id	sid	tid	token	lemma	pos
ap-340	1	1	ap02_02.vp	ap02_02.vp	PROPN
ap-340	1	2	introduction	introduction	NOUN
ap-340	1	3	when	when	SCONJ
ap-340	1	4	solving	solve	VERB
ap-340	1	5	a	a	DET
ap-340	1	6	wide	wide	ADJ
ap-340	1	7	range	range	NOUN
ap-340	1	8	of	of	ADP
ap-340	1	9	problems	problem	NOUN
ap-340	1	10	related	relate	VERB
ap-340	1	11	to	to	ADP
ap-340	1	12	nonlinear	nonlinear	ADJ
ap-340	1	13	acoustics	acoustic	NOUN
ap-340	1	14	,	,	PUNCT
ap-340	1	15	we	we	PRON
ap-340	1	16	may	may	AUX
ap-340	1	17	describe	describe	VERB
ap-340	1	18	the	the	DET
ap-340	1	19	nonlinear	nonlinear	ADJ
ap-340	1	20	sound	sound	ADJ
ap-340	1	21	waves	wave	NOUN
ap-340	1	22	in	in	ADP
ap-340	1	23	fluids	fluid	NOUN
ap-340	1	24	by	by	ADP
ap-340	1	25	using	use	VERB
ap-340	1	26	the	the	DET
ap-340	1	27	burgers	burger	NOUN
ap-340	1	28	model	model	NOUN
ap-340	1	29	equation	equation	NOUN
ap-340	1	30	.	.	PUNCT
ap-340	2	1	this	this	DET
ap-340	2	2	equation	equation	NOUN
ap-340	2	3	is	be	AUX
ap-340	2	4	named	name	VERB
ap-340	2	5	after	after	SCONJ
ap-340	2	6	johannes	johannes	PROPN
ap-340	2	7	martinus	martinus	PROPN
ap-340	2	8	burgers	burger	NOUN
ap-340	2	9	,	,	PUNCT
ap-340	2	10	who	who	PRON
ap-340	2	11	published	publish	VERB
ap-340	2	12	an	an	DET
ap-340	2	13	equation	equation	NOUN
ap-340	2	14	of	of	ADP
ap-340	2	15	this	this	DET
ap-340	2	16	form	form	NOUN
ap-340	2	17	in	in	ADP
ap-340	2	18	his	his	PRON
ap-340	2	19	paper	paper	NOUN
ap-340	2	20	concerning	concern	VERB
ap-340	2	21	turbulent	turbulent	ADJ
ap-340	2	22	phenomena	phenomenon	NOUN
ap-340	2	23	modelling	modelling	NOUN
ap-340	2	24	in	in	ADP
ap-340	2	25	1948	1948	NUM
ap-340	2	26	(	(	PUNCT
ap-340	2	27	see	see	VERB
ap-340	2	28	[	[	X
ap-340	2	29	1	1	NUM
ap-340	2	30	]	]	NUM
ap-340	2	31	)	)	PUNCT
ap-340	2	32	.	.	PUNCT
ap-340	3	1	however	however	ADV
ap-340	3	2	,	,	PUNCT
ap-340	3	3	this	this	DET
ap-340	3	4	type	type	NOUN
ap-340	3	5	of	of	ADP
ap-340	3	6	equation	equation	NOUN
ap-340	3	7	used	use	VERB
ap-340	3	8	in	in	ADP
ap-340	3	9	continuum	continuum	ADJ
ap-340	3	10	mechanics	mechanic	NOUN
ap-340	3	11	was	be	AUX
ap-340	3	12	first	first	ADV
ap-340	3	13	presented	present	VERB
ap-340	3	14	in	in	ADP
ap-340	3	15	a	a	DET
ap-340	3	16	paper	paper	NOUN
ap-340	3	17	published	publish	VERB
ap-340	3	18	in	in	ADP
ap-340	3	19	a	a	DET
ap-340	3	20	meteorology	meteorology	NOUN
ap-340	3	21	journal	journal	NOUN
ap-340	3	22	by	by	ADP
ap-340	3	23	h.	h.	PROPN
ap-340	3	24	bateman	bateman	PROPN
ap-340	3	25	in	in	ADP
ap-340	3	26	1915	1915	NUM
ap-340	3	27	(	(	PUNCT
ap-340	3	28	see	see	VERB
ap-340	3	29	[	[	X
ap-340	3	30	2	2	NUM
ap-340	3	31	]	]	NUM
ap-340	3	32	)	)	PUNCT
ap-340	3	33	.	.	PUNCT
ap-340	4	1	thanks	thank	NOUN
ap-340	4	2	to	to	ADP
ap-340	4	3	the	the	DET
ap-340	4	4	fact	fact	NOUN
ap-340	4	5	that	that	SCONJ
ap-340	4	6	this	this	DET
ap-340	4	7	journal	journal	NOUN
ap-340	4	8	was	be	AUX
ap-340	4	9	not	not	PART
ap-340	4	10	read	read	VERB
ap-340	4	11	by	by	ADP
ap-340	4	12	experts	expert	NOUN
ap-340	4	13	in	in	ADP
ap-340	4	14	continuum	continuum	ADJ
ap-340	4	15	mechanics	mechanic	NOUN
ap-340	4	16	,	,	PUNCT
ap-340	4	17	the	the	DET
ap-340	4	18	equation	equation	NOUN
ap-340	4	19	has	have	AUX
ap-340	4	20	become	become	AUX
ap-340	4	21	known	know	VERB
ap-340	4	22	as	as	ADP
ap-340	4	23	the	the	DET
ap-340	4	24	burgers	burger	NOUN
ap-340	4	25	equation	equation	NOUN
ap-340	4	26	.	.	PUNCT
ap-340	5	1	the	the	DET
ap-340	5	2	possibilities	possibility	NOUN
ap-340	5	3	of	of	ADP
ap-340	5	4	using	use	VERB
ap-340	5	5	this	this	DET
ap-340	5	6	equation	equation	NOUN
ap-340	5	7	in	in	ADP
ap-340	5	8	nonlinear	nonlinear	ADJ
ap-340	5	9	acoustics	acoustic	NOUN
ap-340	5	10	were	be	AUX
ap-340	5	11	probably	probably	ADV
ap-340	5	12	discovered	discover	VERB
ap-340	5	13	by	by	ADP
ap-340	5	14	j.	j.	PROPN
ap-340	5	15	cole	cole	PROPN
ap-340	5	16	in	in	ADP
ap-340	5	17	1949	1949	NUM
ap-340	5	18	.	.	PUNCT
ap-340	6	1	subsequently	subsequently	ADV
ap-340	6	2	e.	e.	PROPN
ap-340	6	3	hopf	hopf	PROPN
ap-340	6	4	(	(	PUNCT
ap-340	6	5	in	in	ADP
ap-340	6	6	1950	1950	NUM
ap-340	6	7	)	)	PUNCT
ap-340	6	8	and	and	CCONJ
ap-340	6	9	j.	j.	PROPN
ap-340	6	10	cole	cole	PROPN
ap-340	6	11	(	(	PUNCT
ap-340	6	12	in	in	ADP
ap-340	6	13	1951	1951	NUM
ap-340	6	14	)	)	PUNCT
ap-340	6	15	published	publish	VERB
ap-340	6	16	the	the	DET
ap-340	6	17	transformation	transformation	NOUN
ap-340	6	18	independently	independently	ADV
ap-340	6	19	in	in	ADP
ap-340	6	20	their	their	PRON
ap-340	6	21	papers	paper	NOUN
ap-340	6	22	(	(	PUNCT
ap-340	6	23	see	see	VERB
ap-340	6	24	[	[	X
ap-340	6	25	3	3	NUM
ap-340	6	26	,	,	PUNCT
ap-340	6	27	4	4	NUM
ap-340	6	28	]	]	NUM
ap-340	6	29	)	)	PUNCT
ap-340	6	30	.	.	PUNCT
ap-340	7	1	the	the	DET
ap-340	7	2	transformation	transformation	NOUN
ap-340	7	3	enables	enable	VERB
ap-340	7	4	us	we	PRON
ap-340	7	5	to	to	PART
ap-340	7	6	find	find	VERB
ap-340	7	7	the	the	DET
ap-340	7	8	general	general	ADJ
ap-340	7	9	analytic	analytic	ADJ
ap-340	7	10	solution	solution	NOUN
ap-340	7	11	of	of	ADP
ap-340	7	12	the	the	DET
ap-340	7	13	burgers	burger	NOUN
ap-340	7	14	equation	equation	NOUN
ap-340	7	15	,	,	PUNCT
ap-340	7	16	as	as	ADP
ap-340	7	17	a	a	DET
ap-340	7	18	result	result	NOUN
ap-340	7	19	of	of	ADP
ap-340	7	20	which	which	PRON
ap-340	7	21	this	this	DET
ap-340	7	22	equation	equation	NOUN
ap-340	7	23	plays	play	VERB
ap-340	7	24	a	a	DET
ap-340	7	25	major	major	ADJ
ap-340	7	26	role	role	NOUN
ap-340	7	27	in	in	ADP
ap-340	7	28	nonlinear	nonlinear	ADJ
ap-340	7	29	acoustics	acoustic	NOUN
ap-340	7	30	.	.	PUNCT
ap-340	8	1	the	the	DET
ap-340	8	2	burgers	burger	NOUN
ap-340	8	3	equation	equation	NOUN
ap-340	8	4	can	can	AUX
ap-340	8	5	be	be	AUX
ap-340	8	6	used	use	VERB
ap-340	8	7	for	for	ADP
ap-340	8	8	modelling	model	VERB
ap-340	8	9	both	both	PRON
ap-340	8	10	travelling	travel	VERB
ap-340	8	11	and	and	CCONJ
ap-340	8	12	standing	stand	VERB
ap-340	8	13	nonlinear	nonlinear	ADJ
ap-340	8	14	plane	plane	NOUN
ap-340	8	15	waves	wave	NOUN
ap-340	8	16	[	[	X
ap-340	8	17	5–8	5–8	NOUN
ap-340	8	18	]	]	PUNCT
ap-340	8	19	.	.	PUNCT
ap-340	9	1	the	the	DET
ap-340	9	2	equation	equation	NOUN
ap-340	9	3	is	be	AUX
ap-340	9	4	the	the	DET
ap-340	9	5	simplest	simple	ADJ
ap-340	9	6	model	model	NOUN
ap-340	9	7	equation	equation	NOUN
ap-340	9	8	that	that	PRON
ap-340	9	9	can	can	AUX
ap-340	9	10	describe	describe	VERB
ap-340	9	11	the	the	DET
ap-340	9	12	second	second	ADJ
ap-340	9	13	order	order	NOUN
ap-340	9	14	nonlinear	nonlinear	ADJ
ap-340	9	15	effects	effect	NOUN
ap-340	9	16	connected	connect	VERB
ap-340	9	17	with	with	ADP
ap-340	9	18	the	the	DET
ap-340	9	19	propagation	propagation	NOUN
ap-340	9	20	of	of	ADP
ap-340	9	21	high	high	ADJ
ap-340	9	22	-	-	PUNCT
ap-340	9	23	amplitude	amplitude	NOUN
ap-340	9	24	(	(	PUNCT
ap-340	9	25	finite	finite	ADJ
ap-340	9	26	-	-	ADJ
ap-340	9	27	amplitude	amplitude	NOUN
ap-340	9	28	waves	wave	NOUN
ap-340	9	29	)	)	PUNCT
ap-340	9	30	plane	plane	NOUN
ap-340	9	31	waves	wave	NOUN
ap-340	9	32	and	and	CCONJ
ap-340	9	33	,	,	PUNCT
ap-340	9	34	in	in	ADP
ap-340	9	35	addition	addition	NOUN
ap-340	9	36	,	,	PUNCT
ap-340	9	37	the	the	DET
ap-340	9	38	dissipative	dissipative	ADJ
ap-340	9	39	effects	effect	NOUN
ap-340	9	40	in	in	ADP
ap-340	9	41	real	real	ADJ
ap-340	9	42	fluids	fluid	NOUN
ap-340	9	43	[	[	X
ap-340	9	44	9–12	9–12	NOUN
ap-340	9	45	]	]	PUNCT
ap-340	9	46	.	.	PUNCT
ap-340	10	1	there	there	PRON
ap-340	10	2	are	be	VERB
ap-340	10	3	several	several	ADJ
ap-340	10	4	approximate	approximate	ADJ
ap-340	10	5	solutions	solution	NOUN
ap-340	10	6	of	of	ADP
ap-340	10	7	the	the	DET
ap-340	10	8	burgers	burger	NOUN
ap-340	10	9	equation	equation	NOUN
ap-340	10	10	(	(	PUNCT
ap-340	10	11	see	see	VERB
ap-340	10	12	[	[	X
ap-340	10	13	13	13	NUM
ap-340	10	14	]	]	NUM
ap-340	10	15	)	)	PUNCT
ap-340	10	16	.	.	PUNCT
ap-340	11	1	these	these	DET
ap-340	11	2	solutions	solution	NOUN
ap-340	11	3	are	be	AUX
ap-340	11	4	always	always	ADV
ap-340	11	5	fixed	fix	VERB
ap-340	11	6	to	to	ADP
ap-340	11	7	areas	area	NOUN
ap-340	11	8	before	before	ADV
ap-340	11	9	and	and	CCONJ
ap-340	11	10	after	after	ADP
ap-340	11	11	the	the	DET
ap-340	11	12	shock	shock	NOUN
ap-340	11	13	formation	formation	NOUN
ap-340	11	14	.	.	PUNCT
ap-340	12	1	for	for	ADP
ap-340	12	2	an	an	DET
ap-340	12	3	area	area	NOUN
ap-340	12	4	where	where	SCONJ
ap-340	12	5	the	the	DET
ap-340	12	6	shock	shock	NOUN
ap-340	12	7	wave	wave	NOUN
ap-340	12	8	is	be	AUX
ap-340	12	9	forming	form	VERB
ap-340	12	10	no	no	DET
ap-340	12	11	approximate	approximate	ADJ
ap-340	12	12	solution	solution	NOUN
ap-340	12	13	has	have	AUX
ap-340	12	14	yet	yet	ADV
ap-340	12	15	been	be	AUX
ap-340	12	16	found	find	VERB
ap-340	12	17	.	.	PUNCT
ap-340	13	1	it	it	PRON
ap-340	13	2	is	be	AUX
ap-340	13	3	therefore	therefore	ADV
ap-340	13	4	necessary	necessary	ADJ
ap-340	13	5	to	to	PART
ap-340	13	6	solve	solve	VERB
ap-340	13	7	the	the	DET
ap-340	13	8	burgers	burger	NOUN
ap-340	13	9	equation	equation	NOUN
ap-340	13	10	numerically	numerically	ADV
ap-340	13	11	in	in	ADP
ap-340	13	12	this	this	DET
ap-340	13	13	area	area	NOUN
ap-340	13	14	(	(	PUNCT
ap-340	13	15	see	see	VERB
ap-340	13	16	[	[	X
ap-340	13	17	14,15	14,15	NUM
ap-340	13	18	]	]	PUNCT
ap-340	13	19	)	)	PUNCT
ap-340	13	20	.	.	PUNCT
ap-340	14	1	numerical	numerical	ADJ
ap-340	14	2	solutions	solution	NOUN
ap-340	14	3	themselves	themselves	PRON
ap-340	14	4	have	have	VERB
ap-340	14	5	difficulties	difficulty	NOUN
ap-340	14	6	with	with	ADP
ap-340	14	7	stability	stability	NOUN
ap-340	14	8	and	and	CCONJ
ap-340	14	9	accuracy	accuracy	NOUN
ap-340	14	10	.	.	PUNCT
ap-340	15	1	a	a	DET
ap-340	15	2	numerical	numerical	ADJ
ap-340	15	3	solution	solution	NOUN
ap-340	15	4	of	of	ADP
ap-340	15	5	the	the	DET
ap-340	15	6	burgers	burger	NOUN
ap-340	15	7	equation	equation	NOUN
ap-340	15	8	is	be	AUX
ap-340	15	9	discussed	discuss	VERB
ap-340	15	10	in	in	ADP
ap-340	15	11	this	this	DET
ap-340	15	12	paper	paper	NOUN
ap-340	15	13	.	.	PUNCT
ap-340	16	1	burgers	burger	NOUN
ap-340	16	2	equation	equation	NOUN
ap-340	16	3	a	a	DET
ap-340	16	4	complete	complete	ADJ
ap-340	16	5	system	system	NOUN
ap-340	16	6	of	of	ADP
ap-340	16	7	equations	equation	NOUN
ap-340	16	8	which	which	PRON
ap-340	16	9	describes	describe	VERB
ap-340	16	10	the	the	DET
ap-340	16	11	propagation	propagation	NOUN
ap-340	16	12	of	of	ADP
ap-340	16	13	waves	wave	NOUN
ap-340	16	14	in	in	ADP
ap-340	16	15	thermo	thermo	NOUN
ap-340	16	16	-	-	PUNCT
ap-340	16	17	viscous	viscous	ADJ
ap-340	16	18	fluids	fluid	NOUN
ap-340	16	19	consists	consist	VERB
ap-340	16	20	of	of	ADP
ap-340	16	21	the	the	DET
ap-340	16	22	navier	navier	NOUN
ap-340	16	23	-	-	PUNCT
ap-340	16	24	stokes	stoke	NOUN
ap-340	16	25	equation	equation	NOUN
ap-340	16	26	,	,	PUNCT
ap-340	16	27	the	the	DET
ap-340	16	28	equation	equation	NOUN
ap-340	16	29	of	of	ADP
ap-340	16	30	continuity	continuity	NOUN
ap-340	16	31	,	,	PUNCT
ap-340	16	32	the	the	DET
ap-340	16	33	heat	heat	NOUN
ap-340	16	34	-	-	PUNCT
ap-340	16	35	transfer	transfer	NOUN
ap-340	16	36	equation	equation	NOUN
ap-340	16	37	and	and	CCONJ
ap-340	16	38	the	the	DET
ap-340	16	39	thermodynamic	thermodynamic	ADJ
ap-340	16	40	state	state	NOUN
ap-340	16	41	equations	equation	NOUN
ap-340	16	42	.	.	PUNCT
ap-340	17	1	unfortunately	unfortunately	ADV
ap-340	17	2	,	,	PUNCT
ap-340	17	3	no	no	DET
ap-340	17	4	general	general	ADJ
ap-340	17	5	solution	solution	NOUN
ap-340	17	6	of	of	ADP
ap-340	17	7	this	this	DET
ap-340	17	8	system	system	NOUN
ap-340	17	9	has	have	AUX
ap-340	17	10	yet	yet	ADV
ap-340	17	11	been	be	AUX
ap-340	17	12	found	find	VERB
ap-340	17	13	,	,	PUNCT
ap-340	17	14	and	and	CCONJ
ap-340	17	15	if	if	SCONJ
ap-340	17	16	we	we	PRON
ap-340	17	17	were	be	AUX
ap-340	17	18	to	to	PART
ap-340	17	19	consider	consider	VERB
ap-340	17	20	all	all	DET
ap-340	17	21	these	these	DET
ap-340	17	22	equations	equation	NOUN
ap-340	17	23	in	in	ADP
ap-340	17	24	their	their	PRON
ap-340	17	25	full	full	ADJ
ap-340	17	26	form	form	NOUN
ap-340	17	27	,	,	PUNCT
ap-340	17	28	many	many	ADJ
ap-340	17	29	problems	problem	NOUN
ap-340	17	30	would	would	AUX
ap-340	17	31	arise	arise	VERB
ap-340	17	32	even	even	ADV
ap-340	17	33	with	with	ADP
ap-340	17	34	a	a	DET
ap-340	17	35	numerical	numerical	ADJ
ap-340	17	36	solution	solution	NOUN
ap-340	17	37	(	(	PUNCT
ap-340	17	38	the	the	DET
ap-340	17	39	large	large	ADJ
ap-340	17	40	number	number	NOUN
ap-340	17	41	of	of	ADP
ap-340	17	42	operations	operation	NOUN
ap-340	17	43	required	require	VERB
ap-340	17	44	,	,	PUNCT
ap-340	17	45	instability	instability	NOUN
ap-340	17	46	,	,	PUNCT
ap-340	17	47	etc	etc	X
ap-340	17	48	.	.	X
ap-340	17	49	)	)	PUNCT
ap-340	17	50	.	.	PUNCT
ap-340	18	1	for	for	ADP
ap-340	18	2	these	these	DET
ap-340	18	3	reasons	reason	NOUN
ap-340	18	4	,	,	PUNCT
ap-340	18	5	it	it	PRON
ap-340	18	6	is	be	AUX
ap-340	18	7	advisable	advisable	ADJ
ap-340	18	8	to	to	PART
ap-340	18	9	approximate	approximate	VERB
ap-340	18	10	this	this	DET
ap-340	18	11	system	system	NOUN
ap-340	18	12	by	by	ADP
ap-340	18	13	an	an	DET
ap-340	18	14	appropriate	appropriate	ADJ
ap-340	18	15	model	model	NOUN
ap-340	18	16	equation	equation	NOUN
ap-340	18	17	in	in	ADP
ap-340	18	18	a	a	DET
ap-340	18	19	given	give	VERB
ap-340	18	20	approximation	approximation	NOUN
ap-340	18	21	,	,	PUNCT
ap-340	18	22	e.g.	e.g.	ADV
ap-340	18	23	,	,	PUNCT
ap-340	18	24	the	the	DET
ap-340	18	25	quasi	quasi	ADJ
ap-340	18	26	-	-	ADJ
ap-340	18	27	linear	linear	ADJ
ap-340	18	28	homogeneous	homogeneous	ADJ
ap-340	18	29	burgers	burger	NOUN
ap-340	18	30	equation	equation	NOUN
ap-340	18	31	(	(	PUNCT
ap-340	18	32	see	see	VERB
ap-340	18	33	[	[	X
ap-340	18	34	13,16	13,16	NUM
ap-340	18	35	]	]	PUNCT
ap-340	18	36	)	)	PUNCT
ap-340	18	37	.	.	PUNCT
ap-340	19	1	homogeneous	homogeneous	ADJ
ap-340	19	2	burgers	burger	NOUN
ap-340	19	3	equation	equation	NOUN
ap-340	19	4	�	�	PROPN
ap-340	19	5	�	�	PROPN
ap-340	19	6	�	�	PROPN
ap-340	19	7	�	�	PROPN
ap-340	19	8	�	�	PROPN
ap-340	19	9	�	�	PROPN
ap-340	19	10	�	�	PROPN
ap-340	19	11	�	�	PROPN
ap-340	19	12	�	�	PROPN
ap-340	19	13	�	�	PROPN
ap-340	19	14	v	v	NOUN
ap-340	19	15	x	x	PROPN
ap-340	19	16	c	c	NOUN
ap-340	19	17	v	v	ADP
ap-340	19	18	v	v	PROPN
ap-340	19	19	b	b	PROPN
ap-340	19	20	c	c	NOUN
ap-340	19	21	v	v	PRON
ap-340	19	22	�	�	PROPN
ap-340	19	23	�	�	PROPN
ap-340	19	24	�	�	PROPN
ap-340	19	25	0	0	NUM
ap-340	19	26	2	2	NUM
ap-340	19	27	0	0	NUM
ap-340	19	28	0	0	NUM
ap-340	19	29	3	3	NUM
ap-340	19	30	2	2	NUM
ap-340	19	31	22	22	NUM
ap-340	19	32	0	0	NUM
ap-340	19	33	,	,	PUNCT
ap-340	19	34	(	(	PUNCT
ap-340	19	35	1	1	X
ap-340	19	36	)	)	PUNCT
ap-340	19	37	here	here	ADV
ap-340	19	38	v	v	NOUN
ap-340	19	39	is	be	AUX
ap-340	19	40	acoustic	acoustic	ADJ
ap-340	19	41	velocity	velocity	NOUN
ap-340	19	42	,	,	PUNCT
ap-340	19	43	�	�	PROPN
ap-340	19	44	is	be	AUX
ap-340	19	45	retarded	retarded	ADJ
ap-340	19	46	time	time	NOUN
ap-340	19	47	,	,	PUNCT
ap-340	19	48	�	�	PROPN
ap-340	19	49	�	�	PROPN
ap-340	19	50	�	�	PROPN
ap-340	19	51	t	t	PROPN
ap-340	19	52	x	x	SYM
ap-340	19	53	c0	c0	PROPN
ap-340	19	54	,	,	PUNCT
ap-340	19	55	where	where	SCONJ
ap-340	19	56	t	t	PROPN
ap-340	19	57	is	be	AUX
ap-340	19	58	time	time	NOUN
ap-340	19	59	,	,	PUNCT
ap-340	19	60	x	x	X
ap-340	19	61	is	be	AUX
ap-340	19	62	the	the	DET
ap-340	19	63	distance	distance	NOUN
ap-340	19	64	from	from	ADP
ap-340	19	65	the	the	DET
ap-340	19	66	sound	sound	NOUN
ap-340	19	67	source	source	NOUN
ap-340	19	68	,	,	PUNCT
ap-340	19	69	c0	c0	PROPN
ap-340	19	70	is	be	AUX
ap-340	19	71	the	the	DET
ap-340	19	72	velocity	velocity	NOUN
ap-340	19	73	of	of	ADP
ap-340	19	74	sound	sound	ADJ
ap-340	19	75	propagation	propagation	NOUN
ap-340	19	76	in	in	ADP
ap-340	19	77	the	the	DET
ap-340	19	78	linear	linear	PROPN
ap-340	19	79	approximation	approximation	NOUN
ap-340	19	80	,	,	PUNCT
ap-340	19	81	b	b	PROPN
ap-340	19	82	is	be	AUX
ap-340	19	83	the	the	DET
ap-340	19	84	dissipation	dissipation	NOUN
ap-340	19	85	coefficient	coefficient	NOUN
ap-340	19	86	,	,	PUNCT
ap-340	19	87	�	�	PROPN
ap-340	19	88	0	0	NUM
ap-340	19	89	is	be	AUX
ap-340	19	90	density	density	NOUN
ap-340	19	91	of	of	ADP
ap-340	19	92	medium	medium	NOUN
ap-340	19	93	,	,	PUNCT
ap-340	19	94	�	�	PROPN
ap-340	19	95	is	be	AUX
ap-340	19	96	nonlinearity	nonlinearity	NOUN
ap-340	19	97	coefficient	coefficient	NOUN
ap-340	19	98	.	.	PUNCT
ap-340	20	1	for	for	ADP
ap-340	20	2	the	the	DET
ap-340	20	3	calculations	calculation	NOUN
ap-340	20	4	that	that	PRON
ap-340	20	5	follow	follow	VERB
ap-340	20	6	it	it	PRON
ap-340	20	7	is	be	AUX
ap-340	20	8	advisable	advisable	ADJ
ap-340	20	9	to	to	PART
ap-340	20	10	rewrite	rewrite	VERB
ap-340	20	11	the	the	DET
ap-340	20	12	equation	equation	NOUN
ap-340	20	13	in	in	ADP
ap-340	20	14	the	the	DET
ap-340	20	15	following	follow	VERB
ap-340	20	16	dimensionless	dimensionless	NOUN
ap-340	20	17	(	(	PUNCT
ap-340	20	18	normed	normed	ADJ
ap-340	20	19	)	)	PUNCT
ap-340	20	20	form	form	NOUN
ap-340	20	21	:	:	PUNCT
ap-340	20	22	�	�	PROPN
ap-340	20	23	�	�	PROPN
ap-340	20	24	�	�	PROPN
ap-340	20	25	�	�	PROPN
ap-340	20	26	�	�	PROPN
ap-340	20	27	�	�	PROPN
ap-340	20	28	v	v	ADP
ap-340	20	29	s	s	NOUN
ap-340	20	30	v	v	NOUN
ap-340	20	31	v	v	ADP
ap-340	20	32	y	y	PROPN
ap-340	20	33	g	g	PROPN
ap-340	20	34	v	v	NUM
ap-340	20	35	y	y	PROPN
ap-340	20	36	�	�	PROPN
ap-340	20	37	�	�	PROPN
ap-340	20	38	�	�	PROPN
ap-340	20	39	1	1	NUM
ap-340	20	40	0	0	NUM
ap-340	20	41	0	0	NUM
ap-340	20	42	2	2	NUM
ap-340	20	43	2	2	NUM
ap-340	20	44	(	(	PUNCT
ap-340	20	45	2	2	NUM
ap-340	20	46	)	)	PUNCT
ap-340	20	47	where	where	SCONJ
ap-340	20	48	y	y	PROPN
ap-340	20	49	�	�	PROPN
ap-340	20	50	�	�	PROPN
ap-340	20	51	�	�	PROPN
ap-340	20	52	;	;	NOUN
ap-340	20	53	s	s	PROPN
ap-340	20	54	v	v	NOUN
ap-340	20	55	c	c	NOUN
ap-340	20	56	x	x	SYM
ap-340	20	57	�	�	PROPN
ap-340	20	58	�	�	PROPN
ap-340	20	59	�	�	PROPN
ap-340	20	60	m	m	PROPN
ap-340	20	61	0	0	NUM
ap-340	20	62	2	2	NUM
ap-340	20	63	;	;	NOUN
ap-340	20	64	v	v	ADP
ap-340	20	65	v	v	ADP
ap-340	20	66	v	v	PRON
ap-340	20	67	�	�	PROPN
ap-340	20	68	m	m	PRON
ap-340	20	69	;	;	NOUN
ap-340	20	70	g	g	PROPN
ap-340	20	71	v	v	ADP
ap-340	20	72	c	c	PROPN
ap-340	20	73	b0	b0	NOUN
ap-340	20	74	0	0	NUM
ap-340	20	75	02	02	NUM
ap-340	20	76	�	�	PROPN
ap-340	20	77	�	�	PROPN
ap-340	20	78	�	�	PROPN
ap-340	20	79	�	�	PROPN
ap-340	20	80	m	m	PROPN
ap-340	20	81	,	,	PUNCT
ap-340	20	82	g0	g0	PROPN
ap-340	20	83	represents	represent	VERB
ap-340	20	84	the	the	DET
ap-340	20	85	goldberg	goldberg	PROPN
ap-340	20	86	number	number	NOUN
ap-340	20	87	,	,	PUNCT
ap-340	20	88	vm	vm	PROPN
ap-340	20	89	is	be	AUX
ap-340	20	90	the	the	DET
ap-340	20	91	velocity	velocity	NOUN
ap-340	20	92	amplitude	amplitude	NOUN
ap-340	20	93	of	of	ADP
ap-340	20	94	the	the	DET
ap-340	20	95	sound	sound	ADJ
ap-340	20	96	source	source	NOUN
ap-340	20	97	and	and	CCONJ
ap-340	20	98	�	�	PROPN
ap-340	20	99	is	be	AUX
ap-340	20	100	the	the	DET
ap-340	20	101	annular	annular	ADJ
ap-340	20	102	frequency	frequency	NOUN
ap-340	20	103	of	of	ADP
ap-340	20	104	the	the	DET
ap-340	20	105	sound	sound	ADJ
ap-340	20	106	source	source	NOUN
ap-340	20	107	.	.	PUNCT
ap-340	21	1	the	the	DET
ap-340	21	2	burgers	burger	NOUN
ap-340	21	3	equation	equation	NOUN
ap-340	21	4	(	(	PUNCT
ap-340	21	5	1	1	X
ap-340	21	6	)	)	PUNCT
ap-340	21	7	is	be	AUX
ap-340	21	8	a	a	DET
ap-340	21	9	parabolic	parabolic	ADJ
ap-340	21	10	equation	equation	NOUN
ap-340	21	11	which	which	PRON
ap-340	21	12	takes	take	VERB
ap-340	21	13	a	a	DET
ap-340	21	14	hyperbolic	hyperbolic	ADJ
ap-340	21	15	form	form	NOUN
ap-340	21	16	in	in	ADP
ap-340	21	17	the	the	DET
ap-340	21	18	case	case	NOUN
ap-340	21	19	of	of	ADP
ap-340	21	20	an	an	DET
ap-340	21	21	ideal	ideal	ADJ
ap-340	21	22	fluid	fluid	NOUN
ap-340	21	23	.	.	PUNCT
ap-340	22	1	the	the	DET
ap-340	22	2	homogeneous	homogeneous	ADJ
ap-340	22	3	burgers	burger	NOUN
ap-340	22	4	equation	equation	NOUN
ap-340	22	5	(	(	PUNCT
ap-340	22	6	1	1	X
ap-340	22	7	)	)	PUNCT
ap-340	22	8	describes	describe	VERB
ap-340	22	9	nonlinear	nonlinear	ADJ
ap-340	22	10	plane	plane	NOUN
ap-340	22	11	travelling	travel	VERB
ap-340	22	12	waves	wave	NOUN
ap-340	22	13	.	.	PUNCT
ap-340	23	1	cole	cole	NOUN
ap-340	23	2	-	-	PUNCT
ap-340	23	3	hopf	hopf	PROPN
ap-340	23	4	transformation	transformation	NOUN
ap-340	23	5	v	v	ADP
ap-340	23	6	g	g	PROPN
ap-340	23	7	u	u	PROPN
ap-340	23	8	u	u	PROPN
ap-340	23	9	y	y	PROPN
ap-340	23	10	�	�	PROPN
ap-340	23	11	2	2	NUM
ap-340	23	12	0	0	NUM
ap-340	23	13	�	�	PROPN
ap-340	23	14	�	�	PROPN
ap-340	23	15	.	.	PUNCT
ap-340	24	1	(	(	PUNCT
ap-340	24	2	3	3	X
ap-340	24	3	)	)	PUNCT
ap-340	24	4	using	use	VERB
ap-340	24	5	transformation	transformation	NOUN
ap-340	24	6	(	(	PUNCT
ap-340	24	7	3	3	X
ap-340	24	8	)	)	PUNCT
ap-340	24	9	we	we	PRON
ap-340	24	10	can	can	AUX
ap-340	24	11	transform	transform	VERB
ap-340	24	12	the	the	DET
ap-340	24	13	burgers	burger	NOUN
ap-340	24	14	equation	equation	NOUN
ap-340	24	15	(	(	PUNCT
ap-340	24	16	2	2	NUM
ap-340	24	17	)	)	PUNCT
ap-340	24	18	to	to	ADP
ap-340	24	19	the	the	DET
ap-340	24	20	linear	linear	ADJ
ap-340	24	21	diffusion	diffusion	NOUN
ap-340	24	22	equation	equation	NOUN
ap-340	24	23	[	[	X
ap-340	24	24	17	17	NUM
ap-340	24	25	]	]	X
ap-340	24	26	:	:	PUNCT
ap-340	24	27	�	�	PROPN
ap-340	24	28	�	�	PROPN
ap-340	24	29	�	�	PROPN
ap-340	24	30	�	�	PROPN
ap-340	24	31	u	u	PROPN
ap-340	24	32	s	s	PROPN
ap-340	24	33	g	g	NOUN
ap-340	24	34	u	u	X
ap-340	24	35	y	y	PROPN
ap-340	24	36	�	�	PROPN
ap-340	24	37	1	1	NUM
ap-340	24	38	0	0	NUM
ap-340	24	39	2	2	NUM
ap-340	24	40	2	2	NUM
ap-340	24	41	(	(	PUNCT
ap-340	24	42	4	4	NUM
ap-340	24	43	)	)	PUNCT
ap-340	24	44	©	©	PROPN
ap-340	24	45	czech	czech	PROPN
ap-340	24	46	technical	technical	PROPN
ap-340	24	47	university	university	PROPN
ap-340	24	48	publishing	publishing	NOUN
ap-340	24	49	house	house	NOUN
ap-340	24	50	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-340	24	51	71	71	NUM
ap-340	24	52	acta	acta	PROPN
ap-340	24	53	polytechnica	polytechnica	PROPN
ap-340	24	54	vol	vol	NOUN
ap-340	24	55	.	.	PUNCT
ap-340	25	1	42	42	NUM
ap-340	25	2	no	no	NOUN
ap-340	25	3	.	.	PUNCT
ap-340	26	1	2/2002	2/2002	NUM
ap-340	26	2	solution	solution	NOUN
ap-340	26	3	of	of	ADP
ap-340	26	4	the	the	DET
ap-340	26	5	burgers	burger	NOUN
ap-340	26	6	equation	equation	NOUN
ap-340	26	7	in	in	ADP
ap-340	26	8	the	the	DET
ap-340	26	9	time	time	NOUN
ap-340	26	10	domain	domain	PROPN
ap-340	26	11	m.	m.	NOUN
ap-340	26	12	bednařík	bednařík	PROPN
ap-340	26	13	,	,	PUNCT
ap-340	26	14	p.	p.	PROPN
ap-340	26	15	koníček	koníček	PROPN
ap-340	26	16	,	,	PUNCT
ap-340	26	17	m.	m.	NOUN
ap-340	26	18	červenka	červenka	PROPN
ap-340	26	19	this	this	DET
ap-340	26	20	paper	paper	NOUN
ap-340	26	21	deals	deal	NOUN
ap-340	26	22	with	with	ADP
ap-340	26	23	a	a	DET
ap-340	26	24	theoretical	theoretical	ADJ
ap-340	26	25	description	description	NOUN
ap-340	26	26	of	of	ADP
ap-340	26	27	the	the	DET
ap-340	26	28	propagation	propagation	NOUN
ap-340	26	29	of	of	ADP
ap-340	26	30	a	a	DET
ap-340	26	31	finite	finite	ADJ
ap-340	26	32	amplitude	amplitude	NOUN
ap-340	26	33	acoustic	acoustic	ADJ
ap-340	26	34	waves	wave	NOUN
ap-340	26	35	.	.	PUNCT
ap-340	27	1	the	the	DET
ap-340	27	2	theory	theory	NOUN
ap-340	27	3	based	base	VERB
ap-340	27	4	on	on	ADP
ap-340	27	5	the	the	DET
ap-340	27	6	homogeneous	homogeneous	ADJ
ap-340	27	7	burgers	burger	NOUN
ap-340	27	8	equation	equation	NOUN
ap-340	27	9	of	of	ADP
ap-340	27	10	the	the	DET
ap-340	27	11	second	second	ADJ
ap-340	27	12	order	order	NOUN
ap-340	27	13	of	of	ADP
ap-340	27	14	accuracy	accuracy	NOUN
ap-340	27	15	is	be	AUX
ap-340	27	16	presented	present	VERB
ap-340	27	17	here	here	ADV
ap-340	27	18	.	.	PUNCT
ap-340	28	1	this	this	DET
ap-340	28	2	equation	equation	NOUN
ap-340	28	3	takes	take	VERB
ap-340	28	4	into	into	ADP
ap-340	28	5	account	account	NOUN
ap-340	28	6	both	both	DET
ap-340	28	7	nonlinear	nonlinear	ADJ
ap-340	28	8	effects	effect	NOUN
ap-340	28	9	and	and	CCONJ
ap-340	28	10	dissipation	dissipation	NOUN
ap-340	28	11	.	.	PUNCT
ap-340	29	1	the	the	DET
ap-340	29	2	method	method	NOUN
ap-340	29	3	for	for	ADP
ap-340	29	4	solving	solve	VERB
ap-340	29	5	this	this	DET
ap-340	29	6	equation	equation	NOUN
ap-340	29	7	,	,	PUNCT
ap-340	29	8	using	use	VERB
ap-340	29	9	the	the	DET
ap-340	29	10	well	well	ADV
ap-340	29	11	-	-	PUNCT
ap-340	29	12	known	know	VERB
ap-340	29	13	cole	cole	NOUN
ap-340	29	14	-	-	PUNCT
ap-340	29	15	hopf	hopf	ADJ
ap-340	29	16	transformation	transformation	NOUN
ap-340	29	17	,	,	PUNCT
ap-340	29	18	is	be	AUX
ap-340	29	19	presented	present	VERB
ap-340	29	20	.	.	PUNCT
ap-340	30	1	two	two	NUM
ap-340	30	2	methods	method	NOUN
ap-340	30	3	for	for	ADP
ap-340	30	4	numerical	numerical	ADJ
ap-340	30	5	solution	solution	NOUN
ap-340	30	6	of	of	ADP
ap-340	30	7	these	these	DET
ap-340	30	8	equations	equation	NOUN
ap-340	30	9	in	in	ADP
ap-340	30	10	the	the	DET
ap-340	30	11	time	time	NOUN
ap-340	30	12	domain	domain	NOUN
ap-340	30	13	are	be	AUX
ap-340	30	14	presented	present	VERB
ap-340	30	15	.	.	PUNCT
ap-340	31	1	the	the	DET
ap-340	31	2	first	first	ADJ
ap-340	31	3	is	be	AUX
ap-340	31	4	based	base	VERB
ap-340	31	5	on	on	ADP
ap-340	31	6	the	the	DET
ap-340	31	7	simple	simple	ADJ
ap-340	31	8	simpson	simpson	PROPN
ap-340	31	9	method	method	PROPN
ap-340	31	10	,	,	PUNCT
ap-340	31	11	which	which	PRON
ap-340	31	12	is	be	AUX
ap-340	31	13	suitable	suitable	ADJ
ap-340	31	14	for	for	ADP
ap-340	31	15	smaller	small	ADJ
ap-340	31	16	goldberg	goldberg	PROPN
ap-340	31	17	numbers	number	NOUN
ap-340	31	18	.	.	PUNCT
ap-340	32	1	the	the	DET
ap-340	32	2	second	second	ADJ
ap-340	32	3	uses	use	VERB
ap-340	32	4	the	the	DET
ap-340	32	5	more	more	ADV
ap-340	32	6	advanced	advanced	ADJ
ap-340	32	7	saddle	saddle	NOUN
ap-340	32	8	point	point	NOUN
ap-340	32	9	method	method	NOUN
ap-340	32	10	,	,	PUNCT
ap-340	32	11	and	and	CCONJ
ap-340	32	12	is	be	AUX
ap-340	32	13	appropriate	appropriate	ADJ
ap-340	32	14	for	for	ADP
ap-340	32	15	large	large	ADJ
ap-340	32	16	goldberg	goldberg	PROPN
ap-340	32	17	numbers	number	NOUN
ap-340	32	18	.	.	PUNCT
ap-340	33	1	keywords	keyword	NOUN
ap-340	33	2	:	:	PUNCT
ap-340	33	3	burgers	burger	NOUN
ap-340	33	4	equation	equation	NOUN
ap-340	33	5	,	,	PUNCT
ap-340	33	6	cole	cole	NOUN
ap-340	33	7	-	-	PUNCT
ap-340	33	8	hopf	hopf	ADJ
ap-340	33	9	transformation	transformation	NOUN
ap-340	33	10	,	,	PUNCT
ap-340	33	11	saddle	saddle	NOUN
ap-340	33	12	point	point	NOUN
ap-340	33	13	method	method	NOUN
ap-340	33	14	,	,	PUNCT
ap-340	33	15	nonlinearity	nonlinearity	NOUN
ap-340	33	16	.	.	PUNCT
ap-340	34	1	solution	solution	NOUN
ap-340	34	2	of	of	ADP
ap-340	34	3	the	the	DET
ap-340	34	4	burgers	burger	NOUN
ap-340	34	5	equation	equation	NOUN
ap-340	34	6	the	the	DET
ap-340	34	7	solution	solution	NOUN
ap-340	34	8	of	of	ADP
ap-340	34	9	the	the	DET
ap-340	34	10	diffusion	diffusion	NOUN
ap-340	34	11	equation	equation	NOUN
ap-340	34	12	(	(	PUNCT
ap-340	34	13	4	4	X
ap-340	34	14	)	)	PUNCT
ap-340	34	15	is	be	AUX
ap-340	34	16	given	give	VERB
ap-340	34	17	by	by	ADP
ap-340	34	18	the	the	DET
ap-340	34	19	poisson	poisson	NOUN
ap-340	34	20	integral	integral	ADJ
ap-340	34	21	,	,	PUNCT
ap-340	34	22	thus	thus	ADV
ap-340	34	23	the	the	DET
ap-340	34	24	solution	solution	NOUN
ap-340	34	25	of	of	ADP
ap-340	34	26	the	the	DET
ap-340	34	27	burgers	burger	NOUN
ap-340	34	28	equation	equation	NOUN
ap-340	34	29	can	can	AUX
ap-340	34	30	be	be	AUX
ap-340	34	31	written	write	VERB
ap-340	34	32	as	as	ADP
ap-340	34	33	the	the	DET
ap-340	34	34	fraction	fraction	NOUN
ap-340	34	35	of	of	ADP
ap-340	34	36	two	two	NUM
ap-340	34	37	integrals	integral	NOUN
ap-340	34	38	with	with	ADP
ap-340	34	39	infinite	infinite	ADJ
ap-340	34	40	limits	limit	NOUN
ap-340	34	41	:	:	PUNCT
ap-340	34	42	�	�	PROPN
ap-340	34	43	�	�	PROPN
ap-340	34	44	�	�	PROPN
ap-340	34	45	�	�	PROPN
ap-340	34	46	v	v	ADP
ap-340	34	47	y	y	PROPN
ap-340	35	1	z	z	PROPN
ap-340	35	2	s	s	PROPN
ap-340	35	3	g	g	PROPN
ap-340	35	4	y	y	PROPN
ap-340	35	5	z	z	PROPN
ap-340	35	6	s	s	PROPN
ap-340	35	7	g	g	PROPN
ap-340	35	8	v	v	ADP
ap-340	35	9	y	y	PROPN
ap-340	35	10	y	y	PROPN
ap-340	35	11	z	z	PROPN
ap-340	35	12	g	g	PROPN
ap-340	35	13	z	z	PROPN
ap-340	35	14	�	�	PROPN
ap-340	35	15	�	�	PROPN
ap-340	35	16	�	�	PROPN
ap-340	35	17	�	�	PROPN
ap-340	35	18	�	�	PROPN
ap-340	35	19	�	�	PROPN
ap-340	35	20	�	�	PROPN
ap-340	35	21	�	�	PROPN
ap-340	35	22	�	�	PROPN
ap-340	35	23	�	�	PROPN
ap-340	35	24	�	�	PROPN
ap-340	35	25	�	�	PROPN
ap-340	35	26	�	�	PROPN
ap-340	35	27	�	�	PROPN
ap-340	35	28	exp	exp	NOUN
ap-340	35	29	,	,	PUNCT
ap-340	35	30	exp	exp	NOUN
ap-340	35	31	0	0	NUM
ap-340	36	1	2	2	NUM
ap-340	36	2	0	0	NUM
ap-340	36	3	04	04	NUM
ap-340	36	4	2	2	NUM
ap-340	36	5	0	0	NUM
ap-340	36	6	d	d	NOUN
ap-340	36	7	d	d	X
ap-340	36	8	�	�	PROPN
ap-340	36	9	�	�	PROPN
ap-340	36	10	�	�	PROPN
ap-340	36	11	�	�	PROPN
ap-340	36	12	0	0	NUM
ap-340	36	13	2	2	NUM
ap-340	36	14	0	0	NUM
ap-340	36	15	04	04	NUM
ap-340	36	16	2	2	NUM
ap-340	36	17	0	0	NUM
ap-340	37	1	y	y	PROPN
ap-340	37	2	z	z	PROPN
ap-340	37	3	s	s	PROPN
ap-340	37	4	g	g	PROPN
ap-340	37	5	v	v	ADP
ap-340	37	6	y	y	PROPN
ap-340	37	7	y	y	PROPN
ap-340	37	8	z	z	PROPN
ap-340	37	9	z	z	PROPN
ap-340	37	10	�	�	PROPN
ap-340	37	11	�	�	PROPN
ap-340	37	12	�	�	PROPN
ap-340	37	13	�	�	PROPN
ap-340	37	14	�	�	PROPN
ap-340	37	15	�	�	PROPN
ap-340	37	16	�	�	PROPN
ap-340	37	17	�	�	PROPN
ap-340	37	18	�	�	PROPN
ap-340	37	19	�	�	PROPN
ap-340	37	20	,	,	PUNCT
ap-340	37	21	d	d	PROPN
ap-340	37	22	d	d	X
ap-340	37	23	(	(	PUNCT
ap-340	37	24	5	5	NUM
ap-340	37	25	)	)	PUNCT
ap-340	37	26	where	where	SCONJ
ap-340	37	27	v(0	v(0	PROPN
ap-340	37	28	,	,	PUNCT
ap-340	37	29	y	y	PROPN
ap-340	37	30	)	)	PUNCT
ap-340	37	31	is	be	AUX
ap-340	37	32	the	the	DET
ap-340	37	33	given	give	VERB
ap-340	37	34	boundary	boundary	ADJ
ap-340	37	35	condition	condition	NOUN
ap-340	37	36	.	.	PUNCT
ap-340	38	1	in	in	ADP
ap-340	38	2	most	most	ADJ
ap-340	38	3	cases	case	NOUN
ap-340	38	4	the	the	DET
ap-340	38	5	integrals	integral	NOUN
ap-340	38	6	in	in	ADP
ap-340	38	7	equation	equation	NOUN
ap-340	38	8	(	(	PUNCT
ap-340	38	9	5	5	X
ap-340	38	10	)	)	PUNCT
ap-340	38	11	can	can	AUX
ap-340	38	12	not	not	PART
ap-340	38	13	be	be	AUX
ap-340	38	14	solved	solve	VERB
ap-340	38	15	analytically	analytically	ADV
ap-340	38	16	.	.	PUNCT
ap-340	39	1	numerical	numerical	ADJ
ap-340	39	2	integration	integration	NOUN
ap-340	39	3	it	it	PRON
ap-340	39	4	is	be	AUX
ap-340	39	5	necessary	necessary	ADJ
ap-340	39	6	to	to	PART
ap-340	39	7	integrate	integrate	VERB
ap-340	39	8	eq	eq	ADP
ap-340	39	9	.	.	PUNCT
ap-340	40	1	(	(	PUNCT
ap-340	40	2	5	5	NUM
ap-340	40	3	)	)	PUNCT
ap-340	40	4	only	only	ADV
ap-340	40	5	in	in	ADP
ap-340	40	6	intervals	interval	NOUN
ap-340	40	7	�	�	PROPN
ap-340	40	8	�	�	PROPN
ap-340	40	9	�	�	PROPN
ap-340	40	10	�	�	PROPN
ap-340	40	11	q	q	PROPN
ap-340	40	12	qi	qi	PROPN
ap-340	40	13	i	i	NOUN
ap-340	40	14	1	1	NUM
ap-340	40	15	2	2	NUM
ap-340	40	16	,	,	PUNCT
ap-340	40	17	where	where	SCONJ
ap-340	40	18	the	the	DET
ap-340	40	19	value	value	NOUN
ap-340	40	20	of	of	ADP
ap-340	40	21	an	an	DET
ap-340	40	22	integrand	integrand	NOUN
ap-340	40	23	is	be	AUX
ap-340	40	24	less	less	ADJ
ap-340	40	25	than	than	ADP
ap-340	40	26	a	a	DET
ap-340	40	27	chosen	choose	VERB
ap-340	40	28	parameter	parameter	NOUN
ap-340	40	29	�	�	PROPN
ap-340	40	30	.	.	PUNCT
ap-340	41	1	in	in	ADP
ap-340	41	2	general	general	ADJ
ap-340	41	3	,	,	PUNCT
ap-340	41	4	it	it	PRON
ap-340	41	5	is	be	AUX
ap-340	41	6	necessary	necessary	ADJ
ap-340	41	7	to	to	PART
ap-340	41	8	determine	determine	VERB
ap-340	41	9	these	these	DET
ap-340	41	10	intervals	interval	NOUN
ap-340	41	11	numerically	numerically	ADV
ap-340	41	12	.	.	PUNCT
ap-340	42	1	when	when	SCONJ
ap-340	42	2	we	we	PRON
ap-340	42	3	can	can	AUX
ap-340	42	4	express	express	VERB
ap-340	42	5	the	the	DET
ap-340	42	6	approximate	approximate	ADJ
ap-340	42	7	solution	solution	NOUN
ap-340	42	8	of	of	ADP
ap-340	42	9	the	the	DET
ap-340	42	10	burgers	burger	NOUN
ap-340	42	11	equation	equation	NOUN
ap-340	42	12	in	in	ADP
ap-340	42	13	the	the	DET
ap-340	42	14	following	follow	VERB
ap-340	42	15	form	form	NOUN
ap-340	42	16	�	�	PROPN
ap-340	42	17	�	�	PROPN
ap-340	42	18	�	�	PROPN
ap-340	42	19	�	�	PROPN
ap-340	42	20	�	�	PROPN
ap-340	42	21	�	�	PROPN
ap-340	42	22	�	�	PROPN
ap-340	42	23	�	�	PROPN
ap-340	42	24	v	v	ADP
ap-340	42	25	y	y	PROPN
ap-340	42	26	z	z	PROPN
ap-340	42	27	s	s	PROPN
ap-340	42	28	g	g	PROPN
ap-340	42	29	y	y	PROPN
ap-340	42	30	z	z	PROPN
ap-340	42	31	s	s	PROPN
ap-340	42	32	g	g	PROPN
ap-340	42	33	v	v	ADP
ap-340	42	34	y	y	PROPN
ap-340	42	35	y	y	PROPN
ap-340	42	36	z	z	PROPN
ap-340	42	37	z	z	NOUN
ap-340	42	38	q	q	X
ap-340	43	1	q	q	X
ap-340	44	1	i	i	PRON
ap-340	44	2	i	i	PRON
ap-340	45	1	i	i	PRON
ap-340	45	2	�	�	PROPN
ap-340	45	3	�	�	PROPN
ap-340	45	4	�	�	PROPN
ap-340	45	5	�	�	PROPN
ap-340	45	6	�	�	PROPN
ap-340	45	7	�	�	PROPN
ap-340	45	8	�	�	PROPN
ap-340	45	9	�	�	PROPN
ap-340	45	10	�	�	PROPN
ap-340	45	11	�	�	PROPN
ap-340	45	12	�	�	PROPN
ap-340	45	13	exp	exp	NOUN
ap-340	45	14	,	,	PUNCT
ap-340	45	15	0	0	NUM
ap-340	45	16	2	2	NUM
ap-340	45	17	0	0	NUM
ap-340	45	18	04	04	NUM
ap-340	45	19	2	2	NUM
ap-340	45	20	0	0	NUM
ap-340	45	21	1	1	NUM
ap-340	45	22	2	2	NUM
ap-340	45	23	d	d	NOUN
ap-340	45	24	d	d	X
ap-340	45	25	�	�	PROPN
ap-340	45	26	�	�	PROPN
ap-340	45	27	�	�	PROPN
ap-340	45	28	�	�	PROPN
ap-340	45	29	�	�	PROPN
ap-340	45	30	�	�	PROPN
ap-340	45	31	�	�	PROPN
ap-340	45	32	�	�	PROPN
ap-340	45	33	1	1	NUM
ap-340	45	34	0	0	NUM
ap-340	45	35	2	2	NUM
ap-340	45	36	0	0	NUM
ap-340	45	37	01	01	NUM
ap-340	45	38	4	4	NUM
ap-340	45	39	2	2	NUM
ap-340	45	40	0	0	NUM
ap-340	45	41	1	1	NUM
ap-340	45	42	2	2	NUM
ap-340	45	43	n	n	NOUN
ap-340	45	44	z	z	NOUN
ap-340	45	45	q	q	NOUN
ap-340	45	46	q	q	X
ap-340	45	47	i	i	PRON
ap-340	45	48	n	n	CCONJ
ap-340	45	49	g	g	PROPN
ap-340	45	50	y	y	PROPN
ap-340	45	51	z	z	PROPN
ap-340	45	52	s	s	PROPN
ap-340	45	53	g	g	PROPN
ap-340	45	54	v	v	ADP
ap-340	45	55	y	y	PROPN
ap-340	45	56	y	y	PROPN
ap-340	45	57	z	z	PROPN
ap-340	46	1	i	i	PRON
ap-340	46	2	i	i	PRON
ap-340	46	3	�	�	PROPN
ap-340	46	4	�	�	PROPN
ap-340	46	5	�	�	PROPN
ap-340	46	6	�	�	PROPN
ap-340	46	7	�	�	PROPN
ap-340	46	8	�	�	PROPN
ap-340	46	9	�	�	PROPN
ap-340	46	10	�	�	PROPN
ap-340	46	11	�	�	PROPN
ap-340	46	12	�	�	PROPN
ap-340	46	13	�	�	PROPN
ap-340	46	14	exp	exp	NOUN
ap-340	46	15	,	,	PUNCT
ap-340	46	16	d	d	PROPN
ap-340	46	17	d	d	X
ap-340	46	18	.(6	.(6	NOUN
ap-340	46	19	)	)	PUNCT
ap-340	46	20	in	in	ADP
ap-340	46	21	the	the	DET
ap-340	46	22	special	special	ADJ
ap-340	46	23	cases	case	NOUN
ap-340	46	24	g0	g0	ADJ
ap-340	46	25	1	1	NUM
ap-340	46	26	�	�	PROPN
ap-340	46	27	or	or	CCONJ
ap-340	46	28	roughly	roughly	ADV
ap-340	46	29	s	s	X
ap-340	46	30	<	<	X
ap-340	46	31	10	10	NUM
ap-340	46	32	,	,	PUNCT
ap-340	46	33	the	the	DET
ap-340	46	34	integration	integration	NOUN
ap-340	46	35	limits	limit	NOUN
ap-340	46	36	analytically	analytically	ADV
ap-340	46	37	can	can	AUX
ap-340	46	38	be	be	AUX
ap-340	46	39	determined	determine	VERB
ap-340	46	40	,	,	PUNCT
ap-340	46	41	using	use	VERB
ap-340	46	42	the	the	DET
ap-340	46	43	following	follow	VERB
ap-340	46	44	speculation	speculation	NOUN
ap-340	46	45	:	:	PUNCT
ap-340	46	46	the	the	DET
ap-340	46	47	integrand	integrand	PROPN
ap-340	46	48	contains	contain	VERB
ap-340	46	49	the	the	DET
ap-340	46	50	exponential	exponential	ADJ
ap-340	46	51	function	function	NOUN
ap-340	46	52	which	which	PRON
ap-340	46	53	for	for	ADP
ap-340	46	54	values	value	NOUN
ap-340	46	55	of	of	ADP
ap-340	46	56	z	z	NOUN
ap-340	46	57	drawing	draw	VERB
ap-340	46	58	apart	apart	ADV
ap-340	46	59	from	from	ADP
ap-340	46	60	the	the	DET
ap-340	46	61	value	value	NOUN
ap-340	46	62	of	of	ADP
ap-340	46	63	y	y	PROPN
ap-340	46	64	falls	fall	VERB
ap-340	46	65	to	to	ADP
ap-340	46	66	zero	zero	NUM
ap-340	46	67	very	very	ADV
ap-340	46	68	quickly	quickly	ADV
ap-340	46	69	.	.	PUNCT
ap-340	47	1	let	let	VERB
ap-340	47	2	us	we	PRON
ap-340	47	3	choose	choose	VERB
ap-340	47	4	a	a	DET
ap-340	47	5	small	small	ADJ
ap-340	47	6	parameter	parameter	NOUN
ap-340	47	7	1	1	NUM
ap-340	47	8	0	0	NUM
ap-340	47	9	�	�	PROPN
ap-340	47	10	�	�	PROPN
ap-340	47	11	�	�	PROPN
ap-340	47	12	,	,	PUNCT
ap-340	47	13	�	�	PROPN
ap-340	47	14	�	�	PROPN
ap-340	47	15	exp	exp	NOUN
ap-340	47	16	�	�	PROPN
ap-340	47	17	�	�	PROPN
ap-340	47	18	�	�	PROPN
ap-340	47	19	�	�	PROPN
ap-340	47	20	�	�	PROPN
ap-340	47	21	�	�	PROPN
ap-340	47	22	�	�	PROPN
ap-340	47	23	�	�	PROPN
ap-340	47	24	�	�	PROPN
ap-340	47	25	y	y	PROPN
ap-340	47	26	z	z	PROPN
ap-340	47	27	g	g	PROPN
ap-340	47	28	s	s	PROPN
ap-340	47	29	2	2	NUM
ap-340	47	30	0	0	NUM
ap-340	47	31	4	4	NUM
ap-340	47	32	.	.	PUNCT
ap-340	48	1	(	(	PUNCT
ap-340	48	2	7	7	NUM
ap-340	48	3	)	)	PUNCT
ap-340	48	4	then	then	ADV
ap-340	48	5	we	we	PRON
ap-340	48	6	are	be	AUX
ap-340	48	7	able	able	ADJ
ap-340	48	8	to	to	PART
ap-340	48	9	calculate	calculate	VERB
ap-340	48	10	the	the	DET
ap-340	48	11	limits	limit	NOUN
ap-340	48	12	from	from	ADP
ap-340	48	13	the	the	DET
ap-340	48	14	equation	equation	NOUN
ap-340	48	15	as	as	ADP
ap-340	48	16	q	q	PROPN
ap-340	48	17	y	y	PROPN
ap-340	48	18	s	s	PROPN
ap-340	48	19	g12	g12	NOUN
ap-340	48	20	0	0	NUM
ap-340	48	21	2	2	NUM
ap-340	48	22	,	,	PUNCT
ap-340	48	23	ln	ln	PROPN
ap-340	48	24	�	�	PROPN
ap-340	48	25	�	�	PROPN
ap-340	48	26	�	�	PROPN
ap-340	48	27	�	�	PROPN
ap-340	48	28	.	.	PUNCT
ap-340	49	1	(	(	PUNCT
ap-340	49	2	8)	8)	NUM
ap-340	49	3	the	the	DET
ap-340	49	4	integration	integration	NOUN
ap-340	49	5	itself	itself	PRON
ap-340	49	6	can	can	AUX
ap-340	49	7	be	be	AUX
ap-340	49	8	performed	perform	VERB
ap-340	49	9	by	by	ADP
ap-340	49	10	means	mean	NOUN
ap-340	49	11	of	of	ADP
ap-340	49	12	the	the	DET
ap-340	49	13	simpson	simpson	PROPN
ap-340	49	14	method	method	PROPN
ap-340	49	15	,	,	PUNCT
ap-340	49	16	which	which	PRON
ap-340	49	17	is	be	AUX
ap-340	49	18	based	base	VERB
ap-340	49	19	on	on	ADP
ap-340	49	20	approximating	approximate	VERB
ap-340	49	21	the	the	DET
ap-340	49	22	integrated	integrate	VERB
ap-340	49	23	function	function	NOUN
ap-340	49	24	in	in	ADP
ap-340	49	25	the	the	DET
ap-340	49	26	segments	segment	NOUN
ap-340	49	27	by	by	ADP
ap-340	49	28	parts	part	NOUN
ap-340	49	29	of	of	ADP
ap-340	49	30	a	a	DET
ap-340	49	31	parabola	parabola	PROPN
ap-340	49	32	�	�	PROPN
ap-340	49	33	�	�	PROPN
ap-340	49	34	�	�	PROPN
ap-340	49	35	�	�	PROPN
ap-340	49	36	�	�	PROPN
ap-340	49	37	�	�	PROPN
ap-340	49	38	�	�	PROPN
ap-340	49	39	�	�	PROPN
ap-340	49	40	f	f	PROPN
ap-340	49	41	z	z	PROPN
ap-340	49	42	z	z	PROPN
ap-340	49	43	q	q	NOUN
ap-340	49	44	q	q	PROPN
ap-340	50	1	n	n	PROPN
ap-340	50	2	f	f	NOUN
ap-340	50	3	z	z	NOUN
ap-340	50	4	f	f	PROPN
ap-340	51	1	z	z	NOUN
ap-340	51	2	f	f	PROPN
ap-340	52	1	z	z	NOUN
ap-340	52	2	q	q	NOUN
ap-340	52	3	q	q	PUNCT
ap-340	53	1	d	d	NOUN
ap-340	53	2	1	1	NUM
ap-340	53	3	2	2	NUM
ap-340	53	4	2	2	NUM
ap-340	53	5	1	1	NUM
ap-340	53	6	0	0	NUM
ap-340	53	7	1	1	NUM
ap-340	53	8	23	23	NUM
ap-340	53	9	4	4	NUM
ap-340	53	10	2	2	NUM
ap-340	53	11	�	�	PROPN
ap-340	53	12	�	�	PROPN
ap-340	53	13	�	�	PROPN
ap-340	53	14	�	�	PROPN
ap-340	53	15	�	�	PROPN
ap-340	53	16	�	�	PROPN
ap-340	53	17	�	�	PROPN
ap-340	53	18	[	[	PUNCT
ap-340	53	19	�	�	PROPN
ap-340	53	20	�	�	PROPN
ap-340	53	21	�	�	PROPN
ap-340	53	22	�	�	PROPN
ap-340	53	23	�	�	PROPN
ap-340	53	24	�	�	PROPN
ap-340	53	25	�	�	PROPN
ap-340	53	26	�	�	PROPN
ap-340	53	27	�	�	PROPN
ap-340	53	28	�	�	PROPN
ap-340	53	29	�	�	PROPN
ap-340	53	30	�	�	PROPN
ap-340	53	31	2	2	NUM
ap-340	53	32	42	42	NUM
ap-340	53	33	1f	1f	NUM
ap-340	53	34	z	z	NOUN
ap-340	54	1	f	f	PROPN
ap-340	54	2	z	z	NOUN
ap-340	54	3	f	f	PROPN
ap-340	54	4	zn	zn	PROPN
ap-340	54	5	n	n	PROPN
ap-340	54	6	n	n	PROPN
ap-340	54	7	]	]	PUNCT
ap-340	54	8	,	,	PUNCT
ap-340	54	9	(	(	PUNCT
ap-340	54	10	9	9	X
ap-340	54	11	)	)	PUNCT
ap-340	54	12	where	where	SCONJ
ap-340	54	13	n	n	PRON
ap-340	54	14	�	�	PROPN
ap-340	54	15	2k	2k	NUM
ap-340	54	16	,	,	PUNCT
ap-340	54	17	k	k	PROPN
ap-340	54	18	n	n	CCONJ
ap-340	54	19	�	�	PROPN
ap-340	54	20	is	be	AUX
ap-340	54	21	the	the	DET
ap-340	54	22	number	number	NOUN
ap-340	54	23	of	of	ADP
ap-340	54	24	equidistant	equidistant	ADJ
ap-340	54	25	intervals	interval	NOUN
ap-340	54	26	and	and	CCONJ
ap-340	54	27	�	�	PROPN
ap-340	54	28	�	�	PROPN
ap-340	54	29	z	z	PROPN
ap-340	54	30	q	q	NOUN
ap-340	55	1	i	i	PRON
ap-340	55	2	q	q	PROPN
ap-340	55	3	q	q	PROPN
ap-340	55	4	ni	ni	PROPN
ap-340	55	5	�	�	PROPN
ap-340	55	6	�	�	PROPN
ap-340	55	7	�	�	PROPN
ap-340	55	8	1	1	NUM
ap-340	55	9	2	2	NUM
ap-340	55	10	1	1	NUM
ap-340	55	11	.	.	PUNCT
ap-340	56	1	however	however	ADV
ap-340	56	2	,	,	PUNCT
ap-340	56	3	there	there	PRON
ap-340	56	4	is	be	VERB
ap-340	56	5	a	a	DET
ap-340	56	6	problem	problem	NOUN
ap-340	56	7	with	with	ADP
ap-340	56	8	floating	float	VERB
ap-340	56	9	-	-	PUNCT
ap-340	56	10	point	point	NOUN
ap-340	56	11	arithmetic	arithmetic	ADJ
ap-340	56	12	,	,	PUNCT
ap-340	56	13	especially	especially	ADV
ap-340	56	14	for	for	ADP
ap-340	56	15	large	large	ADJ
ap-340	56	16	values	value	NOUN
ap-340	56	17	of	of	ADP
ap-340	56	18	the	the	DET
ap-340	56	19	number	number	NOUN
ap-340	56	20	g0	g0	NOUN
ap-340	56	21	.	.	PUNCT
ap-340	57	1	when	when	SCONJ
ap-340	57	2	calculating	calculate	VERB
ap-340	57	3	the	the	DET
ap-340	57	4	integral	integral	ADJ
ap-340	57	5	,	,	PUNCT
ap-340	57	6	we	we	PRON
ap-340	57	7	add	add	VERB
ap-340	57	8	terms	term	NOUN
ap-340	57	9	according	accord	VERB
ap-340	57	10	to	to	ADP
ap-340	57	11	(	(	PUNCT
ap-340	57	12	9	9	NUM
ap-340	57	13	)	)	PUNCT
ap-340	57	14	,	,	PUNCT
ap-340	57	15	and	and	CCONJ
ap-340	57	16	after	after	ADP
ap-340	57	17	a	a	DET
ap-340	57	18	short	short	ADJ
ap-340	57	19	time	time	NOUN
ap-340	57	20	(	(	PUNCT
ap-340	57	21	especially	especially	ADV
ap-340	57	22	after	after	ADP
ap-340	57	23	integrating	integrate	VERB
ap-340	57	24	one	one	NUM
ap-340	57	25	of	of	ADP
ap-340	57	26	the	the	DET
ap-340	57	27	maxima	maxima	NOUN
ap-340	57	28	)	)	PUNCT
ap-340	57	29	the	the	DET
ap-340	57	30	partial	partial	NOUN
ap-340	57	31	is	be	AUX
ap-340	57	32	result	result	NOUN
ap-340	57	33	much	much	ADV
ap-340	57	34	larger	large	ADJ
ap-340	57	35	than	than	ADP
ap-340	57	36	the	the	DET
ap-340	57	37	next	next	ADJ
ap-340	57	38	added	add	VERB
ap-340	57	39	terms	term	NOUN
ap-340	57	40	.	.	PUNCT
ap-340	58	1	thus	thus	ADV
ap-340	58	2	these	these	DET
ap-340	58	3	terms	term	NOUN
ap-340	58	4	are	be	AUX
ap-340	58	5	not	not	PART
ap-340	58	6	taken	take	VERB
ap-340	58	7	into	into	ADP
ap-340	58	8	account	account	NOUN
ap-340	58	9	,	,	PUNCT
ap-340	58	10	and	and	CCONJ
ap-340	58	11	the	the	DET
ap-340	58	12	result	result	NOUN
ap-340	58	13	is	be	AUX
ap-340	58	14	not	not	PART
ap-340	58	15	accurate	accurate	ADJ
ap-340	58	16	.	.	PUNCT
ap-340	59	1	if	if	SCONJ
ap-340	59	2	the	the	DET
ap-340	59	3	accuracy	accuracy	NOUN
ap-340	59	4	of	of	ADP
ap-340	59	5	18	18	NUM
ap-340	59	6	valid	valid	ADJ
ap-340	59	7	digits	digit	NOUN
ap-340	59	8	is	be	AUX
ap-340	59	9	used	use	VERB
ap-340	59	10	,	,	PUNCT
ap-340	59	11	we	we	PRON
ap-340	59	12	can	can	AUX
ap-340	59	13	calculate	calculate	VERB
ap-340	59	14	for	for	ADP
ap-340	59	15	values	value	NOUN
ap-340	59	16	of	of	ADP
ap-340	59	17	g0	g0	NOUN
ap-340	59	18	up	up	ADP
ap-340	59	19	to	to	ADP
ap-340	59	20	approximately	approximately	ADV
ap-340	59	21	600	600	NUM
ap-340	59	22	.	.	PUNCT
ap-340	60	1	if	if	SCONJ
ap-340	60	2	it	it	PRON
ap-340	60	3	were	be	AUX
ap-340	60	4	necessary	necessary	ADJ
ap-340	60	5	to	to	PART
ap-340	60	6	use	use	VERB
ap-340	60	7	this	this	DET
ap-340	60	8	method	method	NOUN
ap-340	60	9	for	for	ADP
ap-340	60	10	larger	large	ADJ
ap-340	60	11	values	value	NOUN
ap-340	60	12	of	of	ADP
ap-340	60	13	g0	g0	NOUN
ap-340	60	14	,	,	PUNCT
ap-340	60	15	we	we	PRON
ap-340	60	16	would	would	AUX
ap-340	60	17	have	have	VERB
ap-340	60	18	to	to	PART
ap-340	60	19	use	use	VERB
ap-340	60	20	some	some	DET
ap-340	60	21	suitable	suitable	ADJ
ap-340	60	22	software	software	NOUN
ap-340	60	23	that	that	PRON
ap-340	60	24	allows	allow	VERB
ap-340	60	25	calculations	calculation	NOUN
ap-340	60	26	of	of	ADP
ap-340	60	27	high	high	ADJ
ap-340	60	28	precision	precision	NOUN
ap-340	60	29	,	,	PUNCT
ap-340	60	30	e.g.	e.g.	ADV
ap-340	60	31	,	,	PUNCT
ap-340	60	32	the	the	DET
ap-340	60	33	free	free	ADJ
ap-340	60	34	library	library	NOUN
ap-340	60	35	gnu	gnu	PROPN
ap-340	60	36	mp	mp	PROPN
ap-340	60	37	.	.	PROPN
ap-340	60	38	saddle	saddle	PROPN
ap-340	60	39	point	point	NOUN
ap-340	60	40	method	method	NOUN
ap-340	60	41	if	if	SCONJ
ap-340	60	42	we	we	PRON
ap-340	60	43	study	study	VERB
ap-340	60	44	the	the	DET
ap-340	60	45	integrand	integrand	NOUN
ap-340	60	46	properties	property	NOUN
ap-340	60	47	,	,	PUNCT
ap-340	60	48	the	the	DET
ap-340	60	49	calculation	calculation	NOUN
ap-340	60	50	can	can	AUX
ap-340	60	51	be	be	AUX
ap-340	60	52	significantly	significantly	ADV
ap-340	60	53	simplified	simplify	VERB
ap-340	60	54	and	and	CCONJ
ap-340	60	55	the	the	DET
ap-340	60	56	problems	problem	NOUN
ap-340	60	57	caused	cause	VERB
ap-340	60	58	by	by	ADP
ap-340	60	59	processing	process	VERB
ap-340	60	60	numbers	number	NOUN
ap-340	60	61	in	in	ADP
ap-340	60	62	high	high	ADJ
ap-340	60	63	precision	precision	NOUN
ap-340	60	64	can	can	AUX
ap-340	60	65	be	be	AUX
ap-340	60	66	avoided	avoid	VERB
ap-340	60	67	[	[	PUNCT
ap-340	60	68	17	17	NUM
ap-340	60	69	]	]	PUNCT
ap-340	60	70	.	.	PUNCT
ap-340	61	1	when	when	SCONJ
ap-340	61	2	using	use	VERB
ap-340	61	3	the	the	DET
ap-340	61	4	saddle	saddle	NOUN
ap-340	61	5	point	point	NOUN
ap-340	61	6	method	method	NOUN
ap-340	61	7	,	,	PUNCT
ap-340	61	8	the	the	DET
ap-340	61	9	accuracy	accuracy	NOUN
ap-340	61	10	of	of	ADP
ap-340	61	11	the	the	DET
ap-340	61	12	values	value	NOUN
ap-340	61	13	of	of	ADP
ap-340	61	14	the	the	DET
ap-340	61	15	integrals	integral	NOUN
ap-340	61	16	obtained	obtain	VERB
ap-340	61	17	in	in	ADP
ap-340	61	18	equation	equation	NOUN
ap-340	61	19	(	(	PUNCT
ap-340	61	20	5	5	NUM
ap-340	61	21	)	)	PUNCT
ap-340	61	22	improves	improve	VERB
ap-340	61	23	with	with	ADP
ap-340	61	24	increasing	increase	VERB
ap-340	61	25	goldberg	goldberg	PROPN
ap-340	61	26	number	number	NOUN
ap-340	61	27	g0	g0	PROPN
ap-340	61	28	.	.	PUNCT
ap-340	62	1	for	for	ADP
ap-340	62	2	easier	easy	ADJ
ap-340	62	3	orientation	orientation	NOUN
ap-340	62	4	we	we	PRON
ap-340	62	5	express	express	VERB
ap-340	62	6	equation	equation	NOUN
ap-340	62	7	(	(	PUNCT
ap-340	62	8	5	5	NUM
ap-340	62	9	)	)	PUNCT
ap-340	62	10	in	in	ADP
ap-340	62	11	the	the	DET
ap-340	62	12	following	follow	VERB
ap-340	62	13	form	form	NOUN
ap-340	62	14	�	�	PROPN
ap-340	62	15	�	�	PROPN
ap-340	62	16	�	�	PROPN
ap-340	62	17	�	�	PROPN
ap-340	62	18	�	�	PROPN
ap-340	62	19	�	�	PROPN
ap-340	62	20	v	v	ADP
ap-340	62	21	f	f	PROPN
ap-340	62	22	z	z	PROPN
ap-340	62	23	s	s	PROPN
ap-340	62	24	y	y	PROPN
ap-340	62	25	g	g	PROPN
ap-340	62	26	f	f	PROPN
ap-340	62	27	z	z	PROPN
ap-340	62	28	s	s	PROPN
ap-340	62	29	y	y	PROPN
ap-340	62	30	z	z	PROPN
ap-340	62	31	g	g	PROPN
ap-340	62	32	f	f	PROPN
ap-340	62	33	z	z	PROPN
ap-340	62	34	s	s	PROPN
ap-340	62	35	y	y	PROPN
ap-340	62	36	�	�	PROPN
ap-340	62	37	�	�	PROPN
ap-340	62	38	�	�	PROPN
ap-340	62	39	�	�	PROPN
ap-340	62	40	�	�	PROPN
ap-340	62	41	�	�	PROPN
ap-340	62	42	�	�	PROPN
ap-340	62	43	�	�	PROPN
ap-340	62	44	�	�	PROPN
ap-340	62	45	�	�	PROPN
ap-340	62	46	�	�	PROPN
ap-340	62	47	�	�	PROPN
ap-340	62	48	;	;	PROPN
ap-340	62	49	,	,	PUNCT
ap-340	62	50	exp	exp	NOUN
ap-340	62	51	;	;	NOUN
ap-340	62	52	,	,	PUNCT
ap-340	62	53	exp	exp	NOUN
ap-340	62	54	;	;	NOUN
ap-340	62	55	,	,	PUNCT
ap-340	62	56	0	0	NUM
ap-340	62	57	0	0	NUM
ap-340	62	58	2	2	NUM
ap-340	62	59	2	2	NUM
ap-340	62	60	d	d	PROPN
ap-340	62	61	�	�	PROPN
ap-340	62	62	�	�	PROPN
ap-340	62	63	�	�	PROPN
ap-340	62	64	�	�	PROPN
ap-340	62	65	�	�	PROPN
ap-340	62	66	dz	dz	PROPN
ap-340	62	67	(	(	PUNCT
ap-340	62	68	10	10	NUM
ap-340	62	69	)	)	PUNCT
ap-340	62	70	where	where	SCONJ
ap-340	62	71	�	�	PROPN
ap-340	62	72	�	�	PROPN
ap-340	62	73	f	f	PROPN
ap-340	62	74	z	z	PROPN
ap-340	62	75	s	s	PROPN
ap-340	62	76	y	y	PROPN
ap-340	62	77	y	y	PROPN
ap-340	62	78	z	z	PROPN
ap-340	62	79	s	s	PROPN
ap-340	62	80	;	;	NOUN
ap-340	62	81	,	,	PUNCT
ap-340	62	82	�	�	PROPN
ap-340	62	83	�	�	PROPN
ap-340	62	84	,	,	PUNCT
ap-340	62	85	�	�	PROPN
ap-340	62	86	�	�	PROPN
ap-340	62	87	�	�	PROPN
ap-340	62	88	�	�	PROPN
ap-340	62	89	�	�	PROPN
ap-340	62	90	�	�	PROPN
ap-340	62	91	f	f	PROPN
ap-340	62	92	z	z	PROPN
ap-340	62	93	s	s	PROPN
ap-340	62	94	y	y	PROPN
ap-340	62	95	y	y	PROPN
ap-340	62	96	z	z	PROPN
ap-340	62	97	s	s	PROPN
ap-340	62	98	v	v	PROPN
ap-340	62	99	y	y	PROPN
ap-340	62	100	y	y	PROPN
ap-340	62	101	z	z	PROPN
ap-340	62	102	;	;	PROPN
ap-340	62	103	,	,	PUNCT
ap-340	62	104	,	,	PUNCT
ap-340	62	105	�	�	PROPN
ap-340	62	106	�	�	PROPN
ap-340	62	107	�	�	PROPN
ap-340	62	108	2	2	NUM
ap-340	62	109	0	0	NUM
ap-340	62	110	2	2	NUM
ap-340	62	111	0	0	NUM
ap-340	62	112	d	d	NOUN
ap-340	62	113	,	,	PUNCT
ap-340	62	114	(	(	PUNCT
ap-340	62	115	11	11	NUM
ap-340	62	116	)	)	PUNCT
ap-340	62	117	here	here	ADV
ap-340	62	118	s	s	X
ap-340	62	119	and	and	CCONJ
ap-340	62	120	y	y	PROPN
ap-340	62	121	represent	represent	VERB
ap-340	62	122	the	the	DET
ap-340	62	123	parameters	parameter	NOUN
ap-340	62	124	.	.	PUNCT
ap-340	63	1	figs	fig	NOUN
ap-340	63	2	.	.	PUNCT
ap-340	64	1	1–3	1–3	NUM
ap-340	64	2	show	show	VERB
ap-340	64	3	the	the	DET
ap-340	64	4	courses	course	NOUN
ap-340	64	5	of	of	ADP
ap-340	64	6	the	the	DET
ap-340	64	7	integrands	integrand	NOUN
ap-340	64	8	for	for	ADP
ap-340	64	9	different	different	ADJ
ap-340	64	10	goldberg	goldberg	PROPN
ap-340	64	11	numbers	number	NOUN
ap-340	64	12	(	(	PUNCT
ap-340	64	13	g0	g0	PROPN
ap-340	64	14	�	�	PROPN
ap-340	64	15	10	10	NUM
ap-340	64	16	,	,	PUNCT
ap-340	64	17	50	50	NUM
ap-340	64	18	,	,	PUNCT
ap-340	64	19	500	500	NUM
ap-340	64	20	)	)	PUNCT
ap-340	64	21	at	at	ADP
ap-340	64	22	the	the	DET
ap-340	64	23	various	various	ADJ
ap-340	64	24	distances	distance	NOUN
ap-340	64	25	(	(	PUNCT
ap-340	64	26	s	s	NOUN
ap-340	64	27	�	�	PROPN
ap-340	64	28	1	1	NUM
ap-340	64	29	,	,	PUNCT
ap-340	64	30	10	10	NUM
ap-340	64	31	,	,	PUNCT
ap-340	64	32	50	50	NUM
ap-340	64	33	)	)	PUNCT
ap-340	64	34	for	for	ADP
ap-340	64	35	a	a	DET
ap-340	64	36	harmonic	harmonic	ADJ
ap-340	64	37	boundary	boundary	ADJ
ap-340	64	38	condition	condition	NOUN
ap-340	64	39	.	.	PUNCT
ap-340	65	1	it	it	PRON
ap-340	65	2	is	be	AUX
ap-340	65	3	obvious	obvious	ADJ
ap-340	65	4	from	from	ADP
ap-340	65	5	the	the	DET
ap-340	65	6	shape	shape	NOUN
ap-340	65	7	of	of	ADP
ap-340	65	8	these	these	DET
ap-340	65	9	three	three	NUM
ap-340	65	10	-	-	PUNCT
ap-340	65	11	dimensional	dimensional	ADJ
ap-340	65	12	graphs	graph	NOUN
ap-340	65	13	that	that	SCONJ
ap-340	65	14	the	the	DET
ap-340	65	15	courses	course	NOUN
ap-340	65	16	of	of	ADP
ap-340	65	17	the	the	DET
ap-340	65	18	integrands	integrand	NOUN
ap-340	65	19	have	have	VERB
ap-340	65	20	significant	significant	ADJ
ap-340	65	21	extrema	extrema	NOUN
ap-340	65	22	(	(	PUNCT
ap-340	65	23	maxima	maxima	NOUN
ap-340	65	24	)	)	PUNCT
ap-340	65	25	.	.	PUNCT
ap-340	66	1	consequently	consequently	ADV
ap-340	66	2	we	we	PRON
ap-340	66	3	can	can	AUX
ap-340	66	4	restrict	restrict	VERB
ap-340	66	5	the	the	DET
ap-340	66	6	integration	integration	NOUN
ap-340	66	7	limits	limit	NOUN
ap-340	66	8	to	to	ADP
ap-340	66	9	their	their	PRON
ap-340	66	10	close	close	ADJ
ap-340	66	11	neighbourhood	neighbourhood	NOUN
ap-340	66	12	.	.	PUNCT
ap-340	67	1	further	far	ADV
ap-340	67	2	,	,	PUNCT
ap-340	67	3	we	we	PRON
ap-340	67	4	can	can	AUX
ap-340	67	5	see	see	VERB
ap-340	67	6	that	that	SCONJ
ap-340	67	7	when	when	SCONJ
ap-340	67	8	the	the	DET
ap-340	67	9	goldberg	goldberg	PROPN
ap-340	67	10	number	number	NOUN
ap-340	67	11	increases	increase	VERB
ap-340	67	12	,	,	PUNCT
ap-340	67	13	the	the	DET
ap-340	67	14	values	value	NOUN
ap-340	67	15	of	of	ADP
ap-340	67	16	the	the	DET
ap-340	67	17	integrand	integrand	ADJ
ap-340	67	18	extrema	extrema	NOUN
ap-340	67	19	also	also	ADV
ap-340	67	20	increase	increase	VERB
ap-340	67	21	and	and	CCONJ
ap-340	67	22	diminish	diminish	VERB
ap-340	67	23	to	to	ADP
ap-340	67	24	zero	zero	NUM
ap-340	67	25	from	from	ADP
ap-340	67	26	these	these	DET
ap-340	67	27	ex72	ex72	PROPN
ap-340	67	28	acta	acta	PROPN
ap-340	67	29	polytechnica	polytechnica	PROPN
ap-340	67	30	vol	vol	NOUN
ap-340	67	31	.	.	PUNCT
ap-340	68	1	42	42	NUM
ap-340	68	2	no	no	NOUN
ap-340	68	3	.	.	PUNCT
ap-340	69	1	2/2002	2/2002	NUM
ap-340	69	2	fig	fig	NOUN
ap-340	69	3	.	.	PUNCT
ap-340	70	1	1	1	NUM
ap-340	70	2	:	:	PUNCT
ap-340	70	3	space	space	NOUN
ap-340	70	4	evolution	evolution	NOUN
ap-340	70	5	of	of	ADP
ap-340	70	6	integrand	integrand	PROPN
ap-340	70	7	,	,	PUNCT
ap-340	70	8	g0	g0	PROPN
ap-340	70	9	�	�	PROPN
ap-340	70	10	10	10	NUM
ap-340	70	11	,	,	PUNCT
ap-340	70	12	s	s	VERB
ap-340	70	13	�	�	PROPN
ap-340	70	14	1	1	NUM
ap-340	70	15	,	,	PUNCT
ap-340	70	16	10	10	NUM
ap-340	70	17	,	,	PUNCT
ap-340	70	18	50	50	NUM
ap-340	70	19	trema	trema	NOUN
ap-340	70	20	more	more	ADV
ap-340	70	21	rapidly	rapidly	ADV
ap-340	70	22	(	(	PUNCT
ap-340	70	23	the	the	DET
ap-340	70	24	course	course	NOUN
ap-340	70	25	of	of	ADP
ap-340	70	26	the	the	DET
ap-340	70	27	integrand	integrand	NOUN
ap-340	70	28	is	be	AUX
ap-340	70	29	narrower	narrow	ADJ
ap-340	70	30	)	)	PUNCT
ap-340	70	31	.	.	PUNCT
ap-340	71	1	these	these	DET
ap-340	71	2	pictures	picture	NOUN
ap-340	71	3	also	also	ADV
ap-340	71	4	show	show	VERB
ap-340	71	5	that	that	SCONJ
ap-340	71	6	,	,	PUNCT
ap-340	71	7	on	on	ADP
ap-340	71	8	the	the	DET
ap-340	71	9	contrary	contrary	NOUN
ap-340	71	10	,	,	PUNCT
ap-340	71	11	in	in	ADP
ap-340	71	12	the	the	DET
ap-340	71	13	case	case	NOUN
ap-340	71	14	of	of	ADP
ap-340	71	15	increasing	increase	VERB
ap-340	71	16	dimensionless	dimensionless	ADJ
ap-340	71	17	distance	distance	NOUN
ap-340	71	18	s	s	VERB
ap-340	71	19	near	near	ADJ
ap-340	71	20	to	to	ADP
ap-340	71	21	the	the	DET
ap-340	71	22	extreme	extreme	NOUN
ap-340	71	23	,	,	PUNCT
ap-340	71	24	the	the	DET
ap-340	71	25	integrand	integrand	NOUN
ap-340	71	26	falls	fall	VERB
ap-340	71	27	more	more	ADV
ap-340	71	28	slowly	slowly	ADV
ap-340	71	29	and	and	CCONJ
ap-340	71	30	the	the	DET
ap-340	71	31	course	course	NOUN
ap-340	71	32	of	of	ADP
ap-340	71	33	integrand	integrand	NOUN
ap-340	71	34	spreads	spread	NOUN
ap-340	71	35	(	(	PUNCT
ap-340	71	36	the	the	DET
ap-340	71	37	extrema	extrema	NOUN
ap-340	71	38	are	be	AUX
ap-340	71	39	not	not	PART
ap-340	71	40	so	so	ADV
ap-340	71	41	significant	significant	ADJ
ap-340	71	42	)	)	PUNCT
ap-340	71	43	.	.	PUNCT
ap-340	72	1	consequently	consequently	ADV
ap-340	72	2	we	we	PRON
ap-340	72	3	need	need	VERB
ap-340	72	4	to	to	PART
ap-340	72	5	take	take	VERB
ap-340	72	6	into	into	ADP
ap-340	72	7	account	account	NOUN
ap-340	72	8	two	two	NUM
ap-340	72	9	maxima	maxima	NOUN
ap-340	72	10	for	for	ADP
ap-340	72	11	certain	certain	ADJ
ap-340	72	12	(	(	PUNCT
ap-340	72	13	appointed	appointed	ADJ
ap-340	72	14	)	)	PUNCT
ap-340	72	15	values	value	NOUN
ap-340	72	16	of	of	ADP
ap-340	72	17	dimensionless	dimensionless	ADJ
ap-340	72	18	time	time	NOUN
ap-340	72	19	to	to	PART
ap-340	72	20	do	do	VERB
ap-340	72	21	the	the	DET
ap-340	72	22	integration	integration	NOUN
ap-340	72	23	(	(	PUNCT
ap-340	72	24	the	the	DET
ap-340	72	25	maxima	maxima	NOUN
ap-340	72	26	superimpose	superimpose	NOUN
ap-340	72	27	in	in	ADP
ap-340	72	28	the	the	DET
ap-340	72	29	direction	direction	NOUN
ap-340	72	30	of	of	ADP
ap-340	72	31	the	the	DET
ap-340	72	32	z	z	NOUN
ap-340	72	33	axis	axis	NOUN
ap-340	72	34	)	)	PUNCT
ap-340	72	35	.	.	PUNCT
ap-340	73	1	let	let	VERB
ap-340	73	2	us	we	PRON
ap-340	73	3	now	now	ADV
ap-340	73	4	analyse	analyse	VERB
ap-340	73	5	the	the	DET
ap-340	73	6	relation	relation	NOUN
ap-340	73	7	(	(	PUNCT
ap-340	73	8	5	5	NUM
ap-340	73	9	)	)	PUNCT
ap-340	73	10	for	for	ADP
ap-340	73	11	g0	g0	ADJ
ap-340	73	12	1	1	NUM
ap-340	73	13	�	�	PROPN
ap-340	73	14	and	and	CCONJ
ap-340	73	15	constant	constant	ADJ
ap-340	73	16	s	s	NOUN
ap-340	73	17	and	and	CCONJ
ap-340	73	18	y.	y.	NOUN
ap-340	73	19	in	in	ADP
ap-340	73	20	this	this	DET
ap-340	73	21	case	case	NOUN
ap-340	73	22	the	the	DET
ap-340	73	23	largest	large	ADJ
ap-340	73	24	contributions	contribution	NOUN
ap-340	73	25	of	of	ADP
ap-340	73	26	both	both	DET
ap-340	73	27	integrands	integrand	NOUN
ap-340	73	28	come	come	VERB
ap-340	73	29	from	from	ADP
ap-340	73	30	the	the	DET
ap-340	73	31	extrema	extrema	NOUN
ap-340	73	32	of	of	ADP
ap-340	73	33	the	the	DET
ap-340	73	34	function	function	NOUN
ap-340	73	35	f(z	f(z	PROPN
ap-340	73	36	;	;	PUNCT
ap-340	73	37	s	s	X
ap-340	73	38	,	,	PUNCT
ap-340	73	39	y	y	PROPN
ap-340	73	40	)	)	PUNCT
ap-340	73	41	.	.	PUNCT
ap-340	74	1	from	from	ADP
ap-340	74	2	the	the	DET
ap-340	74	3	condition	condition	NOUN
ap-340	74	4	�	�	PROPN
ap-340	74	5	�	�	PROPN
ap-340	74	6	�	�	PROPN
ap-340	74	7	�	�	PROPN
ap-340	74	8	�	�	PROPN
ap-340	74	9	�	�	PROPN
ap-340	74	10	�	�	PROPN
ap-340	74	11	�	�	PROPN
ap-340	74	12	�	�	PROPN
ap-340	74	13	�	�	PROPN
ap-340	74	14	f	f	PROPN
ap-340	74	15	z	z	PROPN
ap-340	74	16	s	s	PROPN
ap-340	74	17	y	y	PROPN
ap-340	74	18	z	z	PROPN
ap-340	74	19	z	z	PROPN
ap-340	74	20	y	y	PROPN
ap-340	74	21	z	z	PROPN
ap-340	74	22	s	s	PROPN
ap-340	74	23	v	v	PROPN
ap-340	74	24	y	y	PROPN
ap-340	74	25	y	y	PROPN
ap-340	74	26	z	z	PROPN
ap-340	74	27	;	;	PROPN
ap-340	74	28	,	,	PUNCT
ap-340	74	29	,	,	PUNCT
ap-340	74	30	�	�	PROPN
ap-340	74	31	�	�	PROPN
ap-340	74	32	�	�	PROPN
ap-340	74	33	�	�	PROPN
ap-340	74	34	�	�	PROPN
ap-340	74	35	�	�	PROPN
ap-340	74	36	�	�	PROPN
ap-340	74	37	�	�	PROPN
ap-340	74	38	�	�	PROPN
ap-340	74	39	�	�	PROPN
ap-340	74	40	2	2	NUM
ap-340	74	41	0	0	NUM
ap-340	74	42	2	2	NUM
ap-340	74	43	0	0	NUM
ap-340	74	44	0d	0d	NOUN
ap-340	74	45	(	(	PUNCT
ap-340	74	46	12	12	NUM
ap-340	74	47	)	)	PUNCT
ap-340	74	48	we	we	PRON
ap-340	74	49	obtain	obtain	VERB
ap-340	74	50	�	�	PROPN
ap-340	74	51	�	�	PROPN
ap-340	74	52	y	y	PROPN
ap-340	74	53	z	z	PROPN
ap-340	74	54	s	s	PROPN
ap-340	74	55	v	v	PROPN
ap-340	74	56	z	z	PROPN
ap-340	74	57	�	�	PROPN
ap-340	74	58	�	�	PROPN
ap-340	74	59	�	�	PROPN
ap-340	74	60	0	0	NUM
ap-340	74	61	0	0	NUM
ap-340	74	62	,	,	PUNCT
ap-340	74	63	.	.	PUNCT
ap-340	75	1	(	(	PUNCT
ap-340	75	2	13	13	NUM
ap-340	75	3	)	)	PUNCT
ap-340	75	4	let	let	VERB
ap-340	75	5	us	we	PRON
ap-340	75	6	mark	mark	VERB
ap-340	75	7	the	the	DET
ap-340	75	8	solutions	solution	NOUN
ap-340	75	9	of	of	ADP
ap-340	75	10	equation	equation	NOUN
ap-340	75	11	(	(	PUNCT
ap-340	75	12	13	13	NUM
ap-340	75	13	)	)	PUNCT
ap-340	75	14	z0	z0	NOUN
ap-340	75	15	and	and	CCONJ
ap-340	75	16	select	select	VERB
ap-340	75	17	only	only	ADV
ap-340	75	18	those	those	PRON
ap-340	75	19	which	which	PRON
ap-340	75	20	represent	represent	VERB
ap-340	75	21	maxima	maxima	NOUN
ap-340	75	22	of	of	ADP
ap-340	75	23	the	the	DET
ap-340	75	24	integrands	integrands	PROPN
ap-340	75	25	�	�	PROPN
ap-340	75	26	�	�	PROPN
ap-340	75	27	�	�	PROPN
ap-340	75	28	�	�	PROPN
ap-340	75	29	�	�	PROPN
ap-340	75	30	�	�	PROPN
ap-340	75	31	�	�	PROPN
ap-340	75	32	�	�	PROPN
ap-340	75	33	�	�	PROPN
ap-340	75	34	�	�	PROPN
ap-340	75	35	�	�	PROPN
ap-340	75	36	�	�	PROPN
ap-340	75	37	�	�	PROPN
ap-340	75	38	�	�	PROPN
ap-340	75	39	�	�	PROPN
ap-340	75	40	f	f	PROPN
ap-340	75	41	z	z	PROPN
ap-340	75	42	s	s	PROPN
ap-340	75	43	y	y	PROPN
ap-340	75	44	z	z	PROPN
ap-340	75	45	s	s	PROPN
ap-340	75	46	v	v	ADP
ap-340	75	47	z	z	NOUN
ap-340	75	48	z	z	NOUN
ap-340	75	49	0	0	NUM
ap-340	75	50	2	2	NUM
ap-340	75	51	00	00	NUM
ap-340	75	52	1	1	NUM
ap-340	75	53	0	0	NUM
ap-340	75	54	0	0	NUM
ap-340	75	55	;	;	NOUN
ap-340	75	56	,	,	PUNCT
ap-340	75	57	,	,	PUNCT
ap-340	75	58	.	.	PUNCT
ap-340	76	1	(	(	PUNCT
ap-340	76	2	14	14	NUM
ap-340	76	3	)	)	PUNCT
ap-340	76	4	now	now	ADV
ap-340	76	5	the	the	DET
ap-340	76	6	contribution	contribution	NOUN
ap-340	76	7	of	of	ADP
ap-340	76	8	the	the	DET
ap-340	76	9	neighbourhood	neighbourhood	NOUN
ap-340	76	10	of	of	ADP
ap-340	76	11	this	this	DET
ap-340	76	12	extreme	extreme	NOUN
ap-340	76	13	can	can	AUX
ap-340	76	14	be	be	AUX
ap-340	76	15	expressed	express	VERB
ap-340	76	16	if	if	SCONJ
ap-340	76	17	we	we	PRON
ap-340	76	18	expand	expand	VERB
ap-340	76	19	the	the	DET
ap-340	76	20	function	function	NOUN
ap-340	76	21	f(z	f(z	PROPN
ap-340	76	22	;	;	PUNCT
ap-340	76	23	s	s	X
ap-340	76	24	,	,	PUNCT
ap-340	76	25	y	y	NOUN
ap-340	76	26	)	)	PUNCT
ap-340	76	27	into	into	ADP
ap-340	76	28	the	the	DET
ap-340	76	29	taylor	taylor	PROPN
ap-340	76	30	series	series	NOUN
ap-340	76	31	at	at	ADP
ap-340	76	32	the	the	DET
ap-340	76	33	point	point	NOUN
ap-340	76	34	z	z	PROPN
ap-340	76	35	�	�	PROPN
ap-340	76	36	z0	z0	PROPN
ap-340	76	37	and	and	CCONJ
ap-340	76	38	we	we	PRON
ap-340	76	39	consider	consider	VERB
ap-340	76	40	only	only	ADV
ap-340	76	41	the	the	DET
ap-340	76	42	first	first	ADJ
ap-340	76	43	three	three	NUM
ap-340	76	44	terms	term	NOUN
ap-340	76	45	(	(	PUNCT
ap-340	76	46	the	the	DET
ap-340	76	47	quadratic	quadratic	ADJ
ap-340	76	48	order	order	NOUN
ap-340	76	49	)	)	PUNCT
ap-340	76	50	.	.	PUNCT
ap-340	77	1	for	for	ADP
ap-340	77	2	the	the	DET
ap-340	77	3	function	function	NOUN
ap-340	77	4	f(z	f(z	PROPN
ap-340	77	5	;	;	PUNCT
ap-340	77	6	s	s	X
ap-340	77	7	,	,	PUNCT
ap-340	77	8	y	y	PROPN
ap-340	77	9	)	)	PUNCT
ap-340	77	10	we	we	PRON
ap-340	77	11	shall	shall	AUX
ap-340	77	12	omit	omit	VERB
ap-340	77	13	writing	write	VERB
ap-340	77	14	parameters	parameter	NOUN
ap-340	77	15	s	s	PART
ap-340	77	16	and	and	CCONJ
ap-340	77	17	y	y	PROPN
ap-340	77	18	;	;	PUNCT
ap-340	77	19	�	�	PROPN
ap-340	77	20	�	�	PROPN
ap-340	77	21	�	�	PROPN
ap-340	77	22	f	f	PROPN
ap-340	77	23	z	z	PROPN
ap-340	77	24	and	and	CCONJ
ap-340	77	25	�	�	PROPN
ap-340	77	26	�	�	PROPN
ap-340	77	27	�	�	PROPN
ap-340	77	28	�	�	PROPN
ap-340	77	29	f	f	PROPN
ap-340	77	30	z	z	PROPN
ap-340	77	31	will	will	AUX
ap-340	77	32	have	have	VERB
ap-340	77	33	the	the	DET
ap-340	77	34	meaning	meaning	NOUN
ap-340	77	35	of	of	ADP
ap-340	77	36	the	the	DET
ap-340	77	37	first	first	ADJ
ap-340	77	38	and	and	CCONJ
ap-340	77	39	second	second	ADJ
ap-340	77	40	derivation	derivation	NOUN
ap-340	77	41	of	of	ADP
ap-340	77	42	this	this	DET
ap-340	77	43	function	function	NOUN
ap-340	77	44	with	with	ADP
ap-340	77	45	respect	respect	NOUN
ap-340	77	46	to	to	ADP
ap-340	77	47	variable	variable	ADJ
ap-340	77	48	z.	z.	PROPN
ap-340	77	49	�	�	PROPN
ap-340	77	50	�	�	PROPN
ap-340	77	51	�	�	PROPN
ap-340	77	52	�	�	PROPN
ap-340	77	53	�	�	PROPN
ap-340	77	54	�	�	PROPN
ap-340	77	55	�	�	PROPN
ap-340	77	56	�	�	PROPN
ap-340	77	57	�	�	PROPN
ap-340	77	58	�	�	PROPN
ap-340	77	59	�	�	PROPN
ap-340	77	60	�	�	PROPN
ap-340	77	61	�	�	PROPN
ap-340	77	62	�	�	PROPN
ap-340	77	63	�	�	PROPN
ap-340	77	64	�	�	PROPN
ap-340	77	65	�	�	PROPN
ap-340	77	66	�	�	PROPN
ap-340	78	1	f	f	PROPN
ap-340	78	2	z	z	PROPN
ap-340	79	1	f	f	PROPN
ap-340	79	2	z	z	NOUN
ap-340	79	3	f	f	PROPN
ap-340	80	1	z	z	NOUN
ap-340	80	2	z	z	NOUN
ap-340	80	3	z	z	NOUN
ap-340	81	1	f	f	PROPN
ap-340	81	2	z	z	NOUN
ap-340	81	3	z	z	NOUN
ap-340	81	4	z	z	NOUN
ap-340	82	1	f	f	NOUN
ap-340	82	2	z	z	NOUN
ap-340	82	3	f	f	PROPN
ap-340	82	4	z	z	PROPN
ap-340	82	5	z	z	PROPN
ap-340	82	6	z	z	PROPN
ap-340	82	7	�	�	PROPN
ap-340	82	8	,	,	PUNCT
ap-340	82	9	�	�	PROPN
ap-340	82	10	�	�	PROPN
ap-340	82	11	�	�	PROPN
ap-340	82	12	�	�	PROPN
ap-340	82	13	�	�	PROPN
ap-340	82	14	�	�	PROPN
ap-340	82	15	�	�	PROPN
ap-340	82	16	�	�	PROPN
ap-340	82	17	�	�	PROPN
ap-340	82	18	�	�	PROPN
ap-340	82	19	�	�	PROPN
ap-340	82	20	�	�	PROPN
ap-340	82	21	�	�	PROPN
ap-340	82	22	�	�	PROPN
ap-340	82	23	0	0	NUM
ap-340	82	24	0	0	NUM
ap-340	82	25	0	0	NUM
ap-340	82	26	0	0	NUM
ap-340	82	27	0	0	NUM
ap-340	82	28	2	2	NUM
ap-340	82	29	0	0	NUM
ap-340	82	30	0	0	NUM
ap-340	82	31	0	0	NUM
ap-340	82	32	2	2	NUM
ap-340	82	33	1	1	NUM
ap-340	82	34	2	2	NUM
ap-340	82	35	1	1	NUM
ap-340	82	36	2	2	NUM
ap-340	82	37	(	(	PUNCT
ap-340	82	38	15	15	NUM
ap-340	82	39	)	)	PUNCT
ap-340	82	40	because	because	SCONJ
ap-340	82	41	at	at	ADP
ap-340	82	42	the	the	DET
ap-340	82	43	stationary	stationary	ADJ
ap-340	82	44	point	point	NOUN
ap-340	82	45	there	there	PRON
ap-340	82	46	is	be	VERB
ap-340	82	47	always	always	ADV
ap-340	82	48	�	�	PROPN
ap-340	82	49	�	�	PROPN
ap-340	82	50	�	�	PROPN
ap-340	82	51	�	�	PROPN
ap-340	82	52	f	f	PROPN
ap-340	82	53	z0	z0	PROPN
ap-340	82	54	0	0	PROPN
ap-340	82	55	.	.	PUNCT
ap-340	83	1	now	now	ADV
ap-340	83	2	we	we	PRON
ap-340	83	3	substitute	substitute	VERB
ap-340	83	4	this	this	DET
ap-340	83	5	expansion	expansion	NOUN
ap-340	83	6	into	into	ADP
ap-340	83	7	the	the	DET
ap-340	83	8	integral	integral	ADJ
ap-340	83	9	�	�	PROPN
ap-340	83	10	�	�	PROPN
ap-340	83	11	exp	exp	NOUN
ap-340	83	12	�	�	PROPN
ap-340	83	13	�	�	PROPN
ap-340	83	14	�	�	PROPN
ap-340	83	15	�	�	PROPN
ap-340	83	16	�	�	PROPN
ap-340	83	17	�	�	PROPN
ap-340	83	18	�	�	PROPN
ap-340	83	19	�	�	PROPN
ap-340	83	20	g	g	PROPN
ap-340	83	21	f	f	PROPN
ap-340	83	22	z	z	PROPN
ap-340	83	23	z0	z0	PROPN
ap-340	83	24	2	2	NUM
ap-340	83	25	d	d	NOUN
ap-340	83	26	(	(	PUNCT
ap-340	83	27	16	16	NUM
ap-340	83	28	)	)	PUNCT
ap-340	83	29	which	which	PRON
ap-340	83	30	we	we	PRON
ap-340	83	31	rearrange	rearrange	VERB
ap-340	83	32	by	by	ADP
ap-340	83	33	means	mean	NOUN
ap-340	83	34	of	of	ADP
ap-340	83	35	the	the	DET
ap-340	83	36	well	well	ADV
ap-340	83	37	-	-	PUNCT
ap-340	83	38	known	know	VERB
ap-340	83	39	laplace	laplace	NOUN
ap-340	83	40	-	-	PUNCT
ap-340	83	41	gauss	gauss	NOUN
ap-340	83	42	integral	integral	ADJ
ap-340	83	43	e	e	PROPN
ap-340	83	44	da	da	PROPN
ap-340	83	45	x2	x2	PROPN
ap-340	83	46	�	�	PROPN
ap-340	83	47	�	�	PROPN
ap-340	83	48	�	�	PROPN
ap-340	83	49	�	�	PROPN
ap-340	83	50	�	�	PROPN
ap-340	83	51	�	�	PROPN
ap-340	83	52	2	2	NUM
ap-340	83	53	0z	0z	NOUN
ap-340	83	54	a	a	DET
ap-340	83	55	a	a	NOUN
ap-340	83	56	,	,	PUNCT
ap-340	83	57	(	(	PUNCT
ap-340	83	58	17	17	NUM
ap-340	83	59	)	)	PUNCT
ap-340	83	60	to	to	ADP
ap-340	83	61	the	the	DET
ap-340	83	62	form	form	NOUN
ap-340	83	63	�	�	PROPN
ap-340	83	64	�	�	PROPN
ap-340	83	65	�	�	PROPN
ap-340	83	66	�	�	PROPN
ap-340	83	67	4	4	NUM
ap-340	83	68	1	1	NUM
ap-340	83	69	20	20	NUM
ap-340	83	70	0	0	NUM
ap-340	83	71	0	0	NUM
ap-340	83	72	0	0	NUM
ap-340	84	1	g	g	NOUN
ap-340	84	2	f	f	PROPN
ap-340	84	3	z	z	NOUN
ap-340	84	4	g	g	PROPN
ap-340	84	5	f	f	PROPN
ap-340	84	6	z	z	PROPN
ap-340	84	7	�	�	PROPN
ap-340	84	8	�	�	PROPN
ap-340	84	9	�	�	PROPN
ap-340	84	10	�	�	PROPN
ap-340	84	11	�	�	PROPN
ap-340	84	12	�	�	PROPN
ap-340	84	13	�	�	PROPN
ap-340	84	14	exp	exp	NOUN
ap-340	84	15	.	.	PUNCT
ap-340	85	1	(	(	PUNCT
ap-340	85	2	18	18	NUM
ap-340	85	3	)	)	PUNCT
ap-340	85	4	now	now	ADV
ap-340	85	5	let	let	VERB
ap-340	85	6	us	we	PRON
ap-340	85	7	suppose	suppose	VERB
ap-340	85	8	that	that	SCONJ
ap-340	85	9	there	there	PRON
ap-340	85	10	exists	exist	VERB
ap-340	85	11	only	only	ADV
ap-340	85	12	one	one	NUM
ap-340	85	13	maximum	maximum	ADJ
ap-340	85	14	,	,	PUNCT
ap-340	85	15	z0	z0	PROPN
ap-340	85	16	,	,	PUNCT
ap-340	85	17	that	that	PRON
ap-340	85	18	fulfils	fulfil	VERB
ap-340	85	19	condition	condition	NOUN
ap-340	85	20	(	(	PUNCT
ap-340	85	21	13	13	NUM
ap-340	85	22	)	)	PUNCT
ap-340	85	23	,	,	PUNCT
ap-340	85	24	and	and	CCONJ
ap-340	85	25	let	let	VERB
ap-340	85	26	us	we	PRON
ap-340	85	27	substitute	substitute	VERB
ap-340	85	28	this	this	DET
ap-340	85	29	representation	representation	NOUN
ap-340	85	30	of	of	ADP
ap-340	85	31	integral	integral	ADJ
ap-340	85	32	(	(	PUNCT
ap-340	85	33	16	16	NUM
ap-340	85	34	)	)	PUNCT
ap-340	85	35	into	into	ADP
ap-340	85	36	the	the	DET
ap-340	85	37	numerator	numerator	NOUN
ap-340	85	38	of	of	ADP
ap-340	85	39	relation	relation	NOUN
ap-340	85	40	(	(	PUNCT
ap-340	85	41	5	5	NUM
ap-340	85	42	)	)	PUNCT
ap-340	85	43	.	.	PUNCT
ap-340	86	1	we	we	PRON
ap-340	86	2	can	can	AUX
ap-340	86	3	see	see	VERB
ap-340	86	4	that	that	SCONJ
ap-340	86	5	this	this	DET
ap-340	86	6	term	term	NOUN
ap-340	86	7	is	be	AUX
ap-340	86	8	multiplied	multiply	VERB
ap-340	86	9	by	by	ADP
ap-340	86	10	the	the	DET
ap-340	86	11	function	function	NOUN
ap-340	86	12	f(z	f(z	PROPN
ap-340	86	13	)	)	PUNCT
ap-340	86	14	here	here	ADV
ap-340	86	15	.	.	PUNCT
ap-340	87	1	the	the	DET
ap-340	87	2	value	value	NOUN
ap-340	87	3	of	of	ADP
ap-340	87	4	this	this	DET
ap-340	87	5	function	function	NOUN
ap-340	87	6	does	do	AUX
ap-340	87	7	not	not	PART
ap-340	87	8	vary	vary	VERB
ap-340	87	9	significantly	significantly	ADV
ap-340	87	10	in	in	ADP
ap-340	87	11	the	the	DET
ap-340	87	12	neighbourhood	neighbourhood	NOUN
ap-340	87	13	of	of	ADP
ap-340	87	14	the	the	DET
ap-340	87	15	extreme	extreme	NOUN
ap-340	87	16	.	.	PUNCT
ap-340	88	1	then	then	ADV
ap-340	88	2	we	we	PRON
ap-340	88	3	can	can	AUX
ap-340	88	4	treat	treat	VERB
ap-340	88	5	this	this	DET
ap-340	88	6	function	function	NOUN
ap-340	88	7	as	as	ADP
ap-340	88	8	a	a	DET
ap-340	88	9	constant	constant	ADJ
ap-340	88	10	with	with	ADP
ap-340	88	11	value	value	NOUN
ap-340	88	12	f(z0	f(z0	NOUN
ap-340	88	13	)	)	PUNCT
ap-340	88	14	(	(	PUNCT
ap-340	88	15	this	this	DET
ap-340	88	16	assumption	assumption	NOUN
ap-340	88	17	is	be	AUX
ap-340	88	18	satisfied	satisfied	ADJ
ap-340	88	19	because	because	SCONJ
ap-340	88	20	these	these	DET
ap-340	88	21	extrema	extrema	NOUN
ap-340	88	22	are	be	AUX
ap-340	88	23	narrow	narrow	ADJ
ap-340	88	24	in	in	ADP
ap-340	88	25	comparison	comparison	NOUN
ap-340	88	26	with	with	ADP
ap-340	88	27	the	the	DET
ap-340	88	28	behaviour	behaviour	NOUN
ap-340	88	29	of	of	ADP
ap-340	88	30	the	the	DET
ap-340	88	31	function	function	NOUN
ap-340	88	32	)	)	PUNCT
ap-340	88	33	.	.	PUNCT
ap-340	89	1	on	on	ADP
ap-340	89	2	the	the	DET
ap-340	89	3	basis	basis	NOUN
ap-340	89	4	of	of	ADP
ap-340	89	5	the	the	DET
ap-340	89	6	foregoing	foregoing	NOUN
ap-340	89	7	reasoning	reasoning	NOUN
ap-340	89	8	we	we	PRON
ap-340	89	9	can	can	AUX
ap-340	89	10	write	write	VERB
ap-340	89	11	the	the	DET
ap-340	89	12	numerator	numerator	NOUN
ap-340	89	13	of	of	ADP
ap-340	89	14	term	term	NOUN
ap-340	89	15	(	(	PUNCT
ap-340	89	16	5	5	NUM
ap-340	89	17	)	)	PUNCT
ap-340	89	18	as	as	SCONJ
ap-340	89	19	�	�	PROPN
ap-340	89	20	�	�	PROPN
ap-340	89	21	�	�	PROPN
ap-340	89	22	�	�	PROPN
ap-340	90	1	y	y	PROPN
ap-340	90	2	z	z	PROPN
ap-340	90	3	s	s	PROPN
ap-340	90	4	g	g	PROPN
ap-340	90	5	f	f	PROPN
ap-340	90	6	z	z	PROPN
ap-340	90	7	z	z	PROPN
ap-340	90	8	y	y	PROPN
ap-340	90	9	z	z	PROPN
ap-340	90	10	s	s	PROPN
ap-340	90	11	g	g	PROPN
ap-340	90	12	f	f	PROPN
ap-340	90	13	z	z	PROPN
ap-340	90	14	g	g	PROPN
ap-340	90	15	�	�	PROPN
ap-340	90	16	�	�	PROPN
ap-340	90	17	�	�	PROPN
ap-340	90	18	�	�	PROPN
ap-340	90	19	�	�	PROPN
ap-340	90	20	�	�	PROPN
ap-340	90	21	�	�	PROPN
ap-340	90	22	�	�	PROPN
ap-340	90	23	�	�	PROPN
ap-340	90	24	�	�	PROPN
ap-340	90	25	�	�	PROPN
ap-340	90	26	�	�	PROPN
ap-340	90	27	�	�	PROPN
ap-340	90	28	�	�	PROPN
ap-340	90	29	�	�	PROPN
ap-340	90	30	exp	exp	NOUN
ap-340	90	31	�	�	PROPN
ap-340	90	32	�	�	PROPN
ap-340	90	33	exp	exp	NOUN
ap-340	90	34	0	0	NUM
ap-340	90	35	0	0	NUM
ap-340	90	36	0	0	NUM
ap-340	90	37	0	0	NUM
ap-340	90	38	0	0	NUM
ap-340	90	39	2	2	NUM
ap-340	90	40	4	4	NUM
ap-340	90	41	1	1	NUM
ap-340	90	42	d	d	PROPN
ap-340	90	43	�	�	X
ap-340	90	44	�	�	PROPN
ap-340	90	45	2	2	NUM
ap-340	90	46	0f	0f	NOUN
ap-340	90	47	z	z	PROPN
ap-340	90	48	�	�	PROPN
ap-340	90	49	�	�	PROPN
ap-340	90	50	�	�	PROPN
ap-340	90	51	�	�	PROPN
ap-340	90	52	(	(	PUNCT
ap-340	90	53	19	19	NUM
ap-340	90	54	)	)	PUNCT
ap-340	90	55	and	and	CCONJ
ap-340	90	56	the	the	DET
ap-340	90	57	denominator	denominator	NOUN
ap-340	90	58	can	can	AUX
ap-340	90	59	be	be	AUX
ap-340	90	60	written	write	VERB
ap-340	90	61	as	as	ADP
ap-340	90	62	�	�	PROPN
ap-340	90	63	�	�	PROPN
ap-340	90	64	�	�	PROPN
ap-340	90	65	�	�	PROPN
ap-340	90	66	�	�	PROPN
ap-340	90	67	�	�	PROPN
ap-340	90	68	exp	exp	NOUN
ap-340	90	69	�	�	PROPN
ap-340	90	70	exp	exp	NOUN
ap-340	90	71	�	�	PROPN
ap-340	90	72	�	�	PROPN
ap-340	90	73	�	�	PROPN
ap-340	90	74	�	�	PROPN
ap-340	90	75	�	�	PROPN
ap-340	90	76	�	�	PROPN
ap-340	90	77	�	�	PROPN
ap-340	90	78	�	�	PROPN
ap-340	90	79	�	�	PROPN
ap-340	90	80	�	�	PROPN
ap-340	90	81	�	�	PROPN
ap-340	90	82	�	�	PROPN
ap-340	90	83	�	�	PROPN
ap-340	90	84	�	�	PROPN
ap-340	90	85	�	�	PROPN
ap-340	90	86	�	�	PROPN
ap-340	90	87	g	g	PROPN
ap-340	90	88	f	f	PROPN
ap-340	91	1	z	z	PROPN
ap-340	91	2	z	z	PROPN
ap-340	92	1	g	g	PROPN
ap-340	92	2	f	f	PROPN
ap-340	92	3	z	z	NOUN
ap-340	92	4	g	g	PROPN
ap-340	92	5	f	f	PROPN
ap-340	92	6	z0	z0	PROPN
ap-340	92	7	0	0	NUM
ap-340	92	8	0	0	NUM
ap-340	92	9	0	0	NUM
ap-340	92	10	02	02	NUM
ap-340	92	11	4	4	NUM
ap-340	92	12	1	1	NUM
ap-340	92	13	2	2	NUM
ap-340	92	14	d	d	NOUN
ap-340	92	15	.	.	PUNCT
ap-340	93	1	(	(	PUNCT
ap-340	93	2	20	20	NUM
ap-340	93	3	)	)	PUNCT
ap-340	93	4	then	then	ADV
ap-340	93	5	we	we	PRON
ap-340	93	6	have	have	VERB
ap-340	93	7	v	v	NUM
ap-340	93	8	y	y	PROPN
ap-340	93	9	z	z	PROPN
ap-340	93	10	s	s	PROPN
ap-340	93	11	�	�	PROPN
ap-340	93	12	�	�	PROPN
ap-340	93	13	�	�	PROPN
ap-340	93	14	0	0	NUM
ap-340	93	15	,	,	PUNCT
ap-340	93	16	(	(	PUNCT
ap-340	93	17	21	21	NUM
ap-340	93	18	)	)	PUNCT
ap-340	93	19	where	where	SCONJ
ap-340	93	20	z0	z0	PROPN
ap-340	93	21	is	be	AUX
ap-340	93	22	given	give	VERB
ap-340	93	23	by	by	ADP
ap-340	93	24	expressions	expression	NOUN
ap-340	93	25	(	(	PUNCT
ap-340	93	26	13	13	NUM
ap-340	93	27	)	)	PUNCT
ap-340	93	28	and	and	CCONJ
ap-340	93	29	(	(	PUNCT
ap-340	93	30	14	14	NUM
ap-340	93	31	)	)	PUNCT
ap-340	93	32	.	.	PUNCT
ap-340	94	1	©	©	PROPN
ap-340	94	2	czech	czech	PROPN
ap-340	94	3	technical	technical	PROPN
ap-340	94	4	university	university	PROPN
ap-340	94	5	publishing	publishing	NOUN
ap-340	94	6	house	house	NOUN
ap-340	94	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-340	94	8	73	73	NUM
ap-340	94	9	acta	acta	PROPN
ap-340	94	10	polytechnica	polytechnica	PROPN
ap-340	94	11	vol	vol	NOUN
ap-340	94	12	.	.	PUNCT
ap-340	95	1	42	42	NUM
ap-340	95	2	no	no	NOUN
ap-340	95	3	.	.	PUNCT
ap-340	96	1	2/2002	2/2002	NUM
ap-340	96	2	fig	fig	NOUN
ap-340	96	3	.	.	PUNCT
ap-340	97	1	2	2	NUM
ap-340	97	2	:	:	PUNCT
ap-340	97	3	space	space	NOUN
ap-340	97	4	evolution	evolution	NOUN
ap-340	97	5	of	of	ADP
ap-340	97	6	integrand	integrand	PROPN
ap-340	97	7	,	,	PUNCT
ap-340	97	8	g0	g0	PROPN
ap-340	97	9	�	�	PROPN
ap-340	97	10	50	50	NUM
ap-340	97	11	,	,	PUNCT
ap-340	97	12	s	s	VERB
ap-340	97	13	�	�	PROPN
ap-340	97	14	1	1	NUM
ap-340	97	15	,	,	PUNCT
ap-340	97	16	10	10	NUM
ap-340	97	17	,	,	PUNCT
ap-340	97	18	50	50	NUM
ap-340	97	19	fig	fig	NOUN
ap-340	97	20	.	.	PUNCT
ap-340	98	1	3	3	NUM
ap-340	98	2	:	:	PUNCT
ap-340	98	3	space	space	NOUN
ap-340	98	4	evolution	evolution	NOUN
ap-340	98	5	of	of	ADP
ap-340	98	6	integrand	integrand	PROPN
ap-340	98	7	,	,	PUNCT
ap-340	98	8	g0	g0	PROPN
ap-340	98	9	�	�	PROPN
ap-340	98	10	500	500	NUM
ap-340	98	11	,	,	PUNCT
ap-340	98	12	s	s	VERB
ap-340	98	13	�	�	PROPN
ap-340	98	14	1	1	NUM
ap-340	98	15	,	,	PUNCT
ap-340	98	16	10	10	NUM
ap-340	98	17	,	,	PUNCT
ap-340	98	18	50	50	NUM
ap-340	98	19	however	however	ADV
ap-340	98	20	,	,	PUNCT
ap-340	98	21	relation	relation	NOUN
ap-340	98	22	(	(	PUNCT
ap-340	98	23	21	21	NUM
ap-340	98	24	)	)	PUNCT
ap-340	98	25	can	can	AUX
ap-340	98	26	give	give	VERB
ap-340	98	27	wrong	wrong	ADJ
ap-340	98	28	solutions	solution	NOUN
ap-340	98	29	in	in	ADP
ap-340	98	30	certain	certain	ADJ
ap-340	98	31	cases	case	NOUN
ap-340	98	32	.	.	PUNCT
ap-340	99	1	the	the	DET
ap-340	99	2	explanation	explanation	NOUN
ap-340	99	3	is	be	AUX
ap-340	99	4	that	that	SCONJ
ap-340	99	5	there	there	PRON
ap-340	99	6	are	be	VERB
ap-340	99	7	more	more	ADJ
ap-340	99	8	stationary	stationary	ADJ
ap-340	99	9	points	point	NOUN
ap-340	99	10	satisfying	satisfy	VERB
ap-340	99	11	equation	equation	NOUN
ap-340	99	12	(	(	PUNCT
ap-340	99	13	13	13	NUM
ap-340	99	14	)	)	PUNCT
ap-340	99	15	and	and	CCONJ
ap-340	99	16	condition	condition	NOUN
ap-340	99	17	(	(	PUNCT
ap-340	99	18	14	14	NUM
ap-340	99	19	)	)	PUNCT
ap-340	99	20	,	,	PUNCT
ap-340	99	21	usually	usually	ADV
ap-340	99	22	two	two	NUM
ap-340	99	23	.	.	PUNCT
ap-340	100	1	now	now	ADV
ap-340	100	2	let	let	VERB
ap-340	100	3	us	we	PRON
ap-340	100	4	suppose	suppose	VERB
ap-340	100	5	two	two	NUM
ap-340	100	6	maxima	maxima	NOUN
ap-340	100	7	z1	z1	NOUN
ap-340	100	8	and	and	CCONJ
ap-340	100	9	z2	z2	NOUN
ap-340	100	10	,	,	PUNCT
ap-340	100	11	when	when	SCONJ
ap-340	100	12	z	z	NOUN
ap-340	100	13	z1	z1	VERB
ap-340	100	14	2	2	NUM
ap-340	100	15	�	�	PROPN
ap-340	100	16	.	.	PUNCT
ap-340	101	1	their	their	PRON
ap-340	101	2	contributions	contribution	NOUN
ap-340	101	3	are	be	AUX
ap-340	101	4	determined	determine	VERB
ap-340	101	5	by	by	ADP
ap-340	101	6	relations	relation	NOUN
ap-340	101	7	(	(	PUNCT
ap-340	101	8	19	19	NUM
ap-340	101	9	)	)	PUNCT
ap-340	101	10	and	and	CCONJ
ap-340	101	11	(	(	PUNCT
ap-340	101	12	20	20	NUM
ap-340	101	13	)	)	PUNCT
ap-340	101	14	,	,	PUNCT
ap-340	101	15	and	and	CCONJ
ap-340	101	16	thus	thus	ADV
ap-340	101	17	:	:	PUNCT
ap-340	101	18	�	�	PROPN
ap-340	101	19	�	�	PROPN
ap-340	101	20	�	�	PROPN
ap-340	101	21	�	�	PROPN
ap-340	101	22	�	�	PROPN
ap-340	101	23	�	�	PROPN
ap-340	101	24	v	v	ADP
ap-340	101	25	y	y	PROPN
ap-340	101	26	z	z	PROPN
ap-340	101	27	s	s	PROPN
ap-340	101	28	g	g	PROPN
ap-340	101	29	f	f	PROPN
ap-340	101	30	z	z	PROPN
ap-340	101	31	g	g	PROPN
ap-340	102	1	f	f	PROPN
ap-340	102	2	z	z	NOUN
ap-340	102	3	g	g	PROPN
ap-340	103	1	f	f	PROPN
ap-340	103	2	z	z	PROPN
ap-340	103	3	i	i	PRON
ap-340	103	4	�	�	PROPN
ap-340	103	5	�	�	PROPN
ap-340	103	6	�	�	PROPN
ap-340	103	7	�	�	PROPN
ap-340	103	8	�	�	PROPN
ap-340	103	9	�	�	PROPN
ap-340	103	10	�	�	PROPN
ap-340	103	11	�	�	PROPN
ap-340	103	12	�	�	PROPN
ap-340	103	13	�	�	PROPN
ap-340	103	14	�	�	PROPN
ap-340	103	15	�	�	PROPN
ap-340	103	16	�	�	PROPN
ap-340	104	1	i	i	PRON
ap-340	104	2	i	i	PRON
ap-340	105	1	i	i	PRON
ap-340	105	2	i	i	VERB
ap-340	105	3	4	4	NUM
ap-340	105	4	1	1	NUM
ap-340	105	5	2	2	NUM
ap-340	105	6	4	4	NUM
ap-340	105	7	1	1	NUM
ap-340	105	8	0	0	NUM
ap-340	105	9	0	0	NUM
ap-340	105	10	1	1	NUM
ap-340	105	11	2	2	NUM
ap-340	105	12	0	0	NUM
ap-340	105	13	exp	exp	NOUN
ap-340	105	14	ex	ex	PRON
ap-340	105	15	�	�	PROPN
ap-340	105	16	�	�	PROPN
ap-340	105	17	p	p	PROPN
ap-340	105	18	�	�	PROPN
ap-340	105	19	�	�	PROPN
ap-340	105	20	�	�	PROPN
ap-340	105	21	�	�	PROPN
ap-340	105	22	�	�	PROPN
ap-340	105	23	�	�	PROPN
ap-340	105	24	�	�	PROPN
ap-340	106	1	g	g	PROPN
ap-340	106	2	f	f	PROPN
ap-340	107	1	z	z	NOUN
ap-340	108	1	i	i	NOUN
ap-340	108	2	0	0	NUM
ap-340	108	3	1	1	NUM
ap-340	108	4	2	2	NUM
ap-340	108	5	i	i	NOUN
ap-340	108	6	2	2	NUM
ap-340	108	7	.	.	PUNCT
ap-340	109	1	(	(	PUNCT
ap-340	109	2	22	22	NUM
ap-340	109	3	)	)	PUNCT
ap-340	109	4	this	this	DET
ap-340	109	5	expression	expression	NOUN
ap-340	109	6	can	can	AUX
ap-340	109	7	be	be	AUX
ap-340	109	8	extended	extend	VERB
ap-340	109	9	to	to	ADP
ap-340	109	10	an	an	DET
ap-340	109	11	arbitrary	arbitrary	ADJ
ap-340	109	12	number	number	NOUN
ap-340	109	13	of	of	ADP
ap-340	109	14	maxima	maxima	NOUN
ap-340	109	15	zi	zi	NOUN
ap-340	109	16	.	.	PUNCT
ap-340	110	1	when	when	SCONJ
ap-340	110	2	�	�	PROPN
ap-340	110	3	�	�	PROPN
ap-340	110	4	�	�	PROPN
ap-340	110	5	�	�	PROPN
ap-340	110	6	f	f	PROPN
ap-340	110	7	z	z	PROPN
ap-340	110	8	f	f	PROPN
ap-340	110	9	z1	z1	PROPN
ap-340	110	10	2	2	NUM
ap-340	110	11	�	�	PROPN
ap-340	110	12	,	,	PUNCT
ap-340	110	13	the	the	DET
ap-340	110	14	contribution	contribution	NOUN
ap-340	110	15	of	of	ADP
ap-340	110	16	one	one	NUM
ap-340	110	17	extreme	extreme	NOUN
ap-340	110	18	becomes	become	VERB
ap-340	110	19	very	very	ADV
ap-340	110	20	high	high	ADJ
ap-340	110	21	due	due	ADJ
ap-340	110	22	to	to	ADP
ap-340	110	23	large	large	ADJ
ap-340	110	24	g0	g0	NOUN
ap-340	110	25	–	–	PUNCT
ap-340	110	26	for	for	ADP
ap-340	110	27	example	example	NOUN
ap-340	110	28	in	in	ADP
ap-340	110	29	the	the	DET
ap-340	110	30	case	case	NOUN
ap-340	110	31	g0	g0	PROPN
ap-340	110	32	�	�	PROPN
ap-340	110	33	20000	20000	NUM
ap-340	110	34	and	and	CCONJ
ap-340	110	35	�	�	PROPN
ap-340	110	36	�	�	PROPN
ap-340	110	37	�	�	PROPN
ap-340	110	38	�	�	PROPN
ap-340	110	39	f	f	PROPN
ap-340	110	40	z	z	PROPN
ap-340	110	41	f	f	PROPN
ap-340	110	42	z1	z1	VERB
ap-340	110	43	2	2	NUM
ap-340	110	44	1	1	NUM
ap-340	110	45	�	�	PROPN
ap-340	110	46	�	�	PROPN
ap-340	110	47	this	this	DET
ap-340	110	48	rate	rate	NOUN
ap-340	110	49	is	be	AUX
ap-340	110	50	equal	equal	ADJ
ap-340	110	51	toe10000	toe10000	NOUN
ap-340	110	52	1	1	NUM
ap-340	110	53	:	:	PUNCT
ap-340	110	54	.	.	PUNCT
ap-340	111	1	for	for	ADP
ap-340	111	2	this	this	DET
ap-340	111	3	reason	reason	NOUN
ap-340	111	4	,	,	PUNCT
ap-340	111	5	we	we	PRON
ap-340	111	6	can	can	AUX
ap-340	111	7	use	use	VERB
ap-340	111	8	the	the	DET
ap-340	111	9	approximate	approximate	ADJ
ap-340	111	10	solution	solution	NOUN
ap-340	111	11	in	in	ADP
ap-340	111	12	some	some	DET
ap-340	111	13	circumstances	circumstance	NOUN
ap-340	111	14	.	.	PUNCT
ap-340	112	1	�	�	PROPN
ap-340	112	2	�	�	PROPN
ap-340	112	3	�	�	PROPN
ap-340	112	4	�	�	PROPN
ap-340	112	5	�	�	PROPN
ap-340	112	6	�	�	PROPN
ap-340	112	7	�	�	PROPN
ap-340	112	8	�	�	PROPN
ap-340	112	9	v	v	ADP
ap-340	112	10	y	y	PROPN
ap-340	112	11	z	z	PROPN
ap-340	112	12	s	s	PROPN
ap-340	113	1	f	f	PROPN
ap-340	113	2	z	z	PROPN
ap-340	113	3	f	f	PROPN
ap-340	113	4	z	z	PROPN
ap-340	113	5	v	v	PROPN
ap-340	113	6	y	y	PROPN
ap-340	113	7	z	z	PROPN
ap-340	113	8	s	s	PROPN
ap-340	113	9	f	f	PROPN
ap-340	113	10	z	z	PROPN
ap-340	113	11	f	f	PROPN
ap-340	113	12	z	z	PROPN
ap-340	113	13	�	�	PROPN
ap-340	113	14	,	,	PUNCT
ap-340	113	15	�	�	PROPN
ap-340	113	16	,	,	PUNCT
ap-340	113	17	.	.	PUNCT
ap-340	113	18	�	�	PROPN
ap-340	113	19	�	�	PROPN
ap-340	113	20	�	�	PROPN
ap-340	113	21	�	�	PROPN
ap-340	113	22	�	�	PROPN
ap-340	113	23	�	�	PROPN
ap-340	113	24	1	1	NUM
ap-340	113	25	1	1	NUM
ap-340	113	26	2	2	NUM
ap-340	113	27	2	2	NUM
ap-340	113	28	2	2	NUM
ap-340	113	29	1	1	NUM
ap-340	113	30	when	when	SCONJ
ap-340	113	31	and	and	CCONJ
ap-340	113	32	when	when	SCONJ
ap-340	113	33	(	(	PUNCT
ap-340	113	34	23	23	NUM
ap-340	113	35	)	)	PUNCT
ap-340	113	36	examples	example	NOUN
ap-340	113	37	of	of	ADP
ap-340	113	38	the	the	DET
ap-340	113	39	solution	solution	NOUN
ap-340	113	40	of	of	ADP
ap-340	113	41	the	the	DET
ap-340	113	42	burgers	burger	NOUN
ap-340	113	43	equation	equation	NOUN
ap-340	113	44	figure	figure	VERB
ap-340	113	45	4	4	NUM
ap-340	113	46	a	a	PRON
ap-340	113	47	)	)	PUNCT
ap-340	113	48	shows	show	VERB
ap-340	113	49	waveforms	waveform	NOUN
ap-340	113	50	with	with	ADP
ap-340	113	51	the	the	DET
ap-340	113	52	harmonic	harmonic	ADJ
ap-340	113	53	boundary	boundary	ADJ
ap-340	113	54	condition	condition	NOUN
ap-340	113	55	when	when	SCONJ
ap-340	113	56	g0	g0	PROPN
ap-340	113	57	�	�	PROPN
ap-340	113	58	1500	1500	NUM
ap-340	113	59	.	.	PUNCT
ap-340	114	1	the	the	DET
ap-340	114	2	waveforms	waveform	NOUN
ap-340	114	3	are	be	AUX
ap-340	114	4	calculated	calculate	VERB
ap-340	114	5	using	use	VERB
ap-340	114	6	the	the	DET
ap-340	114	7	saddle	saddle	NOUN
ap-340	114	8	point	point	NOUN
ap-340	114	9	method	method	NOUN
ap-340	114	10	at	at	ADP
ap-340	114	11	dimensionless	dimensionless	ADJ
ap-340	114	12	distances	distance	NOUN
ap-340	114	13	which	which	PRON
ap-340	114	14	were	be	AUX
ap-340	114	15	chosen	choose	VERB
ap-340	114	16	in	in	ADP
ap-340	114	17	order	order	NOUN
ap-340	114	18	to	to	PART
ap-340	114	19	show	show	VERB
ap-340	114	20	the	the	DET
ap-340	114	21	development	development	NOUN
ap-340	114	22	of	of	ADP
ap-340	114	23	a	a	DET
ap-340	114	24	nonlinear	nonlinear	ADJ
ap-340	114	25	wave	wave	NOUN
ap-340	114	26	.	.	PUNCT
ap-340	115	1	figure	figure	VERB
ap-340	115	2	4	4	NUM
ap-340	115	3	b	b	NOUN
ap-340	115	4	)	)	PUNCT
ap-340	115	5	shows	show	VERB
ap-340	115	6	waveforms	waveform	NOUN
ap-340	115	7	for	for	ADP
ap-340	115	8	the	the	DET
ap-340	115	9	identical	identical	ADJ
ap-340	115	10	boundary	boundary	ADJ
ap-340	115	11	condition	condition	NOUN
ap-340	115	12	at	at	ADP
ap-340	115	13	the	the	DET
ap-340	115	14	same	same	ADJ
ap-340	115	15	distances	distance	NOUN
ap-340	115	16	as	as	ADP
ap-340	115	17	in	in	ADP
ap-340	115	18	figure	figure	NOUN
ap-340	115	19	4	4	NUM
ap-340	115	20	a	a	NOUN
ap-340	115	21	)	)	PUNCT
ap-340	115	22	,	,	PUNCT
ap-340	115	23	but	but	CCONJ
ap-340	115	24	for	for	ADP
ap-340	115	25	g0	g0	PROPN
ap-340	115	26	�	�	PROPN
ap-340	115	27	50	50	NUM
ap-340	115	28	.	.	PUNCT
ap-340	116	1	direct	direct	ADJ
ap-340	116	2	integration	integration	NOUN
ap-340	116	3	was	be	AUX
ap-340	116	4	used	use	VERB
ap-340	116	5	in	in	ADP
ap-340	116	6	this	this	DET
ap-340	116	7	case	case	NOUN
ap-340	116	8	.	.	PUNCT
ap-340	117	1	we	we	PRON
ap-340	117	2	can	can	AUX
ap-340	117	3	see	see	VERB
ap-340	117	4	that	that	SCONJ
ap-340	117	5	the	the	DET
ap-340	117	6	dissipation	dissipation	NOUN
ap-340	117	7	effect	effect	NOUN
ap-340	117	8	is	be	AUX
ap-340	117	9	stronger	strong	ADJ
ap-340	117	10	in	in	ADP
ap-340	117	11	this	this	DET
ap-340	117	12	case	case	NOUN
ap-340	117	13	,	,	PUNCT
ap-340	117	14	and	and	CCONJ
ap-340	117	15	therefore	therefore	ADV
ap-340	117	16	the	the	DET
ap-340	117	17	width	width	NOUN
ap-340	117	18	of	of	ADP
ap-340	117	19	the	the	DET
ap-340	117	20	shock	shock	NOUN
ap-340	117	21	front	front	NOUN
ap-340	117	22	is	be	AUX
ap-340	117	23	more	more	ADV
ap-340	117	24	significant	significant	ADJ
ap-340	117	25	.	.	PUNCT
ap-340	118	1	figure	figure	NOUN
ap-340	118	2	5	5	NUM
ap-340	118	3	compares	compare	VERB
ap-340	118	4	the	the	DET
ap-340	118	5	time	time	NOUN
ap-340	118	6	domain	domain	NOUN
ap-340	118	7	solution	solution	NOUN
ap-340	118	8	(	(	PUNCT
ap-340	118	9	saddle	saddle	NOUN
ap-340	118	10	point	point	NOUN
ap-340	118	11	method	method	NOUN
ap-340	118	12	)	)	PUNCT
ap-340	118	13	with	with	ADP
ap-340	118	14	the	the	DET
ap-340	118	15	frequency	frequency	NOUN
ap-340	118	16	domain	domain	NOUN
ap-340	118	17	solution	solution	NOUN
ap-340	118	18	of	of	ADP
ap-340	118	19	the	the	DET
ap-340	118	20	burgers	burger	NOUN
ap-340	118	21	equation	equation	NOUN
ap-340	118	22	(	(	PUNCT
ap-340	118	23	see	see	VERB
ap-340	118	24	[	[	X
ap-340	118	25	18	18	NUM
ap-340	118	26	]	]	NUM
ap-340	118	27	)	)	PUNCT
ap-340	118	28	.	.	PUNCT
ap-340	119	1	conclusion	conclusion	NOUN
ap-340	119	2	this	this	DET
ap-340	119	3	paper	paper	NOUN
ap-340	119	4	analyses	analyse	VERB
ap-340	119	5	a	a	DET
ap-340	119	6	method	method	NOUN
ap-340	119	7	for	for	ADP
ap-340	119	8	solving	solve	VERB
ap-340	119	9	the	the	DET
ap-340	119	10	burgers	burger	NOUN
ap-340	119	11	equation	equation	NOUN
ap-340	119	12	in	in	ADP
ap-340	119	13	the	the	DET
ap-340	119	14	time	time	NOUN
ap-340	119	15	domain	domain	NOUN
ap-340	119	16	by	by	ADP
ap-340	119	17	means	mean	NOUN
ap-340	119	18	of	of	ADP
ap-340	119	19	the	the	DET
ap-340	119	20	cole	cole	NOUN
ap-340	119	21	-	-	PUNCT
ap-340	119	22	hopf	hopf	ADJ
ap-340	119	23	transformation	transformation	NOUN
ap-340	119	24	.	.	PUNCT
ap-340	120	1	however	however	ADV
ap-340	120	2	,	,	PUNCT
ap-340	120	3	this	this	DET
ap-340	120	4	method	method	NOUN
ap-340	120	5	poses	pose	VERB
ap-340	120	6	problems	problem	NOUN
ap-340	120	7	connected	connect	VERB
ap-340	120	8	with	with	ADP
ap-340	120	9	the	the	DET
ap-340	120	10	numerical	numerical	ADJ
ap-340	120	11	solution	solution	NOUN
ap-340	120	12	of	of	ADP
ap-340	120	13	the	the	DET
ap-340	120	14	poisson	poisson	NOUN
ap-340	120	15	integral	integral	ADJ
ap-340	120	16	for	for	ADP
ap-340	120	17	the	the	DET
ap-340	120	18	case	case	NOUN
ap-340	120	19	g0	g0	PROPN
ap-340	120	20	�	�	PROPN
ap-340	120	21	1	1	NUM
ap-340	120	22	.	.	PUNCT
ap-340	121	1	the	the	DET
ap-340	121	2	first	first	ADJ
ap-340	121	3	way	way	NOUN
ap-340	121	4	to	to	PART
ap-340	121	5	solve	solve	VERB
ap-340	121	6	these	these	DET
ap-340	121	7	problems	problem	NOUN
ap-340	121	8	is	be	AUX
ap-340	121	9	based	base	VERB
ap-340	121	10	on	on	ADP
ap-340	121	11	the	the	DET
ap-340	121	12	application	application	NOUN
ap-340	121	13	of	of	ADP
ap-340	121	14	an	an	DET
ap-340	121	15	appropriate	appropriate	ADJ
ap-340	121	16	software	software	NOUN
ap-340	121	17	instrument	instrument	NOUN
ap-340	121	18	(	(	PUNCT
ap-340	121	19	e.g.	e.g.	ADV
ap-340	121	20	,	,	PUNCT
ap-340	121	21	the	the	DET
ap-340	121	22	74	74	NUM
ap-340	121	23	acta	acta	PROPN
ap-340	121	24	polytechnica	polytechnica	PROPN
ap-340	121	25	vol	vol	NOUN
ap-340	121	26	.	.	PUNCT
ap-340	122	1	42	42	NUM
ap-340	122	2	no	no	NOUN
ap-340	122	3	.	.	PUNCT
ap-340	123	1	2/2002	2/2002	NUM
ap-340	123	2	a	a	PRON
ap-340	123	3	)	)	PUNCT
ap-340	123	4	b	b	NOUN
ap-340	123	5	)	)	PUNCT
ap-340	123	6	fig	fig	NOUN
ap-340	123	7	.	.	PUNCT
ap-340	124	1	4	4	NUM
ap-340	124	2	:	:	PUNCT
ap-340	124	3	waveforms	waveform	NOUN
ap-340	124	4	at	at	ADP
ap-340	124	5	distances	distance	NOUN
ap-340	124	6	s	s	PROPN
ap-340	124	7	�	�	PROPN
ap-340	124	8	0	0	NUM
ap-340	124	9	,	,	PUNCT
ap-340	124	10	1	1	NUM
ap-340	124	11	,	,	PUNCT
ap-340	124	12	4	4	NUM
ap-340	124	13	,	,	PUNCT
ap-340	124	14	10	10	NUM
ap-340	124	15	,	,	PUNCT
ap-340	124	16	20	20	NUM
ap-340	124	17	for	for	ADP
ap-340	124	18	a	a	DET
ap-340	124	19	)	)	PUNCT
ap-340	124	20	g0	g0	PROPN
ap-340	124	21	�	�	PROPN
ap-340	124	22	1500	1500	NUM
ap-340	124	23	b	b	NOUN
ap-340	124	24	)	)	PUNCT
ap-340	124	25	g0	g0	NOUN
ap-340	124	26	�	�	PROPN
ap-340	124	27	50	50	NUM
ap-340	124	28	fig	fig	NOUN
ap-340	124	29	.	.	PUNCT
ap-340	125	1	5	5	NUM
ap-340	125	2	:	:	PUNCT
ap-340	125	3	comparison	comparison	NOUN
ap-340	125	4	between	between	ADP
ap-340	125	5	the	the	DET
ap-340	125	6	time	time	NOUN
ap-340	125	7	domain	domain	NOUN
ap-340	125	8	solution	solution	NOUN
ap-340	125	9	and	and	CCONJ
ap-340	125	10	the	the	DET
ap-340	125	11	frequency	frequency	NOUN
ap-340	125	12	domain	domain	NOUN
ap-340	125	13	solution	solution	NOUN
ap-340	125	14	of	of	ADP
ap-340	125	15	the	the	DET
ap-340	125	16	burgers	burger	NOUN
ap-340	125	17	equation	equation	NOUN
ap-340	125	18	,	,	PUNCT
ap-340	125	19	g0	g0	PROPN
ap-340	125	20	�	�	PROPN
ap-340	125	21	1000	1000	NUM
ap-340	125	22	,	,	PUNCT
ap-340	125	23	s	s	VERB
ap-340	125	24	�	�	PROPN
ap-340	125	25	1.1	1.1	NUM
ap-340	125	26	and	and	CCONJ
ap-340	125	27	s	s	NOUN
ap-340	125	28	�	�	PROPN
ap-340	125	29	3	3	NUM
ap-340	125	30	,	,	PUNCT
ap-340	125	31	m	m	VERB
ap-340	125	32	represents	represent	VERB
ap-340	125	33	number	number	NOUN
ap-340	125	34	of	of	ADP
ap-340	125	35	harmonics	harmonic	NOUN
ap-340	125	36	free	free	ADJ
ap-340	125	37	library	library	PROPN
ap-340	125	38	gnu	gnu	PROPN
ap-340	125	39	mp	mp	PROPN
ap-340	125	40	)	)	PUNCT
ap-340	125	41	,	,	PUNCT
ap-340	125	42	which	which	PRON
ap-340	125	43	enables	enable	VERB
ap-340	125	44	calculation	calculation	NOUN
ap-340	125	45	with	with	ADP
ap-340	125	46	accuracy	accuracy	NOUN
ap-340	125	47	to	to	ADP
ap-340	125	48	an	an	DET
ap-340	125	49	arbitrary	arbitrary	ADJ
ap-340	125	50	number	number	NOUN
ap-340	125	51	of	of	ADP
ap-340	125	52	valid	valid	ADJ
ap-340	125	53	digits	digit	NOUN
ap-340	125	54	.	.	PUNCT
ap-340	126	1	the	the	DET
ap-340	126	2	next	next	ADJ
ap-340	126	3	way	way	NOUN
ap-340	126	4	involves	involve	VERB
ap-340	126	5	applying	apply	VERB
ap-340	126	6	the	the	DET
ap-340	126	7	saddle	saddle	NOUN
ap-340	126	8	-	-	PUNCT
ap-340	126	9	point	point	NOUN
ap-340	126	10	method	method	NOUN
ap-340	126	11	,	,	PUNCT
ap-340	126	12	which	which	PRON
ap-340	126	13	becomes	become	VERB
ap-340	126	14	more	more	ADV
ap-340	126	15	accurate	accurate	ADJ
ap-340	126	16	the	the	DET
ap-340	126	17	larger	large	ADJ
ap-340	126	18	the	the	DET
ap-340	126	19	goldberg	goldberg	PROPN
ap-340	126	20	numbers	number	NOUN
ap-340	126	21	are	be	AUX
ap-340	126	22	.	.	PUNCT
ap-340	127	1	the	the	DET
ap-340	127	2	solution	solution	NOUN
ap-340	127	3	in	in	ADP
ap-340	127	4	the	the	DET
ap-340	127	5	time	time	NOUN
ap-340	127	6	domain	domain	NOUN
ap-340	127	7	enables	enable	VERB
ap-340	127	8	us	we	PRON
ap-340	127	9	to	to	PART
ap-340	127	10	find	find	VERB
ap-340	127	11	the	the	DET
ap-340	127	12	proper	proper	ADJ
ap-340	127	13	parameters	parameter	NOUN
ap-340	127	14	of	of	ADP
ap-340	127	15	the	the	DET
ap-340	127	16	numerical	numerical	ADJ
ap-340	127	17	frequency	frequency	PROPN
ap-340	127	18	correction	correction	NOUN
ap-340	127	19	that	that	PRON
ap-340	127	20	is	be	AUX
ap-340	127	21	often	often	ADV
ap-340	127	22	used	use	VERB
ap-340	127	23	for	for	ADP
ap-340	127	24	solving	solve	VERB
ap-340	127	25	the	the	DET
ap-340	127	26	burgers	burger	NOUN
ap-340	127	27	equation	equation	NOUN
ap-340	127	28	in	in	ADP
ap-340	127	29	the	the	DET
ap-340	127	30	frequency	frequency	NOUN
ap-340	127	31	domain	domain	NOUN
ap-340	127	32	.	.	PUNCT
ap-340	128	1	when	when	SCONJ
ap-340	128	2	we	we	PRON
ap-340	128	3	compare	compare	VERB
ap-340	128	4	the	the	DET
ap-340	128	5	results	result	NOUN
ap-340	128	6	of	of	ADP
ap-340	128	7	the	the	DET
ap-340	128	8	solutions	solution	NOUN
ap-340	128	9	of	of	ADP
ap-340	128	10	the	the	DET
ap-340	128	11	burgers	burger	NOUN
ap-340	128	12	equation	equation	NOUN
ap-340	128	13	obtained	obtain	VERB
ap-340	128	14	in	in	ADP
ap-340	128	15	the	the	DET
ap-340	128	16	time	time	NOUN
ap-340	128	17	domain	domain	NOUN
ap-340	128	18	and	and	CCONJ
ap-340	128	19	in	in	ADP
ap-340	128	20	the	the	DET
ap-340	128	21	frequency	frequency	NOUN
ap-340	128	22	domain	domain	NOUN
ap-340	128	23	,	,	PUNCT
ap-340	128	24	it	it	PRON
ap-340	128	25	is	be	AUX
ap-340	128	26	evident	evident	ADJ
ap-340	128	27	that	that	SCONJ
ap-340	128	28	they	they	PRON
ap-340	128	29	are	be	AUX
ap-340	128	30	almost	almost	ADV
ap-340	128	31	identical	identical	ADJ
ap-340	128	32	in	in	ADP
ap-340	128	33	the	the	DET
ap-340	128	34	case	case	NOUN
ap-340	128	35	when	when	SCONJ
ap-340	128	36	the	the	DET
ap-340	128	37	number	number	NOUN
ap-340	128	38	of	of	ADP
ap-340	128	39	used	use	VERB
ap-340	128	40	harmonics	harmonic	NOUN
ap-340	128	41	in	in	ADP
ap-340	128	42	the	the	DET
ap-340	128	43	frequency	frequency	NOUN
ap-340	128	44	domain	domain	NOUN
ap-340	128	45	exceeds	exceed	VERB
ap-340	128	46	250	250	NUM
ap-340	128	47	,	,	PUNCT
ap-340	128	48	but	but	CCONJ
ap-340	128	49	the	the	DET
ap-340	128	50	calculation	calculation	NOUN
ap-340	128	51	is	be	AUX
ap-340	128	52	noticeably	noticeably	ADV
ap-340	128	53	longer	long	ADJ
ap-340	128	54	.	.	PUNCT
ap-340	129	1	acknowledgment	acknowledgment	VERB
ap-340	129	2	the	the	DET
ap-340	129	3	research	research	NOUN
ap-340	129	4	was	be	AUX
ap-340	129	5	supported	support	VERB
ap-340	129	6	by	by	ADP
ap-340	129	7	ctu	ctu	NOUN
ap-340	129	8	research	research	NOUN
ap-340	129	9	program	program	NOUN
ap-340	129	10	16	16	NUM
ap-340	129	11	:	:	PUNCT
ap-340	129	12	cez	cez	PROPN
ap-340	129	13	:	:	PUNCT
ap-340	129	14	j04/98:212300016	j04/98:212300016	PROPN
ap-340	129	15	and	and	CCONJ
ap-340	129	16	by	by	ADP
ap-340	129	17	gacr	gacr	PROPN
ap-340	129	18	grant	grant	PROPN
ap-340	129	19	202/01/1372	202/01/1372	PROPN
ap-340	129	20	.	.	PUNCT
ap-340	130	1	references	reference	NOUN
ap-340	130	2	[	[	X
ap-340	130	3	1	1	NUM
ap-340	130	4	]	]	PUNCT
ap-340	130	5	burgers	burger	NOUN
ap-340	130	6	,	,	PUNCT
ap-340	130	7	j.	j.	PROPN
ap-340	130	8	m.	m.	PROPN
ap-340	130	9	:	:	PUNCT
ap-340	130	10	a	a	DET
ap-340	130	11	mathematical	mathematical	ADJ
ap-340	130	12	model	model	NOUN
ap-340	130	13	illustrating	illustrate	VERB
ap-340	130	14	the	the	DET
ap-340	130	15	theory	theory	NOUN
ap-340	130	16	of	of	ADP
ap-340	130	17	turbulence	turbulence	NOUN
ap-340	130	18	.	.	PUNCT
ap-340	131	1	advances	advance	NOUN
ap-340	131	2	in	in	ADP
ap-340	131	3	applied	apply	VERB
ap-340	131	4	mechanics	mechanic	NOUN
ap-340	131	5	,	,	PUNCT
ap-340	131	6	1948	1948	NUM
ap-340	131	7	,	,	PUNCT
ap-340	131	8	vol.1	vol.1	NUM
ap-340	131	9	,	,	PUNCT
ap-340	131	10	p.	p.	NOUN
ap-340	131	11	171–199	171–199	NUM
ap-340	131	12	.	.	PUNCT
ap-340	132	1	[	[	X
ap-340	132	2	2	2	NUM
ap-340	132	3	]	]	SYM
ap-340	132	4	bateman	bateman	PROPN
ap-340	132	5	,	,	PUNCT
ap-340	132	6	h.	h.	PROPN
ap-340	132	7	:	:	PUNCT
ap-340	132	8	some	some	DET
ap-340	132	9	recent	recent	ADJ
ap-340	132	10	researches	research	NOUN
ap-340	132	11	on	on	ADP
ap-340	132	12	the	the	DET
ap-340	132	13	motions	motion	NOUN
ap-340	132	14	of	of	ADP
ap-340	132	15	fluids	fluid	NOUN
ap-340	132	16	.	.	PUNCT
ap-340	133	1	monthly	monthly	ADJ
ap-340	133	2	weather	weather	NOUN
ap-340	133	3	review	review	PROPN
ap-340	133	4	,	,	PUNCT
ap-340	133	5	1915	1915	NUM
ap-340	133	6	,	,	PUNCT
ap-340	133	7	vol	vol	NOUN
ap-340	133	8	.	.	PROPN
ap-340	133	9	43	43	NUM
ap-340	133	10	,	,	PUNCT
ap-340	133	11	p.	p.	NOUN
ap-340	133	12	163–170	163–170	NUM
ap-340	133	13	.	.	PUNCT
ap-340	134	1	[	[	X
ap-340	134	2	3	3	NUM
ap-340	134	3	]	]	X
ap-340	134	4	hopf	hopf	ADJ
ap-340	134	5	,	,	PUNCT
ap-340	134	6	e.	e.	PROPN
ap-340	134	7	:	:	PUNCT
ap-340	134	8	the	the	DET
ap-340	134	9	partial	partial	ADJ
ap-340	134	10	differential	differential	NOUN
ap-340	134	11	equation	equation	NOUN
ap-340	134	12	u	u	NOUN
ap-340	134	13	uu	uu	INTJ
ap-340	134	14	ut	ut	PROPN
ap-340	134	15	x	x	SYM
ap-340	134	16	xx	xx	PROPN
ap-340	134	17	�	�	PROPN
ap-340	134	18	�	�	PROPN
ap-340	134	19	.	.	PUNCT
ap-340	135	1	comm	comm	NOUN
ap-340	135	2	.	.	PUNCT
ap-340	136	1	pure	pure	ADJ
ap-340	136	2	and	and	CCONJ
ap-340	136	3	appl	appl	PROPN
ap-340	136	4	.	.	PROPN
ap-340	136	5	math	math	PROPN
ap-340	136	6	.	.	PUNCT
ap-340	136	7	,	,	PUNCT
ap-340	136	8	1950	1950	NUM
ap-340	136	9	,	,	PUNCT
ap-340	136	10	vol	vol	NOUN
ap-340	136	11	.	.	NOUN
ap-340	137	1	3	3	NUM
ap-340	137	2	,	,	PUNCT
ap-340	137	3	p.	p.	NOUN
ap-340	137	4	201–230	201–230	NUM
ap-340	137	5	.	.	PUNCT
ap-340	138	1	[	[	X
ap-340	138	2	4	4	NUM
ap-340	138	3	]	]	X
ap-340	138	4	cole	cole	PROPN
ap-340	138	5	,	,	PUNCT
ap-340	138	6	j.	j.	PROPN
ap-340	138	7	d.	d.	PROPN
ap-340	138	8	:	:	PUNCT
ap-340	138	9	on	on	ADP
ap-340	138	10	a	a	DET
ap-340	138	11	quasi	quasi	ADJ
ap-340	138	12	-	-	ADJ
ap-340	138	13	linear	linear	ADJ
ap-340	138	14	parabolic	parabolic	ADJ
ap-340	138	15	equation	equation	NOUN
ap-340	138	16	occurring	occur	VERB
ap-340	138	17	in	in	ADP
ap-340	138	18	aerodynamics	aerodynamic	NOUN
ap-340	138	19	.	.	PUNCT
ap-340	139	1	q.	q.	PROPN
ap-340	139	2	appl	appl	PROPN
ap-340	139	3	.	.	PROPN
ap-340	139	4	math	math	PROPN
ap-340	139	5	.	.	PUNCT
ap-340	139	6	,	,	PUNCT
ap-340	139	7	1951	1951	NUM
ap-340	139	8	,	,	PUNCT
ap-340	139	9	vol	vol	NOUN
ap-340	139	10	.	.	NOUN
ap-340	139	11	9	9	NUM
ap-340	139	12	,	,	PUNCT
ap-340	139	13	p.	p.	NOUN
ap-340	139	14	225–236	225–236	NUM
ap-340	139	15	.	.	PUNCT
ap-340	140	1	[	[	X
ap-340	140	2	5	5	NUM
ap-340	140	3	]	]	PUNCT
ap-340	140	4	koníček	koníček	PROPN
ap-340	140	5	,	,	PUNCT
ap-340	140	6	p.	p.	PROPN
ap-340	140	7	,	,	PUNCT
ap-340	140	8	bednařík	bednařík	PROPN
ap-340	140	9	,	,	PUNCT
ap-340	140	10	m.	m.	NOUN
ap-340	140	11	,	,	PUNCT
ap-340	140	12	červenka	červenka	NOUN
ap-340	140	13	,	,	PUNCT
ap-340	140	14	m.	m.	NOUN
ap-340	140	15	:	:	PUNCT
ap-340	140	16	finite	finite	ADJ
ap-340	140	17	-	-	ADJ
ap-340	140	18	amplitude	amplitude	ADJ
ap-340	140	19	acoustic	acoustic	ADJ
ap-340	140	20	waves	wave	NOUN
ap-340	140	21	in	in	ADP
ap-340	140	22	a	a	DET
ap-340	140	23	liquid	liquid	NOUN
ap-340	140	24	-	-	PUNCT
ap-340	140	25	filled	fill	VERB
ap-340	140	26	tube	tube	NOUN
ap-340	140	27	.	.	PUNCT
ap-340	141	1	hydroacoustics	hydroacoustic	NOUN
ap-340	141	2	(	(	PUNCT
ap-340	141	3	editors	editor	NOUN
ap-340	141	4	:	:	PUNCT
ap-340	141	5	e.	e.	PROPN
ap-340	141	6	kozaczka	kozaczka	PROPN
ap-340	141	7	,	,	PUNCT
ap-340	141	8	g.	g.	PROPN
ap-340	141	9	grelowska	grelowska	PROPN
ap-340	141	10	)	)	PUNCT
ap-340	141	11	,	,	PUNCT
ap-340	141	12	gdynia	gdynia	PROPN
ap-340	141	13	:	:	PUNCT
ap-340	141	14	naval	naval	PROPN
ap-340	141	15	academy	academy	PROPN
ap-340	141	16	,	,	PUNCT
ap-340	141	17	2000	2000	NUM
ap-340	141	18	,	,	PUNCT
ap-340	141	19	p.	p.	NOUN
ap-340	141	20	85–88	85–88	NUM
ap-340	141	21	.	.	PUNCT
ap-340	142	1	[	[	X
ap-340	142	2	6	6	NUM
ap-340	142	3	]	]	X
ap-340	142	4	bednařík	bednařík	NOUN
ap-340	142	5	,	,	PUNCT
ap-340	142	6	m.	m.	NOUN
ap-340	142	7	:	:	PUNCT
ap-340	142	8	description	description	NOUN
ap-340	142	9	of	of	ADP
ap-340	142	10	plane	plane	NOUN
ap-340	142	11	finite	finite	ADJ
ap-340	142	12	-	-	ADJ
ap-340	142	13	amplitude	amplitude	ADJ
ap-340	142	14	traveling	travel	VERB
ap-340	142	15	waves	wave	NOUN
ap-340	142	16	in	in	ADP
ap-340	142	17	air	air	NOUN
ap-340	142	18	-	-	PUNCT
ap-340	142	19	filled	fill	VERB
ap-340	142	20	tubes	tube	NOUN
ap-340	142	21	.	.	PUNCT
ap-340	143	1	acoustica	acoustica	PROPN
ap-340	143	2	,	,	PUNCT
ap-340	143	3	1996	1996	NUM
ap-340	143	4	,	,	PUNCT
ap-340	143	5	vol	vol	NOUN
ap-340	143	6	.	.	PROPN
ap-340	143	7	82	82	NUM
ap-340	143	8	,	,	PUNCT
ap-340	143	9	p.	p.	NOUN
ap-340	143	10	196	196	NUM
ap-340	143	11	.	.	PUNCT
ap-340	144	1	[	[	X
ap-340	144	2	7	7	NUM
ap-340	144	3	]	]	X
ap-340	144	4	bednařík	bednařík	NOUN
ap-340	144	5	,	,	PUNCT
ap-340	144	6	m.	m.	NOUN
ap-340	144	7	:	:	PUNCT
ap-340	144	8	description	description	NOUN
ap-340	144	9	of	of	ADP
ap-340	144	10	high	high	ADJ
ap-340	144	11	-	-	PUNCT
ap-340	144	12	intensity	intensity	NOUN
ap-340	144	13	sound	sound	NOUN
ap-340	144	14	fields	field	NOUN
ap-340	144	15	in	in	ADP
ap-340	144	16	fluids	fluid	NOUN
ap-340	144	17	.	.	PUNCT
ap-340	145	1	proceedings	proceeding	NOUN
ap-340	145	2	of	of	ADP
ap-340	145	3	the	the	DET
ap-340	145	4	31st	31st	ADJ
ap-340	145	5	conference	conference	NOUN
ap-340	145	6	on	on	ADP
ap-340	145	7	acoustics	acoustic	NOUN
ap-340	145	8	,	,	PUNCT
ap-340	145	9	prague	prague	NOUN
ap-340	145	10	,	,	PUNCT
ap-340	145	11	1994	1994	NUM
ap-340	145	12	,	,	PUNCT
ap-340	145	13	p.	p.	NOUN
ap-340	145	14	134–138	134–138	NUM
ap-340	145	15	.	.	PUNCT
ap-340	146	1	[	[	X
ap-340	146	2	8	8	NUM
ap-340	146	3	]	]	X
ap-340	146	4	ochmann	ochmann	NOUN
ap-340	146	5	,	,	PUNCT
ap-340	146	6	m.	m.	NOUN
ap-340	146	7	:	:	PUNCT
ap-340	146	8	nonlinear	nonlinear	ADJ
ap-340	146	9	resonant	resonant	ADJ
ap-340	146	10	oscilllations	oscilllation	NOUN
ap-340	146	11	in	in	ADP
ap-340	146	12	closed	closed	ADJ
ap-340	146	13	tubes	tube	NOUN
ap-340	146	14	–	–	PUNCT
ap-340	146	15	an	an	DET
ap-340	146	16	application	application	NOUN
ap-340	146	17	of	of	ADP
ap-340	146	18	the	the	DET
ap-340	146	19	averaging	averaging	NOUN
ap-340	146	20	method	method	NOUN
ap-340	146	21	.	.	PUNCT
ap-340	147	1	j.	j.	PROPN
ap-340	147	2	acoust	acoust	PROPN
ap-340	147	3	.	.	PUNCT
ap-340	148	1	soc	soc	PROPN
ap-340	148	2	.	.	PUNCT
ap-340	149	1	am	be	AUX
ap-340	149	2	.	.	PROPN
ap-340	149	3	,	,	PUNCT
ap-340	149	4	1985	1985	NUM
ap-340	149	5	,	,	PUNCT
ap-340	149	6	vol	vol	NOUN
ap-340	149	7	.	.	PROPN
ap-340	149	8	77	77	NUM
ap-340	149	9	,	,	PUNCT
ap-340	149	10	p.	p.	NOUN
ap-340	149	11	61–66	61–66	NUM
ap-340	149	12	.	.	PUNCT
ap-340	150	1	[	[	X
ap-340	150	2	9	9	NUM
ap-340	150	3	]	]	SYM
ap-340	150	4	bednařík	bednařík	NOUN
ap-340	150	5	,	,	PUNCT
ap-340	150	6	m.	m.	NOUN
ap-340	150	7	:	:	PUNCT
ap-340	150	8	description	description	NOUN
ap-340	150	9	of	of	ADP
ap-340	150	10	nonlinear	nonlinear	ADJ
ap-340	150	11	waves	wave	NOUN
ap-340	150	12	in	in	ADP
ap-340	150	13	gas	gas	NOUN
ap-340	150	14	-	-	PUNCT
ap-340	150	15	filled	fill	VERB
ap-340	150	16	tubes	tube	NOUN
ap-340	150	17	by	by	ADP
ap-340	150	18	the	the	DET
ap-340	150	19	burgers	burger	NOUN
ap-340	150	20	and	and	CCONJ
ap-340	150	21	the	the	DET
ap-340	150	22	kzk	kzk	PROPN
ap-340	150	23	equations	equation	NOUN
ap-340	150	24	with	with	ADP
ap-340	150	25	a	a	DET
ap-340	150	26	fractional	fractional	ADJ
ap-340	150	27	derivative	derivative	NOUN
ap-340	150	28	.	.	PUNCT
ap-340	151	1	proceedings	proceeding	NOUN
ap-340	151	2	of	of	ADP
ap-340	151	3	the	the	DET
ap-340	151	4	16th	16th	ADJ
ap-340	151	5	ica	ica	PROPN
ap-340	151	6	,	,	PUNCT
ap-340	151	7	ica	ica	PROPN
ap-340	151	8	,	,	PUNCT
ap-340	151	9	seattle	seattle	PROPN
ap-340	151	10	,	,	PUNCT
ap-340	151	11	1998	1998	NUM
ap-340	151	12	,	,	PUNCT
ap-340	151	13	p.	p.	NOUN
ap-340	151	14	2307–2308	2307–2308	NUM
ap-340	151	15	.	.	PUNCT
ap-340	152	1	[	[	X
ap-340	152	2	10	10	NUM
ap-340	152	3	]	]	X
ap-340	152	4	blackstock	blackstock	PROPN
ap-340	152	5	,	,	PUNCT
ap-340	152	6	d.	d.	PROPN
ap-340	152	7	t.	t.	PROPN
ap-340	152	8	:	:	PUNCT
ap-340	152	9	connection	connection	NOUN
ap-340	152	10	between	between	ADP
ap-340	152	11	the	the	DET
ap-340	152	12	fay	fay	NOUN
ap-340	152	13	and	and	CCONJ
ap-340	152	14	fubuini	fubuini	ADJ
ap-340	152	15	solution	solution	NOUN
ap-340	152	16	for	for	ADP
ap-340	152	17	plane	plane	NOUN
ap-340	152	18	sound	sound	NOUN
ap-340	152	19	waves	wave	NOUN
ap-340	152	20	of	of	ADP
ap-340	152	21	finite	finite	ADJ
ap-340	152	22	amplitude	amplitude	NOUN
ap-340	152	23	.	.	PUNCT
ap-340	153	1	j.	j.	PROPN
ap-340	153	2	acoust	acoust	PROPN
ap-340	153	3	.	.	PUNCT
ap-340	154	1	soc	soc	PROPN
ap-340	154	2	.	.	PUNCT
ap-340	155	1	am	be	AUX
ap-340	155	2	.	.	PROPN
ap-340	155	3	,	,	PUNCT
ap-340	155	4	1966	1966	NUM
ap-340	155	5	,	,	PUNCT
ap-340	155	6	vol	vol	NOUN
ap-340	155	7	.	.	PROPN
ap-340	155	8	39	39	NUM
ap-340	155	9	,	,	PUNCT
ap-340	155	10	p.	p.	NOUN
ap-340	155	11	1019–1026	1019–1026	NUM
ap-340	155	12	.	.	PUNCT
ap-340	156	1	[	[	X
ap-340	156	2	11	11	NUM
ap-340	156	3	]	]	PUNCT
ap-340	156	4	blackstock	blackstock	PROPN
ap-340	156	5	,	,	PUNCT
ap-340	156	6	d.	d.	PROPN
ap-340	156	7	t.	t.	PROPN
ap-340	156	8	:	:	PUNCT
ap-340	156	9	thermoviscous	thermoviscous	ADJ
ap-340	156	10	attenuation	attenuation	NOUN
ap-340	156	11	of	of	ADP
ap-340	156	12	plane	plane	NOUN
ap-340	156	13	,	,	PUNCT
ap-340	156	14	periodic	periodic	ADJ
ap-340	156	15	,	,	PUNCT
ap-340	156	16	finite	finite	ADJ
ap-340	156	17	-	-	ADJ
ap-340	156	18	amplitude	amplitude	ADJ
ap-340	156	19	sound	sound	NOUN
ap-340	156	20	waves	wave	NOUN
ap-340	156	21	.	.	PUNCT
ap-340	157	1	j.	j.	PROPN
ap-340	157	2	acoust	acoust	PROPN
ap-340	157	3	.	.	PUNCT
ap-340	158	1	soc	soc	PROPN
ap-340	158	2	.	.	PUNCT
ap-340	159	1	am	be	AUX
ap-340	159	2	.	.	PROPN
ap-340	159	3	,	,	PUNCT
ap-340	159	4	1964	1964	NUM
ap-340	159	5	,	,	PUNCT
ap-340	159	6	vol	vol	NOUN
ap-340	159	7	.	.	PROPN
ap-340	160	1	36	36	NUM
ap-340	160	2	,	,	PUNCT
ap-340	161	1	p.	p.	NOUN
ap-340	161	2	534–542	534–542	NUM
ap-340	161	3	.	.	PUNCT
ap-340	162	1	[	[	X
ap-340	162	2	12	12	NUM
ap-340	162	3	]	]	X
ap-340	162	4	webster	webster	PROPN
ap-340	162	5	,	,	PUNCT
ap-340	162	6	d.	d.	PROPN
ap-340	162	7	a.	a.	PROPN
ap-340	162	8	,	,	PUNCT
ap-340	162	9	blackstock	blackstock	PROPN
ap-340	162	10	,	,	PUNCT
ap-340	162	11	d.	d.	PROPN
ap-340	162	12	t.	t.	PROPN
ap-340	162	13	:	:	PUNCT
ap-340	162	14	finite	finite	ADJ
ap-340	162	15	-	-	ADJ
ap-340	162	16	amplitude	amplitude	NOUN
ap-340	162	17	saturation	saturation	NOUN
ap-340	162	18	of	of	ADP
ap-340	162	19	plane	plane	NOUN
ap-340	162	20	sound	sound	NOUN
ap-340	162	21	waves	wave	NOUN
ap-340	162	22	in	in	ADP
ap-340	162	23	air	air	NOUN
ap-340	162	24	.	.	PUNCT
ap-340	163	1	j.	j.	PROPN
ap-340	163	2	acoust	acoust	PROPN
ap-340	163	3	.	.	PUNCT
ap-340	164	1	soc	soc	PROPN
ap-340	164	2	.	.	PUNCT
ap-340	165	1	am	be	AUX
ap-340	165	2	.	.	PROPN
ap-340	165	3	,	,	PUNCT
ap-340	165	4	1977	1977	NUM
ap-340	165	5	,	,	PUNCT
ap-340	165	6	vol	vol	NOUN
ap-340	165	7	.	.	PROPN
ap-340	166	1	62	62	NUM
ap-340	166	2	,	,	PUNCT
ap-340	167	1	p.	p.	NOUN
ap-340	167	2	518–523	518–523	NUM
ap-340	167	3	.	.	PUNCT
ap-340	168	1	[	[	X
ap-340	168	2	13	13	NUM
ap-340	168	3	]	]	X
ap-340	168	4	hamilton	hamilton	PROPN
ap-340	168	5	,	,	PUNCT
ap-340	168	6	m.	m.	PROPN
ap-340	168	7	f.	f.	PROPN
ap-340	168	8	,	,	PUNCT
ap-340	168	9	blackstock	blackstock	PROPN
ap-340	168	10	,	,	PUNCT
ap-340	168	11	d.	d.	PROPN
ap-340	168	12	t.	t.	PROPN
ap-340	168	13	:	:	PUNCT
ap-340	168	14	nonlinear	nonlinear	ADJ
ap-340	168	15	acoustic	acoustic	ADJ
ap-340	168	16	.	.	PUNCT
ap-340	169	1	usa	usa	NOUN
ap-340	169	2	:	:	PUNCT
ap-340	169	3	academic	academic	ADJ
ap-340	169	4	press	press	NOUN
ap-340	169	5	,	,	PUNCT
ap-340	169	6	1998	1998	NUM
ap-340	169	7	,	,	PUNCT
ap-340	169	8	p.	p.	NOUN
ap-340	169	9	117–139	117–139	NUM
ap-340	169	10	.	.	PUNCT
ap-340	170	1	[	[	X
ap-340	170	2	14	14	NUM
ap-340	170	3	]	]	X
ap-340	170	4	bednařík	bednařík	NOUN
ap-340	170	5	,	,	PUNCT
ap-340	170	6	m.	m.	NOUN
ap-340	170	7	:	:	PUNCT
ap-340	170	8	nonlinear	nonlinear	ADJ
ap-340	170	9	propagation	propagation	NOUN
ap-340	170	10	of	of	ADP
ap-340	170	11	waves	wave	NOUN
ap-340	170	12	in	in	ADP
ap-340	170	13	hard	hard	ADV
ap-340	170	14	-	-	PUNCT
ap-340	170	15	walled	wall	VERB
ap-340	170	16	ducts	duct	NOUN
ap-340	170	17	.	.	PUNCT
ap-340	170	18	proceedings	proceeding	NOUN
ap-340	170	19	of	of	ADP
ap-340	170	20	the	the	DET
ap-340	170	21	ctu	ctu	NOUN
ap-340	170	22	workshop	workshop	NOUN
ap-340	170	23	,	,	PUNCT
ap-340	170	24	prague	prague	NOUN
ap-340	170	25	:	:	PUNCT
ap-340	170	26	ctu	ctu	PROPN
ap-340	170	27	,	,	PUNCT
ap-340	170	28	1995	1995	NUM
ap-340	170	29	,	,	PUNCT
ap-340	170	30	p.	p.	NOUN
ap-340	170	31	91–92	91–92	NUM
ap-340	170	32	.	.	PUNCT
ap-340	171	1	[	[	X
ap-340	171	2	15	15	NUM
ap-340	171	3	]	]	X
ap-340	171	4	mitome	mitome	NOUN
ap-340	171	5	,	,	PUNCT
ap-340	171	6	h.	h.	PROPN
ap-340	171	7	:	:	PUNCT
ap-340	171	8	an	an	DET
ap-340	171	9	exact	exact	ADJ
ap-340	171	10	solution	solution	NOUN
ap-340	171	11	for	for	ADP
ap-340	171	12	finite	finite	ADJ
ap-340	171	13	-	-	ADJ
ap-340	171	14	amplitude	amplitude	ADJ
ap-340	171	15	plane	plane	NOUN
ap-340	171	16	sound	sound	NOUN
ap-340	171	17	waves	wave	NOUN
ap-340	171	18	in	in	ADP
ap-340	171	19	a	a	DET
ap-340	171	20	dissipative	dissipative	ADJ
ap-340	171	21	fluid	fluid	NOUN
ap-340	171	22	.	.	PUNCT
ap-340	172	1	j.	j.	PROPN
ap-340	172	2	acoust	acoust	PROPN
ap-340	172	3	.	.	PUNCT
ap-340	173	1	soc	soc	PROPN
ap-340	173	2	.	.	PUNCT
ap-340	174	1	am	be	AUX
ap-340	174	2	.	.	PROPN
ap-340	174	3	,	,	PUNCT
ap-340	174	4	1989	1989	NUM
ap-340	174	5	,	,	PUNCT
ap-340	174	6	vol	vol	NOUN
ap-340	174	7	.	.	PROPN
ap-340	174	8	86	86	NUM
ap-340	174	9	,	,	PUNCT
ap-340	174	10	no	no	INTJ
ap-340	174	11	.	.	NOUN
ap-340	174	12	6	6	NUM
ap-340	174	13	,	,	PUNCT
ap-340	174	14	p.	p.	NOUN
ap-340	174	15	2334–2338	2334–2338	NUM
ap-340	174	16	.	.	PUNCT
ap-340	175	1	[	[	X
ap-340	175	2	16	16	NUM
ap-340	175	3	]	]	PUNCT
ap-340	175	4	makarov	makarov	PROPN
ap-340	175	5	,	,	PUNCT
ap-340	175	6	s.	s.	PROPN
ap-340	175	7	,	,	PUNCT
ap-340	175	8	ochmann	ochmann	NOUN
ap-340	175	9	,	,	PUNCT
ap-340	175	10	m.	m.	NOUN
ap-340	175	11	:	:	PUNCT
ap-340	175	12	nonlinear	nonlinear	ADJ
ap-340	175	13	and	and	CCONJ
ap-340	175	14	thermoviscous	thermoviscous	ADJ
ap-340	175	15	phenomena	phenomenon	NOUN
ap-340	175	16	in	in	ADP
ap-340	175	17	acoustics	acoustic	NOUN
ap-340	175	18	2	2	NUM
ap-340	175	19	.	.	X
ap-340	175	20	acustica	acustica	PROPN
ap-340	175	21	,	,	PUNCT
ap-340	175	22	1997	1997	NUM
ap-340	175	23	,	,	PUNCT
ap-340	175	24	vol	vol	NOUN
ap-340	175	25	.	.	PROPN
ap-340	175	26	83	83	NUM
ap-340	175	27	,	,	PUNCT
ap-340	175	28	p.	p.	NOUN
ap-340	175	29	197–222	197–222	NUM
ap-340	175	30	.	.	PUNCT
ap-340	176	1	[	[	X
ap-340	176	2	17	17	NUM
ap-340	176	3	]	]	PUNCT
ap-340	176	4	whitham	whitham	NOUN
ap-340	176	5	,	,	PUNCT
ap-340	176	6	g.	g.	PROPN
ap-340	176	7	b.	b.	PROPN
ap-340	176	8	:	:	PUNCT
ap-340	177	1	linear	linear	ADJ
ap-340	177	2	and	and	CCONJ
ap-340	177	3	nonlinear	nonlinear	ADJ
ap-340	177	4	waves	wave	NOUN
ap-340	177	5	.	.	PUNCT
ap-340	178	1	new	new	PROPN
ap-340	178	2	york	york	PROPN
ap-340	178	3	:	:	PUNCT
ap-340	178	4	john	john	PROPN
ap-340	178	5	willey	willey	PROPN
ap-340	178	6	,	,	PUNCT
ap-340	178	7	1974	1974	NUM
ap-340	178	8	,	,	PUNCT
ap-340	178	9	p.	p.	NOUN
ap-340	178	10	152–157	152–157	NUM
ap-340	178	11	.	.	PUNCT
ap-340	179	1	[	[	X
ap-340	179	2	18	18	NUM
ap-340	179	3	]	]	X
ap-340	179	4	trivett	trivett	NOUN
ap-340	179	5	,	,	PUNCT
ap-340	179	6	d.	d.	PROPN
ap-340	179	7	h.	h.	PROPN
ap-340	179	8	,	,	PUNCT
ap-340	179	9	van	van	PROPN
ap-340	179	10	buren	buren	PROPN
ap-340	179	11	,	,	PUNCT
ap-340	179	12	a.	a.	PROPN
ap-340	179	13	l.	l.	PROPN
ap-340	179	14	:	:	PUNCT
ap-340	179	15	propagation	propagation	NOUN
ap-340	179	16	of	of	ADP
ap-340	179	17	plane	plane	NOUN
ap-340	179	18	,	,	PUNCT
ap-340	179	19	cylindrical	cylindrical	ADJ
ap-340	179	20	,	,	PUNCT
ap-340	179	21	and	and	CCONJ
ap-340	179	22	spherical	spherical	ADJ
ap-340	179	23	finite	finite	ADJ
ap-340	179	24	amplitude	amplitude	NOUN
ap-340	179	25	waves	wave	NOUN
ap-340	179	26	.	.	PUNCT
ap-340	180	1	j.	j.	PROPN
ap-340	180	2	acoust	acoust	PROPN
ap-340	180	3	.	.	PUNCT
ap-340	181	1	soc	soc	PROPN
ap-340	181	2	.	.	PUNCT
ap-340	182	1	am	be	AUX
ap-340	182	2	.	.	PROPN
ap-340	182	3	,	,	PUNCT
ap-340	182	4	1981	1981	NUM
ap-340	182	5	,	,	PUNCT
ap-340	182	6	vol	vol	NOUN
ap-340	182	7	.	.	PROPN
ap-340	183	1	69	69	NUM
ap-340	183	2	,	,	PUNCT
ap-340	183	3	no	no	INTJ
ap-340	183	4	.	.	NOUN
ap-340	183	5	4	4	NUM
ap-340	183	6	,	,	PUNCT
ap-340	183	7	p.	p.	NOUN
ap-340	183	8	943–949	943–949	NUM
ap-340	183	9	.	.	PUNCT
ap-340	184	1	dr	dr	PROPN
ap-340	184	2	.	.	PROPN
ap-340	184	3	ing	ing	PROPN
ap-340	184	4	.	.	PUNCT
ap-340	185	1	michal	michal	PROPN
ap-340	185	2	bednařík	bednařík	PROPN
ap-340	185	3	e	e	PROPN
ap-340	185	4	-	-	NOUN
ap-340	185	5	mail	mail	NOUN
ap-340	185	6	:	:	PUNCT
ap-340	185	7	bednarik@fel.cvut.cz	bednarik@fel.cvut.cz	PROPN
ap-340	185	8	dr	dr	PROPN
ap-340	185	9	.	.	PROPN
ap-340	185	10	mgr	mgr	PROPN
ap-340	185	11	.	.	PUNCT
ap-340	186	1	petr	petr	PROPN
ap-340	186	2	koníček	koníček	PROPN
ap-340	186	3	e	e	PROPN
ap-340	186	4	-	-	NOUN
ap-340	186	5	mail	mail	NOUN
ap-340	186	6	:	:	PUNCT
ap-340	186	7	konicek@fel.cvut.cz	konicek@fel.cvut.cz	PROPN
ap-340	186	8	ing	ing	PROPN
ap-340	186	9	.	.	PROPN
ap-340	187	1	milan	milan	PROPN
ap-340	187	2	červenka	červenka	PROPN
ap-340	187	3	e	e	NOUN
ap-340	187	4	-	-	NOUN
ap-340	187	5	mail	mail	NOUN
ap-340	187	6	:	:	PUNCT
ap-340	187	7	cervenm3@fel.cvut.cz	cervenm3@fel.cvut.cz	PROPN
ap-340	187	8	department	department	PROPN
ap-340	187	9	of	of	ADP
ap-340	187	10	physics	physics	PROPN
ap-340	187	11	czech	czech	PROPN
ap-340	187	12	technical	technical	PROPN
ap-340	187	13	university	university	PROPN
ap-340	187	14	in	in	ADP
ap-340	187	15	prague	prague	PROPN
ap-340	187	16	faculty	faculty	NOUN
ap-340	187	17	of	of	ADP
ap-340	187	18	electrical	electrical	ADJ
ap-340	187	19	engineering	engineering	NOUN
ap-340	187	20	technická	technická	NOUN
ap-340	187	21	2	2	NUM
ap-340	187	22	166	166	NUM
ap-340	187	23	27	27	NUM
ap-340	187	24	praha	praha	NOUN
ap-340	187	25	6	6	NUM
ap-340	187	26	,	,	PUNCT
ap-340	187	27	czech	czech	PROPN
ap-340	187	28	republic	republic	NOUN
ap-340	187	29	©	©	PROPN
ap-340	187	30	czech	czech	PROPN
ap-340	187	31	technical	technical	PROPN
ap-340	187	32	university	university	PROPN
ap-340	187	33	publishing	publishing	NOUN
ap-340	187	34	house	house	NOUN
ap-340	187	35	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-340	187	36	75	75	NUM
ap-340	187	37	acta	acta	PROPN
ap-340	187	38	polytechnica	polytechnica	PROPN
ap-340	187	39	vol	vol	NOUN
ap-340	187	40	.	.	PUNCT
ap-340	188	1	42	42	NUM
ap-340	188	2	no	no	NOUN
ap-340	188	3	.	.	PUNCT
ap-340	189	1	2/2002	2/2002	NUM
ap-340	189	2	table	table	NOUN
ap-340	189	3	of	of	ADP
ap-340	189	4	contents	content	NOUN
ap-340	189	5	concept	concept	NOUN
ap-340	189	6	design	design	NOUN
ap-340	189	7	and	and	CCONJ
ap-340	189	8	reliability	reliability	NOUN
ap-340	189	9	3	3	NUM
ap-340	189	10	g.	g.	PROPN
ap-340	189	11	cooper	cooper	PROPN
ap-340	189	12	,	,	PUNCT
ap-340	189	13	g.	g.	PROPN
ap-340	189	14	thompson	thompson	PROPN
ap-340	189	15	the	the	DET
ap-340	189	16	impact	impact	NOUN
ap-340	189	17	of	of	ADP
ap-340	189	18	odors	odor	NOUN
ap-340	189	19	13	13	NUM
ap-340	189	20	m.	m.	NOUN
ap-340	189	21	v.	v.	ADP
ap-340	189	22	jokl	jokl	ADJ
ap-340	189	23	optimization	optimization	NOUN
ap-340	189	24	of	of	ADP
ap-340	189	25	the	the	DET
ap-340	189	26	odor	odor	NOUN
ap-340	189	27	microclimate	microclimate	NOUN
ap-340	189	28	23	23	NUM
ap-340	189	29	m.	m.	NOUN
ap-340	189	30	v.	v.	ADP
ap-340	189	31	jokl	jokl	PROPN
ap-340	189	32	a	a	DET
ap-340	189	33	low	low	ADJ
ap-340	189	34	-	-	PUNCT
ap-340	189	35	complexity	complexity	NOUN
ap-340	189	36	wavelet	wavelet	NOUN
ap-340	189	37	based	base	VERB
ap-340	189	38	algorithm	algorithm	NOUN
ap-340	189	39	for	for	ADP
ap-340	189	40	inter	inter	ADJ
ap-340	189	41	-	-	ADJ
ap-340	189	42	frame	frame	ADJ
ap-340	189	43	image	image	NOUN
ap-340	189	44	prediction	prediction	NOUN
ap-340	189	45	30	30	NUM
ap-340	189	46	a.	a.	NOUN
ap-340	189	47	k.	k.	PROPN
ap-340	189	48	haghi	haghi	PROPN
ap-340	189	49	sampling	sample	VERB
ap-340	189	50	by	by	ADP
ap-340	189	51	fluidics	fluidic	NOUN
ap-340	189	52	and	and	CCONJ
ap-340	189	53	microfluidics	microfluidic	NOUN
ap-340	189	54	41	41	NUM
ap-340	189	55	v.	v.	ADP
ap-340	189	56	tesaø	tesaø	NOUN
ap-340	189	57	mixing	mix	VERB
ap-340	189	58	suspensions	suspension	NOUN
ap-340	189	59	in	in	ADP
ap-340	189	60	slender	slender	ADJ
ap-340	189	61	tanks	tank	NOUN
ap-340	189	62	50	50	NUM
ap-340	189	63	f.	f.	PROPN
ap-340	189	64	rieger	rieger	PROPN
ap-340	189	65	,	,	PUNCT
ap-340	189	66	e.	e.	PROPN
ap-340	189	67	rzyski	rzyski	PROPN
ap-340	189	68	formation	formation	NOUN
ap-340	189	69	of	of	ADP
ap-340	189	70	haloforms	haloform	NOUN
ap-340	189	71	during	during	ADP
ap-340	189	72	chlorination	chlorination	NOUN
ap-340	189	73	of	of	ADP
ap-340	189	74	natural	natural	ADJ
ap-340	189	75	waters	water	NOUN
ap-340	189	76	56	56	NUM
ap-340	189	77	a.	a.	NOUN
ap-340	189	78	grünwald	grünwald	NOUN
ap-340	189	79	,	,	PUNCT
ap-340	189	80	b.	b.	PROPN
ap-340	190	1	š•astný	š•astný	PROPN
ap-340	190	2	,	,	PUNCT
ap-340	190	3	k.	k.	PROPN
ap-340	190	4	slavíèková	slavíèková	PROPN
ap-340	190	5	,	,	PUNCT
ap-340	190	6	m.	m.	NOUN
ap-340	190	7	slavíèek	slavíèek	NOUN
ap-340	190	8	reducing	reduce	VERB
ap-340	190	9	ultrasonic	ultrasonic	ADJ
ap-340	190	10	signal	signal	NOUN
ap-340	190	11	noise	noise	NOUN
ap-340	190	12	by	by	ADP
ap-340	190	13	algorithms	algorithm	NOUN
ap-340	190	14	based	base	VERB
ap-340	190	15	on	on	ADP
ap-340	190	16	wavelet	wavelet	NOUN
ap-340	190	17	thresholding	thresholde	VERB
ap-340	190	18	60	60	NUM
ap-340	190	19	m.	m.	NOUN
ap-340	190	20	kreidl	kreidl	NOUN
ap-340	190	21	,	,	PUNCT
ap-340	190	22	p.	p.	PROPN
ap-340	190	23	houfek	houfek	NOUN
ap-340	190	24	optimisation	optimisation	NOUN
ap-340	190	25	and	and	CCONJ
ap-340	190	26	just	just	ADV
ap-340	190	27	-	-	PUNCT
ap-340	190	28	in	in	ADP
ap-340	190	29	-	-	PUNCT
ap-340	190	30	time	time	NOUN
ap-340	190	31	66	66	NUM
ap-340	190	32	v.	v.	ADP
ap-340	190	33	beran	beran	PROPN
ap-340	190	34	solution	solution	NOUN
ap-340	190	35	of	of	ADP
ap-340	190	36	the	the	DET
ap-340	190	37	burgers	burger	NOUN
ap-340	190	38	equation	equation	NOUN
ap-340	190	39	in	in	ADP
ap-340	190	40	the	the	DET
ap-340	190	41	time	time	NOUN
ap-340	190	42	domain	domain	NOUN
ap-340	190	43	71	71	NUM
ap-340	190	44	m.	m.	NOUN
ap-340	190	45	bednaøík	bednaøík	NOUN
ap-340	190	46	,	,	PUNCT
ap-340	190	47	p.	p.	PROPN
ap-340	190	48	koníèek	koníèek	PROPN
ap-340	190	49	,	,	PUNCT
ap-340	190	50	m.	m.	NOUN
ap-340	190	51	èervenka	èervenka	NOUN