id	sid	tid	token	lemma	pos
ap-368	1	1	ap02_04.vp	ap02_04.vp	NOUN
ap-368	1	2	1	1	NUM
ap-368	1	3	introduction	introduction	NOUN
ap-368	1	4	propagation	propagation	NOUN
ap-368	1	5	of	of	ADP
ap-368	1	6	nonlinear	nonlinear	ADJ
ap-368	1	7	sound	sound	ADJ
ap-368	1	8	waves	wave	NOUN
ap-368	1	9	in	in	ADP
ap-368	1	10	waveguides	waveguide	NOUN
ap-368	1	11	is	be	AUX
ap-368	1	12	a	a	DET
ap-368	1	13	very	very	ADV
ap-368	1	14	interesting	interesting	ADJ
ap-368	1	15	physical	physical	ADJ
ap-368	1	16	problem	problem	NOUN
ap-368	1	17	.	.	PUNCT
ap-368	2	1	in	in	ADP
ap-368	2	2	the	the	DET
ap-368	2	3	case	case	NOUN
ap-368	2	4	that	that	SCONJ
ap-368	2	5	nonlinear	nonlinear	ADJ
ap-368	2	6	waves	wave	NOUN
ap-368	2	7	travel	travel	VERB
ap-368	2	8	in	in	ADP
ap-368	2	9	a	a	DET
ap-368	2	10	gas	gas	NOUN
ap-368	2	11	-	-	PUNCT
ap-368	2	12	filled	fill	VERB
ap-368	2	13	waveguide	waveguide	NOUN
ap-368	2	14	,	,	PUNCT
ap-368	2	15	we	we	PRON
ap-368	2	16	can	can	AUX
ap-368	2	17	observe	observe	VERB
ap-368	2	18	phenomena	phenomena	NOUN
ap-368	2	19	such	such	ADJ
ap-368	2	20	as	as	ADP
ap-368	2	21	nonlinear	nonlinear	ADJ
ap-368	2	22	distortion	distortion	NOUN
ap-368	2	23	,	,	PUNCT
ap-368	2	24	nonlinear	nonlinear	ADJ
ap-368	2	25	absorption	absorption	NOUN
ap-368	2	26	,	,	PUNCT
ap-368	2	27	diffraction	diffraction	NOUN
ap-368	2	28	,	,	PUNCT
ap-368	2	29	lateral	lateral	ADJ
ap-368	2	30	dispersion	dispersion	NOUN
ap-368	2	31	,	,	PUNCT
ap-368	2	32	boundary	boundary	ADJ
ap-368	2	33	layer	layer	NOUN
ap-368	2	34	effects	effect	NOUN
ap-368	2	35	,	,	PUNCT
ap-368	2	36	etc	etc	X
ap-368	2	37	.	.	X
ap-368	3	1	all	all	DET
ap-368	3	2	these	these	DET
ap-368	3	3	phenomena	phenomenon	NOUN
ap-368	3	4	can	can	AUX
ap-368	3	5	be	be	AUX
ap-368	3	6	described	describe	VERB
ap-368	3	7	by	by	ADP
ap-368	3	8	means	mean	NOUN
ap-368	3	9	of	of	ADP
ap-368	3	10	the	the	DET
ap-368	3	11	complete	complete	ADJ
ap-368	3	12	system	system	NOUN
ap-368	3	13	of	of	ADP
ap-368	3	14	the	the	DET
ap-368	3	15	equations	equation	NOUN
ap-368	3	16	of	of	ADP
ap-368	3	17	hydrodynamics	hydrodynamic	NOUN
ap-368	3	18	,	,	PUNCT
ap-368	3	19	see	see	VERB
ap-368	3	20	e.g.	e.g.	ADV
ap-368	3	21	[	[	X
ap-368	3	22	1]–[4	1]–[4	NUM
ap-368	3	23	]	]	X
ap-368	3	24	:	:	PUNCT
ap-368	3	25	the	the	DET
ap-368	3	26	navier	navier	NOUN
ap-368	3	27	-	-	PUNCT
ap-368	3	28	stokes	stokes	PROPN
ap-368	3	29	momentum	momentum	NOUN
ap-368	3	30	equation	equation	NOUN
ap-368	3	31	,	,	PUNCT
ap-368	3	32	the	the	DET
ap-368	3	33	continuity	continuity	NOUN
ap-368	3	34	(	(	PUNCT
ap-368	3	35	mass	mass	NOUN
ap-368	3	36	conservation	conservation	NOUN
ap-368	3	37	)	)	PUNCT
ap-368	3	38	equation	equation	NOUN
ap-368	3	39	,	,	PUNCT
ap-368	3	40	the	the	DET
ap-368	3	41	heat	heat	NOUN
ap-368	3	42	transfer	transfer	NOUN
ap-368	3	43	(	(	PUNCT
ap-368	3	44	entropy	entropy	NOUN
ap-368	3	45	)	)	PUNCT
ap-368	3	46	equation	equation	NOUN
ap-368	3	47	and	and	CCONJ
ap-368	3	48	the	the	DET
ap-368	3	49	state	state	NOUN
ap-368	3	50	equations	equation	NOUN
ap-368	3	51	.	.	PUNCT
ap-368	4	1	unfortunately	unfortunately	ADV
ap-368	4	2	,	,	PUNCT
ap-368	4	3	there	there	PRON
ap-368	4	4	is	be	VERB
ap-368	4	5	no	no	DET
ap-368	4	6	known	know	VERB
ap-368	4	7	general	general	ADJ
ap-368	4	8	solution	solution	NOUN
ap-368	4	9	of	of	ADP
ap-368	4	10	this	this	DET
ap-368	4	11	system	system	NOUN
ap-368	4	12	of	of	ADP
ap-368	4	13	equations	equation	NOUN
ap-368	4	14	,	,	PUNCT
ap-368	4	15	and	and	CCONJ
ap-368	4	16	numerical	numerical	ADJ
ap-368	4	17	solutions	solution	NOUN
ap-368	4	18	bring	bring	VERB
ap-368	4	19	many	many	ADJ
ap-368	4	20	problems	problem	NOUN
ap-368	4	21	regarding	regard	VERB
ap-368	4	22	stability	stability	NOUN
ap-368	4	23	of	of	ADP
ap-368	4	24	the	the	DET
ap-368	4	25	solutions	solution	NOUN
ap-368	4	26	and	and	CCONJ
ap-368	4	27	their	their	PRON
ap-368	4	28	time	time	NOUN
ap-368	4	29	consumption	consumption	NOUN
ap-368	4	30	.	.	PUNCT
ap-368	5	1	consequently	consequently	ADV
ap-368	5	2	,	,	PUNCT
ap-368	5	3	it	it	PRON
ap-368	5	4	is	be	AUX
ap-368	5	5	sensible	sensible	ADJ
ap-368	5	6	to	to	PART
ap-368	5	7	simplify	simplify	VERB
ap-368	5	8	the	the	DET
ap-368	5	9	fundamental	fundamental	ADJ
ap-368	5	10	system	system	NOUN
ap-368	5	11	of	of	ADP
ap-368	5	12	equations	equation	NOUN
ap-368	5	13	if	if	SCONJ
ap-368	5	14	we	we	PRON
ap-368	5	15	ignore	ignore	VERB
ap-368	5	16	some	some	DET
ap-368	5	17	phenomena	phenomenon	NOUN
ap-368	5	18	or	or	CCONJ
ap-368	5	19	consider	consider	VERB
ap-368	5	20	some	some	PRON
ap-368	5	21	of	of	ADP
ap-368	5	22	them	they	PRON
ap-368	5	23	weak	weak	ADJ
ap-368	5	24	.	.	PUNCT
ap-368	6	1	this	this	DET
ap-368	6	2	simplification	simplification	NOUN
ap-368	6	3	leads	lead	VERB
ap-368	6	4	to	to	ADP
ap-368	6	5	the	the	DET
ap-368	6	6	derivation	derivation	NOUN
ap-368	6	7	of	of	ADP
ap-368	6	8	model	model	NOUN
ap-368	6	9	equations	equation	NOUN
ap-368	6	10	of	of	ADP
ap-368	6	11	nonlinear	nonlinear	ADJ
ap-368	6	12	acoustics	acoustic	NOUN
ap-368	6	13	.	.	PUNCT
ap-368	7	1	there	there	PRON
ap-368	7	2	have	have	AUX
ap-368	7	3	been	be	AUX
ap-368	7	4	a	a	DET
ap-368	7	5	number	number	NOUN
ap-368	7	6	of	of	ADP
ap-368	7	7	papers	paper	NOUN
ap-368	7	8	devoted	devote	VERB
ap-368	7	9	to	to	ADP
ap-368	7	10	various	various	ADJ
ap-368	7	11	aspects	aspect	NOUN
ap-368	7	12	of	of	ADP
ap-368	7	13	the	the	DET
ap-368	7	14	propagation	propagation	NOUN
ap-368	7	15	of	of	ADP
ap-368	7	16	nonlinear	nonlinear	ADJ
ap-368	7	17	waves	wave	NOUN
ap-368	7	18	in	in	ADP
ap-368	7	19	waveguides	waveguide	NOUN
ap-368	7	20	.	.	PUNCT
ap-368	8	1	the	the	DET
ap-368	8	2	viscous	viscous	ADJ
ap-368	8	3	and	and	CCONJ
ap-368	8	4	thermal	thermal	ADJ
ap-368	8	5	dissipative	dissipative	ADJ
ap-368	8	6	effects	effect	NOUN
ap-368	8	7	on	on	ADP
ap-368	8	8	the	the	DET
ap-368	8	9	nonlinear	nonlinear	ADJ
ap-368	8	10	propagation	propagation	NOUN
ap-368	8	11	of	of	ADP
ap-368	8	12	plane	plane	NOUN
ap-368	8	13	waves	wave	NOUN
ap-368	8	14	in	in	ADP
ap-368	8	15	hard	hard	ADV
ap-368	8	16	-	-	PUNCT
ap-368	8	17	walled	wall	VERB
ap-368	8	18	ducts	duct	NOUN
ap-368	8	19	are	be	AUX
ap-368	8	20	treated	treat	VERB
ap-368	8	21	for	for	ADP
ap-368	8	22	instance	instance	NOUN
ap-368	8	23	in	in	ADP
ap-368	8	24	papers	paper	NOUN
ap-368	8	25	[	[	X
ap-368	8	26	5	5	NUM
ap-368	8	27	]	]	PUNCT
ap-368	8	28	,	,	PUNCT
ap-368	9	1	[	[	X
ap-368	9	2	6	6	NUM
ap-368	9	3	]	]	PUNCT
ap-368	9	4	,	,	PUNCT
ap-368	9	5	[	[	X
ap-368	9	6	7	7	NUM
ap-368	9	7	]	]	PUNCT
ap-368	9	8	.	.	PUNCT
ap-368	10	1	the	the	DET
ap-368	10	2	authors	author	NOUN
ap-368	10	3	deal	deal	VERB
ap-368	10	4	with	with	ADP
ap-368	10	5	the	the	DET
ap-368	10	6	dependence	dependence	NOUN
ap-368	10	7	of	of	ADP
ap-368	10	8	the	the	DET
ap-368	10	9	frequency	frequency	NOUN
ap-368	10	10	on	on	ADP
ap-368	10	11	the	the	DET
ap-368	10	12	dissipative	dissipative	ADJ
ap-368	10	13	and	and	CCONJ
ap-368	10	14	dispersive	dispersive	ADJ
ap-368	10	15	effects	effect	NOUN
ap-368	10	16	induced	induce	VERB
ap-368	10	17	by	by	ADP
ap-368	10	18	the	the	DET
ap-368	10	19	acoustic	acoustic	ADJ
ap-368	10	20	boundary	boundary	ADJ
ap-368	10	21	layer	layer	NOUN
ap-368	10	22	.	.	PUNCT
ap-368	11	1	experimental	experimental	ADJ
ap-368	11	2	results	result	NOUN
ap-368	11	3	focused	focus	VERB
ap-368	11	4	on	on	ADP
ap-368	11	5	propagation	propagation	NOUN
ap-368	11	6	of	of	ADP
ap-368	11	7	finite	finite	ADJ
ap-368	11	8	-	-	ADJ
ap-368	11	9	amplitude	amplitude	ADJ
ap-368	11	10	plane	plane	NOUN
ap-368	11	11	waves	wave	NOUN
ap-368	11	12	in	in	ADP
ap-368	11	13	circular	circular	ADJ
ap-368	11	14	ducts	duct	NOUN
ap-368	11	15	are	be	AUX
ap-368	11	16	presented	present	VERB
ap-368	11	17	in	in	ADP
ap-368	11	18	[	[	X
ap-368	11	19	8	8	NUM
ap-368	11	20	]	]	PUNCT
ap-368	11	21	and	and	CCONJ
ap-368	12	1	[	[	X
ap-368	12	2	9	9	NUM
ap-368	12	3	]	]	PUNCT
ap-368	12	4	.	.	PUNCT
ap-368	13	1	here	here	ADV
ap-368	13	2	,	,	PUNCT
ap-368	13	3	a	a	DET
ap-368	13	4	very	very	ADV
ap-368	13	5	good	good	ADJ
ap-368	13	6	agreement	agreement	NOUN
ap-368	13	7	is	be	AUX
ap-368	13	8	demonstrated	demonstrate	VERB
ap-368	13	9	between	between	ADP
ap-368	13	10	experimental	experimental	ADJ
ap-368	13	11	data	datum	NOUN
ap-368	13	12	and	and	CCONJ
ap-368	13	13	results	result	NOUN
ap-368	13	14	obtained	obtain	VERB
ap-368	13	15	by	by	ADP
ap-368	13	16	means	mean	NOUN
ap-368	13	17	of	of	ADP
ap-368	13	18	the	the	DET
ap-368	13	19	rudnick	rudnick	NOUN
ap-368	13	20	decay	decay	NOUN
ap-368	13	21	model	model	NOUN
ap-368	13	22	for	for	ADP
ap-368	13	23	the	the	DET
ap-368	13	24	fundamental	fundamental	ADJ
ap-368	13	25	harmonic	harmonic	NOUN
ap-368	13	26	.	.	PUNCT
ap-368	14	1	burns	burn	VERB
ap-368	14	2	in	in	ADP
ap-368	14	3	[	[	X
ap-368	14	4	10	10	NUM
ap-368	14	5	]	]	PUNCT
ap-368	14	6	obtained	obtain	VERB
ap-368	14	7	a	a	DET
ap-368	14	8	fourth	fourth	ADJ
ap-368	14	9	-	-	PUNCT
ap-368	14	10	order	order	NOUN
ap-368	14	11	perturbation	perturbation	NOUN
ap-368	14	12	solution	solution	NOUN
ap-368	14	13	for	for	ADP
ap-368	14	14	finite	finite	ADJ
ap-368	14	15	-	-	ADJ
ap-368	14	16	amplitude	amplitude	NOUN
ap-368	14	17	waves	wave	NOUN
ap-368	14	18	.	.	PUNCT
ap-368	15	1	however	however	ADV
ap-368	15	2	,	,	PUNCT
ap-368	15	3	his	his	PRON
ap-368	15	4	expansion	expansion	NOUN
ap-368	15	5	breaks	break	VERB
ap-368	15	6	down	down	ADP
ap-368	15	7	for	for	ADP
ap-368	15	8	large	large	ADJ
ap-368	15	9	times	time	NOUN
ap-368	15	10	because	because	SCONJ
ap-368	15	11	it	it	PRON
ap-368	15	12	contains	contain	VERB
ap-368	15	13	secular	secular	ADJ
ap-368	15	14	terms	term	NOUN
ap-368	15	15	.	.	PUNCT
ap-368	16	1	he	he	PRON
ap-368	16	2	took	take	VERB
ap-368	16	3	into	into	ADP
ap-368	16	4	account	account	NOUN
ap-368	16	5	dissipation	dissipation	NOUN
ap-368	16	6	,	,	PUNCT
ap-368	16	7	but	but	CCONJ
ap-368	16	8	he	he	PRON
ap-368	16	9	neglected	neglect	VERB
ap-368	16	10	mainstream	mainstream	NOUN
ap-368	16	11	dissipation	dissipation	NOUN
ap-368	16	12	with	with	ADP
ap-368	16	13	respect	respect	NOUN
ap-368	16	14	to	to	ADP
ap-368	16	15	boundary	boundary	ADJ
ap-368	16	16	dissipation	dissipation	NOUN
ap-368	16	17	.	.	PUNCT
ap-368	17	1	keller	keller	PROPN
ap-368	17	2	and	and	CCONJ
ap-368	17	3	millmann	millmann	VERB
ap-368	17	4	in	in	ADP
ap-368	17	5	[	[	X
ap-368	17	6	11	11	NUM
ap-368	17	7	]	]	PUNCT
ap-368	17	8	found	find	VERB
ap-368	17	9	the	the	DET
ap-368	17	10	solution	solution	NOUN
ap-368	17	11	of	of	ADP
ap-368	17	12	the	the	DET
ap-368	17	13	model	model	NOUN
ap-368	17	14	equation	equation	NOUN
ap-368	17	15	for	for	ADP
ap-368	17	16	inviscid	inviscid	ADJ
ap-368	17	17	isentropic	isentropic	NOUN
ap-368	17	18	fluids	fluid	NOUN
ap-368	17	19	,	,	PUNCT
ap-368	17	20	where	where	SCONJ
ap-368	17	21	they	they	PRON
ap-368	17	22	used	use	VERB
ap-368	17	23	perturbation	perturbation	NOUN
ap-368	17	24	expansion	expansion	NOUN
ap-368	17	25	adapted	adapt	VERB
ap-368	17	26	to	to	PART
ap-368	17	27	eliminate	eliminate	VERB
ap-368	17	28	secular	secular	ADJ
ap-368	17	29	terms	term	NOUN
ap-368	17	30	and	and	CCONJ
ap-368	17	31	determined	determine	VERB
ap-368	17	32	the	the	DET
ap-368	17	33	nonlinear	nonlinear	ADJ
ap-368	17	34	wavenumber	wavenumber	NOUN
ap-368	17	35	shift	shift	NOUN
ap-368	17	36	for	for	ADP
ap-368	17	37	dispersive	dispersive	ADJ
ap-368	17	38	modes	mode	NOUN
ap-368	17	39	.	.	PUNCT
ap-368	18	1	in	in	ADP
ap-368	18	2	[	[	X
ap-368	18	3	12	12	NUM
ap-368	18	4	]	]	PUNCT
ap-368	18	5	,	,	PUNCT
ap-368	18	6	keller	keller	PROPN
ap-368	18	7	utilized	utilize	VERB
ap-368	18	8	the	the	DET
ap-368	18	9	results	result	NOUN
ap-368	18	10	from	from	ADP
ap-368	18	11	[	[	X
ap-368	18	12	11	11	NUM
ap-368	18	13	]	]	PUNCT
ap-368	18	14	.	.	PUNCT
ap-368	19	1	he	he	PRON
ap-368	19	2	rewrote	rewrite	VERB
ap-368	19	3	the	the	DET
ap-368	19	4	results	result	NOUN
ap-368	19	5	in	in	ADP
ap-368	19	6	a	a	DET
ap-368	19	7	form	form	NOUN
ap-368	19	8	that	that	PRON
ap-368	19	9	is	be	AUX
ap-368	19	10	useful	useful	ADJ
ap-368	19	11	near	near	ADP
ap-368	19	12	the	the	DET
ap-368	19	13	cutoff	cutoff	NOUN
ap-368	19	14	frequency	frequency	NOUN
ap-368	19	15	,	,	PUNCT
ap-368	19	16	in	in	ADP
ap-368	19	17	order	order	NOUN
ap-368	19	18	to	to	PART
ap-368	19	19	show	show	VERB
ap-368	19	20	that	that	SCONJ
ap-368	19	21	the	the	DET
ap-368	19	22	cutoff	cutoff	NOUN
ap-368	19	23	frequencies	frequency	NOUN
ap-368	19	24	and	and	CCONJ
ap-368	19	25	resonant	resonant	ADJ
ap-368	19	26	frequencies	frequency	NOUN
ap-368	19	27	of	of	ADP
ap-368	19	28	modes	mode	NOUN
ap-368	19	29	in	in	ADP
ap-368	19	30	acoustic	acoustic	ADJ
ap-368	19	31	waveguides	waveguide	NOUN
ap-368	19	32	of	of	ADP
ap-368	19	33	finite	finite	ADJ
ap-368	19	34	length	length	NOUN
ap-368	19	35	depend	depend	VERB
ap-368	19	36	upon	upon	SCONJ
ap-368	19	37	the	the	DET
ap-368	19	38	mode	mode	NOUN
ap-368	19	39	amplitude	amplitude	NOUN
ap-368	19	40	.	.	PUNCT
ap-368	20	1	nayfeh	nayfeh	PROPN
ap-368	20	2	along	along	ADP
ap-368	20	3	with	with	ADP
ap-368	20	4	tsai	tsai	PROPN
ap-368	20	5	in	in	ADP
ap-368	20	6	[	[	X
ap-368	20	7	13	13	NUM
ap-368	20	8	]	]	PUNCT
ap-368	20	9	presented	present	VERB
ap-368	20	10	the	the	DET
ap-368	20	11	nonlinear	nonlinear	ADJ
ap-368	20	12	effects	effect	NOUN
ap-368	20	13	of	of	ADP
ap-368	20	14	gas	gas	NOUN
ap-368	20	15	motion	motion	NOUN
ap-368	20	16	as	as	ADV
ap-368	20	17	well	well	ADV
ap-368	20	18	as	as	ADP
ap-368	20	19	the	the	DET
ap-368	20	20	non	non	ADJ
ap-368	20	21	-	-	ADJ
ap-368	20	22	linear	linear	ADJ
ap-368	20	23	acoustic	acoustic	ADJ
ap-368	20	24	lining	lining	NOUN
ap-368	20	25	material	material	NOUN
ap-368	20	26	properties	property	NOUN
ap-368	20	27	on	on	ADP
ap-368	20	28	wave	wave	NOUN
ap-368	20	29	propagation	propagation	NOUN
ap-368	20	30	and	and	CCONJ
ap-368	20	31	attenuation	attenuation	NOUN
ap-368	20	32	in	in	ADP
ap-368	20	33	circular	circular	ADJ
ap-368	20	34	ducts	duct	NOUN
ap-368	20	35	.	.	PUNCT
ap-368	21	1	they	they	PRON
ap-368	21	2	obtained	obtain	VERB
ap-368	21	3	a	a	DET
ap-368	21	4	second	second	ADJ
ap-368	21	5	-	-	PUNCT
ap-368	21	6	order	order	NOUN
ap-368	21	7	uniformly	uniformly	ADV
ap-368	21	8	valid	valid	ADJ
ap-368	21	9	expansion	expansion	NOUN
ap-368	21	10	by	by	ADP
ap-368	21	11	using	use	VERB
ap-368	21	12	the	the	DET
ap-368	21	13	method	method	NOUN
ap-368	21	14	of	of	ADP
ap-368	21	15	multiple	multiple	ADJ
ap-368	21	16	scales	scale	NOUN
ap-368	21	17	.	.	PUNCT
ap-368	22	1	these	these	DET
ap-368	22	2	authors	author	NOUN
ap-368	22	3	presented	present	VERB
ap-368	22	4	[	[	X
ap-368	22	5	14	14	NUM
ap-368	22	6	]	]	PUNCT
ap-368	22	7	,	,	PUNCT
ap-368	22	8	where	where	SCONJ
ap-368	22	9	they	they	PRON
ap-368	22	10	investigated	investigate	VERB
ap-368	22	11	nonlinear	nonlinear	ADJ
ap-368	22	12	propagation	propagation	NOUN
ap-368	22	13	in	in	ADP
ap-368	22	14	a	a	DET
ap-368	22	15	rectangular	rectangular	ADJ
ap-368	22	16	duct	duct	NOUN
ap-368	22	17	whose	whose	DET
ap-368	22	18	side	side	NOUN
ap-368	22	19	walls	wall	NOUN
ap-368	22	20	were	be	AUX
ap-368	22	21	also	also	ADV
ap-368	22	22	acoustically	acoustically	ADV
ap-368	22	23	treated	treat	VERB
ap-368	22	24	by	by	ADP
ap-368	22	25	means	mean	NOUN
ap-368	22	26	of	of	ADP
ap-368	22	27	the	the	DET
ap-368	22	28	method	method	NOUN
ap-368	22	29	of	of	ADP
ap-368	22	30	multiple	multiple	ADJ
ap-368	22	31	scales	scale	NOUN
ap-368	22	32	.	.	PUNCT
ap-368	23	1	ginsberg	ginsberg	PROPN
ap-368	23	2	in	in	ADP
ap-368	23	3	[	[	X
ap-368	23	4	15	15	NUM
ap-368	23	5	]	]	PUNCT
ap-368	23	6	dealt	deal	VERB
ap-368	23	7	with	with	ADP
ap-368	23	8	nonlinear	nonlinear	ADJ
ap-368	23	9	propagation	propagation	NOUN
ap-368	23	10	in	in	ADP
ap-368	23	11	rectangular	rectangular	ADJ
ap-368	23	12	ducts	duct	NOUN
ap-368	23	13	.	.	PUNCT
ap-368	24	1	he	he	PRON
ap-368	24	2	determined	determine	VERB
ap-368	24	3	by	by	ADP
ap-368	24	4	an	an	DET
ap-368	24	5	asymptotic	asymptotic	ADJ
ap-368	24	6	method	method	NOUN
ap-368	24	7	the	the	DET
ap-368	24	8	nonlinear	nonlinear	ADJ
ap-368	24	9	two	two	NUM
ap-368	24	10	-	-	PUNCT
ap-368	24	11	dimensional	dimensional	ADJ
ap-368	24	12	acoustic	acoustic	ADJ
ap-368	24	13	waves	wave	NOUN
ap-368	24	14	that	that	PRON
ap-368	24	15	occur	occur	VERB
ap-368	24	16	within	within	ADP
ap-368	24	17	a	a	DET
ap-368	24	18	rectangular	rectangular	ADJ
ap-368	24	19	duct	duct	NOUN
ap-368	24	20	of	of	ADP
ap-368	24	21	semi	semi	ADJ
ap-368	24	22	-	-	ADJ
ap-368	24	23	infinite	infinite	ADJ
ap-368	24	24	length	length	NOUN
ap-368	24	25	as	as	ADP
ap-368	24	26	the	the	DET
ap-368	24	27	result	result	NOUN
ap-368	24	28	of	of	ADP
ap-368	24	29	periodic	periodic	ADJ
ap-368	24	30	excitation	excitation	NOUN
ap-368	24	31	.	.	PUNCT
ap-368	25	1	in	in	ADP
ap-368	25	2	[	[	X
ap-368	25	3	16	16	NUM
ap-368	25	4	]	]	PUNCT
ap-368	25	5	,	,	PUNCT
ap-368	25	6	he	he	PRON
ap-368	25	7	utilized	utilize	VERB
ap-368	25	8	the	the	DET
ap-368	25	9	perturbation	perturbation	NOUN
ap-368	25	10	method	method	NOUN
ap-368	25	11	of	of	ADP
ap-368	25	12	renormalization	renormalization	NOUN
ap-368	25	13	to	to	PART
ap-368	25	14	study	study	VERB
ap-368	25	15	the	the	DET
ap-368	25	16	nonlinearity	nonlinearity	NOUN
ap-368	25	17	effect	effect	NOUN
ap-368	25	18	on	on	ADP
ap-368	25	19	a	a	DET
ap-368	25	20	hard	hard	ADV
ap-368	25	21	-	-	PUNCT
ap-368	25	22	walled	wall	VERB
ap-368	25	23	rectangular	rectangular	ADJ
ap-368	25	24	waveguide	waveguide	NOUN
ap-368	25	25	.	.	PUNCT
ap-368	26	1	nonlinear	nonlinear	ADJ
ap-368	26	2	wave	wave	NOUN
ap-368	26	3	interaction	interaction	NOUN
ap-368	26	4	in	in	ADP
ap-368	26	5	a	a	DET
ap-368	26	6	rectangular	rectangular	ADJ
ap-368	26	7	duct	duct	NOUN
ap-368	26	8	was	be	AUX
ap-368	26	9	also	also	ADV
ap-368	26	10	investigated	investigate	VERB
ap-368	26	11	by	by	ADP
ap-368	26	12	hamilton	hamilton	PROPN
ap-368	26	13	and	and	CCONJ
ap-368	26	14	tencate	tencate	VERB
ap-368	26	15	in	in	ADP
ap-368	26	16	[	[	X
ap-368	26	17	17	17	NUM
ap-368	26	18	]	]	PUNCT
ap-368	26	19	and	and	CCONJ
ap-368	26	20	[	[	X
ap-368	26	21	18	18	NUM
ap-368	26	22	]	]	PUNCT
ap-368	26	23	.	.	PUNCT
ap-368	27	1	multiharmonic	multiharmonic	ADJ
ap-368	27	2	excitation	excitation	NOUN
ap-368	27	3	of	of	ADP
ap-368	27	4	a	a	DET
ap-368	27	5	hard	hard	ADV
ap-368	27	6	-	-	PUNCT
ap-368	27	7	walled	wall	VERB
ap-368	27	8	circular	circular	ADJ
ap-368	27	9	duct	duct	NOUN
ap-368	27	10	was	be	AUX
ap-368	27	11	treated	treat	VERB
ap-368	27	12	by	by	ADP
ap-368	27	13	nayfeh	nayfeh	PROPN
ap-368	27	14	in	in	ADP
ap-368	27	15	[	[	X
ap-368	27	16	19	19	NUM
ap-368	27	17	]	]	PUNCT
ap-368	27	18	.	.	PUNCT
ap-368	28	1	he	he	PRON
ap-368	28	2	used	use	VERB
ap-368	28	3	the	the	DET
ap-368	28	4	method	method	NOUN
ap-368	28	5	of	of	ADP
ap-368	28	6	multiple	multiple	ADJ
ap-368	28	7	scales	scale	NOUN
ap-368	28	8	to	to	PART
ap-368	28	9	derive	derive	VERB
ap-368	28	10	a	a	DET
ap-368	28	11	nonlinear	nonlinear	ADJ
ap-368	28	12	schrödinger	schrödinger	ADJ
ap-368	28	13	equation	equation	NOUN
ap-368	28	14	for	for	ADP
ap-368	28	15	temporal	temporal	ADJ
ap-368	28	16	and	and	CCONJ
ap-368	28	17	spatial	spatial	ADJ
ap-368	28	18	modulation	modulation	NOUN
ap-368	28	19	of	of	ADP
ap-368	28	20	the	the	DET
ap-368	28	21	amplitudes	amplitude	NOUN
ap-368	28	22	and	and	CCONJ
ap-368	28	23	the	the	DET
ap-368	28	24	phases	phase	NOUN
ap-368	28	25	of	of	ADP
ap-368	28	26	waves	wave	NOUN
ap-368	28	27	propagating	propagate	VERB
ap-368	28	28	in	in	ADP
ap-368	28	29	a	a	DET
ap-368	28	30	hard	hard	ADV
ap-368	28	31	-	-	PUNCT
ap-368	28	32	walled	wall	VERB
ap-368	28	33	duct	duct	NOUN
ap-368	28	34	.	.	PUNCT
ap-368	29	1	foda	foda	PROPN
ap-368	29	2	presented	present	VERB
ap-368	29	3	his	his	PRON
ap-368	29	4	work	work	NOUN
ap-368	29	5	in	in	ADP
ap-368	29	6	[	[	X
ap-368	29	7	20	20	NUM
ap-368	29	8	]	]	PUNCT
ap-368	29	9	,	,	PUNCT
ap-368	29	10	which	which	PRON
ap-368	29	11	is	be	AUX
ap-368	29	12	concerned	concern	VERB
ap-368	29	13	with	with	ADP
ap-368	29	14	the	the	DET
ap-368	29	15	nonlinear	nonlinear	ADJ
ap-368	29	16	interactions	interaction	NOUN
ap-368	29	17	and	and	CCONJ
ap-368	29	18	propagation	propagation	NOUN
ap-368	29	19	of	of	ADP
ap-368	29	20	two	two	NUM
ap-368	29	21	primary	primary	ADJ
ap-368	29	22	waves	wave	NOUN
ap-368	29	23	in	in	ADP
ap-368	29	24	higher	high	ADJ
ap-368	29	25	order	order	NOUN
ap-368	29	26	modes	mode	NOUN
ap-368	29	27	of	of	ADP
ap-368	29	28	a	a	DET
ap-368	29	29	circular	circular	ADJ
ap-368	29	30	duct	duct	NOUN
ap-368	29	31	,	,	PUNCT
ap-368	29	32	each	each	PRON
ap-368	29	33	at	at	ADP
ap-368	29	34	an	an	DET
ap-368	29	35	arbitrary	arbitrary	ADJ
ap-368	29	36	different	different	ADJ
ap-368	29	37	frequency	frequency	NOUN
ap-368	29	38	and	and	CCONJ
ap-368	29	39	finite	finite	ADJ
ap-368	29	40	amplitude	amplitude	NOUN
ap-368	29	41	.	.	PUNCT
ap-368	30	1	he	he	PRON
ap-368	30	2	used	use	VERB
ap-368	30	3	the	the	DET
ap-368	30	4	renormalization	renormalization	NOUN
ap-368	30	5	method	method	NOUN
ap-368	30	6	to	to	PART
ap-368	30	7	annihilate	annihilate	VERB
ap-368	30	8	the	the	DET
ap-368	30	9	secular	secular	ADJ
ap-368	30	10	terms	term	NOUN
ap-368	30	11	in	in	ADP
ap-368	30	12	the	the	DET
ap-368	30	13	obtained	obtain	VERB
ap-368	30	14	expression	expression	NOUN
ap-368	30	15	.	.	PUNCT
ap-368	31	1	if	if	SCONJ
ap-368	31	2	we	we	PRON
ap-368	31	3	take	take	VERB
ap-368	31	4	no	no	DET
ap-368	31	5	diffraction	diffraction	NOUN
ap-368	31	6	effects	effect	NOUN
ap-368	31	7	into	into	ADP
ap-368	31	8	account	account	NOUN
ap-368	31	9	,	,	PUNCT
ap-368	31	10	we	we	PRON
ap-368	31	11	can	can	AUX
ap-368	31	12	use	use	VERB
ap-368	31	13	the	the	DET
ap-368	31	14	generalized	generalize	VERB
ap-368	31	15	burgers	burger	NOUN
ap-368	31	16	equation	equation	NOUN
ap-368	31	17	to	to	PART
ap-368	31	18	describe	describe	VERB
ap-368	31	19	nonlinear	nonlinear	ADJ
ap-368	31	20	plane	plane	NOUN
ap-368	31	21	waves	wave	NOUN
ap-368	31	22	in	in	ADP
ap-368	31	23	circular	circular	ADJ
ap-368	31	24	ducts	duct	NOUN
ap-368	31	25	.	.	PUNCT
ap-368	32	1	it	it	PRON
ap-368	32	2	is	be	AUX
ap-368	32	3	the	the	DET
ap-368	32	4	burgers	burger	NOUN
ap-368	32	5	equation	equation	NOUN
ap-368	32	6	that	that	PRON
ap-368	32	7	is	be	AUX
ap-368	32	8	supplemented	supplement	VERB
ap-368	32	9	by	by	ADP
ap-368	32	10	the	the	DET
ap-368	32	11	term	term	NOUN
ap-368	32	12	that	that	PRON
ap-368	32	13	represents	represent	VERB
ap-368	32	14	boundary	boundary	ADJ
ap-368	32	15	layer	layer	NOUN
ap-368	32	16	effects	effect	NOUN
ap-368	32	17	,	,	PUNCT
ap-368	32	18	see	see	VERB
ap-368	32	19	[	[	X
ap-368	32	20	21]–[25	21]–[25	NUM
ap-368	32	21	]	]	PUNCT
ap-368	32	22	.	.	PUNCT
ap-368	33	1	the	the	DET
ap-368	33	2	generalized	generalize	VERB
ap-368	33	3	burgers	burger	NOUN
ap-368	33	4	equation	equation	NOUN
ap-368	33	5	enables	enable	VERB
ap-368	33	6	the	the	DET
ap-368	33	7	description	description	NOUN
ap-368	33	8	of	of	ADP
ap-368	33	9	dissipative	dissipative	ADJ
ap-368	33	10	and	and	CCONJ
ap-368	33	11	dispersive	dispersive	ADJ
ap-368	33	12	effects	effect	NOUN
ap-368	33	13	that	that	PRON
ap-368	33	14	are	be	AUX
ap-368	33	15	caused	cause	VERB
ap-368	33	16	by	by	ADP
ap-368	33	17	the	the	DET
ap-368	33	18	boundary	boundary	ADJ
ap-368	33	19	layer	layer	NOUN
ap-368	33	20	.	.	PUNCT
ap-368	34	1	asymptotic	asymptotic	ADJ
ap-368	34	2	and	and	CCONJ
ap-368	34	3	numerical	numerical	ADJ
ap-368	34	4	solutions	solution	NOUN
ap-368	34	5	of	of	ADP
ap-368	34	6	this	this	DET
ap-368	34	7	equation	equation	NOUN
ap-368	34	8	were	be	AUX
ap-368	34	9	presented	present	VERB
ap-368	34	10	by	by	ADP
ap-368	34	11	sugimoto	sugimoto	PROPN
ap-368	34	12	[	[	X
ap-368	34	13	26	26	NUM
ap-368	34	14	]	]	PUNCT
ap-368	34	15	.	.	PUNCT
ap-368	35	1	in	in	ADP
ap-368	35	2	[	[	X
ap-368	35	3	27	27	NUM
ap-368	35	4	]	]	PUNCT
ap-368	35	5	,	,	PUNCT
ap-368	35	6	there	there	PRON
ap-368	35	7	is	be	VERB
ap-368	35	8	a	a	DET
ap-368	35	9	description	description	NOUN
ap-368	35	10	of	of	ADP
ap-368	35	11	the	the	DET
ap-368	35	12	solution	solution	NOUN
ap-368	35	13	of	of	ADP
ap-368	35	14	the	the	DET
ap-368	35	15	burgers	burger	NOUN
ap-368	35	16	equation	equation	NOUN
ap-368	35	17	in	in	ADP
ap-368	35	18	the	the	DET
ap-368	35	19	time	time	NOUN
ap-368	35	20	domain	domain	NOUN
ap-368	35	21	.	.	PUNCT
ap-368	36	1	the	the	DET
ap-368	36	2	approximate	approximate	ADJ
ap-368	36	3	solutions	solution	NOUN
ap-368	36	4	of	of	ADP
ap-368	36	5	the	the	DET
ap-368	36	6	generalized	generalize	VERB
ap-368	36	7	burgers	burger	NOUN
ap-368	36	8	equation	equation	NOUN
ap-368	36	9	for	for	ADP
ap-368	36	10	harmonic	harmonic	ADJ
ap-368	36	11	excitation	excitation	NOUN
ap-368	36	12	in	in	ADP
ap-368	36	13	both	both	CCONJ
ap-368	36	14	the	the	DET
ap-368	36	15	preshock	preshock	NOUN
ap-368	36	16	and	and	CCONJ
ap-368	36	17	the	the	DET
ap-368	36	18	postshock	postshock	NOUN
ap-368	36	19	region	region	NOUN
ap-368	36	20	are	be	AUX
ap-368	36	21	presented	present	VERB
ap-368	36	22	in	in	ADP
ap-368	36	23	[	[	X
ap-368	36	24	28	28	NUM
ap-368	36	25	]	]	PUNCT
ap-368	36	26	.	.	PUNCT
ap-368	37	1	in	in	ADP
ap-368	37	2	the	the	DET
ap-368	37	3	case	case	NOUN
ap-368	37	4	that	that	SCONJ
ap-368	37	5	only	only	ADV
ap-368	37	6	weak	weak	ADJ
ap-368	37	7	18	18	NUM
ap-368	37	8	©	©	PROPN
ap-368	37	9	czech	czech	PROPN
ap-368	37	10	technical	technical	PROPN
ap-368	37	11	university	university	PROPN
ap-368	37	12	publishing	publishing	NOUN
ap-368	37	13	house	house	NOUN
ap-368	37	14	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	37	15	acta	acta	PROPN
ap-368	37	16	polytechnica	polytechnica	PROPN
ap-368	37	17	vol	vol	NOUN
ap-368	37	18	.	.	PUNCT
ap-368	37	19	42	42	NUM
ap-368	38	1	no	no	INTJ
ap-368	38	2	.	.	PUNCT
ap-368	39	1	4/2002	4/2002	DET
ap-368	39	2	propagation	propagation	NOUN
ap-368	39	3	of	of	ADP
ap-368	39	4	quasi	quasi	ADJ
ap-368	39	5	-	-	ADJ
ap-368	39	6	plane	plane	ADJ
ap-368	39	7	nonlinear	nonlinear	ADJ
ap-368	39	8	waves	wave	NOUN
ap-368	39	9	in	in	ADP
ap-368	39	10	tubes	tube	NOUN
ap-368	39	11	p.	p.	PROPN
ap-368	39	12	koníček	koníček	PROPN
ap-368	39	13	,	,	PUNCT
ap-368	39	14	m.	m.	NOUN
ap-368	39	15	bednařík	bednařík	PROPN
ap-368	39	16	,	,	PUNCT
ap-368	39	17	m.	m.	NOUN
ap-368	39	18	červenka	červenka	PROPN
ap-368	39	19	this	this	DET
ap-368	39	20	paper	paper	NOUN
ap-368	39	21	deals	deal	NOUN
ap-368	39	22	with	with	ADP
ap-368	39	23	possibilities	possibility	NOUN
ap-368	39	24	of	of	ADP
ap-368	39	25	using	use	VERB
ap-368	39	26	the	the	DET
ap-368	39	27	generalized	generalize	VERB
ap-368	39	28	burgers	burger	NOUN
ap-368	39	29	equation	equation	NOUN
ap-368	39	30	and	and	CCONJ
ap-368	39	31	the	the	DET
ap-368	39	32	kzk	kzk	PRON
ap-368	39	33	equation	equation	NOUN
ap-368	39	34	to	to	PART
ap-368	39	35	describe	describe	VERB
ap-368	39	36	nonlinear	nonlinear	ADJ
ap-368	39	37	waves	wave	NOUN
ap-368	39	38	in	in	ADP
ap-368	39	39	circular	circular	ADJ
ap-368	39	40	ducts	duct	NOUN
ap-368	39	41	.	.	PUNCT
ap-368	40	1	a	a	DET
ap-368	40	2	new	new	ADJ
ap-368	40	3	method	method	NOUN
ap-368	40	4	for	for	ADP
ap-368	40	5	calculating	calculate	VERB
ap-368	40	6	of	of	ADP
ap-368	40	7	diffraction	diffraction	NOUN
ap-368	40	8	effects	effect	NOUN
ap-368	40	9	taking	take	VERB
ap-368	40	10	into	into	ADP
ap-368	40	11	account	account	NOUN
ap-368	40	12	boundary	boundary	ADJ
ap-368	40	13	layer	layer	NOUN
ap-368	40	14	effects	effect	NOUN
ap-368	40	15	is	be	AUX
ap-368	40	16	described	describe	VERB
ap-368	40	17	.	.	PUNCT
ap-368	41	1	the	the	DET
ap-368	41	2	results	result	NOUN
ap-368	41	3	of	of	ADP
ap-368	41	4	numerical	numerical	ADJ
ap-368	41	5	solutions	solution	NOUN
ap-368	41	6	of	of	ADP
ap-368	41	7	the	the	DET
ap-368	41	8	model	model	NOUN
ap-368	41	9	equations	equation	NOUN
ap-368	41	10	are	be	AUX
ap-368	41	11	compared	compare	VERB
ap-368	41	12	.	.	PUNCT
ap-368	42	1	finally	finally	ADV
ap-368	42	2	,	,	PUNCT
ap-368	42	3	the	the	DET
ap-368	42	4	limits	limit	NOUN
ap-368	42	5	of	of	ADP
ap-368	42	6	validity	validity	NOUN
ap-368	42	7	of	of	ADP
ap-368	42	8	the	the	DET
ap-368	42	9	used	use	VERB
ap-368	42	10	model	model	NOUN
ap-368	42	11	equations	equation	NOUN
ap-368	42	12	are	be	AUX
ap-368	42	13	discussed	discuss	VERB
ap-368	42	14	with	with	ADP
ap-368	42	15	respect	respect	NOUN
ap-368	42	16	to	to	ADP
ap-368	42	17	boundary	boundary	ADJ
ap-368	42	18	conditions	condition	NOUN
ap-368	42	19	and	and	CCONJ
ap-368	42	20	the	the	DET
ap-368	42	21	radius	radius	NOUN
ap-368	42	22	of	of	ADP
ap-368	42	23	the	the	DET
ap-368	42	24	circular	circular	ADJ
ap-368	42	25	duct	duct	NOUN
ap-368	42	26	.	.	PUNCT
ap-368	43	1	the	the	DET
ap-368	43	2	limits	limit	NOUN
ap-368	43	3	of	of	ADP
ap-368	43	4	applicability	applicability	NOUN
ap-368	43	5	of	of	ADP
ap-368	43	6	the	the	DET
ap-368	43	7	kzk	kzk	VERB
ap-368	43	8	equation	equation	NOUN
ap-368	43	9	and	and	CCONJ
ap-368	43	10	the	the	DET
ap-368	43	11	gbe	gbe	NOUN
ap-368	43	12	equation	equation	NOUN
ap-368	43	13	for	for	ADP
ap-368	43	14	describing	describe	VERB
ap-368	43	15	nonlinear	nonlinear	ADJ
ap-368	43	16	waves	wave	NOUN
ap-368	43	17	in	in	ADP
ap-368	43	18	tubes	tube	NOUN
ap-368	43	19	are	be	AUX
ap-368	43	20	discussed	discuss	VERB
ap-368	43	21	.	.	PUNCT
ap-368	44	1	keywords	keyword	NOUN
ap-368	44	2	:	:	PUNCT
ap-368	44	3	nonlinear	nonlinear	ADJ
ap-368	44	4	acoustics	acoustic	NOUN
ap-368	44	5	,	,	PUNCT
ap-368	44	6	khokhlov	khokhlov	PROPN
ap-368	44	7	-	-	PUNCT
ap-368	44	8	zabolotskaya	zabolotskaya	NOUN
ap-368	44	9	-	-	PUNCT
ap-368	44	10	kuznetsov	kuznetsov	NOUN
ap-368	44	11	equation	equation	NOUN
ap-368	44	12	,	,	PUNCT
ap-368	44	13	generalized	generalize	VERB
ap-368	44	14	burgers	burger	NOUN
ap-368	44	15	equation	equation	NOUN
ap-368	44	16	.	.	PUNCT
ap-368	45	1	diffraction	diffraction	NOUN
ap-368	45	2	effects	effect	NOUN
ap-368	45	3	are	be	AUX
ap-368	45	4	considered	consider	VERB
ap-368	45	5	,	,	PUNCT
ap-368	45	6	the	the	DET
ap-368	45	7	kzk	kzk	PRON
ap-368	45	8	equation	equation	NOUN
ap-368	45	9	can	can	AUX
ap-368	45	10	be	be	AUX
ap-368	45	11	used	use	VERB
ap-368	45	12	,	,	PUNCT
ap-368	45	13	see	see	VERB
ap-368	45	14	[	[	X
ap-368	45	15	22	22	NUM
ap-368	45	16	]	]	PUNCT
ap-368	45	17	,	,	PUNCT
ap-368	45	18	[	[	X
ap-368	45	19	25	25	NUM
ap-368	45	20	]	]	PUNCT
ap-368	45	21	,	,	PUNCT
ap-368	45	22	[	[	X
ap-368	45	23	29	29	NUM
ap-368	45	24	]	]	PUNCT
ap-368	45	25	.	.	PUNCT
ap-368	46	1	however	however	ADV
ap-368	46	2	,	,	PUNCT
ap-368	46	3	the	the	DET
ap-368	46	4	boundary	boundary	ADJ
ap-368	46	5	layer	layer	NOUN
ap-368	46	6	is	be	AUX
ap-368	46	7	incorporated	incorporate	VERB
ap-368	46	8	into	into	ADP
ap-368	46	9	the	the	DET
ap-368	46	10	boundary	boundary	ADJ
ap-368	46	11	condition	condition	NOUN
ap-368	46	12	in	in	ADP
ap-368	46	13	[	[	X
ap-368	46	14	22	22	NUM
ap-368	46	15	]	]	PUNCT
ap-368	46	16	and	and	CCONJ
ap-368	46	17	[	[	X
ap-368	46	18	25	25	NUM
ap-368	46	19	]	]	PUNCT
ap-368	46	20	.	.	PUNCT
ap-368	47	1	2	2	NUM
ap-368	47	2	basic	basic	ADJ
ap-368	47	3	equations	equation	NOUN
ap-368	47	4	from	from	ADP
ap-368	47	5	the	the	DET
ap-368	47	6	equations	equation	NOUN
ap-368	47	7	of	of	ADP
ap-368	47	8	continuum	continuum	ADJ
ap-368	47	9	mechanics	mechanic	NOUN
ap-368	47	10	we	we	PRON
ap-368	47	11	can	can	AUX
ap-368	47	12	obtain	obtain	VERB
ap-368	47	13	in	in	ADP
ap-368	47	14	quadratic	quadratic	ADJ
ap-368	47	15	approximation	approximation	NOUN
ap-368	47	16	an	an	DET
ap-368	47	17	equation	equation	NOUN
ap-368	47	18	describing	describe	VERB
ap-368	47	19	weakly	weakly	ADJ
ap-368	47	20	nonlinear	nonlinear	ADJ
ap-368	47	21	waves	wave	NOUN
ap-368	47	22	in	in	ADP
ap-368	47	23	thermo	thermo	NOUN
ap-368	47	24	-	-	PUNCT
ap-368	47	25	viscous	viscous	ADJ
ap-368	47	26	fluids	fluid	NOUN
ap-368	47	27	�	�	PROPN
ap-368	47	28	�	�	PROPN
ap-368	47	29	�	�	PROPN
ap-368	47	30	�	�	PROPN
ap-368	47	31	�	�	PROPN
ap-368	47	32	�	�	PROPN
ap-368	47	33	�	�	PROPN
ap-368	47	34	�	�	PROPN
ap-368	47	35	�	�	PROPN
ap-368	47	36	�	�	PROPN
ap-368	47	37	�	�	PROPN
ap-368	47	38	�	�	PROPN
ap-368	47	39	�	�	PROPN
ap-368	47	40	�	�	PROPN
ap-368	47	41	�	�	PROPN
ap-368	47	42	�	�	PROPN
ap-368	47	43	�	�	PROPN
ap-368	47	44	�	�	PROPN
ap-368	47	45	0	0	NUM
ap-368	47	46	2	2	NUM
ap-368	47	47	2	2	NUM
ap-368	47	48	0	0	NUM
ap-368	47	49	0	0	NUM
ap-368	47	50	2	2	NUM
ap-368	47	51	0	0	NUM
ap-368	47	52	0	0	NUM
ap-368	47	53	2	2	NUM
ap-368	47	54	2	2	NUM
ap-368	47	55	2	2	NUM
ap-368	47	56	2	2	NUM
ap-368	48	1	t	t	NOUN
ap-368	48	2	c	c	NOUN
ap-368	48	3	t	t	PROPN
ap-368	48	4	c	c	PROPN
ap-368	48	5	t	t	PROPN
ap-368	48	6	�	�	PROPN
ap-368	48	7	�	�	PROPN
ap-368	48	8	�	�	PROPN
ap-368	48	9	�	�	PROPN
ap-368	48	10	�	�	PROPN
ap-368	48	11	�	�	PROPN
ap-368	48	12	�	�	PROPN
ap-368	48	13	�	�	PROPN
ap-368	48	14	�	�	PROPN
ap-368	48	15	�	�	PROPN
ap-368	48	16	�	�	PROPN
ap-368	48	17	�	�	PROPN
ap-368	48	18	�	�	PROPN
ap-368	48	19	�	�	PROPN
ap-368	48	20	�	�	PROPN
ap-368	48	21	�	�	PROPN
ap-368	48	22	�	�	PROPN
ap-368	48	23	�	�	PROPN
ap-368	48	24	�	�	PROPN
ap-368	48	25	�	�	PROPN
ap-368	48	26	�	�	PROPN
ap-368	48	27	�	�	PROPN
ap-368	48	28	�	�	PROPN
ap-368	48	29	�	�	PROPN
ap-368	48	30	l	l	PROPN
ap-368	48	31	t	t	PROPN
ap-368	48	32	b	b	PROPN
ap-368	48	33	c	c	NOUN
ap-368	48	34	t	t	NOUN
ap-368	48	35	o	o	X
ap-368	48	36	0	0	NUM
ap-368	48	37	2	2	NUM
ap-368	48	38	3	3	NUM
ap-368	48	39	3	3	NUM
ap-368	48	40	(	(	PUNCT
ap-368	48	41	)	)	PUNCT
ap-368	48	42	.	.	PUNCT
ap-368	49	1	(	(	PUNCT
ap-368	49	2	1	1	X
ap-368	49	3	)	)	PUNCT
ap-368	49	4	here	here	ADV
ap-368	49	5	�	�	PROPN
ap-368	49	6	is	be	AUX
ap-368	49	7	the	the	DET
ap-368	49	8	velocity	velocity	NOUN
ap-368	49	9	potential	potential	NOUN
ap-368	49	10	,	,	PUNCT
ap-368	49	11	t	t	PROPN
ap-368	49	12	is	be	AUX
ap-368	49	13	time	time	NOUN
ap-368	49	14	,	,	PUNCT
ap-368	49	15	c0	c0	PROPN
ap-368	49	16	is	be	AUX
ap-368	49	17	the	the	DET
ap-368	49	18	small	small	ADJ
ap-368	49	19	-	-	PUNCT
ap-368	49	20	signal	signal	NOUN
ap-368	49	21	sound	sound	NOUN
ap-368	49	22	speed	speed	NOUN
ap-368	49	23	,	,	PUNCT
ap-368	49	24	b	b	NOUN
ap-368	49	25	is	be	AUX
ap-368	49	26	the	the	DET
ap-368	49	27	dissipation	dissipation	NOUN
ap-368	49	28	coefficient	coefficient	NOUN
ap-368	49	29	of	of	ADP
ap-368	49	30	the	the	DET
ap-368	49	31	medium	medium	ADJ
ap-368	49	32	,	,	PUNCT
ap-368	49	33	�	�	PROPN
ap-368	49	34	0	0	NUM
ap-368	49	35	is	be	AUX
ap-368	49	36	the	the	DET
ap-368	49	37	ambient	ambient	ADJ
ap-368	49	38	density	density	NOUN
ap-368	49	39	,	,	PUNCT
ap-368	49	40	�	�	PROPN
ap-368	49	41	is	be	AUX
ap-368	49	42	the	the	DET
ap-368	49	43	adiabatic	adiabatic	ADJ
ap-368	49	44	index	index	NOUN
ap-368	49	45	,	,	PUNCT
ap-368	49	46	equal	equal	ADJ
ap-368	49	47	to	to	ADP
ap-368	49	48	the	the	DET
ap-368	49	49	ratio	ratio	NOUN
ap-368	49	50	of	of	ADP
ap-368	49	51	the	the	DET
ap-368	49	52	specific	specific	ADJ
ap-368	49	53	heat	heat	NOUN
ap-368	49	54	at	at	ADP
ap-368	49	55	constant	constant	ADJ
ap-368	49	56	pressure	pressure	NOUN
ap-368	49	57	cp	cp	INTJ
ap-368	49	58	to	to	ADP
ap-368	49	59	that	that	PRON
ap-368	49	60	at	at	ADP
ap-368	49	61	constant	constant	ADJ
ap-368	49	62	volume	volume	NOUN
ap-368	49	63	,	,	PUNCT
ap-368	49	64	cv	cv	PROPN
ap-368	49	65	,	,	PUNCT
ap-368	49	66	and	and	CCONJ
ap-368	49	67	l	l	NOUN
ap-368	49	68	is	be	AUX
ap-368	49	69	the	the	DET
ap-368	49	70	second	second	ADJ
ap-368	49	71	-	-	PUNCT
ap-368	49	72	order	order	NOUN
ap-368	49	73	lagrangian	lagrangian	ADJ
ap-368	49	74	density	density	NOUN
ap-368	49	75	,	,	PUNCT
ap-368	49	76	which	which	PRON
ap-368	49	77	is	be	AUX
ap-368	49	78	given	give	VERB
ap-368	49	79	as	as	ADP
ap-368	49	80	�	�	PROPN
ap-368	49	81	�	�	PROPN
ap-368	50	1	l	l	PROPN
ap-368	50	2	c	c	PROPN
ap-368	50	3	t	t	PROPN
ap-368	50	4	�	�	PROPN
ap-368	50	5	�	�	PROPN
ap-368	50	6	�	�	PROPN
ap-368	50	7	�	�	PROPN
ap-368	50	8	�	�	PROPN
ap-368	50	9	�	�	PROPN
ap-368	50	10	�	�	PROPN
ap-368	50	11	�	�	PROPN
ap-368	50	12	�	�	PROPN
ap-368	50	13	�	�	PROPN
ap-368	50	14	�	�	PROPN
ap-368	50	15	�	�	PROPN
ap-368	50	16	�	�	PROPN
ap-368	50	17	0	0	NUM
ap-368	50	18	2	2	NUM
ap-368	50	19	0	0	NUM
ap-368	50	20	0	0	NUM
ap-368	50	21	2	2	NUM
ap-368	50	22	2	2	NUM
ap-368	50	23	2	2	NUM
ap-368	50	24	2	2	NUM
ap-368	50	25	.	.	PUNCT
ap-368	51	1	(	(	PUNCT
ap-368	51	2	2	2	X
ap-368	51	3	)	)	PUNCT
ap-368	51	4	the	the	DET
ap-368	51	5	symbol	symbol	NOUN
ap-368	51	6	�	�	PROPN
ap-368	51	7	represents	represent	VERB
ap-368	51	8	the	the	DET
ap-368	51	9	laplacian	laplacian	ADJ
ap-368	51	10	operator	operator	NOUN
ap-368	51	11	and	and	CCONJ
ap-368	51	12	the	the	DET
ap-368	51	13	symbol	symbol	NOUN
ap-368	51	14	�	�	PROPN
ap-368	51	15	is	be	AUX
ap-368	51	16	the	the	DET
ap-368	51	17	gradient	gradient	ADJ
ap-368	51	18	operator	operator	NOUN
ap-368	51	19	.	.	PUNCT
ap-368	52	1	the	the	DET
ap-368	52	2	operators	operator	NOUN
ap-368	52	3	are	be	AUX
ap-368	52	4	defined	define	VERB
ap-368	52	5	for	for	ADP
ap-368	52	6	axisymmetric	axisymmetric	ADJ
ap-368	52	7	waves	wave	NOUN
ap-368	52	8	in	in	ADP
ap-368	52	9	the	the	DET
ap-368	52	10	cylindrical	cylindrical	ADJ
ap-368	52	11	coordinates	coordinate	NOUN
ap-368	52	12	by	by	ADP
ap-368	52	13	�	�	PROPN
ap-368	52	14	�	�	PROPN
ap-368	52	15	�	�	PROPN
ap-368	52	16	�	�	PROPN
ap-368	52	17	�	�	PROPN
ap-368	52	18	�	�	PROPN
ap-368	52	19	�	�	PROPN
ap-368	52	20	�	�	PROPN
ap-368	52	21	�	�	PROPN
ap-368	52	22	�	�	PROPN
ap-368	52	23	2	2	NUM
ap-368	52	24	2	2	NUM
ap-368	52	25	2	2	NUM
ap-368	52	26	2	2	NUM
ap-368	52	27	1	1	NUM
ap-368	52	28	z	z	NOUN
ap-368	52	29	r	r	NOUN
ap-368	52	30	r	r	NOUN
ap-368	52	31	r	r	NOUN
ap-368	52	32	,	,	PUNCT
ap-368	52	33	(	(	PUNCT
ap-368	52	34	3	3	X
ap-368	52	35	)	)	PUNCT
ap-368	52	36	�	�	PROPN
ap-368	52	37	�	�	PROPN
ap-368	52	38	�	�	PROPN
ap-368	52	39	e	e	PROPN
ap-368	52	40	ez	ez	PROPN
ap-368	52	41	r	r	PROPN
ap-368	52	42	�	�	PROPN
ap-368	52	43	�	�	PROPN
ap-368	52	44	�	�	PROPN
ap-368	52	45	�	�	PROPN
ap-368	52	46	z	z	PROPN
ap-368	52	47	r	r	NOUN
ap-368	52	48	,	,	PUNCT
ap-368	52	49	(	(	PUNCT
ap-368	52	50	4	4	NUM
ap-368	52	51	)	)	PUNCT
ap-368	52	52	where	where	SCONJ
ap-368	52	53	z	z	NOUN
ap-368	52	54	is	be	AUX
ap-368	52	55	the	the	DET
ap-368	52	56	coordinate	coordinate	NOUN
ap-368	52	57	along	along	ADP
ap-368	52	58	the	the	DET
ap-368	52	59	axis	axis	NOUN
ap-368	52	60	of	of	ADP
ap-368	52	61	the	the	DET
ap-368	52	62	tube	tube	NOUN
ap-368	52	63	,	,	PUNCT
ap-368	52	64	r	r	NOUN
ap-368	52	65	is	be	AUX
ap-368	52	66	the	the	DET
ap-368	52	67	coordinate	coordinate	NOUN
ap-368	52	68	perpendicular	perpendicular	NOUN
ap-368	52	69	to	to	ADP
ap-368	52	70	the	the	DET
ap-368	52	71	axis	axis	NOUN
ap-368	52	72	of	of	ADP
ap-368	52	73	the	the	DET
ap-368	52	74	tube	tube	NOUN
ap-368	52	75	,	,	PUNCT
ap-368	52	76	ez	ez	PROPN
ap-368	52	77	is	be	AUX
ap-368	52	78	the	the	DET
ap-368	52	79	unit	unit	NOUN
ap-368	52	80	vector	vector	NOUN
ap-368	52	81	along	along	ADP
ap-368	52	82	the	the	DET
ap-368	52	83	z	z	NOUN
ap-368	52	84	axis	axis	NOUN
ap-368	52	85	and	and	CCONJ
ap-368	52	86	er	er	INTJ
ap-368	52	87	is	be	AUX
ap-368	52	88	the	the	DET
ap-368	52	89	unit	unit	NOUN
ap-368	52	90	vector	vector	NOUN
ap-368	52	91	along	along	ADP
ap-368	52	92	the	the	DET
ap-368	52	93	r	r	NOUN
ap-368	52	94	axis	axis	NOUN
ap-368	52	95	.	.	PUNCT
ap-368	53	1	we	we	PRON
ap-368	53	2	shall	shall	AUX
ap-368	53	3	assume	assume	VERB
ap-368	53	4	that	that	SCONJ
ap-368	53	5	the	the	DET
ap-368	53	6	profile	profile	NOUN
ap-368	53	7	of	of	ADP
ap-368	53	8	the	the	DET
ap-368	53	9	wave	wave	NOUN
ap-368	53	10	distorts	distort	VERB
ap-368	53	11	slowly	slowly	ADV
ap-368	53	12	as	as	SCONJ
ap-368	53	13	it	it	PRON
ap-368	53	14	propagates	propagate	VERB
ap-368	53	15	in	in	ADP
ap-368	53	16	the	the	DET
ap-368	53	17	positive	positive	ADJ
ap-368	53	18	z	z	NOUN
ap-368	53	19	direction	direction	NOUN
ap-368	53	20	.	.	PUNCT
ap-368	54	1	the	the	DET
ap-368	54	2	term	term	NOUN
ap-368	54	3	“	"	PUNCT
ap-368	54	4	slowly	slowly	ADV
ap-368	54	5	”	"	PUNCT
ap-368	54	6	means	mean	VERB
ap-368	54	7	that	that	SCONJ
ap-368	54	8	the	the	DET
ap-368	54	9	wave	wave	NOUN
ap-368	54	10	must	must	AUX
ap-368	54	11	travel	travel	VERB
ap-368	54	12	a	a	DET
ap-368	54	13	distance	distance	NOUN
ap-368	54	14	of	of	ADP
ap-368	54	15	many	many	ADJ
ap-368	54	16	wavelengths	wavelength	NOUN
ap-368	54	17	�	�	PROPN
ap-368	54	18	for	for	ADP
ap-368	54	19	its	its	PRON
ap-368	54	20	profile	profile	NOUN
ap-368	54	21	to	to	PART
ap-368	54	22	be	be	AUX
ap-368	54	23	distorted	distort	VERB
ap-368	54	24	significantly	significantly	ADV
ap-368	54	25	.	.	PUNCT
ap-368	55	1	then	then	ADV
ap-368	55	2	it	it	PRON
ap-368	55	3	is	be	AUX
ap-368	55	4	reasonable	reasonable	ADJ
ap-368	55	5	to	to	PART
ap-368	55	6	seek	seek	VERB
ap-368	55	7	a	a	DET
ap-368	55	8	solution	solution	NOUN
ap-368	55	9	having	have	VERB
ap-368	55	10	this	this	DET
ap-368	55	11	functional	functional	ADJ
ap-368	55	12	form	form	NOUN
ap-368	55	13	�	�	PROPN
ap-368	55	14	�	�	PROPN
ap-368	55	15	�	�	PROPN
ap-368	55	16	�	�	PROPN
ap-368	55	17	�	�	PROPN
ap-368	55	18	�	�	PROPN
ap-368	55	19	�	�	PROPN
ap-368	55	20	�	�	PROPN
ap-368	55	21	�	�	PROPN
ap-368	55	22	�	�	PROPN
ap-368	55	23	�	�	PROPN
ap-368	55	24	,	,	PUNCT
ap-368	55	25	,	,	PUNCT
ap-368	55	26	,	,	PUNCT
ap-368	55	27	,	,	PUNCT
ap-368	55	28	,	,	PUNCT
ap-368	55	29	,	,	PUNCT
ap-368	55	30	z	z	NOUN
ap-368	55	31	r	r	NOUN
ap-368	55	32	t	t	NOUN
ap-368	55	33	z	z	NOUN
ap-368	55	34	c	c	NOUN
ap-368	55	35	z	z	NOUN
ap-368	55	36	z	z	NOUN
ap-368	55	37	r	r	NOUN
ap-368	55	38	r1	r1	NOUN
ap-368	55	39	1	1	NUM
ap-368	55	40	0	0	NUM
ap-368	55	41	1	1	NUM
ap-368	55	42	1	1	NUM
ap-368	55	43	(	(	PUNCT
ap-368	55	44	5	5	NUM
ap-368	55	45	)	)	PUNCT
ap-368	55	46	where	where	SCONJ
ap-368	55	47	�	�	PROPN
ap-368	55	48	is	be	AUX
ap-368	55	49	retarded	retarded	ADJ
ap-368	55	50	time	time	NOUN
ap-368	55	51	and	and	CCONJ
ap-368	55	52	is	be	AUX
ap-368	55	53	the	the	DET
ap-368	55	54	small	small	ADJ
ap-368	55	55	dimensionless	dimensionless	NOUN
ap-368	55	56	parameter	parameter	NOUN
ap-368	55	57	which	which	PRON
ap-368	55	58	is	be	AUX
ap-368	55	59	given	give	VERB
ap-368	55	60	by	by	ADP
ap-368	55	61	the	the	DET
ap-368	55	62	acoustic	acoustic	ADJ
ap-368	55	63	mach	mach	NOUN
ap-368	55	64	number	number	NOUN
ap-368	55	65	–	–	PUNCT
ap-368	55	66	the	the	DET
ap-368	55	67	ratio	ratio	NOUN
ap-368	55	68	of	of	ADP
ap-368	55	69	the	the	DET
ap-368	55	70	particle	particle	NOUN
ap-368	55	71	velocity	velocity	NOUN
ap-368	55	72	amplitude	amplitude	NOUN
ap-368	55	73	vm	vm	PROPN
ap-368	55	74	to	to	ADP
ap-368	55	75	the	the	DET
ap-368	55	76	small	small	ADJ
ap-368	55	77	-	-	PUNCT
ap-368	55	78	signal	signal	NOUN
ap-368	55	79	sound	sound	NOUN
ap-368	55	80	speed	speed	NOUN
ap-368	55	81	c0	c0	NOUN
ap-368	55	82	.	.	PUNCT
ap-368	56	1	if	if	SCONJ
ap-368	56	2	we	we	PRON
ap-368	56	3	use	use	VERB
ap-368	56	4	the	the	DET
ap-368	56	5	new	new	ADJ
ap-368	56	6	coordinate	coordinate	NOUN
ap-368	56	7	system	system	NOUN
ap-368	56	8	(	(	PUNCT
ap-368	56	9	�	�	PROPN
ap-368	56	10	,	,	PUNCT
ap-368	56	11	z1	z1	NOUN
ap-368	56	12	,	,	PUNCT
ap-368	56	13	r1	r1	PROPN
ap-368	56	14	)	)	PUNCT
ap-368	56	15	,	,	PUNCT
ap-368	56	16	then	then	ADV
ap-368	56	17	transformation	transformation	NOUN
ap-368	56	18	of	of	ADP
ap-368	56	19	the	the	DET
ap-368	56	20	partial	partial	ADJ
ap-368	56	21	derivatives	derivative	NOUN
ap-368	56	22	yields	yield	VERB
ap-368	56	23	�	�	PROPN
ap-368	56	24	�	�	PROPN
ap-368	56	25	�	�	PROPN
ap-368	56	26	�	�	PROPN
ap-368	56	27	�	�	PROPN
ap-368	56	28	�	�	PROPN
ap-368	56	29	�	�	PROPN
ap-368	56	30	z	z	PROPN
ap-368	56	31	c	c	PROPN
ap-368	56	32	z	z	PROPN
ap-368	56	33	�	�	PROPN
ap-368	56	34	�	�	PROPN
ap-368	56	35	�	�	PROPN
ap-368	56	36	1	1	NUM
ap-368	56	37	0	0	NUM
ap-368	56	38	1	1	NUM
ap-368	56	39	,	,	PUNCT
ap-368	56	40	(	(	PUNCT
ap-368	56	41	6	6	NUM
ap-368	56	42	)	)	PUNCT
ap-368	56	43	�	�	PROPN
ap-368	56	44	�	�	PROPN
ap-368	56	45	�	�	PROPN
ap-368	56	46	�	�	PROPN
ap-368	56	47	�	�	PROPN
ap-368	56	48	�	�	PROPN
ap-368	56	49	�	�	PROPN
ap-368	56	50	�	�	PROPN
ap-368	56	51	�	�	PROPN
ap-368	56	52	�	�	PROPN
ap-368	56	53	�	�	PROPN
ap-368	56	54	2	2	NUM
ap-368	56	55	2	2	NUM
ap-368	56	56	0	0	NUM
ap-368	56	57	2	2	NUM
ap-368	56	58	2	2	NUM
ap-368	56	59	0	0	NUM
ap-368	56	60	2	2	NUM
ap-368	56	61	1	1	NUM
ap-368	56	62	2	2	NUM
ap-368	56	63	2	2	NUM
ap-368	56	64	1	1	NUM
ap-368	56	65	2	2	NUM
ap-368	56	66	1	1	NUM
ap-368	56	67	z	z	NOUN
ap-368	56	68	c	c	NOUN
ap-368	56	69	c	c	NOUN
ap-368	56	70	z	z	NOUN
ap-368	56	71	z	z	PROPN
ap-368	56	72	�	�	PROPN
ap-368	56	73	�	�	PROPN
ap-368	56	74	�	�	PROPN
ap-368	56	75	,	,	PUNCT
ap-368	56	76	(	(	PUNCT
ap-368	56	77	7	7	X
ap-368	56	78	)	)	PUNCT
ap-368	56	79	�	�	PROPN
ap-368	56	80	�	�	PROPN
ap-368	56	81	�	�	PROPN
ap-368	56	82	�	�	PROPN
ap-368	56	83	�	�	PROPN
ap-368	56	84	�	�	PROPN
ap-368	56	85	�	�	PROPN
ap-368	56	86	�	�	PROPN
ap-368	56	87	�	�	PROPN
ap-368	56	88	�	�	PROPN
ap-368	56	89	t	t	PROPN
ap-368	56	90	t	t	PROPN
ap-368	56	91	�	�	PROPN
ap-368	56	92	�	�	PROPN
ap-368	56	93	,	,	PUNCT
ap-368	56	94	,	,	PUNCT
ap-368	56	95	2	2	NUM
ap-368	56	96	2	2	NUM
ap-368	56	97	2	2	NUM
ap-368	56	98	2	2	NUM
ap-368	56	99	(	(	PUNCT
ap-368	56	100	8)	8)	NUM
ap-368	56	101	�	�	PROPN
ap-368	56	102	�	�	PROPN
ap-368	56	103	�	�	PROPN
ap-368	56	104	�	�	PROPN
ap-368	56	105	�	�	PROPN
ap-368	56	106	�	�	PROPN
ap-368	56	107	�	�	PROPN
ap-368	56	108	�	�	PROPN
ap-368	56	109	�	�	PROPN
ap-368	56	110	�	�	PROPN
ap-368	56	111	r	r	NOUN
ap-368	56	112	r	r	NOUN
ap-368	56	113	r	r	NOUN
ap-368	56	114	r	r	NOUN
ap-368	56	115	�	�	PROPN
ap-368	56	116	�	�	PROPN
ap-368	56	117	,	,	PUNCT
ap-368	56	118	.	.	PUNCT
ap-368	57	1	2	2	NUM
ap-368	57	2	2	2	NUM
ap-368	57	3	2	2	NUM
ap-368	57	4	(	(	PUNCT
ap-368	57	5	9	9	NUM
ap-368	57	6	)	)	PUNCT
ap-368	57	7	substitution	substitution	NOUN
ap-368	57	8	of	of	ADP
ap-368	57	9	the	the	DET
ap-368	57	10	partial	partial	ADJ
ap-368	57	11	derivatives	derivative	NOUN
ap-368	57	12	(	(	PUNCT
ap-368	57	13	6	6	NUM
ap-368	57	14	)	)	PUNCT
ap-368	57	15	into	into	ADP
ap-368	57	16	the	the	DET
ap-368	57	17	operator	operator	NOUN
ap-368	57	18	(	(	PUNCT
ap-368	57	19	4	4	X
ap-368	57	20	)	)	PUNCT
ap-368	57	21	gives	give	VERB
ap-368	57	22	�	�	PROPN
ap-368	57	23	�	�	PROPN
ap-368	57	24	�	�	PROPN
ap-368	57	25	�	�	PROPN
ap-368	57	26	�	�	PROPN
ap-368	57	27	�	�	PROPN
ap-368	57	28	�	�	PROPN
ap-368	57	29	�	�	PROPN
ap-368	57	30	�	�	PROPN
ap-368	57	31	�	�	PROPN
ap-368	57	32	�	�	PROPN
ap-368	57	33	�	�	PROPN
ap-368	57	34	ez	ez	PROPN
ap-368	57	35	1	1	NUM
ap-368	57	36	0	0	NUM
ap-368	57	37	1c	1c	NOUN
ap-368	57	38	z	z	PROPN
ap-368	57	39	�	�	PROPN
ap-368	57	40	�	�	PROPN
ap-368	57	41	�	�	PROPN
ap-368	57	42	�	�	PROPN
ap-368	57	43	�	�	PROPN
ap-368	57	44	.	.	PUNCT
ap-368	58	1	(	(	PUNCT
ap-368	58	2	10	10	NUM
ap-368	58	3	)	)	PUNCT
ap-368	58	4	here	here	ADV
ap-368	58	5	�	�	PROPN
ap-368	58	6	denotes	denote	VERB
ap-368	58	7	directions	direction	NOUN
ap-368	58	8	transverse	transverse	NOUN
ap-368	58	9	to	to	ADP
ap-368	58	10	propagation	propagation	NOUN
ap-368	58	11	.	.	PUNCT
ap-368	59	1	we	we	PRON
ap-368	59	2	can	can	AUX
ap-368	59	3	write	write	VERB
ap-368	59	4	the	the	DET
ap-368	59	5	linear	linear	ADJ
ap-368	59	6	wave	wave	NOUN
ap-368	59	7	equation	equation	NOUN
ap-368	59	8	directly	directly	ADV
ap-368	59	9	from	from	ADP
ap-368	59	10	eq	eq	ADP
ap-368	59	11	.	.	PUNCT
ap-368	60	1	(	(	PUNCT
ap-368	60	2	1	1	X
ap-368	60	3	)	)	PUNCT
ap-368	60	4	�	�	PROPN
ap-368	60	5	�	�	PROPN
ap-368	60	6	�	�	PROPN
ap-368	60	7	�	�	PROPN
ap-368	60	8	2	2	NUM
ap-368	60	9	2	2	NUM
ap-368	60	10	0	0	NUM
ap-368	60	11	2	2	NUM
ap-368	60	12	t	t	NOUN
ap-368	60	13	c	c	NOUN
ap-368	60	14	o	o	ADJ
ap-368	60	15	�	�	PROPN
ap-368	60	16	�	�	PROPN
ap-368	60	17	�	�	PROPN
ap-368	60	18	�	�	PROPN
ap-368	60	19	�	�	PROPN
ap-368	60	20	(	(	PUNCT
ap-368	60	21	)	)	PUNCT
ap-368	60	22	.	.	PUNCT
ap-368	61	1	(	(	PUNCT
ap-368	61	2	11	11	NUM
ap-368	61	3	)	)	PUNCT
ap-368	61	4	if	if	SCONJ
ap-368	61	5	we	we	PRON
ap-368	61	6	use	use	VERB
ap-368	61	7	the	the	DET
ap-368	61	8	operator	operator	NOUN
ap-368	61	9	(	(	PUNCT
ap-368	61	10	10	10	NUM
ap-368	61	11	)	)	PUNCT
ap-368	61	12	in	in	ADP
ap-368	61	13	eq	eq	ADP
ap-368	61	14	.	.	PUNCT
ap-368	62	1	(	(	PUNCT
ap-368	62	2	11	11	NUM
ap-368	62	3	)	)	PUNCT
ap-368	62	4	for	for	ADP
ap-368	62	5	the	the	DET
ap-368	62	6	divergence	divergence	NOUN
ap-368	62	7	operator	operator	NOUN
ap-368	62	8	,	,	PUNCT
ap-368	62	9	then	then	ADV
ap-368	62	10	after	after	ADP
ap-368	62	11	neglecting	neglect	VERB
ap-368	62	12	a	a	DET
ap-368	62	13	quadratic	quadratic	ADJ
ap-368	62	14	order	order	NOUN
ap-368	62	15	term	term	NOUN
ap-368	62	16	we	we	PRON
ap-368	62	17	obtain	obtain	VERB
ap-368	62	18	�	�	PROPN
ap-368	62	19	�	�	PROPN
ap-368	62	20	�	�	PROPN
ap-368	62	21	�	�	PROPN
ap-368	62	22	�	�	PROPN
ap-368	62	23	�	�	PROPN
ap-368	62	24	�	�	PROPN
ap-368	62	25	�	�	PROPN
ap-368	62	26	�	�	PROPN
ap-368	62	27	�	�	PROPN
ap-368	62	28	2	2	NUM
ap-368	62	29	2	2	NUM
ap-368	62	30	0	0	NUM
ap-368	62	31	2	2	NUM
ap-368	62	32	0	0	NUM
ap-368	62	33	2	2	NUM
ap-368	62	34	�	�	PROPN
ap-368	62	35	�	�	PROPN
ap-368	62	36	�	�	PROPN
ap-368	62	37	�	�	PROPN
ap-368	62	38	�	�	PROPN
ap-368	62	39	�	�	PROPN
ap-368	62	40	�	�	PROPN
ap-368	62	41	�	�	PROPN
ap-368	62	42	�	�	PROPN
ap-368	62	43	c	c	PROPN
ap-368	62	44	z	z	NOUN
ap-368	62	45	c	c	NOUN
ap-368	62	46	o	o	NOUN
ap-368	62	47	(	(	PUNCT
ap-368	62	48	)	)	PUNCT
ap-368	62	49	(	(	PUNCT
ap-368	62	50	12	12	NUM
ap-368	62	51	)	)	PUNCT
ap-368	62	52	if	if	SCONJ
ap-368	62	53	we	we	PRON
ap-368	62	54	suppose	suppose	VERB
ap-368	62	55	the	the	DET
ap-368	62	56	transverse	transverse	NOUN
ap-368	62	57	partial	partial	ADJ
ap-368	62	58	velocity	velocity	NOUN
ap-368	62	59	v	v	ADP
ap-368	62	60	�	�	PROPN
ap-368	62	61	�	�	PROPN
ap-368	62	62	�	�	PROPN
ap-368	62	63	�	�	PROPN
ap-368	62	64	�	�	PROPN
ap-368	62	65	~	~	PUNCT
ap-368	62	66	2	2	NUM
ap-368	62	67	(	(	PUNCT
ap-368	62	68	13	13	NUM
ap-368	62	69	)	)	PUNCT
ap-368	62	70	then	then	ADV
ap-368	62	71	we	we	PRON
ap-368	62	72	can	can	AUX
ap-368	62	73	omit	omit	VERB
ap-368	62	74	the	the	DET
ap-368	62	75	last	last	ADJ
ap-368	62	76	term	term	NOUN
ap-368	62	77	in	in	ADP
ap-368	62	78	eq	eq	ADP
ap-368	62	79	.	.	PUNCT
ap-368	63	1	(	(	PUNCT
ap-368	63	2	12	12	NUM
ap-368	63	3	):	):	PUNCT
ap-368	63	4	�	�	PROPN
ap-368	63	5	�	�	PROPN
ap-368	63	6	�	�	PROPN
ap-368	63	7	�	�	PROPN
ap-368	63	8	�	�	PROPN
ap-368	63	9	�	�	PROPN
ap-368	63	10	t	t	PROPN
ap-368	63	11	c	c	PROPN
ap-368	63	12	z	z	PROPN
ap-368	63	13	o	o	X
ap-368	63	14	�	�	PROPN
ap-368	63	15	�	�	PROPN
ap-368	63	16	�	�	PROPN
ap-368	63	17	0	0	NUM
ap-368	63	18	(	(	PUNCT
ap-368	63	19	)	)	PUNCT
ap-368	63	20	.	.	PUNCT
ap-368	64	1	(	(	PUNCT
ap-368	64	2	14	14	NUM
ap-368	64	3	)	)	PUNCT
ap-368	64	4	equation	equation	NOUN
ap-368	64	5	(	(	PUNCT
ap-368	64	6	14	14	NUM
ap-368	64	7	)	)	PUNCT
ap-368	64	8	represents	represent	VERB
ap-368	64	9	the	the	DET
ap-368	64	10	plane	plane	NOUN
ap-368	64	11	progressive	progressive	ADJ
ap-368	64	12	wave	wave	NOUN
ap-368	64	13	impedance	impedance	NOUN
ap-368	64	14	relation	relation	NOUN
ap-368	64	15	.	.	PUNCT
ap-368	65	1	when	when	SCONJ
ap-368	65	2	conditions	condition	NOUN
ap-368	65	3	(	(	PUNCT
ap-368	65	4	13	13	NUM
ap-368	65	5	)	)	PUNCT
ap-368	65	6	and	and	CCONJ
ap-368	65	7	(	(	PUNCT
ap-368	65	8	14	14	NUM
ap-368	65	9	)	)	PUNCT
ap-368	65	10	are	be	AUX
ap-368	65	11	satisfied	satisfied	ADJ
ap-368	65	12	we	we	PRON
ap-368	65	13	can	can	AUX
ap-368	65	14	suppose	suppose	VERB
ap-368	65	15	l	l	PROPN
ap-368	65	16	�	�	PROPN
ap-368	65	17	0	0	PUNCT
ap-368	66	1	+	+	CCONJ
ap-368	66	2	o	o	NOUN
ap-368	66	3	(	(	PUNCT
ap-368	66	4	3	3	NUM
ap-368	66	5	)	)	PUNCT
ap-368	66	6	.	.	PUNCT
ap-368	67	1	this	this	PRON
ap-368	67	2	enables	enable	VERB
ap-368	67	3	us	we	PRON
ap-368	67	4	to	to	PART
ap-368	67	5	modify	modify	VERB
ap-368	67	6	eq	eq	ADP
ap-368	67	7	.	.	PUNCT
ap-368	68	1	(	(	PUNCT
ap-368	68	2	1	1	X
ap-368	68	3	)	)	PUNCT
ap-368	68	4	�	�	PROPN
ap-368	68	5	�	�	PROPN
ap-368	68	6	�	�	PROPN
ap-368	68	7	�	�	PROPN
ap-368	68	8	�	�	PROPN
ap-368	68	9	�	�	PROPN
ap-368	68	10	�	�	PROPN
ap-368	68	11	�	�	PROPN
ap-368	68	12	�	�	PROPN
ap-368	68	13	�	�	PROPN
ap-368	68	14	�	�	PROPN
ap-368	68	15	�	�	PROPN
ap-368	68	16	�	�	PROPN
ap-368	68	17	2	2	NUM
ap-368	68	18	2	2	NUM
ap-368	68	19	0	0	NUM
ap-368	68	20	2	2	NUM
ap-368	68	21	0	0	NUM
ap-368	68	22	2	2	NUM
ap-368	68	23	2	2	NUM
ap-368	68	24	21	21	NUM
ap-368	68	25	2	2	NUM
ap-368	68	26	t	t	NOUN
ap-368	68	27	c	c	NOUN
ap-368	69	1	t	t	PROPN
ap-368	69	2	c	c	PROPN
ap-368	69	3	t	t	PROPN
ap-368	69	4	z	z	PROPN
ap-368	69	5	�	�	PROPN
ap-368	69	6	�	�	PROPN
ap-368	69	7	�	�	PROPN
ap-368	69	8	�	�	PROPN
ap-368	69	9	�	�	PROPN
ap-368	69	10	�	�	PROPN
ap-368	69	11	�	�	PROPN
ap-368	69	12	�	�	PROPN
ap-368	69	13	�	�	PROPN
ap-368	69	14	�	�	PROPN
ap-368	69	15	�	�	PROPN
ap-368	69	16	�	�	PROPN
ap-368	69	17	�	�	PROPN
ap-368	69	18	�	�	PROPN
ap-368	69	19	�	�	PROPN
ap-368	69	20	�	�	PROPN
ap-368	69	21	�	�	PROPN
ap-368	69	22	�	�	PROPN
ap-368	69	23	�	�	PROPN
ap-368	69	24	�	�	PROPN
ap-368	69	25	�	�	PROPN
ap-368	69	26	�	�	PROPN
ap-368	69	27	�	�	PROPN
ap-368	70	1	b	b	PROPN
ap-368	70	2	c	c	NOUN
ap-368	70	3	t	t	PROPN
ap-368	70	4	o	o	X
ap-368	70	5	�	�	PROPN
ap-368	70	6	�	�	PROPN
ap-368	70	7	�	�	PROPN
ap-368	70	8	�	�	PROPN
ap-368	70	9	0	0	NUM
ap-368	70	10	0	0	NUM
ap-368	70	11	2	2	NUM
ap-368	70	12	3	3	NUM
ap-368	70	13	3	3	NUM
ap-368	70	14	(	(	PUNCT
ap-368	70	15	)	)	PUNCT
ap-368	70	16	.	.	PUNCT
ap-368	71	1	(	(	PUNCT
ap-368	71	2	15	15	X
ap-368	71	3	)	)	PUNCT
ap-368	71	4	substituting	substitute	VERB
ap-368	71	5	relation	relation	NOUN
ap-368	71	6	(	(	PUNCT
ap-368	71	7	14	14	NUM
ap-368	71	8	)	)	PUNCT
ap-368	71	9	to	to	ADP
ap-368	71	10	the	the	DET
ap-368	71	11	second	second	ADJ
ap-368	71	12	-	-	PUNCT
ap-368	71	13	order	order	NOUN
ap-368	71	14	term	term	NOUN
ap-368	71	15	of	of	ADP
ap-368	71	16	eq	eq	PROPN
ap-368	71	17	.	.	PUNCT
ap-368	72	1	(	(	PUNCT
ap-368	72	2	15	15	NUM
ap-368	72	3	)	)	PUNCT
ap-368	72	4	we	we	PRON
ap-368	72	5	get	get	VERB
ap-368	72	6	�	�	PROPN
ap-368	72	7	�	�	PROPN
ap-368	72	8	�	�	PROPN
ap-368	72	9	�	�	PROPN
ap-368	72	10	�	�	PROPN
ap-368	72	11	�	�	PROPN
ap-368	72	12	�	�	PROPN
ap-368	72	13	�	�	PROPN
ap-368	72	14	�	�	PROPN
ap-368	72	15	�	�	PROPN
ap-368	72	16	�	�	PROPN
ap-368	72	17	�	�	PROPN
ap-368	72	18	�	�	PROPN
ap-368	72	19	�	�	PROPN
ap-368	72	20	�	�	PROPN
ap-368	72	21	�	�	PROPN
ap-368	72	22	�	�	PROPN
ap-368	72	23	2	2	NUM
ap-368	72	24	2	2	NUM
ap-368	72	25	0	0	NUM
ap-368	72	26	2	2	NUM
ap-368	72	27	2	2	NUM
ap-368	72	28	2	2	NUM
ap-368	72	29	0	0	NUM
ap-368	72	30	2	2	NUM
ap-368	72	31	2	2	NUM
ap-368	72	32	2	2	NUM
ap-368	72	33	1	1	NUM
ap-368	72	34	t	t	NOUN
ap-368	72	35	c	c	NOUN
ap-368	72	36	z	z	NOUN
ap-368	72	37	c	c	NOUN
ap-368	72	38	r	r	NOUN
ap-368	72	39	r	r	NOUN
ap-368	72	40	r	r	NOUN
ap-368	72	41	t	t	PROPN
ap-368	72	42	�	�	PROPN
ap-368	72	43	�	�	PROPN
ap-368	72	44	�	�	PROPN
ap-368	72	45	�	�	PROPN
ap-368	72	46	�	�	PROPN
ap-368	72	47	�	�	PROPN
ap-368	72	48	�	�	PROPN
ap-368	72	49	�	�	PROPN
ap-368	72	50	�	�	PROPN
ap-368	72	51	�	�	PROPN
ap-368	72	52	�	�	PROPN
ap-368	72	53	�	�	PROPN
ap-368	72	54	�	�	PROPN
ap-368	72	55	�	�	PROPN
ap-368	72	56	�	�	PROPN
ap-368	72	57	�	�	PROPN
ap-368	72	58	z	z	PROPN
ap-368	72	59	b	b	PROPN
ap-368	73	1	c	c	PROPN
ap-368	73	2	t	t	PROPN
ap-368	73	3	o	o	NOUN
ap-368	73	4	�	�	PROPN
ap-368	73	5	�	�	PROPN
ap-368	73	6	�	�	PROPN
ap-368	73	7	�	�	PROPN
ap-368	73	8	�	�	PROPN
ap-368	73	9	�	�	PROPN
ap-368	73	10	2	2	NUM
ap-368	73	11	0	0	NUM
ap-368	73	12	0	0	NUM
ap-368	73	13	2	2	NUM
ap-368	73	14	3	3	NUM
ap-368	73	15	3	3	NUM
ap-368	73	16	(	(	PUNCT
ap-368	73	17	)	)	PUNCT
ap-368	73	18	,	,	PUNCT
ap-368	73	19	(	(	PUNCT
ap-368	73	20	16	16	NUM
ap-368	73	21	)	)	PUNCT
ap-368	73	22	where	where	SCONJ
ap-368	73	23	�	�	PROPN
ap-368	73	24	�	�	PROPN
ap-368	73	25	�	�	PROPN
ap-368	73	26	�	�	PROPN
ap-368	73	27	�	�	PROPN
ap-368	73	28	�	�	PROPN
ap-368	73	29	1	1	NUM
ap-368	73	30	2	2	NUM
ap-368	73	31	is	be	AUX
ap-368	73	32	the	the	DET
ap-368	73	33	coefficient	coefficient	NOUN
ap-368	73	34	of	of	ADP
ap-368	73	35	nonlinearity	nonlinearity	NOUN
ap-368	73	36	.	.	PUNCT
ap-368	74	1	after	after	ADP
ap-368	74	2	using	use	VERB
ap-368	74	3	the	the	DET
ap-368	74	4	transformation	transformation	NOUN
ap-368	74	5	of	of	ADP
ap-368	74	6	derivatives	derivative	NOUN
ap-368	74	7	(	(	PUNCT
ap-368	74	8	6	6	NUM
ap-368	74	9	)	)	PUNCT
ap-368	74	10	we	we	PRON
ap-368	74	11	can	can	AUX
ap-368	74	12	neglect	neglect	VERB
ap-368	74	13	the	the	DET
ap-368	74	14	cubic	cubic	ADJ
ap-368	74	15	and	and	CCONJ
ap-368	74	16	higher	high	ADJ
ap-368	74	17	terms	term	NOUN
ap-368	74	18	.	.	PUNCT
ap-368	75	1	this	this	PRON
ap-368	75	2	yields	yield	VERB
ap-368	75	3	the	the	DET
ap-368	75	4	well	well	ADV
ap-368	75	5	-	-	PUNCT
ap-368	75	6	known	know	VERB
ap-368	75	7	kzk	kzk	NOUN
ap-368	75	8	(	(	PUNCT
ap-368	75	9	khokhlov	khokhlov	PROPN
ap-368	75	10	-	-	PUNCT
ap-368	75	11	zabolotskaya	zabolotskaya	NOUN
ap-368	75	12	-	-	PUNCT
ap-368	75	13	kuznetsov	kuznetsov	NOUN
ap-368	75	14	)	)	PUNCT
ap-368	75	15	equation	equation	NOUN
ap-368	75	16	�	�	PROPN
ap-368	75	17	�	�	PROPN
ap-368	75	18	�	�	PROPN
ap-368	75	19	�	�	PROPN
ap-368	75	20	�	�	PROPN
ap-368	75	21	�	�	PROPN
ap-368	75	22	�	�	PROPN
ap-368	75	23	�	�	PROPN
ap-368	75	24	�	�	PROPN
ap-368	75	25	�	�	PROPN
ap-368	75	26	�	�	PROPN
ap-368	75	27	�	�	PROPN
ap-368	75	28	�	�	PROPN
ap-368	75	29	�	�	PROPN
ap-368	75	30	v	v	ADP
ap-368	75	31	z	z	NOUN
ap-368	75	32	c	c	NOUN
ap-368	75	33	v	v	ADP
ap-368	75	34	v	v	PROPN
ap-368	75	35	b	b	PROPN
ap-368	75	36	c	c	NOUN
ap-368	75	37	v	v	NOUN
ap-368	75	38	c	c	NOUN
ap-368	75	39	z	z	NOUN
ap-368	75	40	z	z	NOUN
ap-368	75	41	z	z	NOUN
ap-368	75	42	z	z	PROPN
ap-368	75	43	�	�	PROPN
ap-368	75	44	�	�	PROPN
ap-368	75	45	�	�	PROPN
ap-368	75	46	�	�	PROPN
ap-368	75	47	�	�	PROPN
ap-368	75	48	�	�	PROPN
ap-368	75	49	�	�	PROPN
ap-368	75	50	�	�	PROPN
ap-368	75	51	�	�	PROPN
ap-368	75	52	2	2	NUM
ap-368	75	53	2	2	NUM
ap-368	75	54	2	2	NUM
ap-368	75	55	0	0	NUM
ap-368	75	56	2	2	NUM
ap-368	75	57	0	0	NUM
ap-368	75	58	0	0	NUM
ap-368	75	59	3	3	NUM
ap-368	75	60	2	2	NUM
ap-368	75	61	2	2	NUM
ap-368	75	62	0	0	NUM
ap-368	75	63	2	2	NUM
ap-368	75	64	2	2	NUM
ap-368	75	65	1v	1v	NUM
ap-368	75	66	r	r	NOUN
ap-368	75	67	r	r	NOUN
ap-368	75	68	v	v	NOUN
ap-368	75	69	r	r	NOUN
ap-368	75	70	oz	oz	NOUN
ap-368	75	71	z	z	PROPN
ap-368	75	72	�	�	PROPN
ap-368	75	73	�	�	PROPN
ap-368	75	74	�	�	PROPN
ap-368	75	75	�	�	PROPN
ap-368	75	76	�	�	PROPN
ap-368	75	77	�	�	PROPN
ap-368	75	78	�	�	PROPN
ap-368	75	79	�	�	PROPN
ap-368	75	80	�	�	PROPN
ap-368	75	81	�	�	PROPN
ap-368	75	82	(	(	PUNCT
ap-368	75	83	)	)	PUNCT
ap-368	75	84	,	,	PUNCT
ap-368	75	85	(	(	PUNCT
ap-368	75	86	17	17	NUM
ap-368	75	87	)	)	PUNCT
ap-368	75	88	where	where	SCONJ
ap-368	75	89	v	v	X
ap-368	75	90	zz	zz	PROPN
ap-368	75	91	�	�	PROPN
ap-368	75	92	�	�	PROPN
ap-368	75	93	�	�	PROPN
ap-368	75	94	�	�	PROPN
ap-368	75	95	is	be	AUX
ap-368	75	96	the	the	DET
ap-368	75	97	z	z	NOUN
ap-368	75	98	component	component	NOUN
ap-368	75	99	of	of	ADP
ap-368	75	100	the	the	DET
ap-368	75	101	particle	particle	NOUN
ap-368	75	102	velocity	velocity	NOUN
ap-368	75	103	v	v	ADP
ap-368	75	104	e	e	PROPN
ap-368	75	105	v	v	ADP
ap-368	75	106	�	�	PROPN
ap-368	75	107	�	�	PROPN
ap-368	75	108	�	�	PROPN
ap-368	75	109	z	z	PROPN
ap-368	75	110	zv	zv	NOUN
ap-368	75	111	.	.	PUNCT
ap-368	76	1	the	the	DET
ap-368	76	2	kzk	kzk	PROPN
ap-368	76	3	eqatuion	eqatuion	NOUN
ap-368	76	4	was	be	AUX
ap-368	76	5	derived	derive	VERB
ap-368	76	6	on	on	ADP
ap-368	76	7	the	the	DET
ap-368	76	8	condition	condition	NOUN
ap-368	76	9	that	that	SCONJ
ap-368	76	10	vz	vz	PROPN
ap-368	76	11	~	~	PUNCT
ap-368	76	12	and	and	CCONJ
ap-368	76	13	v	v	ADP
ap-368	76	14	�	�	X
ap-368	76	15	~	~	PUNCT
ap-368	76	16	2	2	NUM
ap-368	76	17	(	(	PUNCT
ap-368	76	18	i.e.	i.e.	X
ap-368	76	19	vz	vz	X
ap-368	76	20	�	�	PROPN
ap-368	76	21	v	v	PROPN
ap-368	76	22	�	�	PROPN
ap-368	76	23	)	)	PUNCT
ap-368	76	24	.	.	PUNCT
ap-368	77	1	vz	vz	PROPN
ap-368	77	2	and	and	CCONJ
ap-368	77	3	v	v	NOUN
ap-368	77	4	�	�	PROPN
ap-368	77	5	are	be	AUX
ap-368	77	6	connected	connect	VERB
ap-368	77	7	by	by	ADP
ap-368	77	8	the	the	DET
ap-368	77	9	irrotationality	irrotationality	NOUN
ap-368	77	10	condition	condition	NOUN
ap-368	77	11	of	of	ADP
ap-368	77	12	the	the	DET
ap-368	77	13	velocity	velocity	NOUN
ap-368	77	14	field	field	NOUN
ap-368	77	15	�	�	PROPN
ap-368	77	16	�	�	PROPN
ap-368	77	17	�	�	PROPN
ap-368	77	18	�	�	PROPN
ap-368	77	19	�	�	PROPN
ap-368	77	20	v	v	ADP
ap-368	77	21	c	c	NOUN
ap-368	77	22	v	v	NOUN
ap-368	77	23	r	r	NOUN
ap-368	77	24	z	z	PROPN
ap-368	77	25	�	�	PROPN
ap-368	77	26	�	�	PROPN
ap-368	77	27	�	�	PROPN
ap-368	77	28	0	0	NUM
ap-368	77	29	0	0	NUM
ap-368	77	30	.	.	PUNCT
ap-368	78	1	(	(	PUNCT
ap-368	78	2	18	18	NUM
ap-368	78	3	)	)	PUNCT
ap-368	78	4	if	if	SCONJ
ap-368	78	5	we	we	PRON
ap-368	78	6	do	do	AUX
ap-368	78	7	not	not	PART
ap-368	78	8	take	take	VERB
ap-368	78	9	into	into	ADP
ap-368	78	10	account	account	NOUN
ap-368	78	11	the	the	DET
ap-368	78	12	wall	wall	NOUN
ap-368	78	13	friction	friction	NOUN
ap-368	78	14	we	we	PRON
ap-368	78	15	have	have	VERB
ap-368	78	16	to	to	PART
ap-368	78	17	use	use	VERB
ap-368	78	18	for	for	ADP
ap-368	78	19	the	the	DET
ap-368	78	20	solution	solution	NOUN
ap-368	78	21	of	of	ADP
ap-368	78	22	the	the	DET
ap-368	78	23	kzk	kzk	NOUN
ap-368	78	24	the	the	DET
ap-368	78	25	following	following	ADJ
ap-368	78	26	boundary	boundary	ADJ
ap-368	78	27	conditions	condition	NOUN
ap-368	78	28	�	�	PROPN
ap-368	78	29	�	�	PROPN
ap-368	78	30	�	�	PROPN
ap-368	78	31	�	�	PROPN
ap-368	78	32	v	v	NOUN
ap-368	78	33	z	z	NOUN
ap-368	78	34	r	r	NOUN
ap-368	78	35	f	f	NOUN
ap-368	78	36	r	r	NOUN
ap-368	78	37	zz	zz	PROPN
ap-368	78	38	,	,	PUNCT
ap-368	78	39	,	,	PUNCT
ap-368	78	40	,	,	PUNCT
ap-368	78	41	�	�	PROPN
ap-368	78	42	�	�	PROPN
ap-368	78	43	�	�	PROPN
ap-368	78	44	�	�	PROPN
ap-368	78	45	at	at	ADP
ap-368	78	46	0	0	NUM
ap-368	78	47	,	,	PUNCT
ap-368	78	48	(	(	PUNCT
ap-368	78	49	19	19	NUM
ap-368	78	50	)	)	PUNCT
ap-368	78	51	©	©	PROPN
ap-368	78	52	czech	czech	PROPN
ap-368	78	53	technical	technical	PROPN
ap-368	78	54	university	university	PROPN
ap-368	78	55	publishing	publishing	NOUN
ap-368	78	56	house	house	NOUN
ap-368	78	57	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	78	58	19	19	NUM
ap-368	78	59	acta	acta	PROPN
ap-368	78	60	polytechnica	polytechnica	PROPN
ap-368	78	61	vol	vol	NOUN
ap-368	78	62	.	.	PUNCT
ap-368	79	1	42	42	NUM
ap-368	79	2	no	no	INTJ
ap-368	79	3	.	.	PUNCT
ap-368	80	1	4/2002	4/2002	PRON
ap-368	80	2	�	�	PROPN
ap-368	80	3	�	�	PROPN
ap-368	80	4	v	v	NOUN
ap-368	80	5	r	r	NOUN
ap-368	80	6	rz	rz	NOUN
ap-368	80	7	�	�	PROPN
ap-368	80	8	�	�	PROPN
ap-368	80	9	0	0	NUM
ap-368	80	10	0at	0at	NOUN
ap-368	80	11	,	,	PUNCT
ap-368	80	12	(	(	PUNCT
ap-368	80	13	20	20	NUM
ap-368	80	14	)	)	PUNCT
ap-368	80	15	�	�	PROPN
ap-368	80	16	�	�	PROPN
ap-368	80	17	v	v	ADP
ap-368	80	18	r	r	NOUN
ap-368	80	19	r	r	NOUN
ap-368	80	20	rz	rz	NOUN
ap-368	80	21	�	�	PROPN
ap-368	80	22	�	�	PROPN
ap-368	80	23	0	0	NUM
ap-368	80	24	0at	0at	NOUN
ap-368	80	25	,	,	PUNCT
ap-368	80	26	(	(	PUNCT
ap-368	80	27	21	21	NUM
ap-368	80	28	)	)	PUNCT
ap-368	80	29	where	where	SCONJ
ap-368	80	30	r0	r0	NOUN
ap-368	80	31	is	be	AUX
ap-368	80	32	the	the	DET
ap-368	80	33	tube	tube	NOUN
ap-368	80	34	radius	radius	NOUN
ap-368	80	35	and	and	CCONJ
ap-368	80	36	�	�	PROPN
ap-368	80	37	�	�	PROPN
ap-368	80	38	f	f	PROPN
ap-368	80	39	r	r	PROPN
ap-368	80	40	,	,	PUNCT
ap-368	80	41	�	�	PROPN
ap-368	80	42	represents	represent	VERB
ap-368	80	43	the	the	DET
ap-368	80	44	prescribed	prescribed	ADJ
ap-368	80	45	sound	sound	NOUN
ap-368	80	46	field	field	NOUN
ap-368	80	47	at	at	ADP
ap-368	80	48	z	z	PROPN
ap-368	80	49	�	�	PROPN
ap-368	80	50	0	0	NUM
ap-368	80	51	.	.	PUNCT
ap-368	81	1	if	if	SCONJ
ap-368	81	2	we	we	PRON
ap-368	81	3	assume	assume	VERB
ap-368	81	4	the	the	DET
ap-368	81	5	wall	wall	PROPN
ap-368	81	6	friction	friction	NOUN
ap-368	81	7	in	in	ADP
ap-368	81	8	the	the	DET
ap-368	81	9	case	case	NOUN
ap-368	81	10	that	that	SCONJ
ap-368	81	11	nonlinear	nonlinear	ADJ
ap-368	81	12	waves	wave	NOUN
ap-368	81	13	propagate	propagate	VERB
ap-368	81	14	in	in	ADP
ap-368	81	15	a	a	DET
ap-368	81	16	rigid	rigid	ADJ
ap-368	81	17	tube	tube	NOUN
ap-368	81	18	,	,	PUNCT
ap-368	81	19	then	then	ADV
ap-368	81	20	a	a	DET
ap-368	81	21	thin	thin	ADJ
ap-368	81	22	boundary	boundary	ADJ
ap-368	81	23	layer	layer	NOUN
ap-368	81	24	appears	appear	VERB
ap-368	81	25	near	near	ADP
ap-368	81	26	the	the	DET
ap-368	81	27	tube	tube	NOUN
ap-368	81	28	wall	wall	NOUN
ap-368	81	29	.	.	PUNCT
ap-368	82	1	within	within	ADP
ap-368	82	2	the	the	DET
ap-368	82	3	boundary	boundary	ADJ
ap-368	82	4	layer	layer	NOUN
ap-368	82	5	,	,	PUNCT
ap-368	82	6	the	the	DET
ap-368	82	7	velocity	velocity	NOUN
ap-368	82	8	component	component	NOUN
ap-368	82	9	in	in	ADP
ap-368	82	10	the	the	DET
ap-368	82	11	direction	direction	NOUN
ap-368	82	12	of	of	ADP
ap-368	82	13	the	the	DET
ap-368	82	14	tube	tube	NOUN
ap-368	82	15	axis	axis	NOUN
ap-368	82	16	decreases	decrease	VERB
ap-368	82	17	from	from	ADP
ap-368	82	18	a	a	DET
ap-368	82	19	mainstream	mainstream	NOUN
ap-368	82	20	value	value	NOUN
ap-368	82	21	to	to	ADP
ap-368	82	22	zero	zero	NUM
ap-368	82	23	at	at	ADP
ap-368	82	24	the	the	DET
ap-368	82	25	tube	tube	NOUN
ap-368	82	26	wall	wall	NOUN
ap-368	82	27	.	.	PUNCT
ap-368	83	1	the	the	DET
ap-368	83	2	boundary	boundary	ADJ
ap-368	83	3	layer	layer	NOUN
ap-368	83	4	affects	affect	VERB
ap-368	83	5	the	the	DET
ap-368	83	6	acoustic	acoustic	ADJ
ap-368	83	7	waves	wave	NOUN
ap-368	83	8	not	not	PART
ap-368	83	9	just	just	ADV
ap-368	83	10	near	near	ADP
ap-368	83	11	the	the	DET
ap-368	83	12	walls	wall	NOUN
ap-368	83	13	but	but	CCONJ
ap-368	83	14	in	in	ADP
ap-368	83	15	the	the	DET
ap-368	83	16	entire	entire	ADJ
ap-368	83	17	volume	volume	NOUN
ap-368	83	18	.	.	PUNCT
ap-368	84	1	the	the	DET
ap-368	84	2	boundary	boundary	ADJ
ap-368	84	3	layer	layer	NOUN
ap-368	84	4	causes	cause	VERB
ap-368	84	5	both	both	PRON
ap-368	84	6	energy	energy	NOUN
ap-368	84	7	dissipation	dissipation	NOUN
ap-368	84	8	and	and	CCONJ
ap-368	84	9	wave	wave	NOUN
ap-368	84	10	dispersion	dispersion	NOUN
ap-368	84	11	.	.	PUNCT
ap-368	85	1	if	if	SCONJ
ap-368	85	2	the	the	DET
ap-368	85	3	boundary	boundary	ADJ
ap-368	85	4	layer	layer	NOUN
ap-368	85	5	is	be	AUX
ap-368	85	6	assumed	assume	VERB
ap-368	85	7	to	to	PART
ap-368	85	8	have	have	VERB
ap-368	85	9	a	a	DET
ap-368	85	10	small	small	ADJ
ap-368	85	11	displacement	displacement	ADJ
ap-368	85	12	effect	effect	NOUN
ap-368	85	13	on	on	ADP
ap-368	85	14	the	the	DET
ap-368	85	15	mainstream	mainstream	NOUN
ap-368	85	16	,	,	PUNCT
ap-368	85	17	the	the	DET
ap-368	85	18	following	follow	VERB
ap-368	85	19	relation	relation	NOUN
ap-368	85	20	can	can	AUX
ap-368	85	21	be	be	AUX
ap-368	85	22	obtained	obtain	VERB
ap-368	85	23	,	,	PUNCT
ap-368	85	24	see	see	VERB
ap-368	85	25	[	[	X
ap-368	85	26	24	24	NUM
ap-368	85	27	]	]	PUNCT
ap-368	85	28	�	�	PROPN
ap-368	85	29	�	�	PROPN
ap-368	85	30	�	�	PROPN
ap-368	85	31	�	�	PROPN
ap-368	85	32	�	�	PROPN
ap-368	85	33	�	�	PROPN
ap-368	85	34	�	�	PROPN
ap-368	85	35	�	�	PROPN
ap-368	85	36	�	�	PROPN
ap-368	85	37	�	�	PROPN
ap-368	85	38	�	�	PROPN
ap-368	85	39	�	�	PROPN
ap-368	85	40	r	r	NOUN
ap-368	85	41	v	v	NOUN
ap-368	85	42	z	z	NOUN
ap-368	85	43	r	r	NOUN
ap-368	85	44	r	r	NOUN
ap-368	85	45	b	b	PROPN
ap-368	85	46	v	v	NOUN
ap-368	85	47	z	z	NOUN
ap-368	85	48	r	r	NOUN
ap-368	85	49	r	r	NOUN
ap-368	85	50	r	r	NOUN
ap-368	85	51	r	r	NOUN
ap-368	85	52	z	z	PROPN
ap-368	85	53	�	�	PROPN
ap-368	85	54	�	�	PROPN
ap-368	85	55	�	�	PROPN
ap-368	85	56	�	�	PROPN
ap-368	85	57	�	�	PROPN
ap-368	85	58	�	�	PROPN
ap-368	85	59	�	�	PROPN
ap-368	85	60	�	�	PROPN
ap-368	85	61	�	�	PROPN
ap-368	85	62	0	0	NUM
ap-368	85	63	1	1	NUM
ap-368	85	64	2	2	NUM
ap-368	85	65	1	1	NUM
ap-368	85	66	2	2	NUM
ap-368	85	67	0	0	NUM
ap-368	85	68	0	0	NUM
ap-368	85	69	r	r	NOUN
ap-368	85	70	,	,	PUNCT
ap-368	85	71	,	,	PUNCT
ap-368	85	72	,	,	PUNCT
ap-368	85	73	,	,	PUNCT
ap-368	85	74	.	.	PUNCT
ap-368	86	1	(	(	PUNCT
ap-368	86	2	22	22	NUM
ap-368	86	3	)	)	PUNCT
ap-368	86	4	here	here	ADV
ap-368	86	5	b	b	X
ap-368	86	6	is	be	AUX
ap-368	86	7	the	the	DET
ap-368	86	8	coefficient	coefficient	NOUN
ap-368	86	9	which	which	PRON
ap-368	86	10	is	be	AUX
ap-368	86	11	given	give	VERB
ap-368	86	12	as	as	ADP
ap-368	86	13	b	b	PROPN
ap-368	86	14	c	c	PROPN
ap-368	87	1	c	c	PROPN
ap-368	87	2	cp	cp	INTJ
ap-368	87	3	�	�	PROPN
ap-368	87	4	�	�	PROPN
ap-368	87	5	�	�	PROPN
ap-368	87	6	�	�	PROPN
ap-368	87	7	�	�	PROPN
ap-368	87	8	�	�	PROPN
ap-368	87	9	�	�	PROPN
ap-368	87	10	�	�	PROPN
ap-368	87	11	�	�	PROPN
ap-368	87	12	2	2	NUM
ap-368	87	13	1	1	NUM
ap-368	87	14	0	0	NUM
ap-368	87	15	2	2	NUM
ap-368	87	16	0	0	NUM
ap-368	87	17	2	2	NUM
ap-368	87	18	t	t	NOUN
ap-368	87	19	pr	pr	NOUN
ap-368	87	20	(	(	PUNCT
ap-368	87	21	23	23	NUM
ap-368	87	22	)	)	PUNCT
ap-368	87	23	where	where	SCONJ
ap-368	87	24	�	�	PROPN
ap-368	87	25	is	be	AUX
ap-368	87	26	the	the	DET
ap-368	87	27	kinematic	kinematic	ADJ
ap-368	87	28	viscosity	viscosity	NOUN
ap-368	87	29	,	,	PUNCT
ap-368	87	30	pr	pr	NOUN
ap-368	87	31	is	be	AUX
ap-368	87	32	the	the	DET
ap-368	87	33	prandtl	prandtl	NOUN
ap-368	87	34	number	number	NOUN
ap-368	87	35	,	,	PUNCT
ap-368	87	36	the	the	DET
ap-368	87	37	fractional	fractional	ADJ
ap-368	87	38	derivative	derivative	NOUN
ap-368	87	39	of	of	ADP
ap-368	87	40	the	the	DET
ap-368	87	41	order1	order1	NOUN
ap-368	87	42	2	2	NUM
ap-368	87	43	in	in	ADP
ap-368	87	44	eq	eq	ADP
ap-368	87	45	.	.	PUNCT
ap-368	88	1	(	(	PUNCT
ap-368	88	2	22	22	NUM
ap-368	88	3	)	)	PUNCT
ap-368	88	4	represents	represent	VERB
ap-368	88	5	the	the	DET
ap-368	88	6	following	follow	VERB
ap-368	88	7	integrodifferential	integrodifferential	ADJ
ap-368	88	8	operator	operator	NOUN
ap-368	88	9	�	�	PROPN
ap-368	88	10	�	�	PROPN
ap-368	88	11	�	�	PROPN
ap-368	88	12	�	�	PROPN
ap-368	88	13	�	�	PROPN
ap-368	88	14	�	�	PROPN
ap-368	88	15	�	�	PROPN
ap-368	88	16	�	�	PROPN
ap-368	88	17	�	�	PROPN
ap-368	88	18	�	�	PROPN
ap-368	88	19	�	�	PROPN
ap-368	88	20	�	�	PROPN
ap-368	88	21	�	�	PROPN
ap-368	88	22	�	�	PROPN
ap-368	88	23	�	�	PROPN
ap-368	88	24	�	�	PROPN
ap-368	88	25	�	�	PROPN
ap-368	88	26	�	�	PROPN
ap-368	88	27	1	1	NUM
ap-368	88	28	2	2	NUM
ap-368	88	29	1	1	NUM
ap-368	88	30	2	2	NUM
ap-368	88	31	0	0	NUM
ap-368	88	32	01	01	NUM
ap-368	88	33	v	v	NOUN
ap-368	88	34	z	z	NOUN
ap-368	88	35	r	r	NOUN
ap-368	88	36	r	r	NOUN
ap-368	88	37	v	v	NOUN
ap-368	88	38	z	z	NOUN
ap-368	88	39	r	r	NOUN
ap-368	88	40	r	r	NOUN
ap-368	88	41	z	z	NOUN
ap-368	88	42	z	z	NOUN
ap-368	88	43	,	,	PUNCT
ap-368	88	44	,	,	PUNCT
ap-368	88	45	,	,	PUNCT
ap-368	88	46	,	,	PUNCT
ap-368	88	47	�	�	PROPN
ap-368	88	48	�	�	PROPN
ap-368	88	49	�	�	PROPN
ap-368	88	50	�	�	PROPN
ap-368	88	51	�	�	PROPN
ap-368	88	52	�	�	PROPN
ap-368	88	53	�	�	PROPN
ap-368	88	54	�	�	PROPN
ap-368	88	55	�	�	PROPN
ap-368	88	56	�	�	PROPN
ap-368	88	57	�	�	PROPN
ap-368	88	58	�	�	PROPN
ap-368	88	59	(	(	PUNCT
ap-368	88	60	24	24	NUM
ap-368	88	61	)	)	PUNCT
ap-368	88	62	and	and	CCONJ
ap-368	88	63	�	�	PROPN
ap-368	88	64	t	t	PROPN
ap-368	88	65	is	be	AUX
ap-368	88	66	the	the	DET
ap-368	88	67	thermal	thermal	ADJ
ap-368	88	68	expansion	expansion	NOUN
ap-368	88	69	coefficient	coefficient	NOUN
ap-368	88	70	of	of	ADP
ap-368	88	71	the	the	DET
ap-368	88	72	fluid	fluid	ADJ
ap-368	88	73	�	�	PROPN
ap-368	88	74	�	�	PROPN
ap-368	88	75	�	�	PROPN
ap-368	88	76	�	�	PROPN
ap-368	88	77	�	�	PROPN
ap-368	88	78	t	t	PROPN
ap-368	88	79	�	�	PROPN
ap-368	88	80	�	�	PROPN
ap-368	88	81	�	�	PROPN
ap-368	88	82	�	�	PROPN
ap-368	88	83	�	�	PROPN
ap-368	88	84	�	�	PROPN
ap-368	88	85	�	�	PROPN
ap-368	89	1	1	1	NUM
ap-368	89	2	0	0	NUM
ap-368	89	3	0	0	NUM
ap-368	89	4	t	t	PROPN
ap-368	89	5	p	p	PROPN
ap-368	89	6	t	t	PROPN
ap-368	89	7	t	t	PROPN
ap-368	89	8	,	,	PUNCT
ap-368	89	9	,	,	PUNCT
ap-368	89	10	(	(	PUNCT
ap-368	89	11	25	25	NUM
ap-368	89	12	)	)	PUNCT
ap-368	89	13	where	where	SCONJ
ap-368	89	14	t	t	PROPN
ap-368	89	15	is	be	AUX
ap-368	89	16	temperature	temperature	NOUN
ap-368	89	17	.	.	PUNCT
ap-368	90	1	if	if	SCONJ
ap-368	90	2	we	we	PRON
ap-368	90	3	suppose	suppose	VERB
ap-368	90	4	a	a	DET
ap-368	90	5	perfect	perfect	ADJ
ap-368	90	6	gas	gas	NOUN
ap-368	90	7	then	then	ADV
ap-368	90	8	�	�	PROPN
ap-368	90	9	�	�	PROPN
ap-368	90	10	t	t	PROPN
ap-368	90	11	p	p	X
ap-368	90	12	c	c	PROPN
ap-368	90	13	c	c	NOUN
ap-368	90	14	0	0	NUM
ap-368	90	15	2	2	NUM
ap-368	90	16	1	1	NUM
ap-368	90	17	�	�	PROPN
ap-368	90	18	�	�	PROPN
ap-368	90	19	.	.	PUNCT
ap-368	91	1	(	(	PUNCT
ap-368	91	2	26	26	NUM
ap-368	91	3	)	)	PUNCT
ap-368	91	4	relation	relation	NOUN
ap-368	91	5	(	(	PUNCT
ap-368	91	6	22	22	NUM
ap-368	91	7	)	)	PUNCT
ap-368	91	8	is	be	AUX
ap-368	91	9	valid	valid	ADJ
ap-368	91	10	on	on	ADP
ap-368	91	11	condition	condition	NOUN
ap-368	91	12	that	that	SCONJ
ap-368	91	13	�	�	PROPN
ap-368	91	14	�	�	PROPN
ap-368	91	15	r0	r0	PROPN
ap-368	91	16	,	,	PUNCT
ap-368	91	17	�	�	PROPN
ap-368	91	18	�	�	PROPN
ap-368	91	19	�	�	PROPN
ap-368	91	20	,	,	PUNCT
ap-368	91	21	(	(	PUNCT
ap-368	91	22	27	27	NUM
ap-368	91	23	)	)	PUNCT
ap-368	91	24	where	where	SCONJ
ap-368	91	25	�	�	PROPN
ap-368	91	26	is	be	AUX
ap-368	91	27	the	the	DET
ap-368	91	28	boundary	boundary	ADJ
ap-368	91	29	layer	layer	NOUN
ap-368	91	30	thickness	thickness	PROPN
ap-368	91	31	�	�	PROPN
ap-368	91	32	�	�	PROPN
ap-368	91	33	�	�	PROPN
ap-368	91	34	�	�	PROPN
ap-368	91	35	~	~	PUNCT
ap-368	91	36	,	,	PUNCT
ap-368	91	37	(	(	PUNCT
ap-368	91	38	28	28	NUM
ap-368	91	39	)	)	PUNCT
ap-368	91	40	where	where	SCONJ
ap-368	91	41	�	�	PROPN
ap-368	91	42	is	be	AUX
ap-368	91	43	an	an	DET
ap-368	91	44	angular	angular	ADJ
ap-368	91	45	frequency	frequency	NOUN
ap-368	91	46	.	.	PUNCT
ap-368	91	47	differentiating	differentiate	VERB
ap-368	91	48	eq.(14	eq.(14	NOUN
ap-368	91	49	)	)	PUNCT
ap-368	91	50	with	with	ADP
ap-368	91	51	respect	respect	NOUN
ap-368	91	52	to	to	ADP
ap-368	91	53	r	r	NOUN
ap-368	91	54	,	,	PUNCT
ap-368	91	55	we	we	PRON
ap-368	91	56	get	get	VERB
ap-368	91	57	the	the	DET
ap-368	91	58	equation	equation	NOUN
ap-368	91	59	(	(	PUNCT
ap-368	91	60	the	the	DET
ap-368	91	61	irrotationality	irrotationality	NOUN
ap-368	91	62	condition	condition	NOUN
ap-368	91	63	)	)	PUNCT
ap-368	91	64	�	�	PROPN
ap-368	91	65	�	�	PROPN
ap-368	91	66	�	�	PROPN
ap-368	91	67	�	�	PROPN
ap-368	91	68	�	�	PROPN
ap-368	91	69	v	v	ADP
ap-368	91	70	r	r	NOUN
ap-368	91	71	c	c	NOUN
ap-368	91	72	vz	vz	SYM
ap-368	91	73	r	r	X
ap-368	91	74	�	�	X
ap-368	91	75	�	�	PROPN
ap-368	91	76	1	1	NUM
ap-368	91	77	0	0	NUM
ap-368	91	78	.	.	PUNCT
ap-368	92	1	(	(	PUNCT
ap-368	92	2	29	29	NUM
ap-368	92	3	)	)	PUNCT
ap-368	92	4	if	if	SCONJ
ap-368	92	5	we	we	PRON
ap-368	92	6	take	take	VERB
ap-368	92	7	into	into	ADP
ap-368	92	8	account	account	PROPN
ap-368	92	9	eqs	eqs	PROPN
ap-368	92	10	.	.	PUNCT
ap-368	93	1	(	(	PUNCT
ap-368	93	2	29	29	NUM
ap-368	93	3	)	)	PUNCT
ap-368	93	4	and	and	CCONJ
ap-368	93	5	(	(	PUNCT
ap-368	93	6	22	22	NUM
ap-368	93	7	)	)	PUNCT
ap-368	93	8	,	,	PUNCT
ap-368	93	9	we	we	PRON
ap-368	93	10	can	can	AUX
ap-368	93	11	modify	modify	VERB
ap-368	93	12	boundary	boundary	ADJ
ap-368	93	13	condition	condition	NOUN
ap-368	93	14	(	(	PUNCT
ap-368	93	15	21	21	NUM
ap-368	93	16	)	)	PUNCT
ap-368	93	17	for	for	ADP
ap-368	93	18	tubes	tube	NOUN
ap-368	93	19	with	with	ADP
ap-368	93	20	wall	wall	NOUN
ap-368	93	21	friction	friction	NOUN
ap-368	93	22	as	as	SCONJ
ap-368	93	23	follows	follow	VERB
ap-368	93	24	�	�	PROPN
ap-368	93	25	�	�	PROPN
ap-368	93	26	�	�	PROPN
ap-368	93	27	�	�	PROPN
ap-368	93	28	�	�	PROPN
ap-368	93	29	�	�	PROPN
ap-368	93	30	�	�	PROPN
ap-368	93	31	�	�	PROPN
ap-368	93	32	�	�	PROPN
ap-368	93	33	�	�	PROPN
ap-368	93	34	�	�	PROPN
ap-368	93	35	�	�	PROPN
ap-368	93	36	�	�	PROPN
ap-368	93	37	�	�	PROPN
ap-368	93	38	�	�	PROPN
ap-368	93	39	�	�	PROPN
ap-368	93	40	�	�	PROPN
ap-368	93	41	�	�	PROPN
ap-368	93	42	v	v	ADP
ap-368	93	43	r	r	NOUN
ap-368	93	44	b	b	PROPN
ap-368	93	45	c	c	NOUN
ap-368	93	46	v	v	NOUN
ap-368	93	47	z	z	NOUN
ap-368	93	48	r	r	NOUN
ap-368	93	49	b	b	PROPN
ap-368	93	50	c	c	NOUN
ap-368	93	51	v	v	NOUN
ap-368	93	52	z	z	NOUN
ap-368	93	53	z	z	NOUN
ap-368	93	54	z	z	NOUN
ap-368	93	55	�	�	PROPN
ap-368	93	56	�	�	PROPN
ap-368	93	57	�	�	PROPN
ap-368	93	58	�	�	PROPN
ap-368	93	59	�	�	PROPN
ap-368	93	60	�	�	PROPN
ap-368	93	61	�	�	PROPN
ap-368	93	62	�	�	PROPN
ap-368	93	63	�	�	PROPN
ap-368	93	64	�	�	PROPN
ap-368	93	65	�	�	PROPN
ap-368	93	66	�	�	PROPN
ap-368	93	67	0	0	NUM
ap-368	93	68	0	0	NUM
ap-368	93	69	2	2	NUM
ap-368	93	70	2	2	NUM
ap-368	93	71	3	3	NUM
ap-368	93	72	2	2	NUM
ap-368	93	73	,	,	PUNCT
ap-368	93	74	,	,	PUNCT
ap-368	93	75	d	d	PROPN
ap-368	93	76	�	�	PROPN
ap-368	93	77	�	�	PROPN
ap-368	93	78	3	3	NUM
ap-368	93	79	2	2	NUM
ap-368	93	80	0at	0at	NOUN
ap-368	93	81	r	r	NOUN
ap-368	93	82	=	=	NOUN
ap-368	93	83	r	r	NOUN
ap-368	93	84	.	.	PUNCT
ap-368	94	1	(	(	PUNCT
ap-368	94	2	30	30	NUM
ap-368	94	3	)	)	PUNCT
ap-368	94	4	after	after	ADP
ap-368	94	5	space	space	NOUN
ap-368	94	6	-	-	PUNCT
ap-368	94	7	averaging	averaging	NOUN
ap-368	94	8	over	over	ADP
ap-368	94	9	a	a	DET
ap-368	94	10	whole	whole	ADJ
ap-368	94	11	tube	tube	NOUN
ap-368	94	12	cross	cross	NOUN
ap-368	94	13	section	section	NOUN
ap-368	94	14	,	,	PUNCT
ap-368	94	15	if	if	SCONJ
ap-368	94	16	we	we	PRON
ap-368	94	17	take	take	VERB
ap-368	94	18	into	into	ADP
ap-368	94	19	account	account	NOUN
ap-368	94	20	boundary	boundary	ADJ
ap-368	94	21	condition	condition	NOUN
ap-368	94	22	(	(	PUNCT
ap-368	94	23	30	30	NUM
ap-368	94	24	)	)	PUNCT
ap-368	94	25	,	,	PUNCT
ap-368	94	26	the	the	DET
ap-368	94	27	kzk	kzk	PRON
ap-368	94	28	equation	equation	NOUN
ap-368	94	29	is	be	AUX
ap-368	94	30	reduced	reduce	VERB
ap-368	94	31	to	to	ADP
ap-368	94	32	the	the	DET
ap-368	94	33	generalized	generalize	VERB
ap-368	94	34	burgers	burger	NOUN
ap-368	94	35	equation	equation	NOUN
ap-368	94	36	(	(	PUNCT
ap-368	94	37	gbe	gbe	PROPN
ap-368	94	38	)	)	PUNCT
ap-368	94	39	�	�	PROPN
ap-368	94	40	�	�	PROPN
ap-368	94	41	�	�	PROPN
ap-368	94	42	�	�	PROPN
ap-368	94	43	�	�	PROPN
ap-368	94	44	�	�	PROPN
ap-368	94	45	�	�	PROPN
ap-368	94	46	�	�	PROPN
ap-368	94	47	�	�	PROPN
ap-368	94	48	�	�	PROPN
ap-368	94	49	�	�	PROPN
ap-368	94	50	�	�	PROPN
ap-368	94	51	�	�	PROPN
ap-368	94	52	v	v	ADP
ap-368	94	53	z	z	NOUN
ap-368	94	54	c	c	NOUN
ap-368	94	55	v	v	ADP
ap-368	94	56	v	v	PROPN
ap-368	94	57	b	b	PROPN
ap-368	94	58	v	v	ADP
ap-368	94	59	b	b	PROPN
ap-368	94	60	c	c	PROPN
ap-368	94	61	vz	vz	PROPN
ap-368	94	62	z	z	PROPN
ap-368	94	63	z	z	PROPN
ap-368	94	64	z	z	PROPN
ap-368	94	65	�	�	PROPN
ap-368	94	66	�	�	PROPN
ap-368	94	67	�	�	PROPN
ap-368	94	68	�	�	PROPN
ap-368	94	69	0	0	NUM
ap-368	94	70	2	2	NUM
ap-368	94	71	0	0	NUM
ap-368	94	72	0	0	NUM
ap-368	94	73	3	3	NUM
ap-368	94	74	22	22	NUM
ap-368	94	75	2	2	NUM
ap-368	94	76	1	1	NUM
ap-368	94	77	2	2	NUM
ap-368	94	78	1	1	NUM
ap-368	94	79	2	2	NUM
ap-368	94	80	,	,	PUNCT
ap-368	94	81	(	(	PUNCT
ap-368	94	82	31	31	NUM
ap-368	94	83	)	)	PUNCT
ap-368	94	84	where	where	SCONJ
ap-368	94	85	�	�	PROPN
ap-368	94	86	�	�	PROPN
ap-368	94	87	b	b	PROPN
ap-368	94	88	b	b	PROPN
ap-368	94	89	r0	r0	NOUN
ap-368	94	90	.	.	PUNCT
ap-368	95	1	the	the	DET
ap-368	95	2	solution	solution	NOUN
ap-368	95	3	of	of	ADP
ap-368	95	4	the	the	DET
ap-368	95	5	linearized	linearize	VERB
ap-368	95	6	gbe	gbe	NOUN
ap-368	95	7	for	for	ADP
ap-368	95	8	the	the	DET
ap-368	95	9	boundary	boundary	ADJ
ap-368	95	10	condition	condition	NOUN
ap-368	95	11	�	�	PROPN
ap-368	95	12	�	�	PROPN
ap-368	95	13	�	�	PROPN
ap-368	95	14	�	�	PROPN
ap-368	95	15	v	v	NOUN
ap-368	95	16	vz	vz	PROPN
ap-368	95	17	zm0	zm0	PROPN
ap-368	95	18	,	,	PUNCT
ap-368	95	19	sin	sin	PROPN
ap-368	95	20	�	�	PROPN
ap-368	95	21	�	�	PROPN
ap-368	95	22	�	�	PROPN
ap-368	95	23	�	�	PROPN
ap-368	95	24	can	can	AUX
ap-368	95	25	be	be	AUX
ap-368	95	26	expressed	express	VERB
ap-368	95	27	as	as	ADP
ap-368	95	28	�	�	PROPN
ap-368	95	29	�	�	PROPN
ap-368	95	30	�	�	PROPN
ap-368	95	31	�	�	PROPN
ap-368	95	32	�	�	PROPN
ap-368	95	33	�	�	PROPN
ap-368	95	34	v	v	NOUN
ap-368	95	35	v	v	PROPN
ap-368	95	36	z	z	PROPN
ap-368	95	37	zz	zz	PROPN
ap-368	95	38	zm	zm	PROPN
ap-368	95	39	�	�	PROPN
ap-368	95	40	�	�	PROPN
ap-368	95	41	�	�	PROPN
ap-368	95	42	�	�	PROPN
ap-368	95	43	exp	exp	NOUN
ap-368	95	44	sin	sin	PROPN
ap-368	95	45	�	�	PROPN
ap-368	95	46	�	�	PROPN
ap-368	95	47	�	�	PROPN
ap-368	95	48	�	�	PROPN
ap-368	95	49	�	�	PROPN
ap-368	95	50	b	b	PROPN
ap-368	95	51	b	b	PROPN
ap-368	95	52	.	.	PUNCT
ap-368	96	1	(	(	PUNCT
ap-368	96	2	32	32	NUM
ap-368	96	3	)	)	PUNCT
ap-368	96	4	where	where	SCONJ
ap-368	96	5	�	�	PROPN
ap-368	96	6	is	be	AUX
ap-368	96	7	the	the	DET
ap-368	96	8	attenuation	attenuation	NOUN
ap-368	96	9	coefficient	coefficient	NOUN
ap-368	96	10	for	for	ADP
ap-368	96	11	the	the	DET
ap-368	96	12	classical	classical	ADJ
ap-368	96	13	thermo	thermo	NOUN
ap-368	96	14	-	-	PUNCT
ap-368	96	15	viscous	viscous	ADJ
ap-368	96	16	loss	loss	NOUN
ap-368	96	17	mechanism	mechanism	NOUN
ap-368	96	18	�	�	PROPN
ap-368	96	19	�	�	PROPN
ap-368	96	20	�	�	PROPN
ap-368	96	21	�	�	PROPN
ap-368	96	22	b	b	PROPN
ap-368	96	23	c	c	PROPN
ap-368	96	24	2	2	NUM
ap-368	96	25	0	0	NUM
ap-368	96	26	0	0	NUM
ap-368	96	27	32	32	NUM
ap-368	96	28	(	(	PUNCT
ap-368	96	29	33	33	NUM
ap-368	96	30	)	)	PUNCT
ap-368	96	31	and	and	CCONJ
ap-368	96	32	the	the	DET
ap-368	96	33	attenuation	attenuation	NOUN
ap-368	96	34	coefficient	coefficient	PROPN
ap-368	96	35	�	�	PROPN
ap-368	96	36	b	b	PROPN
ap-368	96	37	represents	represent	VERB
ap-368	96	38	the	the	DET
ap-368	96	39	losses	loss	NOUN
ap-368	96	40	due	due	ADP
ap-368	96	41	to	to	ADP
ap-368	96	42	the	the	DET
ap-368	96	43	wall	wall	PROPN
ap-368	96	44	friction	friction	PROPN
ap-368	96	45	�	�	PROPN
ap-368	96	46	�	�	PROPN
ap-368	96	47	b	b	PROPN
ap-368	96	48	�	�	PROPN
ap-368	96	49	�	�	PROPN
ap-368	96	50	b	b	PROPN
ap-368	96	51	.	.	PUNCT
ap-368	97	1	(	(	PUNCT
ap-368	97	2	34	34	NUM
ap-368	97	3	)	)	PUNCT
ap-368	97	4	the	the	DET
ap-368	97	5	ratio	ratio	NOUN
ap-368	97	6	of	of	ADP
ap-368	97	7	the	the	DET
ap-368	97	8	two	two	NUM
ap-368	97	9	attenuation	attenuation	NOUN
ap-368	97	10	coefficients	coefficient	NOUN
ap-368	97	11	can	can	AUX
ap-368	97	12	be	be	AUX
ap-368	97	13	written	write	VERB
ap-368	97	14	as	as	ADP
ap-368	97	15	�	�	PROPN
ap-368	97	16	�	�	PROPN
ap-368	97	17	�	�	PROPN
ap-368	97	18	�	�	PROPN
ap-368	97	19	�	�	PROPN
ap-368	97	20	b	b	PROPN
ap-368	97	21	~	~	PUNCT
ap-368	97	22	�	�	PROPN
ap-368	97	23	r0	r0	NOUN
ap-368	97	24	.	.	PUNCT
ap-368	98	1	(	(	PUNCT
ap-368	98	2	35	35	NUM
ap-368	98	3	)	)	PUNCT
ap-368	98	4	it	it	PRON
ap-368	98	5	is	be	AUX
ap-368	98	6	obvious	obvious	ADJ
ap-368	98	7	that	that	SCONJ
ap-368	98	8	�	�	PROPN
ap-368	98	9	�	�	PROPN
ap-368	98	10	�	�	PROPN
ap-368	98	11	1for	1for	PROPN
ap-368	98	12	high	high	ADJ
ap-368	98	13	frequencies	frequency	NOUN
ap-368	98	14	but	but	CCONJ
ap-368	98	15	r0	r0	PROPN
ap-368	98	16	�	�	PROPN
ap-368	98	17	�	�	PROPN
ap-368	98	18	1	1	NUM
ap-368	98	19	because	because	SCONJ
ap-368	98	20	the	the	DET
ap-368	98	21	first	first	ADJ
ap-368	98	22	of	of	ADP
ap-368	98	23	the	the	DET
ap-368	98	24	conditions	condition	NOUN
ap-368	98	25	(	(	PUNCT
ap-368	98	26	27	27	NUM
ap-368	98	27	)	)	PUNCT
ap-368	98	28	has	have	VERB
ap-368	98	29	to	to	PART
ap-368	98	30	be	be	AUX
ap-368	98	31	satisfied	satisfied	ADJ
ap-368	98	32	.	.	PUNCT
ap-368	99	1	this	this	PRON
ap-368	99	2	means	mean	VERB
ap-368	99	3	that	that	SCONJ
ap-368	99	4	the	the	DET
ap-368	99	5	classical	classical	ADJ
ap-368	99	6	thermo	thermo	NOUN
ap-368	99	7	-	-	PUNCT
ap-368	99	8	viscous	viscous	ADJ
ap-368	99	9	losses	loss	NOUN
ap-368	99	10	dominate	dominate	VERB
ap-368	99	11	for	for	ADP
ap-368	99	12	high	high	ADJ
ap-368	99	13	frequencies	frequency	NOUN
ap-368	99	14	in	in	ADP
ap-368	99	15	comparison	comparison	NOUN
ap-368	99	16	to	to	ADP
ap-368	99	17	the	the	DET
ap-368	99	18	boundary	boundary	ADJ
ap-368	99	19	layer	layer	NOUN
ap-368	99	20	losses	loss	NOUN
ap-368	99	21	.	.	PUNCT
ap-368	100	1	consequently	consequently	ADV
ap-368	100	2	,	,	PUNCT
ap-368	100	3	the	the	DET
ap-368	100	4	condition	condition	NOUN
ap-368	100	5	�	�	PROPN
ap-368	100	6	�	�	PROPN
ap-368	100	7	�	�	PROPN
ap-368	100	8	1	1	NUM
ap-368	100	9	can	can	AUX
ap-368	100	10	not	not	PART
ap-368	100	11	be	be	AUX
ap-368	100	12	satisfied	satisfied	ADJ
ap-368	100	13	for	for	ADP
ap-368	100	14	higher	high	ADJ
ap-368	100	15	wave	wave	NOUN
ap-368	100	16	form	form	NOUN
ap-368	100	17	harmonics	harmonic	NOUN
ap-368	100	18	.	.	PUNCT
ap-368	101	1	3	3	NUM
ap-368	101	2	conditions	condition	NOUN
ap-368	101	3	for	for	ADP
ap-368	101	4	the	the	DET
ap-368	101	5	quasi	quasi	ADJ
ap-368	101	6	-	-	ADJ
ap-368	101	7	plane	plane	ADJ
ap-368	101	8	wave	wave	NOUN
ap-368	101	9	in	in	ADP
ap-368	101	10	a	a	DET
ap-368	101	11	tube	tube	NOUN
ap-368	101	12	the	the	DET
ap-368	101	13	condition	condition	NOUN
ap-368	101	14	for	for	ADP
ap-368	101	15	validity	validity	NOUN
ap-368	101	16	of	of	ADP
ap-368	101	17	the	the	DET
ap-368	101	18	kzk	kzk	PRON
ap-368	101	19	equation	equation	NOUN
ap-368	101	20	in	in	ADP
ap-368	101	21	a	a	DET
ap-368	101	22	tube	tube	NOUN
ap-368	101	23	is	be	AUX
ap-368	101	24	given	give	VERB
ap-368	101	25	by	by	ADP
ap-368	101	26	the	the	DET
ap-368	101	27	relation	relation	NOUN
ap-368	101	28	between	between	ADP
ap-368	101	29	the	the	DET
ap-368	101	30	values	value	NOUN
ap-368	101	31	of	of	ADP
ap-368	101	32	the	the	DET
ap-368	101	33	longitudinal	longitudinal	ADJ
ap-368	101	34	and	and	CCONJ
ap-368	101	35	transverse	transverse	ADJ
ap-368	101	36	velocity	velocity	NOUN
ap-368	101	37	components	component	NOUN
ap-368	101	38	v	v	ADP
ap-368	101	39	�	�	PROPN
ap-368	101	40	v	v	PROPN
ap-368	101	41	�	�	PROPN
ap-368	101	42	.	.	PUNCT
ap-368	102	1	this	this	DET
ap-368	102	2	condition	condition	NOUN
ap-368	102	3	follows	follow	VERB
ap-368	102	4	from	from	ADP
ap-368	102	5	the	the	DET
ap-368	102	6	derivation	derivation	NOUN
ap-368	102	7	of	of	ADP
ap-368	102	8	the	the	DET
ap-368	102	9	kzk	kzk	PRON
ap-368	102	10	equation	equation	NOUN
ap-368	102	11	in	in	ADP
ap-368	102	12	the	the	DET
ap-368	102	13	tube	tube	NOUN
ap-368	102	14	given	give	VERB
ap-368	102	15	above	above	ADV
ap-368	102	16	,	,	PUNCT
ap-368	102	17	see	see	VERB
ap-368	102	18	section	section	NOUN
ap-368	102	19	basic	basic	ADJ
ap-368	102	20	equations	equation	NOUN
ap-368	102	21	.	.	PUNCT
ap-368	103	1	the	the	DET
ap-368	103	2	transverse	transverse	NOUN
ap-368	103	3	velocity	velocity	NOUN
ap-368	103	4	component	component	NOUN
ap-368	103	5	relates	relate	VERB
ap-368	103	6	to	to	PART
ap-368	103	7	transverse	transverse	VERB
ap-368	103	8	diffraction	diffraction	NOUN
ap-368	103	9	.	.	PUNCT
ap-368	104	1	the	the	DET
ap-368	104	2	value	value	NOUN
ap-368	104	3	of	of	ADP
ap-368	104	4	v	v	PROPN
ap-368	104	5	�	�	PROPN
ap-368	104	6	depends	depend	VERB
ap-368	104	7	on	on	ADP
ap-368	104	8	wave	wave	NOUN
ap-368	104	9	frequency	frequency	NOUN
ap-368	104	10	,	,	PUNCT
ap-368	104	11	the	the	DET
ap-368	104	12	non	non	ADJ
ap-368	104	13	-	-	ADJ
ap-368	104	14	quasi	quasi	ADJ
ap-368	104	15	planar	planar	ADJ
ap-368	104	16	boundary	boundary	ADJ
ap-368	104	17	condition	condition	NOUN
ap-368	104	18	,	,	PUNCT
ap-368	104	19	the	the	DET
ap-368	104	20	tube	tube	NOUN
ap-368	104	21	radius	radius	NOUN
ap-368	104	22	and	and	CCONJ
ap-368	104	23	the	the	DET
ap-368	104	24	boundary	boundary	ADJ
ap-368	104	25	layer	layer	NOUN
ap-368	104	26	.	.	PUNCT
ap-368	105	1	supposing	suppose	VERB
ap-368	105	2	that	that	SCONJ
ap-368	105	3	the	the	DET
ap-368	105	4	tube	tube	NOUN
ap-368	105	5	is	be	AUX
ap-368	105	6	narrow	narrow	ADJ
ap-368	105	7	,	,	PUNCT
ap-368	105	8	the	the	DET
ap-368	105	9	influence	influence	NOUN
ap-368	105	10	of	of	ADP
ap-368	105	11	the	the	DET
ap-368	105	12	boundary	boundary	ADJ
ap-368	105	13	layer	layer	NOUN
ap-368	105	14	is	be	AUX
ap-368	105	15	significant	significant	ADJ
ap-368	105	16	.	.	PUNCT
ap-368	106	1	let	let	VERB
ap-368	106	2	us	we	PRON
ap-368	106	3	assume	assume	VERB
ap-368	106	4	that	that	SCONJ
ap-368	106	5	the	the	DET
ap-368	106	6	source	source	NOUN
ap-368	106	7	frequency	frequency	NOUN
ap-368	106	8	is	be	AUX
ap-368	106	9	lower	low	ADJ
ap-368	106	10	than	than	ADP
ap-368	106	11	the	the	DET
ap-368	106	12	cut	cut	VERB
ap-368	106	13	-	-	PUNCT
ap-368	106	14	off	off	ADP
ap-368	106	15	frequency	frequency	NOUN
ap-368	106	16	,	,	PUNCT
ap-368	106	17	thus	thus	ADV
ap-368	106	18	only	only	ADV
ap-368	106	19	plane	plane	NOUN
ap-368	106	20	-	-	PUNCT
ap-368	106	21	wave	wave	NOUN
ap-368	106	22	mode	mode	NOUN
ap-368	106	23	propagation	propagation	NOUN
ap-368	106	24	is	be	AUX
ap-368	106	25	possible	possible	ADJ
ap-368	106	26	.	.	PUNCT
ap-368	107	1	then	then	ADV
ap-368	107	2	the	the	DET
ap-368	107	3	diffraction	diffraction	NOUN
ap-368	107	4	is	be	AUX
ap-368	107	5	given	give	VERB
ap-368	107	6	by	by	ADP
ap-368	107	7	the	the	DET
ap-368	107	8	influence	influence	NOUN
ap-368	107	9	of	of	ADP
ap-368	107	10	the	the	DET
ap-368	107	11	boundary	boundary	ADJ
ap-368	107	12	layer	layer	NOUN
ap-368	107	13	only	only	ADV
ap-368	107	14	.	.	PUNCT
ap-368	108	1	when	when	SCONJ
ap-368	108	2	we	we	PRON
ap-368	108	3	now	now	ADV
ap-368	108	4	gradually	gradually	ADV
ap-368	108	5	increase	increase	VERB
ap-368	108	6	the	the	DET
ap-368	108	7	frequency	frequency	NOUN
ap-368	108	8	,	,	PUNCT
ap-368	108	9	the	the	DET
ap-368	108	10	transverse	transverse	NOUN
ap-368	108	11	component	component	NOUN
ap-368	108	12	of	of	ADP
ap-368	108	13	velocity	velocity	NOUN
ap-368	108	14	v	v	ADP
ap-368	108	15	�	�	PROPN
ap-368	108	16	also	also	ADV
ap-368	108	17	gradually	gradually	ADV
ap-368	108	18	rises	rise	VERB
ap-368	108	19	.	.	PUNCT
ap-368	109	1	as	as	ADV
ap-368	109	2	soon	soon	ADV
ap-368	109	3	as	as	SCONJ
ap-368	109	4	the	the	DET
ap-368	109	5	frequency	frequency	NOUN
ap-368	109	6	exceeds	exceed	VERB
ap-368	109	7	the	the	DET
ap-368	109	8	cut	cut	VERB
ap-368	109	9	-	-	PUNCT
ap-368	109	10	off	off	ADP
ap-368	109	11	frequency	frequency	NOUN
ap-368	109	12	of	of	ADP
ap-368	109	13	the	the	DET
ap-368	109	14	tube	tube	NOUN
ap-368	109	15	,	,	PUNCT
ap-368	109	16	the	the	DET
ap-368	109	17	transverse	transverse	NOUN
ap-368	109	18	mode	mode	NOUN
ap-368	109	19	arises	arise	VERB
ap-368	109	20	,	,	PUNCT
ap-368	109	21	thus	thus	ADV
ap-368	109	22	the	the	DET
ap-368	109	23	effect	effect	NOUN
ap-368	109	24	of	of	ADP
ap-368	109	25	transverse	transverse	NOUN
ap-368	109	26	diffraction	diffraction	NOUN
ap-368	109	27	increases	increase	VERB
ap-368	109	28	considerably	considerably	ADV
ap-368	109	29	and	and	CCONJ
ap-368	109	30	the	the	DET
ap-368	109	31	transverse	transverse	NOUN
ap-368	109	32	component	component	NOUN
ap-368	109	33	of	of	ADP
ap-368	109	34	the	the	DET
ap-368	109	35	20	20	NUM
ap-368	109	36	©	©	PROPN
ap-368	109	37	czech	czech	PROPN
ap-368	109	38	technical	technical	PROPN
ap-368	109	39	university	university	PROPN
ap-368	109	40	publishing	publishing	NOUN
ap-368	109	41	house	house	NOUN
ap-368	109	42	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	109	43	acta	acta	PROPN
ap-368	109	44	polytechnica	polytechnica	PROPN
ap-368	109	45	vol	vol	NOUN
ap-368	109	46	.	.	PUNCT
ap-368	110	1	42	42	NUM
ap-368	110	2	no	no	INTJ
ap-368	110	3	.	.	PUNCT
ap-368	111	1	4/2002	4/2002	DET
ap-368	111	2	velocity	velocity	NOUN
ap-368	111	3	significantly	significantly	ADV
ap-368	111	4	rises	rise	VERB
ap-368	111	5	.	.	PUNCT
ap-368	112	1	oscillations	oscillation	NOUN
ap-368	112	2	appear	appear	VERB
ap-368	112	3	on	on	ADP
ap-368	112	4	the	the	DET
ap-368	112	5	propagation	propagation	NOUN
ap-368	112	6	curves	curve	NOUN
ap-368	112	7	for	for	ADP
ap-368	112	8	the	the	DET
ap-368	112	9	harmonic	harmonic	ADJ
ap-368	112	10	amplitudes	amplitude	NOUN
ap-368	112	11	which	which	PRON
ap-368	112	12	were	be	AUX
ap-368	112	13	obtained	obtain	VERB
ap-368	112	14	by	by	ADP
ap-368	112	15	means	mean	NOUN
ap-368	112	16	of	of	ADP
ap-368	112	17	a	a	DET
ap-368	112	18	numerical	numerical	ADJ
ap-368	112	19	solution	solution	NOUN
ap-368	112	20	of	of	ADP
ap-368	112	21	the	the	DET
ap-368	112	22	kzk	kzk	PRON
ap-368	112	23	equation	equation	NOUN
ap-368	112	24	and	and	CCONJ
ap-368	112	25	consequently	consequently	ADV
ap-368	112	26	the	the	DET
ap-368	112	27	kzk	kzk	PRON
ap-368	112	28	equation	equation	NOUN
ap-368	112	29	loses	lose	VERB
ap-368	112	30	its	its	PRON
ap-368	112	31	accuracy	accuracy	NOUN
ap-368	112	32	.	.	PUNCT
ap-368	113	1	this	this	PRON
ap-368	113	2	means	mean	VERB
ap-368	113	3	that	that	SCONJ
ap-368	113	4	in	in	ADP
ap-368	113	5	the	the	DET
ap-368	113	6	case	case	NOUN
ap-368	113	7	of	of	ADP
ap-368	113	8	a	a	DET
ap-368	113	9	narrow	narrow	ADJ
ap-368	113	10	tube	tube	NOUN
ap-368	113	11	we	we	PRON
ap-368	113	12	can	can	AUX
ap-368	113	13	study	study	VERB
ap-368	113	14	wave	wave	NOUN
ap-368	113	15	propagation	propagation	NOUN
ap-368	113	16	only	only	ADV
ap-368	113	17	below	below	ADP
ap-368	113	18	the	the	DET
ap-368	113	19	cut	cut	VERB
ap-368	113	20	-	-	PUNCT
ap-368	113	21	off	off	ADP
ap-368	113	22	frequency	frequency	NOUN
ap-368	113	23	.	.	PUNCT
ap-368	114	1	in	in	ADP
ap-368	114	2	addition	addition	NOUN
ap-368	114	3	,	,	PUNCT
ap-368	114	4	it	it	PRON
ap-368	114	5	is	be	AUX
ap-368	114	6	not	not	PART
ap-368	114	7	possible	possible	ADJ
ap-368	114	8	to	to	PART
ap-368	114	9	study	study	VERB
ap-368	114	10	wave	wave	NOUN
ap-368	114	11	propagation	propagation	NOUN
ap-368	114	12	if	if	SCONJ
ap-368	114	13	we	we	PRON
ap-368	114	14	use	use	VERB
ap-368	114	15	a	a	DET
ap-368	114	16	boundary	boundary	ADJ
ap-368	114	17	condition	condition	NOUN
ap-368	114	18	of	of	ADP
ap-368	114	19	any	any	DET
ap-368	114	20	distinct	distinct	ADJ
ap-368	114	21	velocity	velocity	NOUN
ap-368	114	22	distribution	distribution	NOUN
ap-368	114	23	along	along	ADP
ap-368	114	24	the	the	DET
ap-368	114	25	tube	tube	NOUN
ap-368	114	26	radius	radius	NOUN
ap-368	114	27	(	(	PUNCT
ap-368	114	28	non	non	ADJ
ap-368	114	29	-	-	ADJ
ap-368	114	30	quasi	quasi	ADJ
ap-368	114	31	planar	planar	ADJ
ap-368	114	32	boundary	boundary	ADJ
ap-368	114	33	condition	condition	NOUN
ap-368	114	34	)	)	PUNCT
ap-368	114	35	.	.	PUNCT
ap-368	115	1	the	the	DET
ap-368	115	2	influence	influence	NOUN
ap-368	115	3	of	of	ADP
ap-368	115	4	the	the	DET
ap-368	115	5	boundary	boundary	ADJ
ap-368	115	6	layer	layer	NOUN
ap-368	115	7	is	be	AUX
ap-368	115	8	less	less	ADV
ap-368	115	9	significant	significant	ADJ
ap-368	115	10	in	in	ADP
ap-368	115	11	wide	wide	ADJ
ap-368	115	12	tubes	tube	NOUN
ap-368	115	13	.	.	PUNCT
ap-368	116	1	the	the	DET
ap-368	116	2	amplitudes	amplitude	NOUN
ap-368	116	3	of	of	ADP
ap-368	116	4	transverse	transverse	NOUN
ap-368	116	5	components	component	NOUN
ap-368	116	6	of	of	ADP
ap-368	116	7	velocity	velocity	NOUN
ap-368	116	8	are	be	AUX
ap-368	116	9	much	much	ADV
ap-368	116	10	lower	low	ADJ
ap-368	116	11	than	than	ADP
ap-368	116	12	in	in	ADP
ap-368	116	13	the	the	DET
ap-368	116	14	case	case	NOUN
ap-368	116	15	of	of	ADP
ap-368	116	16	narrow	narrow	ADJ
ap-368	116	17	tubes	tube	NOUN
ap-368	116	18	.	.	PUNCT
ap-368	117	1	therefore	therefore	ADV
ap-368	117	2	the	the	DET
ap-368	117	3	propagation	propagation	NOUN
ap-368	117	4	can	can	AUX
ap-368	117	5	be	be	AUX
ap-368	117	6	studied	study	VERB
ap-368	117	7	far	far	ADV
ap-368	117	8	above	above	ADP
ap-368	117	9	the	the	DET
ap-368	117	10	cut	cut	VERB
ap-368	117	11	-	-	PUNCT
ap-368	117	12	off	off	ADP
ap-368	117	13	frequency	frequency	NOUN
ap-368	117	14	even	even	ADV
ap-368	117	15	with	with	ADP
ap-368	117	16	distinct	distinct	ADJ
ap-368	117	17	velocity	velocity	NOUN
ap-368	117	18	distribution	distribution	NOUN
ap-368	117	19	along	along	ADP
ap-368	117	20	the	the	DET
ap-368	117	21	tube	tube	NOUN
ap-368	117	22	radius	radius	NOUN
ap-368	117	23	for	for	ADP
ap-368	117	24	the	the	DET
ap-368	117	25	boundary	boundary	ADJ
ap-368	117	26	condition	condition	NOUN
ap-368	117	27	.	.	PUNCT
ap-368	118	1	however	however	ADV
ap-368	118	2	,	,	PUNCT
ap-368	118	3	the	the	DET
ap-368	118	4	kzk	kzk	PRON
ap-368	118	5	equation	equation	NOUN
ap-368	118	6	can	can	AUX
ap-368	118	7	not	not	PART
ap-368	118	8	be	be	AUX
ap-368	118	9	used	use	VERB
ap-368	118	10	for	for	ADP
ap-368	118	11	the	the	DET
ap-368	118	12	boundary	boundary	ADJ
ap-368	118	13	condition	condition	NOUN
ap-368	118	14	with	with	ADP
ap-368	118	15	distinct	distinct	ADJ
ap-368	118	16	velocity	velocity	NOUN
ap-368	118	17	distribution	distribution	NOUN
ap-368	118	18	along	along	ADP
ap-368	118	19	the	the	DET
ap-368	118	20	radius	radius	NOUN
ap-368	118	21	when	when	SCONJ
ap-368	118	22	the	the	DET
ap-368	118	23	source	source	NOUN
ap-368	118	24	frequency	frequency	NOUN
ap-368	118	25	is	be	AUX
ap-368	118	26	less	less	ADJ
ap-368	118	27	than	than	ADP
ap-368	118	28	the	the	DET
ap-368	118	29	cut	cut	VERB
ap-368	118	30	-	-	PUNCT
ap-368	118	31	off	off	ADP
ap-368	118	32	frequency	frequency	NOUN
ap-368	118	33	for	for	ADP
ap-368	118	34	a	a	DET
ap-368	118	35	given	give	VERB
ap-368	118	36	tube	tube	NOUN
ap-368	118	37	.	.	PUNCT
ap-368	119	1	this	this	DET
ap-368	119	2	restriction	restriction	NOUN
ap-368	119	3	holds	hold	VERB
ap-368	119	4	for	for	ADP
ap-368	119	5	any	any	DET
ap-368	119	6	tube	tube	NOUN
ap-368	119	7	radius	radius	NOUN
ap-368	119	8	.	.	PUNCT
ap-368	120	1	if	if	SCONJ
ap-368	120	2	the	the	DET
ap-368	120	3	used	use	VERB
ap-368	120	4	frequency	frequency	NOUN
ap-368	120	5	is	be	AUX
ap-368	120	6	less	less	ADJ
ap-368	120	7	than	than	ADP
ap-368	120	8	the	the	DET
ap-368	120	9	cut	cut	VERB
ap-368	120	10	-	-	PUNCT
ap-368	120	11	off	off	ADP
ap-368	120	12	frequency	frequency	NOUN
ap-368	120	13	,	,	PUNCT
ap-368	120	14	then	then	ADV
ap-368	120	15	all	all	DET
ap-368	120	16	higher	high	ADJ
ap-368	120	17	modes	mode	NOUN
ap-368	120	18	are	be	AUX
ap-368	120	19	evanescent	evanescent	NOUN
ap-368	120	20	and	and	CCONJ
ap-368	120	21	only	only	ADV
ap-368	120	22	the	the	DET
ap-368	120	23	plane	plane	NOUN
ap-368	120	24	wave	wave	NOUN
ap-368	120	25	propagates	propagate	VERB
ap-368	120	26	along	along	ADP
ap-368	120	27	the	the	DET
ap-368	120	28	waveguide	waveguide	NOUN
ap-368	120	29	.	.	PUNCT
ap-368	121	1	however	however	ADV
ap-368	121	2	,	,	PUNCT
ap-368	121	3	the	the	DET
ap-368	121	4	kzk	kzk	PRON
ap-368	121	5	equation	equation	NOUN
ap-368	121	6	can	can	AUX
ap-368	121	7	not	not	PART
ap-368	121	8	describe	describe	VERB
ap-368	121	9	this	this	DET
ap-368	121	10	process	process	NOUN
ap-368	121	11	because	because	SCONJ
ap-368	121	12	the	the	DET
ap-368	121	13	transverse	transverse	NOUN
ap-368	121	14	component	component	NOUN
ap-368	121	15	of	of	ADP
ap-368	121	16	the	the	DET
ap-368	121	17	velocity	velocity	NOUN
ap-368	121	18	is	be	AUX
ap-368	121	19	large	large	ADJ
ap-368	121	20	and	and	CCONJ
ap-368	121	21	we	we	PRON
ap-368	121	22	can	can	AUX
ap-368	121	23	not	not	PART
ap-368	121	24	consider	consider	VERB
ap-368	121	25	the	the	DET
ap-368	121	26	kzk	kzk	DET
ap-368	121	27	equation	equation	NOUN
ap-368	121	28	to	to	PART
ap-368	121	29	be	be	AUX
ap-368	121	30	valid	valid	ADJ
ap-368	121	31	.	.	PUNCT
ap-368	122	1	the	the	DET
ap-368	122	2	cut	cut	VERB
ap-368	122	3	-	-	PUNCT
ap-368	122	4	off	off	ADP
ap-368	122	5	frequency	frequency	NOUN
ap-368	122	6	of	of	ADP
ap-368	122	7	the	the	DET
ap-368	122	8	first	first	ADJ
ap-368	122	9	symmetric	symmetric	ADJ
ap-368	122	10	mode	mode	NOUN
ap-368	122	11	in	in	ADP
ap-368	122	12	a	a	DET
ap-368	122	13	circular	circular	ADJ
ap-368	122	14	waveguide	waveguide	NOUN
ap-368	122	15	is	be	AUX
ap-368	122	16	given	give	VERB
ap-368	122	17	by	by	ADP
ap-368	122	18	the	the	DET
ap-368	122	19	formula	formula	NOUN
ap-368	122	20	f	f	PROPN
ap-368	122	21	c	c	PROPN
ap-368	122	22	k	k	PROPN
ap-368	122	23	c	c	PROPN
ap-368	122	24	rm1	rm1	PROPN
ap-368	122	25	�	�	PROPN
ap-368	122	26	�	�	PROPN
ap-368	122	27	�	�	PROPN
ap-368	122	28	0	0	NUM
ap-368	122	29	1	1	NUM
ap-368	122	30	0	0	NUM
ap-368	122	31	02	02	NUM
ap-368	122	32	2	2	NUM
ap-368	122	33	�	�	PROPN
ap-368	122	34	�	�	PROPN
ap-368	122	35	�	�	PROPN
ap-368	122	36	�	�	PROPN
ap-368	122	37	,	,	PUNCT
ap-368	122	38	(	(	PUNCT
ap-368	122	39	36	36	NUM
ap-368	122	40	)	)	PUNCT
ap-368	122	41	where	where	SCONJ
ap-368	122	42	k1	k1	PROPN
ap-368	122	43	is	be	AUX
ap-368	122	44	the	the	DET
ap-368	122	45	radial	radial	ADJ
ap-368	122	46	wave	wave	NOUN
ap-368	122	47	number	number	NOUN
ap-368	122	48	of	of	ADP
ap-368	122	49	the	the	DET
ap-368	122	50	first	first	ADJ
ap-368	122	51	mode	mode	NOUN
ap-368	122	52	and	and	CCONJ
ap-368	122	53	�	�	PROPN
ap-368	122	54	�	�	PROPN
ap-368	122	55	�	�	PROPN
ap-368	122	56	�	�	PROPN
ap-368	122	57	�	�	PROPN
ap-368	122	58	.38317	.38317	PROPN
ap-368	122	59	is	be	AUX
ap-368	122	60	the	the	DET
ap-368	122	61	first	first	ADJ
ap-368	122	62	zero	zero	NUM
ap-368	122	63	point	point	NOUN
ap-368	122	64	of	of	ADP
ap-368	122	65	the	the	DET
ap-368	122	66	bessel	bessel	NOUN
ap-368	122	67	function	function	VERB
ap-368	122	68	derivative	derivative	NOUN
ap-368	122	69	:	:	PUNCT
ap-368	122	70	�	�	PROPN
ap-368	122	71	�	�	PROPN
ap-368	122	72	�	�	PROPN
ap-368	122	73	�	�	PROPN
ap-368	122	74	�	�	PROPN
ap-368	122	75	j0	j0	PROPN
ap-368	122	76	0	0	NUM
ap-368	122	77	�	�	PROPN
ap-368	122	78	�	�	PROPN
ap-368	122	79	.	.	PUNCT
ap-368	123	1	now	now	ADV
ap-368	123	2	,	,	PUNCT
ap-368	123	3	let	let	VERB
ap-368	123	4	us	we	PRON
ap-368	123	5	suppose	suppose	VERB
ap-368	123	6	that	that	SCONJ
ap-368	123	7	the	the	DET
ap-368	123	8	time	time	NOUN
ap-368	123	9	dependency	dependency	NOUN
ap-368	123	10	of	of	ADP
ap-368	123	11	the	the	DET
ap-368	123	12	dimensionless	dimensionless	NOUN
ap-368	123	13	longitudinal	longitudinal	ADJ
ap-368	123	14	component	component	NOUN
ap-368	123	15	near	near	ADP
ap-368	123	16	the	the	DET
ap-368	123	17	source	source	NOUN
ap-368	123	18	is	be	AUX
ap-368	123	19	given	give	VERB
ap-368	123	20	as	as	ADP
ap-368	123	21	�	�	PROPN
ap-368	123	22	�	�	PROPN
ap-368	123	23	�	�	PROPN
ap-368	123	24	�	�	PROPN
ap-368	123	25	v	v	NOUN
ap-368	123	26	g	g	PROPN
ap-368	123	27	�	�	PROPN
ap-368	123	28	0	0	NUM
ap-368	123	29	�	�	PROPN
ap-368	123	30	�	�	PROPN
ap-368	123	31	sin	sin	NOUN
ap-368	123	32	,	,	PUNCT
ap-368	123	33	(	(	PUNCT
ap-368	123	34	37	37	NUM
ap-368	123	35	)	)	PUNCT
ap-368	123	36	where	where	SCONJ
ap-368	123	37	�	�	PROPN
ap-368	123	38	�	�	PROPN
ap-368	123	39	r	r	NOUN
ap-368	123	40	r0	r0	NOUN
ap-368	123	41	and	and	CCONJ
ap-368	123	42	�	�	PROPN
ap-368	123	43	�	�	PROPN
ap-368	123	44	�	�	PROPN
ap-368	123	45	�	�	PROPN
ap-368	123	46	is	be	AUX
ap-368	123	47	the	the	DET
ap-368	123	48	dimensionless	dimensionless	ADJ
ap-368	123	49	retarded	retarded	ADJ
ap-368	123	50	time	time	NOUN
ap-368	123	51	,	,	PUNCT
ap-368	123	52	which	which	PRON
ap-368	123	53	means	mean	VERB
ap-368	123	54	that	that	SCONJ
ap-368	123	55	we	we	PRON
ap-368	123	56	suppose	suppose	VERB
ap-368	123	57	a	a	DET
ap-368	123	58	mono	mono	NOUN
ap-368	123	59	-	-	PUNCT
ap-368	123	60	frequency	frequency	NOUN
ap-368	123	61	harmonic	harmonic	ADJ
ap-368	123	62	source	source	NOUN
ap-368	123	63	.	.	PUNCT
ap-368	124	1	here	here	ADV
ap-368	124	2	�	�	PROPN
ap-368	124	3	�	�	PROPN
ap-368	124	4	g0	g0	PROPN
ap-368	124	5	�	�	PROPN
ap-368	124	6	represents	represent	VERB
ap-368	124	7	the	the	DET
ap-368	124	8	function	function	NOUN
ap-368	124	9	describing	describe	VERB
ap-368	124	10	the	the	DET
ap-368	124	11	distribution	distribution	NOUN
ap-368	124	12	of	of	ADP
ap-368	124	13	the	the	DET
ap-368	124	14	longitudinal	longitudinal	ADJ
ap-368	124	15	component	component	NOUN
ap-368	124	16	along	along	ADP
ap-368	124	17	the	the	DET
ap-368	124	18	radius	radius	NOUN
ap-368	124	19	.	.	PUNCT
ap-368	125	1	then	then	ADV
ap-368	125	2	for	for	ADP
ap-368	125	3	the	the	DET
ap-368	125	4	transverse	transverse	NOUN
ap-368	125	5	component	component	NOUN
ap-368	125	6	of	of	ADP
ap-368	125	7	the	the	DET
ap-368	125	8	velocity	velocity	NOUN
ap-368	125	9	we	we	PRON
ap-368	125	10	have	have	VERB
ap-368	125	11	�	�	PROPN
ap-368	125	12	�	�	PROPN
ap-368	125	13	w	w	NOUN
ap-368	125	14	c	c	NOUN
ap-368	125	15	r	r	NOUN
ap-368	125	16	g	g	PROPN
ap-368	125	17	�	�	PROPN
ap-368	125	18	0	0	NUM
ap-368	125	19	0	0	SYM
ap-368	125	20	0	0	NUM
ap-368	125	21	�	�	PROPN
ap-368	125	22	�	�	PROPN
ap-368	125	23	�	�	PROPN
ap-368	125	24	�	�	PROPN
ap-368	125	25	�	�	PROPN
ap-368	125	26	,	,	PUNCT
ap-368	125	27	(	(	PUNCT
ap-368	125	28	38	38	NUM
ap-368	125	29	)	)	PUNCT
ap-368	125	30	where	where	SCONJ
ap-368	125	31	w	w	NOUN
ap-368	125	32	is	be	AUX
ap-368	125	33	the	the	DET
ap-368	125	34	dimensionless	dimensionless	ADJ
ap-368	125	35	transverse	transverse	NOUN
ap-368	125	36	component	component	NOUN
ap-368	125	37	of	of	ADP
ap-368	125	38	the	the	DET
ap-368	125	39	velocity	velocity	NOUN
ap-368	125	40	normalized	normalize	VERB
ap-368	125	41	in	in	ADP
ap-368	125	42	the	the	DET
ap-368	125	43	same	same	ADJ
ap-368	125	44	way	way	NOUN
ap-368	125	45	as	as	SCONJ
ap-368	125	46	the	the	DET
ap-368	125	47	longitudinal	longitudinal	ADJ
ap-368	125	48	component	component	NOUN
ap-368	125	49	v.	v.	ADP
ap-368	125	50	assuming	assume	VERB
ap-368	125	51	wave	wave	NOUN
ap-368	125	52	propagation	propagation	NOUN
ap-368	125	53	with	with	ADP
ap-368	125	54	frequency	frequency	NOUN
ap-368	125	55	�	�	PROPN
ap-368	125	56	f	f	PROPN
ap-368	125	57	equal	equal	ADJ
ap-368	125	58	to	to	ADP
ap-368	125	59	one	one	NUM
ap-368	125	60	half	half	NOUN
ap-368	125	61	of	of	ADP
ap-368	125	62	the	the	DET
ap-368	125	63	cut	cut	NOUN
ap-368	125	64	-	-	PUNCT
ap-368	125	65	off	off	ADP
ap-368	125	66	frequency	frequency	NOUN
ap-368	125	67	�	�	PROPN
ap-368	125	68	�	�	PROPN
ap-368	125	69	�	�	PROPN
ap-368	125	70	f	f	PROPN
ap-368	125	71	f	f	PROPN
ap-368	125	72	c	c	NOUN
ap-368	125	73	r	r	NOUN
ap-368	125	74	1	1	NUM
ap-368	125	75	2	2	NUM
ap-368	125	76	38317	38317	NUM
ap-368	125	77	4	4	NUM
ap-368	125	78	0	0	NUM
ap-368	125	79	0	0	NUM
ap-368	125	80	m1	m1	PROPN
ap-368	125	81	.	.	PUNCT
ap-368	126	1	�	�	PROPN
ap-368	126	2	(	(	PUNCT
ap-368	126	3	39	39	NUM
ap-368	126	4	)	)	PUNCT
ap-368	126	5	we	we	PRON
ap-368	126	6	can	can	AUX
ap-368	126	7	see	see	VERB
ap-368	126	8	that	that	PRON
ap-368	126	9	w	w	NOUN
ap-368	126	10	is	be	AUX
ap-368	126	11	equal	equal	ADJ
ap-368	126	12	to	to	ADP
ap-368	126	13	�	�	PROPN
ap-368	126	14	�	�	PROPN
ap-368	126	15	�	�	PROPN
ap-368	126	16	�	�	PROPN
ap-368	127	1	w	w	ADP
ap-368	127	2	g	g	PROPN
ap-368	127	3	g	g	PROPN
ap-368	127	4	�	�	PROPN
ap-368	127	5	�	�	PROPN
ap-368	127	6	2	2	NUM
ap-368	127	7	38317	38317	NUM
ap-368	127	8	05220	05220	NUM
ap-368	127	9	0	0	NUM
ap-368	127	10	.	.	PUNCT
ap-368	127	11	.	.	PUNCT
ap-368	128	1	�	�	PROPN
ap-368	128	2	�	�	PROPN
ap-368	128	3	�	�	PROPN
ap-368	128	4	�	�	PROPN
ap-368	128	5	�	�	PROPN
ap-368	128	6	�	�	PROPN
ap-368	128	7	�	�	PROPN
ap-368	128	8	�	�	PROPN
ap-368	128	9	.	.	PUNCT
ap-368	129	1	(	(	PUNCT
ap-368	129	2	40	40	NUM
ap-368	129	3	)	)	PUNCT
ap-368	129	4	taking	take	VERB
ap-368	129	5	into	into	ADP
ap-368	129	6	account	account	NOUN
ap-368	129	7	the	the	DET
ap-368	129	8	fact	fact	NOUN
ap-368	129	9	that	that	SCONJ
ap-368	129	10	the	the	DET
ap-368	129	11	maximum	maximum	NOUN
ap-368	129	12	of	of	ADP
ap-368	129	13	the	the	DET
ap-368	129	14	derivative	derivative	NOUN
ap-368	129	15	of	of	ADP
ap-368	129	16	the	the	DET
ap-368	129	17	commonly	commonly	ADV
ap-368	129	18	used	use	VERB
ap-368	129	19	velocity	velocity	NOUN
ap-368	129	20	distributions	distribution	NOUN
ap-368	129	21	(	(	PUNCT
ap-368	129	22	gauss	gauss	ADJ
ap-368	129	23	,	,	PUNCT
ap-368	129	24	fermi	fermi	NOUN
ap-368	129	25	)	)	PUNCT
ap-368	129	26	at	at	ADP
ap-368	129	27	the	the	DET
ap-368	129	28	boundary	boundary	NOUN
ap-368	129	29	of	of	ADP
ap-368	129	30	a	a	DET
ap-368	129	31	tube	tube	NOUN
ap-368	129	32	is	be	AUX
ap-368	129	33	of	of	ADP
ap-368	129	34	the	the	DET
ap-368	129	35	order	order	NOUN
ap-368	129	36	o(1	o(1	NOUN
ap-368	129	37	)	)	PUNCT
ap-368	129	38	,	,	PUNCT
ap-368	129	39	we	we	PRON
ap-368	129	40	can	can	AUX
ap-368	129	41	see	see	VERB
ap-368	129	42	that	that	SCONJ
ap-368	129	43	the	the	DET
ap-368	129	44	values	value	NOUN
ap-368	129	45	of	of	ADP
ap-368	129	46	v	v	NOUN
ap-368	129	47	�	�	PROPN
ap-368	129	48	and	and	CCONJ
ap-368	129	49	vz	vz	NOUN
ap-368	129	50	are	be	AUX
ap-368	129	51	comparable	comparable	ADJ
ap-368	129	52	.	.	PUNCT
ap-368	130	1	therefore	therefore	ADV
ap-368	130	2	the	the	DET
ap-368	130	3	validity	validity	NOUN
ap-368	130	4	condition	condition	NOUN
ap-368	130	5	of	of	ADP
ap-368	130	6	the	the	DET
ap-368	130	7	kzk	kzk	PRON
ap-368	130	8	equation	equation	NOUN
ap-368	130	9	is	be	AUX
ap-368	130	10	not	not	PART
ap-368	130	11	fulfilled	fulfil	VERB
ap-368	130	12	.	.	PUNCT
ap-368	131	1	we	we	PRON
ap-368	131	2	can	can	AUX
ap-368	131	3	say	say	VERB
ap-368	131	4	that	that	SCONJ
ap-368	131	5	the	the	DET
ap-368	131	6	kzk	kzk	PRON
ap-368	131	7	equation	equation	NOUN
ap-368	131	8	is	be	AUX
ap-368	131	9	valid	valid	ADJ
ap-368	131	10	only	only	ADV
ap-368	131	11	for	for	ADP
ap-368	131	12	a	a	DET
ap-368	131	13	moderate	moderate	ADJ
ap-368	131	14	distribution	distribution	NOUN
ap-368	131	15	along	along	ADP
ap-368	131	16	the	the	DET
ap-368	131	17	tube	tube	NOUN
ap-368	131	18	radius	radius	NOUN
ap-368	131	19	below	below	ADP
ap-368	131	20	the	the	DET
ap-368	131	21	cut	cut	VERB
ap-368	131	22	-	-	PUNCT
ap-368	131	23	off	off	ADP
ap-368	131	24	frequency	frequency	NOUN
ap-368	131	25	(	(	PUNCT
ap-368	131	26	for	for	ADP
ap-368	131	27	instance	instance	NOUN
ap-368	131	28	,	,	PUNCT
ap-368	131	29	a	a	DET
ap-368	131	30	plane	plane	NOUN
ap-368	131	31	wave	wave	NOUN
ap-368	131	32	which	which	PRON
ap-368	131	33	is	be	AUX
ap-368	131	34	affected	affect	VERB
ap-368	131	35	by	by	ADP
ap-368	131	36	the	the	DET
ap-368	131	37	boundary	boundary	ADJ
ap-368	131	38	layer	layer	NOUN
ap-368	131	39	)	)	PUNCT
ap-368	131	40	.	.	PUNCT
ap-368	132	1	we	we	PRON
ap-368	132	2	often	often	ADV
ap-368	132	3	read	read	VERB
ap-368	132	4	(	(	PUNCT
ap-368	132	5	e.g.	e.g.	ADV
ap-368	132	6	,	,	PUNCT
ap-368	132	7	in	in	ADP
ap-368	132	8	[	[	PUNCT
ap-368	132	9	4	4	NUM
ap-368	132	10	]	]	PUNCT
ap-368	132	11	,	,	PUNCT
ap-368	132	12	[	[	X
ap-368	132	13	29	29	NUM
ap-368	132	14	]	]	PUNCT
ap-368	132	15	)	)	PUNCT
ap-368	132	16	the	the	DET
ap-368	132	17	condition	condition	NOUN
ap-368	132	18	kr0	kr0	PROPN
ap-368	132	19	�	�	PROPN
ap-368	132	20	1	1	NUM
ap-368	132	21	from	from	ADP
ap-368	132	22	which	which	PRON
ap-368	132	23	follows	follow	VERB
ap-368	132	24	the	the	DET
ap-368	132	25	relation	relation	NOUN
ap-368	132	26	between	between	ADP
ap-368	132	27	wave	wave	NOUN
ap-368	132	28	vector	vector	NOUN
ap-368	132	29	components	component	NOUN
ap-368	132	30	k	k	PROPN
ap-368	132	31	�	�	PROPN
ap-368	132	32	k	k	PROPN
ap-368	132	33	�	�	PROPN
ap-368	132	34	.	.	PUNCT
ap-368	133	1	this	this	PRON
ap-368	133	2	means	mean	VERB
ap-368	133	3	that	that	SCONJ
ap-368	133	4	a	a	DET
ap-368	133	5	sound	sound	ADJ
ap-368	133	6	wave	wave	NOUN
ap-368	133	7	is	be	AUX
ap-368	133	8	quasi	quasi	ADJ
ap-368	133	9	-	-	ADJ
ap-368	133	10	plane	plane	NOUN
ap-368	133	11	and	and	CCONJ
ap-368	133	12	diffraction	diffraction	NOUN
ap-368	133	13	effects	effect	NOUN
ap-368	133	14	are	be	AUX
ap-368	133	15	weak	weak	ADJ
ap-368	133	16	in	in	ADP
ap-368	133	17	tubes	tube	NOUN
ap-368	133	18	.	.	PUNCT
ap-368	134	1	with	with	ADP
ap-368	134	2	regard	regard	NOUN
ap-368	134	3	to	to	ADP
ap-368	134	4	the	the	DET
ap-368	134	5	text	text	NOUN
ap-368	134	6	above	above	ADP
ap-368	134	7	we	we	PRON
ap-368	134	8	can	can	AUX
ap-368	134	9	say	say	VERB
ap-368	134	10	that	that	SCONJ
ap-368	134	11	the	the	DET
ap-368	134	12	condition	condition	NOUN
ap-368	134	13	kr0	kr0	PROPN
ap-368	134	14	�	�	PROPN
ap-368	134	15	1	1	NUM
ap-368	134	16	represents	represent	VERB
ap-368	134	17	only	only	ADV
ap-368	134	18	a	a	DET
ap-368	134	19	sufficient	sufficient	ADJ
ap-368	134	20	,	,	PUNCT
ap-368	134	21	but	but	CCONJ
ap-368	134	22	not	not	PART
ap-368	134	23	a	a	DET
ap-368	134	24	necessary	necessary	ADJ
ap-368	134	25	,	,	PUNCT
ap-368	134	26	condition	condition	NOUN
ap-368	134	27	for	for	ADP
ap-368	134	28	the	the	DET
ap-368	134	29	use	use	NOUN
ap-368	134	30	of	of	ADP
ap-368	134	31	the	the	DET
ap-368	134	32	kzk	kzk	PRON
ap-368	134	33	equation	equation	NOUN
ap-368	134	34	as	as	ADP
ap-368	134	35	a	a	DET
ap-368	134	36	model	model	NOUN
ap-368	134	37	equation	equation	NOUN
ap-368	134	38	for	for	ADP
ap-368	134	39	nonlinear	nonlinear	ADJ
ap-368	134	40	waves	wave	NOUN
ap-368	134	41	propagating	propagate	VERB
ap-368	134	42	in	in	ADP
ap-368	134	43	tubes	tube	NOUN
ap-368	134	44	.	.	PUNCT
ap-368	135	1	4	4	NUM
ap-368	135	2	numerical	numerical	ADJ
ap-368	135	3	solution	solution	NOUN
ap-368	135	4	equation	equation	NOUN
ap-368	135	5	(	(	PUNCT
ap-368	135	6	17	17	NUM
ap-368	135	7	)	)	PUNCT
ap-368	135	8	was	be	AUX
ap-368	135	9	solved	solve	VERB
ap-368	135	10	in	in	ADP
ap-368	135	11	the	the	DET
ap-368	135	12	frequency	frequency	NOUN
ap-368	135	13	domain	domain	NOUN
ap-368	135	14	.	.	PUNCT
ap-368	136	1	when	when	SCONJ
ap-368	136	2	the	the	DET
ap-368	136	3	solution	solution	NOUN
ap-368	136	4	is	be	AUX
ap-368	136	5	periodic	periodic	ADJ
ap-368	136	6	in	in	ADP
ap-368	136	7	time	time	NOUN
ap-368	136	8	(	(	PUNCT
ap-368	136	9	i.e.	i.e.	X
ap-368	136	10	,	,	PUNCT
ap-368	136	11	the	the	DET
ap-368	136	12	sound	sound	ADJ
ap-368	136	13	source	source	NOUN
ap-368	136	14	is	be	AUX
ap-368	136	15	periodic	periodic	ADJ
ap-368	136	16	in	in	ADP
ap-368	136	17	time	time	NOUN
ap-368	136	18	)	)	PUNCT
ap-368	136	19	,	,	PUNCT
ap-368	136	20	it	it	PRON
ap-368	136	21	can	can	AUX
ap-368	136	22	be	be	AUX
ap-368	136	23	expressed	express	VERB
ap-368	136	24	in	in	ADP
ap-368	136	25	the	the	DET
ap-368	136	26	form	form	NOUN
ap-368	136	27	of	of	ADP
ap-368	136	28	fourier	fourier	ADJ
ap-368	136	29	series	series	NOUN
ap-368	136	30	.	.	PUNCT
ap-368	137	1	for	for	ADP
ap-368	137	2	a	a	DET
ap-368	137	3	numerical	numerical	ADJ
ap-368	137	4	solution	solution	NOUN
ap-368	137	5	it	it	PRON
ap-368	137	6	was	be	AUX
ap-368	137	7	necessary	necessary	ADJ
ap-368	137	8	to	to	PART
ap-368	137	9	truncate	truncate	VERB
ap-368	137	10	the	the	DET
ap-368	137	11	infinite	infinite	ADJ
ap-368	137	12	number	number	NOUN
ap-368	137	13	of	of	ADP
ap-368	137	14	terms	term	NOUN
ap-368	137	15	in	in	ADP
ap-368	137	16	the	the	DET
ap-368	137	17	fourier	fourier	NOUN
ap-368	137	18	series	series	NOUN
ap-368	137	19	to	to	ADP
ap-368	137	20	*	*	NOUN
ap-368	137	21	terms	term	NOUN
ap-368	137	22	.	.	PUNCT
ap-368	138	1	then	then	ADV
ap-368	138	2	the	the	DET
ap-368	138	3	solution	solution	NOUN
ap-368	138	4	was	be	AUX
ap-368	138	5	sought	seek	VERB
ap-368	138	6	in	in	ADP
ap-368	138	7	the	the	DET
ap-368	138	8	form	form	NOUN
ap-368	138	9	�	�	PROPN
ap-368	138	10	�	�	PROPN
ap-368	138	11	�	�	PROPN
ap-368	138	12	�	�	PROPN
ap-368	138	13	�	�	PROPN
ap-368	138	14	�	�	PROPN
ap-368	138	15	v	v	NOUN
ap-368	138	16	g	g	NOUN
ap-368	138	17	n	n	PROPN
ap-368	138	18	h	h	NOUN
ap-368	138	19	nn	nn	PROPN
ap-368	138	20	n	n	CCONJ
ap-368	138	21	n	n	PRON
ap-368	138	22	m	m	PROPN
ap-368	138	23	�	�	PROPN
ap-368	138	24	�	�	PROPN
ap-368	138	25	�	�	PROPN
ap-368	138	26	�	�	PROPN
ap-368	138	27	�	�	PROPN
ap-368	138	28	�	�	PROPN
ap-368	138	29	�	�	PROPN
ap-368	138	30	�	�	PROPN
ap-368	138	31	�	�	PROPN
ap-368	138	32	�	�	PROPN
ap-368	138	33	,	,	PUNCT
ap-368	138	34	,	,	PUNCT
ap-368	138	35	,	,	PUNCT
ap-368	138	36	sin	sin	NOUN
ap-368	138	37	,	,	PUNCT
ap-368	138	38	cos	cos	PROPN
ap-368	138	39	�	�	PROPN
ap-368	138	40	�	�	PROPN
ap-368	138	41	�	�	PROPN
ap-368	138	42	1	1	NUM
ap-368	138	43	,	,	PUNCT
ap-368	138	44	(	(	PUNCT
ap-368	138	45	41	41	NUM
ap-368	138	46	)	)	PUNCT
ap-368	138	47	where	where	SCONJ
ap-368	138	48	�	�	PROPN
ap-368	138	49	�	�	PROPN
ap-368	138	50	�	�	PROPN
ap-368	138	51	�	�	PROPN
ap-368	138	52	z	z	PROPN
ap-368	138	53	v	v	NOUN
ap-368	138	54	czm	czm	NOUN
ap-368	138	55	0	0	NUM
ap-368	138	56	2	2	NUM
ap-368	138	57	and	and	CCONJ
ap-368	138	58	�	�	PROPN
ap-368	138	59	�	�	PROPN
ap-368	138	60	r	r	NOUN
ap-368	138	61	r0	r0	NOUN
ap-368	138	62	are	be	AUX
ap-368	138	63	dimensionless	dimensionless	ADJ
ap-368	138	64	coordinates	coordinate	NOUN
ap-368	138	65	.	.	PUNCT
ap-368	139	1	the	the	DET
ap-368	139	2	finite	finite	ADJ
ap-368	139	3	number	number	NOUN
ap-368	139	4	of	of	ADP
ap-368	139	5	terms	term	NOUN
ap-368	139	6	in	in	ADP
ap-368	139	7	series	series	NOUN
ap-368	139	8	(	(	PUNCT
ap-368	139	9	41	41	NUM
ap-368	139	10	)	)	PUNCT
ap-368	139	11	causes	cause	VERB
ap-368	139	12	instability	instability	NOUN
ap-368	139	13	in	in	ADP
ap-368	139	14	the	the	DET
ap-368	139	15	numerical	numerical	ADJ
ap-368	139	16	solution	solution	NOUN
ap-368	139	17	.	.	PUNCT
ap-368	140	1	when	when	SCONJ
ap-368	140	2	the	the	DET
ap-368	140	3	solution	solution	NOUN
ap-368	140	4	is	be	AUX
ap-368	140	5	approaching	approach	VERB
ap-368	140	6	the	the	DET
ap-368	140	7	region	region	NOUN
ap-368	140	8	of	of	ADP
ap-368	140	9	shock	shock	NOUN
ap-368	140	10	wave	wave	NOUN
ap-368	140	11	formation	formation	NOUN
ap-368	140	12	,	,	PUNCT
ap-368	140	13	all	all	DET
ap-368	140	14	harmonics	harmonic	NOUN
ap-368	140	15	are	be	AUX
ap-368	140	16	excited	excited	ADJ
ap-368	140	17	and	and	CCONJ
ap-368	140	18	the	the	DET
ap-368	140	19	energy	energy	NOUN
ap-368	140	20	flow	flow	NOUN
ap-368	140	21	stops	stop	VERB
ap-368	140	22	with	with	ADP
ap-368	140	23	the	the	DET
ap-368	140	24	last	last	ADJ
ap-368	140	25	harmonic	harmonic	NOUN
ap-368	140	26	,	,	PUNCT
ap-368	140	27	i.e.	i.e.	X
ap-368	140	28	,	,	PUNCT
ap-368	140	29	the	the	DET
ap-368	140	30	m	m	NOUN
ap-368	140	31	-	-	PUNCT
ap-368	140	32	th	th	VERB
ap-368	140	33	harmonic	harmonic	NOUN
ap-368	140	34	.	.	PUNCT
ap-368	141	1	this	this	DET
ap-368	141	2	effect	effect	NOUN
ap-368	141	3	causes	cause	VERB
ap-368	141	4	the	the	DET
ap-368	141	5	gibbs	gibbs	PROPN
ap-368	141	6	oscillations	oscillation	NOUN
ap-368	141	7	in	in	ADP
ap-368	141	8	the	the	DET
ap-368	141	9	numerical	numerical	ADJ
ap-368	141	10	solution	solution	NOUN
ap-368	141	11	.	.	PUNCT
ap-368	142	1	these	these	DET
ap-368	142	2	oscillations	oscillation	NOUN
ap-368	142	3	were	be	AUX
ap-368	142	4	damped	damp	VERB
ap-368	142	5	by	by	ADP
ap-368	142	6	the	the	DET
ap-368	142	7	method	method	NOUN
ap-368	142	8	described	describe	VERB
ap-368	142	9	,	,	PUNCT
ap-368	142	10	e.g.	e.g.	ADV
ap-368	142	11	,	,	PUNCT
ap-368	142	12	by	by	ADP
ap-368	142	13	fenlon	fenlon	NOUN
ap-368	142	14	[	[	X
ap-368	142	15	31	31	NUM
ap-368	142	16	]	]	PUNCT
ap-368	142	17	.	.	PUNCT
ap-368	143	1	each	each	DET
ap-368	143	2	harmonic	harmonic	NOUN
ap-368	143	3	was	be	AUX
ap-368	143	4	multiplied	multiply	VERB
ap-368	143	5	by	by	ADP
ap-368	143	6	the	the	DET
ap-368	143	7	coefficient	coefficient	NOUN
ap-368	143	8	�	�	PROPN
ap-368	143	9	n	n	CCONJ
ap-368	143	10	given	give	VERB
ap-368	143	11	by	by	ADP
ap-368	143	12	�	�	PROPN
ap-368	143	13	�	�	PROPN
ap-368	143	14	�	�	PROPN
ap-368	143	15	n	n	CCONJ
ap-368	143	16	�	�	PROPN
ap-368	143	17	sin	sin	PROPN
ap-368	143	18	nh	nh	PROPN
ap-368	143	19	nh	nh	PROPN
ap-368	143	20	,	,	PUNCT
ap-368	143	21	(	(	PUNCT
ap-368	143	22	42	42	NUM
ap-368	143	23	)	)	PUNCT
ap-368	143	24	where	where	SCONJ
ap-368	143	25	h	h	NOUN
ap-368	143	26	is	be	AUX
ap-368	143	27	the	the	DET
ap-368	143	28	frequency	frequency	NOUN
ap-368	143	29	damping	damp	VERB
ap-368	143	30	coefficient	coefficient	NOUN
ap-368	143	31	.	.	PUNCT
ap-368	144	1	this	this	PRON
ap-368	144	2	causes	cause	VERB
ap-368	144	3	the	the	DET
ap-368	144	4	additional	additional	ADJ
ap-368	144	5	artificial	artificial	ADJ
ap-368	144	6	attenuation	attenuation	NOUN
ap-368	144	7	of	of	ADP
ap-368	144	8	the	the	DET
ap-368	144	9	solution	solution	NOUN
ap-368	144	10	.	.	PUNCT
ap-368	145	1	the	the	DET
ap-368	145	2	value	value	NOUN
ap-368	145	3	of	of	ADP
ap-368	145	4	h	h	NOUN
ap-368	145	5	was	be	AUX
ap-368	145	6	chosen	choose	VERB
ap-368	145	7	so	so	SCONJ
ap-368	145	8	that	that	SCONJ
ap-368	145	9	gibbs	gibbs	PROPN
ap-368	145	10	oscillations	oscillation	NOUN
ap-368	145	11	practically	practically	ADV
ap-368	145	12	did	do	AUX
ap-368	145	13	not	not	PART
ap-368	145	14	arise	arise	VERB
ap-368	145	15	.	.	PUNCT
ap-368	146	1	during	during	ADP
ap-368	146	2	the	the	DET
ap-368	146	3	assembling	assembling	NOUN
ap-368	146	4	of	of	ADP
ap-368	146	5	the	the	DET
ap-368	146	6	numerical	numerical	ADJ
ap-368	146	7	schema	schema	NOUN
ap-368	146	8	we	we	PRON
ap-368	146	9	proceeded	proceed	VERB
ap-368	146	10	from	from	ADP
ap-368	146	11	the	the	DET
ap-368	146	12	well	well	ADV
ap-368	146	13	known	know	VERB
ap-368	146	14	bergen	bergen	PROPN
ap-368	146	15	code	code	NOUN
ap-368	146	16	[	[	X
ap-368	146	17	32	32	NUM
ap-368	146	18	]	]	PUNCT
ap-368	146	19	,	,	PUNCT
ap-368	146	20	which	which	PRON
ap-368	146	21	was	be	AUX
ap-368	146	22	extended	extend	VERB
ap-368	146	23	by	by	ADP
ap-368	146	24	terms	term	NOUN
ap-368	146	25	including	include	VERB
ap-368	146	26	the	the	DET
ap-368	146	27	boundary	boundary	ADJ
ap-368	146	28	layer	layer	NOUN
ap-368	146	29	influence	influence	NOUN
ap-368	146	30	.	.	PUNCT
ap-368	147	1	simple	simple	ADJ
ap-368	147	2	iteration	iteration	NOUN
ap-368	147	3	by	by	ADP
ap-368	147	4	the	the	DET
ap-368	147	5	lu	lu	PROPN
ap-368	147	6	decomposition	decomposition	NOUN
ap-368	147	7	method	method	NOUN
ap-368	147	8	was	be	AUX
ap-368	147	9	used	use	VERB
ap-368	147	10	to	to	PART
ap-368	147	11	calculate	calculate	VERB
ap-368	147	12	the	the	DET
ap-368	147	13	solution	solution	NOUN
ap-368	147	14	in	in	ADP
ap-368	147	15	the	the	DET
ap-368	147	16	next	next	ADJ
ap-368	147	17	layer	layer	NOUN
ap-368	147	18	.	.	PUNCT
ap-368	148	1	if	if	SCONJ
ap-368	148	2	we	we	PRON
ap-368	148	3	use	use	VERB
ap-368	148	4	lu	lu	NOUN
ap-368	148	5	decomposition	decomposition	NOUN
ap-368	148	6	,	,	PUNCT
ap-368	148	7	then	then	ADV
ap-368	148	8	the	the	DET
ap-368	148	9	calculations	calculation	NOUN
ap-368	148	10	take	take	VERB
ap-368	148	11	approximately	approximately	ADV
ap-368	148	12	three	three	NUM
ap-368	148	13	times	time	NOUN
ap-368	148	14	longer	long	ADV
ap-368	148	15	than	than	ADP
ap-368	148	16	in	in	ADP
ap-368	148	17	the	the	DET
ap-368	148	18	case	case	NOUN
ap-368	148	19	of	of	ADP
ap-368	148	20	calculation	calculation	NOUN
ap-368	148	21	by	by	ADP
ap-368	148	22	means	mean	NOUN
ap-368	148	23	of	of	ADP
ap-368	148	24	simple	simple	ADJ
ap-368	148	25	iteration	iteration	NOUN
ap-368	148	26	.	.	PUNCT
ap-368	149	1	however	however	ADV
ap-368	149	2	,	,	PUNCT
ap-368	149	3	lu	lu	PROPN
ap-368	149	4	decomposition	decomposition	NOUN
ap-368	149	5	is	be	AUX
ap-368	149	6	not	not	PART
ap-368	149	7	restricted	restrict	VERB
ap-368	149	8	by	by	ADP
ap-368	149	9	the	the	DET
ap-368	149	10	condition	condition	NOUN
ap-368	149	11	on	on	ADP
ap-368	149	12	the	the	DET
ap-368	149	13	step	step	NOUN
ap-368	149	14	size	size	NOUN
ap-368	149	15	in	in	ADP
ap-368	149	16	the	the	DET
ap-368	149	17	direction	direction	NOUN
ap-368	149	18	of	of	ADP
ap-368	149	19	propagation	propagation	NOUN
ap-368	149	20	.	.	PUNCT
ap-368	150	1	application	application	NOUN
ap-368	150	2	of	of	ADP
ap-368	150	3	this	this	DET
ap-368	150	4	method	method	NOUN
ap-368	150	5	is	be	AUX
ap-368	150	6	very	very	ADV
ap-368	150	7	convenient	convenient	ADJ
ap-368	150	8	in	in	ADP
ap-368	150	9	the	the	DET
ap-368	150	10	case	case	NOUN
ap-368	150	11	when	when	SCONJ
ap-368	150	12	it	it	PRON
ap-368	150	13	is	be	AUX
ap-368	150	14	necessary	necessary	ADJ
ap-368	150	15	to	to	PART
ap-368	150	16	carry	carry	VERB
ap-368	150	17	out	out	ADP
ap-368	150	18	a	a	DET
ap-368	150	19	very	very	ADV
ap-368	150	20	large	large	ADJ
ap-368	150	21	number	number	NOUN
ap-368	150	22	of	of	ADP
ap-368	150	23	iterations	iteration	NOUN
ap-368	150	24	by	by	ADP
ap-368	150	25	means	mean	NOUN
ap-368	150	26	of	of	ADP
ap-368	150	27	the	the	DET
ap-368	150	28	simple	simple	ADJ
ap-368	150	29	iteration	iteration	NOUN
ap-368	150	30	method	method	NOUN
ap-368	150	31	.	.	PUNCT
ap-368	151	1	for	for	ADP
ap-368	151	2	example	example	NOUN
ap-368	151	3	,	,	PUNCT
ap-368	151	4	we	we	PRON
ap-368	151	5	need	need	VERB
ap-368	151	6	500000	500000	NUM
ap-368	151	7	steps	step	NOUN
ap-368	151	8	for	for	ADP
ap-368	151	9	the	the	DET
ap-368	151	10	simple	simple	ADJ
ap-368	151	11	iteration	iteration	NOUN
ap-368	151	12	method	method	NOUN
ap-368	151	13	and	and	CCONJ
ap-368	151	14	only	only	ADV
ap-368	151	15	400	400	NUM
ap-368	151	16	steps	step	NOUN
ap-368	151	17	for	for	ADP
ap-368	151	18	lu	lu	NOUN
ap-368	151	19	decomposition	decomposition	NOUN
ap-368	151	20	for	for	ADP
ap-368	151	21	a	a	DET
ap-368	151	22	tube	tube	NOUN
ap-368	151	23	4	4	NUM
ap-368	151	24	mm	mm	NOUN
ap-368	151	25	in	in	ADP
ap-368	151	26	radius	radius	NOUN
ap-368	151	27	.	.	PUNCT
ap-368	152	1	the	the	DET
ap-368	152	2	burgers	burger	NOUN
ap-368	152	3	equation	equation	NOUN
ap-368	152	4	was	be	AUX
ap-368	152	5	solved	solve	VERB
ap-368	152	6	in	in	ADP
ap-368	152	7	the	the	DET
ap-368	152	8	frequency	frequency	NOUN
ap-368	152	9	domain	domain	NOUN
ap-368	152	10	by	by	ADP
ap-368	152	11	means	mean	NOUN
ap-368	152	12	of	of	ADP
ap-368	152	13	the	the	DET
ap-368	152	14	standard	standard	ADJ
ap-368	152	15	runge	runge	NOUN
ap-368	152	16	-	-	PUNCT
ap-368	152	17	kutta	kutta	NOUN
ap-368	152	18	method	method	NOUN
ap-368	152	19	of	of	ADP
ap-368	152	20	the	the	DET
ap-368	152	21	fourth	fourth	ADJ
ap-368	152	22	order	order	NOUN
ap-368	152	23	.	.	PUNCT
ap-368	153	1	©	©	PROPN
ap-368	153	2	czech	czech	PROPN
ap-368	153	3	technical	technical	PROPN
ap-368	153	4	university	university	PROPN
ap-368	153	5	publishing	publishing	NOUN
ap-368	153	6	house	house	NOUN
ap-368	153	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	153	8	21	21	NUM
ap-368	153	9	acta	acta	PROPN
ap-368	153	10	polytechnica	polytechnica	PROPN
ap-368	153	11	vol	vol	NOUN
ap-368	153	12	.	.	PUNCT
ap-368	154	1	42	42	NUM
ap-368	154	2	no	no	INTJ
ap-368	154	3	.	.	PUNCT
ap-368	155	1	4/2002	4/2002	NUM
ap-368	155	2	5	5	NUM
ap-368	155	3	results	result	NOUN
ap-368	155	4	of	of	ADP
ap-368	155	5	a	a	DET
ap-368	155	6	numerical	numerical	ADJ
ap-368	155	7	solution	solution	NOUN
ap-368	155	8	of	of	ADP
ap-368	155	9	the	the	DET
ap-368	155	10	kzk	kzk	PRON
ap-368	155	11	equation	equation	NOUN
ap-368	155	12	5.1	5.1	NUM
ap-368	155	13	a	a	DET
ap-368	155	14	narrow	narrow	ADJ
ap-368	155	15	tube	tube	NOUN
ap-368	155	16	the	the	DET
ap-368	155	17	presented	present	VERB
ap-368	155	18	distributions	distribution	NOUN
ap-368	155	19	represent	represent	VERB
ap-368	155	20	the	the	DET
ap-368	155	21	deformation	deformation	NOUN
ap-368	155	22	of	of	ADP
ap-368	155	23	a	a	DET
ap-368	155	24	plane	plane	NOUN
ap-368	155	25	wave	wave	NOUN
ap-368	155	26	under	under	ADP
ap-368	155	27	the	the	DET
ap-368	155	28	influence	influence	NOUN
ap-368	155	29	of	of	ADP
ap-368	155	30	the	the	DET
ap-368	155	31	boundary	boundary	ADJ
ap-368	155	32	layer	layer	NOUN
ap-368	155	33	for	for	ADP
ap-368	155	34	a	a	DET
ap-368	155	35	narrow	narrow	ADJ
ap-368	155	36	tube	tube	NOUN
ap-368	155	37	,	,	PUNCT
ap-368	155	38	where	where	SCONJ
ap-368	155	39	the	the	DET
ap-368	155	40	boundary	boundary	ADJ
ap-368	155	41	layer	layer	NOUN
ap-368	155	42	effect	effect	NOUN
ap-368	155	43	is	be	AUX
ap-368	155	44	very	very	ADV
ap-368	155	45	important	important	ADJ
ap-368	155	46	.	.	PUNCT
ap-368	156	1	the	the	DET
ap-368	156	2	calculations	calculation	NOUN
ap-368	156	3	are	be	AUX
ap-368	156	4	done	do	VERB
ap-368	156	5	for	for	ADP
ap-368	156	6	particle	particle	NOUN
ap-368	156	7	velocity	velocity	NOUN
ap-368	156	8	amplitude	amplitude	NOUN
ap-368	156	9	vm	vm	PROPN
ap-368	156	10	�	�	PROPN
ap-368	156	11	2.76	2.76	NUM
ap-368	156	12	m	m	PROPN
ap-368	156	13	�	�	PROPN
ap-368	156	14	s	s	PART
ap-368	156	15	�	�	NOUN
ap-368	156	16	1	1	NUM
ap-368	156	17	,	,	PUNCT
ap-368	156	18	tube	tube	NOUN
ap-368	156	19	radius	radius	NOUN
ap-368	156	20	r0	r0	PROPN
ap-368	156	21	�	�	PROPN
ap-368	156	22	0.004	0.004	NUM
ap-368	156	23	m	m	NOUN
ap-368	156	24	,	,	PUNCT
ap-368	156	25	and	and	CCONJ
ap-368	156	26	for	for	ADP
ap-368	156	27	the	the	DET
ap-368	156	28	following	follow	VERB
ap-368	156	29	six	six	NUM
ap-368	156	30	frequencies	frequency	NOUN
ap-368	156	31	1	1	NUM
ap-368	156	32	khz	khz	NOUN
ap-368	156	33	,	,	PUNCT
ap-368	156	34	10	10	NUM
ap-368	156	35	khz	khz	NOUN
ap-368	156	36	,	,	PUNCT
ap-368	156	37	40	40	NUM
ap-368	156	38	khz	khz	NOUN
ap-368	156	39	,	,	PUNCT
ap-368	156	40	60	60	NUM
ap-368	156	41	khz	khz	NOUN
ap-368	156	42	,	,	PUNCT
ap-368	156	43	100	100	NUM
ap-368	156	44	khz	khz	NOUN
ap-368	156	45	and	and	CCONJ
ap-368	156	46	500	500	NUM
ap-368	156	47	khz	khz	NOUN
ap-368	156	48	.	.	PUNCT
ap-368	157	1	the	the	DET
ap-368	157	2	cut	cut	VERB
ap-368	157	3	-	-	PUNCT
ap-368	157	4	off	off	ADP
ap-368	157	5	frequency	frequency	NOUN
ap-368	157	6	of	of	ADP
ap-368	157	7	the	the	DET
ap-368	157	8	first	first	ADJ
ap-368	157	9	symmetric	symmetric	ADJ
ap-368	157	10	mode	mode	NOUN
ap-368	157	11	for	for	ADP
ap-368	157	12	the	the	DET
ap-368	157	13	given	give	VERB
ap-368	157	14	tube	tube	NOUN
ap-368	157	15	is	be	AUX
ap-368	157	16	approximately	approximately	ADV
ap-368	157	17	equal	equal	ADJ
ap-368	157	18	to	to	ADP
ap-368	157	19	52	52	NUM
ap-368	157	20	khz	khz	NOUN
ap-368	157	21	.	.	PUNCT
ap-368	158	1	the	the	DET
ap-368	158	2	first	first	ADJ
ap-368	158	3	100	100	NUM
ap-368	158	4	harmonics	harmonic	NOUN
ap-368	158	5	were	be	AUX
ap-368	158	6	used	use	VERB
ap-368	158	7	in	in	ADP
ap-368	158	8	the	the	DET
ap-368	158	9	numerical	numerical	ADJ
ap-368	158	10	calculation	calculation	NOUN
ap-368	158	11	,	,	PUNCT
ap-368	158	12	the	the	DET
ap-368	158	13	numerical	numerical	ADJ
ap-368	158	14	step	step	NOUN
ap-368	158	15	in	in	ADP
ap-368	158	16	the	the	DET
ap-368	158	17	direction	direction	NOUN
ap-368	158	18	of	of	ADP
ap-368	158	19	the	the	DET
ap-368	158	20	wave	wave	NOUN
ap-368	158	21	propagation	propagation	NOUN
ap-368	158	22	was	be	AUX
ap-368	158	23	�	�	PROPN
ap-368	158	24	�	�	PROPN
ap-368	158	25	�	�	PROPN
ap-368	158	26	0.01	0.01	NUM
ap-368	158	27	for	for	ADP
ap-368	158	28	the	the	DET
ap-368	158	29	burgers	burger	NOUN
ap-368	158	30	equation	equation	NOUN
ap-368	158	31	.	.	PUNCT
ap-368	159	1	the	the	DET
ap-368	159	2	value	value	NOUN
ap-368	159	3	of	of	ADP
ap-368	159	4	the	the	DET
ap-368	159	5	numerical	numerical	ADJ
ap-368	159	6	step	step	NOUN
ap-368	159	7	for	for	ADP
ap-368	159	8	the	the	DET
ap-368	159	9	kzk	kzk	PRON
ap-368	159	10	equation	equation	NOUN
ap-368	159	11	was	be	AUX
ap-368	159	12	determined	determine	VERB
ap-368	159	13	from	from	ADP
ap-368	159	14	this	this	DET
ap-368	159	15	step	step	NOUN
ap-368	159	16	,	,	PUNCT
ap-368	159	17	so	so	CCONJ
ap-368	159	18	the	the	DET
ap-368	159	19	total	total	ADJ
ap-368	159	20	number	number	NOUN
ap-368	159	21	of	of	ADP
ap-368	159	22	steps	step	NOUN
ap-368	159	23	was	be	AUX
ap-368	159	24	identical	identical	ADJ
ap-368	159	25	for	for	ADP
ap-368	159	26	the	the	DET
ap-368	159	27	gbe	gbe	PROPN
ap-368	159	28	and	and	CCONJ
ap-368	159	29	kzk	kzk	VERB
ap-368	159	30	equation	equation	NOUN
ap-368	159	31	.	.	PUNCT
ap-368	160	1	the	the	DET
ap-368	160	2	kzk	kzk	PROPN
ap-368	160	3	equation	equation	NOUN
ap-368	160	4	was	be	AUX
ap-368	160	5	solved	solve	VERB
ap-368	160	6	with	with	ADP
ap-368	160	7	the	the	DET
ap-368	160	8	plane	plane	NOUN
ap-368	160	9	boundary	boundary	ADJ
ap-368	160	10	condition	condition	NOUN
ap-368	160	11	.	.	PUNCT
ap-368	161	1	the	the	DET
ap-368	161	2	numerical	numerical	ADJ
ap-368	161	3	step	step	NOUN
ap-368	161	4	in	in	ADP
ap-368	161	5	the	the	DET
ap-368	161	6	direction	direction	NOUN
ap-368	161	7	of	of	ADP
ap-368	161	8	the	the	DET
ap-368	161	9	tube	tube	NOUN
ap-368	161	10	radius	radius	NOUN
ap-368	161	11	was	be	AUX
ap-368	161	12	chosen	choose	VERB
ap-368	161	13	�	�	PROPN
ap-368	161	14	�	�	PROPN
ap-368	161	15	�	�	PROPN
ap-368	161	16	0.05	0.05	NUM
ap-368	161	17	.	.	PUNCT
ap-368	162	1	the	the	DET
ap-368	162	2	calculations	calculation	NOUN
ap-368	162	3	are	be	AUX
ap-368	162	4	realized	realize	VERB
ap-368	162	5	for	for	ADP
ap-368	162	6	the	the	DET
ap-368	162	7	case	case	NOUN
ap-368	162	8	of	of	ADP
ap-368	162	9	propagation	propagation	NOUN
ap-368	162	10	in	in	ADP
ap-368	162	11	air	air	NOUN
ap-368	162	12	.	.	PUNCT
ap-368	163	1	the	the	DET
ap-368	163	2	source	source	NOUN
ap-368	163	3	oscillated	oscillate	VERB
ap-368	163	4	harmonically	harmonically	ADV
ap-368	163	5	with	with	ADP
ap-368	163	6	one	one	NUM
ap-368	163	7	frequency	frequency	NOUN
ap-368	163	8	.	.	PUNCT
ap-368	164	1	for	for	ADP
ap-368	164	2	all	all	DET
ap-368	164	3	calculations	calculation	NOUN
ap-368	164	4	we	we	PRON
ap-368	164	5	used	use	VERB
ap-368	164	6	the	the	DET
ap-368	164	7	numerical	numerical	ADJ
ap-368	164	8	attenuation	attenuation	PROPN
ap-368	164	9	coefficient	coefficient	PROPN
ap-368	164	10	h	h	PROPN
ap-368	164	11	�	�	PROPN
ap-368	164	12	40	40	NUM
ap-368	164	13	.	.	PUNCT
ap-368	165	1	figures	figure	NOUN
ap-368	165	2	1–3	1–3	NUM
ap-368	165	3	contain	contain	VERB
ap-368	165	4	three	three	NUM
ap-368	165	5	curves	curve	NOUN
ap-368	165	6	:	:	PUNCT
ap-368	165	7	curve	curve	NOUN
ap-368	165	8	1	1	NUM
ap-368	165	9	is	be	AUX
ap-368	165	10	the	the	DET
ap-368	165	11	numerical	numerical	ADJ
ap-368	165	12	solution	solution	NOUN
ap-368	165	13	of	of	ADP
ap-368	165	14	the	the	DET
ap-368	165	15	gbe	gbe	NOUN
ap-368	165	16	,	,	PUNCT
ap-368	165	17	curve	curve	NOUN
ap-368	165	18	2	2	NUM
ap-368	165	19	is	be	AUX
ap-368	165	20	the	the	DET
ap-368	165	21	longitudinal	longitudinal	ADJ
ap-368	165	22	component	component	NOUN
ap-368	165	23	of	of	ADP
ap-368	165	24	the	the	DET
ap-368	165	25	velocity	velocity	NOUN
ap-368	165	26	obtained	obtain	VERB
ap-368	165	27	by	by	ADP
ap-368	165	28	the	the	DET
ap-368	165	29	numerical	numerical	ADJ
ap-368	165	30	solution	solution	NOUN
ap-368	165	31	of	of	ADP
ap-368	165	32	the	the	DET
ap-368	165	33	kzk	kzk	PRON
ap-368	165	34	equation	equation	NOUN
ap-368	165	35	,	,	PUNCT
ap-368	165	36	and	and	CCONJ
ap-368	165	37	curve	curve	NOUN
ap-368	165	38	3	3	NUM
ap-368	165	39	represents	represent	VERB
ap-368	165	40	the	the	DET
ap-368	165	41	transverse	transverse	NOUN
ap-368	165	42	velocity	velocity	NOUN
ap-368	165	43	component	component	NOUN
ap-368	165	44	which	which	PRON
ap-368	165	45	is	be	AUX
ap-368	165	46	calculated	calculate	VERB
ap-368	165	47	from	from	ADP
ap-368	165	48	the	the	DET
ap-368	165	49	longitudinal	longitudinal	ADJ
ap-368	165	50	velocity	velocity	NOUN
ap-368	165	51	across	across	ADP
ap-368	165	52	the	the	DET
ap-368	165	53	tube	tube	NOUN
ap-368	165	54	radius	radius	NOUN
ap-368	165	55	using	use	VERB
ap-368	165	56	eq	eq	X
ap-368	165	57	.	.	PUNCT
ap-368	166	1	(	(	PUNCT
ap-368	166	2	18	18	NUM
ap-368	166	3	)	)	PUNCT
ap-368	166	4	.	.	PUNCT
ap-368	167	1	the	the	DET
ap-368	167	2	values	value	NOUN
ap-368	167	3	of	of	ADP
ap-368	167	4	curve	curve	NOUN
ap-368	167	5	3	3	NUM
ap-368	167	6	are	be	AUX
ap-368	167	7	multiplied	multiply	VERB
ap-368	167	8	100	100	NUM
ap-368	167	9	times	time	NOUN
ap-368	167	10	and	and	CCONJ
ap-368	167	11	calibrated	calibrate	VERB
ap-368	167	12	in	in	ADP
ap-368	167	13	the	the	DET
ap-368	167	14	same	same	ADJ
ap-368	167	15	way	way	NOUN
ap-368	167	16	as	as	SCONJ
ap-368	167	17	the	the	DET
ap-368	167	18	longitudinal	longitudinal	ADJ
ap-368	167	19	component	component	NOUN
ap-368	167	20	of	of	ADP
ap-368	167	21	the	the	DET
ap-368	167	22	velocity	velocity	NOUN
ap-368	167	23	to	to	PART
ap-368	167	24	enable	enable	VERB
ap-368	167	25	the	the	DET
ap-368	167	26	two	two	NUM
ap-368	167	27	velocity	velocity	NOUN
ap-368	167	28	components	component	NOUN
ap-368	167	29	to	to	PART
ap-368	167	30	be	be	AUX
ap-368	167	31	compared	compare	VERB
ap-368	167	32	easily	easily	ADV
ap-368	167	33	.	.	PUNCT
ap-368	168	1	curves	curve	NOUN
ap-368	168	2	2	2	NUM
ap-368	168	3	and	and	CCONJ
ap-368	168	4	3	3	NUM
ap-368	168	5	are	be	AUX
ap-368	168	6	depicted	depict	VERB
ap-368	168	7	for	for	ADP
ap-368	168	8	the	the	DET
ap-368	168	9	radius	radius	PROPN
ap-368	168	10	�	�	PROPN
ap-368	168	11	�	�	PROPN
ap-368	168	12	05	05	NUM
ap-368	168	13	.	.	PUNCT
ap-368	168	14	.	.	PUNCT
ap-368	169	1	owing	owe	VERB
ap-368	169	2	to	to	ADP
ap-368	169	3	the	the	DET
ap-368	169	4	fact	fact	NOUN
ap-368	169	5	that	that	SCONJ
ap-368	169	6	the	the	DET
ap-368	169	7	resultant	resultant	NOUN
ap-368	169	8	space	space	NOUN
ap-368	169	9	evolutions	evolution	NOUN
ap-368	169	10	correspond	correspond	VERB
ap-368	169	11	to	to	ADP
ap-368	169	12	practically	practically	ADV
ap-368	169	13	plane	plane	NOUN
ap-368	169	14	waves	wave	NOUN
ap-368	169	15	,	,	PUNCT
ap-368	169	16	the	the	DET
ap-368	169	17	choice	choice	NOUN
ap-368	169	18	of	of	ADP
ap-368	169	19	this	this	DET
ap-368	169	20	radius	radius	NOUN
ap-368	169	21	is	be	AUX
ap-368	169	22	not	not	PART
ap-368	169	23	important	important	ADJ
ap-368	169	24	.	.	PUNCT
ap-368	170	1	figures	figure	NOUN
ap-368	170	2	1–3	1–3	NUM
ap-368	170	3	contain	contain	VERB
ap-368	170	4	the	the	DET
ap-368	170	5	first	first	ADJ
ap-368	170	6	harmonic	harmonic	NOUN
ap-368	170	7	.	.	PUNCT
ap-368	171	1	the	the	DET
ap-368	171	2	graphs	graph	NOUN
ap-368	171	3	illustrate	illustrate	VERB
ap-368	171	4	the	the	DET
ap-368	171	5	speculation	speculation	NOUN
ap-368	171	6	about	about	ADP
ap-368	171	7	the	the	DET
ap-368	171	8	validity	validity	NOUN
ap-368	171	9	of	of	ADP
ap-368	171	10	the	the	DET
ap-368	171	11	kzk	kzk	PRON
ap-368	171	12	equation	equation	NOUN
ap-368	171	13	for	for	ADP
ap-368	171	14	a	a	DET
ap-368	171	15	narrow	narrow	ADJ
ap-368	171	16	tube	tube	NOUN
ap-368	171	17	,	,	PUNCT
ap-368	171	18	where	where	SCONJ
ap-368	171	19	the	the	DET
ap-368	171	20	influence	influence	NOUN
ap-368	171	21	of	of	ADP
ap-368	171	22	the	the	DET
ap-368	171	23	boundary	boundary	ADJ
ap-368	171	24	layer	layer	NOUN
ap-368	171	25	is	be	AUX
ap-368	171	26	dominant	dominant	ADJ
ap-368	171	27	.	.	PUNCT
ap-368	172	1	we	we	PRON
ap-368	172	2	see	see	VERB
ap-368	172	3	that	that	SCONJ
ap-368	172	4	with	with	ADP
ap-368	172	5	increasing	increase	VERB
ap-368	172	6	frequency	frequency	NOUN
ap-368	172	7	the	the	DET
ap-368	172	8	transversal	transversal	ADJ
ap-368	172	9	velocity	velocity	NOUN
ap-368	172	10	component	component	NOUN
ap-368	172	11	progressively	progressively	ADV
ap-368	172	12	rises	rise	VERB
ap-368	172	13	.	.	PUNCT
ap-368	173	1	we	we	PRON
ap-368	173	2	can	can	AUX
ap-368	173	3	observe	observe	VERB
ap-368	173	4	the	the	DET
ap-368	173	5	significant	significant	ADJ
ap-368	173	6	growth	growth	NOUN
ap-368	173	7	of	of	ADP
ap-368	173	8	the	the	DET
ap-368	173	9	transversal	transversal	ADJ
ap-368	173	10	velocity	velocity	NOUN
ap-368	173	11	component	component	NOUN
ap-368	173	12	when	when	SCONJ
ap-368	173	13	the	the	DET
ap-368	173	14	cut	cut	VERB
ap-368	173	15	-	-	PUNCT
ap-368	173	16	off	off	ADP
ap-368	173	17	frequency	frequency	NOUN
ap-368	173	18	is	be	AUX
ap-368	173	19	exceeded	exceed	VERB
ap-368	173	20	.	.	PUNCT
ap-368	174	1	the	the	DET
ap-368	174	2	first	first	ADJ
ap-368	174	3	oscillations	oscillation	NOUN
ap-368	174	4	of	of	ADP
ap-368	174	5	the	the	DET
ap-368	174	6	transversal	transversal	ADJ
ap-368	174	7	velocity	velocity	NOUN
ap-368	174	8	component	component	NOUN
ap-368	174	9	are	be	AUX
ap-368	174	10	noticeable	noticeable	ADJ
ap-368	174	11	in	in	ADP
ap-368	174	12	the	the	DET
ap-368	174	13	case	case	NOUN
ap-368	174	14	of	of	ADP
ap-368	174	15	60	60	NUM
ap-368	174	16	khz	khz	NOUN
ap-368	174	17	.	.	PUNCT
ap-368	175	1	these	these	DET
ap-368	175	2	oscillations	oscillation	NOUN
ap-368	175	3	still	still	ADV
ap-368	175	4	grow	grow	VERB
ap-368	175	5	and	and	CCONJ
ap-368	175	6	they	they	PRON
ap-368	175	7	are	be	AUX
ap-368	175	8	conspicuous	conspicuous	ADJ
ap-368	175	9	when	when	SCONJ
ap-368	175	10	the	the	DET
ap-368	175	11	frequency	frequency	NOUN
ap-368	175	12	is	be	AUX
ap-368	175	13	equal	equal	ADJ
ap-368	175	14	to	to	ADP
ap-368	175	15	100	100	NUM
ap-368	175	16	khz	khz	NOUN
ap-368	175	17	.	.	PUNCT
ap-368	176	1	the	the	DET
ap-368	176	2	longitudinal	longitudinal	ADJ
ap-368	176	3	component	component	NOUN
ap-368	176	4	of	of	ADP
ap-368	176	5	the	the	DET
ap-368	176	6	velocity	velocity	NOUN
ap-368	176	7	was	be	AUX
ap-368	176	8	scarely	scarely	ADV
ap-368	176	9	affected	affect	VERB
ap-368	176	10	,	,	PUNCT
ap-368	176	11	as	as	SCONJ
ap-368	176	12	can	can	AUX
ap-368	176	13	be	be	AUX
ap-368	176	14	seen	see	VERB
ap-368	176	15	from	from	ADP
ap-368	176	16	the	the	DET
ap-368	176	17	comparison	comparison	NOUN
ap-368	176	18	with	with	ADP
ap-368	176	19	the	the	DET
ap-368	176	20	velocity	velocity	NOUN
ap-368	176	21	from	from	ADP
ap-368	176	22	gbe	gbe	PROPN
ap-368	176	23	.	.	PUNCT
ap-368	177	1	the	the	DET
ap-368	177	2	further	further	ADJ
ap-368	177	3	increase	increase	NOUN
ap-368	177	4	in	in	ADP
ap-368	177	5	frequency	frequency	NOUN
ap-368	177	6	causes	cause	VERB
ap-368	177	7	the	the	DET
ap-368	177	8	lon22	lon22	PROPN
ap-368	177	9	©	©	PROPN
ap-368	177	10	czech	czech	PROPN
ap-368	177	11	technical	technical	PROPN
ap-368	177	12	university	university	PROPN
ap-368	177	13	publishing	publishing	NOUN
ap-368	177	14	house	house	NOUN
ap-368	177	15	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	177	16	acta	acta	PROPN
ap-368	177	17	polytechnica	polytechnica	PROPN
ap-368	177	18	vol	vol	NOUN
ap-368	177	19	.	.	PUNCT
ap-368	178	1	42	42	NUM
ap-368	178	2	no	no	INTJ
ap-368	178	3	.	.	PUNCT
ap-368	179	1	4/2002	4/2002	NUM
ap-368	179	2	fig	fig	NOUN
ap-368	179	3	.	.	PUNCT
ap-368	180	1	1	1	NUM
ap-368	180	2	:	:	PUNCT
ap-368	180	3	solution	solution	NOUN
ap-368	180	4	from	from	ADP
ap-368	180	5	the	the	DET
ap-368	180	6	gbe	gbe	NOUN
ap-368	180	7	(	(	PUNCT
ap-368	180	8	line	line	NOUN
ap-368	180	9	1	1	NUM
ap-368	180	10	)	)	PUNCT
ap-368	180	11	,	,	PUNCT
ap-368	180	12	longitudinal	longitudinal	ADJ
ap-368	180	13	(	(	PUNCT
ap-368	180	14	line	line	NOUN
ap-368	180	15	2	2	NUM
ap-368	180	16	)	)	PUNCT
ap-368	180	17	and	and	CCONJ
ap-368	180	18	transversal	transversal	NOUN
ap-368	180	19	(	(	PUNCT
ap-368	180	20	line	line	NOUN
ap-368	180	21	3	3	NUM
ap-368	180	22	)	)	PUNCT
ap-368	180	23	velocity	velocity	NOUN
ap-368	180	24	component	component	NOUN
ap-368	180	25	from	from	ADP
ap-368	180	26	the	the	DET
ap-368	180	27	kzk	kzk	PRON
ap-368	180	28	equation	equation	NOUN
ap-368	180	29	for	for	ADP
ap-368	180	30	the	the	DET
ap-368	180	31	source	source	NOUN
ap-368	180	32	frequency	frequency	NOUN
ap-368	180	33	1khz	1khz	NOUN
ap-368	180	34	and	and	CCONJ
ap-368	180	35	10khz	10khz	NOUN
ap-368	180	36	(	(	PUNCT
ap-368	180	37	first	first	ADJ
ap-368	180	38	harmonic	harmonic	ADJ
ap-368	180	39	)	)	PUNCT
ap-368	180	40	fig	fig	NOUN
ap-368	180	41	.	.	PUNCT
ap-368	181	1	2	2	NUM
ap-368	181	2	:	:	PUNCT
ap-368	181	3	solution	solution	NOUN
ap-368	181	4	from	from	ADP
ap-368	181	5	the	the	DET
ap-368	181	6	gbe	gbe	NOUN
ap-368	181	7	(	(	PUNCT
ap-368	181	8	line	line	NOUN
ap-368	181	9	1	1	NUM
ap-368	181	10	)	)	PUNCT
ap-368	181	11	,	,	PUNCT
ap-368	181	12	longitudinal	longitudinal	ADJ
ap-368	181	13	(	(	PUNCT
ap-368	181	14	line	line	NOUN
ap-368	181	15	2	2	NUM
ap-368	181	16	)	)	PUNCT
ap-368	181	17	and	and	CCONJ
ap-368	181	18	transversal	transversal	NOUN
ap-368	181	19	(	(	PUNCT
ap-368	181	20	line	line	NOUN
ap-368	181	21	3	3	NUM
ap-368	181	22	)	)	PUNCT
ap-368	181	23	velocity	velocity	NOUN
ap-368	181	24	component	component	NOUN
ap-368	181	25	from	from	ADP
ap-368	181	26	the	the	DET
ap-368	181	27	kzk	kzk	PRON
ap-368	181	28	equation	equation	NOUN
ap-368	181	29	for	for	ADP
ap-368	181	30	the	the	DET
ap-368	181	31	source	source	NOUN
ap-368	181	32	frequency	frequency	NOUN
ap-368	181	33	40khz	40khz	NOUN
ap-368	181	34	and	and	CCONJ
ap-368	181	35	60khz	60khz	NOUN
ap-368	181	36	(	(	PUNCT
ap-368	181	37	first	first	ADJ
ap-368	181	38	harmonic	harmonic	ADJ
ap-368	181	39	)	)	PUNCT
ap-368	181	40	gitudinal	gitudinal	ADJ
ap-368	181	41	component	component	NOUN
ap-368	181	42	of	of	ADP
ap-368	181	43	velocity	velocity	NOUN
ap-368	181	44	also	also	ADV
ap-368	181	45	to	to	PART
ap-368	181	46	become	become	AUX
ap-368	181	47	disrupted	disrupt	VERB
ap-368	181	48	,	,	PUNCT
ap-368	181	49	as	as	SCONJ
ap-368	181	50	can	can	AUX
ap-368	181	51	be	be	AUX
ap-368	181	52	seen	see	VERB
ap-368	181	53	for	for	ADP
ap-368	181	54	frequency	frequency	NOUN
ap-368	181	55	equal	equal	ADJ
ap-368	181	56	to	to	ADP
ap-368	181	57	500	500	NUM
ap-368	181	58	khz	khz	NOUN
ap-368	181	59	.	.	PUNCT
ap-368	182	1	these	these	DET
ap-368	182	2	variations	variation	NOUN
ap-368	182	3	are	be	AUX
ap-368	182	4	readily	readily	ADV
ap-368	182	5	noticeable	noticeable	ADJ
ap-368	182	6	,	,	PUNCT
ap-368	182	7	especially	especially	ADV
ap-368	182	8	for	for	ADP
ap-368	182	9	the	the	DET
ap-368	182	10	first	first	ADJ
ap-368	182	11	harmonic	harmonic	NOUN
ap-368	182	12	,	,	PUNCT
ap-368	182	13	and	and	CCONJ
ap-368	182	14	they	they	PRON
ap-368	182	15	are	be	AUX
ap-368	182	16	weaker	weak	ADJ
ap-368	182	17	for	for	ADP
ap-368	182	18	higher	high	ADJ
ap-368	182	19	harmonics	harmonic	NOUN
ap-368	182	20	.	.	PUNCT
ap-368	183	1	the	the	DET
ap-368	183	2	presented	present	VERB
ap-368	183	3	phenomena	phenomenon	NOUN
ap-368	183	4	are	be	AUX
ap-368	183	5	in	in	ADP
ap-368	183	6	harmony	harmony	NOUN
ap-368	183	7	with	with	ADP
ap-368	183	8	the	the	DET
ap-368	183	9	deductions	deduction	NOUN
ap-368	183	10	mentioned	mention	VERB
ap-368	183	11	above	above	ADV
ap-368	183	12	.	.	PUNCT
ap-368	184	1	5.2	5.2	NUM
ap-368	184	2	a	a	DET
ap-368	184	3	wide	wide	ADJ
ap-368	184	4	tube	tube	NOUN
ap-368	184	5	results	result	NOUN
ap-368	184	6	for	for	ADP
ap-368	184	7	a	a	DET
ap-368	184	8	tube	tube	NOUN
ap-368	184	9	with	with	ADP
ap-368	184	10	radius	radius	NOUN
ap-368	184	11	r0	r0	PROPN
ap-368	184	12	�	�	PROPN
ap-368	184	13	0.5	0.5	NUM
ap-368	184	14	m	m	NOUN
ap-368	184	15	are	be	AUX
ap-368	184	16	also	also	ADV
ap-368	184	17	presented	present	VERB
ap-368	184	18	.	.	PUNCT
ap-368	185	1	the	the	DET
ap-368	185	2	calculations	calculation	NOUN
ap-368	185	3	were	be	AUX
ap-368	185	4	made	make	VERB
ap-368	185	5	for	for	ADP
ap-368	185	6	frequency	frequency	NOUN
ap-368	185	7	100	100	NUM
ap-368	185	8	khz	khz	NOUN
ap-368	185	9	.	.	PUNCT
ap-368	186	1	the	the	DET
ap-368	186	2	cut	cut	VERB
ap-368	186	3	-	-	PUNCT
ap-368	186	4	off	off	ADP
ap-368	186	5	frequency	frequency	NOUN
ap-368	186	6	of	of	ADP
ap-368	186	7	the	the	DET
ap-368	186	8	first	first	ADJ
ap-368	186	9	symmetric	symmetric	ADJ
ap-368	186	10	mode	mode	NOUN
ap-368	186	11	for	for	ADP
ap-368	186	12	this	this	DET
ap-368	186	13	tube	tube	NOUN
ap-368	186	14	is	be	AUX
ap-368	186	15	approximately	approximately	ADV
ap-368	186	16	equal	equal	ADJ
ap-368	186	17	to	to	ADP
ap-368	186	18	911	911	NUM
ap-368	186	19	hz	hz	NOUN
ap-368	186	20	,	,	PUNCT
ap-368	186	21	thus	thus	ADV
ap-368	186	22	the	the	DET
ap-368	186	23	frequency	frequency	NOUN
ap-368	186	24	of	of	ADP
ap-368	186	25	the	the	DET
ap-368	186	26	described	describe	VERB
ap-368	186	27	waves	wave	NOUN
ap-368	186	28	is	be	AUX
ap-368	186	29	considerably	considerably	ADV
ap-368	186	30	higher	high	ADJ
ap-368	186	31	than	than	ADP
ap-368	186	32	the	the	DET
ap-368	186	33	cut	cut	VERB
ap-368	186	34	-	-	PUNCT
ap-368	186	35	off	off	ADP
ap-368	186	36	frequency	frequency	NOUN
ap-368	186	37	.	.	PUNCT
ap-368	187	1	the	the	DET
ap-368	187	2	fermi	fermi	NOUN
ap-368	187	3	distribution	distribution	NOUN
ap-368	187	4	was	be	AUX
ap-368	187	5	chosen	choose	VERB
ap-368	187	6	as	as	ADP
ap-368	187	7	the	the	DET
ap-368	187	8	initial	initial	ADJ
ap-368	187	9	condition	condition	NOUN
ap-368	187	10	for	for	ADP
ap-368	187	11	the	the	DET
ap-368	187	12	kzk	kzk	VERB
ap-368	187	13	equation	equation	NOUN
ap-368	187	14	.	.	PUNCT
ap-368	188	1	all	all	DET
ap-368	188	2	other	other	ADJ
ap-368	188	3	parameters	parameter	NOUN
ap-368	188	4	of	of	ADP
ap-368	188	5	the	the	DET
ap-368	188	6	computation	computation	NOUN
ap-368	188	7	were	be	AUX
ap-368	188	8	the	the	DET
ap-368	188	9	same	same	ADJ
ap-368	188	10	as	as	ADP
ap-368	188	11	in	in	ADP
ap-368	188	12	the	the	DET
ap-368	188	13	previous	previous	ADJ
ap-368	188	14	case	case	NOUN
ap-368	188	15	of	of	ADP
ap-368	188	16	the	the	DET
ap-368	188	17	narrow	narrow	ADJ
ap-368	188	18	tube	tube	NOUN
ap-368	188	19	.	.	PUNCT
ap-368	189	1	figures	figure	NOUN
ap-368	189	2	4	4	NUM
ap-368	189	3	and	and	CCONJ
ap-368	189	4	5	5	NUM
ap-368	189	5	contain	contain	VERB
ap-368	189	6	the	the	DET
ap-368	189	7	propagation	propagation	NOUN
ap-368	189	8	curves	curve	NOUN
ap-368	189	9	of	of	ADP
ap-368	189	10	the	the	DET
ap-368	189	11	first	first	ADJ
ap-368	189	12	four	four	NUM
ap-368	189	13	harmonics	harmonic	NOUN
ap-368	189	14	.	.	PUNCT
ap-368	190	1	the	the	DET
ap-368	190	2	distributions	distribution	NOUN
ap-368	190	3	in	in	ADP
ap-368	190	4	these	these	DET
ap-368	190	5	figuresare	figuresare	NOUN
ap-368	190	6	plotted	plot	VERB
ap-368	190	7	for	for	ADP
ap-368	190	8	�	�	PROPN
ap-368	190	9	�	�	PROPN
ap-368	190	10	08	08	NUM
ap-368	190	11	.	.	PROPN
ap-368	190	12	,	,	PUNCT
ap-368	190	13	which	which	PRON
ap-368	190	14	corresponds	correspond	VERB
ap-368	190	15	to	to	ADP
ap-368	190	16	the	the	DET
ap-368	190	17	value	value	NOUN
ap-368	190	18	,	,	PUNCT
ap-368	190	19	at	at	ADP
ap-368	190	20	which	which	PRON
ap-368	190	21	the	the	DET
ap-368	190	22	fermi	fermi	NOUN
ap-368	190	23	©	©	PROPN
ap-368	190	24	czech	czech	PROPN
ap-368	190	25	technical	technical	PROPN
ap-368	190	26	university	university	PROPN
ap-368	190	27	publishing	publishing	NOUN
ap-368	190	28	house	house	NOUN
ap-368	190	29	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	190	30	23	23	NUM
ap-368	190	31	acta	acta	PROPN
ap-368	190	32	polytechnica	polytechnica	PROPN
ap-368	190	33	vol	vol	NOUN
ap-368	190	34	.	.	PUNCT
ap-368	191	1	42	42	NUM
ap-368	191	2	no	no	INTJ
ap-368	191	3	.	.	PUNCT
ap-368	192	1	4/2002	4/2002	NUM
ap-368	192	2	fig	fig	NOUN
ap-368	192	3	.	.	PUNCT
ap-368	193	1	3	3	NUM
ap-368	193	2	:	:	PUNCT
ap-368	193	3	solution	solution	NOUN
ap-368	193	4	from	from	ADP
ap-368	193	5	the	the	DET
ap-368	193	6	gbe	gbe	NOUN
ap-368	193	7	(	(	PUNCT
ap-368	193	8	line	line	NOUN
ap-368	193	9	1	1	NUM
ap-368	193	10	)	)	PUNCT
ap-368	193	11	,	,	PUNCT
ap-368	193	12	longitudinal	longitudinal	ADJ
ap-368	193	13	(	(	PUNCT
ap-368	193	14	line	line	NOUN
ap-368	193	15	2	2	NUM
ap-368	193	16	)	)	PUNCT
ap-368	193	17	and	and	CCONJ
ap-368	193	18	transversal	transversal	NOUN
ap-368	193	19	(	(	PUNCT
ap-368	193	20	line	line	NOUN
ap-368	193	21	3	3	NUM
ap-368	193	22	)	)	PUNCT
ap-368	193	23	velocity	velocity	NOUN
ap-368	193	24	component	component	NOUN
ap-368	193	25	from	from	ADP
ap-368	193	26	the	the	DET
ap-368	193	27	kzk	kzk	PRON
ap-368	193	28	equation	equation	NOUN
ap-368	193	29	for	for	ADP
ap-368	193	30	the	the	DET
ap-368	193	31	source	source	NOUN
ap-368	193	32	frequency	frequency	NOUN
ap-368	193	33	100khz	100khz	NUM
ap-368	193	34	and	and	CCONJ
ap-368	193	35	500khz	500khz	NUM
ap-368	193	36	(	(	PUNCT
ap-368	193	37	first	first	ADJ
ap-368	193	38	harmonic	harmonic	ADJ
ap-368	193	39	)	)	PUNCT
ap-368	193	40	fig	fig	NOUN
ap-368	193	41	.	.	PUNCT
ap-368	194	1	4	4	NUM
ap-368	194	2	:	:	PUNCT
ap-368	194	3	kzk	kzk	ADJ
ap-368	194	4	equation	equation	NOUN
ap-368	194	5	solution	solution	NOUN
ap-368	194	6	of	of	ADP
ap-368	194	7	the	the	DET
ap-368	194	8	longitudinal	longitudinal	ADJ
ap-368	194	9	(	(	PUNCT
ap-368	194	10	line	line	NOUN
ap-368	194	11	1	1	NUM
ap-368	194	12	)	)	PUNCT
ap-368	194	13	and	and	CCONJ
ap-368	194	14	transversal	transversal	NOUN
ap-368	194	15	(	(	PUNCT
ap-368	194	16	line	line	NOUN
ap-368	194	17	2	2	NUM
ap-368	194	18	)	)	PUNCT
ap-368	194	19	velocity	velocity	NOUN
ap-368	194	20	component	component	NOUN
ap-368	194	21	of	of	ADP
ap-368	194	22	the	the	DET
ap-368	194	23	first	first	ADJ
ap-368	194	24	and	and	CCONJ
ap-368	194	25	second	second	ADJ
ap-368	194	26	harmonic	harmonic	ADJ
ap-368	194	27	fig	fig	NOUN
ap-368	194	28	.	.	PUNCT
ap-368	195	1	5	5	NUM
ap-368	195	2	:	:	PUNCT
ap-368	195	3	kzk	kzk	ADJ
ap-368	195	4	equation	equation	NOUN
ap-368	195	5	solution	solution	NOUN
ap-368	195	6	of	of	ADP
ap-368	195	7	the	the	DET
ap-368	195	8	longitudinal	longitudinal	ADJ
ap-368	195	9	(	(	PUNCT
ap-368	195	10	line	line	NOUN
ap-368	195	11	1	1	NUM
ap-368	195	12	)	)	PUNCT
ap-368	195	13	and	and	CCONJ
ap-368	195	14	transversal	transversal	NOUN
ap-368	195	15	(	(	PUNCT
ap-368	195	16	line	line	NOUN
ap-368	195	17	2	2	NUM
ap-368	195	18	)	)	PUNCT
ap-368	195	19	velocity	velocity	NOUN
ap-368	195	20	component	component	NOUN
ap-368	195	21	of	of	ADP
ap-368	195	22	the	the	DET
ap-368	195	23	third	third	ADJ
ap-368	195	24	and	and	CCONJ
ap-368	195	25	fourth	fourth	ADJ
ap-368	195	26	harmonic	harmonic	ADJ
ap-368	195	27	distribution	distribution	NOUN
ap-368	195	28	derivative	derivative	NOUN
ap-368	195	29	has	have	VERB
ap-368	195	30	its	its	PRON
ap-368	195	31	maximum	maximum	ADJ
ap-368	195	32	.	.	PUNCT
ap-368	196	1	figures	figure	NOUN
ap-368	197	1	6-–9	6-–9	NUM
ap-368	197	2	contain	contain	VERB
ap-368	197	3	the	the	DET
ap-368	197	4	space	space	NOUN
ap-368	197	5	evolutions	evolution	NOUN
ap-368	197	6	of	of	ADP
ap-368	197	7	the	the	DET
ap-368	197	8	first	first	ADJ
ap-368	197	9	four	four	NUM
ap-368	197	10	harmonics	harmonic	NOUN
ap-368	197	11	for	for	ADP
ap-368	197	12	both	both	CCONJ
ap-368	197	13	the	the	DET
ap-368	197	14	longitudinal	longitudinal	ADJ
ap-368	197	15	and	and	CCONJ
ap-368	197	16	the	the	DET
ap-368	197	17	transverse	transverse	NOUN
ap-368	197	18	velocity	velocity	NOUN
ap-368	197	19	components	component	NOUN
ap-368	197	20	.	.	PUNCT
ap-368	198	1	6	6	NUM
ap-368	198	2	summary	summary	NOUN
ap-368	198	3	this	this	DET
ap-368	198	4	paper	paper	NOUN
ap-368	198	5	shows	show	VERB
ap-368	198	6	the	the	DET
ap-368	198	7	derivation	derivation	NOUN
ap-368	198	8	of	of	ADP
ap-368	198	9	the	the	DET
ap-368	198	10	kzk	kzk	PRON
ap-368	198	11	equation	equation	NOUN
ap-368	198	12	in	in	ADP
ap-368	198	13	the	the	DET
ap-368	198	14	parabolic	parabolic	NOUN
ap-368	198	15	approximation	approximation	NOUN
ap-368	198	16	.	.	PUNCT
ap-368	199	1	the	the	DET
ap-368	199	2	following	follow	VERB
ap-368	199	3	validity	validity	NOUN
ap-368	199	4	condition	condition	NOUN
ap-368	199	5	of	of	ADP
ap-368	199	6	this	this	DET
ap-368	199	7	equation	equation	NOUN
ap-368	199	8	for	for	ADP
ap-368	199	9	the	the	DET
ap-368	199	10	waveguide	waveguide	NOUN
ap-368	199	11	has	have	VERB
ap-368	199	12	to	to	PART
ap-368	199	13	be	be	AUX
ap-368	199	14	satisfied	satisfied	ADJ
ap-368	199	15	v	v	ADP
ap-368	199	16	~	~	PUNCT
ap-368	199	17	,	,	PUNCT
ap-368	199	18	v	v	X
ap-368	199	19	�	�	X
ap-368	199	20	~	~	PUNCT
ap-368	199	21	(	(	PUNCT
ap-368	199	22	that	that	PRON
ap-368	199	23	is	be	AUX
ap-368	199	24	v	v	ADP
ap-368	199	25	�	�	PROPN
ap-368	199	26	v	v	NOUN
ap-368	199	27	�	�	PROPN
ap-368	199	28	)	)	PUNCT
ap-368	199	29	.	.	PUNCT
ap-368	200	1	the	the	DET
ap-368	200	2	validity	validity	NOUN
ap-368	200	3	conditions	condition	NOUN
ap-368	200	4	of	of	ADP
ap-368	200	5	the	the	DET
ap-368	200	6	kzk	kzk	PRON
ap-368	200	7	equation	equation	NOUN
ap-368	200	8	in	in	ADP
ap-368	200	9	the	the	DET
ap-368	200	10	case	case	NOUN
ap-368	200	11	of	of	ADP
ap-368	200	12	the	the	DET
ap-368	200	13	description	description	NOUN
ap-368	200	14	of	of	ADP
ap-368	200	15	quasi	quasi	ADJ
ap-368	200	16	-	-	ADJ
ap-368	200	17	linear	linear	ADJ
ap-368	200	18	waves	wave	NOUN
ap-368	200	19	propagation	propagation	NOUN
ap-368	200	20	in	in	ADP
ap-368	200	21	the	the	DET
ap-368	200	22	circular	circular	ADJ
ap-368	200	23	waveguide	waveguide	NOUN
ap-368	200	24	are	be	AUX
ap-368	200	25	further	far	ADV
ap-368	200	26	discussed	discuss	VERB
ap-368	200	27	by	by	ADP
ap-368	200	28	means	mean	NOUN
ap-368	200	29	of	of	ADP
ap-368	200	30	these	these	DET
ap-368	200	31	conditions	condition	NOUN
ap-368	200	32	.	.	PUNCT
ap-368	201	1	it	it	PRON
ap-368	201	2	is	be	AUX
ap-368	201	3	shown	show	VERB
ap-368	201	4	that	that	SCONJ
ap-368	201	5	the	the	DET
ap-368	201	6	condition	condition	NOUN
ap-368	201	7	kr0	kr0	PROPN
ap-368	201	8	�	�	NOUN
ap-368	201	9	1	1	NUM
ap-368	201	10	represents	represent	VERB
ap-368	201	11	only	only	ADV
ap-368	201	12	the	the	DET
ap-368	201	13	sufficient	sufficient	ADJ
ap-368	201	14	condition	condition	NOUN
ap-368	201	15	for	for	ADP
ap-368	201	16	validity	validity	NOUN
ap-368	201	17	of	of	ADP
ap-368	201	18	the	the	DET
ap-368	201	19	kzk	kzk	PROPN
ap-368	201	20	equation	equation	NOUN
ap-368	201	21	.	.	PUNCT
ap-368	202	1	the	the	DET
ap-368	202	2	equation	equation	NOUN
ap-368	202	3	remains	remain	VERB
ap-368	202	4	valid	valid	ADJ
ap-368	202	5	in	in	ADP
ap-368	202	6	the	the	DET
ap-368	202	7	case	case	NOUN
ap-368	202	8	of	of	ADP
ap-368	202	9	the	the	DET
ap-368	202	10	small	small	ADJ
ap-368	202	11	radius	radius	NOUN
ap-368	202	12	waveguide	waveguide	NOUN
ap-368	202	13	(	(	PUNCT
ap-368	202	14	and	and	CCONJ
ap-368	202	15	consequently	consequently	ADV
ap-368	202	16	with	with	ADP
ap-368	202	17	strong	strong	ADJ
ap-368	202	18	influence	influence	NOUN
ap-368	202	19	of	of	ADP
ap-368	202	20	the	the	DET
ap-368	202	21	boundary	boundary	ADJ
ap-368	202	22	layer	layer	NOUN
ap-368	202	23	)	)	PUNCT
ap-368	202	24	for	for	ADP
ap-368	202	25	frequencies	frequency	NOUN
ap-368	202	26	below	below	ADP
ap-368	202	27	the	the	DET
ap-368	202	28	cut	cut	VERB
ap-368	202	29	-	-	PUNCT
ap-368	202	30	off	off	ADP
ap-368	202	31	frequency	frequency	NOUN
ap-368	202	32	though	though	SCONJ
ap-368	202	33	kr0<1	kr0<1	PROPN
ap-368	202	34	under	under	ADP
ap-368	202	35	the	the	DET
ap-368	202	36	condition	condition	NOUN
ap-368	202	37	that	that	SCONJ
ap-368	202	38	v	v	ADP
ap-368	202	39	�	�	PROPN
ap-368	202	40	v	v	PROPN
ap-368	202	41	�	�	PROPN
ap-368	202	42	.	.	PUNCT
ap-368	203	1	24	24	NUM
ap-368	203	2	©	©	PROPN
ap-368	203	3	czech	czech	PROPN
ap-368	203	4	technical	technical	PROPN
ap-368	203	5	university	university	PROPN
ap-368	203	6	publishing	publishing	NOUN
ap-368	203	7	house	house	NOUN
ap-368	203	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	203	9	acta	acta	PROPN
ap-368	203	10	polytechnica	polytechnica	PROPN
ap-368	203	11	vol	vol	NOUN
ap-368	203	12	.	.	PUNCT
ap-368	204	1	42	42	NUM
ap-368	204	2	no	no	INTJ
ap-368	204	3	.	.	PUNCT
ap-368	205	1	4/2002	4/2002	NUM
ap-368	205	2	fig	fig	NOUN
ap-368	205	3	.	.	PUNCT
ap-368	206	1	6	6	NUM
ap-368	206	2	:	:	PUNCT
ap-368	206	3	kzk	kzk	ADJ
ap-368	206	4	equation	equation	NOUN
ap-368	206	5	solution	solution	NOUN
ap-368	206	6	of	of	ADP
ap-368	206	7	the	the	DET
ap-368	206	8	longitudinal	longitudinal	ADJ
ap-368	206	9	(	(	PUNCT
ap-368	206	10	v1	v1	NOUN
ap-368	206	11	)	)	PUNCT
ap-368	206	12	and	and	CCONJ
ap-368	206	13	transversal	transversal	NOUN
ap-368	206	14	(	(	PUNCT
ap-368	206	15	w1	w1	NOUN
ap-368	206	16	)	)	PUNCT
ap-368	206	17	velocity	velocity	NOUN
ap-368	206	18	component	component	NOUN
ap-368	206	19	of	of	ADP
ap-368	206	20	the	the	DET
ap-368	206	21	first	first	ADJ
ap-368	206	22	harmonic	harmonic	ADJ
ap-368	206	23	fig	fig	NOUN
ap-368	206	24	.	.	PUNCT
ap-368	207	1	7	7	NUM
ap-368	207	2	:	:	PUNCT
ap-368	207	3	kzk	kzk	ADJ
ap-368	207	4	equation	equation	NOUN
ap-368	207	5	solution	solution	NOUN
ap-368	207	6	of	of	ADP
ap-368	207	7	the	the	DET
ap-368	207	8	longitudinal	longitudinal	ADJ
ap-368	207	9	(	(	PUNCT
ap-368	207	10	v2	v2	NOUN
ap-368	207	11	)	)	PUNCT
ap-368	207	12	and	and	CCONJ
ap-368	207	13	transversal	transversal	NOUN
ap-368	207	14	(	(	PUNCT
ap-368	207	15	w2	w2	NOUN
ap-368	207	16	)	)	PUNCT
ap-368	207	17	velocity	velocity	NOUN
ap-368	207	18	component	component	NOUN
ap-368	207	19	of	of	ADP
ap-368	207	20	the	the	DET
ap-368	207	21	second	second	ADJ
ap-368	207	22	harmonic	harmonic	ADJ
ap-368	207	23	fig	fig	NOUN
ap-368	207	24	.	.	PUNCT
ap-368	208	1	8	8	NUM
ap-368	208	2	:	:	PUNCT
ap-368	208	3	kzk	kzk	ADJ
ap-368	208	4	equation	equation	NOUN
ap-368	208	5	solution	solution	NOUN
ap-368	208	6	of	of	ADP
ap-368	208	7	the	the	DET
ap-368	208	8	longitudinal	longitudinal	ADJ
ap-368	208	9	(	(	PUNCT
ap-368	208	10	v3	v3	PROPN
ap-368	208	11	)	)	PUNCT
ap-368	208	12	and	and	CCONJ
ap-368	208	13	transversal	transversal	NOUN
ap-368	208	14	(	(	PUNCT
ap-368	208	15	w3	w3	PROPN
ap-368	208	16	)	)	PUNCT
ap-368	208	17	velocity	velocity	NOUN
ap-368	208	18	component	component	NOUN
ap-368	208	19	of	of	ADP
ap-368	208	20	the	the	DET
ap-368	208	21	third	third	ADJ
ap-368	208	22	harmonic	harmonic	NOUN
ap-368	208	23	the	the	DET
ap-368	208	24	results	result	NOUN
ap-368	208	25	of	of	ADP
ap-368	208	26	numerical	numerical	ADJ
ap-368	208	27	solution	solution	NOUN
ap-368	208	28	of	of	ADP
ap-368	208	29	the	the	DET
ap-368	208	30	kzk	kzk	PRON
ap-368	208	31	equation	equation	NOUN
ap-368	208	32	are	be	AUX
ap-368	208	33	presented	present	VERB
ap-368	208	34	for	for	ADP
ap-368	208	35	waveguides	waveguide	NOUN
ap-368	208	36	of	of	ADP
ap-368	208	37	both	both	CCONJ
ap-368	208	38	small	small	ADJ
ap-368	208	39	and	and	CCONJ
ap-368	208	40	large	large	ADJ
ap-368	208	41	radius	radius	NOUN
ap-368	208	42	which	which	PRON
ap-368	208	43	demonstrate	demonstrate	VERB
ap-368	208	44	these	these	DET
ap-368	208	45	two	two	NUM
ap-368	208	46	cases	case	NOUN
ap-368	208	47	.	.	PUNCT
ap-368	209	1	the	the	DET
ap-368	209	2	numerical	numerical	ADJ
ap-368	209	3	solution	solution	NOUN
ap-368	209	4	of	of	ADP
ap-368	209	5	the	the	DET
ap-368	209	6	kzk	kzk	PRON
ap-368	209	7	equation	equation	NOUN
ap-368	209	8	was	be	AUX
ap-368	209	9	performed	perform	VERB
ap-368	209	10	by	by	ADP
ap-368	209	11	means	mean	NOUN
ap-368	209	12	of	of	ADP
ap-368	209	13	a	a	DET
ap-368	209	14	method	method	NOUN
ap-368	209	15	based	base	VERB
ap-368	209	16	on	on	ADP
ap-368	209	17	the	the	DET
ap-368	209	18	bergen	bergen	PROPN
ap-368	209	19	code	code	NOUN
ap-368	210	1	[	[	X
ap-368	210	2	32	32	NUM
ap-368	210	3	]	]	PUNCT
ap-368	210	4	,	,	PUNCT
ap-368	211	1	which	which	PRON
ap-368	211	2	was	be	AUX
ap-368	211	3	modified	modify	VERB
ap-368	211	4	by	by	ADP
ap-368	211	5	the	the	DET
ap-368	211	6	authors	author	NOUN
ap-368	211	7	because	because	SCONJ
ap-368	211	8	it	it	PRON
ap-368	211	9	was	be	AUX
ap-368	211	10	necessary	necessary	ADJ
ap-368	211	11	to	to	PART
ap-368	211	12	incorporate	incorporate	VERB
ap-368	211	13	the	the	DET
ap-368	211	14	boundary	boundary	ADJ
ap-368	211	15	condition	condition	NOUN
ap-368	211	16	,	,	PUNCT
ap-368	211	17	taking	take	VERB
ap-368	211	18	into	into	ADP
ap-368	211	19	account	account	NOUN
ap-368	211	20	the	the	DET
ap-368	211	21	boundary	boundary	ADJ
ap-368	211	22	layer	layer	NOUN
ap-368	211	23	at	at	ADP
ap-368	211	24	the	the	DET
ap-368	211	25	waveguide	waveguide	ADJ
ap-368	211	26	lateral	lateral	ADJ
ap-368	211	27	walls	wall	NOUN
ap-368	212	1	.	.	PUNCT
ap-368	213	1	the	the	DET
ap-368	213	2	new	new	ADJ
ap-368	213	3	method	method	NOUN
ap-368	213	4	for	for	ADP
ap-368	213	5	calculating	calculate	VERB
ap-368	213	6	the	the	DET
ap-368	213	7	diffraction	diffraction	NOUN
ap-368	213	8	effects	effect	NOUN
ap-368	213	9	generated	generate	VERB
ap-368	213	10	by	by	ADP
ap-368	213	11	the	the	DET
ap-368	213	12	boundary	boundary	ADJ
ap-368	213	13	layer	layer	NOUN
ap-368	213	14	effects	effect	NOUN
ap-368	213	15	is	be	AUX
ap-368	213	16	described	describe	VERB
ap-368	213	17	in	in	ADP
ap-368	213	18	the	the	DET
ap-368	213	19	text	text	NOUN
ap-368	213	20	.	.	PUNCT
ap-368	214	1	when	when	SCONJ
ap-368	214	2	the	the	DET
ap-368	214	3	plane	plane	NOUN
ap-368	214	4	wave	wave	NOUN
ap-368	214	5	with	with	ADP
ap-368	214	6	a	a	DET
ap-368	214	7	frequency	frequency	NOUN
ap-368	214	8	below	below	ADP
ap-368	214	9	the	the	DET
ap-368	214	10	cut	cut	VERB
ap-368	214	11	-	-	PUNCT
ap-368	214	12	off	off	ADP
ap-368	214	13	frequency	frequency	NOUN
ap-368	214	14	propagates	propagate	VERB
ap-368	214	15	in	in	ADP
ap-368	214	16	a	a	DET
ap-368	214	17	small	small	ADJ
ap-368	214	18	radius	radius	NOUN
ap-368	214	19	tube	tube	NOUN
ap-368	214	20	,	,	PUNCT
ap-368	214	21	then	then	ADV
ap-368	214	22	its	its	PRON
ap-368	214	23	space	space	NOUN
ap-368	214	24	evolution	evolution	NOUN
ap-368	214	25	along	along	ADP
ap-368	214	26	the	the	DET
ap-368	214	27	radius	radius	NOUN
ap-368	214	28	varies	vary	VERB
ap-368	214	29	only	only	ADV
ap-368	214	30	a	a	DET
ap-368	214	31	little	little	ADJ
ap-368	214	32	and	and	CCONJ
ap-368	214	33	the	the	DET
ap-368	214	34	results	result	NOUN
ap-368	214	35	of	of	ADP
ap-368	214	36	the	the	DET
ap-368	214	37	kzk	kzk	NOUN
ap-368	214	38	and	and	CCONJ
ap-368	214	39	the	the	DET
ap-368	214	40	burgers	burger	NOUN
ap-368	214	41	equation	equation	NOUN
ap-368	214	42	are	be	AUX
ap-368	214	43	comparable	comparable	ADJ
ap-368	214	44	.	.	PUNCT
ap-368	215	1	solving	solve	VERB
ap-368	215	2	the	the	DET
ap-368	215	3	kzk	kzk	DET
ap-368	215	4	equation	equation	NOUN
ap-368	215	5	also	also	ADV
ap-368	215	6	enables	enable	VERB
ap-368	215	7	us	we	PRON
ap-368	215	8	to	to	PART
ap-368	215	9	get	get	VERB
ap-368	215	10	the	the	DET
ap-368	215	11	distribution	distribution	NOUN
ap-368	215	12	of	of	ADP
ap-368	215	13	the	the	DET
ap-368	215	14	perpendicular	perpendicular	ADJ
ap-368	215	15	component	component	NOUN
ap-368	215	16	of	of	ADP
ap-368	215	17	velocity	velocity	NOUN
ap-368	215	18	.	.	PUNCT
ap-368	216	1	by	by	ADP
ap-368	216	2	means	mean	NOUN
ap-368	216	3	of	of	ADP
ap-368	216	4	the	the	DET
ap-368	216	5	perpendicular	perpendicular	ADJ
ap-368	216	6	component	component	NOUN
ap-368	216	7	of	of	ADP
ap-368	216	8	the	the	DET
ap-368	216	9	velocity	velocity	NOUN
ap-368	216	10	we	we	PRON
ap-368	216	11	can	can	AUX
ap-368	216	12	see	see	VERB
ap-368	216	13	whether	whether	SCONJ
ap-368	216	14	the	the	DET
ap-368	216	15	validity	validity	NOUN
ap-368	216	16	limits	limit	NOUN
ap-368	216	17	of	of	ADP
ap-368	216	18	the	the	DET
ap-368	216	19	kzk	kzk	PRON
ap-368	216	20	are	be	AUX
ap-368	216	21	fulfilled	fulfil	VERB
ap-368	216	22	.	.	PUNCT
ap-368	217	1	in	in	ADP
ap-368	217	2	the	the	DET
ap-368	217	3	waveguide	waveguide	NOUN
ap-368	217	4	of	of	ADP
ap-368	217	5	the	the	DET
ap-368	217	6	large	large	ADJ
ap-368	217	7	radius	radius	NOUN
ap-368	217	8	we	we	PRON
ap-368	217	9	can	can	AUX
ap-368	217	10	describe	describe	VERB
ap-368	217	11	by	by	ADP
ap-368	217	12	means	mean	NOUN
ap-368	217	13	of	of	ADP
ap-368	217	14	the	the	DET
ap-368	217	15	kzk	kzk	DET
ap-368	217	16	equation	equation	NOUN
ap-368	217	17	the	the	DET
ap-368	217	18	high	high	ADJ
ap-368	217	19	frequency	frequency	NOUN
ap-368	217	20	wave	wave	NOUN
ap-368	217	21	propagation	propagation	NOUN
ap-368	217	22	for	for	ADP
ap-368	217	23	non	non	ADJ
ap-368	217	24	-	-	ADJ
ap-368	217	25	planar	planar	ADJ
ap-368	217	26	distribution	distribution	NOUN
ap-368	217	27	of	of	ADP
ap-368	217	28	the	the	DET
ap-368	217	29	velocity	velocity	NOUN
ap-368	217	30	along	along	ADP
ap-368	217	31	the	the	DET
ap-368	217	32	tube	tube	NOUN
ap-368	217	33	radius	radius	NOUN
ap-368	217	34	(	(	PUNCT
ap-368	217	35	it	it	PRON
ap-368	217	36	is	be	AUX
ap-368	217	37	no	no	ADV
ap-368	217	38	longer	long	ADV
ap-368	217	39	possible	possible	ADJ
ap-368	217	40	to	to	PART
ap-368	217	41	use	use	VERB
ap-368	217	42	the	the	DET
ap-368	217	43	generalized	generalize	VERB
ap-368	217	44	burgers	burger	NOUN
ap-368	217	45	equation	equation	NOUN
ap-368	217	46	here	here	ADV
ap-368	217	47	)	)	PUNCT
ap-368	217	48	.	.	PUNCT
ap-368	218	1	again	again	ADV
ap-368	218	2	we	we	PRON
ap-368	218	3	can	can	AUX
ap-368	218	4	decide	decide	VERB
ap-368	218	5	from	from	ADP
ap-368	218	6	the	the	DET
ap-368	218	7	magnitude	magnitude	NOUN
ap-368	218	8	of	of	ADP
ap-368	218	9	the	the	DET
ap-368	218	10	perpendicular	perpendicular	ADJ
ap-368	218	11	component	component	NOUN
ap-368	218	12	of	of	ADP
ap-368	218	13	the	the	DET
ap-368	218	14	velocity	velocity	NOUN
ap-368	218	15	whether	whether	SCONJ
ap-368	218	16	we	we	PRON
ap-368	218	17	will	will	AUX
ap-368	218	18	use	use	VERB
ap-368	218	19	the	the	DET
ap-368	218	20	kzk	kzk	PRON
ap-368	218	21	equation	equation	NOUN
ap-368	218	22	within	within	ADP
ap-368	218	23	the	the	DET
ap-368	218	24	limits	limit	NOUN
ap-368	218	25	of	of	ADP
ap-368	218	26	its	its	PRON
ap-368	218	27	validity	validity	NOUN
ap-368	218	28	for	for	ADP
ap-368	218	29	the	the	DET
ap-368	218	30	given	give	VERB
ap-368	218	31	parameters	parameter	NOUN
ap-368	218	32	f	f	X
ap-368	218	33	,	,	PUNCT
ap-368	218	34	r0	r0	NOUN
ap-368	218	35	,	,	PUNCT
ap-368	218	36	vm	vm	PROPN
ap-368	218	37	and	and	CCONJ
ap-368	218	38	for	for	ADP
ap-368	218	39	the	the	DET
ap-368	218	40	given	give	VERB
ap-368	218	41	velocity	velocity	NOUN
ap-368	218	42	distribution	distribution	NOUN
ap-368	218	43	along	along	ADP
ap-368	218	44	the	the	DET
ap-368	218	45	radius	radius	NOUN
ap-368	218	46	near	near	ADP
ap-368	218	47	the	the	DET
ap-368	218	48	source	source	NOUN
ap-368	218	49	.	.	PUNCT
ap-368	219	1	acknowledgments	acknowledgment	NOUN
ap-368	219	2	this	this	DET
ap-368	219	3	work	work	NOUN
ap-368	219	4	was	be	AUX
ap-368	219	5	supported	support	VERB
ap-368	219	6	by	by	ADP
ap-368	219	7	gacr	gacr	NOUN
ap-368	219	8	grant	grant	NOUN
ap-368	219	9	no	no	INTJ
ap-368	219	10	.	.	PUNCT
ap-368	220	1	202/01/1372	202/01/1372	NOUN
ap-368	220	2	and	and	CCONJ
ap-368	220	3	by	by	ADP
ap-368	220	4	ctu	ctu	NOUN
ap-368	220	5	research	research	NOUN
ap-368	220	6	program	program	NOUN
ap-368	220	7	16	16	NUM
ap-368	220	8	:	:	PUNCT
ap-368	220	9	cez	cez	PROPN
ap-368	220	10	:	:	PUNCT
ap-368	220	11	j04/98:212300016	j04/98:212300016	PROPN
ap-368	220	12	.	.	PUNCT
ap-368	221	1	references	reference	NOUN
ap-368	221	2	[	[	X
ap-368	221	3	1	1	NUM
ap-368	221	4	]	]	PUNCT
ap-368	221	5	landau	landau	NOUN
ap-368	221	6	,	,	PUNCT
ap-368	221	7	l.	l.	PROPN
ap-368	221	8	d.	d.	PROPN
ap-368	221	9	,	,	PUNCT
ap-368	221	10	lifshitz	lifshitz	PROPN
ap-368	221	11	,	,	PUNCT
ap-368	221	12	e.	e.	PROPN
ap-368	221	13	m.	m.	PROPN
ap-368	221	14	:	:	PUNCT
ap-368	221	15	fluid	fluid	ADJ
ap-368	221	16	mechanics	mechanic	NOUN
ap-368	221	17	,	,	PUNCT
ap-368	221	18	(	(	PUNCT
ap-368	221	19	2nd	2nd	ADJ
ap-368	221	20	ed	ed	NOUN
ap-368	221	21	.	.	PUNCT
ap-368	221	22	)	)	PUNCT
ap-368	221	23	.	.	PUNCT
ap-368	222	1	new	new	PROPN
ap-368	222	2	york	york	PROPN
ap-368	222	3	:	:	PUNCT
ap-368	222	4	pergamon	pergamon	PROPN
ap-368	222	5	press	press	PROPN
ap-368	222	6	,	,	PUNCT
ap-368	222	7	1987	1987	NUM
ap-368	222	8	.	.	PUNCT
ap-368	223	1	[	[	X
ap-368	223	2	2	2	NUM
ap-368	223	3	]	]	PUNCT
ap-368	223	4	rudenko	rudenko	NOUN
ap-368	223	5	,	,	PUNCT
ap-368	223	6	o.	o.	PROPN
ap-368	223	7	v.	v.	PROPN
ap-368	223	8	,	,	PUNCT
ap-368	223	9	soluyan	soluyan	PROPN
ap-368	223	10	,	,	PUNCT
ap-368	223	11	s.	s.	PROPN
ap-368	223	12	i.	i.	PROPN
ap-368	223	13	:	:	PUNCT
ap-368	223	14	theoretical	theoretical	ADJ
ap-368	223	15	foundations	foundation	NOUN
ap-368	223	16	of	of	ADP
ap-368	223	17	nonlinear	nonlinear	ADJ
ap-368	223	18	acoustics	acoustic	NOUN
ap-368	223	19	.	.	PUNCT
ap-368	224	1	new	new	PROPN
ap-368	224	2	york	york	PROPN
ap-368	224	3	:	:	PUNCT
ap-368	224	4	plenum	plenum	PROPN
ap-368	224	5	,	,	PUNCT
ap-368	224	6	1977	1977	NUM
ap-368	224	7	.	.	PUNCT
ap-368	225	1	[	[	X
ap-368	225	2	3	3	NUM
ap-368	225	3	]	]	X
ap-368	225	4	naugolnykh	naugolnykh	NOUN
ap-368	225	5	,	,	PUNCT
ap-368	225	6	k.	k.	PROPN
ap-368	225	7	,	,	PUNCT
ap-368	225	8	ostrovsky	ostrovsky	PROPN
ap-368	225	9	,	,	PUNCT
ap-368	225	10	l.	l.	PROPN
ap-368	225	11	:	:	PUNCT
ap-368	225	12	nonlinear	nonlinear	ADJ
ap-368	225	13	wave	wave	NOUN
ap-368	225	14	processes	process	NOUN
ap-368	225	15	in	in	ADP
ap-368	225	16	acoustics	acoustic	NOUN
ap-368	225	17	.	.	PUNCT
ap-368	226	1	usa	usa	PROPN
ap-368	226	2	:	:	PUNCT
ap-368	226	3	cambridge	cambridge	PROPN
ap-368	226	4	university	university	PROPN
ap-368	226	5	press	press	NOUN
ap-368	226	6	,	,	PUNCT
ap-368	226	7	1998	1998	NUM
ap-368	226	8	.	.	PUNCT
ap-368	227	1	[	[	X
ap-368	227	2	4	4	NUM
ap-368	227	3	]	]	X
ap-368	227	4	hamilton	hamilton	PROPN
ap-368	227	5	,	,	PUNCT
ap-368	227	6	m.	m.	PROPN
ap-368	227	7	f.	f.	PROPN
ap-368	227	8	,	,	PUNCT
ap-368	227	9	blackstock	blackstock	PROPN
ap-368	227	10	,	,	PUNCT
ap-368	227	11	d.	d.	PROPN
ap-368	227	12	t.	t.	PROPN
ap-368	227	13	:	:	PUNCT
ap-368	227	14	nonlinear	nonlinear	ADJ
ap-368	227	15	acoustics	acoustic	NOUN
ap-368	227	16	.	.	PUNCT
ap-368	228	1	usa	usa	NOUN
ap-368	228	2	:	:	PUNCT
ap-368	228	3	academic	academic	ADJ
ap-368	228	4	press	press	NOUN
ap-368	228	5	,	,	PUNCT
ap-368	228	6	1998	1998	NUM
ap-368	228	7	.	.	PUNCT
ap-368	229	1	[	[	X
ap-368	229	2	5	5	NUM
ap-368	229	3	]	]	X
ap-368	229	4	chester	chester	NOUN
ap-368	229	5	,	,	PUNCT
ap-368	229	6	w.	w.	PROPN
ap-368	229	7	:	:	PUNCT
ap-368	229	8	resonant	resonant	VERB
ap-368	229	9	oscillations	oscillation	NOUN
ap-368	229	10	in	in	ADP
ap-368	229	11	closed	closed	ADJ
ap-368	229	12	tubes	tube	NOUN
ap-368	229	13	.	.	PUNCT
ap-368	230	1	j.	j.	PROPN
ap-368	230	2	fluid	fluid	PROPN
ap-368	230	3	mech	mech	NOUN
ap-368	230	4	.	.	PUNCT
ap-368	230	5	,	,	PUNCT
ap-368	230	6	1964	1964	NUM
ap-368	230	7	,	,	PUNCT
ap-368	230	8	vol	vol	NOUN
ap-368	230	9	.	.	PROPN
ap-368	230	10	18	18	NUM
ap-368	230	11	,	,	PUNCT
ap-368	230	12	p.	p.	NOUN
ap-368	230	13	44–64	44–64	NUM
ap-368	230	14	.	.	PUNCT
ap-368	231	1	[	[	X
ap-368	231	2	6	6	NUM
ap-368	231	3	]	]	PUNCT
ap-368	231	4	blackstock	blackstock	PROPN
ap-368	231	5	,	,	PUNCT
ap-368	231	6	d.	d.	PROPN
ap-368	231	7	t.	t.	PROPN
ap-368	231	8	:	:	PUNCT
ap-368	231	9	nonlinear	nonlinear	ADJ
ap-368	231	10	acoustics	acoustic	NOUN
ap-368	231	11	(	(	PUNCT
ap-368	231	12	theoretical	theoretical	ADJ
ap-368	231	13	)	)	PUNCT
ap-368	231	14	.	.	PUNCT
ap-368	232	1	(	(	PUNCT
ap-368	232	2	3rd	3rd	ADJ
ap-368	232	3	ed	ed	NOUN
ap-368	232	4	.	.	PUNCT
ap-368	232	5	)	)	PUNCT
ap-368	233	1	american	american	PROPN
ap-368	233	2	institute	institute	PROPN
ap-368	233	3	of	of	ADP
ap-368	233	4	physics	physics	PROPN
ap-368	233	5	handbook	handbook	PROPN
ap-368	233	6	,	,	PUNCT
ap-368	233	7	new	new	PROPN
ap-368	233	8	york	york	PROPN
ap-368	233	9	:	:	PUNCT
ap-368	233	10	mc	mc	PROPN
ap-368	233	11	graw	graw	PROPN
ap-368	233	12	hill	hill	PROPN
ap-368	233	13	,	,	PUNCT
ap-368	233	14	1972	1972	NUM
ap-368	233	15	.	.	PUNCT
ap-368	234	1	[	[	X
ap-368	234	2	7	7	NUM
ap-368	234	3	]	]	X
ap-368	234	4	coppens	coppen	NOUN
ap-368	234	5	,	,	PUNCT
ap-368	234	6	a.	a.	PROPN
ap-368	234	7	b.	b.	PROPN
ap-368	234	8	:	:	PUNCT
ap-368	234	9	theoretical	theoretical	ADJ
ap-368	234	10	study	study	NOUN
ap-368	234	11	of	of	ADP
ap-368	234	12	finite	finite	ADJ
ap-368	234	13	-	-	ADJ
ap-368	234	14	amplitude	amplitude	ADJ
ap-368	234	15	traveling	travel	VERB
ap-368	234	16	waves	wave	NOUN
ap-368	234	17	in	in	ADP
ap-368	234	18	rigid	rigid	ADJ
ap-368	234	19	-	-	PUNCT
ap-368	234	20	walled	wall	VERB
ap-368	234	21	ducts	duct	NOUN
ap-368	234	22	:	:	PUNCT
ap-368	234	23	behaviour	behaviour	NOUN
ap-368	234	24	for	for	ADP
ap-368	234	25	strengths	strength	NOUN
ap-368	234	26	precluding	preclude	VERB
ap-368	234	27	shock	shock	NOUN
ap-368	234	28	formation	formation	NOUN
ap-368	234	29	.	.	PUNCT
ap-368	235	1	j.	j.	PROPN
ap-368	235	2	acoust	acoust	PROPN
ap-368	235	3	.	.	PUNCT
ap-368	236	1	soc	soc	PROPN
ap-368	236	2	.	.	PUNCT
ap-368	237	1	am	be	AUX
ap-368	237	2	.	.	PROPN
ap-368	237	3	,	,	PUNCT
ap-368	237	4	1971	1971	NUM
ap-368	237	5	,	,	PUNCT
ap-368	237	6	vol	vol	NOUN
ap-368	237	7	.	.	PROPN
ap-368	237	8	49	49	NUM
ap-368	237	9	(	(	PUNCT
ap-368	237	10	1	1	NUM
ap-368	237	11	-	-	PUNCT
ap-368	237	12	part	part	NOUN
ap-368	237	13	2	2	NUM
ap-368	237	14	)	)	PUNCT
ap-368	237	15	,	,	PUNCT
ap-368	238	1	p.	p.	NOUN
ap-368	238	2	306–318	306–318	NUM
ap-368	238	3	.	.	PUNCT
ap-368	239	1	[	[	X
ap-368	239	2	8	8	NUM
ap-368	239	3	]	]	X
ap-368	239	4	webster	webster	PROPN
ap-368	239	5	,	,	PUNCT
ap-368	239	6	d.	d.	PROPN
ap-368	239	7	a.	a.	PROPN
ap-368	239	8	,	,	PUNCT
ap-368	239	9	blackstock	blackstock	PROPN
ap-368	239	10	,	,	PUNCT
ap-368	239	11	d.	d.	PROPN
ap-368	239	12	t.	t.	PROPN
ap-368	239	13	:	:	PUNCT
ap-368	239	14	finite	finite	ADJ
ap-368	239	15	-	-	ADJ
ap-368	239	16	amplitude	amplitude	NOUN
ap-368	239	17	saturation	saturation	NOUN
ap-368	239	18	of	of	ADP
ap-368	239	19	plane	plane	NOUN
ap-368	239	20	sound	sound	NOUN
ap-368	239	21	waves	wave	NOUN
ap-368	239	22	in	in	ADP
ap-368	239	23	air	air	NOUN
ap-368	239	24	.	.	PUNCT
ap-368	240	1	j.	j.	PROPN
ap-368	240	2	acoust	acoust	PROPN
ap-368	240	3	.	.	PUNCT
ap-368	241	1	soc	soc	PROPN
ap-368	241	2	.	.	PUNCT
ap-368	242	1	am	be	AUX
ap-368	242	2	.	.	PROPN
ap-368	242	3	,	,	PUNCT
ap-368	242	4	1977	1977	NUM
ap-368	242	5	,	,	PUNCT
ap-368	242	6	vol	vol	NOUN
ap-368	242	7	.	.	PROPN
ap-368	243	1	62	62	NUM
ap-368	243	2	,	,	PUNCT
ap-368	243	3	no	no	INTJ
ap-368	243	4	.	.	NOUN
ap-368	243	5	3	3	NUM
ap-368	243	6	,	,	PUNCT
ap-368	243	7	p.	p.	NOUN
ap-368	243	8	518–523	518–523	NUM
ap-368	243	9	.	.	PUNCT
ap-368	244	1	[	[	X
ap-368	244	2	9	9	NUM
ap-368	244	3	]	]	X
ap-368	244	4	gaete	gaete	ADJ
ap-368	244	5	-	-	PUNCT
ap-368	244	6	garreton	garreton	NOUN
ap-368	244	7	,	,	PUNCT
ap-368	244	8	l.	l.	PROPN
ap-368	244	9	,	,	PUNCT
ap-368	244	10	gallego	gallego	NOUN
ap-368	244	11	-	-	PUNCT
ap-368	244	12	juarez	juarez	PROPN
ap-368	244	13	,	,	PUNCT
ap-368	244	14	j.	j.	PROPN
ap-368	244	15	a.	a.	PROPN
ap-368	244	16	:	:	PUNCT
ap-368	244	17	propagation	propagation	NOUN
ap-368	244	18	of	of	ADP
ap-368	244	19	finite	finite	ADJ
ap-368	244	20	-	-	ADJ
ap-368	244	21	amplitude	amplitude	ADJ
ap-368	244	22	ultrasonic	ultrasonic	ADJ
ap-368	244	23	waves	wave	NOUN
ap-368	244	24	in	in	ADP
ap-368	244	25	air	air	NOUN
ap-368	244	26	-	-	PUNCT
ap-368	244	27	ii	ii	NOUN
ap-368	244	28	.	.	PUNCT
ap-368	245	1	plane	plane	NOUN
ap-368	245	2	waves	wave	NOUN
ap-368	245	3	in	in	ADP
ap-368	245	4	a	a	DET
ap-368	245	5	tube	tube	NOUN
ap-368	245	6	.	.	PUNCT
ap-368	246	1	j.	j.	PROPN
ap-368	246	2	acoust	acoust	PROPN
ap-368	246	3	.	.	PUNCT
ap-368	247	1	soc	soc	PROPN
ap-368	247	2	.	.	PUNCT
ap-368	248	1	am	be	AUX
ap-368	248	2	.	.	PROPN
ap-368	248	3	,	,	PUNCT
ap-368	248	4	1983	1983	NUM
ap-368	248	5	,	,	PUNCT
ap-368	248	6	vol	vol	NOUN
ap-368	248	7	.	.	PROPN
ap-368	249	1	73	73	NUM
ap-368	249	2	,	,	PUNCT
ap-368	249	3	no	no	INTJ
ap-368	249	4	.	.	NOUN
ap-368	249	5	3	3	NUM
ap-368	249	6	,	,	PUNCT
ap-368	250	1	p.	p.	NOUN
ap-368	250	2	768–773	768–773	NUM
ap-368	250	3	.	.	PUNCT
ap-368	251	1	[	[	X
ap-368	251	2	10	10	NUM
ap-368	251	3	]	]	PUNCT
ap-368	251	4	burns	burn	NOUN
ap-368	251	5	,	,	PUNCT
ap-368	251	6	s.	s.	PROPN
ap-368	251	7	h.	h.	PROPN
ap-368	251	8	:	:	PUNCT
ap-368	251	9	finite	finite	ADJ
ap-368	251	10	-	-	ADJ
ap-368	251	11	amplitude	amplitude	NOUN
ap-368	251	12	distortion	distortion	NOUN
ap-368	251	13	in	in	ADP
ap-368	251	14	air	air	NOUN
ap-368	251	15	at	at	ADP
ap-368	251	16	high	high	ADJ
ap-368	251	17	acoustic	acoustic	ADJ
ap-368	251	18	pressures	pressure	NOUN
ap-368	251	19	.	.	PUNCT
ap-368	252	1	j.	j.	PROPN
ap-368	252	2	acoust	acoust	PROPN
ap-368	252	3	.	.	PUNCT
ap-368	253	1	soc	soc	PROPN
ap-368	253	2	.	.	PUNCT
ap-368	254	1	am	be	AUX
ap-368	254	2	.	.	PROPN
ap-368	254	3	,	,	PUNCT
ap-368	254	4	1967	1967	NUM
ap-368	254	5	,	,	PUNCT
ap-368	254	6	vol	vol	NOUN
ap-368	254	7	.	.	PROPN
ap-368	255	1	41	41	NUM
ap-368	255	2	(	(	PUNCT
ap-368	255	3	4	4	NUM
ap-368	255	4	-	-	PUNCT
ap-368	255	5	part	part	NOUN
ap-368	255	6	2	2	NUM
ap-368	255	7	)	)	PUNCT
ap-368	255	8	,	,	PUNCT
ap-368	255	9	p.	p.	NOUN
ap-368	255	10	1157–1169	1157–1169	NUM
ap-368	255	11	.	.	PUNCT
ap-368	256	1	[	[	X
ap-368	256	2	11	11	NUM
ap-368	256	3	]	]	X
ap-368	256	4	keller	keller	PROPN
ap-368	256	5	,	,	PUNCT
ap-368	256	6	j.	j.	PROPN
ap-368	256	7	b.	b.	PROPN
ap-368	256	8	,	,	PUNCT
ap-368	256	9	millmann	millmann	PROPN
ap-368	256	10	,	,	PUNCT
ap-368	256	11	m.	m.	PROPN
ap-368	256	12	h.	h.	PROPN
ap-368	256	13	:	:	PUNCT
ap-368	256	14	finite	finite	ADJ
ap-368	256	15	-	-	ADJ
ap-368	256	16	amplitude	amplitude	ADJ
ap-368	256	17	sound	sound	NOUN
ap-368	256	18	wave	wave	NOUN
ap-368	256	19	propagation	propagation	NOUN
ap-368	256	20	in	in	ADP
ap-368	256	21	a	a	DET
ap-368	256	22	waveguide	waveguide	NOUN
ap-368	256	23	.	.	PUNCT
ap-368	257	1	j.	j.	PROPN
ap-368	257	2	acoust	acoust	PROPN
ap-368	257	3	.	.	PUNCT
ap-368	258	1	soc	soc	PROPN
ap-368	258	2	.	.	PUNCT
ap-368	259	1	am	be	AUX
ap-368	259	2	.	.	PROPN
ap-368	259	3	,	,	PUNCT
ap-368	259	4	1971	1971	NUM
ap-368	259	5	,	,	PUNCT
ap-368	259	6	vol	vol	NOUN
ap-368	259	7	.	.	PROPN
ap-368	259	8	49	49	NUM
ap-368	259	9	(	(	PUNCT
ap-368	259	10	1	1	NUM
ap-368	259	11	-	-	NUM
ap-368	259	12	part2	part2	NOUN
ap-368	259	13	)	)	PUNCT
ap-368	259	14	,	,	PUNCT
ap-368	260	1	p.	p.	NOUN
ap-368	260	2	329–333	329–333	NUM
ap-368	260	3	.	.	PUNCT
ap-368	261	1	[	[	X
ap-368	261	2	12	12	NUM
ap-368	261	3	]	]	X
ap-368	261	4	keller	keller	PROPN
ap-368	261	5	,	,	PUNCT
ap-368	261	6	j.	j.	PROPN
ap-368	261	7	b.	b.	PROPN
ap-368	261	8	:	:	PUNCT
ap-368	261	9	nonlinear	nonlinear	NOUN
ap-368	261	10	forced	force	VERB
ap-368	261	11	and	and	CCONJ
ap-368	261	12	free	free	ADJ
ap-368	261	13	vibrations	vibration	NOUN
ap-368	261	14	in	in	ADP
ap-368	261	15	acoustic	acoustic	ADJ
ap-368	261	16	waveguides	waveguide	NOUN
ap-368	261	17	.	.	PUNCT
ap-368	262	1	j.	j.	PROPN
ap-368	262	2	acoust	acoust	PROPN
ap-368	262	3	.	.	PUNCT
ap-368	263	1	soc	soc	PROPN
ap-368	263	2	.	.	PUNCT
ap-368	264	1	am	be	AUX
ap-368	264	2	.	.	PROPN
ap-368	264	3	,	,	PUNCT
ap-368	264	4	1974	1974	NUM
ap-368	264	5	,	,	PUNCT
ap-368	264	6	vol	vol	NOUN
ap-368	264	7	.	.	PROPN
ap-368	265	1	55	55	NUM
ap-368	265	2	,	,	PUNCT
ap-368	265	3	no	no	INTJ
ap-368	265	4	.	.	NOUN
ap-368	265	5	3	3	NUM
ap-368	265	6	,	,	PUNCT
ap-368	265	7	p.	p.	NOUN
ap-368	265	8	524–527	524–527	NUM
ap-368	265	9	.	.	PUNCT
ap-368	266	1	[	[	X
ap-368	266	2	13	13	NUM
ap-368	266	3	]	]	PUNCT
ap-368	266	4	nayfeh	nayfeh	NOUN
ap-368	266	5	,	,	PUNCT
ap-368	266	6	a.	a.	PROPN
ap-368	266	7	h.	h.	PROPN
ap-368	266	8	,	,	PUNCT
ap-368	266	9	tsai	tsai	PROPN
ap-368	266	10	,	,	PUNCT
ap-368	266	11	m.	m.	PROPN
ap-368	266	12	s.	s.	PROPN
ap-368	266	13	:	:	PUNCT
ap-368	266	14	non	non	ADJ
ap-368	266	15	-	-	ADJ
ap-368	266	16	linear	linear	ADJ
ap-368	266	17	wave	wave	NOUN
ap-368	266	18	propagation	propagation	NOUN
ap-368	266	19	in	in	ADP
ap-368	266	20	acoustically	acoustically	ADV
ap-368	266	21	lined	line	VERB
ap-368	266	22	circular	circular	ADJ
ap-368	266	23	ducts	duct	NOUN
ap-368	266	24	.	.	PUNCT
ap-368	267	1	j.	j.	PROPN
ap-368	267	2	of	of	ADP
ap-368	267	3	sound	sound	PROPN
ap-368	267	4	and	and	CCONJ
ap-368	267	5	vib	vib	PROPN
ap-368	267	6	.	.	PROPN
ap-368	267	7	,	,	PUNCT
ap-368	267	8	1971	1971	NUM
ap-368	267	9	,	,	PUNCT
ap-368	267	10	vol	vol	NOUN
ap-368	267	11	.	.	PROPN
ap-368	267	12	36	36	NUM
ap-368	267	13	,	,	PUNCT
ap-368	267	14	no	no	INTJ
ap-368	267	15	.	.	NOUN
ap-368	267	16	1	1	NUM
ap-368	267	17	,	,	PUNCT
ap-368	267	18	p.	p.	NOUN
ap-368	267	19	77–89	77–89	NUM
ap-368	267	20	.	.	PUNCT
ap-368	268	1	[	[	X
ap-368	268	2	14	14	NUM
ap-368	268	3	]	]	X
ap-368	268	4	nayfeh	nayfeh	NOUN
ap-368	268	5	,	,	PUNCT
ap-368	268	6	a.	a.	PROPN
ap-368	268	7	h.	h.	PROPN
ap-368	268	8	,	,	PUNCT
ap-368	268	9	tsai	tsai	PROPN
ap-368	268	10	,	,	PUNCT
ap-368	268	11	m.	m.	PROPN
ap-368	268	12	s.	s.	PROPN
ap-368	268	13	:	:	PUNCT
ap-368	268	14	nonlinear	nonlinear	ADJ
ap-368	268	15	acoustic	acoustic	ADJ
ap-368	268	16	propagation	propagation	NOUN
ap-368	268	17	in	in	ADP
ap-368	268	18	two	two	NUM
ap-368	268	19	-	-	PUNCT
ap-368	268	20	dimensional	dimensional	ADJ
ap-368	268	21	ducts	duct	NOUN
ap-368	268	22	.	.	PUNCT
ap-368	269	1	j.	j.	PROPN
ap-368	269	2	acoust	acoust	PROPN
ap-368	269	3	.	.	PUNCT
ap-368	270	1	soc	soc	PROPN
ap-368	270	2	.	.	PUNCT
ap-368	271	1	am	be	AUX
ap-368	271	2	.	.	PROPN
ap-368	271	3	,	,	PUNCT
ap-368	271	4	1974	1974	NUM
ap-368	271	5	,	,	PUNCT
ap-368	271	6	vol	vol	NOUN
ap-368	271	7	.	.	PROPN
ap-368	272	1	55	55	NUM
ap-368	272	2	,	,	PUNCT
ap-368	272	3	no	no	INTJ
ap-368	272	4	.	.	NOUN
ap-368	272	5	6	6	NUM
ap-368	272	6	,	,	PUNCT
ap-368	272	7	p.	p.	NOUN
ap-368	272	8	1127–1133	1127–1133	NUM
ap-368	272	9	.	.	PUNCT
ap-368	273	1	[	[	X
ap-368	273	2	15	15	NUM
ap-368	273	3	]	]	X
ap-368	273	4	ginsberg	ginsberg	PROPN
ap-368	273	5	,	,	PUNCT
ap-368	273	6	j.	j.	PROPN
ap-368	273	7	h.	h.	PROPN
ap-368	273	8	:	:	PUNCT
ap-368	273	9	finite	finite	VERB
ap-368	273	10	amplitude	amplitude	NOUN
ap-368	273	11	two	two	NUM
ap-368	273	12	-	-	PUNCT
ap-368	273	13	dimensional	dimensional	ADJ
ap-368	273	14	waves	wave	NOUN
ap-368	273	15	in	in	ADP
ap-368	273	16	a	a	DET
ap-368	273	17	rectangular	rectangular	ADJ
ap-368	273	18	duct	duct	NOUN
ap-368	273	19	induced	induce	VERB
ap-368	273	20	by	by	ADP
ap-368	273	21	arbitrary	arbitrary	ADJ
ap-368	273	22	periodic	periodic	ADJ
ap-368	273	23	excitation	excitation	NOUN
ap-368	273	24	.	.	PUNCT
ap-368	274	1	j.	j.	PROPN
ap-368	274	2	acoust	acoust	PROPN
ap-368	274	3	.	.	PUNCT
ap-368	275	1	soc	soc	PROPN
ap-368	275	2	.	.	PUNCT
ap-368	276	1	am	be	AUX
ap-368	276	2	.	.	PROPN
ap-368	276	3	,	,	PUNCT
ap-368	276	4	1978	1978	NUM
ap-368	276	5	,	,	PUNCT
ap-368	276	6	vol	vol	NOUN
ap-368	276	7	.	.	PROPN
ap-368	277	1	65	65	NUM
ap-368	277	2	,	,	PUNCT
ap-368	277	3	no	no	INTJ
ap-368	277	4	.	.	NOUN
ap-368	277	5	5	5	NUM
ap-368	277	6	,	,	PUNCT
ap-368	277	7	p.	p.	NOUN
ap-368	277	8	1127–1133	1127–1133	NUM
ap-368	277	9	.	.	PUNCT
ap-368	278	1	[	[	X
ap-368	278	2	16	16	NUM
ap-368	278	3	]	]	PUNCT
ap-368	278	4	ginsberg	ginsberg	PROPN
ap-368	278	5	,	,	PUNCT
ap-368	278	6	j.	j.	PROPN
ap-368	278	7	h.	h.	PROPN
ap-368	278	8	,	,	PUNCT
ap-368	278	9	miao	miao	PROPN
ap-368	278	10	,	,	PUNCT
ap-368	278	11	h.	h.	PROPN
ap-368	278	12	c.	c.	PROPN
ap-368	278	13	:	:	PUNCT
ap-368	278	14	finite	finite	VERB
ap-368	278	15	amplitude	amplitude	NOUN
ap-368	278	16	distortion	distortion	NOUN
ap-368	278	17	and	and	CCONJ
ap-368	278	18	dispersion	dispersion	NOUN
ap-368	278	19	of	of	ADP
ap-368	278	20	a	a	DET
ap-368	278	21	nonplanar	nonplanar	ADJ
ap-368	278	22	mode	mode	NOUN
ap-368	278	23	in	in	ADP
ap-368	278	24	a	a	DET
ap-368	278	25	waveguide	waveguide	NOUN
ap-368	278	26	.	.	PUNCT
ap-368	279	1	j.	j.	PROPN
ap-368	279	2	acoust.soc	acoust.soc	PROPN
ap-368	279	3	.	.	PUNCT
ap-368	280	1	am	be	AUX
ap-368	280	2	.	.	PROPN
ap-368	280	3	,	,	PUNCT
ap-368	280	4	1986	1986	NUM
ap-368	280	5	,	,	PUNCT
ap-368	280	6	vol	vol	NOUN
ap-368	280	7	.	.	PROPN
ap-368	280	8	80	80	NUM
ap-368	280	9	,	,	PUNCT
ap-368	280	10	no	no	INTJ
ap-368	280	11	.	.	NOUN
ap-368	280	12	3	3	NUM
ap-368	280	13	,	,	PUNCT
ap-368	280	14	p.	p.	NOUN
ap-368	280	15	911–920	911–920	NUM
ap-368	280	16	.	.	PUNCT
ap-368	281	1	[	[	X
ap-368	281	2	17	17	NUM
ap-368	281	3	]	]	X
ap-368	281	4	hamilton	hamilton	PROPN
ap-368	281	5	,	,	PUNCT
ap-368	281	6	m.	m.	PROPN
ap-368	281	7	f.	f.	PROPN
ap-368	281	8	,	,	PUNCT
ap-368	281	9	tencate	tencate	PROPN
ap-368	281	10	j.	j.	PROPN
ap-368	281	11	a.	a.	PROPN
ap-368	281	12	:	:	PUNCT
ap-368	281	13	sum	sum	NOUN
ap-368	281	14	and	and	CCONJ
ap-368	281	15	difference	difference	NOUN
ap-368	281	16	frequency	frequency	NOUN
ap-368	281	17	generation	generation	NOUN
ap-368	281	18	due	due	ADP
ap-368	281	19	to	to	ADP
ap-368	281	20	noncollinear	noncollinear	ADJ
ap-368	281	21	wave	wave	NOUN
ap-368	281	22	interaction	interaction	NOUN
ap-368	281	23	in	in	ADP
ap-368	281	24	a	a	DET
ap-368	281	25	rectangular	rectangular	ADJ
ap-368	281	26	duct	duct	NOUN
ap-368	281	27	.	.	PUNCT
ap-368	282	1	j.	j.	PROPN
ap-368	282	2	acoust	acoust	PROPN
ap-368	282	3	.	.	PUNCT
ap-368	283	1	soc	soc	PROPN
ap-368	283	2	.	.	PUNCT
ap-368	284	1	am	be	AUX
ap-368	284	2	.	.	PROPN
ap-368	284	3	,	,	PUNCT
ap-368	284	4	1987	1987	NUM
ap-368	284	5	,	,	PUNCT
ap-368	284	6	vol	vol	NOUN
ap-368	284	7	.	.	PROPN
ap-368	284	8	81	81	NUM
ap-368	284	9	,	,	PUNCT
ap-368	284	10	no	no	INTJ
ap-368	284	11	.	.	NOUN
ap-368	284	12	6	6	NUM
ap-368	284	13	,	,	PUNCT
ap-368	284	14	p.	p.	NOUN
ap-368	284	15	1703–1712	1703–1712	NUM
ap-368	284	16	.	.	PUNCT
ap-368	285	1	[	[	X
ap-368	285	2	18	18	NUM
ap-368	285	3	]	]	X
ap-368	285	4	hamilton	hamilton	PROPN
ap-368	285	5	,	,	PUNCT
ap-368	285	6	m.	m.	PROPN
ap-368	285	7	f.	f.	PROPN
ap-368	285	8	,	,	PUNCT
ap-368	285	9	tencate	tencate	PROPN
ap-368	285	10	j.	j.	PROPN
ap-368	285	11	a.	a.	PROPN
ap-368	285	12	:	:	PUNCT
ap-368	285	13	finite	finite	VERB
ap-368	285	14	amplitude	amplitude	NOUN
ap-368	285	15	sound	sound	NOUN
ap-368	285	16	near	near	ADP
ap-368	285	17	cutoff	cutoff	NOUN
ap-368	285	18	in	in	ADP
ap-368	285	19	higher	high	ADJ
ap-368	285	20	-	-	PUNCT
ap-368	285	21	order	order	NOUN
ap-368	285	22	modes	mode	NOUN
ap-368	285	23	of	of	ADP
ap-368	285	24	a	a	DET
ap-368	285	25	rectangular	rectangular	ADJ
ap-368	285	26	duct	duct	NOUN
ap-368	285	27	.	.	PUNCT
ap-368	286	1	j.	j.	PROPN
ap-368	286	2	acoust	acoust	PROPN
ap-368	286	3	.	.	PUNCT
ap-368	287	1	soc	soc	PROPN
ap-368	287	2	.	.	PUNCT
ap-368	288	1	am	be	AUX
ap-368	288	2	.	.	PROPN
ap-368	288	3	,	,	PUNCT
ap-368	288	4	1988	1988	NUM
ap-368	288	5	,	,	PUNCT
ap-368	288	6	vol	vol	NOUN
ap-368	288	7	.	.	PROPN
ap-368	288	8	84	84	NUM
ap-368	288	9	,	,	PUNCT
ap-368	288	10	no	no	INTJ
ap-368	288	11	.	.	NOUN
ap-368	288	12	1	1	NUM
ap-368	288	13	,	,	PUNCT
ap-368	288	14	p.	p.	NOUN
ap-368	288	15	327–334	327–334	NUM
ap-368	288	16	.	.	PUNCT
ap-368	289	1	©	©	PROPN
ap-368	289	2	czech	czech	PROPN
ap-368	289	3	technical	technical	PROPN
ap-368	289	4	university	university	PROPN
ap-368	289	5	publishing	publishing	NOUN
ap-368	289	6	house	house	NOUN
ap-368	289	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	289	8	25	25	NUM
ap-368	289	9	acta	acta	PROPN
ap-368	289	10	polytechnica	polytechnica	PROPN
ap-368	289	11	vol	vol	NOUN
ap-368	289	12	.	.	PUNCT
ap-368	290	1	42	42	NUM
ap-368	290	2	no	no	INTJ
ap-368	290	3	.	.	PUNCT
ap-368	291	1	4/2002	4/2002	NUM
ap-368	291	2	fig	fig	NOUN
ap-368	291	3	.	.	PUNCT
ap-368	292	1	9	9	NUM
ap-368	292	2	:	:	PUNCT
ap-368	292	3	kzk	kzk	ADJ
ap-368	292	4	equation	equation	NOUN
ap-368	292	5	solution	solution	NOUN
ap-368	292	6	of	of	ADP
ap-368	292	7	the	the	DET
ap-368	292	8	longitudinal	longitudinal	ADJ
ap-368	292	9	(	(	PUNCT
ap-368	292	10	v4	v4	NOUN
ap-368	292	11	)	)	PUNCT
ap-368	292	12	and	and	CCONJ
ap-368	292	13	transversal	transversal	NOUN
ap-368	292	14	(	(	PUNCT
ap-368	292	15	w4	w4	NOUN
ap-368	292	16	)	)	PUNCT
ap-368	292	17	velocity	velocity	NOUN
ap-368	292	18	component	component	NOUN
ap-368	292	19	of	of	ADP
ap-368	292	20	the	the	DET
ap-368	292	21	fourth	fourth	ADJ
ap-368	292	22	harmonic	harmonic	NOUN
ap-368	292	23	[	[	X
ap-368	292	24	19	19	NUM
ap-368	292	25	]	]	PUNCT
ap-368	292	26	nayfeh	nayfeh	NOUN
ap-368	292	27	,	,	PUNCT
ap-368	292	28	a.	a.	PROPN
ap-368	292	29	h.	h.	PROPN
ap-368	292	30	:	:	PUNCT
ap-368	292	31	nonlinear	nonlinear	ADJ
ap-368	292	32	propagation	propagation	NOUN
ap-368	292	33	of	of	ADP
ap-368	292	34	a	a	DET
ap-368	292	35	wave	wave	NOUN
ap-368	292	36	packet	packet	NOUN
ap-368	292	37	in	in	ADP
ap-368	292	38	a	a	DET
ap-368	292	39	hard	hard	ADV
ap-368	292	40	-	-	PUNCT
ap-368	292	41	walled	wall	VERB
ap-368	292	42	circular	circular	ADJ
ap-368	292	43	duct	duct	NOUN
ap-368	292	44	.	.	PUNCT
ap-368	293	1	j.	j.	PROPN
ap-368	293	2	acoust	acoust	PROPN
ap-368	293	3	.	.	PUNCT
ap-368	294	1	soc	soc	PROPN
ap-368	294	2	.	.	PUNCT
ap-368	295	1	am	be	AUX
ap-368	295	2	.	.	PROPN
ap-368	295	3	,	,	PUNCT
ap-368	295	4	1975	1975	NUM
ap-368	295	5	,	,	PUNCT
ap-368	295	6	vol	vol	NOUN
ap-368	295	7	.	.	PROPN
ap-368	295	8	57	57	NUM
ap-368	295	9	,	,	PUNCT
ap-368	295	10	no	no	INTJ
ap-368	295	11	.	.	NOUN
ap-368	295	12	4	4	NUM
ap-368	295	13	,	,	PUNCT
ap-368	295	14	p.	p.	NOUN
ap-368	295	15	803–809	803–809	NUM
ap-368	295	16	.	.	PUNCT
ap-368	296	1	[	[	X
ap-368	296	2	20	20	NUM
ap-368	296	3	]	]	SYM
ap-368	296	4	foda	foda	PROPN
ap-368	296	5	,	,	PUNCT
ap-368	296	6	m.	m.	NOUN
ap-368	296	7	a.	a.	NOUN
ap-368	296	8	:	:	PUNCT
ap-368	296	9	analysis	analysis	NOUN
ap-368	296	10	of	of	ADP
ap-368	296	11	nonlinear	nonlinear	ADJ
ap-368	296	12	propagation	propagation	NOUN
ap-368	296	13	and	and	CCONJ
ap-368	296	14	interactions	interaction	NOUN
ap-368	296	15	of	of	ADP
ap-368	296	16	higher	high	ADJ
ap-368	296	17	order	order	NOUN
ap-368	296	18	modes	mode	NOUN
ap-368	296	19	in	in	ADP
ap-368	296	20	a	a	DET
ap-368	296	21	circular	circular	ADJ
ap-368	296	22	waveguide	waveguide	NOUN
ap-368	296	23	.	.	PUNCT
ap-368	297	1	acustica	acustica	PROPN
ap-368	297	2	,	,	PUNCT
ap-368	297	3	1998	1998	NUM
ap-368	297	4	,	,	PUNCT
ap-368	297	5	vol	vol	NOUN
ap-368	297	6	.	.	PROPN
ap-368	297	7	84	84	NUM
ap-368	297	8	,	,	PUNCT
ap-368	297	9	no	no	INTJ
ap-368	297	10	.	.	NOUN
ap-368	297	11	1	1	NUM
ap-368	297	12	,	,	PUNCT
ap-368	297	13	p.	p.	NOUN
ap-368	297	14	66–77	66–77	NUM
ap-368	297	15	.	.	PUNCT
ap-368	298	1	[	[	X
ap-368	298	2	21	21	NUM
ap-368	298	3	]	]	X
ap-368	298	4	blackstock	blackstock	PROPN
ap-368	298	5	,	,	PUNCT
ap-368	298	6	d.	d.	PROPN
ap-368	298	7	t.	t.	PROPN
ap-368	298	8	:	:	PUNCT
ap-368	298	9	generalized	generalize	VERB
ap-368	298	10	burgers	burger	NOUN
ap-368	298	11	equation	equation	NOUN
ap-368	298	12	for	for	ADP
ap-368	298	13	plane	plane	NOUN
ap-368	298	14	waves	wave	NOUN
ap-368	298	15	.	.	PUNCT
ap-368	299	1	j.	j.	PROPN
ap-368	299	2	acoust	acoust	PROPN
ap-368	299	3	.	.	PUNCT
ap-368	300	1	soc	soc	PROPN
ap-368	300	2	.	.	PUNCT
ap-368	301	1	am	be	AUX
ap-368	301	2	.	.	PROPN
ap-368	301	3	,	,	PUNCT
ap-368	301	4	1985	1985	NUM
ap-368	301	5	,	,	PUNCT
ap-368	301	6	vol	vol	NOUN
ap-368	301	7	.	.	PROPN
ap-368	302	1	77	77	NUM
ap-368	302	2	,	,	PUNCT
ap-368	302	3	no	no	INTJ
ap-368	302	4	.	.	NOUN
ap-368	302	5	6	6	NUM
ap-368	302	6	,	,	PUNCT
ap-368	302	7	p.	p.	NOUN
ap-368	302	8	2050–2053	2050–2053	NUM
ap-368	302	9	.	.	PUNCT
ap-368	303	1	[	[	X
ap-368	303	2	22	22	NUM
ap-368	303	3	]	]	PUNCT
ap-368	303	4	makarov	makarov	PROPN
ap-368	303	5	,	,	PUNCT
ap-368	303	6	s.	s.	PROPN
ap-368	303	7	n.	n.	PROPN
ap-368	303	8	,	,	PUNCT
ap-368	303	9	vatrushina	vatrushina	PROPN
ap-368	303	10	,	,	PUNCT
ap-368	303	11	e.	e.	PROPN
ap-368	303	12	:	:	PUNCT
ap-368	303	13	effect	effect	NOUN
ap-368	303	14	of	of	ADP
ap-368	303	15	the	the	DET
ap-368	303	16	acoustic	acoustic	ADJ
ap-368	303	17	boundary	boundary	ADJ
ap-368	303	18	layer	layer	NOUN
ap-368	303	19	on	on	ADP
ap-368	303	20	a	a	DET
ap-368	303	21	nonlinear	nonlinear	ADJ
ap-368	303	22	quasiplane	quasiplane	ADJ
ap-368	303	23	wave	wave	NOUN
ap-368	303	24	in	in	ADP
ap-368	303	25	a	a	DET
ap-368	303	26	rigid	rigid	ADJ
ap-368	303	27	-	-	PUNCT
ap-368	303	28	waled	wale	VERB
ap-368	303	29	tube	tube	NOUN
ap-368	303	30	.	.	PUNCT
ap-368	304	1	j.	j.	PROPN
ap-368	304	2	acoust	acoust	PROPN
ap-368	304	3	.	.	PUNCT
ap-368	305	1	soc	soc	PROPN
ap-368	305	2	.	.	PUNCT
ap-368	306	1	am	be	AUX
ap-368	306	2	.	.	PROPN
ap-368	306	3	,	,	PUNCT
ap-368	306	4	1993	1993	NUM
ap-368	306	5	,	,	PUNCT
ap-368	306	6	vol	vol	NOUN
ap-368	306	7	.	.	PROPN
ap-368	307	1	94	94	NUM
ap-368	307	2	,	,	PUNCT
ap-368	307	3	no	no	INTJ
ap-368	307	4	.	.	NOUN
ap-368	307	5	2	2	NUM
ap-368	307	6	,	,	PUNCT
ap-368	307	7	p.	p.	NOUN
ap-368	307	8	1076–1083	1076–1083	NUM
ap-368	307	9	.	.	PUNCT
ap-368	308	1	[	[	X
ap-368	308	2	23	23	NUM
ap-368	308	3	]	]	SYM
ap-368	308	4	konicek	konicek	NOUN
ap-368	308	5	,	,	PUNCT
ap-368	308	6	p.	p.	NOUN
ap-368	308	7	,	,	PUNCT
ap-368	308	8	bednarik	bednarik	PROPN
ap-368	308	9	,	,	PUNCT
ap-368	308	10	m.	m.	NOUN
ap-368	308	11	,	,	PUNCT
ap-368	308	12	cervenka	cervenka	ADJ
ap-368	308	13	,	,	PUNCT
ap-368	308	14	m.	m.	NOUN
ap-368	308	15	:	:	PUNCT
ap-368	308	16	finite	finite	ADJ
ap-368	308	17	-	-	ADJ
ap-368	308	18	amplitude	amplitude	ADJ
ap-368	308	19	acoustic	acoustic	ADJ
ap-368	308	20	waves	wave	NOUN
ap-368	308	21	in	in	ADP
ap-368	308	22	a	a	DET
ap-368	308	23	liquid	liquid	NOUN
ap-368	308	24	-	-	PUNCT
ap-368	308	25	filled	fill	VERB
ap-368	308	26	tube	tube	NOUN
ap-368	308	27	.	.	PUNCT
ap-368	309	1	gdynia	gdynia	PROPN
ap-368	309	2	:	:	PUNCT
ap-368	309	3	naval	naval	PROPN
ap-368	309	4	academy	academy	PROPN
ap-368	309	5	,	,	PUNCT
ap-368	309	6	hydroacoustics	hydroacoustic	NOUN
ap-368	309	7	,	,	PUNCT
ap-368	309	8	2000	2000	NUM
ap-368	309	9	,	,	PUNCT
ap-368	309	10	vol	vol	NOUN
ap-368	309	11	.	.	PROPN
ap-368	309	12	3	3	NUM
ap-368	309	13	,	,	PUNCT
ap-368	309	14	p.	p.	NOUN
ap-368	309	15	85–88	85–88	NUM
ap-368	309	16	.	.	PUNCT
ap-368	310	1	[	[	X
ap-368	310	2	24	24	NUM
ap-368	310	3	]	]	PUNCT
ap-368	310	4	ochmann	ochmann	NOUN
ap-368	310	5	,	,	PUNCT
ap-368	310	6	m.	m.	NOUN
ap-368	310	7	:	:	PUNCT
ap-368	310	8	representation	representation	NOUN
ap-368	310	9	of	of	ADP
ap-368	310	10	absorption	absorption	NOUN
ap-368	310	11	of	of	ADP
ap-368	310	12	nonlinear	nonlinear	ADJ
ap-368	310	13	waves	wave	NOUN
ap-368	310	14	by	by	ADP
ap-368	310	15	fractional	fractional	ADJ
ap-368	310	16	derivatives	derivative	NOUN
ap-368	310	17	.	.	PUNCT
ap-368	311	1	j.	j.	PROPN
ap-368	311	2	acoust	acoust	PROPN
ap-368	311	3	.	.	PUNCT
ap-368	312	1	soc	soc	PROPN
ap-368	312	2	.	.	PUNCT
ap-368	313	1	am	be	AUX
ap-368	313	2	.	.	PROPN
ap-368	313	3	,	,	PUNCT
ap-368	313	4	1993	1993	NUM
ap-368	313	5	,	,	PUNCT
ap-368	314	1	p.	p.	NOUN
ap-368	314	2	3392–3399	3392–3399	NUM
ap-368	314	3	.	.	PUNCT
ap-368	315	1	[	[	X
ap-368	315	2	25	25	NUM
ap-368	315	3	]	]	PUNCT
ap-368	315	4	makarov	makarov	PROPN
ap-368	315	5	,	,	PUNCT
ap-368	315	6	s.	s.	PROPN
ap-368	315	7	,	,	PUNCT
ap-368	315	8	ochmann	ochmann	NOUN
ap-368	315	9	,	,	PUNCT
ap-368	315	10	m.	m.	NOUN
ap-368	315	11	:	:	PUNCT
ap-368	315	12	nonlinear	nonlinear	ADJ
ap-368	315	13	and	and	CCONJ
ap-368	315	14	thermoviscous	thermoviscous	ADJ
ap-368	315	15	phenomena	phenomenon	NOUN
ap-368	315	16	in	in	ADP
ap-368	315	17	acoustics	acoustic	NOUN
ap-368	315	18	.	.	PUNCT
ap-368	316	1	part	part	PROPN
ap-368	316	2	ii	ii	PROPN
ap-368	316	3	,	,	PUNCT
ap-368	316	4	acustica	acustica	PROPN
ap-368	316	5	,	,	PUNCT
ap-368	316	6	1997	1997	NUM
ap-368	316	7	,	,	PUNCT
ap-368	316	8	vol	vol	NOUN
ap-368	316	9	.	.	PROPN
ap-368	316	10	83	83	NUM
ap-368	316	11	,	,	PUNCT
ap-368	316	12	no	no	INTJ
ap-368	316	13	.	.	NOUN
ap-368	316	14	2	2	NUM
ap-368	316	15	,	,	PUNCT
ap-368	316	16	p.	p.	NOUN
ap-368	316	17	197–222	197–222	NUM
ap-368	316	18	.	.	PUNCT
ap-368	317	1	[	[	X
ap-368	317	2	26	26	NUM
ap-368	317	3	]	]	X
ap-368	317	4	sugimoto	sugimoto	PROPN
ap-368	317	5	,	,	PUNCT
ap-368	317	6	n.	n.	NOUN
ap-368	317	7	:	:	PUNCT
ap-368	317	8	burgers	burger	NOUN
ap-368	317	9	equation	equation	NOUN
ap-368	317	10	with	with	ADP
ap-368	317	11	a	a	DET
ap-368	317	12	fractional	fractional	ADJ
ap-368	317	13	derivative	derivative	NOUN
ap-368	317	14	:	:	PUNCT
ap-368	317	15	hereditary	hereditary	ADJ
ap-368	317	16	effects	effect	NOUN
ap-368	317	17	on	on	ADP
ap-368	317	18	nonlinear	nonlinear	ADJ
ap-368	317	19	acoustic	acoustic	ADJ
ap-368	317	20	waves	wave	NOUN
ap-368	317	21	.	.	PUNCT
ap-368	318	1	j.	j.	PROPN
ap-368	318	2	fluid	fluid	PROPN
ap-368	318	3	mech	mech	NOUN
ap-368	318	4	.	.	PUNCT
ap-368	318	5	,	,	PUNCT
ap-368	318	6	1991	1991	NUM
ap-368	318	7	,	,	PUNCT
ap-368	318	8	vol	vol	NOUN
ap-368	318	9	.	.	PROPN
ap-368	318	10	125	125	NUM
ap-368	318	11	,	,	PUNCT
ap-368	318	12	p.	p.	NOUN
ap-368	318	13	631–653	631–653	NUM
ap-368	318	14	.	.	PUNCT
ap-368	319	1	[	[	X
ap-368	319	2	27	27	NUM
ap-368	319	3	]	]	X
ap-368	319	4	bednařík	bednařík	NOUN
ap-368	319	5	,	,	PUNCT
ap-368	319	6	m.	m.	NOUN
ap-368	319	7	,	,	PUNCT
ap-368	319	8	koníček	koníček	PROPN
ap-368	319	9	p.	p.	PROPN
ap-368	319	10	,	,	PUNCT
ap-368	319	11	červenka	červenka	PROPN
ap-368	319	12	m.	m.	NOUN
ap-368	319	13	:	:	PUNCT
ap-368	319	14	solution	solution	NOUN
ap-368	319	15	of	of	ADP
ap-368	319	16	the	the	DET
ap-368	319	17	burgers	burger	NOUN
ap-368	319	18	equation	equation	NOUN
ap-368	319	19	in	in	ADP
ap-368	319	20	the	the	DET
ap-368	319	21	time	time	NOUN
ap-368	319	22	domain	domain	NOUN
ap-368	319	23	.	.	PUNCT
ap-368	320	1	acta	acta	PROPN
ap-368	320	2	polytechnica	polytechnica	PROPN
ap-368	320	3	,	,	PUNCT
ap-368	320	4	2002	2002	NUM
ap-368	320	5	,	,	PUNCT
ap-368	320	6	vol	vol	NOUN
ap-368	320	7	.	.	PROPN
ap-368	321	1	42	42	NUM
ap-368	321	2	,	,	PUNCT
ap-368	321	3	no	no	INTJ
ap-368	321	4	.	.	NOUN
ap-368	321	5	2	2	NUM
ap-368	321	6	,	,	PUNCT
ap-368	321	7	p.	p.	NOUN
ap-368	322	1	71–75	71–75	PROPN
ap-368	322	2	.	.	PUNCT
ap-368	323	1	[	[	X
ap-368	323	2	28	28	NUM
ap-368	323	3	]	]	X
ap-368	323	4	bednarik	bednarik	NOUN
ap-368	323	5	,	,	PUNCT
ap-368	323	6	m.	m.	NOUN
ap-368	323	7	,	,	PUNCT
ap-368	323	8	konicek	konicek	PROPN
ap-368	323	9	,	,	PUNCT
ap-368	323	10	p.	p.	NOUN
ap-368	323	11	:	:	PUNCT
ap-368	323	12	propagation	propagation	NOUN
ap-368	323	13	of	of	ADP
ap-368	323	14	quasiplane	quasiplane	ADJ
ap-368	323	15	nonlinear	nonlinear	ADJ
ap-368	323	16	waves	wave	NOUN
ap-368	323	17	in	in	ADP
ap-368	323	18	tubes	tube	NOUN
ap-368	323	19	and	and	CCONJ
ap-368	323	20	the	the	DET
ap-368	323	21	approximate	approximate	ADJ
ap-368	323	22	solutions	solution	NOUN
ap-368	323	23	of	of	ADP
ap-368	323	24	the	the	DET
ap-368	323	25	generalized	generalize	VERB
ap-368	323	26	burgers	burger	NOUN
ap-368	323	27	equation	equation	NOUN
ap-368	323	28	.	.	PUNCT
ap-368	324	1	j.	j.	PROPN
ap-368	324	2	acoust	acoust	PROPN
ap-368	324	3	.	.	PUNCT
ap-368	325	1	soc	soc	PROPN
ap-368	325	2	.	.	PUNCT
ap-368	326	1	am	be	AUX
ap-368	326	2	.	.	PROPN
ap-368	326	3	,	,	PUNCT
ap-368	326	4	2002	2002	NUM
ap-368	326	5	,	,	PUNCT
ap-368	326	6	vol	vol	NOUN
ap-368	326	7	.	.	PROPN
ap-368	326	8	112	112	NUM
ap-368	326	9	,	,	PUNCT
ap-368	326	10	p.	p.	NOUN
ap-368	326	11	91–98	91–98	NUM
ap-368	326	12	.	.	PUNCT
ap-368	327	1	[	[	X
ap-368	327	2	29	29	NUM
ap-368	327	3	]	]	X
ap-368	327	4	zhileikin	zhileikin	PROPN
ap-368	327	5	,	,	PUNCT
ap-368	327	6	ya	ya	PROPN
ap-368	327	7	.	.	PROPN
ap-368	327	8	m.	m.	PROPN
ap-368	327	9	,	,	PUNCT
ap-368	327	10	zhuravleva	zhuravleva	PROPN
ap-368	327	11	,	,	PUNCT
ap-368	327	12	t.	t.	NOUN
ap-368	327	13	m.	m.	NOUN
ap-368	327	14	,	,	PUNCT
ap-368	327	15	rudenko	rudenko	NOUN
ap-368	327	16	,	,	PUNCT
ap-368	327	17	o.	o.	PROPN
ap-368	327	18	v.	v.	PROPN
ap-368	327	19	:	:	PUNCT
ap-368	327	20	nonlinear	nonlinear	ADJ
ap-368	327	21	effects	effect	NOUN
ap-368	327	22	in	in	ADP
ap-368	327	23	the	the	DET
ap-368	327	24	propagation	propagation	NOUN
ap-368	327	25	of	of	ADP
ap-368	327	26	high	high	ADJ
ap-368	327	27	-	-	PUNCT
ap-368	327	28	frequency	frequency	NOUN
ap-368	327	29	sound	sound	NOUN
ap-368	327	30	waves	wave	NOUN
ap-368	327	31	in	in	ADP
ap-368	327	32	tubes	tube	NOUN
ap-368	327	33	.	.	PUNCT
ap-368	328	1	phys	phy	NOUN
ap-368	328	2	.	.	PUNCT
ap-368	329	1	acoust	acoust	PROPN
ap-368	329	2	.	.	PUNCT
ap-368	329	3	,	,	PUNCT
ap-368	329	4	1980	1980	NUM
ap-368	329	5	,	,	PUNCT
ap-368	329	6	vol	vol	NOUN
ap-368	329	7	.	.	PROPN
ap-368	329	8	26	26	NUM
ap-368	329	9	,	,	PUNCT
ap-368	329	10	p.	p.	NOUN
ap-368	329	11	32–34	32–34	NUM
ap-368	329	12	.	.	PUNCT
ap-368	330	1	[	[	X
ap-368	330	2	30	30	NUM
ap-368	330	3	]	]	X
ap-368	330	4	gonghuan	gonghuan	PROPN
ap-368	330	5	,	,	PUNCT
ap-368	330	6	d.	d.	PROPN
ap-368	330	7	:	:	PUNCT
ap-368	330	8	fourier	fourier	PROPN
ap-368	330	9	series	series	PROPN
ap-368	330	10	solution	solution	NOUN
ap-368	330	11	of	of	ADP
ap-368	330	12	burger	burger	NOUN
ap-368	330	13	’s	’s	PART
ap-368	330	14	equation	equation	NOUN
ap-368	330	15	for	for	ADP
ap-368	330	16	nonlinear	nonlinear	ADJ
ap-368	330	17	acoustics	acoustic	NOUN
ap-368	330	18	in	in	ADP
ap-368	330	19	relaxing	relax	VERB
ap-368	330	20	media	medium	NOUN
ap-368	330	21	.	.	PUNCT
ap-368	331	1	j.	j.	PROPN
ap-368	331	2	acoust	acoust	PROPN
ap-368	331	3	.	.	PUNCT
ap-368	332	1	soc	soc	PROPN
ap-368	332	2	.	.	PUNCT
ap-368	333	1	am	be	AUX
ap-368	333	2	.	.	PROPN
ap-368	333	3	,	,	PUNCT
ap-368	333	4	1985	1985	NUM
ap-368	333	5	,	,	PUNCT
ap-368	333	6	vol	vol	NOUN
ap-368	333	7	.	.	PROPN
ap-368	334	1	77	77	NUM
ap-368	334	2	,	,	PUNCT
ap-368	334	3	no	no	INTJ
ap-368	334	4	.	.	NOUN
ap-368	334	5	3	3	NUM
ap-368	334	6	,	,	PUNCT
ap-368	334	7	p.	p.	NOUN
ap-368	334	8	924–927	924–927	NUM
ap-368	334	9	.	.	PUNCT
ap-368	335	1	[	[	X
ap-368	335	2	31	31	NUM
ap-368	335	3	]	]	PUNCT
ap-368	335	4	fenlon	fenlon	NOUN
ap-368	335	5	,	,	PUNCT
ap-368	335	6	f.	f.	PROPN
ap-368	335	7	h.	h.	PROPN
ap-368	335	8	:	:	PUNCT
ap-368	335	9	a	a	DET
ap-368	335	10	recursive	recursive	ADJ
ap-368	335	11	procedure	procedure	NOUN
ap-368	335	12	for	for	ADP
ap-368	335	13	computing	compute	VERB
ap-368	335	14	the	the	DET
ap-368	335	15	nonlinear	nonlinear	ADJ
ap-368	335	16	spectral	spectral	ADJ
ap-368	335	17	interactions	interaction	NOUN
ap-368	335	18	of	of	ADP
ap-368	335	19	progressive	progressive	ADJ
ap-368	335	20	finite	finite	ADJ
ap-368	335	21	-	-	ADJ
ap-368	335	22	amplitude	amplitude	NOUN
ap-368	335	23	waves	wave	NOUN
ap-368	335	24	in	in	ADP
ap-368	335	25	nondispersive	nondispersive	NOUN
ap-368	335	26	fluids	fluid	NOUN
ap-368	335	27	.	.	PUNCT
ap-368	336	1	j.	j.	PROPN
ap-368	336	2	acoust	acoust	PROPN
ap-368	336	3	.	.	PUNCT
ap-368	337	1	soc	soc	PROPN
ap-368	337	2	.	.	PUNCT
ap-368	338	1	am	be	AUX
ap-368	338	2	.	.	PROPN
ap-368	338	3	,	,	PUNCT
ap-368	338	4	1971	1971	NUM
ap-368	338	5	,	,	PUNCT
ap-368	338	6	vol	vol	NOUN
ap-368	338	7	.	.	PROPN
ap-368	339	1	50	50	NUM
ap-368	339	2	,	,	PUNCT
ap-368	339	3	no	no	INTJ
ap-368	339	4	.	.	NOUN
ap-368	339	5	5	5	NUM
ap-368	339	6	,	,	PUNCT
ap-368	339	7	p.	p.	NOUN
ap-368	339	8	1299–1312	1299–1312	NUM
ap-368	339	9	.	.	PUNCT
ap-368	340	1	[	[	X
ap-368	340	2	32	32	NUM
ap-368	340	3	]	]	PUNCT
ap-368	340	4	aanonsen	aanonsen	PROPN
ap-368	340	5	,	,	PUNCT
ap-368	340	6	s.	s.	PROPN
ap-368	340	7	i.	i.	PROPN
ap-368	340	8	:	:	PUNCT
ap-368	340	9	numerical	numerical	ADJ
ap-368	340	10	computation	computation	NOUN
ap-368	340	11	of	of	ADP
ap-368	340	12	the	the	DET
ap-368	340	13	nearfield	nearfield	NOUN
ap-368	340	14	amplitude	amplitude	NOUN
ap-368	340	15	sound	sound	NOUN
ap-368	340	16	beam	beam	NOUN
ap-368	340	17	.	.	PUNCT
ap-368	341	1	report	report	VERB
ap-368	341	2	no	no	INTJ
ap-368	341	3	.	.	PROPN
ap-368	341	4	73	73	NUM
ap-368	341	5	,	,	PUNCT
ap-368	341	6	university	university	NOUN
ap-368	341	7	of	of	ADP
ap-368	341	8	bergen	bergen	PROPN
ap-368	341	9	,	,	PUNCT
ap-368	341	10	department	department	NOUN
ap-368	341	11	of	of	ADP
ap-368	341	12	mathematics	mathematic	NOUN
ap-368	341	13	,	,	PUNCT
ap-368	341	14	1983	1983	NUM
ap-368	341	15	.	.	PUNCT
ap-368	342	1	dr	dr	PROPN
ap-368	342	2	.	.	PROPN
ap-368	342	3	mgr	mgr	PROPN
ap-368	342	4	.	.	PUNCT
ap-368	343	1	petr	petr	PROPN
ap-368	343	2	koníček	koníček	PROPN
ap-368	343	3	phone	phone	PROPN
ap-368	343	4	:	:	PUNCT
ap-368	343	5	+420	+420	PROPN
ap-368	343	6	224	224	NUM
ap-368	343	7	352	352	NUM
ap-368	343	8	329	329	NUM
ap-368	343	9	e	e	NOUN
ap-368	343	10	-	-	NOUN
ap-368	343	11	mail	mail	NOUN
ap-368	343	12	:	:	PUNCT
ap-368	343	13	konicek@feld.cvut.cz	konicek@feld.cvut.cz	PROPN
ap-368	343	14	dr	dr	PROPN
ap-368	343	15	.	.	PROPN
ap-368	343	16	ing	ing	PROPN
ap-368	343	17	.	.	PUNCT
ap-368	344	1	michal	michal	PROPN
ap-368	344	2	bednařík	bednařík	PROPN
ap-368	344	3	phone	phone	NOUN
ap-368	344	4	:	:	PUNCT
ap-368	344	5	+420	+420	PROPN
ap-368	344	6	224	224	NUM
ap-368	344	7	352	352	NUM
ap-368	344	8	308	308	NUM
ap-368	344	9	e	e	NOUN
ap-368	344	10	-	-	NOUN
ap-368	344	11	mail	mail	NOUN
ap-368	344	12	:	:	PUNCT
ap-368	344	13	bednarik@feld.cvut.cz	bednarik@feld.cvut.cz	SCONJ
ap-368	344	14	ing	ing	PROPN
ap-368	344	15	.	.	PROPN
ap-368	345	1	milan	milan	PROPN
ap-368	345	2	červenka	červenka	PROPN
ap-368	345	3	phone	phone	PROPN
ap-368	345	4	:	:	PUNCT
ap-368	345	5	+420	+420	PROPN
ap-368	345	6	224	224	NUM
ap-368	345	7	353	353	NUM
ap-368	345	8	975	975	NUM
ap-368	345	9	e	e	NOUN
ap-368	345	10	-	-	NOUN
ap-368	345	11	mail	mail	NOUN
ap-368	345	12	:	:	PUNCT
ap-368	345	13	cervenm3@feld.cvut.cz	cervenm3@feld.cvut.cz	PROPN
ap-368	345	14	department	department	NOUN
ap-368	345	15	of	of	ADP
ap-368	345	16	physics	physics	PROPN
ap-368	345	17	czech	czech	PROPN
ap-368	345	18	technical	technical	PROPN
ap-368	345	19	university	university	PROPN
ap-368	345	20	in	in	ADP
ap-368	345	21	prague	prague	PROPN
ap-368	345	22	faculty	faculty	NOUN
ap-368	345	23	of	of	ADP
ap-368	345	24	electrical	electrical	ADJ
ap-368	345	25	engineering	engineering	NOUN
ap-368	345	26	technická	technická	NOUN
ap-368	345	27	2	2	NUM
ap-368	345	28	166	166	NUM
ap-368	345	29	27	27	NUM
ap-368	345	30	prague	prague	NOUN
ap-368	345	31	,	,	PUNCT
ap-368	345	32	czech	czech	PROPN
ap-368	345	33	republic	republic	NOUN
ap-368	345	34	26	26	NUM
ap-368	346	1	©	©	PROPN
ap-368	346	2	czech	czech	PROPN
ap-368	346	3	technical	technical	PROPN
ap-368	346	4	university	university	PROPN
ap-368	346	5	publishing	publishing	NOUN
ap-368	346	6	house	house	NOUN
ap-368	346	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-368	346	8	acta	acta	PROPN
ap-368	346	9	polytechnica	polytechnica	PROPN
ap-368	346	10	vol	vol	NOUN
ap-368	346	11	.	.	PUNCT
ap-368	347	1	42	42	NUM
ap-368	347	2	no	no	INTJ
ap-368	347	3	.	.	PUNCT
ap-368	348	1	4/2002	4/2002	NUM