id	sid	tid	token	lemma	pos
ap-938	1	1	ap07_2-3.vp	ap07_2-3.vp	VERB
ap-938	1	2	in	in	ADP
ap-938	1	3	this	this	DET
ap-938	1	4	paper	paper	NOUN
ap-938	1	5	we	we	PRON
ap-938	1	6	consider	consider	VERB
ap-938	1	7	an	an	DET
ap-938	1	8	example	example	NOUN
ap-938	1	9	of	of	ADP
ap-938	1	10	a	a	DET
ap-938	1	11	quantum	quantum	NOUN
ap-938	1	12	waveguide	waveguide	NOUN
ap-938	1	13	with	with	ADP
ap-938	1	14	a	a	DET
ap-938	1	15	small	small	ADJ
ap-938	1	16	�	�	PROPN
ap-938	1	17	�	�	NOUN
ap-938	1	18	-symmetric	-symmetric	ADJ
ap-938	1	19	perturbation	perturbation	NOUN
ap-938	1	20	.	.	PUNCT
ap-938	2	1	the	the	DET
ap-938	2	2	perturbed	perturb	VERB
ap-938	2	3	system	system	NOUN
ap-938	2	4	is	be	AUX
ap-938	2	5	weakly	weakly	ADJ
ap-938	2	6	non	non	ADJ
ap-938	2	7	-	-	ADJ
ap-938	2	8	self	self	NOUN
ap-938	2	9	-	-	PUNCT
ap-938	2	10	adjoint	adjoint	NOUN
ap-938	2	11	and	and	CCONJ
ap-938	2	12	we	we	PRON
ap-938	2	13	employ	employ	VERB
ap-938	2	14	general	general	ADJ
ap-938	2	15	results	result	NOUN
ap-938	2	16	of	of	ADP
ap-938	2	17	[	[	X
ap-938	2	18	1	1	NUM
ap-938	2	19	,	,	PUNCT
ap-938	2	20	2	2	NUM
ap-938	2	21	]	]	PUNCT
ap-938	2	22	to	to	PART
ap-938	2	23	study	study	VERB
ap-938	2	24	the	the	DET
ap-938	2	25	problem	problem	NOUN
ap-938	2	26	.	.	PUNCT
ap-938	3	1	the	the	DET
ap-938	3	2	main	main	ADJ
ap-938	3	3	aim	aim	NOUN
ap-938	3	4	is	be	AUX
ap-938	3	5	to	to	PART
ap-938	3	6	show	show	VERB
ap-938	3	7	that	that	SCONJ
ap-938	3	8	the	the	DET
ap-938	3	9	technique	technique	NOUN
ap-938	3	10	suggested	suggest	VERB
ap-938	3	11	in	in	ADP
ap-938	3	12	the	the	DET
ap-938	3	13	cited	cite	VERB
ap-938	3	14	works	work	NOUN
ap-938	3	15	can	can	AUX
ap-938	3	16	be	be	AUX
ap-938	3	17	used	use	VERB
ap-938	3	18	effectively	effectively	ADV
ap-938	3	19	in	in	ADP
ap-938	3	20	the	the	DET
ap-938	3	21	perturbation	perturbation	NOUN
ap-938	3	22	theory	theory	NOUN
ap-938	3	23	for	for	ADP
ap-938	3	24	�	�	PROPN
ap-938	3	25	�	�	PROPN
ap-938	3	26	-symmetric	-symmetric	ADJ
ap-938	3	27	operators	operator	NOUN
ap-938	3	28	.	.	PUNCT
ap-938	4	1	let	let	VERB
ap-938	4	2	x	x	SYM
ap-938	4	3	x	x	SYM
ap-938	4	4	x	x	X
ap-938	4	5	�	�	PROPN
ap-938	4	6	(	(	PUNCT
ap-938	4	7	,	,	PUNCT
ap-938	4	8	)	)	PUNCT
ap-938	4	9	1	1	NUM
ap-938	4	10	2	2	NUM
ap-938	4	11	be	be	AUX
ap-938	4	12	cartesian	cartesian	ADJ
ap-938	4	13	coordinates	coordinate	NOUN
ap-938	4	14	in	in	ADP
ap-938	4	15	�	�	PROPN
ap-938	4	16	2	2	NUM
ap-938	4	17	,	,	PUNCT
ap-938	4	18	�	�	PROPN
ap-938	4	19	�	�	PROPN
ap-938	4	20	�	�	PROPN
ap-938	4	21	�	�	PROPN
ap-938	4	22	�	�	PROPN
ap-938	4	23	�	�	PROPN
ap-938	4	24	�	�	PROPN
ap-938	4	25	x	x	SYM
ap-938	4	26	x	x	NOUN
ap-938	4	27	:	:	PUNCT
ap-938	4	28	�	�	PROPN
ap-938	4	29	�	�	PROPN
ap-938	4	30	2	2	NUM
ap-938	4	31	22	22	NUM
ap-938	4	32	be	be	AUX
ap-938	4	33	an	an	DET
ap-938	4	34	infinite	infinite	ADJ
ap-938	4	35	straight	straight	ADJ
ap-938	4	36	strip	strip	NOUN
ap-938	4	37	.	.	PUNCT
ap-938	5	1	by	by	ADP
ap-938	5	2	v	v	NUM
ap-938	5	3	v	v	NUM
ap-938	5	4	x	x	X
ap-938	5	5	�	�	PROPN
ap-938	5	6	(	(	PUNCT
ap-938	5	7	)	)	PUNCT
ap-938	5	8	we	we	PRON
ap-938	5	9	denote	denote	VERB
ap-938	5	10	a	a	DET
ap-938	5	11	real	real	ADV
ap-938	5	12	-	-	PUNCT
ap-938	5	13	valued	value	VERB
ap-938	5	14	function	function	NOUN
ap-938	5	15	defined	define	VERB
ap-938	5	16	on	on	ADP
ap-938	5	17	�	�	PROPN
ap-938	5	18	having	having	AUX
ap-938	5	19	bounded	bound	VERB
ap-938	5	20	support	support	NOUN
ap-938	5	21	and	and	CCONJ
ap-938	5	22	belonging	belong	VERB
ap-938	5	23	to	to	ADP
ap-938	5	24	l	l	PROPN
ap-938	5	25	�	�	PROPN
ap-938	5	26	(	(	PUNCT
ap-938	5	27	)	)	PUNCT
ap-938	5	28	�	�	PROPN
ap-938	5	29	.	.	PUNCT
ap-938	6	1	we	we	PRON
ap-938	6	2	assume	assume	VERB
ap-938	6	3	that	that	SCONJ
ap-938	6	4	it	it	PRON
ap-938	6	5	satisfies	satisfy	VERB
ap-938	6	6	the	the	DET
ap-938	6	7	following	following	ADJ
ap-938	6	8	assumption	assumption	NOUN
ap-938	6	9	,	,	PUNCT
ap-938	6	10	v	v	NOUN
ap-938	6	11	x	x	SYM
ap-938	6	12	x	x	SYM
ap-938	6	13	v	v	NUM
ap-938	6	14	x	x	SYM
ap-938	6	15	x	x	X
ap-938	6	16	(	(	PUNCT
ap-938	6	17	,	,	PUNCT
ap-938	6	18	)	)	PUNCT
ap-938	6	19	(	(	PUNCT
ap-938	6	20	,	,	PUNCT
ap-938	6	21	)	)	PUNCT
ap-938	6	22	�	�	PROPN
ap-938	6	23	�	�	PROPN
ap-938	6	24	�	�	PROPN
ap-938	6	25	1	1	NUM
ap-938	6	26	2	2	NUM
ap-938	6	27	1	1	NUM
ap-938	6	28	2	2	NUM
ap-938	6	29	,	,	PUNCT
ap-938	6	30	x	x	PROPN
ap-938	6	31	�	�	PROPN
ap-938	6	32	�	�	PROPN
ap-938	6	33	.	.	PUNCT
ap-938	7	1	(	(	PUNCT
ap-938	7	2	1	1	X
ap-938	7	3	)	)	PUNCT
ap-938	7	4	the	the	DET
ap-938	7	5	main	main	ADJ
ap-938	7	6	object	object	NOUN
ap-938	7	7	of	of	ADP
ap-938	7	8	our	our	PRON
ap-938	7	9	study	study	NOUN
ap-938	7	10	is	be	AUX
ap-938	7	11	the	the	DET
ap-938	7	12	operator	operator	NOUN
ap-938	7	13	�	�	PROPN
ap-938	7	14	�	�	PROPN
ap-938	7	15	�	�	PROPN
ap-938	7	16	:	:	PUNCT
ap-938	7	17	�	�	PROPN
ap-938	7	18	�	�	PROPN
ap-938	7	19	�	�	PROPN
ap-938	8	1	i	i	PRON
ap-938	8	2	v	v	NOUN
ap-938	8	3	(	(	PUNCT
ap-938	8	4	2	2	NUM
ap-938	8	5	)	)	PUNCT
ap-938	8	6	on	on	ADP
ap-938	8	7	�	�	PROPN
ap-938	8	8	subject	subject	NOUN
ap-938	8	9	to	to	ADP
ap-938	8	10	the	the	DET
ap-938	8	11	dirichlet	dirichlet	PROPN
ap-938	8	12	boundary	boundary	PROPN
ap-938	8	13	condition	condition	NOUN
ap-938	8	14	.	.	PUNCT
ap-938	9	1	we	we	PRON
ap-938	9	2	define	define	VERB
ap-938	9	3	it	it	PRON
ap-938	9	4	rigorously	rigorously	ADV
ap-938	9	5	as	as	ADP
ap-938	9	6	an	an	DET
ap-938	9	7	unbounded	unbounded	ADJ
ap-938	9	8	operator	operator	NOUN
ap-938	9	9	in	in	ADP
ap-938	9	10	l2	l2	NOUN
ap-938	9	11	(	(	PUNCT
ap-938	9	12	)	)	PUNCT
ap-938	9	13	�	�	PROPN
ap-938	9	14	with	with	ADP
ap-938	9	15	the	the	DET
ap-938	9	16	domain	domain	NOUN
ap-938	9	17	w2	w2	NOUN
ap-938	9	18	0	0	NUM
ap-938	9	19	2	2	NUM
ap-938	9	20	,	,	PUNCT
ap-938	9	21	(	(	PUNCT
ap-938	9	22	)	)	PUNCT
ap-938	9	23	�	�	PROPN
ap-938	9	24	,	,	PUNCT
ap-938	9	25	where	where	SCONJ
ap-938	9	26	the	the	DET
ap-938	9	27	latter	latter	ADJ
ap-938	9	28	is	be	AUX
ap-938	9	29	a	a	DET
ap-938	9	30	subspace	subspace	NOUN
ap-938	9	31	of	of	ADP
ap-938	9	32	w2	w2	NOUN
ap-938	9	33	2	2	NUM
ap-938	9	34	(	(	PUNCT
ap-938	9	35	)	)	PUNCT
ap-938	9	36	�	�	PROPN
ap-938	9	37	of	of	ADP
ap-938	9	38	the	the	DET
ap-938	9	39	functions	function	NOUN
ap-938	9	40	vanishing	vanish	VERB
ap-938	9	41	on	on	ADP
ap-938	9	42	�	�	PROPN
ap-938	9	43	�	�	PROPN
ap-938	9	44	.	.	PUNCT
ap-938	10	1	the	the	DET
ap-938	10	2	symbol	symbol	NOUN
ap-938	10	3	�	�	PROPN
ap-938	10	4	indicates	indicate	VERB
ap-938	10	5	a	a	DET
ap-938	10	6	small	small	ADJ
ap-938	10	7	positive	positive	ADJ
ap-938	10	8	parameter	parameter	NOUN
ap-938	10	9	.	.	PUNCT
ap-938	11	1	the	the	DET
ap-938	11	2	dirichlet	dirichlet	PROPN
ap-938	11	3	laplacian	laplacian	PROPN
ap-938	11	4	on	on	ADP
ap-938	11	5	�	�	PROPN
ap-938	11	6	is	be	AUX
ap-938	11	7	a	a	DET
ap-938	11	8	closed	closed	ADJ
ap-938	11	9	operator	operator	NOUN
ap-938	11	10	in	in	ADP
ap-938	11	11	l2	l2	NOUN
ap-938	11	12	(	(	PUNCT
ap-938	11	13	)	)	PUNCT
ap-938	11	14	�	�	PROPN
ap-938	11	15	and	and	CCONJ
ap-938	11	16	the	the	DET
ap-938	11	17	multiplication	multiplication	NOUN
ap-938	11	18	operator	operator	NOUN
ap-938	11	19	by	by	ADP
ap-938	11	20	v	v	NOUN
ap-938	11	21	is	be	AUX
ap-938	11	22	relatively	relatively	ADV
ap-938	11	23	bounded	bound	VERB
ap-938	11	24	.	.	PUNCT
ap-938	12	1	because	because	SCONJ
ap-938	12	2	of	of	ADP
ap-938	12	3	this	this	PRON
ap-938	12	4	the	the	DET
ap-938	12	5	operator	operator	NOUN
ap-938	12	6	�	�	PROPN
ap-938	12	7	�	�	PROPN
ap-938	12	8	is	be	AUX
ap-938	12	9	closed	closed	ADJ
ap-938	12	10	.	.	PUNCT
ap-938	13	1	it	it	PRON
ap-938	13	2	can	can	AUX
ap-938	13	3	also	also	ADV
ap-938	13	4	be	be	AUX
ap-938	13	5	shown	show	VERB
ap-938	13	6	that	that	SCONJ
ap-938	13	7	it	it	PRON
ap-938	13	8	is	be	AUX
ap-938	13	9	m	m	NOUN
ap-938	13	10	-	-	ADJ
ap-938	13	11	sectorial	sectorial	ADJ
ap-938	13	12	.	.	PUNCT
ap-938	14	1	the	the	DET
ap-938	14	2	main	main	ADJ
ap-938	14	3	property	property	NOUN
ap-938	14	4	of	of	ADP
ap-938	14	5	the	the	DET
ap-938	14	6	operator	operator	NOUN
ap-938	14	7	�	�	PROPN
ap-938	14	8	�	�	PROPN
ap-938	14	9	is	be	AUX
ap-938	14	10	�	�	PROPN
ap-938	14	11	�	�	NOUN
ap-938	14	12	-symmetricity	-symmetricity	NOUN
ap-938	14	13	expressed	express	VERB
ap-938	14	14	by	by	ADP
ap-938	14	15	the	the	DET
ap-938	14	16	identity	identity	NOUN
ap-938	14	17	�	�	PROPN
ap-938	14	18	�	�	PROPN
ap-938	14	19	�	�	PROPN
ap-938	14	20	�	�	PROPN
ap-938	14	21	*	*	SYM
ap-938	14	22	�	�	PROPN
ap-938	14	23	�	�	PROPN
ap-938	14	24	�	�	PROPN
ap-938	14	25	�	�	PROPN
ap-938	14	26	1	1	NUM
ap-938	14	27	,	,	PUNCT
ap-938	14	28	where	where	SCONJ
ap-938	14	29	(	(	PUNCT
ap-938	14	30	)	)	PUNCT
ap-938	14	31	(	(	PUNCT
ap-938	14	32	)	)	PUNCT
ap-938	14	33	(	(	PUNCT
ap-938	14	34	,	,	PUNCT
ap-938	14	35	)	)	PUNCT
ap-938	14	36	�	�	PROPN
ap-938	14	37	u	u	NOUN
ap-938	14	38	x	x	SYM
ap-938	14	39	u	u	NOUN
ap-938	14	40	x	x	SYM
ap-938	14	41	x	x	X
ap-938	14	42	�	�	X
ap-938	14	43	�	�	PROPN
ap-938	14	44	1	1	NUM
ap-938	14	45	2	2	NUM
ap-938	14	46	.	.	PUNCT
ap-938	15	1	our	our	PRON
ap-938	15	2	aim	aim	NOUN
ap-938	15	3	is	be	AUX
ap-938	15	4	to	to	PART
ap-938	15	5	study	study	VERB
ap-938	15	6	the	the	DET
ap-938	15	7	spectrum	spectrum	NOUN
ap-938	15	8	of	of	ADP
ap-938	15	9	the	the	DET
ap-938	15	10	operator	operator	NOUN
ap-938	15	11	�	�	PROPN
ap-938	15	12	�	�	PROPN
ap-938	15	13	.	.	PUNCT
ap-938	16	1	we	we	PRON
ap-938	16	2	will	will	AUX
ap-938	16	3	focus	focus	VERB
ap-938	16	4	our	our	PRON
ap-938	16	5	attention	attention	NOUN
ap-938	16	6	on	on	ADP
ap-938	16	7	the	the	DET
ap-938	16	8	continuous	continuous	ADJ
ap-938	16	9	,	,	PUNCT
ap-938	16	10	residual	residual	ADJ
ap-938	16	11	and	and	CCONJ
ap-938	16	12	point	point	NOUN
ap-938	16	13	spectrum	spectrum	NOUN
ap-938	16	14	of	of	ADP
ap-938	16	15	this	this	DET
ap-938	16	16	operator	operator	NOUN
ap-938	16	17	.	.	PUNCT
ap-938	17	1	we	we	PRON
ap-938	17	2	define	define	VERB
ap-938	17	3	these	these	DET
ap-938	17	4	subsets	subset	NOUN
ap-938	17	5	of	of	ADP
ap-938	17	6	the	the	DET
ap-938	17	7	spectrum	spectrum	NOUN
ap-938	17	8	in	in	ADP
ap-938	17	9	accordance	accordance	NOUN
ap-938	17	10	with	with	ADP
ap-938	17	11	[	[	X
ap-938	17	12	3	3	NUM
ap-938	17	13	]	]	PUNCT
ap-938	17	14	.	.	PUNCT
ap-938	18	1	namely	namely	ADV
ap-938	18	2	,	,	PUNCT
ap-938	18	3	the	the	DET
ap-938	18	4	continuous	continuous	ADJ
ap-938	18	5	spectrum	spectrum	NOUN
ap-938	18	6	is	be	AUX
ap-938	18	7	introduced	introduce	VERB
ap-938	18	8	in	in	ADP
ap-938	18	9	terms	term	NOUN
ap-938	18	10	of	of	ADP
ap-938	18	11	singular	singular	ADJ
ap-938	18	12	sequence	sequence	NOUN
ap-938	18	13	,	,	PUNCT
ap-938	18	14	the	the	DET
ap-938	18	15	point	point	NOUN
ap-938	18	16	spectrum	spectrum	NOUN
ap-938	18	17	is	be	AUX
ap-938	18	18	the	the	DET
ap-938	18	19	set	set	NOUN
ap-938	18	20	of	of	ADP
ap-938	18	21	all	all	DET
ap-938	18	22	eigenvalues	eigenvalue	NOUN
ap-938	18	23	,	,	PUNCT
ap-938	18	24	and	and	CCONJ
ap-938	18	25	the	the	DET
ap-938	18	26	residual	residual	ADJ
ap-938	18	27	spectrum	spectrum	NOUN
ap-938	18	28	is	be	AUX
ap-938	18	29	the	the	DET
ap-938	18	30	complement	complement	NOUN
ap-938	18	31	of	of	ADP
ap-938	18	32	the	the	DET
ap-938	18	33	continuous	continuous	ADJ
ap-938	18	34	and	and	CCONJ
ap-938	18	35	point	point	NOUN
ap-938	18	36	spectrum	spectrum	NOUN
ap-938	18	37	with	with	ADP
ap-938	18	38	reference	reference	NOUN
ap-938	18	39	to	to	ADP
ap-938	18	40	the	the	DET
ap-938	18	41	whole	whole	ADJ
ap-938	18	42	spectrum	spectrum	NOUN
ap-938	18	43	.	.	PUNCT
ap-938	19	1	our	our	PRON
ap-938	19	2	first	first	ADJ
ap-938	19	3	result	result	NOUN
ap-938	19	4	describes	describe	VERB
ap-938	19	5	the	the	DET
ap-938	19	6	continuous	continuous	ADJ
ap-938	19	7	and	and	CCONJ
ap-938	19	8	residual	residual	ADJ
ap-938	19	9	spectrum	spectrum	NOUN
ap-938	19	10	of	of	ADP
ap-938	19	11	h	h	PROPN
ap-938	19	12	�	�	PROPN
ap-938	19	13	.	.	PUNCT
ap-938	19	14	theorem	theorem	VERB
ap-938	19	15	1	1	NUM
ap-938	19	16	the	the	DET
ap-938	19	17	residual	residual	ADJ
ap-938	19	18	spectrum	spectrum	NOUN
ap-938	19	19	of	of	ADP
ap-938	19	20	�	�	PROPN
ap-938	19	21	�	�	PROPN
ap-938	19	22	is	be	AUX
ap-938	19	23	empty	empty	ADJ
ap-938	19	24	and	and	CCONJ
ap-938	19	25	the	the	DET
ap-938	19	26	continuous	continuous	ADJ
ap-938	19	27	one	one	NOUN
ap-938	19	28	coincides	coincide	VERB
ap-938	19	29	with	with	ADP
ap-938	19	30	�	�	PROPN
ap-938	19	31	1	1	NUM
ap-938	19	32	,	,	PUNCT
ap-938	19	33	�	�	PROPN
ap-938	19	34	.	.	PUNCT
ap-938	20	1	the	the	DET
ap-938	20	2	proof	proof	NOUN
ap-938	20	3	is	be	AUX
ap-938	20	4	the	the	DET
ap-938	20	5	same	same	ADJ
ap-938	20	6	as	as	ADP
ap-938	20	7	the	the	DET
ap-938	20	8	proof	proof	NOUN
ap-938	20	9	of	of	ADP
ap-938	20	10	similar	similar	ADJ
ap-938	20	11	results	result	NOUN
ap-938	20	12	in	in	ADP
ap-938	20	13	[	[	PUNCT
ap-938	20	14	4];	4];	PROPN
ap-938	20	15	we	we	PRON
ap-938	20	16	therefore	therefore	ADV
ap-938	20	17	do	do	AUX
ap-938	20	18	not	not	PART
ap-938	20	19	give	give	VERB
ap-938	20	20	the	the	DET
ap-938	20	21	proof	proof	NOUN
ap-938	20	22	here	here	ADV
ap-938	20	23	.	.	PUNCT
ap-938	21	1	it	it	PRON
ap-938	21	2	is	be	AUX
ap-938	21	3	well	well	ADV
ap-938	21	4	-	-	PUNCT
ap-938	21	5	known	know	VERB
ap-938	21	6	that	that	SCONJ
ap-938	21	7	the	the	DET
ap-938	21	8	spectrum	spectrum	NOUN
ap-938	21	9	of	of	ADP
ap-938	21	10	operator	operator	NOUN
ap-938	21	11	�	�	PROPN
ap-938	21	12	0	0	NUM
ap-938	21	13	is	be	AUX
ap-938	21	14	purely	purely	ADV
ap-938	21	15	continuous	continuous	ADJ
ap-938	21	16	and	and	CCONJ
ap-938	21	17	coincides	coincide	VERB
ap-938	21	18	with	with	ADP
ap-938	21	19	�	�	PROPN
ap-938	21	20	1	1	NUM
ap-938	21	21	,	,	PUNCT
ap-938	21	22	�	�	PROPN
ap-938	21	23	.	.	PUNCT
ap-938	22	1	the	the	DET
ap-938	22	2	small	small	ADJ
ap-938	22	3	perturbation	perturbation	NOUN
ap-938	22	4	�	�	NOUN
ap-938	22	5	v	v	NOUN
ap-938	22	6	can	can	AUX
ap-938	22	7	generate	generate	VERB
ap-938	22	8	an	an	DET
ap-938	22	9	eigenvalue	eigenvalue	NOUN
ap-938	22	10	converging	converging	NOUN
ap-938	22	11	to	to	ADP
ap-938	22	12	the	the	DET
ap-938	22	13	threshold	threshold	NOUN
ap-938	22	14	of	of	ADP
ap-938	22	15	the	the	DET
ap-938	22	16	continuous	continuous	ADJ
ap-938	22	17	spectrum	spectrum	NOUN
ap-938	22	18	.	.	PUNCT
ap-938	23	1	our	our	PRON
ap-938	23	2	second	second	ADJ
ap-938	23	3	theorem	theorem	ADJ
ap-938	23	4	deals	deal	NOUN
ap-938	23	5	with	with	ADP
ap-938	23	6	the	the	DET
ap-938	23	7	existence	existence	NOUN
ap-938	23	8	and	and	CCONJ
ap-938	23	9	asymptotic	asymptotic	ADJ
ap-938	23	10	behaviour	behaviour	NOUN
ap-938	23	11	of	of	ADP
ap-938	23	12	such	such	DET
ap-938	23	13	an	an	DET
ap-938	23	14	eigenvalue	eigenvalue	NOUN
ap-938	23	15	.	.	PUNCT
ap-938	24	1	before	before	ADP
ap-938	24	2	formulating	formulate	VERB
ap-938	24	3	it	it	PRON
ap-938	24	4	,	,	PUNCT
ap-938	24	5	we	we	PRON
ap-938	24	6	introduce	introduce	VERB
ap-938	24	7	auxiliary	auxiliary	ADJ
ap-938	24	8	notations	notation	NOUN
ap-938	24	9	.	.	PUNCT
ap-938	25	1	we	we	PRON
ap-938	25	2	denote	denote	VERB
ap-938	25	3	�	�	PROPN
ap-938	25	4	�	�	PROPN
ap-938	25	5	�	�	PROPN
ap-938	25	6	�	�	PROPN
ap-938	25	7	�	�	PROPN
ap-938	26	1	j	j	PROPN
ap-938	27	1	j	j	PROPN
ap-938	27	2	j	j	PROPN
ap-938	27	3	x	x	X
ap-938	27	4	jx	jx	PROPN
ap-938	27	5	v	v	INTJ
ap-938	27	6	x	x	SYM
ap-938	27	7	v	v	NOUN
ap-938	27	8	x	x	SYM
ap-938	27	9	x	x	SYM
ap-938	27	10	x	x	SYM
ap-938	27	11	x	x	SYM
ap-938	27	12	u	u	NOUN
ap-938	27	13	(	(	PUNCT
ap-938	27	14	):	):	PUNCT
ap-938	27	15	sin	sin	NOUN
ap-938	27	16	,	,	PUNCT
ap-938	27	17	(	(	PUNCT
ap-938	27	18	):	):	PUNCT
ap-938	27	19	(	(	PUNCT
ap-938	27	20	)	)	PUNCT
ap-938	27	21	(	(	PUNCT
ap-938	27	22	)	)	PUNCT
ap-938	27	23	(	(	PUNCT
ap-938	27	24	)	)	PUNCT
ap-938	27	25	,	,	PUNCT
ap-938	27	26	2	2	NUM
ap-938	27	27	2	2	NUM
ap-938	27	28	1	1	NUM
ap-938	27	29	1	1	NUM
ap-938	27	30	2	2	NUM
ap-938	27	31	2	2	NUM
ap-938	27	32	2	2	NUM
ap-938	27	33	0	0	NUM
ap-938	27	34	1	1	NUM
ap-938	27	35	2	2	NUM
ap-938	27	36	�	�	PROPN
ap-938	27	37	�	�	PROPN
ap-938	27	38	�	�	PROPN
ap-938	27	39	d	d	PROPN
ap-938	27	40	(	(	PUNCT
ap-938	27	41	):	):	PUNCT
ap-938	27	42	(	(	PUNCT
ap-938	27	43	)	)	PUNCT
ap-938	27	44	,	,	PUNCT
ap-938	27	45	(	(	PUNCT
ap-938	27	46	):	):	PUNCT
ap-938	27	47	x	x	PUNCT
ap-938	27	48	x	x	SYM
ap-938	27	49	t	t	NOUN
ap-938	27	50	v	v	NUM
ap-938	27	51	t	t	PROPN
ap-938	27	52	t	t	X
ap-938	27	53	u	u	X
ap-938	28	1	x	x	PROPN
ap-938	28	2	j	j	PROPN
ap-938	28	3	ej	ej	PROPN
ap-938	28	4	j	j	PROPN
ap-938	28	5	x	x	SYM
ap-938	28	6	t	t	PROPN
ap-938	28	7	1	1	NUM
ap-938	28	8	1	1	NUM
ap-938	28	9	1	1	NUM
ap-938	28	10	1	1	NUM
ap-938	28	11	1	1	NUM
ap-938	28	12	1	1	NUM
ap-938	28	13	1	1	NUM
ap-938	28	14	2	2	NUM
ap-938	28	15	1	1	NUM
ap-938	28	16	1	1	NUM
ap-938	28	17	2	2	NUM
ap-938	28	18	1	1	NUM
ap-938	28	19	1	1	NUM
ap-938	28	20	2	2	NUM
ap-938	28	21	1	1	NUM
ap-938	28	22	1	1	NUM
ap-938	28	23	�	�	PROPN
ap-938	28	24	�	�	PROPN
ap-938	28	25	�	�	PROPN
ap-938	28	26	�	�	PROPN
ap-938	28	27	�	�	PROPN
ap-938	28	28	�	�	PROPN
ap-938	28	29	�	�	PROPN
ap-938	28	30	�	�	PROPN
ap-938	28	31	�	�	PROPN
ap-938	28	32	d	d	PROPN
ap-938	28	33	�	�	PROPN
ap-938	28	34	v	v	ADP
ap-938	28	35	t	t	PROPN
ap-938	28	36	tj	tj	PROPN
ap-938	28	37	(	(	PUNCT
ap-938	28	38	)	)	PUNCT
ap-938	28	39	.1	.1	NUM
ap-938	29	1	1d	1d	NUM
ap-938	29	2	�	�	PROPN
ap-938	29	3	�	�	PROPN
ap-938	29	4	employing	employ	VERB
ap-938	29	5	these	these	DET
ap-938	29	6	functions	function	NOUN
ap-938	29	7	,	,	PUNCT
ap-938	29	8	we	we	PRON
ap-938	29	9	define	define	VERB
ap-938	29	10	~	~	PUNCT
ap-938	29	11	(	(	PUNCT
ap-938	29	12	):	):	PUNCT
ap-938	29	13	(	(	PUNCT
ap-938	29	14	)	)	PUNCT
ap-938	29	15	(	(	PUNCT
ap-938	29	16	)	)	PUNCT
ap-938	29	17	(	(	PUNCT
ap-938	29	18	(	(	PUNCT
ap-938	29	19	)	)	PUNCT
ap-938	29	20	(	(	PUNCT
ap-938	29	21	)	)	PUNCT
ap-938	29	22	)	)	PUNCT
ap-938	29	23	(	(	PUNCT
ap-938	29	24	)	)	PUNCT
ap-938	29	25	,	,	PUNCT
ap-938	29	26	~	~	PUNCT
ap-938	29	27	(	(	PUNCT
ap-938	29	28	)	)	PUNCT
ap-938	29	29	v	v	NOUN
ap-938	29	30	x	x	SYM
ap-938	29	31	v	v	NOUN
ap-938	29	32	x	x	SYM
ap-938	29	33	x	x	SYM
ap-938	29	34	v	v	ADP
ap-938	29	35	x	x	SYM
ap-938	29	36	v	v	NOUN
ap-938	29	37	x	x	SYM
ap-938	29	38	x	x	PUNCT
ap-938	29	39	u	u	NOUN
ap-938	29	40	x	x	PROPN
ap-938	29	41	j	j	PROPN
ap-938	29	42	j	j	PROPN
ap-938	29	43	j	j	PROPN
ap-938	29	44	�	�	PROPN
ap-938	29	45	�	�	PROPN
ap-938	29	46	�	�	PROPN
ap-938	29	47	�	�	PROPN
ap-938	29	48	�	�	PROPN
ap-938	29	49	1	1	NUM
ap-938	29	50	2	2	NUM
ap-938	29	51	2	2	NUM
ap-938	29	52	1	1	NUM
ap-938	29	53	1	1	NUM
ap-938	29	54	1	1	NUM
ap-938	29	55	2	2	NUM
ap-938	29	56	�	�	PROPN
ap-938	29	57	�	�	PROPN
ap-938	29	58	:	:	PUNCT
ap-938	29	59	(	(	PUNCT
ap-938	29	60	)	)	PUNCT
ap-938	29	61	(	(	PUNCT
ap-938	29	62	)	)	PUNCT
ap-938	29	63	.	.	PUNCT
ap-938	30	1	�	�	PROPN
ap-938	30	2	�	�	PROPN
ap-938	30	3	�	�	PROPN
ap-938	30	4	u	u	PROPN
ap-938	30	5	x	x	PROPN
ap-938	30	6	xj	xj	PROPN
ap-938	30	7	j	j	PROPN
ap-938	30	8	j	j	PROPN
ap-938	30	9	1	1	NUM
ap-938	30	10	2	2	NUM
ap-938	30	11	2	2	NUM
ap-938	30	12	�	�	NOUN
ap-938	30	13	the	the	DET
ap-938	30	14	function	function	NOUN
ap-938	30	15	~u	~u	NUM
ap-938	30	16	is	be	AUX
ap-938	30	17	well	well	ADV
ap-938	30	18	-	-	PUNCT
ap-938	30	19	defined	define	VERB
ap-938	30	20	and	and	CCONJ
ap-938	30	21	belongs	belong	VERB
ap-938	30	22	to	to	ADP
ap-938	30	23	w2	w2	NOUN
ap-938	30	24	2	2	NUM
ap-938	30	25	(	(	PUNCT
ap-938	30	26	)	)	PUNCT
ap-938	30	27	�	�	PROPN
ap-938	30	28	.	.	PUNCT
ap-938	31	1	it	it	PRON
ap-938	31	2	can	can	AUX
ap-938	31	3	be	be	AUX
ap-938	31	4	shown	show	VERB
ap-938	31	5	that	that	SCONJ
ap-938	31	6	it	it	PRON
ap-938	31	7	is	be	AUX
ap-938	31	8	an	an	DET
ap-938	31	9	exponentially	exponentially	ADV
ap-938	31	10	decaying	decay	VERB
ap-938	31	11	solution	solution	NOUN
ap-938	31	12	to	to	ADP
ap-938	31	13	the	the	DET
ap-938	31	14	problem	problem	NOUN
ap-938	31	15	�	�	PROPN
ap-938	31	16	�	�	PROPN
ap-938	31	17	�	�	PROPN
ap-938	31	18	�	�	PROPN
ap-938	31	19	�	�	PROPN
ap-938	31	20	�	�	PROPN
ap-938	31	21	�	�	PROPN
ap-938	31	22	�	�	PROPN
ap-938	31	23	~	~	PUNCT
ap-938	31	24	~	~	PUNCT
ap-938	32	1	~	~	PUNCT
ap-938	32	2	,	,	PUNCT
ap-938	32	3	~	~	PUNCT
ap-938	32	4	,	,	PUNCT
ap-938	32	5	.	.	PUNCT
ap-938	33	1	u	u	PRON
ap-938	33	2	u	u	NOUN
ap-938	33	3	v	v	NOUN
ap-938	33	4	x	x	SYM
ap-938	33	5	u	u	NOUN
ap-938	33	6	x0	x0	PROPN
ap-938	33	7	�	�	PROPN
ap-938	33	8	(	(	PUNCT
ap-938	33	9	3	3	NUM
ap-938	33	10	)	)	PUNCT
ap-938	33	11	finally	finally	ADV
ap-938	33	12	,	,	PUNCT
ap-938	33	13	we	we	PRON
ap-938	33	14	introduce	introduce	VERB
ap-938	33	15	a	a	DET
ap-938	33	16	number	number	NOUN
ap-938	33	17	k	k	NOUN
ap-938	33	18	by	by	ADP
ap-938	33	19	the	the	DET
ap-938	33	20	formula	formula	NOUN
ap-938	33	21	©	©	PROPN
ap-938	33	22	czech	czech	PROPN
ap-938	33	23	technical	technical	PROPN
ap-938	33	24	university	university	PROPN
ap-938	33	25	publishing	publishing	NOUN
ap-938	33	26	house	house	NOUN
ap-938	33	27	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-938	33	28	57	57	NUM
ap-938	33	29	acta	acta	PROPN
ap-938	33	30	polytechnica	polytechnica	PROPN
ap-938	33	31	vol	vol	NOUN
ap-938	33	32	.	.	PUNCT
ap-938	34	1	47	47	NUM
ap-938	34	2	no	no	INTJ
ap-938	34	3	.	.	PUNCT
ap-938	35	1	2–3/2007	2–3/2007	NUM
ap-938	35	2	on	on	ADP
ap-938	35	3	a	a	DET
ap-938	35	4	quantum	quantum	NOUN
ap-938	35	5	waveguide	waveguide	NOUN
ap-938	35	6	with	with	ADP
ap-938	35	7	a	a	DET
ap-938	35	8	small	small	ADJ
ap-938	35	9	�	�	NOUN
ap-938	35	10	�	�	PROPN
ap-938	35	11	-symmetric	-symmetric	ADJ
ap-938	35	12	perturbation	perturbation	NOUN
ap-938	35	13	d.	d.	PROPN
ap-938	35	14	borisov	borisov	PROPN
ap-938	35	15	we	we	PRON
ap-938	35	16	consider	consider	VERB
ap-938	35	17	a	a	DET
ap-938	35	18	quantum	quantum	NOUN
ap-938	35	19	waveguide	waveguide	NOUN
ap-938	35	20	with	with	ADP
ap-938	35	21	a	a	DET
ap-938	35	22	small	small	ADJ
ap-938	35	23	�	�	NOUN
ap-938	35	24	�	�	NOUN
ap-938	35	25	-symmetric	-symmetric	ADJ
ap-938	35	26	perturbation	perturbation	NOUN
ap-938	35	27	described	describe	VERB
ap-938	35	28	by	by	ADP
ap-938	35	29	a	a	DET
ap-938	35	30	potential	potential	NOUN
ap-938	35	31	.	.	PUNCT
ap-938	36	1	we	we	PRON
ap-938	36	2	study	study	VERB
ap-938	36	3	the	the	DET
ap-938	36	4	spectrum	spectrum	NOUN
ap-938	36	5	of	of	ADP
ap-938	36	6	such	such	DET
ap-938	36	7	a	a	DET
ap-938	36	8	system	system	NOUN
ap-938	36	9	and	and	CCONJ
ap-938	36	10	show	show	VERB
ap-938	36	11	that	that	SCONJ
ap-938	36	12	the	the	DET
ap-938	36	13	perturbation	perturbation	NOUN
ap-938	36	14	can	can	AUX
ap-938	36	15	produce	produce	VERB
ap-938	36	16	eigenvalues	eigenvalue	NOUN
ap-938	36	17	near	near	ADP
ap-938	36	18	the	the	DET
ap-938	36	19	threshold	threshold	NOUN
ap-938	36	20	of	of	ADP
ap-938	36	21	the	the	DET
ap-938	36	22	continuous	continuous	ADJ
ap-938	36	23	spectrum	spectrum	NOUN
ap-938	36	24	.	.	PUNCT
ap-938	37	1	keywords	keyword	NOUN
ap-938	37	2	:	:	PUNCT
ap-938	37	3	waveguide	waveguide	ADJ
ap-938	37	4	,	,	PUNCT
ap-938	37	5	�	�	PROPN
ap-938	37	6	�	�	NOUN
ap-938	37	7	-symmetric	-symmetric	ADJ
ap-938	37	8	potential	potential	NOUN
ap-938	37	9	,	,	PUNCT
ap-938	37	10	spectrum	spectrum	NOUN
ap-938	37	11	k	k	PROPN
ap-938	37	12	u	u	PROPN
ap-938	37	13	v	v	INTJ
ap-938	37	14	ul	ul	NOUN
ap-938	37	15	l	l	NOUN
ap-938	37	16	:	:	PUNCT
ap-938	37	17	(	(	PUNCT
ap-938	37	18	~,~	~,~	NUM
ap-938	37	19	)	)	PUNCT
ap-938	37	20	(	(	PUNCT
ap-938	37	21	)	)	PUNCT
ap-938	37	22	(	(	PUNCT
ap-938	37	23	)	)	PUNCT
ap-938	37	24	�	�	PROPN
ap-938	37	25	�	�	PROPN
ap-938	37	26	�	�	PROPN
ap-938	37	27	1	1	NUM
ap-938	37	28	2	2	NUM
ap-938	37	29	2	2	NUM
ap-938	37	30	2	2	NUM
ap-938	37	31	�	�	PROPN
ap-938	37	32	�	�	PROPN
ap-938	37	33	.	.	PUNCT
ap-938	38	1	we	we	PRON
ap-938	38	2	will	will	AUX
ap-938	38	3	show	show	VERB
ap-938	38	4	below	below	ADP
ap-938	38	5	that	that	PRON
ap-938	38	6	the	the	DET
ap-938	38	7	first	first	ADJ
ap-938	38	8	norm	norm	NOUN
ap-938	38	9	in	in	ADP
ap-938	38	10	this	this	DET
ap-938	38	11	formula	formula	NOUN
ap-938	38	12	is	be	AUX
ap-938	38	13	well	well	ADV
ap-938	38	14	-	-	PUNCT
ap-938	38	15	defined	define	VERB
ap-938	38	16	.	.	PUNCT
ap-938	39	1	theorem	theorem	ADJ
ap-938	39	2	2	2	NUM
ap-938	39	3	if	if	SCONJ
ap-938	39	4	k>0	k>0	ADJ
ap-938	39	5	,	,	PUNCT
ap-938	39	6	there	there	PRON
ap-938	39	7	exists	exist	VERB
ap-938	39	8	the	the	DET
ap-938	39	9	unique	unique	ADJ
ap-938	39	10	eigenvalue	eigenvalue	NOUN
ap-938	39	11	of	of	ADP
ap-938	39	12	the	the	DET
ap-938	39	13	operator	operator	NOUN
ap-938	39	14	�	�	PROPN
ap-938	39	15	�	�	PROPN
ap-938	39	16	,	,	PUNCT
ap-938	39	17	converging	converge	VERB
ap-938	39	18	to	to	ADP
ap-938	39	19	the	the	DET
ap-938	39	20	threshold	threshold	NOUN
ap-938	39	21	of	of	ADP
ap-938	39	22	the	the	DET
ap-938	39	23	continuous	continuous	ADJ
ap-938	39	24	spectrum	spectrum	NOUN
ap-938	39	25	.	.	PUNCT
ap-938	40	1	this	this	DET
ap-938	40	2	eigenvalue	eigenvalue	PROPN
ap-938	40	3	is	be	AUX
ap-938	40	4	simple	simple	ADJ
ap-938	40	5	,	,	PUNCT
ap-938	40	6	real	real	ADJ
ap-938	40	7	and	and	CCONJ
ap-938	40	8	satisfies	satisfy	VERB
ap-938	40	9	the	the	DET
ap-938	40	10	asymptotic	asymptotic	ADJ
ap-938	40	11	formula	formula	NOUN
ap-938	40	12	�	�	PROPN
ap-938	40	13	�	�	PROPN
ap-938	40	14	�	�	PROPN
ap-938	40	15	�	�	PROPN
ap-938	40	16	�	�	PROPN
ap-938	40	17	�	�	PROPN
ap-938	40	18	�	�	PROPN
ap-938	40	19	1	1	NUM
ap-938	40	20	4	4	NUM
ap-938	40	21	0	0	NUM
ap-938	40	22	4	4	NUM
ap-938	40	23	2	2	NUM
ap-938	40	24	5k	5k	NUM
ap-938	40	25	�	�	PROPN
ap-938	40	26	(	(	PUNCT
ap-938	40	27	)	)	PUNCT
ap-938	40	28	,	,	PUNCT
ap-938	40	29	.	.	PUNCT
ap-938	41	1	(	(	PUNCT
ap-938	41	2	4	4	X
ap-938	41	3	)	)	PUNCT
ap-938	41	4	if	if	SCONJ
ap-938	41	5	k<0	k<0	NOUN
ap-938	41	6	,	,	PUNCT
ap-938	41	7	the	the	DET
ap-938	41	8	operator	operator	NOUN
ap-938	41	9	�	�	PROPN
ap-938	41	10	�	�	PROPN
ap-938	41	11	has	have	VERB
ap-938	41	12	no	no	DET
ap-938	41	13	eigenvalues	eigenvalue	NOUN
ap-938	41	14	converging	converge	VERB
ap-938	41	15	to	to	ADP
ap-938	41	16	the	the	DET
ap-938	41	17	threshold	threshold	NOUN
ap-938	41	18	of	of	ADP
ap-938	41	19	the	the	DET
ap-938	41	20	continuous	continuous	ADJ
ap-938	41	21	spectrum	spectrum	NOUN
ap-938	41	22	as	as	ADP
ap-938	41	23	�	�	PROPN
ap-938	41	24	�	�	PROPN
ap-938	41	25	0	0	NUM
ap-938	41	26	.	.	PUNCT
ap-938	42	1	in	in	ADP
ap-938	42	2	particular	particular	ADJ
ap-938	42	3	,	,	PUNCT
ap-938	42	4	if	if	SCONJ
ap-938	42	5	v	v	NOUN
ap-938	42	6	x	x	SYM
ap-938	42	7	v	v	NOUN
ap-938	42	8	x	x	X
ap-938	42	9	(	(	PUNCT
ap-938	42	10	)	)	PUNCT
ap-938	42	11	(	(	PUNCT
ap-938	42	12	)	)	PUNCT
ap-938	42	13	�	�	PROPN
ap-938	42	14	1	1	NUM
ap-938	42	15	1	1	NUM
ap-938	42	16	(	(	PUNCT
ap-938	42	17	5	5	NUM
ap-938	42	18	)	)	PUNCT
ap-938	42	19	the	the	DET
ap-938	42	20	number	number	NOUN
ap-938	42	21	k	k	PROPN
ap-938	42	22	is	be	AUX
ap-938	42	23	positive	positive	ADJ
ap-938	42	24	,	,	PUNCT
ap-938	42	25	and	and	CCONJ
ap-938	42	26	if	if	SCONJ
ap-938	42	27	v1	v1	PROPN
ap-938	42	28	0	0	NUM
ap-938	42	29	�	�	PROPN
ap-938	42	30	(	(	PUNCT
ap-938	42	31	6	6	NUM
ap-938	42	32	)	)	PUNCT
ap-938	42	33	the	the	DET
ap-938	42	34	number	number	NOUN
ap-938	42	35	k	k	PROPN
ap-938	42	36	is	be	AUX
ap-938	42	37	negative	negative	ADJ
ap-938	42	38	.	.	PUNCT
ap-938	43	1	proof	proof	NOUN
ap-938	43	2	.	.	PUNCT
ap-938	44	1	we	we	PRON
ap-938	44	2	introduce	introduce	VERB
ap-938	44	3	the	the	DET
ap-938	44	4	numbers	number	NOUN
ap-938	44	5	k	k	X
ap-938	44	6	v	v	NOUN
ap-938	44	7	x	x	SYM
ap-938	44	8	x	x	X
ap-938	44	9	v	v	NOUN
ap-938	44	10	x	x	SYM
ap-938	44	11	x	x	X
ap-938	44	12	k	k	PUNCT
ap-938	44	13	u	u	NOUN
ap-938	44	14	v	v	NOUN
ap-938	44	15	1	1	NUM
ap-938	44	16	2	2	NUM
ap-938	44	17	1	1	NUM
ap-938	44	18	2	2	NUM
ap-938	44	19	2	2	NUM
ap-938	44	20	2	2	NUM
ap-938	44	21	:	:	PUNCT
ap-938	44	22	,	,	PUNCT
ap-938	44	23	:	:	PUNCT
ap-938	44	24	�	�	PROPN
ap-938	44	25	�	�	PROPN
ap-938	44	26	�	�	PROPN
ap-938	44	27	�	�	PROPN
ap-938	44	28	�	�	PROPN
ap-938	44	29	�	�	PROPN
ap-938	44	30	i	i	PRON
ap-938	44	31	(	(	PUNCT
ap-938	44	32	)	)	PUNCT
ap-938	44	33	(	(	PUNCT
ap-938	44	34	x	x	X
ap-938	44	35	)	)	PUNCT
ap-938	44	36	d	d	NOUN
ap-938	44	37	(	(	PUNCT
ap-938	44	38	)	)	PUNCT
ap-938	44	39	d	d	SYM
ap-938	44	40	1	1	NUM
ap-938	44	41	(	(	PUNCT
ap-938	44	42	1	1	NUM
ap-938	44	43	2	2	NUM
ap-938	44	44	1	1	NUM
ap-938	44	45	1	1	NUM
ap-938	44	46	1	1	NUM
ap-938	44	47	1	1	NUM
ap-938	44	48	1	1	NUM
ap-938	44	49	2	2	NUM
ap-938	44	50	�	�	PROPN
ap-938	44	51	�	�	PROPN
ap-938	44	52	�	�	PROPN
ap-938	44	53	�	�	PROPN
ap-938	44	54	~~	~~	NUM
ap-938	44	55	~~	~~	NUM
ap-938	44	56	.v	.v	ADJ
ap-938	44	57	u	u	NOUN
ap-938	44	58	x	x	X
ap-938	44	59	u	u	NOUN
ap-938	44	60	v	v	NOUN
ap-938	44	61	x	x	SYM
ap-938	44	62	v	v	NOUN
ap-938	44	63	u	u	NOUN
ap-938	44	64	x	x	NOUN
ap-938	44	65	)	)	PUNCT
ap-938	45	1	d	d	X
ap-938	45	2	d	d	NOUN
ap-938	45	3	d1	d1	NOUN
ap-938	45	4	1	1	NUM
ap-938	45	5	1	1	NUM
ap-938	45	6	�	�	PROPN
ap-938	45	7	�	�	PROPN
ap-938	45	8	�	�	PROPN
ap-938	45	9	�	�	PROPN
ap-938	45	10	�	�	PROPN
ap-938	45	11	�	�	PROPN
ap-938	45	12	�	�	PROPN
ap-938	45	13	�	�	PROPN
ap-938	45	14	�	�	PROPN
ap-938	45	15	�	�	PROPN
ap-938	45	16	�	�	PROPN
ap-938	45	17	�	�	PROPN
ap-938	45	18	�	�	PROPN
ap-938	45	19	�	�	PROPN
ap-938	45	20	�	�	PROPN
ap-938	45	21	�	�	PROPN
ap-938	45	22	�	�	PROPN
ap-938	45	23	1	1	NUM
ap-938	45	24	2	2	NUM
ap-938	45	25	�	�	NOUN
ap-938	45	26	it	it	PRON
ap-938	45	27	follows	follow	VERB
ap-938	45	28	from	from	ADP
ap-938	45	29	[	[	X
ap-938	45	30	2	2	NUM
ap-938	45	31	,	,	PUNCT
ap-938	45	32	th	th	NOUN
ap-938	45	33	.	.	NOUN
ap-938	45	34	1	1	NUM
ap-938	45	35	]	]	PUNCT
ap-938	45	36	that	that	SCONJ
ap-938	45	37	if	if	SCONJ
ap-938	45	38	re	re	ADP
ap-938	45	39	k1	k1	PROPN
ap-938	45	40	0	0	NUM
ap-938	45	41	�	�	PROPN
ap-938	45	42	,	,	PUNCT
ap-938	45	43	or	or	CCONJ
ap-938	45	44	re	re	ADP
ap-938	45	45	k1	k1	PROPN
ap-938	45	46	0	0	NUM
ap-938	45	47	�	�	PROPN
ap-938	45	48	,	,	PUNCT
ap-938	45	49	re	re	X
ap-938	45	50	k2	k2	PROPN
ap-938	45	51	0	0	NUM
ap-938	45	52	�	�	PROPN
ap-938	45	53	,	,	PUNCT
ap-938	45	54	(	(	PUNCT
ap-938	45	55	7	7	X
ap-938	45	56	)	)	PUNCT
ap-938	45	57	there	there	PRON
ap-938	45	58	exists	exist	VERB
ap-938	45	59	the	the	DET
ap-938	45	60	unique	unique	ADJ
ap-938	45	61	eigenvalue	eigenvalue	NOUN
ap-938	45	62	of	of	ADP
ap-938	45	63	�	�	PROPN
ap-938	45	64	�	�	PROPN
ap-938	45	65	converging	converge	VERB
ap-938	45	66	to	to	ADP
ap-938	45	67	the	the	DET
ap-938	45	68	threshold	threshold	NOUN
ap-938	45	69	of	of	ADP
ap-938	45	70	the	the	DET
ap-938	45	71	continuous	continuous	ADJ
ap-938	45	72	spectrum	spectrum	NOUN
ap-938	45	73	,	,	PUNCT
ap-938	45	74	and	and	CCONJ
ap-938	45	75	the	the	DET
ap-938	45	76	asymptotics	asymptotic	NOUN
ap-938	45	77	of	of	ADP
ap-938	45	78	this	this	DET
ap-938	45	79	eigenvalue	eigenvalue	NOUN
ap-938	45	80	reads	read	NOUN
ap-938	45	81	as	as	SCONJ
ap-938	45	82	follows	follow	VERB
ap-938	45	83	�	�	PROPN
ap-938	45	84	�	�	PROPN
ap-938	45	85	�	�	PROPN
ap-938	45	86	�	�	PROPN
ap-938	45	87	�	�	PROPN
ap-938	45	88	�	�	PROPN
ap-938	45	89	�	�	PROPN
ap-938	45	90	�	�	PROPN
ap-938	45	91	�	�	PROPN
ap-938	45	92	�	�	PROPN
ap-938	45	93	�	�	PROPN
ap-938	45	94	1	1	NUM
ap-938	45	95	02	02	NUM
ap-938	45	96	1	1	NUM
ap-938	45	97	2	2	NUM
ap-938	45	98	2	2	NUM
ap-938	45	99	3k	3k	NOUN
ap-938	45	100	k	k	PROPN
ap-938	45	101	k	k	PROPN
ap-938	45	102	k	k	PROPN
ap-938	45	103	,	,	PUNCT
ap-938	45	104	(	(	PUNCT
ap-938	45	105	)	)	PUNCT
ap-938	45	106	,	,	PUNCT
ap-938	45	107	�	�	PROPN
ap-938	45	108	.	.	PUNCT
ap-938	46	1	(	(	PUNCT
ap-938	46	2	8)	8)	NUM
ap-938	46	3	it	it	PRON
ap-938	46	4	also	also	ADV
ap-938	46	5	follows	follow	VERB
ap-938	46	6	from	from	ADP
ap-938	46	7	[	[	X
ap-938	46	8	2	2	NUM
ap-938	46	9	,	,	PUNCT
ap-938	46	10	th	th	NOUN
ap-938	46	11	.	.	NOUN
ap-938	46	12	1	1	NUM
ap-938	46	13	]	]	PUNCT
ap-938	46	14	that	that	SCONJ
ap-938	46	15	if	if	SCONJ
ap-938	46	16	re	re	ADP
ap-938	46	17	k1	k1	PROPN
ap-938	46	18	0	0	NUM
ap-938	46	19	�	�	PROPN
ap-938	46	20	,	,	PUNCT
ap-938	46	21	or	or	CCONJ
ap-938	46	22	re	re	ADP
ap-938	46	23	k1	k1	PROPN
ap-938	46	24	0	0	NUM
ap-938	46	25	�	�	PROPN
ap-938	46	26	,	,	PUNCT
ap-938	46	27	re	re	X
ap-938	46	28	k2	k2	PROPN
ap-938	46	29	0	0	NUM
ap-938	46	30	�	�	PROPN
ap-938	46	31	(	(	PUNCT
ap-938	46	32	9	9	NUM
ap-938	46	33	)	)	PUNCT
ap-938	46	34	the	the	DET
ap-938	46	35	operator	operator	NOUN
ap-938	46	36	�	�	PROPN
ap-938	46	37	�	�	PROPN
ap-938	46	38	has	have	AUX
ap-938	46	39	no	no	DET
ap-938	46	40	eigenvalues	eigenvalue	NOUN
ap-938	46	41	converging	converge	VERB
ap-938	46	42	to	to	ADP
ap-938	46	43	the	the	DET
ap-938	46	44	threshold	threshold	NOUN
ap-938	46	45	as	as	ADP
ap-938	46	46	�	�	PROPN
ap-938	46	47	�	�	PROPN
ap-938	46	48	0	0	NUM
ap-938	46	49	.	.	PUNCT
ap-938	47	1	thus	thus	ADV
ap-938	47	2	,	,	PUNCT
ap-938	47	3	it	it	PRON
ap-938	47	4	is	be	AUX
ap-938	47	5	sufficient	sufficient	ADJ
ap-938	47	6	to	to	PART
ap-938	47	7	calculate	calculate	VERB
ap-938	47	8	the	the	DET
ap-938	47	9	numbers	number	NOUN
ap-938	47	10	k1	k1	NOUN
ap-938	47	11	,	,	PUNCT
ap-938	47	12	k2	k2	NOUN
ap-938	47	13	.	.	PUNCT
ap-938	48	1	the	the	DET
ap-938	48	2	identity	identity	NOUN
ap-938	48	3	(	(	PUNCT
ap-938	48	4	1	1	NUM
ap-938	48	5	)	)	PUNCT
ap-938	48	6	implies	imply	VERB
ap-938	48	7	that	that	SCONJ
ap-938	48	8	v1	v1	NOUN
ap-938	48	9	is	be	AUX
ap-938	48	10	an	an	DET
ap-938	48	11	odd	odd	ADJ
ap-938	48	12	function	function	NOUN
ap-938	48	13	,	,	PUNCT
ap-938	48	14	and	and	CCONJ
ap-938	48	15	hence	hence	ADV
ap-938	48	16	k1	k1	PROPN
ap-938	48	17	0	0	NUM
ap-938	48	18	�	�	PROPN
ap-938	48	19	.	.	PUNCT
ap-938	49	1	(	(	PUNCT
ap-938	49	2	10	10	NUM
ap-938	49	3	)	)	PUNCT
ap-938	49	4	therefore	therefore	ADV
ap-938	49	5	,	,	PUNCT
ap-938	49	6	it	it	PRON
ap-938	49	7	is	be	AUX
ap-938	49	8	sufficient	sufficient	ADJ
ap-938	49	9	to	to	PART
ap-938	49	10	calculate	calculate	VERB
ap-938	49	11	k2	k2	NOUN
ap-938	49	12	and	and	CCONJ
ap-938	49	13	check	check	VERB
ap-938	49	14	its	its	PRON
ap-938	49	15	sign	sign	NOUN
ap-938	49	16	.	.	PUNCT
ap-938	50	1	the	the	DET
ap-938	50	2	mean	mean	ADJ
ap-938	50	3	value	value	NOUN
ap-938	50	4	of	of	ADP
ap-938	50	5	v1	v1	NOUN
ap-938	50	6	being	be	AUX
ap-938	50	7	zero	zero	NUM
ap-938	50	8	,	,	PUNCT
ap-938	50	9	the	the	DET
ap-938	50	10	function	function	NOUN
ap-938	50	11	u1	u1	NOUN
ap-938	50	12	is	be	AUX
ap-938	50	13	constant	constant	ADJ
ap-938	50	14	as	as	SCONJ
ap-938	50	15	x1	x1	PROPN
ap-938	50	16	is	be	AUX
ap-938	50	17	large	large	ADJ
ap-938	50	18	enough	enough	ADV
ap-938	50	19	.	.	PUNCT
ap-938	51	1	this	this	PRON
ap-938	51	2	allows	allow	VERB
ap-938	51	3	us	we	PRON
ap-938	51	4	to	to	PART
ap-938	51	5	write	write	VERB
ap-938	51	6	v	v	NUM
ap-938	51	7	u	u	NOUN
ap-938	51	8	x	x	PUNCT
ap-938	51	9	u	u	NOUN
ap-938	51	10	u	u	NOUN
ap-938	51	11	x	x	X
ap-938	51	12	u	u	NOUN
ap-938	51	13	x1	x1	NOUN
ap-938	51	14	1	1	NUM
ap-938	51	15	1	1	NUM
ap-938	51	16	1	1	NUM
ap-938	51	17	1	1	NUM
ap-938	51	18	1	1	NUM
ap-938	51	19	1	1	NUM
ap-938	51	20	2	2	NUM
ap-938	51	21	1d	1d	NUM
ap-938	51	22	d	d	NOUN
ap-938	51	23	d	d	X
ap-938	51	24	�	�	PROPN
ap-938	51	25	�	�	PROPN
ap-938	51	26	�	�	PROPN
ap-938	51	27	�	�	PROPN
ap-938	51	28	�	�	PROPN
ap-938	51	29	�	�	PROPN
ap-938	51	30	�	�	PROPN
ap-938	51	31	�	�	PROPN
ap-938	51	32	�	�	PROPN
ap-938	51	33	�	�	PROPN
ap-938	51	34	�	�	PROPN
ap-938	51	35	�	�	PROPN
ap-938	51	36	(	(	PUNCT
ap-938	51	37	)	)	PUNCT
ap-938	51	38	.	.	PUNCT
ap-938	52	1	(	(	PUNCT
ap-938	52	2	11	11	NUM
ap-938	52	3	)	)	PUNCT
ap-938	52	4	hence	hence	ADV
ap-938	52	5	,	,	PUNCT
ap-938	52	6	k	k	PROPN
ap-938	52	7	k	k	PROPN
ap-938	52	8	2	2	NUM
ap-938	52	9	2	2	NUM
ap-938	52	10	�	�	PROPN
ap-938	52	11	.	.	PUNCT
ap-938	53	1	we	we	PRON
ap-938	53	2	substitute	substitute	VERB
ap-938	53	3	this	this	DET
ap-938	53	4	formula	formula	NOUN
ap-938	53	5	and	and	CCONJ
ap-938	53	6	(	(	PUNCT
ap-938	53	7	10	10	NUM
ap-938	53	8	)	)	PUNCT
ap-938	53	9	into	into	ADP
ap-938	53	10	(	(	PUNCT
ap-938	53	11	8)	8)	NUM
ap-938	53	12	,	,	PUNCT
ap-938	53	13	and	and	CCONJ
ap-938	53	14	by	by	ADP
ap-938	53	15	(	(	PUNCT
ap-938	53	16	7	7	NUM
ap-938	53	17	)	)	PUNCT
ap-938	53	18	,	,	PUNCT
ap-938	53	19	(	(	PUNCT
ap-938	53	20	9	9	X
ap-938	53	21	)	)	PUNCT
ap-938	53	22	we	we	PRON
ap-938	53	23	conclude	conclude	VERB
ap-938	53	24	that	that	SCONJ
ap-938	53	25	if	if	SCONJ
ap-938	53	26	k	k	PROPN
ap-938	53	27	�	�	PROPN
ap-938	53	28	0	0	NUM
ap-938	53	29	,	,	PUNCT
ap-938	53	30	there	there	PRON
ap-938	53	31	exists	exist	VERB
ap-938	53	32	the	the	DET
ap-938	53	33	unique	unique	ADJ
ap-938	53	34	eigenvalue	eigenvalue	NOUN
ap-938	53	35	of	of	ADP
ap-938	53	36	�	�	PROPN
ap-938	53	37	�	�	PROPN
ap-938	53	38	satisfying	satisfying	NOUN
ap-938	53	39	(	(	PUNCT
ap-938	53	40	4	4	NUM
ap-938	53	41	)	)	PUNCT
ap-938	53	42	.	.	PUNCT
ap-938	54	1	if	if	SCONJ
ap-938	54	2	k	k	PROPN
ap-938	54	3	�	�	PROPN
ap-938	54	4	0	0	PROPN
ap-938	54	5	,	,	PUNCT
ap-938	54	6	the	the	DET
ap-938	54	7	operator	operator	NOUN
ap-938	54	8	has	have	AUX
ap-938	54	9	no	no	DET
ap-938	54	10	eigenvalues	eigenvalue	NOUN
ap-938	54	11	converging	converge	VERB
ap-938	54	12	to	to	ADP
ap-938	54	13	the	the	DET
ap-938	54	14	threshold	threshold	NOUN
ap-938	54	15	of	of	ADP
ap-938	54	16	the	the	DET
ap-938	54	17	continuous	continuous	ADJ
ap-938	54	18	spectrum	spectrum	NOUN
ap-938	54	19	.	.	PUNCT
ap-938	55	1	using	use	VERB
ap-938	55	2	(	(	PUNCT
ap-938	55	3	1	1	NUM
ap-938	55	4	)	)	PUNCT
ap-938	55	5	,	,	PUNCT
ap-938	55	6	one	one	PRON
ap-938	55	7	can	can	AUX
ap-938	55	8	check	check	VERB
ap-938	55	9	easily	easily	ADV
ap-938	55	10	that	that	SCONJ
ap-938	55	11	�	�	PROPN
ap-938	55	12	is	be	AUX
ap-938	55	13	an	an	DET
ap-938	55	14	eigenvalue	eigenvalue	PROPN
ap-938	55	15	of	of	ADP
ap-938	55	16	�	�	PROPN
ap-938	55	17	�	�	PROPN
ap-938	55	18	as	as	ADV
ap-938	55	19	well	well	ADV
ap-938	55	20	.	.	PUNCT
ap-938	56	1	it	it	PRON
ap-938	56	2	converges	converge	VERB
ap-938	56	3	to	to	ADP
ap-938	56	4	the	the	DET
ap-938	56	5	threshold	threshold	NOUN
ap-938	56	6	and	and	CCONJ
ap-938	56	7	by	by	ADP
ap-938	56	8	the	the	DET
ap-938	56	9	uniqueness	uniqueness	NOUN
ap-938	56	10	of	of	ADP
ap-938	56	11	such	such	DET
ap-938	56	12	an	an	DET
ap-938	56	13	eigenvalue	eigenvalue	NOUN
ap-938	56	14	we	we	PRON
ap-938	56	15	conclude	conclude	VERB
ap-938	56	16	that	that	SCONJ
ap-938	56	17	this	this	DET
ap-938	56	18	eigenvalue	eigenvalue	NOUN
ap-938	56	19	is	be	AUX
ap-938	56	20	real	real	ADJ
ap-938	56	21	.	.	PUNCT
ap-938	57	1	let	let	VERB
ap-938	57	2	us	we	PRON
ap-938	57	3	prove	prove	VERB
ap-938	57	4	that	that	SCONJ
ap-938	57	5	the	the	DET
ap-938	57	6	conditions	condition	NOUN
ap-938	57	7	(	(	PUNCT
ap-938	57	8	5	5	NUM
ap-938	57	9	)	)	PUNCT
ap-938	57	10	,	,	PUNCT
ap-938	57	11	(	(	PUNCT
ap-938	57	12	6	6	X
ap-938	57	13	)	)	PUNCT
ap-938	57	14	are	be	AUX
ap-938	57	15	sufficient	sufficient	ADJ
ap-938	57	16	for	for	SCONJ
ap-938	57	17	the	the	DET
ap-938	57	18	eigenvalue	eigenvalue	NOUN
ap-938	57	19	to	to	PART
ap-938	57	20	be	be	AUX
ap-938	57	21	present	present	ADJ
ap-938	57	22	or	or	CCONJ
ap-938	57	23	absent	absent	ADJ
ap-938	57	24	.	.	PUNCT
ap-938	58	1	assume	assume	VERB
ap-938	58	2	first	first	ADV
ap-938	58	3	(	(	PUNCT
ap-938	58	4	5	5	NUM
ap-938	58	5	)	)	PUNCT
ap-938	58	6	.	.	PUNCT
ap-938	59	1	in	in	ADP
ap-938	59	2	this	this	DET
ap-938	59	3	case	case	NOUN
ap-938	59	4	~v	~v	X
ap-938	59	5	�	�	PROPN
ap-938	59	6	0	0	NUM
ap-938	59	7	,	,	PUNCT
ap-938	59	8	~u	~u	NUM
ap-938	59	9	�	�	PROPN
ap-938	59	10	0	0	NUM
ap-938	59	11	and	and	CCONJ
ap-938	59	12	k	k	PROPN
ap-938	59	13	u	u	PROPN
ap-938	59	14	l	l	X
ap-938	59	15	�	�	PROPN
ap-938	59	16	�	�	PROPN
ap-938	59	17	�	�	PROPN
ap-938	59	18	1	1	NUM
ap-938	59	19	2	2	NUM
ap-938	59	20	01	01	NUM
ap-938	59	21	2	2	NUM
ap-938	59	22	2	2	NUM
ap-938	59	23	(	(	PUNCT
ap-938	59	24	)	)	PUNCT
ap-938	59	25	�	�	PROPN
ap-938	59	26	(	(	PUNCT
ap-938	59	27	12	12	NUM
ap-938	59	28	)	)	PUNCT
ap-938	59	29	if	if	SCONJ
ap-938	59	30	the	the	DET
ap-938	59	31	relation	relation	NOUN
ap-938	59	32	(	(	PUNCT
ap-938	59	33	6	6	NUM
ap-938	59	34	)	)	PUNCT
ap-938	59	35	holds	hold	VERB
ap-938	59	36	true	true	ADJ
ap-938	59	37	,	,	PUNCT
ap-938	59	38	the	the	DET
ap-938	59	39	function	function	NOUN
ap-938	59	40	u1	u1	NOUN
ap-938	59	41	is	be	AUX
ap-938	59	42	identically	identically	ADV
ap-938	59	43	zero	zero	NUM
ap-938	59	44	,	,	PUNCT
ap-938	59	45	and	and	CCONJ
ap-938	59	46	k	k	X
ap-938	59	47	v	v	NUM
ap-938	59	48	u	u	PROPN
ap-938	59	49	l	l	NOUN
ap-938	59	50	:	:	PUNCT
ap-938	59	51	(	(	PUNCT
ap-938	59	52	~,~	~,~	X
ap-938	59	53	)	)	PUNCT
ap-938	59	54	(	(	PUNCT
ap-938	59	55	)	)	PUNCT
ap-938	59	56	�	�	PROPN
ap-938	59	57	�	�	PROPN
ap-938	59	58	2	2	NUM
ap-938	59	59	�	�	PROPN
ap-938	59	60	employing	employ	VERB
ap-938	59	61	(	(	PUNCT
ap-938	59	62	3	3	NUM
ap-938	59	63	)	)	PUNCT
ap-938	59	64	,	,	PUNCT
ap-938	59	65	by	by	ADP
ap-938	59	66	analogy	analogy	NOUN
ap-938	59	67	with	with	ADP
ap-938	59	68	(	(	PUNCT
ap-938	59	69	11	11	NUM
ap-938	59	70	)	)	PUNCT
ap-938	59	71	in	in	ADP
ap-938	59	72	the	the	DET
ap-938	59	73	same	same	ADJ
ap-938	59	74	way	way	NOUN
ap-938	59	75	we	we	PRON
ap-938	59	76	check	check	VERB
ap-938	59	77	~~	~~	PUNCT
ap-938	59	78	~	~	PUNCT
ap-938	59	79	~	~	PUNCT
ap-938	59	80	(	(	PUNCT
ap-938	59	81	)	)	PUNCT
ap-938	59	82	(	(	PUNCT
ap-938	59	83	)	)	PUNCT
ap-938	59	84	v	v	X
ap-938	59	85	u	u	NOUN
ap-938	59	86	x	x	PUNCT
ap-938	59	87	u	u	NOUN
ap-938	59	88	u	u	NOUN
ap-938	59	89	l	l	NOUN
ap-938	59	90	l	l	NOUN
ap-938	59	91	d	d	X
ap-938	59	92	�	�	PROPN
ap-938	59	93	�	�	PROPN
ap-938	59	94	�	�	PROPN
ap-938	59	95	�	�	PROPN
ap-938	59	96	�	�	PROPN
ap-938	59	97	�	�	PROPN
ap-938	59	98	�	�	PROPN
ap-938	59	99	2	2	NUM
ap-938	59	100	2	2	NUM
ap-938	59	101	2	2	NUM
ap-938	59	102	2	2	NUM
ap-938	59	103	.	.	PUNCT
ap-938	60	1	(	(	PUNCT
ap-938	60	2	13	13	NUM
ap-938	60	3	)	)	PUNCT
ap-938	60	4	it	it	PRON
ap-938	60	5	follows	follow	VERB
ap-938	60	6	from	from	ADP
ap-938	60	7	the	the	DET
ap-938	60	8	definition	definition	NOUN
ap-938	60	9	of	of	ADP
ap-938	60	10	the	the	DET
ap-938	60	11	function	function	NOUN
ap-938	60	12	~	~	PUNCT
ap-938	60	13	(	(	PUNCT
ap-938	60	14	,	,	PUNCT
ap-938	60	15	)	)	PUNCT
ap-938	60	16	u	u	NOUN
ap-938	60	17	x1	x1	PROPN
ap-938	60	18	�	�	PROPN
ap-938	60	19	that	that	PRON
ap-938	60	20	�	�	PROPN
ap-938	60	21	�	�	PROPN
ap-938	60	22	�	�	PROPN
ap-938	60	23	�	�	AUX
ap-938	60	24	~	~	PUNCT
ap-938	60	25	(	(	PUNCT
ap-938	60	26	,	,	PUNCT
ap-938	60	27	)	)	PUNCT
ap-938	60	28	~	~	PUNCT
ap-938	60	29	(	(	PUNCT
ap-938	60	30	,	,	PUNCT
ap-938	60	31	)	)	PUNCT
ap-938	60	32	(	(	PUNCT
ap-938	60	33	,	,	PUNCT
ap-938	60	34	)	)	PUNCT
ap-938	60	35	u	u	NOUN
ap-938	60	36	x	x	PUNCT
ap-938	60	37	x	x	PUNCT
ap-938	60	38	u	u	NOUN
ap-938	60	39	l	l	NOUN
ap-938	60	40	l	l	NOUN
ap-938	60	41	2	2	NUM
ap-938	60	42	1	1	NUM
ap-938	60	43	0	0	NUM
ap-938	60	44	2	2	NUM
ap-938	60	45	0	0	NUM
ap-938	60	46	2	2	NUM
ap-938	60	47	2	2	NUM
ap-938	60	48	2	2	NUM
ap-938	60	49	4	4	NUM
ap-938	60	50	�	�	PROPN
ap-938	60	51	�	�	PROPN
ap-938	60	52	,	,	PUNCT
ap-938	60	53	and	and	CCONJ
ap-938	60	54	hence	hence	ADV
ap-938	60	55	�	�	PROPN
ap-938	60	56	�	�	PROPN
ap-938	60	57	~	~	PUNCT
ap-938	60	58	~	~	PUNCT
ap-938	60	59	(	(	PUNCT
ap-938	60	60	)	)	PUNCT
ap-938	60	61	(	(	PUNCT
ap-938	60	62	)	)	PUNCT
ap-938	60	63	u	u	NOUN
ap-938	60	64	u	u	NOUN
ap-938	60	65	l	l	NOUN
ap-938	60	66	l2	l2	NOUN
ap-938	60	67	2	2	NUM
ap-938	60	68	2	2	NUM
ap-938	60	69	24	24	NUM
ap-938	60	70	�	�	PROPN
ap-938	60	71	�	�	PROPN
ap-938	60	72	.	.	PUNCT
ap-938	61	1	in	in	ADP
ap-938	61	2	view	view	NOUN
ap-938	61	3	of	of	ADP
ap-938	61	4	(	(	PUNCT
ap-938	61	5	12	12	NUM
ap-938	61	6	)	)	PUNCT
ap-938	61	7	,	,	PUNCT
ap-938	61	8	(	(	PUNCT
ap-938	61	9	13	13	NUM
ap-938	61	10	)	)	PUNCT
ap-938	61	11	and	and	CCONJ
ap-938	61	12	this	this	DET
ap-938	61	13	estimate	estimate	NOUN
ap-938	61	14	we	we	PRON
ap-938	61	15	conclude	conclude	VERB
ap-938	61	16	that	that	SCONJ
ap-938	61	17	k	k	PROPN
ap-938	61	18	u	u	PROPN
ap-938	61	19	l	l	PROPN
ap-938	61	20	�	�	PROPN
ap-938	61	21	�	�	PROPN
ap-938	61	22	�	�	PROPN
ap-938	61	23	3	3	NUM
ap-938	61	24	0	0	NUM
ap-938	61	25	2	2	NUM
ap-938	61	26	2~	2~	PROPN
ap-938	61	27	(	(	PUNCT
ap-938	61	28	)	)	PUNCT
ap-938	61	29	�	�	PROPN
ap-938	61	30	.	.	PUNCT
ap-938	62	1	in	in	ADP
ap-938	62	2	conclusion	conclusion	NOUN
ap-938	62	3	,	,	PUNCT
ap-938	62	4	we	we	PRON
ap-938	62	5	observe	observe	VERB
ap-938	62	6	that	that	SCONJ
ap-938	62	7	the	the	DET
ap-938	62	8	results	result	NOUN
ap-938	62	9	of	of	ADP
ap-938	62	10	[	[	X
ap-938	62	11	1	1	NUM
ap-938	62	12	,	,	PUNCT
ap-938	62	13	2	2	NUM
ap-938	62	14	]	]	PUNCT
ap-938	62	15	allow	allow	VERB
ap-938	62	16	one	one	NUM
ap-938	62	17	also	also	ADV
ap-938	62	18	to	to	PART
ap-938	62	19	study	study	VERB
ap-938	62	20	also	also	ADV
ap-938	62	21	the	the	DET
ap-938	62	22	existence	existence	NOUN
ap-938	62	23	of	of	ADP
ap-938	62	24	the	the	DET
ap-938	62	25	eigenvalues	eigenvalue	NOUN
ap-938	62	26	emerging	emerge	VERB
ap-938	62	27	from	from	ADP
ap-938	62	28	the	the	DET
ap-938	62	29	higher	high	ADJ
ap-938	62	30	thresholds	threshold	NOUN
ap-938	62	31	in	in	ADP
ap-938	62	32	the	the	DET
ap-938	62	33	continuous	continuous	ADJ
ap-938	62	34	spectrum	spectrum	NOUN
ap-938	62	35	that	that	PRON
ap-938	62	36	are	be	AUX
ap-938	62	37	j2	j2	PROPN
ap-938	62	38	.	.	PUNCT
ap-938	63	1	it	it	PRON
ap-938	63	2	was	be	AUX
ap-938	63	3	shown	show	VERB
ap-938	63	4	in	in	ADP
ap-938	63	5	[	[	X
ap-938	63	6	2	2	NUM
ap-938	63	7	]	]	PUNCT
ap-938	63	8	,	,	PUNCT
ap-938	63	9	that	that	SCONJ
ap-938	63	10	if	if	SCONJ
ap-938	63	11	it	it	PRON
ap-938	63	12	exists	exist	VERB
ap-938	63	13	,	,	PUNCT
ap-938	63	14	this	this	DET
ap-938	63	15	eigenvalue	eigenvalue	NOUN
ap-938	63	16	is	be	AUX
ap-938	63	17	unique	unique	ADJ
ap-938	63	18	.	.	PUNCT
ap-938	64	1	as	as	ADP
ap-938	64	2	in	in	ADP
ap-938	64	3	theorem	theorem	NOUN
ap-938	64	4	2	2	NUM
ap-938	64	5	,	,	PUNCT
ap-938	64	6	this	this	DET
ap-938	64	7	fact	fact	NOUN
ap-938	64	8	implies	imply	VERB
ap-938	64	9	that	that	SCONJ
ap-938	64	10	the	the	DET
ap-938	64	11	eigenvalue	eigenvalue	NOUN
ap-938	64	12	is	be	AUX
ap-938	64	13	real	real	ADJ
ap-938	64	14	and	and	CCONJ
ap-938	64	15	therefore	therefore	ADV
ap-938	64	16	in	in	ADP
ap-938	64	17	this	this	DET
ap-938	64	18	case	case	NOUN
ap-938	64	19	we	we	PRON
ap-938	64	20	are	be	AUX
ap-938	64	21	dealing	deal	VERB
ap-938	64	22	with	with	ADP
ap-938	64	23	embedded	embed	VERB
ap-938	64	24	eigenvalues	eigenvalue	NOUN
ap-938	64	25	.	.	PUNCT
ap-938	65	1	acknowledgments	acknowledgment	NOUN
ap-938	65	2	this	this	DET
ap-938	65	3	work	work	NOUN
ap-938	65	4	has	have	AUX
ap-938	65	5	been	be	AUX
ap-938	65	6	supported	support	VERB
ap-938	65	7	in	in	ADP
ap-938	65	8	parts	part	NOUN
ap-938	65	9	by	by	ADP
ap-938	65	10	rfbr	rfbr	NOUN
ap-938	65	11	(	(	PUNCT
ap-938	65	12	05	05	NUM
ap-938	65	13	-	-	PUNCT
ap-938	65	14	01	01	NUM
ap-938	65	15	-	-	PUNCT
ap-938	65	16	97912	97912	NUM
ap-938	65	17	)	)	PUNCT
ap-938	65	18	and	and	CCONJ
ap-938	65	19	by	by	ADP
ap-938	65	20	the	the	DET
ap-938	65	21	czech	czech	PROPN
ap-938	65	22	academy	academy	PROPN
ap-938	65	23	of	of	ADP
ap-938	65	24	sciences	sciences	PROPN
ap-938	65	25	and	and	CCONJ
ap-938	65	26	ministry	ministry	PROPN
ap-938	65	27	of	of	ADP
ap-938	65	28	education	education	PROPN
ap-938	65	29	,	,	PUNCT
ap-938	65	30	youth	youth	NOUN
ap-938	65	31	and	and	CCONJ
ap-938	65	32	sports	sport	NOUN
ap-938	65	33	(	(	PUNCT
ap-938	65	34	lc06002	lc06002	NOUN
ap-938	65	35	)	)	PUNCT
ap-938	65	36	.	.	PUNCT
ap-938	66	1	the	the	DET
ap-938	66	2	author	author	NOUN
ap-938	66	3	has	have	AUX
ap-938	66	4	also	also	ADV
ap-938	66	5	been	be	AUX
ap-938	66	6	supported	support	VERB
ap-938	66	7	by	by	ADP
ap-938	66	8	a	a	DET
ap-938	66	9	marie	marie	PROPN
ap-938	66	10	curie	curie	PROPN
ap-938	66	11	international	international	ADJ
ap-938	66	12	fellowship	fellowship	NOUN
ap-938	66	13	within	within	ADP
ap-938	66	14	the	the	DET
ap-938	66	15	6th	6th	ADJ
ap-938	66	16	european	european	ADJ
ap-938	66	17	community	community	NOUN
ap-938	66	18	framework	framework	NOUN
ap-938	66	19	(	(	PUNCT
ap-938	66	20	mif1	mif1	NOUN
ap-938	66	21	-	-	PUNCT
ap-938	66	22	ct-2005	ct-2005	PROPN
ap-938	66	23	-	-	PUNCT
ap-938	66	24	006254	006254	NUM
ap-938	66	25	)	)	PUNCT
ap-938	66	26	and	and	CCONJ
ap-938	66	27	gratefully	gratefully	ADV
ap-938	66	28	acknowledges	acknowledge	VERB
ap-938	66	29	support	support	NOUN
ap-938	66	30	from	from	ADP
ap-938	66	31	the	the	DET
ap-938	66	32	deligne	deligne	NOUN
ap-938	66	33	2004	2004	NUM
ap-938	66	34	balzan	balzan	PROPN
ap-938	66	35	prize	prize	PROPN
ap-938	66	36	in	in	ADP
ap-938	66	37	mathematics	mathematic	NOUN
ap-938	66	38	and	and	CCONJ
ap-938	66	39	from	from	ADP
ap-938	66	40	the	the	DET
ap-938	66	41	the	the	DET
ap-938	66	42	grant	grant	NOUN
ap-938	66	43	of	of	ADP
ap-938	66	44	republic	republic	PROPN
ap-938	66	45	bashkortostan	bashkortostan	PROPN
ap-938	66	46	for	for	ADP
ap-938	66	47	young	young	ADJ
ap-938	66	48	scientists	scientist	NOUN
ap-938	66	49	and	and	CCONJ
ap-938	66	50	young	young	ADJ
ap-938	66	51	scientific	scientific	ADJ
ap-938	66	52	collectives	collective	NOUN
ap-938	66	53	.	.	PUNCT
ap-938	67	1	references	reference	NOUN
ap-938	67	2	[	[	X
ap-938	67	3	1	1	NUM
ap-938	67	4	]	]	X
ap-938	67	5	gadyl’shin	gadyl’shin	NOUN
ap-938	67	6	,	,	PUNCT
ap-938	67	7	r.	r.	PROPN
ap-938	67	8	:	:	PUNCT
ap-938	67	9	on	on	ADP
ap-938	67	10	regular	regular	ADJ
ap-938	67	11	and	and	CCONJ
ap-938	67	12	singular	singular	ADJ
ap-938	67	13	perturbation	perturbation	NOUN
ap-938	67	14	of	of	ADP
ap-938	67	15	acoustic	acoustic	ADJ
ap-938	67	16	and	and	CCONJ
ap-938	67	17	quantum	quantum	ADJ
ap-938	67	18	waveguides	waveguide	NOUN
ap-938	67	19	,	,	PUNCT
ap-938	67	20	comptes	compte	VERB
ap-938	67	21	rendus	rendus	PROPN
ap-938	67	22	méchanique	méchanique	PROPN
ap-938	67	23	,	,	PUNCT
ap-938	67	24	vol	vol	NOUN
ap-938	67	25	.	.	PUNCT
ap-938	68	1	332	332	NUM
ap-938	68	2	(	(	PUNCT
ap-938	68	3	2004	2004	NUM
ap-938	68	4	)	)	PUNCT
ap-938	68	5	,	,	PUNCT
ap-938	68	6	no	no	INTJ
ap-938	68	7	.	.	NOUN
ap-938	68	8	8	8	NUM
ap-938	68	9	,	,	PUNCT
ap-938	68	10	p.	p.	NOUN
ap-938	68	11	647–652	647–652	NUM
ap-938	68	12	.	.	PUNCT
ap-938	69	1	[	[	X
ap-938	69	2	2	2	NUM
ap-938	69	3	]	]	X
ap-938	69	4	gadyl’shin	gadyl’shin	NOUN
ap-938	69	5	,	,	PUNCT
ap-938	69	6	r.	r.	PROPN
ap-938	69	7	:	:	PUNCT
ap-938	69	8	local	local	ADJ
ap-938	69	9	perturbations	perturbation	NOUN
ap-938	69	10	of	of	ADP
ap-938	69	11	quantum	quantum	ADJ
ap-938	69	12	waveguides	waveguide	NOUN
ap-938	69	13	,	,	PUNCT
ap-938	69	14	theor	theor	PROPN
ap-938	69	15	.	.	PUNCT
ap-938	69	16	math	math	NOUN
ap-938	69	17	.	.	PUNCT
ap-938	70	1	phys	phy	NOUN
ap-938	70	2	.	.	PUNCT
ap-938	70	3	,	,	PUNCT
ap-938	70	4	vol	vol	NOUN
ap-938	70	5	.	.	PROPN
ap-938	70	6	145	145	NUM
ap-938	70	7	(	(	PUNCT
ap-938	70	8	2005	2005	NUM
ap-938	70	9	)	)	PUNCT
ap-938	70	10	,	,	PUNCT
ap-938	70	11	no	no	INTJ
ap-938	70	12	.	.	NOUN
ap-938	70	13	3	3	NUM
ap-938	70	14	,	,	PUNCT
ap-938	70	15	p.	p.	NOUN
ap-938	70	16	1678–1690	1678–1690	NUM
ap-938	70	17	.	.	PUNCT
ap-938	71	1	58	58	NUM
ap-938	72	1	©	©	PROPN
ap-938	72	2	czech	czech	PROPN
ap-938	72	3	technical	technical	PROPN
ap-938	72	4	university	university	PROPN
ap-938	72	5	publishing	publishing	NOUN
ap-938	72	6	house	house	NOUN
ap-938	72	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-938	72	8	acta	acta	PROPN
ap-938	72	9	polytechnica	polytechnica	PROPN
ap-938	72	10	vol	vol	NOUN
ap-938	72	11	.	.	PUNCT
ap-938	73	1	47	47	NUM
ap-938	73	2	no	no	INTJ
ap-938	73	3	.	.	PUNCT
ap-938	74	1	2–3/2007	2–3/2007	NUM
ap-938	75	1	[	[	X
ap-938	75	2	3	3	NUM
ap-938	75	3	]	]	PUNCT
ap-938	75	4	glazman	glazman	NOUN
ap-938	75	5	,	,	PUNCT
ap-938	75	6	i.	i.	NOUN
ap-938	75	7	m.	m.	PROPN
ap-938	75	8	:	:	PUNCT
ap-938	75	9	direct	direct	ADJ
ap-938	75	10	methods	method	NOUN
ap-938	75	11	of	of	ADP
ap-938	75	12	qualitative	qualitative	ADJ
ap-938	75	13	spectral	spectral	ADJ
ap-938	75	14	analysis	analysis	NOUN
ap-938	75	15	of	of	ADP
ap-938	75	16	singular	singular	ADJ
ap-938	75	17	differential	differential	NOUN
ap-938	75	18	operators	operator	NOUN
ap-938	75	19	.	.	PUNCT
ap-938	76	1	london	london	PROPN
ap-938	76	2	,	,	PUNCT
ap-938	76	3	oldbourne	oldbourne	ADJ
ap-938	76	4	press	press	NOUN
ap-938	76	5	,	,	PUNCT
ap-938	76	6	1965	1965	NUM
ap-938	76	7	.	.	PUNCT
ap-938	77	1	[	[	X
ap-938	77	2	4	4	NUM
ap-938	77	3	]	]	X
ap-938	77	4	borisov	borisov	PROPN
ap-938	77	5	,	,	PUNCT
ap-938	77	6	d.	d.	PROPN
ap-938	77	7	,	,	PUNCT
ap-938	77	8	krejčiřík	krejčiřík	PROPN
ap-938	77	9	,	,	PUNCT
ap-938	77	10	d.	d.	PROPN
ap-938	77	11	:	:	PUNCT
ap-938	77	12	�	�	PROPN
ap-938	77	13	�	�	PROPN
ap-938	77	14	-symmetric	-symmetric	NOUN
ap-938	77	15	waveguide	waveguide	NOUN
ap-938	77	16	,	,	PUNCT
ap-938	77	17	submitted	submit	VERB
ap-938	77	18	.	.	PUNCT
ap-938	78	1	preprint	preprint	NOUN
ap-938	78	2	:	:	PUNCT
ap-938	78	3	arxiv:0707.3039	arxiv:0707.3039	NOUN
ap-938	78	4	.	.	PUNCT
ap-938	79	1	dr	dr	PROPN
ap-938	79	2	.	.	PROPN
ap-938	79	3	denis	denis	PROPN
ap-938	79	4	i.	i.	PROPN
ap-938	79	5	borisov	borisov	PROPN
ap-938	79	6	phone	phone	PROPN
ap-938	79	7	:	:	PUNCT
ap-938	79	8	+49	+49	NOUN
ap-938	79	9	371	371	NUM
ap-938	79	10	431	431	NUM
ap-938	79	11	3215	3215	NUM
ap-938	79	12	e	e	NOUN
ap-938	79	13	-	-	NOUN
ap-938	79	14	mail	mail	NOUN
ap-938	79	15	:	:	PUNCT
ap-938	79	16	borisovdi@yandex.ru	borisovdi@yandex.ru	PROPN
ap-938	79	17	,	,	PUNCT
ap-938	79	18	borisovdi@ic.bashedu.ru	borisovdi@ic.bashedu.ru	PROPN
ap-938	79	19	faculty	faculty	NOUN
ap-938	79	20	of	of	ADP
ap-938	79	21	mathematics	mathematics	PROPN
ap-938	79	22	chemnitz	chemnitz	PROPN
ap-938	79	23	university	university	PROPN
ap-938	79	24	of	of	ADP
ap-938	79	25	technology	technology	NOUN
ap-938	79	26	reichenhainer	reichenhainer	NOUN
ap-938	79	27	str	str	PROPN
ap-938	79	28	.	.	PUNCT
ap-938	79	29	39	39	NUM
ap-938	79	30	d-09107	d-09107	PROPN
ap-938	79	31	chemnitz	chemnitz	NOUN
ap-938	79	32	,	,	PUNCT
ap-938	79	33	germany	germany	PROPN
ap-938	79	34	©	©	PROPN
ap-938	79	35	czech	czech	PROPN
ap-938	79	36	technical	technical	PROPN
ap-938	79	37	university	university	PROPN
ap-938	79	38	publishing	publishing	NOUN
ap-938	79	39	house	house	NOUN
ap-938	79	40	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-938	79	41	59	59	NUM
ap-938	79	42	acta	acta	PROPN
ap-938	79	43	polytechnica	polytechnica	PROPN
ap-938	79	44	vol	vol	NOUN
ap-938	79	45	.	.	PUNCT
ap-938	80	1	47	47	NUM
ap-938	80	2	no	no	INTJ
ap-938	80	3	.	.	PUNCT
ap-938	81	1	2–3/2007	2–3/2007	NUM