id	sid	tid	token	lemma	pos
ap-2076	1	1	acta	acta	PROPN
ap-2076	1	2	polytechnica	polytechnica	PROPN
ap-2076	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2076	1	4	/	/	SYM
ap-2076	1	5	ap.2014.54.0093	ap.2014.54.0093	ADP
ap-2076	1	6	acta	acta	PROPN
ap-2076	1	7	polytechnica	polytechnica	PROPN
ap-2076	1	8	54(2):93–100	54(2):93–100	PROPN
ap-2076	1	9	,	,	PUNCT
ap-2076	1	10	2014	2014	NUM
ap-2076	1	11	©	©	PROPN
ap-2076	1	12	czech	czech	PROPN
ap-2076	1	13	technical	technical	PROPN
ap-2076	1	14	university	university	PROPN
ap-2076	1	15	in	in	ADP
ap-2076	1	16	prague	prague	PROPN
ap-2076	1	17	,	,	PUNCT
ap-2076	1	18	2014	2014	NUM
ap-2076	1	19	available	available	ADJ
ap-2076	1	20	online	online	ADV
ap-2076	1	21	at	at	ADP
ap-2076	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2076	1	23	eigenvalue	eigenvalue	ADJ
ap-2076	1	24	collision	collision	NOUN
ap-2076	1	25	for	for	ADP
ap-2076	1	26	pt	pt	NOUN
ap-2076	1	27	-	-	ADJ
ap-2076	1	28	symmetric	symmetric	ADJ
ap-2076	1	29	waveguide	waveguide	ADJ
ap-2076	1	30	denis	denis	PROPN
ap-2076	1	31	borisova	borisova	PROPN
ap-2076	1	32	,	,	PUNCT
ap-2076	1	33	b	b	PROPN
ap-2076	1	34	a	a	DET
ap-2076	1	35	institute	institute	NOUN
ap-2076	1	36	of	of	ADP
ap-2076	1	37	mathematics	mathematics	PROPN
ap-2076	1	38	of	of	ADP
ap-2076	1	39	ufa	ufa	PROPN
ap-2076	1	40	scientific	scientific	ADJ
ap-2076	1	41	center	center	NOUN
ap-2076	1	42	of	of	ADP
ap-2076	1	43	ras	ras	PROPN
ap-2076	1	44	,	,	PUNCT
ap-2076	1	45	chernyshevskogo	chernyshevskogo	PROPN
ap-2076	1	46	,	,	PUNCT
ap-2076	1	47	str	str	NOUN
ap-2076	1	48	.	.	PROPN
ap-2076	2	1	112	112	NUM
ap-2076	2	2	,	,	PUNCT
ap-2076	2	3	450008	450008	NUM
ap-2076	2	4	,	,	PUNCT
ap-2076	2	5	ufa	ufa	PROPN
ap-2076	2	6	,	,	PUNCT
ap-2076	2	7	russian	russian	PROPN
ap-2076	2	8	federation	federation	PROPN
ap-2076	2	9	b	b	PROPN
ap-2076	2	10	bashkir	bashkir	VERB
ap-2076	2	11	state	state	NOUN
ap-2076	2	12	pedagogical	pedagogical	ADJ
ap-2076	2	13	university	university	NOUN
ap-2076	2	14	,	,	PUNCT
ap-2076	2	15	october	october	PROPN
ap-2076	2	16	st	st	PROPN
ap-2076	2	17	.	.	PROPN
ap-2076	2	18	3a	3a	NUM
ap-2076	2	19	,	,	PUNCT
ap-2076	2	20	450000	450000	NUM
ap-2076	2	21	,	,	PUNCT
ap-2076	2	22	ufa	ufa	PROPN
ap-2076	2	23	,	,	PUNCT
ap-2076	2	24	russian	russian	PROPN
ap-2076	2	25	federation	federation	PROPN
ap-2076	2	26	correspondence	correspondence	NOUN
ap-2076	2	27	:	:	PUNCT
ap-2076	2	28	borisovdi@yandex.ru	borisovdi@yandex.ru	PROPN
ap-2076	2	29	abstract	abstract	ADJ
ap-2076	2	30	.	.	PUNCT
ap-2076	3	1	we	we	PRON
ap-2076	3	2	consider	consider	VERB
ap-2076	3	3	a	a	DET
ap-2076	3	4	model	model	NOUN
ap-2076	3	5	of	of	ADP
ap-2076	3	6	a	a	DET
ap-2076	3	7	planar	planar	ADJ
ap-2076	3	8	pt	pt	NOUN
ap-2076	3	9	-symmetric	-symmetric	NOUN
ap-2076	3	10	waveguide	waveguide	NOUN
ap-2076	3	11	and	and	CCONJ
ap-2076	3	12	study	study	VERB
ap-2076	3	13	the	the	DET
ap-2076	3	14	phenomenon	phenomenon	NOUN
ap-2076	3	15	of	of	ADP
ap-2076	3	16	the	the	DET
ap-2076	3	17	eigenvalue	eigenvalue	ADJ
ap-2076	3	18	collision	collision	NOUN
ap-2076	3	19	under	under	ADP
ap-2076	3	20	perturbation	perturbation	NOUN
ap-2076	3	21	of	of	ADP
ap-2076	3	22	the	the	DET
ap-2076	3	23	boundary	boundary	ADJ
ap-2076	3	24	conditions	condition	NOUN
ap-2076	3	25	.	.	PUNCT
ap-2076	4	1	this	this	DET
ap-2076	4	2	phenomenon	phenomenon	NOUN
ap-2076	4	3	was	be	AUX
ap-2076	4	4	discovered	discover	VERB
ap-2076	4	5	numerically	numerically	ADV
ap-2076	4	6	in	in	ADP
ap-2076	4	7	previous	previous	ADJ
ap-2076	4	8	works	work	NOUN
ap-2076	4	9	.	.	PUNCT
ap-2076	5	1	the	the	DET
ap-2076	5	2	main	main	ADJ
ap-2076	5	3	result	result	NOUN
ap-2076	5	4	of	of	ADP
ap-2076	5	5	this	this	DET
ap-2076	5	6	work	work	NOUN
ap-2076	5	7	is	be	AUX
ap-2076	5	8	an	an	DET
ap-2076	5	9	analytic	analytic	ADJ
ap-2076	5	10	explanation	explanation	NOUN
ap-2076	5	11	of	of	ADP
ap-2076	5	12	this	this	DET
ap-2076	5	13	phenomenon	phenomenon	NOUN
ap-2076	5	14	.	.	PUNCT
ap-2076	6	1	keywords	keyword	NOUN
ap-2076	6	2	:	:	PUNCT
ap-2076	6	3	pt	pt	ADJ
ap-2076	6	4	-	-	PUNCT
ap-2076	6	5	symmetric	symmetric	ADJ
ap-2076	6	6	operator	operator	NOUN
ap-2076	6	7	,	,	PUNCT
ap-2076	6	8	eigenvalues	eigenvalue	NOUN
ap-2076	6	9	,	,	PUNCT
ap-2076	6	10	perturbation	perturbation	NOUN
ap-2076	6	11	,	,	PUNCT
ap-2076	6	12	asymptotics	asymptotic	NOUN
ap-2076	6	13	.	.	PUNCT
ap-2076	7	1	1	1	X
ap-2076	7	2	.	.	X
ap-2076	7	3	introduction	introduction	NOUN
ap-2076	7	4	and	and	CCONJ
ap-2076	7	5	main	main	ADJ
ap-2076	7	6	results	result	NOUN
ap-2076	7	7	in	in	ADP
ap-2076	7	8	this	this	DET
ap-2076	7	9	paper	paper	NOUN
ap-2076	7	10	we	we	PRON
ap-2076	7	11	study	study	VERB
ap-2076	7	12	a	a	DET
ap-2076	7	13	problem	problem	NOUN
ap-2076	7	14	in	in	ADP
ap-2076	7	15	the	the	DET
ap-2076	7	16	theory	theory	NOUN
ap-2076	7	17	of	of	ADP
ap-2076	7	18	pt	pt	NOUN
ap-2076	7	19	-symmetric	-symmetric	ADJ
ap-2076	7	20	operators	operator	NOUN
ap-2076	7	21	which	which	PRON
ap-2076	7	22	has	have	AUX
ap-2076	7	23	been	be	AUX
ap-2076	7	24	studied	study	VERB
ap-2076	7	25	rather	rather	ADV
ap-2076	7	26	intensively	intensively	ADV
ap-2076	7	27	after	after	ADP
ap-2076	7	28	the	the	DET
ap-2076	7	29	pioneering	pioneer	VERB
ap-2076	7	30	works	work	NOUN
ap-2076	7	31	[	[	X
ap-2076	7	32	12–21	12–21	NUM
ap-2076	7	33	]	]	PUNCT
ap-2076	7	34	.	.	PUNCT
ap-2076	8	1	our	our	PRON
ap-2076	8	2	model	model	NOUN
ap-2076	8	3	is	be	AUX
ap-2076	8	4	introduced	introduce	VERB
ap-2076	8	5	as	as	SCONJ
ap-2076	8	6	follows	follow	VERB
ap-2076	8	7	.	.	PUNCT
ap-2076	9	1	let	let	VERB
ap-2076	9	2	x	x	PUNCT
ap-2076	9	3	=	=	SYM
ap-2076	9	4	(	(	PUNCT
ap-2076	9	5	x1	x1	PROPN
ap-2076	9	6	,	,	PUNCT
ap-2076	9	7	x2	x2	PROPN
ap-2076	9	8	)	)	PUNCT
ap-2076	9	9	be	be	VERB
ap-2076	9	10	cartesian	cartesian	ADJ
ap-2076	9	11	coordinates	coordinate	NOUN
ap-2076	9	12	in	in	ADP
ap-2076	9	13	r2	r2	PROPN
ap-2076	9	14	,	,	PUNCT
ap-2076	9	15	let	let	VERB
ap-2076	9	16	ω	ω	NOUN
ap-2076	9	17	be	be	AUX
ap-2076	9	18	the	the	DET
ap-2076	9	19	strip	strip	NOUN
ap-2076	9	20	{	{	PUNCT
ap-2076	9	21	x	x	X
ap-2076	9	22	:	:	PUNCT
ap-2076	9	23	−d	−d	PROPN
ap-2076	9	24	<	<	X
ap-2076	10	1	x2	x2	X
ap-2076	10	2	<	<	X
ap-2076	10	3	d	d	X
ap-2076	10	4	}	}	PUNCT
ap-2076	10	5	,	,	PUNCT
ap-2076	10	6	d	d	X
ap-2076	10	7	>	>	X
ap-2076	10	8	0	0	NUM
ap-2076	10	9	,	,	PUNCT
ap-2076	10	10	and	and	CCONJ
ap-2076	10	11	let	let	VERB
ap-2076	10	12	α	α	NOUN
ap-2076	10	13	=	=	SYM
ap-2076	10	14	α(x1	α(x1	NOUN
ap-2076	10	15	)	)	PUNCT
ap-2076	10	16	be	be	AUX
ap-2076	10	17	a	a	DET
ap-2076	10	18	function	function	NOUN
ap-2076	10	19	in	in	ADP
ap-2076	10	20	w	w	PROPN
ap-2076	10	21	1	1	NUM
ap-2076	10	22	∞(r	∞(r	NUM
ap-2076	10	23	)	)	PUNCT
ap-2076	10	24	.	.	PUNCT
ap-2076	11	1	we	we	PRON
ap-2076	11	2	consider	consider	VERB
ap-2076	11	3	the	the	DET
ap-2076	11	4	operator	operator	NOUN
ap-2076	11	5	hα	hα	X
ap-2076	11	6	in	in	ADP
ap-2076	11	7	l2(ω	l2(ω	NOUN
ap-2076	11	8	)	)	PUNCT
ap-2076	11	9	acting	act	VERB
ap-2076	11	10	as	as	ADP
ap-2076	11	11	hαu	hαu	NOUN
ap-2076	11	12	=	=	SYM
ap-2076	11	13	−∆u	−∆u	NOUN
ap-2076	11	14	on	on	ADP
ap-2076	11	15	the	the	DET
ap-2076	11	16	functions	function	NOUN
ap-2076	11	17	u	u	PRON
ap-2076	11	18	∈w	∈w	VERB
ap-2076	11	19	2	2	NUM
ap-2076	11	20	2	2	NUM
ap-2076	11	21	(	(	PUNCT
ap-2076	11	22	ω	ω	NOUN
ap-2076	11	23	)	)	PUNCT
ap-2076	11	24	satisfying	satisfy	VERB
ap-2076	11	25	the	the	DET
ap-2076	11	26	non	non	ADJ
ap-2076	11	27	-	-	ADJ
ap-2076	11	28	hermitian	hermitian	ADJ
ap-2076	11	29	boundary	boundary	ADJ
ap-2076	11	30	conditions	condition	NOUN
ap-2076	11	31	(	(	PUNCT
ap-2076	11	32	∂	∂	NUM
ap-2076	11	33	∂x2	∂x2	NOUN
ap-2076	11	34	+	+	SYM
ap-2076	11	35	iα	iα	ADJ
ap-2076	11	36	)	)	PUNCT
ap-2076	11	37	u	u	NOUN
ap-2076	11	38	=	=	NOUN
ap-2076	11	39	0	0	NUM
ap-2076	11	40	on	on	ADP
ap-2076	11	41	∂ω	∂ω	PROPN
ap-2076	11	42	.	.	PUNCT
ap-2076	12	1	(	(	PUNCT
ap-2076	12	2	1.1	1.1	NUM
ap-2076	12	3	)	)	PUNCT
ap-2076	12	4	it	it	PRON
ap-2076	12	5	was	be	AUX
ap-2076	12	6	shown	show	VERB
ap-2076	12	7	in	in	ADP
ap-2076	12	8	[	[	X
ap-2076	12	9	1	1	X
ap-2076	12	10	]	]	PUNCT
ap-2076	12	11	that	that	SCONJ
ap-2076	12	12	this	this	DET
ap-2076	12	13	operator	operator	NOUN
ap-2076	12	14	is	be	AUX
ap-2076	12	15	m	m	NOUN
ap-2076	12	16	-	-	ADJ
ap-2076	12	17	sectorial	sectorial	ADJ
ap-2076	12	18	,	,	PUNCT
ap-2076	12	19	densely	densely	ADV
ap-2076	12	20	defined	define	VERB
ap-2076	12	21	,	,	PUNCT
ap-2076	12	22	and	and	CCONJ
ap-2076	13	1	pt	pt	NOUN
ap-2076	13	2	-symmetric	-symmetric	NOUN
ap-2076	13	3	,	,	PUNCT
ap-2076	13	4	namely	namely	ADV
ap-2076	13	5	,	,	PUNCT
ap-2076	13	6	pt	pt	X
ap-2076	13	7	hα	hα	NOUN
ap-2076	13	8	=	=	SYM
ap-2076	13	9	hαpt	hαpt	PROPN
ap-2076	13	10	,	,	PUNCT
ap-2076	13	11	(	(	PUNCT
ap-2076	13	12	1.2	1.2	NUM
ap-2076	13	13	)	)	PUNCT
ap-2076	14	1	where	where	SCONJ
ap-2076	14	2	(	(	PUNCT
ap-2076	14	3	pu)(x	pu)(x	PROPN
ap-2076	14	4	)	)	PUNCT
ap-2076	14	5	=	=	SYM
ap-2076	14	6	u(x1,−x2	u(x1,−x2	ADJ
ap-2076	14	7	)	)	PUNCT
ap-2076	14	8	,	,	PUNCT
ap-2076	14	9	and	and	CCONJ
ap-2076	14	10	t	t	PROPN
ap-2076	14	11	is	be	AUX
ap-2076	14	12	the	the	DET
ap-2076	14	13	operator	operator	NOUN
ap-2076	14	14	of	of	ADP
ap-2076	14	15	complex	complex	ADJ
ap-2076	14	16	conjugation	conjugation	NOUN
ap-2076	14	17	,	,	PUNCT
ap-2076	14	18	t	t	NOUN
ap-2076	14	19	u	u	NOUN
ap-2076	14	20	=	=	X
ap-2076	14	21	u.	u.	VERB
ap-2076	14	22	it	it	PRON
ap-2076	14	23	was	be	AUX
ap-2076	14	24	also	also	ADV
ap-2076	14	25	proven	prove	VERB
ap-2076	14	26	in	in	ADP
ap-2076	14	27	[	[	X
ap-2076	14	28	1	1	X
ap-2076	14	29	]	]	PUNCT
ap-2076	14	30	that	that	SCONJ
ap-2076	14	31	h∗α	h∗α	PUNCT
ap-2076	14	32	=	=	SYM
ap-2076	14	33	h−α	h−α	NOUN
ap-2076	14	34	,	,	PUNCT
ap-2076	14	35	h∗α	h∗α	PUNCT
ap-2076	14	36	=	=	SYM
ap-2076	14	37	t	t	NOUN
ap-2076	14	38	hαt	hαt	VERB
ap-2076	14	39	=	=	SYM
ap-2076	14	40	phαp	phαp	NOUN
ap-2076	14	41	.	.	PUNCT
ap-2076	15	1	(	(	PUNCT
ap-2076	15	2	1.3	1.3	NUM
ap-2076	15	3	)	)	PUNCT
ap-2076	15	4	a	a	DET
ap-2076	15	5	non	non	ADJ
ap-2076	15	6	-	-	ADJ
ap-2076	15	7	trivial	trivial	ADJ
ap-2076	15	8	question	question	NOUN
ap-2076	15	9	related	relate	VERB
ap-2076	15	10	to	to	ADP
ap-2076	15	11	hα	hα	X
ap-2076	15	12	is	be	AUX
ap-2076	15	13	the	the	DET
ap-2076	15	14	behavior	behavior	NOUN
ap-2076	15	15	of	of	ADP
ap-2076	15	16	its	its	PRON
ap-2076	15	17	eigenvalues	eigenvalue	NOUN
ap-2076	15	18	.	.	PUNCT
ap-2076	16	1	as	as	ADP
ap-2076	16	2	α(x1	α(x1	NOUN
ap-2076	16	3	)	)	PUNCT
ap-2076	16	4	is	be	AUX
ap-2076	16	5	a	a	DET
ap-2076	16	6	small	small	ADJ
ap-2076	16	7	regular	regular	ADJ
ap-2076	16	8	localized	localized	ADJ
ap-2076	16	9	perturbation	perturbation	NOUN
ap-2076	16	10	of	of	ADP
ap-2076	16	11	a	a	DET
ap-2076	16	12	constant	constant	ADJ
ap-2076	16	13	function	function	NOUN
ap-2076	16	14	,	,	PUNCT
ap-2076	16	15	sufficient	sufficient	ADJ
ap-2076	16	16	conditions	condition	NOUN
ap-2076	16	17	were	be	AUX
ap-2076	16	18	obtained	obtain	VERB
ap-2076	16	19	in	in	ADP
ap-2076	16	20	[	[	X
ap-2076	16	21	1	1	NUM
ap-2076	16	22	]	]	PUNCT
ap-2076	16	23	for	for	ADP
ap-2076	16	24	the	the	DET
ap-2076	16	25	existence	existence	NOUN
ap-2076	16	26	and	and	CCONJ
ap-2076	16	27	absence	absence	NOUN
ap-2076	16	28	of	of	ADP
ap-2076	16	29	isolated	isolated	ADJ
ap-2076	16	30	eigenvalues	eigenvalue	NOUN
ap-2076	16	31	near	near	ADP
ap-2076	16	32	the	the	DET
ap-2076	16	33	threshold	threshold	NOUN
ap-2076	16	34	of	of	ADP
ap-2076	16	35	the	the	DET
ap-2076	16	36	essential	essential	ADJ
ap-2076	16	37	spectrum	spectrum	NOUN
ap-2076	16	38	.	.	PUNCT
ap-2076	17	1	similar	similar	ADJ
ap-2076	17	2	results	result	NOUN
ap-2076	17	3	for	for	ADP
ap-2076	17	4	both	both	CCONJ
ap-2076	17	5	regularly	regularly	ADV
ap-2076	17	6	and	and	CCONJ
ap-2076	17	7	singularly	singularly	ADV
ap-2076	17	8	perturbed	perturb	VERB
ap-2076	17	9	models	model	NOUN
ap-2076	17	10	were	be	AUX
ap-2076	17	11	obtained	obtain	VERB
ap-2076	17	12	in	in	ADP
ap-2076	17	13	[	[	X
ap-2076	17	14	2–6	2–6	NOUN
ap-2076	17	15	]	]	X
ap-2076	17	16	.	.	PUNCT
ap-2076	18	1	numerical	numerical	ADJ
ap-2076	18	2	experiments	experiment	NOUN
ap-2076	18	3	performed	perform	VERB
ap-2076	18	4	in	in	ADP
ap-2076	18	5	[	[	X
ap-2076	18	6	6	6	NUM
ap-2076	18	7	,	,	PUNCT
ap-2076	18	8	7	7	NUM
ap-2076	18	9	]	]	PUNCT
ap-2076	18	10	provided	provide	VERB
ap-2076	18	11	a	a	DET
ap-2076	18	12	very	very	ADV
ap-2076	18	13	non	non	ADJ
ap-2076	18	14	-	-	ADJ
ap-2076	18	15	trivial	trivial	ADJ
ap-2076	18	16	picture	picture	NOUN
ap-2076	18	17	of	of	ADP
ap-2076	18	18	the	the	DET
ap-2076	18	19	distribution	distribution	NOUN
ap-2076	18	20	of	of	ADP
ap-2076	18	21	the	the	DET
ap-2076	18	22	eigenvalues	eigenvalue	NOUN
ap-2076	18	23	.	.	PUNCT
ap-2076	19	1	an	an	DET
ap-2076	19	2	interesting	interesting	ADJ
ap-2076	19	3	phenomenon	phenomenon	NOUN
ap-2076	19	4	discovered	discover	VERB
ap-2076	19	5	numerically	numerically	ADV
ap-2076	19	6	in	in	ADP
ap-2076	19	7	[	[	X
ap-2076	19	8	6	6	NUM
ap-2076	19	9	,	,	PUNCT
ap-2076	19	10	7	7	NUM
ap-2076	19	11	]	]	PUNCT
ap-2076	19	12	was	be	AUX
ap-2076	19	13	the	the	DET
ap-2076	19	14	eigenvalue	eigenvalue	PROPN
ap-2076	19	15	collision	collision	NOUN
ap-2076	19	16	.	.	PUNCT
ap-2076	20	1	namely	namely	ADV
ap-2076	20	2	,	,	PUNCT
ap-2076	20	3	let	let	VERB
ap-2076	20	4	t	t	PROPN
ap-2076	20	5	∈	∈	NOUN
ap-2076	20	6	r	r	NOUN
ap-2076	20	7	be	be	AUX
ap-2076	20	8	a	a	DET
ap-2076	20	9	parameter	parameter	NOUN
ap-2076	20	10	,	,	PUNCT
ap-2076	20	11	then	then	ADV
ap-2076	20	12	as	as	ADP
ap-2076	20	13	t	t	PROPN
ap-2076	20	14	increases	increase	NOUN
ap-2076	20	15	,	,	PUNCT
ap-2076	20	16	operator	operator	NOUN
ap-2076	20	17	htα	htα	NOUN
ap-2076	20	18	can	can	AUX
ap-2076	20	19	have	have	VERB
ap-2076	20	20	two	two	NUM
ap-2076	20	21	simple	simple	ADJ
ap-2076	20	22	real	real	ADJ
ap-2076	20	23	isolated	isolate	VERB
ap-2076	20	24	eigenvalues	eigenvalue	NOUN
ap-2076	20	25	meeting	meeting	NOUN
ap-2076	20	26	at	at	ADP
ap-2076	20	27	some	some	DET
ap-2076	20	28	point	point	NOUN
ap-2076	20	29	.	.	PUNCT
ap-2076	21	1	then	then	ADV
ap-2076	21	2	two	two	NUM
ap-2076	21	3	cases	case	NOUN
ap-2076	21	4	are	be	AUX
ap-2076	21	5	possible	possible	ADJ
ap-2076	21	6	.	.	PUNCT
ap-2076	22	1	in	in	ADP
ap-2076	22	2	the	the	DET
ap-2076	22	3	first	first	ADJ
ap-2076	22	4	of	of	ADP
ap-2076	22	5	them	they	PRON
ap-2076	22	6	,	,	PUNCT
ap-2076	22	7	these	these	PRON
ap-2076	22	8	eigenvalues	eigenvalues	AUX
ap-2076	22	9	stay	stay	VERB
ap-2076	22	10	real	real	ADJ
ap-2076	22	11	as	as	ADP
ap-2076	22	12	t	t	PROPN
ap-2076	22	13	increases	increase	NOUN
ap-2076	22	14	and	and	CCONJ
ap-2076	22	15	they	they	PRON
ap-2076	22	16	just	just	ADV
ap-2076	22	17	pass	pass	VERB
ap-2076	22	18	along	along	ADP
ap-2076	22	19	the	the	DET
ap-2076	22	20	real	real	ADJ
ap-2076	22	21	line	line	NOUN
ap-2076	22	22	.	.	PUNCT
ap-2076	23	1	in	in	ADP
ap-2076	23	2	the	the	DET
ap-2076	23	3	second	second	ADJ
ap-2076	23	4	case	case	NOUN
ap-2076	23	5	,	,	PUNCT
ap-2076	23	6	the	the	DET
ap-2076	23	7	eigenvalues	eigenvalue	NOUN
ap-2076	23	8	become	become	VERB
ap-2076	23	9	complex	complex	ADJ
ap-2076	23	10	as	as	ADP
ap-2076	23	11	t	t	NOUN
ap-2076	23	12	increases	increase	NOUN
ap-2076	23	13	and	and	CCONJ
ap-2076	23	14	they	they	PRON
ap-2076	23	15	are	be	AUX
ap-2076	23	16	located	locate	VERB
ap-2076	23	17	symmetrically	symmetrically	ADV
ap-2076	23	18	w.r.t	w.r.t	VERB
ap-2076	23	19	.	.	PUNCT
ap-2076	24	1	the	the	DET
ap-2076	24	2	real	real	ADJ
ap-2076	24	3	axis	axis	NOUN
ap-2076	24	4	.	.	PUNCT
ap-2076	25	1	the	the	DET
ap-2076	25	2	present	present	ADJ
ap-2076	25	3	paper	paper	NOUN
ap-2076	25	4	is	be	AUX
ap-2076	25	5	devoted	devote	VERB
ap-2076	25	6	to	to	ADP
ap-2076	25	7	an	an	DET
ap-2076	25	8	analytic	analytic	ADJ
ap-2076	25	9	study	study	NOUN
ap-2076	25	10	of	of	ADP
ap-2076	25	11	this	this	DET
ap-2076	25	12	phenomenon	phenomenon	NOUN
ap-2076	25	13	.	.	PUNCT
ap-2076	26	1	suppose	suppose	VERB
ap-2076	26	2	λ0	λ0	NOUN
ap-2076	26	3	∈	∈	NOUN
ap-2076	26	4	r	r	NOUN
ap-2076	26	5	is	be	AUX
ap-2076	26	6	an	an	DET
ap-2076	26	7	isolated	isolated	ADJ
ap-2076	26	8	eigenvalue	eigenvalue	NOUN
ap-2076	26	9	of	of	ADP
ap-2076	26	10	hα	hα	PROPN
ap-2076	26	11	,	,	PUNCT
ap-2076	26	12	ε	ε	PROPN
ap-2076	26	13	is	be	AUX
ap-2076	26	14	a	a	DET
ap-2076	26	15	small	small	ADJ
ap-2076	26	16	real	real	ADJ
ap-2076	26	17	parameter	parameter	NOUN
ap-2076	26	18	,	,	PUNCT
ap-2076	26	19	β	β	X
ap-2076	26	20	∈w	∈w	NUM
ap-2076	26	21	2	2	NUM
ap-2076	26	22	∞(r	∞(r	NUM
ap-2076	26	23	)	)	PUNCT
ap-2076	26	24	is	be	AUX
ap-2076	26	25	some	some	DET
ap-2076	26	26	function	function	NOUN
ap-2076	26	27	.	.	PUNCT
ap-2076	27	1	denote	denote	VERB
ap-2076	27	2	γ±	γ±	PROPN
ap-2076	27	3	:	:	PUNCT
ap-2076	27	4	=	=	SYM
ap-2076	27	5	{	{	PUNCT
ap-2076	27	6	x	x	X
ap-2076	27	7	:	:	PUNCT
ap-2076	27	8	x2	x2	NOUN
ap-2076	27	9	=	=	PUNCT
ap-2076	27	10	±d	±d	PROPN
ap-2076	27	11	}	}	PUNCT
ap-2076	27	12	.	.	PUNCT
ap-2076	28	1	our	our	PRON
ap-2076	28	2	first	first	ADJ
ap-2076	28	3	main	main	ADJ
ap-2076	28	4	result	result	NOUN
ap-2076	28	5	describes	describe	VERB
ap-2076	28	6	the	the	DET
ap-2076	28	7	case	case	NOUN
ap-2076	28	8	when	when	SCONJ
ap-2076	28	9	λ0	λ0	NOUN
ap-2076	28	10	is	be	AUX
ap-2076	28	11	an	an	DET
ap-2076	28	12	eigenvalue	eigenvalue	NOUN
ap-2076	28	13	of	of	ADP
ap-2076	28	14	geometric	geometric	ADJ
ap-2076	28	15	multiplicity	multiplicity	NOUN
ap-2076	28	16	two	two	NUM
ap-2076	28	17	.	.	PUNCT
ap-2076	29	1	theorem	theorem	VERB
ap-2076	29	2	1.1	1.1	NUM
ap-2076	29	3	.	.	PUNCT
ap-2076	30	1	assume	assume	VERB
ap-2076	30	2	λ0	λ0	NOUN
ap-2076	30	3	∈	∈	NOUN
ap-2076	30	4	r	r	NOUN
ap-2076	30	5	is	be	AUX
ap-2076	30	6	a	a	DET
ap-2076	30	7	double	double	ADJ
ap-2076	30	8	eigenvalue	eigenvalue	NOUN
ap-2076	30	9	of	of	ADP
ap-2076	30	10	hα	hα	PROPN
ap-2076	30	11	,	,	PUNCT
ap-2076	31	1	ψ±0	ψ±0	X
ap-2076	31	2	are	be	AUX
ap-2076	31	3	the	the	DET
ap-2076	31	4	associated	associate	VERB
ap-2076	31	5	eigenfunctions	eigenfunction	NOUN
ap-2076	31	6	satisfying	satisfy	VERB
ap-2076	31	7	(	(	PUNCT
ap-2076	31	8	ψ±0	ψ±0	X
ap-2076	31	9	,	,	PUNCT
ap-2076	31	10	t	t	PROPN
ap-2076	31	11	ψ	ψ	X
ap-2076	31	12	±	±	PROPN
ap-2076	31	13	0	0	NUM
ap-2076	31	14	)	)	PUNCT
ap-2076	31	15	l2(ω	l2(ω	X
ap-2076	31	16	)	)	PUNCT
ap-2076	31	17	=	=	SYM
ap-2076	31	18	1	1	NUM
ap-2076	31	19	,	,	PUNCT
ap-2076	31	20	(	(	PUNCT
ap-2076	31	21	ψ+	ψ+	X
ap-2076	31	22	0	0	NUM
ap-2076	31	23	,	,	PUNCT
ap-2076	31	24	t	t	NOUN
ap-2076	31	25	ψ	ψ	X
ap-2076	31	26	−	−	PROPN
ap-2076	31	27	0	0	NUM
ap-2076	31	28	)	)	PUNCT
ap-2076	32	1	l2(ω	l2(ω	X
ap-2076	32	2	)	)	PUNCT
ap-2076	32	3	=	=	SYM
ap-2076	33	1	0	0	X
ap-2076	33	2	.	.	PUNCT
ap-2076	34	1	(	(	PUNCT
ap-2076	34	2	1.4	1.4	NUM
ap-2076	34	3	)	)	PUNCT
ap-2076	34	4	suppose	suppose	VERB
ap-2076	34	5	also	also	ADV
ap-2076	34	6	(	(	PUNCT
ap-2076	34	7	b11	b11	PROPN
ap-2076	34	8	−	−	PROPN
ap-2076	34	9	b22)2	b22)2	NOUN
ap-2076	34	10	+	+	NOUN
ap-2076	34	11	4b212	4b212	NUM
ap-2076	34	12	6=	6=	ADP
ap-2076	34	13	0	0	NUM
ap-2076	34	14	,	,	PUNCT
ap-2076	34	15	(	(	PUNCT
ap-2076	34	16	1.5	1.5	NUM
ap-2076	34	17	)	)	PUNCT
ap-2076	34	18	b11	b11	NOUN
ap-2076	34	19	=	=	NOUN
ap-2076	35	1	i	i	PRON
ap-2076	35	2	∫	∫	VERB
ap-2076	35	3	γ+	γ+	X
ap-2076	35	4	β(ψ+	β(ψ+	PROPN
ap-2076	35	5	0	0	NUM
ap-2076	36	1	)	)	PUNCT
ap-2076	36	2	2	2	NUM
ap-2076	36	3	dx1	dx1	PROPN
ap-2076	36	4	−	−	NOUN
ap-2076	37	1	i	i	PRON
ap-2076	37	2	∫	∫	PROPN
ap-2076	37	3	γ−	γ−	PROPN
ap-2076	37	4	β(ψ+	β(ψ+	NOUN
ap-2076	37	5	0	0	NUM
ap-2076	37	6	)	)	SYM
ap-2076	37	7	2	2	NUM
ap-2076	37	8	dx1	dx1	PROPN
ap-2076	37	9	,	,	PUNCT
ap-2076	37	10	b22	b22	PROPN
ap-2076	37	11	=	=	SYM
ap-2076	38	1	i	i	PRON
ap-2076	38	2	∫	∫	VERB
ap-2076	38	3	γ+	γ+	X
ap-2076	38	4	β(ψ−0	β(ψ−0	PROPN
ap-2076	38	5	)	)	PUNCT
ap-2076	38	6	2	2	NUM
ap-2076	39	1	dx1	dx1	PROPN
ap-2076	39	2	−	−	NOUN
ap-2076	40	1	i	i	PRON
ap-2076	40	2	∫	∫	PROPN
ap-2076	40	3	γ−	γ−	PROPN
ap-2076	40	4	β(ψ−0	β(ψ−0	NUM
ap-2076	40	5	)	)	PUNCT
ap-2076	40	6	2	2	NUM
ap-2076	40	7	dx1	dx1	PROPN
ap-2076	40	8	,	,	PUNCT
ap-2076	40	9	b12	b12	NOUN
ap-2076	40	10	=	=	NOUN
ap-2076	41	1	i	i	PRON
ap-2076	41	2	∫	∫	VERB
ap-2076	41	3	γ+	γ+	PUNCT
ap-2076	41	4	βψ+	βψ+	ADJ
ap-2076	41	5	0	0	PUNCT
ap-2076	42	1	ψ	ψ	NOUN
ap-2076	42	2	−	−	PROPN
ap-2076	42	3	0	0	NUM
ap-2076	43	1	dx1	dx1	PROPN
ap-2076	44	1	−	−	PROPN
ap-2076	44	2	i	i	PRON
ap-2076	44	3	∫	∫	VERB
ap-2076	44	4	γ−	γ−	NUM
ap-2076	44	5	βψ+	βψ+	NOUN
ap-2076	44	6	0	0	PUNCT
ap-2076	45	1	ψ	ψ	NOUN
ap-2076	45	2	−	−	PROPN
ap-2076	45	3	0	0	NUM
ap-2076	45	4	dx1	dx1	PROPN
ap-2076	45	5	.	.	PUNCT
ap-2076	46	1	(	(	PUNCT
ap-2076	46	2	1.6	1.6	NUM
ap-2076	46	3	)	)	PUNCT
ap-2076	46	4	93	93	NUM
ap-2076	47	1	http://dx.doi.org/10.14311/ap.2014.54.0093	http://dx.doi.org/10.14311/ap.2014.54.0093	PRON
ap-2076	47	2	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2076	47	3	denis	denis	PROPN
ap-2076	47	4	borisov	borisov	PROPN
ap-2076	47	5	acta	acta	PROPN
ap-2076	47	6	polytechnica	polytechnica	PROPN
ap-2076	47	7	then	then	ADV
ap-2076	47	8	for	for	ADP
ap-2076	47	9	all	all	DET
ap-2076	47	10	sufficiently	sufficiently	ADV
ap-2076	47	11	small	small	ADJ
ap-2076	47	12	ε	ε	X
ap-2076	47	13	the	the	DET
ap-2076	47	14	operator	operator	NOUN
ap-2076	47	15	hα+εβ	hα+εβ	PROPN
ap-2076	47	16	has	have	VERB
ap-2076	47	17	two	two	NUM
ap-2076	47	18	simple	simple	ADJ
ap-2076	47	19	isolated	isolate	VERB
ap-2076	47	20	eigenvalues	eigenvalue	NOUN
ap-2076	47	21	λ±ε	λ±ε	X
ap-2076	47	22	converging	converge	VERB
ap-2076	47	23	to	to	ADP
ap-2076	47	24	λ0	λ0	NOUN
ap-2076	47	25	as	as	ADP
ap-2076	47	26	ε→	ε→	NUM
ap-2076	47	27	0	0	NUM
ap-2076	47	28	.	.	PUNCT
ap-2076	48	1	these	these	DET
ap-2076	48	2	eigenvalues	eigenvalue	NOUN
ap-2076	48	3	are	be	AUX
ap-2076	48	4	holomorphic	holomorphic	ADJ
ap-2076	48	5	w.r.t	w.r.t	NOUN
ap-2076	48	6	.	.	PUNCT
ap-2076	49	1	ε	ε	PROPN
ap-2076	49	2	and	and	CCONJ
ap-2076	49	3	the	the	DET
ap-2076	49	4	first	first	ADJ
ap-2076	49	5	terms	term	NOUN
ap-2076	49	6	of	of	ADP
ap-2076	49	7	their	their	PRON
ap-2076	49	8	taylor	taylor	PROPN
ap-2076	49	9	series	series	NOUN
ap-2076	49	10	are	be	AUX
ap-2076	49	11	λ±ε	λ±ε	PRON
ap-2076	49	12	=	=	PUNCT
ap-2076	49	13	λ0	λ0	NOUN
ap-2076	49	14	+	+	CCONJ
ap-2076	49	15	ελ±1	ελ±1	NOUN
ap-2076	49	16	+	+	NOUN
ap-2076	49	17	o(ε2	o(ε2	NOUN
ap-2076	49	18	)	)	PUNCT
ap-2076	49	19	,	,	PUNCT
ap-2076	49	20	λ±1	λ±1	NOUN
ap-2076	50	1	=	=	SYM
ap-2076	50	2	1	1	NUM
ap-2076	50	3	2(b11	2(b11	NUM
ap-2076	50	4	+	+	CCONJ
ap-2076	50	5	b22)±	b22)±	X
ap-2076	50	6	1	1	NUM
ap-2076	50	7	2	2	NUM
ap-2076	50	8	(	(	PUNCT
ap-2076	50	9	(	(	PUNCT
ap-2076	50	10	b11	b11	NOUN
ap-2076	50	11	−	−	PROPN
ap-2076	50	12	b22)2	b22)2	NOUN
ap-2076	50	13	+	+	NOUN
ap-2076	50	14	4b212	4b212	NUM
ap-2076	50	15	)	)	PUNCT
ap-2076	50	16	1/2	1/2	NUM
ap-2076	50	17	.	.	PUNCT
ap-2076	51	1	(	(	PUNCT
ap-2076	51	2	1.7	1.7	NUM
ap-2076	51	3	)	)	PUNCT
ap-2076	51	4	the	the	DET
ap-2076	51	5	second	second	ADJ
ap-2076	51	6	main	main	ADJ
ap-2076	51	7	result	result	NOUN
ap-2076	51	8	is	be	AUX
ap-2076	51	9	devoted	devote	VERB
ap-2076	51	10	to	to	ADP
ap-2076	51	11	the	the	DET
ap-2076	51	12	case	case	NOUN
ap-2076	51	13	when	when	SCONJ
ap-2076	51	14	the	the	DET
ap-2076	51	15	geometric	geometric	ADJ
ap-2076	51	16	multiplicity	multiplicity	NOUN
ap-2076	51	17	of	of	ADP
ap-2076	51	18	λ0	λ0	NOUN
ap-2076	51	19	is	be	AUX
ap-2076	51	20	one	one	NUM
ap-2076	51	21	but	but	CCONJ
ap-2076	51	22	the	the	DET
ap-2076	51	23	algebraic	algebraic	ADJ
ap-2076	51	24	multiplicity	multiplicity	NOUN
ap-2076	51	25	is	be	AUX
ap-2076	51	26	two	two	NUM
ap-2076	51	27	.	.	PUNCT
ap-2076	52	1	theorem	theorem	VERB
ap-2076	52	2	1.2	1.2	NUM
ap-2076	52	3	.	.	PUNCT
ap-2076	53	1	let	let	VERB
ap-2076	53	2	λ0	λ0	NOUN
ap-2076	53	3	∈	∈	NOUN
ap-2076	53	4	r	r	NOUN
ap-2076	53	5	be	be	VERB
ap-2076	53	6	a	a	DET
ap-2076	53	7	simple	simple	ADJ
ap-2076	53	8	eigenvalue	eigenvalue	NOUN
ap-2076	53	9	of	of	ADP
ap-2076	53	10	hα	hα	NOUN
ap-2076	53	11	and	and	CCONJ
ap-2076	53	12	let	let	VERB
ap-2076	53	13	ψ0	ψ0	ADV
ap-2076	53	14	be	be	AUX
ap-2076	53	15	the	the	DET
ap-2076	53	16	associated	associated	ADJ
ap-2076	53	17	eigenfunction	eigenfunction	NOUN
ap-2076	53	18	.	.	PUNCT
ap-2076	54	1	assume	assume	VERB
ap-2076	54	2	that	that	SCONJ
ap-2076	54	3	the	the	DET
ap-2076	54	4	equation	equation	NOUN
ap-2076	54	5	(	(	PUNCT
ap-2076	54	6	hα	hα	ADP
ap-2076	54	7	−	−	PROPN
ap-2076	54	8	λ0)φ0	λ0)φ0	NOUN
ap-2076	55	1	=	=	PUNCT
ap-2076	55	2	ψ0	ψ0	PROPN
ap-2076	55	3	(	(	PUNCT
ap-2076	55	4	1.8	1.8	NUM
ap-2076	55	5	)	)	PUNCT
ap-2076	55	6	is	be	AUX
ap-2076	55	7	solvable	solvable	ADJ
ap-2076	55	8	and	and	CCONJ
ap-2076	55	9	there	there	PRON
ap-2076	55	10	exists	exist	VERB
ap-2076	55	11	a	a	DET
ap-2076	55	12	solution	solution	NOUN
ap-2076	55	13	satisfying	satisfying	ADJ
ap-2076	55	14	(	(	PUNCT
ap-2076	55	15	φ0	φ0	PROPN
ap-2076	55	16	,	,	PUNCT
ap-2076	55	17	t	t	PROPN
ap-2076	55	18	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	55	19	)	)	PUNCT
ap-2076	55	20	6=	6=	ADP
ap-2076	55	21	0	0	NUM
ap-2076	55	22	,	,	PUNCT
ap-2076	55	23	(	(	PUNCT
ap-2076	55	24	φ0	φ0	VERB
ap-2076	55	25	,	,	PUNCT
ap-2076	55	26	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	55	27	)	)	PUNCT
ap-2076	55	28	=	=	SYM
ap-2076	56	1	0	0	X
ap-2076	56	2	.	.	PUNCT
ap-2076	57	1	(	(	PUNCT
ap-2076	57	2	1.9	1.9	NUM
ap-2076	57	3	)	)	PUNCT
ap-2076	57	4	then	then	ADV
ap-2076	57	5	eigenfunction	eigenfunction	VERB
ap-2076	57	6	ψ0	ψ0	ADV
ap-2076	57	7	can	can	AUX
ap-2076	57	8	be	be	AUX
ap-2076	57	9	chosen	choose	VERB
ap-2076	57	10	so	so	SCONJ
ap-2076	57	11	that	that	SCONJ
ap-2076	57	12	(	(	PUNCT
ap-2076	57	13	φ0	φ0	PROPN
ap-2076	57	14	,	,	PUNCT
ap-2076	57	15	t	t	PROPN
ap-2076	57	16	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	57	17	)	)	PUNCT
ap-2076	57	18	=	=	SYM
ap-2076	57	19	1	1	NUM
ap-2076	57	20	,	,	PUNCT
ap-2076	57	21	(	(	PUNCT
ap-2076	57	22	φ0	φ0	VERB
ap-2076	57	23	,	,	PUNCT
ap-2076	57	24	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	57	25	)	)	PUNCT
ap-2076	57	26	=	=	SYM
ap-2076	57	27	0	0	NUM
ap-2076	57	28	,	,	PUNCT
ap-2076	57	29	(	(	PUNCT
ap-2076	57	30	1.10	1.10	NUM
ap-2076	57	31	)	)	PUNCT
ap-2076	57	32	ψ0	ψ0	NOUN
ap-2076	57	33	=	=	SYM
ap-2076	57	34	pt	pt	PROPN
ap-2076	57	35	ψ0	ψ0	ADJ
ap-2076	57	36	,	,	PUNCT
ap-2076	57	37	φ0	φ0	PROPN
ap-2076	57	38	=	=	PROPN
ap-2076	57	39	pt	pt	PROPN
ap-2076	57	40	φ0	φ0	PROPN
ap-2076	57	41	.	.	PUNCT
ap-2076	58	1	(	(	PUNCT
ap-2076	58	2	1.11	1.11	NUM
ap-2076	58	3	)	)	PUNCT
ap-2076	58	4	suppose	suppose	VERB
ap-2076	58	5	then	then	ADV
ap-2076	58	6	that	that	SCONJ
ap-2076	58	7	this	this	DET
ap-2076	58	8	eigenfunction	eigenfunction	NOUN
ap-2076	58	9	obeys	obey	VERB
ap-2076	58	10	the	the	DET
ap-2076	58	11	inequality∫	inequality∫	ADJ
ap-2076	58	12	γ+	γ+	PUNCT
ap-2076	58	13	βreψ0	βreψ0	PUNCT
ap-2076	59	1	imψ0	imψ0	PROPN
ap-2076	59	2	dx1	dx1	PROPN
ap-2076	60	1	6=	6=	ADP
ap-2076	60	2	0	0	NUM
ap-2076	60	3	.	.	PUNCT
ap-2076	61	1	(	(	PUNCT
ap-2076	61	2	1.12	1.12	NUM
ap-2076	61	3	)	)	PUNCT
ap-2076	61	4	then	then	ADV
ap-2076	61	5	for	for	ADP
ap-2076	61	6	all	all	DET
ap-2076	61	7	sufficiently	sufficiently	ADV
ap-2076	61	8	small	small	ADJ
ap-2076	61	9	ε	ε	X
ap-2076	61	10	the	the	DET
ap-2076	61	11	operator	operator	NOUN
ap-2076	61	12	hα+εβ	hα+εβ	PROPN
ap-2076	61	13	has	have	VERB
ap-2076	61	14	two	two	NUM
ap-2076	61	15	simple	simple	ADJ
ap-2076	61	16	isolated	isolate	VERB
ap-2076	61	17	eigenvalues	eigenvalue	NOUN
ap-2076	61	18	λ±ε	λ±ε	X
ap-2076	61	19	converging	converge	VERB
ap-2076	61	20	to	to	ADP
ap-2076	61	21	λ0	λ0	NOUN
ap-2076	61	22	as	as	ADP
ap-2076	61	23	ε→	ε→	NUM
ap-2076	61	24	0	0	NUM
ap-2076	61	25	.	.	PUNCT
ap-2076	62	1	these	these	DET
ap-2076	62	2	eigenvalues	eigenvalue	NOUN
ap-2076	62	3	are	be	AUX
ap-2076	62	4	real	real	ADJ
ap-2076	62	5	as	as	ADP
ap-2076	62	6	ε	ε	PROPN
ap-2076	62	7	∫	∫	PROPN
ap-2076	62	8	γ+	γ+	X
ap-2076	62	9	βreψ0	βreψ0	PROPN
ap-2076	63	1	imψ0	imψ0	PROPN
ap-2076	63	2	dx1	dx1	PROPN
ap-2076	63	3	<	<	X
ap-2076	63	4	0	0	PROPN
ap-2076	63	5	(	(	PUNCT
ap-2076	63	6	1.13	1.13	NUM
ap-2076	63	7	)	)	PUNCT
ap-2076	63	8	and	and	CCONJ
ap-2076	63	9	are	be	AUX
ap-2076	63	10	complex	complex	ADJ
ap-2076	63	11	as	as	ADP
ap-2076	63	12	ε	ε	PROPN
ap-2076	63	13	∫	∫	PROPN
ap-2076	63	14	γ+	γ+	X
ap-2076	63	15	βreψ0	βreψ0	PROPN
ap-2076	64	1	imψ0	imψ0	PROPN
ap-2076	64	2	dx1	dx1	PROPN
ap-2076	64	3	>	>	X
ap-2076	64	4	0	0	X
ap-2076	64	5	.	.	PUNCT
ap-2076	65	1	(	(	PUNCT
ap-2076	65	2	1.14	1.14	NUM
ap-2076	65	3	)	)	PUNCT
ap-2076	65	4	eigenvalues	eigenvalue	VERB
ap-2076	65	5	λ±ε	λ±ε	X
ap-2076	65	6	are	be	AUX
ap-2076	65	7	holomorphic	holomorphic	ADJ
ap-2076	65	8	w.r.t	w.r.t	NOUN
ap-2076	65	9	.	.	PUNCT
ap-2076	66	1	ε1/2	ε1/2	VERB
ap-2076	66	2	and	and	CCONJ
ap-2076	66	3	the	the	DET
ap-2076	66	4	first	first	ADJ
ap-2076	66	5	terms	term	NOUN
ap-2076	66	6	of	of	ADP
ap-2076	66	7	their	their	PRON
ap-2076	66	8	taylor	taylor	PROPN
ap-2076	66	9	series	series	PROPN
ap-2076	66	10	read	read	VERB
ap-2076	66	11	as	as	ADP
ap-2076	66	12	λ±ε	λ±ε	PROPN
ap-2076	66	13	=	=	PUNCT
ap-2076	66	14	λ0	λ0	NOUN
ap-2076	66	15	+	+	CCONJ
ap-2076	66	16	ε1/2λ±1/2	ε1/2λ±1/2	NOUN
ap-2076	66	17	+	+	NOUN
ap-2076	66	18	o(ε	o(ε	PROPN
ap-2076	66	19	)	)	PUNCT
ap-2076	66	20	,	,	PUNCT
ap-2076	66	21	λ±1/2	λ±1/2	PROPN
ap-2076	66	22	=	=	NOUN
ap-2076	67	1	±2	±2	NOUN
ap-2076	67	2	(	(	PUNCT
ap-2076	67	3	−	−	PROPN
ap-2076	67	4	∫	∫	PROPN
ap-2076	67	5	γ+	γ+	X
ap-2076	67	6	βreψ0	βreψ0	PROPN
ap-2076	67	7	imψ0	imψ0	PROPN
ap-2076	67	8	dx1	dx1	PROPN
ap-2076	67	9	)	)	PUNCT
ap-2076	67	10	1/2	1/2	NUM
ap-2076	67	11	.	.	PUNCT
ap-2076	68	1	(	(	PUNCT
ap-2076	68	2	1.15	1.15	NUM
ap-2076	68	3	)	)	PUNCT
ap-2076	68	4	let	let	VERB
ap-2076	68	5	us	we	PRON
ap-2076	68	6	discuss	discuss	VERB
ap-2076	68	7	the	the	DET
ap-2076	68	8	results	result	NOUN
ap-2076	68	9	of	of	ADP
ap-2076	68	10	these	these	DET
ap-2076	68	11	theorems	theorem	NOUN
ap-2076	68	12	.	.	PUNCT
ap-2076	69	1	the	the	DET
ap-2076	69	2	typical	typical	ADJ
ap-2076	69	3	situation	situation	NOUN
ap-2076	69	4	of	of	ADP
ap-2076	69	5	the	the	DET
ap-2076	69	6	eigenvalue	eigenvalue	ADJ
ap-2076	69	7	collision	collision	NOUN
ap-2076	69	8	is	be	AUX
ap-2076	69	9	that	that	SCONJ
ap-2076	69	10	two	two	NUM
ap-2076	69	11	simple	simple	ADJ
ap-2076	69	12	eigenvalues	eigenvalue	NOUN
ap-2076	69	13	of	of	ADP
ap-2076	69	14	hα+εβ	hα+εβ	PROPN
ap-2076	69	15	converge	converge	NOUN
ap-2076	69	16	to	to	ADP
ap-2076	69	17	the	the	DET
ap-2076	69	18	same	same	ADJ
ap-2076	69	19	limiting	limiting	NOUN
ap-2076	69	20	eigenvalue	eigenvalue	NOUN
ap-2076	69	21	λ0	λ0	NOUN
ap-2076	69	22	of	of	ADP
ap-2076	69	23	hα	hα	ADP
ap-2076	69	24	as	as	ADV
ap-2076	69	25	ε→	ε→	NUM
ap-2076	69	26	0	0	NUM
ap-2076	69	27	.	.	PUNCT
ap-2076	70	1	then	then	ADV
ap-2076	70	2	it	it	PRON
ap-2076	70	3	is	be	AUX
ap-2076	70	4	a	a	DET
ap-2076	70	5	general	general	ADJ
ap-2076	70	6	fact	fact	NOUN
ap-2076	70	7	from	from	ADP
ap-2076	70	8	the	the	DET
ap-2076	70	9	regular	regular	ADJ
ap-2076	70	10	perturbation	perturbation	NOUN
ap-2076	70	11	theory	theory	NOUN
ap-2076	70	12	that	that	SCONJ
ap-2076	70	13	the	the	DET
ap-2076	70	14	algebraic	algebraic	ADJ
ap-2076	70	15	multiplicity	multiplicity	NOUN
ap-2076	70	16	of	of	ADP
ap-2076	70	17	λ0	λ0	NOUN
ap-2076	70	18	should	should	AUX
ap-2076	70	19	be	be	AUX
ap-2076	70	20	two	two	NUM
ap-2076	70	21	.	.	PUNCT
ap-2076	71	1	the	the	DET
ap-2076	71	2	above	above	ADJ
ap-2076	71	3	theorems	theorem	NOUN
ap-2076	71	4	address	address	VERB
ap-2076	71	5	two	two	NUM
ap-2076	71	6	possible	possible	ADJ
ap-2076	71	7	situations	situation	NOUN
ap-2076	71	8	.	.	PUNCT
ap-2076	72	1	in	in	ADP
ap-2076	72	2	the	the	DET
ap-2076	72	3	first	first	ADJ
ap-2076	72	4	of	of	ADP
ap-2076	72	5	them	they	PRON
ap-2076	72	6	the	the	DET
ap-2076	72	7	geometric	geometric	ADJ
ap-2076	72	8	multiplicity	multiplicity	NOUN
ap-2076	72	9	of	of	ADP
ap-2076	72	10	λ0	λ0	NOUN
ap-2076	72	11	is	be	AUX
ap-2076	72	12	two	two	NUM
ap-2076	72	13	,	,	PUNCT
ap-2076	72	14	i.e.	i.e.	X
ap-2076	72	15	,	,	PUNCT
ap-2076	72	16	there	there	PRON
ap-2076	72	17	exist	exist	VERB
ap-2076	72	18	two	two	NUM
ap-2076	72	19	associated	associate	VERB
ap-2076	72	20	linearly	linearly	ADV
ap-2076	72	21	independent	independent	ADJ
ap-2076	72	22	eigenfunctions	eigenfunction	NOUN
ap-2076	72	23	.	.	PUNCT
ap-2076	73	1	as	as	SCONJ
ap-2076	73	2	we	we	PRON
ap-2076	73	3	see	see	VERB
ap-2076	73	4	from	from	ADP
ap-2076	73	5	theorem	theorem	ADJ
ap-2076	73	6	1.1	1.1	NUM
ap-2076	73	7	,	,	PUNCT
ap-2076	73	8	in	in	ADP
ap-2076	73	9	this	this	DET
ap-2076	73	10	situation	situation	NOUN
ap-2076	73	11	the	the	DET
ap-2076	73	12	perturbed	perturb	VERB
ap-2076	73	13	eigenvalues	eigenvalue	NOUN
ap-2076	73	14	are	be	AUX
ap-2076	73	15	holomorphic	holomorphic	ADJ
ap-2076	73	16	w.r.t	w.r.t	NOUN
ap-2076	73	17	.	.	PUNCT
ap-2076	74	1	ε	ε	PROPN
ap-2076	74	2	and	and	CCONJ
ap-2076	74	3	their	their	PRON
ap-2076	74	4	first	first	ADJ
ap-2076	74	5	terms	term	NOUN
ap-2076	74	6	in	in	ADP
ap-2076	74	7	the	the	DET
ap-2076	74	8	taylor	taylor	PROPN
ap-2076	74	9	series	series	NOUN
ap-2076	74	10	are	be	AUX
ap-2076	74	11	given	give	VERB
ap-2076	74	12	by	by	ADP
ap-2076	74	13	(	(	PUNCT
ap-2076	74	14	1.7	1.7	NUM
ap-2076	74	15	right	right	NOUN
ap-2076	74	16	)	)	PUNCT
ap-2076	74	17	.	.	PUNCT
ap-2076	75	1	the	the	DET
ap-2076	75	2	numbers	number	NOUN
ap-2076	75	3	λ±1	λ±1	NOUN
ap-2076	75	4	are	be	AUX
ap-2076	75	5	some	some	DET
ap-2076	75	6	fixed	fix	VERB
ap-2076	75	7	constants	constant	NOUN
ap-2076	75	8	and	and	CCONJ
ap-2076	75	9	they	they	PRON
ap-2076	75	10	can	can	AUX
ap-2076	75	11	be	be	AUX
ap-2076	75	12	either	either	CCONJ
ap-2076	75	13	complex	complex	ADJ
ap-2076	75	14	or	or	CCONJ
ap-2076	75	15	real	real	ADJ
ap-2076	75	16	.	.	PUNCT
ap-2076	76	1	but	but	CCONJ
ap-2076	76	2	an	an	DET
ap-2076	76	3	important	important	ADJ
ap-2076	76	4	issue	issue	NOUN
ap-2076	76	5	is	be	AUX
ap-2076	76	6	that	that	SCONJ
ap-2076	76	7	here	here	ADV
ap-2076	76	8	when	when	SCONJ
ap-2076	76	9	changing	change	VERB
ap-2076	76	10	the	the	DET
ap-2076	76	11	sign	sign	NOUN
ap-2076	76	12	of	of	ADP
ap-2076	76	13	ε	ε	PROPN
ap-2076	76	14	,	,	PUNCT
ap-2076	76	15	the	the	DET
ap-2076	76	16	eigenvalues	eigenvalue	NOUN
ap-2076	76	17	can	can	AUX
ap-2076	76	18	not	not	PART
ap-2076	76	19	bifurcate	bifurcate	VERB
ap-2076	76	20	from	from	ADP
ap-2076	76	21	real	real	ADJ
ap-2076	76	22	line	line	NOUN
ap-2076	76	23	to	to	ADP
ap-2076	76	24	the	the	DET
ap-2076	76	25	complex	complex	ADJ
ap-2076	76	26	plane	plane	NOUN
ap-2076	76	27	or	or	CCONJ
ap-2076	76	28	vice	vice	NOUN
ap-2076	76	29	versa	versa	ADV
ap-2076	76	30	.	.	PUNCT
ap-2076	77	1	this	this	DET
ap-2076	77	2	fact	fact	NOUN
ap-2076	77	3	is	be	AUX
ap-2076	77	4	implied	imply	VERB
ap-2076	77	5	by	by	ADP
ap-2076	77	6	(	(	PUNCT
ap-2076	77	7	1.7	1.7	NUM
ap-2076	77	8	right	right	NOUN
ap-2076	77	9	)	)	PUNCT
ap-2076	77	10	,	,	PUNCT
ap-2076	77	11	namely	namely	ADV
ap-2076	77	12	,	,	PUNCT
ap-2076	77	13	if	if	SCONJ
ap-2076	77	14	λ±1	λ±1	NOUN
ap-2076	77	15	are	be	AUX
ap-2076	77	16	complex	complex	ADJ
ap-2076	77	17	numbers	number	NOUN
ap-2076	77	18	,	,	PUNCT
ap-2076	77	19	then	then	ADV
ap-2076	77	20	λ±ε	λ±ε	PROPN
ap-2076	77	21	are	be	AUX
ap-2076	77	22	also	also	ADV
ap-2076	77	23	complex	complex	ADJ
ap-2076	77	24	for	for	ADP
ap-2076	77	25	both	both	PRON
ap-2076	77	26	ε	ε	PROPN
ap-2076	77	27	<	<	X
ap-2076	77	28	0	0	PROPN
ap-2076	77	29	and	and	CCONJ
ap-2076	77	30	ε	ε	PROPN
ap-2076	77	31	>	>	X
ap-2076	77	32	0	0	PROPN
ap-2076	77	33	.	.	PUNCT
ap-2076	78	1	thus	thus	ADV
ap-2076	78	2	,	,	PUNCT
ap-2076	78	3	in	in	ADP
ap-2076	78	4	this	this	DET
ap-2076	78	5	case	case	NOUN
ap-2076	78	6	we	we	PRON
ap-2076	78	7	do	do	AUX
ap-2076	78	8	not	not	PART
ap-2076	78	9	face	face	VERB
ap-2076	78	10	the	the	DET
ap-2076	78	11	above	above	ADV
ap-2076	78	12	-	-	PUNCT
ap-2076	78	13	mentioned	mention	VERB
ap-2076	78	14	phenomenon	phenomenon	NOUN
ap-2076	78	15	of	of	ADP
ap-2076	78	16	the	the	DET
ap-2076	78	17	eigenvalue	eigenvalue	PROPN
ap-2076	78	18	collision	collision	NOUN
ap-2076	78	19	discovered	discover	VERB
ap-2076	78	20	numerically	numerically	ADV
ap-2076	78	21	in	in	ADP
ap-2076	78	22	[	[	X
ap-2076	78	23	6	6	NUM
ap-2076	78	24	]	]	PUNCT
ap-2076	78	25	,	,	PUNCT
ap-2076	78	26	[	[	X
ap-2076	78	27	7	7	NUM
ap-2076	78	28	]	]	PUNCT
ap-2076	78	29	.	.	PUNCT
ap-2076	79	1	if	if	SCONJ
ap-2076	79	2	λ±1	λ±1	NOUN
ap-2076	79	3	are	be	AUX
ap-2076	79	4	real	real	ADJ
ap-2076	79	5	,	,	PUNCT
ap-2076	79	6	then	then	ADV
ap-2076	79	7	we	we	PRON
ap-2076	79	8	need	need	VERB
ap-2076	79	9	to	to	PART
ap-2076	79	10	calculate	calculate	VERB
ap-2076	79	11	the	the	DET
ap-2076	79	12	next	next	ADJ
ap-2076	79	13	terms	term	NOUN
ap-2076	79	14	of	of	ADP
ap-2076	79	15	their	their	PRON
ap-2076	79	16	taylor	taylor	PROPN
ap-2076	79	17	series	series	NOUN
ap-2076	79	18	to	to	PART
ap-2076	79	19	see	see	VERB
ap-2076	79	20	whether	whether	SCONJ
ap-2076	79	21	they	they	PRON
ap-2076	79	22	are	be	AUX
ap-2076	79	23	complex	complex	ADJ
ap-2076	79	24	or	or	CCONJ
ap-2076	79	25	real	real	ADJ
ap-2076	79	26	.	.	PUNCT
ap-2076	80	1	once	once	ADV
ap-2076	80	2	all	all	DET
ap-2076	80	3	the	the	DET
ap-2076	80	4	terms	term	NOUN
ap-2076	80	5	in	in	ADP
ap-2076	80	6	the	the	DET
ap-2076	80	7	taylor	taylor	PROPN
ap-2076	80	8	series	series	PROPN
ap-2076	80	9	are	be	AUX
ap-2076	80	10	real	real	ADJ
ap-2076	80	11	,	,	PUNCT
ap-2076	80	12	we	we	PRON
ap-2076	80	13	deal	deal	VERB
ap-2076	80	14	with	with	ADP
ap-2076	80	15	two	two	NUM
ap-2076	80	16	real	real	ADJ
ap-2076	80	17	eigenvalues	eigenvalue	NOUN
ap-2076	80	18	which	which	PRON
ap-2076	80	19	just	just	ADV
ap-2076	80	20	pass	pass	VERB
ap-2076	80	21	one	one	NUM
ap-2076	80	22	through	through	ADP
ap-2076	80	23	the	the	DET
ap-2076	80	24	other	other	ADJ
ap-2076	80	25	staying	stay	VERB
ap-2076	80	26	on	on	ADP
ap-2076	80	27	the	the	DET
ap-2076	80	28	real	real	ADJ
ap-2076	80	29	line	line	NOUN
ap-2076	80	30	.	.	PUNCT
ap-2076	81	1	nevertheless	nevertheless	ADV
ap-2076	81	2	,	,	PUNCT
ap-2076	81	3	in	in	ADP
ap-2076	81	4	view	view	NOUN
ap-2076	81	5	of	of	ADP
ap-2076	81	6	formulae	formulae	NOUN
ap-2076	81	7	(	(	PUNCT
ap-2076	81	8	1.6	1.6	NUM
ap-2076	81	9	)	)	PUNCT
ap-2076	81	10	we	we	PRON
ap-2076	81	11	believe	believe	VERB
ap-2076	81	12	that	that	SCONJ
ap-2076	81	13	choosing	choose	VERB
ap-2076	81	14	appropriate	appropriate	ADJ
ap-2076	81	15	β	β	NOUN
ap-2076	81	16	we	we	PRON
ap-2076	81	17	can	can	AUX
ap-2076	81	18	get	get	VERB
ap-2076	81	19	almost	almost	ADV
ap-2076	81	20	any	any	PRON
ap-2076	81	21	value	value	NOUN
ap-2076	81	22	for	for	ADP
ap-2076	81	23	the	the	DET
ap-2076	81	24	quantity	quantity	NOUN
ap-2076	81	25	in	in	ADP
ap-2076	81	26	(	(	PUNCT
ap-2076	81	27	1.5	1.5	NUM
ap-2076	81	28	)	)	PUNCT
ap-2076	81	29	.	.	PUNCT
ap-2076	82	1	in	in	ADP
ap-2076	82	2	a	a	DET
ap-2076	82	3	particular	particular	ADJ
ap-2076	82	4	interesting	interesting	ADJ
ap-2076	82	5	case	case	NOUN
ap-2076	82	6	β	β	X
ap-2076	82	7	=	=	PUNCT
ap-2076	82	8	α	α	PRON
ap-2076	82	9	the	the	DET
ap-2076	82	10	author	author	NOUN
ap-2076	82	11	does	do	AUX
ap-2076	82	12	not	not	PART
ap-2076	82	13	know	know	VERB
ap-2076	82	14	a	a	DET
ap-2076	82	15	way	way	NOUN
ap-2076	82	16	of	of	ADP
ap-2076	82	17	identifying	identify	VERB
ap-2076	82	18	the	the	DET
ap-2076	82	19	sign	sign	NOUN
ap-2076	82	20	of	of	ADP
ap-2076	82	21	(	(	PUNCT
ap-2076	82	22	b11	b11	PROPN
ap-2076	82	23	−	−	PROPN
ap-2076	82	24	b22)2	b22)2	NOUN
ap-2076	82	25	+	+	NOUN
ap-2076	82	26	4b212	4b212	PRON
ap-2076	82	27	or	or	CCONJ
ap-2076	82	28	proving	prove	VERB
ap-2076	82	29	the	the	DET
ap-2076	82	30	reality	reality	NOUN
ap-2076	82	31	of	of	ADP
ap-2076	82	32	the	the	DET
ap-2076	82	33	eigenvalues	eigenvalues	PROPN
ap-2076	82	34	λ±ε	λ±ε	X
ap-2076	82	35	.	.	PUNCT
ap-2076	83	1	theorem	theorem	VERB
ap-2076	83	2	1.2	1.2	NUM
ap-2076	83	3	treats	treat	NOUN
ap-2076	83	4	the	the	DET
ap-2076	83	5	case	case	NOUN
ap-2076	83	6	when	when	SCONJ
ap-2076	83	7	the	the	DET
ap-2076	83	8	geometric	geometric	ADJ
ap-2076	83	9	multiplicity	multiplicity	NOUN
ap-2076	83	10	of	of	ADP
ap-2076	83	11	λ0	λ0	NOUN
ap-2076	83	12	is	be	AUX
ap-2076	83	13	one	one	NUM
ap-2076	83	14	.	.	PUNCT
ap-2076	84	1	then	then	ADV
ap-2076	84	2	the	the	DET
ap-2076	84	3	taylor	taylor	PROPN
ap-2076	84	4	series	series	PROPN
ap-2076	84	5	for	for	ADP
ap-2076	84	6	the	the	DET
ap-2076	84	7	perturbed	perturb	VERB
ap-2076	84	8	eigenvalues	eigenvalue	NOUN
ap-2076	84	9	are	be	AUX
ap-2076	84	10	completely	completely	ADV
ap-2076	84	11	different	different	ADJ
ap-2076	84	12	from	from	ADP
ap-2076	84	13	theorem	theorem	ADJ
ap-2076	84	14	1.1	1.1	NUM
ap-2076	84	15	and	and	CCONJ
ap-2076	84	16	here	here	ADV
ap-2076	84	17	the	the	DET
ap-2076	84	18	expansions	expansion	NOUN
ap-2076	84	19	are	be	AUX
ap-2076	84	20	made	make	VERB
ap-2076	84	21	w.r.t	w.r.t	NOUN
ap-2076	84	22	.	.	PUNCT
ap-2076	85	1	ε1/2	ε1/2	VERB
ap-2076	85	2	.	.	PUNCT
ap-2076	86	1	and	and	CCONJ
ap-2076	86	2	the	the	DET
ap-2076	86	3	presence	presence	NOUN
ap-2076	86	4	of	of	ADP
ap-2076	86	5	this	this	DET
ap-2076	86	6	power	power	NOUN
ap-2076	86	7	perfectly	perfectly	ADV
ap-2076	86	8	explains	explain	VERB
ap-2076	86	9	the	the	DET
ap-2076	86	10	studied	studied	ADJ
ap-2076	86	11	phenomenon	phenomenon	NOUN
ap-2076	86	12	.	.	PUNCT
ap-2076	87	1	namely	namely	ADV
ap-2076	87	2	,	,	PUNCT
ap-2076	87	3	once	once	SCONJ
ap-2076	87	4	ε	ε	PROPN
ap-2076	87	5	is	be	AUX
ap-2076	87	6	positive	positive	ADJ
ap-2076	87	7	,	,	PUNCT
ap-2076	87	8	the	the	DET
ap-2076	87	9	same	same	ADJ
ap-2076	87	10	is	be	AUX
ap-2076	87	11	true	true	ADJ
ap-2076	87	12	for	for	ADP
ap-2076	87	13	ε1/2	ε1/2	ADJ
ap-2076	87	14	,	,	PUNCT
ap-2076	87	15	while	while	SCONJ
ap-2076	87	16	for	for	ADP
ap-2076	87	17	negative	negative	ADJ
ap-2076	87	18	ε	ε	PROPN
ap-2076	87	19	the	the	DET
ap-2076	87	20	square	square	PROPN
ap-2076	87	21	root	root	PROPN
ap-2076	87	22	ε1/2	ε1/2	NOUN
ap-2076	87	23	is	be	AUX
ap-2076	87	24	pure	pure	ADJ
ap-2076	87	25	imaginary	imaginary	ADJ
ap-2076	87	26	.	.	PUNCT
ap-2076	88	1	this	this	PRON
ap-2076	88	2	is	be	AUX
ap-2076	88	3	exactly	exactly	ADV
ap-2076	88	4	what	what	PRON
ap-2076	88	5	is	be	AUX
ap-2076	88	6	needed	need	VERB
ap-2076	88	7	,	,	PUNCT
ap-2076	88	8	once	once	ADV
ap-2076	88	9	ε	ε	PROPN
ap-2076	88	10	changes	change	VERB
ap-2076	88	11	the	the	DET
ap-2076	88	12	sign	sign	NOUN
ap-2076	88	13	,	,	PUNCT
ap-2076	88	14	real	real	ADJ
ap-2076	88	15	eigenvalues	eigenvalue	NOUN
ap-2076	88	16	become	become	VERB
ap-2076	88	17	complex	complex	ADJ
ap-2076	88	18	and	and	CCONJ
ap-2076	88	19	vice	vice	ADV
ap-2076	88	20	versa	versa	ADV
ap-2076	88	21	.	.	PUNCT
ap-2076	89	1	unfortunately	unfortunately	ADV
ap-2076	89	2	,	,	PUNCT
ap-2076	89	3	we	we	PRON
ap-2076	89	4	can	can	AUX
ap-2076	89	5	not	not	PART
ap-2076	89	6	even	even	ADV
ap-2076	89	7	analytically	analytically	ADV
ap-2076	89	8	prove	prove	VERB
ap-2076	89	9	for	for	ADP
ap-2076	89	10	our	our	PRON
ap-2076	89	11	model	model	NOUN
ap-2076	89	12	the	the	DET
ap-2076	89	13	existence	existence	NOUN
ap-2076	89	14	of	of	ADP
ap-2076	89	15	such	such	ADJ
ap-2076	89	16	eigenvalues	eigenvalue	NOUN
ap-2076	89	17	.	.	PUNCT
ap-2076	90	1	we	we	PRON
ap-2076	90	2	can	can	AUX
ap-2076	90	3	just	just	ADV
ap-2076	90	4	state	state	VERB
ap-2076	90	5	that	that	SCONJ
ap-2076	90	6	once	once	SCONJ
ap-2076	90	7	λ0	λ0	NOUN
ap-2076	90	8	has	have	VERB
ap-2076	90	9	geometric	geometric	ADJ
ap-2076	90	10	multiplicity	multiplicity	NOUN
ap-2076	90	11	one	one	NUM
ap-2076	90	12	and	and	CCONJ
ap-2076	90	13	the	the	DET
ap-2076	90	14	associated	associated	ADJ
ap-2076	90	15	eigenfunction	eigenfunction	NOUN
ap-2076	90	16	ψ0	ψ0	ADV
ap-2076	90	17	satisfies	satisfy	VERB
ap-2076	90	18	the	the	DET
ap-2076	90	19	identity	identity	NOUN
ap-2076	90	20	(	(	PUNCT
ap-2076	90	21	ψ0	ψ0	PROPN
ap-2076	90	22	,	,	PUNCT
ap-2076	90	23	t	t	NOUN
ap-2076	90	24	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	90	25	)	)	PUNCT
ap-2076	90	26	=	=	SYM
ap-2076	91	1	0	0	NUM
ap-2076	91	2	,	,	PUNCT
ap-2076	91	3	then	then	ADV
ap-2076	91	4	equation	equation	NOUN
ap-2076	91	5	(	(	PUNCT
ap-2076	91	6	1.8	1.8	NUM
ap-2076	91	7	)	)	PUNCT
ap-2076	91	8	is	be	AUX
ap-2076	91	9	solvable	solvable	ADJ
ap-2076	91	10	(	(	PUNCT
ap-2076	91	11	see	see	VERB
ap-2076	91	12	lemma	lemma	PROPN
ap-2076	91	13	2.1	2.1	NUM
ap-2076	91	14	)	)	PUNCT
ap-2076	91	15	.	.	PUNCT
ap-2076	92	1	and	and	CCONJ
ap-2076	92	2	numerical	numerical	ADJ
ap-2076	92	3	results	result	NOUN
ap-2076	92	4	in	in	ADP
ap-2076	92	5	[	[	X
ap-2076	92	6	6	6	NUM
ap-2076	92	7	]	]	PUNCT
ap-2076	92	8	,	,	PUNCT
ap-2076	92	9	[	[	X
ap-2076	92	10	7	7	X
ap-2076	92	11	]	]	PUNCT
ap-2076	92	12	show	show	VERB
ap-2076	92	13	that	that	SCONJ
ap-2076	92	14	this	this	PRON
ap-2076	92	15	is	be	AUX
ap-2076	92	16	quite	quite	DET
ap-2076	92	17	a	a	DET
ap-2076	92	18	typical	typical	ADJ
ap-2076	92	19	situation	situation	NOUN
ap-2076	92	20	.	.	PUNCT
ap-2076	93	1	our	our	PRON
ap-2076	93	2	next	next	ADJ
ap-2076	93	3	main	main	ADJ
ap-2076	93	4	result	result	NOUN
ap-2076	93	5	provides	provide	VERB
ap-2076	93	6	another	another	DET
ap-2076	93	7	criterion	criterion	NOUN
ap-2076	93	8	identifying	identify	VERB
ap-2076	93	9	the	the	DET
ap-2076	93	10	solvability	solvability	NOUN
ap-2076	93	11	of	of	ADP
ap-2076	93	12	equation	equation	NOUN
ap-2076	93	13	(	(	PUNCT
ap-2076	93	14	1.8	1.8	NUM
ap-2076	93	15	)	)	PUNCT
ap-2076	93	16	94	94	NUM
ap-2076	93	17	vol	vol	NOUN
ap-2076	93	18	.	.	PUNCT
ap-2076	94	1	54	54	NUM
ap-2076	95	1	no	no	NOUN
ap-2076	95	2	.	.	PUNCT
ap-2076	96	1	2/2014	2/2014	NUM
ap-2076	96	2	eigenvalue	eigenvalue	NOUN
ap-2076	96	3	collision	collision	NOUN
ap-2076	96	4	for	for	ADP
ap-2076	96	5	pt	pt	NOUN
ap-2076	96	6	-	-	ADJ
ap-2076	96	7	symmetric	symmetric	ADJ
ap-2076	96	8	waveguide	waveguide	NOUN
ap-2076	96	9	theorem	theorem	NOUN
ap-2076	96	10	1.3	1.3	NUM
ap-2076	96	11	.	.	PUNCT
ap-2076	97	1	suppose	suppose	VERB
ap-2076	97	2	λ0	λ0	NOUN
ap-2076	97	3	is	be	AUX
ap-2076	97	4	a	a	DET
ap-2076	97	5	simple	simple	ADJ
ap-2076	97	6	eigenvalue	eigenvalue	NOUN
ap-2076	97	7	of	of	ADP
ap-2076	97	8	hα	hα	PROPN
ap-2076	97	9	,	,	PUNCT
ap-2076	97	10	the	the	DET
ap-2076	97	11	associated	associated	ADJ
ap-2076	97	12	eigenfunction	eigenfunction	NOUN
ap-2076	97	13	satisfies	satisfy	VERB
ap-2076	97	14	the	the	DET
ap-2076	97	15	estimate∑	estimate∑	PROPN
ap-2076	97	16	γ∈z2	γ∈z2	NOUN
ap-2076	97	17	+	+	CCONJ
ap-2076	97	18	|γ|62	|γ|62	PROPN
ap-2076	97	19	∣∣∣∂γψ0	∣∣∣∂γψ0	NOUN
ap-2076	97	20	∂xγ	∂xγ	NOUN
ap-2076	97	21	(	(	PUNCT
ap-2076	97	22	x	x	NOUN
ap-2076	97	23	)	)	PUNCT
ap-2076	97	24	∣∣∣	∣∣∣	NOUN
ap-2076	97	25	6	6	NUM
ap-2076	97	26	c	c	NOUN
ap-2076	97	27	1	1	NUM
ap-2076	97	28	+	+	CCONJ
ap-2076	97	29	|x1|3	|x1|3	X
ap-2076	97	30	,	,	PUNCT
ap-2076	97	31	x	x	PUNCT
ap-2076	97	32	∈	∈	PROPN
ap-2076	97	33	ω	ω	PROPN
ap-2076	97	34	.	.	PUNCT
ap-2076	98	1	(	(	PUNCT
ap-2076	98	2	1.16	1.16	NUM
ap-2076	98	3	)	)	PUNCT
ap-2076	98	4	then	then	ADV
ap-2076	98	5	equation	equation	NOUN
ap-2076	98	6	(	(	PUNCT
ap-2076	98	7	1.8	1.8	NUM
ap-2076	98	8	)	)	PUNCT
ap-2076	98	9	is	be	AUX
ap-2076	98	10	solvable	solvable	ADJ
ap-2076	98	11	if	if	SCONJ
ap-2076	98	12	and	and	CCONJ
ap-2076	98	13	only	only	ADV
ap-2076	98	14	if∫	if∫	PROPN
ap-2076	98	15	r2	r2	PROPN
ap-2076	98	16	k(x1	k(x1	PROPN
ap-2076	98	17	,	,	PUNCT
ap-2076	98	18	y1	y1	PROPN
ap-2076	98	19	)	)	PUNCT
ap-2076	98	20	(	(	PUNCT
ap-2076	98	21	α(x1)−	α(x1)−	X
ap-2076	98	22	α(y1	α(y1	NOUN
ap-2076	98	23	)	)	PUNCT
ap-2076	98	24	)	)	PUNCT
ap-2076	99	1	reψ0(x1	reψ0(x1	PROPN
ap-2076	99	2	,	,	PUNCT
ap-2076	99	3	d	d	NOUN
ap-2076	99	4	)	)	PUNCT
ap-2076	99	5	imψ0(y1	imψ0(y1	PROPN
ap-2076	99	6	,	,	PUNCT
ap-2076	99	7	d	d	NOUN
ap-2076	99	8	)	)	PUNCT
ap-2076	99	9	dx1	dx1	PROPN
ap-2076	99	10	dy1	dy1	PROPN
ap-2076	99	11	=	=	SYM
ap-2076	99	12	0	0	NUM
ap-2076	99	13	,	,	PUNCT
ap-2076	99	14	(	(	PUNCT
ap-2076	99	15	1.17	1.17	NUM
ap-2076	99	16	)	)	PUNCT
ap-2076	99	17	where	where	SCONJ
ap-2076	99	18	k(x1	k(x1	NOUN
ap-2076	99	19	,	,	PUNCT
ap-2076	99	20	y1	y1	NOUN
ap-2076	99	21	)	)	PUNCT
ap-2076	99	22	:	:	PUNCT
ap-2076	99	23	=	=	PRON
ap-2076	99	24	{	{	PUNCT
ap-2076	99	25	x1	x1	INTJ
ap-2076	99	26	if	if	SCONJ
ap-2076	99	27	y1	y1	PROPN
ap-2076	99	28	<	<	X
ap-2076	99	29	x1	x1	PROPN
ap-2076	99	30	,	,	PUNCT
ap-2076	99	31	−y1	−y1	PROPN
ap-2076	99	32	if	if	SCONJ
ap-2076	99	33	y1	y1	PROPN
ap-2076	99	34	>	>	X
ap-2076	100	1	x1	x1	PROPN
ap-2076	100	2	.	.	PUNCT
ap-2076	101	1	here	here	ADV
ap-2076	101	2	ψ0	ψ0	ADV
ap-2076	101	3	is	be	AUX
ap-2076	101	4	chosen	choose	VERB
ap-2076	101	5	so	so	SCONJ
ap-2076	101	6	that	that	SCONJ
ap-2076	101	7	it	it	PRON
ap-2076	101	8	satisfies	satisfy	VERB
ap-2076	101	9	the	the	DET
ap-2076	101	10	first	first	ADJ
ap-2076	101	11	identity	identity	NOUN
ap-2076	101	12	in	in	ADP
ap-2076	101	13	(	(	PUNCT
ap-2076	101	14	1.11	1.11	NUM
ap-2076	101	15	)	)	PUNCT
ap-2076	101	16	.	.	PUNCT
ap-2076	102	1	assumption	assumption	NOUN
ap-2076	102	2	(	(	PUNCT
ap-2076	102	3	1.16	1.16	NUM
ap-2076	102	4	)	)	PUNCT
ap-2076	102	5	is	be	AUX
ap-2076	102	6	not	not	PART
ap-2076	102	7	very	very	ADV
ap-2076	102	8	restrictive	restrictive	ADJ
ap-2076	102	9	since	since	SCONJ
ap-2076	102	10	usually	usually	ADV
ap-2076	102	11	eigenfunctions	eigenfunction	NOUN
ap-2076	102	12	associated	associate	VERB
ap-2076	102	13	with	with	ADP
ap-2076	102	14	isolated	isolated	ADJ
ap-2076	102	15	eigenvalues	eigenvalue	NOUN
ap-2076	102	16	of	of	ADP
ap-2076	102	17	elliptic	elliptic	ADJ
ap-2076	102	18	operators	operator	NOUN
ap-2076	102	19	decay	decay	VERB
ap-2076	102	20	exponentially	exponentially	ADV
ap-2076	102	21	at	at	ADP
ap-2076	102	22	infinity	infinity	NOUN
ap-2076	102	23	.	.	PUNCT
ap-2076	103	1	the	the	DET
ap-2076	103	2	main	main	ADJ
ap-2076	103	3	condition	condition	NOUN
ap-2076	103	4	here	here	ADV
ap-2076	103	5	is	be	AUX
ap-2076	103	6	(	(	PUNCT
ap-2076	103	7	1.17	1.17	NUM
ap-2076	103	8	)	)	PUNCT
ap-2076	103	9	.	.	PUNCT
ap-2076	104	1	as	as	SCONJ
ap-2076	104	2	we	we	PRON
ap-2076	104	3	shall	shall	AUX
ap-2076	104	4	show	show	VERB
ap-2076	104	5	later	later	ADV
ap-2076	104	6	in	in	ADP
ap-2076	104	7	lemma	lemma	PROPN
ap-2076	104	8	2.1	2.1	NUM
ap-2076	104	9	,	,	PUNCT
ap-2076	104	10	equation	equation	NOUN
ap-2076	104	11	(	(	PUNCT
ap-2076	104	12	1.8	1.8	NUM
ap-2076	104	13	)	)	PUNCT
ap-2076	104	14	is	be	AUX
ap-2076	104	15	solvable	solvable	ADJ
ap-2076	104	16	if	if	SCONJ
ap-2076	104	17	and	and	CCONJ
ap-2076	104	18	only	only	ADV
ap-2076	104	19	if	if	SCONJ
ap-2076	104	20	(	(	PUNCT
ap-2076	104	21	ψ0	ψ0	PROPN
ap-2076	104	22	,	,	PUNCT
ap-2076	104	23	t	t	NOUN
ap-2076	104	24	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	104	25	)	)	PUNCT
ap-2076	104	26	=	=	SYM
ap-2076	105	1	0	0	X
ap-2076	105	2	.	.	PUNCT
ap-2076	106	1	and	and	CCONJ
ap-2076	106	2	we	we	PRON
ap-2076	106	3	rewrite	rewrite	VERB
ap-2076	106	4	this	this	DET
ap-2076	106	5	identity	identity	NOUN
ap-2076	106	6	to	to	ADP
ap-2076	106	7	(	(	PUNCT
ap-2076	106	8	1.17	1.17	NUM
ap-2076	106	9	)	)	PUNCT
ap-2076	106	10	by	by	ADP
ap-2076	106	11	calculating	calculate	VERB
ap-2076	106	12	(	(	PUNCT
ap-2076	106	13	ψ0	ψ0	PROPN
ap-2076	106	14	,	,	PUNCT
ap-2076	106	15	t	t	NOUN
ap-2076	106	16	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	106	17	)	)	PUNCT
ap-2076	106	18	.	.	PUNCT
ap-2076	107	1	the	the	DET
ap-2076	107	2	left	left	ADJ
ap-2076	107	3	hand	hand	NOUN
ap-2076	107	4	side	side	NOUN
ap-2076	107	5	in	in	ADP
ap-2076	107	6	(	(	PUNCT
ap-2076	107	7	1.17	1.17	NUM
ap-2076	107	8	)	)	PUNCT
ap-2076	107	9	is	be	AUX
ap-2076	107	10	simpler	simple	ADJ
ap-2076	107	11	in	in	ADP
ap-2076	107	12	the	the	DET
ap-2076	107	13	sense	sense	NOUN
ap-2076	107	14	that	that	SCONJ
ap-2076	107	15	it	it	PRON
ap-2076	107	16	involves	involve	VERB
ap-2076	107	17	only	only	ADV
ap-2076	107	18	boundary	boundary	ADJ
ap-2076	107	19	integrals	integral	NOUN
ap-2076	107	20	while	while	SCONJ
ap-2076	107	21	(	(	PUNCT
ap-2076	107	22	ψ0	ψ0	PROPN
ap-2076	107	23	,	,	PUNCT
ap-2076	107	24	t	t	PROPN
ap-2076	107	25	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	107	26	)	)	PUNCT
ap-2076	107	27	is	be	AUX
ap-2076	107	28	in	in	ADP
ap-2076	107	29	fact	fact	NOUN
ap-2076	107	30	the	the	DET
ap-2076	107	31	integral	integral	ADJ
ap-2076	107	32	over	over	ADP
ap-2076	107	33	the	the	DET
ap-2076	107	34	whole	whole	ADJ
ap-2076	107	35	strip	strip	PROPN
ap-2076	107	36	ω	ω	PROPN
ap-2076	107	37	.	.	PROPN
ap-2076	108	1	2	2	NUM
ap-2076	108	2	.	.	X
ap-2076	108	3	proofs	proof	NOUN
ap-2076	108	4	of	of	ADP
ap-2076	108	5	main	main	ADJ
ap-2076	108	6	results	result	NOUN
ap-2076	108	7	in	in	ADP
ap-2076	108	8	l2(ω	l2(ω	NOUN
ap-2076	108	9	)	)	PUNCT
ap-2076	108	10	we	we	PRON
ap-2076	108	11	introduce	introduce	VERB
ap-2076	108	12	the	the	DET
ap-2076	108	13	unitary	unitary	ADJ
ap-2076	108	14	operator	operator	NOUN
ap-2076	108	15	(	(	PUNCT
ap-2076	108	16	uεβf)(x	uεβf)(x	NOUN
ap-2076	108	17	)	)	PUNCT
ap-2076	108	18	:	:	PUNCT
ap-2076	108	19	=	=	PUNCT
ap-2076	108	20	e−iεβ(x1)x2f(x	e−iεβ(x1)x2f(x	PROPN
ap-2076	108	21	)	)	PUNCT
ap-2076	108	22	.	.	PUNCT
ap-2076	109	1	then	then	ADV
ap-2076	109	2	it	it	PRON
ap-2076	109	3	is	be	AUX
ap-2076	109	4	easy	easy	ADJ
ap-2076	109	5	to	to	PART
ap-2076	109	6	see	see	VERB
ap-2076	109	7	that	that	SCONJ
ap-2076	109	8	the	the	DET
ap-2076	109	9	spectra	spectra	NOUN
ap-2076	109	10	of	of	ADP
ap-2076	109	11	hα+εβ	hα+εβ	PROPN
ap-2076	109	12	and	and	CCONJ
ap-2076	109	13	u−1	u−1	PROPN
ap-2076	109	14	εβ	εβ	PROPN
ap-2076	109	15	hα+εβuεβ	hα+εβuεβ	VERB
ap-2076	109	16	coincide	coincide	NOUN
ap-2076	109	17	and	and	CCONJ
ap-2076	109	18	u−1	u−1	PROPN
ap-2076	109	19	εβ	εβ	PROPN
ap-2076	109	20	hα+εβuεβ	hα+εβuεβ	VERB
ap-2076	110	1	=	=	PUNCT
ap-2076	110	2	hα	hα	ADP
ap-2076	110	3	−	−	PROPN
ap-2076	110	4	εlε	εlε	NOUN
ap-2076	110	5	,	,	PUNCT
ap-2076	110	6	(	(	PUNCT
ap-2076	110	7	2.1	2.1	NUM
ap-2076	110	8	)	)	PUNCT
ap-2076	110	9	lε	lε	ADP
ap-2076	110	10	:	:	PUNCT
ap-2076	110	11	=	=	SYM
ap-2076	110	12	−2iβ′x2	−2iβ′x2	SYM
ap-2076	110	13	∂	∂	NUM
ap-2076	111	1	∂x1	∂x1	NOUN
ap-2076	111	2	−	−	NUM
ap-2076	111	3	2iβ	2iβ	NOUN
ap-2076	111	4	∂	∂	NUM
ap-2076	111	5	∂x2	∂x2	NOUN
ap-2076	111	6	−	−	NOUN
ap-2076	111	7	εβ2	εβ2	NOUN
ap-2076	111	8	−	−	NOUN
ap-2076	111	9	ε(β′)2x2	ε(β′)2x2	NOUN
ap-2076	111	10	−	−	PROPN
ap-2076	111	11	iβ′′x2	iβ′′x2	ADJ
ap-2076	111	12	.	.	PUNCT
ap-2076	112	1	(	(	PUNCT
ap-2076	112	2	2.2	2.2	NUM
ap-2076	112	3	)	)	PUNCT
ap-2076	112	4	in	in	ADP
ap-2076	112	5	the	the	DET
ap-2076	112	6	proofs	proof	NOUN
ap-2076	112	7	of	of	ADP
ap-2076	112	8	the	the	DET
ap-2076	112	9	main	main	ADJ
ap-2076	112	10	results	result	NOUN
ap-2076	112	11	we	we	PRON
ap-2076	112	12	shall	shall	AUX
ap-2076	112	13	make	make	VERB
ap-2076	112	14	use	use	NOUN
ap-2076	112	15	of	of	ADP
ap-2076	112	16	several	several	ADJ
ap-2076	112	17	auxiliary	auxiliary	ADJ
ap-2076	112	18	lemmata	lemmata	NOUN
ap-2076	112	19	.	.	PUNCT
ap-2076	113	1	lemma	lemma	PROPN
ap-2076	113	2	2.1	2.1	NUM
ap-2076	113	3	.	.	PUNCT
ap-2076	114	1	under	under	ADP
ap-2076	114	2	the	the	DET
ap-2076	114	3	hypothesis	hypothesis	NOUN
ap-2076	114	4	of	of	ADP
ap-2076	114	5	theorem	theorem	ADJ
ap-2076	114	6	1.2	1.2	NUM
ap-2076	114	7	the	the	DET
ap-2076	114	8	equation	equation	NOUN
ap-2076	114	9	(	(	PUNCT
ap-2076	114	10	hα	hα	ADP
ap-2076	114	11	−	−	PROPN
ap-2076	114	12	λ0)u	λ0)u	PROPN
ap-2076	115	1	=	=	SYM
ap-2076	115	2	f	f	PROPN
ap-2076	115	3	(	(	PUNCT
ap-2076	115	4	2.3	2.3	NUM
ap-2076	115	5	)	)	PUNCT
ap-2076	115	6	is	be	AUX
ap-2076	115	7	solvable	solvable	ADJ
ap-2076	115	8	if	if	SCONJ
ap-2076	115	9	and	and	CCONJ
ap-2076	115	10	only	only	ADV
ap-2076	115	11	if	if	SCONJ
ap-2076	115	12	(	(	PUNCT
ap-2076	115	13	f	f	X
ap-2076	115	14	,	,	PUNCT
ap-2076	115	15	t	t	PROPN
ap-2076	115	16	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	115	17	)	)	PUNCT
ap-2076	115	18	=	=	SYM
ap-2076	116	1	0	0	X
ap-2076	116	2	.	.	PUNCT
ap-2076	117	1	(	(	PUNCT
ap-2076	117	2	2.4	2.4	NUM
ap-2076	117	3	)	)	PUNCT
ap-2076	117	4	under	under	ADP
ap-2076	117	5	the	the	DET
ap-2076	117	6	hypothesis	hypothesis	NOUN
ap-2076	117	7	of	of	ADP
ap-2076	117	8	theorem	theorem	ADJ
ap-2076	117	9	1.1	1.1	NUM
ap-2076	117	10	equation	equation	NOUN
ap-2076	117	11	(	(	PUNCT
ap-2076	117	12	2.3	2.3	NUM
ap-2076	117	13	)	)	PUNCT
ap-2076	117	14	is	be	AUX
ap-2076	117	15	solvable	solvable	ADJ
ap-2076	117	16	if	if	SCONJ
ap-2076	117	17	and	and	CCONJ
ap-2076	117	18	only	only	ADV
ap-2076	117	19	if	if	SCONJ
ap-2076	117	20	(	(	PUNCT
ap-2076	117	21	f	f	X
ap-2076	117	22	,	,	PUNCT
ap-2076	117	23	t	t	PROPN
ap-2076	117	24	ψ±0	ψ±0	PUNCT
ap-2076	117	25	)	)	PUNCT
ap-2076	118	1	l2(ω	l2(ω	X
ap-2076	118	2	)	)	PUNCT
ap-2076	118	3	=	=	SYM
ap-2076	118	4	0	0	X
ap-2076	118	5	.	.	PUNCT
ap-2076	118	6	(	(	PUNCT
ap-2076	118	7	2.5	2.5	NUM
ap-2076	118	8	)	)	PUNCT
ap-2076	118	9	proof	proof	NOUN
ap-2076	118	10	.	.	PUNCT
ap-2076	119	1	by	by	ADP
ap-2076	119	2	(	(	PUNCT
ap-2076	119	3	1.3	1.3	NUM
ap-2076	119	4	)	)	PUNCT
ap-2076	119	5	we	we	PRON
ap-2076	119	6	see	see	VERB
ap-2076	119	7	that	that	SCONJ
ap-2076	119	8	under	under	ADP
ap-2076	119	9	the	the	DET
ap-2076	119	10	hypotheses	hypothesis	NOUN
ap-2076	119	11	of	of	ADP
ap-2076	119	12	both	both	DET
ap-2076	119	13	theorems	theorem	NOUN
ap-2076	119	14	1.1	1.1	NUM
ap-2076	119	15	and	and	CCONJ
ap-2076	119	16	1.2	1.2	NUM
ap-2076	119	17	,	,	PUNCT
ap-2076	119	18	λ0	λ0	NOUN
ap-2076	119	19	is	be	AUX
ap-2076	119	20	an	an	DET
ap-2076	119	21	eigenvalue	eigenvalue	NOUN
ap-2076	119	22	of	of	ADP
ap-2076	119	23	h∗α	h∗α	PROPN
ap-2076	119	24	with	with	ADP
ap-2076	119	25	the	the	DET
ap-2076	119	26	associated	associated	ADJ
ap-2076	119	27	eigenfunction(s	eigenfunction(s	PROPN
ap-2076	119	28	)	)	PUNCT
ap-2076	119	29	t	t	PROPN
ap-2076	119	30	ψ0	ψ0	ADV
ap-2076	119	31	or	or	CCONJ
ap-2076	119	32	t	t	NOUN
ap-2076	119	33	ψ±0	ψ±0	PUNCT
ap-2076	119	34	.	.	PUNCT
ap-2076	120	1	then	then	ADV
ap-2076	120	2	the	the	DET
ap-2076	120	3	lemma	lemma	PROPN
ap-2076	120	4	follows	follow	VERB
ap-2076	120	5	from	from	ADP
ap-2076	120	6	[	[	X
ap-2076	120	7	8	8	NUM
ap-2076	120	8	,	,	PUNCT
ap-2076	120	9	ch	ch	NOUN
ap-2076	120	10	.	.	PUNCT
ap-2076	120	11	iii	iii	PROPN
ap-2076	120	12	,	,	PUNCT
ap-2076	120	13	sec	sec	PROPN
ap-2076	120	14	.	.	PROPN
ap-2076	120	15	6.6	6.6	NUM
ap-2076	120	16	,	,	PUNCT
ap-2076	120	17	rem	rem	X
ap-2076	120	18	.	.	NOUN
ap-2076	120	19	6.23	6.23	NUM
ap-2076	120	20	]	]	PUNCT
ap-2076	120	21	.	.	PUNCT
ap-2076	121	1	lemma	lemma	PROPN
ap-2076	121	2	2.2	2.2	NUM
ap-2076	121	3	.	.	PUNCT
ap-2076	121	4	suppose	suppose	VERB
ap-2076	121	5	the	the	DET
ap-2076	121	6	hypothesis	hypothesis	NOUN
ap-2076	121	7	of	of	ADP
ap-2076	121	8	theorem	theorem	NOUN
ap-2076	121	9	1.2	1.2	NUM
ap-2076	121	10	.	.	PUNCT
ap-2076	122	1	then	then	ADV
ap-2076	122	2	eigenfunction	eigenfunction	VERB
ap-2076	122	3	ψ0	ψ0	ADV
ap-2076	122	4	can	can	AUX
ap-2076	122	5	be	be	AUX
ap-2076	122	6	chosen	choose	VERB
ap-2076	122	7	so	so	SCONJ
ap-2076	122	8	that	that	SCONJ
ap-2076	122	9	relations	relation	NOUN
ap-2076	122	10	(	(	PUNCT
ap-2076	122	11	1.10	1.10	NUM
ap-2076	122	12	)	)	PUNCT
ap-2076	122	13	,	,	PUNCT
ap-2076	122	14	(	(	PUNCT
ap-2076	122	15	1.11	1.11	NUM
ap-2076	122	16	)	)	PUNCT
ap-2076	122	17	,	,	PUNCT
ap-2076	122	18	and	and	CCONJ
ap-2076	122	19	(	(	PUNCT
ap-2076	122	20	ψ0	ψ0	PROPN
ap-2076	122	21	,	,	PUNCT
ap-2076	122	22	t	t	NOUN
ap-2076	122	23	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	122	24	)	)	PUNCT
ap-2076	122	25	=	=	SYM
ap-2076	122	26	0	0	NUM
ap-2076	122	27	(	(	PUNCT
ap-2076	122	28	2.6	2.6	NUM
ap-2076	122	29	)	)	PUNCT
ap-2076	122	30	hold	hold	VERB
ap-2076	122	31	true	true	ADJ
ap-2076	122	32	.	.	PUNCT
ap-2076	123	1	the	the	DET
ap-2076	123	2	functions	function	NOUN
ap-2076	123	3	reψ0	reψ0	PROPN
ap-2076	123	4	and	and	CCONJ
ap-2076	123	5	reφ0	reφ0	ADJ
ap-2076	123	6	are	be	AUX
ap-2076	123	7	even	even	ADV
ap-2076	123	8	w.r.t	w.r.t	ADJ
ap-2076	123	9	.	.	PUNCT
ap-2076	124	1	x2	x2	PROPN
ap-2076	124	2	and	and	CCONJ
ap-2076	124	3	imψ0	imψ0	PROPN
ap-2076	124	4	and	and	CCONJ
ap-2076	124	5	imφ0	imφ0	PROPN
ap-2076	124	6	are	be	AUX
ap-2076	124	7	odd	odd	ADJ
ap-2076	124	8	w.r.t	w.r.t	NOUN
ap-2076	124	9	.	.	PUNCT
ap-2076	125	1	x2	x2	INTJ
ap-2076	125	2	.	.	PUNCT
ap-2076	126	1	proof	proof	NOUN
ap-2076	126	2	.	.	PUNCT
ap-2076	127	1	identity	identity	NOUN
ap-2076	127	2	(	(	PUNCT
ap-2076	127	3	2.6	2.6	NUM
ap-2076	127	4	)	)	PUNCT
ap-2076	127	5	follows	follow	VERB
ap-2076	127	6	directly	directly	ADV
ap-2076	127	7	from	from	ADP
ap-2076	127	8	(	(	PUNCT
ap-2076	127	9	2.4	2.4	NUM
ap-2076	127	10	)	)	PUNCT
ap-2076	127	11	applied	apply	VERB
ap-2076	127	12	to	to	ADP
ap-2076	127	13	equation	equation	NOUN
ap-2076	127	14	(	(	PUNCT
ap-2076	127	15	1.8	1.8	NUM
ap-2076	127	16	)	)	PUNCT
ap-2076	127	17	.	.	PUNCT
ap-2076	128	1	since	since	SCONJ
ap-2076	128	2	λ0	λ0	NOUN
ap-2076	128	3	is	be	AUX
ap-2076	128	4	a	a	DET
ap-2076	128	5	real	real	ADJ
ap-2076	128	6	simple	simple	ADJ
ap-2076	128	7	eigenvalue	eigenvalue	NOUN
ap-2076	128	8	and	and	CCONJ
ap-2076	128	9	equation	equation	NOUN
ap-2076	128	10	(	(	PUNCT
ap-2076	128	11	1.8	1.8	NUM
ap-2076	128	12	)	)	PUNCT
ap-2076	128	13	has	have	VERB
ap-2076	128	14	a	a	DET
ap-2076	128	15	unique	unique	ADJ
ap-2076	128	16	solution	solution	NOUN
ap-2076	128	17	satisfying	satisfy	VERB
ap-2076	128	18	the	the	DET
ap-2076	128	19	second	second	ADJ
ap-2076	128	20	identity	identity	NOUN
ap-2076	128	21	in	in	ADP
ap-2076	128	22	(	(	PUNCT
ap-2076	128	23	1.10	1.10	NUM
ap-2076	128	24	)	)	PUNCT
ap-2076	128	25	,	,	PUNCT
ap-2076	128	26	by	by	ADP
ap-2076	128	27	(	(	PUNCT
ap-2076	128	28	1.2	1.2	NUM
ap-2076	128	29	)	)	PUNCT
ap-2076	128	30	we	we	PRON
ap-2076	128	31	have	have	VERB
ap-2076	128	32	(	(	PUNCT
ap-2076	128	33	1.11	1.11	NUM
ap-2076	128	34	)	)	PUNCT
ap-2076	128	35	and	and	CCONJ
ap-2076	128	36	thus	thus	ADV
ap-2076	128	37	reψ0	reψ0	NOUN
ap-2076	128	38	and	and	CCONJ
ap-2076	128	39	reφ0	reφ0	ADJ
ap-2076	128	40	are	be	AUX
ap-2076	128	41	even	even	ADV
ap-2076	128	42	,	,	PUNCT
ap-2076	128	43	while	while	SCONJ
ap-2076	128	44	imψ0	imψ0	PROPN
ap-2076	128	45	and	and	CCONJ
ap-2076	128	46	imφ0	imφ0	PROPN
ap-2076	128	47	are	be	AUX
ap-2076	128	48	odd	odd	ADJ
ap-2076	128	49	w.r.t	w.r.t	NOUN
ap-2076	128	50	.	.	PUNCT
ap-2076	129	1	x2	x2	INTJ
ap-2076	129	2	.	.	PUNCT
ap-2076	130	1	employing	employ	VERB
ap-2076	130	2	this	this	DET
ap-2076	130	3	fact	fact	NOUN
ap-2076	130	4	and	and	CCONJ
ap-2076	130	5	(	(	PUNCT
ap-2076	130	6	1.8	1.8	NUM
ap-2076	130	7	)	)	PUNCT
ap-2076	130	8	,	,	PUNCT
ap-2076	130	9	we	we	PRON
ap-2076	130	10	obtain	obtain	VERB
ap-2076	130	11	(	(	PUNCT
ap-2076	130	12	φ0	φ0	ADJ
ap-2076	130	13	,	,	PUNCT
ap-2076	130	14	t	t	PROPN
ap-2076	130	15	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	130	16	)	)	PUNCT
ap-2076	130	17	=	=	PUNCT
ap-2076	131	1	−	−	PROPN
ap-2076	131	2	∫	∫	PROPN
ap-2076	131	3	ω	ω	PROPN
ap-2076	131	4	φ0(∆	φ0(∆	PROPN
ap-2076	131	5	+	+	CCONJ
ap-2076	131	6	λ0)φ0	λ0)φ0	PROPN
ap-2076	131	7	dx	dx	PROPN
ap-2076	132	1	=	=	PROPN
ap-2076	133	1	i	i	PRON
ap-2076	133	2	∫	∫	PROPN
ap-2076	133	3	γ+	γ+	X
ap-2076	133	4	αφ2	αφ2	PROPN
ap-2076	133	5	0	0	NUM
ap-2076	134	1	dx1	dx1	PROPN
ap-2076	135	1	−	−	PROPN
ap-2076	136	1	i	i	PRON
ap-2076	136	2	∫	∫	PROPN
ap-2076	136	3	γ−	γ−	NUM
ap-2076	136	4	αφ2	αφ2	PROPN
ap-2076	136	5	0	0	NUM
ap-2076	137	1	dx1	dx1	PROPN
ap-2076	137	2	+	+	CCONJ
ap-2076	137	3	∫	∫	PROPN
ap-2076	137	4	ω	ω	PROPN
ap-2076	137	5	(	(	PUNCT
ap-2076	137	6	(	(	PUNCT
ap-2076	137	7	∂φ0	∂φ0	PROPN
ap-2076	137	8	∂x1	∂x1	NOUN
ap-2076	137	9	)	)	PUNCT
ap-2076	137	10	2	2	NUM
ap-2076	137	11	+	+	CCONJ
ap-2076	137	12	(	(	PUNCT
ap-2076	137	13	∂φ0	∂φ0	PROPN
ap-2076	137	14	∂x2	∂x2	NOUN
ap-2076	137	15	)	)	PUNCT
ap-2076	137	16	2	2	NUM
ap-2076	137	17	−	−	NOUN
ap-2076	137	18	λ0φ	λ0φ	NOUN
ap-2076	137	19	2	2	NUM
ap-2076	137	20	0	0	NUM
ap-2076	137	21	)	)	PUNCT
ap-2076	137	22	dx	dx	PROPN
ap-2076	138	1	=	=	SYM
ap-2076	138	2	−4	−4	PROPN
ap-2076	138	3	∫	∫	NOUN
ap-2076	138	4	γ+	γ+	PUNCT
ap-2076	138	5	αreφ0	αreφ0	ADV
ap-2076	138	6	imφ0	imφ0	PROPN
ap-2076	138	7	dx1	dx1	PROPN
ap-2076	139	1	+	+	CCONJ
ap-2076	139	2	∫	∫	PROPN
ap-2076	139	3	ω	ω	INTJ
ap-2076	139	4	(	(	PUNCT
ap-2076	139	5	|∇reφ0|2	|∇reφ0|2	NOUN
ap-2076	139	6	−	−	PROPN
ap-2076	139	7	|∇	|∇	PROPN
ap-2076	139	8	imφ0|2	imφ0|2	PROPN
ap-2076	139	9	)	)	PUNCT
ap-2076	140	1	dx−	dx−	PRON
ap-2076	140	2	λ0	λ0	NOUN
ap-2076	140	3	∫	∫	PROPN
ap-2076	140	4	ω	ω	PROPN
ap-2076	140	5	(	(	PUNCT
ap-2076	140	6	|reφ0|2	|reφ0|2	NOUN
ap-2076	140	7	−	−	NOUN
ap-2076	140	8	|	|	ADV
ap-2076	140	9	imφ0|2	imφ0|2	ADJ
ap-2076	140	10	)	)	PUNCT
ap-2076	140	11	dx	dx	PROPN
ap-2076	140	12	∈	∈	PROPN
ap-2076	140	13	r.	r.	PROPN
ap-2076	140	14	(	(	PUNCT
ap-2076	140	15	2.7	2.7	NUM
ap-2076	140	16	)	)	PUNCT
ap-2076	140	17	hence	hence	ADV
ap-2076	140	18	,	,	PUNCT
ap-2076	140	19	multiplying	multiply	VERB
ap-2076	140	20	function	function	NOUN
ap-2076	140	21	ψ0	ψ0	ADV
ap-2076	140	22	and	and	CCONJ
ap-2076	140	23	φ0	φ0	VERB
ap-2076	140	24	by	by	ADP
ap-2076	140	25	an	an	DET
ap-2076	140	26	appropriate	appropriate	ADJ
ap-2076	140	27	constant	constant	ADJ
ap-2076	140	28	,	,	PUNCT
ap-2076	140	29	we	we	PRON
ap-2076	140	30	can	can	AUX
ap-2076	140	31	easily	easily	ADV
ap-2076	140	32	get	get	VERB
ap-2076	140	33	the	the	DET
ap-2076	140	34	first	first	ADJ
ap-2076	140	35	identity	identity	NOUN
ap-2076	140	36	in	in	ADP
ap-2076	140	37	(	(	PUNCT
ap-2076	140	38	1.10	1.10	NUM
ap-2076	140	39	)	)	PUNCT
ap-2076	140	40	not	not	PART
ap-2076	140	41	spoiling	spoil	VERB
ap-2076	140	42	other	other	ADJ
ap-2076	140	43	established	establish	VERB
ap-2076	140	44	properties	property	NOUN
ap-2076	140	45	of	of	ADP
ap-2076	140	46	φ0	φ0	PROPN
ap-2076	140	47	and	and	CCONJ
ap-2076	140	48	ψ0	ψ0	PROPN
ap-2076	140	49	.	.	PUNCT
ap-2076	141	1	95	95	NUM
ap-2076	141	2	denis	denis	PROPN
ap-2076	141	3	borisov	borisov	PROPN
ap-2076	141	4	acta	acta	PROPN
ap-2076	141	5	polytechnica	polytechnica	PROPN
ap-2076	141	6	lemma	lemma	PROPN
ap-2076	141	7	2.3	2.3	NUM
ap-2076	141	8	.	.	PUNCT
ap-2076	142	1	suppose	suppose	VERB
ap-2076	142	2	the	the	DET
ap-2076	142	3	hypothesis	hypothesis	NOUN
ap-2076	142	4	of	of	ADP
ap-2076	142	5	theorem	theorem	NOUN
ap-2076	142	6	1.2	1.2	NUM
ap-2076	142	7	.	.	PUNCT
ap-2076	143	1	then	then	ADV
ap-2076	143	2	for	for	ADP
ap-2076	143	3	λ	λ	PROPN
ap-2076	143	4	close	close	ADJ
ap-2076	143	5	to	to	PART
ap-2076	143	6	λ0	λ0	VERB
ap-2076	143	7	the	the	DET
ap-2076	143	8	resolvent	resolvent	NOUN
ap-2076	143	9	(	(	PUNCT
ap-2076	143	10	hα	hα	ADP
ap-2076	143	11	−	−	PROPN
ap-2076	143	12	λ)−1	λ)−1	NOUN
ap-2076	143	13	can	can	AUX
ap-2076	143	14	be	be	AUX
ap-2076	143	15	represented	represent	VERB
ap-2076	143	16	as	as	ADP
ap-2076	143	17	(	(	PUNCT
ap-2076	143	18	hα	hα	ADP
ap-2076	143	19	−	−	PROPN
ap-2076	143	20	λ)−1	λ)−1	NOUN
ap-2076	143	21	=	=	X
ap-2076	143	22	p−2	p−2	PROPN
ap-2076	143	23	(	(	PUNCT
ap-2076	143	24	λ−	λ−	PROPN
ap-2076	143	25	λ0)2	λ0)2	X
ap-2076	143	26	+	+	NUM
ap-2076	143	27	p−1	p−1	PROPN
ap-2076	143	28	λ−	λ−	PROPN
ap-2076	143	29	λ0	λ0	NOUN
ap-2076	143	30	+	+	NOUN
ap-2076	143	31	rα(λ	rα(λ	NOUN
ap-2076	143	32	)	)	PUNCT
ap-2076	143	33	,	,	PUNCT
ap-2076	143	34	(	(	PUNCT
ap-2076	143	35	2.8	2.8	NUM
ap-2076	143	36	)	)	PUNCT
ap-2076	144	1	p−2	p−2	NOUN
ap-2076	144	2	=	=	SYM
ap-2076	144	3	ψ0`2	ψ0`2	PROPN
ap-2076	144	4	,	,	PUNCT
ap-2076	144	5	p−1	p−1	NOUN
ap-2076	144	6	=	=	SYM
ap-2076	144	7	φ0`2	φ0`2	PROPN
ap-2076	144	8	+	+	NUM
ap-2076	144	9	ψ0`1	ψ0`1	PROPN
ap-2076	144	10	,	,	PUNCT
ap-2076	144	11	`	`	PUNCT
ap-2076	144	12	2f	2f	NUM
ap-2076	144	13	:	:	PUNCT
ap-2076	144	14	=	=	SYM
ap-2076	144	15	−(f	−(f	PROPN
ap-2076	144	16	,	,	PUNCT
ap-2076	144	17	t	t	PROPN
ap-2076	144	18	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	144	19	)	)	PUNCT
ap-2076	144	20	,	,	PUNCT
ap-2076	144	21	`	`	PUNCT
ap-2076	144	22	1f	1f	NUM
ap-2076	144	23	:	:	PUNCT
ap-2076	144	24	=	=	SYM
ap-2076	145	1	−	−	PROPN
ap-2076	145	2	(	(	PUNCT
ap-2076	145	3	f	f	X
ap-2076	145	4	,	,	PUNCT
ap-2076	145	5	t	t	PROPN
ap-2076	145	6	(	(	PUNCT
ap-2076	145	7	φ0	φ0	PROPN
ap-2076	145	8	−	−	PROPN
ap-2076	145	9	ψ0	ψ0	PROPN
ap-2076	145	10	)	)	PUNCT
ap-2076	145	11	)	)	PUNCT
ap-2076	146	1	l2(ω	l2(ω	ADJ
ap-2076	146	2	)	)	PUNCT
ap-2076	146	3	,	,	PUNCT
ap-2076	146	4	(	(	PUNCT
ap-2076	146	5	2.9	2.9	NUM
ap-2076	146	6	)	)	PUNCT
ap-2076	146	7	where	where	SCONJ
ap-2076	146	8	rα(λ	rα(λ	NOUN
ap-2076	146	9	)	)	PUNCT
ap-2076	146	10	is	be	AUX
ap-2076	146	11	the	the	DET
ap-2076	146	12	reduced	reduce	VERB
ap-2076	146	13	resolvent	resolvent	NOUN
ap-2076	146	14	which	which	PRON
ap-2076	146	15	is	be	AUX
ap-2076	146	16	a	a	DET
ap-2076	146	17	bounded	bounded	ADJ
ap-2076	146	18	and	and	CCONJ
ap-2076	146	19	holomorphic	holomorphic	ADJ
ap-2076	146	20	in	in	ADP
ap-2076	146	21	the	the	DET
ap-2076	146	22	λ	λ	NOUN
ap-2076	146	23	operator	operator	NOUN
ap-2076	146	24	.	.	PUNCT
ap-2076	147	1	proof	proof	NOUN
ap-2076	147	2	.	.	PUNCT
ap-2076	148	1	we	we	PRON
ap-2076	148	2	know	know	VERB
ap-2076	148	3	by	by	ADP
ap-2076	148	4	[	[	X
ap-2076	148	5	8	8	NUM
ap-2076	148	6	,	,	PUNCT
ap-2076	148	7	ch	ch	NOUN
ap-2076	148	8	.	.	PUNCT
ap-2076	148	9	iii	iii	PROPN
ap-2076	148	10	,	,	PUNCT
ap-2076	148	11	sec	sec	PROPN
ap-2076	148	12	.	.	PROPN
ap-2076	148	13	6.5	6.5	NUM
ap-2076	148	14	]	]	PUNCT
ap-2076	148	15	(	(	PUNCT
ap-2076	148	16	see	see	VERB
ap-2076	148	17	also	also	ADV
ap-2076	148	18	the	the	DET
ap-2076	148	19	remark	remark	NOUN
ap-2076	148	20	on	on	ADP
ap-2076	148	21	space	space	NOUN
ap-2076	148	22	m′(0	m′(0	NOUN
ap-2076	148	23	)	)	PUNCT
ap-2076	148	24	in	in	ADP
ap-2076	148	25	the	the	DET
ap-2076	148	26	proof	proof	NOUN
ap-2076	148	27	of	of	ADP
ap-2076	148	28	theorem	theorem	ADJ
ap-2076	148	29	1.7	1.7	NUM
ap-2076	148	30	in	in	ADP
ap-2076	148	31	[	[	X
ap-2076	148	32	8	8	NUM
ap-2076	148	33	,	,	PUNCT
ap-2076	148	34	ch	ch	NOUN
ap-2076	148	35	.	.	PUNCT
ap-2076	149	1	vii	vii	PROPN
ap-2076	149	2	,	,	PUNCT
ap-2076	149	3	sec	sec	PROPN
ap-2076	149	4	.	.	PROPN
ap-2076	149	5	1.3	1.3	NUM
ap-2076	149	6	]	]	PUNCT
ap-2076	149	7	)	)	PUNCT
ap-2076	150	1	that	that	SCONJ
ap-2076	150	2	(	(	PUNCT
ap-2076	150	3	hα	hα	X
ap-2076	150	4	−	−	PROPN
ap-2076	150	5	λ)−1	λ)−1	NOUN
ap-2076	150	6	can	can	AUX
ap-2076	150	7	be	be	AUX
ap-2076	150	8	expanded	expand	VERB
ap-2076	150	9	into	into	ADP
ap-2076	150	10	the	the	DET
ap-2076	150	11	laurent	laurent	PROPN
ap-2076	150	12	series	series	NOUN
ap-2076	150	13	(	(	PUNCT
ap-2076	150	14	hα	hα	ADP
ap-2076	150	15	−	−	PROPN
ap-2076	150	16	λ)−1	λ)−1	NOUN
ap-2076	150	17	=	=	SYM
ap-2076	150	18	n∑	n∑	PROPN
ap-2076	150	19	n=1	n=1	PROPN
ap-2076	150	20	p−n	p−n	NOUN
ap-2076	150	21	(	(	PUNCT
ap-2076	150	22	λ−	λ−	PROPN
ap-2076	150	23	λ0)n	λ0)n	PROPN
ap-2076	150	24	+	+	ADV
ap-2076	150	25	rα(λ	rα(λ	NOUN
ap-2076	150	26	)	)	PUNCT
ap-2076	150	27	,	,	PUNCT
ap-2076	150	28	where	where	SCONJ
ap-2076	150	29	n	n	PRON
ap-2076	150	30	is	be	AUX
ap-2076	150	31	a	a	DET
ap-2076	150	32	fixed	fix	VERB
ap-2076	150	33	number	number	NOUN
ap-2076	150	34	independent	independent	ADJ
ap-2076	150	35	of	of	ADP
ap-2076	150	36	λ	λ	PROPN
ap-2076	150	37	,	,	PUNCT
ap-2076	150	38	rα	rα	ADV
ap-2076	150	39	is	be	AUX
ap-2076	150	40	the	the	DET
ap-2076	150	41	reduced	reduce	VERB
ap-2076	150	42	resolvent	resolvent	NOUN
ap-2076	150	43	which	which	PRON
ap-2076	150	44	is	be	AUX
ap-2076	150	45	a	a	DET
ap-2076	150	46	bounded	bounded	ADJ
ap-2076	150	47	and	and	CCONJ
ap-2076	150	48	holomorphic	holomorphic	ADJ
ap-2076	150	49	in	in	ADP
ap-2076	150	50	λ	λ	NOUN
ap-2076	150	51	operator	operator	NOUN
ap-2076	150	52	.	.	PUNCT
ap-2076	151	1	given	give	VERB
ap-2076	151	2	any	any	DET
ap-2076	151	3	f	f	PROPN
ap-2076	151	4	∈	∈	PROPN
ap-2076	151	5	l2(ω	l2(ω	PROPN
ap-2076	151	6	)	)	PUNCT
ap-2076	151	7	,	,	PUNCT
ap-2076	151	8	we	we	PRON
ap-2076	151	9	then	then	ADV
ap-2076	151	10	have	have	VERB
ap-2076	151	11	u	u	NOUN
ap-2076	151	12	=	=	PUNCT
ap-2076	151	13	(	(	PUNCT
ap-2076	151	14	hα	hα	ADP
ap-2076	151	15	−	−	PROPN
ap-2076	151	16	λ)−1f	λ)−1f	PUNCT
ap-2076	152	1	=	=	SYM
ap-2076	152	2	n∑	n∑	PROPN
ap-2076	152	3	n=1	n=1	PROPN
ap-2076	152	4	u−n	u−n	PROPN
ap-2076	152	5	(	(	PUNCT
ap-2076	152	6	λ−	λ−	PROPN
ap-2076	152	7	λ0)n	λ0)n	NOUN
ap-2076	152	8	+	+	CCONJ
ap-2076	152	9	∞∑	∞∑	NUM
ap-2076	152	10	n=0	n=0	NUM
ap-2076	152	11	(	(	PUNCT
ap-2076	152	12	λ−	λ−	PROPN
ap-2076	152	13	λ0)nun	λ0)nun	PROPN
ap-2076	152	14	.	.	PUNCT
ap-2076	153	1	we	we	PRON
ap-2076	153	2	substitute	substitute	VERB
ap-2076	153	3	this	this	DET
ap-2076	153	4	formula	formula	NOUN
ap-2076	153	5	into	into	ADP
ap-2076	153	6	the	the	DET
ap-2076	153	7	equation	equation	NOUN
ap-2076	153	8	(	(	PUNCT
ap-2076	153	9	hα	hα	ADP
ap-2076	153	10	−	−	PROPN
ap-2076	153	11	λ)u	λ)u	PUNCT
ap-2076	154	1	=	=	PUNCT
ap-2076	154	2	f	f	PROPN
ap-2076	154	3	and	and	CCONJ
ap-2076	154	4	equate	equate	VERB
ap-2076	154	5	the	the	DET
ap-2076	154	6	coefficients	coefficient	NOUN
ap-2076	154	7	at	at	ADP
ap-2076	154	8	the	the	DET
ap-2076	154	9	like	like	ADJ
ap-2076	154	10	powers	power	NOUN
ap-2076	154	11	of	of	ADP
ap-2076	154	12	(	(	PUNCT
ap-2076	154	13	λ−	λ−	PROPN
ap-2076	154	14	λ0	λ0	NOUN
ap-2076	154	15	):	):	PUNCT
ap-2076	154	16	(	(	PUNCT
ap-2076	154	17	hα	hα	ADP
ap-2076	154	18	−	−	PROPN
ap-2076	155	1	λ0)u−n	λ0)u−n	PROPN
ap-2076	155	2	=	=	SYM
ap-2076	155	3	0	0	PROPN
ap-2076	155	4	,	,	PUNCT
ap-2076	155	5	(	(	PUNCT
ap-2076	155	6	hα	hα	ADP
ap-2076	155	7	−	−	PROPN
ap-2076	155	8	λ0)u−k	λ0)u−k	X
ap-2076	155	9	=	=	PUNCT
ap-2076	155	10	u−k−1	u−k−1	PROPN
ap-2076	155	11	,	,	PUNCT
ap-2076	155	12	k	k	PROPN
ap-2076	156	1	=	=	SYM
ap-2076	157	1	1	1	NUM
ap-2076	157	2	,	,	PUNCT
ap-2076	157	3	.	.	PUNCT
ap-2076	157	4	.	.	PUNCT
ap-2076	158	1	.	.	PUNCT
ap-2076	159	1	,	,	PUNCT
ap-2076	160	1	n	n	CCONJ
ap-2076	160	2	−	−	PROPN
ap-2076	160	3	1	1	NUM
ap-2076	160	4	,	,	PUNCT
ap-2076	160	5	(	(	PUNCT
ap-2076	160	6	hα	hα	ADP
ap-2076	160	7	−	−	NOUN
ap-2076	161	1	λ0)u0	λ0)u0	NOUN
ap-2076	161	2	=	=	PUNCT
ap-2076	161	3	f	f	PROPN
ap-2076	162	1	+	+	CCONJ
ap-2076	162	2	u−1	u−1	PROPN
ap-2076	162	3	,	,	PUNCT
ap-2076	162	4	(	(	PUNCT
ap-2076	162	5	hα	hα	ADP
ap-2076	162	6	−	−	PROPN
ap-2076	162	7	λ0)u1	λ0)u1	NOUN
ap-2076	162	8	=	=	SYM
ap-2076	162	9	u0	u0	PROPN
ap-2076	162	10	.	.	PUNCT
ap-2076	163	1	(	(	PUNCT
ap-2076	163	2	2.10	2.10	NUM
ap-2076	163	3	)	)	PUNCT
ap-2076	163	4	this	this	PRON
ap-2076	163	5	implies	imply	VERB
ap-2076	163	6	that	that	SCONJ
ap-2076	163	7	u−n	u−n	NOUN
ap-2076	163	8	=	=	SYM
ap-2076	163	9	ψ0`2f	ψ0`2f	X
ap-2076	163	10	,	,	PUNCT
ap-2076	163	11	u−n+1	u−n+1	PUNCT
ap-2076	163	12	=	=	SYM
ap-2076	163	13	φ0`2f	φ0`2f	NOUN
ap-2076	163	14	+	+	CCONJ
ap-2076	163	15	ψ0`1f	ψ0`1f	ADJ
ap-2076	163	16	,	,	PUNCT
ap-2076	163	17	where	where	SCONJ
ap-2076	163	18	`	`	PUNCT
ap-2076	163	19	i	i	PRON
ap-2076	163	20	are	be	AUX
ap-2076	163	21	some	some	DET
ap-2076	163	22	functionals	functional	NOUN
ap-2076	163	23	on	on	ADP
ap-2076	163	24	l2(ω	l2(ω	NOUN
ap-2076	163	25	)	)	PUNCT
ap-2076	163	26	.	.	PUNCT
ap-2076	164	1	if	if	SCONJ
ap-2076	164	2	n	n	PROPN
ap-2076	164	3	>	>	X
ap-2076	164	4	2	2	NUM
ap-2076	164	5	,	,	PUNCT
ap-2076	164	6	then	then	ADV
ap-2076	164	7	by	by	ADP
ap-2076	164	8	(	(	PUNCT
ap-2076	164	9	1.9	1.9	NUM
ap-2076	164	10	)	)	PUNCT
ap-2076	164	11	and	and	CCONJ
ap-2076	164	12	lemma	lemma	PROPN
ap-2076	164	13	2.1	2.1	NUM
ap-2076	164	14	the	the	DET
ap-2076	164	15	equation	equation	NOUN
ap-2076	164	16	for	for	ADP
ap-2076	164	17	u−n+2	u−n+2	PROPN
ap-2076	164	18	is	be	AUX
ap-2076	164	19	unsolvable	unsolvable	ADJ
ap-2076	164	20	.	.	PUNCT
ap-2076	165	1	hence	hence	ADV
ap-2076	165	2	,	,	PUNCT
ap-2076	165	3	we	we	PRON
ap-2076	165	4	can	can	AUX
ap-2076	165	5	assume	assume	VERB
ap-2076	165	6	n	n	NOUN
ap-2076	165	7	=	=	SYM
ap-2076	165	8	2	2	X
ap-2076	165	9	.	.	X
ap-2076	165	10	writing	write	VERB
ap-2076	165	11	then	then	ADV
ap-2076	165	12	the	the	DET
ap-2076	165	13	solvability	solvability	NOUN
ap-2076	165	14	condition	condition	NOUN
ap-2076	165	15	(	(	PUNCT
ap-2076	165	16	2.4	2.4	NUM
ap-2076	165	17	)	)	PUNCT
ap-2076	165	18	for	for	ADP
ap-2076	165	19	equations	equation	NOUN
ap-2076	165	20	(	(	PUNCT
ap-2076	165	21	2.10	2.10	NUM
ap-2076	165	22	)	)	PUNCT
ap-2076	165	23	and	and	CCONJ
ap-2076	165	24	taking	take	VERB
ap-2076	165	25	into	into	ADP
ap-2076	165	26	consideration	consideration	NOUN
ap-2076	165	27	the	the	DET
ap-2076	165	28	identity	identity	NOUN
ap-2076	165	29	in	in	ADP
ap-2076	165	30	(	(	PUNCT
ap-2076	165	31	1.10	1.10	NUM
ap-2076	165	32	)	)	PUNCT
ap-2076	165	33	,	,	PUNCT
ap-2076	165	34	we	we	PRON
ap-2076	165	35	arrive	arrive	VERB
ap-2076	165	36	easily	easily	ADV
ap-2076	165	37	to	to	ADP
ap-2076	165	38	the	the	DET
ap-2076	165	39	formula	formula	NOUN
ap-2076	165	40	for	for	ADP
ap-2076	165	41	`	`	PUNCT
ap-2076	165	42	2	2	NUM
ap-2076	165	43	in	in	ADP
ap-2076	165	44	(	(	PUNCT
ap-2076	165	45	2.9	2.9	NUM
ap-2076	165	46	)	)	PUNCT
ap-2076	165	47	and	and	CCONJ
ap-2076	165	48	`	`	PUNCT
ap-2076	165	49	1f	1f	NUM
ap-2076	165	50	:	:	PUNCT
ap-2076	165	51	=	=	SYM
ap-2076	165	52	−(u0	−(u0	AUX
ap-2076	165	53	,	,	PUNCT
ap-2076	165	54	t	t	NOUN
ap-2076	165	55	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	165	56	)	)	PUNCT
ap-2076	165	57	,	,	PUNCT
ap-2076	165	58	(	(	PUNCT
ap-2076	165	59	2.11	2.11	NUM
ap-2076	165	60	)	)	PUNCT
ap-2076	165	61	where	where	SCONJ
ap-2076	165	62	u0	u0	ADJ
ap-2076	165	63	is	be	AUX
ap-2076	165	64	the	the	DET
ap-2076	165	65	solution	solution	NOUN
ap-2076	165	66	to	to	ADP
ap-2076	165	67	the	the	DET
ap-2076	165	68	equation	equation	NOUN
ap-2076	165	69	(	(	PUNCT
ap-2076	165	70	hα	hα	ADP
ap-2076	165	71	−	−	NOUN
ap-2076	166	1	λ0)u0	λ0)u0	NOUN
ap-2076	166	2	=	=	PUNCT
ap-2076	166	3	f	f	PROPN
ap-2076	167	1	+	+	CCONJ
ap-2076	167	2	ψ0`2f	ψ0`2f	ADJ
ap-2076	167	3	(	(	PUNCT
ap-2076	167	4	2.12	2.12	NUM
ap-2076	167	5	)	)	PUNCT
ap-2076	167	6	satisfying	satisfying	NOUN
ap-2076	167	7	(	(	PUNCT
ap-2076	167	8	u0	u0	ADJ
ap-2076	167	9	,	,	PUNCT
ap-2076	167	10	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	167	11	)	)	PUNCT
ap-2076	167	12	=	=	SYM
ap-2076	168	1	0	0	X
ap-2076	168	2	.	.	PUNCT
ap-2076	169	1	(	(	PUNCT
ap-2076	169	2	2.13	2.13	NUM
ap-2076	169	3	)	)	PUNCT
ap-2076	169	4	it	it	PRON
ap-2076	169	5	follows	follow	VERB
ap-2076	169	6	from	from	ADP
ap-2076	169	7	(	(	PUNCT
ap-2076	169	8	1.3	1.3	NUM
ap-2076	169	9	)	)	PUNCT
ap-2076	169	10	and	and	CCONJ
ap-2076	169	11	(	(	PUNCT
ap-2076	169	12	1.8	1.8	NUM
ap-2076	169	13	)	)	PUNCT
ap-2076	170	1	that	that	SCONJ
ap-2076	170	2	(	(	PUNCT
ap-2076	170	3	u0	u0	PROPN
ap-2076	170	4	,	,	PUNCT
ap-2076	170	5	t	t	PROPN
ap-2076	170	6	ψ0)l2(ω	ψ0)l2(ω	ADV
ap-2076	170	7	)	)	PUNCT
ap-2076	170	8	=	=	PRON
ap-2076	171	1	(	(	PUNCT
ap-2076	171	2	u0	u0	PROPN
ap-2076	171	3	,	,	PUNCT
ap-2076	171	4	t	t	PROPN
ap-2076	171	5	(	(	PUNCT
ap-2076	171	6	hα	hα	ADP
ap-2076	171	7	−	−	PROPN
ap-2076	171	8	λ0)φ0	λ0)φ0	PROPN
ap-2076	171	9	)	)	PUNCT
ap-2076	172	1	l2(ω	l2(ω	PROPN
ap-2076	172	2	)	)	PUNCT
ap-2076	172	3	=	=	PRON
ap-2076	172	4	(	(	PUNCT
ap-2076	172	5	u0	u0	ADJ
ap-2076	172	6	,	,	PUNCT
ap-2076	172	7	(	(	PUNCT
ap-2076	172	8	hα	hα	ADP
ap-2076	172	9	−	−	PROPN
ap-2076	172	10	λ0)∗t	λ0)∗t	NOUN
ap-2076	172	11	φ0	φ0	PROPN
ap-2076	172	12	)	)	PUNCT
ap-2076	173	1	l2(ω	l2(ω	PROPN
ap-2076	173	2	)	)	PUNCT
ap-2076	174	1	=	=	SYM
ap-2076	174	2	(	(	PUNCT
ap-2076	174	3	(	(	PUNCT
ap-2076	174	4	hα	hα	ADP
ap-2076	174	5	−	−	NOUN
ap-2076	174	6	λ0)u0	λ0)u0	ADV
ap-2076	174	7	,	,	PUNCT
ap-2076	174	8	t	t	PROPN
ap-2076	174	9	φ0	φ0	PROPN
ap-2076	174	10	)	)	PUNCT
ap-2076	175	1	l2(ω	l2(ω	PROPN
ap-2076	175	2	)	)	PUNCT
ap-2076	176	1	=	=	PUNCT
ap-2076	176	2	(	(	PUNCT
ap-2076	176	3	f	f	PROPN
ap-2076	176	4	+	+	CCONJ
ap-2076	176	5	ψ0`2f	ψ0`2f	ADJ
ap-2076	176	6	,	,	PUNCT
ap-2076	176	7	t	t	PROPN
ap-2076	176	8	φ0)l2(ω	φ0)l2(ω	ADV
ap-2076	176	9	)	)	PUNCT
ap-2076	176	10	.	.	PUNCT
ap-2076	177	1	these	these	DET
ap-2076	177	2	identities	identity	NOUN
ap-2076	177	3	,	,	PUNCT
ap-2076	177	4	the	the	DET
ap-2076	177	5	above	above	ADJ
ap-2076	177	6	obtained	obtain	VERB
ap-2076	177	7	formula	formula	NOUN
ap-2076	177	8	for	for	ADP
ap-2076	177	9	`	`	PUNCT
ap-2076	177	10	2	2	NUM
ap-2076	177	11	,	,	PUNCT
ap-2076	177	12	and	and	CCONJ
ap-2076	177	13	(	(	PUNCT
ap-2076	177	14	2.6	2.6	NUM
ap-2076	177	15	)	)	PUNCT
ap-2076	177	16	,	,	PUNCT
ap-2076	177	17	(	(	PUNCT
ap-2076	177	18	2.11	2.11	NUM
ap-2076	177	19	)	)	PUNCT
ap-2076	177	20	imply	imply	VERB
ap-2076	177	21	formula	formula	NOUN
ap-2076	177	22	(	(	PUNCT
ap-2076	177	23	2.12	2.12	NUM
ap-2076	177	24	)	)	PUNCT
ap-2076	177	25	for	for	ADP
ap-2076	177	26	`	`	PUNCT
ap-2076	177	27	1	1	X
ap-2076	177	28	.	.	PUNCT
ap-2076	178	1	lemma	lemma	PROPN
ap-2076	178	2	2.4	2.4	NUM
ap-2076	178	3	.	.	PUNCT
ap-2076	178	4	suppose	suppose	VERB
ap-2076	178	5	the	the	DET
ap-2076	178	6	hypothesis	hypothesis	NOUN
ap-2076	178	7	of	of	ADP
ap-2076	178	8	theorem	theorem	ADJ
ap-2076	178	9	1.1	1.1	NUM
ap-2076	178	10	.	.	PUNCT
ap-2076	179	1	then	then	ADV
ap-2076	179	2	for	for	ADP
ap-2076	179	3	λ	λ	PROPN
ap-2076	179	4	close	close	ADJ
ap-2076	179	5	to	to	PART
ap-2076	179	6	λ0	λ0	VERB
ap-2076	179	7	the	the	DET
ap-2076	179	8	resolvent	resolvent	NOUN
ap-2076	179	9	(	(	PUNCT
ap-2076	179	10	hα	hα	ADP
ap-2076	179	11	−	−	PROPN
ap-2076	179	12	λ)−1	λ)−1	NOUN
ap-2076	179	13	can	can	AUX
ap-2076	179	14	be	be	AUX
ap-2076	179	15	represented	represent	VERB
ap-2076	179	16	as	as	ADP
ap-2076	179	17	(	(	PUNCT
ap-2076	179	18	hα	hα	ADP
ap-2076	179	19	−	−	PROPN
ap-2076	179	20	λ)−1	λ)−1	NOUN
ap-2076	179	21	=	=	SYM
ap-2076	179	22	p−1	p−1	PROPN
ap-2076	179	23	λ−	λ−	PROPN
ap-2076	179	24	λ0	λ0	NOUN
ap-2076	179	25	+	+	NOUN
ap-2076	179	26	rα(λ	rα(λ	NOUN
ap-2076	179	27	)	)	PUNCT
ap-2076	179	28	,	,	PUNCT
ap-2076	179	29	(	(	PUNCT
ap-2076	179	30	2.14	2.14	NUM
ap-2076	179	31	)	)	PUNCT
ap-2076	179	32	p−1	p−1	NOUN
ap-2076	179	33	=	=	PUNCT
ap-2076	179	34	ψ+	ψ+	PUNCT
ap-2076	179	35	0	0	NUM
ap-2076	180	1	`	`	PUNCT
ap-2076	180	2	+	+	NUM
ap-2076	180	3	+	+	CCONJ
ap-2076	180	4	ψ−0	ψ−0	PROPN
ap-2076	180	5	`	`	PUNCT
ap-2076	180	6	−	−	PROPN
ap-2076	180	7	,	,	PUNCT
ap-2076	180	8	`	`	PUNCT
ap-2076	180	9	±f	±f	X
ap-2076	180	10	:	:	PUNCT
ap-2076	180	11	=	=	PUNCT
ap-2076	180	12	−(f	−(f	PROPN
ap-2076	180	13	,	,	PUNCT
ap-2076	180	14	t	t	PROPN
ap-2076	180	15	ψ±0	ψ±0	PUNCT
ap-2076	180	16	)	)	PUNCT
ap-2076	180	17	l2(ω	l2(ω	X
ap-2076	180	18	)	)	PUNCT
ap-2076	180	19	,	,	PUNCT
ap-2076	180	20	(	(	PUNCT
ap-2076	180	21	2.15	2.15	NUM
ap-2076	180	22	)	)	PUNCT
ap-2076	180	23	where	where	SCONJ
ap-2076	180	24	rα(λ	rα(λ	NOUN
ap-2076	180	25	)	)	PUNCT
ap-2076	180	26	is	be	AUX
ap-2076	180	27	the	the	DET
ap-2076	180	28	reduced	reduce	VERB
ap-2076	180	29	resolvent	resolvent	NOUN
ap-2076	180	30	which	which	PRON
ap-2076	180	31	is	be	AUX
ap-2076	180	32	a	a	DET
ap-2076	180	33	bounded	bounded	ADJ
ap-2076	180	34	and	and	CCONJ
ap-2076	180	35	holomorphic	holomorphic	ADJ
ap-2076	180	36	in	in	ADP
ap-2076	180	37	λ	λ	NOUN
ap-2076	180	38	operator	operator	NOUN
ap-2076	180	39	.	.	PUNCT
ap-2076	181	1	the	the	DET
ap-2076	181	2	proof	proof	NOUN
ap-2076	181	3	of	of	ADP
ap-2076	181	4	this	this	DET
ap-2076	181	5	lemma	lemma	PROPN
ap-2076	181	6	is	be	AUX
ap-2076	181	7	similar	similar	ADJ
ap-2076	181	8	to	to	ADP
ap-2076	181	9	that	that	PRON
ap-2076	181	10	of	of	ADP
ap-2076	181	11	lemma	lemma	PROPN
ap-2076	181	12	2.3	2.3	NUM
ap-2076	181	13	,	,	PUNCT
ap-2076	181	14	we	we	PRON
ap-2076	181	15	just	just	ADV
ap-2076	181	16	should	should	AUX
ap-2076	181	17	bear	bear	VERB
ap-2076	181	18	in	in	ADP
ap-2076	181	19	mind	mind	NOUN
ap-2076	181	20	that	that	SCONJ
ap-2076	181	21	due	due	ADP
ap-2076	181	22	to	to	ADP
ap-2076	181	23	(	(	PUNCT
ap-2076	181	24	1.4	1.4	NUM
ap-2076	181	25	)	)	PUNCT
ap-2076	181	26	and	and	CCONJ
ap-2076	181	27	lemma	lemma	PROPN
ap-2076	181	28	2.1	2.1	NUM
ap-2076	181	29	the	the	DET
ap-2076	181	30	equations	equation	NOUN
ap-2076	181	31	(	(	PUNCT
ap-2076	181	32	hα	hα	ADP
ap-2076	181	33	−	−	PROPN
ap-2076	181	34	λ0)u	λ0)u	PROPN
ap-2076	182	1	=	=	PUNCT
ap-2076	182	2	ψ±0	ψ±0	X
ap-2076	182	3	are	be	AUX
ap-2076	182	4	unsolvable	unsolvable	ADJ
ap-2076	182	5	.	.	PUNCT
ap-2076	183	1	we	we	PRON
ap-2076	183	2	proceed	proceed	VERB
ap-2076	183	3	to	to	ADP
ap-2076	183	4	the	the	DET
ap-2076	183	5	proofs	proof	NOUN
ap-2076	183	6	of	of	ADP
ap-2076	183	7	theorems	theorem	NOUN
ap-2076	183	8	1.1	1.1	NUM
ap-2076	183	9	,	,	PUNCT
ap-2076	183	10	1.2	1.2	NUM
ap-2076	183	11	,	,	PUNCT
ap-2076	183	12	1.3	1.3	NUM
ap-2076	183	13	.	.	NOUN
ap-2076	183	14	96	96	NUM
ap-2076	183	15	vol	vol	NOUN
ap-2076	183	16	.	.	PUNCT
ap-2076	184	1	54	54	NUM
ap-2076	184	2	no	no	NOUN
ap-2076	184	3	.	.	PUNCT
ap-2076	185	1	2/2014	2/2014	NUM
ap-2076	185	2	eigenvalue	eigenvalue	NOUN
ap-2076	185	3	collision	collision	NOUN
ap-2076	185	4	for	for	ADP
ap-2076	185	5	pt	pt	NOUN
ap-2076	185	6	-	-	ADJ
ap-2076	185	7	symmetric	symmetric	ADJ
ap-2076	185	8	waveguide	waveguide	ADJ
ap-2076	185	9	proof	proof	NOUN
ap-2076	185	10	of	of	ADP
ap-2076	185	11	theorem	theorem	ADJ
ap-2076	185	12	1.2	1.2	NUM
ap-2076	185	13	.	.	PUNCT
ap-2076	186	1	the	the	DET
ap-2076	186	2	proof	proof	NOUN
ap-2076	186	3	is	be	AUX
ap-2076	186	4	based	base	VERB
ap-2076	186	5	on	on	ADP
ap-2076	186	6	the	the	DET
ap-2076	186	7	modified	modify	VERB
ap-2076	186	8	version	version	NOUN
ap-2076	186	9	of	of	ADP
ap-2076	186	10	the	the	DET
ap-2076	186	11	birman	birman	NOUN
ap-2076	186	12	-	-	PUNCT
ap-2076	186	13	schwinger	schwinger	NOUN
ap-2076	186	14	principle	principle	NOUN
ap-2076	186	15	suggested	suggest	VERB
ap-2076	186	16	in	in	ADP
ap-2076	186	17	[	[	X
ap-2076	186	18	9	9	NUM
ap-2076	186	19	]	]	PUNCT
ap-2076	186	20	in	in	ADP
ap-2076	186	21	the	the	DET
ap-2076	186	22	form	form	NOUN
ap-2076	186	23	developed	develop	VERB
ap-2076	186	24	in	in	ADP
ap-2076	186	25	[	[	X
ap-2076	186	26	10	10	NUM
ap-2076	186	27	]	]	PUNCT
ap-2076	186	28	.	.	PUNCT
ap-2076	187	1	in	in	ADP
ap-2076	187	2	view	view	NOUN
ap-2076	187	3	of	of	ADP
ap-2076	187	4	(	(	PUNCT
ap-2076	187	5	2.1	2.1	NUM
ap-2076	187	6	)	)	PUNCT
ap-2076	187	7	,	,	PUNCT
ap-2076	187	8	the	the	DET
ap-2076	187	9	eigenvalue	eigenvalue	ADJ
ap-2076	187	10	equation	equation	NOUN
ap-2076	187	11	for	for	ADP
ap-2076	187	12	hα+εβ	hα+εβ	PROPN
ap-2076	187	13	is	be	AUX
ap-2076	187	14	equivalent	equivalent	ADJ
ap-2076	187	15	to	to	ADP
ap-2076	187	16	the	the	DET
ap-2076	187	17	same	same	ADJ
ap-2076	187	18	equation	equation	NOUN
ap-2076	187	19	for	for	ADP
ap-2076	187	20	hα	hα	ADP
ap-2076	187	21	−	−	PROPN
ap-2076	187	22	εlε	εlε	NOUN
ap-2076	187	23	.	.	PUNCT
ap-2076	188	1	the	the	DET
ap-2076	188	2	latter	latter	ADJ
ap-2076	188	3	equation	equation	NOUN
ap-2076	188	4	can	can	AUX
ap-2076	188	5	be	be	AUX
ap-2076	188	6	written	write	VERB
ap-2076	188	7	as	as	ADP
ap-2076	188	8	(	(	PUNCT
ap-2076	188	9	hα	hα	ADP
ap-2076	188	10	−	−	PROPN
ap-2076	188	11	λε)ψε	λε)ψε	PUNCT
ap-2076	188	12	=	=	SYM
ap-2076	188	13	εlεψε	εlεψε	PROPN
ap-2076	188	14	.	.	PUNCT
ap-2076	189	1	(	(	PUNCT
ap-2076	189	2	2.16	2.16	NUM
ap-2076	189	3	)	)	PUNCT
ap-2076	189	4	we	we	PRON
ap-2076	189	5	then	then	ADV
ap-2076	189	6	invert	invert	VERB
ap-2076	189	7	the	the	DET
ap-2076	189	8	operator	operator	NOUN
ap-2076	189	9	(	(	PUNCT
ap-2076	189	10	hα	hα	ADP
ap-2076	189	11	−	−	PROPN
ap-2076	189	12	λε	λε	NOUN
ap-2076	189	13	)	)	PUNCT
ap-2076	189	14	by	by	ADP
ap-2076	189	15	lemma	lemma	PROPN
ap-2076	189	16	2.3	2.3	NUM
ap-2076	189	17	and	and	CCONJ
ap-2076	189	18	obtain	obtain	VERB
ap-2076	189	19	ψε	ψε	NOUN
ap-2076	189	20	=	=	PUNCT
ap-2076	189	21	ε	ε	PROPN
ap-2076	189	22	p−2lεψε	p−2lεψε	NOUN
ap-2076	189	23	(	(	PUNCT
ap-2076	189	24	λε	λε	INTJ
ap-2076	189	25	−	−	NOUN
ap-2076	189	26	λ0)2	λ0)2	X
ap-2076	189	27	+	+	CCONJ
ap-2076	189	28	ε	ε	PROPN
ap-2076	189	29	p−1lεψε	p−1lεψε	VERB
ap-2076	189	30	λε	λε	PRON
ap-2076	189	31	−	−	NOUN
ap-2076	189	32	λ0	λ0	NOUN
ap-2076	189	33	+	+	CCONJ
ap-2076	189	34	εrα(λε)ψε	εrα(λε)ψε	PROPN
ap-2076	189	35	.	.	PUNCT
ap-2076	190	1	by	by	ADP
ap-2076	190	2	lemma	lemma	PROPN
ap-2076	190	3	2.3	2.3	NUM
ap-2076	190	4	the	the	DET
ap-2076	190	5	operator	operator	NOUN
ap-2076	190	6	rα(λ	rα(λ	NOUN
ap-2076	190	7	)	)	PUNCT
ap-2076	190	8	is	be	AUX
ap-2076	190	9	bounded	bound	VERB
ap-2076	190	10	uniformly	uniformly	ADV
ap-2076	190	11	in	in	ADP
ap-2076	190	12	λ	λ	PROPN
ap-2076	190	13	close	close	ADJ
ap-2076	190	14	to	to	ADP
ap-2076	190	15	λ0	λ0	NOUN
ap-2076	190	16	and	and	CCONJ
ap-2076	190	17	hence	hence	ADV
ap-2076	190	18	the	the	DET
ap-2076	190	19	inverse	inverse	NOUN
ap-2076	190	20	a(z	a(z	PROPN
ap-2076	190	21	,	,	PUNCT
ap-2076	190	22	ε	ε	PROPN
ap-2076	190	23	)	)	PUNCT
ap-2076	190	24	:	:	PUNCT
ap-2076	190	25	=(	=(	INTJ
ap-2076	190	26	i−	i−	PROPN
ap-2076	190	27	εrα(λ0	εrα(λ0	PROPN
ap-2076	190	28	+	+	PROPN
ap-2076	190	29	z	z	NOUN
ap-2076	190	30	)	)	PUNCT
ap-2076	190	31	)	)	PUNCT
ap-2076	191	1	−1	−1	NOUN
ap-2076	191	2	is	be	AUX
ap-2076	191	3	well	well	ADV
ap-2076	191	4	-	-	PUNCT
ap-2076	191	5	defined	define	VERB
ap-2076	191	6	and	and	CCONJ
ap-2076	191	7	is	be	AUX
ap-2076	191	8	uniformly	uniformly	ADV
ap-2076	191	9	bounded	bound	VERB
ap-2076	191	10	for	for	ADP
ap-2076	191	11	all	all	DET
ap-2076	191	12	λ	λ	NOUN
ap-2076	191	13	close	close	ADJ
ap-2076	191	14	to	to	ADP
ap-2076	191	15	λ0	λ0	NOUN
ap-2076	191	16	and	and	CCONJ
ap-2076	191	17	for	for	ADP
ap-2076	191	18	all	all	DET
ap-2076	191	19	sufficiently	sufficiently	ADV
ap-2076	191	20	small	small	ADJ
ap-2076	191	21	ε	ε	PROPN
ap-2076	191	22	.	.	PUNCT
ap-2076	192	1	we	we	PRON
ap-2076	192	2	apply	apply	VERB
ap-2076	192	3	this	this	DET
ap-2076	192	4	operator	operator	NOUN
ap-2076	192	5	to	to	ADP
ap-2076	192	6	the	the	DET
ap-2076	192	7	latter	latter	ADJ
ap-2076	192	8	equation	equation	NOUN
ap-2076	192	9	and	and	CCONJ
ap-2076	192	10	get	get	VERB
ap-2076	192	11	ψε	ψε	ADJ
ap-2076	192	12	=	=	PUNCT
ap-2076	192	13	ε	ε	PROPN
ap-2076	192	14	z2	z2	PROPN
ap-2076	192	15	ε	ε	PROPN
ap-2076	192	16	a(λ0	a(λ0	NOUN
ap-2076	192	17	+	+	CCONJ
ap-2076	192	18	zε	zε	ADJ
ap-2076	192	19	,	,	PUNCT
ap-2076	192	20	ε)p−2lεψε	ε)p−2lεψε	ADJ
ap-2076	192	21	+	+	CCONJ
ap-2076	192	22	ε	ε	PROPN
ap-2076	192	23	zε	zε	ADJ
ap-2076	192	24	a(λ0	a(λ0	NOUN
ap-2076	192	25	+	+	CCONJ
ap-2076	192	26	zε	zε	ADJ
ap-2076	192	27	,	,	PUNCT
ap-2076	192	28	ε)p−1lεψε	ε)p−1lεψε	PROPN
ap-2076	192	29	,	,	PUNCT
ap-2076	192	30	(	(	PUNCT
ap-2076	192	31	2.17	2.17	NUM
ap-2076	192	32	)	)	PUNCT
ap-2076	192	33	where	where	SCONJ
ap-2076	192	34	we	we	PRON
ap-2076	192	35	denote	denote	VERB
ap-2076	192	36	zε	zε	X
ap-2076	192	37	:	:	PUNCT
ap-2076	192	38	=	=	SYM
ap-2076	192	39	λε	λε	INTJ
ap-2076	192	40	−	−	NOUN
ap-2076	192	41	λ0	λ0	NOUN
ap-2076	192	42	.	.	PUNCT
ap-2076	193	1	then	then	ADV
ap-2076	193	2	we	we	PRON
ap-2076	193	3	apply	apply	VERB
ap-2076	193	4	functionals	functional	NOUN
ap-2076	193	5	`	`	PUNCT
ap-2076	193	6	2lε	2lε	ADV
ap-2076	193	7	,	,	PUNCT
ap-2076	193	8	`	`	PUNCT
ap-2076	193	9	1lε	1lε	NOUN
ap-2076	193	10	to	to	ADP
ap-2076	193	11	the	the	DET
ap-2076	193	12	obtained	obtain	VERB
ap-2076	193	13	equation	equation	NOUN
ap-2076	193	14	and	and	CCONJ
ap-2076	193	15	it	it	PRON
ap-2076	193	16	results	result	VERB
ap-2076	193	17	in	in	ADP
ap-2076	193	18	(	(	PUNCT
ap-2076	193	19	ε	ε	PROPN
ap-2076	193	20	zε	zε	PROPN
ap-2076	193	21	a11(zε	a11(zε	PROPN
ap-2076	193	22	,	,	PUNCT
ap-2076	193	23	ε)−	ε)−	PROPN
ap-2076	193	24	1	1	NUM
ap-2076	193	25	)	)	PUNCT
ap-2076	193	26	x1	x1	PROPN
ap-2076	194	1	+	+	CCONJ
ap-2076	194	2	ε	ε	PROPN
ap-2076	194	3	z2	z2	PROPN
ap-2076	194	4	ε	ε	PROPN
ap-2076	194	5	(	(	PUNCT
ap-2076	194	6	a11(zε	a11(zε	PROPN
ap-2076	194	7	,	,	PUNCT
ap-2076	194	8	ε	ε	PROPN
ap-2076	194	9	)	)	PUNCT
ap-2076	194	10	+	+	CCONJ
ap-2076	194	11	zεa12(zε	zεa12(zε	NUM
ap-2076	194	12	,	,	PUNCT
ap-2076	194	13	ε	ε	PROPN
ap-2076	194	14	)	)	PUNCT
ap-2076	194	15	)	)	PUNCT
ap-2076	195	1	x2	x2	NOUN
ap-2076	196	1	=	=	SYM
ap-2076	196	2	0	0	PROPN
ap-2076	196	3	,	,	PUNCT
ap-2076	196	4	ε	ε	PROPN
ap-2076	196	5	zε	zε	VERB
ap-2076	196	6	a21(zε	a21(zε	NUM
ap-2076	196	7	,	,	PUNCT
ap-2076	196	8	ε)x1	ε)x1	NOUN
ap-2076	196	9	+	+	CCONJ
ap-2076	196	10	(	(	PUNCT
ap-2076	196	11	ε	ε	PROPN
ap-2076	196	12	z2	z2	PROPN
ap-2076	196	13	ε	ε	PROPN
ap-2076	196	14	(	(	PUNCT
ap-2076	196	15	a21(zε	a21(zε	PROPN
ap-2076	196	16	,	,	PUNCT
ap-2076	196	17	ε	ε	PROPN
ap-2076	196	18	)	)	PUNCT
ap-2076	196	19	+	+	NUM
ap-2076	196	20	zεa22(zε	zεa22(zε	NUM
ap-2076	196	21	,	,	PUNCT
ap-2076	196	22	ε	ε	PROPN
ap-2076	196	23	)	)	PUNCT
ap-2076	196	24	)	)	PUNCT
ap-2076	197	1	−	−	PROPN
ap-2076	198	1	1	1	X
ap-2076	198	2	)	)	PUNCT
ap-2076	198	3	x2	x2	NOUN
ap-2076	198	4	=	=	SYM
ap-2076	198	5	0	0	NUM
ap-2076	198	6	,	,	PUNCT
ap-2076	198	7	(	(	PUNCT
ap-2076	198	8	2.18	2.18	NUM
ap-2076	198	9	)	)	PUNCT
ap-2076	198	10	where	where	SCONJ
ap-2076	198	11	xi	xi	X
ap-2076	198	12	=	=	PUNCT
ap-2076	198	13	`	`	PUNCT
ap-2076	198	14	ilεψε	ilεψε	PROPN
ap-2076	198	15	,	,	PUNCT
ap-2076	198	16	and	and	CCONJ
ap-2076	198	17	ai1(z	ai1(z	PROPN
ap-2076	198	18	,	,	PUNCT
ap-2076	198	19	ε	ε	PROPN
ap-2076	198	20	)	)	PUNCT
ap-2076	198	21	:	:	PUNCT
ap-2076	199	1	=	=	PUNCT
ap-2076	199	2	`	`	PUNCT
ap-2076	199	3	ilεa(λ0	ilεa(λ0	VERB
ap-2076	199	4	+	+	CCONJ
ap-2076	199	5	z	z	X
ap-2076	199	6	,	,	PUNCT
ap-2076	199	7	ε)ψ0	ε)ψ0	PROPN
ap-2076	199	8	,	,	PUNCT
ap-2076	199	9	ai2(z	ai2(z	PROPN
ap-2076	199	10	,	,	PUNCT
ap-2076	199	11	ε	ε	PROPN
ap-2076	199	12	)	)	PUNCT
ap-2076	199	13	:	:	PUNCT
ap-2076	199	14	=	=	PUNCT
ap-2076	199	15	`	`	PUNCT
ap-2076	199	16	ilεa(λ0	ilεa(λ0	VERB
ap-2076	200	1	+	+	CCONJ
ap-2076	200	2	z	z	X
ap-2076	200	3	,	,	PUNCT
ap-2076	200	4	ε)φ0	ε)φ0	PROPN
ap-2076	200	5	,	,	PUNCT
ap-2076	200	6	i	i	NOUN
ap-2076	200	7	=	=	NOUN
ap-2076	200	8	1	1	NUM
ap-2076	200	9	,	,	PUNCT
ap-2076	200	10	2	2	NUM
ap-2076	200	11	.	.	PUNCT
ap-2076	201	1	the	the	DET
ap-2076	201	2	obtained	obtain	VERB
ap-2076	201	3	system	system	NOUN
ap-2076	201	4	of	of	ADP
ap-2076	201	5	equations	equation	NOUN
ap-2076	201	6	is	be	AUX
ap-2076	201	7	linear	linear	PROPN
ap-2076	201	8	w.r.t	w.r.t	NOUN
ap-2076	201	9	.	.	PUNCT
ap-2076	202	1	(	(	PUNCT
ap-2076	202	2	x1	x1	PROPN
ap-2076	202	3	,	,	PUNCT
ap-2076	202	4	x2	x2	PROPN
ap-2076	202	5	)	)	PUNCT
ap-2076	202	6	.	.	PUNCT
ap-2076	203	1	we	we	PRON
ap-2076	203	2	need	need	VERB
ap-2076	203	3	a	a	DET
ap-2076	203	4	non	non	ADJ
ap-2076	203	5	-	-	ADJ
ap-2076	203	6	zero	zero	ADJ
ap-2076	203	7	solution	solution	NOUN
ap-2076	203	8	to	to	ADP
ap-2076	203	9	this	this	DET
ap-2076	203	10	system	system	NOUN
ap-2076	203	11	since	since	SCONJ
ap-2076	203	12	otherwise	otherwise	ADV
ap-2076	203	13	by	by	ADP
ap-2076	203	14	(	(	PUNCT
ap-2076	203	15	2.17	2.17	NUM
ap-2076	203	16	)	)	PUNCT
ap-2076	203	17	we	we	PRON
ap-2076	203	18	would	would	AUX
ap-2076	203	19	get	get	VERB
ap-2076	203	20	ψε	ψε	NOUN
ap-2076	203	21	=	=	SYM
ap-2076	203	22	0	0	NUM
ap-2076	203	23	and	and	CCONJ
ap-2076	203	24	ψε	ψε	AUX
ap-2076	203	25	then	then	ADV
ap-2076	203	26	can	can	AUX
ap-2076	203	27	not	not	PART
ap-2076	203	28	be	be	AUX
ap-2076	203	29	an	an	DET
ap-2076	203	30	eigenfunction	eigenfunction	NOUN
ap-2076	203	31	.	.	PUNCT
ap-2076	204	1	system	system	NOUN
ap-2076	204	2	(	(	PUNCT
ap-2076	204	3	2.18	2.18	NUM
ap-2076	204	4	)	)	PUNCT
ap-2076	204	5	has	have	VERB
ap-2076	204	6	a	a	DET
ap-2076	204	7	nonzero	nonzero	ADJ
ap-2076	204	8	solution	solution	NOUN
ap-2076	204	9	if	if	SCONJ
ap-2076	204	10	its	its	PRON
ap-2076	204	11	determinant	determinant	ADJ
ap-2076	204	12	vanishes	vanish	VERB
ap-2076	204	13	.	.	PUNCT
ap-2076	205	1	it	it	PRON
ap-2076	205	2	implies	imply	VERB
ap-2076	205	3	the	the	DET
ap-2076	205	4	equation	equation	NOUN
ap-2076	205	5	z2	z2	PROPN
ap-2076	205	6	ε	ε	PROPN
ap-2076	205	7	−	−	PROPN
ap-2076	205	8	ε	ε	PROPN
ap-2076	205	9	(	(	PUNCT
ap-2076	205	10	a11(zε	a11(zε	PROPN
ap-2076	205	11	,	,	PUNCT
ap-2076	205	12	ε	ε	PROPN
ap-2076	205	13	)	)	PUNCT
ap-2076	205	14	+	+	NOUN
ap-2076	205	15	a22(zε	a22(zε	PROPN
ap-2076	205	16	,	,	PUNCT
ap-2076	205	17	ε	ε	PROPN
ap-2076	205	18	)	)	PUNCT
ap-2076	205	19	)	)	PUNCT
ap-2076	206	1	zε	zε	ADP
ap-2076	206	2	−	−	PROPN
ap-2076	206	3	εa21(zε	εa21(zε	NOUN
ap-2076	206	4	,	,	PUNCT
ap-2076	206	5	ε	ε	PROPN
ap-2076	206	6	)	)	PUNCT
ap-2076	207	1	+	+	X
ap-2076	207	2	ε2(a11(zε	ε2(a11(zε	ADJ
ap-2076	207	3	,	,	PUNCT
ap-2076	207	4	ε)a22(zε	ε)a22(zε	PROPN
ap-2076	207	5	,	,	PUNCT
ap-2076	207	6	ε)−a12(zε	ε)−a12(zε	PROPN
ap-2076	207	7	,	,	PUNCT
ap-2076	207	8	ε)a21(zε	ε)a21(zε	PROPN
ap-2076	207	9	,	,	PUNCT
ap-2076	207	10	ε	ε	PROPN
ap-2076	207	11	)	)	PUNCT
ap-2076	207	12	)	)	PUNCT
ap-2076	208	1	=	=	SYM
ap-2076	208	2	0	0	NUM
ap-2076	208	3	,	,	PUNCT
ap-2076	208	4	which	which	PRON
ap-2076	208	5	is	be	AUX
ap-2076	208	6	equivalent	equivalent	ADJ
ap-2076	208	7	to	to	ADP
ap-2076	208	8	the	the	DET
ap-2076	208	9	following	follow	VERB
ap-2076	208	10	two	two	NUM
ap-2076	208	11	zε	zε	ADJ
ap-2076	208	12	=	=	SYM
ap-2076	208	13	g±(zε	g±(zε	PROPN
ap-2076	208	14	,	,	PUNCT
ap-2076	208	15	ε1/2	ε1/2	NOUN
ap-2076	208	16	)	)	PUNCT
ap-2076	208	17	,	,	PUNCT
ap-2076	208	18	(	(	PUNCT
ap-2076	208	19	2.19	2.19	NUM
ap-2076	208	20	)	)	PUNCT
ap-2076	208	21	where	where	SCONJ
ap-2076	208	22	g±(z	g±(z	PROPN
ap-2076	208	23	,	,	PUNCT
ap-2076	208	24	κ	κ	NOUN
ap-2076	208	25	)	)	PUNCT
ap-2076	208	26	:	:	PUNCT
ap-2076	209	1	=	=	SYM
ap-2076	209	2	κ2(a11(z	κ2(a11(z	PROPN
ap-2076	209	3	,	,	PUNCT
ap-2076	209	4	κ2	κ2	NOUN
ap-2076	209	5	)	)	PUNCT
ap-2076	209	6	+	+	SYM
ap-2076	209	7	a22(z	a22(z	NOUN
ap-2076	209	8	,	,	PUNCT
ap-2076	209	9	κ2	κ2	PROPN
ap-2076	209	10	)	)	PUNCT
ap-2076	209	11	)	)	PUNCT
ap-2076	209	12	2	2	NUM
ap-2076	209	13	±	±	NUM
ap-2076	209	14	κ	κ	NOUN
ap-2076	209	15	(	(	PUNCT
ap-2076	209	16	a21(z	a21(z	NOUN
ap-2076	209	17	,	,	PUNCT
ap-2076	209	18	κ2	κ2	NOUN
ap-2076	209	19	)	)	PUNCT
ap-2076	209	20	+	+	NUM
ap-2076	209	21	κ2	κ2	NOUN
ap-2076	209	22	4	4	NUM
ap-2076	209	23	(	(	PUNCT
ap-2076	209	24	a11(z	a11(z	PROPN
ap-2076	209	25	,	,	PUNCT
ap-2076	209	26	κ2)−a22(z	κ2)−a22(z	NOUN
ap-2076	209	27	,	,	PUNCT
ap-2076	209	28	κ2	κ2	NOUN
ap-2076	209	29	)	)	PUNCT
ap-2076	209	30	)	)	PUNCT
ap-2076	209	31	2	2	NUM
ap-2076	209	32	+	+	NUM
ap-2076	209	33	κ2a12(z	κ2a12(z	NOUN
ap-2076	209	34	,	,	PUNCT
ap-2076	209	35	κ2)a21(z	κ2)a21(z	PROPN
ap-2076	209	36	,	,	PUNCT
ap-2076	209	37	κ2	κ2	NOUN
ap-2076	209	38	)	)	PUNCT
ap-2076	209	39	)	)	PUNCT
ap-2076	209	40	1/2	1/2	NUM
ap-2076	209	41	.	.	PUNCT
ap-2076	210	1	(	(	PUNCT
ap-2076	210	2	2.20	2.20	NUM
ap-2076	210	3	)	)	PUNCT
ap-2076	210	4	here	here	ADV
ap-2076	210	5	the	the	DET
ap-2076	210	6	branch	branch	NOUN
ap-2076	210	7	of	of	ADP
ap-2076	210	8	the	the	DET
ap-2076	210	9	square	square	ADJ
ap-2076	210	10	root	root	NOUN
ap-2076	210	11	is	be	AUX
ap-2076	210	12	fixed	fix	VERB
ap-2076	210	13	by	by	ADP
ap-2076	210	14	the	the	DET
ap-2076	210	15	restriction	restriction	NOUN
ap-2076	210	16	11/2	11/2	NUM
ap-2076	211	1	=	=	SYM
ap-2076	211	2	1	1	X
ap-2076	211	3	.	.	PUNCT
ap-2076	212	1	it	it	PRON
ap-2076	212	2	is	be	AUX
ap-2076	212	3	clear	clear	ADJ
ap-2076	212	4	that	that	SCONJ
ap-2076	212	5	the	the	DET
ap-2076	212	6	functions	function	NOUN
ap-2076	212	7	aij	aij	PROPN
ap-2076	212	8	are	be	AUX
ap-2076	212	9	jointly	jointly	ADV
ap-2076	212	10	holomorphic	holomorphic	ADJ
ap-2076	212	11	w.r.t	w.r.t	NOUN
ap-2076	212	12	.	.	PUNCT
ap-2076	213	1	sufficiently	sufficiently	ADV
ap-2076	213	2	small	small	ADJ
ap-2076	213	3	z	z	NOUN
ap-2076	213	4	and	and	CCONJ
ap-2076	213	5	ε	ε	PROPN
ap-2076	213	6	.	.	PUNCT
ap-2076	214	1	moreover	moreover	ADV
ap-2076	214	2	,	,	PUNCT
ap-2076	214	3	by	by	ADP
ap-2076	214	4	(	(	PUNCT
ap-2076	214	5	2.2	2.2	NUM
ap-2076	214	6	)	)	PUNCT
ap-2076	214	7	a21(0	a21(0	NOUN
ap-2076	214	8	,	,	PUNCT
ap-2076	214	9	ε	ε	PROPN
ap-2076	214	10	)	)	PUNCT
ap-2076	214	11	=	=	PUNCT
ap-2076	214	12	`	`	PUNCT
ap-2076	214	13	2lεa(0	2lεa(0	NUM
ap-2076	214	14	,	,	PUNCT
ap-2076	214	15	ε)ψ0	ε)ψ0	PROPN
ap-2076	214	16	=	=	PUNCT
ap-2076	214	17	i`2	i`2	PROPN
ap-2076	214	18	(	(	PUNCT
ap-2076	214	19	−2β′x2	−2β′x2	NOUN
ap-2076	214	20	∂	∂	NUM
ap-2076	214	21	∂x1	∂x1	NOUN
ap-2076	214	22	−	−	NOUN
ap-2076	214	23	2β	2β	NOUN
ap-2076	214	24	∂	∂	NUM
ap-2076	214	25	∂x2	∂x2	NOUN
ap-2076	214	26	−	−	NOUN
ap-2076	214	27	β′′x2	β′′x2	PUNCT
ap-2076	214	28	)	)	PUNCT
ap-2076	214	29	ψ0	ψ0	ADV
ap-2076	215	1	+	+	ADJ
ap-2076	215	2	o(ε	o(ε	PROPN
ap-2076	215	3	)	)	PUNCT
ap-2076	215	4	.	.	PUNCT
ap-2076	216	1	(	(	PUNCT
ap-2076	216	2	2.21	2.21	NUM
ap-2076	216	3	)	)	PUNCT
ap-2076	216	4	to	to	PART
ap-2076	216	5	calculate	calculate	VERB
ap-2076	216	6	the	the	DET
ap-2076	216	7	first	first	ADJ
ap-2076	216	8	term	term	NOUN
ap-2076	216	9	on	on	ADP
ap-2076	216	10	the	the	DET
ap-2076	216	11	right	right	ADJ
ap-2076	216	12	hand	hand	NOUN
ap-2076	216	13	side	side	NOUN
ap-2076	216	14	of	of	ADP
ap-2076	216	15	this	this	DET
ap-2076	216	16	identity	identity	NOUN
ap-2076	216	17	,	,	PUNCT
ap-2076	216	18	we	we	PRON
ap-2076	216	19	first	first	ADV
ap-2076	216	20	observe	observe	VERB
ap-2076	216	21	that	that	SCONJ
ap-2076	216	22	by	by	ADP
ap-2076	216	23	the	the	DET
ap-2076	216	24	equation	equation	NOUN
ap-2076	216	25	for	for	ADP
ap-2076	216	26	ψ0	ψ0	ADV
ap-2076	216	27	we	we	PRON
ap-2076	216	28	have	have	VERB
ap-2076	216	29	−	−	NUM
ap-2076	216	30	(	(	PUNCT
ap-2076	216	31	2β′x2	2β′x2	NUM
ap-2076	216	32	∂	∂	NUM
ap-2076	216	33	∂x1	∂x1	NOUN
ap-2076	216	34	+	+	CCONJ
ap-2076	216	35	2β	2β	NOUN
ap-2076	216	36	∂	∂	NUM
ap-2076	216	37	∂x2	∂x2	NOUN
ap-2076	216	38	+	+	SYM
ap-2076	216	39	β′′x2	β′′x2	PUNCT
ap-2076	216	40	)	)	PUNCT
ap-2076	217	1	ψ0	ψ0	NOUN
ap-2076	217	2	=	=	PUNCT
ap-2076	218	1	−(∆	−(∆	NOUN
ap-2076	219	1	+	+	CCONJ
ap-2076	219	2	λ0)βx2ψ0	λ0)βx2ψ0	PROPN
ap-2076	220	1	=	=	NOUN
ap-2076	220	2	:	:	PUNCT
ap-2076	220	3	g.	g.	PROPN
ap-2076	220	4	now	now	ADV
ap-2076	220	5	we	we	PRON
ap-2076	220	6	find	find	VERB
ap-2076	220	7	i`2	i`2	NOUN
ap-2076	220	8	g	g	NOUN
ap-2076	220	9	by	by	ADP
ap-2076	220	10	integration	integration	NOUN
ap-2076	220	11	by	by	ADP
ap-2076	220	12	parts	part	NOUN
ap-2076	220	13	i`2	i`2	NOUN
ap-2076	220	14	g	g	PROPN
ap-2076	221	1	=	=	SYM
ap-2076	222	1	∫	∫	PROPN
ap-2076	223	1	ω	ω	NUM
ap-2076	223	2	ψ0(∆	ψ0(∆	PROPN
ap-2076	224	1	+	+	CCONJ
ap-2076	224	2	λ0)βx2ψ0	λ0)βx2ψ0	NOUN
ap-2076	224	3	dx	dx	PROPN
ap-2076	225	1	=	=	NOUN
ap-2076	226	1	i	i	PRON
ap-2076	226	2	∫	∫	VERB
ap-2076	226	3	γ+	γ+	PRON
ap-2076	226	4	(	(	PUNCT
ap-2076	226	5	ψ0	ψ0	PROPN
ap-2076	226	6	∂	∂	NUM
ap-2076	226	7	∂x2	∂x2	NOUN
ap-2076	226	8	βx2ψ0	βx2ψ0	PROPN
ap-2076	226	9	−	−	PROPN
ap-2076	226	10	βx2ψ0	βx2ψ0	PROPN
ap-2076	226	11	∂ψ0	∂ψ0	PROPN
ap-2076	226	12	∂x2	∂x2	NOUN
ap-2076	226	13	)	)	PUNCT
ap-2076	227	1	dx1	dx1	PROPN
ap-2076	228	1	−	−	PROPN
ap-2076	229	1	i	i	PRON
ap-2076	229	2	∫	∫	PROPN
ap-2076	229	3	γ−	γ−	PROPN
ap-2076	229	4	(	(	PUNCT
ap-2076	229	5	ψ0	ψ0	NOUN
ap-2076	229	6	∂	∂	NUM
ap-2076	229	7	∂x2	∂x2	NOUN
ap-2076	229	8	βx2ψ0	βx2ψ0	PROPN
ap-2076	229	9	−	−	PROPN
ap-2076	229	10	βx2ψ0	βx2ψ0	PROPN
ap-2076	229	11	∂ψ0	∂ψ0	PROPN
ap-2076	229	12	∂x2	∂x2	NOUN
ap-2076	229	13	)	)	PUNCT
ap-2076	229	14	dx1	dx1	X
ap-2076	230	1	=	=	PUNCT
ap-2076	231	1	i	i	PRON
ap-2076	231	2	∫	∫	PROPN
ap-2076	231	3	γ+	γ+	PUNCT
ap-2076	231	4	βψ2	βψ2	PROPN
ap-2076	231	5	0	0	PUNCT
ap-2076	232	1	dx1	dx1	PROPN
ap-2076	233	1	−	−	PROPN
ap-2076	234	1	i	i	PRON
ap-2076	234	2	∫	∫	PROPN
ap-2076	234	3	γ−	γ−	NUM
ap-2076	234	4	βψ2	βψ2	NOUN
ap-2076	234	5	0	0	NUM
ap-2076	235	1	dx1	dx1	PROPN
ap-2076	235	2	.	.	PUNCT
ap-2076	236	1	(	(	PUNCT
ap-2076	236	2	2.22	2.22	NUM
ap-2076	236	3	)	)	PUNCT
ap-2076	236	4	together	together	ADV
ap-2076	236	5	with	with	ADP
ap-2076	236	6	lemma	lemma	PROPN
ap-2076	236	7	2.2	2.2	NUM
ap-2076	236	8	this	this	PRON
ap-2076	236	9	implies	imply	VERB
ap-2076	236	10	i`2	i`2	NOUN
ap-2076	236	11	g	g	NOUN
ap-2076	236	12	=	=	PUNCT
ap-2076	236	13	−4	−4	PROPN
ap-2076	237	1	∫	∫	PROPN
ap-2076	237	2	γ+	γ+	X
ap-2076	237	3	βreψ0	βreψ0	PROPN
ap-2076	238	1	imψ0	imψ0	PROPN
ap-2076	238	2	dx1	dx1	PROPN
ap-2076	238	3	.	.	PUNCT
ap-2076	239	1	(	(	PUNCT
ap-2076	239	2	2.23	2.23	NUM
ap-2076	239	3	)	)	PUNCT
ap-2076	239	4	97	97	NUM
ap-2076	239	5	denis	denis	PROPN
ap-2076	239	6	borisov	borisov	PROPN
ap-2076	239	7	acta	acta	PROPN
ap-2076	239	8	polytechnica	polytechnica	PROPN
ap-2076	239	9	hence	hence	ADV
ap-2076	239	10	,	,	PUNCT
ap-2076	239	11	by	by	ADP
ap-2076	239	12	(	(	PUNCT
ap-2076	239	13	2.20	2.20	NUM
ap-2076	239	14	)	)	PUNCT
ap-2076	239	15	,	,	PUNCT
ap-2076	239	16	(	(	PUNCT
ap-2076	239	17	2.22	2.22	NUM
ap-2076	239	18	)	)	PUNCT
ap-2076	239	19	,	,	PUNCT
ap-2076	239	20	(	(	PUNCT
ap-2076	239	21	1.12	1.12	NUM
ap-2076	239	22	)	)	PUNCT
ap-2076	239	23	,	,	PUNCT
ap-2076	239	24	and	and	CCONJ
ap-2076	239	25	the	the	DET
ap-2076	239	26	properties	property	NOUN
ap-2076	239	27	of	of	ADP
ap-2076	239	28	functions	function	NOUN
ap-2076	239	29	aij	aij	PROPN
ap-2076	239	30	we	we	PRON
ap-2076	239	31	conclude	conclude	VERB
ap-2076	239	32	that	that	SCONJ
ap-2076	239	33	functions	function	VERB
ap-2076	239	34	g±	g±	NOUN
ap-2076	239	35	are	be	AUX
ap-2076	239	36	jointly	jointly	ADV
ap-2076	239	37	holomorphic	holomorphic	ADJ
ap-2076	239	38	w.r.t	w.r.t	NOUN
ap-2076	239	39	.	.	PUNCT
ap-2076	240	1	sufficiently	sufficiently	ADV
ap-2076	240	2	small	small	ADJ
ap-2076	240	3	z	z	NOUN
ap-2076	240	4	and	and	CCONJ
ap-2076	240	5	κ	κ	NOUN
ap-2076	240	6	.	.	PUNCT
ap-2076	241	1	applying	apply	VERB
ap-2076	241	2	the	the	DET
ap-2076	241	3	rouché	rouché	NOUN
ap-2076	241	4	theorem	theorem	NOUN
ap-2076	241	5	as	as	ADP
ap-2076	241	6	in	in	ADP
ap-2076	241	7	[	[	X
ap-2076	241	8	10	10	NUM
ap-2076	241	9	,	,	PUNCT
ap-2076	241	10	sec	sec	PROPN
ap-2076	241	11	.	.	PROPN
ap-2076	241	12	4	4	NUM
ap-2076	241	13	]	]	PUNCT
ap-2076	241	14	,	,	PUNCT
ap-2076	241	15	we	we	PRON
ap-2076	241	16	conclude	conclude	VERB
ap-2076	241	17	that	that	SCONJ
ap-2076	241	18	for	for	ADP
ap-2076	241	19	all	all	DET
ap-2076	241	20	sufficiently	sufficiently	ADV
ap-2076	241	21	small	small	ADJ
ap-2076	241	22	κ	κ	ADP
ap-2076	241	23	each	each	PRON
ap-2076	241	24	of	of	ADP
ap-2076	241	25	the	the	DET
ap-2076	241	26	functions	function	NOUN
ap-2076	241	27	z	z	NOUN
ap-2076	241	28	7→	7→	NUM
ap-2076	241	29	z	z	NOUN
ap-2076	241	30	−	−	PROPN
ap-2076	242	1	g±(z	g±(z	PROPN
ap-2076	242	2	,	,	PUNCT
ap-2076	242	3	κ	κ	NOUN
ap-2076	242	4	)	)	PUNCT
ap-2076	242	5	has	have	VERB
ap-2076	242	6	a	a	DET
ap-2076	242	7	simple	simple	ADJ
ap-2076	242	8	zero	zero	NUM
ap-2076	242	9	z±(κ	z±(κ	NOUN
ap-2076	242	10	)	)	PUNCT
ap-2076	242	11	in	in	ADP
ap-2076	242	12	a	a	DET
ap-2076	242	13	small	small	ADJ
ap-2076	242	14	neighborhood	neighborhood	NOUN
ap-2076	242	15	of	of	ADP
ap-2076	242	16	the	the	DET
ap-2076	242	17	origin	origin	NOUN
ap-2076	242	18	.	.	PUNCT
ap-2076	243	1	by	by	ADP
ap-2076	243	2	the	the	DET
ap-2076	243	3	implicit	implicit	ADJ
ap-2076	243	4	function	function	NOUN
ap-2076	243	5	theorem	theorem	VERB
ap-2076	243	6	these	these	DET
ap-2076	243	7	zeroes	zero	NOUN
ap-2076	243	8	are	be	AUX
ap-2076	243	9	holomorphic	holomorphic	ADJ
ap-2076	243	10	w.r.t	w.r.t	NOUN
ap-2076	243	11	.	.	PUNCT
ap-2076	244	1	κ	κ	X
ap-2076	244	2	.	.	PUNCT
ap-2076	245	1	thus	thus	ADV
ap-2076	245	2	,	,	PUNCT
ap-2076	245	3	the	the	DET
ap-2076	245	4	desired	desire	VERB
ap-2076	245	5	solutions	solution	NOUN
ap-2076	245	6	to	to	ADP
ap-2076	245	7	equations	equation	NOUN
ap-2076	245	8	(	(	PUNCT
ap-2076	245	9	2.19	2.19	NUM
ap-2076	245	10	)	)	PUNCT
ap-2076	245	11	are	be	AUX
ap-2076	245	12	z±(ε1/2	z±(ε1/2	NUM
ap-2076	245	13	)	)	PUNCT
ap-2076	245	14	,	,	PUNCT
ap-2076	245	15	and	and	CCONJ
ap-2076	245	16	these	these	DET
ap-2076	245	17	functions	function	NOUN
ap-2076	245	18	are	be	AUX
ap-2076	245	19	holomorphic	holomorphic	ADJ
ap-2076	245	20	w.r.t	w.r.t	NOUN
ap-2076	245	21	.	.	PUNCT
ap-2076	246	1	ε1/2	ε1/2	VERB
ap-2076	246	2	.	.	PUNCT
ap-2076	247	1	moreover	moreover	ADV
ap-2076	247	2	,	,	PUNCT
ap-2076	247	3	it	it	PRON
ap-2076	247	4	follows	follow	VERB
ap-2076	247	5	from	from	ADP
ap-2076	247	6	(	(	PUNCT
ap-2076	247	7	2.19	2.19	NUM
ap-2076	247	8	)	)	PUNCT
ap-2076	247	9	,	,	PUNCT
ap-2076	247	10	(	(	PUNCT
ap-2076	247	11	2.20	2.20	NUM
ap-2076	247	12	)	)	PUNCT
ap-2076	247	13	,	,	PUNCT
ap-2076	247	14	(	(	PUNCT
ap-2076	247	15	2.21	2.21	NUM
ap-2076	247	16	)	)	PUNCT
ap-2076	247	17	,	,	PUNCT
ap-2076	247	18	(	(	PUNCT
ap-2076	247	19	2.22	2.22	NUM
ap-2076	247	20	)	)	PUNCT
ap-2076	247	21	,	,	PUNCT
ap-2076	247	22	(	(	PUNCT
ap-2076	247	23	2.23	2.23	NUM
ap-2076	247	24	)	)	PUNCT
ap-2076	247	25	that	that	PRON
ap-2076	247	26	z±(ε1/2	z±(ε1/2	NUM
ap-2076	247	27	)	)	PUNCT
ap-2076	247	28	=	=	SYM
ap-2076	248	1	g±(0	g±(0	ADJ
ap-2076	248	2	,	,	PUNCT
ap-2076	248	3	ε1/2	ε1/2	NOUN
ap-2076	248	4	)	)	PUNCT
ap-2076	249	1	+	+	VERB
ap-2076	249	2	o(ε	o(ε	PROPN
ap-2076	249	3	)	)	PUNCT
ap-2076	249	4	=	=	SYM
ap-2076	250	1	±ε1/2a	±ε1/2a	NUM
ap-2076	250	2	1/2	1/2	NUM
ap-2076	250	3	21	21	NUM
ap-2076	250	4	(	(	PUNCT
ap-2076	250	5	0	0	NUM
ap-2076	250	6	,	,	PUNCT
ap-2076	250	7	ε	ε	PROPN
ap-2076	250	8	)	)	PUNCT
ap-2076	250	9	+	+	ADJ
ap-2076	250	10	o(ε	o(ε	PROPN
ap-2076	250	11	)	)	PUNCT
ap-2076	250	12	and	and	CCONJ
ap-2076	250	13	then	then	ADV
ap-2076	250	14	the	the	DET
ap-2076	250	15	sought	seek	VERB
ap-2076	250	16	eigenvalues	eigenvalue	NOUN
ap-2076	250	17	are	be	AUX
ap-2076	250	18	λ±ε	λ±ε	PRON
ap-2076	250	19	=	=	PUNCT
ap-2076	250	20	λ0	λ0	NOUN
ap-2076	250	21	+	+	CCONJ
ap-2076	250	22	z±(ε1/2	z±(ε1/2	NUM
ap-2076	250	23	)	)	PUNCT
ap-2076	250	24	.	.	PUNCT
ap-2076	251	1	these	these	DET
ap-2076	251	2	eigenvalues	eigenvalue	NOUN
ap-2076	251	3	are	be	AUX
ap-2076	251	4	holomorphic	holomorphic	ADJ
ap-2076	251	5	w.r.t	w.r.t	NOUN
ap-2076	251	6	.	.	PUNCT
ap-2076	252	1	ε1/2	ε1/2	VERB
ap-2076	252	2	and	and	CCONJ
ap-2076	252	3	obey	obey	VERB
ap-2076	252	4	(	(	PUNCT
ap-2076	252	5	1.15	1.15	NUM
ap-2076	252	6	)	)	PUNCT
ap-2076	252	7	.	.	PUNCT
ap-2076	253	1	let	let	VERB
ap-2076	253	2	us	we	PRON
ap-2076	253	3	prove	prove	VERB
ap-2076	253	4	that	that	SCONJ
ap-2076	253	5	these	these	DET
ap-2076	253	6	eigenvalues	eigenvalue	NOUN
ap-2076	253	7	are	be	AUX
ap-2076	253	8	real	real	ADJ
ap-2076	253	9	as	as	ADP
ap-2076	253	10	(	(	PUNCT
ap-2076	253	11	1.13	1.13	NUM
ap-2076	253	12	)	)	PUNCT
ap-2076	253	13	holds	hold	VERB
ap-2076	253	14	true	true	ADJ
ap-2076	253	15	and	and	CCONJ
ap-2076	253	16	are	be	AUX
ap-2076	253	17	complex	complex	ADJ
ap-2076	253	18	once	once	ADV
ap-2076	253	19	(	(	PUNCT
ap-2076	253	20	1.14	1.14	NUM
ap-2076	253	21	)	)	PUNCT
ap-2076	253	22	is	be	AUX
ap-2076	253	23	satisfied	satisfied	ADJ
ap-2076	253	24	.	.	PUNCT
ap-2076	254	1	the	the	DET
ap-2076	254	2	latter	latter	ADJ
ap-2076	254	3	statement	statement	NOUN
ap-2076	254	4	follows	follow	VERB
ap-2076	254	5	easily	easily	ADV
ap-2076	254	6	from	from	ADP
ap-2076	254	7	formulae	formulae	ADJ
ap-2076	254	8	(	(	PUNCT
ap-2076	254	9	1.15	1.15	NUM
ap-2076	254	10	)	)	PUNCT
ap-2076	254	11	since	since	SCONJ
ap-2076	254	12	in	in	ADP
ap-2076	254	13	this	this	DET
ap-2076	254	14	case	case	NOUN
ap-2076	254	15	ε1/2λ±1/2	ε1/2λ±1/2	NOUN
ap-2076	254	16	are	be	AUX
ap-2076	254	17	two	two	NUM
ap-2076	254	18	imaginary	imaginary	ADJ
ap-2076	254	19	numbers	number	NOUN
ap-2076	254	20	.	.	PUNCT
ap-2076	255	1	to	to	PART
ap-2076	255	2	prove	prove	VERB
ap-2076	255	3	the	the	DET
ap-2076	255	4	reality	reality	NOUN
ap-2076	255	5	,	,	PUNCT
ap-2076	255	6	as	as	SCONJ
ap-2076	255	7	one	one	PRON
ap-2076	255	8	can	can	AUX
ap-2076	255	9	easily	easily	ADV
ap-2076	255	10	make	make	VERB
ap-2076	255	11	sure	sure	ADJ
ap-2076	255	12	,	,	PUNCT
ap-2076	255	13	it	it	PRON
ap-2076	255	14	is	be	AUX
ap-2076	255	15	sufficient	sufficient	ADJ
ap-2076	255	16	to	to	PART
ap-2076	255	17	prove	prove	VERB
ap-2076	255	18	that	that	SCONJ
ap-2076	255	19	functions	function	VERB
ap-2076	255	20	g±(z	g±(z	PROPN
ap-2076	255	21	,	,	PUNCT
ap-2076	255	22	κ	κ	NOUN
ap-2076	255	23	)	)	PUNCT
ap-2076	255	24	are	be	AUX
ap-2076	255	25	real	real	ADJ
ap-2076	255	26	for	for	ADP
ap-2076	255	27	real	real	ADJ
ap-2076	255	28	z	z	NOUN
ap-2076	255	29	and	and	CCONJ
ap-2076	255	30	κ	κ	NOUN
ap-2076	255	31	.	.	PUNCT
ap-2076	256	1	then	then	ADV
ap-2076	256	2	the	the	DET
ap-2076	256	3	existence	existence	NOUN
ap-2076	256	4	of	of	ADP
ap-2076	256	5	a	a	DET
ap-2076	256	6	real	real	ADJ
ap-2076	256	7	root	root	NOUN
ap-2076	256	8	is	be	AUX
ap-2076	256	9	implied	imply	VERB
ap-2076	256	10	easily	easily	ADV
ap-2076	256	11	by	by	ADP
ap-2076	256	12	the	the	DET
ap-2076	256	13	implicit	implicit	ADJ
ap-2076	256	14	function	function	NOUN
ap-2076	256	15	theorem	theorem	VERB
ap-2076	256	16	for	for	ADP
ap-2076	256	17	real	real	ADJ
ap-2076	256	18	functions	function	NOUN
ap-2076	256	19	.	.	PUNCT
ap-2076	257	1	in	in	ADP
ap-2076	257	2	view	view	NOUN
ap-2076	257	3	of	of	ADP
ap-2076	257	4	definition	definition	NOUN
ap-2076	257	5	(	(	PUNCT
ap-2076	257	6	2.20	2.20	NUM
ap-2076	257	7	)	)	PUNCT
ap-2076	257	8	of	of	ADP
ap-2076	257	9	g±	g±	NOUN
ap-2076	257	10	,	,	PUNCT
ap-2076	257	11	the	the	DET
ap-2076	257	12	desired	desire	VERB
ap-2076	257	13	fact	fact	NOUN
ap-2076	257	14	is	be	AUX
ap-2076	257	15	yielded	yield	VERB
ap-2076	257	16	by	by	ADP
ap-2076	257	17	the	the	DET
ap-2076	257	18	similar	similar	ADJ
ap-2076	257	19	reality	reality	NOUN
ap-2076	257	20	of	of	ADP
ap-2076	257	21	aij	aij	PROPN
ap-2076	257	22	.	.	PUNCT
ap-2076	258	1	let	let	VERB
ap-2076	258	2	us	we	PRON
ap-2076	258	3	prove	prove	VERB
ap-2076	258	4	the	the	DET
ap-2076	258	5	latter	latter	ADJ
ap-2076	258	6	.	.	PUNCT
ap-2076	259	1	it	it	PRON
ap-2076	259	2	follows	follow	VERB
ap-2076	259	3	from	from	ADP
ap-2076	259	4	lemma	lemma	PROPN
ap-2076	259	5	2.3	2.3	NUM
ap-2076	259	6	that	that	PRON
ap-2076	259	7	for	for	ADP
ap-2076	259	8	each	each	DET
ap-2076	259	9	f	f	PROPN
ap-2076	259	10	∈	∈	PROPN
ap-2076	259	11	l2(ω	l2(ω	PROPN
ap-2076	259	12	)	)	PUNCT
ap-2076	259	13	the	the	DET
ap-2076	259	14	function	function	NOUN
ap-2076	259	15	rα(λ)f	rα(λ)f	PUNCT
ap-2076	259	16	=	=	PUNCT
ap-2076	259	17	(	(	PUNCT
ap-2076	259	18	hα	hα	ADP
ap-2076	259	19	−	−	PROPN
ap-2076	259	20	λ)−1f	λ)−1f	PUNCT
ap-2076	260	1	−	−	NUM
ap-2076	260	2	p−2f	p−2f	NOUN
ap-2076	260	3	(	(	PUNCT
ap-2076	260	4	λ−	λ−	PROPN
ap-2076	260	5	λ0)2	λ0)2	X
ap-2076	260	6	−	−	PROPN
ap-2076	260	7	p−1f	p−1f	NOUN
ap-2076	261	1	λ−	λ−	PROPN
ap-2076	261	2	λ0	λ0	NOUN
ap-2076	261	3	solves	solve	VERB
ap-2076	261	4	the	the	DET
ap-2076	261	5	equation	equation	NOUN
ap-2076	261	6	(	(	PUNCT
ap-2076	261	7	hα	hα	VERB
ap-2076	261	8	−	−	PROPN
ap-2076	261	9	λ)rα(λ)f	λ)rα(λ)f	NOUN
ap-2076	261	10	=	=	SYM
ap-2076	261	11	f	f	PROPN
ap-2076	261	12	+	+	CCONJ
ap-2076	261	13	ψ0`1f	ψ0`1f	ADJ
ap-2076	261	14	+	+	CCONJ
ap-2076	261	15	φ0`2f	φ0`2f	NOUN
ap-2076	261	16	.	.	PUNCT
ap-2076	262	1	(	(	PUNCT
ap-2076	262	2	2.24	2.24	NUM
ap-2076	262	3	)	)	PUNCT
ap-2076	262	4	employing	employ	VERB
ap-2076	262	5	definition	definition	NOUN
ap-2076	262	6	(	(	PUNCT
ap-2076	262	7	2.2	2.2	NUM
ap-2076	262	8	)	)	PUNCT
ap-2076	262	9	of	of	ADP
ap-2076	262	10	lε	lε	X
ap-2076	262	11	,	,	PUNCT
ap-2076	262	12	we	we	PRON
ap-2076	262	13	check	check	VERB
ap-2076	262	14	easily	easily	ADV
ap-2076	262	15	that	that	SCONJ
ap-2076	262	16	pt	pt	VERB
ap-2076	262	17	lε	lε	NOUN
ap-2076	262	18	=	=	PUNCT
ap-2076	262	19	lεpt	lεpt	ADJ
ap-2076	262	20	.	.	PUNCT
ap-2076	263	1	this	this	DET
ap-2076	263	2	identity	identity	NOUN
ap-2076	263	3	and	and	CCONJ
ap-2076	263	4	(	(	PUNCT
ap-2076	263	5	1.11	1.11	NUM
ap-2076	263	6	)	)	PUNCT
ap-2076	263	7	,	,	PUNCT
ap-2076	263	8	(	(	PUNCT
ap-2076	263	9	2.24	2.24	NUM
ap-2076	263	10	)	)	PUNCT
ap-2076	263	11	yield	yield	NOUN
ap-2076	263	12	that	that	PRON
ap-2076	263	13	for	for	ADP
ap-2076	263	14	z	z	PROPN
ap-2076	263	15	∈	∈	PROPN
ap-2076	263	16	r	r	NOUN
ap-2076	263	17	,	,	PUNCT
ap-2076	263	18	κ	κ	PROPN
ap-2076	263	19	∈	∈	PROPN
ap-2076	263	20	r	r	NOUN
ap-2076	263	21	pt	pt	NOUN
ap-2076	263	22	lεa(λ0	lεa(λ0	NOUN
ap-2076	263	23	+	+	PROPN
ap-2076	263	24	z	z	X
ap-2076	263	25	,	,	PUNCT
ap-2076	263	26	κ)ψ0	κ)ψ0	PROPN
ap-2076	263	27	=	=	PUNCT
ap-2076	264	1	lεa(λ0	lεa(λ0	ADP
ap-2076	264	2	+	+	CCONJ
ap-2076	264	3	z	z	PROPN
ap-2076	264	4	,	,	PUNCT
ap-2076	264	5	κ)ψ0	κ)ψ0	PROPN
ap-2076	264	6	,	,	PUNCT
ap-2076	264	7	pt	pt	X
ap-2076	264	8	lεa(λ0	lεa(λ0	NOUN
ap-2076	264	9	+	+	PROPN
ap-2076	264	10	z	z	X
ap-2076	264	11	,	,	PUNCT
ap-2076	264	12	κ)φ0	κ)φ0	PROPN
ap-2076	264	13	=	=	SYM
ap-2076	264	14	lεa(λ0	lεa(λ0	NOUN
ap-2076	264	15	+	+	CCONJ
ap-2076	264	16	z	z	X
ap-2076	264	17	,	,	PUNCT
ap-2076	264	18	κ)φ0	κ)φ0	PROPN
ap-2076	264	19	.	.	PUNCT
ap-2076	265	1	using	use	VERB
ap-2076	265	2	(	(	PUNCT
ap-2076	265	3	1.11	1.11	NUM
ap-2076	265	4	)	)	PUNCT
ap-2076	265	5	once	once	ADV
ap-2076	265	6	again	again	ADV
ap-2076	265	7	,	,	PUNCT
ap-2076	265	8	for	for	ADP
ap-2076	265	9	z	z	PROPN
ap-2076	265	10	∈	∈	PROPN
ap-2076	265	11	r	r	NOUN
ap-2076	265	12	,	,	PUNCT
ap-2076	265	13	κ	κ	PROPN
ap-2076	265	14	∈	∈	PROPN
ap-2076	265	15	r	r	NOUN
ap-2076	265	16	we	we	PRON
ap-2076	265	17	get	get	VERB
ap-2076	265	18	a11(z	a11(z	ADJ
ap-2076	265	19	,	,	PUNCT
ap-2076	265	20	κ	κ	NOUN
ap-2076	265	21	)	)	PUNCT
ap-2076	265	22	=	=	SYM
ap-2076	265	23	(	(	PUNCT
ap-2076	265	24	pt	pt	INTJ
ap-2076	265	25	lεa(λ0	lεa(λ0	NOUN
ap-2076	265	26	+	+	CCONJ
ap-2076	265	27	z	z	PROPN
ap-2076	265	28	,	,	PUNCT
ap-2076	265	29	κ)ψ0,pψ0	κ)ψ0,pψ0	NOUN
ap-2076	265	30	)	)	PUNCT
ap-2076	265	31	l2(ω	l2(ω	PROPN
ap-2076	265	32	)	)	PUNCT
ap-2076	265	33	=	=	NOUN
ap-2076	265	34	(	(	PUNCT
ap-2076	265	35	t	t	PROPN
ap-2076	265	36	lεa(λ0	lεa(λ0	NOUN
ap-2076	265	37	+	+	CCONJ
ap-2076	265	38	z	z	PROPN
ap-2076	265	39	,	,	PUNCT
ap-2076	265	40	κ)ψ0	κ)ψ0	PROPN
ap-2076	265	41	,	,	PUNCT
ap-2076	265	42	t	t	NOUN
ap-2076	265	43	ψ0	ψ0	ADV
ap-2076	265	44	)	)	PUNCT
ap-2076	266	1	l2(ω	l2(ω	X
ap-2076	266	2	)	)	PUNCT
ap-2076	266	3	=	=	SYM
ap-2076	266	4	a11(z	a11(z	PROPN
ap-2076	266	5	,	,	PUNCT
ap-2076	266	6	κ	κ	NOUN
ap-2076	266	7	)	)	PUNCT
ap-2076	266	8	.	.	PUNCT
ap-2076	267	1	the	the	DET
ap-2076	267	2	reality	reality	NOUN
ap-2076	267	3	of	of	ADP
ap-2076	267	4	other	other	ADJ
ap-2076	267	5	functions	function	NOUN
ap-2076	267	6	aij	aij	PROPN
ap-2076	267	7	can	can	AUX
ap-2076	267	8	be	be	AUX
ap-2076	267	9	proven	prove	VERB
ap-2076	267	10	in	in	ADP
ap-2076	267	11	the	the	DET
ap-2076	267	12	same	same	ADJ
ap-2076	267	13	way	way	NOUN
ap-2076	267	14	.	.	PUNCT
ap-2076	268	1	the	the	DET
ap-2076	268	2	proof	proof	NOUN
ap-2076	268	3	is	be	AUX
ap-2076	268	4	complete	complete	ADJ
ap-2076	268	5	.	.	PUNCT
ap-2076	269	1	proof	proof	NOUN
ap-2076	269	2	of	of	ADP
ap-2076	269	3	theorem	theorem	ADJ
ap-2076	269	4	1.1	1.1	NUM
ap-2076	269	5	.	.	PUNCT
ap-2076	270	1	the	the	DET
ap-2076	270	2	main	main	ADJ
ap-2076	270	3	ideas	idea	NOUN
ap-2076	270	4	here	here	ADV
ap-2076	270	5	are	be	AUX
ap-2076	270	6	the	the	DET
ap-2076	270	7	same	same	ADJ
ap-2076	270	8	as	as	ADP
ap-2076	270	9	in	in	ADP
ap-2076	270	10	the	the	DET
ap-2076	270	11	proof	proof	NOUN
ap-2076	270	12	of	of	ADP
ap-2076	270	13	theorem	theorem	ADJ
ap-2076	270	14	1.2	1.2	NUM
ap-2076	270	15	,	,	PUNCT
ap-2076	270	16	so	so	ADV
ap-2076	270	17	,	,	PUNCT
ap-2076	270	18	we	we	PRON
ap-2076	270	19	focus	focus	VERB
ap-2076	270	20	only	only	ADV
ap-2076	270	21	on	on	ADP
ap-2076	270	22	the	the	DET
ap-2076	270	23	main	main	ADJ
ap-2076	270	24	milestones	milestone	NOUN
ap-2076	270	25	.	.	PUNCT
ap-2076	271	1	we	we	PRON
ap-2076	271	2	again	again	ADV
ap-2076	271	3	begin	begin	VERB
ap-2076	271	4	with	with	ADP
ap-2076	271	5	(	(	PUNCT
ap-2076	271	6	2.1	2.1	NUM
ap-2076	271	7	)	)	PUNCT
ap-2076	271	8	and	and	CCONJ
ap-2076	271	9	invert	invert	NOUN
ap-2076	271	10	(	(	PUNCT
ap-2076	271	11	hε	hε	ADP
ap-2076	271	12	−	−	PROPN
ap-2076	271	13	λε	λε	NOUN
ap-2076	271	14	)	)	PUNCT
ap-2076	271	15	by	by	ADP
ap-2076	271	16	lemma	lemma	PROPN
ap-2076	271	17	2.2	2.2	NUM
ap-2076	271	18	.	.	PUNCT
ap-2076	272	1	it	it	PRON
ap-2076	272	2	leads	lead	VERB
ap-2076	272	3	us	we	PRON
ap-2076	272	4	to	to	ADP
ap-2076	272	5	an	an	DET
ap-2076	272	6	analogue	analogue	NOUN
ap-2076	272	7	of	of	ADP
ap-2076	272	8	equation	equation	NOUN
ap-2076	272	9	(	(	PUNCT
ap-2076	272	10	2.17	2.17	NUM
ap-2076	272	11	)	)	PUNCT
ap-2076	272	12	,	,	PUNCT
ap-2076	272	13	ψε	ψε	PUNCT
ap-2076	272	14	=	=	PUNCT
ap-2076	272	15	ε	ε	X
ap-2076	272	16	zε	zε	ADJ
ap-2076	272	17	a(λ0	a(λ0	NOUN
ap-2076	272	18	+	+	CCONJ
ap-2076	272	19	zε	zε	ADJ
ap-2076	272	20	,	,	PUNCT
ap-2076	272	21	ε)p−1lεψε	ε)p−1lεψε	PROPN
ap-2076	272	22	,	,	PUNCT
ap-2076	272	23	(	(	PUNCT
ap-2076	272	24	2.25	2.25	NUM
ap-2076	272	25	)	)	PUNCT
ap-2076	272	26	where	where	SCONJ
ap-2076	272	27	operator	operator	NOUN
ap-2076	272	28	a	a	PRON
ap-2076	272	29	is	be	AUX
ap-2076	272	30	introduced	introduce	VERB
ap-2076	272	31	in	in	ADP
ap-2076	272	32	the	the	DET
ap-2076	272	33	same	same	ADJ
ap-2076	272	34	way	way	NOUN
ap-2076	272	35	as	as	ADP
ap-2076	272	36	above	above	ADV
ap-2076	272	37	.	.	PUNCT
ap-2076	273	1	we	we	PRON
ap-2076	273	2	then	then	ADV
ap-2076	273	3	apply	apply	VERB
ap-2076	273	4	functionals	functional	NOUN
ap-2076	273	5	`	`	PUNCT
ap-2076	273	6	±lε	±lε	NOUN
ap-2076	273	7	to	to	ADP
ap-2076	273	8	this	this	DET
ap-2076	273	9	equation	equation	NOUN
ap-2076	273	10	(	(	PUNCT
ap-2076	273	11	ε	ε	PROPN
ap-2076	273	12	zε	zε	VERB
ap-2076	273	13	b11(zε	b11(zε	PROPN
ap-2076	273	14	,	,	PUNCT
ap-2076	273	15	ε)−	ε)−	PROPN
ap-2076	273	16	1	1	NUM
ap-2076	273	17	)	)	PUNCT
ap-2076	273	18	x1	x1	PROPN
ap-2076	274	1	+	+	CCONJ
ap-2076	274	2	ε	ε	PROPN
ap-2076	274	3	zε	zε	VERB
ap-2076	274	4	b12(zε	b12(zε	PROPN
ap-2076	274	5	,	,	PUNCT
ap-2076	274	6	ε)x2	ε)x2	PROPN
ap-2076	274	7	=	=	SYM
ap-2076	274	8	0	0	PROPN
ap-2076	274	9	,	,	PUNCT
ap-2076	274	10	ε	ε	PROPN
ap-2076	274	11	zε	zε	VERB
ap-2076	274	12	b21(zε	b21(zε	PROPN
ap-2076	274	13	,	,	PUNCT
ap-2076	274	14	ε)x1	ε)x1	NOUN
ap-2076	274	15	+	+	CCONJ
ap-2076	274	16	(	(	PUNCT
ap-2076	274	17	ε	ε	PROPN
ap-2076	274	18	zε	zε	PROPN
ap-2076	274	19	b22(zε	b22(zε	PROPN
ap-2076	274	20	,	,	PUNCT
ap-2076	274	21	ε)−	ε)−	PROPN
ap-2076	274	22	1	1	NUM
ap-2076	274	23	)	)	PUNCT
ap-2076	274	24	x2	x2	NOUN
ap-2076	275	1	=	=	SYM
ap-2076	275	2	0	0	NUM
ap-2076	275	3	,	,	PUNCT
ap-2076	275	4	(	(	PUNCT
ap-2076	275	5	2.26	2.26	NUM
ap-2076	275	6	)	)	PUNCT
ap-2076	275	7	b11(z	b11(z	PROPN
ap-2076	275	8	,	,	PUNCT
ap-2076	275	9	ε	ε	PROPN
ap-2076	275	10	)	)	PUNCT
ap-2076	275	11	:	:	PUNCT
ap-2076	276	1	=	=	PUNCT
ap-2076	276	2	`	`	PUNCT
ap-2076	276	3	+	+	ADJ
ap-2076	276	4	lεa(λ0	lεa(λ0	NOUN
ap-2076	276	5	+	+	X
ap-2076	276	6	z	z	ADJ
ap-2076	276	7	,	,	PUNCT
ap-2076	276	8	ε)ψ+	ε)ψ+	NUM
ap-2076	276	9	0	0	NUM
ap-2076	276	10	,	,	PUNCT
ap-2076	276	11	b12(z	b12(z	NOUN
ap-2076	276	12	,	,	PUNCT
ap-2076	276	13	ε	ε	PROPN
ap-2076	276	14	)	)	PUNCT
ap-2076	276	15	:	:	PUNCT
ap-2076	277	1	=	=	PUNCT
ap-2076	277	2	`	`	PUNCT
ap-2076	277	3	+	+	ADJ
ap-2076	277	4	lεa(λ0	lεa(λ0	NOUN
ap-2076	277	5	+	+	X
ap-2076	277	6	z	z	ADJ
ap-2076	277	7	,	,	PUNCT
ap-2076	277	8	ε)ψ−0	ε)ψ−0	NOUN
ap-2076	277	9	,	,	PUNCT
ap-2076	277	10	b21(z	b21(z	PROPN
ap-2076	277	11	,	,	PUNCT
ap-2076	277	12	ε	ε	PROPN
ap-2076	277	13	)	)	PUNCT
ap-2076	277	14	:	:	PUNCT
ap-2076	277	15	=	=	PUNCT
ap-2076	277	16	`	`	PUNCT
ap-2076	277	17	−lεa(λ0	−lεa(λ0	ADJ
ap-2076	277	18	+	+	CCONJ
ap-2076	277	19	z	z	ADJ
ap-2076	277	20	,	,	PUNCT
ap-2076	277	21	ε)ψ+	ε)ψ+	NUM
ap-2076	277	22	0	0	NUM
ap-2076	277	23	,	,	PUNCT
ap-2076	277	24	b22(z	b22(z	NOUN
ap-2076	277	25	,	,	PUNCT
ap-2076	277	26	ε	ε	PROPN
ap-2076	277	27	)	)	PUNCT
ap-2076	277	28	:	:	PUNCT
ap-2076	277	29	=	=	PUNCT
ap-2076	277	30	`	`	PUNCT
ap-2076	277	31	−lεa(λ0	−lεa(λ0	ADJ
ap-2076	277	32	+	+	CCONJ
ap-2076	277	33	z	z	X
ap-2076	277	34	,	,	PUNCT
ap-2076	277	35	ε)ψ−0	ε)ψ−0	PROPN
ap-2076	277	36	.	.	PUNCT
ap-2076	278	1	the	the	DET
ap-2076	278	2	determinant	determinant	NOUN
ap-2076	278	3	of	of	ADP
ap-2076	278	4	system	system	NOUN
ap-2076	278	5	(	(	PUNCT
ap-2076	278	6	2.26	2.26	NUM
ap-2076	278	7	)	)	PUNCT
ap-2076	278	8	should	should	AUX
ap-2076	278	9	again	again	ADV
ap-2076	278	10	vanish	vanish	VERB
ap-2076	278	11	and	and	CCONJ
ap-2076	278	12	it	it	PRON
ap-2076	278	13	implies	imply	VERB
ap-2076	278	14	the	the	DET
ap-2076	278	15	equation	equation	NOUN
ap-2076	278	16	z2	z2	PROPN
ap-2076	278	17	ε	ε	PROPN
ap-2076	278	18	−	−	PROPN
ap-2076	278	19	ε	ε	PROPN
ap-2076	278	20	(	(	PUNCT
ap-2076	278	21	b11(zε	b11(zε	PROPN
ap-2076	278	22	,	,	PUNCT
ap-2076	278	23	ε	ε	PROPN
ap-2076	278	24	)	)	PUNCT
ap-2076	279	1	+	+	NOUN
ap-2076	279	2	b22(zε	b22(zε	PROPN
ap-2076	279	3	,	,	PUNCT
ap-2076	279	4	ε	ε	PROPN
ap-2076	279	5	)	)	PUNCT
ap-2076	279	6	)	)	PUNCT
ap-2076	280	1	+	+	CCONJ
ap-2076	280	2	ε2(b11(zε	ε2(b11(zε	NOUN
ap-2076	280	3	,	,	PUNCT
ap-2076	280	4	ε)b22(zε	ε)b22(zε	PROPN
ap-2076	280	5	,	,	PUNCT
ap-2076	280	6	ε)−b12(zε	ε)−b12(zε	PROPN
ap-2076	280	7	,	,	PUNCT
ap-2076	280	8	ε)b21(zε	ε)b21(zε	PROPN
ap-2076	280	9	,	,	PUNCT
ap-2076	280	10	ε	ε	PROPN
ap-2076	280	11	)	)	PUNCT
ap-2076	280	12	)	)	PUNCT
ap-2076	280	13	=	=	SYM
ap-2076	280	14	0	0	NUM
ap-2076	280	15	,	,	PUNCT
ap-2076	280	16	which	which	PRON
ap-2076	280	17	splits	split	VERB
ap-2076	280	18	into	into	ADP
ap-2076	280	19	other	other	ADJ
ap-2076	280	20	two	two	NUM
ap-2076	280	21	zε	zε	ADJ
ap-2076	280	22	=	=	NOUN
ap-2076	280	23	q±(zε	q±(zε	NOUN
ap-2076	280	24	,	,	PUNCT
ap-2076	280	25	ε	ε	PROPN
ap-2076	280	26	)	)	PUNCT
ap-2076	280	27	,	,	PUNCT
ap-2076	280	28	(	(	PUNCT
ap-2076	280	29	2.27	2.27	NUM
ap-2076	280	30	)	)	PUNCT
ap-2076	280	31	q±(z	q±(z	PROPN
ap-2076	280	32	,	,	PUNCT
ap-2076	280	33	ε	ε	PROPN
ap-2076	280	34	)	)	PUNCT
ap-2076	280	35	:	:	PUNCT
ap-2076	280	36	=	=	SYM
ap-2076	280	37	ε	ε	PROPN
ap-2076	280	38	2	2	NUM
ap-2076	280	39	(	(	PUNCT
ap-2076	280	40	b11(zε	b11(zε	PROPN
ap-2076	280	41	,	,	PUNCT
ap-2076	280	42	ε	ε	PROPN
ap-2076	280	43	)	)	PUNCT
ap-2076	280	44	+	+	NOUN
ap-2076	280	45	b22(zε	b22(zε	PROPN
ap-2076	280	46	,	,	PUNCT
ap-2076	280	47	ε	ε	PROPN
ap-2076	280	48	)	)	PUNCT
ap-2076	280	49	)	)	PUNCT
ap-2076	280	50	±	±	NUM
ap-2076	280	51	ε	ε	PROPN
ap-2076	280	52	2	2	NUM
ap-2076	280	53	(	(	PUNCT
ap-2076	280	54	(	(	PUNCT
ap-2076	280	55	b11(z	b11(z	INTJ
ap-2076	280	56	,	,	PUNCT
ap-2076	280	57	ε)−b22(z	ε)−b22(z	NOUN
ap-2076	280	58	,	,	PUNCT
ap-2076	280	59	ε))2	ε))2	NOUN
ap-2076	280	60	+	+	CCONJ
ap-2076	280	61	4b12(z	4b12(z	NOUN
ap-2076	280	62	,	,	PUNCT
ap-2076	280	63	ε)b21(z	ε)b21(z	PROPN
ap-2076	280	64	,	,	PUNCT
ap-2076	280	65	ε	ε	PROPN
ap-2076	280	66	)	)	PUNCT
ap-2076	280	67	)	)	PUNCT
ap-2076	280	68	1/2	1/2	NUM
ap-2076	280	69	.	.	PUNCT
ap-2076	281	1	here	here	ADV
ap-2076	281	2	the	the	DET
ap-2076	281	3	branch	branch	NOUN
ap-2076	281	4	of	of	ADP
ap-2076	281	5	the	the	DET
ap-2076	281	6	square	square	ADJ
ap-2076	281	7	root	root	NOUN
ap-2076	281	8	is	be	AUX
ap-2076	281	9	fixed	fix	VERB
ap-2076	281	10	by	by	ADP
ap-2076	281	11	the	the	DET
ap-2076	281	12	restriction	restriction	NOUN
ap-2076	281	13	11/2	11/2	NUM
ap-2076	281	14	=	=	SYM
ap-2076	282	1	1	1	X
ap-2076	282	2	.	.	PUNCT
ap-2076	282	3	let	let	VERB
ap-2076	282	4	us	we	PRON
ap-2076	282	5	prove	prove	VERB
ap-2076	282	6	that	that	SCONJ
ap-2076	282	7	this	this	DET
ap-2076	282	8	square	square	ADJ
ap-2076	282	9	root	root	NOUN
ap-2076	282	10	is	be	AUX
ap-2076	282	11	jointly	jointly	ADV
ap-2076	282	12	holomorphic	holomorphic	ADJ
ap-2076	282	13	w.r.t	w.r.t	NOUN
ap-2076	282	14	.	.	PUNCT
ap-2076	283	1	z	z	AUX
ap-2076	283	2	and	and	CCONJ
ap-2076	283	3	ε	ε	PROPN
ap-2076	283	4	.	.	PUNCT
ap-2076	283	5	integrating	integrate	VERB
ap-2076	283	6	by	by	ADP
ap-2076	283	7	parts	part	NOUN
ap-2076	283	8	as	as	ADP
ap-2076	283	9	in	in	ADP
ap-2076	283	10	(	(	PUNCT
ap-2076	283	11	2.22	2.22	NUM
ap-2076	283	12	)	)	PUNCT
ap-2076	283	13	and	and	CCONJ
ap-2076	283	14	employing	employ	VERB
ap-2076	283	15	(	(	PUNCT
ap-2076	283	16	1.1	1.1	NUM
ap-2076	283	17	)	)	PUNCT
ap-2076	283	18	,	,	PUNCT
ap-2076	283	19	one	one	PRON
ap-2076	283	20	can	can	AUX
ap-2076	283	21	make	make	VERB
ap-2076	283	22	easily	easily	ADV
ap-2076	283	23	sure	sure	ADJ
ap-2076	283	24	that	that	SCONJ
ap-2076	283	25	bii	bii	NOUN
ap-2076	283	26	=	=	SYM
ap-2076	283	27	bii	bii	PROPN
ap-2076	283	28	+	+	NOUN
ap-2076	283	29	o(ε	o(ε	PROPN
ap-2076	283	30	)	)	PUNCT
ap-2076	283	31	,	,	PUNCT
ap-2076	284	1	i	i	PRON
ap-2076	284	2	=	=	NOUN
ap-2076	284	3	1	1	NUM
ap-2076	284	4	,	,	PUNCT
ap-2076	284	5	2	2	NUM
ap-2076	284	6	,	,	PUNCT
ap-2076	284	7	b12(0	b12(0	NOUN
ap-2076	284	8	,	,	PUNCT
ap-2076	284	9	ε	ε	PROPN
ap-2076	284	10	)	)	PUNCT
ap-2076	284	11	=	=	VERB
ap-2076	284	12	b12	b12	NOUN
ap-2076	284	13	+	+	PROPN
ap-2076	284	14	o(ε	o(ε	PROPN
ap-2076	284	15	)	)	PUNCT
ap-2076	284	16	,	,	PUNCT
ap-2076	284	17	b21(0	b21(0	PROPN
ap-2076	284	18	,	,	PUNCT
ap-2076	284	19	ε	ε	PROPN
ap-2076	284	20	)	)	PUNCT
ap-2076	284	21	=	=	SYM
ap-2076	284	22	b21	b21	PROPN
ap-2076	285	1	+	+	NOUN
ap-2076	285	2	o(ε	o(ε	PROPN
ap-2076	285	3	)	)	PUNCT
ap-2076	285	4	.	.	PUNCT
ap-2076	286	1	(	(	PUNCT
ap-2076	286	2	2.28	2.28	NUM
ap-2076	286	3	)	)	PUNCT
ap-2076	286	4	hence	hence	ADV
ap-2076	286	5	,	,	PUNCT
ap-2076	286	6	by	by	ADP
ap-2076	286	7	assumption	assumption	NOUN
ap-2076	286	8	(	(	PUNCT
ap-2076	286	9	1.5	1.5	NUM
ap-2076	286	10	)	)	PUNCT
ap-2076	286	11	,	,	PUNCT
ap-2076	286	12	functions	function	NOUN
ap-2076	286	13	q±	q±	PROPN
ap-2076	286	14	are	be	AUX
ap-2076	286	15	jointly	jointly	ADV
ap-2076	286	16	holomorphic	holomorphic	ADJ
ap-2076	286	17	w.r.t	w.r.t	NOUN
ap-2076	286	18	.	.	PUNCT
ap-2076	287	1	z	z	AUX
ap-2076	287	2	and	and	CCONJ
ap-2076	287	3	ε	ε	PROPN
ap-2076	287	4	.	.	PUNCT
ap-2076	287	5	proceeding	proceed	VERB
ap-2076	287	6	now	now	ADV
ap-2076	287	7	as	as	ADP
ap-2076	287	8	in	in	ADP
ap-2076	287	9	the	the	DET
ap-2076	287	10	proof	proof	NOUN
ap-2076	287	11	of	of	ADP
ap-2076	287	12	theorem	theorem	ADJ
ap-2076	287	13	1.2	1.2	NUM
ap-2076	287	14	,	,	PUNCT
ap-2076	287	15	we	we	PRON
ap-2076	287	16	arrive	arrive	VERB
ap-2076	287	17	at	at	ADP
ap-2076	287	18	the	the	DET
ap-2076	287	19	statement	statement	NOUN
ap-2076	287	20	of	of	ADP
ap-2076	287	21	theorem	theorem	ADJ
ap-2076	287	22	1.1	1.1	NUM
ap-2076	287	23	.	.	PUNCT
ap-2076	288	1	98	98	NUM
ap-2076	288	2	vol	vol	NOUN
ap-2076	288	3	.	.	PUNCT
ap-2076	289	1	54	54	NUM
ap-2076	289	2	no	no	NOUN
ap-2076	289	3	.	.	PUNCT
ap-2076	290	1	2/2014	2/2014	NUM
ap-2076	290	2	eigenvalue	eigenvalue	NOUN
ap-2076	290	3	collision	collision	NOUN
ap-2076	290	4	for	for	ADP
ap-2076	290	5	pt	pt	NOUN
ap-2076	290	6	-	-	ADJ
ap-2076	290	7	symmetric	symmetric	ADJ
ap-2076	290	8	waveguide	waveguide	ADJ
ap-2076	290	9	proof	proof	NOUN
ap-2076	290	10	of	of	ADP
ap-2076	290	11	theorem	theorem	ADJ
ap-2076	290	12	1.3	1.3	NUM
ap-2076	290	13	.	.	PUNCT
ap-2076	291	1	denote	denote	PROPN
ap-2076	291	2	ψ(x	ψ(x	PROPN
ap-2076	291	3	)	)	PUNCT
ap-2076	292	1	:	:	PUNCT
ap-2076	292	2	=	=	SYM
ap-2076	292	3	1	1	NUM
ap-2076	292	4	2	2	NUM
ap-2076	292	5	∫	∫	NOUN
ap-2076	292	6	x1	x1	PROPN
ap-2076	292	7	−∞	−∞	ADP
ap-2076	292	8	tψ0(t	tψ0(t	PROPN
ap-2076	292	9	,	,	PUNCT
ap-2076	292	10	x2	x2	NUM
ap-2076	292	11	)	)	PUNCT
ap-2076	292	12	dt	dt	PROPN
ap-2076	292	13	.	.	PUNCT
ap-2076	293	1	in	in	ADP
ap-2076	293	2	view	view	NOUN
ap-2076	293	3	of	of	ADP
ap-2076	293	4	(	(	PUNCT
ap-2076	293	5	1.16	1.16	NUM
ap-2076	293	6	)	)	PUNCT
ap-2076	293	7	this	this	DET
ap-2076	293	8	function	function	NOUN
ap-2076	293	9	is	be	AUX
ap-2076	293	10	well	well	ADV
ap-2076	293	11	-	-	PUNCT
ap-2076	293	12	defined	define	VERB
ap-2076	293	13	.	.	PUNCT
ap-2076	294	1	throughout	throughout	ADP
ap-2076	294	2	the	the	DET
ap-2076	294	3	proof	proof	NOUN
ap-2076	294	4	we	we	PRON
ap-2076	294	5	shall	shall	AUX
ap-2076	294	6	deal	deal	VERB
ap-2076	294	7	with	with	ADP
ap-2076	294	8	several	several	ADJ
ap-2076	294	9	integrals	integral	NOUN
ap-2076	294	10	of	of	ADP
ap-2076	294	11	such	such	ADJ
ap-2076	294	12	kind	kind	NOUN
ap-2076	294	13	and	and	CCONJ
ap-2076	294	14	all	all	PRON
ap-2076	294	15	of	of	ADP
ap-2076	294	16	them	they	PRON
ap-2076	294	17	will	will	AUX
ap-2076	294	18	be	be	AUX
ap-2076	294	19	well	well	ADV
ap-2076	294	20	-	-	PUNCT
ap-2076	294	21	defined	define	VERB
ap-2076	294	22	due	due	ADP
ap-2076	294	23	to	to	ADP
ap-2076	294	24	(	(	PUNCT
ap-2076	294	25	1.16	1.16	NUM
ap-2076	294	26	)	)	PUNCT
ap-2076	294	27	.	.	PUNCT
ap-2076	295	1	in	in	ADP
ap-2076	295	2	what	what	PRON
ap-2076	295	3	follows	follow	VERB
ap-2076	295	4	we	we	PRON
ap-2076	295	5	shall	shall	AUX
ap-2076	295	6	not	not	PART
ap-2076	295	7	stress	stress	VERB
ap-2076	295	8	this	this	DET
ap-2076	295	9	fact	fact	NOUN
ap-2076	295	10	anymore	anymore	ADV
ap-2076	295	11	.	.	PUNCT
ap-2076	296	1	employing	employ	VERB
ap-2076	296	2	the	the	DET
ap-2076	296	3	equation	equation	NOUN
ap-2076	296	4	for	for	ADP
ap-2076	296	5	ψ0	ψ0	ADV
ap-2076	296	6	,	,	PUNCT
ap-2076	296	7	integrating	integrate	VERB
ap-2076	296	8	by	by	ADP
ap-2076	296	9	parts	part	NOUN
ap-2076	296	10	,	,	PUNCT
ap-2076	296	11	and	and	CCONJ
ap-2076	296	12	bearing	bear	VERB
ap-2076	296	13	in	in	ADP
ap-2076	296	14	mind	mind	NOUN
ap-2076	296	15	estimates	estimate	NOUN
ap-2076	296	16	(	(	PUNCT
ap-2076	296	17	1.16	1.16	NUM
ap-2076	296	18	)	)	PUNCT
ap-2076	296	19	,	,	PUNCT
ap-2076	296	20	we	we	PRON
ap-2076	296	21	get	get	VERB
ap-2076	296	22	(	(	PUNCT
ap-2076	296	23	∆	∆	X
ap-2076	296	24	+	+	CCONJ
ap-2076	296	25	λ0)ψ	λ0)ψ	ADJ
ap-2076	296	26	=	=	NOUN
ap-2076	297	1	ψ0	ψ0	PROPN
ap-2076	297	2	+	+	ADJ
ap-2076	297	3	1	1	NUM
ap-2076	297	4	2x1	2x1	NUM
ap-2076	297	5	∂ψ0	∂ψ0	NOUN
ap-2076	298	1	∂x1	∂x1	VERB
ap-2076	298	2	+	+	CCONJ
ap-2076	298	3	1	1	NUM
ap-2076	298	4	2	2	NUM
ap-2076	298	5	∫	∫	NOUN
ap-2076	298	6	x1	x1	PROPN
ap-2076	298	7	−∞	−∞	ADP
ap-2076	298	8	t	t	PROPN
ap-2076	298	9	(	(	PUNCT
ap-2076	298	10	∂2	∂2	NUM
ap-2076	298	11	∂x2	∂x2	NOUN
ap-2076	298	12	2	2	NUM
ap-2076	298	13	+	+	NOUN
ap-2076	298	14	λ0	λ0	NOUN
ap-2076	298	15	)	)	PUNCT
ap-2076	298	16	ψ0(t	ψ0(t	NOUN
ap-2076	298	17	,	,	PUNCT
ap-2076	298	18	x2	x2	PROPN
ap-2076	298	19	)	)	PUNCT
ap-2076	298	20	dt	dt	PUNCT
ap-2076	299	1	=	=	PUNCT
ap-2076	300	1	ψ0	ψ0	PROPN
ap-2076	300	2	+	+	ADJ
ap-2076	300	3	1	1	NUM
ap-2076	300	4	2x1	2x1	NUM
ap-2076	300	5	∂ψ0	∂ψ0	NOUN
ap-2076	300	6	∂x1	∂x1	VERB
ap-2076	300	7	−	−	NOUN
ap-2076	300	8	1	1	NUM
ap-2076	300	9	2x1	2x1	NUM
ap-2076	300	10	∫	∫	NOUN
ap-2076	300	11	x1	x1	PROPN
ap-2076	300	12	−∞	−∞	ADP
ap-2076	300	13	∂2ψ0	∂2ψ0	NUM
ap-2076	300	14	∂x2	∂x2	NOUN
ap-2076	300	15	1	1	NUM
ap-2076	300	16	(	(	PUNCT
ap-2076	300	17	t	t	PROPN
ap-2076	300	18	,	,	PUNCT
ap-2076	300	19	x2	x2	PROPN
ap-2076	300	20	)	)	PUNCT
ap-2076	300	21	dt	dt	NOUN
ap-2076	301	1	=	=	PUNCT
ap-2076	301	2	ψ0	ψ0	PROPN
ap-2076	301	3	.	.	PUNCT
ap-2076	302	1	the	the	DET
ap-2076	302	2	proven	prove	VERB
ap-2076	302	3	equation	equation	NOUN
ap-2076	302	4	for	for	ADP
ap-2076	302	5	ψ	ψ	NOUN
ap-2076	302	6	allows	allow	VERB
ap-2076	302	7	us	we	PRON
ap-2076	302	8	to	to	PART
ap-2076	302	9	integrate	integrate	VERB
ap-2076	302	10	once	once	ADV
ap-2076	302	11	again,∫	again,∫	VERB
ap-2076	302	12	ω	ω	NUM
ap-2076	302	13	ψ2	ψ2	NOUN
ap-2076	302	14	0	0	NUM
ap-2076	302	15	dx	dx	PROPN
ap-2076	303	1	=	=	SYM
ap-2076	303	2	∫	∫	PROPN
ap-2076	303	3	ω	ω	NUM
ap-2076	303	4	ψ0(∆	ψ0(∆	PROPN
ap-2076	303	5	+	+	CCONJ
ap-2076	304	1	λ0)ψ	λ0)ψ	ADJ
ap-2076	304	2	dx	dx	PROPN
ap-2076	304	3	=	=	SYM
ap-2076	304	4	∫	∫	PROPN
ap-2076	304	5	γ+	γ+	PRON
ap-2076	304	6	(	(	PUNCT
ap-2076	304	7	ψ0	ψ0	ADV
ap-2076	304	8	∂ψ	∂ψ	ADJ
ap-2076	304	9	∂x2	∂x2	NOUN
ap-2076	304	10	−	−	NOUN
ap-2076	304	11	ψ∂ψ0	ψ∂ψ0	SYM
ap-2076	304	12	∂x2	∂x2	NOUN
ap-2076	304	13	)	)	PUNCT
ap-2076	305	1	dx1	dx1	PROPN
ap-2076	305	2	−	−	PROPN
ap-2076	305	3	∫	∫	PROPN
ap-2076	305	4	γ−	γ−	PROPN
ap-2076	305	5	(	(	PUNCT
ap-2076	305	6	ψ0	ψ0	ADV
ap-2076	305	7	∂ψ	∂ψ	ADJ
ap-2076	305	8	∂x2	∂x2	NOUN
ap-2076	305	9	−	−	NOUN
ap-2076	305	10	ψ∂ψ0	ψ∂ψ0	SYM
ap-2076	305	11	∂x2	∂x2	NOUN
ap-2076	305	12	)	)	PUNCT
ap-2076	305	13	dx1	dx1	PROPN
ap-2076	306	1	=	=	SYM
ap-2076	306	2	∫	∫	PROPN
ap-2076	306	3	γ+	γ+	X
ap-2076	306	4	ψ0	ψ0	ADV
ap-2076	306	5	(	(	PUNCT
ap-2076	306	6	∂ψ	∂ψ	VERB
ap-2076	306	7	∂x2	∂x2	NOUN
ap-2076	306	8	+	+	NOUN
ap-2076	306	9	iαψ	iαψ	ADJ
ap-2076	306	10	)	)	PUNCT
ap-2076	306	11	dx1	dx1	PROPN
ap-2076	307	1	−	−	PROPN
ap-2076	307	2	∫	∫	PROPN
ap-2076	307	3	γ−	γ−	PROPN
ap-2076	307	4	ψ0	ψ0	ADV
ap-2076	307	5	(	(	PUNCT
ap-2076	307	6	∂ψ	∂ψ	VERB
ap-2076	307	7	∂x2	∂x2	NOUN
ap-2076	307	8	+	+	NOUN
ap-2076	307	9	iαψ	iαψ	PROPN
ap-2076	307	10	)	)	PUNCT
ap-2076	307	11	dx1	dx1	PROPN
ap-2076	307	12	.	.	PUNCT
ap-2076	308	1	now	now	ADV
ap-2076	308	2	we	we	PRON
ap-2076	308	3	employ	employ	VERB
ap-2076	308	4	identity	identity	NOUN
ap-2076	308	5	(	(	PUNCT
ap-2076	308	6	1.11	1.11	NUM
ap-2076	308	7	)	)	PUNCT
ap-2076	308	8	and	and	CCONJ
ap-2076	308	9	boundary	boundary	ADJ
ap-2076	308	10	condition	condition	NOUN
ap-2076	308	11	(	(	PUNCT
ap-2076	308	12	1.1	1.1	NUM
ap-2076	308	13	)	)	PUNCT
ap-2076	308	14	for	for	ADP
ap-2076	308	15	ψ0	ψ0	ADV
ap-2076	308	16	to	to	PART
ap-2076	308	17	simplify	simplify	VERB
ap-2076	308	18	the	the	DET
ap-2076	308	19	sum	sum	NOUN
ap-2076	308	20	of	of	ADP
ap-2076	308	21	these	these	DET
ap-2076	308	22	integrals,∫	integrals,∫	NOUN
ap-2076	308	23	ω	ω	NUM
ap-2076	308	24	ψ2	ψ2	NOUN
ap-2076	308	25	0	0	NUM
ap-2076	308	26	dx	dx	PROPN
ap-2076	308	27	=	=	SYM
ap-2076	309	1	−	−	PROPN
ap-2076	309	2	∫	∫	PROPN
ap-2076	309	3	γ+	γ+	PUNCT
ap-2076	309	4	dx1	dx1	PROPN
ap-2076	309	5	reψ0(x1	reψ0(x1	PROPN
ap-2076	309	6	,	,	PUNCT
ap-2076	309	7	d)x1	d)x1	PROPN
ap-2076	309	8	∫	∫	PROPN
ap-2076	310	1	x1	x1	PROPN
ap-2076	310	2	−∞	−∞	X
ap-2076	310	3	(	(	PUNCT
ap-2076	310	4	α(x1)−	α(x1)−	PROPN
ap-2076	310	5	α(y1	α(y1	NOUN
ap-2076	310	6	)	)	PUNCT
ap-2076	310	7	)	)	PUNCT
ap-2076	311	1	imψ0(y1	imψ0(y1	PROPN
ap-2076	311	2	,	,	PUNCT
ap-2076	311	3	d	d	NOUN
ap-2076	311	4	)	)	PUNCT
ap-2076	311	5	dy1	dy1	NOUN
ap-2076	311	6	−	−	PROPN
ap-2076	311	7	∫	∫	PROPN
ap-2076	311	8	γ+	γ+	PUNCT
ap-2076	311	9	dx1	dx1	PROPN
ap-2076	311	10	imψ0(x1	imψ0(x1	PROPN
ap-2076	311	11	,	,	PUNCT
ap-2076	311	12	d)x1	d)x1	PROPN
ap-2076	311	13	∫	∫	PROPN
ap-2076	312	1	x1	x1	PROPN
ap-2076	312	2	−∞	−∞	X
ap-2076	312	3	(	(	PUNCT
ap-2076	312	4	α(x1)−	α(x1)−	PROPN
ap-2076	312	5	α(y1	α(y1	NOUN
ap-2076	312	6	)	)	PUNCT
ap-2076	312	7	)	)	PUNCT
ap-2076	313	1	reψ0(y1	reψ0(y1	PROPN
ap-2076	313	2	,	,	PUNCT
ap-2076	313	3	d	d	NOUN
ap-2076	313	4	)	)	PUNCT
ap-2076	313	5	dy1	dy1	NOUN
ap-2076	313	6	=	=	SYM
ap-2076	314	1	−	−	PROPN
ap-2076	314	2	∫	∫	PROPN
ap-2076	314	3	γ+	γ+	PUNCT
ap-2076	314	4	dx1	dx1	PROPN
ap-2076	314	5	reψ0(x1	reψ0(x1	PROPN
ap-2076	314	6	,	,	PUNCT
ap-2076	314	7	d)x1	d)x1	PROPN
ap-2076	314	8	∫	∫	PROPN
ap-2076	314	9	x1	x1	PROPN
ap-2076	314	10	−∞	−∞	X
ap-2076	314	11	(	(	PUNCT
ap-2076	314	12	α(x1)−	α(x1)−	PROPN
ap-2076	314	13	α(y1	α(y1	NOUN
ap-2076	314	14	)	)	PUNCT
ap-2076	314	15	)	)	PUNCT
ap-2076	314	16	imψ0(y1	imψ0(y1	PROPN
ap-2076	314	17	,	,	PUNCT
ap-2076	314	18	d	d	NOUN
ap-2076	314	19	)	)	PUNCT
ap-2076	314	20	dy1	dy1	NOUN
ap-2076	314	21	+	+	CCONJ
ap-2076	314	22	∫	∫	PROPN
ap-2076	314	23	γ+	γ+	PUNCT
ap-2076	314	24	dx1	dx1	PROPN
ap-2076	314	25	reψ0(x1	reψ0(x1	PROPN
ap-2076	314	26	,	,	PUNCT
ap-2076	314	27	d)x1	d)x1	PROPN
ap-2076	314	28	∫	∫	PROPN
ap-2076	315	1	+	+	NUM
ap-2076	315	2	∞	∞	PROPN
ap-2076	315	3	x1	x1	PROPN
ap-2076	315	4	(	(	PUNCT
ap-2076	315	5	α(x1)−	α(x1)−	X
ap-2076	315	6	α(y1	α(y1	NOUN
ap-2076	315	7	)	)	PUNCT
ap-2076	315	8	)	)	PUNCT
ap-2076	315	9	imψ0(y1	imψ0(y1	PROPN
ap-2076	315	10	,	,	PUNCT
ap-2076	315	11	d	d	NOUN
ap-2076	315	12	)	)	PUNCT
ap-2076	315	13	dy1	dy1	NOUN
ap-2076	315	14	=	=	SYM
ap-2076	316	1	−	−	PROPN
ap-2076	316	2	∫	∫	PROPN
ap-2076	316	3	r2	r2	PROPN
ap-2076	316	4	k(x1	k(x1	PROPN
ap-2076	316	5	,	,	PUNCT
ap-2076	316	6	y1	y1	PROPN
ap-2076	316	7	)	)	PUNCT
ap-2076	316	8	(	(	PUNCT
ap-2076	316	9	α(x1)−	α(x1)−	X
ap-2076	316	10	α(y1	α(y1	NOUN
ap-2076	316	11	)	)	PUNCT
ap-2076	316	12	)	)	PUNCT
ap-2076	317	1	reψ0(y1	reψ0(y1	PROPN
ap-2076	317	2	,	,	PUNCT
ap-2076	317	3	d	d	NOUN
ap-2076	317	4	)	)	PUNCT
ap-2076	317	5	imψ0(y1	imψ0(y1	PROPN
ap-2076	317	6	,	,	PUNCT
ap-2076	317	7	d	d	PROPN
ap-2076	317	8	)	)	PUNCT
ap-2076	317	9	dx1	dx1	PROPN
ap-2076	317	10	dy1	dy1	PROPN
ap-2076	317	11	.	.	PUNCT
ap-2076	318	1	by	by	ADP
ap-2076	318	2	(	(	PUNCT
ap-2076	318	3	2.4	2.4	NUM
ap-2076	318	4	)	)	PUNCT
ap-2076	318	5	we	we	PRON
ap-2076	318	6	then	then	ADV
ap-2076	318	7	conclude	conclude	VERB
ap-2076	318	8	that	that	PRON
ap-2076	318	9	equation	equation	NOUN
ap-2076	318	10	(	(	PUNCT
ap-2076	318	11	1.8	1.8	NUM
ap-2076	318	12	)	)	PUNCT
ap-2076	318	13	is	be	AUX
ap-2076	318	14	solvable	solvable	ADJ
ap-2076	318	15	if	if	SCONJ
ap-2076	318	16	and	and	CCONJ
ap-2076	318	17	only	only	ADV
ap-2076	318	18	if	if	SCONJ
ap-2076	318	19	identity	identity	NOUN
ap-2076	318	20	(	(	PUNCT
ap-2076	318	21	1.17	1.17	NUM
ap-2076	318	22	)	)	PUNCT
ap-2076	318	23	holds	hold	VERB
ap-2076	318	24	true	true	ADJ
ap-2076	318	25	.	.	PUNCT
ap-2076	319	1	remark	remark	VERB
ap-2076	319	2	2.5	2.5	NUM
ap-2076	319	3	.	.	PUNCT
ap-2076	320	1	the	the	DET
ap-2076	320	2	idea	idea	NOUN
ap-2076	320	3	of	of	ADP
ap-2076	320	4	the	the	DET
ap-2076	320	5	latter	latter	ADJ
ap-2076	320	6	proof	proof	NOUN
ap-2076	320	7	was	be	AUX
ap-2076	320	8	borrowed	borrow	VERB
ap-2076	320	9	from	from	ADP
ap-2076	320	10	the	the	DET
ap-2076	320	11	proof	proof	NOUN
ap-2076	320	12	of	of	ADP
ap-2076	320	13	lemma	lemma	PROPN
ap-2076	320	14	2.2	2.2	NUM
ap-2076	320	15	in	in	ADP
ap-2076	320	16	[	[	PUNCT
ap-2076	320	17	11	11	NUM
ap-2076	320	18	]	]	PUNCT
ap-2076	320	19	,	,	PUNCT
ap-2076	320	20	see	see	VERB
ap-2076	320	21	also	also	ADV
ap-2076	320	22	proof	proof	NOUN
ap-2076	320	23	of	of	ADP
ap-2076	320	24	lemma	lemma	PROPN
ap-2076	320	25	3.6	3.6	NUM
ap-2076	320	26	in	in	ADP
ap-2076	320	27	[	[	X
ap-2076	320	28	10	10	NUM
ap-2076	320	29	]	]	PUNCT
ap-2076	320	30	.	.	PUNCT
ap-2076	321	1	acknowledgements	acknowledgement	VERB
ap-2076	321	2	the	the	DET
ap-2076	321	3	author	author	NOUN
ap-2076	321	4	thanks	thank	NOUN
ap-2076	321	5	m.	m.	NOUN
ap-2076	321	6	znojil	znojil	PROPN
ap-2076	321	7	for	for	ADP
ap-2076	321	8	valuable	valuable	ADJ
ap-2076	321	9	discussions	discussion	NOUN
ap-2076	321	10	that	that	PRON
ap-2076	321	11	stimulated	stimulate	VERB
ap-2076	321	12	him	he	PRON
ap-2076	321	13	to	to	PART
ap-2076	321	14	write	write	VERB
ap-2076	321	15	this	this	DET
ap-2076	321	16	paper	paper	NOUN
ap-2076	321	17	.	.	PUNCT
ap-2076	322	1	the	the	DET
ap-2076	322	2	work	work	NOUN
ap-2076	322	3	is	be	AUX
ap-2076	322	4	partially	partially	ADV
ap-2076	322	5	supported	support	VERB
ap-2076	322	6	by	by	ADP
ap-2076	322	7	rfbr	rfbr	NOUN
ap-2076	322	8	,	,	PUNCT
ap-2076	322	9	by	by	ADP
ap-2076	322	10	a	a	DET
ap-2076	322	11	grant	grant	NOUN
ap-2076	322	12	of	of	ADP
ap-2076	322	13	the	the	DET
ap-2076	322	14	president	president	NOUN
ap-2076	322	15	of	of	ADP
ap-2076	322	16	russia	russia	PROPN
ap-2076	322	17	for	for	ADP
ap-2076	322	18	young	young	ADJ
ap-2076	322	19	scientists	scientist	NOUN
ap-2076	322	20	—	—	PUNCT
ap-2076	322	21	doctors	doctor	NOUN
ap-2076	322	22	of	of	ADP
ap-2076	322	23	science	science	NOUN
ap-2076	322	24	(	(	PUNCT
ap-2076	322	25	md-183.2014.1	md-183.2014.1	NOUN
ap-2076	322	26	)	)	PUNCT
ap-2076	322	27	and	and	CCONJ
ap-2076	322	28	by	by	ADP
ap-2076	322	29	the	the	DET
ap-2076	322	30	dynasty	dynasty	PROPN
ap-2076	322	31	foundation	foundation	NOUN
ap-2076	322	32	fellowship	fellowship	NOUN
ap-2076	322	33	for	for	ADP
ap-2076	322	34	young	young	ADJ
ap-2076	322	35	mathematicians	mathematician	NOUN
ap-2076	322	36	.	.	PUNCT
ap-2076	323	1	references	reference	NOUN
ap-2076	323	2	[	[	X
ap-2076	323	3	1	1	X
ap-2076	323	4	]	]	PUNCT
ap-2076	323	5	d.	d.	PROPN
ap-2076	323	6	borisov	borisov	PROPN
ap-2076	323	7	,	,	PUNCT
ap-2076	323	8	d.	d.	PROPN
ap-2076	323	9	krejčiřík	krejčiřík	PROPN
ap-2076	323	10	.	.	PUNCT
ap-2076	324	1	pt	pt	PROPN
ap-2076	324	2	-symmetric	-symmetric	ADJ
ap-2076	324	3	waveguide	waveguide	NOUN
ap-2076	324	4	.	.	PUNCT
ap-2076	325	1	integral	integral	ADJ
ap-2076	325	2	equations	equation	NOUN
ap-2076	325	3	and	and	CCONJ
ap-2076	325	4	operator	operator	NOUN
ap-2076	325	5	theory	theory	NOUN
ap-2076	325	6	.	.	PUNCT
ap-2076	326	1	2008	2008	NUM
ap-2076	326	2	.	.	PUNCT
ap-2076	327	1	v.	v.	ADP
ap-2076	327	2	62	62	NUM
ap-2076	327	3	.	.	PUNCT
ap-2076	328	1	no	no	INTJ
ap-2076	328	2	.	.	NOUN
ap-2076	329	1	4	4	X
ap-2076	329	2	.	.	PUNCT
ap-2076	330	1	p.	p.	NOUN
ap-2076	330	2	489	489	NUM
ap-2076	330	3	-	-	SYM
ap-2076	330	4	515	515	NUM
ap-2076	330	5	.	.	PUNCT
ap-2076	331	1	doi	doi	NOUN
ap-2076	331	2	:	:	PUNCT
ap-2076	331	3	10.1007	10.1007	NUM
ap-2076	331	4	/	/	SYM
ap-2076	331	5	s00020	s00020	NOUN
ap-2076	331	6	-	-	PUNCT
ap-2076	331	7	008	008	NUM
ap-2076	331	8	-	-	PUNCT
ap-2076	331	9	1634	1634	NUM
ap-2076	331	10	-	-	SYM
ap-2076	331	11	1	1	NUM
ap-2076	331	12	[	[	X
ap-2076	331	13	2	2	NUM
ap-2076	331	14	]	]	PUNCT
ap-2076	331	15	d.	d.	PROPN
ap-2076	331	16	borisov	borisov	PROPN
ap-2076	331	17	.	.	PUNCT
ap-2076	332	1	on	on	ADP
ap-2076	332	2	a	a	DET
ap-2076	332	3	pt	pt	NOUN
ap-2076	332	4	-symmetric	-symmetric	NOUN
ap-2076	332	5	waveguide	waveguide	ADJ
ap-2076	332	6	with	with	ADP
ap-2076	332	7	a	a	DET
ap-2076	332	8	pair	pair	NOUN
ap-2076	332	9	of	of	ADP
ap-2076	332	10	small	small	ADJ
ap-2076	332	11	holes.proceedings	holes.proceeding	NOUN
ap-2076	332	12	of	of	ADP
ap-2076	332	13	steklov	steklov	PROPN
ap-2076	332	14	institute	institute	PROPN
ap-2076	332	15	of	of	ADP
ap-2076	332	16	mathematics	mathematics	PROPN
ap-2076	332	17	.	.	PUNCT
ap-2076	333	1	2013	2013	NUM
ap-2076	333	2	.	.	PUNCT
ap-2076	334	1	v.	v.	ADP
ap-2076	334	2	281	281	NUM
ap-2076	334	3	.	.	PUNCT
ap-2076	335	1	no	no	INTJ
ap-2076	335	2	.	.	NOUN
ap-2076	335	3	1	1	NUM
ap-2076	335	4	supplement	supplement	NOUN
ap-2076	335	5	.	.	PUNCT
ap-2076	336	1	p.	p.	NOUN
ap-2076	336	2	5	5	NUM
ap-2076	336	3	-	-	SYM
ap-2076	336	4	21	21	NUM
ap-2076	336	5	;	;	PUNCT
ap-2076	336	6	translated	translate	VERB
ap-2076	336	7	from	from	ADP
ap-2076	336	8	trudy	trudy	PROPN
ap-2076	336	9	instituta	instituta	PROPN
ap-2076	337	1	matematiki	matematiki	PRON
ap-2076	337	2	i	i	PRON
ap-2076	337	3	mekhaniki	mekhaniki	PROPN
ap-2076	337	4	uro	uro	PROPN
ap-2076	337	5	ran	run	VERB
ap-2076	337	6	.	.	PUNCT
ap-2076	338	1	2012	2012	NUM
ap-2076	338	2	.	.	PUNCT
ap-2076	339	1	v.	v.	ADP
ap-2076	339	2	18	18	NUM
ap-2076	339	3	,	,	PUNCT
ap-2076	339	4	no	no	INTJ
ap-2076	339	5	.	.	NOUN
ap-2076	339	6	2	2	X
ap-2076	339	7	.	.	PUNCT
ap-2076	340	1	p.	p.	NOUN
ap-2076	340	2	22	22	NUM
ap-2076	340	3	-	-	SYM
ap-2076	340	4	37	37	NUM
ap-2076	340	5	.	.	PUNCT
ap-2076	341	1	doi	doi	NOUN
ap-2076	341	2	:	:	PUNCT
ap-2076	341	3	10.1134	10.1134	NUM
ap-2076	341	4	/	/	SYM
ap-2076	341	5	s0081543813050027	s0081543813050027	NOUN
ap-2076	342	1	[	[	X
ap-2076	342	2	3	3	X
ap-2076	342	3	]	]	PUNCT
ap-2076	342	4	d.	d.	PROPN
ap-2076	342	5	borisov	borisov	PROPN
ap-2076	342	6	.	.	PUNCT
ap-2076	343	1	discrete	discrete	ADJ
ap-2076	343	2	spectrum	spectrum	NOUN
ap-2076	343	3	of	of	ADP
ap-2076	343	4	thin	thin	ADJ
ap-2076	343	5	pt	pt	X
ap-2076	343	6	-symmetric	-symmetric	ADJ
ap-2076	343	7	waveguide.ufa	waveguide.ufa	X
ap-2076	343	8	mathematical	mathematical	ADJ
ap-2076	343	9	journal	journal	NOUN
ap-2076	343	10	.	.	PUNCT
ap-2076	344	1	2014	2014	NUM
ap-2076	344	2	.	.	PUNCT
ap-2076	345	1	vol	vol	NOUN
ap-2076	345	2	.	.	PROPN
ap-2076	346	1	6	6	NUM
ap-2076	346	2	,	,	PUNCT
ap-2076	346	3	no	no	INTJ
ap-2076	346	4	.	.	NOUN
ap-2076	346	5	1	1	NUM
ap-2076	346	6	,	,	PUNCT
ap-2076	346	7	pp	pp	ADJ
ap-2076	346	8	.	.	PUNCT
ap-2076	347	1	29–55	29–55	NUM
ap-2076	347	2	.	.	PUNCT
ap-2076	348	1	doi	doi	NOUN
ap-2076	348	2	:	:	PUNCT
ap-2076	348	3	10.13108/2014	10.13108/2014	NUM
ap-2076	348	4	-	-	SYM
ap-2076	348	5	6	6	NUM
ap-2076	348	6	-	-	PUNCT
ap-2076	348	7	1	1	NUM
ap-2076	348	8	-	-	SYM
ap-2076	348	9	29	29	NUM
ap-2076	348	10	[	[	X
ap-2076	348	11	4	4	NUM
ap-2076	348	12	]	]	PUNCT
ap-2076	348	13	d.	d.	PROPN
ap-2076	348	14	borisov	borisov	PROPN
ap-2076	348	15	.	.	PUNCT
ap-2076	349	1	on	on	ADP
ap-2076	349	2	a	a	DET
ap-2076	349	3	quantum	quantum	NOUN
ap-2076	349	4	waveguide	waveguide	NOUN
ap-2076	349	5	with	with	ADP
ap-2076	349	6	a	a	DET
ap-2076	349	7	small	small	ADJ
ap-2076	349	8	pt	pt	NOUN
ap-2076	349	9	-symmetric	-symmetric	ADJ
ap-2076	349	10	perturbation.acta	perturbation.acta	PROPN
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ap-2076	349	12	.	.	PUNCT
ap-2076	350	1	2007	2007	NUM
ap-2076	350	2	.	.	PUNCT
ap-2076	351	1	no	no	INTJ
ap-2076	351	2	.	.	NOUN
ap-2076	352	1	2	2	NUM
ap-2076	352	2	-	-	SYM
ap-2076	352	3	3	3	NUM
ap-2076	352	4	.	.	PUNCT
ap-2076	353	1	p.	p.	NOUN
ap-2076	353	2	59	59	NUM
ap-2076	353	3	-	-	SYM
ap-2076	353	4	61	61	NUM
ap-2076	353	5	.	.	PUNCT
ap-2076	354	1	[	[	X
ap-2076	354	2	5	5	X
ap-2076	354	3	]	]	PUNCT
ap-2076	354	4	d.	d.	PROPN
ap-2076	354	5	borisov	borisov	PROPN
ap-2076	354	6	,	,	PUNCT
ap-2076	354	7	d.	d.	PROPN
ap-2076	354	8	krejčiřík	krejčiřík	PROPN
ap-2076	354	9	.	.	PUNCT
ap-2076	355	1	the	the	DET
ap-2076	355	2	effective	effective	ADJ
ap-2076	355	3	hamiltonian	hamiltonian	NOUN
ap-2076	355	4	for	for	ADP
ap-2076	355	5	thin	thin	ADJ
ap-2076	355	6	layers	layer	NOUN
ap-2076	355	7	with	with	ADP
ap-2076	355	8	non	non	ADJ
ap-2076	355	9	-	-	ADJ
ap-2076	355	10	hermitian	hermitian	ADJ
ap-2076	355	11	robin	robin	PROPN
ap-2076	355	12	-	-	PUNCT
ap-2076	355	13	type	type	NOUN
ap-2076	355	14	boundary	boundary	ADJ
ap-2076	355	15	conditions.asymptotic	conditions.asymptotic	ADJ
ap-2076	355	16	analysis	analysis	NOUN
ap-2076	355	17	.	.	PUNCT
ap-2076	355	18	2012	2012	NUM
ap-2076	355	19	.	.	PUNCT
ap-2076	356	1	v.	v.	ADP
ap-2076	356	2	76	76	NUM
ap-2076	356	3	.	.	PUNCT
ap-2076	357	1	no	no	INTJ
ap-2076	357	2	.	.	NOUN
ap-2076	358	1	1	1	X
ap-2076	358	2	.	.	PUNCT
ap-2076	359	1	p.	p.	NOUN
ap-2076	359	2	49	49	NUM
ap-2076	359	3	-	-	SYM
ap-2076	359	4	59	59	NUM
ap-2076	359	5	.	.	PUNCT
ap-2076	360	1	doi	doi	NOUN
ap-2076	360	2	:	:	PUNCT
ap-2076	360	3	10.3233	10.3233	NUM
ap-2076	360	4	/	/	SYM
ap-2076	360	5	asy-2011	asy-2011	NOUN
ap-2076	360	6	-	-	PUNCT
ap-2076	360	7	1061	1061	NUM
ap-2076	361	1	[	[	X
ap-2076	361	2	6	6	NUM
ap-2076	361	3	]	]	PUNCT
ap-2076	361	4	d.	d.	PROPN
ap-2076	361	5	krejčiřík	krejčiřík	PROPN
ap-2076	361	6	and	and	CCONJ
ap-2076	361	7	p.	p.	PROPN
ap-2076	361	8	siegl	siegl	PROPN
ap-2076	361	9	.	.	PUNCT
ap-2076	362	1	pt	pt	NOUN
ap-2076	362	2	-symmetric	-symmetric	ADJ
ap-2076	362	3	models	model	NOUN
ap-2076	362	4	in	in	ADP
ap-2076	362	5	curved	curved	ADJ
ap-2076	362	6	manifolds.journal	manifolds.journal	PROPN
ap-2076	362	7	of	of	ADP
ap-2076	362	8	physics	physics	NOUN
ap-2076	362	9	a	a	PRON
ap-2076	362	10	:	:	PUNCT
ap-2076	362	11	mathematical	mathematical	ADJ
ap-2076	362	12	and	and	CCONJ
ap-2076	362	13	theoretical	theoretical	ADJ
ap-2076	362	14	.	.	PUNCT
ap-2076	363	1	2010	2010	NUM
ap-2076	363	2	.	.	PUNCT
ap-2076	364	1	v.	v.	ADP
ap-2076	364	2	43	43	NUM
ap-2076	364	3	,	,	PUNCT
ap-2076	364	4	no	no	INTJ
ap-2076	364	5	.	.	NOUN
ap-2076	364	6	48	48	NUM
ap-2076	364	7	.	.	PUNCT
ap-2076	365	1	i	i	PROPN
ap-2076	365	2	d	d	PROPN
ap-2076	365	3	485204	485204	NUM
ap-2076	365	4	.	.	PUNCT
ap-2076	366	1	doi	doi	NOUN
ap-2076	366	2	:	:	PUNCT
ap-2076	366	3	10.1088/1751	10.1088/1751	NUM
ap-2076	366	4	-	-	PUNCT
ap-2076	366	5	8113/43/48/485204	8113/43/48/485204	PROPN
ap-2076	366	6	[	[	PUNCT
ap-2076	366	7	7	7	X
ap-2076	366	8	]	]	X
ap-2076	366	9	d.	d.	PROPN
ap-2076	366	10	krejčiřík	krejčiřík	PROPN
ap-2076	366	11	and	and	CCONJ
ap-2076	366	12	m.	m.	NOUN
ap-2076	366	13	tater	tater	NOUN
ap-2076	366	14	.	.	PUNCT
ap-2076	367	1	non	non	ADJ
ap-2076	367	2	-	-	ADJ
ap-2076	367	3	hermitian	hermitian	ADJ
ap-2076	367	4	spectral	spectral	ADJ
ap-2076	367	5	effects	effect	NOUN
ap-2076	367	6	in	in	ADP
ap-2076	367	7	a	a	DET
ap-2076	367	8	pt	pt	NOUN
ap-2076	367	9	-symmetric	-symmetric	ADJ
ap-2076	367	10	waveguide.journal	waveguide.journal	PROPN
ap-2076	367	11	of	of	ADP
ap-2076	367	12	physics	physics	NOUN
ap-2076	367	13	a	a	PRON
ap-2076	367	14	:	:	PUNCT
ap-2076	367	15	mathematical	mathematical	ADJ
ap-2076	367	16	and	and	CCONJ
ap-2076	367	17	theoretical	theoretical	ADJ
ap-2076	367	18	.	.	PUNCT
ap-2076	368	1	2008	2008	NUM
ap-2076	368	2	.	.	PUNCT
ap-2076	369	1	v.	v.	ADP
ap-2076	369	2	41	41	NUM
ap-2076	369	3	,	,	PUNCT
ap-2076	369	4	no	no	INTJ
ap-2076	369	5	.	.	NOUN
ap-2076	369	6	24	24	NUM
ap-2076	369	7	.	.	PUNCT
ap-2076	370	1	i	i	PRON
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ap-2076	370	4	.	.	PUNCT
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ap-2076	371	2	:	:	PUNCT
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ap-2076	371	4	-	-	NUM
ap-2076	371	5	8113/41/24/244013	8113/41/24/244013	NOUN
ap-2076	372	1	[	[	NOUN
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ap-2076	372	3	]	]	PUNCT
ap-2076	372	4	t.	t.	PROPN
ap-2076	372	5	kato	kato	PROPN
ap-2076	372	6	.	.	PUNCT
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ap-2076	372	8	theory	theory	NOUN
ap-2076	372	9	for	for	ADP
ap-2076	372	10	linear	linear	PROPN
ap-2076	372	11	operators	operator	NOUN
ap-2076	372	12	.	.	PUNCT
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ap-2076	373	2	in	in	ADP
ap-2076	373	3	mathematics	mathematic	NOUN
ap-2076	373	4	,	,	PUNCT
ap-2076	373	5	springer	springer	NOUN
ap-2076	373	6	-	-	PUNCT
ap-2076	373	7	verlag	verlag	PROPN
ap-2076	373	8	,	,	PUNCT
ap-2076	373	9	berlin	berlin	PROPN
ap-2076	373	10	.	.	PUNCT
ap-2076	373	11	1995	1995	NUM
ap-2076	373	12	.	.	PUNCT
ap-2076	374	1	99	99	NUM
ap-2076	374	2	http://dx.doi.org/10.1007/s00020-008-1634-1	http://dx.doi.org/10.1007/s00020-008-1634-1	NUM
ap-2076	374	3	http://dx.doi.org/10.1134/s0081543813050027	http://dx.doi.org/10.1134/s0081543813050027	PROPN
ap-2076	374	4	http://dx.doi.org/10.13108/2014-6-1-29	http://dx.doi.org/10.13108/2014-6-1-29	PROPN
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ap-2076	374	6	http://dx.doi.org/10.1088/1751-8113/43/48/485204	http://dx.doi.org/10.1088/1751-8113/43/48/485204	NUM
ap-2076	374	7	http://dx.doi.org/10.1088/1751-8113/41/24/244013	http://dx.doi.org/10.1088/1751-8113/41/24/244013	NUM
ap-2076	374	8	denis	denis	PROPN
ap-2076	374	9	borisov	borisov	PROPN
ap-2076	374	10	acta	acta	PROPN
ap-2076	374	11	polytechnica	polytechnica	PROPN
ap-2076	374	12	[	[	X
ap-2076	374	13	9	9	NUM
ap-2076	374	14	]	]	X
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ap-2076	374	17	gadyl’shin	gadyl’shin	PROPN
ap-2076	374	18	.	.	PUNCT
ap-2076	375	1	local	local	ADJ
ap-2076	375	2	perturbations	perturbation	NOUN
ap-2076	375	3	of	of	ADP
ap-2076	375	4	the	the	DET
ap-2076	375	5	schrödinger	schrödinger	ADJ
ap-2076	375	6	operator	operator	NOUN
ap-2076	375	7	on	on	ADP
ap-2076	375	8	the	the	DET
ap-2076	375	9	axis.theoretical	axis.theoretical	ADJ
ap-2076	375	10	and	and	CCONJ
ap-2076	375	11	mathematical	mathematical	ADJ
ap-2076	375	12	physics	physics	NOUN
ap-2076	375	13	.	.	PUNCT
ap-2076	376	1	2002	2002	NUM
ap-2076	376	2	.	.	PUNCT
ap-2076	377	1	v.	v.	ADP
ap-2076	377	2	132	132	NUM
ap-2076	377	3	,	,	PUNCT
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ap-2076	377	5	.	.	NOUN
ap-2076	377	6	1	1	X
ap-2076	377	7	.	.	PUNCT
ap-2076	378	1	p.	p.	NOUN
ap-2076	378	2	976	976	NUM
ap-2076	378	3	-	-	SYM
ap-2076	378	4	982	982	NUM
ap-2076	378	5	.	.	PUNCT
ap-2076	379	1	doi	doi	NOUN
ap-2076	379	2	:	:	PUNCT
ap-2076	379	3	10.4213	10.4213	NUM
ap-2076	379	4	/	/	SYM
ap-2076	379	5	tmf349	tmf349	NOUN
ap-2076	380	1	[	[	X
ap-2076	380	2	10	10	NUM
ap-2076	380	3	]	]	X
ap-2076	380	4	d.	d.	PROPN
ap-2076	380	5	borisov	borisov	PROPN
ap-2076	380	6	.	.	PUNCT
ap-2076	381	1	discrete	discrete	ADJ
ap-2076	381	2	spectrum	spectrum	NOUN
ap-2076	381	3	of	of	ADP
ap-2076	381	4	a	a	DET
ap-2076	381	5	pair	pair	NOUN
ap-2076	381	6	of	of	ADP
ap-2076	381	7	non	non	ADJ
ap-2076	381	8	-	-	ADJ
ap-2076	381	9	symmetric	symmetric	ADJ
ap-2076	381	10	waveguides	waveguide	NOUN
ap-2076	381	11	coupled	couple	VERB
ap-2076	381	12	by	by	ADP
ap-2076	381	13	a	a	DET
ap-2076	381	14	window.sbornik	window.sbornik	X
ap-2076	381	15	mathematics	mathematic	NOUN
ap-2076	381	16	.	.	PUNCT
ap-2076	382	1	2006	2006	NUM
ap-2076	382	2	.	.	PUNCT
ap-2076	383	1	v.	v.	ADP
ap-2076	383	2	197	197	NUM
ap-2076	383	3	.	.	PUNCT
ap-2076	384	1	no	no	INTJ
ap-2076	384	2	.	.	NOUN
ap-2076	385	1	4	4	X
ap-2076	385	2	.	.	PUNCT
ap-2076	386	1	p.	p.	NOUN
ap-2076	386	2	475	475	NUM
ap-2076	386	3	-	-	SYM
ap-2076	386	4	504	504	NUM
ap-2076	386	5	.	.	PUNCT
ap-2076	387	1	doi	doi	NOUN
ap-2076	387	2	:	:	PUNCT
ap-2076	387	3	10.1070	10.1070	NUM
ap-2076	387	4	/	/	SYM
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ap-2076	387	6	[	[	X
ap-2076	387	7	11	11	NUM
ap-2076	387	8	]	]	PUNCT
ap-2076	387	9	d.	d.	PROPN
ap-2076	387	10	i.	i.	PROPN
ap-2076	387	11	borisov	borisov	PROPN
ap-2076	387	12	.	.	PUNCT
ap-2076	388	1	on	on	ADP
ap-2076	388	2	a	a	DET
ap-2076	388	3	model	model	NOUN
ap-2076	388	4	boundary	boundary	ADJ
ap-2076	388	5	value	value	NOUN
ap-2076	388	6	problem	problem	NOUN
ap-2076	388	7	for	for	ADP
ap-2076	388	8	laplacian	laplacian	NOUN
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ap-2076	388	10	frequently	frequently	ADV
ap-2076	388	11	alternating	alternate	VERB
ap-2076	388	12	type	type	NOUN
ap-2076	388	13	of	of	ADP
ap-2076	388	14	boundary	boundary	ADJ
ap-2076	388	15	condition.asymptotic	condition.asymptotic	ADJ
ap-2076	388	16	analysis	analysis	NOUN
ap-2076	388	17	.	.	PUNCT
ap-2076	389	1	2003	2003	NUM
ap-2076	389	2	.	.	PUNCT
ap-2076	390	1	v.	v.	ADP
ap-2076	390	2	35	35	NUM
ap-2076	390	3	.	.	PUNCT
ap-2076	391	1	no	no	INTJ
ap-2076	391	2	.	.	NOUN
ap-2076	392	1	1	1	X
ap-2076	392	2	.	.	PUNCT
ap-2076	393	1	p.	p.	NOUN
ap-2076	393	2	1	1	NUM
ap-2076	393	3	-	-	SYM
ap-2076	393	4	26	26	NUM
ap-2076	393	5	.	.	PUNCT
ap-2076	394	1	[	[	X
ap-2076	394	2	12	12	NUM
ap-2076	394	3	]	]	X
ap-2076	394	4	c.m	c.m	PROPN
ap-2076	394	5	.	.	PROPN
ap-2076	394	6	bender	bender	PROPN
ap-2076	394	7	,	,	PUNCT
ap-2076	394	8	s.	s.	PROPN
ap-2076	394	9	boettcher	boettcher	PROPN
ap-2076	394	10	.	.	PUNCT
ap-2076	395	1	real	real	ADJ
ap-2076	395	2	spectra	spectra	NOUN
ap-2076	395	3	in	in	ADP
ap-2076	395	4	non	non	ADJ
ap-2076	395	5	-	-	ADJ
ap-2076	395	6	hermitian	hermitian	ADJ
ap-2076	395	7	hamiltonians	hamiltonian	NOUN
ap-2076	395	8	having	have	VERB
ap-2076	395	9	pt	pt	PRON
ap-2076	395	10	symmetry.physics	symmetry.physic	NOUN
ap-2076	395	11	review	review	NOUN
ap-2076	395	12	letters	letter	NOUN
ap-2076	395	13	.	.	PUNCT
ap-2076	396	1	1998	1998	NUM
ap-2076	396	2	.	.	PUNCT
ap-2076	397	1	v.	v.	ADP
ap-2076	397	2	80	80	NUM
ap-2076	397	3	.	.	PUNCT
ap-2076	398	1	no	no	INTJ
ap-2076	398	2	.	.	NOUN
ap-2076	399	1	24	24	NUM
ap-2076	399	2	.	.	PUNCT
ap-2076	400	1	p.	p.	NOUN
ap-2076	400	2	5243	5243	NUM
ap-2076	400	3	-	-	SYM
ap-2076	400	4	5246	5246	NUM
ap-2076	400	5	.	.	PUNCT
ap-2076	401	1	doi	doi	NOUN
ap-2076	401	2	:	:	PUNCT
ap-2076	401	3	10.1103	10.1103	NUM
ap-2076	401	4	/	/	SYM
ap-2076	401	5	physrevlett.80.5243	physrevlett.80.5243	NOUN
ap-2076	402	1	[	[	X
ap-2076	402	2	13	13	NUM
ap-2076	402	3	]	]	PUNCT
ap-2076	402	4	a.	a.	NOUN
ap-2076	402	5	mostafazadeh	mostafazadeh	PROPN
ap-2076	402	6	.	.	PUNCT
ap-2076	403	1	pseudo	pseudo	NOUN
ap-2076	403	2	-	-	NOUN
ap-2076	403	3	hermiticity	hermiticity	NOUN
ap-2076	403	4	versus	versus	ADP
ap-2076	403	5	pt	pt	NOUN
ap-2076	403	6	-	-	PUNCT
ap-2076	403	7	symmetry	symmetry	NOUN
ap-2076	403	8	:	:	PUNCT
ap-2076	403	9	the	the	DET
ap-2076	403	10	necessary	necessary	ADJ
ap-2076	403	11	condition	condition	NOUN
ap-2076	403	12	for	for	ADP
ap-2076	403	13	the	the	DET
ap-2076	403	14	reality	reality	NOUN
ap-2076	403	15	of	of	ADP
ap-2076	403	16	the	the	DET
ap-2076	403	17	spectrum	spectrum	NOUN
ap-2076	403	18	of	of	ADP
ap-2076	403	19	a	a	DET
ap-2076	403	20	non	non	ADJ
ap-2076	403	21	-	-	ADJ
ap-2076	403	22	hermitian	hermitian	ADJ
ap-2076	403	23	hamiltonian.journal	hamiltonian.journal	PROPN
ap-2076	403	24	of	of	ADP
ap-2076	403	25	mathematical	mathematical	ADJ
ap-2076	403	26	physics	physics	NOUN
ap-2076	403	27	.	.	PUNCT
ap-2076	404	1	2002	2002	NUM
ap-2076	404	2	.	.	PUNCT
ap-2076	405	1	v.	v.	ADP
ap-2076	405	2	43	43	NUM
ap-2076	405	3	.	.	PUNCT
ap-2076	406	1	no	no	INTJ
ap-2076	406	2	.	.	NOUN
ap-2076	407	1	1	1	X
ap-2076	407	2	.	.	PUNCT
ap-2076	408	1	p.	p.	NOUN
ap-2076	408	2	205	205	NUM
ap-2076	408	3	-	-	SYM
ap-2076	408	4	214	214	NUM
ap-2076	408	5	.	.	PUNCT
ap-2076	409	1	doi	doi	NOUN
ap-2076	409	2	:	:	PUNCT
ap-2076	409	3	10.1063/1.1418246	10.1063/1.1418246	NUM
ap-2076	409	4	[	[	X
ap-2076	409	5	14	14	NUM
ap-2076	409	6	]	]	PUNCT
ap-2076	409	7	a.	a.	NOUN
ap-2076	409	8	mostafazadeh	mostafazadeh	PROPN
ap-2076	409	9	.	.	PUNCT
ap-2076	410	1	pseudo	pseudo	NOUN
ap-2076	410	2	-	-	NOUN
ap-2076	410	3	hermiticity	hermiticity	NOUN
ap-2076	410	4	versus	versus	ADP
ap-2076	410	5	pt	pt	PROPN
ap-2076	410	6	-	-	PUNCT
ap-2076	410	7	symmetry	symmetry	NOUN
ap-2076	410	8	ii	ii	PROPN
ap-2076	410	9	:	:	PUNCT
ap-2076	410	10	a	a	DET
ap-2076	410	11	complete	complete	ADJ
ap-2076	410	12	characterization	characterization	NOUN
ap-2076	410	13	of	of	ADP
ap-2076	410	14	non	non	ADJ
ap-2076	410	15	-	-	ADJ
ap-2076	410	16	hermitian	hermitian	ADJ
ap-2076	410	17	hamiltonians	hamiltonian	NOUN
ap-2076	410	18	with	with	ADP
ap-2076	410	19	a	a	DET
ap-2076	410	20	real	real	ADJ
ap-2076	410	21	spectrum.journal	spectrum.journal	ADJ
ap-2076	410	22	of	of	ADP
ap-2076	410	23	mathematical	mathematical	ADJ
ap-2076	410	24	physics	physics	NOUN
ap-2076	410	25	.	.	PUNCT
ap-2076	411	1	2002	2002	NUM
ap-2076	411	2	.	.	PUNCT
ap-2076	412	1	v.	v.	ADP
ap-2076	412	2	43	43	NUM
ap-2076	412	3	.	.	PUNCT
ap-2076	413	1	no	no	INTJ
ap-2076	413	2	.	.	NOUN
ap-2076	414	1	5	5	X
ap-2076	414	2	.	.	PUNCT
ap-2076	415	1	p.	p.	NOUN
ap-2076	415	2	2814	2814	NUM
ap-2076	415	3	-	-	SYM
ap-2076	415	4	2816	2816	NUM
ap-2076	415	5	.	.	PUNCT
ap-2076	416	1	doi	doi	NOUN
ap-2076	416	2	:	:	PUNCT
ap-2076	416	3	10.1063/1.1461427	10.1063/1.1461427	NUM
ap-2076	416	4	[	[	SYM
ap-2076	416	5	15	15	NUM
ap-2076	416	6	]	]	PUNCT
ap-2076	416	7	a.	a.	NOUN
ap-2076	416	8	mostafazadeh	mostafazadeh	NOUN
ap-2076	416	9	.	.	PUNCT
ap-2076	417	1	pseudo	pseudo	NOUN
ap-2076	417	2	-	-	NOUN
ap-2076	417	3	hermiticity	hermiticity	NOUN
ap-2076	417	4	versus	versus	ADP
ap-2076	417	5	pt	pt	NOUN
ap-2076	417	6	-	-	PUNCT
ap-2076	417	7	symmetry	symmetry	NOUN
ap-2076	417	8	iii	iii	NOUN
ap-2076	417	9	:	:	PUNCT
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ap-2076	417	11	of	of	ADP
ap-2076	417	12	pseudo	pseudo	NOUN
ap-2076	417	13	-	-	NOUN
ap-2076	417	14	hermiticity	hermiticity	NOUN
ap-2076	417	15	and	and	CCONJ
ap-2076	417	16	the	the	DET
ap-2076	417	17	presence	presence	NOUN
ap-2076	417	18	of	of	ADP
ap-2076	417	19	antilinear	antilinear	ADJ
ap-2076	417	20	symmetries.journal	symmetries.journal	PROPN
ap-2076	417	21	of	of	ADP
ap-2076	417	22	mathematical	mathematical	ADJ
ap-2076	417	23	physics	physics	NOUN
ap-2076	417	24	.	.	PUNCT
ap-2076	418	1	2002	2002	NUM
ap-2076	418	2	.	.	PUNCT
ap-2076	419	1	v.	v.	ADP
ap-2076	419	2	43	43	NUM
ap-2076	419	3	.	.	PUNCT
ap-2076	420	1	no	no	INTJ
ap-2076	420	2	.	.	NOUN
ap-2076	421	1	8	8	NUM
ap-2076	421	2	.	.	PUNCT
ap-2076	422	1	p.	p.	NOUN
ap-2076	422	2	3944	3944	NUM
ap-2076	422	3	-	-	SYM
ap-2076	422	4	3951	3951	NUM
ap-2076	422	5	.	.	PUNCT
ap-2076	423	1	doi	doi	NOUN
ap-2076	423	2	:	:	PUNCT
ap-2076	423	3	10.1063/1.1489072	10.1063/1.1489072	NUM
ap-2076	423	4	[	[	X
ap-2076	423	5	16	16	NUM
ap-2076	423	6	]	]	PUNCT
ap-2076	423	7	a.	a.	NOUN
ap-2076	423	8	mostafazadeh	mostafazadeh	PROPN
ap-2076	423	9	.	.	PUNCT
ap-2076	424	1	on	on	ADP
ap-2076	424	2	the	the	DET
ap-2076	424	3	pseudo	pseudo	NOUN
ap-2076	424	4	-	-	NOUN
ap-2076	424	5	hermiticity	hermiticity	NOUN
ap-2076	424	6	of	of	ADP
ap-2076	424	7	a	a	DET
ap-2076	424	8	class	class	NOUN
ap-2076	424	9	of	of	ADP
ap-2076	424	10	pt	pt	NOUN
ap-2076	424	11	-	-	ADJ
ap-2076	424	12	symmetric	symmetric	ADJ
ap-2076	424	13	hamiltonians	hamiltonian	NOUN
ap-2076	424	14	in	in	ADP
ap-2076	424	15	one	one	NUM
ap-2076	424	16	dimension.modern	dimension.modern	ADJ
ap-2076	424	17	physics	physics	NOUN
ap-2076	424	18	letters	letter	NOUN
ap-2076	424	19	a.	a.	PROPN
ap-2076	424	20	2002	2002	NUM
ap-2076	424	21	.	.	PUNCT
ap-2076	425	1	v.	v.	ADP
ap-2076	425	2	17	17	NUM
ap-2076	425	3	.	.	PUNCT
ap-2076	426	1	no	no	INTJ
ap-2076	426	2	.	.	NOUN
ap-2076	426	3	30	30	NUM
ap-2076	426	4	.	.	PUNCT
ap-2076	427	1	p.	p.	NOUN
ap-2076	427	2	1973	1973	NUM
ap-2076	427	3	-	-	SYM
ap-2076	427	4	1977	1977	NUM
ap-2076	427	5	.	.	PUNCT
ap-2076	428	1	doi	doi	NOUN
ap-2076	428	2	:	:	PUNCT
ap-2076	428	3	10.1142	10.1142	NUM
ap-2076	428	4	/	/	SYM
ap-2076	428	5	s0217732302008472	s0217732302008472	NOUN
ap-2076	429	1	[	[	X
ap-2076	429	2	17	17	NUM
ap-2076	429	3	]	]	PUNCT
ap-2076	429	4	m.	m.	NOUN
ap-2076	429	5	znojil	znojil	PROPN
ap-2076	429	6	.	.	PUNCT
ap-2076	430	1	exact	exact	ADJ
ap-2076	430	2	solution	solution	NOUN
ap-2076	430	3	for	for	ADP
ap-2076	430	4	morse	morse	ADJ
ap-2076	430	5	oscillator	oscillator	NOUN
ap-2076	430	6	in	in	ADP
ap-2076	430	7	pt	pt	ADJ
ap-2076	430	8	-	-	ADJ
ap-2076	430	9	symmetric	symmetric	ADJ
ap-2076	430	10	quantum	quantum	NOUN
ap-2076	430	11	mechanics.physics	mechanics.physic	NOUN
ap-2076	430	12	letters	letter	NOUN
ap-2076	430	13	a.	a.	NOUN
ap-2076	430	14	1999	1999	NUM
ap-2076	430	15	.	.	PUNCT
ap-2076	431	1	v.	v.	ADP
ap-2076	431	2	264	264	NUM
ap-2076	431	3	.	.	PUNCT
ap-2076	432	1	no	no	INTJ
ap-2076	432	2	.	.	NOUN
ap-2076	433	1	2	2	X
ap-2076	433	2	.	.	PUNCT
ap-2076	434	1	p.	p.	NOUN
ap-2076	434	2	108	108	NUM
ap-2076	434	3	-	-	SYM
ap-2076	434	4	111	111	NUM
ap-2076	434	5	.	.	PUNCT
ap-2076	435	1	doi	doi	NOUN
ap-2076	435	2	:	:	PUNCT
ap-2076	435	3	10.1016	10.1016	NUM
ap-2076	435	4	/	/	SYM
ap-2076	435	5	s0375	s0375	VERB
ap-2076	435	6	-	-	PUNCT
ap-2076	435	7	9601(99)00805	9601(99)00805	NUM
ap-2076	435	8	-	-	PUNCT
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ap-2076	435	10	[	[	SYM
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ap-2076	435	12	]	]	PUNCT
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ap-2076	435	14	znojil	znojil	NOUN
ap-2076	435	15	.	.	PUNCT
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ap-2076	436	2	-	-	ADJ
ap-2076	436	3	hermitian	hermitian	ADJ
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ap-2076	436	5	description	description	NOUN
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ap-2076	436	7	the	the	DET
ap-2076	436	8	pt	pt	ADJ
ap-2076	436	9	-	-	PUNCT
ap-2076	436	10	symmetric	symmetric	ADJ
ap-2076	436	11	anharmonic	anharmonic	ADJ
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ap-2076	436	13	of	of	ADP
ap-2076	436	14	physics	physics	NOUN
ap-2076	436	15	a	a	PRON
ap-2076	436	16	:	:	PUNCT
ap-2076	436	17	mathematics	mathematic	NOUN
ap-2076	436	18	and	and	CCONJ
ap-2076	436	19	general	general	ADJ
ap-2076	436	20	.	.	PUNCT
ap-2076	436	21	1999	1999	NUM
ap-2076	436	22	.	.	PUNCT
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ap-2076	437	3	.	.	PUNCT
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ap-2076	439	2	.	.	PUNCT
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ap-2076	440	3	-	-	SYM
ap-2076	440	4	7428	7428	NUM
ap-2076	440	5	.	.	PUNCT
ap-2076	441	1	doi	doi	NOUN
ap-2076	441	2	:	:	PUNCT
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ap-2076	441	4	-	-	SYM
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ap-2076	441	6	[	[	X
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ap-2076	441	8	]	]	PUNCT
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ap-2076	441	10	znojil	znojil	PROPN
ap-2076	441	11	.	.	PUNCT
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ap-2076	442	2	-	-	ADJ
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ap-2076	442	9	.	.	PUNCT
ap-2076	443	1	v.	v.	ADP
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ap-2076	443	3	.	.	PUNCT
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ap-2076	444	2	.	.	NOUN
ap-2076	445	1	3	3	NUM
ap-2076	445	2	-	-	SYM
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ap-2076	445	4	.	.	PUNCT
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ap-2076	446	3	-	-	SYM
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ap-2076	446	5	.	.	PUNCT
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ap-2076	447	2	:	:	PUNCT
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ap-2076	447	8	-	-	SYM
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ap-2076	447	18	.	.	PUNCT
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ap-2076	449	2	.	.	PUNCT
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ap-2076	450	3	.	.	PUNCT
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ap-2076	451	2	.	.	NOUN
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ap-2076	452	2	.	.	PUNCT
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ap-2076	453	3	-	-	SYM
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ap-2076	453	5	.	.	PUNCT
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ap-2076	454	12	.	.	PUNCT
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ap-2076	455	4	non	non	ADJ
ap-2076	455	5	-	-	ADJ
ap-2076	455	6	hermitian	hermitian	ADJ
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ap-2076	455	8	on	on	ADP
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ap-2076	455	12	.	.	PUNCT
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ap-2076	456	2	.	.	PUNCT
ap-2076	457	1	v.	v.	ADP
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ap-2076	458	2	.	.	NOUN
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ap-2076	461	1	-	-	SYM
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ap-2076	461	3	.	.	PUNCT
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ap-2076	462	2	:	:	PUNCT
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ap-2076	462	4	-	-	SYM
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ap-2076	462	6	/	/	SYM
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ap-2076	462	21	acta	acta	PROPN
ap-2076	462	22	polytechnica	polytechnica	PROPN
ap-2076	462	23	54(2):93–100	54(2):93–100	NUM
ap-2076	462	24	,	,	PUNCT
ap-2076	462	25	2014	2014	NUM
ap-2076	462	26	1	1	NUM
ap-2076	462	27	introduction	introduction	NOUN
ap-2076	462	28	and	and	CCONJ
ap-2076	462	29	main	main	ADJ
ap-2076	462	30	results	result	NOUN
ap-2076	462	31	2	2	NUM
ap-2076	462	32	proofs	proof	NOUN
ap-2076	462	33	of	of	ADP
ap-2076	462	34	main	main	ADJ
ap-2076	462	35	results	result	NOUN
ap-2076	462	36	acknowledgements	acknowledgement	NOUN
ap-2076	462	37	references	reference	NOUN