id	sid	tid	token	lemma	pos
ap-1851	1	1	acta	acta	PROPN
ap-1851	1	2	polytechnica	polytechnica	PROPN
ap-1851	1	3	doi:10.14311	doi:10.14311	PROPN
ap-1851	1	4	/	/	PROPN
ap-1851	1	5	ap.2013.53.0416	ap.2013.53.0416	PROPN
ap-1851	1	6	acta	acta	PROPN
ap-1851	1	7	polytechnica	polytechnica	PROPN
ap-1851	1	8	53(5):416–426	53(5):416–426	PROPN
ap-1851	1	9	,	,	PUNCT
ap-1851	1	10	2013	2013	NUM
ap-1851	1	11	©	©	PROPN
ap-1851	1	12	czech	czech	PROPN
ap-1851	1	13	technical	technical	PROPN
ap-1851	1	14	university	university	PROPN
ap-1851	1	15	in	in	ADP
ap-1851	1	16	prague	prague	PROPN
ap-1851	1	17	,	,	PUNCT
ap-1851	1	18	2013	2013	NUM
ap-1851	1	19	available	available	ADJ
ap-1851	1	20	online	online	ADV
ap-1851	1	21	at	at	ADP
ap-1851	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1851	1	23	resonances	resonance	NOUN
ap-1851	1	24	on	on	ADP
ap-1851	1	25	hedgehog	hedgehog	PROPN
ap-1851	1	26	manifolds	manifolds	PROPN
ap-1851	1	27	pavel	pavel	PROPN
ap-1851	1	28	exnera	exnera	NOUN
ap-1851	1	29	,	,	PUNCT
ap-1851	1	30	b,∗	b,∗	NOUN
ap-1851	1	31	,	,	PUNCT
ap-1851	1	32	jiří	jiří	NOUN
ap-1851	1	33	lipovskýc	lipovskýc	NOUN
ap-1851	1	34	a	a	DET
ap-1851	1	35	doppler	doppler	NOUN
ap-1851	1	36	institute	institute	NOUN
ap-1851	1	37	for	for	ADP
ap-1851	1	38	mathematical	mathematical	ADJ
ap-1851	1	39	physics	physics	NOUN
ap-1851	1	40	and	and	CCONJ
ap-1851	1	41	applied	apply	VERB
ap-1851	1	42	mathematics	mathematic	NOUN
ap-1851	1	43	,	,	PUNCT
ap-1851	1	44	czech	czech	PROPN
ap-1851	1	45	technical	technical	PROPN
ap-1851	1	46	university	university	PROPN
ap-1851	1	47	,	,	PUNCT
ap-1851	1	48	břehová	břehová	VERB
ap-1851	1	49	7,11519	7,11519	NUM
ap-1851	1	50	prague	prague	NOUN
ap-1851	1	51	,	,	PUNCT
ap-1851	1	52	czechia	czechia	PROPN
ap-1851	1	53	b	b	PROPN
ap-1851	1	54	department	department	PROPN
ap-1851	1	55	of	of	ADP
ap-1851	1	56	theoretical	theoretical	ADJ
ap-1851	1	57	physics	physics	NOUN
ap-1851	1	58	,	,	PUNCT
ap-1851	1	59	nuclear	nuclear	PROPN
ap-1851	1	60	physics	physics	PROPN
ap-1851	1	61	institute	institute	PROPN
ap-1851	1	62	as	as	ADP
ap-1851	1	63	cr	cr	PROPN
ap-1851	1	64	,	,	PUNCT
ap-1851	1	65	25068	25068	NUM
ap-1851	1	66	řež	řež	NUM
ap-1851	1	67	near	near	ADP
ap-1851	1	68	prague	prague	PROPN
ap-1851	1	69	,	,	PUNCT
ap-1851	1	70	czechia	czechia	PROPN
ap-1851	1	71	c	c	PROPN
ap-1851	1	72	department	department	PROPN
ap-1851	1	73	of	of	ADP
ap-1851	1	74	physics	physics	PROPN
ap-1851	1	75	,	,	PUNCT
ap-1851	1	76	faculty	faculty	NOUN
ap-1851	1	77	of	of	ADP
ap-1851	1	78	science	science	NOUN
ap-1851	1	79	,	,	PUNCT
ap-1851	1	80	university	university	PROPN
ap-1851	1	81	of	of	ADP
ap-1851	1	82	hradec	hradec	PROPN
ap-1851	1	83	králové	králové	PROPN
ap-1851	1	84	,	,	PUNCT
ap-1851	1	85	rokitanského	rokitanského	VERB
ap-1851	1	86	62	62	NUM
ap-1851	1	87	,	,	PUNCT
ap-1851	1	88	50003	50003	NUM
ap-1851	1	89	hradec	hradec	PROPN
ap-1851	1	90	králové	králové	PROPN
ap-1851	1	91	,	,	PUNCT
ap-1851	1	92	czechia	czechia	PROPN
ap-1851	1	93	∗	∗	NOUN
ap-1851	1	94	corresponding	corresponding	ADJ
ap-1851	1	95	author	author	NOUN
ap-1851	1	96	:	:	PUNCT
ap-1851	1	97	exner@ujf.cas.cz	exner@ujf.cas.cz	NOUN
ap-1851	1	98	abstract	abstract	ADJ
ap-1851	1	99	.	.	PUNCT
ap-1851	2	1	we	we	PRON
ap-1851	2	2	discuss	discuss	VERB
ap-1851	2	3	resonances	resonance	NOUN
ap-1851	2	4	for	for	ADP
ap-1851	2	5	a	a	DET
ap-1851	2	6	nonrelativistic	nonrelativistic	ADJ
ap-1851	2	7	and	and	CCONJ
ap-1851	2	8	spinless	spinless	ADJ
ap-1851	2	9	quantum	quantum	NOUN
ap-1851	2	10	particle	particle	NOUN
ap-1851	2	11	confined	confine	VERB
ap-1851	2	12	to	to	ADP
ap-1851	2	13	a	a	DET
ap-1851	2	14	twoor	twoor	ADJ
ap-1851	2	15	three	three	NUM
ap-1851	2	16	-	-	PUNCT
ap-1851	2	17	dimensional	dimensional	ADJ
ap-1851	2	18	riemannian	riemannian	NOUN
ap-1851	2	19	manifold	manifold	NOUN
ap-1851	2	20	to	to	ADP
ap-1851	2	21	which	which	PRON
ap-1851	2	22	a	a	DET
ap-1851	2	23	finite	finite	ADJ
ap-1851	2	24	number	number	NOUN
ap-1851	2	25	of	of	ADP
ap-1851	2	26	semiinfinite	semiinfinite	ADJ
ap-1851	2	27	leads	lead	NOUN
ap-1851	2	28	is	be	AUX
ap-1851	2	29	attached	attach	VERB
ap-1851	2	30	.	.	PUNCT
ap-1851	3	1	resolvent	resolvent	ADJ
ap-1851	3	2	and	and	CCONJ
ap-1851	3	3	scattering	scatter	VERB
ap-1851	3	4	resonances	resonance	NOUN
ap-1851	3	5	are	be	AUX
ap-1851	3	6	shown	show	VERB
ap-1851	3	7	to	to	PART
ap-1851	3	8	coincide	coincide	VERB
ap-1851	3	9	in	in	ADP
ap-1851	3	10	this	this	DET
ap-1851	3	11	situation	situation	NOUN
ap-1851	3	12	.	.	PUNCT
ap-1851	4	1	next	next	ADV
ap-1851	4	2	we	we	PRON
ap-1851	4	3	consider	consider	VERB
ap-1851	4	4	the	the	DET
ap-1851	4	5	resonances	resonance	NOUN
ap-1851	4	6	together	together	ADV
ap-1851	4	7	with	with	ADP
ap-1851	4	8	embedded	embed	VERB
ap-1851	4	9	eigenvalues	eigenvalue	NOUN
ap-1851	4	10	and	and	CCONJ
ap-1851	4	11	ask	ask	VERB
ap-1851	4	12	about	about	ADP
ap-1851	4	13	the	the	DET
ap-1851	4	14	high	high	ADJ
ap-1851	4	15	-	-	PUNCT
ap-1851	4	16	energy	energy	NOUN
ap-1851	4	17	asymptotics	asymptotic	NOUN
ap-1851	4	18	of	of	ADP
ap-1851	4	19	such	such	DET
ap-1851	4	20	a	a	DET
ap-1851	4	21	family	family	NOUN
ap-1851	4	22	.	.	PUNCT
ap-1851	5	1	for	for	ADP
ap-1851	5	2	the	the	DET
ap-1851	5	3	case	case	NOUN
ap-1851	5	4	when	when	SCONJ
ap-1851	5	5	all	all	DET
ap-1851	5	6	the	the	DET
ap-1851	5	7	halflines	halfline	NOUN
ap-1851	5	8	are	be	AUX
ap-1851	5	9	attached	attach	VERB
ap-1851	5	10	at	at	ADP
ap-1851	5	11	a	a	DET
ap-1851	5	12	single	single	ADJ
ap-1851	5	13	point	point	NOUN
ap-1851	5	14	we	we	PRON
ap-1851	5	15	prove	prove	VERB
ap-1851	5	16	that	that	SCONJ
ap-1851	5	17	all	all	DET
ap-1851	5	18	resonances	resonance	NOUN
ap-1851	5	19	are	be	AUX
ap-1851	5	20	in	in	ADP
ap-1851	5	21	the	the	DET
ap-1851	5	22	momentum	momentum	NOUN
ap-1851	5	23	plane	plane	NOUN
ap-1851	5	24	confined	confine	VERB
ap-1851	5	25	to	to	ADP
ap-1851	5	26	a	a	DET
ap-1851	5	27	strip	strip	NOUN
ap-1851	5	28	parallel	parallel	NOUN
ap-1851	5	29	to	to	ADP
ap-1851	5	30	the	the	DET
ap-1851	5	31	real	real	ADJ
ap-1851	5	32	axis	axis	NOUN
ap-1851	5	33	,	,	PUNCT
ap-1851	5	34	in	in	ADP
ap-1851	5	35	contrast	contrast	NOUN
ap-1851	5	36	to	to	ADP
ap-1851	5	37	the	the	DET
ap-1851	5	38	analogous	analogous	ADJ
ap-1851	5	39	asymptotics	asymptotic	NOUN
ap-1851	5	40	in	in	ADP
ap-1851	5	41	some	some	DET
ap-1851	5	42	metric	metric	ADJ
ap-1851	5	43	quantum	quantum	NOUN
ap-1851	5	44	graphs	graph	NOUN
ap-1851	5	45	;	;	PUNCT
ap-1851	5	46	we	we	PRON
ap-1851	5	47	illustrate	illustrate	VERB
ap-1851	5	48	this	this	PRON
ap-1851	5	49	on	on	ADP
ap-1851	5	50	several	several	ADJ
ap-1851	5	51	simple	simple	ADJ
ap-1851	5	52	examples	example	NOUN
ap-1851	5	53	.	.	PUNCT
ap-1851	6	1	on	on	ADP
ap-1851	6	2	the	the	DET
ap-1851	6	3	other	other	ADJ
ap-1851	6	4	hand	hand	NOUN
ap-1851	6	5	,	,	PUNCT
ap-1851	6	6	the	the	DET
ap-1851	6	7	resonance	resonance	NOUN
ap-1851	6	8	behaviour	behaviour	NOUN
ap-1851	6	9	can	can	AUX
ap-1851	6	10	be	be	AUX
ap-1851	6	11	influenced	influence	VERB
ap-1851	6	12	by	by	ADP
ap-1851	6	13	a	a	DET
ap-1851	6	14	magnetic	magnetic	ADJ
ap-1851	6	15	field	field	NOUN
ap-1851	6	16	.	.	PUNCT
ap-1851	7	1	we	we	PRON
ap-1851	7	2	provide	provide	VERB
ap-1851	7	3	an	an	DET
ap-1851	7	4	example	example	NOUN
ap-1851	7	5	of	of	ADP
ap-1851	7	6	such	such	DET
ap-1851	7	7	a	a	DET
ap-1851	7	8	‘	'	PUNCT
ap-1851	7	9	hedgehog	hedgehog	NOUN
ap-1851	7	10	’	'	PUNCT
ap-1851	7	11	manifold	manifold	NOUN
ap-1851	7	12	at	at	ADP
ap-1851	7	13	which	which	PRON
ap-1851	7	14	a	a	DET
ap-1851	7	15	suitable	suitable	ADJ
ap-1851	7	16	aharonov	aharonov	NOUN
ap-1851	7	17	-	-	PUNCT
ap-1851	7	18	bohm	bohm	PROPN
ap-1851	7	19	flux	flux	NOUN
ap-1851	7	20	leads	lead	VERB
ap-1851	7	21	to	to	ADP
ap-1851	7	22	absence	absence	NOUN
ap-1851	7	23	of	of	ADP
ap-1851	7	24	any	any	DET
ap-1851	7	25	true	true	ADJ
ap-1851	7	26	resonance	resonance	NOUN
ap-1851	7	27	,	,	PUNCT
ap-1851	7	28	i.e.	i.e.	X
ap-1851	7	29	that	that	SCONJ
ap-1851	7	30	corresponding	correspond	VERB
ap-1851	7	31	to	to	ADP
ap-1851	7	32	a	a	DET
ap-1851	7	33	pole	pole	NOUN
ap-1851	7	34	outside	outside	ADP
ap-1851	7	35	the	the	DET
ap-1851	7	36	real	real	ADJ
ap-1851	7	37	axis	axis	NOUN
ap-1851	7	38	.	.	PUNCT
ap-1851	8	1	keywords	keyword	NOUN
ap-1851	8	2	:	:	PUNCT
ap-1851	8	3	hedgehog	hedgehog	PROPN
ap-1851	8	4	manifolds	manifold	NOUN
ap-1851	8	5	,	,	PUNCT
ap-1851	8	6	weyl	weyl	ADJ
ap-1851	8	7	asymptotics	asymptotic	NOUN
ap-1851	8	8	,	,	PUNCT
ap-1851	8	9	quantum	quantum	NOUN
ap-1851	8	10	graphs	graph	NOUN
ap-1851	8	11	,	,	PUNCT
ap-1851	8	12	resonances	resonance	NOUN
ap-1851	8	13	.	.	PUNCT
ap-1851	9	1	submitted	submit	VERB
ap-1851	9	2	:	:	PUNCT
ap-1851	9	3	21	21	NUM
ap-1851	9	4	february	february	NOUN
ap-1851	9	5	2013	2013	NUM
ap-1851	9	6	.	.	PUNCT
ap-1851	10	1	accepted	accept	VERB
ap-1851	10	2	:	:	PUNCT
ap-1851	10	3	17	17	NUM
ap-1851	10	4	april	april	PROPN
ap-1851	10	5	2013	2013	NUM
ap-1851	10	6	.	.	PUNCT
ap-1851	11	1	1	1	X
ap-1851	11	2	.	.	X
ap-1851	11	3	introduction	introduction	NOUN
ap-1851	11	4	a	a	DET
ap-1851	11	5	study	study	NOUN
ap-1851	11	6	of	of	ADP
ap-1851	11	7	quantum	quantum	NOUN
ap-1851	11	8	systems	system	NOUN
ap-1851	11	9	the	the	DET
ap-1851	11	10	configuration	configuration	NOUN
ap-1851	11	11	space	space	NOUN
ap-1851	11	12	of	of	ADP
ap-1851	11	13	which	which	PRON
ap-1851	11	14	is	be	AUX
ap-1851	11	15	geometrically	geometrically	ADV
ap-1851	11	16	and	and	CCONJ
ap-1851	11	17	topologically	topologically	ADV
ap-1851	11	18	nontrivial	nontrivial	NOUN
ap-1851	11	19	has	have	AUX
ap-1851	11	20	proved	prove	VERB
ap-1851	11	21	to	to	PART
ap-1851	11	22	be	be	AUX
ap-1851	11	23	a	a	DET
ap-1851	11	24	fruitful	fruitful	ADJ
ap-1851	11	25	subject	subject	NOUN
ap-1851	11	26	both	both	CCONJ
ap-1851	11	27	theoretically	theoretically	ADV
ap-1851	11	28	and	and	CCONJ
ap-1851	11	29	practically	practically	ADV
ap-1851	11	30	.	.	PUNCT
ap-1851	12	1	a	a	DET
ap-1851	12	2	lot	lot	NOUN
ap-1851	12	3	of	of	ADP
ap-1851	12	4	attention	attention	NOUN
ap-1851	12	5	has	have	AUX
ap-1851	12	6	been	be	AUX
ap-1851	12	7	paid	pay	VERB
ap-1851	12	8	to	to	ADP
ap-1851	12	9	quantum	quantum	NOUN
ap-1851	12	10	graphs	graph	NOUN
ap-1851	12	11	—	—	PUNCT
ap-1851	12	12	a	a	DET
ap-1851	12	13	survey	survey	NOUN
ap-1851	12	14	and	and	CCONJ
ap-1851	12	15	a	a	DET
ap-1851	12	16	guide	guide	NOUN
ap-1851	12	17	to	to	PART
ap-1851	12	18	further	further	ADJ
ap-1851	12	19	reading	reading	NOUN
ap-1851	12	20	can	can	AUX
ap-1851	12	21	be	be	AUX
ap-1851	12	22	found	find	VERB
ap-1851	12	23	in	in	ADP
ap-1851	12	24	[	[	X
ap-1851	12	25	6	6	NUM
ap-1851	12	26	,	,	PUNCT
ap-1851	12	27	14	14	NUM
ap-1851	12	28	]	]	PUNCT
ap-1851	12	29	.	.	PUNCT
ap-1851	13	1	together	together	ADV
ap-1851	13	2	with	with	ADP
ap-1851	13	3	this	this	DET
ap-1851	13	4	other	other	ADJ
ap-1851	13	5	systems	system	NOUN
ap-1851	13	6	have	have	AUX
ap-1851	13	7	been	be	AUX
ap-1851	13	8	studied	study	VERB
ap-1851	13	9	which	which	DET
ap-1851	13	10	one	one	PRON
ap-1851	13	11	can	can	AUX
ap-1851	13	12	regard	regard	VERB
ap-1851	13	13	as	as	ADP
ap-1851	13	14	a	a	DET
ap-1851	13	15	generalization	generalization	NOUN
ap-1851	13	16	of	of	ADP
ap-1851	13	17	quantum	quantum	NOUN
ap-1851	13	18	graphs	graph	NOUN
ap-1851	13	19	where	where	SCONJ
ap-1851	13	20	the	the	DET
ap-1851	13	21	‘	'	PUNCT
ap-1851	13	22	edges	edge	NOUN
ap-1851	13	23	’	'	PUNCT
ap-1851	13	24	may	may	AUX
ap-1851	13	25	have	have	VERB
ap-1851	13	26	different	different	ADJ
ap-1851	13	27	dimensions	dimension	NOUN
ap-1851	13	28	;	;	PUNCT
ap-1851	13	29	using	use	VERB
ap-1851	13	30	the	the	DET
ap-1851	13	31	theory	theory	NOUN
ap-1851	13	32	of	of	ADP
ap-1851	13	33	self	self	NOUN
ap-1851	13	34	-	-	PUNCT
ap-1851	13	35	adjoint	adjoint	NOUN
ap-1851	13	36	extensions	extension	NOUN
ap-1851	13	37	one	one	PRON
ap-1851	13	38	can	can	AUX
ap-1851	13	39	construct	construct	VERB
ap-1851	13	40	operator	operator	NOUN
ap-1851	13	41	classes	class	NOUN
ap-1851	13	42	which	which	PRON
ap-1851	13	43	serve	serve	VERB
ap-1851	13	44	as	as	ADP
ap-1851	13	45	hamiltonians	hamiltonian	NOUN
ap-1851	13	46	of	of	ADP
ap-1851	13	47	such	such	ADJ
ap-1851	13	48	models	model	NOUN
ap-1851	13	49	[	[	X
ap-1851	13	50	19	19	NUM
ap-1851	13	51	]	]	PUNCT
ap-1851	13	52	.	.	PUNCT
ap-1851	14	1	one	one	NUM
ap-1851	14	2	sometimes	sometimes	ADV
ap-1851	14	3	uses	use	VERB
ap-1851	14	4	a	a	DET
ap-1851	14	5	pictorial	pictorial	ADJ
ap-1851	14	6	term	term	NOUN
ap-1851	14	7	‘	'	PUNCT
ap-1851	14	8	hedgehog	hedgehog	NOUN
ap-1851	14	9	manifold	manifold	NOUN
ap-1851	14	10	’	'	PUNCT
ap-1851	14	11	for	for	ADP
ap-1851	14	12	a	a	DET
ap-1851	14	13	geometrical	geometrical	ADJ
ap-1851	14	14	construct	construct	NOUN
ap-1851	14	15	consisting	consist	VERB
ap-1851	14	16	of	of	ADP
ap-1851	14	17	riemannian	riemannian	ADJ
ap-1851	14	18	manifolds	manifold	NOUN
ap-1851	14	19	of	of	ADP
ap-1851	14	20	dimension	dimension	NOUN
ap-1851	14	21	two	two	NUM
ap-1851	14	22	or	or	CCONJ
ap-1851	14	23	three	three	NUM
ap-1851	14	24	together	together	ADV
ap-1851	14	25	with	with	ADP
ap-1851	14	26	line	line	NOUN
ap-1851	14	27	segments	segment	NOUN
ap-1851	14	28	attached	attach	VERB
ap-1851	14	29	to	to	ADP
ap-1851	14	30	them	they	PRON
ap-1851	14	31	.	.	PUNCT
ap-1851	15	1	in	in	ADP
ap-1851	15	2	this	this	DET
ap-1851	15	3	paper	paper	NOUN
ap-1851	15	4	we	we	PRON
ap-1851	15	5	consider	consider	VERB
ap-1851	15	6	the	the	DET
ap-1851	15	7	simplest	simple	ADJ
ap-1851	15	8	situation	situation	NOUN
ap-1851	15	9	when	when	SCONJ
ap-1851	15	10	we	we	PRON
ap-1851	15	11	have	have	VERB
ap-1851	15	12	a	a	DET
ap-1851	15	13	single	single	ADJ
ap-1851	15	14	connected	connected	ADJ
ap-1851	15	15	manifold	manifold	NOUN
ap-1851	15	16	to	to	ADP
ap-1851	15	17	which	which	PRON
ap-1851	15	18	a	a	DET
ap-1851	15	19	finite	finite	ADJ
ap-1851	15	20	number	number	NOUN
ap-1851	15	21	of	of	ADP
ap-1851	15	22	semiinfinite	semiinfinite	ADJ
ap-1851	15	23	leads	lead	NOUN
ap-1851	15	24	are	be	AUX
ap-1851	15	25	attached	attach	VERB
ap-1851	15	26	—	—	PUNCT
ap-1851	15	27	one	one	PRON
ap-1851	15	28	is	be	AUX
ap-1851	15	29	especially	especially	ADV
ap-1851	15	30	interested	interested	ADJ
ap-1851	15	31	in	in	ADP
ap-1851	15	32	transport	transport	NOUN
ap-1851	15	33	in	in	ADP
ap-1851	15	34	such	such	DET
ap-1851	15	35	a	a	DET
ap-1851	15	36	system	system	NOUN
ap-1851	15	37	.	.	PUNCT
ap-1851	16	1	particular	particular	ADJ
ap-1851	16	2	models	model	NOUN
ap-1851	16	3	of	of	ADP
ap-1851	16	4	this	this	DET
ap-1851	16	5	type	type	NOUN
ap-1851	16	6	have	have	AUX
ap-1851	16	7	been	be	AUX
ap-1851	16	8	studied	study	VERB
ap-1851	16	9	,	,	PUNCT
ap-1851	16	10	e.g.	e.g.	ADV
ap-1851	16	11	,	,	PUNCT
ap-1851	16	12	in	in	ADP
ap-1851	16	13	[	[	PUNCT
ap-1851	16	14	7	7	NUM
ap-1851	16	15	,	,	PUNCT
ap-1851	16	16	8	8	NUM
ap-1851	16	17	,	,	PUNCT
ap-1851	16	18	18	18	NUM
ap-1851	16	19	,	,	PUNCT
ap-1851	16	20	20	20	NUM
ap-1851	16	21	,	,	PUNCT
ap-1851	16	22	25	25	NUM
ap-1851	16	23	]	]	PUNCT
ap-1851	16	24	.	.	PUNCT
ap-1851	17	1	again	again	ADV
ap-1851	17	2	for	for	ADP
ap-1851	17	3	the	the	DET
ap-1851	17	4	sake	sake	NOUN
ap-1851	17	5	of	of	ADP
ap-1851	17	6	simplicity	simplicity	NOUN
ap-1851	17	7	we	we	PRON
ap-1851	17	8	limit	limit	VERB
ap-1851	17	9	ourselves	ourselves	PRON
ap-1851	17	10	mostly	mostly	ADV
ap-1851	17	11	to	to	ADP
ap-1851	17	12	the	the	DET
ap-1851	17	13	situation	situation	NOUN
ap-1851	17	14	when	when	SCONJ
ap-1851	17	15	there	there	PRON
ap-1851	17	16	are	be	VERB
ap-1851	17	17	no	no	DET
ap-1851	17	18	external	external	ADJ
ap-1851	17	19	fields	field	NOUN
ap-1851	17	20	;	;	PUNCT
ap-1851	17	21	the	the	DET
ap-1851	17	22	hamiltonian	hamiltonian	NOUN
ap-1851	17	23	will	will	AUX
ap-1851	17	24	act	act	VERB
ap-1851	17	25	as	as	ADP
ap-1851	17	26	the	the	DET
ap-1851	17	27	negative	negative	ADJ
ap-1851	17	28	second	second	ADJ
ap-1851	17	29	derivative	derivative	NOUN
ap-1851	17	30	on	on	ADP
ap-1851	17	31	the	the	DET
ap-1851	17	32	halflines	halfline	NOUN
ap-1851	17	33	representing	represent	VERB
ap-1851	17	34	the	the	DET
ap-1851	17	35	leads	lead	NOUN
ap-1851	17	36	and	and	CCONJ
ap-1851	17	37	as	as	ADP
ap-1851	17	38	laplace	laplace	NOUN
ap-1851	17	39	-	-	PUNCT
ap-1851	17	40	beltrami	beltrami	ADJ
ap-1851	17	41	operator	operator	NOUN
ap-1851	17	42	on	on	ADP
ap-1851	17	43	the	the	DET
ap-1851	17	44	manifold	manifold	NOUN
ap-1851	17	45	.	.	PUNCT
ap-1851	18	1	we	we	PRON
ap-1851	18	2	have	have	AUX
ap-1851	18	3	said	say	VERB
ap-1851	18	4	that	that	SCONJ
ap-1851	18	5	quantum	quantum	ADJ
ap-1851	18	6	motion	motion	NOUN
ap-1851	18	7	on	on	ADP
ap-1851	18	8	hedgehog	hedgehog	PROPN
ap-1851	18	9	manifolds	manifold	NOUN
ap-1851	18	10	can	can	AUX
ap-1851	18	11	be	be	AUX
ap-1851	18	12	regarded	regard	VERB
ap-1851	18	13	as	as	ADP
ap-1851	18	14	a	a	DET
ap-1851	18	15	generalization	generalization	NOUN
ap-1851	18	16	of	of	ADP
ap-1851	18	17	quantum	quantum	NOUN
ap-1851	18	18	graphs	graph	NOUN
ap-1851	18	19	.	.	PUNCT
ap-1851	19	1	it	it	PRON
ap-1851	19	2	is	be	AUX
ap-1851	19	3	therefore	therefore	ADV
ap-1851	19	4	useful	useful	ADJ
ap-1851	19	5	to	to	PART
ap-1851	19	6	compare	compare	VERB
ap-1851	19	7	similarities	similarity	NOUN
ap-1851	19	8	and	and	CCONJ
ap-1851	19	9	differences	difference	NOUN
ap-1851	19	10	of	of	ADP
ap-1851	19	11	the	the	DET
ap-1851	19	12	two	two	NUM
ap-1851	19	13	cases	case	NOUN
ap-1851	19	14	,	,	PUNCT
ap-1851	19	15	and	and	CCONJ
ap-1851	19	16	we	we	PRON
ap-1851	19	17	will	will	AUX
ap-1851	19	18	recall	recall	VERB
ap-1851	19	19	at	at	ADP
ap-1851	19	20	appropriate	appropriate	ADJ
ap-1851	19	21	places	place	NOUN
ap-1851	19	22	in	in	ADP
ap-1851	19	23	the	the	DET
ap-1851	19	24	text	text	NOUN
ap-1851	19	25	how	how	SCONJ
ap-1851	19	26	the	the	DET
ap-1851	19	27	claims	claim	NOUN
ap-1851	19	28	look	look	VERB
ap-1851	19	29	when	when	SCONJ
ap-1851	19	30	the	the	DET
ap-1851	19	31	riemannian	riemannian	ADJ
ap-1851	19	32	manifold	manifold	NOUN
ap-1851	19	33	is	be	AUX
ap-1851	19	34	replaced	replace	VERB
ap-1851	19	35	by	by	ADP
ap-1851	19	36	a	a	DET
ap-1851	19	37	compact	compact	ADJ
ap-1851	19	38	metric	metric	ADJ
ap-1851	19	39	graph	graph	NOUN
ap-1851	19	40	.	.	PUNCT
ap-1851	20	1	the	the	DET
ap-1851	20	2	first	first	ADJ
ap-1851	20	3	question	question	NOUN
ap-1851	20	4	one	one	PRON
ap-1851	20	5	has	have	VERB
ap-1851	20	6	to	to	PART
ap-1851	20	7	pose	pose	VERB
ap-1851	20	8	when	when	SCONJ
ap-1851	20	9	resonances	resonance	NOUN
ap-1851	20	10	are	be	AUX
ap-1851	20	11	discussed	discuss	VERB
ap-1851	20	12	is	be	AUX
ap-1851	20	13	what	what	PRON
ap-1851	20	14	is	be	AUX
ap-1851	20	15	meant	mean	VERB
ap-1851	20	16	by	by	ADP
ap-1851	20	17	this	this	PRON
ap-1851	20	18	term1	term1	PROPN
ap-1851	20	19	.	.	PUNCT
ap-1851	21	1	the	the	DET
ap-1851	21	2	two	two	NUM
ap-1851	21	3	prominent	prominent	ADJ
ap-1851	21	4	instances	instance	NOUN
ap-1851	21	5	are	be	AUX
ap-1851	21	6	resolvent	resolvent	ADJ
ap-1851	21	7	resonances	resonance	NOUN
ap-1851	21	8	identified	identify	VERB
ap-1851	21	9	with	with	ADP
ap-1851	21	10	poles	pole	NOUN
ap-1851	21	11	of	of	ADP
ap-1851	21	12	the	the	DET
ap-1851	21	13	analytically	analytically	ADV
ap-1851	21	14	continued	continue	VERB
ap-1851	21	15	resolvent	resolvent	NOUN
ap-1851	21	16	of	of	ADP
ap-1851	21	17	the	the	DET
ap-1851	21	18	hamiltonian	hamiltonian	ADJ
ap-1851	21	19	and	and	CCONJ
ap-1851	21	20	scattering	scatter	VERB
ap-1851	21	21	resonances	resonance	NOUN
ap-1851	21	22	where	where	SCONJ
ap-1851	21	23	we	we	PRON
ap-1851	21	24	look	look	VERB
ap-1851	21	25	instead	instead	ADV
ap-1851	21	26	into	into	ADP
ap-1851	21	27	the	the	DET
ap-1851	21	28	analytical	analytical	ADJ
ap-1851	21	29	structure	structure	NOUN
ap-1851	21	30	of	of	ADP
ap-1851	21	31	the	the	DET
ap-1851	21	32	on	on	ADP
ap-1851	21	33	-	-	PUNCT
ap-1851	21	34	shell	shell	NOUN
ap-1851	21	35	scattering	scattering	NOUN
ap-1851	21	36	operator	operator	NOUN
ap-1851	21	37	.	.	PUNCT
ap-1851	22	1	while	while	SCONJ
ap-1851	22	2	the	the	DET
ap-1851	22	3	two	two	NUM
ap-1851	22	4	often	often	ADV
ap-1851	22	5	coincide	coincide	NOUN
ap-1851	22	6	,	,	PUNCT
ap-1851	22	7	in	in	ADP
ap-1851	22	8	general	general	ADJ
ap-1851	22	9	it	it	PRON
ap-1851	22	10	may	may	AUX
ap-1851	22	11	not	not	PART
ap-1851	22	12	be	be	AUX
ap-1851	22	13	so	so	ADV
ap-1851	22	14	;	;	PUNCT
ap-1851	22	15	recall	recall	VERB
ap-1851	22	16	that	that	SCONJ
ap-1851	22	17	the	the	DET
ap-1851	22	18	former	former	ADJ
ap-1851	22	19	are	be	AUX
ap-1851	22	20	the	the	DET
ap-1851	22	21	property	property	NOUN
ap-1851	22	22	of	of	ADP
ap-1851	22	23	a	a	DET
ap-1851	22	24	single	single	ADJ
ap-1851	22	25	operator	operator	NOUN
ap-1851	22	26	while	while	SCONJ
ap-1851	22	27	the	the	DET
ap-1851	22	28	latter	latter	ADJ
ap-1851	22	29	refer	refer	VERB
ap-1851	22	30	to	to	ADP
ap-1851	22	31	the	the	DET
ap-1851	22	32	pair	pair	NOUN
ap-1851	22	33	of	of	ADP
ap-1851	22	34	full	full	ADJ
ap-1851	22	35	and	and	CCONJ
ap-1851	22	36	unperturbed	unperturbed	ADJ
ap-1851	22	37	hamiltonians	hamiltonian	NOUN
ap-1851	22	38	,	,	PUNCT
ap-1851	22	39	and	and	CCONJ
ap-1851	22	40	often	often	ADV
ap-1851	22	41	also	also	ADV
ap-1851	22	42	a	a	DET
ap-1851	22	43	third	third	ADJ
ap-1851	22	44	one	one	NOUN
ap-1851	22	45	,	,	PUNCT
ap-1851	22	46	an	an	DET
ap-1851	22	47	identification	identification	NOUN
ap-1851	22	48	operator	operator	NOUN
ap-1851	22	49	,	,	PUNCT
ap-1851	22	50	which	which	PRON
ap-1851	22	51	one	one	NOUN
ap-1851	22	52	uses	use	VERB
ap-1851	22	53	if	if	SCONJ
ap-1851	22	54	the	the	DET
ap-1851	22	55	two	two	NUM
ap-1851	22	56	hamiltonians	hamiltonian	NOUN
ap-1851	22	57	act	act	VERB
ap-1851	22	58	on	on	ADP
ap-1851	22	59	different	different	ADJ
ap-1851	22	60	hilbert	hilbert	NOUN
ap-1851	22	61	spaces	space	NOUN
ap-1851	22	62	[	[	X
ap-1851	22	63	27	27	NUM
ap-1851	22	64	]	]	PUNCT
ap-1851	22	65	.	.	PUNCT
ap-1851	23	1	the	the	DET
ap-1851	23	2	first	first	ADJ
ap-1851	23	3	question	question	NOUN
ap-1851	23	4	we	we	PRON
ap-1851	23	5	will	will	AUX
ap-1851	23	6	thus	thus	ADV
ap-1851	23	7	address	address	VERB
ap-1851	23	8	deals	deal	NOUN
ap-1851	23	9	with	with	ADP
ap-1851	23	10	the	the	DET
ap-1851	23	11	two	two	NUM
ap-1851	23	12	resonance	resonance	NOUN
ap-1851	23	13	definitions	definition	NOUN
ap-1851	23	14	for	for	ADP
ap-1851	23	15	quantum	quantum	ADJ
ap-1851	23	16	motion	motion	NOUN
ap-1851	23	17	on	on	ADP
ap-1851	23	18	hedgehog	hedgehog	NOUN
ap-1851	23	19	manifolds	manifold	NOUN
ap-1851	23	20	.	.	PUNCT
ap-1851	23	21	using	use	VERB
ap-1851	23	22	an	an	DET
ap-1851	23	23	exterior	exterior	ADJ
ap-1851	23	24	complex	complex	ADJ
ap-1851	23	25	scaling	scaling	NOUN
ap-1851	23	26	we	we	PRON
ap-1851	23	27	will	will	AUX
ap-1851	23	28	show	show	VERB
ap-1851	23	29	that	that	SCONJ
ap-1851	23	30	in	in	ADP
ap-1851	23	31	this	this	DET
ap-1851	23	32	case	case	NOUN
ap-1851	23	33	both	both	DET
ap-1851	23	34	notions	notion	NOUN
ap-1851	23	35	coincide	coincide	NOUN
ap-1851	23	36	and	and	CCONJ
ap-1851	23	37	one	one	NOUN
ap-1851	23	38	is	be	AUX
ap-1851	23	39	thus	thus	ADV
ap-1851	23	40	allowed	allow	VERB
ap-1851	23	41	to	to	PART
ap-1851	23	42	speak	speak	VERB
ap-1851	23	43	about	about	ADP
ap-1851	23	44	resonances	resonance	NOUN
ap-1851	23	45	without	without	ADP
ap-1851	23	46	a	a	DET
ap-1851	23	47	further	further	ADJ
ap-1851	23	48	specification	specification	NOUN
ap-1851	23	49	.	.	PUNCT
ap-1851	24	1	the	the	DET
ap-1851	24	2	result	result	NOUN
ap-1851	24	3	is	be	AUX
ap-1851	24	4	the	the	DET
ap-1851	24	5	same	same	ADJ
ap-1851	24	6	as	as	ADP
ap-1851	24	7	for	for	ADP
ap-1851	24	8	quantum	quantum	NOUN
ap-1851	24	9	graphs	graph	NOUN
ap-1851	24	10	[	[	X
ap-1851	24	11	15	15	NUM
ap-1851	24	12	,	,	PUNCT
ap-1851	24	13	16	16	NUM
ap-1851	24	14	]	]	PUNCT
ap-1851	24	15	and	and	CCONJ
ap-1851	24	16	,	,	PUNCT
ap-1851	24	17	needless	needless	ADJ
ap-1851	24	18	to	to	PART
ap-1851	24	19	say	say	VERB
ap-1851	24	20	,	,	PUNCT
ap-1851	24	21	in	in	ADP
ap-1851	24	22	many	many	ADJ
ap-1851	24	23	other	other	ADJ
ap-1851	24	24	situations	situation	NOUN
ap-1851	24	25	.	.	PUNCT
ap-1851	25	1	the	the	DET
ap-1851	25	2	next	next	ADJ
ap-1851	25	3	question	question	NOUN
ap-1851	25	4	to	to	PART
ap-1851	25	5	be	be	AUX
ap-1851	25	6	addressed	address	VERB
ap-1851	25	7	in	in	ADP
ap-1851	25	8	this	this	DET
ap-1851	25	9	paper	paper	NOUN
ap-1851	25	10	concerns	concern	VERB
ap-1851	25	11	the	the	DET
ap-1851	25	12	high	high	ADJ
ap-1851	25	13	energy	energy	NOUN
ap-1851	25	14	behaviour	behaviour	NOUN
ap-1851	25	15	of	of	ADP
ap-1851	25	16	the	the	DET
ap-1851	25	17	resonances	resonance	NOUN
ap-1851	25	18	1investigations	1investigations	NUM
ap-1851	25	19	of	of	ADP
ap-1851	25	20	resonances	resonance	NOUN
ap-1851	25	21	in	in	ADP
ap-1851	25	22	quantum	quantum	ADJ
ap-1851	25	23	systems	system	NOUN
ap-1851	25	24	have	have	VERB
ap-1851	25	25	a	a	DET
ap-1851	25	26	long	long	ADJ
ap-1851	25	27	history	history	NOUN
ap-1851	25	28	.	.	PUNCT
ap-1851	26	1	for	for	ADP
ap-1851	26	2	a	a	DET
ap-1851	26	3	survey	survey	NOUN
ap-1851	26	4	of	of	ADP
ap-1851	26	5	classical	classical	ADJ
ap-1851	26	6	results	result	NOUN
ap-1851	26	7	see	see	VERB
ap-1851	26	8	,	,	PUNCT
ap-1851	26	9	e.g.	e.g.	ADV
ap-1851	26	10	,	,	PUNCT
ap-1851	26	11	chap	chap	NOUN
ap-1851	26	12	.	.	PUNCT
ap-1851	26	13	3	3	NUM
ap-1851	26	14	of	of	ADP
ap-1851	26	15	[	[	X
ap-1851	26	16	13	13	NUM
ap-1851	26	17	]	]	PUNCT
ap-1851	26	18	.	.	PUNCT
ap-1851	27	1	there	there	PRON
ap-1851	27	2	are	be	VERB
ap-1851	27	3	also	also	ADV
ap-1851	27	4	various	various	ADJ
ap-1851	27	5	newer	new	ADJ
ap-1851	27	6	results	result	NOUN
ap-1851	27	7	,	,	PUNCT
ap-1851	27	8	in	in	ADP
ap-1851	27	9	particular	particular	ADJ
ap-1851	27	10	,	,	PUNCT
ap-1851	27	11	attention	attention	NOUN
ap-1851	27	12	has	have	AUX
ap-1851	27	13	been	be	AUX
ap-1851	27	14	paid	pay	VERB
ap-1851	27	15	recently	recently	ADV
ap-1851	27	16	to	to	ADP
ap-1851	27	17	perturbation	perturbation	NOUN
ap-1851	27	18	of	of	ADP
ap-1851	27	19	eigenvalues	eigenvalue	NOUN
ap-1851	27	20	near	near	ADP
ap-1851	27	21	the	the	DET
ap-1851	27	22	threshold	threshold	NOUN
ap-1851	27	23	[	[	X
ap-1851	27	24	12	12	NUM
ap-1851	27	25	]	]	PUNCT
ap-1851	27	26	.	.	PUNCT
ap-1851	28	1	416	416	NUM
ap-1851	28	2	http://dx.doi.org/10.14311/ap.2013.53.0416	http://dx.doi.org/10.14311/ap.2013.53.0416	NOUN
ap-1851	28	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	NOUN
ap-1851	28	4	vol	vol	NOUN
ap-1851	28	5	.	.	PUNCT
ap-1851	29	1	53	53	NUM
ap-1851	29	2	no	no	NOUN
ap-1851	29	3	.	.	PUNCT
ap-1851	30	1	5/2013	5/2013	NUM
ap-1851	30	2	resonances	resonance	NOUN
ap-1851	30	3	on	on	ADP
ap-1851	30	4	hedgehog	hedgehog	NOUN
ap-1851	30	5	manifolds	manifold	NOUN
ap-1851	30	6	which	which	PRON
ap-1851	30	7	is	be	AUX
ap-1851	30	8	,	,	PUNCT
ap-1851	30	9	for	for	ADP
ap-1851	30	10	this	this	DET
ap-1851	30	11	purpose	purpose	NOUN
ap-1851	30	12	,	,	PUNCT
ap-1851	30	13	useful	useful	ADJ
ap-1851	30	14	to	to	PART
ap-1851	30	15	count	count	VERB
ap-1851	30	16	together	together	ADV
ap-1851	30	17	with	with	ADP
ap-1851	30	18	the	the	DET
ap-1851	30	19	eigenvalues	eigenvalue	NOUN
ap-1851	30	20	.	.	PUNCT
ap-1851	31	1	note	note	VERB
ap-1851	31	2	that	that	SCONJ
ap-1851	31	3	if	if	SCONJ
ap-1851	31	4	a	a	DET
ap-1851	31	5	hedgehog	hedgehog	NOUN
ap-1851	31	6	manifold	manifold	NOUN
ap-1851	31	7	with	with	ADP
ap-1851	31	8	a	a	DET
ap-1851	31	9	finite	finite	ADJ
ap-1851	31	10	number	number	NOUN
ap-1851	31	11	of	of	ADP
ap-1851	31	12	junctions	junction	NOUN
ap-1851	31	13	is	be	AUX
ap-1851	31	14	compact	compact	ADJ
ap-1851	31	15	having	have	VERB
ap-1851	31	16	finite	finite	ADJ
ap-1851	31	17	line	line	NOUN
ap-1851	31	18	segments	segment	NOUN
ap-1851	31	19	,	,	PUNCT
ap-1851	31	20	its	its	PRON
ap-1851	31	21	spectrum	spectrum	NOUN
ap-1851	31	22	is	be	AUX
ap-1851	31	23	purely	purely	ADV
ap-1851	31	24	discrete	discrete	ADJ
ap-1851	31	25	and	and	CCONJ
ap-1851	31	26	an	an	DET
ap-1851	31	27	easy	easy	ADJ
ap-1851	31	28	estimate	estimate	NOUN
ap-1851	31	29	yields	yield	VERB
ap-1851	31	30	the	the	DET
ap-1851	31	31	spectral	spectral	ADJ
ap-1851	31	32	behaviour	behaviour	NOUN
ap-1851	31	33	at	at	ADP
ap-1851	31	34	high	high	ADJ
ap-1851	31	35	energies	energy	NOUN
ap-1851	31	36	.	.	PUNCT
ap-1851	32	1	it	it	PRON
ap-1851	32	2	follows	follow	VERB
ap-1851	32	3	the	the	DET
ap-1851	32	4	usual	usual	ADJ
ap-1851	32	5	weyl	weyl	X
ap-1851	32	6	’s	’s	PART
ap-1851	32	7	law	law	NOUN
ap-1851	33	1	[	[	X
ap-1851	33	2	30	30	NUM
ap-1851	33	3	]	]	PUNCT
ap-1851	33	4	,	,	PUNCT
ap-1851	33	5	and	and	CCONJ
ap-1851	33	6	moreover	moreover	ADV
ap-1851	33	7	,	,	PUNCT
ap-1851	33	8	it	it	PRON
ap-1851	33	9	is	be	AUX
ap-1851	33	10	determined	determine	VERB
ap-1851	33	11	by	by	ADP
ap-1851	33	12	the	the	DET
ap-1851	33	13	manifold	manifold	ADJ
ap-1851	33	14	component	component	NOUN
ap-1851	33	15	with	with	ADP
ap-1851	33	16	the	the	DET
ap-1851	33	17	highest	high	ADJ
ap-1851	33	18	dimension	dimension	NOUN
ap-1851	33	19	,	,	PUNCT
ap-1851	33	20	that	that	ADV
ap-1851	33	21	is	is	ADV
ap-1851	33	22	,	,	PUNCT
ap-1851	33	23	in	in	ADP
ap-1851	33	24	our	our	PRON
ap-1851	33	25	case	case	NOUN
ap-1851	33	26	,	,	PUNCT
ap-1851	33	27	the	the	DET
ap-1851	33	28	riemannian	riemannian	ADJ
ap-1851	33	29	manifold	manifold	NOUN
ap-1851	33	30	[	[	X
ap-1851	33	31	24	24	NUM
ap-1851	33	32	]	]	PUNCT
ap-1851	33	33	.	.	PUNCT
ap-1851	34	1	if	if	SCONJ
ap-1851	34	2	,	,	PUNCT
ap-1851	34	3	on	on	ADP
ap-1851	34	4	the	the	DET
ap-1851	34	5	other	other	ADJ
ap-1851	34	6	hand	hand	NOUN
ap-1851	34	7	,	,	PUNCT
ap-1851	34	8	the	the	DET
ap-1851	34	9	leads	lead	NOUN
ap-1851	34	10	are	be	AUX
ap-1851	34	11	semiinfinite	semiinfinite	VERB
ap-1851	34	12	,	,	PUNCT
ap-1851	34	13	the	the	DET
ap-1851	34	14	essential	essential	ADJ
ap-1851	34	15	spectrum	spectrum	NOUN
ap-1851	34	16	covers	cover	VERB
ap-1851	34	17	the	the	DET
ap-1851	34	18	positive	positive	ADJ
ap-1851	34	19	real	real	ADJ
ap-1851	34	20	axis	axis	NOUN
ap-1851	34	21	.	.	PUNCT
ap-1851	35	1	in	in	ADP
ap-1851	35	2	contrast	contrast	NOUN
ap-1851	35	3	to	to	ADP
ap-1851	35	4	the	the	DET
ap-1851	35	5	usual	usual	ADJ
ap-1851	35	6	schrödinger	schrödinger	ADJ
ap-1851	35	7	operator	operator	NOUN
ap-1851	35	8	theory	theory	NOUN
ap-1851	35	9	,	,	PUNCT
ap-1851	35	10	it	it	PRON
ap-1851	35	11	often	often	ADV
ap-1851	35	12	contains	contain	VERB
ap-1851	35	13	embedded	embed	VERB
ap-1851	35	14	eigenvalues	eigenvalue	NOUN
ap-1851	35	15	;	;	PUNCT
ap-1851	35	16	this	this	PRON
ap-1851	35	17	happens	happen	VERB
ap-1851	35	18	typically	typically	ADV
ap-1851	35	19	when	when	SCONJ
ap-1851	35	20	the	the	DET
ap-1851	35	21	laplace	laplace	NOUN
ap-1851	35	22	-	-	PUNCT
ap-1851	35	23	beltrami	beltrami	ADJ
ap-1851	35	24	operator	operator	NOUN
ap-1851	35	25	which	which	PRON
ap-1851	35	26	is	be	AUX
ap-1851	35	27	the	the	DET
ap-1851	35	28	manifold	manifold	ADJ
ap-1851	35	29	part	part	NOUN
ap-1851	35	30	of	of	ADP
ap-1851	35	31	the	the	DET
ap-1851	35	32	hamiltonian	hamiltonian	NOUN
ap-1851	35	33	has	have	VERB
ap-1851	35	34	an	an	DET
ap-1851	35	35	eigenfunction	eigenfunction	NOUN
ap-1851	35	36	with	with	ADP
ap-1851	35	37	zeros	zero	NOUN
ap-1851	35	38	at	at	ADP
ap-1851	35	39	the	the	DET
ap-1851	35	40	hedgehog	hedgehog	NOUN
ap-1851	35	41	junctions	junction	NOUN
ap-1851	35	42	.	.	PUNCT
ap-1851	36	1	since	since	SCONJ
ap-1851	36	2	such	such	ADJ
ap-1851	36	3	eigenvalues	eigenvalue	NOUN
ap-1851	36	4	are	be	AUX
ap-1851	36	5	unstable	unstable	ADJ
ap-1851	36	6	—	—	PUNCT
ap-1851	36	7	a	a	DET
ap-1851	36	8	geometrical	geometrical	ADJ
ap-1851	36	9	perturbation	perturbation	NOUN
ap-1851	36	10	turns	turn	VERB
ap-1851	36	11	them	they	PRON
ap-1851	36	12	generically	generically	ADV
ap-1851	36	13	into	into	ADP
ap-1851	36	14	resonances	resonance	NOUN
ap-1851	36	15	—	—	PUNCT
ap-1851	36	16	it	it	PRON
ap-1851	36	17	is	be	AUX
ap-1851	36	18	natural	natural	ADJ
ap-1851	36	19	to	to	PART
ap-1851	36	20	count	count	VERB
ap-1851	36	21	them	they	PRON
ap-1851	36	22	together	together	ADV
ap-1851	36	23	with	with	ADP
ap-1851	36	24	the	the	DET
ap-1851	36	25	‘	'	PUNCT
ap-1851	36	26	true	true	ADJ
ap-1851	36	27	’	'	PUNCT
ap-1851	36	28	resonances	resonance	NOUN
ap-1851	36	29	;	;	PUNCT
ap-1851	36	30	one	one	NUM
ap-1851	36	31	then	then	ADV
ap-1851	36	32	asks	ask	VERB
ap-1851	36	33	about	about	ADP
ap-1851	36	34	the	the	DET
ap-1851	36	35	asymptotics	asymptotic	NOUN
ap-1851	36	36	of	of	ADP
ap-1851	36	37	the	the	DET
ap-1851	36	38	number	number	NOUN
ap-1851	36	39	of	of	ADP
ap-1851	36	40	such	such	ADJ
ap-1851	36	41	singularities	singularity	NOUN
ap-1851	36	42	enclosed	enclose	VERB
ap-1851	36	43	in	in	ADP
ap-1851	36	44	the	the	DET
ap-1851	36	45	circle	circle	NOUN
ap-1851	36	46	of	of	ADP
ap-1851	36	47	radius	radius	NOUN
ap-1851	36	48	r	r	NOUN
ap-1851	36	49	in	in	ADP
ap-1851	36	50	the	the	DET
ap-1851	36	51	momentum	momentum	NOUN
ap-1851	36	52	plane	plane	NOUN
ap-1851	36	53	.	.	PUNCT
ap-1851	37	1	this	this	DET
ap-1851	37	2	question	question	NOUN
ap-1851	37	3	is	be	AUX
ap-1851	37	4	made	make	VERB
ap-1851	37	5	intriguing	intriguing	ADJ
ap-1851	37	6	by	by	ADP
ap-1851	37	7	the	the	DET
ap-1851	37	8	recent	recent	ADJ
ap-1851	37	9	observation	observation	NOUN
ap-1851	37	10	[	[	X
ap-1851	37	11	10	10	NUM
ap-1851	37	12	,	,	PUNCT
ap-1851	37	13	11	11	NUM
ap-1851	37	14	]	]	PUNCT
ap-1851	37	15	that	that	SCONJ
ap-1851	37	16	in	in	ADP
ap-1851	37	17	some	some	DET
ap-1851	37	18	quantum	quantum	NOUN
ap-1851	37	19	graphs	graph	NOUN
ap-1851	37	20	the	the	DET
ap-1851	37	21	asymptotics	asymptotic	NOUN
ap-1851	37	22	may	may	AUX
ap-1851	37	23	not	not	PART
ap-1851	37	24	be	be	AUX
ap-1851	37	25	of	of	ADP
ap-1851	37	26	weyl	weyl	VERB
ap-1851	37	27	type	type	NOUN
ap-1851	37	28	.	.	PUNCT
ap-1851	38	1	the	the	DET
ap-1851	38	2	reason	reason	NOUN
ap-1851	38	3	behind	behind	ADP
ap-1851	38	4	this	this	DET
ap-1851	38	5	effect	effect	NOUN
ap-1851	38	6	is	be	AUX
ap-1851	38	7	that	that	SCONJ
ap-1851	38	8	symmetries	symmetry	NOUN
ap-1851	38	9	,	,	PUNCT
ap-1851	38	10	maybe	maybe	ADV
ap-1851	38	11	not	not	PART
ap-1851	38	12	apparent	apparent	ADJ
ap-1851	38	13	ones	one	NOUN
ap-1851	38	14	,	,	PUNCT
ap-1851	38	15	may	may	AUX
ap-1851	38	16	effectively	effectively	ADV
ap-1851	38	17	diminish	diminish	VERB
ap-1851	38	18	the	the	DET
ap-1851	38	19	graph	graph	NOUN
ap-1851	38	20	size	size	NOUN
ap-1851	38	21	making	make	VERB
ap-1851	38	22	a	a	DET
ap-1851	38	23	part	part	NOUN
ap-1851	38	24	of	of	ADP
ap-1851	38	25	it	it	PRON
ap-1851	38	26	effectively	effectively	ADV
ap-1851	38	27	belongs	belong	VERB
ap-1851	38	28	to	to	ADP
ap-1851	38	29	a	a	DET
ap-1851	38	30	lead	lead	NOUN
ap-1851	38	31	instead	instead	ADV
ap-1851	38	32	.	.	PUNCT
ap-1851	39	1	the	the	DET
ap-1851	39	2	mechanism	mechanism	NOUN
ap-1851	39	3	uses	use	VERB
ap-1851	39	4	the	the	DET
ap-1851	39	5	fact	fact	NOUN
ap-1851	39	6	that	that	SCONJ
ap-1851	39	7	all	all	DET
ap-1851	39	8	the	the	DET
ap-1851	39	9	edges	edge	NOUN
ap-1851	39	10	of	of	ADP
ap-1851	39	11	a	a	DET
ap-1851	39	12	quantum	quantum	NOUN
ap-1851	39	13	graph	graph	NOUN
ap-1851	39	14	are	be	AUX
ap-1851	39	15	one	one	NUM
ap-1851	39	16	-	-	PUNCT
ap-1851	39	17	dimensional	dimensional	ADJ
ap-1851	39	18	,	,	PUNCT
ap-1851	39	19	and	and	CCONJ
ap-1851	39	20	one	one	PRON
ap-1851	39	21	may	may	AUX
ap-1851	39	22	expect	expect	VERB
ap-1851	39	23	that	that	SCONJ
ap-1851	39	24	such	such	DET
ap-1851	39	25	a	a	DET
ap-1851	39	26	thing	thing	NOUN
ap-1851	39	27	would	would	AUX
ap-1851	39	28	not	not	PART
ap-1851	39	29	happen	happen	VERB
ap-1851	39	30	on	on	ADP
ap-1851	39	31	hedgehog	hedgehog	NOUN
ap-1851	39	32	manifolds	manifold	NOUN
ap-1851	39	33	where	where	SCONJ
ap-1851	39	34	the	the	DET
ap-1851	39	35	particles	particle	NOUN
ap-1851	39	36	are	be	AUX
ap-1851	39	37	forced	force	VERB
ap-1851	39	38	to	to	PART
ap-1851	39	39	‘	'	PUNCT
ap-1851	39	40	change	change	VERB
ap-1851	39	41	dimension	dimension	NOUN
ap-1851	39	42	’	'	PUNCT
ap-1851	39	43	at	at	ADP
ap-1851	39	44	the	the	DET
ap-1851	39	45	junctions	junction	NOUN
ap-1851	39	46	.	.	PUNCT
ap-1851	40	1	we	we	PRON
ap-1851	40	2	are	be	AUX
ap-1851	40	3	going	go	VERB
ap-1851	40	4	to	to	PART
ap-1851	40	5	give	give	VERB
ap-1851	40	6	a	a	DET
ap-1851	40	7	partial	partial	ADJ
ap-1851	40	8	confirmation	confirmation	NOUN
ap-1851	40	9	of	of	ADP
ap-1851	40	10	this	this	DET
ap-1851	40	11	conjecture	conjecture	NOUN
ap-1851	40	12	by	by	ADP
ap-1851	40	13	showing	show	VERB
ap-1851	40	14	that	that	SCONJ
ap-1851	40	15	,	,	PUNCT
ap-1851	40	16	in	in	ADP
ap-1851	40	17	contrast	contrast	NOUN
ap-1851	40	18	to	to	ADP
ap-1851	40	19	the	the	DET
ap-1851	40	20	quantum	quantum	NOUN
ap-1851	40	21	-	-	PUNCT
ap-1851	40	22	graph	graph	NOUN
ap-1851	40	23	case	case	NOUN
ap-1851	40	24	,	,	PUNCT
ap-1851	40	25	the	the	DET
ap-1851	40	26	resonances	resonance	NOUN
ap-1851	40	27	can	can	AUX
ap-1851	40	28	not	not	PART
ap-1851	40	29	be	be	AUX
ap-1851	40	30	found	find	VERB
ap-1851	40	31	at	at	ADP
ap-1851	40	32	arbitrary	arbitrary	ADJ
ap-1851	40	33	distance	distance	NOUN
ap-1851	40	34	from	from	ADP
ap-1851	40	35	the	the	DET
ap-1851	40	36	real	real	ADJ
ap-1851	40	37	axis	axis	NOUN
ap-1851	40	38	in	in	ADP
ap-1851	40	39	the	the	DET
ap-1851	40	40	momentum	momentum	NOUN
ap-1851	40	41	plane	plane	NOUN
ap-1851	40	42	as	as	ADV
ap-1851	40	43	long	long	ADV
ap-1851	40	44	as	as	SCONJ
ap-1851	40	45	the	the	DET
ap-1851	40	46	leads	lead	NOUN
ap-1851	40	47	are	be	AUX
ap-1851	40	48	attached	attach	VERB
ap-1851	40	49	at	at	ADP
ap-1851	40	50	a	a	DET
ap-1851	40	51	single	single	ADJ
ap-1851	40	52	point	point	NOUN
ap-1851	40	53	of	of	ADP
ap-1851	40	54	the	the	DET
ap-1851	40	55	manifold	manifold	NOUN
ap-1851	40	56	.	.	PUNCT
ap-1851	41	1	the	the	DET
ap-1851	41	2	third	third	ADJ
ap-1851	41	3	and	and	CCONJ
ap-1851	41	4	the	the	DET
ap-1851	41	5	last	last	ADJ
ap-1851	41	6	question	question	NOUN
ap-1851	41	7	addressed	address	VERB
ap-1851	41	8	here	here	ADV
ap-1851	41	9	is	be	AUX
ap-1851	41	10	again	again	ADV
ap-1851	41	11	inspired	inspire	VERB
ap-1851	41	12	by	by	ADP
ap-1851	41	13	an	an	DET
ap-1851	41	14	observation	observation	NOUN
ap-1851	41	15	about	about	ADP
ap-1851	41	16	quantum	quantum	NOUN
ap-1851	41	17	graphs	graph	NOUN
ap-1851	41	18	.	.	PUNCT
ap-1851	42	1	it	it	PRON
ap-1851	42	2	has	have	AUX
ap-1851	42	3	been	be	AUX
ap-1851	42	4	noted	note	VERB
ap-1851	42	5	that	that	SCONJ
ap-1851	42	6	a	a	DET
ap-1851	42	7	magnetic	magnetic	ADJ
ap-1851	42	8	field	field	NOUN
ap-1851	42	9	can	can	AUX
ap-1851	42	10	change	change	VERB
ap-1851	42	11	the	the	DET
ap-1851	42	12	effective	effective	ADJ
ap-1851	42	13	size	size	NOUN
ap-1851	42	14	of	of	ADP
ap-1851	42	15	some	some	DET
ap-1851	42	16	quantum	quantum	ADJ
ap-1851	42	17	graphs	graph	NOUN
ap-1851	42	18	with	with	ADP
ap-1851	42	19	a	a	DET
ap-1851	42	20	non	non	ADJ
ap-1851	42	21	-	-	ADJ
ap-1851	42	22	weyl	weyl	ADJ
ap-1851	42	23	asymptotics	asymptotic	NOUN
ap-1851	43	1	[	[	X
ap-1851	43	2	17	17	NUM
ap-1851	43	3	]	]	X
ap-1851	43	4	:	:	PUNCT
ap-1851	43	5	if	if	SCONJ
ap-1851	43	6	we	we	PRON
ap-1851	43	7	follow	follow	VERB
ap-1851	43	8	the	the	DET
ap-1851	43	9	resonance	resonance	NOUN
ap-1851	43	10	poles	pole	NOUN
ap-1851	43	11	as	as	ADP
ap-1851	43	12	functions	function	NOUN
ap-1851	43	13	of	of	ADP
ap-1851	43	14	the	the	DET
ap-1851	43	15	field	field	NOUN
ap-1851	43	16	we	we	PRON
ap-1851	43	17	observe	observe	VERB
ap-1851	43	18	that	that	SCONJ
ap-1851	43	19	at	at	ADP
ap-1851	43	20	some	some	DET
ap-1851	43	21	field	field	NOUN
ap-1851	43	22	values	value	NOUN
ap-1851	43	23	they	they	PRON
ap-1851	43	24	move	move	VERB
ap-1851	43	25	to	to	ADP
ap-1851	43	26	(	(	PUNCT
ap-1851	43	27	imaginary	imaginary	ADJ
ap-1851	43	28	)	)	PUNCT
ap-1851	43	29	infinity	infinity	NOUN
ap-1851	43	30	and	and	CCONJ
ap-1851	43	31	the	the	DET
ap-1851	43	32	resonances	resonance	NOUN
ap-1851	43	33	disappear	disappear	VERB
ap-1851	43	34	.	.	PUNCT
ap-1851	44	1	on	on	ADP
ap-1851	44	2	hedgehog	hedgehog	PROPN
ap-1851	44	3	manifolds	manifold	NOUN
ap-1851	44	4	the	the	DET
ap-1851	44	5	situation	situation	NOUN
ap-1851	44	6	is	be	AUX
ap-1851	44	7	different	different	ADJ
ap-1851	44	8	,	,	PUNCT
ap-1851	44	9	though	though	SCONJ
ap-1851	44	10	a	a	DET
ap-1851	44	11	similar	similar	ADJ
ap-1851	44	12	effect	effect	NOUN
ap-1851	44	13	may	may	AUX
ap-1851	44	14	again	again	ADV
ap-1851	44	15	occur	occur	VERB
ap-1851	44	16	;	;	PUNCT
ap-1851	44	17	we	we	PRON
ap-1851	44	18	will	will	AUX
ap-1851	44	19	present	present	VERB
ap-1851	44	20	a	a	DET
ap-1851	44	21	simple	simple	ADJ
ap-1851	44	22	example	example	NOUN
ap-1851	44	23	of	of	ADP
ap-1851	44	24	such	such	DET
ap-1851	44	25	a	a	DET
ap-1851	44	26	system	system	NOUN
ap-1851	44	27	in	in	ADP
ap-1851	44	28	which	which	PRON
ap-1851	44	29	a	a	DET
ap-1851	44	30	suitable	suitable	ADJ
ap-1851	44	31	aharonov	aharonov	NOUN
ap-1851	44	32	-	-	PUNCT
ap-1851	44	33	bohm	bohm	PROPN
ap-1851	44	34	field	field	NOUN
ap-1851	44	35	removes	remove	VERB
ap-1851	44	36	all	all	DET
ap-1851	44	37	the	the	DET
ap-1851	44	38	‘	'	PUNCT
ap-1851	44	39	true	true	ADJ
ap-1851	44	40	’	'	PUNCT
ap-1851	44	41	resonances	resonance	NOUN
ap-1851	44	42	,	,	PUNCT
ap-1851	44	43	i.e.	i.e.	X
ap-1851	44	44	those	those	PRON
ap-1851	44	45	with	with	ADP
ap-1851	44	46	pole	pole	NOUN
ap-1851	44	47	position	position	NOUN
ap-1851	44	48	having	have	VERB
ap-1851	44	49	nonzero	nonzero	ADJ
ap-1851	44	50	imaginary	imaginary	ADJ
ap-1851	44	51	part	part	NOUN
ap-1851	44	52	.	.	PUNCT
ap-1851	45	1	2	2	X
ap-1851	45	2	.	.	X
ap-1851	45	3	description	description	NOUN
ap-1851	45	4	of	of	ADP
ap-1851	45	5	the	the	DET
ap-1851	45	6	model	model	NOUN
ap-1851	45	7	let	let	VERB
ap-1851	45	8	us	we	PRON
ap-1851	45	9	first	first	ADV
ap-1851	45	10	give	give	VERB
ap-1851	45	11	a	a	DET
ap-1851	45	12	proper	proper	ADJ
ap-1851	45	13	meaning	meaning	NOUN
ap-1851	45	14	to	to	ADP
ap-1851	45	15	what	what	PRON
ap-1851	45	16	we	we	PRON
ap-1851	45	17	described	describe	VERB
ap-1851	45	18	above	above	ADV
ap-1851	45	19	as	as	ADP
ap-1851	45	20	quantum	quantum	NOUN
ap-1851	45	21	motion	motion	NOUN
ap-1851	45	22	on	on	ADP
ap-1851	45	23	a	a	DET
ap-1851	45	24	hedgehog	hedgehog	NOUN
ap-1851	45	25	manifold	manifold	NOUN
ap-1851	45	26	;	;	PUNCT
ap-1851	45	27	doing	do	VERB
ap-1851	45	28	so	so	ADV
ap-1851	45	29	we	we	PRON
ap-1851	45	30	generalize	generalize	VERB
ap-1851	45	31	previously	previously	ADV
ap-1851	45	32	used	use	VERB
ap-1851	45	33	definitions	definition	NOUN
ap-1851	45	34	—	—	PUNCT
ap-1851	45	35	see	see	VERB
ap-1851	45	36	,	,	PUNCT
ap-1851	45	37	e.g.	e.g.	ADV
ap-1851	45	38	[	[	X
ap-1851	45	39	7	7	NUM
ap-1851	45	40	,	,	PUNCT
ap-1851	45	41	8	8	NUM
ap-1851	45	42	,	,	PUNCT
ap-1851	45	43	18	18	NUM
ap-1851	45	44	]	]	PUNCT
ap-1851	45	45	—	—	PUNCT
ap-1851	45	46	by	by	ADP
ap-1851	45	47	allowing	allow	VERB
ap-1851	45	48	more	more	ADJ
ap-1851	45	49	than	than	ADP
ap-1851	45	50	a	a	DET
ap-1851	45	51	single	single	ADJ
ap-1851	45	52	semiinfinite	semiinfinite	ADJ
ap-1851	45	53	lead	lead	NOUN
ap-1851	45	54	be	be	AUX
ap-1851	45	55	attached	attach	VERB
ap-1851	45	56	at	at	ADP
ap-1851	45	57	a	a	DET
ap-1851	45	58	point	point	NOUN
ap-1851	45	59	of	of	ADP
ap-1851	45	60	the	the	DET
ap-1851	45	61	manifold	manifold	NOUN
ap-1851	45	62	.	.	PUNCT
ap-1851	46	1	consider	consider	VERB
ap-1851	46	2	a	a	DET
ap-1851	46	3	compact	compact	ADJ
ap-1851	46	4	and	and	CCONJ
ap-1851	46	5	connected	connected	ADJ
ap-1851	46	6	riemannian	riemannian	ADJ
ap-1851	46	7	figure	figure	NOUN
ap-1851	46	8	1	1	NUM
ap-1851	46	9	.	.	NOUN
ap-1851	46	10	example	example	NOUN
ap-1851	46	11	of	of	ADP
ap-1851	46	12	a	a	DET
ap-1851	46	13	hedgehog	hedgehog	NOUN
ap-1851	46	14	manifold	manifold	ADJ
ap-1851	46	15	manifold	manifold	PROPN
ap-1851	46	16	ω	ω	PROPN
ap-1851	46	17	∈	∈	PROPN
ap-1851	46	18	rn	rn	PROPN
ap-1851	46	19	,	,	PUNCT
ap-1851	46	20	n	n	PROPN
ap-1851	46	21	=	=	SYM
ap-1851	46	22	2	2	NUM
ap-1851	46	23	,	,	PUNCT
ap-1851	46	24	3	3	NUM
ap-1851	46	25	,	,	PUNCT
ap-1851	46	26	endowed	endow	VERB
ap-1851	46	27	with	with	ADP
ap-1851	46	28	metric	metric	ADJ
ap-1851	46	29	grs	grs	PROPN
ap-1851	46	30	.	.	PUNCT
ap-1851	47	1	the	the	DET
ap-1851	47	2	manifold	manifold	ADJ
ap-1851	47	3	may	may	AUX
ap-1851	47	4	or	or	CCONJ
ap-1851	47	5	may	may	AUX
ap-1851	47	6	not	not	PART
ap-1851	47	7	have	have	VERB
ap-1851	47	8	a	a	DET
ap-1851	47	9	boundary	boundary	NOUN
ap-1851	47	10	,	,	PUNCT
ap-1851	47	11	in	in	ADP
ap-1851	47	12	the	the	DET
ap-1851	47	13	latter	latter	ADJ
ap-1851	47	14	case	case	NOUN
ap-1851	47	15	we	we	PRON
ap-1851	47	16	suppose	suppose	VERB
ap-1851	47	17	that	that	SCONJ
ap-1851	47	18	∂ω	∂ω	PROPN
ap-1851	47	19	is	be	AUX
ap-1851	47	20	smooth	smooth	ADJ
ap-1851	47	21	.	.	PUNCT
ap-1851	48	1	we	we	PRON
ap-1851	48	2	denote	denote	VERB
ap-1851	48	3	by	by	ADP
ap-1851	48	4	γ	γ	NOUN
ap-1851	48	5	the	the	DET
ap-1851	48	6	geometric	geometric	ADJ
ap-1851	48	7	object	object	NOUN
ap-1851	48	8	consisting	consist	VERB
ap-1851	48	9	of	of	ADP
ap-1851	48	10	ω	ω	PROPN
ap-1851	48	11	and	and	CCONJ
ap-1851	48	12	a	a	DET
ap-1851	48	13	finite	finite	ADJ
ap-1851	48	14	number	number	NOUN
ap-1851	48	15	nj	nj	PROPN
ap-1851	48	16	of	of	ADP
ap-1851	48	17	halflines	halfline	NOUN
ap-1851	48	18	attached	attach	VERB
ap-1851	48	19	at	at	ADP
ap-1851	48	20	points	point	NOUN
ap-1851	48	21	xj	xj	PROPN
ap-1851	48	22	,	,	PUNCT
ap-1851	48	23	j	j	PROPN
ap-1851	48	24	=	=	SYM
ap-1851	48	25	1	1	NUM
ap-1851	48	26	,	,	PUNCT
ap-1851	48	27	.	.	PUNCT
ap-1851	48	28	.	.	PUNCT
ap-1851	49	1	.	.	PUNCT
ap-1851	50	1	,	,	PUNCT
ap-1851	50	2	n	n	X
ap-1851	50	3	belonging	belong	VERB
ap-1851	50	4	to	to	ADP
ap-1851	50	5	a	a	DET
ap-1851	50	6	finite	finite	NOUN
ap-1851	50	7	subset	subset	NOUN
ap-1851	50	8	{	{	PUNCT
ap-1851	50	9	xj	xj	PROPN
ap-1851	50	10	}	}	PUNCT
ap-1851	50	11	of	of	ADP
ap-1851	50	12	the	the	DET
ap-1851	50	13	interior	interior	NOUN
ap-1851	50	14	of	of	ADP
ap-1851	50	15	ω	ω	PROPN
ap-1851	50	16	—	—	PUNCT
ap-1851	50	17	see	see	VERB
ap-1851	50	18	figure	figure	NOUN
ap-1851	50	19	1	1	NUM
ap-1851	50	20	—	—	PUNCT
ap-1851	50	21	we	we	PRON
ap-1851	50	22	will	will	AUX
ap-1851	50	23	employ	employ	VERB
ap-1851	50	24	the	the	DET
ap-1851	50	25	term	term	NOUN
ap-1851	50	26	hedgehog	hedgehog	NOUN
ap-1851	50	27	manifold	manifold	NOUN
ap-1851	50	28	,	,	PUNCT
ap-1851	50	29	or	or	CCONJ
ap-1851	50	30	simply	simply	ADV
ap-1851	50	31	manifold	manifold	ADJ
ap-1851	50	32	if	if	SCONJ
ap-1851	50	33	there	there	PRON
ap-1851	50	34	is	be	VERB
ap-1851	50	35	no	no	DET
ap-1851	50	36	danger	danger	NOUN
ap-1851	50	37	of	of	ADP
ap-1851	50	38	misunderstanding	misunderstanding	NOUN
ap-1851	50	39	.	.	PUNCT
ap-1851	51	1	by	by	ADP
ap-1851	51	2	m	m	PROPN
ap-1851	51	3	=	=	PUNCT
ap-1851	51	4	∑	∑	PUNCT
ap-1851	51	5	j	j	PROPN
ap-1851	51	6	nj	nj	PROPN
ap-1851	51	7	we	we	PRON
ap-1851	51	8	denote	denote	VERB
ap-1851	51	9	the	the	DET
ap-1851	51	10	total	total	ADJ
ap-1851	51	11	number	number	NOUN
ap-1851	51	12	of	of	ADP
ap-1851	51	13	the	the	DET
ap-1851	51	14	halflines	halfline	NOUN
ap-1851	51	15	.	.	PUNCT
ap-1851	52	1	the	the	DET
ap-1851	52	2	hilbert	hilbert	PROPN
ap-1851	52	3	space	space	NOUN
ap-1851	52	4	we	we	PRON
ap-1851	52	5	are	be	AUX
ap-1851	52	6	going	go	VERB
ap-1851	52	7	to	to	PART
ap-1851	52	8	consider	consider	VERB
ap-1851	52	9	consists	consist	NOUN
ap-1851	52	10	of	of	ADP
ap-1851	52	11	direct	direct	ADJ
ap-1851	52	12	sum	sum	NOUN
ap-1851	52	13	of	of	ADP
ap-1851	52	14	the	the	DET
ap-1851	52	15	‘	'	PUNCT
ap-1851	52	16	component	component	NOUN
ap-1851	52	17	’	'	PUNCT
ap-1851	52	18	hilbert	hilbert	NOUN
ap-1851	52	19	spaces	space	NOUN
ap-1851	52	20	,	,	PUNCT
ap-1851	52	21	in	in	ADP
ap-1851	52	22	other	other	ADJ
ap-1851	52	23	words	word	NOUN
ap-1851	52	24	,	,	PUNCT
ap-1851	52	25	its	its	PRON
ap-1851	52	26	elements	element	NOUN
ap-1851	52	27	are	be	AUX
ap-1851	52	28	square	square	ADJ
ap-1851	52	29	integrable	integrable	ADJ
ap-1851	52	30	functions	function	NOUN
ap-1851	52	31	on	on	ADP
ap-1851	52	32	every	every	DET
ap-1851	52	33	component	component	NOUN
ap-1851	52	34	of	of	ADP
ap-1851	52	35	γ	γ	PROPN
ap-1851	52	36	,	,	PUNCT
ap-1851	52	37	h	h	NOUN
ap-1851	52	38	=	=	SYM
ap-1851	53	1	l2(ω,√|g|dx)⊕	l2(ω,√|g|dx)⊕	NOUN
ap-1851	53	2	m⊕	m⊕	VERB
ap-1851	53	3	i=1	i=1	PRON
ap-1851	53	4	l2(r(i	l2(r(i	NOUN
ap-1851	53	5	)	)	PUNCT
ap-1851	54	1	+	+	CCONJ
ap-1851	54	2	)	)	PUNCT
ap-1851	54	3	,	,	PUNCT
ap-1851	54	4	where	where	SCONJ
ap-1851	54	5	g	g	PROPN
ap-1851	54	6	stands	stand	VERB
ap-1851	54	7	for	for	ADP
ap-1851	54	8	det(grs	det(grs	NOUN
ap-1851	54	9	)	)	PUNCT
ap-1851	54	10	and	and	CCONJ
ap-1851	54	11	dx	dx	PROPN
ap-1851	54	12	for	for	ADP
ap-1851	54	13	lebesque	lebesque	ADJ
ap-1851	54	14	measure	measure	NOUN
ap-1851	54	15	on	on	ADP
ap-1851	54	16	rn	rn	PROPN
ap-1851	54	17	.	.	PUNCT
ap-1851	55	1	let	let	VERB
ap-1851	55	2	h0	h0	NOUN
ap-1851	55	3	be	be	AUX
ap-1851	55	4	the	the	DET
ap-1851	55	5	closure	closure	NOUN
ap-1851	55	6	of	of	ADP
ap-1851	55	7	the	the	DET
ap-1851	55	8	laplace	laplace	NOUN
ap-1851	55	9	-	-	PUNCT
ap-1851	55	10	beltrami	beltrami	ADJ
ap-1851	55	11	operator2	operator2	NOUN
ap-1851	55	12	−g−1/2∂r(g1/2grs∂s	−g−1/2∂r(g1/2grs∂s	PROPN
ap-1851	55	13	)	)	PUNCT
ap-1851	55	14	with	with	ADP
ap-1851	55	15	the	the	DET
ap-1851	55	16	domain	domain	NOUN
ap-1851	55	17	consisting	consist	VERB
ap-1851	55	18	of	of	ADP
ap-1851	55	19	functions	function	NOUN
ap-1851	55	20	in	in	ADP
ap-1851	55	21	c∞0	c∞0	PROPN
ap-1851	55	22	(	(	PUNCT
ap-1851	55	23	ω	ω	NOUN
ap-1851	55	24	)	)	PUNCT
ap-1851	55	25	;	;	PUNCT
ap-1851	55	26	if	if	SCONJ
ap-1851	55	27	the	the	DET
ap-1851	55	28	boundary	boundary	NOUN
ap-1851	55	29	of	of	ADP
ap-1851	55	30	ω	ω	PROPN
ap-1851	55	31	is	be	AUX
ap-1851	55	32	nonempty	nonempty	ADJ
ap-1851	55	33	we	we	PRON
ap-1851	55	34	require	require	VERB
ap-1851	55	35	that	that	SCONJ
ap-1851	55	36	they	they	PRON
ap-1851	55	37	satisfy	satisfy	VERB
ap-1851	55	38	at	at	ADP
ap-1851	55	39	it	it	PRON
ap-1851	55	40	appropriate	appropriate	ADJ
ap-1851	55	41	boundary	boundary	ADJ
ap-1851	55	42	conditions	condition	NOUN
ap-1851	55	43	,	,	PUNCT
ap-1851	55	44	either	either	CCONJ
ap-1851	55	45	neumann	neumann	PROPN
ap-1851	55	46	/	/	SYM
ap-1851	55	47	robin	robin	PROPN
ap-1851	55	48	,	,	PUNCT
ap-1851	55	49	(	(	PUNCT
ap-1851	55	50	∂n	∂n	PROPN
ap-1851	55	51	+	+	CCONJ
ap-1851	55	52	γ)f	γ)f	ADJ
ap-1851	55	53	|∂ω	|∂ω	PROPN
ap-1851	55	54	=	=	SYM
ap-1851	55	55	0	0	NUM
ap-1851	55	56	,	,	PUNCT
ap-1851	55	57	or	or	CCONJ
ap-1851	55	58	dirichlet	dirichlet	PROPN
ap-1851	55	59	,	,	PUNCT
ap-1851	55	60	f	f	PROPN
ap-1851	55	61	|∂ω	|∂ω	PROPN
ap-1851	55	62	=	=	SYM
ap-1851	56	1	0	0	X
ap-1851	56	2	.	.	PUNCT
ap-1851	57	1	the	the	DET
ap-1851	57	2	domain	domain	NOUN
ap-1851	57	3	of	of	ADP
ap-1851	57	4	h0	h0	PROPN
ap-1851	57	5	coincides	coincide	VERB
ap-1851	57	6	with	with	ADP
ap-1851	57	7	w	w	PROPN
ap-1851	57	8	2,2(ω	2,2(ω	NUM
ap-1851	57	9	)	)	PUNCT
ap-1851	57	10	which	which	PRON
ap-1851	57	11	,	,	PUNCT
ap-1851	57	12	in	in	ADP
ap-1851	57	13	particular	particular	ADJ
ap-1851	57	14	,	,	PUNCT
ap-1851	57	15	means	mean	VERB
ap-1851	57	16	that	that	SCONJ
ap-1851	57	17	f(x	f(x	PROPN
ap-1851	57	18	)	)	PUNCT
ap-1851	57	19	makes	make	VERB
ap-1851	57	20	sense	sense	NOUN
ap-1851	57	21	for	for	ADP
ap-1851	57	22	f	f	PROPN
ap-1851	57	23	∈	∈	PROPN
ap-1851	57	24	d(h0	d(h0	NOUN
ap-1851	57	25	)	)	PUNCT
ap-1851	57	26	and	and	CCONJ
ap-1851	57	27	x	x	X
ap-1851	57	28	∈	∈	PROPN
ap-1851	57	29	ω	ω	PROPN
ap-1851	57	30	.	.	PUNCT
ap-1851	58	1	the	the	DET
ap-1851	58	2	restriction	restriction	NOUN
ap-1851	58	3	h	h	NOUN
ap-1851	58	4	′0	′0	NOUN
ap-1851	58	5	of	of	ADP
ap-1851	58	6	h0	h0	NOUN
ap-1851	58	7	to	to	ADP
ap-1851	58	8	the	the	DET
ap-1851	58	9	domain	domain	NOUN
ap-1851	58	10	{	{	PUNCT
ap-1851	58	11	f	f	PROPN
ap-1851	58	12	∈	∈	PROPN
ap-1851	58	13	d(h0	d(h0	NOUN
ap-1851	58	14	)	)	PUNCT
ap-1851	58	15	:	:	PUNCT
ap-1851	58	16	f(xj	f(xj	NOUN
ap-1851	58	17	)	)	PUNCT
ap-1851	58	18	=	=	SYM
ap-1851	58	19	0	0	NUM
ap-1851	58	20	,	,	PUNCT
ap-1851	58	21	j	j	PROPN
ap-1851	58	22	=	=	SYM
ap-1851	58	23	1	1	NUM
ap-1851	58	24	,	,	PUNCT
ap-1851	58	25	.	.	PUNCT
ap-1851	58	26	.	.	PUNCT
ap-1851	59	1	.	.	PUNCT
ap-1851	60	1	,	,	PUNCT
ap-1851	60	2	n	n	CCONJ
ap-1851	60	3	}	}	PUNCT
ap-1851	60	4	is	be	AUX
ap-1851	60	5	a	a	DET
ap-1851	60	6	symmetric	symmetric	ADJ
ap-1851	60	7	operator	operator	NOUN
ap-1851	60	8	with	with	ADP
ap-1851	60	9	deficiency	deficiency	NOUN
ap-1851	60	10	indices	index	NOUN
ap-1851	60	11	(	(	PUNCT
ap-1851	60	12	n	n	X
ap-1851	60	13	,	,	PUNCT
ap-1851	60	14	n	n	CCONJ
ap-1851	60	15	)	)	PUNCT
ap-1851	60	16	,	,	PUNCT
ap-1851	60	17	cf	cf	NOUN
ap-1851	60	18	.	.	PUNCT
ap-1851	61	1	[	[	X
ap-1851	61	2	7	7	NUM
ap-1851	61	3	,	,	PUNCT
ap-1851	61	4	8	8	NUM
ap-1851	61	5	]	]	PUNCT
ap-1851	61	6	.	.	PUNCT
ap-1851	62	1	furthermore	furthermore	ADV
ap-1851	62	2	,	,	PUNCT
ap-1851	62	3	we	we	PRON
ap-1851	62	4	denote	denote	VERB
ap-1851	62	5	by	by	ADP
ap-1851	62	6	hi	hi	INTJ
ap-1851	62	7	the	the	DET
ap-1851	62	8	negative	negative	ADJ
ap-1851	62	9	laplacian	laplacian	NOUN
ap-1851	62	10	on	on	ADP
ap-1851	62	11	l2(r(i	l2(r(i	NOUN
ap-1851	62	12	)	)	PUNCT
ap-1851	62	13	+	+	CCONJ
ap-1851	62	14	)	)	PUNCT
ap-1851	62	15	referring	refer	VERB
ap-1851	62	16	to	to	ADP
ap-1851	62	17	the	the	DET
ap-1851	62	18	i	i	PROPN
ap-1851	62	19	-	-	PUNCT
ap-1851	62	20	th	th	X
ap-1851	62	21	halfline	halfline	NOUN
ap-1851	62	22	and	and	CCONJ
ap-1851	62	23	by	by	ADP
ap-1851	62	24	h	h	NOUN
ap-1851	62	25	′i	′i	NOUN
ap-1851	62	26	its	its	PRON
ap-1851	62	27	restriction	restriction	NOUN
ap-1851	62	28	to	to	ADP
ap-1851	62	29	functions	function	NOUN
ap-1851	62	30	which	which	PRON
ap-1851	62	31	vanish	vanish	VERB
ap-1851	62	32	together	together	ADV
ap-1851	62	33	with	with	ADP
ap-1851	62	34	their	their	PRON
ap-1851	62	35	first	first	ADJ
ap-1851	62	36	derivative	derivative	NOUN
ap-1851	62	37	at	at	ADP
ap-1851	62	38	the	the	DET
ap-1851	62	39	halfline	halfline	NOUN
ap-1851	62	40	endpoint	endpoint	NOUN
ap-1851	62	41	.	.	PUNCT
ap-1851	63	1	since	since	SCONJ
ap-1851	63	2	each	each	DET
ap-1851	63	3	h	h	NOUN
ap-1851	63	4	′i	′i	PROPN
ap-1851	63	5	has	have	VERB
ap-1851	63	6	deficiency	deficiency	NOUN
ap-1851	63	7	indices	index	NOUN
ap-1851	63	8	(	(	PUNCT
ap-1851	63	9	1	1	NUM
ap-1851	63	10	,	,	PUNCT
ap-1851	63	11	1	1	NUM
ap-1851	63	12	)	)	PUNCT
ap-1851	63	13	,	,	PUNCT
ap-1851	63	14	the	the	DET
ap-1851	63	15	direct	direct	ADJ
ap-1851	63	16	sum	sum	NOUN
ap-1851	63	17	h	h	NOUN
ap-1851	63	18	′	′	NUM
ap-1851	64	1	=	=	SYM
ap-1851	64	2	h	h	NOUN
ap-1851	64	3	′0	′0	NOUN
ap-1851	64	4	⊕h	⊕h	VERB
ap-1851	64	5	′1	′1	PROPN
ap-1851	64	6	⊕	⊕	PROPN
ap-1851	64	7	·	·	PUNCT
ap-1851	64	8	·	·	PUNCT
ap-1851	64	9	·	·	PUNCT
ap-1851	65	1	⊕h	⊕h	PROPN
ap-1851	65	2	′m	′m	PROPN
ap-1851	65	3	is	be	AUX
ap-1851	65	4	a	a	DET
ap-1851	65	5	symmetric	symmetric	ADJ
ap-1851	65	6	operator	operator	NOUN
ap-1851	65	7	with	with	ADP
ap-1851	65	8	deficiency	deficiency	NOUN
ap-1851	65	9	indices	index	NOUN
ap-1851	65	10	(	(	PUNCT
ap-1851	65	11	n+m	n+m	NUM
ap-1851	65	12	,	,	PUNCT
ap-1851	65	13	n+m	n+m	NUM
ap-1851	65	14	)	)	PUNCT
ap-1851	65	15	.	.	PUNCT
ap-1851	66	1	the	the	DET
ap-1851	66	2	family	family	NOUN
ap-1851	66	3	of	of	ADP
ap-1851	66	4	admissible	admissible	ADJ
ap-1851	66	5	hamiltonians	hamiltonian	NOUN
ap-1851	66	6	for	for	ADP
ap-1851	66	7	quantum	quantum	ADJ
ap-1851	66	8	motion	motion	NOUN
ap-1851	66	9	on	on	ADP
ap-1851	66	10	the	the	DET
ap-1851	66	11	hedgehog	hedgehog	NOUN
ap-1851	66	12	manifold	manifold	ADJ
ap-1851	66	13	γ	γ	X
ap-1851	66	14	can	can	AUX
ap-1851	66	15	be	be	AUX
ap-1851	66	16	identified	identify	VERB
ap-1851	66	17	with	with	ADP
ap-1851	66	18	the	the	DET
ap-1851	66	19	self	self	NOUN
ap-1851	66	20	-	-	PUNCT
ap-1851	66	21	adjoint	adjoint	NOUN
ap-1851	66	22	extensions	extension	NOUN
ap-1851	66	23	of	of	ADP
ap-1851	66	24	the	the	DET
ap-1851	66	25	operator	operator	NOUN
ap-1851	66	26	h	h	NOUN
ap-1851	66	27	′.	′.	NOUN
ap-1851	66	28	the	the	DET
ap-1851	66	29	procedure	procedure	NOUN
ap-1851	66	30	for	for	ADP
ap-1851	66	31	constructing	construct	VERB
ap-1851	66	32	them	they	PRON
ap-1851	66	33	using	use	VERB
ap-1851	66	34	the	the	DET
ap-1851	66	35	2as	2as	NOUN
ap-1851	66	36	mentioned	mention	VERB
ap-1851	66	37	above	above	ADV
ap-1851	66	38	,	,	PUNCT
ap-1851	66	39	we	we	PRON
ap-1851	66	40	make	make	VERB
ap-1851	66	41	this	this	DET
ap-1851	66	42	assumption	assumption	NOUN
ap-1851	66	43	for	for	ADP
ap-1851	66	44	the	the	DET
ap-1851	66	45	sake	sake	NOUN
ap-1851	66	46	of	of	ADP
ap-1851	66	47	simplicity	simplicity	NOUN
ap-1851	66	48	and	and	CCONJ
ap-1851	66	49	most	most	ADJ
ap-1851	66	50	considerations	consideration	NOUN
ap-1851	66	51	below	below	ADP
ap-1851	66	52	extend	extend	VERB
ap-1851	66	53	easily	easily	ADV
ap-1851	66	54	to	to	ADP
ap-1851	66	55	schrödinger	schrödinger	ADJ
ap-1851	66	56	type	type	NOUN
ap-1851	66	57	operators	operator	NOUN
ap-1851	66	58	−g−1/2∂r(g1/2grs∂s	−g−1/2∂r(g1/2grs∂s	PROPN
ap-1851	66	59	)	)	PUNCT
ap-1851	66	60	+	+	X
ap-1851	66	61	v	v	X
ap-1851	66	62	(	(	PUNCT
ap-1851	66	63	x	x	NOUN
ap-1851	66	64	)	)	PUNCT
ap-1851	66	65	provided	provide	VERB
ap-1851	66	66	the	the	DET
ap-1851	66	67	potential	potential	ADJ
ap-1851	66	68	v	v	NOUN
ap-1851	66	69	is	be	AUX
ap-1851	66	70	sufficiently	sufficiently	ADV
ap-1851	66	71	regular	regular	ADJ
ap-1851	66	72	.	.	PUNCT
ap-1851	67	1	417	417	NUM
ap-1851	67	2	p.	p.	PROPN
ap-1851	67	3	exner	exner	NOUN
ap-1851	67	4	,	,	PUNCT
ap-1851	67	5	j.	j.	PROPN
ap-1851	67	6	lipovský	lipovský	PROPN
ap-1851	67	7	acta	acta	PROPN
ap-1851	67	8	polytechnica	polytechnica	PROPN
ap-1851	67	9	boundary	boundary	ADJ
ap-1851	67	10	-	-	PUNCT
ap-1851	67	11	value	value	NOUN
ap-1851	67	12	theory	theory	NOUN
ap-1851	67	13	was	be	AUX
ap-1851	67	14	described	describe	VERB
ap-1851	67	15	in	in	ADP
ap-1851	67	16	detail	detail	NOUN
ap-1851	67	17	in	in	ADP
ap-1851	67	18	[	[	X
ap-1851	67	19	8	8	NUM
ap-1851	67	20	]	]	PUNCT
ap-1851	67	21	.	.	PUNCT
ap-1851	68	1	it	it	PRON
ap-1851	68	2	is	be	AUX
ap-1851	68	3	a	a	DET
ap-1851	68	4	modification	modification	NOUN
ap-1851	68	5	of	of	ADP
ap-1851	68	6	the	the	DET
ap-1851	68	7	analogous	analogous	ADJ
ap-1851	68	8	result	result	NOUN
ap-1851	68	9	from	from	ADP
ap-1851	68	10	the	the	DET
ap-1851	68	11	quantum	quantum	ADJ
ap-1851	68	12	graph	graph	NOUN
ap-1851	68	13	theory	theory	NOUN
ap-1851	68	14	[	[	X
ap-1851	68	15	23	23	NUM
ap-1851	68	16	]	]	PUNCT
ap-1851	68	17	,	,	PUNCT
ap-1851	68	18	and	and	CCONJ
ap-1851	68	19	in	in	ADP
ap-1851	68	20	a	a	DET
ap-1851	68	21	broader	broad	ADJ
ap-1851	68	22	context	context	NOUN
ap-1851	68	23	of	of	ADP
ap-1851	68	24	a	a	DET
ap-1851	68	25	known	know	VERB
ap-1851	68	26	general	general	ADJ
ap-1851	68	27	result	result	NOUN
ap-1851	68	28	[	[	X
ap-1851	68	29	22	22	NUM
ap-1851	68	30	]	]	PUNCT
ap-1851	68	31	.	.	PUNCT
ap-1851	69	1	all	all	DET
ap-1851	69	2	the	the	DET
ap-1851	69	3	extensions	extension	NOUN
ap-1851	69	4	are	be	AUX
ap-1851	69	5	described	describe	VERB
ap-1851	69	6	by	by	ADP
ap-1851	69	7	the	the	DET
ap-1851	69	8	coupling	coupling	NOUN
ap-1851	69	9	conditions	condition	NOUN
ap-1851	69	10	(	(	PUNCT
ap-1851	69	11	u	u	NOUN
ap-1851	69	12	−	−	NOUN
ap-1851	69	13	i)ψ	i)ψ	NOUN
ap-1851	69	14	+	+	CCONJ
ap-1851	70	1	i(u	i(u	PRON
ap-1851	70	2	+	+	PUNCT
ap-1851	70	3	i)ψ′	i)ψ′	PROPN
ap-1851	70	4	=	=	SYM
ap-1851	70	5	0	0	NUM
ap-1851	70	6	,	,	PUNCT
ap-1851	70	7	(	(	PUNCT
ap-1851	70	8	1	1	X
ap-1851	70	9	)	)	PUNCT
ap-1851	70	10	where	where	SCONJ
ap-1851	70	11	u	u	NOUN
ap-1851	70	12	is	be	AUX
ap-1851	70	13	an	an	DET
ap-1851	70	14	(	(	PUNCT
ap-1851	70	15	n+m)×	n+m)×	PROPN
ap-1851	70	16	(	(	PUNCT
ap-1851	70	17	n+m	n+m	NUM
ap-1851	70	18	)	)	PUNCT
ap-1851	70	19	unitary	unitary	ADJ
ap-1851	70	20	matrix	matrix	NOUN
ap-1851	70	21	,	,	PUNCT
ap-1851	70	22	i	i	PRON
ap-1851	70	23	the	the	DET
ap-1851	70	24	corresponding	correspond	VERB
ap-1851	70	25	unit	unit	NOUN
ap-1851	70	26	matrix	matrix	NOUN
ap-1851	70	27	and	and	CCONJ
ap-1851	70	28	ψ	ψ	NOUN
ap-1851	70	29	=	=	SYM
ap-1851	70	30	(	(	PUNCT
ap-1851	70	31	d1(f	d1(f	PROPN
ap-1851	70	32	)	)	PUNCT
ap-1851	70	33	,	,	PUNCT
ap-1851	70	34	.	.	PUNCT
ap-1851	70	35	.	.	PUNCT
ap-1851	70	36	.	.	PUNCT
ap-1851	71	1	,	,	PUNCT
ap-1851	71	2	dn(f	dn(f	PROPN
ap-1851	71	3	)	)	PUNCT
ap-1851	71	4	,	,	PUNCT
ap-1851	71	5	f1(0	f1(0	PROPN
ap-1851	71	6	)	)	PUNCT
ap-1851	71	7	,	,	PUNCT
ap-1851	71	8	.	.	PUNCT
ap-1851	71	9	.	.	PUNCT
ap-1851	72	1	.	.	PUNCT
ap-1851	73	1	,	,	PUNCT
ap-1851	73	2	fn(0	fn(0	NOUN
ap-1851	73	3	)	)	PUNCT
ap-1851	73	4	)	)	PUNCT
ap-1851	74	1	t	t	NOUN
ap-1851	74	2	,	,	PUNCT
ap-1851	74	3	ψ′	ψ′	PUNCT
ap-1851	74	4	=	=	SYM
ap-1851	74	5	(	(	PUNCT
ap-1851	74	6	c1(f	c1(f	NOUN
ap-1851	74	7	)	)	PUNCT
ap-1851	74	8	,	,	PUNCT
ap-1851	74	9	.	.	PUNCT
ap-1851	74	10	.	.	PUNCT
ap-1851	74	11	.	.	PUNCT
ap-1851	75	1	,	,	PUNCT
ap-1851	75	2	cn(f	cn(f	PROPN
ap-1851	75	3	)	)	PUNCT
ap-1851	75	4	,	,	PUNCT
ap-1851	75	5	f	f	PROPN
ap-1851	75	6	′1(0	′1(0	PROPN
ap-1851	75	7	)	)	PUNCT
ap-1851	75	8	,	,	PUNCT
ap-1851	75	9	.	.	PUNCT
ap-1851	75	10	.	.	PUNCT
ap-1851	76	1	.	.	PUNCT
ap-1851	77	1	,	,	PUNCT
ap-1851	77	2	f	f	PROPN
ap-1851	77	3	′n(0	′n(0	PROPN
ap-1851	77	4	)	)	PUNCT
ap-1851	77	5	)	)	PUNCT
ap-1851	78	1	t	t	PROPN
ap-1851	78	2	are	be	AUX
ap-1851	78	3	the	the	DET
ap-1851	78	4	columns	column	NOUN
ap-1851	78	5	of	of	ADP
ap-1851	78	6	(	(	PUNCT
ap-1851	78	7	generalized	generalized	ADJ
ap-1851	78	8	)	)	PUNCT
ap-1851	78	9	boundary	boundary	ADJ
ap-1851	78	10	values	value	NOUN
ap-1851	78	11	.	.	PUNCT
ap-1851	79	1	the	the	DET
ap-1851	79	2	first	first	ADJ
ap-1851	79	3	n	n	NUM
ap-1851	79	4	entries	entry	NOUN
ap-1851	79	5	correspond	correspond	VERB
ap-1851	79	6	to	to	ADP
ap-1851	79	7	the	the	DET
ap-1851	79	8	manifold	manifold	ADJ
ap-1851	79	9	part	part	NOUN
ap-1851	79	10	being	be	AUX
ap-1851	79	11	equal	equal	ADJ
ap-1851	79	12	to	to	ADP
ap-1851	79	13	the	the	DET
ap-1851	79	14	leading	leading	ADJ
ap-1851	79	15	and	and	CCONJ
ap-1851	79	16	next	next	ADJ
ap-1851	79	17	-	-	PUNCT
ap-1851	79	18	to	to	ADP
ap-1851	79	19	-	-	PUNCT
ap-1851	79	20	leading	lead	VERB
ap-1851	79	21	terms	term	NOUN
ap-1851	79	22	of	of	ADP
ap-1851	79	23	the	the	DET
ap-1851	79	24	asymptotics	asymptotic	NOUN
ap-1851	79	25	of	of	ADP
ap-1851	79	26	f(x	f(x	PROPN
ap-1851	79	27	)	)	PUNCT
ap-1851	79	28	on	on	ADP
ap-1851	79	29	ω	ω	PROPN
ap-1851	79	30	in	in	ADP
ap-1851	79	31	the	the	DET
ap-1851	79	32	vicinity	vicinity	NOUN
ap-1851	79	33	of	of	ADP
ap-1851	79	34	xj	xj	PROPN
ap-1851	79	35	,	,	PUNCT
ap-1851	79	36	while	while	SCONJ
ap-1851	79	37	fi(0	fi(0	PROPN
ap-1851	79	38	)	)	PUNCT
ap-1851	79	39	,	,	PUNCT
ap-1851	79	40	f	f	PROPN
ap-1851	79	41	′i(0	′i(0	PROPN
ap-1851	79	42	)	)	PUNCT
ap-1851	79	43	describe	describe	VERB
ap-1851	79	44	the	the	DET
ap-1851	79	45	limits	limit	NOUN
ap-1851	79	46	of	of	ADP
ap-1851	79	47	the	the	DET
ap-1851	79	48	wave	wave	NOUN
ap-1851	79	49	function	function	NOUN
ap-1851	79	50	and	and	CCONJ
ap-1851	79	51	its	its	PRON
ap-1851	79	52	first	first	ADJ
ap-1851	79	53	derivative	derivative	NOUN
ap-1851	79	54	on	on	ADP
ap-1851	79	55	i	i	PROPN
ap-1851	79	56	-	-	PUNCT
ap-1851	79	57	th	th	X
ap-1851	79	58	halfline	halfline	NOUN
ap-1851	79	59	,	,	PUNCT
ap-1851	79	60	respectively	respectively	ADV
ap-1851	79	61	.	.	PUNCT
ap-1851	80	1	more	more	ADV
ap-1851	80	2	precisely	precisely	ADV
ap-1851	80	3	,	,	PUNCT
ap-1851	80	4	according	accord	VERB
ap-1851	80	5	to	to	ADP
ap-1851	80	6	lemma	lemma	PROPN
ap-1851	80	7	4	4	NUM
ap-1851	80	8	in	in	ADP
ap-1851	80	9	[	[	X
ap-1851	80	10	8	8	NUM
ap-1851	80	11	]	]	PUNCT
ap-1851	80	12	,	,	PUNCT
ap-1851	80	13	for	for	ADP
ap-1851	80	14	f	f	PROPN
ap-1851	80	15	∈	∈	PROPN
ap-1851	80	16	d(h∗0	d(h∗0	PROPN
ap-1851	80	17	)	)	PUNCT
ap-1851	80	18	the	the	DET
ap-1851	80	19	asymptotic	asymptotic	ADJ
ap-1851	80	20	expansion	expansion	NOUN
ap-1851	80	21	near	near	ADP
ap-1851	80	22	xj	xj	PROPN
ap-1851	80	23	has	have	VERB
ap-1851	80	24	the	the	DET
ap-1851	80	25	form	form	NOUN
ap-1851	80	26	f(x	f(x	PROPN
ap-1851	80	27	)	)	PUNCT
ap-1851	81	1	=	=	SYM
ap-1851	81	2	cj(f)f0(x	cj(f)f0(x	PROPN
ap-1851	81	3	,	,	PUNCT
ap-1851	81	4	xj	xj	NOUN
ap-1851	81	5	)	)	PUNCT
ap-1851	81	6	+	+	CCONJ
ap-1851	81	7	dj(f	dj(f	X
ap-1851	81	8	)	)	PUNCT
ap-1851	82	1	+	+	SYM
ap-1851	82	2	o(r(x	o(r(x	PROPN
ap-1851	82	3	,	,	PUNCT
ap-1851	82	4	xj	xj	PROPN
ap-1851	82	5	)	)	PUNCT
ap-1851	82	6	)	)	PUNCT
ap-1851	82	7	,	,	PUNCT
ap-1851	82	8	where	where	SCONJ
ap-1851	82	9	f0(x	f0(x	NOUN
ap-1851	82	10	,	,	PUNCT
ap-1851	82	11	xj	xj	PROPN
ap-1851	82	12	)	)	PUNCT
ap-1851	82	13	=	=	PRON
ap-1851	82	14	{	{	PUNCT
ap-1851	82	15	−	−	PROPN
ap-1851	82	16	q2(x	q2(x	PROPN
ap-1851	82	17	,	,	PUNCT
ap-1851	82	18	xj	xj	NOUN
ap-1851	82	19	)	)	PUNCT
ap-1851	82	20	2π	2π	PROPN
ap-1851	82	21	ln	ln	PROPN
ap-1851	82	22	r(x	r(x	PROPN
ap-1851	82	23	,	,	PUNCT
ap-1851	82	24	xj	xj	PROPN
ap-1851	82	25	)	)	PUNCT
ap-1851	82	26	,	,	PUNCT
ap-1851	82	27	n	n	NOUN
ap-1851	82	28	=	=	SYM
ap-1851	82	29	2	2	NUM
ap-1851	82	30	q3(x	q3(x	PROPN
ap-1851	82	31	,	,	PUNCT
ap-1851	82	32	xj	xj	NOUN
ap-1851	82	33	)	)	PUNCT
ap-1851	82	34	4π	4π	NUM
ap-1851	82	35	(	(	PUNCT
ap-1851	82	36	r(x	r(x	PROPN
ap-1851	82	37	,	,	PUNCT
ap-1851	82	38	xj	xj	PROPN
ap-1851	82	39	)	)	PUNCT
ap-1851	82	40	)	)	PUNCT
ap-1851	82	41	−1	−1	NOUN
ap-1851	82	42	,	,	PUNCT
ap-1851	82	43	n	n	NOUN
ap-1851	82	44	=	=	SYM
ap-1851	82	45	3	3	NUM
ap-1851	82	46	(	(	PUNCT
ap-1851	82	47	2	2	NUM
ap-1851	82	48	)	)	PUNCT
ap-1851	82	49	here	here	ADV
ap-1851	82	50	q2	q2	PROPN
ap-1851	82	51	,	,	PUNCT
ap-1851	82	52	q3	q3	PROPN
ap-1851	82	53	are	be	AUX
ap-1851	82	54	continuous	continuous	ADJ
ap-1851	82	55	functions	function	NOUN
ap-1851	82	56	of	of	ADP
ap-1851	82	57	x	x	PUNCT
ap-1851	82	58	with	with	ADP
ap-1851	82	59	qi(xj	qi(xj	PROPN
ap-1851	82	60	,	,	PUNCT
ap-1851	82	61	xj	xj	PROPN
ap-1851	82	62	)	)	PUNCT
ap-1851	82	63	=	=	SYM
ap-1851	82	64	1	1	NUM
ap-1851	82	65	and	and	CCONJ
ap-1851	82	66	r(x	r(x	PROPN
ap-1851	82	67	,	,	PUNCT
ap-1851	82	68	xj	xj	NOUN
ap-1851	82	69	)	)	PUNCT
ap-1851	82	70	denotes	denote	VERB
ap-1851	82	71	the	the	DET
ap-1851	82	72	geodetic	geodetic	ADJ
ap-1851	82	73	distance	distance	NOUN
ap-1851	82	74	between	between	ADP
ap-1851	82	75	x	x	PROPN
ap-1851	82	76	and	and	CCONJ
ap-1851	82	77	xj	xj	PROPN
ap-1851	82	78	.	.	PUNCT
ap-1851	83	1	function	function	PROPN
ap-1851	83	2	f0	f0	PROPN
ap-1851	83	3	is	be	AUX
ap-1851	83	4	the	the	DET
ap-1851	83	5	leading	lead	VERB
ap-1851	83	6	term	term	NOUN
ap-1851	83	7	,	,	PUNCT
ap-1851	83	8	independent	independent	ADJ
ap-1851	83	9	of	of	ADP
ap-1851	83	10	energy	energy	NOUN
ap-1851	83	11	,	,	PUNCT
ap-1851	83	12	of	of	ADP
ap-1851	83	13	the	the	DET
ap-1851	83	14	green	green	ADJ
ap-1851	83	15	function	function	NOUN
ap-1851	83	16	asymptotics	asymptotic	NOUN
ap-1851	83	17	near	near	ADP
ap-1851	83	18	xj	xj	PROPN
ap-1851	83	19	,	,	PUNCT
ap-1851	83	20	i.e.	i.e.	X
ap-1851	83	21	g(x	g(x	X
ap-1851	83	22	,	,	PUNCT
ap-1851	83	23	xj	xj	PROPN
ap-1851	83	24	;	;	PUNCT
ap-1851	83	25	k	k	X
ap-1851	83	26	)	)	PUNCT
ap-1851	83	27	=	=	SYM
ap-1851	83	28	f0(x	f0(x	PROPN
ap-1851	83	29	,	,	PUNCT
ap-1851	83	30	xj	xj	PROPN
ap-1851	83	31	)	)	PUNCT
ap-1851	83	32	+	+	CCONJ
ap-1851	83	33	f1(x	f1(x	PROPN
ap-1851	83	34	,	,	PUNCT
ap-1851	83	35	xj	xj	X
ap-1851	83	36	;	;	PUNCT
ap-1851	83	37	k	k	X
ap-1851	83	38	)	)	PUNCT
ap-1851	84	1	+	+	SYM
ap-1851	84	2	r(x	r(x	PROPN
ap-1851	84	3	,	,	PUNCT
ap-1851	84	4	xj	xj	PROPN
ap-1851	84	5	;	;	PUNCT
ap-1851	84	6	k	k	X
ap-1851	84	7	)	)	PUNCT
ap-1851	84	8	with	with	ADP
ap-1851	84	9	the	the	DET
ap-1851	84	10	remainder	remainder	NOUN
ap-1851	84	11	term	term	NOUN
ap-1851	84	12	r(x	r(x	PROPN
ap-1851	84	13	,	,	PUNCT
ap-1851	84	14	xj	xj	PROPN
ap-1851	84	15	;	;	PUNCT
ap-1851	84	16	k	k	X
ap-1851	84	17	)	)	PUNCT
ap-1851	85	1	=	=	SYM
ap-1851	85	2	o	o	X
ap-1851	85	3	(	(	PUNCT
ap-1851	85	4	r(x	r(x	PROPN
ap-1851	85	5	,	,	PUNCT
ap-1851	85	6	xj	xj	PROPN
ap-1851	85	7	)	)	PUNCT
ap-1851	85	8	)	)	PUNCT
ap-1851	85	9	.	.	PUNCT
ap-1851	86	1	the	the	DET
ap-1851	86	2	self	self	NOUN
ap-1851	86	3	-	-	PUNCT
ap-1851	86	4	adjoint	adjoint	NOUN
ap-1851	86	5	extension	extension	NOUN
ap-1851	86	6	of	of	ADP
ap-1851	86	7	h	h	NOUN
ap-1851	86	8	′	′	NUM
ap-1851	86	9	determined	determine	VERB
ap-1851	86	10	by	by	ADP
ap-1851	86	11	the	the	DET
ap-1851	86	12	condition	condition	NOUN
ap-1851	86	13	(	(	PUNCT
ap-1851	86	14	1	1	X
ap-1851	86	15	)	)	PUNCT
ap-1851	86	16	will	will	AUX
ap-1851	86	17	be	be	AUX
ap-1851	86	18	denoted	denote	VERB
ap-1851	86	19	as	as	ADP
ap-1851	86	20	hu	hu	PROPN
ap-1851	86	21	;	;	PUNCT
ap-1851	86	22	we	we	PRON
ap-1851	86	23	will	will	AUX
ap-1851	86	24	drop	drop	VERB
ap-1851	86	25	the	the	DET
ap-1851	86	26	subscript	subscript	NOUN
ap-1851	86	27	if	if	SCONJ
ap-1851	86	28	the	the	DET
ap-1851	86	29	choice	choice	NOUN
ap-1851	86	30	of	of	ADP
ap-1851	86	31	u	u	NOUN
ap-1851	86	32	is	be	AUX
ap-1851	86	33	either	either	CCONJ
ap-1851	86	34	clear	clear	ADJ
ap-1851	86	35	from	from	ADP
ap-1851	86	36	the	the	DET
ap-1851	86	37	context	context	NOUN
ap-1851	86	38	or	or	CCONJ
ap-1851	86	39	not	not	PART
ap-1851	86	40	important	important	ADJ
ap-1851	86	41	.	.	PUNCT
ap-1851	87	1	not	not	PART
ap-1851	87	2	all	all	DET
ap-1851	87	3	self	self	NOUN
ap-1851	87	4	-	-	PUNCT
ap-1851	87	5	adjoint	adjoint	NOUN
ap-1851	87	6	extensions	extension	NOUN
ap-1851	87	7	,	,	PUNCT
ap-1851	87	8	however	however	ADV
ap-1851	87	9	,	,	PUNCT
ap-1851	87	10	make	make	VERB
ap-1851	87	11	sense	sense	NOUN
ap-1851	87	12	in	in	ADP
ap-1851	87	13	general	general	ADJ
ap-1851	87	14	from	from	ADP
ap-1851	87	15	the	the	DET
ap-1851	87	16	physics	physics	NOUN
ap-1851	87	17	point	point	NOUN
ap-1851	87	18	of	of	ADP
ap-1851	87	19	view	view	NOUN
ap-1851	87	20	.	.	PUNCT
ap-1851	88	1	the	the	DET
ap-1851	88	2	reason	reason	NOUN
ap-1851	88	3	is	be	AUX
ap-1851	88	4	that	that	PRON
ap-1851	88	5	for	for	ADP
ap-1851	88	6	n	n	PRON
ap-1851	88	7	>	>	SYM
ap-1851	88	8	1	1	NUM
ap-1851	88	9	one	one	NUM
ap-1851	88	10	finds	find	VERB
ap-1851	88	11	among	among	ADP
ap-1851	88	12	them	they	PRON
ap-1851	88	13	such	such	ADJ
ap-1851	88	14	extensions	extension	NOUN
ap-1851	88	15	which	which	PRON
ap-1851	88	16	would	would	AUX
ap-1851	88	17	allow	allow	VERB
ap-1851	88	18	the	the	DET
ap-1851	88	19	particle	particle	NOUN
ap-1851	88	20	living	live	VERB
ap-1851	88	21	on	on	ADP
ap-1851	88	22	γ	γ	NOUN
ap-1851	88	23	to	to	PART
ap-1851	88	24	hop	hop	VERB
ap-1851	88	25	from	from	ADP
ap-1851	88	26	one	one	NUM
ap-1851	88	27	junction	junction	NOUN
ap-1851	88	28	to	to	ADP
ap-1851	88	29	another	another	DET
ap-1851	88	30	junction	junction	NOUN
ap-1851	88	31	.	.	PUNCT
ap-1851	89	1	we	we	PRON
ap-1851	89	2	restrict	restrict	VERB
ap-1851	89	3	our	our	PRON
ap-1851	89	4	attention	attention	NOUN
ap-1851	89	5	in	in	ADP
ap-1851	89	6	what	what	PRON
ap-1851	89	7	follows	follow	VERB
ap-1851	89	8	to	to	ADP
ap-1851	89	9	local	local	ADJ
ap-1851	89	10	couplings	coupling	NOUN
ap-1851	89	11	for	for	ADP
ap-1851	89	12	which	which	PRON
ap-1851	89	13	such	such	DET
ap-1851	89	14	a	a	DET
ap-1851	89	15	situation	situation	NOUN
ap-1851	89	16	can	can	AUX
ap-1851	89	17	not	not	PART
ap-1851	89	18	occur	occur	VERB
ap-1851	89	19	.	.	PUNCT
ap-1851	90	1	they	they	PRON
ap-1851	90	2	are	be	AUX
ap-1851	90	3	described	describe	VERB
ap-1851	90	4	by	by	ADP
ap-1851	90	5	matrices	matrix	NOUN
ap-1851	90	6	which	which	PRON
ap-1851	90	7	are	be	AUX
ap-1851	90	8	block	block	NOUN
ap-1851	90	9	diagonal	diagonal	ADJ
ap-1851	90	10	,	,	PUNCT
ap-1851	90	11	so	so	SCONJ
ap-1851	90	12	that	that	SCONJ
ap-1851	90	13	such	such	DET
ap-1851	90	14	a	a	DET
ap-1851	90	15	u	u	NOUN
ap-1851	90	16	does	do	AUX
ap-1851	90	17	not	not	PART
ap-1851	90	18	connect	connect	VERB
ap-1851	90	19	disjoint	disjoint	NOUN
ap-1851	90	20	junction	junction	NOUN
ap-1851	90	21	points	point	NOUN
ap-1851	90	22	xj	xj	PROPN
ap-1851	90	23	.	.	PUNCT
ap-1851	91	1	the	the	DET
ap-1851	91	2	coupling	couple	VERB
ap-1851	91	3	condition	condition	NOUN
ap-1851	91	4	(	(	PUNCT
ap-1851	91	5	1	1	X
ap-1851	91	6	)	)	PUNCT
ap-1851	91	7	is	be	AUX
ap-1851	91	8	then	then	ADV
ap-1851	91	9	a	a	DET
ap-1851	91	10	family	family	NOUN
ap-1851	91	11	of	of	ADP
ap-1851	91	12	n	n	PRON
ap-1851	91	13	conditions	condition	NOUN
ap-1851	91	14	,	,	PUNCT
ap-1851	91	15	each	each	PRON
ap-1851	91	16	referring	refer	VERB
ap-1851	91	17	to	to	ADP
ap-1851	91	18	a	a	DET
ap-1851	91	19	particular	particular	ADJ
ap-1851	91	20	xj	xj	PROPN
ap-1851	91	21	and	and	CCONJ
ap-1851	91	22	coupling	couple	VERB
ap-1851	91	23	the	the	DET
ap-1851	91	24	corresponding	correspond	VERB
ap-1851	91	25	(	(	PUNCT
ap-1851	91	26	sub)columns	sub)columns	PROPN
ap-1851	91	27	ψj	ψj	ADV
ap-1851	91	28	and	and	CCONJ
ap-1851	91	29	ψ′j	ψ′j	VERB
ap-1851	91	30	by	by	ADP
ap-1851	91	31	means	mean	NOUN
ap-1851	91	32	of	of	ADP
ap-1851	91	33	the	the	DET
ap-1851	91	34	respective	respective	ADJ
ap-1851	91	35	block	block	NOUN
ap-1851	91	36	uj	uj	PROPN
ap-1851	91	37	of	of	ADP
ap-1851	91	38	u	u	PROPN
ap-1851	91	39	.	.	PUNCT
ap-1851	92	1	before	before	ADP
ap-1851	92	2	proceeding	proceed	VERB
ap-1851	92	3	further	far	ADV
ap-1851	92	4	we	we	PRON
ap-1851	92	5	will	will	AUX
ap-1851	92	6	mention	mention	VERB
ap-1851	92	7	a	a	DET
ap-1851	92	8	useful	useful	ADJ
ap-1851	92	9	trick	trick	NOUN
ap-1851	92	10	,	,	PUNCT
ap-1851	92	11	known	know	VERB
ap-1851	92	12	from	from	ADP
ap-1851	92	13	quantum	quantum	NOUN
ap-1851	92	14	-	-	PUNCT
ap-1851	92	15	graph	graph	NOUN
ap-1851	92	16	theory	theory	NOUN
ap-1851	92	17	[	[	X
ap-1851	92	18	16	16	NUM
ap-1851	92	19	]	]	X
ap-1851	92	20	,	,	PUNCT
ap-1851	92	21	which	which	PRON
ap-1851	92	22	allows	allow	VERB
ap-1851	92	23	to	to	PART
ap-1851	92	24	study	study	VERB
ap-1851	92	25	a	a	DET
ap-1851	92	26	compact	compact	ADJ
ap-1851	92	27	scatterer	scatterer	NOUN
ap-1851	92	28	with	with	ADP
ap-1851	92	29	leads	lead	NOUN
ap-1851	92	30	looking	look	VERB
ap-1851	92	31	at	at	ADP
ap-1851	92	32	its	its	PRON
ap-1851	92	33	‘	'	PUNCT
ap-1851	92	34	core	core	NOUN
ap-1851	92	35	’	'	PUNCT
ap-1851	92	36	alone	alone	ADV
ap-1851	92	37	replacing	replace	VERB
ap-1851	92	38	the	the	DET
ap-1851	92	39	leads	lead	NOUN
ap-1851	92	40	by	by	ADP
ap-1851	92	41	effective	effective	ADJ
ap-1851	92	42	coupling	coupling	NOUN
ap-1851	92	43	at	at	ADP
ap-1851	92	44	the	the	DET
ap-1851	92	45	points	point	NOUN
ap-1851	92	46	xj	xj	PROPN
ap-1851	92	47	which	which	PRON
ap-1851	92	48	is	be	AUX
ap-1851	92	49	a	a	DET
ap-1851	92	50	non	non	ADJ
ap-1851	92	51	-	-	NOUN
ap-1851	92	52	selfadjoint	selfadjoint	ADJ
ap-1851	92	53	,	,	PUNCT
ap-1851	92	54	energy	energy	NOUN
ap-1851	92	55	-	-	PUNCT
ap-1851	92	56	dependent	dependent	ADJ
ap-1851	92	57	point	point	NOUN
ap-1851	92	58	interaction	interaction	NOUN
ap-1851	92	59	,	,	PUNCT
ap-1851	92	60	namely	namely	ADV
ap-1851	92	61	(	(	PUNCT
ap-1851	92	62	ũj(k)−	ũj(k)−	NOUN
ap-1851	92	63	i	i	PROPN
ap-1851	92	64	)	)	PUNCT
ap-1851	92	65	dj(f	dj(f	PROPN
ap-1851	92	66	)	)	PUNCT
ap-1851	93	1	+	+	CCONJ
ap-1851	93	2	i	i	PRON
ap-1851	93	3	(	(	PUNCT
ap-1851	93	4	ũj(k	ũj(k	X
ap-1851	93	5	)	)	PUNCT
ap-1851	93	6	+	+	CCONJ
ap-1851	93	7	i	i	NOUN
ap-1851	93	8	)	)	PUNCT
ap-1851	93	9	cj(f	cj(f	X
ap-1851	93	10	)	)	PUNCT
ap-1851	93	11	=	=	SYM
ap-1851	93	12	0	0	NUM
ap-1851	93	13	,	,	PUNCT
ap-1851	93	14	(	(	PUNCT
ap-1851	93	15	3	3	X
ap-1851	93	16	)	)	PUNCT
ap-1851	93	17	ũj(k	ũj(k	NOUN
ap-1851	93	18	)	)	PUNCT
ap-1851	93	19	=	=	PUNCT
ap-1851	93	20	u1j	u1j	ADV
ap-1851	93	21	−	−	PROPN
ap-1851	93	22	(	(	PUNCT
ap-1851	93	23	1−	1−	NUM
ap-1851	93	24	k)u2j	k)u2j	NOUN
ap-1851	93	25	[	[	PUNCT
ap-1851	93	26	(	(	PUNCT
ap-1851	93	27	1−	1−	NUM
ap-1851	93	28	k)u4j	k)u4j	NOUN
ap-1851	93	29	−	−	PROPN
ap-1851	93	30	(	(	PUNCT
ap-1851	93	31	k	k	PROPN
ap-1851	93	32	+	+	X
ap-1851	93	33	1)i	1)i	NUM
ap-1851	93	34	]	]	SYM
ap-1851	93	35	−1	−1	NOUN
ap-1851	93	36	u3j	u3j	ADJ
ap-1851	93	37	,	,	PUNCT
ap-1851	93	38	where	where	SCONJ
ap-1851	93	39	u1j	u1j	NOUN
ap-1851	93	40	denotes	denote	VERB
ap-1851	93	41	the	the	DET
ap-1851	93	42	top	top	ADV
ap-1851	93	43	-	-	PUNCT
ap-1851	93	44	left	leave	VERB
ap-1851	93	45	entry	entry	NOUN
ap-1851	93	46	of	of	ADP
ap-1851	93	47	uj	uj	PROPN
ap-1851	93	48	,	,	PUNCT
ap-1851	93	49	u2j	u2j	ADJ
ap-1851	93	50	the	the	DET
ap-1851	93	51	rest	rest	NOUN
ap-1851	93	52	of	of	ADP
ap-1851	93	53	the	the	DET
ap-1851	93	54	first	first	ADJ
ap-1851	93	55	row	row	NOUN
ap-1851	93	56	,	,	PUNCT
ap-1851	93	57	u3j	u3j	ADV
ap-1851	93	58	the	the	DET
ap-1851	93	59	rest	rest	NOUN
ap-1851	93	60	of	of	ADP
ap-1851	93	61	the	the	DET
ap-1851	93	62	first	first	ADJ
ap-1851	93	63	column	column	NOUN
ap-1851	93	64	and	and	CCONJ
ap-1851	93	65	u4j	u4j	PROPN
ap-1851	93	66	is	be	AUX
ap-1851	93	67	nj	nj	PROPN
ap-1851	93	68	×nj	×nj	VERB
ap-1851	93	69	part	part	NOUN
ap-1851	93	70	corresponding	correspond	VERB
ap-1851	93	71	to	to	ADP
ap-1851	93	72	the	the	DET
ap-1851	93	73	coupling	coupling	NOUN
ap-1851	93	74	between	between	ADP
ap-1851	93	75	the	the	DET
ap-1851	93	76	halflines	halfline	NOUN
ap-1851	93	77	attached	attach	VERB
ap-1851	93	78	to	to	ADP
ap-1851	93	79	the	the	DET
ap-1851	93	80	manifold	manifold	NOUN
ap-1851	93	81	.	.	PUNCT
ap-1851	94	1	this	this	PRON
ap-1851	94	2	can	can	AUX
ap-1851	94	3	be	be	AUX
ap-1851	94	4	easily	easily	ADV
ap-1851	94	5	checked	check	VERB
ap-1851	94	6	using	use	VERB
ap-1851	94	7	the	the	DET
ap-1851	94	8	standard	standard	ADJ
ap-1851	94	9	argument	argument	NOUN
ap-1851	94	10	ascribed	ascribe	VERB
ap-1851	94	11	,	,	PUNCT
ap-1851	94	12	in	in	ADP
ap-1851	94	13	different	different	ADJ
ap-1851	94	14	fields	field	NOUN
ap-1851	94	15	,	,	PUNCT
ap-1851	94	16	to	to	ADP
ap-1851	94	17	different	different	ADJ
ap-1851	94	18	people	people	NOUN
ap-1851	94	19	such	such	ADJ
ap-1851	94	20	as	as	ADP
ap-1851	94	21	schur	schur	NOUN
ap-1851	94	22	,	,	PUNCT
ap-1851	94	23	feshbach	feshbach	NOUN
ap-1851	94	24	,	,	PUNCT
ap-1851	94	25	grushin	grushin	NOUN
ap-1851	94	26	,	,	PUNCT
ap-1851	94	27	etc	etc	X
ap-1851	94	28	.	.	X
ap-1851	95	1	3	3	X
ap-1851	95	2	.	.	NOUN
ap-1851	95	3	scattering	scatter	VERB
ap-1851	95	4	and	and	CCONJ
ap-1851	95	5	resolvent	resolvent	ADJ
ap-1851	95	6	resonances	resonance	NOUN
ap-1851	95	7	the	the	DET
ap-1851	95	8	model	model	NOUN
ap-1851	95	9	described	describe	VERB
ap-1851	95	10	in	in	ADP
ap-1851	95	11	the	the	DET
ap-1851	95	12	previous	previous	ADJ
ap-1851	95	13	section	section	NOUN
ap-1851	95	14	provides	provide	VERB
ap-1851	95	15	a	a	DET
ap-1851	95	16	natural	natural	ADJ
ap-1851	95	17	framework	framework	NOUN
ap-1851	95	18	for	for	ADP
ap-1851	95	19	studying	study	VERB
ap-1851	95	20	scattering	scatter	VERB
ap-1851	95	21	on	on	ADP
ap-1851	95	22	the	the	DET
ap-1851	95	23	hedgehog	hedgehog	NOUN
ap-1851	95	24	manifold	manifold	NOUN
ap-1851	95	25	.	.	PUNCT
ap-1851	96	1	the	the	DET
ap-1851	96	2	existence	existence	NOUN
ap-1851	96	3	of	of	ADP
ap-1851	96	4	scattering	scattering	NOUN
ap-1851	96	5	is	be	AUX
ap-1851	96	6	easy	easy	ADJ
ap-1851	96	7	to	to	PART
ap-1851	96	8	establish	establish	VERB
ap-1851	96	9	because	because	SCONJ
ap-1851	96	10	any	any	DET
ap-1851	96	11	hamiltonian	hamiltonian	NOUN
ap-1851	96	12	of	of	ADP
ap-1851	96	13	the	the	DET
ap-1851	96	14	considered	considered	ADJ
ap-1851	96	15	class	class	NOUN
ap-1851	96	16	differs	differ	VERB
ap-1851	96	17	from	from	ADP
ap-1851	96	18	one	one	NUM
ap-1851	96	19	with	with	ADP
ap-1851	96	20	decoupled	decouple	VERB
ap-1851	96	21	leads	lead	NOUN
ap-1851	96	22	by	by	ADP
ap-1851	96	23	a	a	DET
ap-1851	96	24	finite	finite	ADJ
ap-1851	96	25	-	-	ADJ
ap-1851	96	26	rank	rank	ADJ
ap-1851	96	27	perturbation	perturbation	NOUN
ap-1851	96	28	in	in	ADP
ap-1851	96	29	the	the	DET
ap-1851	96	30	resolvent	resolvent	NOUN
ap-1851	96	31	[	[	X
ap-1851	96	32	27	27	NUM
ap-1851	96	33	]	]	PUNCT
ap-1851	96	34	.	.	PUNCT
ap-1851	97	1	finding	find	VERB
ap-1851	97	2	the	the	DET
ap-1851	97	3	on	on	ADP
ap-1851	97	4	-	-	PUNCT
ap-1851	97	5	shell	shell	NOUN
ap-1851	97	6	scattering	scattering	NOUN
ap-1851	97	7	matrix	matrix	NOUN
ap-1851	97	8	is	be	AUX
ap-1851	97	9	computationally	computationally	ADV
ap-1851	97	10	slightly	slightly	ADV
ap-1851	97	11	more	more	ADV
ap-1851	97	12	complicated	complicated	ADJ
ap-1851	97	13	but	but	CCONJ
ap-1851	97	14	simple	simple	ADJ
ap-1851	97	15	in	in	ADP
ap-1851	97	16	principle	principle	NOUN
ap-1851	97	17	.	.	PUNCT
ap-1851	98	1	the	the	DET
ap-1851	98	2	solution	solution	NOUN
ap-1851	98	3	of	of	ADP
ap-1851	98	4	the	the	DET
ap-1851	98	5	sschrödinger	sschrödinger	ADJ
ap-1851	98	6	equation	equation	NOUN
ap-1851	98	7	on	on	ADP
ap-1851	98	8	the	the	DET
ap-1851	98	9	jth	jth	PROPN
ap-1851	98	10	external	external	ADJ
ap-1851	98	11	lead	lead	NOUN
ap-1851	98	12	with	with	ADP
ap-1851	98	13	energy	energy	NOUN
ap-1851	98	14	k2	k2	NOUN
ap-1851	98	15	can	can	AUX
ap-1851	98	16	be	be	AUX
ap-1851	98	17	expressed	express	VERB
ap-1851	98	18	as	as	ADP
ap-1851	98	19	a	a	DET
ap-1851	98	20	linear	linear	ADJ
ap-1851	98	21	combination	combination	NOUN
ap-1851	98	22	of	of	ADP
ap-1851	98	23	the	the	DET
ap-1851	98	24	incoming	incoming	ADJ
ap-1851	98	25	and	and	CCONJ
ap-1851	98	26	outgoing	outgoing	ADJ
ap-1851	98	27	waves	wave	NOUN
ap-1851	98	28	,	,	PUNCT
ap-1851	98	29	aj(k)e−ikx	aj(k)e−ikx	NOUN
ap-1851	98	30	+	+	CCONJ
ap-1851	98	31	bj(k)eikx	bj(k)eikx	ADV
ap-1851	98	32	.	.	PUNCT
ap-1851	99	1	the	the	DET
ap-1851	99	2	scattering	scatter	VERB
ap-1851	99	3	matrix	matrix	NOUN
ap-1851	99	4	then	then	ADV
ap-1851	99	5	maps	map	VERB
ap-1851	99	6	the	the	DET
ap-1851	99	7	vector	vector	NOUN
ap-1851	99	8	of	of	ADP
ap-1851	99	9	incoming	incoming	ADJ
ap-1851	99	10	wave	wave	NOUN
ap-1851	99	11	amplitudes	amplitude	NOUN
ap-1851	99	12	aj	aj	PROPN
ap-1851	99	13	into	into	ADP
ap-1851	99	14	the	the	DET
ap-1851	99	15	vector	vector	NOUN
ap-1851	99	16	of	of	ADP
ap-1851	99	17	outgoing	outgoing	ADJ
ap-1851	99	18	wave	wave	NOUN
ap-1851	99	19	amplitudes	amplitude	NOUN
ap-1851	99	20	bj	bj	VERB
ap-1851	99	21	.	.	PUNCT
ap-1851	100	1	we	we	PRON
ap-1851	100	2	emphasize	emphasize	VERB
ap-1851	100	3	that	that	SCONJ
ap-1851	100	4	our	our	PRON
ap-1851	100	5	convention	convention	NOUN
ap-1851	100	6	,	,	PUNCT
ap-1851	100	7	which	which	PRON
ap-1851	100	8	is	be	AUX
ap-1851	100	9	natural	natural	ADJ
ap-1851	100	10	in	in	ADP
ap-1851	100	11	this	this	DET
ap-1851	100	12	context	context	NOUN
ap-1851	100	13	and	and	CCONJ
ap-1851	100	14	analogous	analogous	ADJ
ap-1851	100	15	to	to	ADP
ap-1851	100	16	the	the	DET
ap-1851	100	17	one	one	NOUN
ap-1851	100	18	used	use	VERB
ap-1851	100	19	in	in	ADP
ap-1851	100	20	quantum	quantum	NOUN
ap-1851	100	21	-	-	PUNCT
ap-1851	100	22	graph	graph	NOUN
ap-1851	100	23	theory	theory	NOUN
ap-1851	100	24	[	[	X
ap-1851	100	25	26	26	NUM
ap-1851	100	26	]	]	PUNCT
ap-1851	100	27	differs	differ	VERB
ap-1851	100	28	from	from	ADP
ap-1851	100	29	the	the	DET
ap-1851	100	30	one	one	NUM
ap-1851	100	31	employed	employ	VERB
ap-1851	100	32	when	when	SCONJ
ap-1851	100	33	scattering	scatter	VERB
ap-1851	100	34	on	on	ADP
ap-1851	100	35	the	the	DET
ap-1851	100	36	real	real	ADJ
ap-1851	100	37	line	line	NOUN
ap-1851	100	38	is	be	AUX
ap-1851	100	39	treated	treat	VERB
ap-1851	100	40	[	[	PUNCT
ap-1851	100	41	29	29	NUM
ap-1851	100	42	]	]	PUNCT
ap-1851	100	43	,	,	PUNCT
ap-1851	100	44	in	in	SCONJ
ap-1851	100	45	that	that	SCONJ
ap-1851	100	46	each	each	DET
ap-1851	100	47	lead	lead	NOUN
ap-1851	100	48	is	be	AUX
ap-1851	100	49	identified	identify	VERB
ap-1851	100	50	with	with	ADP
ap-1851	100	51	the	the	DET
ap-1851	100	52	positive	positive	ADJ
ap-1851	100	53	real	real	ADJ
ap-1851	100	54	halfline	halfline	NOUN
ap-1851	100	55	.	.	PUNCT
ap-1851	101	1	for	for	ADP
ap-1851	101	2	the	the	DET
ap-1851	101	3	case	case	NOUN
ap-1851	101	4	of	of	ADP
ap-1851	101	5	two	two	NUM
ap-1851	101	6	leads	lead	NOUN
ap-1851	101	7	,	,	PUNCT
ap-1851	101	8	in	in	ADP
ap-1851	101	9	particular	particular	ADJ
ap-1851	101	10	,	,	PUNCT
ap-1851	101	11	it	it	PRON
ap-1851	101	12	means	mean	VERB
ap-1851	101	13	that	that	SCONJ
ap-1851	101	14	columns	column	NOUN
ap-1851	101	15	of	of	ADP
ap-1851	101	16	the	the	DET
ap-1851	101	17	2×	2×	NUM
ap-1851	101	18	2	2	NUM
ap-1851	101	19	scattering	scattering	NOUN
ap-1851	101	20	matrix	matrix	NOUN
ap-1851	101	21	are	be	AUX
ap-1851	101	22	interchanged	interchange	VERB
ap-1851	101	23	and	and	CCONJ
ap-1851	101	24	we	we	PRON
ap-1851	101	25	have	have	VERB
ap-1851	101	26	lemma	lemma	PROPN
ap-1851	101	27	3.1	3.1	NUM
ap-1851	101	28	.	.	PUNCT
ap-1851	102	1	the	the	DET
ap-1851	102	2	on	on	ADP
ap-1851	102	3	-	-	PUNCT
ap-1851	102	4	shell	shell	NOUN
ap-1851	102	5	scattering	scattering	NOUN
ap-1851	102	6	matrix	matrix	NOUN
ap-1851	102	7	satisfies	satisfy	VERB
ap-1851	102	8	s(k)−1	s(k)−1	NOUN
ap-1851	102	9	=	=	SYM
ap-1851	102	10	s(−k	s(−k	NOUN
ap-1851	102	11	)	)	PUNCT
ap-1851	102	12	=	=	SYM
ap-1851	102	13	s∗(k̄	s∗(k̄	NOUN
ap-1851	102	14	)	)	PUNCT
ap-1851	102	15	,	,	PUNCT
ap-1851	102	16	where	where	SCONJ
ap-1851	102	17	star	star	NOUN
ap-1851	102	18	and	and	CCONJ
ap-1851	102	19	bar	bar	NOUN
ap-1851	102	20	denote	denote	VERB
ap-1851	102	21	the	the	DET
ap-1851	102	22	hermitian	hermitian	ADJ
ap-1851	102	23	and	and	CCONJ
ap-1851	102	24	complex	complex	ADJ
ap-1851	102	25	conjugation	conjugation	NOUN
ap-1851	102	26	,	,	PUNCT
ap-1851	102	27	respectively	respectively	ADV
ap-1851	102	28	.	.	PUNCT
ap-1851	103	1	proof	proof	NOUN
ap-1851	103	2	.	.	PUNCT
ap-1851	104	1	the	the	DET
ap-1851	104	2	claim	claim	NOUN
ap-1851	104	3	follows	follow	VERB
ap-1851	104	4	directly	directly	ADV
ap-1851	104	5	from	from	ADP
ap-1851	104	6	the	the	DET
ap-1851	104	7	definition	definition	NOUN
ap-1851	104	8	of	of	ADP
ap-1851	104	9	scattering	scatter	VERB
ap-1851	104	10	matrix	matrix	NOUN
ap-1851	104	11	and	and	CCONJ
ap-1851	104	12	from	from	ADP
ap-1851	104	13	the	the	DET
ap-1851	104	14	properties	property	NOUN
ap-1851	104	15	of	of	ADP
ap-1851	104	16	the	the	DET
ap-1851	104	17	schrödinger	schrödinger	ADJ
ap-1851	104	18	equation	equation	NOUN
ap-1851	104	19	and	and	CCONJ
ap-1851	104	20	its	its	PRON
ap-1851	104	21	external	external	ADJ
ap-1851	104	22	solutions	solution	NOUN
ap-1851	104	23	.	.	PUNCT
ap-1851	105	1	since	since	SCONJ
ap-1851	105	2	the	the	DET
ap-1851	105	3	potential	potential	NOUN
ap-1851	105	4	is	be	AUX
ap-1851	105	5	absent	absent	ADJ
ap-1851	105	6	we	we	PRON
ap-1851	105	7	infer	infer	VERB
ap-1851	105	8	that	that	SCONJ
ap-1851	105	9	if	if	SCONJ
ap-1851	105	10	f(k0	f(k0	NOUN
ap-1851	105	11	,	,	PUNCT
ap-1851	105	12	x	x	X
ap-1851	105	13	)	)	PUNCT
ap-1851	105	14	is	be	AUX
ap-1851	105	15	a	a	DET
ap-1851	105	16	solution	solution	NOUN
ap-1851	105	17	of	of	ADP
ap-1851	105	18	the	the	DET
ap-1851	105	19	schrödinger	schrödinger	ADJ
ap-1851	105	20	equation	equation	NOUN
ap-1851	105	21	for	for	ADP
ap-1851	105	22	a	a	DET
ap-1851	105	23	given	give	VERB
ap-1851	105	24	k	k	NOUN
ap-1851	105	25	,	,	PUNCT
ap-1851	105	26	so	so	ADV
ap-1851	105	27	is	be	AUX
ap-1851	105	28	f(−k0	f(−k0	PROPN
ap-1851	105	29	,	,	PUNCT
ap-1851	105	30	x	x	NOUN
ap-1851	105	31	)	)	PUNCT
ap-1851	105	32	.	.	PUNCT
ap-1851	106	1	this	this	PRON
ap-1851	106	2	means	mean	VERB
ap-1851	106	3	that	that	SCONJ
ap-1851	106	4	s(k	s(k	ADV
ap-1851	106	5	)	)	PUNCT
ap-1851	106	6	can	can	AUX
ap-1851	106	7	be	be	AUX
ap-1851	106	8	regarded	regard	VERB
ap-1851	106	9	both	both	PRON
ap-1851	106	10	as	as	ADP
ap-1851	106	11	an	an	DET
ap-1851	106	12	operator	operator	NOUN
ap-1851	106	13	mapping	mapping	NOUN
ap-1851	106	14	{	{	PUNCT
ap-1851	106	15	aj(k	aj(k	NOUN
ap-1851	106	16	)	)	PUNCT
ap-1851	106	17	}	}	PUNCT
ap-1851	106	18	to	to	ADP
ap-1851	106	19	{	{	PUNCT
ap-1851	106	20	bj(k	bj(k	NOUN
ap-1851	106	21	)	)	PUNCT
ap-1851	106	22	}	}	PUNCT
ap-1851	106	23	and	and	CCONJ
ap-1851	106	24	as	as	ADP
ap-1851	106	25	a	a	DET
ap-1851	106	26	map	map	NOUN
ap-1851	106	27	from	from	ADP
ap-1851	106	28	{	{	PUNCT
ap-1851	106	29	bj(−k	bj(−k	NOUN
ap-1851	106	30	)	)	PUNCT
ap-1851	106	31	}	}	PUNCT
ap-1851	106	32	to	to	ADP
ap-1851	106	33	{	{	PUNCT
ap-1851	106	34	aj(−k	aj(−k	NOUN
ap-1851	106	35	)	)	PUNCT
ap-1851	106	36	}	}	PUNCT
ap-1851	106	37	,	,	PUNCT
ap-1851	106	38	i.e.	i.e.	X
ap-1851	106	39	as	as	ADP
ap-1851	106	40	the	the	DET
ap-1851	106	41	inverse	inverse	NOUN
ap-1851	106	42	of	of	ADP
ap-1851	106	43	s(−k	s(−k	NOUN
ap-1851	106	44	)	)	PUNCT
ap-1851	106	45	.	.	PUNCT
ap-1851	107	1	in	in	ADP
ap-1851	107	2	an	an	DET
ap-1851	107	3	similar	similar	ADJ
ap-1851	107	4	way	way	NOUN
ap-1851	107	5	one	one	PRON
ap-1851	107	6	can	can	AUX
ap-1851	107	7	establish	establish	VERB
ap-1851	107	8	the	the	DET
ap-1851	107	9	second	second	ADJ
ap-1851	107	10	identity	identity	NOUN
ap-1851	107	11	.	.	PUNCT
ap-1851	108	1	remark	remark	PROPN
ap-1851	108	2	3.2	3.2	NUM
ap-1851	108	3	.	.	PUNCT
ap-1851	109	1	if	if	SCONJ
ap-1851	109	2	ω	ω	PROPN
ap-1851	109	3	is	be	AUX
ap-1851	109	4	replaced	replace	VERB
ap-1851	109	5	by	by	ADP
ap-1851	109	6	a	a	DET
ap-1851	109	7	compact	compact	ADJ
ap-1851	109	8	metric	metric	ADJ
ap-1851	109	9	graph	graph	NOUN
ap-1851	109	10	and	and	CCONJ
ap-1851	109	11	the	the	DET
ap-1851	109	12	potential	potential	NOUN
ap-1851	109	13	is	be	AUX
ap-1851	109	14	again	again	ADV
ap-1851	109	15	absent	absent	ADJ
ap-1851	109	16	,	,	PUNCT
ap-1851	109	17	the	the	DET
ap-1851	109	18	s	s	NOUN
ap-1851	109	19	-	-	NOUN
ap-1851	109	20	matrix	matrix	NOUN
ap-1851	109	21	can	can	AUX
ap-1851	109	22	be	be	AUX
ap-1851	109	23	written	write	VERB
ap-1851	109	24	as	as	ADP
ap-1851	109	25	s(k	s(k	ADV
ap-1851	109	26	)	)	PUNCT
ap-1851	110	1	=	=	SYM
ap-1851	110	2	−f	−f	NOUN
ap-1851	110	3	(	(	PUNCT
ap-1851	110	4	k)−1	k)−1	PROPN
ap-1851	110	5	·	·	SYM
ap-1851	110	6	f	f	PROPN
ap-1851	110	7	(	(	PUNCT
ap-1851	110	8	−k	−k	PROPN
ap-1851	110	9	)	)	PUNCT
ap-1851	110	10	where	where	SCONJ
ap-1851	110	11	the	the	DET
ap-1851	110	12	m	m	PROPN
ap-1851	110	13	×m	×m	NOUN
ap-1851	110	14	matrix	matrix	NOUN
ap-1851	110	15	f	f	PROPN
ap-1851	110	16	(	(	PUNCT
ap-1851	110	17	k	k	NOUN
ap-1851	110	18	)	)	PUNCT
ap-1851	110	19	is	be	AUX
ap-1851	110	20	an	an	DET
ap-1851	110	21	analogue	analogue	NOUN
ap-1851	110	22	of	of	ADP
ap-1851	110	23	jost	jost	NOUN
ap-1851	110	24	function	function	NOUN
ap-1851	110	25	.	.	PUNCT
ap-1851	111	1	418	418	NUM
ap-1851	111	2	vol	vol	NOUN
ap-1851	111	3	.	.	PUNCT
ap-1851	112	1	53	53	NUM
ap-1851	112	2	no	no	NOUN
ap-1851	112	3	.	.	PUNCT
ap-1851	113	1	5/2013	5/2013	NUM
ap-1851	113	2	resonances	resonance	NOUN
ap-1851	113	3	on	on	ADP
ap-1851	113	4	hedgehog	hedgehog	NOUN
ap-1851	113	5	manifolds	manifold	NOUN
ap-1851	113	6	in	in	ADP
ap-1851	113	7	particular	particular	ADJ
ap-1851	113	8	,	,	PUNCT
ap-1851	113	9	s(k	s(k	ADV
ap-1851	113	10	)	)	PUNCT
ap-1851	113	11	is	be	AUX
ap-1851	113	12	unitary	unitary	ADJ
ap-1851	113	13	for	for	SCONJ
ap-1851	113	14	k	k	PROPN
ap-1851	113	15	∈	∈	PROPN
ap-1851	113	16	r	r	NOUN
ap-1851	113	17	,	,	PUNCT
ap-1851	113	18	however	however	ADV
ap-1851	113	19	,	,	PUNCT
ap-1851	113	20	we	we	PRON
ap-1851	113	21	will	will	AUX
ap-1851	113	22	need	need	VERB
ap-1851	113	23	it	it	PRON
ap-1851	113	24	also	also	ADV
ap-1851	113	25	for	for	ADP
ap-1851	113	26	complex	complex	ADJ
ap-1851	113	27	values	value	NOUN
ap-1851	113	28	of	of	ADP
ap-1851	113	29	k.	k.	NOUN
ap-1851	113	30	by	by	ADP
ap-1851	113	31	a	a	DET
ap-1851	113	32	scattering	scatter	VERB
ap-1851	113	33	resonance	resonance	NOUN
ap-1851	113	34	we	we	PRON
ap-1851	113	35	conventionally	conventionally	ADV
ap-1851	113	36	understand	understand	VERB
ap-1851	113	37	a	a	DET
ap-1851	113	38	pole	pole	NOUN
ap-1851	113	39	of	of	ADP
ap-1851	113	40	the	the	DET
ap-1851	113	41	on	on	ADP
ap-1851	113	42	-	-	PUNCT
ap-1851	113	43	shell	shell	NOUN
ap-1851	113	44	scattering	scattering	NOUN
ap-1851	113	45	matrix	matrix	NOUN
ap-1851	113	46	in	in	ADP
ap-1851	113	47	the	the	DET
ap-1851	113	48	complex	complex	ADJ
ap-1851	113	49	plane	plane	NOUN
ap-1851	113	50	,	,	PUNCT
ap-1851	113	51	more	more	ADV
ap-1851	113	52	precisely	precisely	ADV
ap-1851	113	53	,	,	PUNCT
ap-1851	113	54	the	the	DET
ap-1851	113	55	point	point	NOUN
ap-1851	113	56	at	at	ADP
ap-1851	113	57	which	which	PRON
ap-1851	113	58	some	some	PRON
ap-1851	113	59	of	of	ADP
ap-1851	113	60	its	its	PRON
ap-1851	113	61	entries	entry	NOUN
ap-1851	113	62	have	have	VERB
ap-1851	113	63	a	a	DET
ap-1851	113	64	pole	pole	NOUN
ap-1851	113	65	singularity	singularity	NOUN
ap-1851	113	66	.	.	PUNCT
ap-1851	114	1	a	a	DET
ap-1851	114	2	resolvent	resolvent	ADJ
ap-1851	114	3	resonance	resonance	NOUN
ap-1851	114	4	,	,	PUNCT
ap-1851	114	5	on	on	ADP
ap-1851	114	6	the	the	DET
ap-1851	114	7	other	other	ADJ
ap-1851	114	8	hand	hand	NOUN
ap-1851	114	9	,	,	PUNCT
ap-1851	114	10	is	be	AUX
ap-1851	114	11	identified	identify	VERB
ap-1851	114	12	with	with	ADP
ap-1851	114	13	a	a	DET
ap-1851	114	14	pole	pole	NOUN
ap-1851	114	15	of	of	ADP
ap-1851	114	16	the	the	DET
ap-1851	114	17	resolvent	resolvent	NOUN
ap-1851	114	18	analytically	analytically	ADV
ap-1851	114	19	continued	continue	VERB
ap-1851	114	20	from	from	ADP
ap-1851	114	21	the	the	DET
ap-1851	114	22	upper	upper	ADJ
ap-1851	114	23	complex	complex	ADJ
ap-1851	114	24	halfplane	halfplane	NOUN
ap-1851	114	25	to	to	ADP
ap-1851	114	26	a	a	DET
ap-1851	114	27	region	region	NOUN
ap-1851	114	28	of	of	ADP
ap-1851	114	29	the	the	DET
ap-1851	114	30	lower	low	ADJ
ap-1851	114	31	one	one	NUM
ap-1851	114	32	.	.	PUNCT
ap-1851	115	1	a	a	DET
ap-1851	115	2	convenient	convenient	ADJ
ap-1851	115	3	and	and	CCONJ
ap-1851	115	4	efficient	efficient	ADJ
ap-1851	115	5	way	way	NOUN
ap-1851	115	6	of	of	ADP
ap-1851	115	7	treating	treat	VERB
ap-1851	115	8	resolvent	resolvent	ADJ
ap-1851	115	9	resonances	resonance	NOUN
ap-1851	115	10	is	be	AUX
ap-1851	115	11	the	the	DET
ap-1851	115	12	method	method	NOUN
ap-1851	115	13	of	of	ADP
ap-1851	115	14	exterior	exterior	ADJ
ap-1851	115	15	complex	complex	ADJ
ap-1851	115	16	scaling	scaling	NOUN
ap-1851	115	17	based	base	VERB
ap-1851	115	18	on	on	ADP
ap-1851	115	19	the	the	DET
ap-1851	115	20	ideas	idea	NOUN
ap-1851	115	21	of	of	ADP
ap-1851	115	22	aguilar	aguilar	PROPN
ap-1851	115	23	,	,	PUNCT
ap-1851	115	24	baslev	baslev	NOUN
ap-1851	115	25	,	,	PUNCT
ap-1851	115	26	combes	combe	NOUN
ap-1851	115	27	,	,	PUNCT
ap-1851	115	28	and	and	CCONJ
ap-1851	115	29	simon	simon	PROPN
ap-1851	115	30	—	—	PUNCT
ap-1851	115	31	cf	cf	NOUN
ap-1851	115	32	.	.	PUNCT
ap-1851	116	1	[	[	X
ap-1851	116	2	2	2	NUM
ap-1851	116	3	,	,	PUNCT
ap-1851	116	4	5	5	NUM
ap-1851	116	5	,	,	PUNCT
ap-1851	116	6	28	28	NUM
ap-1851	116	7	]	]	PUNCT
ap-1851	116	8	,	,	PUNCT
ap-1851	116	9	for	for	ADP
ap-1851	116	10	a	a	DET
ap-1851	116	11	recent	recent	ADJ
ap-1851	116	12	application	application	NOUN
ap-1851	116	13	to	to	ADP
ap-1851	116	14	the	the	DET
ap-1851	116	15	case	case	NOUN
ap-1851	116	16	of	of	ADP
ap-1851	116	17	quantum	quantum	NOUN
ap-1851	116	18	graphs	graph	NOUN
ap-1851	116	19	see	see	VERB
ap-1851	116	20	[	[	X
ap-1851	116	21	11	11	NUM
ap-1851	116	22	,	,	PUNCT
ap-1851	116	23	15	15	NUM
ap-1851	116	24	,	,	PUNCT
ap-1851	116	25	16	16	NUM
ap-1851	116	26	]	]	PUNCT
ap-1851	116	27	)	)	PUNCT
ap-1851	116	28	.	.	PUNCT
ap-1851	117	1	resonances	resonance	NOUN
ap-1851	117	2	in	in	ADP
ap-1851	117	3	this	this	DET
ap-1851	117	4	approach	approach	NOUN
ap-1851	117	5	become	become	VERB
ap-1851	117	6	eigenvalues	eigenvalue	NOUN
ap-1851	117	7	of	of	ADP
ap-1851	117	8	the	the	DET
ap-1851	117	9	non	non	ADJ
ap-1851	117	10	-	-	ADJ
ap-1851	117	11	selfadjoint	selfadjoint	ADJ
ap-1851	117	12	operator	operator	NOUN
ap-1851	118	1	hθ	hθ	NOUN
ap-1851	118	2	=	=	SYM
ap-1851	118	3	uθhu−1	uθhu−1	PROPN
ap-1851	118	4	θ	θ	PROPN
ap-1851	118	5	obtained	obtain	VERB
ap-1851	118	6	by	by	ADP
ap-1851	118	7	scaling	scale	VERB
ap-1851	118	8	the	the	DET
ap-1851	118	9	hamiltonian	hamiltonian	NOUN
ap-1851	118	10	outside	outside	ADP
ap-1851	118	11	a	a	DET
ap-1851	118	12	compact	compact	ADJ
ap-1851	118	13	region	region	NOUN
ap-1851	118	14	with	with	ADP
ap-1851	118	15	the	the	DET
ap-1851	118	16	scaling	scale	VERB
ap-1851	118	17	parameter	parameter	NOUN
ap-1851	118	18	taking	take	VERB
ap-1851	118	19	a	a	DET
ap-1851	118	20	complex	complex	ADJ
ap-1851	118	21	value	value	NOUN
ap-1851	118	22	eθ	eθ	PROPN
ap-1851	118	23	;	;	PUNCT
ap-1851	118	24	if	if	SCONJ
ap-1851	118	25	i	i	PRON
ap-1851	118	26	m	m	VERB
ap-1851	118	27	θ	θ	NOUN
ap-1851	118	28	is	be	AUX
ap-1851	118	29	large	large	ADJ
ap-1851	118	30	enough	enough	ADV
ap-1851	118	31	,	,	PUNCT
ap-1851	118	32	the	the	DET
ap-1851	118	33	rotated	rotate	VERB
ap-1851	118	34	essential	essential	ADJ
ap-1851	118	35	spectrum	spectrum	NOUN
ap-1851	118	36	reveals	reveal	VERB
ap-1851	118	37	a	a	DET
ap-1851	118	38	part	part	NOUN
ap-1851	118	39	of	of	ADP
ap-1851	118	40	the	the	DET
ap-1851	118	41	‘	'	PUNCT
ap-1851	118	42	unphysical	unphysical	ADJ
ap-1851	118	43	’	'	PUNCT
ap-1851	118	44	sheet	sheet	NOUN
ap-1851	118	45	with	with	ADP
ap-1851	118	46	the	the	DET
ap-1851	118	47	poles	pole	NOUN
ap-1851	118	48	being	be	AUX
ap-1851	118	49	now	now	ADV
ap-1851	118	50	true	true	ADJ
ap-1851	118	51	eigenvalues	eigenvalue	NOUN
ap-1851	118	52	corresponding	correspond	VERB
ap-1851	118	53	to	to	ADP
ap-1851	118	54	square	square	ADJ
ap-1851	118	55	integrable	integrable	ADJ
ap-1851	118	56	eigenfunctions	eigenfunction	NOUN
ap-1851	118	57	.	.	PUNCT
ap-1851	119	1	in	in	ADP
ap-1851	119	2	the	the	DET
ap-1851	119	3	present	present	ADJ
ap-1851	119	4	case	case	NOUN
ap-1851	119	5	we	we	PRON
ap-1851	119	6	identify	identify	VERB
ap-1851	119	7	,	,	PUNCT
ap-1851	119	8	by	by	ADP
ap-1851	119	9	analogy	analogy	NOUN
ap-1851	119	10	with	with	ADP
ap-1851	119	11	the	the	DET
ap-1851	119	12	quantum	quantum	NOUN
ap-1851	119	13	-	-	PUNCT
ap-1851	119	14	graph	graph	NOUN
ap-1851	119	15	situation	situation	NOUN
ap-1851	119	16	mentioned	mention	VERB
ap-1851	119	17	above	above	ADV
ap-1851	119	18	,	,	PUNCT
ap-1851	119	19	the	the	DET
ap-1851	119	20	exterior	exterior	ADJ
ap-1851	119	21	part	part	NOUN
ap-1851	119	22	of	of	ADP
ap-1851	119	23	γ	γ	NOUN
ap-1851	119	24	with	with	ADP
ap-1851	119	25	the	the	DET
ap-1851	119	26	leads	lead	NOUN
ap-1851	119	27	,	,	PUNCT
ap-1851	119	28	and	and	CCONJ
ap-1851	119	29	scale	scale	VERB
ap-1851	119	30	the	the	DET
ap-1851	119	31	wave	wave	NOUN
ap-1851	119	32	function	function	NOUN
ap-1851	119	33	at	at	ADP
ap-1851	119	34	each	each	PRON
ap-1851	119	35	them	they	PRON
ap-1851	119	36	using	use	VERB
ap-1851	119	37	the	the	DET
ap-1851	119	38	transformation	transformation	NOUN
ap-1851	119	39	(	(	PUNCT
ap-1851	119	40	uθf)(x	uθf)(x	NOUN
ap-1851	119	41	)	)	PUNCT
ap-1851	119	42	=	=	SYM
ap-1851	120	1	eθ/2f(eθx	eθ/2f(eθx	NOUN
ap-1851	120	2	)	)	PUNCT
ap-1851	120	3	,	,	PUNCT
ap-1851	120	4	which	which	PRON
ap-1851	120	5	is	be	AUX
ap-1851	120	6	,	,	PUNCT
ap-1851	120	7	of	of	ADP
ap-1851	120	8	course	course	NOUN
ap-1851	120	9	,	,	PUNCT
ap-1851	120	10	unitary	unitary	ADJ
ap-1851	120	11	for	for	ADP
ap-1851	120	12	real	real	ADJ
ap-1851	120	13	θ	θ	NOUN
ap-1851	120	14	,	,	PUNCT
ap-1851	120	15	while	while	SCONJ
ap-1851	120	16	for	for	ADP
ap-1851	120	17	a	a	DET
ap-1851	120	18	complex	complex	ADJ
ap-1851	120	19	θ	θ	NOUN
ap-1851	120	20	it	it	PRON
ap-1851	120	21	leads	lead	VERB
ap-1851	120	22	to	to	ADP
ap-1851	120	23	the	the	DET
ap-1851	120	24	desired	desire	VERB
ap-1851	120	25	rotation	rotation	NOUN
ap-1851	120	26	of	of	ADP
ap-1851	120	27	the	the	DET
ap-1851	120	28	essential	essential	ADJ
ap-1851	120	29	spectrum	spectrum	NOUN
ap-1851	120	30	.	.	PUNCT
ap-1851	121	1	to	to	PART
ap-1851	121	2	use	use	VERB
ap-1851	121	3	it	it	PRON
ap-1851	121	4	,	,	PUNCT
ap-1851	121	5	we	we	PRON
ap-1851	121	6	first	first	ADV
ap-1851	121	7	state	state	VERB
ap-1851	121	8	a	a	DET
ap-1851	121	9	useful	useful	ADJ
ap-1851	121	10	auxiliary	auxiliary	ADJ
ap-1851	121	11	result	result	NOUN
ap-1851	121	12	.	.	PUNCT
ap-1851	122	1	lemma	lemma	PROPN
ap-1851	122	2	3.3	3.3	NUM
ap-1851	122	3	.	.	PUNCT
ap-1851	123	1	let	let	VERB
ap-1851	123	2	h|ω	h|ω	NOUN
ap-1851	123	3	be	be	AUX
ap-1851	123	4	the	the	DET
ap-1851	123	5	restriction	restriction	NOUN
ap-1851	123	6	of	of	ADP
ap-1851	123	7	an	an	DET
ap-1851	123	8	admissible	admissible	ADJ
ap-1851	123	9	hamiltonian	hamiltonian	NOUN
ap-1851	123	10	to	to	ADP
ap-1851	123	11	ω	ω	NUM
ap-1851	123	12	and	and	CCONJ
ap-1851	123	13	suppose	suppose	VERB
ap-1851	123	14	that	that	SCONJ
ap-1851	123	15	f	f	PROPN
ap-1851	123	16	(	(	PUNCT
ap-1851	123	17	·	·	PUNCT
ap-1851	123	18	,	,	PUNCT
ap-1851	123	19	k	k	NOUN
ap-1851	123	20	)	)	PUNCT
ap-1851	123	21	satisfies	satisfie	NOUN
ap-1851	123	22	h|ωf(x	h|ωf(x	PROPN
ap-1851	123	23	,	,	PUNCT
ap-1851	123	24	k	k	NOUN
ap-1851	123	25	)	)	PUNCT
ap-1851	123	26	=	=	SYM
ap-1851	123	27	k2f(x	k2f(x	PROPN
ap-1851	123	28	,	,	PUNCT
ap-1851	123	29	k	k	NOUN
ap-1851	123	30	)	)	PUNCT
ap-1851	123	31	for	for	ADP
ap-1851	123	32	k2	k2	PROPN
ap-1851	123	33	6∈	6∈	PROPN
ap-1851	123	34	σ(h0	σ(h0	PROPN
ap-1851	123	35	)	)	PUNCT
ap-1851	123	36	,	,	PUNCT
ap-1851	123	37	then	then	ADV
ap-1851	123	38	it	it	PRON
ap-1851	123	39	can	can	AUX
ap-1851	123	40	be	be	AUX
ap-1851	123	41	written	write	VERB
ap-1851	123	42	as	as	ADP
ap-1851	123	43	a	a	DET
ap-1851	123	44	particular	particular	ADJ
ap-1851	123	45	linear	linear	ADJ
ap-1851	123	46	combination	combination	NOUN
ap-1851	123	47	of	of	ADP
ap-1851	123	48	green	green	ADJ
ap-1851	123	49	functions	function	NOUN
ap-1851	123	50	of	of	ADP
ap-1851	123	51	h0	h0	NOUN
ap-1851	123	52	,	,	PUNCT
ap-1851	123	53	namely	namely	ADV
ap-1851	123	54	f(x	f(x	PROPN
ap-1851	123	55	,	,	PUNCT
ap-1851	123	56	k	k	NOUN
ap-1851	123	57	)	)	PUNCT
ap-1851	123	58	=	=	SYM
ap-1851	124	1	n∑	n∑	NOUN
ap-1851	124	2	j=1	j=1	PROPN
ap-1851	124	3	cjg(x	cjg(x	PROPN
ap-1851	124	4	,	,	PUNCT
ap-1851	124	5	xj	xj	PROPN
ap-1851	124	6	;	;	PUNCT
ap-1851	124	7	k	k	X
ap-1851	124	8	)	)	PUNCT
ap-1851	124	9	.	.	PUNCT
ap-1851	125	1	proof	proof	NOUN
ap-1851	125	2	.	.	PUNCT
ap-1851	126	1	the	the	DET
ap-1851	126	2	claim	claim	NOUN
ap-1851	126	3	is	be	AUX
ap-1851	126	4	a	a	DET
ap-1851	126	5	straightforward	straightforward	ADJ
ap-1851	126	6	generalization	generalization	NOUN
ap-1851	126	7	of	of	ADP
ap-1851	126	8	lemma	lemma	PROPN
ap-1851	126	9	2.2	2.2	NUM
ap-1851	126	10	in	in	ADP
ap-1851	126	11	[	[	X
ap-1851	126	12	25	25	NUM
ap-1851	126	13	]	]	PUNCT
ap-1851	126	14	to	to	ADP
ap-1851	126	15	the	the	DET
ap-1851	126	16	situation	situation	NOUN
ap-1851	126	17	where	where	SCONJ
ap-1851	126	18	n	n	X
ap-1851	126	19	>	>	X
ap-1851	126	20	2	2	NUM
ap-1851	126	21	and	and	CCONJ
ap-1851	126	22	more	more	ADJ
ap-1851	126	23	general	general	ADJ
ap-1851	126	24	couplings	coupling	NOUN
ap-1851	126	25	are	be	AUX
ap-1851	126	26	imposed	impose	VERB
ap-1851	126	27	at	at	ADP
ap-1851	126	28	the	the	DET
ap-1851	126	29	junctions	junction	NOUN
ap-1851	126	30	.	.	PUNCT
ap-1851	127	1	suppose	suppose	VERB
ap-1851	127	2	that	that	SCONJ
ap-1851	127	3	k	k	PROPN
ap-1851	127	4	is	be	AUX
ap-1851	127	5	not	not	PART
ap-1851	127	6	an	an	DET
ap-1851	127	7	eigenvalue	eigenvalue	NOUN
ap-1851	127	8	of	of	ADP
ap-1851	127	9	h0	h0	PROPN
ap-1851	127	10	.	.	PUNCT
ap-1851	128	1	the	the	DET
ap-1851	128	2	green	green	ADJ
ap-1851	128	3	functions	function	NOUN
ap-1851	128	4	with	with	ADP
ap-1851	128	5	one	one	NUM
ap-1851	128	6	argument	argument	NOUN
ap-1851	128	7	fixed	fix	VERB
ap-1851	128	8	at	at	ADP
ap-1851	128	9	different	different	ADJ
ap-1851	128	10	points	point	NOUN
ap-1851	128	11	xj	xj	NOUN
ap-1851	128	12	are	be	AUX
ap-1851	128	13	clearly	clearly	ADV
ap-1851	128	14	linearly	linearly	ADV
ap-1851	128	15	independent	independent	ADJ
ap-1851	128	16	,	,	PUNCT
ap-1851	128	17	hence	hence	ADV
ap-1851	128	18	domh	domh	NOUN
ap-1851	128	19	′∗	′∗	X
ap-1851	129	1	=	=	PUNCT
ap-1851	129	2	w	w	PROPN
ap-1851	129	3	2,2(ω	2,2(ω	NUM
ap-1851	129	4	)	)	PUNCT
ap-1851	129	5	⊕	⊕	PROPN
ap-1851	129	6	(	(	PUNCT
ap-1851	129	7	span{g(x	span{g(x	PROPN
ap-1851	129	8	,	,	PUNCT
ap-1851	129	9	xj	xj	PROPN
ap-1851	129	10	;	;	PUNCT
ap-1851	129	11	k)}nj=1	k)}nj=1	PROPN
ap-1851	129	12	)	)	PUNCT
ap-1851	129	13	,	,	PUNCT
ap-1851	129	14	and	and	CCONJ
ap-1851	129	15	without	without	ADP
ap-1851	129	16	loss	loss	NOUN
ap-1851	129	17	of	of	ADP
ap-1851	129	18	generality	generality	NOUN
ap-1851	129	19	one	one	PRON
ap-1851	129	20	can	can	AUX
ap-1851	129	21	write	write	VERB
ap-1851	129	22	f(x	f(x	PROPN
ap-1851	129	23	,	,	PUNCT
ap-1851	129	24	k	k	NOUN
ap-1851	129	25	)	)	PUNCT
ap-1851	130	1	=	=	NOUN
ap-1851	130	2	∑n	∑n	PROPN
ap-1851	130	3	j=1	j=1	PROPN
ap-1851	130	4	cjg(x	cjg(x	PROPN
ap-1851	130	5	,	,	PUNCT
ap-1851	130	6	xj	xj	PROPN
ap-1851	130	7	;	;	PUNCT
ap-1851	130	8	k)+g(x	k)+g(x	PROPN
ap-1851	130	9	)	)	PUNCT
ap-1851	130	10	with	with	ADP
ap-1851	130	11	g	g	PROPN
ap-1851	130	12	∈w	∈w	PROPN
ap-1851	130	13	2,2(ω	2,2(ω	NUM
ap-1851	130	14	)	)	PUNCT
ap-1851	130	15	.	.	PUNCT
ap-1851	131	1	however	however	ADV
ap-1851	131	2	,	,	PUNCT
ap-1851	131	3	then	then	ADV
ap-1851	131	4	we	we	PRON
ap-1851	131	5	would	would	AUX
ap-1851	131	6	have	have	AUX
ap-1851	131	7	h|ωg(x	h|ωg(x	VERB
ap-1851	131	8	)	)	PUNCT
ap-1851	132	1	=	=	PUNCT
ap-1851	132	2	h0g(x	h0g(x	NOUN
ap-1851	132	3	)	)	PUNCT
ap-1851	132	4	=	=	SYM
ap-1851	132	5	k2g(x	k2g(x	PROPN
ap-1851	132	6	)	)	PUNCT
ap-1851	132	7	for	for	ADP
ap-1851	132	8	x	x	SYM
ap-1851	132	9	6=	6=	PROPN
ap-1851	132	10	xj	xj	PROPN
ap-1851	132	11	,	,	PUNCT
ap-1851	132	12	and	and	CCONJ
ap-1851	132	13	since	since	SCONJ
ap-1851	132	14	k2	k2	PROPN
ap-1851	132	15	6∈	6∈	PROPN
ap-1851	132	16	σ(h0	σ(h0	PROPN
ap-1851	132	17	)	)	PUNCT
ap-1851	132	18	and	and	CCONJ
ap-1851	132	19	g	g	PROPN
ap-1851	132	20	∈	∈	PROPN
ap-1851	132	21	w	w	ADP
ap-1851	132	22	2,2(ω	2,2(ω	NUM
ap-1851	132	23	)	)	PUNCT
ap-1851	132	24	by	by	ADP
ap-1851	132	25	assumption	assumption	NOUN
ap-1851	132	26	,	,	PUNCT
ap-1851	132	27	it	it	PRON
ap-1851	132	28	follows	follow	VERB
ap-1851	132	29	that	that	SCONJ
ap-1851	132	30	g	g	PROPN
ap-1851	132	31	=	=	SYM
ap-1851	132	32	0	0	PROPN
ap-1851	132	33	.	.	PUNCT
ap-1851	132	34	theorem	theorem	VERB
ap-1851	132	35	3.4	3.4	NUM
ap-1851	132	36	.	.	PUNCT
ap-1851	133	1	in	in	ADP
ap-1851	133	2	the	the	DET
ap-1851	133	3	described	describe	VERB
ap-1851	133	4	setting	setting	NOUN
ap-1851	133	5	,	,	PUNCT
ap-1851	133	6	the	the	DET
ap-1851	133	7	hedgehog	hedgehog	NOUN
ap-1851	133	8	system	system	NOUN
ap-1851	133	9	has	have	VERB
ap-1851	133	10	a	a	DET
ap-1851	133	11	scattering	scatter	VERB
ap-1851	133	12	resonance	resonance	NOUN
ap-1851	133	13	at	at	ADP
ap-1851	133	14	k0	k0	PROPN
ap-1851	133	15	with	with	ADP
ap-1851	133	16	i	i	PROPN
ap-1851	133	17	m	m	PROPN
ap-1851	133	18	k0	k0	PROPN
ap-1851	133	19	<	<	X
ap-1851	133	20	0	0	PROPN
ap-1851	133	21	and	and	CCONJ
ap-1851	133	22	k2	k2	PROPN
ap-1851	133	23	0	0	PROPN
ap-1851	134	1	6∈	6∈	NOUN
ap-1851	134	2	r	r	NOUN
ap-1851	134	3	iff	iff	PROPN
ap-1851	134	4	there	there	PRON
ap-1851	134	5	is	be	VERB
ap-1851	134	6	a	a	DET
ap-1851	134	7	resolvent	resolvent	ADJ
ap-1851	134	8	resonance	resonance	NOUN
ap-1851	134	9	at	at	ADP
ap-1851	134	10	k0	k0	PROPN
ap-1851	134	11	.	.	PUNCT
ap-1851	135	1	algebraic	algebraic	PROPN
ap-1851	135	2	multiplicities	multiplicity	NOUN
ap-1851	135	3	of	of	ADP
ap-1851	135	4	the	the	DET
ap-1851	135	5	resonances	resonance	NOUN
ap-1851	135	6	defined	define	VERB
ap-1851	135	7	in	in	ADP
ap-1851	135	8	both	both	DET
ap-1851	135	9	ways	way	NOUN
ap-1851	135	10	coincide	coincide	NOUN
ap-1851	135	11	.	.	PUNCT
ap-1851	136	1	proof	proof	NOUN
ap-1851	136	2	.	.	PUNCT
ap-1851	137	1	consider	consider	VERB
ap-1851	137	2	first	first	ADV
ap-1851	137	3	the	the	DET
ap-1851	137	4	scattering	scatter	VERB
ap-1851	137	5	resonances	resonance	NOUN
ap-1851	137	6	.	.	PUNCT
ap-1851	138	1	the	the	DET
ap-1851	138	2	starting	starting	NOUN
ap-1851	138	3	point	point	NOUN
ap-1851	138	4	is	be	AUX
ap-1851	138	5	the	the	DET
ap-1851	138	6	generalized	generalized	ADJ
ap-1851	138	7	eigenfunction	eigenfunction	NOUN
ap-1851	138	8	describing	describe	VERB
ap-1851	138	9	the	the	DET
ap-1851	138	10	scattering	scattering	NOUN
ap-1851	138	11	at	at	ADP
ap-1851	138	12	energy	energy	NOUN
ap-1851	138	13	k2	k2	NOUN
ap-1851	138	14	and	and	CCONJ
ap-1851	138	15	its	its	PRON
ap-1851	138	16	analytical	analytical	ADJ
ap-1851	138	17	continuation	continuation	NOUN
ap-1851	138	18	to	to	ADP
ap-1851	138	19	the	the	DET
ap-1851	138	20	lower	low	ADJ
ap-1851	138	21	complex	complex	ADJ
ap-1851	138	22	halfplane	halfplane	NOUN
ap-1851	138	23	.	.	PUNCT
ap-1851	139	1	from	from	ADP
ap-1851	139	2	the	the	DET
ap-1851	139	3	previous	previous	ADJ
ap-1851	139	4	lemma	lemma	PROPN
ap-1851	139	5	we	we	PRON
ap-1851	139	6	know	know	VERB
ap-1851	139	7	that	that	SCONJ
ap-1851	139	8	for	for	ADP
ap-1851	139	9	k2	k2	PROPN
ap-1851	139	10	6∈	6∈	PROPN
ap-1851	139	11	σ(h0	σ(h0	PROPN
ap-1851	139	12	)	)	PUNCT
ap-1851	139	13	the	the	DET
ap-1851	139	14	restriction	restriction	NOUN
ap-1851	139	15	of	of	ADP
ap-1851	139	16	the	the	DET
ap-1851	139	17	appropriate	appropriate	ADJ
ap-1851	139	18	schrödinger	schrödinger	ADJ
ap-1851	139	19	equation	equation	NOUN
ap-1851	139	20	solution	solution	NOUN
ap-1851	139	21	to	to	ADP
ap-1851	139	22	the	the	DET
ap-1851	139	23	manifold	manifold	NOUN
ap-1851	139	24	is	be	AUX
ap-1851	139	25	a	a	DET
ap-1851	139	26	linear	linear	ADJ
ap-1851	139	27	combination	combination	NOUN
ap-1851	139	28	of	of	ADP
ap-1851	139	29	at	at	ADP
ap-1851	139	30	most	most	ADJ
ap-1851	139	31	n	n	CCONJ
ap-1851	139	32	green	green	ADJ
ap-1851	139	33	functions	function	NOUN
ap-1851	139	34	;	;	PUNCT
ap-1851	139	35	we	we	PRON
ap-1851	139	36	denote	denote	VERB
ap-1851	139	37	the	the	DET
ap-1851	139	38	corresponding	correspond	VERB
ap-1851	139	39	vector	vector	NOUN
ap-1851	139	40	of	of	ADP
ap-1851	139	41	coefficients	coefficient	NOUN
ap-1851	139	42	by	by	ADP
ap-1851	139	43	c.	c.	PROPN
ap-1851	139	44	the	the	DET
ap-1851	139	45	relation	relation	NOUN
ap-1851	139	46	between	between	ADP
ap-1851	139	47	these	these	DET
ap-1851	139	48	coefficients	coefficient	NOUN
ap-1851	139	49	and	and	CCONJ
ap-1851	139	50	amplitudes	amplitude	NOUN
ap-1851	139	51	of	of	ADP
ap-1851	139	52	the	the	DET
ap-1851	139	53	outgoing	outgoing	ADJ
ap-1851	139	54	and	and	CCONJ
ap-1851	139	55	incoming	incoming	ADJ
ap-1851	139	56	wave	wave	NOUN
ap-1851	139	57	is	be	AUX
ap-1851	139	58	given	give	VERB
ap-1851	139	59	by	by	ADP
ap-1851	139	60	(	(	PUNCT
ap-1851	139	61	1	1	NUM
ap-1851	139	62	)	)	PUNCT
ap-1851	139	63	.	.	PUNCT
ap-1851	140	1	using	use	VERB
ap-1851	140	2	a	a	PRON
ap-1851	140	3	as	as	ADP
ap-1851	140	4	a	a	DET
ap-1851	140	5	shortcut	shortcut	NOUN
ap-1851	140	6	for	for	ADP
ap-1851	140	7	the	the	DET
ap-1851	140	8	vector	vector	NOUN
ap-1851	140	9	of	of	ADP
ap-1851	140	10	the	the	DET
ap-1851	140	11	amplitudes	amplitude	NOUN
ap-1851	140	12	of	of	ADP
ap-1851	140	13	the	the	DET
ap-1851	140	14	incoming	incoming	ADJ
ap-1851	140	15	waves	wave	NOUN
ap-1851	140	16	,	,	PUNCT
ap-1851	140	17	(	(	PUNCT
ap-1851	140	18	a1(k	a1(k	NOUN
ap-1851	140	19	)	)	PUNCT
ap-1851	140	20	,	,	PUNCT
ap-1851	140	21	.	.	PUNCT
ap-1851	140	22	.	.	PUNCT
ap-1851	141	1	.	.	PUNCT
ap-1851	142	1	,	,	PUNCT
ap-1851	142	2	am	be	AUX
ap-1851	142	3	(	(	PUNCT
ap-1851	142	4	k	k	NOUN
ap-1851	142	5	)	)	PUNCT
ap-1851	142	6	)	)	PUNCT
ap-1851	143	1	t	t	PROPN
ap-1851	143	2	,	,	PUNCT
ap-1851	143	3	and	and	CCONJ
ap-1851	143	4	similarly	similarly	ADV
ap-1851	143	5	b	b	X
ap-1851	143	6	for	for	ADP
ap-1851	143	7	the	the	DET
ap-1851	143	8	vector	vector	NOUN
ap-1851	143	9	of	of	ADP
ap-1851	143	10	the	the	DET
ap-1851	143	11	amplitudes	amplitude	NOUN
ap-1851	143	12	of	of	ADP
ap-1851	143	13	the	the	DET
ap-1851	143	14	outgoing	outgoing	ADJ
ap-1851	143	15	waves	wave	NOUN
ap-1851	143	16	one	one	NUM
ap-1851	143	17	obtains	obtain	VERB
ap-1851	143	18	in	in	ADP
ap-1851	143	19	general	general	ADJ
ap-1851	143	20	system	system	NOUN
ap-1851	143	21	of	of	ADP
ap-1851	143	22	equations	equation	NOUN
ap-1851	143	23	a(k)a	a(k)a	PROPN
ap-1851	144	1	+	+	ADP
ap-1851	144	2	b(k)b	b(k)b	PROPN
ap-1851	144	3	+	+	CCONJ
ap-1851	144	4	c(k)c	c(k)c	PROPN
ap-1851	144	5	=	=	SYM
ap-1851	144	6	0	0	NUM
ap-1851	144	7	,	,	PUNCT
ap-1851	144	8	(	(	PUNCT
ap-1851	144	9	4	4	NUM
ap-1851	144	10	)	)	PUNCT
ap-1851	144	11	in	in	ADP
ap-1851	144	12	which	which	PRON
ap-1851	144	13	a	a	PRON
ap-1851	144	14	and	and	CCONJ
ap-1851	144	15	b	b	NOUN
ap-1851	144	16	are	be	AUX
ap-1851	144	17	(	(	PUNCT
ap-1851	144	18	n+m)×m	n+m)×m	ADJ
ap-1851	144	19	matrices	matrix	NOUN
ap-1851	144	20	and	and	CCONJ
ap-1851	144	21	c	c	NOUN
ap-1851	144	22	is	be	AUX
ap-1851	144	23	(	(	PUNCT
ap-1851	144	24	n+m)×	n+m)×	PROPN
ap-1851	144	25	n	n	PRON
ap-1851	144	26	matrix	matrix	VERB
ap-1851	144	27	the	the	DET
ap-1851	144	28	elements	element	NOUN
ap-1851	144	29	of	of	ADP
ap-1851	144	30	which	which	PRON
ap-1851	144	31	are	be	AUX
ap-1851	144	32	exponentials	exponential	NOUN
ap-1851	144	33	and	and	CCONJ
ap-1851	144	34	green	green	ADJ
ap-1851	144	35	functions	function	NOUN
ap-1851	144	36	,	,	PUNCT
ap-1851	144	37	regularized	regularize	VERB
ap-1851	144	38	if	if	SCONJ
ap-1851	144	39	needed	need	VERB
ap-1851	144	40	—	—	PUNCT
ap-1851	144	41	recall	recall	VERB
ap-1851	144	42	that	that	SCONJ
ap-1851	144	43	n	n	X
ap-1851	144	44	is	be	AUX
ap-1851	144	45	the	the	DET
ap-1851	144	46	number	number	NOUN
ap-1851	144	47	of	of	ADP
ap-1851	144	48	internal	internal	ADJ
ap-1851	144	49	parameters	parameter	NOUN
ap-1851	144	50	associated	associate	VERB
ap-1851	144	51	with	with	ADP
ap-1851	144	52	the	the	DET
ap-1851	144	53	junctions	junction	NOUN
ap-1851	144	54	and	and	CCONJ
ap-1851	144	55	m	m	NOUN
ap-1851	144	56	is	be	AUX
ap-1851	144	57	the	the	DET
ap-1851	144	58	number	number	NOUN
ap-1851	144	59	of	of	ADP
ap-1851	144	60	the	the	DET
ap-1851	144	61	leads	lead	NOUN
ap-1851	144	62	.	.	PUNCT
ap-1851	145	1	what	what	PRON
ap-1851	145	2	is	be	AUX
ap-1851	145	3	important	important	ADJ
ap-1851	145	4	that	that	SCONJ
ap-1851	145	5	all	all	DET
ap-1851	145	6	the	the	DET
ap-1851	145	7	entries	entry	NOUN
ap-1851	145	8	of	of	ADP
ap-1851	145	9	the	the	DET
ap-1851	145	10	mentioned	mention	VERB
ap-1851	145	11	matrices	matrix	NOUN
ap-1851	145	12	allow	allow	VERB
ap-1851	145	13	for	for	ADP
ap-1851	145	14	an	an	DET
ap-1851	145	15	analytical	analytical	ADJ
ap-1851	145	16	continuation	continuation	NOUN
ap-1851	145	17	which	which	PRON
ap-1851	145	18	makes	make	VERB
ap-1851	145	19	it	it	PRON
ap-1851	145	20	possible	possible	ADJ
ap-1851	145	21	to	to	PART
ap-1851	145	22	ask	ask	VERB
ap-1851	145	23	for	for	ADP
ap-1851	145	24	solution	solution	NOUN
ap-1851	145	25	of	of	ADP
ap-1851	145	26	equations	equation	NOUN
ap-1851	145	27	(	(	PUNCT
ap-1851	145	28	4	4	NUM
ap-1851	145	29	)	)	PUNCT
ap-1851	145	30	for	for	ADP
ap-1851	145	31	k	k	PROPN
ap-1851	145	32	=	=	PROPN
ap-1851	145	33	k0	k0	PROPN
ap-1851	145	34	from	from	ADP
ap-1851	145	35	the	the	DET
ap-1851	145	36	open	open	ADJ
ap-1851	145	37	lower	low	ADJ
ap-1851	145	38	complex	complex	ADJ
ap-1851	145	39	halfplane	halfplane	NOUN
ap-1851	145	40	.	.	PUNCT
ap-1851	146	1	it	it	PRON
ap-1851	146	2	is	be	AUX
ap-1851	146	3	obvious	obvious	ADJ
ap-1851	146	4	that	that	SCONJ
ap-1851	146	5	for	for	ADP
ap-1851	146	6	k2	k2	PROPN
ap-1851	146	7	0	0	NUM
ap-1851	146	8	6∈	6∈	NOUN
ap-1851	146	9	r	r	NOUN
ap-1851	146	10	the	the	DET
ap-1851	146	11	columns	column	NOUN
ap-1851	146	12	of	of	ADP
ap-1851	146	13	c(k0	c(k0	NOUN
ap-1851	146	14	)	)	PUNCT
ap-1851	146	15	have	have	VERB
ap-1851	146	16	to	to	PART
ap-1851	146	17	be	be	AUX
ap-1851	146	18	linearly	linearly	ADV
ap-1851	146	19	independent	independent	ADJ
ap-1851	146	20	;	;	PUNCT
ap-1851	146	21	otherwise	otherwise	ADV
ap-1851	146	22	k2	k2	PROPN
ap-1851	146	23	0	0	NUM
ap-1851	146	24	would	would	AUX
ap-1851	146	25	be	be	AUX
ap-1851	146	26	an	an	DET
ap-1851	146	27	eigenvalue	eigenvalue	NOUN
ap-1851	146	28	of	of	ADP
ap-1851	146	29	h	h	NOUN
ap-1851	146	30	with	with	ADP
ap-1851	146	31	an	an	DET
ap-1851	146	32	eigenfunction	eigenfunction	NOUN
ap-1851	146	33	supported	support	VERB
ap-1851	146	34	on	on	ADP
ap-1851	146	35	the	the	DET
ap-1851	146	36	manifold	manifold	ADJ
ap-1851	146	37	ω	ω	PROPN
ap-1851	146	38	only	only	ADV
ap-1851	146	39	.	.	PUNCT
ap-1851	147	1	hence	hence	ADV
ap-1851	147	2	there	there	PRON
ap-1851	147	3	are	be	VERB
ap-1851	147	4	n	n	ADV
ap-1851	147	5	linearly	linearly	ADV
ap-1851	147	6	independent	independent	ADJ
ap-1851	147	7	rows	row	NOUN
ap-1851	147	8	of	of	ADP
ap-1851	147	9	c(k0	c(k0	NOUN
ap-1851	147	10	)	)	PUNCT
ap-1851	147	11	and	and	CCONJ
ap-1851	147	12	after	after	ADP
ap-1851	147	13	a	a	DET
ap-1851	147	14	rearrangement	rearrangement	NOUN
ap-1851	147	15	in	in	ADP
ap-1851	147	16	equations	equation	NOUN
ap-1851	147	17	(	(	PUNCT
ap-1851	147	18	4	4	X
ap-1851	147	19	)	)	PUNCT
ap-1851	147	20	one	one	NOUN
ap-1851	147	21	is	be	AUX
ap-1851	147	22	able	able	ADJ
ap-1851	147	23	to	to	PART
ap-1851	147	24	express	express	VERB
ap-1851	147	25	c	c	NOUN
ap-1851	147	26	from	from	ADP
ap-1851	147	27	the	the	DET
ap-1851	147	28	first	first	ADJ
ap-1851	147	29	n	n	PROPN
ap-1851	147	30	of	of	ADP
ap-1851	147	31	them	they	PRON
ap-1851	147	32	.	.	PUNCT
ap-1851	148	1	substituting	substitute	VERB
ap-1851	148	2	then	then	ADV
ap-1851	148	3	to	to	ADP
ap-1851	148	4	the	the	DET
ap-1851	148	5	remaining	remain	VERB
ap-1851	148	6	equations	equation	NOUN
ap-1851	148	7	one	one	PRON
ap-1851	148	8	can	can	AUX
ap-1851	148	9	rewrite	rewrite	VERB
ap-1851	148	10	them	they	PRON
ap-1851	148	11	in	in	ADP
ap-1851	148	12	the	the	DET
ap-1851	148	13	form	form	NOUN
ap-1851	148	14	ã(k0)a	ã(k0)a	ADJ
ap-1851	148	15	+	+	NOUN
ap-1851	148	16	b̃(k0)b	b̃(k0)b	PUNCT
ap-1851	148	17	=	=	SYM
ap-1851	148	18	0	0	NUM
ap-1851	148	19	(	(	PUNCT
ap-1851	148	20	5	5	NUM
ap-1851	148	21	)	)	PUNCT
ap-1851	148	22	with	with	ADP
ap-1851	148	23	ã(k0	ã(k0	NOUN
ap-1851	148	24	)	)	PUNCT
ap-1851	148	25	and	and	CCONJ
ap-1851	148	26	b̃(k0	b̃(k0	X
ap-1851	148	27	)	)	PUNCT
ap-1851	148	28	being	be	AUX
ap-1851	148	29	m	m	PROPN
ap-1851	148	30	×	×	NOUN
ap-1851	148	31	m	m	NOUN
ap-1851	148	32	matrices	matrice	VERB
ap-1851	148	33	the	the	DET
ap-1851	148	34	entries	entry	NOUN
ap-1851	148	35	of	of	ADP
ap-1851	148	36	which	which	PRON
ap-1851	148	37	are	be	AUX
ap-1851	148	38	rational	rational	ADJ
ap-1851	148	39	functions	function	NOUN
ap-1851	148	40	of	of	ADP
ap-1851	148	41	the	the	DET
ap-1851	148	42	entries	entry	NOUN
ap-1851	148	43	of	of	ADP
ap-1851	148	44	the	the	DET
ap-1851	148	45	previous	previous	ADJ
ap-1851	148	46	ones	one	NOUN
ap-1851	148	47	.	.	PUNCT
ap-1851	149	1	suppose	suppose	VERB
ap-1851	149	2	that	that	SCONJ
ap-1851	149	3	det	det	NOUN
ap-1851	149	4	ã(k0	ã(k0	NOUN
ap-1851	149	5	)	)	PUNCT
ap-1851	149	6	=	=	SYM
ap-1851	149	7	0	0	NUM
ap-1851	149	8	,	,	PUNCT
ap-1851	149	9	then	then	ADV
ap-1851	149	10	there	there	PRON
ap-1851	149	11	exists	exist	VERB
ap-1851	149	12	a	a	DET
ap-1851	149	13	solution	solution	NOUN
ap-1851	149	14	of	of	ADP
ap-1851	149	15	the	the	DET
ap-1851	149	16	previous	previous	ADJ
ap-1851	149	17	equation	equation	NOUN
ap-1851	149	18	with	with	ADP
ap-1851	149	19	b	b	PROPN
ap-1851	149	20	=	=	SYM
ap-1851	149	21	0	0	NUM
ap-1851	149	22	,	,	PUNCT
ap-1851	149	23	and	and	CCONJ
ap-1851	149	24	consequently	consequently	ADV
ap-1851	149	25	,	,	PUNCT
ap-1851	149	26	k0	k0	PROPN
ap-1851	149	27	is	be	AUX
ap-1851	149	28	an	an	DET
ap-1851	149	29	eigenvalue	eigenvalue	NOUN
ap-1851	149	30	of	of	ADP
ap-1851	149	31	h	h	NOUN
ap-1851	149	32	since	since	SCONJ
ap-1851	149	33	i	i	PRON
ap-1851	149	34	m	m	VERB
ap-1851	149	35	k0	k0	PROPN
ap-1851	149	36	<	<	X
ap-1851	149	37	0	0	PROPN
ap-1851	149	38	and	and	CCONJ
ap-1851	149	39	the	the	DET
ap-1851	149	40	corresponding	corresponding	ADJ
ap-1851	149	41	eigenfunction	eigenfunction	NOUN
ap-1851	149	42	belongs	belong	VERB
ap-1851	149	43	to	to	ADP
ap-1851	149	44	l2	l2	VERB
ap-1851	149	45	,	,	PUNCT
ap-1851	149	46	however	however	ADV
ap-1851	149	47	,	,	PUNCT
ap-1851	149	48	this	this	PRON
ap-1851	149	49	contradicts	contradict	VERB
ap-1851	149	50	to	to	ADP
ap-1851	149	51	the	the	DET
ap-1851	149	52	self	self	NOUN
ap-1851	149	53	-	-	PUNCT
ap-1851	149	54	adjointness	adjointness	NOUN
ap-1851	149	55	of	of	ADP
ap-1851	149	56	h.	h.	PROPN
ap-1851	150	1	now	now	ADV
ap-1851	150	2	it	it	PRON
ap-1851	150	3	is	be	AUX
ap-1851	150	4	sufficient	sufficient	ADJ
ap-1851	150	5	to	to	PART
ap-1851	150	6	note	note	VERB
ap-1851	150	7	that	that	SCONJ
ap-1851	150	8	the	the	DET
ap-1851	150	9	s	s	NOUN
ap-1851	150	10	-	-	NOUN
ap-1851	150	11	matrix	matrix	NOUN
ap-1851	150	12	analytically	analytically	ADV
ap-1851	150	13	continued	continue	VERB
ap-1851	150	14	to	to	PART
ap-1851	150	15	point	point	VERB
ap-1851	150	16	k0	k0	PROPN
ap-1851	150	17	equals	equal	VERB
ap-1851	150	18	−b̃(k0)−1ã(k0	−b̃(k0)−1ã(k0	NOUN
ap-1851	150	19	)	)	PUNCT
ap-1851	150	20	hence	hence	ADV
ap-1851	150	21	its	its	PRON
ap-1851	150	22	pole	pole	NOUN
ap-1851	150	23	singularities	singularity	NOUN
ap-1851	150	24	are	be	AUX
ap-1851	150	25	solutions	solution	NOUN
ap-1851	150	26	of	of	ADP
ap-1851	150	27	the	the	DET
ap-1851	150	28	equation	equation	NOUN
ap-1851	150	29	det	det	PROPN
ap-1851	150	30	b̃(k	b̃(k	PROPN
ap-1851	150	31	)	)	PUNCT
ap-1851	150	32	=	=	SYM
ap-1851	151	1	0	0	X
ap-1851	151	2	.	.	PUNCT
ap-1851	151	3	let	let	VERB
ap-1851	151	4	us	we	PRON
ap-1851	151	5	turn	turn	VERB
ap-1851	151	6	to	to	ADP
ap-1851	151	7	resolvent	resolvent	ADJ
ap-1851	151	8	resonances	resonance	NOUN
ap-1851	151	9	and	and	CCONJ
ap-1851	151	10	consider	consider	VERB
ap-1851	151	11	the	the	DET
ap-1851	151	12	exterior	exterior	ADJ
ap-1851	151	13	complex	complex	ADJ
ap-1851	151	14	scaling	scaling	NOUN
ap-1851	151	15	transformation	transformation	NOUN
ap-1851	151	16	uθ	uθ	ADP
ap-1851	151	17	with	with	ADP
ap-1851	151	18	i	i	PRON
ap-1851	151	19	m	m	VERB
ap-1851	151	20	θ	θ	NOUN
ap-1851	151	21	>	>	X
ap-1851	151	22	0	0	PUNCT
ap-1851	152	1	large	large	ADJ
ap-1851	152	2	enough	enough	ADV
ap-1851	152	3	to	to	PART
ap-1851	152	4	reveal	reveal	VERB
ap-1851	152	5	the	the	DET
ap-1851	152	6	sought	seek	VERB
ap-1851	152	7	pole	pole	NOUN
ap-1851	152	8	on	on	ADP
ap-1851	152	9	the	the	DET
ap-1851	152	10	second	second	ADJ
ap-1851	152	11	sheet	sheet	NOUN
ap-1851	152	12	of	of	ADP
ap-1851	152	13	the	the	DET
ap-1851	152	14	energy	energy	NOUN
ap-1851	152	15	surface	surface	NOUN
ap-1851	152	16	.	.	PUNCT
ap-1851	153	1	choosing	choose	VERB
ap-1851	153	2	arg	arg	NOUN
ap-1851	153	3	θ	θ	PROPN
ap-1851	153	4	>	>	PUNCT
ap-1851	153	5	arg	arg	PROPN
ap-1851	153	6	k0	k0	PROPN
ap-1851	153	7	we	we	PRON
ap-1851	153	8	find	find	VERB
ap-1851	153	9	that	that	SCONJ
ap-1851	153	10	the	the	DET
ap-1851	153	11	solution	solution	NOUN
ap-1851	153	12	aj(k)e−ikx	aj(k)e−ikx	NOUN
ap-1851	153	13	on	on	ADP
ap-1851	153	14	the	the	DET
ap-1851	153	15	j	j	PROPN
ap-1851	153	16	-	-	PUNCT
ap-1851	153	17	th	th	VERB
ap-1851	153	18	lead	lead	NOUN
ap-1851	153	19	,	,	PUNCT
ap-1851	153	20	analytically	analytically	ADV
ap-1851	153	21	continued	continue	VERB
ap-1851	153	22	to	to	ADP
ap-1851	153	23	the	the	DET
ap-1851	153	24	point	point	NOUN
ap-1851	153	25	k	k	PROPN
ap-1851	153	26	=	=	PROPN
ap-1851	153	27	k0	k0	PROPN
ap-1851	153	28	,	,	PUNCT
ap-1851	153	29	is	be	AUX
ap-1851	153	30	after	after	SCONJ
ap-1851	153	31	the	the	DET
ap-1851	153	32	transformation	transformation	NOUN
ap-1851	153	33	by	by	ADP
ap-1851	153	34	uθ	uθ	NOUN
ap-1851	153	35	exponentially	exponentially	ADV
ap-1851	153	36	increasing	increase	VERB
ap-1851	153	37	,	,	PUNCT
ap-1851	153	38	while	while	SCONJ
ap-1851	153	39	bj(k)eikx	bj(k)eikx	ADV
ap-1851	153	40	becomes	become	VERB
ap-1851	153	41	square	square	ADJ
ap-1851	153	42	integrable	integrable	ADJ
ap-1851	153	43	.	.	PUNCT
ap-1851	154	1	this	this	PRON
ap-1851	154	2	means	mean	VERB
ap-1851	154	3	that	that	SCONJ
ap-1851	154	4	solving	solve	VERB
ap-1851	154	5	in	in	ADP
ap-1851	154	6	l2	l2	NOUN
ap-1851	154	7	the	the	DET
ap-1851	154	8	eigenvalue	eigenvalue	PROPN
ap-1851	154	9	problem	problem	NOUN
ap-1851	154	10	for	for	ADP
ap-1851	154	11	the	the	DET
ap-1851	154	12	non	non	ADJ
ap-1851	154	13	-	-	ADJ
ap-1851	154	14	selfadjoint	selfadjoint	ADJ
ap-1851	154	15	operator	operator	NOUN
ap-1851	154	16	hθ	hθ	VERB
ap-1851	154	17	obtained	obtain	VERB
ap-1851	154	18	from	from	ADP
ap-1851	154	19	419	419	NUM
ap-1851	154	20	p.	p.	NOUN
ap-1851	154	21	exner	exner	NOUN
ap-1851	154	22	,	,	PUNCT
ap-1851	154	23	j.	j.	PROPN
ap-1851	154	24	lipovský	lipovský	PROPN
ap-1851	154	25	acta	acta	PROPN
ap-1851	154	26	polytechnica	polytechnica	PROPN
ap-1851	154	27	h	h	PROPN
ap-1851	154	28	=	=	SYM
ap-1851	154	29	hu	hu	PROPN
ap-1851	154	30	one	one	PRON
ap-1851	154	31	has	have	VERB
ap-1851	154	32	to	to	PART
ap-1851	154	33	find	find	VERB
ap-1851	154	34	solutions	solution	NOUN
ap-1851	154	35	of	of	ADP
ap-1851	154	36	(	(	PUNCT
ap-1851	154	37	5	5	NUM
ap-1851	154	38	)	)	PUNCT
ap-1851	154	39	with	with	ADP
ap-1851	154	40	a	a	DET
ap-1851	154	41	=	=	NOUN
ap-1851	154	42	0	0	NUM
ap-1851	154	43	.	.	PUNCT
ap-1851	155	1	this	this	PRON
ap-1851	155	2	leads	lead	VERB
ap-1851	155	3	again	again	ADV
ap-1851	155	4	to	to	ADP
ap-1851	155	5	the	the	DET
ap-1851	155	6	condition	condition	NOUN
ap-1851	155	7	det	det	PROPN
ap-1851	155	8	b̃(k	b̃(k	PROPN
ap-1851	155	9	)	)	PUNCT
ap-1851	155	10	=	=	SYM
ap-1851	155	11	0	0	NUM
ap-1851	155	12	thus	thus	ADV
ap-1851	155	13	concluding	conclude	VERB
ap-1851	155	14	the	the	DET
ap-1851	155	15	proof	proof	NOUN
ap-1851	155	16	.	.	PUNCT
ap-1851	156	1	remarks	remark	VERB
ap-1851	156	2	3.5	3.5	NUM
ap-1851	156	3	.	.	PUNCT
ap-1851	157	1	(	(	PUNCT
ap-1851	157	2	1	1	NUM
ap-1851	157	3	.	.	PUNCT
ap-1851	157	4	)	)	PUNCT
ap-1851	158	1	it	it	PRON
ap-1851	158	2	may	may	AUX
ap-1851	158	3	happen	happen	VERB
ap-1851	158	4	,	,	PUNCT
ap-1851	158	5	of	of	ADP
ap-1851	158	6	course	course	NOUN
ap-1851	158	7	,	,	PUNCT
ap-1851	158	8	that	that	SCONJ
ap-1851	158	9	at	at	ADP
ap-1851	158	10	some	some	DET
ap-1851	158	11	junctions	junction	NOUN
ap-1851	158	12	the	the	DET
ap-1851	158	13	leads	lead	NOUN
ap-1851	158	14	are	be	AUX
ap-1851	158	15	disconnected	disconnect	VERB
ap-1851	158	16	from	from	ADP
ap-1851	158	17	the	the	DET
ap-1851	158	18	manifold	manifold	NOUN
ap-1851	158	19	since	since	SCONJ
ap-1851	158	20	the	the	DET
ap-1851	158	21	conditions	condition	NOUN
ap-1851	158	22	(	(	PUNCT
ap-1851	158	23	1	1	X
ap-1851	158	24	)	)	PUNCT
ap-1851	158	25	are	be	AUX
ap-1851	158	26	locally	locally	ADV
ap-1851	158	27	separating	separate	VERB
ap-1851	158	28	and	and	CCONJ
ap-1851	158	29	define	define	VERB
ap-1851	158	30	a	a	DET
ap-1851	158	31	point	point	NOUN
ap-1851	158	32	interaction	interaction	NOUN
ap-1851	158	33	at	at	ADP
ap-1851	158	34	those	those	DET
ap-1851	158	35	points	point	NOUN
ap-1851	158	36	,	,	PUNCT
ap-1851	158	37	or	or	CCONJ
ap-1851	158	38	that	that	SCONJ
ap-1851	158	39	a	a	DET
ap-1851	158	40	junction	junction	NOUN
ap-1851	158	41	coincides	coincide	VERB
ap-1851	158	42	with	with	ADP
ap-1851	158	43	a	a	DET
ap-1851	158	44	zero	zero	NUM
ap-1851	158	45	of	of	ADP
ap-1851	158	46	an	an	DET
ap-1851	158	47	eigenfunction	eigenfunction	NOUN
ap-1851	158	48	of	of	ADP
ap-1851	158	49	h0	h0	PROPN
ap-1851	158	50	.	.	PUNCT
ap-1851	159	1	in	in	ADP
ap-1851	159	2	such	such	ADJ
ap-1851	159	3	situations	situation	NOUN
ap-1851	159	4	it	it	PRON
ap-1851	159	5	may	may	AUX
ap-1851	159	6	happen	happen	VERB
ap-1851	159	7	that	that	SCONJ
ap-1851	159	8	h	h	NOUN
ap-1851	159	9	has	have	AUX
ap-1851	159	10	eigenvalues	eigenvalue	NOUN
ap-1851	159	11	,	,	PUNCT
ap-1851	159	12	either	either	CCONJ
ap-1851	159	13	positive	positive	ADJ
ap-1851	159	14	,	,	PUNCT
ap-1851	159	15	embedded	embed	VERB
ap-1851	159	16	into	into	ADP
ap-1851	159	17	the	the	DET
ap-1851	159	18	continuous	continuous	ADJ
ap-1851	159	19	spectrum	spectrum	NOUN
ap-1851	159	20	,	,	PUNCT
ap-1851	159	21	or	or	CCONJ
ap-1851	159	22	negative	negative	ADJ
ap-1851	159	23	.	.	PUNCT
ap-1851	160	1	in	in	ADP
ap-1851	160	2	terms	term	NOUN
ap-1851	160	3	of	of	ADP
ap-1851	160	4	the	the	DET
ap-1851	160	5	momentum	momentum	NOUN
ap-1851	160	6	variable	variable	NOUN
ap-1851	160	7	k	k	PROPN
ap-1851	160	8	,	,	PUNCT
ap-1851	160	9	these	these	DET
ap-1851	160	10	eigenvalues	eigenvalue	NOUN
ap-1851	160	11	appear	appear	VERB
ap-1851	160	12	in	in	ADP
ap-1851	160	13	pairs	pair	NOUN
ap-1851	160	14	symmetric	symmetric	ADJ
ap-1851	160	15	w.r.t	w.r.t	NOUN
ap-1851	160	16	.	.	PUNCT
ap-1851	161	1	the	the	DET
ap-1851	161	2	origin	origin	NOUN
ap-1851	161	3	.	.	PUNCT
ap-1851	162	1	(	(	PUNCT
ap-1851	162	2	2	2	NUM
ap-1851	162	3	.	.	PUNCT
ap-1851	162	4	)	)	PUNCT
ap-1851	163	1	in	in	ADP
ap-1851	163	2	the	the	DET
ap-1851	163	3	case	case	NOUN
ap-1851	163	4	of	of	ADP
ap-1851	163	5	separating	separate	VERB
ap-1851	163	6	conditions	condition	NOUN
ap-1851	163	7	(	(	PUNCT
ap-1851	163	8	1	1	X
ap-1851	163	9	)	)	PUNCT
ap-1851	163	10	it	it	PRON
ap-1851	163	11	may	may	AUX
ap-1851	163	12	happen	happen	VERB
ap-1851	163	13	that	that	SCONJ
ap-1851	163	14	the	the	DET
ap-1851	163	15	complex	complex	ADV
ap-1851	163	16	-	-	PUNCT
ap-1851	163	17	scaled	scale	VERB
ap-1851	163	18	operator	operator	NOUN
ap-1851	163	19	hθ	hθ	NOUN
ap-1851	163	20	has	have	VERB
ap-1851	163	21	an	an	DET
ap-1851	163	22	eigenvalue	eigenvalue	NOUN
ap-1851	163	23	in	in	ADP
ap-1851	163	24	k2	k2	PROPN
ap-1851	163	25	0	0	NUM
ap-1851	163	26	with	with	ADP
ap-1851	163	27	eigenfunction	eigenfunction	NOUN
ap-1851	163	28	supported	support	VERB
ap-1851	163	29	outside	outside	ADP
ap-1851	163	30	ω	ω	PROPN
ap-1851	163	31	,	,	PUNCT
ap-1851	163	32	then	then	ADV
ap-1851	163	33	k0	k0	PROPN
ap-1851	163	34	is	be	AUX
ap-1851	163	35	also	also	ADV
ap-1851	163	36	a	a	DET
ap-1851	163	37	pole	pole	NOUN
ap-1851	163	38	of	of	ADP
ap-1851	163	39	s(k	s(k	PROPN
ap-1851	163	40	)	)	PUNCT
ap-1851	163	41	;	;	PUNCT
ap-1851	163	42	the	the	DET
ap-1851	163	43	poles	pole	NOUN
ap-1851	163	44	multiplicities	multiplicitie	VERB
ap-1851	163	45	of	of	ADP
ap-1851	163	46	the	the	DET
ap-1851	163	47	resolvent	resolvent	NOUN
ap-1851	163	48	and	and	CCONJ
ap-1851	163	49	the	the	DET
ap-1851	163	50	scattering	scatter	VERB
ap-1851	163	51	matrix	matrix	NOUN
ap-1851	163	52	may	may	AUX
ap-1851	163	53	differ	differ	VERB
ap-1851	163	54	in	in	ADP
ap-1851	163	55	this	this	DET
ap-1851	163	56	situation	situation	NOUN
ap-1851	163	57	.	.	PUNCT
ap-1851	164	1	(	(	PUNCT
ap-1851	164	2	3	3	NUM
ap-1851	164	3	.	.	PUNCT
ap-1851	164	4	)	)	PUNCT
ap-1851	164	5	in	in	ADP
ap-1851	164	6	the	the	DET
ap-1851	164	7	quantum	quantum	NOUN
ap-1851	164	8	-	-	PUNCT
ap-1851	164	9	graph	graph	NOUN
ap-1851	164	10	analogue	analogue	NOUN
ap-1851	164	11	when	when	SCONJ
ap-1851	164	12	ω	ω	PROPN
ap-1851	164	13	is	be	AUX
ap-1851	164	14	replaced	replace	VERB
ap-1851	164	15	by	by	ADP
ap-1851	164	16	a	a	DET
ap-1851	164	17	compact	compact	ADJ
ap-1851	164	18	metric	metric	ADJ
ap-1851	164	19	graph	graph	NOUN
ap-1851	164	20	the	the	DET
ap-1851	164	21	decomposition	decomposition	NOUN
ap-1851	164	22	of	of	ADP
ap-1851	164	23	lemma	lemma	PROPN
ap-1851	164	24	3.3	3.3	NUM
ap-1851	164	25	can	can	AUX
ap-1851	164	26	not	not	PART
ap-1851	164	27	be	be	AUX
ap-1851	164	28	used	use	VERB
ap-1851	164	29	since	since	SCONJ
ap-1851	164	30	the	the	DET
ap-1851	164	31	deficiency	deficiency	NOUN
ap-1851	164	32	indices	index	NOUN
ap-1851	164	33	of	of	ADP
ap-1851	164	34	h	h	NOUN
ap-1851	164	35	′0	′0	NOUN
ap-1851	164	36	may	may	AUX
ap-1851	164	37	,	,	PUNCT
ap-1851	164	38	in	in	ADP
ap-1851	164	39	general	general	ADJ
ap-1851	164	40	,	,	PUNCT
ap-1851	164	41	exceed	exceed	VERB
ap-1851	164	42	n	n	PRON
ap-1851	164	43	and	and	CCONJ
ap-1851	164	44	one	one	NUM
ap-1851	164	45	can	can	AUX
ap-1851	164	46	have	have	VERB
ap-1851	164	47	extensions	extension	NOUN
ap-1851	164	48	with	with	ADP
ap-1851	164	49	the	the	DET
ap-1851	164	50	wave	wave	NOUN
ap-1851	164	51	functions	function	NOUN
ap-1851	164	52	discontinuous	discontinuous	ADJ
ap-1851	164	53	at	at	ADP
ap-1851	164	54	the	the	DET
ap-1851	164	55	junctions	junction	NOUN
ap-1851	164	56	.	.	PUNCT
ap-1851	165	1	the	the	DET
ap-1851	165	2	role	role	NOUN
ap-1851	165	3	of	of	ADP
ap-1851	165	4	the	the	DET
ap-1851	165	5	internal	internal	ADJ
ap-1851	165	6	parameters	parameter	NOUN
ap-1851	165	7	is	be	AUX
ap-1851	165	8	instead	instead	ADV
ap-1851	165	9	played	play	VERB
ap-1851	165	10	by	by	ADP
ap-1851	165	11	the	the	DET
ap-1851	165	12	coefficients	coefficient	NOUN
ap-1851	165	13	of	of	ADP
ap-1851	165	14	two	two	NUM
ap-1851	165	15	linearly	linearly	ADV
ap-1851	165	16	independent	independent	ADJ
ap-1851	165	17	solutions	solution	NOUN
ap-1851	165	18	on	on	ADP
ap-1851	165	19	each	each	DET
ap-1851	165	20	(	(	PUNCT
ap-1851	165	21	internal	internal	ADJ
ap-1851	165	22	)	)	PUNCT
ap-1851	165	23	edge	edge	NOUN
ap-1851	165	24	.	.	PUNCT
ap-1851	166	1	4	4	X
ap-1851	166	2	.	.	X
ap-1851	166	3	resonance	resonance	NOUN
ap-1851	166	4	asymptotics	asymptotic	VERB
ap-1851	166	5	the	the	DET
ap-1851	166	6	aim	aim	NOUN
ap-1851	166	7	of	of	ADP
ap-1851	166	8	this	this	DET
ap-1851	166	9	section	section	NOUN
ap-1851	166	10	is	be	AUX
ap-1851	166	11	to	to	PART
ap-1851	166	12	say	say	VERB
ap-1851	166	13	something	something	PRON
ap-1851	166	14	about	about	ADP
ap-1851	166	15	the	the	DET
ap-1851	166	16	asymptotic	asymptotic	ADJ
ap-1851	166	17	behaviour	behaviour	NOUN
ap-1851	166	18	of	of	ADP
ap-1851	166	19	the	the	DET
ap-1851	166	20	resolvent	resolvent	ADJ
ap-1851	166	21	poles	pole	NOUN
ap-1851	166	22	with	with	ADP
ap-1851	166	23	respect	respect	NOUN
ap-1851	166	24	to	to	ADP
ap-1851	166	25	an	an	DET
ap-1851	166	26	increasing	increase	VERB
ap-1851	166	27	family	family	NOUN
ap-1851	166	28	of	of	ADP
ap-1851	166	29	regions	region	NOUN
ap-1851	166	30	which	which	PRON
ap-1851	166	31	cover	cover	VERB
ap-1851	166	32	in	in	ADP
ap-1851	166	33	the	the	DET
ap-1851	166	34	limit	limit	NOUN
ap-1851	166	35	the	the	DET
ap-1851	166	36	whole	whole	ADJ
ap-1851	166	37	complex	complex	ADJ
ap-1851	166	38	plane	plane	NOUN
ap-1851	166	39	.	.	PUNCT
ap-1851	167	1	using	use	VERB
ap-1851	167	2	lemma	lemma	PROPN
ap-1851	167	3	3.3	3.3	NUM
ap-1851	167	4	let	let	VERB
ap-1851	167	5	us	we	PRON
ap-1851	167	6	write	write	VERB
ap-1851	167	7	the	the	DET
ap-1851	167	8	manifold	manifold	ADJ
ap-1851	167	9	part	part	NOUN
ap-1851	168	1	f	f	X
ap-1851	168	2	(	(	PUNCT
ap-1851	168	3	·	·	PUNCT
ap-1851	168	4	,	,	PUNCT
ap-1851	168	5	k	k	NOUN
ap-1851	168	6	)	)	PUNCT
ap-1851	168	7	of	of	ADP
ap-1851	168	8	a	a	DET
ap-1851	168	9	function	function	NOUN
ap-1851	168	10	from	from	ADP
ap-1851	168	11	the	the	DET
ap-1851	168	12	deficiency	deficiency	NOUN
ap-1851	168	13	subspace	subspace	NOUN
ap-1851	168	14	of	of	ADP
ap-1851	168	15	h	h	NOUN
ap-1851	168	16	′	′	NUM
ap-1851	168	17	as	as	ADP
ap-1851	168	18	a	a	DET
ap-1851	168	19	linear	linear	ADJ
ap-1851	168	20	combination	combination	NOUN
ap-1851	168	21	of	of	ADP
ap-1851	168	22	green	green	ADJ
ap-1851	168	23	functions	function	NOUN
ap-1851	168	24	of	of	ADP
ap-1851	168	25	hω	hω	ADP
ap-1851	168	26	,	,	PUNCT
ap-1851	168	27	acting	act	VERB
ap-1851	168	28	as	as	ADP
ap-1851	168	29	negative	negative	ADJ
ap-1851	168	30	laplace	laplace	NOUN
ap-1851	168	31	-	-	PUNCT
ap-1851	168	32	beltrami	beltrami	ADJ
ap-1851	168	33	operator	operator	NOUN
ap-1851	168	34	on	on	ADP
ap-1851	168	35	ω	ω	PROPN
ap-1851	168	36	.	.	PROPN
ap-1851	169	1	for	for	ADP
ap-1851	169	2	k2	k2	PROPN
ap-1851	169	3	6∈	6∈	PROPN
ap-1851	169	4	σ(hω	σ(hω	PROPN
ap-1851	169	5	)	)	PUNCT
ap-1851	169	6	and	and	CCONJ
ap-1851	169	7	x	x	X
ap-1851	169	8	in	in	ADP
ap-1851	169	9	the	the	DET
ap-1851	169	10	vicinity	vicinity	NOUN
ap-1851	169	11	of	of	ADP
ap-1851	169	12	the	the	DET
ap-1851	169	13	point	point	NOUN
ap-1851	169	14	xi	xi	INTJ
ap-1851	169	15	we	we	PRON
ap-1851	169	16	then	then	ADV
ap-1851	169	17	have	have	VERB
ap-1851	169	18	f(x	f(x	PROPN
ap-1851	169	19	,	,	PUNCT
ap-1851	169	20	k	k	NOUN
ap-1851	169	21	)	)	PUNCT
ap-1851	169	22	=	=	SYM
ap-1851	170	1	n∑	n∑	NOUN
ap-1851	170	2	j=1	j=1	PROPN
ap-1851	170	3	cjg(x	cjg(x	PROPN
ap-1851	170	4	,	,	PUNCT
ap-1851	170	5	xj	xj	PROPN
ap-1851	170	6	;	;	PUNCT
ap-1851	170	7	k	k	X
ap-1851	170	8	)	)	PUNCT
ap-1851	170	9	=	=	SYM
ap-1851	170	10	cif0(x	cif0(x	NOUN
ap-1851	170	11	,	,	PUNCT
ap-1851	170	12	xi	xi	ADJ
ap-1851	170	13	)	)	PUNCT
ap-1851	170	14	+	+	CCONJ
ap-1851	170	15	cif1(x	cif1(x	NOUN
ap-1851	170	16	,	,	PUNCT
ap-1851	170	17	xi	xi	PROPN
ap-1851	170	18	;	;	PUNCT
ap-1851	170	19	k	k	X
ap-1851	170	20	)	)	PUNCT
ap-1851	171	1	+	+	CCONJ
ap-1851	171	2	n∑	n∑	INTJ
ap-1851	171	3	i	i	PRON
ap-1851	171	4	6	6	NUM
ap-1851	172	1	=	=	NOUN
ap-1851	172	2	j=1	j=1	NOUN
ap-1851	172	3	cjg(xi	cjg(xi	VERB
ap-1851	172	4	,	,	PUNCT
ap-1851	172	5	xj	xj	PROPN
ap-1851	172	6	;	;	PUNCT
ap-1851	172	7	k	k	X
ap-1851	172	8	)	)	PUNCT
ap-1851	173	1	+	+	NOUN
ap-1851	173	2	o	o	X
ap-1851	173	3	(	(	PUNCT
ap-1851	173	4	r(x	r(x	PROPN
ap-1851	173	5	,	,	PUNCT
ap-1851	173	6	xi	xi	ADJ
ap-1851	173	7	)	)	PUNCT
ap-1851	173	8	)	)	PUNCT
ap-1851	173	9	which	which	PRON
ap-1851	173	10	makes	make	VERB
ap-1851	173	11	it	it	PRON
ap-1851	173	12	easy	easy	ADJ
ap-1851	173	13	to	to	PART
ap-1851	173	14	find	find	VERB
ap-1851	173	15	the	the	DET
ap-1851	173	16	generalized	generalized	ADJ
ap-1851	173	17	boundary	boundary	ADJ
ap-1851	173	18	values	value	NOUN
ap-1851	173	19	ci(f	ci(f	PRON
ap-1851	173	20	)	)	PUNCT
ap-1851	173	21	and	and	CCONJ
ap-1851	173	22	di(f	di(f	NOUN
ap-1851	173	23	)	)	PUNCT
ap-1851	173	24	to	to	PART
ap-1851	173	25	be	be	AUX
ap-1851	173	26	inserted	insert	VERB
ap-1851	173	27	into	into	ADP
ap-1851	173	28	the	the	DET
ap-1851	173	29	coupling	coupling	NOUN
ap-1851	173	30	conditions	condition	NOUN
ap-1851	173	31	(	(	PUNCT
ap-1851	173	32	1	1	NUM
ap-1851	173	33	)	)	PUNCT
ap-1851	173	34	,	,	PUNCT
ap-1851	173	35	or	or	CCONJ
ap-1851	173	36	effective	effective	ADJ
ap-1851	173	37	conditions	condition	NOUN
ap-1851	173	38	(	(	PUNCT
ap-1851	173	39	3	3	NUM
ap-1851	173	40	)	)	PUNCT
ap-1851	173	41	.	.	PUNCT
ap-1851	174	1	we	we	PRON
ap-1851	174	2	will	will	AUX
ap-1851	174	3	employ	employ	VERB
ap-1851	174	4	the	the	DET
ap-1851	174	5	latter	latter	ADJ
ap-1851	174	6	with	with	ADP
ap-1851	174	7	matrix	matrix	NOUN
ap-1851	174	8	ũ(k	ũ(k	ADJ
ap-1851	174	9	)	)	PUNCT
ap-1851	174	10	=	=	SYM
ap-1851	174	11	diag	diag	NOUN
ap-1851	174	12	(	(	PUNCT
ap-1851	174	13	ũ1(k	ũ1(k	PROPN
ap-1851	174	14	)	)	PUNCT
ap-1851	174	15	,	,	PUNCT
ap-1851	174	16	.	.	PUNCT
ap-1851	174	17	.	.	PUNCT
ap-1851	175	1	.	.	PUNCT
ap-1851	176	1	,	,	PUNCT
ap-1851	176	2	ũn(k	ũn(k	NOUN
ap-1851	176	3	)	)	PUNCT
ap-1851	176	4	)	)	PUNCT
ap-1851	177	1	whose	whose	DET
ap-1851	177	2	blocks	block	NOUN
ap-1851	177	3	correspond	correspond	VERB
ap-1851	177	4	to	to	ADP
ap-1851	177	5	junctions	junction	NOUN
ap-1851	177	6	of	of	ADP
ap-1851	177	7	γ	γ	X
ap-1851	177	8	.	.	PUNCT
ap-1851	178	1	we	we	PRON
ap-1851	178	2	introduce	introduce	VERB
ap-1851	178	3	q0(k	q0(k	PROPN
ap-1851	178	4	)	)	PUNCT
ap-1851	178	5	=	=	SYM
ap-1851	178	6	{	{	PUNCT
ap-1851	178	7	g(xi	g(xi	PROPN
ap-1851	178	8	,	,	PUNCT
ap-1851	178	9	xj	xj	PROPN
ap-1851	178	10	;	;	PUNCT
ap-1851	178	11	k	k	X
ap-1851	178	12	)	)	PUNCT
ap-1851	178	13	,	,	PUNCT
ap-1851	178	14	i	i	PROPN
ap-1851	178	15	6=	6=	NUM
ap-1851	178	16	j	j	PROPN
ap-1851	178	17	f1(xi	f1(xi	PROPN
ap-1851	178	18	,	,	PUNCT
ap-1851	178	19	xi	xi	PROPN
ap-1851	178	20	;	;	PUNCT
ap-1851	178	21	k	k	X
ap-1851	178	22	)	)	PUNCT
ap-1851	178	23	,	,	PUNCT
ap-1851	178	24	i	i	PRON
ap-1851	178	25	=	=	PUNCT
ap-1851	178	26	j	j	PROPN
ap-1851	178	27	which	which	PRON
ap-1851	178	28	allows	allow	VERB
ap-1851	178	29	us	we	PRON
ap-1851	178	30	to	to	PART
ap-1851	178	31	write	write	VERB
ap-1851	178	32	d(f	d(f	NOUN
ap-1851	178	33	)	)	PUNCT
ap-1851	178	34	=	=	PUNCT
ap-1851	178	35	q0(k)c	q0(k)c	ADV
ap-1851	178	36	,	,	PUNCT
ap-1851	178	37	and	and	CCONJ
ap-1851	178	38	substituting	substitute	VERB
ap-1851	178	39	into	into	ADP
ap-1851	178	40	(	(	PUNCT
ap-1851	178	41	3	3	X
ap-1851	178	42	)	)	PUNCT
ap-1851	178	43	we	we	PRON
ap-1851	178	44	can	can	AUX
ap-1851	178	45	write	write	VERB
ap-1851	178	46	the	the	DET
ap-1851	178	47	solvability	solvability	NOUN
ap-1851	178	48	of	of	ADP
ap-1851	178	49	the	the	DET
ap-1851	178	50	system	system	NOUN
ap-1851	178	51	which	which	PRON
ap-1851	178	52	determines	determine	VERB
ap-1851	178	53	the	the	DET
ap-1851	178	54	resonances	resonance	NOUN
ap-1851	178	55	as	as	ADP
ap-1851	178	56	det	det	PROPN
ap-1851	178	57	[	[	X
ap-1851	178	58	(	(	PUNCT
ap-1851	178	59	ũ(k)−	ũ(k)−	PROPN
ap-1851	178	60	i	i	PRON
ap-1851	178	61	)	)	PUNCT
ap-1851	179	1	q0(k	q0(k	X
ap-1851	179	2	)	)	PUNCT
ap-1851	180	1	+	+	CCONJ
ap-1851	180	2	i	i	PRON
ap-1851	180	3	(	(	PUNCT
ap-1851	180	4	ũ(k	ũ(k	PROPN
ap-1851	180	5	)	)	PUNCT
ap-1851	180	6	+	+	NUM
ap-1851	180	7	i	i	NOUN
ap-1851	180	8	)	)	PUNCT
ap-1851	180	9	]	]	PUNCT
ap-1851	181	1	=	=	PUNCT
ap-1851	181	2	0	0	X
ap-1851	181	3	.	.	PUNCT
ap-1851	182	1	(	(	PUNCT
ap-1851	182	2	6	6	X
ap-1851	182	3	)	)	PUNCT
ap-1851	182	4	we	we	PRON
ap-1851	182	5	note	note	VERB
ap-1851	182	6	that	that	SCONJ
ap-1851	182	7	the	the	DET
ap-1851	182	8	matrices	matrix	NOUN
ap-1851	182	9	ũj(k	ũj(k	VERB
ap-1851	182	10	)	)	PUNCT
ap-1851	182	11	entering	enter	VERB
ap-1851	182	12	this	this	DET
ap-1851	182	13	condition	condition	NOUN
ap-1851	182	14	may	may	AUX
ap-1851	182	15	be	be	AUX
ap-1851	182	16	singular	singular	ADJ
ap-1851	182	17	,	,	PUNCT
ap-1851	182	18	however	however	ADV
ap-1851	182	19	,	,	PUNCT
ap-1851	182	20	this	this	PRON
ap-1851	182	21	may	may	AUX
ap-1851	182	22	happen	happen	VERB
ap-1851	182	23	for	for	ADP
ap-1851	182	24	at	at	ADP
ap-1851	182	25	most	most	ADJ
ap-1851	182	26	m	m	NOUN
ap-1851	182	27	values	value	NOUN
ap-1851	182	28	of	of	ADP
ap-1851	182	29	k	k	NOUN
ap-1851	182	30	,	,	PUNCT
ap-1851	182	31	taking	take	VERB
ap-1851	182	32	all	all	DET
ap-1851	182	33	the	the	DET
ap-1851	182	34	conditions	condition	NOUN
ap-1851	182	35	together	together	ADV
ap-1851	182	36	.	.	PUNCT
ap-1851	183	1	we	we	PRON
ap-1851	183	2	also	also	ADV
ap-1851	183	3	note	note	VERB
ap-1851	183	4	that	that	SCONJ
ap-1851	183	5	if	if	SCONJ
ap-1851	183	6	the	the	DET
ap-1851	183	7	hamiltonian	hamiltonian	ADJ
ap-1851	183	8	h	h	NOUN
ap-1851	183	9	has	have	VERB
ap-1851	183	10	an	an	DET
ap-1851	183	11	eigenvalue	eigenvalue	ADJ
ap-1851	183	12	k2	k2	NOUN
ap-1851	183	13	embedded	embed	VERB
ap-1851	183	14	in	in	ADP
ap-1851	183	15	its	its	PRON
ap-1851	183	16	continuous	continuous	ADJ
ap-1851	183	17	spectrum	spectrum	NOUN
ap-1851	183	18	covering	cover	VERB
ap-1851	183	19	the	the	DET
ap-1851	183	20	interval	interval	NOUN
ap-1851	183	21	r+	r+	NOUN
ap-1851	183	22	,	,	PUNCT
ap-1851	183	23	the	the	DET
ap-1851	183	24	corresponding	correspond	VERB
ap-1851	183	25	k	k	PROPN
ap-1851	183	26	>	>	X
ap-1851	183	27	0	0	PUNCT
ap-1851	183	28	also	also	ADV
ap-1851	183	29	solves	solve	VERB
ap-1851	183	30	the	the	DET
ap-1851	183	31	equation	equation	NOUN
ap-1851	183	32	(	(	PUNCT
ap-1851	183	33	6	6	NUM
ap-1851	183	34	)	)	PUNCT
ap-1851	183	35	.	.	PUNCT
ap-1851	184	1	hence	hence	ADV
ap-1851	184	2	,	,	PUNCT
ap-1851	184	3	as	as	SCONJ
ap-1851	184	4	we	we	PRON
ap-1851	184	5	have	have	AUX
ap-1851	184	6	indicated	indicate	VERB
ap-1851	184	7	in	in	ADP
ap-1851	184	8	the	the	DET
ap-1851	184	9	introduction	introduction	NOUN
ap-1851	184	10	,	,	PUNCT
ap-1851	184	11	from	from	ADP
ap-1851	184	12	now	now	ADV
ap-1851	184	13	on	on	ADV
ap-1851	184	14	—	—	PUNCT
ap-1851	184	15	for	for	ADP
ap-1851	184	16	purpose	purpose	NOUN
ap-1851	184	17	of	of	ADP
ap-1851	184	18	this	this	DET
ap-1851	184	19	section	section	NOUN
ap-1851	184	20	—	—	PUNCT
ap-1851	184	21	we	we	PRON
ap-1851	184	22	will	will	AUX
ap-1851	184	23	include	include	VERB
ap-1851	184	24	such	such	ADJ
ap-1851	184	25	embedded	embed	VERB
ap-1851	184	26	eigenvalues	eigenvalue	NOUN
ap-1851	184	27	among	among	ADP
ap-1851	184	28	resonances	resonance	NOUN
ap-1851	184	29	.	.	PUNCT
ap-1851	185	1	having	having	AUX
ap-1851	185	2	formulated	formulate	VERB
ap-1851	185	3	the	the	DET
ap-1851	185	4	resonance	resonance	NOUN
ap-1851	185	5	condition	condition	NOUN
ap-1851	185	6	we	we	PRON
ap-1851	185	7	can	can	AUX
ap-1851	185	8	ask	ask	VERB
ap-1851	185	9	how	how	SCONJ
ap-1851	185	10	its	its	PRON
ap-1851	185	11	solutions	solution	NOUN
ap-1851	185	12	are	be	AUX
ap-1851	185	13	distributed	distribute	VERB
ap-1851	185	14	.	.	PUNCT
ap-1851	186	1	to	to	PART
ap-1851	186	2	count	count	VERB
ap-1851	186	3	zeros	zero	NOUN
ap-1851	186	4	of	of	ADP
ap-1851	186	5	a	a	DET
ap-1851	186	6	meromorphic	meromorphic	ADJ
ap-1851	186	7	function	function	NOUN
ap-1851	186	8	we	we	PRON
ap-1851	186	9	employ	employ	VERB
ap-1851	186	10	the	the	DET
ap-1851	186	11	following	follow	VERB
ap-1851	186	12	auxiliary	auxiliary	ADJ
ap-1851	186	13	result	result	NOUN
ap-1851	186	14	.	.	PUNCT
ap-1851	187	1	lemma	lemma	PROPN
ap-1851	187	2	4.1	4.1	NUM
ap-1851	187	3	.	.	PUNCT
ap-1851	188	1	let	let	VERB
ap-1851	188	2	g	g	NOUN
ap-1851	188	3	be	be	AUX
ap-1851	188	4	meromorphic	meromorphic	ADJ
ap-1851	188	5	function	function	NOUN
ap-1851	188	6	in	in	ADP
ap-1851	188	7	c	c	PROPN
ap-1851	188	8	and	and	CCONJ
ap-1851	188	9	suppose	suppose	VERB
ap-1851	188	10	that	that	SCONJ
ap-1851	188	11	it	it	PRON
ap-1851	188	12	has	have	VERB
ap-1851	188	13	no	no	DET
ap-1851	188	14	pole	pole	NOUN
ap-1851	188	15	or	or	CCONJ
ap-1851	188	16	zero	zero	NUM
ap-1851	188	17	on	on	ADP
ap-1851	188	18	the	the	DET
ap-1851	188	19	circle	circle	NOUN
ap-1851	188	20	cr	cr	NOUN
ap-1851	189	1	=	=	PUNCT
ap-1851	190	1	{	{	PUNCT
ap-1851	190	2	z	z	NOUN
ap-1851	190	3	:	:	PUNCT
ap-1851	190	4	|z|	|z|	NOUN
ap-1851	190	5	=	=	SYM
ap-1851	190	6	r	r	NOUN
ap-1851	190	7	}	}	PUNCT
ap-1851	190	8	.	.	PUNCT
ap-1851	191	1	then	then	ADV
ap-1851	191	2	the	the	DET
ap-1851	191	3	difference	difference	NOUN
ap-1851	191	4	between	between	ADP
ap-1851	191	5	the	the	DET
ap-1851	191	6	number	number	NOUN
ap-1851	191	7	of	of	ADP
ap-1851	191	8	the	the	DET
ap-1851	191	9	zeros	zero	NOUN
ap-1851	191	10	and	and	CCONJ
ap-1851	191	11	poles	pole	NOUN
ap-1851	191	12	of	of	ADP
ap-1851	191	13	g	g	NOUN
ap-1851	191	14	in	in	ADP
ap-1851	191	15	the	the	DET
ap-1851	191	16	disc	disc	NOUN
ap-1851	191	17	of	of	ADP
ap-1851	191	18	radius	radius	NOUN
ap-1851	191	19	r	r	NOUN
ap-1851	191	20	of	of	ADP
ap-1851	191	21	which	which	PRON
ap-1851	191	22	cr	cr	PROPN
ap-1851	191	23	is	be	AUX
ap-1851	191	24	the	the	DET
ap-1851	191	25	perimeter	perimeter	NOUN
ap-1851	191	26	is	be	AUX
ap-1851	191	27	given	give	VERB
ap-1851	191	28	by∫	by∫	PROPN
ap-1851	191	29	cr	cr	ADP
ap-1851	191	30	g(z)′	g(z)′	PROPN
ap-1851	191	31	g(z	g(z	PROPN
ap-1851	191	32	)	)	PUNCT
ap-1851	191	33	dz	dz	NOUN
ap-1851	191	34	,	,	PUNCT
ap-1851	191	35	with	with	ADP
ap-1851	191	36	prime	prime	ADJ
ap-1851	191	37	denoting	denote	VERB
ap-1851	191	38	the	the	DET
ap-1851	191	39	derivative	derivative	NOUN
ap-1851	191	40	with	with	ADP
ap-1851	191	41	respect	respect	NOUN
ap-1851	191	42	to	to	ADP
ap-1851	191	43	z	z	NOUN
ap-1851	191	44	,	,	PUNCT
ap-1851	191	45	or	or	CCONJ
ap-1851	191	46	equivalently	equivalently	ADV
ap-1851	191	47	,	,	PUNCT
ap-1851	191	48	it	it	PRON
ap-1851	191	49	is	be	AUX
ap-1851	191	50	the	the	DET
ap-1851	191	51	difference	difference	NOUN
ap-1851	191	52	between	between	ADP
ap-1851	191	53	the	the	DET
ap-1851	191	54	number	number	NOUN
ap-1851	191	55	of	of	ADP
ap-1851	191	56	jumps	jump	NOUN
ap-1851	191	57	of	of	ADP
ap-1851	191	58	the	the	DET
ap-1851	191	59	phase	phase	NOUN
ap-1851	191	60	of	of	ADP
ap-1851	191	61	g(z	g(z	PROPN
ap-1851	191	62	)	)	PUNCT
ap-1851	191	63	from	from	ADP
ap-1851	191	64	2π	2π	NUM
ap-1851	191	65	to	to	ADP
ap-1851	191	66	0	0	NUM
ap-1851	191	67	along	along	ADP
ap-1851	191	68	the	the	DET
ap-1851	191	69	circle	circle	NOUN
ap-1851	191	70	cr	cr	PROPN
ap-1851	191	71	and	and	CCONJ
ap-1851	191	72	the	the	DET
ap-1851	191	73	jumps	jump	NOUN
ap-1851	191	74	from	from	ADP
ap-1851	191	75	0	0	NUM
ap-1851	191	76	to	to	ADP
ap-1851	191	77	2π	2π	NOUN
ap-1851	191	78	.	.	PUNCT
ap-1851	192	1	proof	proof	NOUN
ap-1851	192	2	.	.	PUNCT
ap-1851	193	1	the	the	DET
ap-1851	193	2	argument	argument	NOUN
ap-1851	193	3	is	be	AUX
ap-1851	193	4	well	well	ADV
ap-1851	193	5	known	know	VERB
ap-1851	193	6	,	,	PUNCT
ap-1851	193	7	and	and	CCONJ
ap-1851	193	8	we	we	PRON
ap-1851	193	9	present	present	VERB
ap-1851	193	10	it	it	PRON
ap-1851	193	11	just	just	ADV
ap-1851	193	12	for	for	ADP
ap-1851	193	13	the	the	DET
ap-1851	193	14	sake	sake	NOUN
ap-1851	193	15	of	of	ADP
ap-1851	193	16	completeness	completeness	NOUN
ap-1851	193	17	.	.	PUNCT
ap-1851	194	1	suppose	suppose	VERB
ap-1851	194	2	that	that	SCONJ
ap-1851	194	3	g	g	PROPN
ap-1851	194	4	(	(	PUNCT
ap-1851	194	5	·	·	PUNCT
ap-1851	194	6	)	)	PUNCT
ap-1851	194	7	has	have	VERB
ap-1851	194	8	at	at	ADP
ap-1851	194	9	z0	z0	PROPN
ap-1851	194	10	a	a	DET
ap-1851	194	11	zero	zero	NUM
ap-1851	194	12	of	of	ADP
ap-1851	194	13	multiplicity	multiplicity	NOUN
ap-1851	194	14	s	s	NOUN
ap-1851	194	15	,	,	PUNCT
ap-1851	194	16	i.e.	i.e.	X
ap-1851	194	17	g(z	g(z	ADJ
ap-1851	194	18	)	)	PUNCT
ap-1851	195	1	=	=	SYM
ap-1851	196	1	h(z)(z	h(z)(z	NOUN
ap-1851	196	2	−	−	PROPN
ap-1851	196	3	z0)s	z0)s	NOUN
ap-1851	196	4	with	with	ADP
ap-1851	196	5	neither	neither	DET
ap-1851	196	6	h(z	h(z	NOUN
ap-1851	196	7	)	)	PUNCT
ap-1851	196	8	nor	nor	CCONJ
ap-1851	196	9	h(z)′	h(z)′	PROPN
ap-1851	196	10	having	have	VERB
ap-1851	196	11	a	a	DET
ap-1851	196	12	zero	zero	NUM
ap-1851	196	13	or	or	CCONJ
ap-1851	196	14	a	a	DET
ap-1851	196	15	pole	pole	NOUN
ap-1851	196	16	at	at	ADP
ap-1851	196	17	z0	z0	PROPN
ap-1851	196	18	.	.	PUNCT
ap-1851	197	1	using	use	VERB
ap-1851	197	2	g(z)′	g(z)′	PROPN
ap-1851	197	3	g(z	g(z	PROPN
ap-1851	197	4	)	)	PUNCT
ap-1851	198	1	=	=	SYM
ap-1851	198	2	h(z)′	h(z)′	PRON
ap-1851	198	3	h(z	h(z	NOUN
ap-1851	198	4	)	)	PUNCT
ap-1851	199	1	+	+	NUM
ap-1851	199	2	s	s	NOUN
ap-1851	199	3	z	z	NOUN
ap-1851	199	4	−	−	PROPN
ap-1851	199	5	z0	z0	NOUN
ap-1851	199	6	we	we	PRON
ap-1851	199	7	find	find	VERB
ap-1851	199	8	resz0	resz0	PROPN
ap-1851	199	9	g(z)′	g(z)′	PROPN
ap-1851	199	10	g(z	g(z	PROPN
ap-1851	199	11	)	)	PUNCT
ap-1851	199	12	=	=	SYM
ap-1851	199	13	1	1	NUM
ap-1851	199	14	(	(	PUNCT
ap-1851	199	15	s−	s−	PROPN
ap-1851	199	16	1	1	NUM
ap-1851	199	17	)	)	PUNCT
ap-1851	199	18	!	!	PUNCT
ap-1851	200	1	lim	lim	PROPN
ap-1851	200	2	z→z0	z→z0	VERB
ap-1851	200	3	ds−1	ds−1	PROPN
ap-1851	200	4	dzs−1	dzs−1	PROPN
ap-1851	200	5	(	(	PUNCT
ap-1851	200	6	(	(	PUNCT
ap-1851	200	7	z	z	NOUN
ap-1851	200	8	−	−	PROPN
ap-1851	200	9	z0)s	z0)s	PROPN
ap-1851	200	10	g(z)′	g(z)′	PROPN
ap-1851	200	11	g(z	g(z	PROPN
ap-1851	200	12	)	)	PUNCT
ap-1851	200	13	)	)	PUNCT
ap-1851	201	1	=	=	SYM
ap-1851	201	2	s	s	X
ap-1851	201	3	;	;	PUNCT
ap-1851	201	4	a	a	DET
ap-1851	201	5	similar	similar	ADJ
ap-1851	201	6	result	result	NOUN
ap-1851	201	7	differing	differ	VERB
ap-1851	201	8	only	only	ADV
ap-1851	201	9	by	by	ADP
ap-1851	201	10	the	the	DET
ap-1851	201	11	sign	sign	NOUN
ap-1851	201	12	is	be	AUX
ap-1851	201	13	obtained	obtain	VERB
ap-1851	201	14	in	in	ADP
ap-1851	201	15	the	the	DET
ap-1851	201	16	case	case	NOUN
ap-1851	201	17	of	of	ADP
ap-1851	201	18	a	a	DET
ap-1851	201	19	pole	pole	NOUN
ap-1851	201	20	of	of	ADP
ap-1851	201	21	multiplicity	multiplicity	NOUN
ap-1851	201	22	s.	s.	PROPN
ap-1851	201	23	consequently	consequently	ADV
ap-1851	201	24	,	,	PUNCT
ap-1851	201	25	the	the	DET
ap-1851	201	26	function	function	NOUN
ap-1851	201	27	g(·)′/g	g(·)′/g	PROPN
ap-1851	201	28	(	(	PUNCT
ap-1851	201	29	·	·	PUNCT
ap-1851	201	30	)	)	PUNCT
ap-1851	201	31	has	have	AUX
ap-1851	201	32	pole	pole	NOUN
ap-1851	201	33	with	with	ADP
ap-1851	201	34	the	the	DET
ap-1851	201	35	residue	residue	NOUN
ap-1851	201	36	s	s	NOUN
ap-1851	201	37	if	if	SCONJ
ap-1851	201	38	g	g	PROPN
ap-1851	201	39	(	(	PUNCT
ap-1851	201	40	·	·	PUNCT
ap-1851	201	41	)	)	PUNCT
ap-1851	201	42	has	have	VERB
ap-1851	201	43	zero	zero	NUM
ap-1851	201	44	of	of	ADP
ap-1851	201	45	multiplicity	multiplicity	NOUN
ap-1851	201	46	s	s	NOUN
ap-1851	201	47	,	,	PUNCT
ap-1851	201	48	and	and	CCONJ
ap-1851	201	49	it	it	PRON
ap-1851	201	50	has	have	VERB
ap-1851	201	51	pole	pole	NOUN
ap-1851	201	52	with	with	ADP
ap-1851	201	53	the	the	DET
ap-1851	201	54	residue	residue	NOUN
ap-1851	201	55	−s	−s	NOUN
ap-1851	201	56	at	at	ADP
ap-1851	201	57	points	point	NOUN
ap-1851	201	58	where	where	SCONJ
ap-1851	201	59	g	g	NOUN
ap-1851	201	60	(	(	PUNCT
ap-1851	201	61	·	·	PUNCT
ap-1851	201	62	)	)	PUNCT
ap-1851	201	63	has	have	VERB
ap-1851	201	64	pole	pole	NOUN
ap-1851	201	65	of	of	ADP
ap-1851	201	66	multiplicity	multiplicity	NOUN
ap-1851	201	67	s.	s.	PROPN
ap-1851	201	68	furthermore	furthermore	ADV
ap-1851	201	69	,	,	PUNCT
ap-1851	201	70	g(·)′	g(·)′	NOUN
ap-1851	201	71	does	do	AUX
ap-1851	201	72	not	not	PART
ap-1851	201	73	have	have	VERB
ap-1851	201	74	a	a	DET
ap-1851	201	75	pole	pole	NOUN
ap-1851	201	76	at	at	ADP
ap-1851	201	77	z0	z0	PROPN
ap-1851	201	78	as	as	ADV
ap-1851	201	79	long	long	ADV
ap-1851	201	80	as	as	ADP
ap-1851	201	81	g	g	PROPN
ap-1851	201	82	(	(	PUNCT
ap-1851	201	83	·	·	PUNCT
ap-1851	201	84	)	)	PUNCT
ap-1851	201	85	does	do	AUX
ap-1851	201	86	not	not	PART
ap-1851	201	87	which	which	PRON
ap-1851	201	88	can	can	AUX
ap-1851	201	89	be	be	AUX
ap-1851	201	90	easily	easily	ADV
ap-1851	201	91	seen	see	VERB
ap-1851	201	92	from	from	ADP
ap-1851	201	93	the	the	DET
ap-1851	201	94	appropriate	appropriate	ADJ
ap-1851	201	95	laurent	laurent	NOUN
ap-1851	201	96	series	series	NOUN
ap-1851	201	97	.	.	PUNCT
ap-1851	202	1	using	use	VERB
ap-1851	202	2	now	now	ADV
ap-1851	202	3	the	the	DET
ap-1851	202	4	residue	residue	NOUN
ap-1851	202	5	theorem	theorem	VERB
ap-1851	202	6	we	we	PRON
ap-1851	202	7	arrive	arrive	VERB
ap-1851	202	8	at	at	ADP
ap-1851	202	9	the	the	DET
ap-1851	202	10	desired	desire	VERB
ap-1851	202	11	integral	integral	ADJ
ap-1851	202	12	expression	expression	NOUN
ap-1851	202	13	.	.	PUNCT
ap-1851	203	1	the	the	DET
ap-1851	203	2	claim	claim	NOUN
ap-1851	203	3	about	about	ADP
ap-1851	203	4	the	the	DET
ap-1851	203	5	number	number	NOUN
ap-1851	203	6	of	of	ADP
ap-1851	203	7	phase	phase	NOUN
ap-1851	203	8	jumps	jump	VERB
ap-1851	203	9	follows	follow	VERB
ap-1851	203	10	from	from	ADP
ap-1851	203	11	the	the	DET
ap-1851	203	12	fact	fact	NOUN
ap-1851	203	13	that	that	SCONJ
ap-1851	203	14	g′(z)/g(z	g′(z)/g(z	NUM
ap-1851	203	15	)	)	PUNCT
ap-1851	203	16	=	=	PRON
ap-1851	203	17	(	(	PUNCT
ap-1851	203	18	ln	ln	ADJ
ap-1851	203	19	g(z	g(z	PROPN
ap-1851	203	20	)	)	PUNCT
ap-1851	203	21	)	)	PUNCT
ap-1851	203	22	′.	′.	NOUN
ap-1851	203	23	420	420	NUM
ap-1851	203	24	vol	vol	NOUN
ap-1851	203	25	.	.	PUNCT
ap-1851	204	1	53	53	NUM
ap-1851	204	2	no	no	NOUN
ap-1851	204	3	.	.	PUNCT
ap-1851	205	1	5/2013	5/2013	NUM
ap-1851	205	2	resonances	resonance	NOUN
ap-1851	205	3	on	on	ADP
ap-1851	205	4	hedgehog	hedgehog	NOUN
ap-1851	205	5	manifolds	manifold	NOUN
ap-1851	205	6	4.1	4.1	NUM
ap-1851	205	7	.	.	PUNCT
ap-1851	206	1	manifolds	manifold	NOUN
ap-1851	206	2	with	with	ADP
ap-1851	206	3	the	the	DET
ap-1851	206	4	leads	lead	NOUN
ap-1851	206	5	attached	attach	VERB
ap-1851	206	6	at	at	ADP
ap-1851	206	7	a	a	DET
ap-1851	206	8	single	single	ADJ
ap-1851	206	9	point	point	NOUN
ap-1851	206	10	we	we	PRON
ap-1851	206	11	shall	shall	AUX
ap-1851	206	12	consider	consider	VERB
ap-1851	206	13	the	the	DET
ap-1851	206	14	situation	situation	NOUN
ap-1851	206	15	when	when	SCONJ
ap-1851	206	16	γ	γ	PROPN
ap-1851	206	17	has	have	VERB
ap-1851	206	18	a	a	DET
ap-1851	206	19	single	single	ADJ
ap-1851	206	20	junction	junction	NOUN
ap-1851	206	21	,	,	PUNCT
ap-1851	206	22	i.e.	i.e.	X
ap-1851	206	23	there	there	PRON
ap-1851	206	24	is	be	VERB
ap-1851	206	25	a	a	DET
ap-1851	206	26	point	point	NOUN
ap-1851	206	27	x0	x0	PROPN
ap-1851	206	28	∈	∈	PROPN
ap-1851	206	29	ω	ω	X
ap-1851	206	30	at	at	ADP
ap-1851	206	31	which	which	PRON
ap-1851	206	32	all	all	DET
ap-1851	206	33	the	the	DET
ap-1851	206	34	m	m	PROPN
ap-1851	206	35	halfline	halfline	NOUN
ap-1851	206	36	leads	lead	NOUN
ap-1851	206	37	are	be	AUX
ap-1851	206	38	attached	attach	VERB
ap-1851	206	39	.	.	PUNCT
ap-1851	207	1	then	then	ADV
ap-1851	207	2	the	the	DET
ap-1851	207	3	matrix	matrix	NOUN
ap-1851	207	4	functionq0(k	functionq0(k	VERB
ap-1851	207	5	)	)	PUNCT
ap-1851	207	6	is	be	AUX
ap-1851	207	7	reduced	reduce	VERB
ap-1851	207	8	to	to	PART
ap-1851	207	9	dimension	dimension	VERB
ap-1851	207	10	one	one	NUM
ap-1851	207	11	and	and	CCONJ
ap-1851	207	12	it	it	PRON
ap-1851	207	13	coincides	coincide	VERB
ap-1851	207	14	with	with	ADP
ap-1851	207	15	the	the	DET
ap-1851	207	16	regularized	regularize	VERB
ap-1851	207	17	green	green	ADJ
ap-1851	207	18	function	function	NOUN
ap-1851	207	19	f1(x0	f1(x0	PROPN
ap-1851	207	20	,	,	PUNCT
ap-1851	207	21	x0	x0	PROPN
ap-1851	207	22	;	;	PUNCT
ap-1851	207	23	k	k	X
ap-1851	207	24	)	)	PUNCT
ap-1851	207	25	;	;	PUNCT
ap-1851	207	26	for	for	ADP
ap-1851	207	27	simplicity	simplicity	NOUN
ap-1851	207	28	in	in	ADP
ap-1851	207	29	the	the	DET
ap-1851	207	30	rest	rest	NOUN
ap-1851	207	31	of	of	ADP
ap-1851	207	32	this	this	DET
ap-1851	207	33	subsection	subsection	NOUN
ap-1851	207	34	we	we	PRON
ap-1851	207	35	drop	drop	VERB
ap-1851	207	36	x0	x0	PROPN
ap-1851	207	37	from	from	ADP
ap-1851	207	38	the	the	DET
ap-1851	207	39	argument	argument	NOUN
ap-1851	207	40	.	.	PUNCT
ap-1851	208	1	the	the	DET
ap-1851	208	2	resonance	resonance	NOUN
ap-1851	208	3	condition	condition	NOUN
ap-1851	208	4	(	(	PUNCT
ap-1851	208	5	6	6	NUM
ap-1851	208	6	)	)	PUNCT
ap-1851	208	7	then	then	ADV
ap-1851	208	8	becomes	become	VERB
ap-1851	208	9	(	(	PUNCT
ap-1851	208	10	ũ(k	ũ(k	ADJ
ap-1851	208	11	)	)	PUNCT
ap-1851	208	12	−	−	PROPN
ap-1851	208	13	1	1	X
ap-1851	208	14	)	)	PUNCT
ap-1851	208	15	f1(k	f1(k	PROPN
ap-1851	208	16	)	)	PUNCT
ap-1851	209	1	+	+	CCONJ
ap-1851	209	2	i	i	PRON
ap-1851	209	3	(	(	PUNCT
ap-1851	209	4	ũ(k	ũ(k	PROPN
ap-1851	209	5	)	)	PUNCT
ap-1851	209	6	+	+	NUM
ap-1851	209	7	1	1	X
ap-1851	209	8	)	)	PUNCT
ap-1851	209	9	=	=	SYM
ap-1851	209	10	0	0	NUM
ap-1851	209	11	;	;	PUNCT
ap-1851	209	12	we	we	PRON
ap-1851	209	13	use	use	VERB
ap-1851	209	14	the	the	DET
ap-1851	209	15	lower	low	ADJ
ap-1851	209	16	-	-	PUNCT
ap-1851	209	17	case	case	NOUN
ap-1851	209	18	symbol	symbol	NOUN
ap-1851	209	19	to	to	PART
ap-1851	209	20	stress	stress	VERB
ap-1851	209	21	that	that	SCONJ
ap-1851	209	22	ũ(k	ũ(k	NOUN
ap-1851	209	23	)	)	PUNCT
ap-1851	209	24	is	be	AUX
ap-1851	209	25	just	just	ADV
ap-1851	209	26	a	a	DET
ap-1851	209	27	number	number	NOUN
ap-1851	209	28	in	in	ADP
ap-1851	209	29	this	this	DET
ap-1851	209	30	case	case	NOUN
ap-1851	209	31	.	.	PUNCT
ap-1851	210	1	the	the	DET
ap-1851	210	2	aim	aim	NOUN
ap-1851	210	3	is	be	AUX
ap-1851	210	4	now	now	ADV
ap-1851	210	5	to	to	PART
ap-1851	210	6	establish	establish	VERB
ap-1851	210	7	the	the	DET
ap-1851	210	8	high	high	ADJ
ap-1851	210	9	-	-	PUNCT
ap-1851	210	10	energy	energy	NOUN
ap-1851	210	11	asymptotics	asymptotic	NOUN
ap-1851	210	12	.	.	PUNCT
ap-1851	211	1	if	if	SCONJ
ap-1851	211	2	we	we	PRON
ap-1851	211	3	exclude	exclude	VERB
ap-1851	211	4	the	the	DET
ap-1851	211	5	case	case	NOUN
ap-1851	211	6	of	of	ADP
ap-1851	211	7	ũ(k	ũ(k	PROPN
ap-1851	211	8	)	)	PUNCT
ap-1851	211	9	=	=	SYM
ap-1851	211	10	1	1	NUM
ap-1851	211	11	when	when	SCONJ
ap-1851	211	12	the	the	DET
ap-1851	211	13	leads	lead	NOUN
ap-1851	211	14	are	be	AUX
ap-1851	211	15	obviously	obviously	ADV
ap-1851	211	16	decoupled	decouple	VERB
ap-1851	211	17	from	from	ADP
ap-1851	211	18	the	the	DET
ap-1851	211	19	manifold	manifold	NOUN
ap-1851	211	20	and	and	CCONJ
ap-1851	211	21	the	the	DET
ap-1851	211	22	motion	motion	NOUN
ap-1851	211	23	on	on	ADP
ap-1851	211	24	ω	ω	PROPN
ap-1851	211	25	is	be	AUX
ap-1851	211	26	described	describe	VERB
ap-1851	211	27	by	by	ADP
ap-1851	211	28	the	the	DET
ap-1851	211	29	hamiltonian	hamiltonian	PROPN
ap-1851	211	30	h0	h0	PROPN
ap-1851	211	31	,	,	PUNCT
ap-1851	211	32	we	we	PRON
ap-1851	211	33	can	can	AUX
ap-1851	211	34	without	without	ADP
ap-1851	211	35	loss	loss	NOUN
ap-1851	211	36	of	of	ADP
ap-1851	211	37	generality	generality	NOUN
ap-1851	211	38	rewrite	rewrite	VERB
ap-1851	211	39	the	the	DET
ap-1851	211	40	resonance	resonance	NOUN
ap-1851	211	41	condition	condition	NOUN
ap-1851	211	42	as	as	ADP
ap-1851	211	43	f	f	PROPN
ap-1851	211	44	(	(	PUNCT
ap-1851	211	45	k	k	NOUN
ap-1851	211	46	)	)	PUNCT
ap-1851	211	47	:	:	PUNCT
ap-1851	212	1	=	=	PUNCT
ap-1851	212	2	f1(k	f1(k	PROPN
ap-1851	212	3	)	)	PUNCT
ap-1851	212	4	+	+	NUM
ap-1851	212	5	i	i	PRON
ap-1851	212	6	ũ(k	ũ(k	ADJ
ap-1851	212	7	)	)	PUNCT
ap-1851	212	8	+	+	CCONJ
ap-1851	212	9	1	1	NUM
ap-1851	212	10	ũ(k)−	ũ(k)−	PROPN
ap-1851	212	11	1	1	NUM
ap-1851	212	12	=	=	SYM
ap-1851	212	13	0	0	NUM
ap-1851	212	14	.	.	PUNCT
ap-1851	212	15	from	from	ADP
ap-1851	212	16	(	(	PUNCT
ap-1851	212	17	3	3	X
ap-1851	212	18	)	)	PUNCT
ap-1851	212	19	we	we	PRON
ap-1851	212	20	see	see	VERB
ap-1851	212	21	that	that	SCONJ
ap-1851	212	22	ũ	ũ	PROPN
ap-1851	212	23	(	(	PUNCT
ap-1851	212	24	·	·	PUNCT
ap-1851	212	25	)	)	PUNCT
ap-1851	213	1	−	−	NOUN
ap-1851	214	1	i	i	PRON
ap-1851	214	2	is	be	AUX
ap-1851	214	3	a	a	DET
ap-1851	214	4	rational	rational	ADJ
ap-1851	214	5	function	function	NOUN
ap-1851	214	6	.	.	PUNCT
ap-1851	215	1	consequently	consequently	ADV
ap-1851	215	2	,	,	PUNCT
ap-1851	215	3	it	it	PRON
ap-1851	215	4	may	may	AUX
ap-1851	215	5	add	add	VERB
ap-1851	215	6	zeros	zero	NOUN
ap-1851	215	7	or	or	CCONJ
ap-1851	215	8	poles	pole	NOUN
ap-1851	215	9	to	to	ADP
ap-1851	215	10	those	those	PRON
ap-1851	215	11	of	of	ADP
ap-1851	215	12	f1	f1	NOUN
ap-1851	215	13	(	(	PUNCT
ap-1851	215	14	·	·	PUNCT
ap-1851	215	15	)	)	PUNCT
ap-1851	215	16	,	,	PUNCT
ap-1851	215	17	however	however	ADV
ap-1851	215	18	,	,	PUNCT
ap-1851	215	19	their	their	PRON
ap-1851	215	20	number	number	NOUN
ap-1851	215	21	is	be	AUX
ap-1851	215	22	finite	finite	ADJ
ap-1851	215	23	and	and	CCONJ
ap-1851	215	24	bounded	bound	VERB
ap-1851	215	25	by	by	ADP
ap-1851	215	26	m	m	PROPN
ap-1851	215	27	and	and	CCONJ
ap-1851	215	28	n	n	CCONJ
ap-1851	215	29	=	=	SYM
ap-1851	215	30	1	1	NUM
ap-1851	215	31	,	,	PUNCT
ap-1851	215	32	respectively	respectively	ADV
ap-1851	215	33	.	.	PUNCT
ap-1851	216	1	the	the	DET
ap-1851	216	2	main	main	ADJ
ap-1851	216	3	thing	thing	NOUN
ap-1851	216	4	is	be	AUX
ap-1851	216	5	thus	thus	ADV
ap-1851	216	6	to	to	PART
ap-1851	216	7	find	find	VERB
ap-1851	216	8	the	the	DET
ap-1851	216	9	behaviour	behaviour	NOUN
ap-1851	216	10	of	of	ADP
ap-1851	216	11	f1(k	f1(k	NOUN
ap-1851	216	12	)	)	PUNCT
ap-1851	216	13	,	,	PUNCT
ap-1851	216	14	in	in	ADP
ap-1851	216	15	particular	particular	ADJ
ap-1851	216	16	,	,	PUNCT
ap-1851	216	17	its	its	PRON
ap-1851	216	18	asymptotics	asymptotic	NOUN
ap-1851	216	19	for	for	ADP
ap-1851	216	20	k	k	PROPN
ap-1851	216	21	far	far	ADV
ap-1851	216	22	enough	enough	ADV
ap-1851	216	23	from	from	ADP
ap-1851	216	24	the	the	DET
ap-1851	216	25	real	real	ADJ
ap-1851	216	26	axis	axis	NOUN
ap-1851	216	27	.	.	PUNCT
ap-1851	217	1	lemma	lemma	PROPN
ap-1851	217	2	4.2	4.2	NUM
ap-1851	217	3	.	.	PUNCT
ap-1851	218	1	the	the	DET
ap-1851	218	2	asymptotics	asymptotic	NOUN
ap-1851	218	3	of	of	ADP
ap-1851	218	4	the	the	DET
ap-1851	218	5	regularized	regularize	VERB
ap-1851	218	6	green	green	ADJ
ap-1851	218	7	function	function	NOUN
ap-1851	218	8	is	be	AUX
ap-1851	218	9	the	the	DET
ap-1851	218	10	following	following	NOUN
ap-1851	218	11	:	:	PUNCT
ap-1851	218	12	(	(	PUNCT
ap-1851	218	13	1	1	NUM
ap-1851	218	14	.	.	PUNCT
ap-1851	218	15	)	)	PUNCT
ap-1851	219	1	for	for	ADP
ap-1851	219	2	d	d	NOUN
ap-1851	219	3	=	=	SYM
ap-1851	219	4	2	2	NUM
ap-1851	219	5	we	we	PRON
ap-1851	219	6	have	have	VERB
ap-1851	219	7	f1(k	f1(k	NOUN
ap-1851	219	8	)	)	PUNCT
ap-1851	219	9	=	=	SYM
ap-1851	219	10	1	1	NUM
ap-1851	219	11	2π	2π	NOUN
ap-1851	219	12	(	(	PUNCT
ap-1851	219	13	ln(±ik)−	ln(±ik)−	PROPN
ap-1851	219	14	ln	ln	ADJ
ap-1851	219	15	2−	2−	NUM
ap-1851	219	16	γe	γe	NOUN
ap-1851	219	17	)	)	PUNCT
ap-1851	220	1	+	+	VERB
ap-1851	220	2	o(|	o(|	PROPN
ap-1851	220	3	i	i	PRON
ap-1851	220	4	m	m	VERB
ap-1851	220	5	k|−1	k|−1	ADJ
ap-1851	220	6	)	)	PUNCT
ap-1851	221	1	if	if	SCONJ
ap-1851	221	2	∓	∓	PROPN
ap-1851	221	3	i	i	PRON
ap-1851	221	4	m	m	VERB
ap-1851	221	5	k	k	X
ap-1851	221	6	>	>	X
ap-1851	221	7	0	0	NUM
ap-1851	221	8	,	,	PUNCT
ap-1851	221	9	(	(	PUNCT
ap-1851	221	10	2	2	NUM
ap-1851	221	11	.	.	PUNCT
ap-1851	221	12	)	)	PUNCT
ap-1851	221	13	for	for	ADP
ap-1851	221	14	d	d	NOUN
ap-1851	221	15	=	=	SYM
ap-1851	221	16	3	3	NUM
ap-1851	221	17	we	we	PRON
ap-1851	221	18	have	have	VERB
ap-1851	221	19	f1(k	f1(k	NOUN
ap-1851	221	20	)	)	PUNCT
ap-1851	221	21	=	=	SYM
ap-1851	221	22	±	±	NUM
ap-1851	222	1	ik	ik	X
ap-1851	222	2	4π	4π	PROPN
ap-1851	223	1	+	+	CCONJ
ap-1851	224	1	o(|	o(|	PROPN
ap-1851	224	2	i	i	PRON
ap-1851	224	3	m	m	VERB
ap-1851	224	4	k|−1	k|−1	ADJ
ap-1851	224	5	)	)	PUNCT
ap-1851	225	1	if	if	SCONJ
ap-1851	225	2	∓	∓	PROPN
ap-1851	225	3	i	i	PRON
ap-1851	225	4	m	m	VERB
ap-1851	225	5	k	k	X
ap-1851	225	6	>	>	X
ap-1851	225	7	0	0	PROPN
ap-1851	225	8	,	,	PUNCT
ap-1851	225	9	where	where	SCONJ
ap-1851	225	10	γe	γe	PRON
ap-1851	225	11	stands	stand	VERB
ap-1851	225	12	for	for	ADP
ap-1851	225	13	the	the	DET
ap-1851	225	14	euler	euler	PROPN
ap-1851	225	15	constant	constant	ADJ
ap-1851	225	16	.	.	PUNCT
ap-1851	226	1	proof	proof	NOUN
ap-1851	226	2	.	.	PUNCT
ap-1851	227	1	the	the	DET
ap-1851	227	2	claim	claim	NOUN
ap-1851	227	3	can	can	AUX
ap-1851	227	4	be	be	AUX
ap-1851	227	5	easily	easily	ADV
ap-1851	227	6	verified	verify	VERB
ap-1851	227	7	by	by	ADP
ap-1851	227	8	reformulating	reformulate	VERB
ap-1851	227	9	results	result	NOUN
ap-1851	227	10	of	of	ADP
ap-1851	227	11	avramidi	avramidi	NOUN
ap-1851	227	12	[	[	X
ap-1851	227	13	3	3	NUM
ap-1851	227	14	,	,	PUNCT
ap-1851	227	15	4	4	NUM
ap-1851	227	16	]	]	PUNCT
ap-1851	227	17	on	on	ADP
ap-1851	227	18	high	high	ADJ
ap-1851	227	19	-	-	PUNCT
ap-1851	227	20	mass	mass	NOUN
ap-1851	227	21	asymptotics	asymptotic	NOUN
ap-1851	227	22	of	of	ADP
ap-1851	227	23	the	the	DET
ap-1851	227	24	operator	operator	NOUN
ap-1851	227	25	−∆	−∆	NOUN
ap-1851	228	1	+	+	ADJ
ap-1851	228	2	m2	m2	PROPN
ap-1851	228	3	as	as	ADP
ap-1851	228	4	m→∞.	m→∞.	NOUN
ap-1851	228	5	more	more	ADV
ap-1851	228	6	precisely	precisely	ADV
ap-1851	228	7	,	,	PUNCT
ap-1851	228	8	it	it	PRON
ap-1851	228	9	follows	follow	VERB
ap-1851	228	10	from	from	ADP
ap-1851	228	11	the	the	DET
ap-1851	228	12	stated	state	VERB
ap-1851	228	13	asymptotics	asymptotic	NOUN
ap-1851	228	14	of	of	ADP
ap-1851	228	15	equations	equation	NOUN
ap-1851	228	16	(	(	PUNCT
ap-1851	228	17	33	33	NUM
ap-1851	228	18	)	)	PUNCT
ap-1851	228	19	and	and	CCONJ
ap-1851	228	20	(	(	PUNCT
ap-1851	228	21	36	36	NUM
ap-1851	228	22	)	)	PUNCT
ap-1851	228	23	in	in	ADP
ap-1851	228	24	[	[	X
ap-1851	228	25	4	4	X
ap-1851	228	26	]	]	PUNCT
ap-1851	228	27	in	in	ADP
ap-1851	228	28	combination	combination	NOUN
ap-1851	228	29	with	with	ADP
ap-1851	228	30	the	the	DET
ap-1851	228	31	expression	expression	NOUN
ap-1851	228	32	for	for	ADP
ap-1851	228	33	bq	bq	INTJ
ap-1851	228	34	given	give	VERB
ap-1851	228	35	in	in	ADP
ap-1851	228	36	[	[	X
ap-1851	228	37	3	3	NUM
ap-1851	228	38	]	]	PUNCT
ap-1851	228	39	.	.	PUNCT
ap-1851	229	1	the	the	DET
ap-1851	229	2	constant	constant	ADJ
ap-1851	229	3	a0	a0	NOUN
ap-1851	229	4	in	in	ADP
ap-1851	229	5	[	[	X
ap-1851	229	6	4	4	NUM
ap-1851	229	7	]	]	PUNCT
ap-1851	229	8	can	can	AUX
ap-1851	229	9	be	be	AUX
ap-1851	229	10	determined	determine	VERB
ap-1851	229	11	from	from	ADP
ap-1851	229	12	the	the	DET
ap-1851	229	13	form	form	NOUN
ap-1851	229	14	of	of	ADP
ap-1851	229	15	the	the	DET
ap-1851	229	16	singular	singular	ADJ
ap-1851	229	17	parts	part	NOUN
ap-1851	229	18	of	of	ADP
ap-1851	229	19	green	green	ADJ
ap-1851	229	20	function	function	NOUN
ap-1851	229	21	to	to	PART
ap-1851	229	22	fit	fit	VERB
ap-1851	229	23	with	with	ADP
ap-1851	229	24	our	our	PRON
ap-1851	229	25	convention	convention	NOUN
ap-1851	229	26	.	.	PUNCT
ap-1851	230	1	remark	remark	VERB
ap-1851	230	2	4.3	4.3	NUM
ap-1851	230	3	.	.	PUNCT
ap-1851	231	1	in	in	ADP
ap-1851	231	2	the	the	DET
ap-1851	231	3	case	case	NOUN
ap-1851	231	4	of	of	ADP
ap-1851	231	5	a	a	DET
ap-1851	231	6	graph	graph	NOUN
ap-1851	231	7	with	with	ADP
ap-1851	231	8	a	a	DET
ap-1851	231	9	compact	compact	ADJ
ap-1851	231	10	core	core	NOUN
ap-1851	231	11	corresponding	correspond	VERB
ap-1851	231	12	to	to	ADP
ap-1851	231	13	d	d	PROPN
ap-1851	231	14	=	=	SYM
ap-1851	231	15	1	1	NUM
ap-1851	231	16	,	,	PUNCT
ap-1851	231	17	which	which	PRON
ap-1851	231	18	we	we	PRON
ap-1851	231	19	use	use	VERB
ap-1851	231	20	for	for	ADP
ap-1851	231	21	comparison	comparison	NOUN
ap-1851	231	22	,	,	PUNCT
ap-1851	231	23	one	one	PRON
ap-1851	231	24	has	have	VERB
ap-1851	231	25	instead	instead	ADV
ap-1851	231	26	f1(k	f1(k	NOUN
ap-1851	231	27	)	)	PUNCT
ap-1851	231	28	=	=	SYM
ap-1851	231	29	±	±	NOUN
ap-1851	231	30	1	1	NUM
ap-1851	231	31	2ik	2ik	NOUN
ap-1851	231	32	+	+	PROPN
ap-1851	232	1	o(|	o(|	PROPN
ap-1851	232	2	i	i	PRON
ap-1851	232	3	m	m	VERB
ap-1851	232	4	k|−2	k|−2	ADJ
ap-1851	232	5	)	)	PUNCT
ap-1851	232	6	for	for	ADP
ap-1851	232	7	∓	∓	PROPN
ap-1851	233	1	i	i	PRON
ap-1851	233	2	m	m	VERB
ap-1851	233	3	k	k	X
ap-1851	233	4	>	>	X
ap-1851	233	5	0	0	X
ap-1851	233	6	.	.	PUNCT
ap-1851	234	1	now	now	ADV
ap-1851	234	2	we	we	PRON
ap-1851	234	3	can	can	AUX
ap-1851	234	4	use	use	VERB
ap-1851	234	5	the	the	DET
ap-1851	234	6	previous	previous	ADJ
ap-1851	234	7	lemmata	lemmata	NOUN
ap-1851	234	8	to	to	PART
ap-1851	234	9	prove	prove	VERB
ap-1851	234	10	the	the	DET
ap-1851	234	11	main	main	ADJ
ap-1851	234	12	result	result	NOUN
ap-1851	234	13	of	of	ADP
ap-1851	234	14	this	this	DET
ap-1851	234	15	section	section	NOUN
ap-1851	234	16	.	.	PUNCT
ap-1851	235	1	theorem	theorem	VERB
ap-1851	235	2	4.4	4.4	NUM
ap-1851	235	3	.	.	PUNCT
ap-1851	236	1	consider	consider	VERB
ap-1851	236	2	a	a	DET
ap-1851	236	3	manifold	manifold	ADJ
ap-1851	236	4	ω	ω	NOUN
ap-1851	236	5	,	,	PUNCT
ap-1851	236	6	dim	dim	ADJ
ap-1851	236	7	ω	ω	NOUN
ap-1851	236	8	=	=	SYM
ap-1851	236	9	2	2	NUM
ap-1851	236	10	,	,	PUNCT
ap-1851	236	11	and	and	CCONJ
ap-1851	236	12	let	let	VERB
ap-1851	236	13	hu	hu	PROPN
ap-1851	236	14	be	be	AUX
ap-1851	236	15	the	the	DET
ap-1851	236	16	hamiltonian	hamiltonian	NOUN
ap-1851	236	17	on	on	ADP
ap-1851	236	18	ω	ω	PROPN
ap-1851	236	19	with	with	ADP
ap-1851	236	20	several	several	ADJ
ap-1851	236	21	halflines	halfline	NOUN
ap-1851	236	22	attached	attach	VERB
ap-1851	236	23	at	at	ADP
ap-1851	236	24	a	a	DET
ap-1851	236	25	single	single	ADJ
ap-1851	236	26	point	point	NOUN
ap-1851	236	27	by	by	ADP
ap-1851	236	28	coupling	couple	VERB
ap-1851	236	29	condition	condition	NOUN
ap-1851	236	30	(	(	PUNCT
ap-1851	236	31	1	1	NUM
ap-1851	236	32	)	)	PUNCT
ap-1851	236	33	.	.	PUNCT
ap-1851	237	1	then	then	ADV
ap-1851	237	2	all	all	DET
ap-1851	237	3	the	the	DET
ap-1851	237	4	resonances	resonance	NOUN
ap-1851	237	5	of	of	ADP
ap-1851	237	6	this	this	DET
ap-1851	237	7	system	system	NOUN
ap-1851	237	8	are	be	AUX
ap-1851	237	9	located	locate	VERB
ap-1851	237	10	in	in	ADP
ap-1851	237	11	the	the	DET
ap-1851	237	12	k	k	NOUN
ap-1851	237	13	-	-	NOUN
ap-1851	237	14	plane	plane	NOUN
ap-1851	237	15	within	within	ADP
ap-1851	237	16	a	a	DET
ap-1851	237	17	finite	finite	ADJ
ap-1851	237	18	-	-	ADJ
ap-1851	237	19	width	width	ADJ
ap-1851	237	20	strip	strip	NOUN
ap-1851	237	21	parallel	parallel	NOUN
ap-1851	237	22	to	to	ADP
ap-1851	237	23	the	the	DET
ap-1851	237	24	real	real	ADJ
ap-1851	237	25	axis	axis	NOUN
ap-1851	237	26	.	.	PUNCT
ap-1851	238	1	proof	proof	NOUN
ap-1851	238	2	.	.	PUNCT
ap-1851	239	1	from	from	ADP
ap-1851	239	2	equation	equation	NOUN
ap-1851	239	3	(	(	PUNCT
ap-1851	239	4	3	3	X
ap-1851	239	5	)	)	PUNCT
ap-1851	239	6	it	it	PRON
ap-1851	239	7	follows	follow	VERB
ap-1851	239	8	that	that	SCONJ
ap-1851	239	9	ũ(k	ũ(k	NOUN
ap-1851	239	10	)	)	PUNCT
ap-1851	239	11	and	and	CCONJ
ap-1851	239	12	subsequently	subsequently	ADV
ap-1851	239	13	also	also	ADV
ap-1851	239	14	the	the	DET
ap-1851	239	15	expression	expression	NOUN
ap-1851	239	16	i	i	PRON
ap-1851	239	17	(	(	PUNCT
ap-1851	239	18	ũ(k)−	ũ(k)−	PROPN
ap-1851	239	19	1	1	NUM
ap-1851	239	20	)	)	PUNCT
ap-1851	239	21	−1	−1	NOUN
ap-1851	239	22	(	(	PUNCT
ap-1851	239	23	ũ(k	ũ(k	PROPN
ap-1851	239	24	)	)	PUNCT
ap-1851	239	25	+	+	NUM
ap-1851	239	26	1	1	X
ap-1851	239	27	)	)	PUNCT
ap-1851	239	28	is	be	AUX
ap-1851	239	29	a	a	DET
ap-1851	239	30	rational	rational	ADJ
ap-1851	239	31	function	function	NOUN
ap-1851	239	32	of	of	ADP
ap-1851	239	33	the	the	DET
ap-1851	239	34	momentum	momentum	NOUN
ap-1851	239	35	variable	variable	NOUN
ap-1851	240	1	k.	k.	PROPN
ap-1851	240	2	hence	hence	ADV
ap-1851	240	3	there	there	PRON
ap-1851	240	4	exists	exist	VERB
ap-1851	240	5	such	such	DET
ap-1851	240	6	a	a	DET
ap-1851	240	7	constant	constant	ADJ
ap-1851	240	8	c	c	NOUN
ap-1851	240	9	that	that	PRON
ap-1851	240	10	for	for	ADP
ap-1851	240	11	|	|	ADV
ap-1851	240	12	i	i	PRON
ap-1851	240	13	m	m	VERB
ap-1851	240	14	k|	k|	NOUN
ap-1851	240	15	>	>	X
ap-1851	240	16	c	c	X
ap-1851	240	17	the	the	DET
ap-1851	240	18	leading	lead	VERB
ap-1851	240	19	term	term	NOUN
ap-1851	240	20	of	of	ADP
ap-1851	240	21	f	f	PROPN
ap-1851	240	22	(	(	PUNCT
ap-1851	240	23	k	k	NOUN
ap-1851	240	24	)	)	PUNCT
ap-1851	240	25	behaves	behave	VERB
ap-1851	240	26	either	either	CCONJ
ap-1851	240	27	like	like	ADP
ap-1851	240	28	a	a	DET
ap-1851	240	29	multiple	multiple	NOUN
ap-1851	240	30	of	of	ADP
ap-1851	240	31	ln	ln	ADJ
ap-1851	241	1	|	|	ADV
ap-1851	242	1	i	i	PRON
ap-1851	242	2	m	m	VERB
ap-1851	242	3	k|	k|	NOUN
ap-1851	242	4	or	or	CCONJ
ap-1851	242	5	like	like	ADP
ap-1851	242	6	the	the	DET
ap-1851	242	7	leading	lead	VERB
ap-1851	242	8	term	term	NOUN
ap-1851	242	9	of	of	ADP
ap-1851	242	10	previously	previously	ADV
ap-1851	242	11	mentioned	mention	VERB
ap-1851	242	12	rational	rational	ADJ
ap-1851	242	13	function	function	NOUN
ap-1851	242	14	.	.	PUNCT
ap-1851	243	1	the	the	DET
ap-1851	243	2	constant	constant	ADJ
ap-1851	243	3	c	c	NOUN
ap-1851	243	4	can	can	AUX
ap-1851	243	5	be	be	AUX
ap-1851	243	6	chosen	choose	VERB
ap-1851	243	7	such	such	ADJ
ap-1851	243	8	that	that	SCONJ
ap-1851	243	9	the	the	DET
ap-1851	243	10	contribution	contribution	NOUN
ap-1851	243	11	of	of	ADP
ap-1851	243	12	the	the	DET
ap-1851	243	13	rest	rest	NOUN
ap-1851	243	14	of	of	ADP
ap-1851	243	15	f	f	PROPN
ap-1851	243	16	does	do	AUX
ap-1851	243	17	change	change	VERB
ap-1851	243	18	substantially	substantially	ADV
ap-1851	243	19	the	the	DET
ap-1851	243	20	phase	phase	NOUN
ap-1851	243	21	of	of	ADP
ap-1851	243	22	f	f	PROPN
ap-1851	243	23	.	.	PUNCT
ap-1851	244	1	more	more	ADV
ap-1851	244	2	precisely	precisely	ADV
ap-1851	244	3	,	,	PUNCT
ap-1851	244	4	we	we	PRON
ap-1851	244	5	then	then	ADV
ap-1851	244	6	have	have	VERB
ap-1851	244	7	|kn|	|kn|	PROPN
ap-1851	244	8	≥	≥	NOUN
ap-1851	244	9	cn	cn	X
ap-1851	244	10	and∣∣ln	and∣∣ln	ADV
ap-1851	244	11	(	(	PUNCT
ap-1851	244	12	∓ik	∓ik	PROPN
ap-1851	244	13	)	)	PUNCT
ap-1851	244	14	∣∣	∣∣	X
ap-1851	245	1	=	=	PUNCT
ap-1851	245	2	∣∣∣ln	∣∣∣ln	PROPN
ap-1851	245	3	|k|	|k|	PROPN
ap-1851	245	4	∓	∓	PROPN
ap-1851	245	5	π	π	PROPN
ap-1851	245	6	2	2	NUM
ap-1851	245	7	+	+	CCONJ
ap-1851	245	8	arg	arg	NOUN
ap-1851	245	9	k	k	X
ap-1851	245	10	∣∣∣	∣∣∣	X
ap-1851	245	11	≥	≥	NUM
ap-1851	245	12	1	1	NUM
ap-1851	245	13	2	2	NUM
ap-1851	245	14	lnc	lnc	NOUN
ap-1851	245	15	for	for	ADP
ap-1851	245	16	large	large	ADJ
ap-1851	245	17	enough	enough	ADJ
ap-1851	245	18	c	c	NOUN
ap-1851	245	19	,	,	PUNCT
ap-1851	245	20	and	and	CCONJ
ap-1851	245	21	consequently	consequently	ADV
ap-1851	245	22	,	,	PUNCT
ap-1851	245	23	the	the	DET
ap-1851	245	24	dominant	dominant	ADJ
ap-1851	245	25	phase	phase	NOUN
ap-1851	245	26	behaviour	behaviour	NOUN
ap-1851	245	27	of	of	ADP
ap-1851	245	28	ank	ank	PROPN
ap-1851	245	29	n	n	PROPN
ap-1851	245	30	(	(	PUNCT
ap-1851	245	31	1	1	NUM
ap-1851	245	32	+	+	CCONJ
ap-1851	245	33	ln(∓ik	ln(∓ik	NOUN
ap-1851	245	34	)	)	PUNCT
ap-1851	245	35	+	+	CCONJ
ap-1851	245	36	∑n−1	∑n−1	ADP
ap-1851	245	37	j=0	j=0	PROPN
ap-1851	245	38	ajk	ajk	PROPN
ap-1851	245	39	j	j	PROPN
ap-1851	245	40	+	+	PROPN
ap-1851	245	41	o(|k|	o(|k|	X
ap-1851	245	42	)	)	PUNCT
ap-1851	245	43	ankn	ankn	ADJ
ap-1851	245	44	)	)	PUNCT
ap-1851	245	45	and	and	CCONJ
ap-1851	245	46	ln(∓ik	ln(∓ik	NOUN
ap-1851	245	47	)	)	PUNCT
ap-1851	245	48	(	(	PUNCT
ap-1851	245	49	1	1	NUM
ap-1851	245	50	+	+	NUM
ap-1851	245	51	c+o(|k|	c+o(|k|	NOUN
ap-1851	245	52	)	)	PUNCT
ap-1851	245	53	ln(∓ik	ln(∓ik	NOUN
ap-1851	245	54	)	)	PUNCT
ap-1851	245	55	)	)	PUNCT
ap-1851	245	56	is	be	AUX
ap-1851	245	57	determined	determine	VERB
ap-1851	245	58	by	by	ADP
ap-1851	245	59	the	the	DET
ap-1851	245	60	terms	term	NOUN
ap-1851	245	61	in	in	ADP
ap-1851	245	62	front	front	NOUN
ap-1851	245	63	of	of	ADP
ap-1851	245	64	the	the	DET
ap-1851	245	65	brackets	bracket	NOUN
ap-1851	245	66	,	,	PUNCT
ap-1851	245	67	in	in	ADP
ap-1851	245	68	particular	particular	ADJ
ap-1851	245	69	,	,	PUNCT
ap-1851	245	70	there	there	PRON
ap-1851	245	71	are	be	VERB
ap-1851	245	72	finitely	finitely	ADV
ap-1851	245	73	many	many	ADJ
ap-1851	245	74	jumps	jump	NOUN
ap-1851	245	75	of	of	ADP
ap-1851	245	76	the	the	DET
ap-1851	245	77	phase	phase	NOUN
ap-1851	245	78	of	of	ADP
ap-1851	245	79	f	f	PROPN
ap-1851	245	80	between	between	ADP
ap-1851	245	81	zero	zero	NUM
ap-1851	245	82	and	and	CCONJ
ap-1851	245	83	2π	2π	NOUN
ap-1851	245	84	along	along	ADP
ap-1851	245	85	the	the	DET
ap-1851	245	86	part	part	NOUN
ap-1851	245	87	of	of	ADP
ap-1851	245	88	the	the	DET
ap-1851	245	89	circle	circle	NOUN
ap-1851	245	90	|k|	|k|	NOUN
ap-1851	245	91	=	=	SYM
ap-1851	246	1	r	r	NOUN
ap-1851	246	2	in	in	ADP
ap-1851	246	3	the	the	DET
ap-1851	246	4	region	region	NOUN
ap-1851	247	1	|	|	INTJ
ap-1851	247	2	i	i	PRON
ap-1851	247	3	m	m	VERB
ap-1851	247	4	k|	k|	VERB
ap-1851	247	5	>	>	X
ap-1851	247	6	c	c	NOUN
ap-1851	247	7	with	with	ADP
ap-1851	247	8	c	c	NOUN
ap-1851	247	9	sufficiently	sufficiently	ADV
ap-1851	247	10	large	large	ADJ
ap-1851	247	11	.	.	PUNCT
ap-1851	248	1	in	in	ADP
ap-1851	248	2	other	other	ADJ
ap-1851	248	3	words	word	NOUN
ap-1851	248	4	,	,	PUNCT
ap-1851	248	5	all	all	DET
ap-1851	248	6	but	but	ADV
ap-1851	248	7	finitely	finitely	ADV
ap-1851	248	8	many	many	ADJ
ap-1851	248	9	resonances	resonance	NOUN
ap-1851	248	10	can	can	AUX
ap-1851	248	11	be	be	AUX
ap-1851	248	12	found	find	VERB
ap-1851	248	13	within	within	ADP
ap-1851	248	14	the	the	DET
ap-1851	248	15	strip	strip	NOUN
ap-1851	249	1	|	|	INTJ
ap-1851	249	2	i	i	PRON
ap-1851	249	3	m	m	VERB
ap-1851	249	4	k|	k|	VERB
ap-1851	249	5	<	<	X
ap-1851	249	6	c	c	NOUN
ap-1851	249	7	,	,	PUNCT
ap-1851	249	8	hence	hence	ADV
ap-1851	249	9	all	all	DET
ap-1851	249	10	resonances	resonance	NOUN
ap-1851	249	11	are	be	AUX
ap-1851	249	12	located	locate	VERB
ap-1851	249	13	within	within	ADP
ap-1851	249	14	some	some	DET
ap-1851	249	15	strip	strip	NOUN
ap-1851	249	16	parallel	parallel	NOUN
ap-1851	249	17	to	to	ADP
ap-1851	249	18	the	the	DET
ap-1851	249	19	real	real	ADJ
ap-1851	249	20	axis	axis	NOUN
ap-1851	249	21	in	in	ADP
ap-1851	249	22	the	the	DET
ap-1851	249	23	momentum	momentum	NOUN
ap-1851	249	24	plane	plane	NOUN
ap-1851	249	25	.	.	PUNCT
ap-1851	250	1	theorem	theorem	VERB
ap-1851	250	2	4.5	4.5	NUM
ap-1851	250	3	.	.	PUNCT
ap-1851	251	1	let	let	VERB
ap-1851	251	2	d	d	NOUN
ap-1851	251	3	=	=	SYM
ap-1851	251	4	3	3	NUM
ap-1851	251	5	,	,	PUNCT
ap-1851	251	6	and	and	CCONJ
ap-1851	251	7	let	let	VERB
ap-1851	251	8	hu	hu	PROPN
ap-1851	251	9	be	be	AUX
ap-1851	251	10	hamiltonian	hamiltonian	ADJ
ap-1851	251	11	on	on	ADP
ap-1851	251	12	ω	ω	PROPN
ap-1851	251	13	with	with	ADP
ap-1851	251	14	several	several	ADJ
ap-1851	251	15	halflines	halfline	NOUN
ap-1851	251	16	attached	attach	VERB
ap-1851	251	17	at	at	ADP
ap-1851	251	18	one	one	NUM
ap-1851	251	19	point	point	NOUN
ap-1851	251	20	by	by	ADP
ap-1851	251	21	coupling	couple	VERB
ap-1851	251	22	condition	condition	NOUN
ap-1851	251	23	(	(	PUNCT
ap-1851	251	24	1	1	NUM
ap-1851	251	25	)	)	PUNCT
ap-1851	251	26	.	.	PUNCT
ap-1851	252	1	then	then	ADV
ap-1851	252	2	all	all	DET
ap-1851	252	3	resonances	resonance	NOUN
ap-1851	252	4	of	of	ADP
ap-1851	252	5	hu	hu	PROPN
ap-1851	252	6	are	be	AUX
ap-1851	252	7	located	locate	VERB
ap-1851	252	8	within	within	ADP
ap-1851	252	9	a	a	DET
ap-1851	252	10	strip	strip	NOUN
ap-1851	252	11	parallel	parallel	NOUN
ap-1851	252	12	to	to	ADP
ap-1851	252	13	the	the	DET
ap-1851	252	14	real	real	ADJ
ap-1851	252	15	axis	axis	NOUN
ap-1851	252	16	.	.	PUNCT
ap-1851	253	1	proof	proof	NOUN
ap-1851	253	2	.	.	PUNCT
ap-1851	254	1	in	in	ADP
ap-1851	254	2	the	the	DET
ap-1851	254	3	case	case	NOUN
ap-1851	254	4	when	when	SCONJ
ap-1851	254	5	the	the	DET
ap-1851	254	6	coupling	coupling	NOUN
ap-1851	254	7	term	term	NOUN
ap-1851	254	8	does	do	AUX
ap-1851	254	9	not	not	PART
ap-1851	254	10	coincide	coincide	VERB
ap-1851	254	11	with	with	ADP
ap-1851	254	12	the	the	DET
ap-1851	254	13	first	first	ADJ
ap-1851	254	14	term	term	NOUN
ap-1851	254	15	of	of	ADP
ap-1851	254	16	asymptotics	asymptotic	NOUN
ap-1851	254	17	of	of	ADP
ap-1851	254	18	f1	f1	NOUN
ap-1851	254	19	,	,	PUNCT
ap-1851	254	20	i.e.	i.e.	X
ap-1851	254	21	(	(	PUNCT
ap-1851	254	22	ũ(k	ũ(k	ADJ
ap-1851	254	23	)	)	PUNCT
ap-1851	254	24	−	−	NOUN
ap-1851	254	25	1)−1(ũ(k	1)−1(ũ(k	NUM
ap-1851	254	26	)	)	PUNCT
ap-1851	254	27	+	+	CCONJ
ap-1851	254	28	1	1	NUM
ap-1851	254	29	)	)	PUNCT
ap-1851	254	30	6=	6=	ADP
ap-1851	254	31	±	±	NOUN
ap-1851	255	1	k	k	NOUN
ap-1851	256	1	4π	4π	NUM
ap-1851	256	2	,	,	PUNCT
ap-1851	256	3	one	one	PRON
ap-1851	256	4	can	can	AUX
ap-1851	256	5	employ	employ	VERB
ap-1851	256	6	the	the	DET
ap-1851	256	7	same	same	ADJ
ap-1851	256	8	arguments	argument	NOUN
ap-1851	256	9	as	as	ADP
ap-1851	256	10	in	in	ADP
ap-1851	256	11	previous	previous	ADJ
ap-1851	256	12	theorem	theorem	NOUN
ap-1851	256	13	.	.	PUNCT
ap-1851	257	1	let	let	VERB
ap-1851	257	2	us	we	PRON
ap-1851	257	3	check	check	VERB
ap-1851	257	4	that	that	SCONJ
ap-1851	257	5	no	no	DET
ap-1851	257	6	unitary	unitary	ADJ
ap-1851	257	7	matrix	matrix	NOUN
ap-1851	257	8	can	can	AUX
ap-1851	257	9	lead	lead	VERB
ap-1851	257	10	to	to	ADP
ap-1851	257	11	such	such	DET
ap-1851	257	12	an	an	DET
ap-1851	257	13	effective	effective	ADJ
ap-1851	257	14	coupling	coupling	NOUN
ap-1851	257	15	matrix	matrix	NOUN
ap-1851	257	16	.	.	PUNCT
ap-1851	258	1	if	if	SCONJ
ap-1851	258	2	it	it	PRON
ap-1851	258	3	were	be	AUX
ap-1851	258	4	the	the	DET
ap-1851	258	5	case	case	NOUN
ap-1851	258	6	we	we	PRON
ap-1851	258	7	would	would	AUX
ap-1851	258	8	have	have	VERB
ap-1851	258	9	ũ(k	ũ(k	NOUN
ap-1851	258	10	)	)	PUNCT
ap-1851	258	11	=	=	SYM
ap-1851	259	1	−4π	−4π	PROPN
ap-1851	259	2	±	±	NUM
ap-1851	259	3	k	k	NOUN
ap-1851	260	1	4π	4π	NUM
ap-1851	260	2	∓	∓	PROPN
ap-1851	261	1	k	k	X
ap-1851	261	2	.	.	PUNCT
ap-1851	262	1	(	(	PUNCT
ap-1851	262	2	7	7	X
ap-1851	262	3	)	)	PUNCT
ap-1851	262	4	assume	assume	VERB
ap-1851	262	5	that	that	SCONJ
ap-1851	262	6	(	(	PUNCT
ap-1851	262	7	7	7	X
ap-1851	262	8	)	)	PUNCT
ap-1851	262	9	holds	hold	VERB
ap-1851	262	10	true	true	ADJ
ap-1851	262	11	for	for	ADP
ap-1851	262	12	some	some	DET
ap-1851	262	13	unitary	unitary	ADJ
ap-1851	262	14	matrix	matrix	NOUN
ap-1851	262	15	u	u	NOUN
ap-1851	262	16	.	.	PUNCT
ap-1851	263	1	for	for	ADP
ap-1851	263	2	the	the	DET
ap-1851	263	3	upper	upper	ADJ
ap-1851	263	4	sign	sign	NOUN
ap-1851	263	5	the	the	DET
ap-1851	263	6	expression	expression	NOUN
ap-1851	263	7	diverges	diverge	VERB
ap-1851	263	8	at	at	ADP
ap-1851	263	9	k	k	PROPN
ap-1851	263	10	=	=	PUNCT
ap-1851	263	11	4π	4π	NUM
ap-1851	263	12	;	;	PUNCT
ap-1851	263	13	this	this	PRON
ap-1851	263	14	contradicts	contradict	VERB
ap-1851	263	15	the	the	DET
ap-1851	263	16	unitarity	unitarity	NOUN
ap-1851	263	17	of	of	ADP
ap-1851	263	18	u	u	PROPN
ap-1851	263	19	,	,	PUNCT
ap-1851	263	20	by	by	ADP
ap-1851	263	21	which	which	PRON
ap-1851	263	22	its	its	PRON
ap-1851	263	23	modulus	modulus	NOUN
ap-1851	263	24	must	must	AUX
ap-1851	263	25	not	not	PART
ap-1851	263	26	exceed	exceed	VERB
ap-1851	263	27	one	one	NUM
ap-1851	263	28	.	.	PUNCT
ap-1851	264	1	let	let	VERB
ap-1851	264	2	us	we	PRON
ap-1851	264	3	now	now	ADV
ap-1851	264	4	turn	turn	VERB
ap-1851	264	5	to	to	ADP
ap-1851	264	6	the	the	DET
ap-1851	264	7	lower	low	ADJ
ap-1851	264	8	-	-	PUNCT
ap-1851	264	9	sign	sign	NOUN
ap-1851	264	10	case	case	NOUN
ap-1851	264	11	.	.	PUNCT
ap-1851	265	1	using	use	VERB
ap-1851	265	2	u4	u4	PROPN
ap-1851	265	3	=	=	PROPN
ap-1851	265	4	v	v	PROPN
ap-1851	265	5	−1dv	−1dv	NOUN
ap-1851	265	6	,	,	PUNCT
ap-1851	265	7	u2v	u2v	PROPN
ap-1851	265	8	=	=	SYM
ap-1851	265	9	u2v	u2v	NOUN
ap-1851	265	10	−1	−1	NOUN
ap-1851	265	11	and	and	CCONJ
ap-1851	265	12	u3v	u3v	NOUN
ap-1851	265	13	=	=	SYM
ap-1851	265	14	v	v	NUM
ap-1851	265	15	u3	u3	NOUN
ap-1851	265	16	with	with	ADP
ap-1851	265	17	a	a	DET
ap-1851	265	18	diagonal	diagonal	ADJ
ap-1851	265	19	d	d	NOUN
ap-1851	265	20	and	and	CCONJ
ap-1851	265	21	a	a	DET
ap-1851	265	22	unitary	unitary	ADJ
ap-1851	265	23	v	v	NOUN
ap-1851	265	24	,	,	PUNCT
ap-1851	265	25	the	the	DET
ap-1851	265	26	equation	equation	NOUN
ap-1851	265	27	(	(	PUNCT
ap-1851	265	28	7	7	X
ap-1851	265	29	)	)	PUNCT
ap-1851	265	30	becomes	become	VERB
ap-1851	265	31	−4π	−4π	PROPN
ap-1851	265	32	−	−	PROPN
ap-1851	266	1	k	k	NOUN
ap-1851	267	1	4π	4π	NUM
ap-1851	268	1	+	+	CCONJ
ap-1851	268	2	k	k	NOUN
ap-1851	268	3	=	=	SYM
ap-1851	268	4	u1	u1	PROPN
ap-1851	268	5	−	−	PROPN
ap-1851	268	6	u2v	u2v	PROPN
ap-1851	269	1	(	(	PUNCT
ap-1851	269	2	d	d	NOUN
ap-1851	269	3	−	−	PROPN
ap-1851	269	4	1	1	NUM
ap-1851	270	1	+	+	CCONJ
ap-1851	270	2	k	k	PROPN
ap-1851	271	1	1−	1−	NUM
ap-1851	271	2	k	k	NOUN
ap-1851	271	3	i	i	NOUN
ap-1851	271	4	)	)	PUNCT
ap-1851	271	5	−1	−1	NOUN
ap-1851	271	6	u3v	u3v	ADV
ap-1851	271	7	.	.	PUNCT
ap-1851	272	1	let	let	VERB
ap-1851	272	2	us	we	PRON
ap-1851	272	3	find	find	VERB
ap-1851	272	4	how	how	SCONJ
ap-1851	272	5	the	the	DET
ap-1851	272	6	right	right	ADJ
ap-1851	272	7	-	-	PUNCT
ap-1851	272	8	hand	hand	NOUN
ap-1851	272	9	side	side	NOUN
ap-1851	272	10	behaves	behave	VERB
ap-1851	272	11	in	in	ADP
ap-1851	272	12	the	the	DET
ap-1851	272	13	vicinity	vicinity	NOUN
ap-1851	272	14	of	of	ADP
ap-1851	272	15	−4π	−4π	PROPN
ap-1851	272	16	choosing	choose	VERB
ap-1851	272	17	k	k	PROPN
ap-1851	272	18	=	=	PUNCT
ap-1851	273	1	−4π	−4π	PROPN
ap-1851	273	2	+	+	NUM
ap-1851	273	3	ε	ε	PROPN
ap-1851	273	4	.	.	PUNCT
ap-1851	274	1	if	if	SCONJ
ap-1851	274	2	none	none	NOUN
ap-1851	274	3	of	of	ADP
ap-1851	274	4	the	the	DET
ap-1851	274	5	eigenvalues	eigenvalue	NOUN
ap-1851	274	6	of	of	ADP
ap-1851	274	7	d	d	NOUN
ap-1851	274	8	equals	equal	VERB
ap-1851	274	9	1−4π	1−4π	NUM
ap-1851	274	10	1	1	NUM
ap-1851	274	11	+	+	SYM
ap-1851	274	12	4π	4π	NUM
ap-1851	274	13	the	the	DET
ap-1851	274	14	relation	relation	NOUN
ap-1851	274	15	can	can	AUX
ap-1851	274	16	not	not	PART
ap-1851	274	17	be	be	AUX
ap-1851	274	18	valid	valid	ADJ
ap-1851	274	19	as	as	ADP
ap-1851	274	20	ε→	ε→	PROPN
ap-1851	274	21	0	0	NUM
ap-1851	274	22	.	.	PUNCT
ap-1851	275	1	furthermore	furthermore	ADV
ap-1851	275	2	,	,	PUNCT
ap-1851	275	3	combining	combine	VERB
ap-1851	275	4	(	(	PUNCT
ap-1851	275	5	7	7	NUM
ap-1851	275	6	)	)	PUNCT
ap-1851	275	7	with	with	ADP
ap-1851	275	8	421	421	NUM
ap-1851	275	9	p.	p.	NOUN
ap-1851	275	10	exner	exner	NOUN
ap-1851	275	11	,	,	PUNCT
ap-1851	275	12	j.	j.	PROPN
ap-1851	275	13	lipovský	lipovský	PROPN
ap-1851	275	14	acta	acta	PROPN
ap-1851	275	15	polytechnica	polytechnica	PROPN
ap-1851	275	16	the	the	DET
ap-1851	275	17	behaviour	behaviour	NOUN
ap-1851	275	18	of	of	ADP
ap-1851	275	19	the	the	DET
ap-1851	275	20	last	last	ADJ
ap-1851	275	21	expression	expression	NOUN
ap-1851	275	22	as	as	ADP
ap-1851	275	23	k	k	PROPN
ap-1851	275	24	→	→	SYM
ap-1851	275	25	1	1	NUM
ap-1851	275	26	,	,	PUNCT
ap-1851	275	27	we	we	PRON
ap-1851	275	28	find	find	VERB
ap-1851	275	29	u1	u1	NOUN
ap-1851	275	30	=	=	SYM
ap-1851	275	31	1−4π	1−4π	NUM
ap-1851	275	32	1	1	NUM
ap-1851	276	1	+	+	SYM
ap-1851	276	2	4π	4π	NUM
ap-1851	276	3	.	.	PUNCT
ap-1851	277	1	were	be	AUX
ap-1851	277	2	there	there	ADV
ap-1851	277	3	two	two	NUM
ap-1851	277	4	or	or	CCONJ
ap-1851	277	5	more	more	ADJ
ap-1851	277	6	eigenvalues	eigenvalue	NOUN
ap-1851	277	7	of	of	ADP
ap-1851	277	8	d	d	NOUN
ap-1851	277	9	equal	equal	ADJ
ap-1851	277	10	to	to	ADP
ap-1851	277	11	1−4π	1−4π	NUM
ap-1851	277	12	1	1	NUM
ap-1851	278	1	+	+	SYM
ap-1851	278	2	4π	4π	NUM
ap-1851	278	3	,	,	PUNCT
ap-1851	278	4	we	we	PRON
ap-1851	278	5	could	could	AUX
ap-1851	278	6	conclude	conclude	VERB
ap-1851	278	7	that	that	SCONJ
ap-1851	278	8	the	the	DET
ap-1851	278	9	vector	vector	NOUN
ap-1851	278	10	(	(	PUNCT
ap-1851	278	11	u1	u1	NOUN
ap-1851	278	12	,	,	PUNCT
ap-1851	278	13	u3v	u3v	NOUN
ap-1851	278	14	)	)	PUNCT
ap-1851	278	15	t	t	PROPN
ap-1851	278	16	has	have	AUX
ap-1851	278	17	norm	norm	VERB
ap-1851	278	18	bigger	big	ADJ
ap-1851	278	19	than	than	ADP
ap-1851	278	20	one	one	NUM
ap-1851	278	21	,	,	PUNCT
ap-1851	278	22	which	which	PRON
ap-1851	278	23	contradicts	contradict	VERB
ap-1851	278	24	the	the	DET
ap-1851	278	25	unitarity	unitarity	NOUN
ap-1851	278	26	of	of	ADP
ap-1851	278	27	u	u	PROPN
ap-1851	278	28	.	.	PUNCT
ap-1851	279	1	consequently	consequently	ADV
ap-1851	279	2	,	,	PUNCT
ap-1851	279	3	there	there	PRON
ap-1851	279	4	is	be	VERB
ap-1851	279	5	exactly	exactly	ADV
ap-1851	279	6	one	one	NUM
ap-1851	279	7	eigenvalue	eigenvalue	NOUN
ap-1851	279	8	1−4π	1−4π	NUM
ap-1851	279	9	1	1	NUM
ap-1851	279	10	+	+	SYM
ap-1851	279	11	4π	4π	NUM
ap-1851	279	12	of	of	ADP
ap-1851	279	13	matrix	matrix	NOUN
ap-1851	279	14	d.	d.	NOUN
ap-1851	279	15	since	since	SCONJ
ap-1851	279	16	the	the	DET
ap-1851	279	17	rows	row	NOUN
ap-1851	279	18	and	and	CCONJ
ap-1851	279	19	columns	column	NOUN
ap-1851	279	20	of	of	ADP
ap-1851	279	21	u4	u4	PROPN
ap-1851	279	22	can	can	AUX
ap-1851	279	23	be	be	AUX
ap-1851	279	24	rearranged	rearrange	VERB
ap-1851	279	25	,	,	PUNCT
ap-1851	279	26	we	we	PRON
ap-1851	279	27	may	may	AUX
ap-1851	279	28	assume	assume	VERB
ap-1851	279	29	that	that	SCONJ
ap-1851	279	30	it	it	PRON
ap-1851	279	31	is	be	AUX
ap-1851	279	32	the	the	DET
ap-1851	279	33	first	first	ADJ
ap-1851	279	34	eigenvalue	eigenvalue	NOUN
ap-1851	279	35	in	in	ADP
ap-1851	279	36	which	which	DET
ap-1851	279	37	case	case	NOUN
ap-1851	279	38	we	we	PRON
ap-1851	279	39	have	have	VERB
ap-1851	279	40	−	−	NUM
ap-1851	279	41	8π	8π	NUM
ap-1851	279	42	ε	ε	PROPN
ap-1851	279	43	=	=	SYM
ap-1851	279	44	u1	u1	PROPN
ap-1851	279	45	−	−	PROPN
ap-1851	279	46	1	1	NUM
ap-1851	280	1	+	+	NUM
ap-1851	280	2	u	u	SYM
ap-1851	280	3	(	(	PUNCT
ap-1851	280	4	1	1	NUM
ap-1851	280	5	)	)	PUNCT
ap-1851	280	6	2v	2v	PROPN
ap-1851	280	7	u	u	SYM
ap-1851	280	8	(	(	PUNCT
ap-1851	280	9	1	1	NUM
ap-1851	280	10	)	)	PUNCT
ap-1851	280	11	3v	3v	NUM
ap-1851	280	12	(	(	PUNCT
ap-1851	280	13	1	1	NUM
ap-1851	280	14	+	+	SYM
ap-1851	280	15	4π)(1	4π)(1	NUM
ap-1851	281	1	+	+	CCONJ
ap-1851	281	2	4π	4π	NUM
ap-1851	281	3	+	+	CCONJ
ap-1851	281	4	ε	ε	PROPN
ap-1851	281	5	)	)	PUNCT
ap-1851	281	6	2ε	2ε	NOUN
ap-1851	281	7	−	−	PUNCT
ap-1851	281	8	u	u	NOUN
ap-1851	281	9	′2v	′2v	ADP
ap-1851	281	10	(	(	PUNCT
ap-1851	281	11	d′	d′	X
ap-1851	281	12	−	−	PROPN
ap-1851	281	13	1−	1−	NUM
ap-1851	282	1	4π	4π	NUM
ap-1851	282	2	+	+	CCONJ
ap-1851	282	3	ε	ε	PROPN
ap-1851	282	4	1	1	NUM
ap-1851	283	1	+	+	CCONJ
ap-1851	283	2	4π	4π	NUM
ap-1851	283	3	−	−	NOUN
ap-1851	283	4	εi	εi	VERB
ap-1851	283	5	)	)	PUNCT
ap-1851	283	6	−1	−1	NOUN
ap-1851	283	7	u	u	NOUN
ap-1851	283	8	′3v	′3v	PROPN
ap-1851	283	9	,	,	PUNCT
ap-1851	283	10	where	where	SCONJ
ap-1851	283	11	u	u	NOUN
ap-1851	283	12	(	(	PUNCT
ap-1851	283	13	1	1	NUM
ap-1851	283	14	)	)	PUNCT
ap-1851	283	15	2v	2v	PROPN
ap-1851	283	16	and	and	CCONJ
ap-1851	283	17	u	u	PROPN
ap-1851	283	18	(	(	PUNCT
ap-1851	283	19	1	1	NUM
ap-1851	283	20	)	)	PUNCT
ap-1851	283	21	3v	3v	NUM
ap-1851	283	22	are	be	AUX
ap-1851	283	23	the	the	DET
ap-1851	283	24	first	first	ADJ
ap-1851	283	25	entries	entry	NOUN
ap-1851	283	26	of	of	ADP
ap-1851	283	27	u2v	u2v	NUM
ap-1851	283	28	and	and	CCONJ
ap-1851	283	29	u3v	u3v	ADV
ap-1851	283	30	,	,	PUNCT
ap-1851	283	31	and	and	CCONJ
ap-1851	283	32	u	u	NOUN
ap-1851	283	33	′2v	′2v	NOUN
ap-1851	283	34	and	and	CCONJ
ap-1851	283	35	u	u	PROPN
ap-1851	283	36	′3v	′3v	PROPN
ap-1851	283	37	is	be	AUX
ap-1851	283	38	rest	rest	NOUN
ap-1851	283	39	of	of	ADP
ap-1851	283	40	the	the	DET
ap-1851	283	41	row	row	NOUN
ap-1851	283	42	/	/	SYM
ap-1851	283	43	column	column	NOUN
ap-1851	283	44	,	,	PUNCT
ap-1851	283	45	respectively	respectively	ADV
ap-1851	283	46	.	.	PUNCT
ap-1851	284	1	to	to	PART
ap-1851	284	2	match	match	VERB
ap-1851	284	3	the	the	DET
ap-1851	284	4	ε−1	ε−1	PROPN
ap-1851	284	5	terms	term	NOUN
ap-1851	284	6	on	on	ADP
ap-1851	284	7	both	both	DET
ap-1851	284	8	sides	side	NOUN
ap-1851	284	9	of	of	ADP
ap-1851	284	10	the	the	DET
ap-1851	284	11	last	last	ADJ
ap-1851	284	12	equation	equation	NOUN
ap-1851	284	13	,	,	PUNCT
ap-1851	284	14	the	the	DET
ap-1851	284	15	identity	identity	NOUN
ap-1851	284	16	−8π	−8π	X
ap-1851	284	17	=	=	PUNCT
ap-1851	284	18	(	(	PUNCT
ap-1851	284	19	1	1	NUM
ap-1851	284	20	+	+	NUM
ap-1851	284	21	4π)2	4π)2	NUM
ap-1851	284	22	2	2	NUM
ap-1851	284	23	u	u	NOUN
ap-1851	284	24	(	(	PUNCT
ap-1851	284	25	1	1	NUM
ap-1851	284	26	)	)	PUNCT
ap-1851	284	27	2v	2v	PROPN
ap-1851	284	28	u	u	SYM
ap-1851	284	29	(	(	PUNCT
ap-1851	284	30	1	1	NUM
ap-1851	284	31	)	)	PUNCT
ap-1851	284	32	3v	3v	PROPN
ap-1851	284	33	has	have	VERB
ap-1851	284	34	to	to	PART
ap-1851	284	35	be	be	AUX
ap-1851	284	36	valid	valid	ADJ
ap-1851	284	37	.	.	PUNCT
ap-1851	285	1	from	from	ADP
ap-1851	285	2	this	this	PRON
ap-1851	285	3	and	and	CCONJ
ap-1851	285	4	the	the	DET
ap-1851	285	5	unitarity	unitarity	NOUN
ap-1851	285	6	of	of	ADP
ap-1851	285	7	u	u	PRON
ap-1851	285	8	it	it	PRON
ap-1851	285	9	follows	follow	VERB
ap-1851	285	10	that	that	SCONJ
ap-1851	285	11	|u	|u	ADJ
ap-1851	285	12	(	(	PUNCT
ap-1851	285	13	1	1	NUM
ap-1851	285	14	)	)	PUNCT
ap-1851	285	15	2v	2v	NOUN
ap-1851	286	1	|	|	ADV
ap-1851	286	2	=	=	SYM
ap-1851	286	3	|u	|u	ADJ
ap-1851	286	4	(	(	PUNCT
ap-1851	286	5	1	1	NUM
ap-1851	286	6	)	)	PUNCT
ap-1851	286	7	3v	3v	NUM
ap-1851	287	1	|	|	NOUN
ap-1851	287	2	=	=	NOUN
ap-1851	287	3	√	√	NUM
ap-1851	287	4	1−	1−	NUM
ap-1851	287	5	(	(	PUNCT
ap-1851	287	6	1−4π	1−4π	NUM
ap-1851	287	7	1	1	NUM
ap-1851	287	8	+	+	SYM
ap-1851	287	9	4π	4π	NUM
ap-1851	287	10	)	)	PUNCT
ap-1851	287	11	2	2	X
ap-1851	287	12	.	.	PUNCT
ap-1851	288	1	using	use	VERB
ap-1851	288	2	the	the	DET
ap-1851	288	3	unitarity	unitarity	NOUN
ap-1851	288	4	again	again	ADV
ap-1851	288	5	,	,	PUNCT
ap-1851	288	6	we	we	PRON
ap-1851	288	7	note	note	VERB
ap-1851	288	8	that	that	SCONJ
ap-1851	288	9	the	the	DET
ap-1851	288	10	column	column	NOUN
ap-1851	288	11	(	(	PUNCT
ap-1851	288	12	u1	u1	NOUN
ap-1851	288	13	,	,	PUNCT
ap-1851	288	14	u3v	u3v	NOUN
ap-1851	288	15	)	)	PUNCT
ap-1851	288	16	t	t	PROPN
ap-1851	288	17	must	must	AUX
ap-1851	288	18	have	have	VERB
ap-1851	288	19	norm	norm	NOUN
ap-1851	288	20	equal	equal	ADJ
ap-1851	288	21	to	to	ADP
ap-1851	288	22	one	one	NUM
ap-1851	288	23	,	,	PUNCT
ap-1851	288	24	and	and	CCONJ
ap-1851	288	25	since	since	SCONJ
ap-1851	288	26	we	we	PRON
ap-1851	288	27	know	know	VERB
ap-1851	288	28	already	already	ADV
ap-1851	288	29	that	that	DET
ap-1851	288	30	u1	u1	NOUN
ap-1851	288	31	=	=	SYM
ap-1851	288	32	1−4π	1−4π	NUM
ap-1851	288	33	1	1	NUM
ap-1851	288	34	+	+	SYM
ap-1851	288	35	4π	4π	NUM
ap-1851	288	36	,	,	PUNCT
ap-1851	288	37	it	it	PRON
ap-1851	288	38	follows	follow	VERB
ap-1851	288	39	that	that	SCONJ
ap-1851	288	40	u	u	PROPN
ap-1851	288	41	′	′	NUM
ap-1851	289	1	2v	2v	PROPN
ap-1851	289	2	=	=	SYM
ap-1851	289	3	u	u	PROPN
ap-1851	289	4	′3v	′3v	PROPN
ap-1851	289	5	=	=	SYM
ap-1851	289	6	0	0	X
ap-1851	289	7	.	.	PUNCT
ap-1851	289	8	equation	equation	NOUN
ap-1851	289	9	(	(	PUNCT
ap-1851	289	10	7	7	X
ap-1851	289	11	)	)	PUNCT
ap-1851	289	12	now	now	ADV
ap-1851	289	13	becomes	become	VERB
ap-1851	289	14	−	−	PROPN
ap-1851	289	15	4π	4π	NUM
ap-1851	289	16	−	−	PROPN
ap-1851	289	17	k	k	PROPN
ap-1851	290	1	4π	4π	NUM
ap-1851	290	2	+	+	CCONJ
ap-1851	290	3	k	k	X
ap-1851	290	4	=	=	SYM
ap-1851	290	5	1−	1−	NUM
ap-1851	290	6	4π	4π	NUM
ap-1851	290	7	1	1	NUM
ap-1851	290	8	+	+	CCONJ
ap-1851	290	9	4π	4π	NUM
ap-1851	290	10	−	−	PROPN
ap-1851	290	11	(	(	PUNCT
ap-1851	290	12	1−	1−	NUM
ap-1851	290	13	(	(	PUNCT
ap-1851	290	14	1−	1−	NUM
ap-1851	290	15	4π	4π	NUM
ap-1851	290	16	1	1	NUM
ap-1851	291	1	+	+	CCONJ
ap-1851	291	2	4π	4π	NUM
ap-1851	291	3	)	)	PUNCT
ap-1851	291	4	2	2	X
ap-1851	291	5	)	)	PUNCT
ap-1851	291	6	eiϕ	eiϕ	NOUN
ap-1851	291	7	(	(	PUNCT
ap-1851	291	8	1−	1−	NUM
ap-1851	291	9	4π	4π	NUM
ap-1851	291	10	1	1	NUM
ap-1851	292	1	+	+	CCONJ
ap-1851	292	2	4π	4π	NUM
ap-1851	292	3	−	−	NOUN
ap-1851	292	4	1	1	NUM
ap-1851	293	1	+	+	CCONJ
ap-1851	293	2	k	k	PROPN
ap-1851	293	3	1−	1−	NUM
ap-1851	293	4	k	k	NOUN
ap-1851	293	5	)	)	PUNCT
ap-1851	293	6	−1	−1	NOUN
ap-1851	293	7	with	with	ADP
ap-1851	293	8	ϕ	ϕ	NOUN
ap-1851	293	9	being	be	AUX
ap-1851	293	10	the	the	DET
ap-1851	293	11	phase	phase	NOUN
ap-1851	293	12	of	of	ADP
ap-1851	293	13	u	u	NOUN
ap-1851	293	14	(	(	PUNCT
ap-1851	293	15	1	1	NUM
ap-1851	293	16	)	)	PUNCT
ap-1851	293	17	2v	2v	PROPN
ap-1851	293	18	u	u	SYM
ap-1851	293	19	(	(	PUNCT
ap-1851	293	20	1	1	NUM
ap-1851	293	21	)	)	PUNCT
ap-1851	293	22	3v	3v	NUM
ap-1851	293	23	.	.	PUNCT
ap-1851	294	1	this	this	PRON
ap-1851	294	2	clearly	clearly	ADV
ap-1851	294	3	can	can	AUX
ap-1851	294	4	not	not	PART
ap-1851	294	5	be	be	AUX
ap-1851	294	6	true	true	ADJ
ap-1851	294	7	for	for	ADP
ap-1851	294	8	all	all	DET
ap-1851	294	9	k	k	NOUN
ap-1851	294	10	,	,	PUNCT
ap-1851	294	11	which	which	PRON
ap-1851	294	12	can	can	AUX
ap-1851	294	13	be	be	AUX
ap-1851	294	14	seen	see	VERB
ap-1851	294	15	,	,	PUNCT
ap-1851	294	16	for	for	ADP
ap-1851	294	17	instance	instance	NOUN
ap-1851	294	18	,	,	PUNCT
ap-1851	294	19	from	from	ADP
ap-1851	294	20	observing	observe	VERB
ap-1851	294	21	the	the	DET
ap-1851	294	22	limit	limit	NOUN
ap-1851	294	23	k	k	PROPN
ap-1851	294	24	→∞	→∞	NOUN
ap-1851	294	25	;	;	PUNCT
ap-1851	294	26	in	in	ADP
ap-1851	294	27	this	this	DET
ap-1851	294	28	way	way	NOUN
ap-1851	294	29	we	we	PRON
ap-1851	294	30	come	come	VERB
ap-1851	294	31	to	to	ADP
ap-1851	294	32	a	a	DET
ap-1851	294	33	contradiction	contradiction	NOUN
ap-1851	294	34	.	.	PUNCT
ap-1851	295	1	the	the	DET
ap-1851	295	2	two	two	NUM
ap-1851	295	3	previous	previous	ADJ
ap-1851	295	4	claims	claim	NOUN
ap-1851	295	5	show	show	VERB
ap-1851	295	6	that	that	SCONJ
ap-1851	295	7	,	,	PUNCT
ap-1851	295	8	unlike	unlike	ADP
ap-1851	295	9	the	the	DET
ap-1851	295	10	case	case	NOUN
ap-1851	295	11	of	of	ADP
ap-1851	295	12	quantum	quantum	NOUN
ap-1851	295	13	graphs	graph	NOUN
ap-1851	295	14	,	,	PUNCT
ap-1851	295	15	one	one	PRON
ap-1851	295	16	can	can	AUX
ap-1851	295	17	not	not	PART
ap-1851	295	18	find	find	VERB
ap-1851	295	19	a	a	DET
ap-1851	295	20	sequence	sequence	NOUN
ap-1851	295	21	of	of	ADP
ap-1851	295	22	resonances	resonance	NOUN
ap-1851	295	23	which	which	PRON
ap-1851	295	24	would	would	AUX
ap-1851	295	25	escape	escape	VERB
ap-1851	295	26	to	to	ADP
ap-1851	295	27	imaginary	imaginary	ADJ
ap-1851	295	28	infinity	infinity	NOUN
ap-1851	295	29	in	in	ADP
ap-1851	295	30	the	the	DET
ap-1851	295	31	momentum	momentum	NOUN
ap-1851	295	32	plane	plane	NOUN
ap-1851	295	33	;	;	PUNCT
ap-1851	295	34	in	in	ADP
ap-1851	295	35	the	the	DET
ap-1851	295	36	next	next	ADJ
ap-1851	295	37	section	section	NOUN
ap-1851	295	38	we	we	PRON
ap-1851	295	39	provide	provide	VERB
ap-1851	295	40	a	a	DET
ap-1851	295	41	couple	couple	NOUN
ap-1851	295	42	of	of	ADP
ap-1851	295	43	examples	example	NOUN
ap-1851	295	44	illustrating	illustrate	VERB
ap-1851	295	45	the	the	DET
ap-1851	295	46	comparison	comparison	NOUN
ap-1851	295	47	between	between	ADP
ap-1851	295	48	the	the	DET
ap-1851	295	49	one	one	NUM
ap-1851	295	50	-	-	PUNCT
ap-1851	295	51	dimensional	dimensional	ADJ
ap-1851	295	52	case	case	NOUN
ap-1851	295	53	and	and	CCONJ
ap-1851	295	54	the	the	DET
ap-1851	295	55	twoand	twoand	ADJ
ap-1851	295	56	three	three	NUM
ap-1851	295	57	-	-	PUNCT
ap-1851	295	58	dimensional	dimensional	ADJ
ap-1851	295	59	cases	case	NOUN
ap-1851	295	60	.	.	PUNCT
ap-1851	296	1	let	let	VERB
ap-1851	296	2	us	we	PRON
ap-1851	296	3	stress	stress	VERB
ap-1851	296	4	,	,	PUNCT
ap-1851	296	5	however	however	ADV
ap-1851	296	6	,	,	PUNCT
ap-1851	296	7	that	that	SCONJ
ap-1851	296	8	any	any	DET
ap-1851	296	9	such	such	ADJ
ap-1851	296	10	sequence	sequence	NOUN
ap-1851	296	11	tends	tend	VERB
ap-1851	296	12	to	to	PART
ap-1851	296	13	infinity	infinity	VERB
ap-1851	296	14	along	along	ADP
ap-1851	296	15	the	the	DET
ap-1851	296	16	real	real	ADJ
ap-1851	296	17	axis	axis	NOUN
ap-1851	296	18	,	,	PUNCT
ap-1851	296	19	and	and	CCONJ
ap-1851	296	20	thus	thus	ADV
ap-1851	296	21	the	the	DET
ap-1851	296	22	above	above	ADJ
ap-1851	296	23	results	result	NOUN
ap-1851	296	24	do	do	AUX
ap-1851	296	25	not	not	PART
ap-1851	296	26	answer	answer	VERB
ap-1851	296	27	the	the	DET
ap-1851	296	28	question	question	NOUN
ap-1851	296	29	stated	state	VERB
ap-1851	296	30	in	in	ADP
ap-1851	296	31	the	the	DET
ap-1851	296	32	opening	opening	NOUN
ap-1851	296	33	,	,	PUNCT
ap-1851	296	34	namely	namely	ADV
ap-1851	296	35	whether	whether	SCONJ
ap-1851	296	36	the	the	DET
ap-1851	296	37	resonance	resonance	NOUN
ap-1851	296	38	asymptotics	asymptotic	NOUN
ap-1851	296	39	always	always	ADV
ap-1851	296	40	has	have	VERB
ap-1851	296	41	a	a	DET
ap-1851	296	42	weyl	weyl	VERB
ap-1851	296	43	character	character	NOUN
ap-1851	296	44	.	.	PUNCT
ap-1851	297	1	also	also	ADV
ap-1851	297	2	,	,	PUNCT
ap-1851	297	3	we	we	PRON
ap-1851	297	4	postpone	postpone	VERB
ap-1851	297	5	to	to	ADP
ap-1851	297	6	another	another	DET
ap-1851	297	7	paper	paper	NOUN
ap-1851	297	8	discussion	discussion	NOUN
ap-1851	297	9	of	of	ADP
ap-1851	297	10	the	the	DET
ap-1851	297	11	case	case	NOUN
ap-1851	297	12	when	when	SCONJ
ap-1851	297	13	halflines	halfline	NOUN
ap-1851	297	14	are	be	AUX
ap-1851	297	15	attached	attach	VERB
ap-1851	297	16	at	at	ADP
ap-1851	297	17	two	two	NUM
ap-1851	297	18	and	and	CCONJ
ap-1851	297	19	more	more	ADJ
ap-1851	297	20	points	point	NOUN
ap-1851	297	21	;	;	PUNCT
ap-1851	297	22	we	we	PRON
ap-1851	297	23	note	note	VERB
ap-1851	297	24	that	that	SCONJ
ap-1851	297	25	the	the	DET
ap-1851	297	26	green	green	ADJ
ap-1851	297	27	function	function	NOUN
ap-1851	297	28	on	on	ADP
ap-1851	297	29	the	the	DET
ap-1851	297	30	manifold	manifold	NOUN
ap-1851	297	31	between	between	ADP
ap-1851	297	32	two	two	NUM
ap-1851	297	33	distinct	distinct	ADJ
ap-1851	297	34	points	point	NOUN
ap-1851	297	35	does	do	AUX
ap-1851	297	36	not	not	PART
ap-1851	297	37	depend	depend	VERB
ap-1851	297	38	only	only	ADV
ap-1851	297	39	on	on	ADP
ap-1851	297	40	local	local	ADJ
ap-1851	297	41	curvature	curvature	NOUN
ap-1851	297	42	properties	property	NOUN
ap-1851	297	43	,	,	PUNCT
ap-1851	297	44	but	but	CCONJ
ap-1851	297	45	also	also	ADV
ap-1851	297	46	nontrivially	nontrivially	ADV
ap-1851	297	47	on	on	ADP
ap-1851	297	48	the	the	DET
ap-1851	297	49	structure	structure	NOUN
ap-1851	297	50	of	of	ADP
ap-1851	297	51	the	the	DET
ap-1851	297	52	whole	whole	ADJ
ap-1851	297	53	manifold	manifold	NOUN
ap-1851	297	54	.	.	PUNCT
ap-1851	298	1	also	also	ADV
ap-1851	298	2	the	the	DET
ap-1851	298	3	resonance	resonance	NOUN
ap-1851	298	4	trajectories	trajectorie	VERB
ap-1851	298	5	from	from	ADP
ap-1851	298	6	the	the	DET
ap-1851	298	7	fully	fully	ADV
ap-1851	298	8	decoupled	decouple	VERB
ap-1851	298	9	case	case	NOUN
ap-1851	298	10	to	to	ADP
ap-1851	298	11	the	the	DET
ap-1851	298	12	coupled	couple	VERB
ap-1851	298	13	case	case	NOUN
ap-1851	298	14	will	will	AUX
ap-1851	298	15	be	be	AUX
ap-1851	298	16	left	leave	VERB
ap-1851	298	17	for	for	ADP
ap-1851	298	18	another	another	DET
ap-1851	298	19	paper	paper	NOUN
ap-1851	298	20	.	.	PUNCT
ap-1851	299	1	l	l	NOUN
ap-1851	299	2	�	�	PROPN
ap-1851	299	3	l	l	NOUN
ap-1851	299	4	0	0	NUM
ap-1851	299	5	figure	figure	NOUN
ap-1851	299	6	2	2	NUM
ap-1851	299	7	.	.	PUNCT
ap-1851	300	1	a	a	DET
ap-1851	300	2	‘	'	PUNCT
ap-1851	300	3	thin	thin	ADJ
ap-1851	300	4	-	-	PUNCT
ap-1851	300	5	hedgehog	hedgehog	NOUN
ap-1851	300	6	’	'	PUNCT
ap-1851	300	7	manifold	manifold	NOUN
ap-1851	300	8	,	,	PUNCT
ap-1851	300	9	d	d	NOUN
ap-1851	300	10	=	=	SYM
ap-1851	300	11	1	1	NUM
ap-1851	300	12	4.2	4.2	NUM
ap-1851	300	13	.	.	PUNCT
ap-1851	301	1	examples	example	NOUN
ap-1851	301	2	to	to	PART
ap-1851	301	3	illustrate	illustrate	VERB
ap-1851	301	4	how	how	SCONJ
ap-1851	301	5	the	the	DET
ap-1851	301	6	resonance	resonance	NOUN
ap-1851	301	7	asymptotical	asymptotical	ADJ
ap-1851	301	8	behaviour	behaviour	NOUN
ap-1851	301	9	depends	depend	VERB
ap-1851	301	10	on	on	ADP
ap-1851	301	11	the	the	DET
ap-1851	301	12	dimension	dimension	NOUN
ap-1851	301	13	of	of	ADP
ap-1851	301	14	ω	ω	NOUN
ap-1851	301	15	we	we	PRON
ap-1851	301	16	now	now	ADV
ap-1851	301	17	consider	consider	VERB
ap-1851	301	18	two	two	NUM
ap-1851	301	19	examples	example	NOUN
ap-1851	301	20	of	of	ADP
ap-1851	301	21	a	a	DET
ap-1851	301	22	planar	planar	ADJ
ap-1851	301	23	manifold	manifold	NOUN
ap-1851	301	24	with	with	ADP
ap-1851	301	25	dirichlet	dirichlet	PROPN
ap-1851	301	26	boundary	boundary	ADJ
ap-1851	301	27	conditions	condition	NOUN
ap-1851	301	28	in	in	ADP
ap-1851	301	29	dimensions	dimension	NOUN
ap-1851	301	30	one	one	NUM
ap-1851	301	31	and	and	CCONJ
ap-1851	301	32	two	two	NUM
ap-1851	301	33	.	.	PUNCT
ap-1851	302	1	first	first	ADV
ap-1851	302	2	we	we	PRON
ap-1851	302	3	illustrate	illustrate	VERB
ap-1851	302	4	the	the	DET
ap-1851	302	5	difference	difference	NOUN
ap-1851	302	6	between	between	ADP
ap-1851	302	7	dimensions	dimension	NOUN
ap-1851	302	8	one	one	NUM
ap-1851	302	9	and	and	CCONJ
ap-1851	302	10	two	two	NUM
ap-1851	302	11	in	in	ADP
ap-1851	302	12	a	a	DET
ap-1851	302	13	pair	pair	NOUN
ap-1851	302	14	of	of	ADP
ap-1851	302	15	examples	example	NOUN
ap-1851	302	16	,	,	PUNCT
ap-1851	302	17	that	that	SCONJ
ap-1851	302	18	at	at	ADP
ap-1851	302	19	first	first	ADJ
ap-1851	302	20	glance	glance	NOUN
ap-1851	302	21	may	may	AUX
ap-1851	302	22	appear	appear	VERB
ap-1851	302	23	similar	similar	ADJ
ap-1851	302	24	.	.	PUNCT
ap-1851	303	1	in	in	ADP
ap-1851	303	2	the	the	DET
ap-1851	303	3	former	former	ADJ
ap-1851	303	4	case	case	NOUN
ap-1851	303	5	one	one	PRON
ap-1851	303	6	is	be	AUX
ap-1851	303	7	able	able	ADJ
ap-1851	303	8	to	to	PART
ap-1851	303	9	adjust	adjust	VERB
ap-1851	303	10	the	the	DET
ap-1851	303	11	parameters	parameter	NOUN
ap-1851	303	12	to	to	PART
ap-1851	303	13	obtain	obtain	VERB
ap-1851	303	14	a	a	DET
ap-1851	303	15	non	non	ADJ
ap-1851	303	16	-	-	ADJ
ap-1851	303	17	weyl	weyl	ADJ
ap-1851	303	18	graph	graph	NOUN
ap-1851	303	19	for	for	ADP
ap-1851	303	20	which	which	PRON
ap-1851	303	21	one	one	NUM
ap-1851	303	22	half	half	NOUN
ap-1851	303	23	of	of	ADP
ap-1851	303	24	the	the	DET
ap-1851	303	25	resonances	resonance	NOUN
ap-1851	303	26	escape	escape	VERB
ap-1851	303	27	to	to	ADP
ap-1851	303	28	imaginary	imaginary	ADJ
ap-1851	303	29	infinity	infinity	NOUN
ap-1851	303	30	,	,	PUNCT
ap-1851	303	31	hence	hence	ADV
ap-1851	303	32	the	the	DET
ap-1851	303	33	number	number	NOUN
ap-1851	303	34	of	of	ADP
ap-1851	303	35	phase	phase	NOUN
ap-1851	303	36	jumps	jump	VERB
ap-1851	303	37	along	along	ADP
ap-1851	303	38	the	the	DET
ap-1851	303	39	circle	circle	NOUN
ap-1851	303	40	of	of	ADP
ap-1851	303	41	increasing	increase	VERB
ap-1851	303	42	radius	radius	NOUN
ap-1851	303	43	increases	increase	NOUN
ap-1851	303	44	.	.	PUNCT
ap-1851	304	1	on	on	ADP
ap-1851	304	2	the	the	DET
ap-1851	304	3	other	other	ADJ
ap-1851	304	4	hand	hand	NOUN
ap-1851	304	5	,	,	PUNCT
ap-1851	304	6	we	we	PRON
ap-1851	304	7	do	do	AUX
ap-1851	304	8	not	not	PART
ap-1851	304	9	observe	observe	VERB
ap-1851	304	10	such	such	ADJ
ap-1851	304	11	behaviour	behaviour	NOUN
ap-1851	304	12	in	in	ADP
ap-1851	304	13	dimension	dimension	NOUN
ap-1851	304	14	two	two	NUM
ap-1851	304	15	.	.	PUNCT
ap-1851	304	16	example	example	NOUN
ap-1851	304	17	4.6	4.6	NUM
ap-1851	304	18	.	.	PUNCT
ap-1851	305	1	in	in	ADP
ap-1851	305	2	the	the	DET
ap-1851	305	3	case	case	NOUN
ap-1851	305	4	dim	dim	NOUN
ap-1851	305	5	ω	ω	NOUN
ap-1851	305	6	=	=	SYM
ap-1851	305	7	1	1	NUM
ap-1851	305	8	we	we	PRON
ap-1851	305	9	consider	consider	VERB
ap-1851	305	10	an	an	DET
ap-1851	305	11	abscissa	abscissa	NOUN
ap-1851	305	12	of	of	ADP
ap-1851	305	13	length	length	NOUN
ap-1851	305	14	2l	2l	NUM
ap-1851	305	15	with	with	ADP
ap-1851	305	16	m	m	PROPN
ap-1851	305	17	halflines	halfline	NOUN
ap-1851	305	18	attached	attach	VERB
ap-1851	305	19	in	in	ADP
ap-1851	305	20	the	the	DET
ap-1851	305	21	middle	middle	NOUN
ap-1851	305	22	—	—	PUNCT
ap-1851	306	1	cf	cf	NOUN
ap-1851	306	2	.	.	PUNCT
ap-1851	306	3	figure	figure	NOUN
ap-1851	306	4	2	2	NUM
ap-1851	306	5	.	.	PUNCT
ap-1851	307	1	we	we	PRON
ap-1851	307	2	impose	impose	VERB
ap-1851	307	3	dirichlet	dirichlet	PROPN
ap-1851	307	4	boundary	boundary	ADJ
ap-1851	307	5	conditions	condition	NOUN
ap-1851	307	6	at	at	ADP
ap-1851	307	7	its	its	PRON
ap-1851	307	8	endpoints	endpoint	NOUN
ap-1851	307	9	,	,	PUNCT
ap-1851	307	10	f(−l	f(−l	ADP
ap-1851	307	11	)	)	PUNCT
ap-1851	307	12	=	=	SYM
ap-1851	307	13	f(l	f(l	PROPN
ap-1851	307	14	)	)	PUNCT
ap-1851	307	15	=	=	SYM
ap-1851	307	16	0	0	NUM
ap-1851	307	17	,	,	PUNCT
ap-1851	307	18	and	and	CCONJ
ap-1851	307	19	condition	condition	NOUN
ap-1851	307	20	(	(	PUNCT
ap-1851	307	21	1	1	NUM
ap-1851	307	22	)	)	PUNCT
ap-1851	307	23	at	at	ADP
ap-1851	307	24	the	the	DET
ap-1851	307	25	middle	middle	NOUN
ap-1851	307	26	.	.	PUNCT
ap-1851	308	1	the	the	DET
ap-1851	308	2	green	green	ADJ
ap-1851	308	3	function	function	NOUN
ap-1851	308	4	of	of	ADP
ap-1851	308	5	the	the	DET
ap-1851	308	6	operator	operator	NOUN
ap-1851	308	7	h0	h0	NOUN
ap-1851	308	8	is	be	AUX
ap-1851	308	9	given	give	VERB
ap-1851	308	10	by	by	ADP
ap-1851	308	11	g(x	g(x	PROPN
ap-1851	308	12	,	,	PUNCT
ap-1851	308	13	y	y	PROPN
ap-1851	308	14	;	;	PUNCT
ap-1851	308	15	k	k	X
ap-1851	308	16	)	)	PUNCT
ap-1851	308	17	=	=	SYM
ap-1851	308	18	f1(x	f1(x	PROPN
ap-1851	308	19	,	,	PUNCT
ap-1851	308	20	y	y	PROPN
ap-1851	308	21	;	;	PUNCT
ap-1851	308	22	k	k	X
ap-1851	308	23	)	)	PUNCT
ap-1851	308	24	=	=	SYM
ap-1851	308	25	∑	∑	PROPN
ap-1851	308	26	n	n	PRON
ap-1851	308	27	ψ̄n(x)ψn(y	ψ̄n(x)ψn(y	NOUN
ap-1851	308	28	)	)	PUNCT
ap-1851	308	29	λn	λn	ADP
ap-1851	308	30	−	−	PROPN
ap-1851	308	31	k2	k2	X
ap-1851	308	32	=	=	SYM
ap-1851	308	33	1	1	NUM
ap-1851	308	34	l	l	NOUN
ap-1851	308	35	∞∑	∞∑	NUM
ap-1851	308	36	n=1	n=1	PROPN
ap-1851	308	37	cos	cos	PROPN
ap-1851	308	38	(	(	PUNCT
ap-1851	308	39	2n−1)πx	2n−1)πx	NUM
ap-1851	308	40	2l	2l	NOUN
ap-1851	308	41	cos	cos	X
ap-1851	308	42	(	(	PUNCT
ap-1851	308	43	2n−1)πy	2n−1)πy	NUM
ap-1851	308	44	2l	2l	NUM
ap-1851	308	45	(	(	PUNCT
ap-1851	308	46	(	(	PUNCT
ap-1851	308	47	2n−1)π	2n−1)π	NUM
ap-1851	308	48	2l	2l	NOUN
ap-1851	308	49	)	)	PUNCT
ap-1851	308	50	2	2	NUM
ap-1851	308	51	−	−	PROPN
ap-1851	308	52	k2	k2	NOUN
ap-1851	308	53	.	.	PUNCT
ap-1851	309	1	substituting	substituting	NOUN
ap-1851	309	2	,	,	PUNCT
ap-1851	309	3	in	in	ADP
ap-1851	309	4	particular	particular	ADJ
ap-1851	309	5	,	,	PUNCT
ap-1851	309	6	x	x	PUNCT
ap-1851	309	7	=	=	PUNCT
ap-1851	310	1	y	y	NOUN
ap-1851	310	2	=	=	SYM
ap-1851	310	3	0	0	NUM
ap-1851	310	4	one	one	NOUN
ap-1851	310	5	obtains	obtain	VERB
ap-1851	310	6	f1(0	f1(0	PROPN
ap-1851	310	7	,	,	PUNCT
ap-1851	310	8	0	0	NUM
ap-1851	310	9	;	;	PUNCT
ap-1851	310	10	k	k	X
ap-1851	310	11	)	)	PUNCT
ap-1851	310	12	=	=	SYM
ap-1851	310	13	1	1	NUM
ap-1851	310	14	l	l	NOUN
ap-1851	310	15	∞∑	∞∑	NUM
ap-1851	310	16	n=1	n=1	PROPN
ap-1851	310	17	1	1	NUM
ap-1851	310	18	(	(	PUNCT
ap-1851	310	19	(	(	PUNCT
ap-1851	310	20	2n−1)π	2n−1)π	NUM
ap-1851	310	21	2l	2l	NOUN
ap-1851	310	22	)	)	PUNCT
ap-1851	310	23	2	2	NUM
ap-1851	310	24	−	−	PROPN
ap-1851	310	25	k2	k2	X
ap-1851	310	26	=	=	NOUN
ap-1851	310	27	1	1	NUM
ap-1851	310	28	2k	2k	NUM
ap-1851	310	29	tan	tan	PROPN
ap-1851	310	30	kl	kl	PROPN
ap-1851	310	31	.	.	PUNCT
ap-1851	311	1	substituting	substitute	VERB
ap-1851	311	2	this	this	PRON
ap-1851	311	3	into	into	ADP
ap-1851	311	4	the	the	DET
ap-1851	311	5	resonance	resonance	NOUN
ap-1851	311	6	condition	condition	NOUN
ap-1851	311	7	one	one	PRON
ap-1851	311	8	can	can	AUX
ap-1851	311	9	check	check	VERB
ap-1851	311	10	easily	easily	ADV
ap-1851	311	11	that	that	DET
ap-1851	311	12	resonance	resonance	NOUN
ap-1851	311	13	count	count	NOUN
ap-1851	311	14	asymptotics	asymptotic	NOUN
ap-1851	311	15	has	have	VERB
ap-1851	311	16	a	a	DET
ap-1851	311	17	non	non	ADJ
ap-1851	311	18	-	-	ADJ
ap-1851	311	19	weyl	weyl	ADJ
ap-1851	311	20	character	character	NOUN
ap-1851	311	21	if	if	SCONJ
ap-1851	311	22	the	the	DET
ap-1851	311	23	coupling	coupling	NOUN
ap-1851	311	24	is	be	AUX
ap-1851	311	25	chosen	choose	VERB
ap-1851	311	26	as	as	SCONJ
ap-1851	311	27	follows	follow	VERB
ap-1851	311	28	,	,	PUNCT
ap-1851	311	29	i	i	PRON
ap-1851	311	30	ũ(k	ũ(k	PROPN
ap-1851	311	31	)	)	PUNCT
ap-1851	311	32	+	+	CCONJ
ap-1851	311	33	1	1	NUM
ap-1851	311	34	ũ(k)−	ũ(k)−	PROPN
ap-1851	311	35	1	1	NUM
ap-1851	311	36	=	=	SYM
ap-1851	311	37	±	±	NOUN
ap-1851	312	1	i	i	PRON
ap-1851	312	2	2k	2k	VERB
ap-1851	312	3	⇒	⇒	VERB
ap-1851	312	4	ũ(k	ũ(k	PROPN
ap-1851	312	5	)	)	PUNCT
ap-1851	312	6	=	=	SYM
ap-1851	312	7	−2k	−2k	PROPN
ap-1851	312	8	∓	∓	PROPN
ap-1851	312	9	1	1	NUM
ap-1851	312	10	2k	2k	NOUN
ap-1851	312	11	∓	∓	PROPN
ap-1851	312	12	1	1	NUM
ap-1851	312	13	.	.	PUNCT
ap-1851	313	1	the	the	DET
ap-1851	313	2	upper	upper	ADJ
ap-1851	313	3	-	-	PUNCT
ap-1851	313	4	sign	sign	NOUN
ap-1851	313	5	choice	choice	NOUN
ap-1851	313	6	can	can	AUX
ap-1851	313	7	be	be	AUX
ap-1851	313	8	realized	realize	VERB
ap-1851	313	9	,	,	PUNCT
ap-1851	313	10	e.g.	e.g.	ADV
ap-1851	313	11	by	by	ADP
ap-1851	313	12	taking	take	VERB
ap-1851	313	13	m	m	PROPN
ap-1851	313	14	=	=	SYM
ap-1851	313	15	2	2	NUM
ap-1851	313	16	and	and	CCONJ
ap-1851	313	17	connecting	connect	VERB
ap-1851	313	18	the	the	DET
ap-1851	313	19	halflines	halfline	NOUN
ap-1851	313	20	with	with	ADP
ap-1851	313	21	the	the	DET
ap-1851	313	22	abscissa	abscissa	NOUN
ap-1851	313	23	by	by	ADP
ap-1851	313	24	kirchhoff	kirchhoff	NOUN
ap-1851	313	25	conditions	condition	NOUN
ap-1851	313	26	—	—	PUNCT
ap-1851	313	27	see	see	VERB
ap-1851	313	28	[	[	X
ap-1851	313	29	10	10	NUM
ap-1851	313	30	,	,	PUNCT
ap-1851	313	31	11	11	NUM
ap-1851	313	32	]	]	PUNCT
ap-1851	313	33	.	.	PUNCT
ap-1851	314	1	this	this	PRON
ap-1851	314	2	corresponds	correspond	VERB
ap-1851	314	3	to	to	ADP
ap-1851	314	4	a	a	DET
ap-1851	314	5	‘	'	PUNCT
ap-1851	314	6	balanced	balanced	ADJ
ap-1851	314	7	’	'	PUNCT
ap-1851	314	8	vertex	vertex	NOUN
ap-1851	314	9	connecting	connect	VERB
ap-1851	314	10	two	two	NUM
ap-1851	314	11	internal	internal	ADJ
ap-1851	314	12	and	and	CCONJ
ap-1851	314	13	two	two	NUM
ap-1851	314	14	external	external	ADJ
ap-1851	314	15	edges	edge	NOUN
ap-1851	314	16	.	.	PUNCT
ap-1851	315	1	the	the	DET
ap-1851	315	2	phase	phase	NOUN
ap-1851	315	3	of	of	ADP
ap-1851	315	4	the	the	DET
ap-1851	315	5	regularized	regularize	VERB
ap-1851	315	6	green	green	ADJ
ap-1851	315	7	function	function	NOUN
ap-1851	315	8	f1	f1	NOUN
ap-1851	315	9	and	and	CCONJ
ap-1851	315	10	the	the	DET
ap-1851	315	11	left	left	ADJ
ap-1851	315	12	-	-	PUNCT
ap-1851	315	13	hand	hand	NOUN
ap-1851	315	14	side	side	NOUN
ap-1851	315	15	of	of	ADP
ap-1851	315	16	the	the	DET
ap-1851	315	17	resonance	resonance	NOUN
ap-1851	315	18	condition	condition	NOUN
ap-1851	315	19	for	for	ADP
ap-1851	315	20	the	the	DET
ap-1851	315	21	above	above	ADJ
ap-1851	315	22	choice	choice	NOUN
ap-1851	315	23	of	of	ADP
ap-1851	315	24	the	the	DET
ap-1851	315	25	coupling	coupling	NOUN
ap-1851	315	26	,	,	PUNCT
ap-1851	315	27	f1	f1	NOUN
ap-1851	315	28	+	+	CCONJ
ap-1851	315	29	i	i	PROPN
ap-1851	315	30	2k	2k	NUM
ap-1851	315	31	,	,	PUNCT
ap-1851	315	32	can	can	AUX
ap-1851	315	33	be	be	AUX
ap-1851	315	34	seen	see	VERB
ap-1851	315	35	in	in	ADP
ap-1851	315	36	figures	figure	NOUN
ap-1851	315	37	3	3	NUM
ap-1851	315	38	and	and	CCONJ
ap-1851	315	39	4	4	NUM
ap-1851	315	40	,	,	PUNCT
ap-1851	315	41	respectively	respectively	ADV
ap-1851	315	42	;	;	PUNCT
ap-1851	315	43	figure	figure	NOUN
ap-1851	315	44	4	4	NUM
ap-1851	315	45	illustrates	illustrate	VERB
ap-1851	315	46	how	how	SCONJ
ap-1851	315	47	the	the	DET
ap-1851	315	48	number	number	NOUN
ap-1851	315	49	of	of	ADP
ap-1851	315	50	phase	phase	NOUN
ap-1851	315	51	jumps	jump	VERB
ap-1851	315	52	increases	increase	NOUN
ap-1851	315	53	for	for	ADP
ap-1851	315	54	an	an	DET
ap-1851	315	55	increasing	increase	VERB
ap-1851	315	56	radius	radius	NOUN
ap-1851	315	57	of	of	ADP
ap-1851	315	58	the	the	DET
ap-1851	315	59	circle	circle	NOUN
ap-1851	315	60	.	.	PUNCT
ap-1851	316	1	422	422	NUM
ap-1851	316	2	vol	vol	NOUN
ap-1851	316	3	.	.	PUNCT
ap-1851	317	1	53	53	NUM
ap-1851	317	2	no	no	NOUN
ap-1851	317	3	.	.	PUNCT
ap-1851	318	1	5/2013	5/2013	NUM
ap-1851	318	2	resonances	resonance	NOUN
ap-1851	318	3	on	on	ADP
ap-1851	318	4	hedgehog	hedgehog	NOUN
ap-1851	318	5	manifolds	manifold	NOUN
ap-1851	318	6	figure	figure	NOUN
ap-1851	318	7	3	3	NUM
ap-1851	318	8	.	.	NOUN
ap-1851	318	9	phase	phase	NOUN
ap-1851	318	10	of	of	ADP
ap-1851	318	11	the	the	DET
ap-1851	318	12	green	green	ADJ
ap-1851	318	13	function	function	NOUN
ap-1851	318	14	for	for	ADP
ap-1851	318	15	d	d	PROPN
ap-1851	318	16	=	=	SYM
ap-1851	318	17	1	1	NUM
ap-1851	318	18	figure	figure	NOUN
ap-1851	318	19	4	4	NUM
ap-1851	318	20	.	.	NOUN
ap-1851	318	21	phase	phase	NOUN
ap-1851	318	22	of	of	ADP
ap-1851	318	23	the	the	DET
ap-1851	318	24	green	green	ADJ
ap-1851	318	25	function	function	NOUN
ap-1851	318	26	plus	plus	CCONJ
ap-1851	318	27	i	i	PRON
ap-1851	318	28	2k	2k	NUM
ap-1851	318	29	example	example	NOUN
ap-1851	318	30	4.7	4.7	NUM
ap-1851	318	31	.	.	PUNCT
ap-1851	319	1	consider	consider	VERB
ap-1851	319	2	next	next	ADJ
ap-1851	319	3	an	an	DET
ap-1851	319	4	analogous	analogous	ADJ
ap-1851	319	5	situation	situation	NOUN
ap-1851	319	6	in	in	ADP
ap-1851	319	7	two	two	NUM
ap-1851	319	8	dimensions	dimension	NOUN
ap-1851	319	9	—	—	PUNCT
ap-1851	319	10	a	a	DET
ap-1851	319	11	flat	flat	ADJ
ap-1851	319	12	circular	circular	ADJ
ap-1851	319	13	drum	drum	NOUN
ap-1851	319	14	of	of	ADP
ap-1851	319	15	radius	radius	PROPN
ap-1851	319	16	l	l	PROPN
ap-1851	319	17	with	with	ADP
ap-1851	319	18	dirichlet	dirichlet	PROPN
ap-1851	319	19	boundary	boundary	ADJ
ap-1851	319	20	condition	condition	NOUN
ap-1851	319	21	at	at	ADP
ap-1851	319	22	r	r	NOUN
ap-1851	319	23	=	=	SYM
ap-1851	319	24	r	r	NOUN
ap-1851	319	25	and	and	CCONJ
ap-1851	319	26	m	m	PROPN
ap-1851	319	27	halflines	halfline	NOUN
ap-1851	319	28	attached	attach	VERB
ap-1851	319	29	in	in	ADP
ap-1851	319	30	its	its	PRON
ap-1851	319	31	center	center	NOUN
ap-1851	319	32	.	.	PUNCT
ap-1851	320	1	because	because	SCONJ
ap-1851	320	2	of	of	ADP
ap-1851	320	3	the	the	DET
ap-1851	320	4	rotational	rotational	ADJ
ap-1851	320	5	symmetry	symmetry	NOUN
ap-1851	320	6	,	,	PUNCT
ap-1851	320	7	the	the	DET
ap-1851	320	8	green	green	ADJ
ap-1851	320	9	function	function	NOUN
ap-1851	320	10	with	with	ADP
ap-1851	320	11	one	one	NUM
ap-1851	320	12	argument	argument	NOUN
ap-1851	320	13	fixed	fix	VERB
ap-1851	320	14	at	at	ADP
ap-1851	320	15	y	y	PROPN
ap-1851	320	16	=	=	SYM
ap-1851	320	17	0	0	NUM
ap-1851	320	18	can	can	AUX
ap-1851	320	19	be	be	AUX
ap-1851	320	20	expressed	express	VERB
ap-1851	320	21	as	as	ADP
ap-1851	320	22	a	a	DET
ap-1851	320	23	combination	combination	NOUN
ap-1851	320	24	of	of	ADP
ap-1851	320	25	bessel	bessel	NOUN
ap-1851	320	26	functions	function	NOUN
ap-1851	320	27	,	,	PUNCT
ap-1851	320	28	g(x	g(x	NOUN
ap-1851	320	29	,	,	PUNCT
ap-1851	320	30	0	0	NUM
ap-1851	320	31	;	;	PUNCT
ap-1851	320	32	k	k	X
ap-1851	320	33	)	)	PUNCT
ap-1851	320	34	=	=	PUNCT
ap-1851	320	35	−1	−1	NOUN
ap-1851	320	36	4y0(kr	4y0(kr	NOUN
ap-1851	320	37	)	)	PUNCT
ap-1851	321	1	+	+	CCONJ
ap-1851	321	2	c(k)j0(kr	c(k)j0(kr	NOUN
ap-1851	321	3	)	)	PUNCT
ap-1851	321	4	,	,	PUNCT
ap-1851	321	5	where	where	SCONJ
ap-1851	321	6	r	r	NOUN
ap-1851	321	7	:	:	PUNCT
ap-1851	321	8	=	=	SYM
ap-1851	321	9	|x|	|x|	PROPN
ap-1851	321	10	and	and	CCONJ
ap-1851	321	11	j0	j0	PROPN
ap-1851	321	12	and	and	CCONJ
ap-1851	321	13	y0	y0	PROPN
ap-1851	321	14	are	be	AUX
ap-1851	321	15	bessel	bessel	ADJ
ap-1851	321	16	functions	function	NOUN
ap-1851	321	17	of	of	ADP
ap-1851	321	18	the	the	DET
ap-1851	321	19	first	first	ADJ
ap-1851	321	20	and	and	CCONJ
ap-1851	321	21	second	second	ADJ
ap-1851	321	22	kind	kind	NOUN
ap-1851	321	23	,	,	PUNCT
ap-1851	321	24	respectively	respectively	ADV
ap-1851	321	25	.	.	PUNCT
ap-1851	322	1	the	the	DET
ap-1851	322	2	constant	constant	ADJ
ap-1851	322	3	by	by	ADP
ap-1851	322	4	y0	y0	PROPN
ap-1851	322	5	is	be	AUX
ap-1851	322	6	chosen	choose	VERB
ap-1851	322	7	so	so	SCONJ
ap-1851	322	8	that	that	SCONJ
ap-1851	322	9	g	g	PROPN
ap-1851	322	10	satisfies	satisfie	NOUN
ap-1851	322	11	(	(	PUNCT
ap-1851	322	12	2	2	NUM
ap-1851	322	13	)	)	PUNCT
ap-1851	322	14	.	.	PUNCT
ap-1851	323	1	we	we	PRON
ap-1851	323	2	employ	employ	VERB
ap-1851	323	3	the	the	DET
ap-1851	323	4	well	well	ADV
ap-1851	323	5	-	-	PUNCT
ap-1851	323	6	known	know	VERB
ap-1851	323	7	asymptotic	asymptotic	ADJ
ap-1851	323	8	behaviour	behaviour	NOUN
ap-1851	323	9	of	of	ADP
ap-1851	323	10	bessel	bessel	NOUN
ap-1851	323	11	functions	function	NOUN
ap-1851	323	12	,	,	PUNCT
ap-1851	323	13	y0(x	y0(x	NUM
ap-1851	323	14	)	)	PUNCT
ap-1851	323	15	∼	∼	NOUN
ap-1851	323	16	−	−	NOUN
ap-1851	323	17	2	2	NUM
ap-1851	323	18	π	π	NOUN
ap-1851	323	19	(	(	PUNCT
ap-1851	323	20	ln	ln	ADJ
ap-1851	323	21	x/2	x/2	PUNCT
ap-1851	323	22	+	+	CCONJ
ap-1851	323	23	γ	γ	NOUN
ap-1851	323	24	)	)	PUNCT
ap-1851	323	25	,	,	PUNCT
ap-1851	323	26	j0(x	j0(x	NOUN
ap-1851	323	27	)	)	PUNCT
ap-1851	323	28	∼	∼	NOUN
ap-1851	323	29	1	1	NUM
ap-1851	323	30	as	as	ADP
ap-1851	323	31	x→	x→	PROPN
ap-1851	323	32	0	0	NUM
ap-1851	323	33	,	,	PUNCT
ap-1851	323	34	which	which	PRON
ap-1851	323	35	yields	yield	VERB
ap-1851	323	36	the	the	DET
ap-1851	323	37	expression	expression	NOUN
ap-1851	323	38	f1(k	f1(k	NOUN
ap-1851	323	39	)	)	PUNCT
ap-1851	323	40	=	=	SYM
ap-1851	324	1	−	−	PROPN
ap-1851	324	2	1	1	NUM
ap-1851	324	3	2π	2π	NOUN
ap-1851	324	4	(	(	PUNCT
ap-1851	324	5	ln	ln	NOUN
ap-1851	324	6	k	k	NOUN
ap-1851	325	1	−	−	PROPN
ap-1851	325	2	ln	ln	ADJ
ap-1851	325	3	2	2	NUM
ap-1851	325	4	+	+	CCONJ
ap-1851	325	5	γ	γ	X
ap-1851	325	6	)	)	PUNCT
ap-1851	325	7	+	+	NUM
ap-1851	325	8	y0(kr	y0(kr	NOUN
ap-1851	325	9	)	)	PUNCT
ap-1851	325	10	4j0(kr	4j0(kr	NUM
ap-1851	325	11	)	)	PUNCT
ap-1851	325	12	.	.	PUNCT
ap-1851	326	1	using	use	VERB
ap-1851	326	2	the	the	DET
ap-1851	326	3	asymptotics	asymptotic	NOUN
ap-1851	326	4	of	of	ADP
ap-1851	326	5	j0(x	j0(x	NOUN
ap-1851	326	6	)	)	PUNCT
ap-1851	326	7	and	and	CCONJ
ap-1851	326	8	y0(x	y0(x	NUM
ap-1851	326	9	)	)	PUNCT
ap-1851	326	10	as	as	ADP
ap-1851	326	11	x→∞	x→∞	NUM
ap-1851	326	12	,	,	PUNCT
ap-1851	326	13	one	one	PRON
ap-1851	326	14	finds	find	VERB
ap-1851	326	15	that	that	SCONJ
ap-1851	326	16	the	the	DET
ap-1851	326	17	second	second	ADJ
ap-1851	326	18	term	term	NOUN
ap-1851	326	19	on	on	ADP
ap-1851	326	20	the	the	DET
ap-1851	326	21	right	right	ADJ
ap-1851	326	22	-	-	PUNCT
ap-1851	326	23	hand	hand	NOUN
ap-1851	326	24	side	side	NOUN
ap-1851	326	25	behaves	behave	VERB
ap-1851	326	26	as	as	ADP
ap-1851	326	27	1	1	NUM
ap-1851	326	28	4	4	NUM
ap-1851	326	29	tan	tan	NOUN
ap-1851	326	30	(	(	PUNCT
ap-1851	326	31	kr	kr	PROPN
ap-1851	326	32	−	−	PROPN
ap-1851	326	33	π	π	PROPN
ap-1851	326	34	4	4	NUM
ap-1851	326	35	)	)	PUNCT
ap-1851	326	36	and	and	CCONJ
ap-1851	326	37	its	its	PRON
ap-1851	326	38	absolute	absolute	ADJ
ap-1851	326	39	value	value	NOUN
ap-1851	326	40	is	be	AUX
ap-1851	326	41	therefore	therefore	ADV
ap-1851	326	42	bounded	bound	VERB
ap-1851	326	43	for	for	ADP
ap-1851	326	44	k	k	PROPN
ap-1851	326	45	outside	outside	ADP
ap-1851	326	46	the	the	DET
ap-1851	326	47	real	real	ADJ
ap-1851	326	48	axis	axis	NOUN
ap-1851	326	49	.	.	PUNCT
ap-1851	327	1	the	the	DET
ap-1851	327	2	phase	phase	NOUN
ap-1851	327	3	of	of	ADP
ap-1851	327	4	f1	f1	NOUN
ap-1851	327	5	for	for	ADP
ap-1851	327	6	r	r	NOUN
ap-1851	327	7	=	=	PUNCT
ap-1851	327	8	π	π	NOUN
ap-1851	327	9	is	be	AUX
ap-1851	327	10	plotted	plot	VERB
ap-1851	327	11	in	in	ADP
ap-1851	327	12	figure	figure	NOUN
ap-1851	327	13	6	6	NUM
ap-1851	327	14	.	.	PUNCT
ap-1851	328	1	r	r	NOUN
ap-1851	328	2	figure	figure	NOUN
ap-1851	328	3	5	5	NUM
ap-1851	328	4	.	.	PUNCT
ap-1851	329	1	the	the	DET
ap-1851	329	2	hedgehog	hedgehog	PROPN
ap-1851	329	3	manifold	manifold	NOUN
ap-1851	329	4	of	of	ADP
ap-1851	329	5	example	example	NOUN
ap-1851	329	6	4.7	4.7	NUM
ap-1851	329	7	figure	figure	NOUN
ap-1851	329	8	6	6	NUM
ap-1851	329	9	.	.	NOUN
ap-1851	329	10	phase	phase	NOUN
ap-1851	329	11	of	of	ADP
ap-1851	329	12	the	the	DET
ap-1851	329	13	regularized	regularize	VERB
ap-1851	329	14	green	green	ADJ
ap-1851	329	15	function	function	NOUN
ap-1851	329	16	for	for	ADP
ap-1851	329	17	the	the	DET
ap-1851	329	18	hedgehog	hedgehog	NOUN
ap-1851	329	19	manifold	manifold	NOUN
ap-1851	329	20	of	of	ADP
ap-1851	329	21	example	example	NOUN
ap-1851	329	22	4.7	4.7	NUM
ap-1851	329	23	r	r	NOUN
ap-1851	329	24	figure	figure	NOUN
ap-1851	329	25	7	7	NUM
ap-1851	329	26	.	.	PUNCT
ap-1851	329	27	a	a	DET
ap-1851	329	28	disc	disc	NOUN
ap-1851	329	29	with	with	ADP
ap-1851	329	30	a	a	DET
ap-1851	329	31	lead	lead	NOUN
ap-1851	329	32	in	in	ADP
ap-1851	329	33	a	a	DET
ap-1851	329	34	magnetic	magnetic	ADJ
ap-1851	329	35	field	field	NOUN
ap-1851	329	36	5	5	NUM
ap-1851	329	37	.	.	PUNCT
ap-1851	329	38	resonances	resonance	NOUN
ap-1851	329	39	for	for	ADP
ap-1851	329	40	a	a	DET
ap-1851	329	41	hedgehog	hedgehog	NOUN
ap-1851	329	42	manifold	manifold	NOUN
ap-1851	329	43	in	in	ADP
ap-1851	329	44	magnetic	magnetic	ADJ
ap-1851	329	45	field	field	NOUN
ap-1851	329	46	now	now	ADV
ap-1851	329	47	we	we	PRON
ap-1851	329	48	are	be	AUX
ap-1851	329	49	going	go	VERB
ap-1851	329	50	to	to	PART
ap-1851	329	51	present	present	VERB
ap-1851	329	52	an	an	DET
ap-1851	329	53	example	example	NOUN
ap-1851	329	54	showing	show	VERB
ap-1851	329	55	that	that	SCONJ
ap-1851	329	56	an	an	DET
ap-1851	329	57	appropriately	appropriately	ADV
ap-1851	329	58	chosen	choose	VERB
ap-1851	329	59	magnetic	magnetic	ADJ
ap-1851	329	60	field	field	NOUN
ap-1851	329	61	can	can	AUX
ap-1851	329	62	remove	remove	VERB
ap-1851	329	63	all	all	DET
ap-1851	329	64	‘	'	PUNCT
ap-1851	329	65	true	true	ADJ
ap-1851	329	66	resonances	resonance	NOUN
ap-1851	329	67	’	'	PUNCT
ap-1851	329	68	on	on	ADP
ap-1851	329	69	a	a	DET
ap-1851	329	70	hedgehog	hedgehog	NOUN
ap-1851	329	71	manifold	manifold	ADJ
ap-1851	329	72	,	,	PUNCT
ap-1851	329	73	i.e.	i.e.	X
ap-1851	329	74	those	those	PRON
ap-1851	329	75	corresponding	correspond	VERB
ap-1851	329	76	to	to	ADP
ap-1851	329	77	poles	pole	NOUN
ap-1851	329	78	in	in	ADP
ap-1851	329	79	the	the	DET
ap-1851	329	80	open	open	ADJ
ap-1851	329	81	lower	low	ADJ
ap-1851	329	82	complex	complex	ADJ
ap-1851	329	83	halfplane	halfplane	NOUN
ap-1851	329	84	.	.	PUNCT
ap-1851	330	1	we	we	PRON
ap-1851	330	2	note	note	VERB
ap-1851	330	3	that	that	SCONJ
ap-1851	330	4	this	this	PRON
ap-1851	330	5	does	do	AUX
ap-1851	330	6	not	not	PART
ap-1851	330	7	influence	influence	VERB
ap-1851	330	8	the	the	DET
ap-1851	330	9	semiclassical	semiclassical	ADJ
ap-1851	330	10	asymptotics	asymptotic	NOUN
ap-1851	330	11	in	in	ADP
ap-1851	330	12	this	this	DET
ap-1851	330	13	case	case	NOUN
ap-1851	330	14	,	,	PUNCT
ap-1851	330	15	because	because	SCONJ
ap-1851	330	16	the	the	DET
ap-1851	330	17	embedded	embed	VERB
ap-1851	330	18	eigenvalues	eigenvalue	NOUN
ap-1851	330	19	of	of	ADP
ap-1851	330	20	the	the	DET
ap-1851	330	21	system	system	NOUN
ap-1851	330	22	corresponding	correspond	VERB
ap-1851	330	23	to	to	ADP
ap-1851	330	24	higher	high	ADJ
ap-1851	330	25	partial	partial	ADJ
ap-1851	330	26	waves	wave	NOUN
ap-1851	330	27	with	with	ADP
ap-1851	330	28	eigenfunctions	eigenfunction	NOUN
ap-1851	330	29	vanishing	vanish	VERB
ap-1851	330	30	at	at	ADP
ap-1851	330	31	the	the	DET
ap-1851	330	32	junction	junction	NOUN
ap-1851	330	33	will	will	AUX
ap-1851	330	34	persist	persist	VERB
ap-1851	330	35	being	be	AUX
ap-1851	330	36	just	just	ADV
ap-1851	330	37	shifted	shift	VERB
ap-1851	330	38	.	.	PUNCT
ap-1851	331	1	the	the	DET
ap-1851	331	2	manifold	manifold	NOUN
ap-1851	331	3	of	of	ADP
ap-1851	331	4	our	our	PRON
ap-1851	331	5	example	example	NOUN
ap-1851	331	6	will	will	AUX
ap-1851	331	7	consist	consist	VERB
ap-1851	331	8	of	of	ADP
ap-1851	331	9	a	a	DET
ap-1851	331	10	disc	disc	NOUN
ap-1851	331	11	of	of	ADP
ap-1851	331	12	radius	radius	NOUN
ap-1851	331	13	r	r	NOUN
ap-1851	331	14	with	with	ADP
ap-1851	331	15	a	a	DET
ap-1851	331	16	halfline	halfline	NOUN
ap-1851	331	17	lead	lead	NOUN
ap-1851	331	18	attached	attach	VERB
ap-1851	331	19	at	at	ADP
ap-1851	331	20	its	its	PRON
ap-1851	331	21	centre	centre	NOUN
ap-1851	331	22	.	.	PUNCT
ap-1851	332	1	for	for	ADP
ap-1851	332	2	definiteness	definiteness	NOUN
ap-1851	332	3	we	we	PRON
ap-1851	332	4	assume	assume	VERB
ap-1851	332	5	that	that	SCONJ
ap-1851	332	6	it	it	PRON
ap-1851	332	7	is	be	AUX
ap-1851	332	8	perpendicular	perpendicular	ADJ
ap-1851	332	9	to	to	ADP
ap-1851	332	10	the	the	DET
ap-1851	332	11	disc	disc	NOUN
ap-1851	332	12	plane	plane	NOUN
ap-1851	332	13	,	,	PUNCT
ap-1851	332	14	cf	cf	NOUN
ap-1851	332	15	.	.	PUNCT
ap-1851	333	1	figure	figure	NOUN
ap-1851	333	2	7	7	NUM
ap-1851	333	3	.	.	PUNCT
ap-1851	334	1	the	the	DET
ap-1851	334	2	disc	disc	NOUN
ap-1851	334	3	is	be	AUX
ap-1851	334	4	parametrized	parametrize	VERB
ap-1851	334	5	by	by	ADP
ap-1851	334	6	polar	polar	ADJ
ap-1851	334	7	coordinates	coordinate	NOUN
ap-1851	334	8	r	r	NOUN
ap-1851	334	9	,	,	PUNCT
ap-1851	334	10	ϕ	ϕ	NOUN
ap-1851	334	11	,	,	PUNCT
ap-1851	334	12	and	and	CCONJ
ap-1851	334	13	dirichlet	dirichlet	PROPN
ap-1851	334	14	boundary	boundary	ADJ
ap-1851	334	15	conditions	condition	NOUN
ap-1851	334	16	are	be	AUX
ap-1851	334	17	imposed	impose	VERB
ap-1851	334	18	at	at	ADP
ap-1851	334	19	r	r	NOUN
ap-1851	334	20	=	=	PUNCT
ap-1851	334	21	r.	r.	NOUN
ap-1851	334	22	we	we	PRON
ap-1851	334	23	suppose	suppose	VERB
ap-1851	334	24	that	that	SCONJ
ap-1851	334	25	the	the	DET
ap-1851	334	26	system	system	NOUN
ap-1851	334	27	is	be	AUX
ap-1851	334	28	under	under	ADP
ap-1851	334	29	the	the	DET
ap-1851	334	30	influence	influence	NOUN
ap-1851	334	31	of	of	ADP
ap-1851	334	32	a	a	DET
ap-1851	334	33	magnetic	magnetic	ADJ
ap-1851	334	34	field	field	NOUN
ap-1851	334	35	in	in	ADP
ap-1851	334	36	the	the	DET
ap-1851	334	37	form	form	NOUN
ap-1851	334	38	of	of	ADP
ap-1851	334	39	an	an	DET
ap-1851	334	40	aharonov	aharonov	NOUN
ap-1851	334	41	-	-	PUNCT
ap-1851	334	42	bohm	bohm	PROPN
ap-1851	334	43	string	string	NOUN
ap-1851	334	44	which	which	PRON
ap-1851	334	45	coincides	coincide	VERB
ap-1851	334	46	423	423	NUM
ap-1851	334	47	p.	p.	NOUN
ap-1851	334	48	exner	exner	NOUN
ap-1851	334	49	,	,	PUNCT
ap-1851	334	50	j.	j.	PROPN
ap-1851	334	51	lipovský	lipovský	PROPN
ap-1851	334	52	acta	acta	PROPN
ap-1851	334	53	polytechnica	polytechnica	PROPN
ap-1851	334	54	in	in	ADP
ap-1851	334	55	the	the	DET
ap-1851	334	56	‘	'	PUNCT
ap-1851	334	57	upper	upper	ADJ
ap-1851	334	58	’	'	PUNCT
ap-1851	334	59	halfspace	halfspace	NOUN
ap-1851	334	60	with	with	ADP
ap-1851	334	61	the	the	DET
ap-1851	334	62	lead	lead	NOUN
ap-1851	334	63	.	.	PUNCT
ap-1851	335	1	the	the	DET
ap-1851	335	2	effect	effect	NOUN
ap-1851	335	3	of	of	ADP
ap-1851	335	4	an	an	DET
ap-1851	335	5	aharonov	aharonov	NOUN
ap-1851	335	6	-	-	PUNCT
ap-1851	335	7	bohm	bohm	PROPN
ap-1851	335	8	field	field	NOUN
ap-1851	335	9	piercing	pierce	VERB
ap-1851	335	10	a	a	DET
ap-1851	335	11	surface	surface	NOUN
ap-1851	335	12	has	have	AUX
ap-1851	335	13	been	be	AUX
ap-1851	335	14	studied	study	VERB
ap-1851	335	15	in	in	ADP
ap-1851	335	16	numerous	numerous	ADJ
ap-1851	335	17	papers	paper	NOUN
ap-1851	335	18	—	—	PUNCT
ap-1851	335	19	see	see	VERB
ap-1851	335	20	,	,	PUNCT
ap-1851	335	21	e.g.	e.g.	ADV
ap-1851	335	22	,	,	PUNCT
ap-1851	335	23	[	[	X
ap-1851	335	24	1	1	NUM
ap-1851	335	25	,	,	PUNCT
ap-1851	335	26	9	9	NUM
ap-1851	335	27	,	,	PUNCT
ap-1851	335	28	21	21	NUM
ap-1851	335	29	]	]	PUNCT
ap-1851	335	30	—	—	PUNCT
ap-1851	335	31	so	so	ADV
ap-1851	335	32	we	we	PRON
ap-1851	335	33	can	can	AUX
ap-1851	335	34	just	just	ADV
ap-1851	335	35	modify	modify	VERB
ap-1851	335	36	those	those	DET
ap-1851	335	37	results	result	NOUN
ap-1851	335	38	for	for	ADP
ap-1851	335	39	our	our	PRON
ap-1851	335	40	purpose	purpose	NOUN
ap-1851	335	41	.	.	PUNCT
ap-1851	336	1	the	the	DET
ap-1851	336	2	idea	idea	NOUN
ap-1851	336	3	is	be	AUX
ap-1851	336	4	that	that	SCONJ
ap-1851	336	5	the	the	DET
ap-1851	336	6	‘	'	PUNCT
ap-1851	336	7	true	true	ADJ
ap-1851	336	8	’	'	PUNCT
ap-1851	336	9	resonances	resonance	NOUN
ap-1851	336	10	will	will	AUX
ap-1851	336	11	disappear	disappear	VERB
ap-1851	336	12	if	if	SCONJ
ap-1851	336	13	we	we	PRON
ap-1851	336	14	manage	manage	VERB
ap-1851	336	15	to	to	PART
ap-1851	336	16	choose	choose	VERB
ap-1851	336	17	such	such	DET
ap-1851	336	18	a	a	DET
ap-1851	336	19	coupling	coupling	NOUN
ap-1851	336	20	in	in	ADP
ap-1851	336	21	which	which	PRON
ap-1851	336	22	the	the	DET
ap-1851	336	23	radial	radial	ADJ
ap-1851	336	24	part	part	NOUN
ap-1851	336	25	of	of	ADP
ap-1851	336	26	the	the	DET
ap-1851	336	27	disc	disc	NOUN
ap-1851	336	28	wave	wave	NOUN
ap-1851	336	29	function	function	NOUN
ap-1851	336	30	will	will	AUX
ap-1851	336	31	match	match	VERB
ap-1851	336	32	the	the	DET
ap-1851	336	33	halfline	halfline	NOUN
ap-1851	336	34	wave	wave	NOUN
ap-1851	336	35	function	function	NOUN
ap-1851	336	36	in	in	ADP
ap-1851	336	37	a	a	DET
ap-1851	336	38	trivial	trivial	ADJ
ap-1851	336	39	way	way	NOUN
ap-1851	336	40	.	.	PUNCT
ap-1851	337	1	we	we	PRON
ap-1851	337	2	write	write	VERB
ap-1851	337	3	the	the	DET
ap-1851	337	4	hilbert	hilbert	NOUN
ap-1851	337	5	space	space	NOUN
ap-1851	337	6	of	of	ADP
ap-1851	337	7	the	the	DET
ap-1851	337	8	model	model	NOUN
ap-1851	337	9	as	as	ADP
ap-1851	337	10	h	h	NOUN
ap-1851	337	11	=	=	SYM
ap-1851	337	12	l2((0	l2((0	PROPN
ap-1851	337	13	,	,	PUNCT
ap-1851	337	14	r	r	NOUN
ap-1851	337	15	)	)	PUNCT
ap-1851	337	16	,	,	PUNCT
ap-1851	337	17	rdr	rdr	NOUN
ap-1851	337	18	)	)	PUNCT
ap-1851	337	19	⊗	⊗	PROPN
ap-1851	337	20	l2(s1	l2(s1	X
ap-1851	337	21	)	)	PUNCT
ap-1851	337	22	⊕	⊕	PROPN
ap-1851	337	23	l2(r+	l2(r+	PROPN
ap-1851	337	24	)	)	PUNCT
ap-1851	337	25	;	;	PUNCT
ap-1851	337	26	the	the	DET
ap-1851	337	27	admissible	admissible	ADJ
ap-1851	337	28	hamiltonians	hamiltonian	NOUN
ap-1851	337	29	are	be	AUX
ap-1851	337	30	then	then	ADV
ap-1851	337	31	constructed	construct	VERB
ap-1851	337	32	as	as	ADP
ap-1851	337	33	selfadjoint	selfadjoint	NOUN
ap-1851	337	34	extensions	extension	NOUN
ap-1851	337	35	of	of	ADP
ap-1851	337	36	the	the	DET
ap-1851	337	37	operator	operator	NOUN
ap-1851	337	38	ḣα	ḣα	PROPN
ap-1851	337	39	acting	act	VERB
ap-1851	337	40	as	as	ADP
ap-1851	337	41	ḣα	ḣα	PROPN
ap-1851	337	42	(	(	PUNCT
ap-1851	337	43	u	u	NOUN
ap-1851	337	44	f	f	PROPN
ap-1851	337	45	)	)	PUNCT
ap-1851	338	1	=	=	PRON
ap-1851	338	2	(	(	PUNCT
ap-1851	338	3	−∂	−∂	ADV
ap-1851	338	4	2u	2u	VERB
ap-1851	338	5	∂r2	∂r2	PRON
ap-1851	338	6	−	−	ADP
ap-1851	338	7	1	1	NUM
ap-1851	338	8	r	r	NOUN
ap-1851	338	9	∂u	∂u	NOUN
ap-1851	339	1	∂r	∂r	NOUN
ap-1851	340	1	+	+	CCONJ
ap-1851	340	2	1	1	NUM
ap-1851	340	3	r2	r2	NOUN
ap-1851	340	4	(	(	PUNCT
ap-1851	340	5	i	i	PRON
ap-1851	340	6	∂∂ϕ	∂∂ϕ	VERB
ap-1851	341	1	−	−	PROPN
ap-1851	341	2	α	α	NOUN
ap-1851	341	3	)	)	PUNCT
ap-1851	341	4	2	2	NUM
ap-1851	341	5	u	u	NOUN
ap-1851	341	6	−f	−f	PROPN
ap-1851	341	7	′′	′′	PROPN
ap-1851	341	8	)	)	PUNCT
ap-1851	342	1	on	on	ADP
ap-1851	342	2	the	the	DET
ap-1851	342	3	domain	domain	NOUN
ap-1851	342	4	consisting	consist	VERB
ap-1851	342	5	of	of	ADP
ap-1851	342	6	functions	function	NOUN
ap-1851	342	7	(	(	PUNCT
ap-1851	342	8	u	u	NOUN
ap-1851	342	9	f	f	PROPN
ap-1851	342	10	)	)	PUNCT
ap-1851	342	11	with	with	ADP
ap-1851	342	12	u	u	PROPN
ap-1851	342	13	∈	∈	PROPN
ap-1851	342	14	h2	h2	PROPN
ap-1851	342	15	loc	loc	PROPN
ap-1851	342	16	(	(	PUNCT
ap-1851	342	17	br(0	br(0	PROPN
ap-1851	342	18	)	)	PUNCT
ap-1851	342	19	)	)	PUNCT
ap-1851	343	1	satisfying	satisfy	VERB
ap-1851	343	2	u(0	u(0	PROPN
ap-1851	343	3	,	,	PUNCT
ap-1851	343	4	ϕ	ϕ	NOUN
ap-1851	343	5	)	)	PUNCT
ap-1851	343	6	=	=	SYM
ap-1851	343	7	u(r,ϕ	u(r,ϕ	NOUN
ap-1851	343	8	)	)	PUNCT
ap-1851	343	9	=	=	SYM
ap-1851	343	10	0	0	NUM
ap-1851	343	11	and	and	CCONJ
ap-1851	343	12	f	f	PROPN
ap-1851	343	13	∈	∈	PROPN
ap-1851	343	14	h2	h2	PROPN
ap-1851	343	15	loc(r+	loc(r+	X
ap-1851	343	16	)	)	PUNCT
ap-1851	343	17	satisfying	satisfy	VERB
ap-1851	343	18	f(0	f(0	NOUN
ap-1851	343	19	)	)	PUNCT
ap-1851	343	20	=	=	PUNCT
ap-1851	344	1	f	f	PROPN
ap-1851	344	2	′(0	′(0	PROPN
ap-1851	344	3	)	)	PUNCT
ap-1851	345	1	=	=	SYM
ap-1851	345	2	0	0	X
ap-1851	345	3	.	.	PUNCT
ap-1851	346	1	the	the	DET
ap-1851	346	2	parameter	parameter	NOUN
ap-1851	346	3	α	α	PROPN
ap-1851	346	4	in	in	ADP
ap-1851	346	5	the	the	DET
ap-1851	346	6	above	above	ADJ
ap-1851	346	7	expression	expression	NOUN
ap-1851	346	8	is	be	AUX
ap-1851	346	9	the	the	DET
ap-1851	346	10	magnetic	magnetic	ADJ
ap-1851	346	11	flux	flux	NOUN
ap-1851	346	12	of	of	ADP
ap-1851	346	13	the	the	DET
ap-1851	346	14	aharonov	aharonov	PROPN
ap-1851	346	15	-	-	PUNCT
ap-1851	346	16	bohm	bohm	PROPN
ap-1851	346	17	string	string	NOUN
ap-1851	346	18	in	in	ADP
ap-1851	346	19	the	the	DET
ap-1851	346	20	units	unit	NOUN
ap-1851	346	21	of	of	ADP
ap-1851	346	22	the	the	DET
ap-1851	346	23	flux	flux	NOUN
ap-1851	346	24	quantum	quantum	NOUN
ap-1851	346	25	;	;	PUNCT
ap-1851	346	26	since	since	SCONJ
ap-1851	346	27	an	an	DET
ap-1851	346	28	integer	integer	NOUN
ap-1851	346	29	value	value	NOUN
ap-1851	346	30	of	of	ADP
ap-1851	346	31	the	the	DET
ap-1851	346	32	flux	flux	NOUN
ap-1851	346	33	plays	play	VERB
ap-1851	346	34	no	no	DET
ap-1851	346	35	role	role	NOUN
ap-1851	346	36	in	in	ADP
ap-1851	346	37	view	view	NOUN
ap-1851	346	38	of	of	ADP
ap-1851	346	39	the	the	DET
ap-1851	346	40	natural	natural	ADJ
ap-1851	346	41	gauge	gauge	NOUN
ap-1851	346	42	invariance	invariance	NOUN
ap-1851	346	43	we	we	PRON
ap-1851	346	44	may	may	AUX
ap-1851	346	45	restrict	restrict	VERB
ap-1851	346	46	our	our	PRON
ap-1851	346	47	attention	attention	NOUN
ap-1851	346	48	to	to	ADP
ap-1851	346	49	the	the	DET
ap-1851	346	50	values	value	NOUN
ap-1851	346	51	α	α	X
ap-1851	346	52	∈	∈	PROPN
ap-1851	346	53	(	(	PUNCT
ap-1851	346	54	0	0	NUM
ap-1851	346	55	,	,	PUNCT
ap-1851	346	56	1	1	NUM
ap-1851	346	57	)	)	PUNCT
ap-1851	346	58	.	.	PUNCT
ap-1851	347	1	using	use	VERB
ap-1851	347	2	the	the	DET
ap-1851	347	3	partial	partial	ADJ
ap-1851	347	4	-	-	PUNCT
ap-1851	347	5	wave	wave	NOUN
ap-1851	347	6	decomposition	decomposition	NOUN
ap-1851	347	7	together	together	ADV
ap-1851	347	8	with	with	ADP
ap-1851	347	9	the	the	DET
ap-1851	347	10	standard	standard	ADJ
ap-1851	347	11	unitary	unitary	ADJ
ap-1851	347	12	transformation	transformation	NOUN
ap-1851	347	13	(	(	PUNCT
ap-1851	347	14	v	v	NOUN
ap-1851	347	15	u)(r	u)(r	ADJ
ap-1851	347	16	)	)	PUNCT
ap-1851	347	17	=	=	SYM
ap-1851	347	18	r1/2u(r	r1/2u(r	NOUN
ap-1851	347	19	)	)	PUNCT
ap-1851	347	20	to	to	ADP
ap-1851	347	21	the	the	DET
ap-1851	347	22	reduced	reduce	VERB
ap-1851	347	23	radial	radial	ADJ
ap-1851	347	24	functions	function	NOUN
ap-1851	347	25	we	we	PRON
ap-1851	347	26	get	get	VERB
ap-1851	348	1	ḣα	ḣα	PROPN
ap-1851	348	2	=	=	PUNCT
ap-1851	348	3	∞⊕	∞⊕	PROPN
ap-1851	348	4	m=−∞	m=−∞	X
ap-1851	349	1	v	v	X
ap-1851	349	2	−1ḣα	−1ḣα	PROPN
ap-1851	349	3	,	,	PUNCT
ap-1851	350	1	mv	mv	PROPN
ap-1851	350	2	⊗	⊗	PROPN
ap-1851	350	3	i	i	PRON
ap-1851	350	4	where	where	SCONJ
ap-1851	350	5	the	the	DET
ap-1851	350	6	component	component	NOUN
ap-1851	350	7	ḣα	ḣα	PROPN
ap-1851	350	8	,	,	PUNCT
ap-1851	350	9	m	m	VERB
ap-1851	350	10	acts	act	VERB
ap-1851	350	11	on	on	ADP
ap-1851	350	12	the	the	DET
ap-1851	350	13	upper	upper	ADJ
ap-1851	350	14	component	component	NOUN
ap-1851	350	15	of	of	ADP
ap-1851	350	16	ψ	ψ	NOUN
ap-1851	350	17	=	=	PUNCT
ap-1851	350	18	(	(	PUNCT
ap-1851	350	19	φ	φ	PROPN
ap-1851	350	20	f	f	PROPN
ap-1851	350	21	)	)	PUNCT
ap-1851	350	22	as	as	ADP
ap-1851	350	23	ḣα	ḣα	PROPN
ap-1851	350	24	,	,	PUNCT
ap-1851	350	25	mφ	mφ	NOUN
ap-1851	350	26	=	=	NOUN
ap-1851	351	1	−d2φ	−d2φ	PUNCT
ap-1851	352	1	dr2	dr2	PROPN
ap-1851	352	2	+	+	CCONJ
ap-1851	352	3	(	(	PUNCT
ap-1851	352	4	m+	m+	NUM
ap-1851	352	5	α)2	α)2	NOUN
ap-1851	352	6	−	−	PROPN
ap-1851	352	7	1/4	1/4	NUM
ap-1851	352	8	r2	r2	PROPN
ap-1851	352	9	φ	φ	X
ap-1851	352	10	.	.	PUNCT
ap-1851	353	1	(	(	PUNCT
ap-1851	353	2	8)	8)	NUM
ap-1851	353	3	to	to	PART
ap-1851	353	4	construct	construct	VERB
ap-1851	353	5	the	the	DET
ap-1851	353	6	self	self	NOUN
ap-1851	353	7	-	-	PUNCT
ap-1851	353	8	adjoint	adjoint	NOUN
ap-1851	353	9	extensions	extension	NOUN
ap-1851	353	10	of	of	ADP
ap-1851	353	11	ḣα	ḣα	PROPN
ap-1851	353	12	which	which	PRON
ap-1851	353	13	describe	describe	VERB
ap-1851	353	14	the	the	DET
ap-1851	353	15	coupling	coupling	NOUN
ap-1851	353	16	between	between	ADP
ap-1851	353	17	the	the	DET
ap-1851	353	18	disc	disc	NOUN
ap-1851	353	19	and	and	CCONJ
ap-1851	353	20	the	the	DET
ap-1851	353	21	lead	lead	NOUN
ap-1851	353	22	the	the	DET
ap-1851	353	23	following	follow	VERB
ap-1851	353	24	functionals	functional	NOUN
ap-1851	353	25	can	can	AUX
ap-1851	353	26	be	be	AUX
ap-1851	353	27	used	use	VERB
ap-1851	353	28	,	,	PUNCT
ap-1851	353	29	φ−1	φ−1	PROPN
ap-1851	353	30	1	1	NUM
ap-1851	353	31	(	(	PUNCT
ap-1851	353	32	ψ	ψ	NOUN
ap-1851	353	33	)	)	PUNCT
ap-1851	353	34	=	=	SYM
ap-1851	354	1	√	√	PROPN
ap-1851	354	2	π	π	PROPN
ap-1851	354	3	lim	lim	PROPN
ap-1851	354	4	r→0	r→0	VERB
ap-1851	354	5	r1−α	r1−α	VERB
ap-1851	354	6	2π	2π	PROPN
ap-1851	354	7	∫	∫	PROPN
ap-1851	354	8	2π	2π	PROPN
ap-1851	354	9	0	0	NUM
ap-1851	355	1	u(r	u(r	ADV
ap-1851	355	2	,	,	PUNCT
ap-1851	355	3	ϕ)eiϕdϕ	ϕ)eiϕdϕ	PROPN
ap-1851	355	4	,	,	PUNCT
ap-1851	355	5	φ−1	φ−1	PROPN
ap-1851	355	6	2	2	NUM
ap-1851	355	7	(	(	PUNCT
ap-1851	355	8	ψ	ψ	NOUN
ap-1851	355	9	)	)	PUNCT
ap-1851	355	10	=	=	SYM
ap-1851	355	11	√	√	PROPN
ap-1851	355	12	π	π	PROPN
ap-1851	355	13	limr→0	limr→0	PROPN
ap-1851	355	14	r−1+α	r−1+α	ADP
ap-1851	355	15	2π	2π	NOUN
ap-1851	356	1	[	[	X
ap-1851	356	2	∫	∫	X
ap-1851	356	3	2π	2π	NOUN
ap-1851	356	4	0	0	NUM
ap-1851	357	1	u(r	u(r	NOUN
ap-1851	357	2	,	,	PUNCT
ap-1851	357	3	ϕ)eiϕdϕ	ϕ)eiϕdϕ	PROPN
ap-1851	357	4	−2	−2	NOUN
ap-1851	357	5	√	√	VERB
ap-1851	357	6	πr−1+αφ1	πr−1+αφ1	PROPN
ap-1851	357	7	−1(ψ	−1(ψ	NOUN
ap-1851	357	8	)	)	PUNCT
ap-1851	357	9	]	]	PUNCT
ap-1851	357	10	,	,	PUNCT
ap-1851	357	11	φ0	φ0	PROPN
ap-1851	357	12	1(ψ	1(ψ	NUM
ap-1851	357	13	)	)	PUNCT
ap-1851	357	14	=	=	SYM
ap-1851	358	1	√	√	PROPN
ap-1851	358	2	π	π	PROPN
ap-1851	358	3	lim	lim	PROPN
ap-1851	358	4	r→0	r→0	VERB
ap-1851	358	5	rα	rα	ADJ
ap-1851	358	6	2π	2π	PROPN
ap-1851	358	7	∫	∫	PROPN
ap-1851	358	8	2π	2π	PROPN
ap-1851	358	9	0	0	NUM
ap-1851	359	1	u(r	u(r	ADV
ap-1851	359	2	,	,	PUNCT
ap-1851	359	3	ϕ)dϕ	ϕ)dϕ	PROPN
ap-1851	359	4	,	,	PUNCT
ap-1851	359	5	φ0	φ0	PROPN
ap-1851	359	6	2(ψ	2(ψ	NUM
ap-1851	359	7	)	)	PUNCT
ap-1851	359	8	=	=	SYM
ap-1851	360	1	√	√	PROPN
ap-1851	360	2	π	π	PROPN
ap-1851	360	3	limr→0	limr→0	NOUN
ap-1851	360	4	r−α	r−α	VERB
ap-1851	360	5	2π	2π	NOUN
ap-1851	361	1	[	[	X
ap-1851	361	2	∫	∫	X
ap-1851	361	3	2π	2π	NOUN
ap-1851	361	4	0	0	PUNCT
ap-1851	362	1	u(r	u(r	ADV
ap-1851	362	2	,	,	PUNCT
ap-1851	362	3	ϕ)dϕ	ϕ)dϕ	PROPN
ap-1851	362	4	−2	−2	NOUN
ap-1851	363	1	√	√	VERB
ap-1851	363	2	πr−αφ0	πr−αφ0	NUM
ap-1851	363	3	1(ψ	1(ψ	NUM
ap-1851	363	4	)	)	PUNCT
ap-1851	363	5	]	]	PUNCT
ap-1851	364	1	,	,	PUNCT
ap-1851	364	2	φh	φh	NOUN
ap-1851	364	3	1(ψ	1(ψ	NUM
ap-1851	364	4	)	)	PUNCT
ap-1851	364	5	=	=	SYM
ap-1851	364	6	f(0	f(0	NOUN
ap-1851	364	7	)	)	PUNCT
ap-1851	364	8	,	,	PUNCT
ap-1851	364	9	φh	φh	VERB
ap-1851	364	10	2(ψ	2(ψ	NUM
ap-1851	364	11	)	)	PUNCT
ap-1851	365	1	=	=	PUNCT
ap-1851	365	2	f	f	PROPN
ap-1851	365	3	′(0	′(0	NOUN
ap-1851	365	4	)	)	PUNCT
ap-1851	365	5	.	.	PUNCT
ap-1851	366	1	the	the	DET
ap-1851	366	2	first	first	ADJ
ap-1851	366	3	two	two	NUM
ap-1851	366	4	of	of	ADP
ap-1851	366	5	them	they	PRON
ap-1851	366	6	are	be	AUX
ap-1851	366	7	,	,	PUNCT
ap-1851	366	8	by	by	ADP
ap-1851	366	9	analogy	analogy	NOUN
ap-1851	366	10	with	with	ADP
ap-1851	366	11	[	[	X
ap-1851	366	12	9	9	NUM
ap-1851	366	13	]	]	PUNCT
ap-1851	366	14	,	,	PUNCT
ap-1851	366	15	multiples	multiple	NOUN
ap-1851	366	16	of	of	ADP
ap-1851	366	17	the	the	DET
ap-1851	366	18	coefficients	coefficient	NOUN
ap-1851	366	19	of	of	ADP
ap-1851	366	20	the	the	DET
ap-1851	366	21	two	two	NUM
ap-1851	366	22	leading	lead	VERB
ap-1851	366	23	terms	term	NOUN
ap-1851	366	24	of	of	ADP
ap-1851	366	25	asymptotics	asymptotic	NOUN
ap-1851	366	26	as	as	ADP
ap-1851	366	27	r	r	NOUN
ap-1851	366	28	→	→	SYM
ap-1851	366	29	0	0	NUM
ap-1851	366	30	of	of	ADP
ap-1851	366	31	the	the	DET
ap-1851	366	32	wave	wave	NOUN
ap-1851	366	33	functions	function	NOUN
ap-1851	366	34	from	from	ADP
ap-1851	366	35	ḣ∗α	ḣ∗α	NOUN
ap-1851	366	36	belonging	belong	VERB
ap-1851	366	37	to	to	ADP
ap-1851	366	38	the	the	DET
ap-1851	366	39	subspace	subspace	NOUN
ap-1851	366	40	with	with	ADP
ap-1851	366	41	m	m	PROPN
ap-1851	366	42	=	=	SYM
ap-1851	366	43	−1	−1	NOUN
ap-1851	366	44	,	,	PUNCT
ap-1851	366	45	the	the	DET
ap-1851	366	46	second	second	ADJ
ap-1851	366	47	two	two	NUM
ap-1851	366	48	correspond	correspond	NOUN
ap-1851	366	49	to	to	ADP
ap-1851	366	50	the	the	DET
ap-1851	366	51	analogous	analogous	ADJ
ap-1851	366	52	quantities	quantity	NOUN
ap-1851	366	53	in	in	ADP
ap-1851	366	54	the	the	DET
ap-1851	366	55	subspace	subspace	NOUN
ap-1851	366	56	with	with	ADP
ap-1851	366	57	m	m	PROPN
ap-1851	366	58	=	=	SYM
ap-1851	366	59	0	0	NUM
ap-1851	366	60	,	,	PUNCT
ap-1851	366	61	and	and	CCONJ
ap-1851	366	62	the	the	DET
ap-1851	366	63	last	last	ADJ
ap-1851	366	64	two	two	NUM
ap-1851	366	65	are	be	AUX
ap-1851	366	66	the	the	DET
ap-1851	366	67	standard	standard	ADJ
ap-1851	366	68	boundary	boundary	ADJ
ap-1851	366	69	values	value	NOUN
ap-1851	366	70	for	for	ADP
ap-1851	366	71	the	the	DET
ap-1851	366	72	laplacian	laplacian	NOUN
ap-1851	366	73	on	on	ADP
ap-1851	366	74	a	a	DET
ap-1851	366	75	halfline	halfline	NOUN
ap-1851	366	76	.	.	PUNCT
ap-1851	367	1	it	it	PRON
ap-1851	367	2	is	be	AUX
ap-1851	367	3	obvious	obvious	ADJ
ap-1851	367	4	that	that	SCONJ
ap-1851	367	5	if	if	SCONJ
ap-1851	367	6	the	the	DET
ap-1851	367	7	s	s	NOUN
ap-1851	367	8	-	-	PUNCT
ap-1851	367	9	wave	wave	NOUN
ap-1851	367	10	resonances	resonance	NOUN
ap-1851	367	11	should	should	AUX
ap-1851	367	12	be	be	AUX
ap-1851	367	13	absent	absent	ADJ
ap-1851	367	14	,	,	PUNCT
ap-1851	367	15	one	one	PRON
ap-1851	367	16	has	have	VERB
ap-1851	367	17	to	to	PART
ap-1851	367	18	get	get	AUX
ap-1851	367	19	rid	rid	VERB
ap-1851	367	20	of	of	ADP
ap-1851	367	21	the	the	DET
ap-1851	367	22	second	second	ADJ
ap-1851	367	23	term	term	NOUN
ap-1851	367	24	in	in	ADP
ap-1851	367	25	the	the	DET
ap-1851	367	26	expression	expression	NOUN
ap-1851	367	27	(	(	PUNCT
ap-1851	367	28	8)	8)	NUM
ap-1851	367	29	for	for	ADP
ap-1851	367	30	the	the	DET
ap-1851	367	31	m	m	PROPN
ap-1851	367	32	=	=	SYM
ap-1851	367	33	0	0	NUM
ap-1851	367	34	function	function	NOUN
ap-1851	367	35	,	,	PUNCT
ap-1851	367	36	hence	hence	ADV
ap-1851	367	37	we	we	PRON
ap-1851	367	38	will	will	AUX
ap-1851	367	39	restrict	restrict	VERB
ap-1851	367	40	our	our	PRON
ap-1851	367	41	attention	attention	NOUN
ap-1851	367	42	to	to	ADP
ap-1851	367	43	the	the	DET
ap-1851	367	44	case	case	NOUN
ap-1851	367	45	α	α	X
ap-1851	367	46	=	=	SYM
ap-1851	367	47	1/2	1/2	NUM
ap-1851	367	48	.	.	PUNCT
ap-1851	368	1	by	by	ADP
ap-1851	368	2	analogy	analogy	NOUN
ap-1851	368	3	with	with	ADP
ap-1851	368	4	the	the	DET
ap-1851	368	5	case	case	NOUN
ap-1851	368	6	of	of	ADP
ap-1851	368	7	an	an	DET
ap-1851	368	8	aharonov	aharonov	NOUN
ap-1851	368	9	-	-	PUNCT
ap-1851	368	10	bohm	bohm	PROPN
ap-1851	368	11	flux	flux	NOUN
ap-1851	368	12	piercing	pierce	VERB
ap-1851	368	13	a	a	DET
ap-1851	368	14	plane	plane	NOUN
ap-1851	368	15	treated	treat	VERB
ap-1851	368	16	in	in	ADP
ap-1851	368	17	[	[	X
ap-1851	368	18	9	9	NUM
ap-1851	368	19	]	]	PUNCT
ap-1851	368	20	,	,	PUNCT
ap-1851	368	21	one	one	NUM
ap-1851	368	22	obtains	obtain	VERB
ap-1851	368	23	(	(	PUNCT
ap-1851	368	24	ψ1	ψ1	NOUN
ap-1851	368	25	,	,	PUNCT
ap-1851	368	26	hψ2	hψ2	NOUN
ap-1851	368	27	)	)	PUNCT
ap-1851	368	28	=	=	PUNCT
ap-1851	369	1	−	−	PROPN
ap-1851	369	2	∫	∫	PROPN
ap-1851	369	3	2π	2π	PROPN
ap-1851	369	4	0	0	NUM
ap-1851	369	5	∫	∫	NOUN
ap-1851	369	6	r	r	NOUN
ap-1851	369	7	0	0	NUM
ap-1851	369	8	u1	u1	NOUN
ap-1851	369	9	r	r	NOUN
ap-1851	369	10	−1/2	−1/2	VERB
ap-1851	369	11	d2	d2	PROPN
ap-1851	369	12	dr2	dr2	PROPN
ap-1851	369	13	r	r	NOUN
ap-1851	369	14	1/2u2	1/2u2	NUM
ap-1851	369	15	r	r	NOUN
ap-1851	369	16	dr	dr	NOUN
ap-1851	369	17	dϕ	dϕ	NOUN
ap-1851	369	18	−	−	PROPN
ap-1851	369	19	∫	∫	PROPN
ap-1851	369	20	∞	∞	PROPN
ap-1851	369	21	0	0	NUM
ap-1851	369	22	f1f2	f1f2	PUNCT
ap-1851	370	1	′′	′′	PROPN
ap-1851	370	2	dx	dx	PROPN
ap-1851	371	1	=	=	PUNCT
ap-1851	372	1	−	−	PROPN
ap-1851	372	2	∫	∫	PROPN
ap-1851	372	3	2π	2π	PROPN
ap-1851	372	4	0	0	NUM
ap-1851	372	5	∫	∫	NOUN
ap-1851	372	6	r	r	NOUN
ap-1851	372	7	0	0	NUM
ap-1851	372	8	ũ1ũ2	ũ1ũ2	PROPN
ap-1851	372	9	′′	′′	PROPN
ap-1851	372	10	dr	dr	NOUN
ap-1851	372	11	dϕ	dϕ	NOUN
ap-1851	372	12	−	−	PROPN
ap-1851	372	13	∫	∫	PROPN
ap-1851	372	14	∞	∞	PROPN
ap-1851	372	15	0	0	NUM
ap-1851	372	16	f1f2	f1f2	PUNCT
ap-1851	373	1	′′	′′	PROPN
ap-1851	373	2	dx	dx	PROPN
ap-1851	374	1	=	=	PUNCT
ap-1851	375	1	−	−	PROPN
ap-1851	375	2	∫	∫	PROPN
ap-1851	375	3	2π	2π	NOUN
ap-1851	375	4	0	0	NUM
ap-1851	376	1	ũ1ũ2	ũ1ũ2	NOUN
ap-1851	376	2	′	′	NUM
ap-1851	376	3	dϕ	dϕ	NOUN
ap-1851	377	1	+	+	CCONJ
ap-1851	378	1	∫	∫	PROPN
ap-1851	378	2	2π	2π	NOUN
ap-1851	378	3	0	0	NUM
ap-1851	378	4	∫	∫	NOUN
ap-1851	378	5	r	r	NOUN
ap-1851	378	6	0	0	NUM
ap-1851	378	7	ũ1	ũ1	PROPN
ap-1851	378	8	′	′	ADJ
ap-1851	378	9	ũ2	ũ2	PROPN
ap-1851	378	10	′	′	PROPN
ap-1851	378	11	dr	dr	PROPN
ap-1851	378	12	dϕ−	dϕ−	X
ap-1851	378	13	f1(0+)f	f1(0+)f	PROPN
ap-1851	378	14	′2(0	′2(0	PROPN
ap-1851	378	15	+	+	PROPN
ap-1851	378	16	)	)	PUNCT
ap-1851	379	1	+	+	CCONJ
ap-1851	379	2	∫	∫	PROPN
ap-1851	379	3	∞	∞	PROPN
ap-1851	379	4	0	0	NUM
ap-1851	379	5	f1	f1	NOUN
ap-1851	379	6	′	′	NUM
ap-1851	379	7	f2	f2	PROPN
ap-1851	379	8	′	′	NUM
ap-1851	379	9	dx	dx	PROPN
ap-1851	379	10	,	,	PUNCT
ap-1851	379	11	where	where	SCONJ
ap-1851	379	12	ũa	ũa	ADJ
ap-1851	379	13	=	=	SYM
ap-1851	379	14	r1/2ua	r1/2ua	PROPN
ap-1851	379	15	,	,	PUNCT
ap-1851	379	16	a	a	PRON
ap-1851	379	17	=	=	SYM
ap-1851	379	18	1	1	NUM
ap-1851	379	19	,	,	PUNCT
ap-1851	379	20	2	2	NUM
ap-1851	379	21	,	,	PUNCT
ap-1851	379	22	is	be	AUX
ap-1851	379	23	a	a	DET
ap-1851	379	24	multiple	multiple	NOUN
ap-1851	379	25	of	of	ADP
ap-1851	379	26	the	the	DET
ap-1851	379	27	disc	disc	NOUN
ap-1851	379	28	component	component	NOUN
ap-1851	379	29	of	of	ADP
ap-1851	379	30	ua	ua	PROPN
ap-1851	379	31	(	(	PUNCT
ap-1851	379	32	with	with	ADP
ap-1851	379	33	the	the	DET
ap-1851	379	34	prime	prime	NOUN
ap-1851	379	35	denoting	denote	VERB
ap-1851	379	36	the	the	DET
ap-1851	379	37	derivative	derivative	NOUN
ap-1851	379	38	with	with	ADP
ap-1851	379	39	respect	respect	NOUN
ap-1851	379	40	to	to	ADP
ap-1851	379	41	r	r	NOUN
ap-1851	379	42	)	)	PUNCT
ap-1851	379	43	and	and	CCONJ
ap-1851	379	44	fa	fa	PROPN
ap-1851	379	45	is	be	AUX
ap-1851	379	46	the	the	DET
ap-1851	379	47	corresponding	corresponding	ADJ
ap-1851	379	48	halfline	halfline	NOUN
ap-1851	379	49	component	component	NOUN
ap-1851	379	50	.	.	PUNCT
ap-1851	380	1	hence	hence	ADV
ap-1851	380	2	we	we	PRON
ap-1851	380	3	have	have	VERB
ap-1851	380	4	(	(	PUNCT
ap-1851	380	5	ψ1	ψ1	ADJ
ap-1851	380	6	,	,	PUNCT
ap-1851	380	7	hψ2)−	hψ2)−	NOUN
ap-1851	380	8	(	(	PUNCT
ap-1851	380	9	hψ1	hψ1	NOUN
ap-1851	380	10	,	,	PUNCT
ap-1851	380	11	ψ2	ψ2	NOUN
ap-1851	380	12	)	)	PUNCT
ap-1851	381	1	=	=	SYM
ap-1851	381	2	lim	lim	PROPN
ap-1851	381	3	r→0	r→0	VERB
ap-1851	381	4	∫	∫	PROPN
ap-1851	381	5	2π	2π	PROPN
ap-1851	381	6	0	0	PUNCT
ap-1851	382	1	[	[	PUNCT
ap-1851	382	2	ũ1ũ2	ũ1ũ2	ADJ
ap-1851	382	3	′	′	NUM
ap-1851	382	4	−	−	PROPN
ap-1851	382	5	ũ2ũ1	ũ2ũ1	NOUN
ap-1851	382	6	′]dϕ	′]dϕ	PROPN
ap-1851	382	7	+	+	CCONJ
ap-1851	382	8	f2(0+)f	f2(0+)f	PROPN
ap-1851	382	9	′1(0+)−	′1(0+)−	NUM
ap-1851	382	10	f1(0+)f	f1(0+)f	PROPN
ap-1851	382	11	′2(0	′2(0	PROPN
ap-1851	382	12	+	+	PROPN
ap-1851	382	13	)	)	PUNCT
ap-1851	382	14	,	,	PUNCT
ap-1851	382	15	and	and	CCONJ
ap-1851	383	1	using	use	VERB
ap-1851	383	2	asymptotic	asymptotic	ADJ
ap-1851	383	3	expansion	expansion	NOUN
ap-1851	383	4	of	of	ADP
ap-1851	383	5	u	u	NOUN
ap-1851	383	6	near	near	ADP
ap-1851	383	7	r	r	NOUN
ap-1851	383	8	=	=	SYM
ap-1851	383	9	0	0	NUM
ap-1851	383	10	,	,	PUNCT
ap-1851	383	11	√	√	NUM
ap-1851	383	12	πu(r	πu(r	NUM
ap-1851	383	13	,	,	PUNCT
ap-1851	383	14	θ	θ	X
ap-1851	383	15	)	)	PUNCT
ap-1851	383	16	=	=	SYM
ap-1851	384	1	(	(	PUNCT
ap-1851	384	2	φ−1	φ−1	PROPN
ap-1851	384	3	1	1	NUM
ap-1851	384	4	(	(	PUNCT
ap-1851	384	5	ψ)r−1/2	ψ)r−1/2	PUNCT
ap-1851	384	6	+	+	CCONJ
ap-1851	384	7	φ−1	φ−1	PROPN
ap-1851	384	8	2	2	NUM
ap-1851	384	9	(	(	PUNCT
ap-1851	384	10	ψ)r1/2)e−iθ	ψ)r1/2)e−iθ	PROPN
ap-1851	384	11	+	+	CCONJ
ap-1851	384	12	φ0	φ0	PROPN
ap-1851	384	13	1(ψ)r−1/2	1(ψ)r−1/2	PROPN
ap-1851	384	14	+	+	CCONJ
ap-1851	384	15	φ0	φ0	PROPN
ap-1851	384	16	2(ψ)r1/2	2(ψ)r1/2	PROPN
ap-1851	384	17	,	,	PUNCT
ap-1851	384	18	−2r	−2r	PROPN
ap-1851	384	19	√	√	NUM
ap-1851	384	20	πu′(r	πu′(r	PROPN
ap-1851	384	21	,	,	PUNCT
ap-1851	384	22	θ	θ	NOUN
ap-1851	384	23	)	)	PUNCT
ap-1851	384	24	=	=	SYM
ap-1851	384	25	(	(	PUNCT
ap-1851	384	26	φ−1	φ−1	PROPN
ap-1851	384	27	1	1	NUM
ap-1851	384	28	(	(	PUNCT
ap-1851	384	29	ψ)r−1/2	ψ)r−1/2	NUM
ap-1851	384	30	−	−	PROPN
ap-1851	384	31	φ−1	φ−1	PROPN
ap-1851	384	32	2	2	NUM
ap-1851	384	33	(	(	PUNCT
ap-1851	384	34	ψ)r1/2)e−iθ	ψ)r1/2)e−iθ	PROPN
ap-1851	384	35	+	+	PROPN
ap-1851	384	36	φ0	φ0	PROPN
ap-1851	384	37	1(ψ)r−1/2	1(ψ)r−1/2	PROPN
ap-1851	384	38	−	−	PROPN
ap-1851	384	39	φ0	φ0	PROPN
ap-1851	384	40	2(ψ)r1/2	2(ψ)r1/2	PROPN
ap-1851	384	41	,	,	PUNCT
ap-1851	384	42	one	one	PRON
ap-1851	384	43	finds	find	VERB
ap-1851	384	44	(	(	PUNCT
ap-1851	384	45	ψ1	ψ1	NOUN
ap-1851	384	46	,	,	PUNCT
ap-1851	384	47	hψ2)−	hψ2)−	NOUN
ap-1851	384	48	(	(	PUNCT
ap-1851	384	49	hψ1	hψ1	NOUN
ap-1851	384	50	,	,	PUNCT
ap-1851	384	51	ψ2	ψ2	NOUN
ap-1851	384	52	)	)	PUNCT
ap-1851	384	53	=	=	PUNCT
ap-1851	384	54	φ1(ψ1)∗φ2(ψ2)−	φ1(ψ1)∗φ2(ψ2)−	VERB
ap-1851	384	55	φ1(ψ2)∗φ2(ψ1	φ1(ψ2)∗φ2(ψ1	NOUN
ap-1851	384	56	)	)	PUNCT
ap-1851	384	57	,	,	PUNCT
ap-1851	384	58	where	where	SCONJ
ap-1851	384	59	φa(ψ	φa(ψ	NUM
ap-1851	384	60	)	)	PUNCT
ap-1851	384	61	=	=	SYM
ap-1851	385	1	(	(	PUNCT
ap-1851	385	2	φh	φh	ADP
ap-1851	385	3	a	a	PRON
ap-1851	385	4	,	,	PUNCT
ap-1851	385	5	φ0	φ0	PROPN
ap-1851	385	6	a	a	NOUN
ap-1851	385	7	,	,	PUNCT
ap-1851	385	8	φ−1	φ−1	PROPN
ap-1851	385	9	a	a	PRON
ap-1851	385	10	)	)	PUNCT
ap-1851	385	11	t	t	NOUN
ap-1851	385	12	for	for	ADP
ap-1851	385	13	a	a	DET
ap-1851	385	14	=	=	SYM
ap-1851	385	15	1	1	NUM
ap-1851	385	16	,	,	PUNCT
ap-1851	385	17	2	2	NUM
ap-1851	385	18	.	.	PUNCT
ap-1851	385	19	consequently	consequently	ADV
ap-1851	385	20	,	,	PUNCT
ap-1851	385	21	to	to	PART
ap-1851	385	22	get	get	VERB
ap-1851	385	23	a	a	DET
ap-1851	385	24	self	self	NOUN
ap-1851	385	25	-	-	PUNCT
ap-1851	385	26	adjoint	adjoint	NOUN
ap-1851	385	27	hamiltonian	hamiltonian	NOUN
ap-1851	385	28	one	one	PRON
ap-1851	385	29	has	have	VERB
ap-1851	385	30	to	to	PART
ap-1851	385	31	impose	impose	VERB
ap-1851	385	32	coupling	couple	VERB
ap-1851	385	33	conditions	condition	NOUN
ap-1851	385	34	similar	similar	ADJ
ap-1851	385	35	to	to	ADP
ap-1851	385	36	(	(	PUNCT
ap-1851	385	37	1	1	NUM
ap-1851	385	38	)	)	PUNCT
ap-1851	385	39	,	,	PUNCT
ap-1851	385	40	namely	namely	ADV
ap-1851	385	41	(	(	PUNCT
ap-1851	385	42	u	u	NOUN
ap-1851	385	43	−	−	NOUN
ap-1851	385	44	i)φ1(ψ	i)φ1(ψ	NOUN
ap-1851	385	45	)	)	PUNCT
ap-1851	385	46	+	+	CCONJ
ap-1851	386	1	i(u	i(u	PROPN
ap-1851	386	2	+	+	PROPN
ap-1851	386	3	i)φ2(ψ	i)φ2(ψ	NOUN
ap-1851	386	4	)	)	PUNCT
ap-1851	387	1	=	=	SYM
ap-1851	387	2	0	0	PUNCT
ap-1851	387	3	(	(	PUNCT
ap-1851	387	4	9	9	NUM
ap-1851	387	5	)	)	PUNCT
ap-1851	387	6	with	with	ADP
ap-1851	387	7	a	a	DET
ap-1851	387	8	unitary	unitary	ADJ
ap-1851	387	9	u	u	NOUN
ap-1851	387	10	.	.	PUNCT
ap-1851	388	1	we	we	PRON
ap-1851	388	2	choose	choose	VERB
ap-1851	388	3	the	the	DET
ap-1851	388	4	latter	latter	ADJ
ap-1851	388	5	in	in	ADP
ap-1851	388	6	the	the	DET
ap-1851	388	7	form	form	NOUN
ap-1851	388	8	u	u	NOUN
ap-1851	388	9	=	=	NOUN
ap-1851	388	10	0	0	ADP
ap-1851	388	11	1	1	NUM
ap-1851	388	12	0	0	NUM
ap-1851	388	13	1	1	NUM
ap-1851	388	14	0	0	NUM
ap-1851	388	15	0	0	NUM
ap-1851	388	16	0	0	NUM
ap-1851	388	17	0	0	NUM
ap-1851	388	18	eiρ	eiρ	NOUN
ap-1851	388	19			PROPN
ap-1851	388	20	,	,	PUNCT
ap-1851	388	21	(	(	PUNCT
ap-1851	388	22	10	10	NUM
ap-1851	388	23	)	)	PUNCT
ap-1851	388	24	i.e.	i.e.	X
ap-1851	388	25	the	the	DET
ap-1851	388	26	nonradial	nonradial	ADJ
ap-1851	388	27	part	part	NOUN
ap-1851	388	28	(	(	PUNCT
ap-1851	388	29	m	m	NOUN
ap-1851	388	30	=	=	SYM
ap-1851	388	31	−1	−1	NOUN
ap-1851	388	32	)	)	PUNCT
ap-1851	388	33	of	of	ADP
ap-1851	388	34	the	the	DET
ap-1851	388	35	disc	disc	NOUN
ap-1851	388	36	wave	wave	NOUN
ap-1851	388	37	function	function	NOUN
ap-1851	388	38	is	be	AUX
ap-1851	388	39	coupled	couple	VERB
ap-1851	388	40	to	to	ADP
ap-1851	388	41	neither	neither	PRON
ap-1851	388	42	of	of	ADP
ap-1851	388	43	the	the	DET
ap-1851	388	44	other	other	ADJ
ap-1851	388	45	two	two	NUM
ap-1851	388	46	,	,	PUNCT
ap-1851	388	47	while	while	SCONJ
ap-1851	388	48	the	the	DET
ap-1851	388	49	radial	radial	ADJ
ap-1851	388	50	part	part	NOUN
ap-1851	388	51	(	(	PUNCT
ap-1851	388	52	m	m	PROPN
ap-1851	388	53	=	=	NOUN
ap-1851	388	54	0	0	NUM
ap-1851	388	55	)	)	PUNCT
ap-1851	388	56	is	be	AUX
ap-1851	388	57	coupled	couple	VERB
ap-1851	388	58	to	to	ADP
ap-1851	388	59	the	the	DET
ap-1851	388	60	halfline	halfline	NOUN
ap-1851	388	61	via	via	ADP
ap-1851	388	62	424	424	NUM
ap-1851	388	63	vol	vol	NOUN
ap-1851	388	64	.	.	PUNCT
ap-1851	389	1	53	53	NUM
ap-1851	389	2	no	no	NOUN
ap-1851	389	3	.	.	PUNCT
ap-1851	390	1	5/2013	5/2013	NUM
ap-1851	390	2	resonances	resonance	NOUN
ap-1851	390	3	on	on	ADP
ap-1851	390	4	hedgehog	hedgehog	PROPN
ap-1851	390	5	manifolds	manifolds	PROPN
ap-1851	390	6	kirchhoff	kirchhoff	PROPN
ap-1851	390	7	’s	’s	PART
ap-1851	390	8	(	(	PUNCT
ap-1851	390	9	free	free	ADJ
ap-1851	390	10	)	)	PUNCT
ap-1851	390	11	coupling	coupling	NOUN
ap-1851	390	12	.	.	PUNCT
ap-1851	391	1	to	to	PART
ap-1851	391	2	see	see	VERB
ap-1851	391	3	that	that	SCONJ
ap-1851	391	4	this	this	DET
ap-1851	391	5	choice	choice	NOUN
ap-1851	391	6	kills	kill	VERB
ap-1851	391	7	all	all	DET
ap-1851	391	8	the	the	DET
ap-1851	391	9	‘	'	PUNCT
ap-1851	391	10	true	true	ADJ
ap-1851	391	11	’	'	PUNCT
ap-1851	391	12	resonances	resonance	NOUN
ap-1851	391	13	,	,	PUNCT
ap-1851	391	14	we	we	PRON
ap-1851	391	15	choose	choose	VERB
ap-1851	391	16	the	the	DET
ap-1851	391	17	ansatz	ansatz	ADJ
ap-1851	391	18	f(x	f(x	NOUN
ap-1851	391	19	)	)	PUNCT
ap-1851	391	20	=	=	PUNCT
ap-1851	391	21	a	a	DET
ap-1851	391	22	sin	sin	NOUN
ap-1851	391	23	kx+	kx+	PROPN
ap-1851	391	24	b	b	PROPN
ap-1851	391	25	cos	cos	PROPN
ap-1851	391	26	kx	kx	PROPN
ap-1851	391	27	,	,	PUNCT
ap-1851	391	28	u(r	u(r	PROPN
ap-1851	391	29	)	)	PUNCT
ap-1851	392	1	=	=	SYM
ap-1851	393	1	r−1/2(c	r−1/2(c	NOUN
ap-1851	393	2	sin	sin	NOUN
ap-1851	393	3	k(r−	k(r−	PROPN
ap-1851	393	4	r	r	NOUN
ap-1851	393	5	)	)	PUNCT
ap-1851	393	6	)	)	PUNCT
ap-1851	394	1	which	which	PRON
ap-1851	394	2	yields	yield	VERB
ap-1851	394	3	the	the	DET
ap-1851	394	4	boundary	boundary	ADJ
ap-1851	394	5	values	value	NOUN
ap-1851	394	6	φ1(ψ	φ1(ψ	NOUN
ap-1851	394	7	)	)	PUNCT
ap-1851	395	1	=	=	PUNCT
ap-1851	395	2	(	(	PUNCT
ap-1851	395	3	b	b	NOUN
ap-1851	395	4	,	,	PUNCT
ap-1851	395	5	c	c	NOUN
ap-1851	395	6	√	√	PROPN
ap-1851	395	7	π	π	PROPN
ap-1851	395	8	sin	sin	VERB
ap-1851	395	9	kr	kr	PROPN
ap-1851	395	10	,	,	PUNCT
ap-1851	395	11	0)t	0)t	NOUN
ap-1851	395	12	,	,	PUNCT
ap-1851	395	13	φ2(ψ	φ2(ψ	NOUN
ap-1851	395	14	)	)	PUNCT
ap-1851	395	15	=	=	VERB
ap-1851	396	1	k(a,−c	k(a,−c	NOUN
ap-1851	396	2	√	√	PROPN
ap-1851	396	3	π	π	PROPN
ap-1851	396	4	cos	cos	PROPN
ap-1851	396	5	kr	kr	PROPN
ap-1851	396	6	,	,	PUNCT
ap-1851	396	7	0)t	0)t	PROPN
ap-1851	396	8	.	.	PUNCT
ap-1851	397	1	it	it	PRON
ap-1851	397	2	follows	follow	VERB
ap-1851	397	3	now	now	ADV
ap-1851	397	4	from	from	ADP
ap-1851	397	5	the	the	DET
ap-1851	397	6	coupling	coupling	NOUN
ap-1851	397	7	conditions	condition	NOUN
ap-1851	397	8	that	that	PRON
ap-1851	397	9	b	b	X
ap-1851	397	10	=	=	SYM
ap-1851	397	11	c	c	NOUN
ap-1851	397	12	√	√	PROPN
ap-1851	397	13	π	π	PROPN
ap-1851	397	14	sin	sin	VERB
ap-1851	397	15	kr	kr	PROPN
ap-1851	397	16	,	,	PUNCT
ap-1851	397	17	a	a	DET
ap-1851	397	18	=	=	X
ap-1851	397	19	c	c	NOUN
ap-1851	397	20	√	√	PROPN
ap-1851	397	21	π	π	PROPN
ap-1851	397	22	cos	cos	PROPN
ap-1851	397	23	kr	kr	PROPN
ap-1851	397	24	,	,	PUNCT
ap-1851	397	25	hence	hence	ADV
ap-1851	397	26	f(x	f(x	NOUN
ap-1851	397	27	)	)	PUNCT
ap-1851	397	28	=	=	PUNCT
ap-1851	398	1	c	c	NOUN
ap-1851	398	2	√	√	NUM
ap-1851	398	3	π	π	PROPN
ap-1851	398	4	sin	sin	VERB
ap-1851	398	5	k(r+	k(r+	NOUN
ap-1851	398	6	x	x	X
ap-1851	398	7	)	)	PUNCT
ap-1851	398	8	,	,	PUNCT
ap-1851	398	9	thus	thus	ADV
ap-1851	398	10	for	for	ADP
ap-1851	398	11	any	any	DET
ap-1851	398	12	k	k	PROPN
ap-1851	398	13	6∈	6∈	PROPN
ap-1851	398	14	r	r	NOUN
ap-1851	398	15	and	and	CCONJ
ap-1851	398	16	c	c	PROPN
ap-1851	398	17	6=	6=	ADP
ap-1851	398	18	0	0	NUM
ap-1851	399	1	the	the	DET
ap-1851	399	2	function	function	NOUN
ap-1851	399	3	f	f	PROPN
ap-1851	399	4	necessarily	necessarily	ADV
ap-1851	399	5	contains	contain	VERB
ap-1851	399	6	a	a	DET
ap-1851	399	7	nontrivial	nontrivial	ADJ
ap-1851	399	8	part	part	NOUN
ap-1851	399	9	of	of	ADP
ap-1851	399	10	the	the	DET
ap-1851	399	11	wave	wave	NOUN
ap-1851	399	12	e−ikx	e−ikx	NOUN
ap-1851	399	13	.	.	PUNCT
ap-1851	400	1	however	however	ADV
ap-1851	400	2	,	,	PUNCT
ap-1851	400	3	as	as	SCONJ
ap-1851	400	4	we	we	PRON
ap-1851	400	5	have	have	AUX
ap-1851	400	6	argued	argue	VERB
ap-1851	400	7	above	above	ADV
ap-1851	400	8	,	,	PUNCT
ap-1851	400	9	a	a	DET
ap-1851	400	10	resolvent	resolvent	ADJ
ap-1851	400	11	resonance	resonance	NOUN
ap-1851	400	12	can	can	AUX
ap-1851	400	13	must	must	AUX
ap-1851	400	14	have	have	VERB
ap-1851	400	15	the	the	DET
ap-1851	400	16	asymptotics	asymptotic	NOUN
ap-1851	400	17	eikx	eikx	VERB
ap-1851	400	18	only	only	ADV
ap-1851	400	19	.	.	PUNCT
ap-1851	401	1	in	in	ADP
ap-1851	401	2	this	this	DET
ap-1851	401	3	way	way	NOUN
ap-1851	401	4	we	we	PRON
ap-1851	401	5	come	come	VERB
ap-1851	401	6	to	to	ADP
ap-1851	401	7	the	the	DET
ap-1851	401	8	indicated	indicate	VERB
ap-1851	401	9	conclusion	conclusion	NOUN
ap-1851	401	10	:	:	PUNCT
ap-1851	401	11	proposition	proposition	NOUN
ap-1851	401	12	5.1	5.1	NUM
ap-1851	401	13	.	.	PUNCT
ap-1851	402	1	the	the	DET
ap-1851	402	2	described	describe	VERB
ap-1851	402	3	system	system	NOUN
ap-1851	402	4	has	have	VERB
ap-1851	402	5	no	no	DET
ap-1851	402	6	true	true	ADJ
ap-1851	402	7	resonances	resonance	NOUN
ap-1851	402	8	for	for	ADP
ap-1851	402	9	the	the	DET
ap-1851	402	10	coupling	coupling	NOUN
ap-1851	402	11	corresponding	correspond	VERB
ap-1851	402	12	to	to	ADP
ap-1851	402	13	matrix	matrix	VERB
ap-1851	402	14	(	(	PUNCT
ap-1851	402	15	10	10	NUM
ap-1851	402	16	)	)	PUNCT
ap-1851	402	17	and	and	CCONJ
ap-1851	402	18	magnetic	magnetic	ADJ
ap-1851	402	19	flux	flux	NOUN
ap-1851	402	20	α	α	NOUN
ap-1851	403	1	=	=	NOUN
ap-1851	403	2	1	1	NUM
ap-1851	403	3	2	2	NUM
ap-1851	403	4	.	.	PUNCT
ap-1851	404	1	since	since	SCONJ
ap-1851	404	2	the	the	DET
ap-1851	404	3	effect	effect	NOUN
ap-1851	404	4	occurs	occur	VERB
ap-1851	404	5	at	at	ADP
ap-1851	404	6	a	a	DET
ap-1851	404	7	particular	particular	ADJ
ap-1851	404	8	value	value	NOUN
ap-1851	404	9	of	of	ADP
ap-1851	404	10	the	the	DET
ap-1851	404	11	magnetic	magnetic	ADJ
ap-1851	404	12	flux	flux	NOUN
ap-1851	404	13	,	,	PUNCT
ap-1851	404	14	it	it	PRON
ap-1851	404	15	is	be	AUX
ap-1851	404	16	also	also	ADV
ap-1851	404	17	interesting	interesting	ADJ
ap-1851	404	18	to	to	PART
ap-1851	404	19	ask	ask	VERB
ap-1851	404	20	what	what	PRON
ap-1851	404	21	happens	happen	VERB
ap-1851	404	22	if	if	SCONJ
ap-1851	404	23	the	the	DET
ap-1851	404	24	field	field	NOUN
ap-1851	404	25	changes	change	VERB
ap-1851	404	26	,	,	PUNCT
ap-1851	404	27	so	so	SCONJ
ap-1851	404	28	that	that	SCONJ
ap-1851	404	29	α	α	PROPN
ap-1851	404	30	runs	run	VERB
ap-1851	404	31	from	from	ADP
ap-1851	404	32	zero	zero	NUM
ap-1851	404	33	to	to	ADP
ap-1851	404	34	1	1	NUM
ap-1851	404	35	2	2	NUM
ap-1851	404	36	.	.	PUNCT
ap-1851	405	1	the	the	DET
ap-1851	405	2	symmetry	symmetry	NOUN
ap-1851	405	3	of	of	ADP
ap-1851	405	4	the	the	DET
ap-1851	405	5	problem	problem	NOUN
ap-1851	405	6	allows	allow	VERB
ap-1851	405	7	us	we	PRON
ap-1851	405	8	to	to	PART
ap-1851	405	9	use	use	VERB
ap-1851	405	10	the	the	DET
ap-1851	405	11	ansatz	ansatz	ADJ
ap-1851	405	12	u(r	u(r	NOUN
ap-1851	405	13	,	,	PUNCT
ap-1851	405	14	ϕ	ϕ	NOUN
ap-1851	405	15	)	)	PUNCT
ap-1851	405	16	=	=	SYM
ap-1851	405	17	r(r	r(r	PROPN
ap-1851	405	18	)	)	PUNCT
ap-1851	405	19	eimϕ	eimϕ	PROPN
ap-1851	405	20	;	;	PUNCT
ap-1851	405	21	this	this	PRON
ap-1851	405	22	shows	show	VERB
ap-1851	405	23	that	that	SCONJ
ap-1851	405	24	one	one	PRON
ap-1851	405	25	has	have	VERB
ap-1851	405	26	to	to	PART
ap-1851	405	27	solve	solve	VERB
ap-1851	405	28	the	the	DET
ap-1851	405	29	equation	equation	NOUN
ap-1851	405	30	−∂	−∂	NOUN
ap-1851	405	31	2r(r	2r(r	NUM
ap-1851	405	32	)	)	PUNCT
ap-1851	406	1	∂r2	∂r2	PROPN
ap-1851	406	2	−	−	NOUN
ap-1851	406	3	1	1	NUM
ap-1851	406	4	r	r	NOUN
ap-1851	406	5	∂r(r	∂r(r	NOUN
ap-1851	406	6	)	)	PUNCT
ap-1851	406	7	∂r	∂r	PROPN
ap-1851	407	1	+	+	CCONJ
ap-1851	407	2	1	1	NUM
ap-1851	407	3	r2	r2	NOUN
ap-1851	407	4	(	(	PUNCT
ap-1851	407	5	m+	m+	NUM
ap-1851	407	6	α)2r(r	α)2r(r	NOUN
ap-1851	407	7	)	)	PUNCT
ap-1851	407	8	=	=	SYM
ap-1851	407	9	k2r(r	k2r(r	NOUN
ap-1851	407	10	)	)	PUNCT
ap-1851	407	11	which	which	PRON
ap-1851	407	12	can	can	AUX
ap-1851	407	13	be	be	AUX
ap-1851	407	14	easily	easily	ADV
ap-1851	407	15	transformed	transform	VERB
ap-1851	407	16	into	into	ADP
ap-1851	407	17	bessel	bessel	ADJ
ap-1851	407	18	equation	equation	NOUN
ap-1851	407	19	in	in	ADP
ap-1851	407	20	the	the	DET
ap-1851	407	21	variable	variable	ADJ
ap-1851	407	22	kr	kr	PROPN
ap-1851	407	23	with	with	ADP
ap-1851	407	24	the	the	DET
ap-1851	407	25	constant	constant	ADJ
ap-1851	407	26	(	(	PUNCT
ap-1851	407	27	m+	m+	NUM
ap-1851	407	28	α	α	NOUN
ap-1851	407	29	)	)	PUNCT
ap-1851	407	30	.	.	PUNCT
ap-1851	408	1	hence	hence	ADV
ap-1851	408	2	the	the	DET
ap-1851	408	3	radial	radial	ADJ
ap-1851	408	4	part	part	NOUN
ap-1851	408	5	of	of	ADP
ap-1851	408	6	the	the	DET
ap-1851	408	7	wavefunction	wavefunction	NOUN
ap-1851	408	8	on	on	ADP
ap-1851	408	9	the	the	DET
ap-1851	408	10	disc	disc	NOUN
ap-1851	408	11	is	be	AUX
ap-1851	408	12	given	give	VERB
ap-1851	408	13	as	as	ADP
ap-1851	408	14	a	a	DET
ap-1851	408	15	combination	combination	NOUN
ap-1851	408	16	of	of	ADP
ap-1851	408	17	bessel	bessel	NOUN
ap-1851	408	18	functions	function	NOUN
ap-1851	408	19	and	and	CCONJ
ap-1851	408	20	u(r	u(r	NOUN
ap-1851	408	21	,	,	PUNCT
ap-1851	408	22	ϕ	ϕ	NOUN
ap-1851	408	23	)	)	PUNCT
ap-1851	408	24	=	=	PUNCT
ap-1851	409	1	∑	∑	PROPN
ap-1851	409	2	m	m	PROPN
ap-1851	409	3	(	(	PUNCT
ap-1851	409	4	a1mjm+α(kr	a1mjm+α(kr	ADJ
ap-1851	409	5	)	)	PUNCT
ap-1851	409	6	+	+	NUM
ap-1851	409	7	a2mym+α(kr	a2mym+α(kr	NOUN
ap-1851	409	8	)	)	PUNCT
ap-1851	409	9	)	)	PUNCT
ap-1851	409	10	eimϕ.	eimϕ.	ADV
ap-1851	409	11	we	we	PRON
ap-1851	409	12	employ	employ	VERB
ap-1851	409	13	the	the	DET
ap-1851	409	14	behaviour	behaviour	NOUN
ap-1851	409	15	of	of	ADP
ap-1851	409	16	bessel	bessel	NOUN
ap-1851	409	17	functions	function	NOUN
ap-1851	409	18	in	in	ADP
ap-1851	409	19	the	the	DET
ap-1851	409	20	vicinity	vicinity	NOUN
ap-1851	409	21	of	of	ADP
ap-1851	409	22	zero	zero	NUM
ap-1851	409	23	,	,	PUNCT
ap-1851	409	24	jα(x	jα(x	NOUN
ap-1851	409	25	)	)	PUNCT
ap-1851	410	1	≈	≈	PROPN
ap-1851	410	2	1	1	NUM
ap-1851	410	3	γ(α+	γ(α+	PRON
ap-1851	410	4	1	1	NUM
ap-1851	410	5	)	)	PUNCT
ap-1851	410	6	(	(	PUNCT
ap-1851	410	7	x	x	SYM
ap-1851	410	8	2	2	X
ap-1851	410	9	)	)	PUNCT
ap-1851	410	10	α	α	NOUN
ap-1851	410	11	,	,	PUNCT
ap-1851	410	12	yα(x	yα(x	PUNCT
ap-1851	410	13	)	)	PUNCT
ap-1851	411	1	≈	≈	PROPN
ap-1851	411	2	−γ(α	−γ(α	ADJ
ap-1851	411	3	)	)	PUNCT
ap-1851	412	1	π	π	PROPN
ap-1851	412	2	(	(	PUNCT
ap-1851	412	3	2	2	NUM
ap-1851	412	4	x	x	SYM
ap-1851	412	5	)	)	PUNCT
ap-1851	412	6	α	α	PROPN
ap-1851	412	7	,	,	PUNCT
ap-1851	412	8	which	which	PRON
ap-1851	412	9	yields	yield	VERB
ap-1851	412	10	the	the	DET
ap-1851	412	11	values	value	NOUN
ap-1851	412	12	of	of	ADP
ap-1851	412	13	the	the	DET
ap-1851	412	14	above	above	ADJ
ap-1851	412	15	functionals	functional	NOUN
ap-1851	412	16	,	,	PUNCT
ap-1851	412	17	φ0	φ0	PROPN
ap-1851	412	18	1	1	NUM
ap-1851	412	19	=	=	SYM
ap-1851	412	20	√	√	PROPN
ap-1851	412	21	π	π	PROPN
ap-1851	412	22	lim	lim	PROPN
ap-1851	412	23	r→0	r→0	VERB
ap-1851	412	24	rα	rα	PROPN
ap-1851	412	25	2π	2π	PROPN
ap-1851	412	26	2π−γ(α	2π−γ(α	NUM
ap-1851	412	27	)	)	PUNCT
ap-1851	413	1	π	π	PROPN
ap-1851	413	2	a20	a20	NOUN
ap-1851	413	3	(	(	PUNCT
ap-1851	413	4	2	2	NUM
ap-1851	413	5	kr	kr	NOUN
ap-1851	413	6	)	)	PUNCT
ap-1851	413	7	α	α	NOUN
ap-1851	413	8	=	=	PUNCT
ap-1851	414	1	−γ(α)√	−γ(α)√	PROPN
ap-1851	414	2	π	π	X
ap-1851	414	3	(	(	PUNCT
ap-1851	414	4	2	2	NUM
ap-1851	414	5	k	k	NOUN
ap-1851	414	6	)	)	PUNCT
ap-1851	414	7	α	α	PROPN
ap-1851	414	8	a20	a20	PROPN
ap-1851	414	9	,	,	PUNCT
ap-1851	414	10	φ0	φ0	PROPN
ap-1851	414	11	2	2	NUM
ap-1851	414	12	=	=	SYM
ap-1851	414	13	√	√	PROPN
ap-1851	414	14	π	π	PROPN
ap-1851	414	15	lim	lim	PROPN
ap-1851	414	16	r→0	r→0	VERB
ap-1851	414	17	r−α	r−α	VERB
ap-1851	414	18	2π	2π	PROPN
ap-1851	414	19	2πa10	2πa10	ADP
ap-1851	414	20	1	1	NUM
ap-1851	414	21	γ(α+	γ(α+	DET
ap-1851	414	22	1	1	NUM
ap-1851	414	23	)	)	PUNCT
ap-1851	414	24	(	(	PUNCT
ap-1851	414	25	kr	kr	PROPN
ap-1851	414	26	2	2	NUM
ap-1851	414	27	)	)	PUNCT
ap-1851	414	28	α	α	NOUN
ap-1851	414	29	=	=	PUNCT
ap-1851	415	1	√	√	PROPN
ap-1851	415	2	π	π	PROPN
ap-1851	415	3	γ(α+	γ(α+	X
ap-1851	415	4	1	1	NUM
ap-1851	415	5	)	)	PUNCT
ap-1851	415	6	(	(	PUNCT
ap-1851	415	7	k	k	NOUN
ap-1851	415	8	2	2	X
ap-1851	415	9	)	)	PUNCT
ap-1851	415	10	α	α	NOUN
ap-1851	415	11	a10	a10	NOUN
ap-1851	415	12	,	,	PUNCT
ap-1851	415	13	-8	-8	NOUN
ap-1851	416	1	-7	-7	INTJ
ap-1851	417	1	-6	-6	INTJ
ap-1851	417	2	-5	-5	INTJ
ap-1851	417	3	-4	-4	INTJ
ap-1851	417	4	-3	-3	INTJ
ap-1851	417	5	-2	-2	INTJ
ap-1851	417	6	-1	-1	NOUN
ap-1851	417	7	0	0	NUM
ap-1851	417	8	0	0	NUM
ap-1851	417	9	0.05	0.05	NUM
ap-1851	417	10	0.1	0.1	NUM
ap-1851	417	11	0.15	0.15	NUM
ap-1851	417	12	0.2	0.2	NUM
ap-1851	417	13	0.25	0.25	NUM
ap-1851	417	14	0.3	0.3	NUM
ap-1851	417	15	0.35	0.35	NUM
ap-1851	417	16	0.4	0.4	NUM
ap-1851	417	17	0.45	0.45	NUM
ap-1851	417	18	0.5	0.5	NUM
ap-1851	417	19	figure	figure	NOUN
ap-1851	417	20	8	8	NUM
ap-1851	417	21	.	.	PUNCT
ap-1851	418	1	trajectory	trajectory	NOUN
ap-1851	418	2	of	of	ADP
ap-1851	418	3	a	a	DET
ap-1851	418	4	resonance	resonance	NOUN
ap-1851	418	5	for	for	ADP
ap-1851	418	6	α	α	NOUN
ap-1851	418	7	running	run	VERB
ap-1851	418	8	from	from	ADP
ap-1851	418	9	zero	zero	NUM
ap-1851	418	10	to	to	ADP
ap-1851	418	11	1	1	NUM
ap-1851	418	12	2	2	NUM
ap-1851	418	13	.	.	PUNCT
ap-1851	419	1	φ−1	φ−1	PROPN
ap-1851	419	2	1	1	NUM
ap-1851	419	3	=	=	SYM
ap-1851	419	4	√	√	PROPN
ap-1851	419	5	π	π	PROPN
ap-1851	419	6	lim	lim	PROPN
ap-1851	419	7	r→0	r→0	VERB
ap-1851	419	8	r1−α	r1−α	VERB
ap-1851	419	9	2π	2π	PROPN
ap-1851	419	10	2π	2π	PROPN
ap-1851	419	11	1	1	NUM
ap-1851	419	12	γ(α	γ(α	NOUN
ap-1851	419	13	)	)	PUNCT
ap-1851	419	14	(	(	PUNCT
ap-1851	419	15	kr	kr	PROPN
ap-1851	419	16	2	2	NUM
ap-1851	419	17	)	)	PUNCT
ap-1851	419	18	−1+α	−1+α	PROPN
ap-1851	420	1	a1−1	a1−1	NOUN
ap-1851	420	2	=	=	PUNCT
ap-1851	420	3	√	√	PROPN
ap-1851	420	4	π	π	PROPN
ap-1851	420	5	γ(α	γ(α	PROPN
ap-1851	420	6	)	)	PUNCT
ap-1851	420	7	(	(	PUNCT
ap-1851	420	8	2	2	NUM
ap-1851	420	9	k	k	NOUN
ap-1851	420	10	)	)	PUNCT
ap-1851	420	11	1−α	1−α	NUM
ap-1851	420	12	a1−1	a1−1	PROPN
ap-1851	420	13	,	,	PUNCT
ap-1851	420	14	φ−1	φ−1	PROPN
ap-1851	420	15	2	2	NUM
ap-1851	420	16	=	=	SYM
ap-1851	420	17	−	−	NOUN
ap-1851	420	18	√	√	PROPN
ap-1851	421	1	π	π	PROPN
ap-1851	421	2	lim	lim	PROPN
ap-1851	421	3	r→0	r→0	VERB
ap-1851	421	4	r−1+α	r−1+α	PROPN
ap-1851	421	5	2π	2π	NUM
ap-1851	421	6	2πγ(α−	2πγ(α−	NUM
ap-1851	421	7	1	1	NUM
ap-1851	421	8	)	)	PUNCT
ap-1851	421	9	π	π	PROPN
ap-1851	421	10	(	(	PUNCT
ap-1851	421	11	2	2	NUM
ap-1851	421	12	kr	kr	NOUN
ap-1851	421	13	)	)	PUNCT
ap-1851	422	1	−1+α	−1+α	PROPN
ap-1851	422	2	a2−1	a2−1	NOUN
ap-1851	422	3	=	=	SYM
ap-1851	422	4	−γ(α−	−γ(α−	NOUN
ap-1851	423	1	1)√	1)√	NUM
ap-1851	423	2	π	π	PROPN
ap-1851	423	3	(	(	PUNCT
ap-1851	423	4	k	k	NOUN
ap-1851	423	5	2	2	NUM
ap-1851	423	6	)	)	PUNCT
ap-1851	423	7	1−α	1−α	NUM
ap-1851	423	8	a2−1	a2−1	NOUN
ap-1851	423	9	.	.	PUNCT
ap-1851	424	1	the	the	DET
ap-1851	424	2	resonance	resonance	NOUN
ap-1851	424	3	equation	equation	NOUN
ap-1851	424	4	is	be	AUX
ap-1851	424	5	then	then	ADV
ap-1851	424	6	given	give	VERB
ap-1851	424	7	by	by	ADP
ap-1851	424	8	eq	eq	PROPN
ap-1851	424	9	.	.	PUNCT
ap-1851	425	1	(	(	PUNCT
ap-1851	425	2	9	9	NUM
ap-1851	425	3	)	)	PUNCT
ap-1851	425	4	and	and	CCONJ
ap-1851	425	5	dirichlet	dirichlet	PROPN
ap-1851	425	6	condition	condition	NOUN
ap-1851	425	7	at	at	ADP
ap-1851	425	8	the	the	DET
ap-1851	425	9	disc	disc	NOUN
ap-1851	425	10	boundary	boundary	NOUN
ap-1851	425	11	,	,	PUNCT
ap-1851	425	12	a10jα(kr	a10jα(kr	NOUN
ap-1851	425	13	)	)	PUNCT
ap-1851	425	14	+	+	NUM
ap-1851	425	15	a20yα(kr	a20yα(kr	NOUN
ap-1851	425	16	)	)	PUNCT
ap-1851	425	17	=	=	SYM
ap-1851	425	18	0	0	NUM
ap-1851	425	19	,	,	PUNCT
ap-1851	425	20	a1−1jα−1(kr	a1−1jα−1(kr	NOUN
ap-1851	425	21	)	)	PUNCT
ap-1851	425	22	+	+	CCONJ
ap-1851	425	23	a2−1yα−1(kr	a2−1yα−1(kr	NOUN
ap-1851	425	24	)	)	PUNCT
ap-1851	425	25	=	=	SYM
ap-1851	426	1	0	0	X
ap-1851	426	2	.	.	PUNCT
ap-1851	427	1	in	in	ADP
ap-1851	427	2	a	a	DET
ap-1851	427	3	particular	particular	ADJ
ap-1851	427	4	case	case	NOUN
ap-1851	427	5	of	of	ADP
ap-1851	427	6	u	u	NOUN
ap-1851	427	7	=	=	PUNCT
ap-1851	427	8	(	(	PUNCT
ap-1851	427	9	0	0	NUM
ap-1851	427	10	1	1	NUM
ap-1851	427	11	0	0	NUM
ap-1851	427	12	1	1	NUM
ap-1851	427	13	0	0	NUM
ap-1851	427	14	0	0	NUM
ap-1851	427	15	0	0	NUM
ap-1851	427	16	0	0	NUM
ap-1851	427	17	eiρ	eiρ	NOUN
ap-1851	427	18	)	)	PUNCT
ap-1851	427	19	resonances	resonance	NOUN
ap-1851	427	20	are	be	AUX
ap-1851	427	21	obtained	obtain	VERB
ap-1851	427	22	as	as	ADP
ap-1851	427	23	solutions	solution	NOUN
ap-1851	427	24	to	to	ADP
ap-1851	427	25	the	the	DET
ap-1851	427	26	condition	condition	NOUN
ap-1851	427	27	det	det	NOUN
ap-1851	427	28	[	[	X
ap-1851	427	29	(	(	PUNCT
ap-1851	427	30	−1	−1	NOUN
ap-1851	427	31	1	1	NUM
ap-1851	427	32	1	1	NUM
ap-1851	427	33	−1	−1	NOUN
ap-1851	427	34	)	)	PUNCT
ap-1851	427	35	(	(	PUNCT
ap-1851	427	36	1	1	NUM
ap-1851	427	37	0	0	NUM
ap-1851	427	38	0	0	NUM
ap-1851	427	39	−γ(α)√	−γ(α)√	NOUN
ap-1851	427	40	π	π	NOUN
ap-1851	427	41	(	(	PUNCT
ap-1851	427	42	2	2	NUM
ap-1851	427	43	k	k	NOUN
ap-1851	427	44	)	)	PUNCT
ap-1851	427	45	α	α	PROPN
ap-1851	427	46	jα(kr	jα(kr	PROPN
ap-1851	427	47	)	)	PUNCT
ap-1851	427	48	)	)	PUNCT
ap-1851	428	1	+	+	CCONJ
ap-1851	428	2	i	i	PRON
ap-1851	428	3	(	(	PUNCT
ap-1851	428	4	1	1	NUM
ap-1851	428	5	1	1	NUM
ap-1851	428	6	1	1	NUM
ap-1851	428	7	1	1	NUM
ap-1851	428	8	)	)	PUNCT
ap-1851	428	9	(	(	PUNCT
ap-1851	428	10	ik	ik	X
ap-1851	428	11	0	0	NUM
ap-1851	428	12	0	0	NUM
ap-1851	428	13	√	√	PROPN
ap-1851	428	14	π	π	PROPN
ap-1851	428	15	γ(α+1	γ(α+1	NOUN
ap-1851	428	16	)	)	PUNCT
ap-1851	428	17	(	(	PUNCT
ap-1851	428	18	k	k	NOUN
ap-1851	428	19	2	2	X
ap-1851	428	20	)	)	PUNCT
ap-1851	428	21	α	α	PROPN
ap-1851	428	22	yα(kr	yα(kr	PROPN
ap-1851	428	23	)	)	PUNCT
ap-1851	428	24	)	)	PUNCT
ap-1851	428	25	]	]	PUNCT
ap-1851	429	1	=	=	PUNCT
ap-1851	429	2	0	0	NUM
ap-1851	429	3	,	,	PUNCT
ap-1851	429	4	which	which	PRON
ap-1851	429	5	can	can	AUX
ap-1851	429	6	be	be	AUX
ap-1851	429	7	rewritten	rewrite	VERB
ap-1851	429	8	as	as	ADP
ap-1851	429	9	i	i	PRON
ap-1851	429	10	√	√	PUNCT
ap-1851	429	11	π	π	PROPN
ap-1851	429	12	γ(α+	γ(α+	ADP
ap-1851	429	13	1	1	NUM
ap-1851	429	14	)	)	PUNCT
ap-1851	429	15	(	(	PUNCT
ap-1851	429	16	k	k	NOUN
ap-1851	429	17	2	2	X
ap-1851	429	18	)	)	PUNCT
ap-1851	429	19	α	α	PROPN
ap-1851	429	20	yα(kr	yα(kr	PROPN
ap-1851	429	21	)	)	PUNCT
ap-1851	430	1	+	+	CCONJ
ap-1851	430	2	k	k	SYM
ap-1851	430	3	γ(α)√	γ(α)√	NOUN
ap-1851	430	4	π	π	X
ap-1851	430	5	(	(	PUNCT
ap-1851	430	6	2	2	NUM
ap-1851	430	7	k	k	NOUN
ap-1851	430	8	)	)	PUNCT
ap-1851	430	9	α	α	PROPN
ap-1851	430	10	jα(kr	jα(kr	PROPN
ap-1851	430	11	)	)	PUNCT
ap-1851	430	12	=	=	SYM
ap-1851	431	1	0	0	X
ap-1851	431	2	.	.	PUNCT
ap-1851	432	1	in	in	ADP
ap-1851	432	2	particular	particular	ADJ
ap-1851	432	3	,	,	PUNCT
ap-1851	432	4	for	for	ADP
ap-1851	432	5	α	α	NOUN
ap-1851	432	6	=	=	SYM
ap-1851	432	7	1/2	1/2	NUM
ap-1851	432	8	it	it	PRON
ap-1851	432	9	gives	give	VERB
ap-1851	432	10	sin	sin	NOUN
ap-1851	432	11	kr−	kr−	PROPN
ap-1851	432	12	i	i	PRON
ap-1851	432	13	cos	cos	VERB
ap-1851	432	14	kr√	kr√	NOUN
ap-1851	432	15	πr	πr	NOUN
ap-1851	432	16	=	=	SYM
ap-1851	432	17	0	0	NUM
ap-1851	432	18	showing	show	VERB
ap-1851	432	19	again	again	ADV
ap-1851	432	20	that	that	SCONJ
ap-1851	432	21	there	there	PRON
ap-1851	432	22	are	be	VERB
ap-1851	432	23	no	no	DET
ap-1851	432	24	resonances	resonance	NOUN
ap-1851	432	25	for	for	ADP
ap-1851	432	26	α	α	NOUN
ap-1851	432	27	=	=	SYM
ap-1851	432	28	1/2	1/2	NUM
ap-1851	432	29	.	.	PUNCT
ap-1851	433	1	for	for	ADP
ap-1851	433	2	other	other	ADJ
ap-1851	433	3	values	value	NOUN
ap-1851	433	4	of	of	ADP
ap-1851	433	5	α	α	PRON
ap-1851	433	6	the	the	DET
ap-1851	433	7	condition	condition	NOUN
ap-1851	433	8	can	can	AUX
ap-1851	433	9	be	be	AUX
ap-1851	433	10	solved	solve	VERB
ap-1851	433	11	numerically	numerically	ADV
ap-1851	433	12	.	.	PUNCT
ap-1851	434	1	in	in	ADP
ap-1851	434	2	figure	figure	NOUN
ap-1851	434	3	8	8	NUM
ap-1851	434	4	we	we	PRON
ap-1851	434	5	plot	plot	VERB
ap-1851	434	6	the	the	DET
ap-1851	434	7	trajectory	trajectory	NOUN
ap-1851	434	8	of	of	ADP
ap-1851	434	9	one	one	NUM
ap-1851	434	10	of	of	ADP
ap-1851	434	11	the	the	DET
ap-1851	434	12	resonances	resonance	NOUN
ap-1851	434	13	as	as	ADP
ap-1851	434	14	the	the	DET
ap-1851	434	15	value	value	NOUN
ap-1851	434	16	of	of	ADP
ap-1851	434	17	α	α	PROPN
ap-1851	434	18	increases	increase	NOUN
ap-1851	434	19	from	from	ADP
ap-1851	434	20	zero	zero	NUM
ap-1851	434	21	to	to	ADP
ap-1851	434	22	1	1	NUM
ap-1851	434	23	2	2	NUM
ap-1851	434	24	.	.	PUNCT
ap-1851	435	1	the	the	DET
ap-1851	435	2	step	step	NOUN
ap-1851	435	3	is	be	AUX
ap-1851	435	4	taken	take	VERB
ap-1851	435	5	to	to	PART
ap-1851	435	6	be	be	AUX
ap-1851	435	7	0.01	0.01	NUM
ap-1851	435	8	for	for	ADP
ap-1851	435	9	values	value	NOUN
ap-1851	435	10	until	until	ADP
ap-1851	435	11	α	α	NOUN
ap-1851	435	12	=	=	NOUN
ap-1851	435	13	0.49	0.49	NUM
ap-1851	435	14	,	,	PUNCT
ap-1851	435	15	which	which	PRON
ap-1851	435	16	corresponds	correspond	VERB
ap-1851	435	17	to	to	ADP
ap-1851	435	18	the	the	DET
ap-1851	435	19	sharp	sharp	ADJ
ap-1851	435	20	bend	bend	NOUN
ap-1851	435	21	of	of	ADP
ap-1851	435	22	the	the	DET
ap-1851	435	23	curve	curve	NOUN
ap-1851	435	24	,	,	PUNCT
ap-1851	435	25	and	and	CCONJ
ap-1851	435	26	from	from	ADP
ap-1851	435	27	this	this	DET
ap-1851	435	28	point	point	NOUN
ap-1851	435	29	on	on	ADP
ap-1851	435	30	the	the	DET
ap-1851	435	31	linear	linear	ADJ
ap-1851	435	32	step	step	NOUN
ap-1851	435	33	is	be	AUX
ap-1851	435	34	replaced	replace	VERB
ap-1851	435	35	by	by	ADP
ap-1851	435	36	a	a	DET
ap-1851	435	37	sequence	sequence	NOUN
ap-1851	435	38	of	of	ADP
ap-1851	435	39	exponentially	exponentially	ADV
ap-1851	435	40	increasing	increase	VERB
ap-1851	435	41	density	density	NOUN
ap-1851	435	42	accumulating	accumulate	VERB
ap-1851	435	43	at	at	ADP
ap-1851	435	44	α	α	NOUN
ap-1851	435	45	=	=	SYM
ap-1851	435	46	1	1	NUM
ap-1851	435	47	2	2	NUM
ap-1851	435	48	.	.	PUNCT
ap-1851	435	49	425	425	NUM
ap-1851	435	50	p.	p.	PROPN
ap-1851	435	51	exner	exner	NOUN
ap-1851	435	52	,	,	PUNCT
ap-1851	435	53	j.	j.	PROPN
ap-1851	435	54	lipovský	lipovský	PROPN
ap-1851	435	55	acta	acta	PROPN
ap-1851	435	56	polytechnica	polytechnica	PROPN
ap-1851	435	57	acknowledgements	acknowledgement	NOUN
ap-1851	435	58	we	we	PRON
ap-1851	435	59	thank	thank	VERB
ap-1851	435	60	the	the	DET
ap-1851	435	61	referees	referee	NOUN
ap-1851	435	62	for	for	ADP
ap-1851	435	63	useful	useful	ADJ
ap-1851	435	64	remarks	remark	NOUN
ap-1851	435	65	.	.	PUNCT
ap-1851	436	1	this	this	DET
ap-1851	436	2	research	research	NOUN
ap-1851	436	3	was	be	AUX
ap-1851	436	4	supported	support	VERB
ap-1851	436	5	by	by	ADP
ap-1851	436	6	the	the	DET
ap-1851	436	7	czech	czech	PROPN
ap-1851	436	8	science	science	NOUN
ap-1851	436	9	foundation	foundation	PROPN
ap-1851	436	10	within	within	ADP
ap-1851	436	11	project	project	NOUN
ap-1851	436	12	p203/11/0701	p203/11/0701	PROPN
ap-1851	436	13	and	and	CCONJ
ap-1851	436	14	the	the	DET
ap-1851	436	15	development	development	NOUN
ap-1851	436	16	of	of	ADP
ap-1851	436	17	postdoc	postdoc	ADJ
ap-1851	436	18	activities	activity	NOUN
ap-1851	436	19	project	project	NOUN
ap-1851	436	20	at	at	ADP
ap-1851	436	21	the	the	DET
ap-1851	436	22	university	university	NOUN
ap-1851	436	23	of	of	ADP
ap-1851	436	24	the	the	DET
ap-1851	436	25	hradec	hradec	PROPN
ap-1851	436	26	králové	králové	PROPN
ap-1851	436	27	,	,	PUNCT
ap-1851	436	28	cz.1.07/2.3.00/30.0015	cz.1.07/2.3.00/30.0015	PROPN
ap-1851	436	29	.	.	PUNCT
ap-1851	437	1	references	reference	NOUN
ap-1851	437	2	[	[	X
ap-1851	437	3	1	1	NUM
ap-1851	437	4	]	]	X
ap-1851	437	5	r.	r.	PROPN
ap-1851	437	6	adami	adami	PROPN
ap-1851	437	7	,	,	PUNCT
ap-1851	437	8	a.	a.	PROPN
ap-1851	437	9	teta	teta	PROPN
ap-1851	437	10	:	:	PUNCT
ap-1851	437	11	on	on	ADP
ap-1851	437	12	the	the	DET
ap-1851	437	13	aharonov	aharonov	PROPN
ap-1851	437	14	-	-	PUNCT
ap-1851	437	15	bohm	bohm	PROPN
ap-1851	437	16	hamiltonian	hamiltonian	NOUN
ap-1851	437	17	,	,	PUNCT
ap-1851	437	18	lett	lett	PROPN
ap-1851	437	19	.	.	PUNCT
ap-1851	437	20	math	math	NOUN
ap-1851	437	21	.	.	PUNCT
ap-1851	438	1	phys	phy	NOUN
ap-1851	438	2	.	.	PUNCT
ap-1851	439	1	43	43	NUM
ap-1851	439	2	,	,	PUNCT
ap-1851	439	3	43–54	43–54	NUM
ap-1851	439	4	,	,	PUNCT
ap-1851	439	5	1998	1998	NUM
ap-1851	439	6	.	.	PUNCT
ap-1851	440	1	[	[	X
ap-1851	440	2	2	2	X
ap-1851	440	3	]	]	PUNCT
ap-1851	440	4	j.	j.	PROPN
ap-1851	440	5	aguilar	aguilar	PROPN
ap-1851	440	6	,	,	PUNCT
ap-1851	440	7	j.-m	j.-m	PROPN
ap-1851	440	8	.	.	PUNCT
ap-1851	441	1	combes	comb	VERB
ap-1851	441	2	:	:	PUNCT
ap-1851	441	3	a	a	DET
ap-1851	441	4	class	class	NOUN
ap-1851	441	5	of	of	ADP
ap-1851	441	6	analytic	analytic	ADJ
ap-1851	441	7	perturbations	perturbation	NOUN
ap-1851	441	8	for	for	ADP
ap-1851	441	9	one	one	NUM
ap-1851	441	10	-	-	PUNCT
ap-1851	441	11	body	body	NOUN
ap-1851	441	12	schrödinger	schrödinger	ADJ
ap-1851	441	13	operators	operator	NOUN
ap-1851	441	14	,	,	PUNCT
ap-1851	441	15	commun	commun	PROPN
ap-1851	441	16	.	.	PUNCT
ap-1851	441	17	math	math	NOUN
ap-1851	441	18	.	.	PUNCT
ap-1851	442	1	phys	phy	NOUN
ap-1851	442	2	.	.	PUNCT
ap-1851	443	1	22	22	NUM
ap-1851	443	2	,	,	PUNCT
ap-1851	443	3	269–279	269–279	NUM
ap-1851	443	4	,	,	PUNCT
ap-1851	443	5	1971	1971	NUM
ap-1851	443	6	.	.	PUNCT
ap-1851	444	1	[	[	X
ap-1851	444	2	3	3	NUM
ap-1851	444	3	]	]	X
ap-1851	444	4	i.g	i.g	PROPN
ap-1851	444	5	.	.	PROPN
ap-1851	444	6	avramidi	avramidi	PROPN
ap-1851	444	7	:	:	PUNCT
ap-1851	444	8	a	a	DET
ap-1851	444	9	covariant	covariant	ADJ
ap-1851	444	10	technique	technique	NOUN
ap-1851	444	11	for	for	ADP
ap-1851	444	12	the	the	DET
ap-1851	444	13	calculation	calculation	NOUN
ap-1851	444	14	of	of	ADP
ap-1851	444	15	the	the	DET
ap-1851	444	16	one	one	NUM
ap-1851	444	17	-	-	PUNCT
ap-1851	444	18	loop	loop	NOUN
ap-1851	444	19	effective	effective	ADJ
ap-1851	444	20	action	action	NOUN
ap-1851	444	21	.	.	PUNCT
ap-1851	445	1	nuclear	nuclear	ADJ
ap-1851	445	2	physics	physics	PROPN
ap-1851	445	3	b	b	PROPN
ap-1851	445	4	355	355	NUM
ap-1851	445	5	,	,	PUNCT
ap-1851	445	6	712–754	712–754	NUM
ap-1851	445	7	,	,	PUNCT
ap-1851	445	8	1991	1991	NUM
ap-1851	445	9	.	.	PUNCT
ap-1851	446	1	[	[	X
ap-1851	446	2	4	4	NUM
ap-1851	446	3	]	]	X
ap-1851	446	4	i.g	i.g	PROPN
ap-1851	446	5	.	.	PROPN
ap-1851	446	6	avramidi	avramidi	PROPN
ap-1851	446	7	:	:	PUNCT
ap-1851	446	8	green	green	ADJ
ap-1851	446	9	functions	function	NOUN
ap-1851	446	10	of	of	ADP
ap-1851	446	11	higher	high	ADJ
ap-1851	446	12	-	-	PUNCT
ap-1851	446	13	order	order	NOUN
ap-1851	446	14	differential	differential	NOUN
ap-1851	446	15	operators	operator	NOUN
ap-1851	446	16	,	,	PUNCT
ap-1851	446	17	j.	j.	PROPN
ap-1851	446	18	math	math	PROPN
ap-1851	446	19	.	.	PUNCT
ap-1851	447	1	phys	phy	NOUN
ap-1851	447	2	.	.	PUNCT
ap-1851	448	1	39	39	NUM
ap-1851	448	2	,	,	PUNCT
ap-1851	448	3	2889–2909	2889–2909	NUM
ap-1851	448	4	,	,	PUNCT
ap-1851	448	5	1998	1998	NUM
ap-1851	448	6	.	.	PUNCT
ap-1851	449	1	[	[	X
ap-1851	449	2	5	5	X
ap-1851	449	3	]	]	PUNCT
ap-1851	449	4	e.	e.	PROPN
ap-1851	449	5	baslev	baslev	PROPN
ap-1851	449	6	,	,	PUNCT
ap-1851	449	7	j.-m	j.-m	PROPN
ap-1851	449	8	.	.	PUNCT
ap-1851	450	1	combes	combes	PROPN
ap-1851	450	2	:	:	PUNCT
ap-1851	450	3	spectral	spectral	ADJ
ap-1851	450	4	properties	property	NOUN
ap-1851	450	5	of	of	ADP
ap-1851	450	6	many	many	ADJ
ap-1851	450	7	body	body	NOUN
ap-1851	450	8	schrödinger	schrödinger	NOUN
ap-1851	450	9	operators	operator	NOUN
ap-1851	450	10	with	with	ADP
ap-1851	450	11	dilation	dilation	NOUN
ap-1851	450	12	analytic	analytic	ADJ
ap-1851	450	13	interactions	interaction	NOUN
ap-1851	450	14	,	,	PUNCT
ap-1851	450	15	commun	commun	PROPN
ap-1851	450	16	.	.	PUNCT
ap-1851	450	17	math	math	NOUN
ap-1851	450	18	.	.	PUNCT
ap-1851	451	1	phys	phy	NOUN
ap-1851	451	2	.	.	PUNCT
ap-1851	452	1	22	22	NUM
ap-1851	452	2	,	,	PUNCT
ap-1851	452	3	280–294	280–294	NUM
ap-1851	452	4	,	,	PUNCT
ap-1851	452	5	1971	1971	NUM
ap-1851	452	6	.	.	PUNCT
ap-1851	453	1	[	[	X
ap-1851	453	2	6	6	NUM
ap-1851	453	3	]	]	PUNCT
ap-1851	453	4	g.	g.	NOUN
ap-1851	453	5	berkolaiko	berkolaiko	NOUN
ap-1851	453	6	,	,	PUNCT
ap-1851	453	7	p.	p.	PROPN
ap-1851	453	8	kuchment	kuchment	NOUN
ap-1851	453	9	:	:	PUNCT
ap-1851	453	10	introduction	introduction	NOUN
ap-1851	453	11	to	to	ADP
ap-1851	453	12	quantum	quantum	NOUN
ap-1851	453	13	graphs	graph	NOUN
ap-1851	453	14	,	,	PUNCT
ap-1851	453	15	ams	am	NOUN
ap-1851	453	16	“	"	PUNCT
ap-1851	453	17	mathematical	mathematical	ADJ
ap-1851	453	18	surveys	survey	NOUN
ap-1851	453	19	and	and	CCONJ
ap-1851	453	20	monographs	monograph	NOUN
ap-1851	453	21	”	"	PUNCT
ap-1851	453	22	series	series	NOUN
ap-1851	453	23	,	,	PUNCT
ap-1851	453	24	vol	vol	NOUN
ap-1851	453	25	.	.	PROPN
ap-1851	453	26	186	186	NUM
ap-1851	453	27	,	,	PUNCT
ap-1851	453	28	providence	providence	NOUN
ap-1851	453	29	,	,	PUNCT
ap-1851	453	30	r.i	r.i	PROPN
ap-1851	453	31	.	.	PROPN
ap-1851	453	32	,	,	PUNCT
ap-1851	453	33	2013	2013	NUM
ap-1851	454	1	[	[	X
ap-1851	454	2	7	7	X
ap-1851	454	3	]	]	X
ap-1851	454	4	j.	j.	PROPN
ap-1851	454	5	brüning	brüning	PROPN
ap-1851	454	6	,	,	PUNCT
ap-1851	454	7	p.	p.	PROPN
ap-1851	454	8	exner	exner	PROPN
ap-1851	454	9	,	,	PUNCT
ap-1851	454	10	v.a	v.a	PROPN
ap-1851	454	11	.	.	PROPN
ap-1851	454	12	geyler	geyler	NOUN
ap-1851	454	13	:	:	PUNCT
ap-1851	454	14	large	large	ADJ
ap-1851	454	15	gaps	gap	NOUN
ap-1851	454	16	in	in	ADP
ap-1851	454	17	point	point	NOUN
ap-1851	454	18	-	-	PUNCT
ap-1851	454	19	coupled	couple	VERB
ap-1851	454	20	periodic	periodic	ADJ
ap-1851	454	21	systems	system	NOUN
ap-1851	454	22	of	of	ADP
ap-1851	454	23	manifolds	manifold	NOUN
ap-1851	454	24	,	,	PUNCT
ap-1851	454	25	j.	j.	PROPN
ap-1851	454	26	phys	phys	PROPN
ap-1851	454	27	.	.	PUNCT
ap-1851	455	1	a	a	DET
ap-1851	455	2	:	:	PUNCT
ap-1851	455	3	math	math	NOUN
ap-1851	455	4	.	.	PUNCT
ap-1851	456	1	gen	gen	PROPN
ap-1851	456	2	36	36	NUM
ap-1851	456	3	,	,	PUNCT
ap-1851	456	4	4890	4890	NUM
ap-1851	456	5	,	,	PUNCT
ap-1851	456	6	2003	2003	NUM
ap-1851	456	7	.	.	PUNCT
ap-1851	457	1	[	[	X
ap-1851	457	2	8	8	X
ap-1851	457	3	]	]	X
ap-1851	457	4	j.	j.	PROPN
ap-1851	457	5	brüning	brüning	PROPN
ap-1851	457	6	,	,	PUNCT
ap-1851	457	7	v.	v.	ADP
ap-1851	457	8	geyler	geyler	NOUN
ap-1851	457	9	:	:	PUNCT
ap-1851	457	10	scattering	scatter	VERB
ap-1851	457	11	on	on	ADP
ap-1851	457	12	compact	compact	ADJ
ap-1851	457	13	manifolds	manifold	NOUN
ap-1851	457	14	with	with	ADP
ap-1851	457	15	infinitely	infinitely	ADV
ap-1851	457	16	thin	thin	ADJ
ap-1851	457	17	horns	horn	NOUN
ap-1851	457	18	,	,	PUNCT
ap-1851	457	19	j.	j.	PROPN
ap-1851	457	20	math	math	PROPN
ap-1851	457	21	.	.	PUNCT
ap-1851	458	1	phys	phy	NOUN
ap-1851	458	2	.	.	PUNCT
ap-1851	459	1	44	44	NUM
ap-1851	459	2	,	,	PUNCT
ap-1851	459	3	371–405	371–405	NUM
ap-1851	459	4	,	,	PUNCT
ap-1851	459	5	2003	2003	NUM
ap-1851	459	6	.	.	PUNCT
ap-1851	460	1	[	[	X
ap-1851	460	2	9	9	NUM
ap-1851	460	3	]	]	X
ap-1851	460	4	l.	l.	PROPN
ap-1851	460	5	dabrowski	dabrowski	PROPN
ap-1851	460	6	,	,	PUNCT
ap-1851	460	7	p.	p.	PROPN
ap-1851	460	8	šťovíček	šťovíček	PROPN
ap-1851	460	9	:	:	PUNCT
ap-1851	460	10	aharonov	aharonov	NOUN
ap-1851	460	11	-	-	PUNCT
ap-1851	460	12	bohm	bohm	PROPN
ap-1851	460	13	effect	effect	NOUN
ap-1851	460	14	with	with	ADP
ap-1851	460	15	δ	δ	NOUN
ap-1851	460	16	-	-	PUNCT
ap-1851	460	17	type	type	NOUN
ap-1851	460	18	interaction	interaction	NOUN
ap-1851	460	19	,	,	PUNCT
ap-1851	460	20	j.	j.	PROPN
ap-1851	460	21	math	math	PROPN
ap-1851	460	22	.	.	PUNCT
ap-1851	461	1	phys	phy	NOUN
ap-1851	461	2	.	.	PUNCT
ap-1851	462	1	36	36	NUM
ap-1851	462	2	,	,	PUNCT
ap-1851	462	3	47–62	47–62	NUM
ap-1851	462	4	,	,	PUNCT
ap-1851	462	5	1998	1998	NUM
ap-1851	462	6	.	.	PUNCT
ap-1851	463	1	[	[	X
ap-1851	463	2	10	10	NUM
ap-1851	463	3	]	]	X
ap-1851	463	4	e.b	e.b	PROPN
ap-1851	463	5	.	.	PUNCT
ap-1851	463	6	davies	davy	NOUN
ap-1851	463	7	,	,	PUNCT
ap-1851	463	8	p.	p.	PROPN
ap-1851	463	9	exner	exner	NOUN
ap-1851	463	10	,	,	PUNCT
ap-1851	463	11	j.	j.	PROPN
ap-1851	463	12	lipovský	lipovský	PROPN
ap-1851	463	13	:	:	PUNCT
ap-1851	463	14	non	non	ADJ
ap-1851	463	15	-	-	ADJ
ap-1851	463	16	weyl	weyl	ADJ
ap-1851	463	17	asymptotics	asymptotic	NOUN
ap-1851	463	18	for	for	ADP
ap-1851	463	19	quantum	quantum	NOUN
ap-1851	463	20	graphs	graph	NOUN
ap-1851	463	21	with	with	ADP
ap-1851	463	22	general	general	ADJ
ap-1851	463	23	coupling	coupling	NOUN
ap-1851	463	24	conditions	condition	NOUN
ap-1851	463	25	,	,	PUNCT
ap-1851	463	26	j.	j.	PROPN
ap-1851	463	27	phys	phys	PROPN
ap-1851	463	28	.	.	PUNCT
ap-1851	464	1	a	a	DET
ap-1851	464	2	:	:	PUNCT
ap-1851	464	3	math	math	NOUN
ap-1851	464	4	.	.	PUNCT
ap-1851	465	1	theor	theor	PROPN
ap-1851	465	2	.	.	PROPN
ap-1851	466	1	43	43	NUM
ap-1851	466	2	,	,	PUNCT
ap-1851	466	3	474013	474013	NUM
ap-1851	466	4	,	,	PUNCT
ap-1851	466	5	2010	2010	NUM
ap-1851	466	6	.	.	PUNCT
ap-1851	467	1	[	[	X
ap-1851	467	2	11	11	NUM
ap-1851	467	3	]	]	X
ap-1851	467	4	e.b	e.b	PROPN
ap-1851	467	5	.	.	PUNCT
ap-1851	467	6	davies	davy	NOUN
ap-1851	467	7	,	,	PUNCT
ap-1851	467	8	a.	a.	NOUN
ap-1851	467	9	pushnitski	pushnitski	NOUN
ap-1851	467	10	:	:	PUNCT
ap-1851	467	11	non	non	ADJ
ap-1851	467	12	-	-	ADJ
ap-1851	467	13	weyl	weyl	ADJ
ap-1851	467	14	resonance	resonance	NOUN
ap-1851	467	15	asymptotics	asymptotic	NOUN
ap-1851	467	16	for	for	ADP
ap-1851	467	17	quantum	quantum	NOUN
ap-1851	467	18	graphs	graph	NOUN
ap-1851	467	19	.	.	PUNCT
ap-1851	468	1	analysis	analysis	NOUN
ap-1851	468	2	and	and	CCONJ
ap-1851	468	3	pde	pde	NOUN
ap-1851	468	4	4	4	NUM
ap-1851	468	5	,	,	PUNCT
ap-1851	468	6	no	no	INTJ
ap-1851	468	7	.	.	NOUN
ap-1851	468	8	5	5	NUM
ap-1851	468	9	,	,	PUNCT
ap-1851	468	10	729–756	729–756	NUM
ap-1851	468	11	,	,	PUNCT
ap-1851	468	12	2011	2011	NUM
ap-1851	468	13	.	.	PUNCT
ap-1851	469	1	[	[	X
ap-1851	469	2	12	12	NUM
ap-1851	469	3	]	]	X
ap-1851	469	4	v.	v.	ADP
ap-1851	469	5	dinu	dinu	PROPN
ap-1851	469	6	,	,	PUNCT
ap-1851	469	7	a.	a.	PROPN
ap-1851	469	8	jensen	jensen	PROPN
ap-1851	469	9	,	,	PUNCT
ap-1851	469	10	g.	g.	PROPN
ap-1851	469	11	nenciu	nenciu	PROPN
ap-1851	469	12	:	:	PUNCT
ap-1851	469	13	non	non	ADJ
ap-1851	469	14	-	-	ADJ
ap-1851	469	15	exponential	exponential	ADJ
ap-1851	469	16	decay	decay	NOUN
ap-1851	469	17	laws	law	NOUN
ap-1851	469	18	in	in	ADP
ap-1851	469	19	perturbation	perturbation	NOUN
ap-1851	469	20	theory	theory	NOUN
ap-1851	469	21	of	of	ADP
ap-1851	469	22	near	near	ADJ
ap-1851	469	23	threshold	threshold	NOUN
ap-1851	469	24	eigenvalues	eigenvalue	VERB
ap-1851	469	25	j.	j.	PROPN
ap-1851	469	26	math	math	PROPN
ap-1851	469	27	.	.	PUNCT
ap-1851	470	1	phys	phy	NOUN
ap-1851	470	2	.	.	PUNCT
ap-1851	471	1	50	50	NUM
ap-1851	471	2	,	,	PUNCT
ap-1851	471	3	013516	013516	NUM
ap-1851	471	4	,	,	PUNCT
ap-1851	471	5	2009	2009	NUM
ap-1851	471	6	.	.	PUNCT
ap-1851	472	1	[	[	X
ap-1851	472	2	13	13	NUM
ap-1851	472	3	]	]	PUNCT
ap-1851	472	4	p.	p.	NOUN
ap-1851	472	5	exner	exner	NOUN
ap-1851	472	6	:	:	PUNCT
ap-1851	472	7	open	open	ADJ
ap-1851	472	8	quantum	quantum	NOUN
ap-1851	472	9	system	system	NOUN
ap-1851	472	10	and	and	CCONJ
ap-1851	472	11	feynman	feynman	PROPN
ap-1851	472	12	integrals	integral	NOUN
ap-1851	472	13	,	,	PUNCT
ap-1851	472	14	reidel	reidel	PROPN
ap-1851	472	15	,	,	PUNCT
ap-1851	472	16	dordrecht	dordrecht	NOUN
ap-1851	472	17	1985	1985	NUM
ap-1851	472	18	.	.	PUNCT
ap-1851	473	1	[	[	X
ap-1851	473	2	14	14	NUM
ap-1851	473	3	]	]	X
ap-1851	473	4	p.	p.	NOUN
ap-1851	473	5	exner	exner	PROPN
ap-1851	473	6	,	,	PUNCT
ap-1851	473	7	j.p	j.p	PROPN
ap-1851	473	8	.	.	PROPN
ap-1851	473	9	keating	keating	PROPN
ap-1851	473	10	,	,	PUNCT
ap-1851	473	11	p.	p.	PROPN
ap-1851	473	12	kuchment	kuchment	NOUN
ap-1851	473	13	,	,	PUNCT
ap-1851	473	14	t.	t.	PROPN
ap-1851	473	15	sunada	sunada	PROPN
ap-1851	473	16	,	,	PUNCT
ap-1851	473	17	a.	a.	PROPN
ap-1851	473	18	teplyaev	teplyaev	PROPN
ap-1851	473	19	,	,	PUNCT
ap-1851	473	20	eds	eds	PROPN
ap-1851	473	21	.	.	PUNCT
ap-1851	473	22	:	:	PUNCT
ap-1851	473	23	analysis	analysis	NOUN
ap-1851	473	24	on	on	ADP
ap-1851	473	25	graphs	graph	NOUN
ap-1851	473	26	and	and	CCONJ
ap-1851	473	27	applications	application	NOUN
ap-1851	473	28	,	,	PUNCT
ap-1851	473	29	proceedings	proceeding	NOUN
ap-1851	473	30	of	of	ADP
ap-1851	473	31	the	the	DET
ap-1851	473	32	isaac	isaac	PROPN
ap-1851	473	33	newton	newton	PROPN
ap-1851	473	34	institute	institute	PROPN
ap-1851	473	35	programme	programme	PROPN
ap-1851	473	36	,	,	PUNCT
ap-1851	473	37	january	january	PROPN
ap-1851	473	38	8	8	NUM
ap-1851	473	39	–	–	PUNCT
ap-1851	473	40	june	june	PROPN
ap-1851	473	41	29	29	NUM
ap-1851	473	42	,	,	PUNCT
ap-1851	473	43	2007	2007	NUM
ap-1851	473	44	;	;	PUNCT
ap-1851	473	45	670	670	NUM
ap-1851	473	46	p.	p.	NOUN
ap-1851	473	47	;	;	PUNCT
ap-1851	473	48	ams	am	NOUN
ap-1851	473	49	“	"	PUNCT
ap-1851	473	50	proceedings	proceeding	NOUN
ap-1851	473	51	of	of	ADP
ap-1851	473	52	symposia	symposia	NOUN
ap-1851	473	53	in	in	ADP
ap-1851	473	54	pure	pure	ADJ
ap-1851	473	55	mathematics	mathematic	NOUN
ap-1851	473	56	”	"	PUNCT
ap-1851	473	57	series	series	NOUN
ap-1851	473	58	,	,	PUNCT
ap-1851	473	59	vol	vol	NOUN
ap-1851	473	60	.	.	PROPN
ap-1851	473	61	77	77	NUM
ap-1851	473	62	,	,	PUNCT
ap-1851	473	63	providence	providence	NOUN
ap-1851	473	64	,	,	PUNCT
ap-1851	473	65	r.i	r.i	PROPN
ap-1851	473	66	.	.	PROPN
ap-1851	473	67	,	,	PUNCT
ap-1851	473	68	2008	2008	NUM
ap-1851	474	1	[	[	X
ap-1851	474	2	15	15	NUM
ap-1851	474	3	]	]	X
ap-1851	474	4	p.	p.	NOUN
ap-1851	474	5	exner	exner	PROPN
ap-1851	474	6	,	,	PUNCT
ap-1851	474	7	j.	j.	PROPN
ap-1851	474	8	lipovský	lipovský	PROPN
ap-1851	474	9	:	:	PUNCT
ap-1851	474	10	equivalence	equivalence	NOUN
ap-1851	474	11	of	of	ADP
ap-1851	474	12	resolvent	resolvent	ADJ
ap-1851	474	13	and	and	CCONJ
ap-1851	474	14	scattering	scatter	VERB
ap-1851	474	15	resonances	resonance	NOUN
ap-1851	474	16	on	on	ADP
ap-1851	474	17	quantum	quantum	NOUN
ap-1851	474	18	graphs	graph	NOUN
ap-1851	474	19	,	,	PUNCT
ap-1851	474	20	in	in	ADP
ap-1851	474	21	adventures	adventure	NOUN
ap-1851	474	22	in	in	ADP
ap-1851	474	23	mathematical	mathematical	ADJ
ap-1851	474	24	physics	physics	NOUN
ap-1851	474	25	(	(	PUNCT
ap-1851	474	26	proceedings	proceeding	NOUN
ap-1851	474	27	,	,	PUNCT
ap-1851	474	28	cergy	cergy	NOUN
ap-1851	474	29	-	-	PUNCT
ap-1851	474	30	pontoise	pontoise	NOUN
ap-1851	474	31	2006	2006	NUM
ap-1851	474	32	)	)	PUNCT
ap-1851	474	33	,	,	PUNCT
ap-1851	474	34	vol	vol	NOUN
ap-1851	474	35	.	.	PROPN
ap-1851	475	1	447	447	NUM
ap-1851	475	2	,	,	PUNCT
ap-1851	475	3	pp	pp	ADJ
ap-1851	475	4	.	.	PUNCT
ap-1851	476	1	73–81	73–81	NUM
ap-1851	476	2	;	;	PUNCT
ap-1851	476	3	ams	am	NOUN
ap-1851	476	4	,	,	PUNCT
ap-1851	476	5	providence	providence	NOUN
ap-1851	476	6	,	,	PUNCT
ap-1851	476	7	r.i	r.i	PROPN
ap-1851	476	8	.	.	PROPN
ap-1851	476	9	,	,	PUNCT
ap-1851	476	10	2007	2007	NUM
ap-1851	476	11	.	.	PUNCT
ap-1851	477	1	[	[	X
ap-1851	477	2	16	16	NUM
ap-1851	477	3	]	]	PUNCT
ap-1851	477	4	p.	p.	NOUN
ap-1851	477	5	exner	exner	PROPN
ap-1851	477	6	,	,	PUNCT
ap-1851	477	7	j.	j.	PROPN
ap-1851	477	8	lipovský	lipovský	PROPN
ap-1851	477	9	:	:	PUNCT
ap-1851	477	10	resonances	resonance	NOUN
ap-1851	477	11	from	from	ADP
ap-1851	477	12	perturbations	perturbation	NOUN
ap-1851	477	13	of	of	ADP
ap-1851	477	14	quantum	quantum	NOUN
ap-1851	477	15	graphs	graph	NOUN
ap-1851	477	16	with	with	ADP
ap-1851	477	17	rationally	rationally	ADV
ap-1851	477	18	related	relate	VERB
ap-1851	477	19	edges	edge	NOUN
ap-1851	477	20	,	,	PUNCT
ap-1851	477	21	j.	j.	PROPN
ap-1851	477	22	phys	phys	PROPN
ap-1851	477	23	.	.	PUNCT
ap-1851	478	1	a	a	DET
ap-1851	478	2	:	:	PUNCT
ap-1851	478	3	math	math	NOUN
ap-1851	478	4	.	.	PUNCT
ap-1851	479	1	theor	theor	PROPN
ap-1851	479	2	.	.	PROPN
ap-1851	480	1	43	43	NUM
ap-1851	480	2	,	,	PUNCT
ap-1851	480	3	105301	105301	NUM
ap-1851	480	4	,	,	PUNCT
ap-1851	480	5	2010	2010	NUM
ap-1851	480	6	.	.	PUNCT
ap-1851	481	1	[	[	X
ap-1851	481	2	17	17	NUM
ap-1851	481	3	]	]	X
ap-1851	481	4	p.	p.	NOUN
ap-1851	481	5	exner	exner	PROPN
ap-1851	481	6	,	,	PUNCT
ap-1851	481	7	j.	j.	PROPN
ap-1851	481	8	lipovský	lipovský	PROPN
ap-1851	481	9	:	:	PUNCT
ap-1851	481	10	non	non	ADJ
ap-1851	481	11	-	-	ADJ
ap-1851	481	12	weyl	weyl	ADJ
ap-1851	481	13	resonance	resonance	NOUN
ap-1851	481	14	asymptotics	asymptotic	NOUN
ap-1851	481	15	for	for	ADP
ap-1851	481	16	quantum	quantum	NOUN
ap-1851	481	17	graphs	graph	NOUN
ap-1851	481	18	in	in	ADP
ap-1851	481	19	a	a	DET
ap-1851	481	20	magnetic	magnetic	ADJ
ap-1851	481	21	field	field	NOUN
ap-1851	481	22	,	,	PUNCT
ap-1851	481	23	phys	phy	NOUN
ap-1851	481	24	.	.	PUNCT
ap-1851	482	1	lett	lett	PROPN
ap-1851	482	2	.	.	PUNCT
ap-1851	483	1	a	a	DET
ap-1851	483	2	375	375	NUM
ap-1851	483	3	,	,	PUNCT
ap-1851	483	4	805–807	805–807	NUM
ap-1851	483	5	,	,	PUNCT
ap-1851	483	6	2011	2011	NUM
ap-1851	483	7	.	.	PUNCT
ap-1851	484	1	[	[	X
ap-1851	484	2	18	18	NUM
ap-1851	484	3	]	]	PUNCT
ap-1851	484	4	p.	p.	NOUN
ap-1851	484	5	exner	exner	PROPN
ap-1851	484	6	,	,	PUNCT
ap-1851	484	7	m.	m.	NOUN
ap-1851	484	8	tater	tater	NOUN
ap-1851	484	9	,	,	PUNCT
ap-1851	484	10	d.	d.	PROPN
ap-1851	484	11	vaněk	vaněk	PROPN
ap-1851	484	12	:	:	PUNCT
ap-1851	484	13	a	a	DET
ap-1851	484	14	single	single	ADJ
ap-1851	484	15	-	-	PUNCT
ap-1851	484	16	mode	mode	NOUN
ap-1851	484	17	quantum	quantum	NOUN
ap-1851	484	18	transport	transport	NOUN
ap-1851	484	19	in	in	ADP
ap-1851	484	20	serial	serial	ADJ
ap-1851	484	21	-	-	PUNCT
ap-1851	484	22	structure	structure	NOUN
ap-1851	484	23	geometric	geometric	ADJ
ap-1851	484	24	scatterers	scatterer	NOUN
ap-1851	484	25	,	,	PUNCT
ap-1851	484	26	j.	j.	PROPN
ap-1851	484	27	math	math	PROPN
ap-1851	484	28	.	.	PUNCT
ap-1851	485	1	phys	phy	NOUN
ap-1851	485	2	.	.	PUNCT
ap-1851	486	1	42	42	NUM
ap-1851	486	2	,	,	PUNCT
ap-1851	486	3	4050–4078	4050–4078	NUM
ap-1851	486	4	,	,	PUNCT
ap-1851	486	5	2001	2001	NUM
ap-1851	486	6	.	.	PUNCT
ap-1851	487	1	[	[	X
ap-1851	487	2	19	19	NUM
ap-1851	487	3	]	]	PUNCT
ap-1851	487	4	p.	p.	NOUN
ap-1851	487	5	exner	exner	NOUN
ap-1851	487	6	,	,	PUNCT
ap-1851	487	7	p.	p.	PROPN
ap-1851	487	8	šeba	šeba	PROPN
ap-1851	487	9	:	:	PUNCT
ap-1851	487	10	quantum	quantum	NOUN
ap-1851	487	11	motion	motion	NOUN
ap-1851	487	12	on	on	ADP
ap-1851	487	13	a	a	DET
ap-1851	487	14	halfline	halfline	NOUN
ap-1851	487	15	connected	connect	VERB
ap-1851	487	16	to	to	ADP
ap-1851	487	17	a	a	DET
ap-1851	487	18	plane	plane	NOUN
ap-1851	487	19	,	,	PUNCT
ap-1851	487	20	j.	j.	PROPN
ap-1851	487	21	math	math	PROPN
ap-1851	487	22	.	.	PUNCT
ap-1851	488	1	phys	phy	NOUN
ap-1851	488	2	.	.	PUNCT
ap-1851	489	1	28	28	NUM
ap-1851	489	2	,	,	PUNCT
ap-1851	489	3	386–391	386–391	NUM
ap-1851	489	4	;	;	PUNCT
ap-1851	489	5	erratum	erratum	PROPN
ap-1851	489	6	p.	p.	PROPN
ap-1851	489	7	2254	2254	NUM
ap-1851	489	8	,	,	PUNCT
ap-1851	489	9	1987	1987	NUM
ap-1851	489	10	.	.	PUNCT
ap-1851	490	1	[	[	X
ap-1851	490	2	20	20	NUM
ap-1851	490	3	]	]	PUNCT
ap-1851	490	4	p.	p.	NOUN
ap-1851	490	5	exner	exner	NOUN
ap-1851	490	6	,	,	PUNCT
ap-1851	490	7	p.	p.	PROPN
ap-1851	490	8	šeba	šeba	PROPN
ap-1851	490	9	:	:	PUNCT
ap-1851	490	10	resonance	resonance	NOUN
ap-1851	490	11	statistics	statistic	NOUN
ap-1851	490	12	in	in	ADP
ap-1851	490	13	a	a	DET
ap-1851	490	14	microwave	microwave	NOUN
ap-1851	490	15	cavity	cavity	NOUN
ap-1851	490	16	with	with	ADP
ap-1851	490	17	a	a	DET
ap-1851	490	18	thin	thin	ADJ
ap-1851	490	19	antenna	antenna	NOUN
ap-1851	490	20	,	,	PUNCT
ap-1851	490	21	phys	phy	NOUN
ap-1851	490	22	.	.	PUNCT
ap-1851	491	1	lett	lett	PROPN
ap-1851	491	2	.	.	PUNCT
ap-1851	492	1	a228	a228	PROPN
ap-1851	492	2	,	,	PUNCT
ap-1851	492	3	146–150	146–150	NUM
ap-1851	492	4	,	,	PUNCT
ap-1851	492	5	1997	1997	NUM
ap-1851	492	6	.	.	PUNCT
ap-1851	493	1	[	[	X
ap-1851	493	2	21	21	NUM
ap-1851	493	3	]	]	X
ap-1851	493	4	p.	p.	NOUN
ap-1851	493	5	exner	exner	NOUN
ap-1851	493	6	,	,	PUNCT
ap-1851	493	7	p.	p.	PROPN
ap-1851	493	8	šťovíček	šťovíček	PROPN
ap-1851	493	9	,	,	PUNCT
ap-1851	493	10	p.	p.	PROPN
ap-1851	493	11	vytřas	vytřas	NOUN
ap-1851	493	12	:	:	PUNCT
ap-1851	493	13	generalized	generalize	VERB
ap-1851	493	14	boundary	boundary	ADJ
ap-1851	493	15	conditions	condition	NOUN
ap-1851	493	16	for	for	ADP
ap-1851	493	17	the	the	DET
ap-1851	493	18	aharonov	aharonov	PROPN
ap-1851	493	19	-	-	PUNCT
ap-1851	493	20	bohm	bohm	PROPN
ap-1851	493	21	effect	effect	NOUN
ap-1851	493	22	combined	combine	VERB
ap-1851	493	23	with	with	ADP
ap-1851	493	24	a	a	DET
ap-1851	493	25	homogeneous	homogeneous	ADJ
ap-1851	493	26	magnetic	magnetic	ADJ
ap-1851	493	27	field	field	NOUN
ap-1851	493	28	,	,	PUNCT
ap-1851	493	29	j.	j.	PROPN
ap-1851	493	30	math	math	PROPN
ap-1851	493	31	.	.	PUNCT
ap-1851	494	1	phys	phy	NOUN
ap-1851	494	2	.	.	PUNCT
ap-1851	495	1	43	43	NUM
ap-1851	495	2	,	,	PUNCT
ap-1851	495	3	2151–2168	2151–2168	NOUN
ap-1851	495	4	,	,	PUNCT
ap-1851	495	5	2002	2002	NUM
ap-1851	495	6	.	.	PUNCT
ap-1851	496	1	[	[	X
ap-1851	496	2	22	22	NUM
ap-1851	496	3	]	]	X
ap-1851	496	4	v.i	v.i	PROPN
ap-1851	496	5	.	.	PROPN
ap-1851	496	6	gorbachuk	gorbachuk	PROPN
ap-1851	496	7	,	,	PUNCT
ap-1851	496	8	m.l	m.l	PROPN
ap-1851	496	9	.	.	PROPN
ap-1851	496	10	gorbachuk	gorbachuk	PROPN
ap-1851	496	11	:	:	PUNCT
ap-1851	496	12	boundary	boundary	ADJ
ap-1851	496	13	value	value	NOUN
ap-1851	496	14	problems	problem	NOUN
ap-1851	496	15	for	for	ADP
ap-1851	496	16	operator	operator	NOUN
ap-1851	496	17	differential	differential	NOUN
ap-1851	496	18	equations	equation	NOUN
ap-1851	496	19	,	,	PUNCT
ap-1851	496	20	kluwer	kluwer	NOUN
ap-1851	496	21	,	,	PUNCT
ap-1851	496	22	dordrecht	dordrecht	PROPN
ap-1851	496	23	1991	1991	NUM
ap-1851	496	24	.	.	PUNCT
ap-1851	497	1	[	[	X
ap-1851	497	2	23	23	NUM
ap-1851	497	3	]	]	X
ap-1851	497	4	m.	m.	NOUN
ap-1851	497	5	harmer	harmer	PROPN
ap-1851	497	6	:	:	PUNCT
ap-1851	497	7	hermitian	hermitian	PROPN
ap-1851	497	8	symplectic	symplectic	ADJ
ap-1851	497	9	geometry	geometry	NOUN
ap-1851	497	10	and	and	CCONJ
ap-1851	497	11	extension	extension	NOUN
ap-1851	497	12	theory	theory	NOUN
ap-1851	497	13	,	,	PUNCT
ap-1851	497	14	j.	j.	PROPN
ap-1851	497	15	phys	phys	PROPN
ap-1851	497	16	.	.	PUNCT
ap-1851	498	1	a	a	DET
ap-1851	498	2	:	:	PUNCT
ap-1851	498	3	math	math	NOUN
ap-1851	498	4	.	.	PUNCT
ap-1851	499	1	gen	gen	PROPN
ap-1851	499	2	.	.	PROPN
ap-1851	499	3	33	33	NUM
ap-1851	499	4	,	,	PUNCT
ap-1851	499	5	9193–9203	9193–9203	NUM
ap-1851	499	6	,	,	PUNCT
ap-1851	499	7	2000	2000	NUM
ap-1851	499	8	.	.	PUNCT
ap-1851	500	1	[	[	X
ap-1851	500	2	24	24	NUM
ap-1851	500	3	]	]	X
ap-1851	500	4	v.ya	v.ya	PROPN
ap-1851	500	5	.	.	PUNCT
ap-1851	500	6	ivrii	ivrii	PROPN
ap-1851	500	7	:	:	PUNCT
ap-1851	501	1	the	the	DET
ap-1851	501	2	second	second	ADJ
ap-1851	501	3	term	term	NOUN
ap-1851	501	4	of	of	ADP
ap-1851	501	5	the	the	DET
ap-1851	501	6	spectral	spectral	ADJ
ap-1851	501	7	asymptotics	asymptotic	NOUN
ap-1851	501	8	for	for	ADP
ap-1851	501	9	a	a	DET
ap-1851	501	10	laplace	laplace	NOUN
ap-1851	501	11	-	-	PUNCT
ap-1851	501	12	beltrami	beltrami	ADJ
ap-1851	501	13	operator	operator	NOUN
ap-1851	501	14	on	on	ADP
ap-1851	501	15	manifolds	manifold	NOUN
ap-1851	501	16	with	with	ADP
ap-1851	501	17	boundary	boundary	ADJ
ap-1851	501	18	,	,	PUNCT
ap-1851	501	19	funktsional	funktsional	ADJ
ap-1851	501	20	.	.	PUNCT
ap-1851	502	1	anal	anal	NOUN
ap-1851	502	2	.	.	PUNCT
ap-1851	503	1	i	i	PRON
ap-1851	503	2	prilozhen	prilozhen	VERB
ap-1851	503	3	14	14	NUM
ap-1851	503	4	(	(	PUNCT
ap-1851	503	5	3	3	NUM
ap-1851	503	6	)	)	PUNCT
ap-1851	503	7	,	,	PUNCT
ap-1851	503	8	25–34	25–34	NUM
ap-1851	503	9	,	,	PUNCT
ap-1851	503	10	1980	1980	NUM
ap-1851	503	11	.	.	PUNCT
ap-1851	504	1	[	[	X
ap-1851	504	2	25	25	NUM
ap-1851	504	3	]	]	PUNCT
ap-1851	504	4	a.	a.	NOUN
ap-1851	504	5	kiselev	kiselev	PROPN
ap-1851	504	6	:	:	PUNCT
ap-1851	504	7	some	some	DET
ap-1851	504	8	examples	example	NOUN
ap-1851	504	9	in	in	ADP
ap-1851	504	10	one	one	NUM
ap-1851	504	11	-	-	PUNCT
ap-1851	504	12	dimensional	dimensional	ADJ
ap-1851	504	13	‘	'	PUNCT
ap-1851	504	14	geometric	geometric	ADJ
ap-1851	504	15	’	'	PUNCT
ap-1851	504	16	scattering	scatter	VERB
ap-1851	504	17	on	on	ADP
ap-1851	504	18	manifolds	manifold	NOUN
ap-1851	504	19	,	,	PUNCT
ap-1851	504	20	j.	j.	PROPN
ap-1851	504	21	math	math	PROPN
ap-1851	504	22	.	.	PUNCT
ap-1851	505	1	anal	anal	PROPN
ap-1851	505	2	.	.	PUNCT
ap-1851	506	1	appl	appl	PROPN
ap-1851	506	2	.	.	PROPN
ap-1851	506	3	212	212	NUM
ap-1851	506	4	,	,	PUNCT
ap-1851	506	5	263–280	263–280	NUM
ap-1851	506	6	,	,	PUNCT
ap-1851	506	7	1997	1997	NUM
ap-1851	506	8	.	.	PUNCT
ap-1851	507	1	[	[	X
ap-1851	507	2	26	26	NUM
ap-1851	507	3	]	]	PUNCT
ap-1851	507	4	v.	v.	PROPN
ap-1851	507	5	kostrykin	kostrykin	PROPN
ap-1851	507	6	,	,	PUNCT
ap-1851	507	7	r.	r.	PROPN
ap-1851	507	8	schrader	schrader	PROPN
ap-1851	507	9	:	:	PUNCT
ap-1851	507	10	kirchhoff	kirchhoff	PROPN
ap-1851	507	11	’s	’s	PART
ap-1851	507	12	rule	rule	NOUN
ap-1851	507	13	for	for	ADP
ap-1851	507	14	quantum	quantum	ADJ
ap-1851	507	15	wires	wire	NOUN
ap-1851	507	16	,	,	PUNCT
ap-1851	507	17	j.	j.	PROPN
ap-1851	507	18	phys	phys	PROPN
ap-1851	507	19	.	.	PUNCT
ap-1851	508	1	a	a	DET
ap-1851	508	2	:	:	PUNCT
ap-1851	508	3	math	math	NOUN
ap-1851	508	4	.	.	PUNCT
ap-1851	509	1	gen	gen	PROPN
ap-1851	509	2	.	.	PROPN
ap-1851	509	3	32	32	NUM
ap-1851	509	4	,	,	PUNCT
ap-1851	509	5	595–630	595–630	NUM
ap-1851	509	6	,	,	PUNCT
ap-1851	509	7	1999	1999	NUM
ap-1851	509	8	.	.	PUNCT
ap-1851	510	1	[	[	X
ap-1851	510	2	27	27	NUM
ap-1851	510	3	]	]	PUNCT
ap-1851	510	4	m.	m.	NOUN
ap-1851	510	5	reed	reed	PROPN
ap-1851	510	6	,	,	PUNCT
ap-1851	510	7	b.	b.	PROPN
ap-1851	510	8	simon	simon	PROPN
ap-1851	510	9	:	:	PUNCT
ap-1851	510	10	methods	method	NOUN
ap-1851	510	11	of	of	ADP
ap-1851	510	12	modern	modern	ADJ
ap-1851	510	13	mathematical	mathematical	ADJ
ap-1851	510	14	physics	physics	PROPN
ap-1851	510	15	,	,	PUNCT
ap-1851	510	16	iii	iii	PROPN
ap-1851	510	17	.	.	PUNCT
ap-1851	510	18	scattering	scatter	VERB
ap-1851	510	19	theory	theory	NOUN
ap-1851	510	20	,	,	PUNCT
ap-1851	510	21	academic	academic	ADJ
ap-1851	510	22	press	press	NOUN
ap-1851	510	23	,	,	PUNCT
ap-1851	510	24	new	new	PROPN
ap-1851	510	25	york	york	PROPN
ap-1851	510	26	1979	1979	NUM
ap-1851	510	27	.	.	PUNCT
ap-1851	511	1	[	[	X
ap-1851	511	2	28	28	NUM
ap-1851	511	3	]	]	X
ap-1851	511	4	b.	b.	PROPN
ap-1851	511	5	simon	simon	PROPN
ap-1851	511	6	:	:	PUNCT
ap-1851	511	7	quadratic	quadratic	ADJ
ap-1851	511	8	form	form	NOUN
ap-1851	511	9	techniques	technique	NOUN
ap-1851	511	10	and	and	CCONJ
ap-1851	511	11	the	the	DET
ap-1851	511	12	balslevcombes	balslevcombe	NOUN
ap-1851	511	13	theorem	theorem	VERB
ap-1851	511	14	,	,	PUNCT
ap-1851	511	15	commun	commun	PROPN
ap-1851	511	16	.	.	PUNCT
ap-1851	511	17	math	math	NOUN
ap-1851	511	18	.	.	PUNCT
ap-1851	512	1	phys	phy	NOUN
ap-1851	512	2	.	.	PUNCT
ap-1851	513	1	27	27	NUM
ap-1851	513	2	,	,	PUNCT
ap-1851	513	3	1–9	1–9	NUM
ap-1851	513	4	,	,	PUNCT
ap-1851	513	5	1972	1972	NUM
ap-1851	513	6	.	.	PUNCT
ap-1851	514	1	[	[	X
ap-1851	514	2	29	29	NUM
ap-1851	514	3	]	]	PUNCT
ap-1851	514	4	s.-h	s.-h	NOUN
ap-1851	514	5	.	.	PUNCT
ap-1851	514	6	tang	tang	PROPN
ap-1851	514	7	,	,	PUNCT
ap-1851	514	8	m.	m.	NOUN
ap-1851	514	9	zworski	zworski	PROPN
ap-1851	514	10	.	.	PUNCT
ap-1851	515	1	potential	potential	ADJ
ap-1851	515	2	scattering	scattering	NOUN
ap-1851	515	3	on	on	ADP
ap-1851	515	4	the	the	DET
ap-1851	515	5	real	real	ADJ
ap-1851	515	6	line	line	NOUN
ap-1851	515	7	,	,	PUNCT
ap-1851	515	8	lecture	lecture	NOUN
ap-1851	515	9	notes	note	NOUN
ap-1851	515	10	,	,	PUNCT
ap-1851	515	11	http://math.berkeley.edu/~zworski/tz1.pdf	http://math.berkeley.edu/~zworski/tz1.pdf	PROPN
ap-1851	515	12	.	.	PUNCT
ap-1851	516	1	[	[	X
ap-1851	516	2	30	30	NUM
ap-1851	516	3	]	]	X
ap-1851	516	4	h.	h.	PROPN
ap-1851	516	5	weyl	weyl	PROPN
ap-1851	516	6	:	:	PUNCT
ap-1851	516	7	über	über	NOUN
ap-1851	516	8	die	die	VERB
ap-1851	516	9	asymptotische	asymptotische	PROPN
ap-1851	516	10	verteilung	verteilung	PROPN
ap-1851	516	11	der	der	PROPN
ap-1851	516	12	eigenwerte	eigenwerte	PROPN
ap-1851	516	13	,	,	PUNCT
ap-1851	516	14	nachrichten	nachrichten	PROPN
ap-1851	516	15	von	von	PROPN
ap-1851	516	16	der	der	PROPN
ap-1851	516	17	gesellschaft	gesellschaft	PROPN
ap-1851	516	18	der	der	NOUN
ap-1851	516	19	wissenschaften	wissenschaften	VERB
ap-1851	516	20	zu	zu	NOUN
ap-1851	516	21	göttingen	göttingen	NOUN
ap-1851	516	22	,	,	PUNCT
ap-1851	516	23	mathematisch	mathematisch	NOUN
ap-1851	516	24	-	-	PUNCT
ap-1851	516	25	physikalische	physikalische	NOUN
ap-1851	516	26	klasse	klasse	NOUN
ap-1851	516	27	2	2	NUM
ap-1851	516	28	,	,	PUNCT
ap-1851	516	29	110–117	110–117	NUM
ap-1851	516	30	,	,	PUNCT
ap-1851	516	31	1911	1911	NUM
ap-1851	516	32	.	.	PUNCT
ap-1851	517	1	426	426	NUM
ap-1851	517	2	acta	acta	PROPN
ap-1851	517	3	polytechnica	polytechnica	PROPN
ap-1851	517	4	53(5):416–426	53(5):416–426	PROPN
ap-1851	517	5	,	,	PUNCT
ap-1851	517	6	2013	2013	NUM
ap-1851	517	7	1	1	NUM
ap-1851	517	8	introduction	introduction	NOUN
ap-1851	517	9	2	2	NUM
ap-1851	517	10	description	description	NOUN
ap-1851	517	11	of	of	ADP
ap-1851	517	12	the	the	DET
ap-1851	517	13	model	model	NOUN
ap-1851	517	14	3	3	NUM
ap-1851	517	15	scattering	scattering	NOUN
ap-1851	517	16	and	and	CCONJ
ap-1851	517	17	resolvent	resolvent	ADJ
ap-1851	517	18	resonances	resonance	NOUN
ap-1851	517	19	4	4	NUM
ap-1851	517	20	resonance	resonance	NOUN
ap-1851	517	21	asymptotics	asymptotic	VERB
ap-1851	517	22	4.1	4.1	NUM
ap-1851	517	23	manifolds	manifold	NOUN
ap-1851	517	24	with	with	ADP
ap-1851	517	25	the	the	DET
ap-1851	517	26	leads	lead	NOUN
ap-1851	517	27	attached	attach	VERB
ap-1851	517	28	at	at	ADP
ap-1851	517	29	a	a	DET
ap-1851	517	30	single	single	ADJ
ap-1851	517	31	point	point	NOUN
ap-1851	517	32	4.2	4.2	NUM
ap-1851	517	33	examples	example	NOUN
ap-1851	517	34	5	5	NUM
ap-1851	517	35	resonances	resonance	NOUN
ap-1851	517	36	for	for	ADP
ap-1851	517	37	a	a	DET
ap-1851	517	38	hedgehog	hedgehog	NOUN
ap-1851	517	39	manifold	manifold	NOUN
ap-1851	517	40	in	in	ADP
ap-1851	517	41	magnetic	magnetic	ADJ
ap-1851	517	42	field	field	NOUN
ap-1851	517	43	acknowledgements	acknowledgement	NOUN
ap-1851	517	44	references	reference	NOUN