VERB
uiug.30112106882779	105	7	on	on	ADP
uiug.30112106882779	105	8	to	to	ADP
uiug.30112106882779	105	9	w(2ab	w(2ab	PROPN
uiug.30112106882779	105	10	)	)	PUNCT
uiug.30112106882779	105	11	,	,	PUNCT
uiug.30112106882779	105	12	and	and	CCONJ
uiug.30112106882779	105	13	in	in	ADP
uiug.30112106882779	105	14	like	like	INTJ
uiug.30112106882779	105	15	manner	manner	NOUN
uiug.30112106882779	105	16	the	the	DET
uiug.30112106882779	105	17	progress	progress	NOUN
uiug.30112106882779	105	18	of	of	ADP
uiug.30112106882779	105	19	w(b	w(b	PROPN
uiug.30112106882779	105	20	)	)	PUNCT
uiug.30112106882779	105	21	=	=	PROPN
uiug.30112106882779	105	22	wr	wr	PROPN
uiug.30112106882779	105	23	iy	iy	PROPN
uiug.30112106882779	105	24	on	on	ADP
uiug.30112106882779	105	25	the	the	DET
uiug.30112106882779	105	26	ywr	ywr	ADJ
uiug.30112106882779	105	27	-	-	PUNCT
uiug.30112106882779	105	28	plane	plane	NOUN
uiug.30112106882779	105	29	is	be	AUX
uiug.30112106882779	105	30	tracked	track	VERB
uiug.30112106882779	105	31	.	.	PUNCT
uiug.30112106882779	106	1	the	the	DET
uiug.30112106882779	106	2	chief	chief	ADJ
uiug.30112106882779	106	3	difficulties	difficulty	NOUN
uiug.30112106882779	106	4	are	be	AUX
uiug.30112106882779	106	5	found	find	VERB
uiug.30112106882779	106	6	in	in	ADP
uiug.30112106882779	106	7	scaling	scale	VERB
uiug.30112106882779	106	8	the	the	DET
uiug.30112106882779	106	9	large	large	ADJ
uiug.30112106882779	106	10	numbers	number	NOUN
uiug.30112106882779	106	11	which	which	PRON
uiug.30112106882779	106	12	arise	arise	VERB
uiug.30112106882779	106	13	for	for	ADP
uiug.30112106882779	106	14	large	large	ADJ
uiug.30112106882779	106	15	n	n	NOUN
uiug.30112106882779	106	16	and	and	CCONJ
uiug.30112106882779	106	17	in	in	ADP
uiug.30112106882779	106	18	the	the	DET
uiug.30112106882779	106	19	necessity	necessity	NOUN
uiug.30112106882779	106	20	of	of	ADP
uiug.30112106882779	106	21	iteration	iteration	NOUN
uiug.30112106882779	106	22	to	to	PART
uiug.30112106882779	106	23	sharpen	sharpen	VERB
uiug.30112106882779	106	24	the	the	DET
uiug.30112106882779	106	25	values	value	NOUN
uiug.30112106882779	106	26	of	of	ADP
uiug.30112106882779	106	27	w(b	w(b	PROPN
uiug.30112106882779	106	28	)	)	PUNCT
uiug.30112106882779	106	29	.	.	PUNCT
uiug.30112106882779	107	1	a	a	DET
uiug.30112106882779	107	2	sample	sample	NOUN
uiug.30112106882779	107	3	fortran	fortran	PROPN
uiug.30112106882779	107	4	program	program	NOUN
uiug.30112106882779	107	5	is	be	AUX
uiug.30112106882779	107	6	shown	show	VERB
uiug.30112106882779	107	7	in	in	ADP
uiug.30112106882779	107	8	appendix	appendix	ADJ
uiug.30112106882779	107	9	a.	a.	NOUN
uiug.30112106882779	107	10	=	=	PUNCT
uiug.30112106882779	107	11	use	use	NOUN
uiug.30112106882779	107	12	of	of	ADP
uiug.30112106882779	107	13	the	the	DET
uiug.30112106882779	107	14	recursion	recursion	NOUN
uiug.30112106882779	107	15	equation	equation	NOUN
uiug.30112106882779	107	16	(	(	PUNCT
uiug.30112106882779	107	17	5	5	X
uiug.30112106882779	107	18	)	)	PUNCT
uiug.30112106882779	107	19	simplifies	simplify	VERB
uiug.30112106882779	107	20	the	the	DET
uiug.30112106882779	107	21	task	task	NOUN
uiug.30112106882779	107	22	of	of	ADP
uiug.30112106882779	107	23	finding	find	VERB
uiug.30112106882779	107	24	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	107	25	for	for	ADP
uiug.30112106882779	107	26	the	the	DET
uiug.30112106882779	107	27	b	b	NOUN
uiug.30112106882779	107	28	=	=	SYM
uiug.30112106882779	107	29	0	0	NUM
uiug.30112106882779	107	30	(	(	PUNCT
uiug.30112106882779	107	31	collisionless	collisionless	NOUN
uiug.30112106882779	107	32	)	)	PUNCT
uiug.30112106882779	107	33	case	case	NOUN
uiug.30112106882779	107	34	of	of	ADP
uiug.30112106882779	107	35	equation	equation	NOUN
uiug.30112106882779	107	36	(	(	PUNCT
uiug.30112106882779	107	37	4	4	NUM
uiug.30112106882779	107	38	)	)	PUNCT
uiug.30112106882779	107	39	.	.	PUNCT
uiug.30112106882779	108	1	easy	easy	ADJ
uiug.30112106882779	108	2	evaluation	evaluation	NOUN
uiug.30112106882779	108	3	of	of	ADP
uiug.30112106882779	108	4	dn+1(w	dn+1(w	SPACE
uiug.30112106882779	108	5	)	)	PUNCT
uiug.30112106882779	108	6	at	at	ADP
uiug.30112106882779	108	7	any	any	DET
uiug.30112106882779	108	8	n	n	NOUN
uiug.30112106882779	108	9	per	per	ADP
uiug.30112106882779	108	10	.	.	PUNCT
uiug.30112106882779	108	11	mits	mit	VERB
uiug.30112106882779	108	12	a	a	DET
uiug.30112106882779	108	13	movement	movement	NOUN
uiug.30112106882779	108	14	from	from	ADP
uiug.30112106882779	108	15	w	w	PROPN
uiug.30112106882779	108	16	=	=	SYM
uiug.30112106882779	108	17	0	0	NUM
uiug.30112106882779	108	18	in	in	ADP
uiug.30112106882779	108	19	steps	step	NOUN
uiug.30112106882779	108	20	of	of	ADP
uiug.30112106882779	108	21	aw	aw	INTJ
uiug.30112106882779	108	22	>	>	SYM
uiug.30112106882779	108	23	0	0	NUM
uiug.30112106882779	108	24	.	.	PUNCT
uiug.30112106882779	109	1	sign	sign	VERB
uiug.30112106882779	109	2	changes	change	NOUN
uiug.30112106882779	109	3	of	of	ADP
uiug.30112106882779	109	4	dn+1(w	dn+1(w	SPACE
uiug.30112106882779	109	5	)	)	PUNCT
uiug.30112106882779	109	6	localize	localize	VERB
uiug.30112106882779	109	7	each	each	DET
uiug.30112106882779	109	8	root	root	NOUN
uiug.30112106882779	109	9	within	within	ADP
uiug.30112106882779	109	10	aw	aw	INTJ
uiug.30112106882779	109	11	,	,	PUNCT
uiug.30112106882779	109	12	and	and	CCONJ
uiug.30112106882779	109	13	iteration	iteration	NOUN
uiug.30112106882779	109	14	sharpens	sharpen	VERB
uiug.30112106882779	109	15	the	the	DET
uiug.30112106882779	109	16	root	root	NOUN
uiug.30112106882779	109	17	.	.	PUNCT
uiug.30112106882779	110	1	the	the	DET
uiug.30112106882779	110	2	tridiagonal	tridiagonal	ADJ
uiug.30112106882779	110	3	form	form	NOUN
uiug.30112106882779	110	4	of	of	ADP
uiug.30112106882779	110	5	the	the	DET
uiug.30112106882779	110	6	matrix	matrix	NOUN
uiug.30112106882779	110	7	in	in	ADP
uiug.30112106882779	110	8	equation	equation	NOUN
uiug.30112106882779	110	9	(	(	PUNCT
uiug.30112106882779	110	10	4	4	X
uiug.30112106882779	110	11	)	)	PUNCT
uiug.30112106882779	110	12	makes	make	VERB
uiug.30112106882779	110	13	trivial	trivial	ADJ
uiug.30112106882779	110	14	(	(	PUNCT
uiug.30112106882779	110	15	for	for	ADP
uiug.30112106882779	110	16	k	k	X
uiug.30112106882779	110	17	=	=	SYM
uiug.30112106882779	110	18	0.5	0.5	NUM
uiug.30112106882779	110	19	)	)	PUNCT
uiug.30112106882779	110	20	the	the	DET
uiug.30112106882779	110	21	calculation	calculation	NOUN
uiug.30112106882779	110	22	of	of	ADP
uiug.30112106882779	110	23	the	the	DET
uiug.30112106882779	110	24	corresponding	correspond	VERB
uiug.30112106882779	110	25	eigenvectors	eigenvector	NOUN
uiug.30112106882779	110	26	.	.	PUNCT
uiug.30112106882779	111	1	in	in	ADP
uiug.30112106882779	111	2	reference	reference	NOUN
uiug.30112106882779	111	3	5	5	NUM
uiug.30112106882779	111	4	,	,	PUNCT
uiug.30112106882779	111	5	histograms	histogram	NOUN
uiug.30112106882779	111	6	corresponding	correspond	VERB
uiug.30112106882779	111	7	to	to	ADP
uiug.30112106882779	111	8	an	an	DET
uiug.30112106882779	111	9	initial	initial	ADJ
uiug.30112106882779	111	10	cos(kx	cos(kx	NOUN
uiug.30112106882779	111	11	)	)	PUNCT
uiug.30112106882779	111	12	spatial	spatial	ADJ
uiug.30112106882779	111	13	disturbance	disturbance	NOUN
uiug.30112106882779	111	14	of	of	ADP
uiug.30112106882779	111	15	plasma	plasma	NOUN
uiug.30112106882779	111	16	density	density	NOUN
uiug.30112106882779	111	17	were	be	AUX
uiug.30112106882779	111	18	constructed	construct	VERB
uiug.30112106882779	111	19	from	from	ADP
uiug.30112106882779	111	20	the	the	DET
uiug.30112106882779	111	21	eigenvectors	eigenvector	NOUN
uiug.30112106882779	111	22	of	of	ADP
uiug.30112106882779	111	23	the	the	DET
uiug.30112106882779	111	24	matrix	matrix	NOUN
uiug.30112106882779	111	25	of	of	ADP
uiug.30112106882779	111	26	equation	equation	NOUN
uiug.30112106882779	111	27	(	(	PUNCT
uiug.30112106882779	111	28	4	4	NUM
uiug.30112106882779	111	29	)	)	PUNCT
uiug.30112106882779	111	30	.	.	PUNCT
uiug.30112106882779	112	1	full	full	ADJ
uiug.30112106882779	112	2	matrix	matrix	NOUN
uiug.30112106882779	112	3	methods	method	NOUN
uiug.30112106882779	112	4	were	be	AUX
uiug.30112106882779	112	5	barely	barely	ADV
uiug.30112106882779	112	6	adequate	adequate	ADJ
uiug.30112106882779	112	7	to	to	PART
uiug.30112106882779	112	8	yield	yield	VERB
uiug.30112106882779	112	9	histograms	histogram	NOUN
uiug.30112106882779	112	10	for	for	ADP
uiug.30112106882779	112	11	the	the	DET
uiug.30112106882779	112	12	case	case	NOUN
uiug.30112106882779	112	13	of	of	ADP
uiug.30112106882779	112	14	truncation	truncation	NOUN
uiug.30112106882779	112	15	8	8	NUM
uiug.30112106882779	112	16	at	at	ADP
uiug.30112106882779	112	17	n	n	NOUN
uiug.30112106882779	112	18	=	=	ADP
uiug.30112106882779	112	19	99	99	NUM
uiug.30112106882779	112	20	,	,	PUNCT
uiug.30112106882779	112	21	and	and	CCONJ
uiug.30112106882779	112	22	then	then	ADV
uiug.30112106882779	112	23	only	only	ADV
uiug.30112106882779	112	24	because	because	SCONJ
uiug.30112106882779	112	25	b	b	NOUN
uiug.30112106882779	112	26	=	=	SYM
uiug.30112106882779	112	27	0	0	NUM
uiug.30112106882779	112	28	produces	produce	VERB
uiug.30112106882779	112	29	real	real	ADJ
uiug.30112106882779	112	30	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	112	31	and	and	CCONJ
uiug.30112106882779	112	32	eigenvectors	eigenvector	NOUN
uiug.30112106882779	112	33	.	.	PUNCT
uiug.30112106882779	113	1	with	with	ADP
uiug.30112106882779	113	2	the	the	DET
uiug.30112106882779	113	3	recursion	recursion	NOUN
uiug.30112106882779	113	4	methods	method	NOUN
uiug.30112106882779	113	5	,	,	PUNCT
uiug.30112106882779	113	6	histograms	histogram	NOUN
uiug.30112106882779	113	7	for	for	ADP
uiug.30112106882779	113	8	n	n	CCONJ
uiug.30112106882779	113	9	>	>	X
uiug.30112106882779	113	10	103	103	NUM
uiug.30112106882779	113	11	have	have	AUX
uiug.30112106882779	113	12	now	now	ADV
uiug.30112106882779	113	13	been	be	AUX
uiug.30112106882779	113	14	constructed	construct	VERB
uiug.30112106882779	113	15	.	.	PUNCT
uiug.30112106882779	114	1	the	the	DET
uiug.30112106882779	114	2	oscillations	oscillation	NOUN
uiug.30112106882779	114	3	in	in	ADP
uiug.30112106882779	114	4	density	density	NOUN
uiug.30112106882779	114	5	which	which	PRON
uiug.30112106882779	114	6	follow	follow	VERB
uiug.30112106882779	114	7	an	an	DET
uiug.30112106882779	114	8	initial	initial	ADJ
uiug.30112106882779	114	9	cos(kx	cos(kx	NOUN
uiug.30112106882779	114	10	)	)	PUNCT
uiug.30112106882779	114	11	spatial	spatial	ADJ
uiug.30112106882779	114	12	density	density	NOUN
uiug.30112106882779	114	13	perturbation	perturbation	NOUN
uiug.30112106882779	114	14	may	may	AUX
uiug.30112106882779	114	15	be	be	AUX
uiug.30112106882779	114	16	represented	represent	VERB
uiug.30112106882779	114	17	exactly	exactly	ADV
uiug.30112106882779	114	18	by	by	ADP
uiug.30112106882779	114	19	the	the	DET
uiug.30112106882779	114	20	following	follow	VERB
uiug.30112106882779	114	21	fourier	fourier	NOUN
uiug.30112106882779	114	22	integral	integral	ADJ
uiug.30112106882779	114	23	over	over	ADP
uiug.30112106882779	114	24	a	a	DET
uiug.30112106882779	114	25	real	real	ADJ
uiug.30112106882779	114	26	phase	phase	NOUN
uiug.30112106882779	114	27	velocity	velocity	NOUN
uiug.30112106882779	114	28	w	w	NOUN
uiug.30112106882779	114	29	:	:	PUNCT
uiug.30112106882779	114	30	n(k	n(k	PROPN
uiug.30112106882779	114	31	,	,	PUNCT
uiug.30112106882779	114	32	t	t	PROPN
uiug.30112106882779	114	33	)	)	PUNCT
uiug.30112106882779	114	34	=	=	PROPN
uiug.30112106882779	114	35	s	s	VERB
uiug.30112106882779	114	36	+	+	PROPN
uiug.30112106882779	114	37	(	(	PUNCT
uiug.30112106882779	114	38	w)exp(ikwt)dw	w)exp(ikwt)dw	PROPN
uiug.30112106882779	114	39	n	n	NOUN
uiug.30112106882779	114	40	(	(	PUNCT
uiug.30112106882779	114	41	7	7	NUM
uiug.30112106882779	114	42	)	)	PUNCT
uiug.30112106882779	114	43	7	7	NUM
uiug.30112106882779	114	44	where	where	SCONJ
uiug.30112106882779	114	45	kw	kw	PROPN
uiug.30112106882779	114	46	=	=	X
uiug.30112106882779	114	47	w	w	PROPN
uiug.30112106882779	114	48	,	,	PUNCT
uiug.30112106882779	114	49	a	a	DET
uiug.30112106882779	114	50	real	real	ADJ
uiug.30112106882779	114	51	frequency	frequency	NOUN
uiug.30112106882779	114	52	.	.	PUNCT
uiug.30112106882779	115	1	the	the	DET
uiug.30112106882779	115	2	reality	reality	NOUN
uiug.30112106882779	115	3	of	of	ADP
uiug.30112106882779	115	4	the	the	DET
uiug.30112106882779	115	5	fourier	fourier	NOUN
uiug.30112106882779	115	6	-	-	PUNCT
uiug.30112106882779	115	7	hermite	hermite	NOUN
uiug.30112106882779	115	8	eigenfrequencies	eigenfrequencie	NOUN
uiug.30112106882779	115	9	for	for	ADP
uiug.30112106882779	115	10	b	b	NOUN
uiug.30112106882779	115	11	=	=	SYM
uiug.30112106882779	115	12	0	0	NUM
uiug.30112106882779	115	13	permits	permit	VERB
uiug.30112106882779	115	14	the	the	DET
uiug.30112106882779	115	15	construction	construction	NOUN
uiug.30112106882779	115	16	of	of	ADP
uiug.30112106882779	115	17	a	a	DET
uiug.30112106882779	115	18	histogram	histogram	NOUN
uiug.30112106882779	115	19	analogous	analogous	NOUN
uiug.30112106882779	115	20	to	to	ADP
uiug.30112106882779	115	21	4(w	4(w	NUM
uiug.30112106882779	115	22	)	)	PUNCT
uiug.30112106882779	115	23	in	in	ADP
uiug.30112106882779	115	24	equation	equation	NOUN
uiug.30112106882779	115	25	(	(	PUNCT
uiug.30112106882779	115	26	7	7	NUM
uiug.30112106882779	115	27	)	)	PUNCT
uiug.30112106882779	115	28	.	.	PUNCT
uiug.30112106882779	116	1	in	in	ADP
uiug.30112106882779	116	2	the	the	DET
uiug.30112106882779	116	3	limit	limit	NOUN
uiug.30112106882779	116	4	of	of	ADP
uiug.30112106882779	116	5	infinite	infinite	PROPN
uiug.30112106882779	116	6	n	n	CCONJ
uiug.30112106882779	116	7	the	the	DET
uiug.30112106882779	116	8	histogram	histogram	NOUN
uiug.30112106882779	116	9	approaches	approach	VERB
uiug.30112106882779	116	10	¥	¥	PROPN
uiug.30112106882779	116	11	(	(	PUNCT
uiug.30112106882779	116	12	w	w	NOUN
uiug.30112106882779	116	13	)	)	PUNCT
uiug.30112106882779	116	14	.	.	PUNCT
uiug.30112106882779	117	1	in	in	ADP
uiug.30112106882779	117	2	appendix	appendix	PROPN
uiug.30112106882779	117	3	b	b	PROPN
uiug.30112106882779	117	4	the	the	DET
uiug.30112106882779	117	5	derivation	derivation	NOUN
uiug.30112106882779	117	6	oft	oft	ADV
uiug.30112106882779	117	7	is	be	AUX
uiug.30112106882779	117	8	given	give	VERB
uiug.30112106882779	117	9	.	.	PUNCT
uiug.30112106882779	118	1	as	as	SCONJ
uiug.30112106882779	118	2	shown	show	VERB
uiug.30112106882779	118	3	in	in	ADP
uiug.30112106882779	118	4	reference	reference	NOUN
uiug.30112106882779	118	5	5	5	NUM
uiug.30112106882779	118	6	,	,	PUNCT
uiug.30112106882779	118	7	the	the	DET
uiug.30112106882779	118	8	ordinate	ordinate	NOUN
uiug.30112106882779	118	9	of	of	ADP
uiug.30112106882779	118	10	the	the	DET
uiug.30112106882779	118	11	histogram	histogram	NOUN
uiug.30112106882779	118	12	between	between	ADP
uiug.30112106882779	118	13	the	the	DET
uiug.30112106882779	118	14	jth	jth	PROPN
uiug.30112106882779	118	15	and	and	CCONJ
uiug.30112106882779	118	16	(	(	PUNCT
uiug.30112106882779	118	17	i	i	NOUN
uiug.30112106882779	118	18	+	+	CCONJ
uiug.30112106882779	118	19	1)th	1)th	NUM
uiug.30112106882779	118	20	eigenvelocities	eigenvelocitie	NOUN
uiug.30112106882779	118	21	may	may	AUX
uiug.30112106882779	118	22	be	be	AUX
uiug.30112106882779	118	23	assigned	assign	VERB
uiug.30112106882779	118	24	as	as	ADP
uiug.30112106882779	118	25	!	!	PUNCT
uiug.30112106882779	119	1	+	+	CCONJ
uiug.30112106882779	119	2	(	(	PUNCT
uiug.30112106882779	119	3	2	2	NUM
uiug.30112106882779	119	4	2	2	NUM
uiug.30112106882779	119	5	vj,0	vj,0	PROPN
uiug.30112106882779	119	6	+	+	PROPN
uiug.30112106882779	119	7	vj+1,0	vj+1,0	NOUN
uiug.30112106882779	119	8	)	)	PUNCT
uiug.30112106882779	120	1	wj+1	wj+1	PROPN
uiug.30112106882779	120	2	w	w	PROPN
uiug.30112106882779	120	3	;	;	PUNCT
uiug.30112106882779	120	4	1,0	1,0	NUM
uiug.30112106882779	120	5	)	)	PUNCT
uiug.30112106882779	120	6	w	w	PROPN
uiug.30112106882779	120	7	4j	4j	NOUN
uiug.30112106882779	120	8	j	j	NOUN
uiug.30112106882779	120	9	,	,	PUNCT
uiug.30112106882779	120	10	j+1	j+1	PROPN
uiug.30112106882779	120	11	(	(	PUNCT
uiug.30112106882779	120	12	wj+1	wj+1	PROPN
uiug.30112106882779	120	13	>	>	X
uiug.30112106882779	120	14	w	w	PROPN
uiug.30112106882779	120	15	;	;	PUNCT
uiug.30112106882779	120	16	0	0	NUM
uiug.30112106882779	120	17	;	;	PUNCT
uiug.30112106882779	120	18	j	j	PROPN
uiug.30112106882779	120	19	=	=	PROPN
uiug.30112106882779	120	20	0,1,2	0,1,2	PROPN
uiug.30112106882779	120	21	,	,	PUNCT
uiug.30112106882779	120	22	.	.	PUNCT
uiug.30112106882779	120	23	.	.	PUNCT
uiug.30112106882779	121	1	.	.	PUNCT
uiug.30112106882779	121	2	,	,	PUNCT
uiug.30112106882779	121	3	n	n	CCONJ
uiug.30112106882779	121	4	)	)	PUNCT
uiug.30112106882779	121	5	where	where	SCONJ
uiug.30112106882779	121	6	v	v	PROPN
uiug.30112106882779	121	7	is	be	AUX
uiug.30112106882779	121	8	the	the	DET
uiug.30112106882779	121	9	first	first	ADJ
uiug.30112106882779	121	10	component	component	NOUN
uiug.30112106882779	121	11	of	of	ADP
uiug.30112106882779	121	12	the	the	DET
uiug.30112106882779	121	13	normalized	normalized	ADJ
uiug.30112106882779	121	14	eigenvector	eigenvector	NOUN
uiug.30112106882779	121	15	corresponding	correspond	VERB
uiug.30112106882779	121	16	to	to	ADP
uiug.30112106882779	121	17	the	the	DET
uiug.30112106882779	121	18	nth	nth	PROPN
uiug.30112106882779	121	19	eigenvelocity	eigenvelocity	PROPN
uiug.30112106882779	121	20	w	w	PROPN
uiug.30112106882779	121	21	found	find	VERB
uiug.30112106882779	121	22	by	by	ADP
uiug.30112106882779	121	23	solving	solve	VERB
uiug.30112106882779	121	24	'	'	PUNCT
uiug.30112106882779	121	25	n,0	n,0	PROPN
uiug.30112106882779	121	26	n	n	ADP
uiug.30112106882779	121	27	w	w	PROPN
uiug.30112106882779	121	28	(	(	PUNCT
uiug.30112106882779	121	29	1	1	NUM
uiug.30112106882779	121	30	+	+	CCONJ
uiug.30112106882779	121	31	k-2)1/2	k-2)1/2	PROPN
uiug.30112106882779	122	1	0	0	NUM
uiug.30112106882779	122	2	0	0	NUM
uiug.30112106882779	122	3	0	0	NUM
uiug.30112106882779	123	1	(	(	PUNCT
uiug.30112106882779	123	2	1	1	NUM
uiug.30112106882779	123	3	+	+	CCONJ
uiug.30112106882779	123	4	k-2)1/2	k-2)1/2	PROPN
uiug.30112106882779	123	5	in	in	ADP
uiug.30112106882779	123	6	w	w	NOUN
uiug.30112106882779	123	7	0	0	SYM
uiug.30112106882779	123	8	0	0	NUM
uiug.30112106882779	124	1	det	det	PROPN
uiug.30112106882779	124	2	0	0	PUNCT
uiug.30112106882779	125	1	v2	v2	PROPN
uiug.30112106882779	125	2	w	w	NOUN
uiug.30112106882779	125	3	0	0	NUM
uiug.30112106882779	125	4	=	=	SYM
uiug.30112106882779	125	5	0	0	NUM
uiug.30112106882779	125	6	=	=	SYM
uiug.30112106882779	125	7	(	(	PUNCT
uiug.30112106882779	125	8	8)	8)	NUM
uiug.30112106882779	125	9	0	0	NUM
uiug.30112106882779	125	10	0	0	NUM
uiug.30112106882779	125	11	nl/2	nl/2	PROPN
uiug.30112106882779	125	12	0	0	NUM
uiug.30112106882779	125	13	0	0	NUM
uiug.30112106882779	125	14	0	0	NUM
uiug.30112106882779	125	15	n1/2	n1/2	NUM
uiug.30112106882779	125	16	w	w	PROPN
uiug.30112106882779	125	17	equation	equation	NOUN
uiug.30112106882779	125	18	(	(	PUNCT
uiug.30112106882779	125	19	8)	8)	NUM
uiug.30112106882779	125	20	is	be	AUX
uiug.30112106882779	125	21	derived	derive	VERB
uiug.30112106882779	125	22	by	by	ADP
uiug.30112106882779	125	23	similarity	similarity	NOUN
uiug.30112106882779	125	24	transformations	transformation	NOUN
uiug.30112106882779	125	25	of	of	ADP
uiug.30112106882779	125	26	the	the	DET
uiug.30112106882779	125	27	matrix	matrix	NOUN
uiug.30112106882779	125	28	of	of	ADP
uiug.30112106882779	125	29	equation	equation	NOUN
uiug.30112106882779	125	30	(	(	PUNCT
uiug.30112106882779	125	31	4	4	NUM
uiug.30112106882779	125	32	)	)	PUNCT
uiug.30112106882779	125	33	and	and	CCONJ
uiug.30112106882779	125	34	by	by	ADP
uiug.30112106882779	125	35	the	the	DET
uiug.30112106882779	125	36	introduction	introduction	NOUN
uiug.30112106882779	125	37	of	of	ADP
uiug.30112106882779	125	38	the	the	DET
uiug.30112106882779	125	39	phase	phase	NOUN
uiug.30112106882779	125	40	velocity	velocity	NOUN
uiug.30112106882779	125	41	w	w	NOUN
uiug.30112106882779	125	42	/	/	SYM
uiug.30112106882779	125	43	k.	k.	NOUN
uiug.30112106882779	125	44	results	result	NOUN
uiug.30112106882779	125	45	and	and	CCONJ
uiug.30112106882779	125	46	discussion	discussion	NOUN
uiug.30112106882779	125	47	the	the	DET
uiug.30112106882779	125	48	behavior	behavior	NOUN
uiug.30112106882779	125	49	of	of	ADP
uiug.30112106882779	125	50	the	the	DET
uiug.30112106882779	125	51	fourier	fourier	ADJ
uiug.30112106882779	125	52	-	-	PUNCT
uiug.30112106882779	125	53	hermite	hermite	NOUN
uiug.30112106882779	125	54	poles	pole	NOUN
uiug.30112106882779	125	55	with	with	ADP
uiug.30112106882779	125	56	vanishing	vanish	VERB
uiug.30112106882779	125	57	collisions	collision	NOUN
uiug.30112106882779	125	58	is	be	AUX
uiug.30112106882779	125	59	indicated	indicate	VERB
uiug.30112106882779	125	60	in	in	ADP
uiug.30112106882779	125	61	figures	figure	NOUN
uiug.30112106882779	125	62	2	2	NUM
uiug.30112106882779	125	63	and	and	CCONJ
uiug.30112106882779	125	64	3	3	NUM
uiug.30112106882779	125	65	for	for	ADP
uiug.30112106882779	125	66	approximations	approximation	NOUN
uiug.30112106882779	125	67	up	up	ADP
uiug.30112106882779	125	68	to	to	ADP
uiug.30112106882779	125	69	n	n	NOUN
uiug.30112106882779	125	70	=	=	ADP
uiug.30112106882779	125	71	1023	1023	NUM
uiug.30112106882779	125	72	.	.	PUNCT
uiug.30112106882779	126	1	in	in	ADP
uiug.30112106882779	126	2	figure	figure	NOUN
uiug.30112106882779	126	3	2	2	NUM
uiug.30112106882779	126	4	the	the	DET
uiug.30112106882779	126	5	behavior	behavior	NOUN
uiug.30112106882779	126	6	of	of	ADP
uiug.30112106882779	126	7	the	the	DET
uiug.30112106882779	126	8	real	real	ADJ
uiug.30112106882779	126	9	=	=	ADJ
uiug.30112106882779	126	10	part	part	NOUN
uiug.30112106882779	126	11	of	of	ADP
uiug.30112106882779	126	12	the	the	DET
uiug.30112106882779	126	13	eigenfrequency	eigenfrequency	NOUN
uiug.30112106882779	126	14	is	be	AUX
uiug.30112106882779	126	15	shown	show	VERB
uiug.30112106882779	126	16	.	.	PUNCT
uiug.30112106882779	127	1	a	a	DET
uiug.30112106882779	127	2	scale	scale	NOUN
uiug.30112106882779	127	3	to	to	PART
uiug.30112106882779	127	4	accommodate	accommodate	VERB
uiug.30112106882779	127	5	all	all	DET
uiug.30112106882779	127	6	the	the	DET
uiug.30112106882779	127	7	values	value	NOUN
uiug.30112106882779	127	8	of	of	ADP
uiug.30112106882779	127	9	n	n	X
uiug.30112106882779	127	10	has	have	AUX
uiug.30112106882779	127	11	been	be	AUX
uiug.30112106882779	127	12	used	use	VERB
uiug.30112106882779	127	13	in	in	ADP
uiug.30112106882779	127	14	figure	figure	NOUN
uiug.30112106882779	127	15	2(a	2(a	NUM
uiug.30112106882779	127	16	)	)	PUNCT
uiug.30112106882779	127	17	.	.	PUNCT
uiug.30112106882779	128	1	the	the	DET
uiug.30112106882779	128	2	extreme	extreme	ADJ
uiug.30112106882779	128	3	deviations	deviation	NOUN
uiug.30112106882779	128	4	by	by	ADP
uiug.30112106882779	128	5	which	which	PRON
uiug.30112106882779	128	6	the	the	DET
uiug.30112106882779	128	7	curves	curve	NOUN
uiug.30112106882779	128	8	reach	reach	VERB
uiug.30112106882779	128	9	fourier9	fourier9	NOUN
uiug.30112106882779	128	10	=	=	VERB
uiug.30112106882779	129	1	hermite	hermite	PROPN
uiug.30112106882779	129	2	values	value	NOUN
uiug.30112106882779	129	3	at	at	ADP
uiug.30112106882779	129	4	n	n	NOUN
uiug.30112106882779	129	5	=	=	ADP
uiug.30112106882779	129	6	255	255	NUM
uiug.30112106882779	129	7	and	and	CCONJ
uiug.30112106882779	129	8	511	511	NUM
uiug.30112106882779	129	9	as	as	ADP
uiug.30112106882779	129	10	b	b	NOUN
uiug.30112106882779	129	11	goes	go	VERB
uiug.30112106882779	129	12	to	to	ADP
uiug.30112106882779	129	13	zero	zero	NUM
uiug.30112106882779	129	14	are	be	AUX
uiug.30112106882779	129	15	quite	quite	ADV
uiug.30112106882779	129	16	striking	striking	ADJ
uiug.30112106882779	129	17	.	.	PUNCT
uiug.30112106882779	130	1	the	the	DET
uiug.30112106882779	130	2	curve	curve	NOUN
uiug.30112106882779	130	3	for	for	ADP
uiug.30112106882779	130	4	n	n	NOUN
uiug.30112106882779	130	5	=	=	SYM
uiug.30112106882779	130	6	1023	1023	NUM
uiug.30112106882779	130	7	lies	lie	NOUN
uiug.30112106882779	130	8	so	so	ADV
uiug.30112106882779	130	9	nearly	nearly	ADV
uiug.30112106882779	130	10	on	on	ADP
uiug.30112106882779	130	11	a	a	DET
uiug.30112106882779	130	12	straight	straight	ADJ
uiug.30112106882779	130	13	line	line	NOUN
uiug.30112106882779	130	14	to	to	ADP
uiug.30112106882779	130	15	the	the	DET
uiug.30112106882779	130	16	landau	landau	PROPN
uiug.30112106882779	130	17	value	value	NOUN
uiug.30112106882779	130	18	that	that	SCONJ
uiug.30112106882779	130	19	it	it	PRON
uiug.30112106882779	130	20	would	would	AUX
uiug.30112106882779	130	21	not	not	PART
uiug.30112106882779	130	22	show	show	VERB
uiug.30112106882779	130	23	in	in	ADP
uiug.30112106882779	130	24	figure	figure	NOUN
uiug.30112106882779	130	25	2(a	2(a	NUM
uiug.30112106882779	130	26	)	)	PUNCT
uiug.30112106882779	130	27	.	.	PUNCT
uiug.30112106882779	131	1	therefore	therefore	ADV
uiug.30112106882779	131	2	,	,	PUNCT
uiug.30112106882779	131	3	the	the	DET
uiug.30112106882779	131	4	behavior	behavior	NOUN
uiug.30112106882779	131	5	for	for	ADP
uiug.30112106882779	131	6	the	the	DET
uiug.30112106882779	131	7	three	three	NUM
uiug.30112106882779	131	8	highest	high	ADJ
uiug.30112106882779	131	9	values	value	NOUN
uiug.30112106882779	131	10	of	of	ADP
uiug.30112106882779	131	11	n	n	CCONJ
uiug.30112106882779	131	12	is	be	AUX
uiug.30112106882779	131	13	shown	show	VERB
uiug.30112106882779	131	14	at	at	ADP
uiug.30112106882779	131	15	larger	large	ADJ
uiug.30112106882779	131	16	scale	scale	NOUN
uiug.30112106882779	131	17	in	in	ADP
uiug.30112106882779	131	18	figure	figure	NOUN
uiug.30112106882779	131	19	2(b	2(b	NUM
uiug.30112106882779	131	20	)	)	PUNCT
uiug.30112106882779	131	21	.	.	PUNCT
uiug.30112106882779	132	1	for	for	ADP
uiug.30112106882779	132	2	n	n	NOUN
uiug.30112106882779	132	3	=	=	SYM
uiug.30112106882779	132	4	1023	1023	NUM
uiug.30112106882779	132	5	it	it	PRON
uiug.30112106882779	132	6	can	can	AUX
uiug.30112106882779	132	7	be	be	AUX
uiug.30112106882779	132	8	seen	see	VERB
uiug.30112106882779	132	9	that	that	SCONJ
uiug.30112106882779	132	10	the	the	DET
uiug.30112106882779	132	11	chance	chance	NOUN
uiug.30112106882779	132	12	closeness	closeness	NOUN
uiug.30112106882779	132	13	of	of	ADP
uiug.30112106882779	132	14	the	the	DET
uiug.30112106882779	132	15	fourier	fourier	NOUN
uiug.30112106882779	132	16	-	-	PUNCT
uiug.30112106882779	132	17	hermite	hermite	NOUN
uiug.30112106882779	132	18	root	root	NOUN
uiug.30112106882779	132	19	to	to	ADP
uiug.30112106882779	132	20	the	the	DET
uiug.30112106882779	132	21	landau	landau	NOUN
uiug.30112106882779	132	22	value	value	NOUN
uiug.30112106882779	132	23	causes	cause	VERB
uiug.30112106882779	132	24	a	a	DET
uiug.30112106882779	132	25	nearly	nearly	ADV
uiug.30112106882779	132	26	straight	straight	ADJ
uiug.30112106882779	132	27	approach	approach	NOUN
uiug.30112106882779	132	28	to	to	ADP
uiug.30112106882779	132	29	the	the	DET
uiug.30112106882779	132	30	landau	landau	NOUN
uiug.30112106882779	132	31	value	value	NOUN
uiug.30112106882779	132	32	.	.	PUNCT
uiug.30112106882779	133	1	actually	actually	ADV
uiug.30112106882779	133	2	,	,	PUNCT
uiug.30112106882779	133	3	a	a	DET
uiug.30112106882779	133	4	deviation	deviation	NOUN
uiug.30112106882779	133	5	from	from	ADP
uiug.30112106882779	133	6	a	a	DET
uiug.30112106882779	133	7	straight	straight	ADJ
uiug.30112106882779	133	8	approach	approach	NOUN
uiug.30112106882779	133	9	starts	start	VERB
uiug.30112106882779	133	10	at	at	ADP
uiug.30112106882779	133	11	about	about	ADP
uiug.30112106882779	133	12	b	b	PROPN
uiug.30112106882779	133	13	=	=	SYM
uiug.30112106882779	133	14	0.0006	0.0006	NUM
uiug.30112106882779	133	15	.	.	PUNCT
uiug.30112106882779	134	1	in	in	ADP
uiug.30112106882779	134	2	figure	figure	NOUN
uiug.30112106882779	134	3	3	3	NUM
uiug.30112106882779	134	4	the	the	DET
uiug.30112106882779	134	5	behavior	behavior	NOUN
uiug.30112106882779	134	6	of	of	ADP
uiug.30112106882779	134	7	the	the	DET
uiug.30112106882779	134	8	damping	damping	NOUN
uiug.30112106882779	134	9	is	be	AUX
uiug.30112106882779	134	10	shown	show	VERB
uiug.30112106882779	134	11	for	for	ADP
uiug.30112106882779	134	12	vanishing	vanish	VERB
uiug.30112106882779	134	13	collisions	collision	NOUN
uiug.30112106882779	134	14	.	.	PUNCT
uiug.30112106882779	135	1	again	again	ADV
uiug.30112106882779	135	2	the	the	DET
uiug.30112106882779	135	3	two	two	NUM
uiug.30112106882779	135	4	parts	part	NOUN
uiug.30112106882779	135	5	of	of	ADP
uiug.30112106882779	135	6	the	the	DET
uiug.30112106882779	135	7	figure	figure	NOUN
uiug.30112106882779	135	8	are	be	AUX
uiug.30112106882779	135	9	small	small	ADJ
uiug.30112106882779	135	10	-	-	PUNCT
uiug.30112106882779	135	11	scale	scale	NOUN
uiug.30112106882779	135	12	and	and	CCONJ
uiug.30112106882779	135	13	large	large	ADJ
uiug.30112106882779	135	14	-	-	PUNCT
uiug.30112106882779	135	15	scale	scale	NOUN
uiug.30112106882779	135	16	graphs	graph	NOUN
uiug.30112106882779	135	17	.	.	PUNCT
uiug.30112106882779	136	1	the	the	DET
uiug.30112106882779	136	2	curves	curve	NOUN
uiug.30112106882779	136	3	for	for	ADP
uiug.30112106882779	136	4	the	the	DET
uiug.30112106882779	136	5	higher	high	ADJ
uiug.30112106882779	136	6	n	n	CCONJ
uiug.30112106882779	136	7	can	can	AUX
uiug.30112106882779	136	8	be	be	AUX
uiug.30112106882779	136	9	clearly	clearly	ADV
uiug.30112106882779	136	10	seen	see	VERB
uiug.30112106882779	136	11	only	only	ADV
uiug.30112106882779	136	12	in	in	ADP
uiug.30112106882779	136	13	the	the	DET
uiug.30112106882779	136	14	large	large	ADJ
uiug.30112106882779	136	15	-	-	PUNCT
uiug.30112106882779	136	16	scale	scale	NOUN
uiug.30112106882779	136	17	graph	graph	NOUN
uiug.30112106882779	136	18	of	of	ADP
uiug.30112106882779	136	19	figure	figure	NOUN
uiug.30112106882779	136	20	3(b	3(b	NUM
uiug.30112106882779	136	21	)	)	PUNCT
uiug.30112106882779	136	22	.	.	PUNCT
uiug.30112106882779	137	1	in	in	ADP
uiug.30112106882779	137	2	every	every	DET
uiug.30112106882779	137	3	case	case	NOUN
uiug.30112106882779	137	4	the	the	DET
uiug.30112106882779	137	5	sharp	sharp	ADJ
uiug.30112106882779	137	6	swerve	swerve	NOUN
uiug.30112106882779	137	7	toward	toward	ADP
uiug.30112106882779	137	8	y	y	PROPN
uiug.30112106882779	137	9	=	=	NOUN
uiug.30112106882779	137	10	0	0	NUM
uiug.30112106882779	137	11	from	from	ADP
uiug.30112106882779	137	12	a	a	DET
uiug.30112106882779	137	13	straight	straight	ADJ
uiug.30112106882779	137	14	approach	approach	NOUN
uiug.30112106882779	137	15	to	to	ADP
uiug.30112106882779	137	16	the	the	DET
uiug.30112106882779	137	17	landau	landau	NOUN
uiug.30112106882779	137	18	value	value	NOUN
uiug.30112106882779	137	19	is	be	AUX
uiug.30112106882779	137	20	striking	strike	VERB
uiug.30112106882779	137	21	.	.	PUNCT
uiug.30112106882779	138	1	it	it	PRON
uiug.30112106882779	138	2	is	be	AUX
uiug.30112106882779	138	3	clear	clear	ADJ
uiug.30112106882779	138	4	from	from	ADP
uiug.30112106882779	138	5	figures	figure	NOUN
uiug.30112106882779	138	6	2	2	NUM
uiug.30112106882779	138	7	and	and	CCONJ
uiug.30112106882779	138	8	3	3	NUM
uiug.30112106882779	138	9	that	that	PRON
uiug.30112106882779	138	10	,	,	PUNCT
uiug.30112106882779	138	11	numerically	numerically	ADV
uiug.30112106882779	138	12	,	,	PUNCT
uiug.30112106882779	138	13	the	the	DET
uiug.30112106882779	138	14	connection	connection	NOUN
uiug.30112106882779	138	15	between	between	ADP
uiug.30112106882779	138	16	the	the	DET
uiug.30112106882779	138	17	van	van	PROPN
uiug.30112106882779	138	18	kampen	kampen	PROPN
uiug.30112106882779	138	19	and	and	CCONJ
uiug.30112106882779	138	20	landau	landau	NOUN
uiug.30112106882779	138	21	representations	representation	NOUN
uiug.30112106882779	138	22	has	have	AUX
uiug.30112106882779	138	23	been	be	AUX
uiug.30112106882779	138	24	demonstrated	demonstrate	VERB
uiug.30112106882779	138	25	within	within	ADP
uiug.30112106882779	138	26	the	the	DET
uiug.30112106882779	138	27	fourierhermite	fourierhermite	NOUN
uiug.30112106882779	138	28	representation	representation	NOUN
uiug.30112106882779	138	29	.	.	PUNCT
uiug.30112106882779	139	1	moreover	moreover	ADV
uiug.30112106882779	139	2	,	,	PUNCT
uiug.30112106882779	139	3	the	the	DET
uiug.30112106882779	139	4	pathological	pathological	ADJ
uiug.30112106882779	139	5	character	character	NOUN
uiug.30112106882779	139	6	of	of	ADP
uiug.30112106882779	139	7	the	the	DET
uiug.30112106882779	139	8	curves	curve	NOUN
uiug.30112106882779	139	9	wr(b	wr(b	ADV
uiug.30112106882779	139	10	)	)	PUNCT
uiug.30112106882779	139	11	and	and	CCONJ
uiug.30112106882779	139	12	7(b	7(b	NUM
uiug.30112106882779	139	13	)	)	PUNCT
uiug.30112106882779	139	14	for	for	ADP
uiug.30112106882779	139	15	large	large	ADJ
uiug.30112106882779	139	16	values	value	NOUN
uiug.30112106882779	139	17	of	of	ADP
uiug.30112106882779	139	18	n	n	CCONJ
uiug.30112106882779	139	19	as	as	ADP
uiug.30112106882779	139	20	b	b	PROPN
uiug.30112106882779	139	21	goes	go	VERB
uiug.30112106882779	139	22	to	to	ADP
uiug.30112106882779	139	23	zero	zero	NUM
uiug.30112106882779	139	24	clearly	clearly	ADV
uiug.30112106882779	139	25	indicates	indicate	VERB
uiug.30112106882779	139	26	the	the	DET
uiug.30112106882779	139	27	nonuniformly	nonuniformly	ADV
uiug.30112106882779	139	28	convergent	convergent	ADJ
uiug.30112106882779	139	29	behavior	behavior	NOUN
uiug.30112106882779	139	30	of	of	ADP
uiug.30112106882779	139	31	the	the	DET
uiug.30112106882779	139	32	approximation	approximation	NOUN
uiug.30112106882779	139	33	curve	curve	NOUN
uiug.30112106882779	139	34	in	in	ADP
uiug.30112106882779	139	35	the	the	DET
uiug.30112106882779	139	36	limit	limit	NOUN
uiug.30112106882779	139	37	of	of	ADP
uiug.30112106882779	139	38	infinite	infinite	PROPN
uiug.30112106882779	139	39	nat	nat	PROPN
uiug.30112106882779	139	40	vanishing	vanish	VERB
uiug.30112106882779	139	41	b.	b.	PROPN
uiug.30112106882779	139	42	in	in	ADP
uiug.30112106882779	139	43	figure	figure	NOUN
uiug.30112106882779	139	44	4	4	NUM
uiug.30112106882779	139	45	a	a	DET
uiug.30112106882779	139	46	histogram	histogram	NOUN
uiug.30112106882779	139	47	for	for	ADP
uiug.30112106882779	139	48	n	n	NOUN
uiug.30112106882779	139	49	=	=	SYM
uiug.30112106882779	139	50	1023	1023	NUM
uiug.30112106882779	139	51	is	be	AUX
uiug.30112106882779	139	52	shown	show	VERB
uiug.30112106882779	139	53	along	along	ADP
uiug.30112106882779	139	54	with	with	ADP
uiug.30112106882779	139	55	one	one	NUM
uiug.30112106882779	139	56	for	for	ADP
uiug.30112106882779	139	57	n	n	CCONJ
uiug.30112106882779	139	58	=	=	SYM
uiug.30112106882779	139	59	99	99	NUM
uiug.30112106882779	139	60	that	that	PRON
uiug.30112106882779	139	61	was	be	AUX
uiug.30112106882779	139	62	presented	present	VERB
uiug.30112106882779	139	63	in	in	ADP
uiug.30112106882779	139	64	reference	reference	NOUN
uiug.30112106882779	139	65	5	5	NUM
uiug.30112106882779	139	66	.	.	PUNCT
uiug.30112106882779	140	1	the	the	DET
uiug.30112106882779	140	2	curve	curve	NOUN
uiug.30112106882779	140	3	is	be	AUX
uiug.30112106882779	140	4	symmetrical	symmetrical	ADJ
uiug.30112106882779	140	5	about	about	ADP
uiug.30112106882779	140	6	i	i	PRON
uiug.30112106882779	140	7	=	=	PUNCT
uiug.30112106882779	140	8	0	0	NUM
uiug.30112106882779	140	9	,	,	PUNCT
uiug.30112106882779	140	10	so	so	SCONJ
uiug.30112106882779	140	11	only	only	ADV
uiug.30112106882779	140	12	the	the	DET
uiug.30112106882779	140	13	positive	positive	ADJ
uiug.30112106882779	140	14	half	half	NOUN
uiug.30112106882779	140	15	is	be	AUX
uiug.30112106882779	140	16	shown	show	VERB
uiug.30112106882779	140	17	.	.	PUNCT
uiug.30112106882779	141	1	although	although	SCONJ
uiug.30112106882779	141	2	a	a	DET
uiug.30112106882779	141	3	better	well	ADJ
uiug.30112106882779	141	4	representation	representation	NOUN
uiug.30112106882779	141	5	of	of	ADP
uiug.30112106882779	141	6	the	the	DET
uiug.30112106882779	141	7	curve	curve	NOUN
uiug.30112106882779	141	8	for	for	ADP
uiug.30112106882779	141	9	n	n	CCONJ
uiug.30112106882779	141	10	=	=	SYM
uiug.30112106882779	141	11	6	6	NUM
uiug.30112106882779	141	12	is	be	AUX
uiug.30112106882779	141	13	obtained	obtain	VERB
uiug.30112106882779	141	14	with	with	ADP
uiug.30112106882779	141	15	n	n	NOUN
uiug.30112106882779	141	16	=	=	SYM
uiug.30112106882779	141	17	1023	1023	NUM
uiug.30112106882779	141	18	than	than	ADP
uiug.30112106882779	141	19	with	with	ADP
uiug.30112106882779	141	20	n	n	CCONJ
uiug.30112106882779	141	21	=	=	SYM
uiug.30112106882779	141	22	99	99	NUM
uiug.30112106882779	141	23	,	,	PUNCT
uiug.30112106882779	141	24	the	the	DET
uiug.30112106882779	141	25	peak	peak	NOUN
uiug.30112106882779	141	26	is	be	AUX
uiug.30112106882779	141	27	still	still	ADV
uiug.30112106882779	141	28	rather	rather	ADV
uiug.30112106882779	141	29	crudely	crudely	ADV
uiug.30112106882779	141	30	modeled	model	VERB
uiug.30112106882779	141	31	despite	despite	SCONJ
uiug.30112106882779	141	32	a	a	DET
uiug.30112106882779	141	33	tenfold	tenfold	ADJ
uiug.30112106882779	141	34	increase	increase	NOUN
uiug.30112106882779	141	35	in	in	ADP
uiug.30112106882779	141	36	the	the	DET
uiug.30112106882779	141	37	number	number	NOUN
uiug.30112106882779	141	38	of	of	ADP
uiug.30112106882779	141	39	terms	term	NOUN
uiug.30112106882779	141	40	in	in	ADP
uiug.30112106882779	141	41	the	the	DET
uiug.30112106882779	141	42	fourier	fourier	ADJ
uiug.30112106882779	141	43	-	-	PUNCT
uiug.30112106882779	141	44	hermite	hermite	NOUN
uiug.30112106882779	141	45	expansion	expansion	NOUN
uiug.30112106882779	141	46	.	.	PUNCT
uiug.30112106882779	142	1	the	the	DET
uiug.30112106882779	142	2	root	root	NOUN
uiug.30112106882779	142	3	separation	separation	NOUN
uiug.30112106882779	142	4	diminishes	diminish	VERB
uiug.30112106882779	142	5	so	so	ADV
uiug.30112106882779	142	6	slowly	slowly	ADV
uiug.30112106882779	142	7	with	with	ADP
uiug.30112106882779	142	8	increasing	increase	VERB
uiug.30112106882779	142	9	n	n	CCONJ
uiug.30112106882779	142	10	that	that	SCONJ
uiug.30112106882779	142	11	most	most	ADJ
uiug.30112106882779	142	12	roots	root	NOUN
uiug.30112106882779	142	13	can	can	AUX
uiug.30112106882779	142	14	make	make	VERB
uiug.30112106882779	142	15	only	only	ADV
uiug.30112106882779	142	16	negligible	negligible	ADJ
uiug.30112106882779	142	17	contributions	contribution	NOUN
uiug.30112106882779	142	18	to	to	ADP
uiug.30112106882779	142	19	the	the	DET
uiug.30112106882779	142	20	peak	peak	NOUN
uiug.30112106882779	142	21	.	.	PUNCT
uiug.30112106882779	143	1	the	the	DET
uiug.30112106882779	143	2	advantage	advantage	NOUN
uiug.30112106882779	143	3	of	of	ADP
uiug.30112106882779	143	4	a	a	DET
uiug.30112106882779	143	5	collision	collision	NOUN
uiug.30112106882779	143	6	term	term	NOUN
uiug.30112106882779	143	7	barely	barely	ADV
uiug.30112106882779	143	8	large	large	ADJ
uiug.30112106882779	143	9	enough	enough	ADV
uiug.30112106882779	143	10	to	to	PART
uiug.30112106882779	143	11	move	move	VERB
uiug.30112106882779	143	12	a	a	DET
uiug.30112106882779	143	13	root	root	NOUN
uiug.30112106882779	143	14	very	very	ADV
uiug.30112106882779	143	15	close	close	ADV
uiug.30112106882779	143	16	to	to	ADP
uiug.30112106882779	143	17	the	the	DET
uiug.30112106882779	143	18	landau	landau	NOUN
uiug.30112106882779	143	19	pole	pole	NOUN
uiug.30112106882779	143	20	is	be	AUX
uiug.30112106882779	143	21	suggested	suggest	VERB
uiug.30112106882779	143	22	by	by	ADP
uiug.30112106882779	143	23	figure	figure	NOUN
uiug.30112106882779	143	24	4	4	NUM
uiug.30112106882779	143	25	.	.	PUNCT
uiug.30112106882779	144	1	with	with	ADP
uiug.30112106882779	144	2	a	a	DET
uiug.30112106882779	144	3	small	small	ADJ
uiug.30112106882779	144	4	collision	collision	NOUN
uiug.30112106882779	144	5	term	term	NOUN
uiug.30112106882779	144	6	,	,	PUNCT
uiug.30112106882779	144	7	a	a	DET
uiug.30112106882779	144	8	single	single	ADJ
uiug.30112106882779	144	9	fourierhermite	fourierhermite	NOUN
uiug.30112106882779	144	10	root	root	NOUN
uiug.30112106882779	144	11	can	can	AUX
uiug.30112106882779	144	12	well	well	ADV
uiug.30112106882779	144	13	represent	represent	VERB
uiug.30112106882779	144	14	the	the	DET
uiug.30112106882779	144	15	landau	landau	NOUN
uiug.30112106882779	144	16	damping	damp	VERB
uiug.30112106882779	144	17	,	,	PUNCT
uiug.30112106882779	144	18	which	which	PRON
uiug.30112106882779	144	19	is	be	AUX
uiug.30112106882779	144	20	the	the	DET
uiug.30112106882779	144	21	most	most	ADV
uiug.30112106882779	144	22	prominent	prominent	ADJ
uiug.30112106882779	144	23	feature	feature	NOUN
uiug.30112106882779	144	24	of	of	ADP
uiug.30112106882779	144	25	the	the	DET
uiug.30112106882779	144	26	behavior	behavior	NOUN
uiug.30112106882779	144	27	of	of	ADP
uiug.30112106882779	144	28	the	the	DET
uiug.30112106882779	144	29	plasma	plasma	NOUN
uiug.30112106882779	144	30	at	at	ADP
uiug.30112106882779	144	31	long	long	ADJ
uiug.30112106882779	144	32	times	time	NOUN
uiug.30112106882779	144	33	for	for	ADP
uiug.30112106882779	144	34	weak	weak	ADJ
uiug.30112106882779	144	35	initial	initial	ADJ
uiug.30112106882779	144	36	disturbances	disturbance	NOUN
uiug.30112106882779	144	37	of	of	ADP
uiug.30112106882779	144	38	the	the	DET
uiug.30112106882779	144	39	plasma	plasma	NOUN
uiug.30112106882779	144	40	.	.	PUNCT
uiug.30112106882779	145	1	concluding	conclude	VERB
uiug.30112106882779	145	2	remark	remark	NOUN
uiug.30112106882779	145	3	in	in	ADP
uiug.30112106882779	145	4	addition	addition	NOUN
uiug.30112106882779	145	5	to	to	ADP
uiug.30112106882779	145	6	yielding	yield	VERB
uiug.30112106882779	145	7	conclusive	conclusive	ADJ
uiug.30112106882779	145	8	indications	indication	NOUN
uiug.30112106882779	145	9	of	of	ADP
uiug.30112106882779	145	10	the	the	DET
uiug.30112106882779	145	11	nonuniformly	nonuniformly	ADV
uiug.30112106882779	145	12	convergent	convergent	ADJ
uiug.30112106882779	145	13	behavior	behavior	NOUN
uiug.30112106882779	145	14	of	of	ADP
uiug.30112106882779	145	15	the	the	DET
uiug.30112106882779	145	16	fourier	fourier	NOUN
uiug.30112106882779	145	17	-	-	PUNCT
uiug.30112106882779	145	18	hermite	hermite	NOUN
uiug.30112106882779	145	19	expansion	expansion	NOUN
uiug.30112106882779	145	20	as	as	SCONJ
uiug.30112106882779	145	21	order	order	NOUN
uiug.30112106882779	145	22	increases	increase	NOUN
uiug.30112106882779	145	23	to	to	ADP
uiug.30112106882779	145	24	infinity	infinity	NOUN
uiug.30112106882779	145	25	and	and	CCONJ
uiug.30112106882779	145	26	collisions	collision	NOUN
uiug.30112106882779	145	27	decrease	decrease	NOUN
uiug.30112106882779	146	1	,	,	PUNCT
uiug.30112106882779	146	2	the	the	DET
uiug.30112106882779	146	3	results	result	NOUN
uiug.30112106882779	146	4	have	have	AUX
uiug.30112106882779	146	5	provided	provide	VERB
uiug.30112106882779	146	6	a	a	DET
uiug.30112106882779	146	7	guide	guide	NOUN
uiug.30112106882779	146	8	to	to	ADP
uiug.30112106882779	146	9	the	the	DET
uiug.30112106882779	146	10	choice	choice	NOUN
uiug.30112106882779	146	11	of	of	ADP
uiug.30112106882779	146	12	the	the	DET
uiug.30112106882779	146	13	size	size	NOUN
uiug.30112106882779	146	14	of	of	ADP
uiug.30112106882779	146	15	collision	collision	NOUN
uiug.30112106882779	146	16	term	term	NOUN
uiug.30112106882779	146	17	that	that	PRON
uiug.30112106882779	146	18	best	well	ADV
uiug.30112106882779	146	19	simulates	simulate	VERB
uiug.30112106882779	146	20	the	the	DET
uiug.30112106882779	146	21	secular	secular	ADJ
uiug.30112106882779	146	22	behavior	behavior	NOUN
uiug.30112106882779	146	23	of	of	ADP
uiug.30112106882779	146	24	the	the	DET
uiug.30112106882779	146	25	plasma	plasma	NOUN
uiug.30112106882779	146	26	.	.	PUNCT
uiug.30112106882779	147	1	langley	langley	PROPN
uiug.30112106882779	147	2	research	research	PROPN
uiug.30112106882779	147	3	center	center	NOUN
uiug.30112106882779	147	4	,	,	PUNCT
uiug.30112106882779	147	5	national	national	ADJ
uiug.30112106882779	147	6	aeronautics	aeronautic	NOUN
uiug.30112106882779	147	7	and	and	CCONJ
uiug.30112106882779	147	8	space	space	PROPN
uiug.30112106882779	147	9	administration	administration	PROPN
uiug.30112106882779	147	10	,	,	PUNCT
uiug.30112106882779	147	11	hampton	hampton	PROPN
uiug.30112106882779	147	12	,	,	PUNCT
uiug.30112106882779	147	13	va	va	PROPN
uiug.30112106882779	147	14	.	.	PROPN
uiug.30112106882779	147	15	,	,	PUNCT
uiug.30112106882779	147	16	march	march	PROPN
uiug.30112106882779	147	17	23	23	NUM
uiug.30112106882779	147	18	,	,	PUNCT
uiug.30112106882779	147	19	1972	1972	NUM
uiug.30112106882779	147	20	.	.	PUNCT
uiug.30112106882779	148	1	10	10	NUM
uiug.30112106882779	148	2	appendix	appendix	NOUN
uiug.30112106882779	148	3	a	a	DET
uiug.30112106882779	148	4	calculation	calculation	NOUN
uiug.30112106882779	148	5	of	of	ADP
uiug.30112106882779	148	6	eigenvalues	eigenvalue	NOUN
uiug.30112106882779	148	7	the	the	DET
uiug.30112106882779	148	8	fortran	fortran	PROPN
uiug.30112106882779	148	9	iv	iv	PROPN
uiug.30112106882779	148	10	computer	computer	NOUN
uiug.30112106882779	148	11	program	program	NOUN
uiug.30112106882779	148	12	used	use	VERB
uiug.30112106882779	148	13	to	to	PART
uiug.30112106882779	148	14	compute	compute	VERB
uiug.30112106882779	148	15	the	the	DET
uiug.30112106882779	148	16	curves	curve	NOUN
uiug.30112106882779	148	17	for	for	ADP
uiug.30112106882779	148	18	n	n	NOUN
uiug.30112106882779	148	19	=	=	SYM
uiug.30112106882779	148	20	1023	1023	NUM
uiug.30112106882779	148	21	in	in	ADP
uiug.30112106882779	148	22	figures	figure	NOUN
uiug.30112106882779	148	23	2	2	NUM
uiug.30112106882779	148	24	and	and	CCONJ
uiug.30112106882779	148	25	3	3	NUM
uiug.30112106882779	148	26	follows	follow	NOUN
uiug.30112106882779	148	27	.	.	PUNCT
uiug.30112106882779	149	1	although	although	SCONJ
uiug.30112106882779	149	2	the	the	DET
uiug.30112106882779	149	3	dimensions	dimension	NOUN
uiug.30112106882779	149	4	100	100	NUM
uiug.30112106882779	149	5	and	and	CCONJ
uiug.30112106882779	149	6	1024	1024	NUM
uiug.30112106882779	149	7	have	have	AUX
uiug.30112106882779	149	8	been	be	AUX
uiug.30112106882779	149	9	used	use	VERB
uiug.30112106882779	149	10	respectively	respectively	ADV
uiug.30112106882779	149	11	for	for	ADP
uiug.30112106882779	149	12	arrays	array	NOUN
uiug.30112106882779	149	13	app	app	NOUN
uiug.30112106882779	149	14	(	(	PUNCT
uiug.30112106882779	149	15	corresponding	correspond	VERB
uiug.30112106882779	149	16	to	to	ADP
uiug.30112106882779	149	17	successive	successive	ADJ
uiug.30112106882779	149	18	root	root	NOUN
uiug.30112106882779	149	19	approximations	approximation	NOUN
uiug.30112106882779	149	20	)	)	PUNCT
uiug.30112106882779	149	21	and	and	CCONJ
uiug.30112106882779	149	22	det	det	PROPN
uiug.30112106882779	149	23	(	(	PUNCT
uiug.30112106882779	149	24	corresponding	correspond	VERB
uiug.30112106882779	149	25	to	to	ADP
uiug.30112106882779	149	26	the	the	DET
uiug.30112106882779	149	27	successive	successive	ADJ
uiug.30112106882779	149	28	determinants	determinant	NOUN
uiug.30112106882779	149	29	in	in	ADP
uiug.30112106882779	149	30	the	the	DET
uiug.30112106882779	149	31	recursive	recursive	ADJ
uiug.30112106882779	149	32	process	process	NOUN
uiug.30112106882779	149	33	)	)	PUNCT
uiug.30112106882779	149	34	,	,	PUNCT
uiug.30112106882779	149	35	these	these	DET
uiug.30112106882779	149	36	locations	location	NOUN
uiug.30112106882779	149	37	are	be	AUX
uiug.30112106882779	149	38	a	a	DET
uiug.30112106882779	149	39	luxury	luxury	NOUN
uiug.30112106882779	149	40	for	for	ADP
uiug.30112106882779	149	41	diagnostic	diagnostic	ADJ
uiug.30112106882779	149	42	purposes	purpose	NOUN
uiug.30112106882779	149	43	.	.	PUNCT
uiug.30112106882779	150	1	several	several	ADJ
uiug.30112106882779	150	2	locations	location	NOUN
uiug.30112106882779	150	3	would	would	AUX
uiug.30112106882779	150	4	suffice	suffice	VERB
uiug.30112106882779	150	5	if	if	SCONJ
uiug.30112106882779	150	6	the	the	DET
uiug.30112106882779	150	7	successive	successive	ADJ
uiug.30112106882779	150	8	root	root	NOUN
uiug.30112106882779	150	9	approximations	approximation	NOUN
uiug.30112106882779	150	10	and	and	CCONJ
uiug.30112106882779	150	11	higher	high	ADJ
uiug.30112106882779	150	12	order	order	NOUN
uiug.30112106882779	150	13	determinants	determinant	NOUN
uiug.30112106882779	150	14	were	be	AUX
uiug.30112106882779	150	15	written	write	VERB
uiug.30112106882779	150	16	over	over	ADP
uiug.30112106882779	150	17	the	the	DET
uiug.30112106882779	150	18	earlier	early	ADJ
uiug.30112106882779	150	19	values	value	NOUN
uiug.30112106882779	150	20	.	.	PUNCT
uiug.30112106882779	151	1	for	for	SCONJ
uiug.30112106882779	151	2	the	the	DET
uiug.30112106882779	151	3	case	case	NOUN
uiug.30112106882779	151	4	shown	show	VERB
uiug.30112106882779	151	5	,	,	PUNCT
uiug.30112106882779	151	6	central	central	ADJ
uiug.30112106882779	151	7	processor	processor	NOUN
uiug.30112106882779	151	8	time	time	NOUN
uiug.30112106882779	151	9	on	on	ADP
uiug.30112106882779	151	10	the	the	DET
uiug.30112106882779	151	11	cdc	cdc	PROPN
uiug.30112106882779	151	12	6600	6600	NUM
uiug.30112106882779	151	13	computer	computer	NOUN
uiug.30112106882779	151	14	was	be	AUX
uiug.30112106882779	151	15	less	less	ADJ
uiug.30112106882779	151	16	than	than	ADP
uiug.30112106882779	151	17	30	30	NUM
uiug.30112106882779	151	18	seconds	second	NOUN
uiug.30112106882779	151	19	.	.	PUNCT
uiug.30112106882779	152	1	program	program	NOUN
uiug.30112106882779	152	2	chase	chase	NOUN
uiug.30112106882779	152	3	(	(	PUNCT
uiug.30112106882779	152	4	input	input	NOUN
uiug.30112106882779	152	5	,	,	PUNCT
uiug.30112106882779	152	6	output	output	NOUN
uiug.30112106882779	152	7	)	)	PUNCT
uiug.30112106882779	152	8	,	,	PUNCT
uiug.30112106882779	152	9	*	*	PUNCT
uiug.30112106882779	152	10	tracks	track	VERB
uiug.30112106882779	152	11	f	f	PROPN
uiug.30112106882779	152	12	-	-	PUNCT
uiug.30112106882779	152	13	h	h	NOUN
uiug.30112106882779	152	14	roots	root	NOUN
uiug.30112106882779	152	15	into	into	ADP
uiug.30112106882779	152	16	complex	complex	ADJ
uiug.30112106882779	152	17	plane	plane	NOUN
uiug.30112106882779	152	18	as	as	ADP
uiug.30112106882779	152	19	b	b	NOUN
uiug.30112106882779	152	20	increases	increase	NOUN
uiug.30112106882779	152	21	from	from	ADP
uiug.30112106882779	152	22	zero	zero	NUM
uiug.30112106882779	152	23	,	,	PUNCT
uiug.30112106882779	152	24	complex	complex	ADJ
uiug.30112106882779	152	25	d	d	PROPN
uiug.30112106882779	152	26	,	,	PUNCT
uiug.30112106882779	152	27	omega	omega	NOUN
uiug.30112106882779	152	28	,	,	PUNCT
uiug.30112106882779	152	29	derd	derd	PROPN
uiug.30112106882779	152	30	,	,	PUNCT
uiug.30112106882779	152	31	deltom	deltom	PROPN
uiug.30112106882779	152	32	,	,	PUNCT
uiug.30112106882779	152	33	delmeg	delmeg	PROPN
uiug.30112106882779	152	34	,	,	PUNCT
uiug.30112106882779	152	35	app	app	PROPN
uiug.30112106882779	152	36	,	,	PUNCT
uiug.30112106882779	152	37	det	det	PROPN
uiug.30112106882779	152	38	,	,	PUNCT
uiug.30112106882779	152	39	omegao	omegao	ADJ
uiug.30112106882779	152	40	,	,	PUNCT
uiug.30112106882779	152	41	complex	complex	ADJ
uiug.30112106882779	152	42	derni	derni	NOUN
uiug.30112106882779	152	43	,	,	PUNCT
uiug.30112106882779	152	44	dern2	dern2	PROPN
uiug.30112106882779	152	45	,	,	PUNCT
uiug.30112106882779	152	46	real	real	ADJ
uiug.30112106882779	152	47	keksor	keksor	NOUN
uiug.30112106882779	152	48	,	,	PUNCT
uiug.30112106882779	152	49	common	common	ADJ
uiug.30112106882779	152	50	ksqr.b	ksqr.b	PROPN
uiug.30112106882779	152	51	,	,	PUNCT
uiug.30112106882779	152	52	is	be	AUX
uiug.30112106882779	152	53	,	,	PUNCT
uiug.30112106882779	152	54	scale	scale	NOUN
uiug.30112106882779	152	55	,	,	PUNCT
uiug.30112106882779	152	56	dimension	dimension	NOUN
uiug.30112106882779	152	57	app	app	NOUN
uiug.30112106882779	152	58	(	(	PUNCT
uiug.30112106882779	152	59	100	100	NUM
uiug.30112106882779	152	60	)	)	PUNCT
uiug.30112106882779	152	61	,	,	PUNCT
uiug.30112106882779	152	62	det	det	PROPN
uiug.30112106882779	152	63	(	(	PUNCT
uiug.30112106882779	152	64	1024	1024	NUM
uiug.30112106882779	152	65	)	)	PUNCT
uiug.30112106882779	152	66	,	,	PUNCT
uiug.30112106882779	152	67	k=5,-01	k=5,-01	PROPN
uiug.30112106882779	152	68	,	,	PUNCT
uiug.30112106882779	152	69	*	*	PUNCT
uiug.30112106882779	152	70	value	value	NOUN
uiug.30112106882779	152	71	of	of	ADP
uiug.30112106882779	152	72	nas	nas	PROPN
uiug.30112106882779	152	73	used	use	VERB
uiug.30112106882779	152	74	below	below	ADP
uiug.30112106882779	152	75	corresponds	correspond	NOUN
uiug.30112106882779	152	76	to	to	ADP
uiug.30112106882779	152	77	(	(	PUNCT
uiug.30112106882779	152	78	n-1	n-1	PROPN
uiug.30112106882779	152	79	)	)	PUNCT
uiug.30112106882779	152	80	hermite	hermite	PROPN
uiug.30112106882779	152	81	functions	function	NOUN
uiug.30112106882779	152	82	,	,	PUNCT
uiug.30112106882779	152	83	n=1024	n=1024	PROPN
uiug.30112106882779	152	84	,	,	PUNCT
uiug.30112106882779	152	85	*	*	NOUN
uiug.30112106882779	152	86	landau	landau	NOUN
uiug.30112106882779	152	87	pole	pole	NOUN
uiug.30112106882779	152	88	for	for	ADP
uiug.30112106882779	152	89	k=0.5	k=0.5	PROPN
uiug.30112106882779	152	90	is	be	AUX
uiug.30112106882779	152	91	at	at	ADP
uiug.30112106882779	152	92	(	(	PUNCT
uiug.30112106882779	152	93	1.41566	1.41566	NUM
uiug.30112106882779	152	94	,	,	PUNCT
uiug.30112106882779	152	95	.15336	.15336	PROPN
uiug.30112106882779	152	96	)	)	PUNCT
uiug.30112106882779	152	97	,	,	PUNCT
uiug.30112106882779	152	98	*	*	PUNCT
uiug.30112106882779	152	99	fourier	fourier	ADJ
uiug.30112106882779	152	100	-	-	PUNCT
uiug.30112106882779	152	101	hermite	hermite	NOUN
uiug.30112106882779	152	102	eigenvalue	eigenvalue	NOUN
uiug.30112106882779	152	103	nearest	nearest	ADP
uiug.30112106882779	152	104	real	real	ADJ
uiug.30112106882779	152	105	part	part	NOUN
uiug.30112106882779	152	106	of	of	ADP
uiug.30112106882779	152	107	landau	landau	NOUN
uiug.30112106882779	152	108	pole	pole	NOUN
uiug.30112106882779	152	109	,	,	PUNCT
uiug.30112106882779	152	110	omegao=	omegao=	NUM
uiug.30112106882779	152	111	(	(	PUNCT
uiug.30112106882779	152	112	1.41424,0	1.41424,0	NUM
uiug.30112106882779	152	113	.	.	PUNCT
uiug.30112106882779	152	114	)	)	PUNCT
uiug.30112106882779	152	115	,	,	PUNCT
uiug.30112106882779	152	116	print	print	PROPN
uiug.30112106882779	152	117	900	900	NUM
uiug.30112106882779	152	118	,	,	PUNCT
uiug.30112106882779	152	119	nok	nok	PROPN
uiug.30112106882779	152	120	,	,	PUNCT
uiug.30112106882779	152	121	*	*	NOUN
uiug.30112106882779	152	122	maximum	maximum	NOUN
uiug.30112106882779	152	123	number	number	NOUN
uiug.30112106882779	152	124	of	of	ADP
uiug.30112106882779	152	125	iterations	iteration	NOUN
uiug.30112106882779	152	126	allowed	allow	VERB
uiug.30112106882779	152	127	to	to	PART
uiug.30112106882779	152	128	fix	fix	VERB
uiug.30112106882779	152	129	omega	omega	NOUN
uiug.30112106882779	152	130	,	,	PUNCT
uiug.30112106882779	152	131	noit=100	noit=100	PROPN
uiug.30112106882779	152	132	,	,	PUNCT
uiug.30112106882779	152	133	*	*	NOUN
uiug.30112106882779	152	134	sharpness	sharpness	ADJ
uiug.30112106882779	152	135	criterion	criterion	NOUN
uiug.30112106882779	152	136	for	for	ADP
uiug.30112106882779	152	137	omega	omega	NOUN
uiug.30112106882779	152	138	,	,	PUNCT
uiug.30112106882779	152	139	cvlim=	cvlim=	NUM
uiug.30112106882779	152	140	2.f-09	2.f-09	NUM
uiug.30112106882779	152	141	,	,	PUNCT
uiug.30112106882779	152	142	*	*	NOUN
uiug.30112106882779	152	143	step	step	NOUN
uiug.30112106882779	152	144	size	size	NOUN
uiug.30112106882779	152	145	in	in	ADP
uiug.30112106882779	152	146	approximate	approximate	ADJ
uiug.30112106882779	152	147	derivative	derivative	NOUN
uiug.30112106882779	152	148	,	,	PUNCT
uiug.30112106882779	152	149	deltom=	deltom=	PRON
uiug.30112106882779	152	150	(	(	PUNCT
uiug.30112106882779	152	151	0.,1.f-05	0.,1.f-05	NUM
uiug.30112106882779	152	152	)	)	PUNCT
uiug.30112106882779	152	153	,	,	PUNCT
uiug.30112106882779	152	154	*	*	PUNCT
uiug.30112106882779	152	155	b	b	X
uiug.30112106882779	152	156	-	-	PUNCT
uiug.30112106882779	152	157	range	range	NOUN
uiug.30112106882779	152	158	and	and	CCONJ
uiug.30112106882779	152	159	step	step	NOUN
uiug.30112106882779	152	160	size	size	NOUN
uiug.30112106882779	152	161	,	,	PUNCT
uiug.30112106882779	152	162	bmin=.0002	bmin=.0002	PROPN
uiug.30112106882779	152	163	,	,	PUNCT
uiug.30112106882779	152	164	deltro.00002	deltro.00002	SPACE
uiug.30112106882779	152	165	,	,	PUNCT
uiug.30112106882779	152	166	bmax=	bmax=	PROPN
uiug.30112106882779	152	167	.0013	.0013	PROPN
uiug.30112106882779	152	168	,	,	PUNCT
uiug.30112106882779	152	169	ksorok*k	ksorok*k	PROPN
uiug.30112106882779	152	170	,	,	PUNCT
uiug.30112106882779	152	171	omega=	omega=	X
uiug.30112106882779	152	172	omegao	omegao	NOUN
uiug.30112106882779	152	173	,	,	PUNCT
uiug.30112106882779	152	174	b	b	NOUN
uiug.30112106882779	152	175	=	=	SYM
uiug.30112106882779	152	176	amin	amin	NOUN
uiug.30112106882779	152	177	-	-	PUNCT
uiug.30112106882779	152	178	deltb	deltb	NOUN
uiug.30112106882779	152	179	,	,	PUNCT
uiug.30112106882779	152	180	*	*	PUNCT
uiug.30112106882779	152	181	loop	loop	NOUN
uiug.30112106882779	152	182	on	on	ADP
uiug.30112106882779	152	183	e	e	NOUN
uiug.30112106882779	152	184	,	,	PUNCT
uiug.30112106882779	152	185	1	1	NUM
uiug.30112106882779	152	186	bebudeltb	bebudeltb	NOUN
uiug.30112106882779	152	187	.	.	PUNCT
uiug.30112106882779	153	1	*	*	PUNCT
uiug.30112106882779	153	2	newton	newton	PROPN
uiug.30112106882779	153	3	-	-	PUNCT
uiug.30112106882779	153	4	raphson	raphson	PROPN
uiug.30112106882779	153	5	loop	loop	PROPN
uiug.30112106882779	153	6	,	,	PUNCT
uiug.30112106882779	153	7	do21=1	do21=1	SPACE
uiug.30112106882779	153	8	,	,	PUNCT
uiug.30112106882779	153	9	no	no	INTJ
uiug.30112106882779	153	10	it	it	PRON
uiug.30112106882779	153	11	.	.	PUNCT
uiug.30112106882779	154	1	*	*	PUNCT
uiug.30112106882779	154	2	w2	w2	PROPN
uiug.30112106882779	154	3	,	,	PUNCT
uiug.30112106882779	154	4	derno	derno	NOUN
uiug.30112106882779	154	5	=	=	NOUN
uiug.30112106882779	154	6	d	d	NOUN
uiug.30112106882779	154	7	(	(	PUNCT
uiug.30112106882779	154	8	n	n	X
uiug.30112106882779	154	9	,	,	PUNCT
uiug.30112106882779	154	10	omega+del	omega+del	PROPN
uiug.30112106882779	154	11	tom	tom	PROPN
uiug.30112106882779	154	12	,	,	PUNCT
uiug.30112106882779	154	13	det	det	PROPN
uiug.30112106882779	154	14	)	)	PUNCT
uiug.30112106882779	154	15	,	,	PUNCT
uiug.30112106882779	154	16	*	*	PUNCT
uiug.30112106882779	154	17	number	number	NOUN
uiug.30112106882779	154	18	of	of	ADP
uiug.30112106882779	154	19	scalings	scaling	NOUN
uiug.30112106882779	154	20	,	,	PUNCT
uiug.30112106882779	154	21	is2	is2	PROPN
uiug.30112106882779	154	22	=	=	NOUN
uiug.30112106882779	154	23	is	be	AUX
uiug.30112106882779	154	24	,	,	PUNCT
uiug.30112106882779	154	25	ܙ	ܙ	ADV
uiug.30112106882779	154	26	1	1	NUM
uiug.30112106882779	154	27	ܐܙܙ	ܐܙܙ	PROPN
uiug.30112106882779	154	28	*	*	PUNCT
uiug.30112106882779	154	29	dern1	dern1	PROPN
uiug.30112106882779	154	30	=	=	NOUN
uiug.30112106882779	154	31	d	d	NOUN
uiug.30112106882779	154	32	(	(	PUNCT
uiug.30112106882779	154	33	n	n	PROPN
uiug.30112106882779	154	34	,	,	PUNCT
uiug.30112106882779	154	35	omegadet	omegadet	PROPN
uiug.30112106882779	154	36	)	)	PUNCT
uiug.30112106882779	154	37	,	,	PUNCT
uiug.30112106882779	154	38	is1	is1	NOUN
uiug.30112106882779	154	39	=	=	PROPN
uiug.30112106882779	154	40	is	be	AUX
uiug.30112106882779	154	41	,	,	PUNCT
uiug.30112106882779	154	42	11	11	NUM
uiug.30112106882779	154	43	appendix	appendix	NOUN
uiug.30112106882779	154	44	a	a	DET
uiug.30112106882779	154	45	concluded	conclude	VERB
uiug.30112106882779	154	46	*	*	NOUN
uiug.30112106882779	154	47	check	check	NOUN
uiug.30112106882779	154	48	to	to	PART
uiug.30112106882779	154	49	insure	insure	VERB
uiug.30112106882779	154	50	same	same	ADJ
uiug.30112106882779	154	51	scaling	scaling	NOUN
uiug.30112106882779	154	52	on	on	ADP
uiug.30112106882779	154	53	w2	w2	PROPN
uiug.30112106882779	154	54	,	,	PUNCT
uiug.30112106882779	154	55	w1	w1	PROPN
uiug.30112106882779	154	56	,	,	PUNCT
uiug.30112106882779	154	57	if(is2.equisi	if(is2.equisi	PROPN
uiug.30112106882779	154	58	)	)	PUNCT
uiug.30112106882779	154	59	go	go	VERB
uiug.30112106882779	154	60	to	to	ADP
uiug.30112106882779	154	61	4	4	NUM
uiug.30112106882779	154	62	.	.	PUNCT
uiug.30112106882779	155	1	if	if	SCONJ
uiug.30112106882779	155	2	(	(	PUNCT
uiug.30112106882779	155	3	is2	is2	NOUN
uiug.30112106882779	155	4	-	-	PUNCT
uiug.30112106882779	155	5	isi.gt.n	isi.gt.n	VERB
uiug.30112106882779	155	6	)	)	PUNCT
uiug.30112106882779	155	7	go	go	VERB
uiug.30112106882779	155	8	to	to	ADP
uiug.30112106882779	155	9	6	6	NUM
uiug.30112106882779	155	10	,	,	PUNCT
uiug.30112106882779	155	11	cern?=dern2	cern?=dern2	SPACE
uiug.30112106882779	155	12	*	*	PUNCT
uiug.30112106882779	155	13	scale	scale	PROPN
uiug.30112106882779	155	14	,	,	PUNCT
uiug.30112106882779	155	15	go	go	VERB
uiug.30112106882779	155	16	to	to	ADP
uiug.30112106882779	155	17	4	4	NUM
uiug.30112106882779	155	18	,	,	PUNCT
uiug.30112106882779	155	19	6	6	NUM
uiug.30112106882779	155	20	derni	derni	ADJ
uiug.30112106882779	155	21	=	=	PROPN
uiug.30112106882779	155	22	derni	derni	PROPN
uiug.30112106882779	155	23	scale	scale	PROPN
uiug.30112106882779	155	24	,	,	PUNCT
uiug.30112106882779	155	25	*	*	PUNCT
uiug.30112106882779	155	26	approximate	approximate	ADJ
uiug.30112106882779	155	27	derivative	derivative	ADJ
uiug.30112106882779	155	28	(	(	PUNCT
uiug.30112106882779	155	29	w2	w2	PROPN
uiug.30112106882779	155	30	-	-	PUNCT
uiug.30112106882779	155	31	wi	wi	PROPN
uiug.30112106882779	155	32	/	/	PUNCT
uiug.30112106882779	155	33	deltom	deltom	PROPN
uiug.30112106882779	155	34	,	,	PUNCT
uiug.30112106882779	155	35	4	4	NUM
uiug.30112106882779	155	36	derde	derde	X
uiug.30112106882779	155	37	(	(	PUNCT
uiug.30112106882779	155	38	dern2	dern2	PROPN
uiug.30112106882779	155	39	-	-	PUNCT
uiug.30112106882779	155	40	derni	derni	PROPN
uiug.30112106882779	155	41	)	)	PUNCT
uiug.30112106882779	155	42	del	del	PROPN
uiug.30112106882779	155	43	tcm	tcm	PROPN
uiug.30112106882779	155	44	,	,	PUNCT
uiug.30112106882779	155	45	*	*	PROPN
uiug.30112106882779	155	46	newton	newton	PROPN
uiug.30112106882779	155	47	-	-	PUNCT
uiug.30112106882779	155	48	raphson	raphson	PROPN
uiug.30112106882779	155	49	root	root	NOUN
uiug.30112106882779	155	50	increment	increment	NOUN
uiug.30112106882779	155	51	,	,	PUNCT
uiug.30112106882779	155	52	delmeg	delmeg	PROPN
uiug.30112106882779	155	53	=	=	SYM
uiug.30112106882779	155	54	dern1	dern1	PROPN
uiug.30112106882779	155	55	/depd	/depd	NOUN
uiug.30112106882779	155	56	,	,	PUNCT
uiug.30112106882779	155	57	omega	omega	NOUN
uiug.30112106882779	155	58	omega	omega	NOUN
uiug.30112106882779	155	59	-	-	PUNCT
uiug.30112106882779	155	60	delmeg	delmeg	PROPN
uiug.30112106882779	155	61	,	,	PUNCT
uiug.30112106882779	155	62	app	app	PROPN
uiug.30112106882779	155	63	(	(	PUNCT
uiug.30112106882779	155	64	i	i	NOUN
uiug.30112106882779	155	65	)	)	PUNCT
uiug.30112106882779	155	66	=	=	VERB
uiug.30112106882779	156	1	omega	omega	NOUN
uiug.30112106882779	156	2	,	,	PUNCT
uiug.30112106882779	156	3	*	*	PUNCT
uiug.30112106882779	156	4	check	check	VERB
uiug.30112106882779	156	5	on	on	ADP
uiug.30112106882779	156	6	improvement	improvement	NOUN
uiug.30112106882779	156	7	of	of	ADP
uiug.30112106882779	156	8	omega	omega	NOUN
uiug.30112106882779	156	9	,	,	PUNCT
uiug.30112106882779	156	10	2	2	NUM
uiug.30112106882779	156	11	if(cabs	if(cab	NOUN
uiug.30112106882779	156	12	(	(	PUNCT
uiug.30112106882779	156	13	delmeg)olt.cvlimi	delmeg)olt.cvlimi	PROPN
uiug.30112106882779	156	14	go	go	VERB
uiug.30112106882779	156	15	to	to	ADP
uiug.30112106882779	156	16	3	3	NUM
uiug.30112106882779	156	17	,	,	PUNCT
uiug.30112106882779	156	18	)	)	PUNCT
uiug.30112106882779	156	19	3	3	NUM
uiug.30112106882779	156	20	print	print	NOUN
uiug.30112106882779	156	21	100,3,1	100,3,1	NUM
uiug.30112106882779	156	22	,	,	PUNCT
uiug.30112106882779	156	23	omega	omega	NOUN
uiug.30112106882779	156	24	,	,	PUNCT
uiug.30112106882779	156	25	print	print	PROPN
uiug.30112106882779	156	26	101.is	101.is	NUM
uiug.30112106882779	156	27	,	,	PUNCT
uiug.30112106882779	156	28	100	100	NUM
uiug.30112106882779	156	29	formato	formato	NOUN
uiug.30112106882779	156	30	3h	3h	X
uiug.30112106882779	156	31	b	b	X
uiug.30112106882779	156	32	=	=	SYM
uiug.30112106882779	156	33	f10.6,5x11	f10.6,5x11	X
uiug.30112106882779	156	34	hiterations	hiteration	NOUN
uiug.30112106882779	156	35	=	=	VERB
uiug.30112106882779	156	36	13,5x6home	13,5x6home	NUM
uiug.30112106882779	156	37	ga	ga	NOUN
uiug.30112106882779	156	38	=	=	PROPN
uiug.30112106882779	156	39	f11.8	f11.8	SPACE
uiug.30112106882779	156	40	,	,	PUNCT
uiug.30112106882779	156	41	f11.8	f11.8	SPACE
uiug.30112106882779	156	42	)	)	PUNCT
uiug.30112106882779	156	43	,	,	PUNCT
uiug.30112106882779	156	44	=	=	PROPN
uiug.30112106882779	156	45	101	101	NUM
uiug.30112106882779	156	46	format	format	NOUN
uiug.30112106882779	156	47	(	(	PUNCT
uiug.30112106882779	156	48	1x3his=13	1x3his=13	NUM
uiug.30112106882779	156	49	)	)	PUNCT
uiug.30112106882779	156	50	,	,	PUNCT
uiug.30112106882779	156	51	900	900	NUM
uiug.30112106882779	156	52	format(1/3h	format(1/3h	NOUN
uiug.30112106882779	156	53	n=1	n=1	PROPN
uiug.30112106882779	156	54	4/3h	4/3h	NUM
uiug.30112106882779	157	1	k	k	X
uiug.30112106882779	157	2	=	=	NOUN
uiug.30112106882779	157	3	f6.3/1	f6.3/1	PROPN
uiug.30112106882779	157	4	)	)	PUNCT
uiug.30112106882779	157	5	,	,	PUNCT
uiug.30112106882779	157	6	if	if	SCONJ
uiug.30112106882779	157	7	(	(	PUNCT
uiug.30112106882779	157	8	b.lt.bmax	b.lt.bmax	NOUN
uiug.30112106882779	157	9	-	-	PUNCT
uiug.30112106882779	157	10	deltb/2	deltb/2	NOUN
uiug.30112106882779	157	11	.	.	PROPN
uiug.30112106882779	157	12	)	)	PUNCT
uiug.30112106882779	157	13	,	,	PUNCT
uiug.30112106882779	157	14	2	2	NUM
uiug.30112106882779	157	15	go	go	VERB
uiug.30112106882779	157	16	to	to	ADP
uiug.30112106882779	157	17	1.4	1.4	NUM
uiug.30112106882779	157	18	stop	stop	NOUN
uiug.30112106882779	157	19	,	,	PUNCT
uiug.30112106882779	157	20	enn	enn	PROPN
uiug.30112106882779	157	21	,	,	PUNCT
uiug.30112106882779	157	22	*	*	PUNCT
uiug.30112106882779	157	23	subprogram	subprogram	NOUN
uiug.30112106882779	157	24	for	for	ADP
uiug.30112106882779	157	25	dispersion	dispersion	NOUN
uiug.30112106882779	157	26	determinant	determinant	ADJ
uiug.30112106882779	157	27	,	,	PUNCT
uiug.30112106882779	157	28	complex	complex	ADJ
uiug.30112106882779	157	29	function	function	NOUN
uiug.30112106882779	157	30	d(iord	d(iord	PROPN
uiug.30112106882779	157	31	,	,	PUNCT
uiug.30112106882779	157	32	omega	omega	NOUN
uiug.30112106882779	157	33	,	,	PUNCT
uiug.30112106882779	157	34	det	det	PROPN
uiug.30112106882779	157	35	)	)	PUNCT
uiug.30112106882779	157	36	,	,	PUNCT
uiug.30112106882779	157	37	complex	complex	ADJ
uiug.30112106882779	157	38	omega	omega	NOUN
uiug.30112106882779	157	39	,	,	PUNCT
uiug.30112106882779	157	40	det	det	PROPN
uiug.30112106882779	157	41	,	,	PUNCT
uiug.30112106882779	157	42	real	real	ADJ
uiug.30112106882779	157	43	ksqr	ksqr	NOUN
uiug.30112106882779	157	44	,	,	PUNCT
uiug.30112106882779	157	45	common	common	ADJ
uiug.30112106882779	157	46	ksqr	ksqr	NOUN
uiug.30112106882779	157	47	,	,	PUNCT
uiug.30112106882779	157	48	b	b	NOUN
uiug.30112106882779	157	49	,	,	PUNCT
uiug.30112106882779	157	50	is	be	AUX
uiug.30112106882779	157	51	,	,	PUNCT
uiug.30112106882779	157	52	scale	scale	NOUN
uiug.30112106882779	157	53	,	,	PUNCT
uiug.30112106882779	157	54	dimension	dimension	NOUN
uiug.30112106882779	157	55	det	det	PROPN
uiug.30112106882779	157	56	i	i	PROPN
uiug.30112106882779	157	57	ord	ord	PROPN
uiug.30112106882779	157	58	)	)	PUNCT
uiug.30112106882779	157	59	,	,	PUNCT
uiug.30112106882779	157	60	*	*	PUNCT
uiug.30112106882779	157	61	first	first	ADV
uiug.30112106882779	157	62	determinants	determinant	NOUN
uiug.30112106882779	157	63	,	,	PUNCT
uiug.30112106882779	157	64	det	det	PROPN
uiug.30112106882779	157	65	(	(	PUNCT
uiug.30112106882779	157	66	1	1	NUM
uiug.30112106882779	157	67	)	)	PUNCT
uiug.30112106882779	157	68	=	=	SYM
uiug.30112106882779	157	69	omega	omega	NOUN
uiug.30112106882779	157	70	,	,	PUNCT
uiug.30112106882779	157	71	det	det	PROPN
uiug.30112106882779	157	72	(	(	PUNCT
uiug.30112106882779	157	73	?	?	PUNCT
uiug.30112106882779	157	74	)	)	PUNCT
uiug.30112106882779	158	1	=	=	PUNCT
uiug.30112106882779	159	1	omega	omega	NOUN
uiug.30112106882779	159	2	*	*	PUNCT
uiug.30112106882779	159	3	(	(	PUNCT
uiug.30112106882779	159	4	omega+cmplx(0.,1.0)*b)-(1	omega+cmplx(0.,1.0)*b)-(1	PROPN
uiug.30112106882779	159	5	.	.	PUNCT
uiug.30112106882779	160	1	+	+	PROPN
uiug.30112106882779	160	2	k	k	PROPN
uiug.30112106882779	160	3	sqr	sqr	PROPN
uiug.30112106882779	160	4	)	)	PUNCT
uiug.30112106882779	160	5	,	,	PUNCT
uiug.30112106882779	160	6	scalf=1.f-18	scalf=1.f-18	PROPN
uiug.30112106882779	160	7	,	,	PUNCT
uiug.30112106882779	160	8	is=0	is=0	NUM
uiug.30112106882779	160	9	*	*	SYM
uiug.30112106882779	160	10	re	re	PROPN
uiug.30112106882779	160	11	cursion	cursion	NOUN
uiug.30112106882779	160	12	loop	loop	PROPN
uiug.30112106882779	160	13	,	,	PUNCT
uiug.30112106882779	160	14	doi	doi	PROPN
uiug.30112106882779	160	15	1	1	NUM
uiug.30112106882779	160	16	-	-	SYM
uiug.30112106882779	160	17	3	3	NUM
uiug.30112106882779	160	18	,	,	PUNCT
uiug.30112106882779	160	19	i	i	PROPN
uiug.30112106882779	160	20	ord	ord	PROPN
uiug.30112106882779	160	21	,	,	PUNCT
uiug.30112106882779	160	22	det	det	PROPN
uiug.30112106882779	160	23	(	(	PUNCT
uiug.30112106882779	160	24	i	i	NOUN
uiug.30112106882779	160	25	)	)	PUNCT
uiug.30112106882779	161	1	=	=	PROPN
uiug.30112106882779	161	2	det	det	PROPN
uiug.30112106882779	161	3	(	(	PUNCT
uiug.30112106882779	161	4	1	1	NUM
uiug.30112106882779	161	5	-	-	SYM
uiug.30112106882779	161	6	1	1	NUM
uiug.30112106882779	161	7	)	)	PUNCT
uiug.30112106882779	161	8	*	*	PUNCT
uiug.30112106882779	161	9	(	(	PUNCT
uiug.30112106882779	161	10	omega+float	omega+float	PROPN
uiug.30112106882779	161	11	(	(	PUNCT
uiug.30112106882779	161	12	1	1	NUM
uiug.30112106882779	161	13	-	-	SYM
uiug.30112106882779	161	14	1)*cmplx(0.,1.)*b)-float(i-1	1)*cmplx(0.,1.)*b)-float(i-1	NUM
uiug.30112106882779	161	15	)	)	PUNCT
uiug.30112106882779	161	16	*	*	PROPN
uiug.30112106882779	161	17	,	,	PUNCT
uiug.30112106882779	161	18	2k	2k	NUM
uiug.30112106882779	161	19	sqr*det(1	sqr*det(1	NOUN
uiug.30112106882779	161	20	-	-	SYM
uiug.30112106882779	161	21	2	2	NUM
uiug.30112106882779	161	22	)	)	PUNCT
uiug.30112106882779	161	23	,	,	PUNCT
uiug.30112106882779	161	24	*	*	PUNCT
uiug.30112106882779	161	25	check	check	VERB
uiug.30112106882779	161	26	on	on	ADP
uiug.30112106882779	161	27	size	size	NOUN
uiug.30112106882779	161	28	of	of	ADP
uiug.30112106882779	161	29	d	d	NOUN
uiug.30112106882779	161	30	,	,	PUNCT
uiug.30112106882779	161	31	if(cabs	if(cabs	PROPN
uiug.30112106882779	161	32	(	(	PUNCT
uiug.30112106882779	161	33	det(i)volt.1.e18	det(i)volt.1.e18	PROPN
uiug.30112106882779	161	34	)	)	PUNCT
uiug.30112106882779	161	35	go	go	VERB
uiug.30112106882779	161	36	to	to	ADP
uiug.30112106882779	161	37	1	1	NUM
uiug.30112106882779	161	38	,	,	PUNCT
uiug.30112106882779	161	39	*	*	PUNCT
uiug.30112106882779	161	40	scaling	scaling	NOUN
uiug.30112106882779	161	41	of	of	ADP
uiug.30112106882779	161	42	d.	d.	PROPN
uiug.30112106882779	161	43	,	,	PUNCT
uiug.30112106882779	161	44	2	2	NUM
uiug.30112106882779	161	45	det(i	det(i	PROPN
uiug.30112106882779	161	46	)	)	PUNCT
uiug.30112106882779	161	47	=	=	PROPN
uiug.30112106882779	161	48	dft	dft	PROPN
uiug.30112106882779	161	49	(	(	PUNCT
uiug.30112106882779	161	50	!	!	PUNCT
uiug.30112106882779	161	51	)	)	PUNCT
uiug.30112106882779	162	1	*	*	PUNCT
uiug.30112106882779	162	2	scale	scale	PROPN
uiug.30112106882779	162	3	,	,	PUNCT
uiug.30112106882779	162	4	det(i-1)=det	det(i-1)=det	NOUN
uiug.30112106882779	162	5	(	(	PUNCT
uiug.30112106882779	162	6	1	1	NUM
uiug.30112106882779	162	7	-	-	SYM
uiug.30112106882779	162	8	1)*scale	1)*scale	NUM
uiug.30112106882779	162	9	,	,	PUNCT
uiug.30112106882779	162	10	*	*	VERB
uiug.30112106882779	162	11	scaling	scaling	NOUN
uiug.30112106882779	162	12	count	count	NOUN
uiug.30112106882779	162	13	,	,	PUNCT
uiug.30112106882779	162	14	is=15	is=15	PROPN
uiug.30112106882779	162	15	+	+	PROPN
uiug.30112106882779	162	16	1	1	NUM
uiug.30112106882779	162	17	,	,	PUNCT
uiug.30112106882779	162	18	1	1	NUM
uiug.30112106882779	162	19	continue	continue	VERB
uiug.30112106882779	162	20	,	,	PUNCT
uiug.30112106882779	162	21	d	d	NOUN
uiug.30112106882779	162	22	=	=	PROPN
uiug.30112106882779	162	23	detci	detci	PROPN
uiug.30112106882779	162	24	ord	ord	PROPN
uiug.30112106882779	162	25	)	)	PUNCT
uiug.30112106882779	162	26	.	.	PUNCT
uiug.30112106882779	163	1	return	return	VERB
uiug.30112106882779	163	2	end	end	NOUN
uiug.30112106882779	163	3	,	,	PUNCT
uiug.30112106882779	163	4	12	12	NUM
uiug.30112106882779	163	5	appendix	appendix	ADJ
uiug.30112106882779	163	6	b	b	NOUN
uiug.30112106882779	163	7	derivation	derivation	NOUN
uiug.30112106882779	163	8	of	of	ADP
uiug.30112106882779	163	9	kla	kla	PROPN
uiug.30112106882779	163	10	)	)	PUNCT
uiug.30112106882779	163	11	the	the	DET
uiug.30112106882779	163	12	linearized	linearize	VERB
uiug.30112106882779	163	13	one	one	NUM
uiug.30112106882779	163	14	-	-	PUNCT
uiug.30112106882779	163	15	dimensional	dimensional	ADJ
uiug.30112106882779	163	16	vlasov	vlasov	NOUN
uiug.30112106882779	163	17	equations	equation	NOUN
uiug.30112106882779	163	18	,	,	PUNCT
uiug.30112106882779	163	19	in	in	ADP
uiug.30112106882779	163	20	natural	natural	ADJ
uiug.30112106882779	163	21	units	unit	NOUN
uiug.30112106882779	163	22	,	,	PUNCT
uiug.30112106882779	163	23	for	for	ADP
uiug.30112106882779	163	24	the	the	DET
uiug.30112106882779	163	25	electronic	electronic	ADJ
uiug.30112106882779	163	26	perturbation	perturbation	NOUN
uiug.30112106882779	163	27	f	f	PROPN
uiug.30112106882779	163	28	on	on	ADP
uiug.30112106882779	163	29	a	a	DET
uiug.30112106882779	163	30	uniform	uniform	ADJ
uiug.30112106882779	163	31	ionic	ionic	ADJ
uiug.30112106882779	163	32	background	background	NOUN
uiug.30112106882779	163	33	distribution	distribution	NOUN
uiug.30112106882779	163	34	are	be	AUX
uiug.30112106882779	163	35	af	af	ADV
uiug.30112106882779	163	36	af	af	INTJ
uiug.30112106882779	163	37	+	+	ADP
uiug.30112106882779	163	38	v	v	NOUN
uiug.30112106882779	163	39	at	at	ADP
uiug.30112106882779	163	40	ef	ef	PROPN
uiug.30112106882779	163	41	'	'	PUNCT
uiug.30112106882779	163	42	=	=	NOUN
uiug.30112106882779	163	43	0	0	NUM
uiug.30112106882779	163	44	(	(	PUNCT
uiug.30112106882779	163	45	bla	bla	NOUN
uiug.30112106882779	163	46	)	)	PUNCT
uiug.30112106882779	163	47	əx	əx	ADP
uiug.30112106882779	163	48	әe	әe	PROPN
uiug.30112106882779	163	49	ax	ax	PROPN
uiug.30112106882779	163	50	ii	ii	PROPN
uiug.30112106882779	163	51	s	s	X
uiug.30112106882779	163	52	f	f	PROPN
uiug.30112106882779	163	53	dx	dx	PROPN
uiug.30112106882779	163	54	(	(	PUNCT
uiug.30112106882779	163	55	b1b	b1b	X
uiug.30112106882779	163	56	)	)	PUNCT
uiug.30112106882779	163	57	where	where	SCONJ
uiug.30112106882779	163	58	f	f	PROPN
uiug.30112106882779	163	59	is	be	AUX
uiug.30112106882779	163	60	the	the	DET
uiug.30112106882779	163	61	unperturbed	unperturbed	ADJ
uiug.30112106882779	163	62	velocity	velocity	NOUN
uiug.30112106882779	163	63	distribution	distribution	NOUN
uiug.30112106882779	163	64	of	of	ADP
uiug.30112106882779	163	65	the	the	DET
uiug.30112106882779	163	66	electrons	electron	NOUN
uiug.30112106882779	163	67	.	.	PUNCT
uiug.30112106882779	164	1	the	the	DET
uiug.30112106882779	164	2	fourier	fourier	NOUN
uiug.30112106882779	164	3	-	-	PUNCT
uiug.30112106882779	164	4	laplace	laplace	NOUN
uiug.30112106882779	164	5	transform	transform	NOUN
uiug.30112106882779	164	6	of	of	ADP
uiug.30112106882779	164	7	f(x	f(x	PROPN
uiug.30112106882779	164	8	,	,	PUNCT
uiug.30112106882779	164	9	v	v	NOUN
uiug.30112106882779	164	10	,	,	PUNCT
uiug.30112106882779	164	11	t	t	PROPN
uiug.30112106882779	164	12	)	)	PUNCT
uiug.30112106882779	164	13	may	may	AUX
uiug.30112106882779	164	14	be	be	AUX
uiug.30112106882779	164	15	written	write	VERB
uiug.30112106882779	164	16	as	as	ADP
uiug.30112106882779	164	17	f(8,5	f(8,5	PROPN
uiug.30112106882779	164	18	)	)	PUNCT
uiug.30112106882779	164	19	=	=	PROPN
uiug.30112106882779	164	20	z1	z1	PROPN
uiug.30112106882779	165	1	so	so	ADV
uiug.30112106882779	165	2	at	at	ADP
uiug.30112106882779	165	3	sdx	sdx	PROPN
uiug.30112106882779	165	4	e	e	PROPN
uiug.30112106882779	165	5	-	-	PROPN
uiug.30112106882779	165	6	ste+{kx	ste+{kx	PROPN
uiug.30112106882779	165	7	f(x	f(x	PROPN
uiug.30112106882779	165	8	,	,	PUNCT
uiug.30112106882779	165	9	v	v	NOUN
uiug.30112106882779	165	10	,	,	PUNCT
uiug.30112106882779	165	11	t	t	PROPN
uiug.30112106882779	165	12	)	)	PUNCT
uiug.30112106882779	165	13	xsc	xsc	PROPN
uiug.30112106882779	165	14	ks	ks	PROPN
uiug.30112106882779	165	15	)	)	PUNCT
uiug.30112106882779	165	16	dt	dt	PROPN
uiug.30112106882779	165	17	211	211	NUM
uiug.30112106882779	165	18	where	where	SCONJ
uiug.30112106882779	165	19	the	the	DET
uiug.30112106882779	165	20	same	same	ADJ
uiug.30112106882779	165	21	symbol	symbol	NOUN
uiug.30112106882779	165	22	f	f	PROPN
uiug.30112106882779	165	23	is	be	AUX
uiug.30112106882779	165	24	used	use	VERB
uiug.30112106882779	165	25	for	for	ADP
uiug.30112106882779	165	26	both	both	DET
uiug.30112106882779	165	27	function	function	NOUN
uiug.30112106882779	165	28	and	and	CCONJ
uiug.30112106882779	165	29	transform	transform	NOUN
uiug.30112106882779	165	30	.	.	PUNCT
uiug.30112106882779	166	1	the	the	DET
uiug.30112106882779	166	2	corresponding	correspond	VERB
uiug.30112106882779	166	3	inverse	inverse	NOUN
uiug.30112106882779	166	4	is	be	AUX
uiug.30112106882779	166	5	+100	+100	NUM
uiug.30112106882779	166	6	+	+	NUM
uiug.30112106882779	166	7	8	8	NUM
uiug.30112106882779	166	8	f(x	f(x	NUM
uiug.30112106882779	166	9	,	,	PUNCT
uiug.30112106882779	166	10	v	v	NOUN
uiug.30112106882779	166	11	,	,	PUNCT
uiug.30112106882779	166	12	t	t	PROPN
uiug.30112106882779	166	13	)	)	PUNCT
uiug.30112106882779	166	14	1	1	NUM
uiug.30112106882779	166	15	20i	20i	NUM
uiug.30112106882779	166	16	ds	ds	PROPN
uiug.30112106882779	166	17	s	s	PART
uiug.30112106882779	166	18	dk	dk	PROPN
uiug.30112106882779	166	19	e+ste	e+ste	ADJ
uiug.30112106882779	166	20	-	-	PUNCT
uiug.30112106882779	166	21	ikx	ikx	NOUN
uiug.30112106882779	166	22	f(k	f(k	PROPN
uiug.30112106882779	166	23	,	,	PUNCT
uiug.30112106882779	166	24	s	s	PART
uiug.30112106882779	166	25	)	)	PUNCT
uiug.30112106882779	166	26	-100	-100	NUM
uiug.30112106882779	166	27	+	+	NUM
uiug.30112106882779	166	28	0	0	NUM
uiug.30112106882779	166	29	where	where	SCONJ
uiug.30112106882779	166	30	the	the	DET
uiug.30112106882779	166	31	integral	integral	NOUN
uiug.30112106882779	166	32	on	on	ADP
uiug.30112106882779	166	33	s	s	VERB
uiug.30112106882779	166	34	is	be	AUX
uiug.30112106882779	166	35	known	know	VERB
uiug.30112106882779	166	36	as	as	ADP
uiug.30112106882779	166	37	bromwich	bromwich	PROPN
uiug.30112106882779	166	38	's	's	PART
uiug.30112106882779	166	39	integral	integral	ADJ
uiug.30112106882779	166	40	.	.	PUNCT
uiug.30112106882779	167	1	on	on	ADP
uiug.30112106882779	167	2	application	application	NOUN
uiug.30112106882779	167	3	of	of	ADP
uiug.30112106882779	167	4	the	the	DET
uiug.30112106882779	167	5	fourierlaplace	fourierlaplace	NOUN
uiug.30112106882779	167	6	transform	transform	NOUN
uiug.30112106882779	167	7	to	to	ADP
uiug.30112106882779	167	8	equations	equation	NOUN
uiug.30112106882779	167	9	(	(	PUNCT
uiug.30112106882779	167	10	b1	b1	PROPN
uiug.30112106882779	167	11	)	)	PUNCT
uiug.30112106882779	167	12	,	,	PUNCT
uiug.30112106882779	167	13	the	the	DET
uiug.30112106882779	167	14	result	result	NOUN
uiug.30112106882779	167	15	is	be	AUX
uiug.30112106882779	167	16	s	s	PROPN
uiug.30112106882779	167	17	f(k	f(k	PROPN
uiug.30112106882779	167	18	,	,	PUNCT
uiug.30112106882779	167	19	s	s	PART
uiug.30112106882779	167	20	)	)	PUNCT
uiug.30112106882779	167	21	ikv	ikv	PROPN
uiug.30112106882779	167	22	f(k	f(k	PROPN
uiug.30112106882779	167	23	,	,	PUNCT
uiug.30112106882779	167	24	s	s	PART
uiug.30112106882779	167	25	)	)	PUNCT
uiug.30112106882779	167	26	f	f	PROPN
uiug.30112106882779	167	27	'	'	PUNCT
uiug.30112106882779	167	28	eſk	eſk	PROPN
uiug.30112106882779	167	29	,	,	PUNCT
uiug.30112106882779	167	30	s	s	PROPN
uiug.30112106882779	167	31	)	)	PUNCT
uiug.30112106882779	167	32	=	=	PROPN
uiug.30112106882779	167	33	fo(k	fo(k	PROPN
uiug.30112106882779	167	34	,	,	PUNCT
uiug.30112106882779	167	35	v	v	NOUN
uiug.30112106882779	167	36	)	)	PUNCT
uiug.30112106882779	167	37	(	(	PUNCT
uiug.30112106882779	167	38	b2a	b2a	NOUN
uiug.30112106882779	167	39	)	)	PUNCT
uiug.30112106882779	167	40	tik	tik	PROPN
uiug.30112106882779	167	41	e(k,5	e(k,5	PROPN
uiug.30112106882779	167	42	)	)	PUNCT
uiug.30112106882779	168	1	=	=	PROPN
uiug.30112106882779	169	1	sº	sº	PROPN
uiug.30112106882779	169	2	f(k	f(k	PROPN
uiug.30112106882779	169	3	,	,	PUNCT
uiug.30112106882779	169	4	s)dv	s)dv	PROPN
uiug.30112106882779	169	5	=	=	SYM
uiug.30112106882779	169	6	n(k,8	n(k,8	PROPN
uiug.30112106882779	169	7	)	)	PUNCT
uiug.30112106882779	169	8	(	(	PUNCT
uiug.30112106882779	169	9	b2b	b2b	PROPN
uiug.30112106882779	169	10	)	)	PUNCT
uiug.30112106882779	169	11	to	to	PART
uiug.30112106882779	169	12	obtain	obtain	VERB
uiug.30112106882779	169	13	equations	equation	NOUN
uiug.30112106882779	169	14	(	(	PUNCT
uiug.30112106882779	169	15	b2	b2	X
uiug.30112106882779	169	16	)	)	PUNCT
uiug.30112106882779	169	17	the	the	DET
uiug.30112106882779	169	18	usual	usual	ADJ
uiug.30112106882779	169	19	relations	relation	NOUN
uiug.30112106882779	169	20	l	l	NOUN
uiug.30112106882779	169	21	of	of	ADP
uiug.30112106882779	169	22	at	at	ADP
uiug.30112106882779	169	23	s{{f	s{{f	NOUN
uiug.30112106882779	169	24	}	}	PUNCT
uiug.30112106882779	169	25	f(x	f(x	PROPN
uiug.30112106882779	169	26	,	,	PUNCT
uiug.30112106882779	169	27	v,0	v,0	PROPN
uiug.30112106882779	169	28	)	)	PUNCT
uiug.30112106882779	169	29	3	3	NUM
uiug.30112106882779	170	1	af	af	PROPN
uiug.30112106882779	170	2	ax	ax	PROPN
uiug.30112106882779	170	3	-ik7{f	-ik7{f	NOUN
uiug.30112106882779	170	4	}	}	PUNCT
uiug.30112106882779	170	5	13	13	NUM
uiug.30112106882779	170	6	appendix	appendix	PROPN
uiug.30112106882779	170	7	b	b	NOUN
uiug.30112106882779	170	8	–	–	PUNCT
uiug.30112106882779	170	9	continued	continue	VERB
uiug.30112106882779	170	10	are	be	AUX
uiug.30112106882779	170	11	employed	employ	VERB
uiug.30112106882779	170	12	.	.	PUNCT
uiug.30112106882779	171	1	the	the	DET
uiug.30112106882779	171	2	notation	notation	NOUN
uiug.30112106882779	171	3	fo(k	fo(k	PROPN
uiug.30112106882779	171	4	,	,	PUNCT
uiug.30112106882779	171	5	v	v	NOUN
uiug.30112106882779	171	6	)	)	PUNCT
uiug.30112106882779	171	7	refers	refer	VERB
uiug.30112106882779	171	8	to	to	ADP
uiug.30112106882779	171	9	3{f(x	3{f(x	NUM
uiug.30112106882779	171	10	,	,	PUNCT
uiug.30112106882779	171	11	v,0	v,0	PROPN
uiug.30112106882779	171	12	)	)	PUNCT
uiug.30112106882779	171	13	,	,	PUNCT
uiug.30112106882779	171	14	the	the	DET
uiug.30112106882779	171	15	fourier	fourier	NOUN
uiug.30112106882779	171	16	transform	transform	NOUN
uiug.30112106882779	171	17	of	of	ADP
uiug.30112106882779	171	18	the	the	DET
uiug.30112106882779	171	19	initial	initial	ADJ
uiug.30112106882779	171	20	conditions	condition	NOUN
uiug.30112106882779	171	21	.	.	PUNCT
uiug.30112106882779	172	1	in	in	ADP
uiug.30112106882779	172	2	equations	equation	NOUN
uiug.30112106882779	172	3	(	(	PUNCT
uiug.30112106882779	172	4	b2	b2	NOUN
uiug.30112106882779	172	5	)	)	PUNCT
uiug.30112106882779	172	6	,	,	PUNCT
uiug.30112106882779	172	7	f(k	f(k	PROPN
uiug.30112106882779	172	8	,	,	PUNCT
uiug.30112106882779	172	9	s	s	PART
uiug.30112106882779	172	10	)	)	PUNCT
uiug.30112106882779	172	11	has	have	VERB
uiug.30112106882779	172	12	an	an	DET
uiug.30112106882779	172	13	implicit	implicit	ADJ
uiug.30112106882779	172	14	dependence	dependence	NOUN
uiug.30112106882779	172	15	on	on	ADP
uiug.30112106882779	172	16	velocity	velocity	NOUN
uiug.30112106882779	172	17	v	v	NOUN
uiug.30112106882779	172	18	,	,	PUNCT
uiug.30112106882779	172	19	but	but	CCONJ
uiug.30112106882779	172	20	n(k	n(k	PROPN
uiug.30112106882779	172	21	,	,	PUNCT
uiug.30112106882779	172	22	s	s	PART
uiug.30112106882779	172	23	)	)	PUNCT
uiug.30112106882779	172	24	and	and	CCONJ
uiug.30112106882779	172	25	e(k	e(k	PROPN
uiug.30112106882779	172	26	,	,	PUNCT
uiug.30112106882779	172	27	s	s	PUNCT
uiug.30112106882779	172	28	)	)	PUNCT
uiug.30112106882779	172	29	do	do	VERB
uiug.30112106882779	172	30	not	not	PART
uiug.30112106882779	172	31	,	,	PUNCT
uiug.30112106882779	172	32	since	since	SCONJ
uiug.30112106882779	172	33	only	only	ADV
uiug.30112106882779	172	34	in	in	ADP
uiug.30112106882779	172	35	equation	equation	NOUN
uiug.30112106882779	172	36	(	(	PUNCT
uiug.30112106882779	172	37	b2b	b2b	PROPN
uiug.30112106882779	172	38	)	)	PUNCT
uiug.30112106882779	172	39	has	have	VERB
uiug.30112106882779	172	40	velocity	velocity	NOUN
uiug.30112106882779	172	41	been	be	AUX
uiug.30112106882779	172	42	integrated	integrate	VERB
uiug.30112106882779	172	43	upon	upon	SCONJ
uiug.30112106882779	172	44	.	.	PUNCT
uiug.30112106882779	173	1	v	v	NOUN
uiug.30112106882779	173	2	to	to	PART
uiug.30112106882779	173	3	find	find	VERB
uiug.30112106882779	173	4	if	if	SCONJ
uiug.30112106882779	173	5	one	one	NUM
uiug.30112106882779	173	6	first	first	ADJ
uiug.30112106882779	173	7	solves	solve	VERB
uiug.30112106882779	173	8	for	for	ADP
uiug.30112106882779	173	9	f(k	f(k	PROPN
uiug.30112106882779	173	10	,	,	PUNCT
uiug.30112106882779	173	11	s	s	PART
uiug.30112106882779	173	12	)	)	PUNCT
uiug.30112106882779	173	13	in	in	ADP
uiug.30112106882779	173	14	equation	equation	NOUN
uiug.30112106882779	173	15	(	(	PUNCT
uiug.30112106882779	173	16	b2a	b2a	NOUN
uiug.30112106882779	173	17	)	)	PUNCT
uiug.30112106882779	173	18	,	,	PUNCT
uiug.30112106882779	173	19	then	then	ADV
uiug.30112106882779	173	20	integrates	integrate	VERB
uiug.30112106882779	173	21	over	over	ADP
uiug.30112106882779	173	22	n(k	n(k	PROPN
uiug.30112106882779	173	23	,	,	PUNCT
uiug.30112106882779	173	24	s	s	PART
uiug.30112106882779	173	25	)	)	PUNCT
uiug.30112106882779	173	26	from	from	ADP
uiug.30112106882779	173	27	equation	equation	NOUN
uiug.30112106882779	173	28	(	(	PUNCT
uiug.30112106882779	173	29	b2b	b2b	PROPN
uiug.30112106882779	173	30	)	)	PUNCT
uiug.30112106882779	173	31	,	,	PUNCT
uiug.30112106882779	173	32	and	and	CCONJ
uiug.30112106882779	173	33	,	,	PUNCT
uiug.30112106882779	173	34	finally	finally	ADV
uiug.30112106882779	173	35	,	,	PUNCT
uiug.30112106882779	173	36	substitutes	substitutes	PROPN
uiug.30112106882779	173	37	s	s	PART
uiug.30112106882779	173	38	=	=	PROPN
uiug.30112106882779	173	39	iw	iw	PROPN
uiug.30112106882779	173	40	,	,	PUNCT
uiug.30112106882779	173	41	the	the	DET
uiug.30112106882779	173	42	result	result	NOUN
uiug.30112106882779	173	43	is	be	AUX
uiug.30112106882779	173	44	1	1	NUM
uiug.30112106882779	173	45	j	j	PROPN
uiug.30112106882779	173	46	n(k	n(k	PROPN
uiug.30112106882779	173	47	,	,	PUNCT
uiug.30112106882779	173	48	s	s	PART
uiug.30112106882779	173	49	)	)	PUNCT
uiug.30112106882779	173	50	i(k	i(k	PROPN
uiug.30112106882779	173	51	,	,	PUNCT
uiug.30112106882779	173	52	s	s	NOUN
uiug.30112106882779	173	53	)	)	PUNCT
uiug.30112106882779	173	54	e(k	e(k	PROPN
uiug.30112106882779	173	55	,	,	PUNCT
uiug.30112106882779	173	56	s	s	PUNCT
uiug.30112106882779	173	57	)	)	PUNCT
uiug.30112106882779	173	58	=	=	NOUN
uiug.30112106882779	173	59	1.s	1.s	NUM
uiug.30112106882779	173	60	is	be	AUX
uiug.30112106882779	173	61	fok	fok	ADJ
uiug.30112106882779	173	62	,	,	PUNCT
uiug.30112106882779	173	63	v)dv	v)dv	PROPN
uiug.30112106882779	173	64	w	w	X
uiug.30112106882779	173	65	kv	kv	PROPN
uiug.30112106882779	173	66	f'dy	f'dy	X
uiug.30112106882779	173	67	ky	ky	PROPN
uiug.30112106882779	173	68	(	(	PUNCT
uiug.30112106882779	173	69	s	s	X
uiug.30112106882779	173	70	=	=	X
uiug.30112106882779	173	71	i	i	PROPN
uiug.30112106882779	173	72	d	d	NOUN
uiug.30112106882779	173	73	)	)	PUNCT
uiug.30112106882779	173	74	1	1	NUM
uiug.30112106882779	173	75	+	+	NUM
uiug.30112106882779	173	76	11	11	NUM
uiug.30112106882779	173	77	w	w	NOUN
uiug.30112106882779	173	78	where	where	SCONJ
uiug.30112106882779	173	79	the	the	DET
uiug.30112106882779	173	80	denominator	denominator	PROPN
uiug.30112106882779	173	81	elk	elk	PROPN
uiug.30112106882779	173	82	,	,	PUNCT
uiug.30112106882779	173	83	s	s	PROPN
uiug.30112106882779	173	84	)	)	PUNCT
uiug.30112106882779	173	85	is	be	AUX
uiug.30112106882779	173	86	the	the	DET
uiug.30112106882779	173	87	so	so	ADV
uiug.30112106882779	173	88	-	-	PUNCT
uiug.30112106882779	173	89	called	call	VERB
uiug.30112106882779	173	90	plasma	plasma	NOUN
uiug.30112106882779	173	91	dielectric	dielectric	NOUN
uiug.30112106882779	173	92	constant	constant	ADJ
uiug.30112106882779	173	93	.	.	PUNCT
uiug.30112106882779	174	1	under	under	ADP
uiug.30112106882779	174	2	an	an	DET
uiug.30112106882779	174	3	initial	initial	ADJ
uiug.30112106882779	174	4	cos(kx	cos(kx	VERB
uiug.30112106882779	174	5	)	)	PUNCT
uiug.30112106882779	174	6	density	density	NOUN
uiug.30112106882779	174	7	perturbation	perturbation	NOUN
uiug.30112106882779	174	8	the	the	DET
uiug.30112106882779	174	9	assumed	assume	VERB
uiug.30112106882779	174	10	maxwellian	maxwellian	ADJ
uiug.30112106882779	174	11	electronic	electronic	ADJ
uiug.30112106882779	174	12	velocity	velocity	NOUN
uiug.30112106882779	174	13	distribution	distribution	NOUN
uiug.30112106882779	174	14	f	f	X
uiug.30112106882779	174	15	=	=	SYM
uiug.30112106882779	174	16	1	1	NUM
uiug.30112106882779	175	1	|	|	PROPN
uiug.30112106882779	175	2	v	v	NOUN
uiug.30112106882779	175	3	exp(-v2/2	exp(-v2/2	PROPN
uiug.30112106882779	175	4	)	)	PUNCT
uiug.30112106882779	176	1	2	2	NUM
uiug.30112106882779	176	2	tt	tt	PROPN
uiug.30112106882779	176	3	is	be	AUX
uiug.30112106882779	176	4	untouched	untouched	ADJ
uiug.30112106882779	176	5	.	.	PUNCT
uiug.30112106882779	177	1	thus	thus	ADV
uiug.30112106882779	177	2	fo(k	fo(k	PROPN
uiug.30112106882779	177	3	,	,	PUNCT
uiug.30112106882779	177	4	v	v	NOUN
uiug.30112106882779	177	5	)	)	PUNCT
uiug.30112106882779	177	6	=	=	X
uiug.30112106882779	178	1	f	f	PROPN
uiug.30112106882779	178	2	=	=	X
uiug.30112106882779	178	3	f	f	X
uiug.30112106882779	178	4	'	'	PUNCT
uiug.30112106882779	178	5	<	<	X
uiug.30112106882779	178	6	and	and	CCONJ
uiug.30112106882779	178	7	in	in	ADP
uiug.30112106882779	178	8	terms	term	NOUN
uiug.30112106882779	178	9	of	of	ADP
uiug.30112106882779	178	10	f	f	X
uiug.30112106882779	178	11	'	'	PUNCT
uiug.30112106882779	178	12	,	,	PUNCT
uiug.30112106882779	178	13	1	1	NUM
uiug.30112106882779	178	14	som	som	NOUN
uiug.30112106882779	178	15	1	1	NUM
uiug.30112106882779	178	16	-f	-f	X
uiug.30112106882779	178	17	'	'	PUNCT
uiug.30112106882779	178	18	w	w	X
uiug.30112106882779	178	19	kv	kv	ADV
uiug.30112106882779	178	20	dv	dv	PROPN
uiug.30112106882779	178	21	v	v	PROPN
uiug.30112106882779	178	22	ܚ	ܚ	PROPN
uiug.30112106882779	178	23	n(k	n(k	PROPN
uiug.30112106882779	178	24	,	,	PUNCT
uiug.30112106882779	178	25	s	s	PART
uiug.30112106882779	178	26	)	)	PUNCT
uiug.30112106882779	178	27	sº	sº	PROPN
uiug.30112106882779	178	28	sf'dv	sf'dv	PROPN
uiug.30112106882779	178	29	1	1	PROPN
uiug.30112106882779	178	30	+	+	CCONJ
uiug.30112106882779	178	31	k	k	X
uiug.30112106882779	178	32	w	w	X
uiug.30112106882779	178	33	kv	kv	PROPN
uiug.30112106882779	178	34	in	in	ADP
uiug.30112106882779	178	35	the	the	DET
uiug.30112106882779	178	36	integral	integral	NOUN
uiug.30112106882779	178	37	of	of	ADP
uiug.30112106882779	178	38	the	the	DET
uiug.30112106882779	178	39	numerator	numerator	NOUN
uiug.30112106882779	178	40	of	of	ADP
uiug.30112106882779	178	41	n(k	n(k	PROPN
uiug.30112106882779	178	42	,	,	PUNCT
uiug.30112106882779	178	43	s	s	PART
uiug.30112106882779	178	44	)	)	PUNCT
uiug.30112106882779	178	45	the	the	DET
uiug.30112106882779	178	46	coefficient	coefficient	NOUN
uiug.30112106882779	178	47	of	of	ADP
uiug.30112106882779	178	48	-f	-f	SPACE
uiug.30112106882779	178	49	'	'	PUNCT
uiug.30112106882779	178	50	may	may	AUX
uiug.30112106882779	178	51	be	be	AUX
uiug.30112106882779	178	52	written	write	VERB
uiug.30112106882779	178	53	as	as	ADP
uiug.30112106882779	178	54	11	11	NUM
uiug.30112106882779	178	55	vw	vw	PRON
uiug.30112106882779	178	56	kv	kv	X
uiug.30112106882779	178	57	k	k	PROPN
uiug.30112106882779	178	58	-1	-1	PROPN
uiug.30112106882779	178	59	1	1	NUM
uiug.30112106882779	179	1	+	+	NUM
uiug.30112106882779	179	2	w10	w10	NOUN
uiug.30112106882779	179	3	ky	ky	X
uiug.30112106882779	179	4	w	w	PROPN
uiug.30112106882779	179	5	kv	kv	PROPN
uiug.30112106882779	180	1	so	so	SCONJ
uiug.30112106882779	180	2	that	that	SCONJ
uiug.30112106882779	180	3	n(k	n(k	PROPN
uiug.30112106882779	180	4	,	,	PUNCT
uiug.30112106882779	180	5	s	s	AUX
uiug.30112106882779	180	6	)	)	PUNCT
uiug.30112106882779	180	7	may	may	AUX
uiug.30112106882779	180	8	be	be	AUX
uiug.30112106882779	180	9	written	write	VERB
uiug.30112106882779	180	10	in	in	ADP
uiug.30112106882779	180	11	terms	term	NOUN
uiug.30112106882779	180	12	of	of	ADP
uiug.30112106882779	180	13	e(k	e(k	PROPN
uiug.30112106882779	180	14	,	,	PUNCT
uiug.30112106882779	180	15	w	w	PROPN
uiug.30112106882779	180	16	)	)	PUNCT
uiug.30112106882779	180	17	and	and	CCONJ
uiug.30112106882779	180	18	e(k,0	e(k,0	PROPN
uiug.30112106882779	180	19	):	):	PUNCT
uiug.30112106882779	180	20	eo	eo	PROPN
uiug.30112106882779	180	21	n(k	n(k	PROPN
uiug.30112106882779	180	22	,	,	PUNCT
uiug.30112106882779	180	23	s	s	PART
uiug.30112106882779	180	24	)	)	PUNCT
uiug.30112106882779	180	25	ik2	ik2	PRON
uiug.30112106882779	180	26	€	€	PROPN
uiug.30112106882779	180	27	(	(	PUNCT
uiug.30112106882779	180	28	kw	kw	X
uiug.30112106882779	180	29	)	)	PUNCT
uiug.30112106882779	180	30	€	€	SYM
uiug.30112106882779	180	31	(	(	PUNCT
uiug.30112106882779	180	32	k,0	k,0	X
uiug.30112106882779	180	33	)	)	PUNCT
uiug.30112106882779	180	34	ik2	ik2	PRON
uiug.30112106882779	180	35	€	€	PROPN
uiug.30112106882779	180	36	(	(	PUNCT
uiug.30112106882779	180	37	k	k	PROPN
uiug.30112106882779	180	38	,	,	PUNCT
uiug.30112106882779	180	39	w	w	PROPN
uiug.30112106882779	180	40	)	)	PUNCT
uiug.30112106882779	180	41	ليا	ليا	NOUN
uiug.30112106882779	180	42	e	e	NOUN
uiug.30112106882779	180	43	14	14	NUM
uiug.30112106882779	180	44	appendix	appendix	PROPN
uiug.30112106882779	180	45	b	b	NOUN
uiug.30112106882779	180	46	continued	continue	VERB
uiug.30112106882779	180	47	by	by	ADP
uiug.30112106882779	180	48	means	mean	NOUN
uiug.30112106882779	180	49	of	of	ADP
uiug.30112106882779	180	50	a	a	DET
uiug.30112106882779	180	51	change	change	NOUN
uiug.30112106882779	180	52	in	in	ADP
uiug.30112106882779	180	53	variable	variable	ADJ
uiug.30112106882779	180	54	w	w	PROPN
uiug.30112106882779	180	55	=	=	X
uiug.30112106882779	180	56	v	v	NOUN
uiug.30112106882779	180	57	/	/	SYM
uiug.30112106882779	180	58	v2	v2	NOUN
uiug.30112106882779	180	59	,	,	PUNCT
uiug.30112106882779	180	60	and	and	CCONJ
uiug.30112106882779	180	61	the	the	DET
uiug.30112106882779	180	62	substitution	substitution	NOUN
uiug.30112106882779	180	63	w	w	X
uiug.30112106882779	180	64	u	u	PROPN
uiug.30112106882779	180	65	il	il	PROPN
uiug.30112106882779	180	66	1	1	PROPN
uiug.30112106882779	180	67	u	u	PROPN
uiug.30112106882779	180	68	w	w	X
uiug.30112106882779	180	69	m	m	VERB
uiug.30112106882779	180	70	w	w	ADP
uiug.30112106882779	180	71	the	the	DET
uiug.30112106882779	180	72	dielectric	dielectric	ADJ
uiug.30112106882779	180	73	constant	constant	ADJ
uiug.30112106882779	180	74	e(kw	e(kw	NOUN
uiug.30112106882779	180	75	)	)	PUNCT
uiug.30112106882779	180	76	may	may	AUX
uiug.30112106882779	180	77	be	be	AUX
uiug.30112106882779	180	78	expressed	express	VERB
uiug.30112106882779	180	79	in	in	ADP
uiug.30112106882779	180	80	terms	term	NOUN
uiug.30112106882779	180	81	of	of	ADP
uiug.30112106882779	180	82	the	the	DET
uiug.30112106882779	180	83	complex	complex	ADJ
uiug.30112106882779	180	84	function	function	NOUN
uiug.30112106882779	180	85	e	e	PROPN
uiug.30112106882779	180	86	-	-	PROPN
uiug.30112106882779	180	87	t2	t2	PROPN
uiug.30112106882779	180	88	e	e	X
uiug.30112106882779	180	89	)	)	PUNCT
uiug.30112106882779	181	1	=	=	PUNCT
uiug.30112106882779	181	2	1st	1st	PROPN
uiug.30112106882779	181	3	z(u	z(u	SPACE
uiug.30112106882779	181	4	)	)	PUNCT
uiug.30112106882779	182	1	dt	dt	PROPN
uiug.30112106882779	182	2	t	t	PROPN
uiug.30112106882779	182	3	u	u	PROPN
uiug.30112106882779	182	4	m	m	PROPN
uiug.30112106882779	182	5	im(u	im(u	PROPN
uiug.30112106882779	182	6	)	)	PUNCT
uiug.30112106882779	182	7	<	<	X
uiug.30112106882779	182	8	0	0	NUM
uiug.30112106882779	182	9	;	;	PUNCT
uiug.30112106882779	182	10	h	h	NOUN
uiug.30112106882779	182	11	=	=	X
uiug.30112106882779	182	12	x	x	PUNCT
uiug.30112106882779	183	1	+	+	CCONJ
uiug.30112106882779	183	2	iy	iy	INTJ
uiug.30112106882779	183	3	kv2	kv2	PROPN
uiug.30112106882779	183	4	iy	iy	PROPN
uiug.30112106882779	183	5	as	as	ADP
uiug.30112106882779	183	6	k2	k2	PROPN
uiug.30112106882779	183	7	e(k	e(k	PROPN
uiug.30112106882779	183	8	,	,	PUNCT
uiug.30112106882779	183	9	y	y	PROPN
uiug.30112106882779	183	10	)	)	PUNCT
uiug.30112106882779	183	11	=	=	PROPN
uiug.30112106882779	183	12	1	1	NUM
uiug.30112106882779	184	1	+	+	CCONJ
uiug.30112106882779	184	2	k2	k2	PROPN
uiug.30112106882779	184	3	+	+	CCONJ
uiug.30112106882779	184	4	u	u	PROPN
uiug.30112106882779	184	5	z(u	z(u	PROPN
uiug.30112106882779	184	6	)	)	PUNCT
uiug.30112106882779	184	7	in	in	ADP
uiug.30112106882779	184	8	terms	term	NOUN
uiug.30112106882779	184	9	of	of	ADP
uiug.30112106882779	184	10	z	z	PROPN
uiug.30112106882779	184	11	=	=	NOUN
uiug.30112106882779	184	12	zr	zr	INTJ
uiug.30112106882779	184	13	+	+	CCONJ
uiug.30112106882779	184	14	izi	izi	ADJ
uiug.30112106882779	184	15	,	,	PUNCT
uiug.30112106882779	184	16	kểer	kểer	ADJ
uiug.30112106882779	184	17	=	=	NOUN
uiug.30112106882779	184	18	1	1	NUM
uiug.30112106882779	184	19	+	+	CCONJ
uiug.30112106882779	184	20	k2	k2	ADJ
uiug.30112106882779	184	21	+	+	X
uiug.30112106882779	184	22	xzr	xzr	NOUN
uiug.30112106882779	184	23	y2i	y2i	NOUN
uiug.30112106882779	184	24	kểe	kểe	NOUN
uiug.30112106882779	184	25	;	;	PUNCT
uiug.30112106882779	184	26	=	=	PUNCT
uiug.30112106882779	184	27	y2	y2	PROPN
uiug.30112106882779	184	28	+	+	CCONJ
uiug.30112106882779	184	29	xz	xz	PROPN
uiug.30112106882779	184	30	;	;	PUNCT
uiug.30112106882779	184	31	r	r	X
uiug.30112106882779	184	32	the	the	DET
uiug.30112106882779	184	33	function	function	NOUN
uiug.30112106882779	184	34	z	z	PROPN
uiug.30112106882779	184	35	is	be	AUX
uiug.30112106882779	184	36	related	relate	VERB
uiug.30112106882779	184	37	to	to	ADP
uiug.30112106882779	184	38	the	the	DET
uiug.30112106882779	184	39	complementary	complementary	ADJ
uiug.30112106882779	184	40	error	error	NOUN
uiug.30112106882779	184	41	function	function	NOUN
uiug.30112106882779	184	42	by	by	ADP
uiug.30112106882779	184	43	z(z	z(z	NOUN
uiug.30112106882779	184	44	)	)	PUNCT
uiug.30112106882779	184	45	=	=	PROPN
uiug.30112106882779	185	1	yt	yt	PROPN
uiug.30112106882779	185	2	e	e	X
uiug.30112106882779	185	3	-	-	PROPN
uiug.30112106882779	185	4	zerfc(-iz	zerfc(-iz	NUM
uiug.30112106882779	185	5	)	)	PUNCT
uiug.30112106882779	185	6	-22	-22	NUM
uiug.30112106882779	185	7	on	on	ADP
uiug.30112106882779	185	8	the	the	DET
uiug.30112106882779	185	9	real	real	ADJ
uiug.30112106882779	185	10	axis	axis	NOUN
uiug.30112106882779	185	11	of	of	ADP
uiug.30112106882779	185	12	the	the	DET
uiug.30112106882779	185	13	l	l	NOUN
uiug.30112106882779	185	14	-	-	PUNCT
uiug.30112106882779	185	15	plane	plane	NOUN
uiug.30112106882779	185	16	,	,	PUNCT
uiug.30112106882779	185	17	y	y	PROPN
uiug.30112106882779	185	18	=	=	SYM
uiug.30112106882779	185	19	0	0	NUM
uiug.30112106882779	185	20	;	;	PUNCT
uiug.30112106882779	185	21	so	so	CCONJ
uiug.30112106882779	185	22	for	for	ADP
uiug.30112106882779	185	23	real	real	NOUN
uiug.30112106882779	185	24	x	x	PUNCT
uiug.30112106882779	185	25	=	=	X
uiug.30112106882779	185	26	w	w	PROPN
uiug.30112106882779	185	27	/	/	SYM
uiug.30112106882779	185	28	k	k	PROPN
uiug.30112106882779	185	29	,	,	PUNCT
uiug.30112106882779	185	30	k2	k2	PROPN
uiug.30112106882779	185	31	epſk	epſk	PROPN
uiug.30112106882779	185	32	,	,	PUNCT
uiug.30112106882779	185	33	w	w	PROPN
uiug.30112106882779	185	34	)	)	PUNCT
uiug.30112106882779	185	35	=	=	SYM
uiug.30112106882779	185	36	1	1	NUM
uiug.30112106882779	186	1	+	+	CCONJ
uiug.30112106882779	186	2	k2	k2	ADJ
uiug.30112106882779	187	1	+	+	CCONJ
uiug.30112106882779	187	2	<	<	X
uiug.30112106882779	187	3	/	/	PUNCT
uiug.30112106882779	187	4	<	<	X
uiug.30112106882779	187	5	l	l	PROPN
uiug.30112106882779	187	6	z	z	PROPN
uiug.30112106882779	187	7	je	je	PROPN
uiug.30112106882779	187	8	zr	zr	INTJ
uiug.30112106882779	187	9	(	(	PUNCT
uiug.30112106882779	187	10	(	(	PUNCT
uiug.30112106882779	187	11	b3a	b3a	ADV
uiug.30112106882779	187	12	)	)	PUNCT
uiug.30112106882779	187	13	v2	v2	NOUN
uiug.30112106882779	187	14	12670k	12670k	NOUN
uiug.30112106882779	187	15	,	,	PUNCT
uiug.30112106882779	187	16	w	w	PROPN
uiug.30112106882779	187	17	)	)	PUNCT
uiug.30112106882779	187	18	zi	zi	PROPN
uiug.30112106882779	187	19	(	(	PUNCT
uiug.30112106882779	187	20	b3b	b3b	PROPN
uiug.30112106882779	187	21	)	)	PUNCT
uiug.30112106882779	187	22	k2	k2	PROPN
uiug.30112106882779	187	23	r(k,0	r(k,0	PROPN
uiug.30112106882779	187	24	)	)	PUNCT
uiug.30112106882779	187	25	=	=	PROPN
uiug.30112106882779	187	26	1	1	NUM
uiug.30112106882779	187	27	+	+	CCONJ
uiug.30112106882779	187	28	k2	k2	PROPN
uiug.30112106882779	187	29	(	(	PUNCT
uiug.30112106882779	187	30	b3c	b3c	NOUN
uiug.30112106882779	187	31	)	)	PUNCT
uiug.30112106882779	187	32	r	r	NOUN
uiug.30112106882779	187	33	k2	k2	PROPN
uiug.30112106882779	187	34	€	€	PROPN
uiug.30112106882779	187	35	(	(	PUNCT
uiug.30112106882779	187	36	k,0	k,0	X
uiug.30112106882779	187	37	)	)	PUNCT
uiug.30112106882779	187	38	=	=	PROPN
uiug.30112106882779	187	39	0	0	NUM
uiug.30112106882779	187	40	(	(	PUNCT
uiug.30112106882779	187	41	b3d	b3d	NOUN
uiug.30112106882779	187	42	)	)	PUNCT
uiug.30112106882779	187	43	inversion	inversion	NOUN
uiug.30112106882779	187	44	by	by	ADP
uiug.30112106882779	187	45	bromwich	bromwich	PROPN
uiug.30112106882779	187	46	's	's	PART
uiug.30112106882779	187	47	integral	integral	NOUN
uiug.30112106882779	187	48	with	with	ADP
uiug.30112106882779	187	49	the	the	DET
uiug.30112106882779	187	50	contour	contour	NOUN
uiug.30112106882779	187	51	along	along	ADP
uiug.30112106882779	187	52	the	the	DET
uiug.30112106882779	187	53	imaginary	imaginary	ADJ
uiug.30112106882779	187	54	axis	axis	NOUN
uiug.30112106882779	187	55	of	of	ADP
uiug.30112106882779	187	56	the	the	DET
uiug.30112106882779	187	57	s	s	NOUN
uiug.30112106882779	187	58	-	-	PUNCT
uiug.30112106882779	187	59	plane	plane	NOUN
uiug.30112106882779	187	60	(	(	PUNCT
uiug.30112106882779	187	61	8	8	NUM
uiug.30112106882779	187	62	=	=	SYM
uiug.30112106882779	187	63	0	0	NUM
uiug.30112106882779	187	64	)	)	PUNCT
uiug.30112106882779	187	65	yields	yield	VERB
uiug.30112106882779	187	66	15	15	NUM
uiug.30112106882779	187	67	appendix	appendix	PROPN
uiug.30112106882779	187	68	b	b	NOUN
uiug.30112106882779	187	69	–	–	PUNCT
uiug.30112106882779	187	70	concluded	conclude	VERB
uiug.30112106882779	187	71	e	e	PROPN
uiug.30112106882779	187	72	nľk	nľk	PROPN
uiug.30112106882779	187	73	,	,	PUNCT
uiug.30112106882779	187	74	t	t	PROPN
uiug.30112106882779	187	75	)	)	PUNCT
uiug.30112106882779	187	76	=	=	PUNCT
uiug.30112106882779	188	1	hk2	hk2	NOUN
uiug.30112106882779	188	2	sono	sono	PROPN
uiug.30112106882779	188	3	rimasto	rimasto	PROPN
uiug.30112106882779	188	4	ciutaw	ciutaw	PROPN
uiug.30112106882779	188	5	the	the	DET
uiug.30112106882779	188	6	er	er	INTJ
uiug.30112106882779	188	7	+	+	PROPN
uiug.30112106882779	188	8	10	10	NUM
uiug.30112106882779	189	1	i	i	PRON
uiug.30112106882779	189	2	r	r	X
uiug.30112106882779	189	3	n	n	X
uiug.30112106882779	189	4	(	(	PUNCT
uiug.30112106882779	189	5	=	=	PROPN
uiug.30112106882779	189	6	ik2	ik2	ADP
uiug.30112106882779	189	7	21	21	NUM
uiug.30112106882779	189	8	eiwtdw	eiwtdw	NOUN
uiug.30112106882779	189	9	=	=	VERB
uiug.30112106882779	189	10	so	so	ADV
uiug.30112106882779	189	11	(	(	PUNCT
uiug.30112106882779	189	12	b4	b4	PROPN
uiug.30112106882779	189	13	)	)	PUNCT
uiug.30112106882779	189	14	21	21	NUM
uiug.30112106882779	189	15	we	we	PRON
uiug.30112106882779	189	16	3	3	NUM
uiug.30112106882779	189	17	at	at	ADV
uiug.30112106882779	189	18	all	all	ADV
uiug.30112106882779	189	19	t<0	t<0	ADJ
uiug.30112106882779	189	20	,	,	PUNCT
uiug.30112106882779	189	21	n(k	n(k	PROPN
uiug.30112106882779	189	22	,	,	PUNCT
uiug.30112106882779	189	23	t	t	PROPN
uiug.30112106882779	189	24	)	)	PUNCT
uiug.30112106882779	189	25	=	=	PROPN
uiug.30112106882779	189	26	0	0	NUM
uiug.30112106882779	189	27	;	;	PUNCT
uiug.30112106882779	189	28	thus	thus	ADV
uiug.30112106882779	189	29	0	0	PUNCT
uiug.30112106882779	189	30	r	r	X
uiug.30112106882779	189	31	+	+	X
uiug.30112106882779	189	32	iº	iº	NOUN
uiug.30112106882779	189	33	;	;	PUNCT
uiug.30112106882779	189	34	i	i	PRON
uiug.30112106882779	189	35	-iwtdw	-iwtdw	VERB
uiug.30112106882779	189	36	0	0	PUNCT
uiug.30112106882779	189	37	=	=	PUNCT
uiug.30112106882779	189	38	=	=	PUNCT
uiug.30112106882779	189	39	:	:	PUNCT
uiug.30112106882779	189	40	s	s	X
uiug.30112106882779	189	41	(	(	PUNCT
uiug.30112106882779	189	42	t	t	PROPN
uiug.30112106882779	189	43	>	>	SYM
uiug.30112106882779	189	44	0	0	NUM
uiug.30112106882779	189	45	)	)	PUNCT
uiug.30112106882779	189	46	3	3	NUM
uiug.30112106882779	189	47	taking	take	VERB
uiug.30112106882779	189	48	the	the	DET
uiug.30112106882779	189	49	complex	complex	ADJ
uiug.30112106882779	189	50	conjugate	conjugate	NOUN
uiug.30112106882779	189	51	yields	yield	NOUN
uiug.30112106882779	189	52	noo	noo	PROPN
uiug.30112106882779	189	53	ir	ir	INTJ
uiug.30112106882779	189	54	ør	ør	INTJ
uiug.30112106882779	189	55	iq	iq	INTJ
uiug.30112106882779	190	1	i	i	PRON
uiug.30112106882779	190	2	ciwtaw	ciwtaw	PROPN
uiug.30112106882779	190	3	0	0	PUNCT
uiug.30112106882779	191	1	so	so	ADV
uiug.30112106882779	191	2	(	(	PUNCT
uiug.30112106882779	191	3	t	t	PROPN
uiug.30112106882779	191	4	>	>	SYM
uiug.30112106882779	191	5	0	0	NUM
uiug.30112106882779	191	6	)	)	PUNCT
uiug.30112106882779	191	7	subtraction	subtraction	NOUN
uiug.30112106882779	191	8	of	of	ADP
uiug.30112106882779	191	9	ik2/29	ik2/29	PRON
uiug.30112106882779	191	10	times	time	NOUN
uiug.30112106882779	191	11	this	this	DET
uiug.30112106882779	191	12	null	null	ADJ
uiug.30112106882779	191	13	member	member	NOUN
uiug.30112106882779	191	14	from	from	ADP
uiug.30112106882779	191	15	equation	equation	PROPN
uiug.30112106882779	191	16	(	(	PUNCT
uiug.30112106882779	191	17	b4	b4	PROPN
uiug.30112106882779	191	18	)	)	PUNCT
uiug.30112106882779	191	19	for	for	ADP
uiug.30112106882779	191	20	n(k	n(k	PROPN
uiug.30112106882779	191	21	,	,	PUNCT
uiug.30112106882779	191	22	t	t	PROPN
uiug.30112106882779	191	23	)	)	PUNCT
uiug.30112106882779	191	24	yields	yield	VERB
uiug.30112106882779	191	25	n(x	n(x	PROPN
uiug.30112106882779	191	26	,	,	PUNCT
uiug.30112106882779	191	27	t	t	PROPN
uiug.30112106882779	191	28	)	)	PUNCT
uiug.30112106882779	191	29	=	=	X
uiug.30112106882779	191	30	ke	ke	PROPN
uiug.30112106882779	191	31	go	go	VERB
uiug.30112106882779	191	32	or	or	CCONJ
uiug.30112106882779	191	33	less	less	ADV
uiug.30112106882779	191	34	etwtdw	etwtdw	ADJ
uiug.30112106882779	191	35	=	=	NOUN
uiug.30112106882779	192	1	s	s	VERB
uiug.30112106882779	192	2	piwtaw	piwtaw	PROPN
uiug.30112106882779	192	3	=	=	PROPN
uiug.30112106882779	192	4	sa	sa	PROPN
uiug.30112106882779	192	5	mweiwtaw	mweiwtaw	PROPN
uiug.30112106882779	192	6	vi(w	vi(w	SPACE
uiug.30112106882779	192	7	)	)	PUNCT
uiug.30112106882779	193	1	nk	nk	ADP
uiug.30112106882779	193	2	=	=	PUNCT
uiug.30112106882779	193	3	writing	write	VERB
uiug.30112106882779	193	4	4	4	NUM
uiug.30112106882779	193	5	pi	pi	NOUN
uiug.30112106882779	193	6	in	in	ADP
uiug.30112106882779	193	7	terms	term	NOUN
uiug.30112106882779	193	8	of	of	ADP
uiug.30112106882779	193	9	the	the	DET
uiug.30112106882779	193	10	values	value	NOUN
uiug.30112106882779	193	11	of	of	ADP
uiug.30112106882779	193	12	er	er	INTJ
uiug.30112106882779	193	13	and	and	CCONJ
uiug.30112106882779	193	14	ti	ti	PROPN
uiug.30112106882779	193	15	given	give	VERB
uiug.30112106882779	193	16	in	in	ADP
uiug.30112106882779	193	17	equation	equation	NOUN
uiug.30112106882779	193	18	(	(	PUNCT
uiug.30112106882779	193	19	b3	b3	PROPN
uiug.30112106882779	193	20	)	)	PUNCT
uiug.30112106882779	193	21	yields	yield	NOUN
uiug.30112106882779	193	22	+	+	ADP
uiug.30112106882779	193	23	n	n	ADP
uiug.30112106882779	193	24	1	1	NUM
uiug.30112106882779	193	25	+	+	CCONJ
uiug.30112106882779	194	1	k-2	k-2	PROPN
uiug.30112106882779	194	2	z	z	PROPN
uiug.30112106882779	194	3	(	(	PUNCT
uiug.30112106882779	194	4	)	)	PUNCT
uiug.30112106882779	194	5	tv2	tv2	NOUN
uiug.30112106882779	194	6	2(kw	2(kw	NUM
uiug.30112106882779	194	7	)	)	PUNCT
uiug.30112106882779	194	8	+	+	CCONJ
uiug.30112106882779	194	9	¢{(kw	¢{(kw	SPACE
uiug.30112106882779	194	10	)	)	PUNCT
uiug.30112106882779	194	11	€	€	SYM
uiug.30112106882779	194	12	kv2	kv2	NOUN
uiug.30112106882779	194	13	#	#	SYM
uiug.30112106882779	194	14	w	w	PROPN
uiug.30112106882779	194	15	)	)	PUNCT
uiug.30112106882779	194	16	1k	1k	NUM
uiug.30112106882779	194	17	where	where	SCONJ
uiug.30112106882779	194	18	the	the	DET
uiug.30112106882779	194	19	function	function	NOUN
uiug.30112106882779	194	20	z+	z+	VERB
uiug.30112106882779	194	21	=	=	SYM
uiug.30112106882779	194	22	-z	-z	PUNCT
uiug.30112106882779	194	23	*	*	PUNCT
uiug.30112106882779	194	24	is	be	AUX
uiug.30112106882779	194	25	one	one	NUM
uiug.30112106882779	194	26	available	available	ADJ
uiug.30112106882779	194	27	on	on	ADP
uiug.30112106882779	194	28	the	the	DET
uiug.30112106882779	194	29	computer	computer	NOUN
uiug.30112106882779	194	30	library	library	NOUN
uiug.30112106882779	194	31	tape	tape	NOUN
uiug.30112106882779	194	32	at	at	ADP
uiug.30112106882779	194	33	langley	langley	PROPN
uiug.30112106882779	194	34	research	research	NOUN
uiug.30112106882779	194	35	center	center	NOUN
uiug.30112106882779	194	36	.	.	PUNCT
uiug.30112106882779	195	1	the	the	DET
uiug.30112106882779	195	2	substitution	substitution	NOUN
uiug.30112106882779	195	3	w	w	PROPN
uiug.30112106882779	195	4	=	=	PROPN
uiug.30112106882779	195	5	kx	kx	PROPN
uiug.30112106882779	195	6	(	(	PUNCT
uiug.30112106882779	195	7	using	use	VERB
uiug.30112106882779	195	8	the	the	DET
uiug.30112106882779	195	9	same	same	ADJ
uiug.30112106882779	195	10	symbol	symbol	NOUN
uiug.30112106882779	195	11	for	for	ADP
uiug.30112106882779	195	12	*	*	NOUN
uiug.30112106882779	195	13	)	)	PUNCT
uiug.30112106882779	195	14	yields	yield	NOUN
uiug.30112106882779	195	15	n(k	n(k	PROPN
uiug.30112106882779	195	16	,	,	PUNCT
uiug.30112106882779	195	17	t	t	PROPN
uiug.30112106882779	195	18	)	)	PUNCT
uiug.30112106882779	195	19	=	=	PROPN
uiug.30112106882779	195	20	s	s	VERB
uiug.30112106882779	195	21	«	«	PUNCT
uiug.30112106882779	195	22	(	(	PUNCT
uiug.30112106882779	195	23	)	)	PUNCT
uiug.30112106882779	195	24	eikata	eikata	PROPN
uiug.30112106882779	195	25	where	where	SCONJ
uiug.30112106882779	195	26	+	+	ADV
uiug.30112106882779	195	27	ry	ry	INTJ
uiug.30112106882779	195	28	zi	zi	PROPN
uiug.30112106882779	195	29	/	/	PUNCT
uiug.30112106882779	195	30	+	+	PROPN
uiug.30112106882779	195	31	(	(	PUNCT
uiug.30112106882779	195	32	a	a	X
uiug.30112106882779	195	33	)	)	PUNCT
uiug.30112106882779	195	34	=	=	NOUN
uiug.30112106882779	195	35	1+k-2	1+k-2	NUM
uiug.30112106882779	195	36	712	712	NUM
uiug.30112106882779	195	37	2	2	NUM
uiug.30112106882779	195	38	ni	ni	X
uiug.30112106882779	195	39	-2	-2	NOUN
uiug.30112106882779	195	40	+	+	CCONJ
uiug.30112106882779	195	41	e	e	NOUN
uiug.30112106882779	195	42	!	!	PUNCT
uiug.30112106882779	196	1	r	r	NOUN
uiug.30112106882779	197	1	i	i	PRON
uiug.30112106882779	197	2	is	be	AUX
uiug.30112106882779	197	3	the	the	DET
uiug.30112106882779	197	4	function	function	NOUN
uiug.30112106882779	197	5	corresponding	correspond	VERB
uiug.30112106882779	197	6	to	to	ADP
uiug.30112106882779	197	7	infinite	infinite	PROPN
uiug.30112106882779	197	8	n	n	PROPN
uiug.30112106882779	197	9	that	that	PRON
uiug.30112106882779	197	10	is	be	AUX
uiug.30112106882779	197	11	plotted	plot	VERB
uiug.30112106882779	197	12	in	in	ADP
uiug.30112106882779	197	13	figure	figure	NOUN
uiug.30112106882779	197	14	4	4	NUM
uiug.30112106882779	197	15	.	.	PUNCT
uiug.30112106882779	197	16	16	16	NUM
uiug.30112106882779	197	17	references	reference	NOUN
uiug.30112106882779	197	18	1	1	NUM
uiug.30112106882779	197	19	.	.	PUNCT
uiug.30112106882779	198	1	landau	landau	PROPN
uiug.30112106882779	198	2	,	,	PUNCT
uiug.30112106882779	198	3	l.	l.	PROPN
uiug.30112106882779	198	4	:	:	PUNCT
uiug.30112106882779	198	5	on	on	ADP
uiug.30112106882779	198	6	the	the	DET
uiug.30112106882779	198	7	vibrations	vibration	NOUN
uiug.30112106882779	198	8	of	of	ADP
uiug.30112106882779	198	9	the	the	DET
uiug.30112106882779	198	10	electronic	electronic	ADJ
uiug.30112106882779	198	11	plasma	plasma	NOUN
uiug.30112106882779	198	12	.	.	PUNCT
uiug.30112106882779	199	1	j.	j.	PROPN
uiug.30112106882779	199	2	phys	phys	PROPN
uiug.30112106882779	199	3	.	.	PUNCT
uiug.30112106882779	200	1	(	(	PUNCT
uiug.30112106882779	200	2	ussr	ussr	PROPN
uiug.30112106882779	200	3	)	)	PUNCT
uiug.30112106882779	200	4	,	,	PUNCT
uiug.30112106882779	200	5	vol	vol	NOUN
uiug.30112106882779	200	6	.	.	PUNCT
uiug.30112106882779	201	1	x	x	PROPN
uiug.30112106882779	201	2	,	,	PUNCT
uiug.30112106882779	201	3	no	no	INTJ
uiug.30112106882779	201	4	.	.	NOUN
uiug.30112106882779	201	5	1	1	NUM
uiug.30112106882779	201	6	,	,	PUNCT
uiug.30112106882779	201	7	1946	1946	NUM
uiug.30112106882779	201	8	,	,	PUNCT
uiug.30112106882779	201	9	pp	pp	PROPN
uiug.30112106882779	201	10	.	.	PROPN
uiug.30112106882779	202	1	25	25	NUM
uiug.30112106882779	202	2	-	-	SYM
uiug.30112106882779	202	3	34	34	NUM
uiug.30112106882779	202	4	.	.	PUNCT
uiug.30112106882779	203	1	2	2	NUM
uiug.30112106882779	203	2	.	.	X
uiug.30112106882779	203	3	van	van	PROPN
uiug.30112106882779	203	4	kampen	kampen	PROPN
uiug.30112106882779	203	5	,	,	PUNCT
uiug.30112106882779	203	6	n.	n.	PROPN
uiug.30112106882779	203	7	g.	g.	PROPN
uiug.30112106882779	203	8	:	:	PUNCT
uiug.30112106882779	203	9	on	on	ADP
uiug.30112106882779	203	10	the	the	DET
uiug.30112106882779	203	11	theory	theory	NOUN
uiug.30112106882779	203	12	of	of	ADP
uiug.30112106882779	203	13	stationary	stationary	ADJ
uiug.30112106882779	203	14	waves	wave	NOUN
uiug.30112106882779	203	15	in	in	ADP
uiug.30112106882779	203	16	plasmas	plasmas	PROPN
uiug.30112106882779	203	17	.	.	PROPN
uiug.30112106882779	204	1	physica	physica	PROPN
uiug.30112106882779	204	2	,	,	PUNCT
uiug.30112106882779	204	3	vol	vol	NOUN
uiug.30112106882779	204	4	.	.	PROPN
uiug.30112106882779	204	5	21	21	NUM
uiug.30112106882779	204	6	,	,	PUNCT
uiug.30112106882779	204	7	no	no	NOUN
uiug.30112106882779	204	8	.	.	NOUN
uiug.30112106882779	204	9	12	12	NUM
uiug.30112106882779	204	10	,	,	PUNCT
uiug.30112106882779	204	11	dec	dec	PROPN
uiug.30112106882779	204	12	.	.	PROPN
uiug.30112106882779	204	13	1955	1955	NUM
uiug.30112106882779	204	14	,	,	PUNCT
uiug.30112106882779	204	15	pp	pp	PROPN
uiug.30112106882779	204	16	.	.	PUNCT
uiug.30112106882779	204	17	949	949	NUM
uiug.30112106882779	204	18	-	-	SYM
uiug.30112106882779	204	19	963	963	NUM
uiug.30112106882779	204	20	.	.	NOUN
uiug.30112106882779	204	21	3	3	NUM
uiug.30112106882779	204	22	.	.	X
uiug.30112106882779	204	23	grant	grant	PROPN
uiug.30112106882779	204	24	,	,	PUNCT
uiug.30112106882779	204	25	frederick	frederick	PROPN
uiug.30112106882779	204	26	c.	c.	PROPN
uiug.30112106882779	204	27	;	;	PUNCT
uiug.30112106882779	204	28	and	and	CCONJ
uiug.30112106882779	204	29	feix	feix	PROPN
uiug.30112106882779	204	30	,	,	PUNCT
uiug.30112106882779	204	31	marc	marc	PROPN
uiug.30112106882779	204	32	r.	r.	PROPN
uiug.30112106882779	204	33	:	:	PUNCT
uiug.30112106882779	204	34	transition	transition	NOUN
uiug.30112106882779	204	35	between	between	ADP
uiug.30112106882779	204	36	landau	landau	NOUN
uiug.30112106882779	204	37	and	and	CCONJ
uiug.30112106882779	204	38	van	van	PROPN
uiug.30112106882779	204	39	kampen	kampen	PROPN
uiug.30112106882779	204	40	treatments	treatment	NOUN
uiug.30112106882779	204	41	of	of	ADP
uiug.30112106882779	204	42	the	the	DET
uiug.30112106882779	204	43	vlasov	vlasov	NOUN
uiug.30112106882779	204	44	equation	equation	NOUN
uiug.30112106882779	204	45	.	.	PUNCT
uiug.30112106882779	205	1	phys	phys	PROPN
uiug.30112106882779	205	2	.	.	PUNCT
uiug.30112106882779	205	3	fluids	fluids	PROPN
uiug.30112106882779	205	4	,	,	PUNCT
uiug.30112106882779	205	5	vol	vol	NOUN
uiug.30112106882779	205	6	.	.	PROPN
uiug.30112106882779	205	7	10	10	NUM
uiug.30112106882779	205	8	,	,	PUNCT
uiug.30112106882779	205	9	no	no	NOUN
uiug.30112106882779	205	10	.	.	NOUN
uiug.30112106882779	205	11	6	6	NUM
uiug.30112106882779	205	12	,	,	PUNCT
uiug.30112106882779	205	13	june	june	PROPN
uiug.30112106882779	205	14	1967	1967	NUM
uiug.30112106882779	205	15	,	,	PUNCT
uiug.30112106882779	205	16	pp	pp	PROPN
uiug.30112106882779	205	17	.	.	PUNCT
uiug.30112106882779	205	18	1356	1356	NUM
uiug.30112106882779	205	19	-	-	SYM
uiug.30112106882779	205	20	1357	1357	NUM
uiug.30112106882779	205	21	.	.	PUNCT
uiug.30112106882779	206	1	4	4	X
uiug.30112106882779	206	2	.	.	X
uiug.30112106882779	206	3	grant	grant	PROPN
uiug.30112106882779	206	4	,	,	PUNCT
uiug.30112106882779	206	5	frederick	frederick	PROPN
uiug.30112106882779	206	6	cyril	cyril	PROPN
uiug.30112106882779	206	7	:	:	PUNCT
uiug.30112106882779	206	8	fourier	fourier	ADJ
uiug.30112106882779	206	9	-	-	PUNCT
uiug.30112106882779	206	10	hermite	hermite	NOUN
uiug.30112106882779	206	11	representation	representation	NOUN
uiug.30112106882779	206	12	of	of	ADP
uiug.30112106882779	206	13	the	the	DET
uiug.30112106882779	206	14	one	one	NUM
uiug.30112106882779	206	15	-	-	PUNCT
uiug.30112106882779	206	16	dimensional	dimensional	ADJ
uiug.30112106882779	206	17	vlasov	vlasov	NOUN
uiug.30112106882779	206	18	equations	equation	NOUN
uiug.30112106882779	206	19	.	.	PUNCT
uiug.30112106882779	207	1	ph	ph	PROPN
uiug.30112106882779	207	2	.	.	PUNCT
uiug.30112106882779	208	1	d.	d.	PROPN
uiug.30112106882779	208	2	thesis	thesis	PROPN
uiug.30112106882779	208	3	,	,	PUNCT
uiug.30112106882779	208	4	virginia	virginia	PROPN
uiug.30112106882779	208	5	polytechnic	polytechnic	PROPN
uiug.30112106882779	208	6	inst	inst	ADP
uiug.30112106882779	208	7	.	.	PUNCT
uiug.30112106882779	208	8	,	,	PUNCT
uiug.30112106882779	208	9	1967	1967	NUM
uiug.30112106882779	208	10	.	.	PUNCT
uiug.30112106882779	209	1	5	5	X
uiug.30112106882779	209	2	.	.	X
uiug.30112106882779	209	3	grant	grant	PROPN
uiug.30112106882779	209	4	,	,	PUNCT
uiug.30112106882779	209	5	frederick	frederick	PROPN
uiug.30112106882779	209	6	c.	c.	PROPN
uiug.30112106882779	209	7	;	;	PUNCT
uiug.30112106882779	209	8	and	and	CCONJ
uiug.30112106882779	209	9	feix	feix	PROPN
uiug.30112106882779	209	10	,	,	PUNCT
uiug.30112106882779	209	11	marc	marc	PROPN
uiug.30112106882779	209	12	r.	r.	PROPN
uiug.30112106882779	209	13	;	;	PUNCT
uiug.30112106882779	209	14	fourier	fourier	ADJ
uiug.30112106882779	209	15	-	-	PUNCT
uiug.30112106882779	209	16	hermite	hermite	NOUN
uiug.30112106882779	209	17	solutions	solution	NOUN
uiug.30112106882779	209	18	of	of	ADP
uiug.30112106882779	209	19	the	the	DET
uiug.30112106882779	209	20	vlasov	vlasov	NOUN
uiug.30112106882779	209	21	equations	equation	NOUN
uiug.30112106882779	209	22	in	in	ADP
uiug.30112106882779	209	23	the	the	DET
uiug.30112106882779	209	24	linearized	linearize	VERB
uiug.30112106882779	209	25	limit	limit	NOUN
uiug.30112106882779	209	26	.	.	PUNCT
uiug.30112106882779	210	1	phys	phys	PROPN
uiug.30112106882779	210	2	.	.	PUNCT
uiug.30112106882779	210	3	fluids	fluids	PROPN
uiug.30112106882779	210	4	,	,	PUNCT
uiug.30112106882779	210	5	vol	vol	NOUN
uiug.30112106882779	210	6	.	.	PROPN
uiug.30112106882779	210	7	10	10	NUM
uiug.30112106882779	210	8	,	,	PUNCT
uiug.30112106882779	210	9	no	no	NOUN
uiug.30112106882779	210	10	.	.	NOUN
uiug.30112106882779	210	11	4	4	NUM
uiug.30112106882779	210	12	,	,	PUNCT
uiug.30112106882779	210	13	apr	apr	PROPN
uiug.30112106882779	210	14	.	.	PROPN
uiug.30112106882779	210	15	1967	1967	NUM
uiug.30112106882779	210	16	,	,	PUNCT
uiug.30112106882779	210	17	pp	pp	PROPN
uiug.30112106882779	210	18	.	.	PROPN
uiug.30112106882779	210	19	696	696	NUM
uiug.30112106882779	210	20	-	-	SYM
uiug.30112106882779	210	21	702	702	NUM
uiug.30112106882779	210	22	.	.	PROPN
uiug.30112106882779	210	23	6	6	NUM
uiug.30112106882779	210	24	.	.	PROPN
uiug.30112106882779	210	25	lenard	lenard	PROPN
uiug.30112106882779	210	26	,	,	PUNCT
uiug.30112106882779	210	27	a.	a.	PROPN
uiug.30112106882779	210	28	;	;	PUNCT
uiug.30112106882779	210	29	and	and	CCONJ
uiug.30112106882779	210	30	bernstein	bernstein	PROPN
uiug.30112106882779	210	31	,	,	PUNCT
uiug.30112106882779	210	32	ira	ira	PROPN
uiug.30112106882779	210	33	b.	b.	PROPN
uiug.30112106882779	210	34	:	:	PUNCT
uiug.30112106882779	210	35	plasma	plasma	NOUN
uiug.30112106882779	210	36	oscillations	oscillation	NOUN
uiug.30112106882779	210	37	with	with	ADP
uiug.30112106882779	210	38	diffusion	diffusion	NOUN
uiug.30112106882779	210	39	in	in	ADP
uiug.30112106882779	210	40	velocity	velocity	NOUN
uiug.30112106882779	210	41	space	space	NOUN
uiug.30112106882779	210	42	.	.	PUNCT
uiug.30112106882779	211	1	phys	phys	PROPN
uiug.30112106882779	211	2	.	.	PUNCT
uiug.30112106882779	212	1	rev	rev	PROPN
uiug.30112106882779	212	2	.	.	PROPN
uiug.30112106882779	212	3	,	,	PUNCT
uiug.30112106882779	212	4	vol	vol	NOUN
uiug.30112106882779	212	5	.	.	PROPN
uiug.30112106882779	213	1	112	112	NUM
uiug.30112106882779	213	2	,	,	PUNCT
uiug.30112106882779	213	3	no	no	NOUN
uiug.30112106882779	213	4	.	.	NOUN
uiug.30112106882779	213	5	5	5	NUM
uiug.30112106882779	213	6	,	,	PUNCT
uiug.30112106882779	213	7	dec	dec	PROPN
uiug.30112106882779	213	8	.	.	PROPN
uiug.30112106882779	213	9	1	1	NUM
uiug.30112106882779	213	10	,	,	PUNCT
uiug.30112106882779	213	11	1958	1958	NUM
uiug.30112106882779	213	12	,	,	PUNCT
uiug.30112106882779	213	13	pp	pp	PROPN
uiug.30112106882779	213	14	.	.	PUNCT
uiug.30112106882779	214	1	1456	1456	NUM
uiug.30112106882779	214	2	-	-	SYM
uiug.30112106882779	214	3	1459	1459	NUM
uiug.30112106882779	214	4	.	.	PUNCT
uiug.30112106882779	215	1	7	7	NUM
uiug.30112106882779	215	2	.	.	X
uiug.30112106882779	215	3	faddeev	faddeev	PROPN
uiug.30112106882779	215	4	,	,	PUNCT
uiug.30112106882779	215	5	d.	d.	PROPN
uiug.30112106882779	215	6	k.	k.	PROPN
uiug.30112106882779	215	7	;	;	PUNCT
uiug.30112106882779	215	8	and	and	CCONJ
uiug.30112106882779	215	9	faddeeva	faddeeva	PROPN
uiug.30112106882779	215	10	,	,	PUNCT
uiug.30112106882779	215	11	v.	v.	PROPN
uiug.30112106882779	215	12	n.	n.	PROPN
uiug.30112106882779	215	13	(	(	PUNCT
uiug.30112106882779	215	14	robert	robert	PROPN
uiug.30112106882779	215	15	c.	c.	PROPN
uiug.30112106882779	215	16	williams	williams	PROPN
uiug.30112106882779	215	17	,	,	PUNCT
uiug.30112106882779	215	18	trans	trans	PROPN
uiug.30112106882779	215	19	.	.	PROPN
uiug.30112106882779	215	20	):	):	PUNCT
uiug.30112106882779	215	21	computational	computational	ADJ
uiug.30112106882779	215	22	methods	method	NOUN
uiug.30112106882779	215	23	of	of	ADP
uiug.30112106882779	215	24	linear	linear	ADJ
uiug.30112106882779	215	25	algebra	algebra	PROPN
uiug.30112106882779	215	26	.	.	PUNCT
uiug.30112106882779	216	1	w.	w.	PROPN
uiug.30112106882779	216	2	h.	h.	PROPN
uiug.30112106882779	216	3	freeman	freeman	PROPN
uiug.30112106882779	216	4	and	and	CCONJ
uiug.30112106882779	216	5	co.	co.	PROPN
uiug.30112106882779	216	6	,	,	PUNCT
uiug.30112106882779	216	7	c.1963	c.1963	SPACE
uiug.30112106882779	216	8	.	.	PROPN
uiug.30112106882779	217	1	17	17	NUM
uiug.30112106882779	217	2	2.0	2.0	NUM
uiug.30112106882779	217	3	b	b	NOUN
uiug.30112106882779	217	4	=	=	PUNCT
uiug.30112106882779	217	5	.020.015	.020.015	NUM
uiug.30112106882779	217	6	.010	.010	NUM
uiug.30112106882779	217	7	.005	.005	NUM
uiug.30112106882779	217	8	y	y	PROPN
uiug.30112106882779	217	9	te	te	PROPN
uiug.30112106882779	217	10	landau	landau	PROPN
uiug.30112106882779	217	11	pole	pole	PROPN
uiug.30112106882779	217	12	z	z	PROPN
uiug.30112106882779	217	13	w	w	NOUN
uiug.30112106882779	217	14	-	-	NOUN
uiug.30112106882779	217	15	plane	plane	NOUN
uiug.30112106882779	217	16	1.0	1.0	NUM
uiug.30112106882779	217	17	wr	wr	PROPN
uiug.30112106882779	217	18	-.6	-.6	X
uiug.30112106882779	217	19	-.4	-.4	PUNCT
uiug.30112106882779	218	1	-.2	-.2	PUNCT
uiug.30112106882779	218	2	0	0	PUNCT
uiug.30112106882779	218	3	y	y	PROPN
uiug.30112106882779	218	4	figure	figure	NOUN
uiug.30112106882779	218	5	1.movement	1.movement	NUM
uiug.30112106882779	218	6	of	of	ADP
uiug.30112106882779	218	7	fourier	fourier	NOUN
uiug.30112106882779	218	8	-	-	PUNCT
uiug.30112106882779	218	9	hermite	hermite	NOUN
uiug.30112106882779	218	10	poles	pole	NOUN
uiug.30112106882779	218	11	into	into	ADP
uiug.30112106882779	218	12	complex	complex	ADJ
uiug.30112106882779	218	13	frequency	frequency	NOUN
uiug.30112106882779	218	14	plane	plane	NOUN
uiug.30112106882779	218	15	as	as	ADP
uiug.30112106882779	218	16	collisions	collision	NOUN
uiug.30112106882779	218	17	increase	increase	NOUN
uiug.30112106882779	218	18	.	.	PUNCT
uiug.30112106882779	219	1	n	n	CCONJ
uiug.30112106882779	220	1	=	=	X
uiug.30112106882779	220	2	63	63	NUM
uiug.30112106882779	220	3	;	;	PUNCT
uiug.30112106882779	220	4	k	k	X
uiug.30112106882779	220	5	=	=	NOUN
uiug.30112106882779	220	6	0.5	0.5	NUM
uiug.30112106882779	220	7	.	.	PUNCT
uiug.30112106882779	220	8	18	18	NUM
uiug.30112106882779	220	9	1.57	1.57	NUM
uiug.30112106882779	220	10	n	n	CCONJ
uiug.30112106882779	220	11	=	=	X
uiug.30112106882779	220	12	255	255	NUM
uiug.30112106882779	220	13	n	n	CCONJ
uiug.30112106882779	220	14	=	=	SYM
uiug.30112106882779	220	15	511	511	NUM
uiug.30112106882779	220	16	landau	landau	NOUN
uiug.30112106882779	220	17	value	value	NOUN
uiug.30112106882779	220	18	wp	wp	PROPN
uiug.30112106882779	220	19	1.4	1.4	NUM
uiug.30112106882779	220	20	n	n	CCONJ
uiug.30112106882779	220	21	=	=	X
uiug.30112106882779	220	22	31	31	NUM
uiug.30112106882779	220	23	n	n	CCONJ
uiug.30112106882779	220	24	=	=	PUNCT
uiug.30112106882779	220	25	63	63	NUM
uiug.30112106882779	220	26	n	n	CCONJ
uiug.30112106882779	220	27	=	=	X
uiug.30112106882779	220	28	127	127	NUM
uiug.30112106882779	220	29	1.3	1.3	NUM
uiug.30112106882779	220	30	0	0	NUM
uiug.30112106882779	220	31	1	1	NUM
uiug.30112106882779	220	32	.04	.04	NUM
uiug.30112106882779	220	33	.02	.02	NUM
uiug.30112106882779	220	34	.06	.06	NUM
uiug.30112106882779	220	35	.08	.08	NUM
uiug.30112106882779	220	36	.10	.10	NUM
uiug.30112106882779	220	37	b	b	NOUN
uiug.30112106882779	220	38	(	(	PUNCT
uiug.30112106882779	220	39	a	a	X
uiug.30112106882779	220	40	)	)	PUNCT
uiug.30112106882779	220	41	wide	wide	ADJ
uiug.30112106882779	220	42	range	range	NOUN
uiug.30112106882779	220	43	of	of	ADP
uiug.30112106882779	220	44	n.	n.	PROPN
uiug.30112106882779	220	45	1.46	1.46	NUM
uiug.30112106882779	220	46	n	n	CCONJ
uiug.30112106882779	220	47	=	=	X
uiug.30112106882779	220	48	255	255	NUM
uiug.30112106882779	220	49	1.44	1.44	NUM
uiug.30112106882779	220	50	-n	-n	NOUN
uiug.30112106882779	220	51	=	=	SYM
uiug.30112106882779	220	52	511	511	NUM
uiug.30112106882779	220	53	wp	wp	PROPN
uiug.30112106882779	220	54	landau	landau	NOUN
uiug.30112106882779	220	55	value	value	NOUN
uiug.30112106882779	220	56	1.42	1.42	NUM
uiug.30112106882779	220	57	zn	zn	X
uiug.30112106882779	220	58	n	n	X
uiug.30112106882779	220	59	=	=	X
uiug.30112106882779	220	60	1023	1023	NUM
uiug.30112106882779	220	61	1.40	1.40	NUM
uiug.30112106882779	220	62	0	0	NUM
uiug.30112106882779	220	63	.001	.001	NUM
uiug.30112106882779	220	64	.002	.002	NUM
uiug.30112106882779	220	65	b	b	NOUN
uiug.30112106882779	220	66	(	(	PUNCT
uiug.30112106882779	220	67	b	b	NOUN
uiug.30112106882779	220	68	)	)	PUNCT
uiug.30112106882779	220	69	higher	high	ADJ
uiug.30112106882779	220	70	values	value	NOUN
uiug.30112106882779	220	71	of	of	ADP
uiug.30112106882779	220	72	n	n	NOUN
uiug.30112106882779	220	73	;	;	PUNCT
uiug.30112106882779	220	74	expanded	expand	VERB
uiug.30112106882779	220	75	scale	scale	NOUN
uiug.30112106882779	220	76	.	.	PUNCT
uiug.30112106882779	221	1	figure	figure	VERB
uiug.30112106882779	221	2	2.real	2.real	NUM
uiug.30112106882779	221	3	part	part	NOUN
uiug.30112106882779	221	4	of	of	ADP
uiug.30112106882779	221	5	complex	complex	ADJ
uiug.30112106882779	221	6	frequency	frequency	NOUN
uiug.30112106882779	221	7	as	as	ADP
uiug.30112106882779	221	8	a	a	DET
uiug.30112106882779	221	9	function	function	NOUN
uiug.30112106882779	221	10	of	of	ADP
uiug.30112106882779	221	11	collision	collision	NOUN
uiug.30112106882779	221	12	parameter	parameter	PROPN
uiug.30112106882779	221	13	b.	b.	PROPN
uiug.30112106882779	221	14	k	k	PROPN
uiug.30112106882779	221	15	=	=	PROPN
uiug.30112106882779	221	16	0.5	0.5	NUM
uiug.30112106882779	221	17	.	.	PUNCT
uiug.30112106882779	221	18	19	19	NUM
uiug.30112106882779	221	19	landau	landau	NOUN
uiug.30112106882779	221	20	value	value	NOUN
uiug.30112106882779	221	21	n	n	CCONJ
uiug.30112106882779	221	22	=	=	PUNCT
uiug.30112106882779	221	23	31	31	NUM
uiug.30112106882779	221	24	n	n	CCONJ
uiug.30112106882779	221	25	=	=	SYM
uiug.30112106882779	221	26	63	63	NUM
uiug.30112106882779	221	27	.1	.1	NUM
uiug.30112106882779	221	28	n	n	CCONJ
uiug.30112106882779	221	29	=	=	X
uiug.30112106882779	221	30	127	127	NUM
uiug.30112106882779	221	31	n	n	CCONJ
uiug.30112106882779	221	32	=	=	X
uiug.30112106882779	221	33	255	255	NUM
uiug.30112106882779	221	34	0	0	NUM
uiug.30112106882779	221	35	.02	.02	NUM
uiug.30112106882779	221	36	.04	.04	PROPN
uiug.30112106882779	221	37	.06	.06	NUM
uiug.30112106882779	221	38	.08	.08	NUM
uiug.30112106882779	221	39	.10	.10	NUM
uiug.30112106882779	221	40	b	b	NOUN
uiug.30112106882779	221	41	(	(	PUNCT
uiug.30112106882779	221	42	a	a	X
uiug.30112106882779	221	43	)	)	PUNCT
uiug.30112106882779	221	44	lower	low	ADJ
uiug.30112106882779	221	45	values	value	NOUN
uiug.30112106882779	221	46	of	of	ADP
uiug.30112106882779	221	47	n.	n.	PROPN
uiug.30112106882779	221	48	.16	.16	PROPN
uiug.30112106882779	221	49	landau	landau	PROPN
uiug.30112106882779	221	50	value	value	PROPN
uiug.30112106882779	221	51	y	y	PROPN
uiug.30112106882779	221	52	.154	.154	PUNCT
uiug.30112106882779	222	1	y	y	PROPN
uiug.30112106882779	222	2	en	en	PROPN
uiug.30112106882779	222	3	=	=	PRON
uiug.30112106882779	222	4	511	511	NUM
uiug.30112106882779	222	5	n	n	CCONJ
uiug.30112106882779	222	6	=	=	SYM
uiug.30112106882779	222	7	1023	1023	NUM
uiug.30112106882779	222	8	.144	.144	NUM
uiug.30112106882779	222	9	.002	.002	NUM
uiug.30112106882779	222	10	.001	.001	PUNCT
uiug.30112106882779	222	11	b	b	NOUN
uiug.30112106882779	222	12	(	(	PUNCT
uiug.30112106882779	222	13	b	b	NOUN
uiug.30112106882779	222	14	)	)	PUNCT
uiug.30112106882779	222	15	higher	high	ADJ
uiug.30112106882779	222	16	values	value	NOUN
uiug.30112106882779	222	17	of	of	ADP
uiug.30112106882779	222	18	n	n	NOUN
uiug.30112106882779	222	19	;	;	PUNCT
uiug.30112106882779	222	20	expanded	expand	VERB
uiug.30112106882779	222	21	scale	scale	NOUN
uiug.30112106882779	222	22	.	.	PUNCT
uiug.30112106882779	223	1	figure	figure	NOUN
uiug.30112106882779	223	2	3.damping	3.damping	NUM
uiug.30112106882779	223	3	part	part	NOUN
uiug.30112106882779	223	4	of	of	ADP
uiug.30112106882779	223	5	complex	complex	ADJ
uiug.30112106882779	223	6	frequency	frequency	NOUN
uiug.30112106882779	223	7	as	as	ADP
uiug.30112106882779	223	8	a	a	DET
uiug.30112106882779	223	9	function	function	NOUN
uiug.30112106882779	223	10	of	of	ADP
uiug.30112106882779	223	11	collision	collision	NOUN
uiug.30112106882779	223	12	parameter	parameter	PROPN
uiug.30112106882779	223	13	b.	b.	PROPN
uiug.30112106882779	223	14	k	k	PROPN
uiug.30112106882779	223	15	=	=	PROPN
uiug.30112106882779	223	16	0.5	0.5	NUM
uiug.30112106882779	223	17	.	.	PUNCT
uiug.30112106882779	224	1	20	20	NUM
uiug.30112106882779	224	2	.4	.4	NUM
uiug.30112106882779	224	3	n	n	CCONJ
uiug.30112106882779	224	4	=	=	PUNCT
uiug.30112106882779	224	5	00	00	PUNCT
uiug.30112106882779	225	1	=	=	SYM
uiug.30112106882779	225	2	12	12	NUM
uiug.30112106882779	225	3	.3	.3	NUM
uiug.30112106882779	225	4	.2	.2	NUM
uiug.30112106882779	225	5	.1	.1	NUM
uiug.30112106882779	225	6	0	0	NUM
uiug.30112106882779	225	7	1	1	NUM
uiug.30112106882779	225	8	2	2	NUM
uiug.30112106882779	225	9	.	.	NUM
uiug.30112106882779	225	10	3	3	NUM
uiug.30112106882779	225	11	4	4	NUM
uiug.30112106882779	225	12	(	(	PUNCT
uiug.30112106882779	225	13	a	a	NOUN
uiug.30112106882779	225	14	)	)	PUNCT
uiug.30112106882779	225	15	n	n	CCONJ
uiug.30112106882779	225	16	=	=	SYM
uiug.30112106882779	225	17	99	99	NUM
uiug.30112106882779	225	18	.	.	PUNCT
uiug.30112106882779	226	1	.4	.4	NUM
uiug.30112106882779	226	2	n	n	CCONJ
uiug.30112106882779	226	3	=	=	PUNCT
uiug.30112106882779	226	4	00	00	PUNCT
uiug.30112106882779	226	5	.3	.3	NUM
uiug.30112106882779	227	1	.2	.2	NUM
uiug.30112106882779	227	2	.1	.1	NUM
uiug.30112106882779	227	3	0	0	NUM
uiug.30112106882779	227	4	1	1	NUM
uiug.30112106882779	227	5	2	2	NUM
uiug.30112106882779	227	6	3	3	NUM
uiug.30112106882779	227	7	4	4	NUM
uiug.30112106882779	227	8	λ	λ	NOUN
uiug.30112106882779	227	9	(	(	PUNCT
uiug.30112106882779	227	10	b	b	NOUN
uiug.30112106882779	227	11	)	)	PUNCT
uiug.30112106882779	227	12	n	n	CCONJ
uiug.30112106882779	227	13	=	=	X
uiug.30112106882779	227	14	1023	1023	NUM
uiug.30112106882779	227	15	.	.	PUNCT
uiug.30112106882779	228	1	figure	figure	VERB
uiug.30112106882779	228	2	4.exact	4.exact	NUM
uiug.30112106882779	228	3	fourier	fourier	NOUN
uiug.30112106882779	228	4	transform	transform	NOUN
uiug.30112106882779	228	5	compared	compare	VERB
uiug.30112106882779	228	6	with	with	ADP
uiug.30112106882779	228	7	corresponding	corresponding	ADJ
uiug.30112106882779	228	8	fourier	fourier	NOUN
uiug.30112106882779	228	9	-	-	PUNCT
uiug.30112106882779	228	10	hermite	hermite	NOUN
uiug.30112106882779	228	11	histograms	histogram	NOUN
uiug.30112106882779	228	12	for	for	ADP
uiug.30112106882779	228	13	initial	initial	ADJ
uiug.30112106882779	228	14	cos(kx	cos(kx	PROPN
uiug.30112106882779	228	15	)	)	PUNCT
uiug.30112106882779	228	16	density	density	NOUN
uiug.30112106882779	228	17	disturbance	disturbance	NOUN
uiug.30112106882779	228	18	.	.	PUNCT
uiug.30112106882779	229	1	k	k	PROPN
uiug.30112106882779	229	2	=	=	PROPN
uiug.30112106882779	229	3	0.5	0.5	NUM
uiug.30112106882779	229	4	.	.	PUNCT
uiug.30112106882779	230	1	nasa	nasa	PROPN
uiug.30112106882779	230	2	-	-	PUNCT
uiug.30112106882779	230	3	langley	langley	PROPN
uiug.30112106882779	230	4	,	,	PUNCT
uiug.30112106882779	230	5	1972	1972	NUM
uiug.30112106882779	230	6	25	25	NUM
uiug.30112106882779	230	7	l-8141	l-8141	NUM
uiug.30112106882779	230	8	21	21	NUM
uiug.30112106882779	230	9	一	一	NOUN
uiug.30112106882779	230	10	​	​	PROPN
uiug.30112106882779	230	11	national	national	ADJ
uiug.30112106882779	230	12	aeronautics	aeronautic	NOUN
uiug.30112106882779	230	13	and	and	CCONJ
uiug.30112106882779	230	14	space	space	PROPN
uiug.30112106882779	230	15	admistration	admistration	PROPN
uiug.30112106882779	230	16	washington	washington	PROPN
uiug.30112106882779	230	17	,	,	PUNCT
uiug.30112106882779	230	18	d.c	d.c	PROPN
uiug.30112106882779	230	19	.	.	PROPN
uiug.30112106882779	230	20	20546	20546	NUM
uiug.30112106882779	230	21	postage	postage	NOUN
uiug.30112106882779	230	22	and	and	CCONJ
uiug.30112106882779	230	23	fees	fee	NOUN
uiug.30112106882779	230	24	paid	pay	VERB
uiug.30112106882779	230	25	national	national	ADJ
uiug.30112106882779	230	26	aeronautics	aeronautic	NOUN
uiug.30112106882779	230	27	and	and	CCONJ
uiug.30112106882779	230	28	space	space	PROPN
uiug.30112106882779	230	29	administration	administration	PROPN
uiug.30112106882779	230	30	2	2	NUM
uiug.30112106882779	230	31	official	official	ADJ
uiug.30112106882779	230	32	business	business	NOUN
uiug.30112106882779	230	33	penalty	penalty	NOUN
uiug.30112106882779	230	34	for	for	ADP
uiug.30112106882779	230	35	private	private	ADJ
uiug.30112106882779	230	36	use	use	NOUN
uiug.30112106882779	230	37	$	$	SYM
uiug.30112106882779	230	38	300	300	NUM
uiug.30112106882779	230	39	first	first	ADJ
uiug.30112106882779	230	40	class	class	NOUN
uiug.30112106882779	230	41	mail	mail	NOUN
uiug.30112106882779	230	42	u.s.mail	u.s.mail	NOUN
uiug.30112106882779	230	43	postmaster	postmaster	NOUN
uiug.30112106882779	230	44	:	:	PUNCT
uiug.30112106882779	230	45	if	if	SCONJ
uiug.30112106882779	230	46	undeliverable	undeliverable	ADJ
uiug.30112106882779	230	47	(	(	PUNCT
uiug.30112106882779	230	48	section	section	NOUN
uiug.30112106882779	230	49	14	14	NUM
uiug.30112106882779	230	50	postal	postal	ADJ
uiug.30112106882779	230	51	manual	manual	NOUN
uiug.30112106882779	230	52	)	)	PUNCT
uiug.30112106882779	230	53	do	do	AUX
uiug.30112106882779	230	54	not	not	PART
uiug.30112106882779	230	55	rec	rec	VERB
uiug.30112106882779	230	56	"	"	PUNCT
uiug.30112106882779	230	57	the	the	DET
uiug.30112106882779	230	58	aeronautical	aeronautical	ADJ
uiug.30112106882779	230	59	and	and	CCONJ
uiug.30112106882779	230	60	space	space	NOUN
uiug.30112106882779	230	61	activities	activity	NOUN
uiug.30112106882779	230	62	of	of	ADP
uiug.30112106882779	230	63	the	the	DET
uiug.30112106882779	230	64	united	united	PROPN
uiug.30112106882779	230	65	states	states	PROPN
uiug.30112106882779	230	66	shall	shall	AUX
uiug.30112106882779	230	67	be	be	AUX
uiug.30112106882779	230	68	conducted	conduct	VERB
uiug.30112106882779	230	69	so	so	SCONJ
uiug.30112106882779	230	70	as	as	SCONJ
uiug.30112106882779	230	71	to	to	PART
uiug.30112106882779	230	72	contribute	contribute	VERB
uiug.30112106882779	230	73	...	...	PUNCT
uiug.30112106882779	230	74	to	to	ADP
uiug.30112106882779	230	75	the	the	DET
uiug.30112106882779	230	76	expansion	expansion	NOUN
uiug.30112106882779	230	77	of	of	ADP
uiug.30112106882779	230	78	human	human	ADJ
uiug.30112106882779	230	79	knowledge	knowledge	NOUN
uiug.30112106882779	230	80	of	of	ADP
uiug.30112106882779	230	81	phenomena	phenomenon	NOUN
uiug.30112106882779	230	82	in	in	ADP
uiug.30112106882779	230	83	the	the	DET
uiug.30112106882779	230	84	atmosphere	atmosphere	NOUN
uiug.30112106882779	230	85	and	and	CCONJ
uiug.30112106882779	230	86	space	space	NOUN
uiug.30112106882779	230	87	.	.	PUNCT
uiug.30112106882779	231	1	the	the	DET
uiug.30112106882779	231	2	administration	administration	NOUN
uiug.30112106882779	231	3	shall	shall	AUX
uiug.30112106882779	231	4	provide	provide	VERB
uiug.30112106882779	231	5	for	for	ADP
uiug.30112106882779	231	6	the	the	DET
uiug.30112106882779	231	7	widest	widest	ADJ
uiug.30112106882779	231	8	practicable	practicable	ADJ
uiug.30112106882779	231	9	and	and	CCONJ
uiug.30112106882779	231	10	appropriate	appropriate	ADJ
uiug.30112106882779	231	11	dissemination	dissemination	NOUN
uiug.30112106882779	231	12	of	of	ADP
uiug.30112106882779	231	13	information	information	NOUN
uiug.30112106882779	231	14	concerning	concern	VERB
uiug.30112106882779	231	15	its	its	PRON
uiug.30112106882779	231	16	activities	activity	NOUN
uiug.30112106882779	231	17	and	and	CCONJ
uiug.30112106882779	231	18	the	the	DET
uiug.30112106882779	231	19	results	result	NOUN
uiug.30112106882779	231	20	thereof	thereof	ADV
uiug.30112106882779	231	21	.	.	PUNCT
uiug.30112106882779	231	22	"	"	PUNCT
uiug.30112106882779	232	1	national	national	PROPN
uiug.30112106882779	232	2	aeronautics	aeronautic	NOUN
uiug.30112106882779	232	3	and	and	CCONJ
uiug.30112106882779	232	4	space	space	NOUN
uiug.30112106882779	232	5	act	act	NOUN
uiug.30112106882779	232	6	of	of	ADP
uiug.30112106882779	232	7	1958	1958	NUM
uiug.30112106882779	232	8	nasa	nasa	PROPN
uiug.30112106882779	232	9	scientific	scientific	ADJ
uiug.30112106882779	232	10	and	and	CCONJ
uiug.30112106882779	232	11	technical	technical	ADJ
uiug.30112106882779	232	12	publications	publication	NOUN
uiug.30112106882779	232	13	technical	technical	ADJ
uiug.30112106882779	232	14	reports	report	NOUN
uiug.30112106882779	232	15	:	:	PUNCT
uiug.30112106882779	232	16	scientific	scientific	ADJ
uiug.30112106882779	232	17	and	and	CCONJ
uiug.30112106882779	232	18	technical	technical	ADJ
uiug.30112106882779	232	19	information	information	NOUN
uiug.30112106882779	232	20	considered	consider	VERB
uiug.30112106882779	232	21	important	important	ADJ
uiug.30112106882779	232	22	,	,	PUNCT
uiug.30112106882779	232	23	complete	complete	ADJ
uiug.30112106882779	232	24	,	,	PUNCT
uiug.30112106882779	232	25	and	and	CCONJ
uiug.30112106882779	232	26	a	a	DET
uiug.30112106882779	232	27	lasting	last	VERB
uiug.30112106882779	232	28	contribution	contribution	NOUN
uiug.30112106882779	232	29	to	to	ADP
uiug.30112106882779	232	30	existing	exist	VERB
uiug.30112106882779	232	31	knowledge	knowledge	NOUN
uiug.30112106882779	232	32	technical	technical	ADJ
uiug.30112106882779	232	33	translations	translation	NOUN
uiug.30112106882779	232	34	:	:	PUNCT
uiug.30112106882779	232	35	information	information	NOUN
uiug.30112106882779	232	36	published	publish	VERB
uiug.30112106882779	232	37	in	in	ADP
uiug.30112106882779	232	38	a	a	DET
uiug.30112106882779	232	39	foreign	foreign	ADJ
uiug.30112106882779	232	40	language	language	NOUN
uiug.30112106882779	232	41	considered	consider	VERB
uiug.30112106882779	232	42	to	to	ADP
uiug.30112106882779	232	43	merit	merit	NOUN
uiug.30112106882779	232	44	nasa	nasa	PROPN
uiug.30112106882779	232	45	distribution	distribution	NOUN
uiug.30112106882779	232	46	in	in	ADP
uiug.30112106882779	232	47	english	english	PROPN
uiug.30112106882779	232	48	.	.	PUNCT
uiug.30112106882779	233	1	a	a	DET
uiug.30112106882779	233	2	technical	technical	ADJ
uiug.30112106882779	233	3	notes	note	NOUN
uiug.30112106882779	233	4	:	:	PUNCT
uiug.30112106882779	233	5	information	information	NOUN
uiug.30112106882779	233	6	less	less	ADV
uiug.30112106882779	233	7	broad	broad	ADJ
uiug.30112106882779	233	8	in	in	ADP
uiug.30112106882779	233	9	scope	scope	NOUN
uiug.30112106882779	233	10	but	but	CCONJ
uiug.30112106882779	233	11	nevertheless	nevertheless	ADV
uiug.30112106882779	233	12	of	of	ADP
uiug.30112106882779	233	13	importance	importance	NOUN
uiug.30112106882779	233	14	as	as	ADP
uiug.30112106882779	233	15	a	a	DET
uiug.30112106882779	233	16	contribution	contribution	NOUN
uiug.30112106882779	233	17	to	to	ADP
uiug.30112106882779	233	18	existing	exist	VERB
uiug.30112106882779	233	19	knowledge	knowledge	NOUN
uiug.30112106882779	233	20	.	.	PUNCT
uiug.30112106882779	234	1	technical	technical	ADJ
uiug.30112106882779	234	2	memorandums	memorandum	NOUN
uiug.30112106882779	234	3	:	:	PUNCT
uiug.30112106882779	234	4	information	information	NOUN
uiug.30112106882779	234	5	receiving	receive	VERB
uiug.30112106882779	234	6	limited	limited	ADJ
uiug.30112106882779	234	7	distribution	distribution	NOUN
uiug.30112106882779	234	8	because	because	SCONJ
uiug.30112106882779	234	9	of	of	ADP
uiug.30112106882779	234	10	preliminary	preliminary	ADJ
uiug.30112106882779	234	11	data	datum	NOUN
uiug.30112106882779	234	12	,	,	PUNCT
uiug.30112106882779	234	13	security	security	NOUN
uiug.30112106882779	234	14	classification	classification	NOUN
uiug.30112106882779	234	15	,	,	PUNCT
uiug.30112106882779	234	16	or	or	CCONJ
uiug.30112106882779	234	17	other	other	ADJ
uiug.30112106882779	234	18	reasons	reason	NOUN
uiug.30112106882779	234	19	.	.	PUNCT
uiug.30112106882779	235	1	contractor	contractor	NOUN
uiug.30112106882779	235	2	reports	report	NOUN
uiug.30112106882779	235	3	:	:	PUNCT
uiug.30112106882779	235	4	scientific	scientific	ADJ
uiug.30112106882779	235	5	and	and	CCONJ
uiug.30112106882779	235	6	technical	technical	ADJ
uiug.30112106882779	235	7	information	information	NOUN
uiug.30112106882779	235	8	generated	generate	VERB
uiug.30112106882779	235	9	under	under	ADP
uiug.30112106882779	235	10	a	a	DET
uiug.30112106882779	235	11	nasa	nasa	PROPN
uiug.30112106882779	235	12	contract	contract	NOUN
uiug.30112106882779	235	13	or	or	CCONJ
uiug.30112106882779	235	14	grant	grant	NOUN
uiug.30112106882779	235	15	and	and	CCONJ
uiug.30112106882779	235	16	considered	consider	VERB
uiug.30112106882779	235	17	an	an	DET
uiug.30112106882779	235	18	important	important	ADJ
uiug.30112106882779	235	19	contribution	contribution	NOUN
uiug.30112106882779	235	20	to	to	ADP
uiug.30112106882779	235	21	existing	exist	VERB
uiug.30112106882779	235	22	knowledge	knowledge	NOUN
uiug.30112106882779	235	23	.	.	PUNCT
uiug.30112106882779	236	1	special	special	ADJ
uiug.30112106882779	236	2	publications	publication	NOUN
uiug.30112106882779	236	3	:	:	PUNCT
uiug.30112106882779	236	4	information	information	NOUN
uiug.30112106882779	236	5	derived	derive	VERB
uiug.30112106882779	236	6	from	from	ADP
uiug.30112106882779	236	7	or	or	CCONJ
uiug.30112106882779	236	8	of	of	ADP
uiug.30112106882779	236	9	value	value	NOUN
uiug.30112106882779	236	10	to	to	ADP
uiug.30112106882779	236	11	nasa	nasa	PROPN
uiug.30112106882779	236	12	activities	activity	NOUN
uiug.30112106882779	236	13	.	.	PUNCT
uiug.30112106882779	237	1	publications	publication	NOUN
uiug.30112106882779	237	2	include	include	VERB
uiug.30112106882779	237	3	conference	conference	NOUN
uiug.30112106882779	237	4	proceedings	proceeding	NOUN
uiug.30112106882779	237	5	,	,	PUNCT
uiug.30112106882779	237	6	monographs	monograph	NOUN
uiug.30112106882779	237	7	,	,	PUNCT
uiug.30112106882779	237	8	data	datum	NOUN
uiug.30112106882779	237	9	compilations	compilation	NOUN
uiug.30112106882779	237	10	,	,	PUNCT
uiug.30112106882779	237	11	handbooks	handbook	NOUN
uiug.30112106882779	237	12	,	,	PUNCT
uiug.30112106882779	237	13	sourcebooks	sourcebook	NOUN
uiug.30112106882779	237	14	,	,	PUNCT
uiug.30112106882779	237	15	and	and	CCONJ
uiug.30112106882779	237	16	special	special	ADJ
uiug.30112106882779	237	17	bibliographies	bibliography	NOUN
uiug.30112106882779	237	18	.	.	PUNCT
uiug.30112106882779	238	1	technology	technology	NOUN
uiug.30112106882779	238	2	utilization	utilization	NOUN
uiug.30112106882779	238	3	publications	publication	NOUN
uiug.30112106882779	238	4	:	:	PUNCT
uiug.30112106882779	238	5	information	information	NOUN
uiug.30112106882779	238	6	on	on	ADP
uiug.30112106882779	238	7	technology	technology	NOUN
uiug.30112106882779	238	8	used	use	VERB
uiug.30112106882779	238	9	by	by	ADP
uiug.30112106882779	238	10	nasa	nasa	PROPN
uiug.30112106882779	238	11	that	that	PRON
uiug.30112106882779	238	12	may	may	AUX
uiug.30112106882779	238	13	be	be	AUX
uiug.30112106882779	238	14	of	of	ADP
uiug.30112106882779	238	15	particular	particular	ADJ
uiug.30112106882779	238	16	interest	interest	NOUN
uiug.30112106882779	238	17	in	in	ADP
uiug.30112106882779	238	18	commercial	commercial	ADJ
uiug.30112106882779	238	19	and	and	CCONJ
uiug.30112106882779	238	20	other	other	ADJ
uiug.30112106882779	238	21	non	non	ADJ
uiug.30112106882779	238	22	-	-	ADJ
uiug.30112106882779	238	23	aerospace	aerospace	ADJ
uiug.30112106882779	238	24	applications	application	NOUN
uiug.30112106882779	238	25	.	.	PUNCT
uiug.30112106882779	239	1	publications	publication	NOUN
uiug.30112106882779	239	2	include	include	VERB
uiug.30112106882779	239	3	tech	tech	NOUN
uiug.30112106882779	239	4	briefs	brief	NOUN
uiug.30112106882779	239	5	,	,	PUNCT
uiug.30112106882779	239	6	technology	technology	NOUN
uiug.30112106882779	239	7	utilization	utilization	NOUN
uiug.30112106882779	239	8	reports	report	NOUN
uiug.30112106882779	239	9	and	and	CCONJ
uiug.30112106882779	239	10	technology	technology	NOUN
uiug.30112106882779	239	11	surveys	survey	NOUN
uiug.30112106882779	239	12	.	.	PUNCT
uiug.30112106882779	240	1	details	detail	NOUN
uiug.30112106882779	240	2	on	on	ADP
uiug.30112106882779	240	3	the	the	DET
uiug.30112106882779	240	4	availability	availability	NOUN
uiug.30112106882779	240	5	of	of	ADP
uiug.30112106882779	240	6	these	these	DET
uiug.30112106882779	240	7	publications	publication	NOUN
uiug.30112106882779	240	8	may	may	AUX
uiug.30112106882779	240	9	be	be	AUX
uiug.30112106882779	240	10	obtained	obtain	VERB
uiug.30112106882779	240	11	from	from	ADP
uiug.30112106882779	240	12	:	:	PUNCT
uiug.30112106882779	240	13	scientific	scientific	ADJ
uiug.30112106882779	240	14	and	and	CCONJ
uiug.30112106882779	240	15	technical	technical	ADJ
uiug.30112106882779	240	16	information	information	NOUN
uiug.30112106882779	240	17	office	office	NOUN
uiug.30112106882779	240	18	national	national	ADJ
uiug.30112106882779	240	19	aeronautics	aeronautic	NOUN
uiug.30112106882779	240	20	and	and	CCONJ
uiug.30112106882779	240	21	space	space	PROPN
uiug.30112106882779	240	22	administration	administration	PROPN
uiug.30112106882779	240	23	washington	washington	PROPN
uiug.30112106882779	240	24	,	,	PUNCT
uiug.30112106882779	240	25	d.c	d.c	PROPN
uiug.30112106882779	240	26	.	.	PROPN
uiug.30112106882779	241	1	20546	20546	NUM
uiug.30112106882779	241	2	29	29	NUM
uiug.30112106882779	241	3	30	30	NUM