id	sid	tid	token	lemma	pos
ap-180	1	1	ap1_01.vp	ap1_01.vp	PRON
ap-180	1	2	18	18	NUM
ap-180	1	3	©	©	PROPN
ap-180	1	4	czech	czech	PROPN
ap-180	1	5	technical	technical	PROPN
ap-180	1	6	university	university	PROPN
ap-180	1	7	publishing	publishing	NOUN
ap-180	1	8	house	house	NOUN
ap-180	1	9	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-180	1	10	acta	acta	PROPN
ap-180	1	11	polytechnica	polytechnica	PROPN
ap-180	1	12	vol	vol	NOUN
ap-180	1	13	.	.	PUNCT
ap-180	2	1	41	41	NUM
ap-180	2	2	no.1/2001	no.1/2001	NOUN
ap-180	2	3	1	1	NUM
ap-180	2	4	introduction	introduction	NOUN
ap-180	2	5	linear	linear	ADJ
ap-180	2	6	formulation	formulation	NOUN
ap-180	2	7	of	of	ADP
ap-180	2	8	the	the	DET
ap-180	2	9	eigenvalue	eigenvalue	PROPN
ap-180	2	10	problem	problem	NOUN
ap-180	2	11	for	for	ADP
ap-180	2	12	a	a	DET
ap-180	2	13	vertical	vertical	ADJ
ap-180	2	14	rod	rod	NOUN
ap-180	2	15	loaded	load	VERB
ap-180	2	16	with	with	ADP
ap-180	2	17	its	its	PRON
ap-180	2	18	own	own	ADJ
ap-180	2	19	weight	weight	NOUN
ap-180	2	20	has	have	VERB
ap-180	2	21	apparent	apparent	ADJ
ap-180	2	22	drawbacks	drawback	NOUN
ap-180	2	23	,	,	PUNCT
ap-180	2	24	e.g.	e.g.	ADV
ap-180	2	25	,	,	PUNCT
ap-180	2	26	a	a	X
ap-180	2	27	)	)	PUNCT
ap-180	2	28	all	all	DET
ap-180	2	29	the	the	DET
ap-180	2	30	critical	critical	ADJ
ap-180	2	31	lengths	length	NOUN
ap-180	2	32	of	of	ADP
ap-180	2	33	the	the	DET
ap-180	2	34	rod	rod	NOUN
ap-180	2	35	(	(	PUNCT
ap-180	2	36	i.e.	i.e.	X
ap-180	2	37	,	,	PUNCT
ap-180	2	38	the	the	DET
ap-180	2	39	eigenvalues	eigenvalue	NOUN
ap-180	2	40	)	)	PUNCT
ap-180	2	41	compose	compose	VERB
ap-180	2	42	a	a	DET
ap-180	2	43	discrete	discrete	ADJ
ap-180	2	44	set	set	NOUN
ap-180	2	45	,	,	PUNCT
ap-180	2	46	outside	outside	ADP
ap-180	2	47	of	of	ADP
ap-180	2	48	which	which	PRON
ap-180	2	49	all	all	DET
ap-180	2	50	the	the	DET
ap-180	2	51	lengths	length	NOUN
ap-180	2	52	are	be	AUX
ap-180	2	53	noncritical	noncritical	ADJ
ap-180	2	54	,	,	PUNCT
ap-180	2	55	i.e.	i.e.	X
ap-180	2	56	,	,	PUNCT
ap-180	2	57	nonzero	nonzero	ADJ
ap-180	2	58	deflections	deflection	NOUN
ap-180	2	59	are	be	AUX
ap-180	2	60	impossible	impossible	ADJ
ap-180	2	61	,	,	PUNCT
ap-180	2	62	and	and	CCONJ
ap-180	2	63	b	b	X
ap-180	2	64	)	)	PUNCT
ap-180	2	65	all	all	DET
ap-180	2	66	the	the	DET
ap-180	2	67	critical	critical	ADJ
ap-180	2	68	deflections	deflection	NOUN
ap-180	2	69	(	(	PUNCT
ap-180	2	70	i.e.	i.e.	X
ap-180	2	71	,	,	PUNCT
ap-180	2	72	the	the	DET
ap-180	2	73	eigenfunctions	eigenfunction	NOUN
ap-180	2	74	)	)	PUNCT
ap-180	2	75	are	be	AUX
ap-180	2	76	of	of	ADP
ap-180	2	77	an	an	DET
ap-180	2	78	arbitrary	arbitrary	ADJ
ap-180	2	79	magnitude	magnitude	NOUN
ap-180	2	80	.	.	PUNCT
ap-180	3	1	to	to	ADP
ap-180	3	2	a	a	DET
ap-180	3	3	certain	certain	ADJ
ap-180	3	4	extent	extent	NOUN
ap-180	3	5	,	,	PUNCT
ap-180	3	6	they	they	PRON
ap-180	3	7	may	may	AUX
ap-180	3	8	be	be	AUX
ap-180	3	9	eliminated	eliminate	VERB
ap-180	3	10	using	use	VERB
ap-180	3	11	the	the	DET
ap-180	3	12	precise	precise	ADJ
ap-180	3	13	(	(	PUNCT
ap-180	3	14	nonlinear	nonlinear	ADJ
ap-180	3	15	)	)	PUNCT
ap-180	3	16	form	form	NOUN
ap-180	3	17	of	of	ADP
ap-180	3	18	the	the	DET
ap-180	3	19	curvature	curvature	NOUN
ap-180	3	20	.	.	PUNCT
ap-180	4	1	the	the	DET
ap-180	4	2	nonlinear	nonlinear	ADJ
ap-180	4	3	problem	problem	NOUN
ap-180	4	4	was	be	AUX
ap-180	4	5	solved	solve	VERB
ap-180	4	6	long	long	ADV
ap-180	4	7	ago	ago	ADV
ap-180	4	8	by	by	ADP
ap-180	4	9	l.	l.	PROPN
ap-180	4	10	euler	euler	PROPN
ap-180	4	11	(	(	PUNCT
ap-180	4	12	1744	1744	NUM
ap-180	4	13	)	)	PUNCT
ap-180	4	14	and	and	CCONJ
ap-180	4	15	by	by	ADP
ap-180	4	16	j.	j.	PROPN
ap-180	4	17	l.	l.	PROPN
ap-180	4	18	lagrange	lagrange	PROPN
ap-180	4	19	(	(	PUNCT
ap-180	4	20	1773	1773	NUM
ap-180	4	21	)	)	PUNCT
ap-180	4	22	,	,	PUNCT
ap-180	4	23	who	who	PRON
ap-180	4	24	gave	give	VERB
ap-180	4	25	the	the	DET
ap-180	4	26	solution	solution	NOUN
ap-180	4	27	of	of	ADP
ap-180	4	28	the	the	DET
ap-180	4	29	simplest	simple	ADJ
ap-180	4	30	problem	problem	NOUN
ap-180	4	31	for	for	ADP
ap-180	4	32	a	a	DET
ap-180	4	33	homogeneous	homogeneous	ADJ
ap-180	4	34	rod	rod	NOUN
ap-180	4	35	loaded	load	VERB
ap-180	4	36	with	with	ADP
ap-180	4	37	a	a	DET
ap-180	4	38	longitudinal	longitudinal	ADJ
ap-180	4	39	force	force	NOUN
ap-180	4	40	(	(	PUNCT
ap-180	4	41	neglecting	neglect	VERB
ap-180	4	42	its	its	PRON
ap-180	4	43	own	own	ADJ
ap-180	4	44	weight	weight	NOUN
ap-180	4	45	)	)	PUNCT
ap-180	4	46	in	in	ADP
ap-180	4	47	the	the	DET
ap-180	4	48	form	form	NOUN
ap-180	4	49	of	of	ADP
ap-180	4	50	elliptic	elliptic	ADJ
ap-180	4	51	functions	function	NOUN
ap-180	4	52	.	.	PUNCT
ap-180	5	1	detailed	detailed	ADJ
ap-180	5	2	analysis	analysis	NOUN
ap-180	5	3	of	of	ADP
ap-180	5	4	the	the	DET
ap-180	5	5	problem	problem	NOUN
ap-180	5	6	was	be	AUX
ap-180	5	7	published	publish	VERB
ap-180	5	8	e.g.	e.g.	ADV
ap-180	5	9	,	,	PUNCT
ap-180	5	10	in	in	ADP
ap-180	5	11	[	[	PUNCT
ap-180	5	12	1	1	NUM
ap-180	5	13	]	]	PUNCT
ap-180	5	14	,	,	PUNCT
ap-180	5	15	[	[	X
ap-180	5	16	2	2	NUM
ap-180	5	17	]	]	PUNCT
ap-180	5	18	and	and	CCONJ
ap-180	5	19	it	it	PRON
ap-180	5	20	is	be	AUX
ap-180	5	21	mentioned	mention	VERB
ap-180	5	22	in	in	ADP
ap-180	5	23	the	the	DET
ap-180	5	24	first	first	ADJ
ap-180	5	25	part	part	NOUN
ap-180	5	26	of	of	ADP
ap-180	5	27	the	the	DET
ap-180	5	28	paper	paper	NOUN
ap-180	5	29	as	as	ADP
ap-180	5	30	an	an	DET
ap-180	5	31	introduction	introduction	NOUN
ap-180	5	32	to	to	ADP
ap-180	5	33	the	the	DET
ap-180	5	34	bifurcation	bifurcation	NOUN
ap-180	5	35	problem	problem	NOUN
ap-180	5	36	.	.	PUNCT
ap-180	6	1	the	the	DET
ap-180	6	2	second	second	ADJ
ap-180	6	3	part	part	NOUN
ap-180	6	4	of	of	ADP
ap-180	6	5	this	this	DET
ap-180	6	6	paper	paper	NOUN
ap-180	6	7	contains	contain	VERB
ap-180	6	8	the	the	DET
ap-180	6	9	formulation	formulation	NOUN
ap-180	6	10	of	of	ADP
ap-180	6	11	nonlinear	nonlinear	ADJ
ap-180	6	12	eigenvalue	eigenvalue	PROPN
ap-180	6	13	problem	problem	NOUN
ap-180	6	14	for	for	ADP
ap-180	6	15	a	a	DET
ap-180	6	16	vertical	vertical	ADJ
ap-180	6	17	homogeneous	homogeneous	ADJ
ap-180	6	18	rod	rod	NOUN
ap-180	6	19	loaded	load	VERB
ap-180	6	20	with	with	ADP
ap-180	6	21	its	its	PRON
ap-180	6	22	own	own	ADJ
ap-180	6	23	weight	weight	NOUN
ap-180	6	24	only	only	ADV
ap-180	6	25	,	,	PUNCT
ap-180	6	26	and	and	CCONJ
ap-180	6	27	the	the	DET
ap-180	6	28	corresponding	corresponding	ADJ
ap-180	6	29	linear	linear	PROPN
ap-180	6	30	problem	problem	NOUN
ap-180	6	31	is	be	AUX
ap-180	6	32	solved	solve	VERB
ap-180	6	33	.	.	PUNCT
ap-180	7	1	the	the	DET
ap-180	7	2	last	last	ADJ
ap-180	7	3	part	part	NOUN
ap-180	7	4	is	be	AUX
ap-180	7	5	devoted	devote	VERB
ap-180	7	6	to	to	ADP
ap-180	7	7	applications	application	NOUN
ap-180	7	8	of	of	ADP
ap-180	7	9	bifurcation	bifurcation	NOUN
ap-180	7	10	theory	theory	NOUN
ap-180	7	11	(	(	PUNCT
ap-180	7	12	see	see	VERB
ap-180	7	13	e.g.	e.g.	ADV
ap-180	7	14	,	,	PUNCT
ap-180	7	15	[	[	X
ap-180	7	16	3	3	NUM
ap-180	7	17	]	]	PUNCT
ap-180	7	18	,	,	PUNCT
ap-180	7	19	[	[	X
ap-180	7	20	4	4	NUM
ap-180	7	21	]	]	PUNCT
ap-180	7	22	)	)	PUNCT
ap-180	7	23	to	to	ADP
ap-180	7	24	the	the	DET
ap-180	7	25	nonlinear	nonlinear	ADJ
ap-180	7	26	problem	problem	NOUN
ap-180	7	27	and	and	CCONJ
ap-180	7	28	the	the	DET
ap-180	7	29	approximate	approximate	ADJ
ap-180	7	30	solution	solution	NOUN
ap-180	7	31	of	of	ADP
ap-180	7	32	the	the	DET
ap-180	7	33	problem	problem	NOUN
ap-180	7	34	is	be	AUX
ap-180	7	35	found	find	VERB
ap-180	7	36	.	.	PUNCT
ap-180	8	1	all	all	DET
ap-180	8	2	the	the	DET
ap-180	8	3	computations	computation	NOUN
ap-180	8	4	and	and	CCONJ
ap-180	8	5	pictures	picture	NOUN
ap-180	8	6	were	be	AUX
ap-180	8	7	performed	perform	VERB
ap-180	8	8	with	with	ADP
ap-180	8	9	use	use	NOUN
ap-180	8	10	of	of	ADP
ap-180	8	11	the	the	DET
ap-180	8	12	maple	maple	NOUN
ap-180	8	13	v	v	PROPN
ap-180	8	14	software	software	NOUN
ap-180	8	15	.	.	PUNCT
ap-180	9	1	2	2	NUM
ap-180	9	2	critical	critical	ADJ
ap-180	9	3	load	load	NOUN
ap-180	9	4	of	of	ADP
ap-180	9	5	a	a	DET
ap-180	9	6	column	column	NOUN
ap-180	9	7	in	in	ADP
ap-180	9	8	view	view	NOUN
ap-180	9	9	of	of	ADP
ap-180	9	10	nonlinear	nonlinear	ADJ
ap-180	9	11	theory	theory	NOUN
ap-180	9	12	the	the	DET
ap-180	9	13	problem	problem	NOUN
ap-180	9	14	of	of	ADP
ap-180	9	15	finding	find	VERB
ap-180	9	16	the	the	DET
ap-180	9	17	critical	critical	ADJ
ap-180	9	18	vertical	vertical	ADJ
ap-180	9	19	load	load	NOUN
ap-180	9	20	,	,	PUNCT
ap-180	9	21	which	which	PRON
ap-180	9	22	is	be	AUX
ap-180	9	23	applied	apply	VERB
ap-180	9	24	to	to	ADP
ap-180	9	25	the	the	DET
ap-180	9	26	free	free	ADJ
ap-180	9	27	end	end	NOUN
ap-180	9	28	of	of	ADP
ap-180	9	29	a	a	DET
ap-180	9	30	vertical	vertical	ADJ
ap-180	9	31	homogeneous	homogeneous	ADJ
ap-180	9	32	rod	rod	NOUN
ap-180	9	33	of	of	ADP
ap-180	9	34	uniform	uniform	PROPN
ap-180	9	35	cross	cross	PROPN
ap-180	9	36	section	section	NOUN
ap-180	9	37	fixed	fix	VERB
ap-180	9	38	at	at	ADP
ap-180	9	39	the	the	DET
ap-180	9	40	bottom	bottom	NOUN
ap-180	9	41	is	be	AUX
ap-180	9	42	a	a	DET
ap-180	9	43	well	well	ADV
ap-180	9	44	-	-	PUNCT
ap-180	9	45	known	know	VERB
ap-180	9	46	eigenvalue	eigenvalue	NOUN
ap-180	9	47	problem	problem	NOUN
ap-180	9	48	that	that	PRON
ap-180	9	49	has	have	AUX
ap-180	9	50	been	be	AUX
ap-180	9	51	explicitly	explicitly	ADV
ap-180	9	52	solved	solve	VERB
ap-180	9	53	in	in	ADP
ap-180	9	54	many	many	ADJ
ap-180	9	55	mechanics	mechanic	NOUN
ap-180	9	56	textbooks	textbook	NOUN
ap-180	9	57	.	.	PUNCT
ap-180	10	1	the	the	DET
ap-180	10	2	example	example	NOUN
ap-180	10	3	is	be	AUX
ap-180	10	4	mentioned	mention	VERB
ap-180	10	5	here	here	ADV
ap-180	10	6	to	to	PART
ap-180	10	7	illustrate	illustrate	VERB
ap-180	10	8	the	the	DET
ap-180	10	9	differences	difference	NOUN
ap-180	10	10	between	between	ADP
ap-180	10	11	the	the	DET
ap-180	10	12	results	result	NOUN
ap-180	10	13	of	of	ADP
ap-180	10	14	linear	linear	ADJ
ap-180	10	15	and	and	CCONJ
ap-180	10	16	nonlinear	nonlinear	ADJ
ap-180	10	17	theories	theory	NOUN
ap-180	10	18	.	.	PUNCT
ap-180	11	1	if	if	SCONJ
ap-180	11	2	we	we	PRON
ap-180	11	3	denote	denote	VERB
ap-180	11	4	the	the	DET
ap-180	11	5	horizontal	horizontal	ADJ
ap-180	11	6	deflection	deflection	NOUN
ap-180	11	7	of	of	ADP
ap-180	11	8	the	the	DET
ap-180	11	9	column	column	NOUN
ap-180	11	10	by	by	ADP
ap-180	11	11	w	w	PROPN
ap-180	11	12	(	(	PUNCT
ap-180	11	13	only	only	ADV
ap-180	11	14	such	such	ADJ
ap-180	11	15	displacements	displacement	NOUN
ap-180	11	16	are	be	AUX
ap-180	11	17	taken	take	VERB
ap-180	11	18	into	into	ADP
ap-180	11	19	account	account	NOUN
ap-180	11	20	)	)	PUNCT
ap-180	11	21	,	,	PUNCT
ap-180	11	22	its	its	PRON
ap-180	11	23	curvature	curvature	NOUN
ap-180	11	24	by	by	ADP
ap-180	11	25	�	�	PROPN
ap-180	11	26	�	�	PROPN
ap-180	11	27	the	the	DET
ap-180	11	28	variable	variable	ADJ
ap-180	11	29	length	length	NOUN
ap-180	11	30	measured	measure	VERB
ap-180	11	31	from	from	ADP
ap-180	11	32	the	the	DET
ap-180	11	33	free	free	ADJ
ap-180	11	34	end	end	NOUN
ap-180	11	35	by	by	ADP
ap-180	11	36	s	s	PROPN
ap-180	11	37	,	,	PUNCT
ap-180	11	38	the	the	DET
ap-180	11	39	length	length	NOUN
ap-180	11	40	of	of	ADP
ap-180	11	41	the	the	DET
ap-180	11	42	whole	whole	ADJ
ap-180	11	43	rod	rod	NOUN
ap-180	11	44	by	by	ADP
ap-180	11	45	l	l	PROPN
ap-180	11	46	,	,	PUNCT
ap-180	11	47	the	the	DET
ap-180	11	48	angle	angle	NOUN
ap-180	11	49	between	between	ADP
ap-180	11	50	the	the	DET
ap-180	11	51	x	x	NOUN
ap-180	11	52	-	-	NOUN
ap-180	11	53	axis	axis	NOUN
ap-180	11	54	and	and	CCONJ
ap-180	11	55	the	the	DET
ap-180	11	56	tangent	tangent	ADJ
ap-180	11	57	line	line	NOUN
ap-180	11	58	at	at	ADP
ap-180	11	59	the	the	DET
ap-180	11	60	point	point	NOUN
ap-180	11	61	s	s	NOUN
ap-180	11	62	of	of	ADP
ap-180	11	63	the	the	DET
ap-180	11	64	rod	rod	NOUN
ap-180	11	65	by	by	ADP
ap-180	11	66	�	�	PROPN
ap-180	11	67	(	(	PUNCT
ap-180	11	68	s	s	NOUN
ap-180	11	69	)	)	PUNCT
ap-180	11	70	,	,	PUNCT
ap-180	11	71	the	the	DET
ap-180	11	72	equation	equation	NOUN
ap-180	11	73	of	of	ADP
ap-180	11	74	the	the	DET
ap-180	11	75	moments	moment	NOUN
ap-180	11	76	is	be	AUX
ap-180	11	77	�	�	PROPN
ap-180	11	78	�	�	PROPN
ap-180	11	79	�	�	PROPN
ap-180	11	80	�	�	PROPN
ap-180	11	81	�	�	PROPN
ap-180	11	82	�	�	PROPN
ap-180	11	83	ei	ei	PROPN
ap-180	11	84	p	p	X
ap-180	11	85	w	w	PROPN
ap-180	11	86	s	s	PROPN
ap-180	11	87	w	w	PROPN
ap-180	11	88	�	�	PROPN
ap-180	11	89	�	�	PROPN
ap-180	11	90	�	�	PROPN
ap-180	11	91	0	0	NUM
ap-180	11	92	,	,	PUNCT
ap-180	11	93	where	where	SCONJ
ap-180	11	94	e	e	NOUN
ap-180	11	95	is	be	AUX
ap-180	11	96	young	young	ADJ
ap-180	11	97	’s	’s	PART
ap-180	11	98	modulus	modulus	NOUN
ap-180	11	99	,	,	PUNCT
ap-180	11	100	i	i	PRON
ap-180	11	101	is	be	AUX
ap-180	11	102	the	the	DET
ap-180	11	103	moment	moment	NOUN
ap-180	11	104	of	of	ADP
ap-180	11	105	inertia	inertia	NOUN
ap-180	11	106	and	and	CCONJ
ap-180	11	107	p	p	NOUN
ap-180	11	108	is	be	AUX
ap-180	11	109	the	the	DET
ap-180	11	110	above	above	ADJ
ap-180	11	111	mentioned	mention	VERB
ap-180	11	112	load	load	NOUN
ap-180	11	113	(	(	PUNCT
ap-180	11	114	in	in	ADP
ap-180	11	115	the	the	DET
ap-180	11	116	direction	direction	NOUN
ap-180	11	117	x	x	PUNCT
ap-180	11	118	of	of	ADP
ap-180	11	119	the	the	DET
ap-180	11	120	column	column	NOUN
ap-180	11	121	)	)	PUNCT
ap-180	11	122	.	.	PUNCT
ap-180	12	1	differentiating	differentiate	VERB
ap-180	12	2	(	(	PUNCT
ap-180	12	3	by	by	ADP
ap-180	12	4	s	s	NOUN
ap-180	12	5	)	)	PUNCT
ap-180	12	6	the	the	DET
ap-180	12	7	equation	equation	NOUN
ap-180	12	8	and	and	CCONJ
ap-180	12	9	substituting	substitute	VERB
ap-180	12	10	the	the	DET
ap-180	12	11	relations	relation	NOUN
ap-180	12	12	�	�	PROPN
ap-180	12	13	�	�	PROPN
ap-180	12	14	1	1	NUM
ap-180	12	15	�	�	PROPN
ap-180	12	16	�	�	PROPN
ap-180	12	17	�	�	PROPN
ap-180	12	18	�	�	PROPN
ap-180	12	19	�	�	PROPN
ap-180	12	20	�	�	PROPN
ap-180	12	21	d	d	PROPN
ap-180	13	1	d	d	PROPN
ap-180	13	2	d	d	X
ap-180	13	3	ds	ds	PROPN
ap-180	13	4	w	w	NOUN
ap-180	13	5	s	s	PROPN
ap-180	13	6	s	s	NOUN
ap-180	13	7	,	,	PUNCT
ap-180	13	8	sin	sin	NOUN
ap-180	13	9	,	,	PUNCT
ap-180	13	10	(	(	PUNCT
ap-180	13	11	1	1	X
ap-180	13	12	)	)	PUNCT
ap-180	13	13	into	into	ADP
ap-180	13	14	it	it	PRON
ap-180	13	15	,	,	PUNCT
ap-180	13	16	we	we	PRON
ap-180	13	17	get	get	VERB
ap-180	13	18	d	d	PROPN
ap-180	13	19	d	d	PROPN
ap-180	13	20	2	2	NUM
ap-180	13	21	�	�	PROPN
ap-180	13	22	�	�	PROPN
ap-180	13	23	s	s	PART
ap-180	13	24	p2	p2	PROPN
ap-180	13	25	2	2	NUM
ap-180	13	26	0	0	NUM
ap-180	13	27	�	�	PROPN
ap-180	13	28	�	�	PROPN
ap-180	13	29	sin	sin	NOUN
ap-180	13	30	,	,	PUNCT
ap-180	13	31	(	(	PUNCT
ap-180	13	32	2	2	X
ap-180	13	33	)	)	PUNCT
ap-180	13	34	where	where	SCONJ
ap-180	13	35	p	p	PROPN
ap-180	13	36	p	p	PROPN
ap-180	13	37	ei2	ei2	PROPN
ap-180	13	38	�	�	PROPN
ap-180	13	39	.	.	PUNCT
ap-180	14	1	in	in	ADP
ap-180	14	2	the	the	DET
ap-180	14	3	case	case	NOUN
ap-180	14	4	of	of	ADP
ap-180	14	5	small	small	ADJ
ap-180	14	6	deflections	deflection	NOUN
ap-180	14	7	,	,	PUNCT
ap-180	14	8	the	the	DET
ap-180	14	9	equation	equation	NOUN
ap-180	14	10	may	may	AUX
ap-180	14	11	be	be	AUX
ap-180	14	12	approximated	approximate	VERB
ap-180	14	13	by	by	ADP
ap-180	14	14	the	the	DET
ap-180	14	15	linear	linear	ADJ
ap-180	14	16	equation	equation	NOUN
ap-180	14	17	d	d	PROPN
ap-180	14	18	d	d	PROPN
ap-180	14	19	2	2	NUM
ap-180	14	20	�	�	PROPN
ap-180	14	21	�	�	PROPN
ap-180	14	22	s	s	PART
ap-180	14	23	p2	p2	PROPN
ap-180	14	24	2	2	NUM
ap-180	14	25	0	0	NUM
ap-180	14	26	�	�	PROPN
ap-180	14	27	�	�	PROPN
ap-180	14	28	,	,	PUNCT
ap-180	14	29	having	have	VERB
ap-180	14	30	(	(	PUNCT
ap-180	14	31	together	together	ADV
ap-180	14	32	with	with	ADP
ap-180	14	33	the	the	DET
ap-180	14	34	appropriate	appropriate	ADJ
ap-180	14	35	boundary	boundary	ADJ
ap-180	14	36	conditions	condition	NOUN
ap-180	14	37	)	)	PUNCT
ap-180	14	38	the	the	DET
ap-180	14	39	discrete	discrete	ADJ
ap-180	14	40	set	set	NOUN
ap-180	14	41	of	of	ADP
ap-180	14	42	eigenvalues	eigenvalue	VERB
ap-180	14	43	�	�	PROPN
ap-180	14	44	�	�	PROPN
ap-180	14	45	p	p	PROPN
ap-180	14	46	k	k	PROPN
ap-180	14	47	l	l	NOUN
ap-180	14	48	kk	kk	NOUN
ap-180	14	49	2	2	NUM
ap-180	14	50	22	22	NUM
ap-180	14	51	1	1	NUM
ap-180	14	52	2	2	NUM
ap-180	14	53	1	1	NUM
ap-180	14	54	2	2	NUM
ap-180	14	55	�	�	PROPN
ap-180	14	56	�	�	PROPN
ap-180	14	57	�	�	PROPN
ap-180	14	58	�	�	PROPN
ap-180	14	59	�	�	PROPN
ap-180	14	60	�	�	PROPN
ap-180	14	61	�	�	PROPN
ap-180	14	62	�	�	PROPN
ap-180	14	63	,	,	PUNCT
ap-180	14	64	,	,	PUNCT
ap-180	14	65	,	,	PUNCT
ap-180	14	66	and	and	CCONJ
ap-180	14	67	corresponding	correspond	VERB
ap-180	14	68	eigenfunctions	eigenfunction	NOUN
ap-180	14	69	with	with	ADP
ap-180	14	70	an	an	DET
ap-180	14	71	arbitrary	arbitrary	ADJ
ap-180	14	72	magnitude	magnitude	NOUN
ap-180	14	73	.	.	PUNCT
ap-180	15	1	but	but	CCONJ
ap-180	15	2	these	these	DET
ap-180	15	3	results	result	NOUN
ap-180	15	4	do	do	AUX
ap-180	15	5	not	not	PART
ap-180	15	6	correspond	correspond	VERB
ap-180	15	7	to	to	ADP
ap-180	15	8	reality	reality	NOUN
ap-180	15	9	(	(	PUNCT
ap-180	15	10	see	see	VERB
ap-180	15	11	the	the	DET
ap-180	15	12	introduction	introduction	NOUN
ap-180	15	13	)	)	PUNCT
ap-180	15	14	.	.	PUNCT
ap-180	16	1	for	for	ADP
ap-180	16	2	this	this	DET
ap-180	16	3	reason	reason	NOUN
ap-180	16	4	many	many	ADJ
ap-180	16	5	engineers	engineer	NOUN
ap-180	16	6	and	and	CCONJ
ap-180	16	7	mathematicians	mathematician	NOUN
ap-180	16	8	have	have	AUX
ap-180	16	9	tried	try	VERB
ap-180	16	10	to	to	PART
ap-180	16	11	solve	solve	VERB
ap-180	16	12	the	the	DET
ap-180	16	13	nonlinear	nonlinear	ADJ
ap-180	16	14	equation	equation	NOUN
ap-180	16	15	(	(	PUNCT
ap-180	16	16	2	2	NUM
ap-180	16	17	)	)	PUNCT
ap-180	16	18	.	.	PUNCT
ap-180	17	1	using	use	VERB
ap-180	17	2	the	the	DET
ap-180	17	3	identity	identity	NOUN
ap-180	17	4	d	d	NOUN
ap-180	17	5	d	d	PROPN
ap-180	17	6	d	d	PROPN
ap-180	17	7	d	d	PROPN
ap-180	17	8	d	d	PROPN
ap-180	17	9	d	d	PROPN
ap-180	17	10	d	d	PROPN
ap-180	17	11	d	d	PROPN
ap-180	17	12	d	d	X
ap-180	17	13	d	d	PROPN
ap-180	17	14	2	2	NUM
ap-180	17	15	�	�	PROPN
ap-180	17	16	�	�	PROPN
ap-180	17	17	�	�	PROPN
ap-180	17	18	�	�	PROPN
ap-180	17	19	�	�	PROPN
ap-180	17	20	�	�	PROPN
ap-180	17	21	�	�	PROPN
ap-180	17	22	s	s	PART
ap-180	17	23	s	s	PROPN
ap-180	17	24	s2	s2	NOUN
ap-180	17	25	2	2	NUM
ap-180	17	26	1	1	NUM
ap-180	17	27	1	1	NUM
ap-180	17	28	1	1	NUM
ap-180	17	29	2	2	NUM
ap-180	17	30	�	�	PROPN
ap-180	17	31	�	�	PROPN
ap-180	17	32	�	�	PROPN
ap-180	17	33	�	�	PROPN
ap-180	17	34	�	�	PROPN
ap-180	17	35	�	�	PROPN
ap-180	17	36	�	�	PROPN
ap-180	17	37	�	�	PROPN
ap-180	17	38	�	�	PROPN
ap-180	17	39	�	�	PROPN
ap-180	17	40	�	�	PROPN
ap-180	17	41	�	�	PROPN
ap-180	17	42	�	�	PROPN
ap-180	17	43	�	�	PROPN
ap-180	17	44	�	�	PROPN
ap-180	17	45	�	�	PROPN
ap-180	17	46	�	�	PROPN
ap-180	17	47	�	�	PROPN
ap-180	17	48	on	on	ADP
ap-180	17	49	the	the	DET
ap-180	17	50	left	left	ADJ
ap-180	17	51	hand	hand	NOUN
ap-180	17	52	side	side	NOUN
ap-180	17	53	of	of	ADP
ap-180	17	54	(	(	PUNCT
ap-180	17	55	2	2	NUM
ap-180	17	56	)	)	PUNCT
ap-180	17	57	,	,	PUNCT
ap-180	17	58	integrating	integrate	VERB
ap-180	17	59	by	by	ADP
ap-180	17	60	�	�	PROPN
ap-180	17	61	and	and	CCONJ
ap-180	17	62	taking	take	VERB
ap-180	17	63	into	into	ADP
ap-180	17	64	account	account	NOUN
ap-180	17	65	the	the	DET
ap-180	17	66	boundary	boundary	ADJ
ap-180	17	67	condition	condition	NOUN
ap-180	17	68	�	�	PROPN
ap-180	17	69	(	(	PUNCT
ap-180	17	70	0)=	0)=	PROPN
ap-180	17	71	�	�	X
ap-180	17	72	0	0	NUM
ap-180	17	73	,	,	PUNCT
ap-180	17	74	1/	1/	NUM
ap-180	17	75	�	�	PROPN
ap-180	17	76	(	(	PUNCT
ap-180	17	77	�	�	NOUN
ap-180	17	78	0)=0	0)=0	NUM
ap-180	17	79	,	,	PUNCT
ap-180	17	80	we	we	PRON
ap-180	17	81	get	get	VERB
ap-180	17	82	�	�	PROPN
ap-180	17	83	�	�	PROPN
ap-180	17	84	�	�	PROPN
ap-180	17	85	�	�	PROPN
ap-180	17	86	1	1	NUM
ap-180	17	87	2	2	NUM
ap-180	17	88	2	2	NUM
ap-180	17	89	2	2	NUM
ap-180	17	90	�	�	PROPN
ap-180	17	91	�	�	PROPN
ap-180	17	92	�	�	PROPN
ap-180	17	93	�	�	PROPN
ap-180	17	94	�	�	PROPN
ap-180	17	95	�	�	PROPN
ap-180	17	96	�	�	PROPN
ap-180	17	97	p	p	PROPN
ap-180	17	98	cos	cos	PROPN
ap-180	17	99	cos	cos	PROPN
ap-180	17	100	.	.	PUNCT
ap-180	18	1	(	(	PUNCT
ap-180	18	2	3	3	X
ap-180	18	3	)	)	PUNCT
ap-180	18	4	computing	compute	VERB
ap-180	18	5	�	�	PROPN
ap-180	18	6	�	�	PROPN
ap-180	18	7	�	�	PROPN
ap-180	19	1	d	d	PROPN
ap-180	19	2	d	d	X
ap-180	19	3	s	s	VERB
ap-180	19	4	from	from	ADP
ap-180	19	5	(	(	PUNCT
ap-180	19	6	3	3	NUM
ap-180	19	7	)	)	PUNCT
ap-180	19	8	,	,	PUNCT
ap-180	19	9	we	we	PRON
ap-180	19	10	must	must	AUX
ap-180	19	11	choose	choose	VERB
ap-180	19	12	the	the	DET
ap-180	19	13	sign	sign	NOUN
ap-180	19	14	in	in	ADP
ap-180	19	15	front	front	NOUN
ap-180	19	16	of	of	ADP
ap-180	19	17	the	the	DET
ap-180	19	18	root	root	NOUN
ap-180	19	19	.	.	PUNCT
ap-180	20	1	as	as	SCONJ
ap-180	20	2	the	the	DET
ap-180	20	3	most	most	ADV
ap-180	20	4	important	important	ADJ
ap-180	20	5	eigenvalue	eigenvalue	NOUN
ap-180	20	6	is	be	AUX
ap-180	20	7	the	the	DET
ap-180	20	8	smallest	small	ADJ
ap-180	20	9	one	one	NOUN
ap-180	20	10	,	,	PUNCT
ap-180	20	11	we	we	PRON
ap-180	20	12	choose	choose	VERB
ap-180	20	13	the	the	DET
ap-180	20	14	minus	minus	ADJ
ap-180	20	15	sign	sign	NOUN
ap-180	20	16	on	on	ADP
ap-180	20	17	the	the	DET
ap-180	20	18	whole	whole	ADJ
ap-180	20	19	interval	interval	NOUN
ap-180	20	20	(	(	PUNCT
ap-180	20	21	0	0	NUM
ap-180	20	22	,	,	PUNCT
ap-180	20	23	�	�	PROPN
ap-180	20	24	0	0	NUM
ap-180	20	25	)	)	PUNCT
ap-180	20	26	,	,	PUNCT
ap-180	20	27	and	and	CCONJ
ap-180	20	28	then	then	ADV
ap-180	20	29	we	we	PRON
ap-180	20	30	will	will	AUX
ap-180	20	31	consider	consider	VERB
ap-180	20	32	the	the	DET
ap-180	20	33	smallest	small	ADJ
ap-180	20	34	critical	critical	ADJ
ap-180	20	35	force	force	NOUN
ap-180	20	36	and	and	CCONJ
ap-180	20	37	its	its	PRON
ap-180	20	38	right	right	ADJ
ap-180	20	39	neighborhood	neighborhood	NOUN
ap-180	20	40	.	.	PUNCT
ap-180	21	1	integrating	integrate	VERB
ap-180	21	2	the	the	DET
ap-180	21	3	root	root	NOUN
ap-180	21	4	of	of	ADP
ap-180	21	5	(	(	PUNCT
ap-180	21	6	3	3	NUM
ap-180	21	7	)	)	PUNCT
ap-180	21	8	and	and	CCONJ
ap-180	21	9	taking	take	VERB
ap-180	21	10	into	into	ADP
ap-180	21	11	account	account	NOUN
ap-180	21	12	the	the	DET
ap-180	21	13	boundary	boundary	ADJ
ap-180	21	14	condition	condition	NOUN
ap-180	21	15	s(0)=	s(0)=	NOUN
ap-180	21	16	l	l	NOUN
ap-180	21	17	,	,	PUNCT
ap-180	21	18	we	we	PRON
ap-180	21	19	get	get	VERB
ap-180	21	20	the	the	DET
ap-180	21	21	implicit	implicit	ADJ
ap-180	21	22	form	form	NOUN
ap-180	21	23	of	of	ADP
ap-180	21	24	the	the	DET
ap-180	21	25	function	function	NOUN
ap-180	21	26	�	�	PROPN
ap-180	21	27	=	=	SYM
ap-180	21	28	�	�	PROPN
ap-180	21	29	(	(	PUNCT
ap-180	21	30	s	s	NUM
ap-180	21	31	):	):	PUNCT
ap-180	21	32	critical	critical	ADJ
ap-180	21	33	length	length	NOUN
ap-180	21	34	of	of	ADP
ap-180	21	35	a	a	DET
ap-180	21	36	column	column	NOUN
ap-180	21	37	in	in	ADP
ap-180	21	38	view	view	NOUN
ap-180	21	39	of	of	ADP
ap-180	21	40	bifurcation	bifurcation	NOUN
ap-180	21	41	theory	theory	NOUN
ap-180	21	42	m.	m.	NOUN
ap-180	21	43	kopáčková	kopáčková	PROPN
ap-180	21	44	the	the	DET
ap-180	21	45	paper	paper	NOUN
ap-180	21	46	investigates	investigate	VERB
ap-180	21	47	nonlinear	nonlinear	PROPN
ap-180	21	48	eigenvalue	eigenvalue	PROPN
ap-180	21	49	problem	problem	NOUN
ap-180	21	50	for	for	ADP
ap-180	21	51	a	a	DET
ap-180	21	52	vertical	vertical	ADJ
ap-180	21	53	homogeneous	homogeneous	ADJ
ap-180	21	54	rod	rod	NOUN
ap-180	21	55	loaded	load	VERB
ap-180	21	56	with	with	ADP
ap-180	21	57	its	its	PRON
ap-180	21	58	own	own	ADJ
ap-180	21	59	weight	weight	NOUN
ap-180	21	60	only	only	ADV
ap-180	21	61	.	.	PUNCT
ap-180	22	1	the	the	DET
ap-180	22	2	critical	critical	ADJ
ap-180	22	3	length	length	NOUN
ap-180	22	4	of	of	ADP
ap-180	22	5	the	the	DET
ap-180	22	6	rod	rod	NOUN
ap-180	22	7	,	,	PUNCT
ap-180	22	8	for	for	ADP
ap-180	22	9	which	which	PRON
ap-180	22	10	the	the	DET
ap-180	22	11	rod	rod	NOUN
ap-180	22	12	loses	lose	VERB
ap-180	22	13	its	its	PRON
ap-180	22	14	stability	stability	NOUN
ap-180	22	15	,	,	PUNCT
ap-180	22	16	is	be	AUX
ap-180	22	17	found	find	VERB
ap-180	22	18	by	by	ADP
ap-180	22	19	use	use	NOUN
ap-180	22	20	of	of	ADP
ap-180	22	21	bifurcation	bifurcation	NOUN
ap-180	22	22	theory	theory	NOUN
ap-180	22	23	.	.	PUNCT
ap-180	23	1	dependence	dependence	NOUN
ap-180	23	2	of	of	ADP
ap-180	23	3	maximal	maximal	ADJ
ap-180	23	4	deflections	deflection	NOUN
ap-180	23	5	of	of	ADP
ap-180	23	6	the	the	DET
ap-180	23	7	rods	rod	NOUN
ap-180	23	8	on	on	ADP
ap-180	23	9	their	their	PRON
ap-180	23	10	lengths	length	NOUN
ap-180	23	11	is	be	AUX
ap-180	23	12	given	give	VERB
ap-180	23	13	.	.	PUNCT
ap-180	24	1	keywords	keyword	NOUN
ap-180	24	2	:	:	PUNCT
ap-180	24	3	critical	critical	ADJ
ap-180	24	4	length	length	NOUN
ap-180	24	5	of	of	ADP
ap-180	24	6	column	column	NOUN
ap-180	24	7	,	,	PUNCT
ap-180	24	8	eigenvalue	eigenvalue	PROPN
ap-180	24	9	problem	problem	NOUN
ap-180	24	10	,	,	PUNCT
ap-180	24	11	bifurcation	bifurcation	NOUN
ap-180	24	12	theory	theory	NOUN
ap-180	24	13	,	,	PUNCT
ap-180	24	14	approximation	approximation	NOUN
ap-180	24	15	of	of	ADP
ap-180	24	16	solution	solution	NOUN
ap-180	24	17	,	,	PUNCT
ap-180	24	18	bessel	bessel	ADJ
ap-180	24	19	function	function	NOUN
ap-180	24	20	.	.	PUNCT
ap-180	25	1	�	�	PROPN
ap-180	25	2	�	�	PROPN
ap-180	25	3	l	l	NOUN
ap-180	25	4	s	s	PART
ap-180	25	5	p	p	X
ap-180	25	6	d	d	PROPN
ap-180	25	7	�	�	PROPN
ap-180	25	8	�	�	PROPN
ap-180	25	9	�	�	PROPN
ap-180	25	10	�	�	PROPN
ap-180	25	11	�	�	PROPN
ap-180	25	12	�	�	PROPN
ap-180	25	13	�	�	PROPN
ap-180	25	14	�	�	PROPN
ap-180	25	15	�	�	PROPN
ap-180	25	16	1	1	NUM
ap-180	25	17	2	2	NUM
ap-180	25	18	00	00	PUNCT
ap-180	25	19	cos	cos	PROPN
ap-180	25	20	cos	cos	PROPN
ap-180	25	21	.	.	PUNCT
ap-180	26	1	(	(	PUNCT
ap-180	26	2	4	4	X
ap-180	26	3	)	)	PUNCT
ap-180	26	4	the	the	DET
ap-180	26	5	value	value	NOUN
ap-180	26	6	�	�	PROPN
ap-180	26	7	�	�	PROPN
ap-180	26	8	is	be	AUX
ap-180	26	9	obtained	obtain	VERB
ap-180	26	10	by	by	ADP
ap-180	26	11	use	use	NOUN
ap-180	26	12	of	of	ADP
ap-180	26	13	the	the	DET
ap-180	26	14	substitution	substitution	NOUN
ap-180	26	15	sin	sin	NOUN
ap-180	26	16	sin	sin	NOUN
ap-180	26	17	sin	sin	PROPN
ap-180	26	18	�	�	PROPN
ap-180	26	19	�	�	PROPN
ap-180	26	20	2	2	NUM
ap-180	26	21	2	2	NUM
ap-180	26	22	0	0	NUM
ap-180	26	23	�	�	PROPN
ap-180	26	24	�	�	PROPN
ap-180	26	25	in	in	ADP
ap-180	26	26	(	(	PUNCT
ap-180	26	27	4	4	NUM
ap-180	26	28	)	)	PUNCT
ap-180	26	29	and	and	CCONJ
ap-180	26	30	limiting	limit	VERB
ap-180	26	31	the	the	DET
ap-180	26	32	result	result	NOUN
ap-180	26	33	for	for	ADP
ap-180	26	34	�	�	PROPN
ap-180	26	35	�	�	PROPN
ap-180	26	36	0	0	NUM
ap-180	26	37	,	,	PUNCT
ap-180	26	38	s	s	PART
ap-180	26	39	0	0	NUM
ap-180	26	40	:	:	PUNCT
ap-180	26	41	lp	lp	PROPN
ap-180	26	42	�	�	PROPN
ap-180	26	43	�	�	PROPN
ap-180	26	44	�	�	PROPN
ap-180	26	45	�	�	PROPN
ap-180	26	46	�	�	PROPN
ap-180	26	47	�	�	PROPN
ap-180	26	48	�	�	PROPN
ap-180	26	49	d	d	PROPN
ap-180	26	50	�	�	PROPN
ap-180	26	51	�	�	PROPN
ap-180	26	52	1	1	NUM
ap-180	26	53	2	2	NUM
ap-180	26	54	0	0	NUM
ap-180	26	55	20	20	NUM
ap-180	26	56	2	2	NUM
ap-180	26	57	sin	sin	NOUN
ap-180	26	58	sin	sin	NOUN
ap-180	26	59	�	�	PROPN
ap-180	26	60	�	�	PROPN
ap-180	26	61	,	,	PUNCT
ap-180	26	62	(	(	PUNCT
ap-180	26	63	5	5	X
ap-180	26	64	)	)	PUNCT
ap-180	26	65	which	which	PRON
ap-180	26	66	is	be	AUX
ap-180	26	67	the	the	DET
ap-180	26	68	implicit	implicit	ADJ
ap-180	26	69	form	form	NOUN
ap-180	26	70	of	of	ADP
ap-180	26	71	the	the	DET
ap-180	26	72	function	function	NOUN
ap-180	26	73	�	�	NOUN
ap-180	26	74	0(p	0(p	NOUN
ap-180	26	75	)	)	PUNCT
ap-180	26	76	.	.	PUNCT
ap-180	27	1	it	it	PRON
ap-180	27	2	is	be	AUX
ap-180	27	3	seen	see	VERB
ap-180	27	4	,	,	PUNCT
ap-180	27	5	that	that	SCONJ
ap-180	27	6	the	the	DET
ap-180	27	7	smallest	small	ADJ
ap-180	27	8	p	p	X
ap-180	27	9	satisfying	satisfy	VERB
ap-180	27	10	(	(	PUNCT
ap-180	27	11	5	5	NUM
ap-180	27	12	)	)	PUNCT
ap-180	27	13	is	be	AUX
ap-180	27	14	the	the	DET
ap-180	27	15	smallest	small	ADJ
ap-180	27	16	eigenvalue	eigenvalue	ADJ
ap-180	27	17	p1	p1	NOUN
ap-180	27	18	of	of	ADP
ap-180	27	19	the	the	DET
ap-180	27	20	linear	linear	ADJ
ap-180	27	21	problem	problem	NOUN
ap-180	27	22	with	with	ADP
ap-180	27	23	corresponding	corresponding	ADJ
ap-180	27	24	�	�	PROPN
ap-180	27	25	0=0	0=0	NUM
ap-180	27	26	.	.	PUNCT
ap-180	28	1	the	the	DET
ap-180	28	2	dependence	dependence	NOUN
ap-180	28	3	of	of	ADP
ap-180	28	4	the	the	DET
ap-180	28	5	maximum	maximum	ADJ
ap-180	28	6	deflections	deflection	NOUN
ap-180	28	7	w0	w0	PROPN
ap-180	28	8	w(0	w(0	PROPN
ap-180	28	9	)	)	PUNCT
ap-180	28	10	on	on	ADP
ap-180	28	11	the	the	DET
ap-180	28	12	force	force	NOUN
ap-180	28	13	p	p	NOUN
ap-180	28	14	,	,	PUNCT
ap-180	28	15	resp	resp	NOUN
ap-180	28	16	.	.	PUNCT
ap-180	29	1	p	p	NOUN
ap-180	29	2	is	be	AUX
ap-180	29	3	given	give	VERB
ap-180	29	4	by	by	ADP
ap-180	29	5	the	the	DET
ap-180	29	6	formula	formula	NOUN
ap-180	29	7	�	�	PROPN
ap-180	29	8	�	�	PROPN
ap-180	29	9	w	w	PROPN
ap-180	29	10	p	p	X
ap-180	29	11	p	p	X
ap-180	29	12	0	0	NUM
ap-180	29	13	02	02	NUM
ap-180	29	14	2	2	NUM
ap-180	29	15	�	�	PROPN
ap-180	29	16	sin	sin	PROPN
ap-180	29	17	�	�	PROPN
ap-180	29	18	,	,	PUNCT
ap-180	29	19	which	which	PRON
ap-180	29	20	is	be	AUX
ap-180	29	21	obtained	obtain	VERB
ap-180	29	22	by	by	ADP
ap-180	29	23	integrating	integrate	VERB
ap-180	29	24	the	the	DET
ap-180	29	25	second	second	ADJ
ap-180	29	26	equality	equality	NOUN
ap-180	29	27	of	of	ADP
ap-180	29	28	(	(	PUNCT
ap-180	29	29	1	1	NUM
ap-180	29	30	)	)	PUNCT
ap-180	29	31	with	with	ADP
ap-180	29	32	the	the	DET
ap-180	29	33	use	use	NOUN
ap-180	29	34	of	of	ADP
ap-180	29	35	(	(	PUNCT
ap-180	29	36	3	3	NUM
ap-180	29	37	)	)	PUNCT
ap-180	29	38	and	and	CCONJ
ap-180	29	39	the	the	DET
ap-180	29	40	fact	fact	NOUN
ap-180	30	1	d	d	X
ap-180	30	2	d	d	NOUN
ap-180	31	1	d	d	PROPN
ap-180	31	2	d	d	PROPN
ap-180	31	3	d	d	PROPN
ap-180	31	4	d	d	PROPN
ap-180	31	5	d	d	PROPN
ap-180	31	6	d	d	X
ap-180	31	7	w	w	PROPN
ap-180	31	8	s	s	PROPN
ap-180	31	9	w	w	PROPN
ap-180	31	10	s	s	PROPN
ap-180	31	11	w	w	PROPN
ap-180	31	12	�	�	PROPN
ap-180	31	13	�	�	PROPN
ap-180	31	14	�	�	PROPN
ap-180	31	15	�	�	PROPN
ap-180	31	16	�	�	PROPN
ap-180	31	17	�	�	PROPN
ap-180	31	18	�	�	PROPN
ap-180	31	19	�	�	PROPN
ap-180	31	20	1	1	NUM
ap-180	31	21	and	and	CCONJ
ap-180	31	22	limiting	limit	VERB
ap-180	31	23	the	the	DET
ap-180	31	24	result	result	NOUN
ap-180	31	25	for	for	ADP
ap-180	31	26	�	�	PROPN
ap-180	31	27	�	�	PROPN
ap-180	31	28	0	0	NUM
ap-180	31	29	,	,	PUNCT
ap-180	31	30	s	s	PART
ap-180	31	31	0	0	NUM
ap-180	31	32	(	(	PUNCT
ap-180	31	33	see	see	VERB
ap-180	31	34	the	the	DET
ap-180	31	35	fig	fig	NOUN
ap-180	31	36	.	.	PUNCT
ap-180	32	1	1	1	NUM
ap-180	32	2	)	)	PUNCT
ap-180	32	3	.	.	PUNCT
ap-180	33	1	the	the	DET
ap-180	33	2	dependence	dependence	NOUN
ap-180	33	3	of	of	ADP
ap-180	33	4	the	the	DET
ap-180	33	5	ratio	ratio	NOUN
ap-180	33	6	�	�	PROPN
ap-180	33	7	�	�	PROPN
ap-180	33	8	�	�	PROPN
ap-180	33	9	�	�	PROPN
ap-180	33	10	r	r	NOUN
ap-180	33	11	p	p	NOUN
ap-180	33	12	l	l	NOUN
ap-180	33	13	x	x	PUNCT
ap-180	33	14	l	l	NOUN
ap-180	33	15	l	l	X
ap-180	33	16	�	�	PROPN
ap-180	33	17	�	�	PROPN
ap-180	33	18	on	on	ADP
ap-180	33	19	p	p	PROPN
ap-180	33	20	is	be	AUX
ap-180	33	21	given	give	VERB
ap-180	33	22	by	by	ADP
ap-180	33	23	the	the	DET
ap-180	33	24	following	follow	VERB
ap-180	33	25	formula	formula	NOUN
ap-180	33	26	�	�	PROPN
ap-180	33	27	�	�	PROPN
ap-180	33	28	r	r	PROPN
ap-180	33	29	p	p	PROPN
ap-180	33	30	lp	lp	PROPN
ap-180	33	31	�	�	PROPN
ap-180	33	32	�	�	PROPN
ap-180	33	33	�	�	PROPN
ap-180	33	34	�	�	PROPN
ap-180	33	35	�	�	PROPN
ap-180	33	36	�	�	PROPN
ap-180	33	37	�	�	PROPN
ap-180	33	38	�	�	PROPN
ap-180	33	39	�	�	PROPN
ap-180	33	40	�	�	PROPN
ap-180	33	41	�	�	PROPN
ap-180	33	42	�	�	PROPN
ap-180	33	43	�	�	PROPN
ap-180	33	44	�	�	PROPN
ap-180	33	45	1	1	NUM
ap-180	33	46	1	1	NUM
ap-180	33	47	2	2	NUM
ap-180	33	48	1	1	NUM
ap-180	33	49	2	2	NUM
ap-180	33	50	1	1	NUM
ap-180	33	51	1	1	NUM
ap-180	33	52	2	2	NUM
ap-180	33	53	0	0	NUM
ap-180	33	54	2	2	NUM
ap-180	33	55	0	0	NUM
ap-180	33	56	2	2	NUM
ap-180	33	57	sin	sin	NOUN
ap-180	33	58	sin	sin	NOUN
ap-180	33	59	sin	sin	NOUN
ap-180	33	60	sin	sin	PROPN
ap-180	33	61	�	�	PROPN
ap-180	33	62	�	�	PROPN
ap-180	33	63	�	�	PROPN
ap-180	33	64	�	�	PROPN
ap-180	33	65	�	�	PROPN
ap-180	33	66	�	�	PROPN
ap-180	33	67	�	�	PROPN
ap-180	33	68	�	�	PROPN
ap-180	33	69	�	�	PROPN
ap-180	33	70	�	�	PROPN
ap-180	33	71	�	�	PROPN
ap-180	33	72	�	�	PROPN
ap-180	33	73	d	d	PROPN
ap-180	33	74	�	�	PROPN
ap-180	33	75	�	�	PROPN
ap-180	33	76	0	0	NUM
ap-180	33	77	2	2	NUM
ap-180	33	78	,	,	PUNCT
ap-180	33	79	which	which	PRON
ap-180	33	80	is	be	AUX
ap-180	33	81	calculated	calculate	VERB
ap-180	33	82	(	(	PUNCT
ap-180	33	83	similarly	similarly	ADV
ap-180	33	84	as	as	ADP
ap-180	33	85	w0	w0	NOUN
ap-180	33	86	)	)	PUNCT
ap-180	33	87	integrating	integrate	VERB
ap-180	33	88	the	the	DET
ap-180	33	89	equality	equality	NOUN
ap-180	33	90	�	�	PROPN
ap-180	33	91	�	�	PROPN
ap-180	33	92	d	d	PROPN
ap-180	33	93	d	d	X
ap-180	33	94	x	x	X
ap-180	33	95	s	s	PROPN
ap-180	33	96	s	s	X
ap-180	33	97	�	�	PROPN
ap-180	33	98	cos	cos	PROPN
ap-180	33	99	�	�	PROPN
ap-180	33	100	,	,	PUNCT
ap-180	33	101	and	and	CCONJ
ap-180	33	102	limiting	limit	VERB
ap-180	33	103	the	the	DET
ap-180	33	104	result	result	NOUN
ap-180	33	105	for	for	ADP
ap-180	33	106	�	�	PROPN
ap-180	33	107	�	�	PROPN
ap-180	33	108	�	�	PROPN
ap-180	33	109	,	,	PUNCT
ap-180	33	110	s	s	PART
ap-180	33	111	0	0	NUM
ap-180	33	112	(	(	PUNCT
ap-180	33	113	see	see	VERB
ap-180	33	114	fig	fig	NOUN
ap-180	33	115	.	.	PUNCT
ap-180	34	1	2	2	NUM
ap-180	34	2	)	)	PUNCT
ap-180	34	3	.	.	PUNCT
ap-180	35	1	two	two	NUM
ap-180	35	2	improvements	improvement	NOUN
ap-180	35	3	comparing	compare	VERB
ap-180	35	4	with	with	ADP
ap-180	35	5	the	the	DET
ap-180	35	6	linear	linear	PROPN
ap-180	35	7	theory	theory	NOUN
ap-180	35	8	are	be	AUX
ap-180	35	9	evident	evident	ADJ
ap-180	35	10	:	:	PUNCT
ap-180	35	11	1	1	X
ap-180	35	12	.	.	X
ap-180	35	13	if	if	SCONJ
ap-180	35	14	p	p	NOUN
ap-180	35	15	tends	tend	VERB
ap-180	35	16	to	to	ADP
ap-180	35	17	the	the	DET
ap-180	35	18	first	first	ADJ
ap-180	35	19	eigenvalue	eigenvalue	PROPN
ap-180	35	20	p1	p1	NOUN
ap-180	35	21	=	=	SYM
ap-180	35	22	p	p	PROPN
ap-180	35	23	/2l	/2l	PUNCT
ap-180	35	24	of	of	ADP
ap-180	35	25	the	the	DET
ap-180	35	26	linear	linear	ADJ
ap-180	35	27	problem	problem	NOUN
ap-180	35	28	from	from	ADP
ap-180	35	29	the	the	DET
ap-180	35	30	right	right	ADJ
ap-180	35	31	hand	hand	NOUN
ap-180	35	32	side	side	NOUN
ap-180	35	33	of	of	ADP
ap-180	35	34	the	the	DET
ap-180	35	35	interval	interval	NOUN
ap-180	35	36	,	,	PUNCT
ap-180	35	37	the	the	DET
ap-180	35	38	maximum	maximum	ADJ
ap-180	35	39	deflection	deflection	NOUN
ap-180	35	40	w0	w0	PROPN
ap-180	35	41	tends	tend	VERB
ap-180	35	42	to	to	ADP
ap-180	35	43	zero	zero	NUM
ap-180	35	44	,	,	PUNCT
ap-180	35	45	whereas	whereas	SCONJ
ap-180	35	46	no	no	DET
ap-180	35	47	deflection	deflection	NOUN
ap-180	35	48	of	of	ADP
ap-180	35	49	the	the	DET
ap-180	35	50	rod	rod	NOUN
ap-180	35	51	exists	exist	VERB
ap-180	35	52	for	for	ADP
ap-180	35	53	p	p	PROPN
ap-180	35	54	�	�	PROPN
ap-180	35	55	p1	p1	PROPN
ap-180	35	56	.	.	PROPN
ap-180	36	1	2	2	NUM
ap-180	36	2	.	.	X
ap-180	36	3	for	for	ADP
ap-180	36	4	every	every	DET
ap-180	36	5	p	p	PROPN
ap-180	36	6	�	�	PROPN
ap-180	36	7	p1	p1	PROPN
ap-180	36	8	there	there	ADV
ap-180	36	9	exists	exist	VERB
ap-180	36	10	the	the	DET
ap-180	36	11	unique	unique	ADJ
ap-180	36	12	solution	solution	NOUN
ap-180	36	13	w	w	PROPN
ap-180	36	14	(	(	PUNCT
ap-180	36	15	�	�	PROPN
ap-180	36	16	)	)	PUNCT
ap-180	36	17	,	,	PUNCT
ap-180	36	18	�	�	PROPN
ap-180	36	19	(	(	PUNCT
ap-180	36	20	0	0	NUM
ap-180	36	21	,	,	PUNCT
ap-180	36	22	�	�	NOUN
ap-180	36	23	0	0	NUM
ap-180	36	24	]	]	PUNCT
ap-180	36	25	with	with	ADP
ap-180	36	26	maximum	maximum	ADJ
ap-180	36	27	deflection	deflection	NOUN
ap-180	36	28	w0(p	w0(p	NUM
ap-180	36	29	)	)	PUNCT
ap-180	36	30	.	.	PUNCT
ap-180	37	1	the	the	DET
ap-180	37	2	same	same	ADJ
ap-180	37	3	considerations	consideration	NOUN
ap-180	37	4	hold	hold	VERB
ap-180	37	5	for	for	ADP
ap-180	37	6	pk	pk	NOUN
ap-180	37	7	,	,	PUNCT
ap-180	37	8	k	k	PROPN
ap-180	37	9	=	=	SYM
ap-180	37	10	2	2	NUM
ap-180	37	11	,	,	PUNCT
ap-180	37	12	3	3	NUM
ap-180	37	13	,	,	PUNCT
ap-180	37	14	…	…	PUNCT
ap-180	37	15	3	3	NUM
ap-180	37	16	critical	critical	ADJ
ap-180	37	17	lengths	length	NOUN
ap-180	37	18	of	of	ADP
ap-180	37	19	a	a	DET
ap-180	37	20	column	column	NOUN
ap-180	37	21	bent	bent	ADJ
ap-180	37	22	with	with	ADP
ap-180	37	23	its	its	PRON
ap-180	37	24	own	own	ADJ
ap-180	37	25	weight	weight	NOUN
ap-180	37	26	–	–	PUNCT
ap-180	37	27	nonlinear	nonlinear	ADJ
ap-180	37	28	formulation	formulation	NOUN
ap-180	37	29	and	and	CCONJ
ap-180	37	30	some	some	DET
ap-180	37	31	results	result	NOUN
ap-180	37	32	of	of	ADP
ap-180	37	33	linear	linear	ADJ
ap-180	37	34	theory	theory	NOUN
ap-180	37	35	in	in	ADP
ap-180	37	36	the	the	DET
ap-180	37	37	further	further	ADJ
ap-180	37	38	discussion	discussion	NOUN
ap-180	37	39	we	we	PRON
ap-180	37	40	answer	answer	VERB
ap-180	37	41	the	the	DET
ap-180	37	42	question	question	NOUN
ap-180	37	43	which	which	DET
ap-180	37	44	length	length	NOUN
ap-180	37	45	of	of	ADP
ap-180	37	46	a	a	DET
ap-180	37	47	homogeneous	homogeneous	ADJ
ap-180	37	48	column	column	NOUN
ap-180	37	49	of	of	ADP
ap-180	37	50	a	a	DET
ap-180	37	51	constant	constant	ADJ
ap-180	37	52	cross	cross	NOUN
ap-180	37	53	section	section	NOUN
ap-180	37	54	is	be	AUX
ap-180	37	55	bent	bent	ADJ
ap-180	37	56	with	with	ADP
ap-180	37	57	its	its	PRON
ap-180	37	58	own	own	ADJ
ap-180	37	59	weight	weight	NOUN
ap-180	37	60	only	only	ADV
ap-180	37	61	,	,	PUNCT
ap-180	37	62	i.e.	i.e.	X
ap-180	37	63	,	,	PUNCT
ap-180	37	64	finding	find	VERB
ap-180	37	65	the	the	DET
ap-180	37	66	smallest	small	ADJ
ap-180	37	67	l	l	NOUN
ap-180	37	68	,	,	PUNCT
ap-180	37	69	for	for	ADP
ap-180	37	70	which	which	PRON
ap-180	37	71	there	there	PRON
ap-180	37	72	exists	exist	VERB
ap-180	37	73	nonzero	nonzero	PROPN
ap-180	37	74	deflection	deflection	PROPN
ap-180	37	75	w	w	PROPN
ap-180	37	76	of	of	ADP
ap-180	37	77	the	the	DET
ap-180	37	78	column	column	NOUN
ap-180	37	79	.	.	PUNCT
ap-180	38	1	let	let	VERB
ap-180	38	2	us	we	PRON
ap-180	38	3	consider	consider	VERB
ap-180	38	4	the	the	DET
ap-180	38	5	equality	equality	NOUN
ap-180	38	6	of	of	ADP
ap-180	38	7	the	the	DET
ap-180	38	8	moments	moment	NOUN
ap-180	38	9	in	in	ADP
ap-180	38	10	the	the	DET
ap-180	38	11	form	form	NOUN
ap-180	38	12	�	�	PROPN
ap-180	38	13	�	�	PROPN
ap-180	38	14	�	�	PROPN
ap-180	38	15	�	�	PROPN
ap-180	38	16	�	�	PROPN
ap-180	38	17	�	�	PROPN
ap-180	38	18	�	�	PROPN
ap-180	38	19	�	�	PROPN
ap-180	38	20	ei	ei	NOUN
ap-180	38	21	fs	fs	ADP
ap-180	38	22	w	w	PROPN
ap-180	38	23	s	s	PROPN
ap-180	38	24	w	w	PROPN
ap-180	38	25	s	s	PROPN
ap-180	38	26	,	,	PUNCT
ap-180	38	27	l	l	PROPN
ap-180	38	28	s	s	PROPN
ap-180	38	29	�	�	PROPN
ap-180	38	30	�	�	PROPN
ap-180	38	31	�	�	PROPN
ap-180	38	32	�	�	PROPN
ap-180	38	33	�	�	PROPN
ap-180	38	34	�	�	PROPN
ap-180	38	35	�	�	PROPN
ap-180	38	36	d	d	PROPN
ap-180	38	37	,	,	PUNCT
ap-180	38	38	0	0	NUM
ap-180	38	39	0	0	NUM
ap-180	38	40	,	,	PUNCT
ap-180	38	41	where	where	SCONJ
ap-180	38	42	f	f	PROPN
ap-180	38	43	is	be	AUX
ap-180	38	44	the	the	DET
ap-180	38	45	density	density	NOUN
ap-180	38	46	of	of	ADP
ap-180	38	47	the	the	DET
ap-180	38	48	column	column	NOUN
ap-180	38	49	and	and	CCONJ
ap-180	38	50	s	s	NOUN
ap-180	38	51	is	be	AUX
ap-180	38	52	its	its	PRON
ap-180	38	53	cross	cross	NOUN
ap-180	38	54	section	section	NOUN
ap-180	38	55	(	(	PUNCT
ap-180	38	56	the	the	DET
ap-180	38	57	other	other	ADJ
ap-180	38	58	notation	notation	NOUN
ap-180	38	59	coincides	coincide	VERB
ap-180	38	60	with	with	ADP
ap-180	38	61	that	that	PRON
ap-180	38	62	of	of	ADP
ap-180	38	63	part	part	NOUN
ap-180	38	64	1	1	NUM
ap-180	38	65	)	)	PUNCT
ap-180	38	66	.	.	PUNCT
ap-180	39	1	differentiating	differentiate	VERB
ap-180	39	2	the	the	DET
ap-180	39	3	equation	equation	NOUN
ap-180	39	4	and	and	CCONJ
ap-180	39	5	substituting	substitute	VERB
ap-180	39	6	the	the	DET
ap-180	39	7	relations	relation	NOUN
ap-180	39	8	�	�	PROPN
ap-180	39	9	�	�	PROPN
ap-180	39	10	1	1	NUM
ap-180	39	11	�	�	PROPN
ap-180	39	12	�	�	PROPN
ap-180	39	13	�	�	PROPN
ap-180	39	14	�	�	PROPN
ap-180	39	15	�	�	PROPN
ap-180	39	16	�	�	PROPN
ap-180	40	1	d	d	PROPN
ap-180	40	2	d	d	PROPN
ap-180	40	3	d	d	X
ap-180	40	4	ds	ds	PROPN
ap-180	40	5	w	w	PROPN
ap-180	40	6	s	s	PROPN
ap-180	40	7	s	s	NOUN
ap-180	40	8	,	,	PUNCT
ap-180	40	9	sin	sin	VERB
ap-180	40	10	into	into	ADP
ap-180	40	11	it	it	PRON
ap-180	40	12	,	,	PUNCT
ap-180	40	13	we	we	PRON
ap-180	40	14	get	get	VERB
ap-180	40	15	�	�	PROPN
ap-180	40	16	�	�	PROPN
ap-180	40	17	d	d	PROPN
ap-180	40	18	d	d	PROPN
ap-180	40	19	2	2	NUM
ap-180	40	20	�	�	PROPN
ap-180	40	21	�	�	PROPN
ap-180	40	22	s	s	PART
ap-180	40	23	fs	fs	ADP
ap-180	40	24	ei	ei	NOUN
ap-180	40	25	s	s	PROPN
ap-180	40	26	s2	s2	PROPN
ap-180	40	27	0	0	NUM
ap-180	40	28	�	�	PROPN
ap-180	40	29	�	�	PROPN
ap-180	40	30	sin	sin	NOUN
ap-180	40	31	.	.	PUNCT
ap-180	41	1	to	to	PART
ap-180	41	2	eliminate	eliminate	VERB
ap-180	41	3	the	the	DET
ap-180	41	4	unknown	unknown	ADJ
ap-180	41	5	length	length	NOUN
ap-180	41	6	l	l	NOUN
ap-180	41	7	of	of	ADP
ap-180	41	8	the	the	DET
ap-180	41	9	column	column	NOUN
ap-180	41	10	,	,	PUNCT
ap-180	41	11	we	we	PRON
ap-180	41	12	transform	transform	VERB
ap-180	41	13	s	s	PRON
ap-180	41	14	to	to	ADP
ap-180	41	15	the	the	DET
ap-180	41	16	new	new	ADJ
ap-180	41	17	variable	variable	NOUN
ap-180	41	18	s	s	PART
ap-180	41	19	/	/	SYM
ap-180	41	20	l	l	NOUN
ap-180	41	21	(	(	PUNCT
ap-180	41	22	denoting	denote	VERB
ap-180	41	23	it	it	PRON
ap-180	41	24	again	again	ADV
ap-180	41	25	s	s	VERB
ap-180	41	26	)	)	PUNCT
ap-180	41	27	in	in	ADP
ap-180	41	28	the	the	DET
ap-180	41	29	last	last	ADJ
ap-180	41	30	equation	equation	NOUN
ap-180	41	31	and	and	CCONJ
ap-180	41	32	we	we	PRON
ap-180	41	33	denote	denote	VERB
ap-180	41	34	the	the	DET
ap-180	41	35	unknown	unknown	ADJ
ap-180	41	36	function	function	NOUN
ap-180	41	37	�	�	PROPN
ap-180	41	38	in	in	ADP
ap-180	41	39	the	the	DET
ap-180	41	40	new	new	ADJ
ap-180	41	41	variable	variable	NOUN
ap-180	41	42	by	by	ADP
ap-180	41	43	u(s	u(s	PROPN
ap-180	41	44	)	)	PUNCT
ap-180	41	45	.	.	PUNCT
ap-180	42	1	thus	thus	ADV
ap-180	42	2	,	,	PUNCT
ap-180	42	3	we	we	PRON
ap-180	42	4	get	get	VERB
ap-180	42	5	the	the	DET
ap-180	42	6	equation	equation	NOUN
ap-180	42	7	�	�	PROPN
ap-180	42	8	�	�	PROPN
ap-180	42	9	�	�	PROPN
ap-180	42	10	�	�	PROPN
ap-180	42	11	�	�	PROPN
ap-180	42	12	�	�	PROPN
ap-180	42	13	d	d	PROPN
ap-180	42	14	d	d	PROPN
ap-180	42	15	2	2	NUM
ap-180	42	16	2	2	NUM
ap-180	42	17	0	0	NUM
ap-180	42	18	0	0	NUM
ap-180	42	19	1	1	NUM
ap-180	42	20	u	u	NOUN
ap-180	42	21	s	s	PART
ap-180	42	22	s	s	X
ap-180	42	23	s	s	X
ap-180	42	24	u	u	NOUN
ap-180	42	25	s	s	NOUN
ap-180	42	26	s	s	PROPN
ap-180	42	27	�	�	PROPN
ap-180	42	28	�	�	PROPN
ap-180	42	29	�	�	PROPN
ap-180	42	30	�	�	PROPN
ap-180	42	31	sin	sin	NOUN
ap-180	42	32	,	,	PUNCT
ap-180	42	33	,	,	PUNCT
ap-180	42	34	,	,	PUNCT
ap-180	42	35	(	(	PUNCT
ap-180	42	36	6	6	X
ap-180	42	37	)	)	PUNCT
ap-180	42	38	acta	acta	PROPN
ap-180	42	39	polytechnica	polytechnica	PROPN
ap-180	42	40	vol	vol	NOUN
ap-180	42	41	.	.	PUNCT
ap-180	43	1	41	41	NUM
ap-180	43	2	no.1/2001	no.1/2001	NOUN
ap-180	43	3	©	©	PROPN
ap-180	43	4	czech	czech	PROPN
ap-180	43	5	technical	technical	PROPN
ap-180	43	6	university	university	PROPN
ap-180	43	7	publishing	publishing	NOUN
ap-180	43	8	house	house	NOUN
ap-180	43	9	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-180	43	10	19	19	NUM
ap-180	43	11	fig	fig	NOUN
ap-180	43	12	.	.	PUNCT
ap-180	44	1	1	1	NUM
ap-180	44	2	:	:	PUNCT
ap-180	44	3	dependence	dependence	NOUN
ap-180	44	4	of	of	ADP
ap-180	44	5	the	the	DET
ap-180	44	6	maximum	maximum	ADJ
ap-180	44	7	deflections	deflection	NOUN
ap-180	44	8	w	w	VERB
ap-180	44	9	on	on	ADP
ap-180	44	10	the	the	DET
ap-180	44	11	force	force	NOUN
ap-180	44	12	p	p	X
ap-180	44	13	(	(	PUNCT
ap-180	44	14	l	l	NOUN
ap-180	44	15	=	=	SYM
ap-180	44	16	�	�	PROPN
ap-180	44	17	/2	/2	NUM
ap-180	44	18	)	)	PUNCT
ap-180	44	19	fig	fig	NOUN
ap-180	44	20	.	.	PUNCT
ap-180	45	1	2	2	NUM
ap-180	45	2	:	:	PUNCT
ap-180	45	3	dependence	dependence	NOUN
ap-180	45	4	of	of	ADP
ap-180	45	5	the	the	DET
ap-180	45	6	relative	relative	ADJ
ap-180	45	7	extension	extension	NOUN
ap-180	45	8	r	r	NOUN
ap-180	45	9	on	on	ADP
ap-180	45	10	the	the	DET
ap-180	45	11	force	force	NOUN
ap-180	45	12	p	p	X
ap-180	45	13	(	(	PUNCT
ap-180	45	14	l	l	NOUN
ap-180	45	15	=	=	SYM
ap-180	45	16	�	�	PROPN
ap-180	45	17	/2	/2	NUM
ap-180	45	18	)	)	PUNCT
ap-180	45	19	where	where	SCONJ
ap-180	45	20	�	�	PROPN
ap-180	45	21	�	�	PROPN
ap-180	45	22	fsl	fsl	PROPN
ap-180	45	23	ei	ei	ADP
ap-180	45	24	3	3	NUM
ap-180	45	25	(	(	PUNCT
ap-180	45	26	7	7	NUM
ap-180	45	27	)	)	PUNCT
ap-180	45	28	is	be	AUX
ap-180	45	29	an	an	DET
ap-180	45	30	unknown	unknown	ADJ
ap-180	45	31	eigenvalue	eigenvalue	NOUN
ap-180	45	32	of	of	ADP
ap-180	45	33	the	the	DET
ap-180	45	34	problem	problem	NOUN
ap-180	45	35	to	to	ADP
ap-180	45	36	equation	equation	NOUN
ap-180	45	37	(	(	PUNCT
ap-180	45	38	6	6	NUM
ap-180	45	39	)	)	PUNCT
ap-180	45	40	and	and	CCONJ
ap-180	45	41	to	to	ADP
ap-180	45	42	the	the	DET
ap-180	45	43	boundary	boundary	ADJ
ap-180	45	44	conditions	condition	NOUN
ap-180	45	45	�	�	PROPN
ap-180	45	46	�	�	PROPN
ap-180	45	47	�	�	PROPN
ap-180	45	48	�	�	PROPN
ap-180	45	49	�	�	PROPN
ap-180	45	50	�	�	PROPN
ap-180	45	51	�	�	PROPN
ap-180	45	52	u	u	NOUN
ap-180	45	53	u0	u0	ADJ
ap-180	45	54	0	0	NUM
ap-180	45	55	1	1	NUM
ap-180	45	56	0	0	NUM
ap-180	45	57	,	,	PUNCT
ap-180	45	58	.	.	PUNCT
ap-180	46	1	(	(	PUNCT
ap-180	46	2	8)	8)	NUM
ap-180	46	3	the	the	DET
ap-180	46	4	first	first	ADJ
ap-180	46	5	condition	condition	NOUN
ap-180	46	6	follows	follow	VERB
ap-180	46	7	from	from	ADP
ap-180	46	8	the	the	DET
ap-180	46	9	assumption	assumption	NOUN
ap-180	46	10	that	that	SCONJ
ap-180	46	11	upper	upper	ADJ
ap-180	46	12	end	end	NOUN
ap-180	46	13	of	of	ADP
ap-180	46	14	the	the	DET
ap-180	46	15	column	column	NOUN
ap-180	46	16	is	be	AUX
ap-180	46	17	free	free	ADJ
ap-180	46	18	of	of	ADP
ap-180	46	19	tension	tension	NOUN
ap-180	46	20	,	,	PUNCT
ap-180	46	21	i.e.	i.e.	X
ap-180	46	22	,	,	PUNCT
ap-180	46	23	1/	1/	NUM
ap-180	46	24	�	�	PROPN
ap-180	46	25	=	=	SYM
ap-180	46	26	0	0	NUM
ap-180	46	27	,	,	PUNCT
ap-180	46	28	and	and	CCONJ
ap-180	46	29	the	the	DET
ap-180	46	30	second	second	ADJ
ap-180	46	31	condition	condition	NOUN
ap-180	46	32	expresses	express	VERB
ap-180	46	33	the	the	DET
ap-180	46	34	fixed	fixed	ADJ
ap-180	46	35	end	end	NOUN
ap-180	46	36	at	at	ADP
ap-180	46	37	the	the	DET
ap-180	46	38	bottom	bottom	NOUN
ap-180	46	39	.	.	PUNCT
ap-180	47	1	in	in	ADP
ap-180	47	2	the	the	DET
ap-180	47	3	case	case	NOUN
ap-180	47	4	of	of	ADP
ap-180	47	5	small	small	ADJ
ap-180	47	6	deflections	deflection	NOUN
ap-180	47	7	,	,	PUNCT
ap-180	47	8	equation	equation	NOUN
ap-180	47	9	(	(	PUNCT
ap-180	47	10	6	6	NUM
ap-180	47	11	)	)	PUNCT
ap-180	47	12	may	may	AUX
ap-180	47	13	be	be	AUX
ap-180	47	14	linearized	linearize	VERB
ap-180	47	15	using	use	VERB
ap-180	47	16	the	the	DET
ap-180	47	17	following	follow	VERB
ap-180	47	18	approximations	approximation	NOUN
ap-180	47	19	�	�	PROPN
ap-180	47	20	�	�	PROPN
ap-180	47	21	sin	sin	NOUN
ap-180	47	22	.	.	PUNCT
ap-180	47	23	.	.	PUNCT
ap-180	48	1	�	�	PROPN
ap-180	48	2	�	�	PROPN
ap-180	48	3	�	�	PROPN
ap-180	48	4	�	�	PROPN
ap-180	48	5	�	�	PROPN
ap-180	48	6	w	w	PROPN
ap-180	48	7	s	s	PROPN
ap-180	48	8	.	.	PUNCT
ap-180	49	1	thus	thus	ADV
ap-180	49	2	,	,	PUNCT
ap-180	49	3	we	we	PRON
ap-180	49	4	get	get	VERB
ap-180	49	5	the	the	DET
ap-180	49	6	linear	linear	PROPN
ap-180	49	7	eigenvalue	eigenvalue	PROPN
ap-180	49	8	problem	problem	NOUN
ap-180	49	9	�	�	PROPN
ap-180	49	10	�	�	PROPN
ap-180	49	11	�	�	PROPN
ap-180	49	12	�	�	PROPN
ap-180	49	13	�	�	PROPN
ap-180	49	14	�	�	PROPN
ap-180	49	15	�	�	PROPN
ap-180	49	16	�	�	PROPN
ap-180	49	17	�	�	PROPN
ap-180	49	18	�	�	PROPN
ap-180	49	19	d	d	PROPN
ap-180	49	20	d	d	PROPN
ap-180	50	1	d	d	PROPN
ap-180	50	2	d	d	PROPN
ap-180	50	3	2	2	NUM
ap-180	50	4	2	2	NUM
ap-180	50	5	0	0	NUM
ap-180	50	6	0	0	NUM
ap-180	50	7	1	1	NUM
ap-180	50	8	0	0	NUM
ap-180	50	9	0	0	NUM
ap-180	50	10	1	1	NUM
ap-180	50	11	0	0	NUM
ap-180	50	12	v	v	NOUN
ap-180	50	13	s	s	AUX
ap-180	50	14	s	s	NOUN
ap-180	50	15	s	s	X
ap-180	50	16	v	v	NOUN
ap-180	50	17	s	s	NOUN
ap-180	50	18	s	s	NOUN
ap-180	50	19	v	v	NOUN
ap-180	50	20	s	s	NOUN
ap-180	50	21	v	v	PRON
ap-180	50	22	�	�	PROPN
ap-180	50	23	�	�	PROPN
ap-180	50	24	�	�	PROPN
ap-180	50	25	�	�	PROPN
ap-180	50	26	�	�	PROPN
ap-180	50	27	�	�	PROPN
ap-180	50	28	,	,	PUNCT
ap-180	50	29	,	,	PUNCT
ap-180	50	30	,	,	PUNCT
ap-180	50	31	,	,	PUNCT
ap-180	50	32	,	,	PUNCT
ap-180	50	33	(	(	PUNCT
ap-180	50	34	9	9	X
ap-180	50	35	)	)	PUNCT
ap-180	50	36	here	here	ADV
ap-180	50	37	we	we	PRON
ap-180	50	38	denoted	denote	VERB
ap-180	50	39	v(s	v(s	NOUN
ap-180	50	40	)	)	PUNCT
ap-180	50	41	=	=	SYM
ap-180	50	42	�	�	PROPN
ap-180	50	43	w	w	PROPN
ap-180	50	44	(	(	PUNCT
ap-180	50	45	s	s	NOUN
ap-180	50	46	)	)	PUNCT
ap-180	50	47	.	.	PUNCT
ap-180	51	1	the	the	DET
ap-180	51	2	solutions	solution	NOUN
ap-180	51	3	of	of	ADP
ap-180	51	4	(	(	PUNCT
ap-180	51	5	9	9	NUM
ap-180	51	6	)	)	PUNCT
ap-180	51	7	are	be	AUX
ap-180	51	8	the	the	DET
ap-180	51	9	discrete	discrete	ADJ
ap-180	51	10	set	set	NOUN
ap-180	51	11	of	of	ADP
ap-180	51	12	the	the	DET
ap-180	51	13	eigenvalues	eigenvalue	NOUN
ap-180	51	14	�	�	PROPN
ap-180	51	15	n	n	CCONJ
ap-180	51	16	nz	nz	PROPN
ap-180	51	17	n	n	CCONJ
ap-180	51	18	�	�	PROPN
ap-180	51	19	�	�	PROPN
ap-180	51	20	9	9	NUM
ap-180	51	21	4	4	NUM
ap-180	51	22	0	0	NUM
ap-180	51	23	1	1	NUM
ap-180	51	24	2	2	NUM
ap-180	51	25	,	,	PUNCT
ap-180	51	26	,	,	PUNCT
ap-180	51	27	,	,	PUNCT
ap-180	51	28	and	and	CCONJ
ap-180	51	29	the	the	DET
ap-180	51	30	corresponding	correspond	VERB
ap-180	51	31	eigenfunctions	eigenfunction	NOUN
ap-180	51	32	�	�	PROPN
ap-180	51	33	�	�	PROPN
ap-180	51	34	�	�	PROPN
ap-180	51	35	�	�	PROPN
ap-180	51	36	v	v	NOUN
ap-180	51	37	s	s	PART
ap-180	51	38	c	c	NOUN
ap-180	51	39	s	s	PROPN
ap-180	51	40	j	j	PROPN
ap-180	51	41	z	z	PROPN
ap-180	51	42	s	s	PROPN
ap-180	51	43	nn	nn	PROPN
ap-180	51	44	n	n	CCONJ
ap-180	51	45	�	�	PROPN
ap-180	51	46	�	�	PROPN
ap-180	51	47	�	�	PROPN
ap-180	51	48	1	1	NUM
ap-180	51	49	3	3	NUM
ap-180	51	50	3	3	NUM
ap-180	51	51	2	2	NUM
ap-180	51	52	0	0	NUM
ap-180	51	53	1	1	NUM
ap-180	51	54	,	,	PUNCT
ap-180	51	55	,	,	PUNCT
ap-180	51	56	,	,	PUNCT
ap-180	51	57	where	where	SCONJ
ap-180	51	58	zn	zn	PROPN
ap-180	51	59	(	(	PUNCT
ap-180	51	60	n	n	NOUN
ap-180	51	61	=	=	SYM
ap-180	51	62	0	0	NUM
ap-180	51	63	,	,	PUNCT
ap-180	51	64	1	1	NUM
ap-180	51	65	,	,	PUNCT
ap-180	51	66	…	…	PUNCT
ap-180	51	67	)	)	PUNCT
ap-180	51	68	are	be	AUX
ap-180	51	69	all	all	DET
ap-180	51	70	the	the	DET
ap-180	51	71	roots	root	NOUN
ap-180	51	72	of	of	ADP
ap-180	51	73	the	the	DET
ap-180	51	74	bessel	bessel	NOUN
ap-180	51	75	function	function	NOUN
ap-180	51	76	�	�	PROPN
ap-180	51	77	�	�	PROPN
ap-180	51	78	j	j	PROPN
ap-180	51	79	z	z	PROPN
ap-180	51	80	�	�	PROPN
ap-180	51	81	1	1	NUM
ap-180	51	82	3	3	NUM
ap-180	51	83	and	and	CCONJ
ap-180	51	84	c	c	PROPN
ap-180	51	85	is	be	AUX
ap-180	51	86	an	an	DET
ap-180	51	87	arbitrary	arbitrary	ADJ
ap-180	51	88	constant	constant	ADJ
ap-180	51	89	.	.	PUNCT
ap-180	52	1	the	the	DET
ap-180	52	2	first	first	ADJ
ap-180	52	3	three	three	NUM
ap-180	52	4	eigenfunctions	eigenfunction	NOUN
ap-180	52	5	v0	v0	NOUN
ap-180	52	6	,	,	PUNCT
ap-180	52	7	v1	v1	NOUN
ap-180	52	8	,	,	PUNCT
ap-180	52	9	v2	v2	PROPN
ap-180	52	10	of	of	ADP
ap-180	52	11	the	the	DET
ap-180	52	12	problem	problem	NOUN
ap-180	52	13	(	(	PUNCT
ap-180	52	14	where	where	SCONJ
ap-180	52	15	c	c	PROPN
ap-180	52	16	is	be	AUX
ap-180	52	17	chosen	choose	VERB
ap-180	52	18	in	in	ADP
ap-180	52	19	such	such	DET
ap-180	52	20	a	a	DET
ap-180	52	21	way	way	NOUN
ap-180	52	22	that	that	PRON
ap-180	52	23	vi	vi	PROPN
ap-180	52	24	(	(	PUNCT
ap-180	52	25	0	0	NUM
ap-180	52	26	)	)	PUNCT
ap-180	52	27	=	=	SYM
ap-180	53	1	1	1	NUM
ap-180	53	2	,	,	PUNCT
ap-180	53	3	i	i	PRON
ap-180	53	4	=	=	NOUN
ap-180	53	5	0	0	NUM
ap-180	53	6	,	,	PUNCT
ap-180	53	7	1	1	NUM
ap-180	53	8	,	,	PUNCT
ap-180	53	9	2	2	NUM
ap-180	53	10	)	)	PUNCT
ap-180	53	11	are	be	AUX
ap-180	53	12	given	give	VERB
ap-180	53	13	in	in	ADP
ap-180	53	14	fig	fig	NOUN
ap-180	53	15	.	.	PUNCT
ap-180	54	1	3	3	NUM
ap-180	54	2	,	,	PUNCT
ap-180	54	3	whereas	whereas	SCONJ
ap-180	54	4	the	the	DET
ap-180	54	5	corresponding	corresponding	ADJ
ap-180	54	6	deflections	deflection	NOUN
ap-180	54	7	w0	w0	PROPN
ap-180	54	8	,	,	PUNCT
ap-180	54	9	w1	w1	NOUN
ap-180	54	10	,	,	PUNCT
ap-180	54	11	w2	w2	NOUN
ap-180	54	12	are	be	AUX
ap-180	54	13	drawn	draw	VERB
ap-180	54	14	in	in	ADP
ap-180	54	15	fig	fig	NOUN
ap-180	54	16	.	.	PUNCT
ap-180	55	1	4	4	X
ap-180	55	2	.	.	X
ap-180	55	3	the	the	DET
ap-180	55	4	critical	critical	ADJ
ap-180	55	5	lengths	length	NOUN
ap-180	55	6	of	of	ADP
ap-180	55	7	the	the	DET
ap-180	55	8	column	column	NOUN
ap-180	55	9	are	be	AUX
ap-180	55	10	determined	determine	VERB
ap-180	55	11	by	by	ADP
ap-180	55	12	the	the	DET
ap-180	55	13	eigenvalues	eigenvalue	NOUN
ap-180	55	14	�	�	NOUN
ap-180	55	15	n	n	NUM
ap-180	55	16	and	and	CCONJ
ap-180	55	17	the	the	DET
ap-180	55	18	relation	relation	NOUN
ap-180	55	19	(	(	PUNCT
ap-180	55	20	7	7	NUM
ap-180	55	21	)	)	PUNCT
ap-180	55	22	,	,	PUNCT
ap-180	55	23	i.e.	i.e.	X
ap-180	55	24	,	,	PUNCT
ap-180	55	25	l	l	NOUN
ap-180	55	26	eiz	eiz	PROPN
ap-180	55	27	fsn	fsn	PROPN
ap-180	55	28	n3	n3	PROPN
ap-180	55	29	29	29	NUM
ap-180	55	30	4	4	NUM
ap-180	55	31	�	�	PROPN
ap-180	55	32	.	.	PUNCT
ap-180	56	1	the	the	DET
ap-180	56	2	length	length	NOUN
ap-180	56	3	for	for	ADP
ap-180	56	4	which	which	PRON
ap-180	56	5	the	the	DET
ap-180	56	6	homogeneous	homogeneous	ADJ
ap-180	56	7	column	column	NOUN
ap-180	56	8	loses	lose	VERB
ap-180	56	9	its	its	PRON
ap-180	56	10	stability	stability	NOUN
ap-180	56	11	(	(	PUNCT
ap-180	56	12	i.e.	i.e.	X
ap-180	56	13	,	,	PUNCT
ap-180	56	14	nonzero	nonzero	ADJ
ap-180	56	15	deflection	deflection	NOUN
ap-180	56	16	of	of	ADP
ap-180	56	17	the	the	DET
ap-180	56	18	column	column	NOUN
ap-180	56	19	exists	exist	VERB
ap-180	56	20	without	without	ADP
ap-180	56	21	any	any	DET
ap-180	56	22	force	force	NOUN
ap-180	56	23	apart	apart	ADV
ap-180	56	24	from	from	ADP
ap-180	56	25	its	its	PRON
ap-180	56	26	own	own	ADJ
ap-180	56	27	weight	weight	NOUN
ap-180	56	28	)	)	PUNCT
ap-180	56	29	,	,	PUNCT
ap-180	56	30	l	l	NOUN
ap-180	56	31	eiz	eiz	AUX
ap-180	56	32	fs0	fs0	NOUN
ap-180	56	33	0	0	NUM
ap-180	56	34	2	2	NUM
ap-180	56	35	1	1	NUM
ap-180	56	36	3	3	NUM
ap-180	56	37	9	9	NUM
ap-180	56	38	4	4	NUM
ap-180	56	39	�	�	PROPN
ap-180	56	40	�	�	PROPN
ap-180	56	41	�	�	PROPN
ap-180	56	42	�	�	PROPN
ap-180	56	43	�	�	PROPN
ap-180	56	44	�	�	PROPN
ap-180	56	45	corresponds	correspond	VERB
ap-180	56	46	to	to	ADP
ap-180	56	47	the	the	DET
ap-180	56	48	smallest	small	ADJ
ap-180	56	49	eigenvalue	eigenvalue	PROPN
ap-180	56	50	�	�	PROPN
ap-180	56	51	�	�	PROPN
ap-180	56	52	of	of	ADP
ap-180	56	53	the	the	DET
ap-180	56	54	above	above	ADJ
ap-180	56	55	problem	problem	NOUN
ap-180	56	56	,	,	PUNCT
ap-180	56	57	where	where	SCONJ
ap-180	56	58	�	�	X
ap-180	56	59	0	0	SYM
ap-180	56	60	0	0	NUM
ap-180	56	61	29	29	NUM
ap-180	56	62	4	4	NUM
ap-180	56	63	7	7	NUM
ap-180	56	64	83734744	83734744	NUM
ap-180	56	65	�	�	PROPN
ap-180	56	66	�	�	PROPN
ap-180	56	67	z	z	PROPN
ap-180	56	68	.	.	PUNCT
ap-180	57	1	(	(	PUNCT
ap-180	57	2	10	10	NUM
ap-180	57	3	)	)	PUNCT
ap-180	57	4	and	and	CCONJ
ap-180	57	5	the	the	DET
ap-180	57	6	corresponding	corresponding	ADJ
ap-180	57	7	eigenfunction	eigenfunction	NOUN
ap-180	57	8	is	be	AUX
ap-180	57	9	of	of	ADP
ap-180	57	10	the	the	DET
ap-180	57	11	form	form	NOUN
ap-180	57	12	�	�	PROPN
ap-180	57	13	�	�	PROPN
ap-180	57	14	�	�	PROPN
ap-180	57	15	�	�	PROPN
ap-180	57	16	�	�	PROPN
ap-180	57	17	�	�	PROPN
ap-180	57	18	v	v	NOUN
ap-180	57	19	s	s	NOUN
ap-180	57	20	s	s	PROPN
ap-180	57	21	j	j	PROPN
ap-180	57	22	s	s	PROPN
ap-180	57	23	s0	s0	PROPN
ap-180	57	24	1	1	NUM
ap-180	57	25	3	3	NUM
ap-180	57	26	3	3	NUM
ap-180	57	27	2186635086	2186635086	NUM
ap-180	57	28	0	0	NUM
ap-180	57	29	1	1	NUM
ap-180	57	30	�	�	PROPN
ap-180	57	31	�	�	PROPN
ap-180	57	32	�	�	PROPN
ap-180	57	33	.	.	PUNCT
ap-180	58	1	,	,	PUNCT
ap-180	58	2	,	,	PUNCT
ap-180	58	3	.	.	PUNCT
ap-180	59	1	(	(	PUNCT
ap-180	59	2	11	11	NUM
ap-180	59	3	)	)	PUNCT
ap-180	59	4	4	4	NUM
ap-180	59	5	the	the	DET
ap-180	59	6	solution	solution	NOUN
ap-180	59	7	of	of	ADP
ap-180	59	8	the	the	DET
ap-180	59	9	bifurcation	bifurcation	NOUN
ap-180	59	10	problem	problem	NOUN
ap-180	59	11	the	the	DET
ap-180	59	12	assumption	assumption	NOUN
ap-180	59	13	of	of	ADP
ap-180	59	14	small	small	ADJ
ap-180	59	15	deflections	deflection	NOUN
ap-180	59	16	,	,	PUNCT
ap-180	59	17	and	and	CCONJ
ap-180	59	18	then	then	ADV
ap-180	59	19	the	the	DET
ap-180	59	20	validity	validity	NOUN
ap-180	59	21	of	of	ADP
ap-180	59	22	linear	linear	PROPN
ap-180	59	23	theory	theory	NOUN
ap-180	59	24	,	,	PUNCT
ap-180	59	25	implies	imply	VERB
ap-180	59	26	the	the	DET
ap-180	59	27	same	same	ADJ
ap-180	59	28	insufficiency	insufficiency	NOUN
ap-180	59	29	as	as	ADP
ap-180	59	30	that	that	PRON
ap-180	59	31	mentioned	mention	VERB
ap-180	59	32	in	in	ADP
ap-180	59	33	the	the	DET
ap-180	59	34	introduction	introduction	NOUN
ap-180	59	35	.	.	PUNCT
ap-180	60	1	to	to	PART
ap-180	60	2	remove	remove	VERB
ap-180	60	3	it	it	PRON
ap-180	60	4	,	,	PUNCT
ap-180	60	5	we	we	PRON
ap-180	60	6	have	have	VERB
ap-180	60	7	to	to	PART
ap-180	60	8	take	take	VERB
ap-180	60	9	into	into	ADP
ap-180	60	10	account	account	NOUN
ap-180	60	11	the	the	DET
ap-180	60	12	nonlinear	nonlinear	ADJ
ap-180	60	13	equation	equation	NOUN
ap-180	60	14	(	(	PUNCT
ap-180	60	15	6	6	NUM
ap-180	60	16	)	)	PUNCT
ap-180	60	17	representing	represent	VERB
ap-180	60	18	together	together	ADV
ap-180	60	19	with	with	ADP
ap-180	60	20	the	the	DET
ap-180	60	21	boundary	boundary	ADJ
ap-180	60	22	conditions	condition	NOUN
ap-180	60	23	(	(	PUNCT
ap-180	60	24	8)	8)	NUM
ap-180	60	25	the	the	DET
ap-180	60	26	problem	problem	NOUN
ap-180	60	27	of	of	ADP
ap-180	60	28	a	a	DET
ap-180	60	29	bifurcation	bifurcation	NOUN
ap-180	60	30	of	of	ADP
ap-180	60	31	the	the	DET
ap-180	60	32	nonlinear	nonlinear	ADJ
ap-180	60	33	operator	operator	NOUN
ap-180	60	34	l(u	l(u	PROPN
ap-180	60	35	)	)	PUNCT
ap-180	60	36	–	–	PUNCT
ap-180	60	37	f(u	f(u	PROPN
ap-180	60	38	,	,	PUNCT
ap-180	60	39	t	t	PROPN
ap-180	60	40	)	)	PUNCT
ap-180	60	41	(	(	PUNCT
ap-180	60	42	given	give	VERB
ap-180	60	43	below	below	ADV
ap-180	60	44	)	)	PUNCT
ap-180	60	45	at	at	ADP
ap-180	60	46	the	the	DET
ap-180	60	47	point	point	NOUN
ap-180	60	48	[	[	X
ap-180	60	49	0	0	NUM
ap-180	60	50	,	,	PUNCT
ap-180	60	51	0	0	NUM
ap-180	60	52	]	]	PUNCT
ap-180	60	53	,	,	PUNCT
ap-180	60	54	(	(	PUNCT
ap-180	60	55	where	where	SCONJ
ap-180	60	56	l(0	l(0	PROPN
ap-180	60	57	)	)	PUNCT
ap-180	60	58	–	–	PUNCT
ap-180	60	59	f(0	f(0	NOUN
ap-180	60	60	,	,	PUNCT
ap-180	60	61	t	t	PROPN
ap-180	60	62	)	)	PUNCT
ap-180	60	63	=	=	NOUN
ap-180	60	64	0	0	NUM
ap-180	60	65	)	)	PUNCT
ap-180	60	66	,	,	PUNCT
ap-180	60	67	i.e.	i.e.	X
ap-180	60	68	,	,	PUNCT
ap-180	60	69	there	there	PRON
ap-180	60	70	exists	exist	VERB
ap-180	60	71	a	a	DET
ap-180	60	72	nonzero	nonzero	ADJ
ap-180	60	73	solution	solution	NOUN
ap-180	60	74	of	of	ADP
ap-180	60	75	the	the	DET
ap-180	60	76	equation	equation	NOUN
ap-180	60	77	(	(	PUNCT
ap-180	60	78	14	14	NUM
ap-180	60	79	)	)	PUNCT
ap-180	60	80	(	(	PUNCT
ap-180	60	81	see	see	VERB
ap-180	60	82	below	below	ADV
ap-180	60	83	)	)	PUNCT
ap-180	60	84	in	in	ADP
ap-180	60	85	every	every	DET
ap-180	60	86	neighborhood	neighborhood	NOUN
ap-180	60	87	of	of	ADP
ap-180	60	88	[	[	X
ap-180	60	89	0	0	NUM
ap-180	60	90	,	,	PUNCT
ap-180	60	91	0	0	NUM
ap-180	60	92	]	]	PUNCT
ap-180	60	93	.	.	PUNCT
ap-180	61	1	every	every	DET
ap-180	61	2	eigenvalue	eigenvalue	PROPN
ap-180	61	3	�	�	PROPN
ap-180	61	4	n	n	PART
ap-180	61	5	gives	give	VERB
ap-180	61	6	a	a	DET
ap-180	61	7	bifurcation	bifurcation	NOUN
ap-180	61	8	point	point	NOUN
ap-180	61	9	[	[	X
ap-180	61	10	0	0	NUM
ap-180	61	11	,	,	PUNCT
ap-180	61	12	�	�	PROPN
ap-180	61	13	n	n	CCONJ
ap-180	61	14	]	]	PUNCT
ap-180	61	15	and	and	CCONJ
ap-180	61	16	the	the	DET
ap-180	61	17	solution	solution	NOUN
ap-180	61	18	of	of	ADP
ap-180	61	19	the	the	DET
ap-180	61	20	problem	problem	NOUN
ap-180	61	21	is	be	AUX
ap-180	61	22	similar	similar	ADJ
ap-180	61	23	to	to	ADP
ap-180	61	24	each	each	DET
ap-180	61	25	other	other	ADJ
ap-180	61	26	f	f	NOUN
ap-180	61	27	o	o	NOUN
ap-180	61	28	r	r	NOUN
ap-180	61	29	n	n	NOUN
ap-180	61	30	=	=	SYM
ap-180	61	31	0	0	NUM
ap-180	61	32	,	,	PUNCT
ap-180	61	33	1	1	NUM
ap-180	61	34	,	,	PUNCT
ap-180	61	35	…	…	PUNCT
ap-180	61	36	then	then	ADV
ap-180	61	37	,	,	PUNCT
ap-180	61	38	we	we	PRON
ap-180	61	39	choose	choose	VERB
ap-180	61	40	the	the	DET
ap-180	61	41	smallest	small	ADJ
ap-180	61	42	eigenvalue	eigenvalue	ADJ
ap-180	61	43	�	�	NOUN
ap-180	61	44	0	0	NUM
ap-180	61	45	,	,	PUNCT
ap-180	61	46	because	because	SCONJ
ap-180	61	47	this	this	DET
ap-180	61	48	number	number	NOUN
ap-180	61	49	determines	determine	VERB
ap-180	61	50	the	the	DET
ap-180	61	51	loss	loss	NOUN
ap-180	61	52	of	of	ADP
ap-180	61	53	stability	stability	NOUN
ap-180	61	54	of	of	ADP
ap-180	61	55	the	the	DET
ap-180	61	56	column	column	NOUN
ap-180	61	57	.	.	PUNCT
ap-180	62	1	equation	equation	NOUN
ap-180	62	2	(	(	PUNCT
ap-180	62	3	1	1	X
ap-180	62	4	)	)	PUNCT
ap-180	62	5	may	may	AUX
ap-180	62	6	be	be	AUX
ap-180	62	7	rewritten	rewrite	VERB
ap-180	62	8	into	into	ADP
ap-180	62	9	the	the	DET
ap-180	62	10	form	form	NOUN
ap-180	62	11	�	�	PROPN
ap-180	62	12	�	�	PROPN
ap-180	62	13	�	�	PROPN
ap-180	62	14	�	�	PROPN
ap-180	62	15	�	�	PROPN
ap-180	62	16	�	�	PROPN
ap-180	62	17	�	�	PROPN
ap-180	62	18	�	�	PROPN
ap-180	62	19	�	�	PROPN
ap-180	62	20	�	�	PROPN
ap-180	62	21	�	�	PROPN
ap-180	62	22	�	�	PROPN
ap-180	62	23	�	�	PROPN
ap-180	62	24	�	�	PROPN
ap-180	62	25	�	�	PROPN
ap-180	62	26	�	�	PROPN
ap-180	62	27	�	�	PROPN
ap-180	62	28	�	�	PROPN
ap-180	62	29	u	u	NOUN
ap-180	62	30	s	s	PART
ap-180	62	31	s	s	X
ap-180	62	32	u	u	NOUN
ap-180	62	33	s	s	NOUN
ap-180	62	34	s	s	X
ap-180	62	35	u	u	NOUN
ap-180	62	36	s	s	PROPN
ap-180	62	37	u	u	X
ap-180	62	38	s	s	NOUN
ap-180	62	39	s	s	PROPN
ap-180	62	40	�	�	PROPN
ap-180	62	41	�	�	PROPN
ap-180	62	42	�	�	PROPN
ap-180	62	43	0	0	NUM
ap-180	62	44	0	0	NUM
ap-180	62	45	0	0	NUM
ap-180	62	46	1sin	1sin	NOUN
ap-180	62	47	,	,	PUNCT
ap-180	62	48	,	,	PUNCT
ap-180	62	49	.	.	PUNCT
ap-180	63	1	(	(	PUNCT
ap-180	63	2	12	12	NUM
ap-180	63	3	)	)	PUNCT
ap-180	63	4	let	let	VERB
ap-180	63	5	us	we	PRON
ap-180	63	6	denote	denote	VERB
ap-180	63	7	by	by	ADP
ap-180	63	8	l(u	l(u	PROPN
ap-180	63	9	)	)	PUNCT
ap-180	63	10	the	the	DET
ap-180	63	11	linear	linear	ADJ
ap-180	63	12	operator	operator	NOUN
ap-180	63	13	as	as	ADP
ap-180	63	14	the	the	DET
ap-180	63	15	closure	closure	NOUN
ap-180	63	16	(	(	PUNCT
ap-180	63	17	in	in	ADP
ap-180	63	18	h1(0	h1(0	PROPN
ap-180	63	19	,	,	PUNCT
ap-180	63	20	1	1	NUM
ap-180	63	21	)	)	PUNCT
ap-180	63	22	)	)	PUNCT
ap-180	63	23	of	of	ADP
ap-180	63	24	the	the	DET
ap-180	63	25	operator	operator	NOUN
ap-180	63	26	given	give	VERB
ap-180	63	27	by	by	ADP
ap-180	63	28	the	the	DET
ap-180	63	29	values	value	NOUN
ap-180	63	30	�	�	PROPN
ap-180	63	31	�	�	PROPN
ap-180	63	32	�	�	PROPN
ap-180	63	33	�	�	PROPN
ap-180	63	34	�	�	PROPN
ap-180	63	35	�	�	PROPN
ap-180	64	1	lu	lu	PROPN
ap-180	64	2	s	s	VERB
ap-180	64	3	u	u	NOUN
ap-180	64	4	s	s	PROPN
ap-180	64	5	s	s	X
ap-180	64	6	u	u	NOUN
ap-180	64	7	s	s	PROPN
ap-180	64	8	�	�	PROPN
ap-180	64	9	�	�	PROPN
ap-180	64	10	�	�	PROPN
ap-180	64	11	�	�	PROPN
ap-180	64	12	�	�	PROPN
ap-180	64	13	0	0	NUM
ap-180	64	14	for	for	ADP
ap-180	64	15	the	the	DET
ap-180	64	16	functions	function	NOUN
ap-180	64	17	satisfying	satisfy	VERB
ap-180	64	18	boundary	boundary	ADJ
ap-180	64	19	conditions	condition	NOUN
ap-180	64	20	(	(	PUNCT
ap-180	64	21	8)	8)	NUM
ap-180	64	22	and	and	CCONJ
ap-180	64	23	�	�	PROPN
ap-180	64	24	�	�	PROPN
ap-180	64	25	�	�	PROPN
ap-180	64	26	�	�	PROPN
ap-180	64	27	�	�	PROPN
ap-180	64	28	�	�	PROPN
ap-180	64	29	�	�	PROPN
ap-180	64	30	�	�	PROPN
ap-180	64	31	�	�	PROPN
ap-180	64	32	�	�	PROPN
ap-180	64	33	�	�	PROPN
ap-180	64	34	�	�	PROPN
ap-180	65	1	f	f	PROPN
ap-180	65	2	u	u	PROPN
ap-180	66	1	t	t	PROPN
ap-180	66	2	s	s	PART
ap-180	66	3	u	u	NOUN
ap-180	66	4	s	s	PROPN
ap-180	66	5	u	u	X
ap-180	66	6	s	s	PROPN
ap-180	66	7	u	u	X
ap-180	66	8	s	s	PROPN
ap-180	66	9	,	,	PUNCT
ap-180	66	10	sin	sin	NOUN
ap-180	66	11	sin	sin	NOUN
ap-180	66	12	,	,	PUNCT
ap-180	66	13	�	�	PROPN
ap-180	66	14	�	�	PROPN
ap-180	66	15	�	�	PROPN
ap-180	66	16	0	0	NUM
ap-180	66	17	�	�	PROPN
ap-180	66	18	(	(	PUNCT
ap-180	66	19	13	13	NUM
ap-180	66	20	)	)	PUNCT
ap-180	66	21	where	where	SCONJ
ap-180	66	22	=	=	PUNCT
ap-180	66	23	�	�	PROPN
ap-180	66	24	�	�	PROPN
ap-180	66	25	�	�	PROPN
ap-180	66	26	0	0	NUM
ap-180	66	27	.	.	PUNCT
ap-180	67	1	now	now	ADV
ap-180	67	2	,	,	PUNCT
ap-180	67	3	we	we	PRON
ap-180	67	4	may	may	AUX
ap-180	67	5	reduce	reduce	VERB
ap-180	67	6	the	the	DET
ap-180	67	7	problem	problem	NOUN
ap-180	67	8	of	of	ADP
ap-180	67	9	finding	find	VERB
ap-180	67	10	nonzero	nonzero	PROPN
ap-180	67	11	solutions	solution	NOUN
ap-180	67	12	to	to	ADP
ap-180	67	13	(	(	PUNCT
ap-180	67	14	6	6	NUM
ap-180	67	15	)	)	PUNCT
ap-180	67	16	,	,	PUNCT
ap-180	67	17	(	(	PUNCT
ap-180	67	18	8)	8)	NUM
ap-180	67	19	for	for	ADP
ap-180	67	20	�	�	PROPN
ap-180	67	21	near	near	ADP
ap-180	67	22	to	to	ADP
ap-180	67	23	�	�	PROPN
ap-180	67	24	0	0	NUM
ap-180	67	25	to	to	ADP
ap-180	67	26	solving	solve	VERB
ap-180	67	27	the	the	DET
ap-180	67	28	equation	equation	NOUN
ap-180	67	29	�	�	PROPN
ap-180	67	30	�	�	PROPN
ap-180	67	31	lu	lu	PROPN
ap-180	67	32	f	f	PROPN
ap-180	67	33	u	u	PROPN
ap-180	67	34	�	�	PROPN
ap-180	67	35	,	,	PUNCT
ap-180	67	36	(	(	PUNCT
ap-180	67	37	14	14	NUM
ap-180	67	38	)	)	PUNCT
ap-180	67	39	(	(	PUNCT
ap-180	67	40	in	in	ADP
ap-180	67	41	l2(0	l2(0	NOUN
ap-180	67	42	,	,	PUNCT
ap-180	67	43	1	1	NUM
ap-180	67	44	)	)	PUNCT
ap-180	67	45	)	)	PUNCT
ap-180	67	46	for	for	ADP
ap-180	67	47	sufficiently	sufficiently	ADV
ap-180	67	48	small	small	ADJ
ap-180	67	49	.	.	PUNCT
ap-180	68	1	all	all	DET
ap-180	68	2	the	the	DET
ap-180	68	3	solutions	solution	NOUN
ap-180	68	4	of	of	ADP
ap-180	68	5	the	the	DET
ap-180	68	6	homogeneous	homogeneous	ADJ
ap-180	68	7	equation	equation	NOUN
ap-180	68	8	lu	lu	PROPN
ap-180	68	9	�	�	PROPN
ap-180	68	10	0	0	NUM
ap-180	68	11	form	form	VERB
ap-180	68	12	a	a	DET
ap-180	68	13	one	one	NUM
ap-180	68	14	-	-	PUNCT
ap-180	68	15	dimensional	dimensional	ADJ
ap-180	68	16	subspace	subspace	NOUN
ap-180	68	17	n	n	PROPN
ap-180	68	18	of	of	ADP
ap-180	68	19	the	the	DET
ap-180	68	20	eigenfunctions	eigenfunction	NOUN
ap-180	68	21	v0(s	v0(s	NOUN
ap-180	68	22	)	)	PUNCT
ap-180	68	23	given	give	VERB
ap-180	68	24	by	by	ADP
ap-180	68	25	the	the	DET
ap-180	68	26	formula	formula	NOUN
ap-180	68	27	(	(	PUNCT
ap-180	68	28	11	11	NUM
ap-180	68	29	)	)	PUNCT
ap-180	68	30	corresponding	correspond	VERB
ap-180	68	31	to	to	ADP
ap-180	68	32	the	the	DET
ap-180	68	33	eigenvalue	eigenvalue	PROPN
ap-180	68	34	�	�	PROPN
ap-180	68	35	0	0	NUM
ap-180	68	36	.	.	PUNCT
ap-180	69	1	any	any	DET
ap-180	69	2	solution	solution	NOUN
ap-180	69	3	u(s	u(s	ADJ
ap-180	69	4	)	)	PUNCT
ap-180	69	5	to	to	ADP
ap-180	69	6	the	the	DET
ap-180	69	7	equation	equation	NOUN
ap-180	69	8	20	20	NUM
ap-180	69	9	©	©	PROPN
ap-180	69	10	czech	czech	PROPN
ap-180	69	11	technical	technical	PROPN
ap-180	69	12	university	university	PROPN
ap-180	69	13	publishing	publishing	NOUN
ap-180	69	14	house	house	NOUN
ap-180	69	15	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-180	69	16	acta	acta	PROPN
ap-180	69	17	polytechnica	polytechnica	PROPN
ap-180	69	18	vol	vol	NOUN
ap-180	69	19	.	.	PUNCT
ap-180	69	20	41	41	NUM
ap-180	69	21	no.1/2001	no.1/2001	NOUN
ap-180	69	22	fig	fig	NOUN
ap-180	69	23	.	.	PUNCT
ap-180	70	1	3	3	NUM
ap-180	70	2	:	:	PUNCT
ap-180	70	3	three	three	NUM
ap-180	70	4	eigenfunctions	eigenfunction	NOUN
ap-180	70	5	v0	v0	NOUN
ap-180	70	6	,	,	PUNCT
ap-180	70	7	v1	v1	NOUN
ap-180	70	8	,	,	PUNCT
ap-180	70	9	v2	v2	PROPN
ap-180	70	10	of	of	ADP
ap-180	70	11	the	the	DET
ap-180	70	12	linear	linear	PROPN
ap-180	70	13	program	program	NOUN
ap-180	70	14	fig	fig	NOUN
ap-180	70	15	.	.	PUNCT
ap-180	71	1	4	4	NUM
ap-180	71	2	:	:	SYM
ap-180	71	3	three	three	NUM
ap-180	71	4	deflections	deflection	NOUN
ap-180	71	5	of	of	ADP
ap-180	71	6	the	the	DET
ap-180	71	7	column	column	NOUN
ap-180	71	8	�	�	PROPN
ap-180	71	9	�	�	PROPN
ap-180	71	10	�	�	PROPN
ap-180	71	11	�	�	PROPN
ap-180	71	12	�	�	PROPN
ap-180	71	13	�	�	PROPN
ap-180	71	14	lu	lu	PROPN
ap-180	71	15	s	s	PROPN
ap-180	71	16	f	f	PROPN
ap-180	71	17	s	s	PROPN
ap-180	71	18	s	s	PROPN
ap-180	71	19	�	�	PROPN
ap-180	71	20	�	�	PROPN
ap-180	71	21	,	,	PUNCT
ap-180	71	22	,	,	PUNCT
ap-180	71	23	0	0	NUM
ap-180	71	24	1	1	NUM
ap-180	71	25	(	(	PUNCT
ap-180	71	26	15	15	NUM
ap-180	71	27	)	)	PUNCT
ap-180	71	28	exists	exist	VERB
ap-180	71	29	and	and	CCONJ
ap-180	71	30	is	be	AUX
ap-180	71	31	of	of	ADP
ap-180	71	32	the	the	DET
ap-180	71	33	form	form	NOUN
ap-180	71	34	�	�	PROPN
ap-180	71	35	�	�	PROPN
ap-180	71	36	�	�	PROPN
ap-180	71	37	�	�	PROPN
ap-180	71	38	�	�	PROPN
ap-180	71	39	�	�	PROPN
ap-180	71	40	�	�	PROPN
ap-180	71	41	�	�	PROPN
ap-180	71	42	�	�	PROPN
ap-180	71	43	�	�	PROPN
ap-180	71	44	�	�	PROPN
ap-180	71	45	�	�	PROPN
ap-180	71	46	�	�	PROPN
ap-180	71	47	�	�	PROPN
ap-180	71	48	�	�	PROPN
ap-180	71	49	�	�	PROPN
ap-180	71	50	u	u	PROPN
ap-180	71	51	s	s	PROPN
ap-180	71	52	b	b	PROPN
ap-180	71	53	f	f	X
ap-180	71	54	v	v	ADP
ap-180	71	55	u	u	PROPN
ap-180	71	56	s	s	PROPN
ap-180	71	57	v	v	NOUN
ap-180	71	58	s	s	X
ap-180	71	59	u	u	NOUN
ap-180	71	60	cv	cv	PROPN
ap-180	71	61	s	s	PROPN
ap-180	71	62	s	s	PROPN
ap-180	71	63	�	�	PROPN
ap-180	71	64	�	�	PROPN
ap-180	71	65	�	�	PROPN
ap-180	71	66	�	�	PROPN
ap-180	71	67	�	�	PROPN
ap-180	71	68	�	�	PROPN
ap-180	71	69	�	�	PROPN
ap-180	71	70	�	�	PROPN
ap-180	71	71	0	0	NUM
ap-180	71	72	0	0	NUM
ap-180	71	73	0	0	NUM
ap-180	71	74	0	0	NUM
ap-180	71	75	0	0	NUM
ap-180	71	76	0d	0d	NOUN
ap-180	71	77	(	(	PUNCT
ap-180	71	78	16	16	NUM
ap-180	71	79	)	)	PUNCT
ap-180	71	80	if	if	SCONJ
ap-180	71	81	and	and	CCONJ
ap-180	71	82	only	only	ADV
ap-180	71	83	if	if	SCONJ
ap-180	71	84	the	the	DET
ap-180	71	85	function	function	NOUN
ap-180	71	86	f	f	PROPN
ap-180	71	87	is	be	AUX
ap-180	71	88	orthogonal	orthogonal	ADJ
ap-180	71	89	to	to	PART
ap-180	71	90	v0	v0	VERB
ap-180	71	91	in	in	ADP
ap-180	71	92	l2(0	l2(0	NOUN
ap-180	71	93	,	,	PUNCT
ap-180	71	94	1	1	NUM
ap-180	71	95	)	)	PUNCT
ap-180	71	96	,	,	PUNCT
ap-180	71	97	i.e.	i.e.	X
ap-180	71	98	,	,	PUNCT
ap-180	71	99	�	�	PROPN
ap-180	71	100	�	�	PROPN
ap-180	71	101	�	�	PROPN
ap-180	71	102	�	�	PROPN
ap-180	71	103	f	f	PROPN
ap-180	71	104	s	s	PROPN
ap-180	71	105	v	v	NOUN
ap-180	71	106	s	s	NOUN
ap-180	71	107	s0	s0	NOUN
ap-180	71	108	0	0	NUM
ap-180	71	109	1	1	NUM
ap-180	71	110	0d	0d	NUM
ap-180	71	111	�	�	PROPN
ap-180	71	112	�	�	PROPN
ap-180	71	113	,	,	PUNCT
ap-180	71	114	(	(	PUNCT
ap-180	71	115	17	17	NUM
ap-180	71	116	)	)	PUNCT
ap-180	71	117	where	where	SCONJ
ap-180	71	118	c	c	NOUN
ap-180	71	119	is	be	AUX
ap-180	71	120	an	an	DET
ap-180	71	121	arbitrary	arbitrary	ADJ
ap-180	71	122	constant	constant	ADJ
ap-180	71	123	,	,	PUNCT
ap-180	71	124	�	�	PROPN
ap-180	71	125	�	�	PROPN
ap-180	71	126	�	�	PROPN
ap-180	71	127	�	�	PROPN
ap-180	71	128	b	b	PROPN
ap-180	71	129	u	u	NOUN
ap-180	71	130	s	s	PROPN
ap-180	71	131	s	s	PROPN
ap-180	71	132	j	j	PROPN
ap-180	71	133	z	z	PROPN
ap-180	71	134	s	s	PROPN
ap-180	71	135	�	�	PROPN
ap-180	71	136	�	�	PROPN
ap-180	71	137	2	2	NUM
ap-180	71	138	3	3	NUM
ap-180	71	139	3	3	NUM
ap-180	71	140	0	0	NUM
ap-180	71	141	1	1	NUM
ap-180	71	142	3	3	NUM
ap-180	71	143	0	0	NUM
ap-180	71	144	3	3	NUM
ap-180	71	145	2	2	NUM
ap-180	71	146	�	�	PROPN
ap-180	71	147	,	,	PUNCT
ap-180	71	148	.	.	PUNCT
ap-180	72	1	u0	u0	PROPN
ap-180	72	2	is	be	AUX
ap-180	72	3	a	a	DET
ap-180	72	4	solution	solution	NOUN
ap-180	72	5	of	of	ADP
ap-180	72	6	�	�	PROPN
ap-180	72	7	�	�	PROPN
ap-180	72	8	�	�	PROPN
ap-180	72	9	�	�	PROPN
ap-180	72	10	�	�	PROPN
ap-180	72	11	�	�	PROPN
ap-180	72	12	�	�	PROPN
ap-180	72	13	�	�	PROPN
ap-180	72	14	u	u	NOUN
ap-180	72	15	s	s	PROPN
ap-180	72	16	s	s	X
ap-180	72	17	u	u	NOUN
ap-180	72	18	s	s	NOUN
ap-180	72	19	�	�	PROPN
ap-180	72	20	0	0	NUM
ap-180	72	21	0	0	NUM
ap-180	72	22	,	,	PUNCT
ap-180	72	23	representing	represent	VERB
ap-180	72	24	together	together	ADV
ap-180	72	25	with	with	ADP
ap-180	72	26	v0	v0	PROPN
ap-180	72	27	a	a	DET
ap-180	72	28	fundamental	fundamental	ADJ
ap-180	72	29	system	system	NOUN
ap-180	72	30	of	of	ADP
ap-180	72	31	solutions	solution	NOUN
ap-180	72	32	to	to	ADP
ap-180	72	33	the	the	DET
ap-180	72	34	above	above	ADJ
ap-180	72	35	equation	equation	NOUN
ap-180	72	36	.	.	PUNCT
ap-180	73	1	formula	formula	NOUN
ap-180	73	2	(	(	PUNCT
ap-180	73	3	16	16	NUM
ap-180	73	4	)	)	PUNCT
ap-180	73	5	is	be	AUX
ap-180	73	6	easily	easily	ADV
ap-180	73	7	obtained	obtain	VERB
ap-180	73	8	by	by	ADP
ap-180	73	9	solving	solve	VERB
ap-180	73	10	the	the	DET
ap-180	73	11	linear	linear	ADJ
ap-180	73	12	problem	problem	NOUN
ap-180	73	13	(	(	PUNCT
ap-180	73	14	15	15	NUM
ap-180	73	15	)	)	PUNCT
ap-180	73	16	,	,	PUNCT
ap-180	73	17	(	(	PUNCT
ap-180	73	18	8)	8)	NUM
ap-180	73	19	with	with	ADP
ap-180	73	20	the	the	DET
ap-180	73	21	use	use	NOUN
ap-180	73	22	of	of	ADP
ap-180	73	23	variation	variation	NOUN
ap-180	73	24	of	of	ADP
ap-180	73	25	parameters	parameter	NOUN
ap-180	73	26	.	.	PUNCT
ap-180	74	1	as	as	SCONJ
ap-180	74	2	operator	operator	NOUN
ap-180	74	3	l	l	NOUN
ap-180	74	4	is	be	AUX
ap-180	74	5	not	not	PART
ap-180	74	6	invertible	invertible	ADJ
ap-180	74	7	,	,	PUNCT
ap-180	74	8	we	we	PRON
ap-180	74	9	split	split	VERB
ap-180	74	10	equation	equation	NOUN
ap-180	74	11	(	(	PUNCT
ap-180	74	12	14	14	NUM
ap-180	74	13	)	)	PUNCT
ap-180	74	14	into	into	ADP
ap-180	74	15	two	two	NUM
ap-180	74	16	equations	equation	NOUN
ap-180	74	17	:	:	PUNCT
ap-180	74	18	�	�	PROPN
ap-180	74	19	�	�	PROPN
ap-180	74	20	�	�	PROPN
ap-180	74	21	�	�	PROPN
ap-180	74	22	�	�	PROPN
ap-180	74	23	�	�	PROPN
ap-180	74	24	q	q	PROPN
ap-180	74	25	lu	lu	PROPN
ap-180	74	26	q	q	PROPN
ap-180	74	27	f	f	PROPN
ap-180	74	28	u	u	PROPN
ap-180	74	29	t	t	PROPN
ap-180	74	30	�	�	PROPN
ap-180	74	31	,	,	PUNCT
ap-180	74	32	,	,	PUNCT
ap-180	74	33	(	(	PUNCT
ap-180	74	34	18	18	NUM
ap-180	74	35	)	)	PUNCT
ap-180	74	36	�	�	PROPN
ap-180	74	37	�	�	PROPN
ap-180	74	38	�	�	PROPN
ap-180	74	39	�	�	PROPN
ap-180	74	40	�	�	PROPN
ap-180	74	41	�	�	PROPN
ap-180	74	42	i	i	PRON
ap-180	74	43	q	q	NOUN
ap-180	75	1	lu	lu	INTJ
ap-180	75	2	f	f	PROPN
ap-180	75	3	u	u	PROPN
ap-180	75	4	t	t	PROPN
ap-180	75	5	�	�	PROPN
ap-180	75	6	�	�	PROPN
ap-180	75	7	�	�	PROPN
ap-180	75	8	�	�	PROPN
ap-180	75	9	,	,	PUNCT
ap-180	75	10	0	0	NUM
ap-180	75	11	,	,	PUNCT
ap-180	75	12	(	(	PUNCT
ap-180	75	13	19	19	NUM
ap-180	75	14	)	)	PUNCT
ap-180	75	15	where	where	SCONJ
ap-180	75	16	q	q	NOUN
ap-180	75	17	is	be	AUX
ap-180	75	18	a	a	DET
ap-180	75	19	projector	projector	NOUN
ap-180	75	20	operator	operator	NOUN
ap-180	75	21	of	of	ADP
ap-180	75	22	l2(0	l2(0	NOUN
ap-180	75	23	,	,	PUNCT
ap-180	75	24	1	1	NUM
ap-180	75	25	)	)	PUNCT
ap-180	75	26	on	on	ADP
ap-180	75	27	�	�	PROPN
ap-180	75	28	�	�	PROPN
ap-180	75	29	�	�	PROPN
ap-180	75	30	�	�	PROPN
ap-180	75	31	�	�	PROPN
ap-180	75	32	�	�	PROPN
ap-180	75	33	n	n	PROPN
ap-180	75	34	f	f	NOUN
ap-180	75	35	l	l	NOUN
ap-180	76	1	f	f	PROPN
ap-180	76	2	s	s	PROPN
ap-180	76	3	v	v	NOUN
ap-180	76	4	s	s	X
ap-180	76	5	s	s	PROPN
ap-180	76	6	�	�	PROPN
ap-180	76	7	�	�	PROPN
ap-180	76	8	�	�	PROPN
ap-180	76	9	�	�	PROPN
ap-180	76	10	�	�	PROPN
ap-180	76	11	�	�	PROPN
ap-180	76	12	�	�	PROPN
ap-180	76	13	�	�	PROPN
ap-180	76	14	�	�	PROPN
ap-180	76	15	�	�	PROPN
ap-180	76	16	�	�	PROPN
ap-180	76	17	�	�	PROPN
ap-180	76	18	�	�	PROPN
ap-180	76	19	�	�	PROPN
ap-180	76	20	�	�	PROPN
ap-180	76	21	2	2	NUM
ap-180	76	22	0	0	NUM
ap-180	76	23	0	0	NUM
ap-180	76	24	1	1	NUM
ap-180	76	25	0	0	NUM
ap-180	76	26	1	1	NUM
ap-180	76	27	0	0	NUM
ap-180	76	28	,	,	PUNCT
ap-180	76	29	:	:	PUNCT
ap-180	77	1	d	d	X
ap-180	77	2	.	.	PUNCT
ap-180	78	1	due	due	ADP
ap-180	78	2	to	to	ADP
ap-180	78	3	the	the	DET
ap-180	78	4	uniqueness	uniqueness	NOUN
ap-180	78	5	of	of	ADP
ap-180	78	6	the	the	DET
ap-180	78	7	solution	solution	NOUN
ap-180	78	8	to	to	ADP
ap-180	78	9	(	(	PUNCT
ap-180	78	10	15	15	NUM
ap-180	78	11	)	)	PUNCT
ap-180	78	12	in	in	ADP
ap-180	78	13	n	n	PRON
ap-180	78	14	�	�	PROPN
ap-180	78	15	,	,	PUNCT
ap-180	78	16	the	the	DET
ap-180	78	17	operator	operator	NOUN
ap-180	78	18	q(lu	q(lu	NUM
ap-180	78	19	)	)	PUNCT
ap-180	78	20	is	be	AUX
ap-180	78	21	invertible	invertible	ADJ
ap-180	78	22	in	in	ADP
ap-180	78	23	n	n	PRON
ap-180	78	24	�	�	PROPN
ap-180	78	25	.	.	PUNCT
ap-180	79	1	then	then	ADV
ap-180	79	2	the	the	DET
ap-180	79	3	solution	solution	NOUN
ap-180	79	4	u(s	u(s	PROPN
ap-180	79	5	)	)	PUNCT
ap-180	79	6	of	of	ADP
ap-180	79	7	(	(	PUNCT
ap-180	79	8	14	14	NUM
ap-180	79	9	)	)	PUNCT
ap-180	79	10	may	may	AUX
ap-180	79	11	be	be	AUX
ap-180	79	12	rewritten	rewrite	VERB
ap-180	79	13	in	in	ADP
ap-180	79	14	the	the	DET
ap-180	79	15	form	form	NOUN
ap-180	79	16	�	�	PROPN
ap-180	79	17	�	�	PROPN
ap-180	79	18	u	u	NOUN
ap-180	79	19	u	u	PROPN
ap-180	79	20	u	u	X
ap-180	79	21	u	u	NOUN
ap-180	79	22	�	�	PROPN
ap-180	79	23	�	�	PROPN
ap-180	79	24	1	1	NUM
ap-180	79	25	2	2	NUM
ap-180	79	26	2	2	NUM
ap-180	79	27	where	where	SCONJ
ap-180	79	28	u1(u2	u1(u2	NOUN
ap-180	79	29	)	)	PUNCT
ap-180	79	30	is	be	AUX
ap-180	79	31	the	the	DET
ap-180	79	32	solution	solution	NOUN
ap-180	79	33	of	of	ADP
ap-180	79	34	(	(	PUNCT
ap-180	79	35	18	18	NUM
ap-180	79	36	)	)	PUNCT
ap-180	79	37	for	for	ADP
ap-180	79	38	fixed	fixed	ADJ
ap-180	79	39	but	but	CCONJ
ap-180	79	40	arbitrary	arbitrary	ADJ
ap-180	79	41	u2	u2	NOUN
ap-180	79	42	,	,	PUNCT
ap-180	79	43	and	and	CCONJ
ap-180	79	44	u2	u2	NOUN
ap-180	79	45	is	be	AUX
ap-180	79	46	afterwards	afterwards	ADV
ap-180	79	47	obtained	obtain	VERB
ap-180	79	48	as	as	ADP
ap-180	79	49	a	a	DET
ap-180	79	50	solution	solution	NOUN
ap-180	79	51	of	of	ADP
ap-180	79	52	(	(	PUNCT
ap-180	79	53	19	19	NUM
ap-180	79	54	)	)	PUNCT
ap-180	79	55	where	where	SCONJ
ap-180	79	56	u1	u1	NOUN
ap-180	79	57	=	=	SYM
ap-180	79	58	u1(u2	u1(u2	PROPN
ap-180	79	59	)	)	PUNCT
ap-180	79	60	was	be	AUX
ap-180	79	61	substituted	substitute	VERB
ap-180	79	62	.	.	PUNCT
ap-180	80	1	now	now	ADV
ap-180	80	2	,	,	PUNCT
ap-180	80	3	we	we	PRON
ap-180	80	4	will	will	AUX
ap-180	80	5	compute	compute	VERB
ap-180	80	6	u1	u1	NOUN
ap-180	80	7	,	,	PUNCT
ap-180	80	8	u2	u2	NOUN
ap-180	80	9	solving	solving	NOUN
ap-180	80	10	problems	problem	NOUN
ap-180	80	11	(	(	PUNCT
ap-180	80	12	18	18	NUM
ap-180	80	13	)	)	PUNCT
ap-180	80	14	,	,	PUNCT
ap-180	80	15	(	(	PUNCT
ap-180	80	16	19	19	NUM
ap-180	80	17	)	)	PUNCT
ap-180	80	18	,	,	PUNCT
ap-180	80	19	or	or	CCONJ
ap-180	80	20	,	,	PUNCT
ap-180	80	21	more	more	ADV
ap-180	80	22	precisely	precisely	ADV
ap-180	80	23	,	,	PUNCT
ap-180	80	24	their	their	PRON
ap-180	80	25	approximations	approximation	NOUN
ap-180	80	26	.	.	PUNCT
ap-180	81	1	let	let	VERB
ap-180	81	2	us	we	PRON
ap-180	81	3	introduce	introduce	VERB
ap-180	81	4	a	a	DET
ap-180	81	5	sufficiently	sufficiently	ADV
ap-180	81	6	small	small	ADJ
ap-180	81	7	parameter	parameter	NOUN
ap-180	81	8	t	t	PROPN
ap-180	81	9	and	and	CCONJ
ap-180	81	10	use	use	VERB
ap-180	81	11	the	the	DET
ap-180	81	12	following	follow	VERB
ap-180	81	13	series	series	PROPN
ap-180	81	14	�	�	PROPN
ap-180	81	15	�	�	PROPN
ap-180	81	16	�	�	PROPN
ap-180	81	17	�	�	PROPN
ap-180	81	18	�	�	PROPN
ap-180	81	19	�	�	PROPN
ap-180	81	20	�	�	PROPN
ap-180	81	21	�	�	PROPN
ap-180	81	22	�	�	PROPN
ap-180	81	23	�	�	PROPN
ap-180	81	24	�	�	PROPN
ap-180	81	25	�	�	PROPN
ap-180	81	26	�	�	PROPN
ap-180	81	27	�	�	PROPN
ap-180	81	28	�	�	PROPN
ap-180	81	29	�	�	PROPN
ap-180	81	30	�	�	PROPN
ap-180	81	31	�	�	PROPN
ap-180	81	32	�	�	PROPN
ap-180	81	33	�	�	PROPN
ap-180	81	34	�	�	PROPN
ap-180	81	35	�	�	PROPN
ap-180	81	36	1	1	NUM
ap-180	81	37	2	2	NUM
ap-180	81	38	2	2	NUM
ap-180	81	39	3	3	NUM
ap-180	81	40	3	3	NUM
ap-180	81	41	0	0	NUM
ap-180	81	42	2	2	NUM
ap-180	81	43	2	2	NUM
ap-180	81	44	3	3	NUM
ap-180	81	45	3	3	NUM
ap-180	81	46	t	t	NOUN
ap-180	81	47	t	t	PROPN
ap-180	81	48	t	t	PROPN
ap-180	81	49	u	u	PROPN
ap-180	81	50	s	s	PROPN
ap-180	81	51	v	v	NOUN
ap-180	81	52	s	s	X
ap-180	81	53	t	t	NOUN
ap-180	81	54	u	u	PROPN
ap-180	81	55	s	s	PROPN
ap-180	81	56	t	t	NOUN
ap-180	81	57	u	u	PROPN
ap-180	81	58	s	s	PROPN
ap-180	81	59	t	t	X
ap-180	81	60	u	u	X
ap-180	81	61	u	u	PROPN
ap-180	81	62	,	,	PUNCT
ap-180	81	63	,	,	PUNCT
ap-180	81	64	sin	sin	NOUN
ap-180	81	65	u	u	NOUN
ap-180	81	66	u3	u3	NOUN
ap-180	81	67	5	5	NUM
ap-180	81	68	3	3	NUM
ap-180	81	69	5	5	NUM
ap-180	81	70	!	!	PUNCT
ap-180	81	71	!	!	PUNCT
ap-180	82	1	�	�	PROPN
ap-180	82	2	�	�	PROPN
ap-180	82	3	(	(	PUNCT
ap-180	82	4	20	20	NUM
ap-180	82	5	)	)	PUNCT
ap-180	82	6	in	in	ADP
ap-180	82	7	(	(	PUNCT
ap-180	82	8	12	12	NUM
ap-180	82	9	)	)	PUNCT
ap-180	82	10	.	.	PUNCT
ap-180	83	1	comparing	compare	VERB
ap-180	83	2	the	the	DET
ap-180	83	3	coefficients	coefficient	NOUN
ap-180	83	4	corresponding	correspond	VERB
ap-180	83	5	to	to	ADP
ap-180	83	6	the	the	DET
ap-180	83	7	same	same	ADJ
ap-180	83	8	power	power	NOUN
ap-180	83	9	tn	tn	PROPN
ap-180	83	10	,	,	PUNCT
ap-180	83	11	n	n	NOUN
ap-180	83	12	=	=	SYM
ap-180	83	13	1	1	NUM
ap-180	83	14	,	,	PUNCT
ap-180	83	15	2	2	NUM
ap-180	83	16	,	,	PUNCT
ap-180	83	17	3	3	NUM
ap-180	83	18	,	,	PUNCT
ap-180	83	19	…	…	PUNCT
ap-180	83	20	,	,	PUNCT
ap-180	83	21	we	we	PRON
ap-180	83	22	get	get	VERB
ap-180	83	23	an	an	DET
ap-180	83	24	infinite	infinite	ADJ
ap-180	83	25	system	system	NOUN
ap-180	83	26	of	of	ADP
ap-180	83	27	equations	equation	NOUN
ap-180	83	28	,	,	PUNCT
ap-180	83	29	three	three	NUM
ap-180	83	30	of	of	ADP
ap-180	83	31	which	which	PRON
ap-180	83	32	are	be	AUX
ap-180	83	33	written	write	VERB
ap-180	83	34	below	below	ADP
ap-180	83	35	�	�	PROPN
ap-180	83	36	�	�	PROPN
ap-180	83	37	�	�	PROPN
ap-180	83	38	�	�	PROPN
ap-180	83	39	�	�	PROPN
ap-180	83	40	�	�	PROPN
ap-180	83	41	�	�	PROPN
ap-180	83	42	�	�	PROPN
ap-180	83	43	v	v	NOUN
ap-180	83	44	s	s	NOUN
ap-180	83	45	s	s	NOUN
ap-180	83	46	v	v	NOUN
ap-180	83	47	s0	s0	NOUN
ap-180	83	48	0	0	NUM
ap-180	83	49	0	0	NUM
ap-180	83	50	0	0	NUM
ap-180	83	51	�	�	PROPN
ap-180	83	52	,	,	PUNCT
ap-180	83	53	(	(	PUNCT
ap-180	84	1	21	21	NUM
ap-180	84	2	)	)	PUNCT
ap-180	84	3	�	�	PROPN
ap-180	84	4	�	�	PROPN
ap-180	84	5	�	�	PROPN
ap-180	84	6	�	�	PROPN
ap-180	84	7	�	�	PROPN
ap-180	84	8	�	�	PROPN
ap-180	84	9	�	�	PROPN
ap-180	84	10	�	�	PROPN
ap-180	84	11	�	�	PROPN
ap-180	84	12	�	�	PROPN
ap-180	84	13	�	�	PROPN
ap-180	84	14	u	u	NOUN
ap-180	84	15	s	s	PART
ap-180	84	16	s	s	X
ap-180	84	17	u	u	NOUN
ap-180	84	18	s	s	PROPN
ap-180	84	19	v	v	PROPN
ap-180	84	20	s2	s2	NOUN
ap-180	84	21	0	0	NUM
ap-180	84	22	2	2	NUM
ap-180	84	23	0	0	NUM
ap-180	84	24	�	�	PROPN
ap-180	84	25	�	�	PROPN
ap-180	84	26	,	,	PUNCT
ap-180	84	27	(	(	PUNCT
ap-180	84	28	22	22	NUM
ap-180	84	29	)	)	PUNCT
ap-180	84	30	�	�	PROPN
ap-180	84	31	�	�	PROPN
ap-180	84	32	�	�	PROPN
ap-180	84	33	�	�	PROPN
ap-180	84	34	�	�	PROPN
ap-180	84	35	�	�	PROPN
ap-180	84	36	�	�	PROPN
ap-180	84	37	�	�	PROPN
ap-180	84	38	�	�	PROPN
ap-180	84	39	�	�	PROPN
ap-180	84	40	�	�	PROPN
ap-180	84	41	�	�	PROPN
ap-180	84	42	�	�	PROPN
ap-180	84	43	�	�	PROPN
ap-180	84	44	�	�	PROPN
ap-180	84	45	�	�	PROPN
ap-180	84	46	�	�	PROPN
ap-180	84	47	u	u	NOUN
ap-180	84	48	s	s	PART
ap-180	84	49	s	s	X
ap-180	84	50	u	u	NOUN
ap-180	84	51	s	s	NOUN
ap-180	84	52	s	s	PROPN
ap-180	84	53	v	v	NUM
ap-180	84	54	v	v	ADP
ap-180	84	55	u	u	PROPN
ap-180	84	56	v3	v3	PROPN
ap-180	84	57	0	0	NUM
ap-180	84	58	3	3	NUM
ap-180	84	59	0	0	NUM
ap-180	84	60	0	0	NUM
ap-180	84	61	2	2	NUM
ap-180	84	62	0	0	NUM
ap-180	84	63	3	3	NUM
ap-180	84	64	0	0	NUM
ap-180	84	65	3	3	NUM
ap-180	84	66	2	2	NUM
ap-180	84	67	6	6	NUM
ap-180	84	68	�	�	PROPN
ap-180	84	69	�	�	PROPN
ap-180	84	70	�	�	PROPN
ap-180	84	71	�	�	PROPN
ap-180	84	72	�	�	PROPN
ap-180	84	73	.	.	PUNCT
ap-180	85	1	(	(	PUNCT
ap-180	85	2	23	23	X
ap-180	85	3	)	)	PUNCT
ap-180	85	4	other	other	ADJ
ap-180	85	5	equations	equation	NOUN
ap-180	85	6	may	may	AUX
ap-180	85	7	easily	easily	ADV
ap-180	85	8	be	be	AUX
ap-180	85	9	obtained	obtain	VERB
ap-180	85	10	continuing	continue	VERB
ap-180	85	11	the	the	DET
ap-180	85	12	computations	computation	NOUN
ap-180	85	13	.	.	PUNCT
ap-180	86	1	(	(	PUNCT
ap-180	86	2	21	21	NUM
ap-180	86	3	)	)	PUNCT
ap-180	86	4	is	be	AUX
ap-180	86	5	automatically	automatically	ADV
ap-180	86	6	satisfied	satisfied	ADJ
ap-180	86	7	due	due	ADP
ap-180	86	8	to	to	PART
ap-180	86	9	(	(	PUNCT
ap-180	86	10	11	11	NUM
ap-180	86	11	)	)	PUNCT
ap-180	86	12	.	.	PUNCT
ap-180	87	1	any	any	DET
ap-180	87	2	solution	solution	NOUN
ap-180	87	3	of	of	ADP
ap-180	87	4	(	(	PUNCT
ap-180	87	5	21	21	NUM
ap-180	87	6	)	)	PUNCT
ap-180	87	7	is	be	AUX
ap-180	87	8	of	of	ADP
ap-180	87	9	the	the	DET
ap-180	87	10	form	form	NOUN
ap-180	87	11	(	(	PUNCT
ap-180	87	12	16	16	NUM
ap-180	87	13	)	)	PUNCT
ap-180	87	14	for	for	ADP
ap-180	87	15	f	f	PROPN
ap-180	87	16	(	(	PUNCT
ap-180	87	17	s	s	X
ap-180	87	18	)	)	PUNCT
ap-180	87	19	=	=	NOUN
ap-180	87	20	�	�	PROPN
ap-180	87	21	1v0(s	1v0(s	NUM
ap-180	87	22	)	)	PUNCT
ap-180	87	23	satisfying	satisfying	NOUN
ap-180	87	24	(	(	PUNCT
ap-180	87	25	17	17	NUM
ap-180	87	26	)	)	PUNCT
ap-180	87	27	,	,	PUNCT
ap-180	87	28	which	which	PRON
ap-180	87	29	implies	imply	VERB
ap-180	87	30	1=	1=	X
ap-180	87	31	0	0	NUM
ap-180	87	32	.	.	PUNCT
ap-180	88	1	in	in	ADP
ap-180	88	2	this	this	DET
ap-180	88	3	case	case	NOUN
ap-180	88	4	,	,	PUNCT
ap-180	88	5	the	the	DET
ap-180	88	6	only	only	ADJ
ap-180	88	7	solution	solution	NOUN
ap-180	88	8	u2	u2	PROPN
ap-180	88	9	�	�	PROPN
ap-180	88	10	n	n	CCONJ
ap-180	88	11	�	�	PROPN
ap-180	88	12	is	be	AUX
ap-180	88	13	u2	u2	PROPN
ap-180	88	14	(	(	PUNCT
ap-180	88	15	s	s	NOUN
ap-180	88	16	)	)	PUNCT
ap-180	88	17	�	�	PROPN
ap-180	88	18	0	0	NUM
ap-180	88	19	.	.	PUNCT
ap-180	89	1	substituting	substitute	VERB
ap-180	89	2	these	these	DET
ap-180	89	3	values	value	NOUN
ap-180	89	4	into	into	ADP
ap-180	89	5	(	(	PUNCT
ap-180	89	6	23	23	NUM
ap-180	89	7	)	)	PUNCT
ap-180	89	8	,	,	PUNCT
ap-180	89	9	we	we	PRON
ap-180	89	10	get	get	VERB
ap-180	89	11	the	the	DET
ap-180	89	12	equation	equation	NOUN
ap-180	89	13	for	for	ADP
ap-180	89	14	u3	u3	PROPN
ap-180	89	15	:	:	PUNCT
ap-180	90	1	�	�	PROPN
ap-180	90	2	�	�	PROPN
ap-180	90	3	�	�	PROPN
ap-180	90	4	�	�	PROPN
ap-180	90	5	�	�	PROPN
ap-180	90	6	�	�	PROPN
ap-180	90	7	�	�	PROPN
ap-180	90	8	�	�	PROPN
ap-180	90	9	�	�	PROPN
ap-180	90	10	�	�	PROPN
ap-180	90	11	�	�	PROPN
ap-180	90	12	�	�	PROPN
ap-180	90	13	�	�	PROPN
ap-180	90	14	�	�	PROPN
ap-180	90	15	�	�	PROPN
ap-180	90	16	�	�	PROPN
ap-180	90	17	u	u	NOUN
ap-180	90	18	s	s	PART
ap-180	90	19	s	s	X
ap-180	90	20	u	u	NOUN
ap-180	90	21	s	s	NOUN
ap-180	90	22	s	s	X
ap-180	90	23	v	v	NOUN
ap-180	90	24	v	v	ADP
ap-180	90	25	s3	s3	PROPN
ap-180	90	26	0	0	NUM
ap-180	90	27	3	3	NUM
ap-180	90	28	0	0	NUM
ap-180	90	29	0	0	NUM
ap-180	90	30	2	2	NUM
ap-180	90	31	02	02	NUM
ap-180	90	32	0	0	NUM
ap-180	90	33	1	1	NUM
ap-180	90	34	�	�	PROPN
ap-180	90	35	�	�	PROPN
ap-180	90	36	�	�	PROPN
ap-180	90	37	,	,	PUNCT
ap-180	90	38	,	,	PUNCT
ap-180	90	39	.	.	PUNCT
ap-180	91	1	(	(	PUNCT
ap-180	91	2	24	24	NUM
ap-180	91	3	)	)	PUNCT
ap-180	91	4	and	and	CCONJ
ap-180	91	5	again	again	ADV
ap-180	91	6	,	,	PUNCT
ap-180	91	7	any	any	DET
ap-180	91	8	solution	solution	NOUN
ap-180	91	9	of	of	ADP
ap-180	91	10	(	(	PUNCT
ap-180	91	11	24	24	NUM
ap-180	91	12	)	)	PUNCT
ap-180	91	13	satisfying	satisfying	NOUN
ap-180	91	14	(	(	PUNCT
ap-180	91	15	8)	8)	NUM
ap-180	91	16	is	be	AUX
ap-180	91	17	of	of	ADP
ap-180	91	18	the	the	DET
ap-180	91	19	form	form	NOUN
ap-180	91	20	(	(	PUNCT
ap-180	91	21	16	16	NUM
ap-180	91	22	)	)	PUNCT
ap-180	91	23	under	under	ADP
ap-180	91	24	the	the	DET
ap-180	91	25	assumption	assumption	NOUN
ap-180	91	26	(	(	PUNCT
ap-180	91	27	17	17	NUM
ap-180	91	28	)	)	PUNCT
ap-180	91	29	on	on	ADP
ap-180	91	30	the	the	DET
ap-180	91	31	right	right	ADJ
ap-180	91	32	hand	hand	NOUN
ap-180	91	33	side	side	NOUN
ap-180	91	34	of	of	ADP
ap-180	91	35	(	(	PUNCT
ap-180	91	36	24	24	NUM
ap-180	91	37	)	)	PUNCT
ap-180	91	38	,	,	PUNCT
ap-180	91	39	which	which	PRON
ap-180	91	40	determines	determine	VERB
ap-180	91	41	the	the	DET
ap-180	91	42	unique	unique	ADJ
ap-180	91	43	2	2	NUM
ap-180	91	44	.	.	PUNCT
ap-180	92	1	the	the	DET
ap-180	92	2	constant	constant	ADJ
ap-180	92	3	c	c	NOUN
ap-180	92	4	from	from	ADP
ap-180	92	5	(	(	PUNCT
ap-180	92	6	16	16	NUM
ap-180	92	7	)	)	PUNCT
ap-180	92	8	is	be	AUX
ap-180	92	9	determined	determine	VERB
ap-180	92	10	by	by	ADP
ap-180	92	11	the	the	DET
ap-180	92	12	condition	condition	NOUN
ap-180	92	13	u3	u3	PROPN
ap-180	92	14	n	n	PRON
ap-180	92	15	�	�	PROPN
ap-180	92	16	.	.	PUNCT
ap-180	93	1	the	the	DET
ap-180	93	2	computation	computation	NOUN
ap-180	93	3	of	of	ADP
ap-180	93	4	n	n	CCONJ
ap-180	93	5	,	,	PUNCT
ap-180	93	6	un(s	un(s	NUM
ap-180	93	7	)	)	PUNCT
ap-180	93	8	(	(	PUNCT
ap-180	93	9	n	n	NOUN
ap-180	93	10	=	=	SYM
ap-180	93	11	2	2	NUM
ap-180	93	12	,	,	PUNCT
ap-180	93	13	3	3	NUM
ap-180	93	14	,	,	PUNCT
ap-180	93	15	…	…	PUNCT
ap-180	93	16	)	)	PUNCT
ap-180	93	17	gives	give	VERB
ap-180	93	18	approximations	approximation	NOUN
ap-180	93	19	of	of	ADP
ap-180	93	20	the	the	DET
ap-180	93	21	solution	solution	NOUN
ap-180	93	22	u(s	u(s	PROPN
ap-180	93	23	)	)	PUNCT
ap-180	93	24	of	of	ADP
ap-180	93	25	(	(	PUNCT
ap-180	93	26	14	14	NUM
ap-180	93	27	)	)	PUNCT
ap-180	93	28	,	,	PUNCT
ap-180	93	29	whereas	whereas	SCONJ
ap-180	93	30	n	n	CCONJ
ap-180	93	31	,	,	PUNCT
ap-180	93	32	un+1(s	un+1(s	PROPN
ap-180	93	33	)	)	PUNCT
ap-180	93	34	is	be	AUX
ap-180	93	35	a	a	DET
ap-180	93	36	zero	zero	NUM
ap-180	93	37	for	for	ADP
ap-180	93	38	odd	odd	ADJ
ap-180	93	39	indices	index	NOUN
ap-180	93	40	n.	n.	VERB
ap-180	93	41	the	the	DET
ap-180	93	42	approximations	approximation	NOUN
ap-180	93	43	�	�	PROPN
ap-180	93	44	�	�	PROPN
ap-180	93	45	�	�	PROPN
ap-180	93	46	�	�	PROPN
ap-180	93	47	�	�	PROPN
ap-180	93	48	�	�	PROPN
ap-180	93	49	u	u	NOUN
ap-180	93	50	s	s	PROPN
ap-180	93	51	v	v	NOUN
ap-180	93	52	s	s	X
ap-180	93	53	t	t	NOUN
ap-180	93	54	u	u	PROPN
ap-180	93	55	s	s	PROPN
ap-180	93	56	t	t	PROPN
ap-180	93	57	�	�	PROPN
ap-180	93	58	�	�	PROPN
ap-180	93	59	0	0	NUM
ap-180	93	60	3	3	NUM
ap-180	93	61	3	3	NUM
ap-180	93	62	�	�	PROPN
ap-180	93	63	(	(	PUNCT
ap-180	93	64	25	25	NUM
ap-180	93	65	)	)	PUNCT
ap-180	93	66	for	for	ADP
ap-180	93	67	the	the	DET
ap-180	93	68	values	value	NOUN
ap-180	93	69	of	of	ADP
ap-180	93	70	parameter	parameter	NOUN
ap-180	93	71	t	t	PROPN
ap-180	93	72	=	=	SYM
ap-180	93	73	±0.5	±0.5	PROPN
ap-180	93	74	,	,	PUNCT
ap-180	93	75	±1.0	±1.0	PROPN
ap-180	93	76	,	,	PUNCT
ap-180	93	77	±1.5	±1.5	PROPN
ap-180	93	78	are	be	AUX
ap-180	93	79	given	give	VERB
ap-180	93	80	in	in	ADP
ap-180	93	81	fig	fig	NOUN
ap-180	93	82	.	.	PUNCT
ap-180	94	1	5	5	X
ap-180	94	2	.	.	PUNCT
ap-180	94	3	the	the	DET
ap-180	94	4	dependence	dependence	NOUN
ap-180	94	5	of	of	ADP
ap-180	94	6	two	two	NUM
ap-180	94	7	approximations	approximation	NOUN
ap-180	94	8	of	of	ADP
ap-180	94	9	�	�	PROPN
ap-180	94	10	(	(	PUNCT
ap-180	94	11	denoted	denote	VERB
ap-180	94	12	by	by	ADP
ap-180	94	13	l1	l1	PROPN
ap-180	94	14	,	,	PUNCT
ap-180	94	15	l2	l2	NOUN
ap-180	94	16	on	on	ADP
ap-180	94	17	the	the	DET
ap-180	94	18	picture	picture	NOUN
ap-180	94	19	6	6	NUM
ap-180	94	20	):	):	PUNCT
ap-180	94	21	�	�	PROPN
ap-180	94	22	�	�	PROPN
ap-180	94	23	�	�	PROPN
ap-180	94	24	�	�	PROPN
ap-180	94	25	0	0	NUM
ap-180	94	26	2	2	NUM
ap-180	94	27	�	�	PROPN
ap-180	94	28	t	t	PROPN
ap-180	94	29	,	,	PUNCT
ap-180	94	30	�	�	PROPN
ap-180	94	31	�	�	PROPN
ap-180	94	32	�	�	PROPN
ap-180	94	33	�	�	PROPN
ap-180	94	34	�	�	PROPN
ap-180	94	35	0	0	NUM
ap-180	94	36	2	2	NUM
ap-180	94	37	4	4	NUM
ap-180	94	38	�	�	PROPN
ap-180	94	39	�	�	PROPN
ap-180	94	40	t	t	PROPN
ap-180	94	41	t	t	PROPN
ap-180	94	42	(	(	PUNCT
ap-180	94	43	26	26	NUM
ap-180	94	44	)	)	PUNCT
ap-180	94	45	is	be	AUX
ap-180	94	46	shown	show	VERB
ap-180	94	47	in	in	ADP
ap-180	94	48	fig	fig	NOUN
ap-180	94	49	.	.	PUNCT
ap-180	95	1	6	6	NUM
ap-180	95	2	.	.	X
ap-180	95	3	excluding	exclude	VERB
ap-180	95	4	parameter	parameter	NOUN
ap-180	95	5	t	t	PROPN
ap-180	95	6	from	from	ADP
ap-180	95	7	(	(	PUNCT
ap-180	95	8	25	25	NUM
ap-180	95	9	)	)	PUNCT
ap-180	95	10	and	and	CCONJ
ap-180	95	11	(	(	PUNCT
ap-180	95	12	26	26	NUM
ap-180	95	13	)	)	PUNCT
ap-180	95	14	,	,	PUNCT
ap-180	95	15	we	we	PRON
ap-180	95	16	get	get	VERB
ap-180	95	17	the	the	DET
ap-180	95	18	maximum	maximum	ADJ
ap-180	95	19	angle	angle	NOUN
ap-180	95	20	�	�	PROPN
ap-180	95	21	0	0	NUM
ap-180	95	22	(	(	PUNCT
ap-180	95	23	denoted	denote	VERB
ap-180	95	24	by	by	ADP
ap-180	95	25	u0	u0	NOUN
ap-180	95	26	in	in	ADP
ap-180	95	27	fig	fig	NOUN
ap-180	95	28	.	.	PUNCT
ap-180	96	1	7	7	NUM
ap-180	96	2	)	)	PUNCT
ap-180	96	3	as	as	ADP
ap-180	96	4	a	a	DET
ap-180	96	5	function	function	NOUN
ap-180	96	6	of	of	ADP
ap-180	96	7	the	the	DET
ap-180	96	8	length	length	NOUN
ap-180	96	9	l	l	NOUN
ap-180	96	10	of	of	ADP
ap-180	96	11	the	the	DET
ap-180	96	12	column	column	NOUN
ap-180	96	13	(	(	PUNCT
ap-180	96	14	see	see	VERB
ap-180	96	15	fig	fig	NOUN
ap-180	96	16	.	.	PUNCT
ap-180	97	1	7	7	NUM
ap-180	97	2	)	)	PUNCT
ap-180	97	3	.	.	PUNCT
ap-180	98	1	©	©	PROPN
ap-180	98	2	czech	czech	PROPN
ap-180	98	3	technical	technical	PROPN
ap-180	98	4	university	university	PROPN
ap-180	98	5	publishing	publishing	NOUN
ap-180	98	6	house	house	NOUN
ap-180	98	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-180	98	8	21	21	NUM
ap-180	98	9	acta	acta	PROPN
ap-180	98	10	polytechnica	polytechnica	PROPN
ap-180	98	11	vol	vol	NOUN
ap-180	98	12	.	.	PUNCT
ap-180	99	1	41	41	NUM
ap-180	99	2	no.1/2001	no.1/2001	NOUN
ap-180	99	3	fig	fig	NOUN
ap-180	99	4	.	.	PUNCT
ap-180	100	1	5	5	NUM
ap-180	100	2	:	:	PUNCT
ap-180	100	3	the	the	DET
ap-180	100	4	approximate	approximate	ADJ
ap-180	100	5	solutions	solution	NOUN
ap-180	100	6	u(s	u(s	ADJ
ap-180	100	7	)	)	PUNCT
ap-180	100	8	for	for	ADP
ap-180	100	9	t	t	NOUN
ap-180	100	10	=	=	SYM
ap-180	100	11	±0.5	±0.5	PROPN
ap-180	100	12	,	,	PUNCT
ap-180	100	13	±1.0	±1.0	PROPN
ap-180	100	14	,	,	PUNCT
ap-180	100	15	±1.5	±1.5	PROPN
ap-180	100	16	fig	fig	NOUN
ap-180	100	17	.	.	PUNCT
ap-180	101	1	6	6	NUM
ap-180	101	2	:	:	SYM
ap-180	101	3	two	two	NUM
ap-180	101	4	approximations	approximation	NOUN
ap-180	101	5	of	of	ADP
ap-180	101	6	�	�	PROPN
ap-180	101	7	:	:	PUNCT
ap-180	101	8	l1	l1	PROPN
ap-180	101	9	,	,	PUNCT
ap-180	101	10	l2	l2	NOUN
ap-180	101	11	5	5	NUM
ap-180	101	12	conclusions	conclusion	NOUN
ap-180	101	13	the	the	DET
ap-180	101	14	last	last	ADJ
ap-180	101	15	figure	figure	NOUN
ap-180	101	16	illustrates	illustrate	VERB
ap-180	101	17	the	the	DET
ap-180	101	18	fact	fact	NOUN
ap-180	101	19	that	that	SCONJ
ap-180	101	20	the	the	DET
ap-180	101	21	nonlinear	nonlinear	ADJ
ap-180	101	22	theory	theory	NOUN
ap-180	101	23	gives	give	VERB
ap-180	101	24	reasonable	reasonable	ADJ
ap-180	101	25	results	result	NOUN
ap-180	101	26	:	:	PUNCT
ap-180	101	27	a	a	X
ap-180	101	28	)	)	PUNCT
ap-180	101	29	the	the	DET
ap-180	101	30	deflections	deflection	NOUN
ap-180	101	31	of	of	ADP
ap-180	101	32	the	the	DET
ap-180	101	33	column	column	NOUN
ap-180	101	34	loaded	load	VERB
ap-180	101	35	with	with	ADP
ap-180	101	36	its	its	PRON
ap-180	101	37	own	own	ADJ
ap-180	101	38	weight	weight	NOUN
ap-180	101	39	are	be	AUX
ap-180	101	40	zero	zero	NUM
ap-180	101	41	for	for	ADP
ap-180	101	42	�	�	PROPN
ap-180	101	43	�	�	PROPN
ap-180	101	44	�	�	PROPN
ap-180	101	45	�	�	PROPN
ap-180	101	46	(	(	PUNCT
ap-180	101	47	the	the	DET
ap-180	101	48	first	first	ADJ
ap-180	101	49	eigenvalue	eigenvalue	NOUN
ap-180	101	50	of	of	ADP
ap-180	101	51	the	the	DET
ap-180	101	52	linear	linear	PROPN
ap-180	101	53	problem	problem	NOUN
ap-180	101	54	)	)	PUNCT
ap-180	101	55	,	,	PUNCT
ap-180	101	56	b	b	X
ap-180	101	57	)	)	PUNCT
ap-180	101	58	the	the	DET
ap-180	101	59	maximum	maximum	ADJ
ap-180	101	60	deflection	deflection	NOUN
ap-180	101	61	increases	increase	VERB
ap-180	101	62	continuously	continuously	ADV
ap-180	101	63	with	with	ADP
ap-180	101	64	increasing	increase	VERB
ap-180	101	65	length	length	NOUN
ap-180	101	66	of	of	ADP
ap-180	101	67	the	the	DET
ap-180	101	68	column	column	NOUN
ap-180	101	69	.	.	PUNCT
ap-180	102	1	formula	formula	NOUN
ap-180	102	2	(	(	PUNCT
ap-180	102	3	25	25	NUM
ap-180	102	4	)	)	PUNCT
ap-180	102	5	represents	represent	VERB
ap-180	102	6	the	the	DET
ap-180	102	7	solution	solution	NOUN
ap-180	102	8	of	of	ADP
ap-180	102	9	the	the	DET
ap-180	102	10	problem	problem	NOUN
ap-180	102	11	as	as	ADP
ap-180	102	12	the	the	DET
ap-180	102	13	sum	sum	NOUN
ap-180	102	14	of	of	ADP
ap-180	102	15	the	the	DET
ap-180	102	16	first	first	ADJ
ap-180	102	17	eigenfunction	eigenfunction	NOUN
ap-180	102	18	v0(s	v0(s	PROPN
ap-180	102	19	)	)	PUNCT
ap-180	102	20	of	of	ADP
ap-180	102	21	the	the	DET
ap-180	102	22	linear	linear	ADJ
ap-180	102	23	problem	problem	NOUN
ap-180	102	24	multiplied	multiply	VERB
ap-180	102	25	by	by	ADP
ap-180	102	26	parameter	parameter	PROPN
ap-180	102	27	t	t	PROPN
ap-180	102	28	:	:	PUNCT
ap-180	102	29	t	t	PROPN
ap-180	102	30	0	0	NUM
ap-180	102	31	for	for	ADP
ap-180	102	32	�	�	PROPN
ap-180	102	33	�	�	PROPN
ap-180	102	34	0	0	NUM
ap-180	102	35	and	and	CCONJ
ap-180	102	36	“	"	PUNCT
ap-180	102	37	a	a	DET
ap-180	102	38	perturbation	perturbation	NOUN
ap-180	102	39	”	"	PUNCT
ap-180	102	40	,	,	PUNCT
ap-180	102	41	which	which	PRON
ap-180	102	42	is	be	AUX
ap-180	102	43	orthogonal	orthogonal	ADJ
ap-180	102	44	to	to	PART
ap-180	102	45	v0	v0	VERB
ap-180	102	46	in	in	ADP
ap-180	102	47	l2	l2	NOUN
ap-180	102	48	.	.	PUNCT
ap-180	103	1	the	the	DET
ap-180	103	2	above	above	ADJ
ap-180	103	3	mentioned	mention	VERB
ap-180	103	4	method	method	NOUN
ap-180	103	5	is	be	AUX
ap-180	103	6	applicable	applicable	ADJ
ap-180	103	7	to	to	ADP
ap-180	103	8	other	other	ADJ
ap-180	103	9	stability	stability	NOUN
ap-180	103	10	problems	problem	NOUN
ap-180	103	11	described	describe	VERB
ap-180	103	12	by	by	ADP
ap-180	103	13	nonlinear	nonlinear	ADJ
ap-180	103	14	ordinary	ordinary	ADJ
ap-180	103	15	and	and	CCONJ
ap-180	103	16	partial	partial	ADJ
ap-180	103	17	differential	differential	NOUN
ap-180	103	18	equations	equation	NOUN
ap-180	103	19	,	,	PUNCT
ap-180	103	20	e.g.	e.g.	ADV
ap-180	103	21	,	,	PUNCT
ap-180	103	22	lateral	lateral	ADJ
ap-180	103	23	buckling	buckling	NOUN
ap-180	103	24	.	.	PUNCT
ap-180	104	1	acknowledgement	acknowledgement	NOUN
ap-180	104	2	the	the	DET
ap-180	104	3	author	author	NOUN
ap-180	104	4	is	be	AUX
ap-180	104	5	grateful	grateful	ADJ
ap-180	104	6	to	to	PART
ap-180	104	7	prof	prof	VERB
ap-180	104	8	.	.	PUNCT
ap-180	105	1	j.	j.	PROPN
ap-180	105	2	šejnoha	šejnoha	PROPN
ap-180	105	3	for	for	ADP
ap-180	105	4	his	his	PRON
ap-180	105	5	stimulating	stimulate	VERB
ap-180	105	6	discussions	discussion	NOUN
ap-180	105	7	and	and	CCONJ
ap-180	105	8	valuable	valuable	ADJ
ap-180	105	9	advice	advice	NOUN
ap-180	105	10	.	.	PUNCT
ap-180	106	1	the	the	DET
ap-180	106	2	research	research	NOUN
ap-180	106	3	of	of	ADP
ap-180	106	4	the	the	DET
ap-180	106	5	author	author	NOUN
ap-180	106	6	was	be	AUX
ap-180	106	7	supported	support	VERB
ap-180	106	8	by	by	ADP
ap-180	106	9	the	the	DET
ap-180	106	10	foundation	foundation	NOUN
ap-180	106	11	of	of	ADP
ap-180	106	12	the	the	DET
ap-180	106	13	ministry	ministry	PROPN
ap-180	106	14	of	of	ADP
ap-180	106	15	education	education	NOUN
ap-180	106	16	in	in	ADP
ap-180	106	17	the	the	DET
ap-180	106	18	project	project	NOUN
ap-180	106	19	“	"	PUNCT
ap-180	106	20	výzkumný	výzkumný	X
ap-180	106	21	záměr	záměr	ADV
ap-180	106	22	no	no	INTJ
ap-180	106	23	.	.	PUNCT
ap-180	106	24	j04/98:210000001	j04/98:210000001	NOUN
ap-180	106	25	”	"	PUNCT
ap-180	106	26	.	.	PUNCT
ap-180	107	1	references	reference	NOUN
ap-180	107	2	[	[	X
ap-180	107	3	1	1	NUM
ap-180	107	4	]	]	X
ap-180	107	5	rzhanicyn	rzhanicyn	NOUN
ap-180	107	6	,	,	PUNCT
ap-180	107	7	a.	a.	PROPN
ap-180	107	8	r.	r.	PROPN
ap-180	107	9	:	:	PUNCT
ap-180	107	10	ustoichivost	ustoichivost	PROPN
ap-180	107	11	ravnoviesija	ravnoviesija	PROPN
ap-180	107	12	uprugich	uprugich	PROPN
ap-180	107	13	sistem	sistem	PROPN
ap-180	107	14	.	.	PUNCT
ap-180	108	1	moskva	moskva	PROPN
ap-180	108	2	1955	1955	NUM
ap-180	109	1	[	[	X
ap-180	109	2	2	2	NUM
ap-180	109	3	]	]	PUNCT
ap-180	109	4	collatz	collatz	NOUN
ap-180	109	5	,	,	PUNCT
ap-180	109	6	l.	l.	PROPN
ap-180	109	7	:	:	PUNCT
ap-180	109	8	eigenwertaufgaben	eigenwertaufgaben	PROPN
ap-180	109	9	mit	mit	PROPN
ap-180	109	10	technischen	technischen	NOUN
ap-180	109	11	anwendungen	anwendungen	NOUN
ap-180	109	12	.	.	PUNCT
ap-180	110	1	leipzig	leipzig	NOUN
ap-180	110	2	1963	1963	NUM
ap-180	110	3	[	[	X
ap-180	110	4	3	3	NUM
ap-180	110	5	]	]	X
ap-180	110	6	nirenberg	nirenberg	PROPN
ap-180	110	7	,	,	PUNCT
ap-180	110	8	l.	l.	PROPN
ap-180	110	9	:	:	PUNCT
ap-180	110	10	topics	topic	NOUN
ap-180	110	11	in	in	ADP
ap-180	110	12	nonlinear	nonlinear	ADJ
ap-180	110	13	functional	functional	ADJ
ap-180	110	14	analysis	analysis	NOUN
ap-180	110	15	.	.	PUNCT
ap-180	111	1	new	new	PROPN
ap-180	111	2	york	york	PROPN
ap-180	111	3	1974	1974	NUM
ap-180	112	1	[	[	X
ap-180	112	2	4	4	NUM
ap-180	112	3	]	]	X
ap-180	112	4	krasnoselskij	krasnoselskij	NOUN
ap-180	112	5	,	,	PUNCT
ap-180	112	6	m.	m.	NOUN
ap-180	112	7	a.	a.	PROPN
ap-180	112	8	,	,	PUNCT
ap-180	112	9	zabrejko	zabrejko	NOUN
ap-180	112	10	,	,	PUNCT
ap-180	112	11	p.	p.	PROPN
ap-180	112	12	p.	p.	NOUN
ap-180	112	13	:	:	PUNCT
ap-180	112	14	geometricheskije	geometricheskije	VERB
ap-180	112	15	metody	metody	ADJ
ap-180	112	16	nelinejnogo	nelinejnogo	PROPN
ap-180	112	17	analiza	analiza	PROPN
ap-180	112	18	.	.	PUNCT
ap-180	113	1	moskva	moskva	PROPN
ap-180	113	2	1975	1975	NUM
ap-180	114	1	[	[	X
ap-180	114	2	5	5	NUM
ap-180	114	3	]	]	X
ap-180	114	4	char	char	NOUN
ap-180	114	5	,	,	PUNCT
ap-180	114	6	b.	b.	PROPN
ap-180	114	7	w.	w.	PROPN
ap-180	114	8	,	,	PUNCT
ap-180	114	9	geddes	geddes	PROPN
ap-180	114	10	,	,	PUNCT
ap-180	114	11	k.	k.	PROPN
ap-180	114	12	o.	o.	PROPN
ap-180	114	13	,	,	PUNCT
ap-180	114	14	gonet	gonet	PROPN
ap-180	114	15	,	,	PUNCT
ap-180	114	16	g.	g.	PROPN
ap-180	114	17	h.	h.	PROPN
ap-180	114	18	,	,	PUNCT
ap-180	114	19	leong	leong	PROPN
ap-180	114	20	,	,	PUNCT
ap-180	114	21	b.	b.	PROPN
ap-180	114	22	l.	l.	PROPN
ap-180	114	23	,	,	PUNCT
ap-180	114	24	monagan	monagan	NOUN
ap-180	114	25	,	,	PUNCT
ap-180	114	26	m.	m.	PROPN
ap-180	114	27	b.	b.	PROPN
ap-180	114	28	,	,	PUNCT
ap-180	114	29	watt	watt	PROPN
ap-180	114	30	,	,	PUNCT
ap-180	114	31	s.	s.	PROPN
ap-180	114	32	m.	m.	PROPN
ap-180	114	33	:	:	PUNCT
ap-180	114	34	first	first	ADV
ap-180	114	35	leaves	leave	VERB
ap-180	114	36	:	:	PUNCT
ap-180	114	37	a	a	DET
ap-180	114	38	tutorial	tutorial	ADJ
ap-180	114	39	introduction	introduction	NOUN
ap-180	114	40	to	to	ADP
ap-180	114	41	maple	maple	PROPN
ap-180	114	42	v.	v.	ADP
ap-180	114	43	springer	springer	NOUN
ap-180	114	44	-	-	PUNCT
ap-180	114	45	verlag	verlag	PROPN
ap-180	114	46	1992	1992	NUM
ap-180	114	47	rndr	rndr	PROPN
ap-180	114	48	.	.	PUNCT
ap-180	115	1	marie	marie	PROPN
ap-180	115	2	kopáčková	kopáčková	PROPN
ap-180	115	3	,	,	PUNCT
ap-180	115	4	csc	csc	PROPN
ap-180	115	5	.	.	PROPN
ap-180	115	6	department	department	PROPN
ap-180	115	7	of	of	ADP
ap-180	115	8	mathematics	mathematics	PROPN
ap-180	115	9	phone:+420	phone:+420	NOUN
ap-180	115	10	2	2	NUM
ap-180	115	11	2435	2435	NUM
ap-180	115	12	4385	4385	NUM
ap-180	115	13	e	e	NOUN
ap-180	115	14	-	-	NOUN
ap-180	115	15	mail	mail	NOUN
ap-180	115	16	:	:	PUNCT
ap-180	115	17	marie.kopackova@fsv.cvut.cz	marie.kopackova@fsv.cvut.cz	NUM
ap-180	115	18	czech	czech	PROPN
ap-180	115	19	technical	technical	PROPN
ap-180	115	20	university	university	PROPN
ap-180	115	21	in	in	ADP
ap-180	115	22	prague	prague	PROPN
ap-180	115	23	faculty	faculty	NOUN
ap-180	115	24	of	of	ADP
ap-180	115	25	civil	civil	ADJ
ap-180	115	26	engineering	engineering	NOUN
ap-180	115	27	thákurova	thákurova	PROPN
ap-180	115	28	7	7	NUM
ap-180	115	29	,	,	PUNCT
ap-180	115	30	166	166	NUM
ap-180	115	31	29	29	NUM
ap-180	115	32	praha	praha	NOUN
ap-180	115	33	6	6	NUM
ap-180	115	34	,	,	PUNCT
ap-180	115	35	czech	czech	PROPN
ap-180	115	36	republic	republic	NOUN
ap-180	115	37	22	22	NUM
ap-180	115	38	©	©	PROPN
ap-180	115	39	czech	czech	PROPN
ap-180	115	40	technical	technical	PROPN
ap-180	115	41	university	university	PROPN
ap-180	115	42	publishing	publishing	NOUN
ap-180	115	43	house	house	NOUN
ap-180	115	44	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-180	115	45	acta	acta	PROPN
ap-180	115	46	polytechnica	polytechnica	PROPN
ap-180	115	47	vol	vol	NOUN
ap-180	115	48	.	.	PUNCT
ap-180	116	1	41	41	NUM
ap-180	116	2	no.1/2001	no.1/2001	NOUN
ap-180	116	3	fig	fig	NOUN
ap-180	116	4	.	.	PUNCT
ap-180	117	1	7	7	NUM
ap-180	117	2	:	:	PUNCT
ap-180	117	3	graph	graph	NOUN
ap-180	117	4	of	of	ADP
ap-180	117	5	the	the	DET
ap-180	117	6	maximum	maximum	ADJ
ap-180	117	7	angle	angle	PROPN
ap-180	117	8	�	�	PROPN
ap-180	117	9	0	0	SYM
ap-180	117	10	(	(	PUNCT
ap-180	117	11	l	l	NOUN
ap-180	117	12	)	)	PUNCT
ap-180	117	13	u(l	u(l	NOUN
ap-180	117	14	)	)	PUNCT