id	sid	tid	token	lemma	pos
ap-1275	1	1	ap-5-10.dvi	ap-5-10.dvi	PROPN
ap-1275	1	2	acta	acta	PROPN
ap-1275	1	3	polytechnica	polytechnica	PROPN
ap-1275	1	4	vol	vol	NOUN
ap-1275	1	5	.	.	PROPN
ap-1275	2	1	50	50	NUM
ap-1275	2	2	no	no	NOUN
ap-1275	2	3	.	.	PUNCT
ap-1275	3	1	5/2010	5/2010	PRON
ap-1275	3	2	root	root	NOUN
ap-1275	3	3	asymptotics	asymptotic	NOUN
ap-1275	3	4	for	for	ADP
ap-1275	3	5	the	the	DET
ap-1275	3	6	eigenfunctions	eigenfunction	NOUN
ap-1275	3	7	of	of	ADP
ap-1275	3	8	univariate	univariate	ADJ
ap-1275	3	9	differential	differential	ADJ
ap-1275	3	10	operators	operator	NOUN
ap-1275	3	11	b.	b.	PROPN
ap-1275	3	12	shapiro	shapiro	PROPN
ap-1275	3	13	abstract	abstract	PROPN
ap-1275	3	14	this	this	DET
ap-1275	3	15	paper	paper	NOUN
ap-1275	3	16	is	be	AUX
ap-1275	3	17	a	a	DET
ap-1275	3	18	brief	brief	ADJ
ap-1275	3	19	survey	survey	NOUN
ap-1275	3	20	of	of	ADP
ap-1275	3	21	the	the	DET
ap-1275	3	22	research	research	NOUN
ap-1275	3	23	conducted	conduct	VERB
ap-1275	3	24	by	by	ADP
ap-1275	3	25	the	the	DET
ap-1275	3	26	author	author	NOUN
ap-1275	3	27	and	and	CCONJ
ap-1275	3	28	his	his	PRON
ap-1275	3	29	collaborators	collaborator	NOUN
ap-1275	3	30	in	in	ADP
ap-1275	3	31	the	the	DET
ap-1275	3	32	field	field	NOUN
ap-1275	3	33	of	of	ADP
ap-1275	3	34	root	root	NOUN
ap-1275	3	35	asymptotics	asymptotic	NOUN
ap-1275	3	36	of	of	ADP
ap-1275	3	37	(	(	PUNCT
ap-1275	3	38	mostly	mostly	ADV
ap-1275	3	39	polynomial	polynomial	ADJ
ap-1275	3	40	)	)	PUNCT
ap-1275	3	41	eigenfunctions	eigenfunction	NOUN
ap-1275	3	42	of	of	ADP
ap-1275	3	43	linear	linear	ADJ
ap-1275	3	44	univariate	univariate	ADJ
ap-1275	3	45	differential	differential	ADJ
ap-1275	3	46	operators	operator	NOUN
ap-1275	3	47	with	with	ADP
ap-1275	3	48	polynomial	polynomial	ADJ
ap-1275	3	49	coefficients	coefficient	NOUN
ap-1275	3	50	.	.	PUNCT
ap-1275	4	1	keywords	keyword	NOUN
ap-1275	4	2	:	:	PUNCT
ap-1275	4	3	root	root	NOUN
ap-1275	4	4	-	-	PUNCT
ap-1275	4	5	counting	count	VERB
ap-1275	4	6	measure	measure	NOUN
ap-1275	4	7	,	,	PUNCT
ap-1275	4	8	exactly	exactly	ADV
ap-1275	4	9	solvable	solvable	ADJ
ap-1275	4	10	operator	operator	NOUN
ap-1275	4	11	,	,	PUNCT
ap-1275	4	12	schrödinger	schrödinger	NOUN
ap-1275	4	13	equation	equation	NOUN
ap-1275	4	14	.	.	PUNCT
ap-1275	5	1	1	1	NUM
ap-1275	5	2	objective	objective	ADJ
ap-1275	5	3	study	study	NOUN
ap-1275	5	4	asymptotic	asymptotic	ADJ
ap-1275	5	5	properties	property	NOUN
ap-1275	5	6	of	of	ADP
ap-1275	5	7	sequences	sequence	NOUN
ap-1275	5	8	{	{	PUNCT
ap-1275	5	9	pn(z	pn(z	PROPN
ap-1275	5	10	)	)	PUNCT
ap-1275	5	11	}	}	PUNCT
ap-1275	5	12	,	,	PUNCT
ap-1275	5	13	of	of	ADP
ap-1275	5	14	polynomials	polynomial	NOUN
ap-1275	5	15	/	/	SYM
ap-1275	5	16	entire	entire	ADJ
ap-1275	5	17	functions	function	NOUN
ap-1275	5	18	in	in	ADP
ap-1275	5	19	z	z	NOUN
ap-1275	5	20	which	which	PRON
ap-1275	5	21	either	either	CCONJ
ap-1275	5	22	1	1	X
ap-1275	5	23	.	.	NUM
ap-1275	5	24	are	be	AUX
ap-1275	5	25	polynomial	polynomial	ADJ
ap-1275	5	26	/	/	SYM
ap-1275	5	27	entire	entire	ADJ
ap-1275	5	28	eigenfunctions	eigenfunction	NOUN
ap-1275	5	29	of	of	ADP
ap-1275	5	30	a	a	DET
ap-1275	5	31	univariate	univariate	ADJ
ap-1275	5	32	linear	linear	ADJ
ap-1275	5	33	ordinary	ordinary	ADJ
ap-1275	5	34	differential	differential	ADJ
ap-1275	5	35	operator	operator	NOUN
ap-1275	5	36	with	with	ADP
ap-1275	5	37	polynomial	polynomial	ADJ
ap-1275	5	38	coefficients	coefficient	NOUN
ap-1275	5	39	;	;	PUNCT
ap-1275	5	40	or	or	CCONJ
ap-1275	5	41	2	2	NUM
ap-1275	5	42	.	.	X
ap-1275	5	43	are	be	AUX
ap-1275	5	44	polynomial	polynomial	ADJ
ap-1275	5	45	solutions	solution	NOUN
ap-1275	5	46	of	of	ADP
ap-1275	5	47	more	more	ADJ
ap-1275	5	48	general	general	ADJ
ap-1275	5	49	pencils	pencil	NOUN
ap-1275	5	50	of	of	ADP
ap-1275	5	51	such	such	ADJ
ap-1275	5	52	operators	operator	NOUN
ap-1275	5	53	,	,	PUNCT
ap-1275	5	54	e.g.	e.g.	ADV
ap-1275	5	55	homogenized	homogenize	VERB
ap-1275	5	56	spectral	spectral	ADJ
ap-1275	5	57	problems	problem	NOUN
ap-1275	5	58	and	and	CCONJ
ap-1275	5	59	heine	heine	PROPN
ap-1275	5	60	-	-	PUNCT
ap-1275	5	61	stieltjes	stieltjes	PROPN
ap-1275	5	62	spectral	spectral	ADJ
ap-1275	5	63	problems	problem	NOUN
ap-1275	5	64	;	;	PUNCT
ap-1275	5	65	or	or	CCONJ
ap-1275	5	66	3	3	X
ap-1275	5	67	.	.	X
ap-1275	5	68	satisfy	satisfy	VERB
ap-1275	5	69	a	a	DET
ap-1275	5	70	finite	finite	ADJ
ap-1275	5	71	recurrence	recurrence	NOUN
ap-1275	5	72	relation	relation	NOUN
ap-1275	5	73	with	with	ADP
ap-1275	5	74	(	(	PUNCT
ap-1275	5	75	in	in	ADP
ap-1275	5	76	general	general	ADJ
ap-1275	5	77	)	)	PUNCT
ap-1275	5	78	varying	vary	VERB
ap-1275	5	79	coefficients	coefficient	NOUN
ap-1275	5	80	.	.	PUNCT
ap-1275	6	1	2	2	NUM
ap-1275	6	2	basic	basic	ADJ
ap-1275	6	3	notions	notion	NOUN
ap-1275	6	4	and	and	CCONJ
ap-1275	6	5	examples	example	NOUN
ap-1275	6	6	definition	definition	NOUN
ap-1275	6	7	1	1	NUM
ap-1275	6	8	an	an	DET
ap-1275	6	9	operator	operator	NOUN
ap-1275	6	10	t	t	PROPN
ap-1275	6	11	=	=	SYM
ap-1275	6	12	k∑	k∑	PROPN
ap-1275	6	13	i=1	i=1	PROPN
ap-1275	6	14	qi(z	qi(z	X
ap-1275	6	15	)	)	PUNCT
ap-1275	6	16	di	di	X
ap-1275	6	17	dzi	dzi	PROPN
ap-1275	6	18	is	be	AUX
ap-1275	6	19	called	call	VERB
ap-1275	6	20	exactly	exactly	ADV
ap-1275	6	21	solvable	solvable	ADJ
ap-1275	6	22	if	if	SCONJ
ap-1275	6	23	degqi(z	degqi(z	NOUN
ap-1275	6	24	)	)	PUNCT
ap-1275	6	25	≤	≤	NOUN
ap-1275	7	1	i	i	PRON
ap-1275	7	2	and	and	CCONJ
ap-1275	7	3	there	there	PRON
ap-1275	7	4	exists	exist	VERB
ap-1275	7	5	at	at	ADP
ap-1275	7	6	least	least	ADV
ap-1275	7	7	one	one	NUM
ap-1275	7	8	value	value	NOUN
ap-1275	7	9	i	i	PRON
ap-1275	7	10	such	such	ADJ
ap-1275	7	11	that	that	DET
ap-1275	7	12	degqi(z	degqi(z	NOUN
ap-1275	7	13	)	)	PUNCT
ap-1275	7	14	=	=	SYM
ap-1275	7	15	i.	i.	NOUN
ap-1275	7	16	obviously	obviously	ADV
ap-1275	7	17	,	,	PUNCT
ap-1275	7	18	t	t	PROPN
ap-1275	7	19	(	(	PUNCT
ap-1275	7	20	zj	zj	PROPN
ap-1275	7	21	)	)	PUNCT
ap-1275	7	22	=	=	PUNCT
ap-1275	7	23	ajz	ajz	PROPN
ap-1275	7	24	j	j	NOUN
ap-1275	7	25	+	+	CCONJ
ap-1275	7	26	lower	low	ADJ
ap-1275	7	27	order	order	NOUN
ap-1275	7	28	terms	term	NOUN
ap-1275	7	29	,	,	PUNCT
ap-1275	7	30	i.e.	i.e.	X
ap-1275	7	31	t	t	NOUN
ap-1275	7	32	acts	act	VERB
ap-1275	7	33	by	by	ADP
ap-1275	7	34	an	an	DET
ap-1275	7	35	(	(	PUNCT
ap-1275	7	36	infinite	infinite	NOUN
ap-1275	7	37	)	)	PUNCT
ap-1275	7	38	triangular	triangular	NOUN
ap-1275	7	39	matrix	matrix	NOUN
ap-1275	7	40	in	in	ADP
ap-1275	7	41	the	the	DET
ap-1275	7	42	monomial	monomial	ADJ
ap-1275	7	43	basis	basis	NOUN
ap-1275	7	44	{	{	PUNCT
ap-1275	7	45	1	1	NUM
ap-1275	7	46	,	,	PUNCT
ap-1275	7	47	z	z	NOUN
ap-1275	7	48	,	,	PUNCT
ap-1275	7	49	,	,	PUNCT
ap-1275	7	50	z2	z2	PROPN
ap-1275	7	51	,	,	PUNCT
ap-1275	7	52	.	.	PUNCT
ap-1275	7	53	.	.	PUNCT
ap-1275	8	1	.	.	PUNCT
ap-1275	8	2	}	}	PUNCT
ap-1275	9	1	of	of	ADP
ap-1275	9	2	c[z	c[z	PROPN
ap-1275	9	3	]	]	PUNCT
ap-1275	9	4	.	.	PUNCT
ap-1275	10	1	lemma	lemma	PROPN
ap-1275	10	2	1	1	NUM
ap-1275	10	3	for	for	ADP
ap-1275	10	4	any	any	DET
ap-1275	10	5	exactly	exactly	ADV
ap-1275	10	6	solvable	solvable	ADJ
ap-1275	10	7	t	t	NOUN
ap-1275	10	8	and	and	CCONJ
ap-1275	10	9	sufficiently	sufficiently	ADV
ap-1275	10	10	large	large	ADJ
ap-1275	10	11	n	n	CCONJ
ap-1275	10	12	there	there	ADV
ap-1275	10	13	exists	exist	VERB
ap-1275	10	14	a	a	DET
ap-1275	10	15	unique	unique	ADJ
ap-1275	10	16	(	(	PUNCT
ap-1275	10	17	up	up	ADP
ap-1275	10	18	to	to	ADP
ap-1275	10	19	a	a	DET
ap-1275	10	20	scalar	scalar	ADJ
ap-1275	10	21	)	)	PUNCT
ap-1275	10	22	eigenpolynomial	eigenpolynomial	ADJ
ap-1275	10	23	pn(z	pn(z	PUNCT
ap-1275	10	24	)	)	PUNCT
ap-1275	10	25	of	of	ADP
ap-1275	10	26	degree	degree	NOUN
ap-1275	10	27	n.	n.	PROPN
ap-1275	10	28	typical	typical	ADJ
ap-1275	10	29	problem	problem	NOUN
ap-1275	10	30	.	.	PUNCT
ap-1275	11	1	given	give	VERB
ap-1275	11	2	an	an	DET
ap-1275	11	3	exactly	exactly	ADV
ap-1275	11	4	solvable	solvable	ADJ
ap-1275	11	5	t	t	NOUN
ap-1275	11	6	describe	describe	VERB
ap-1275	11	7	the	the	DET
ap-1275	11	8	root	root	NOUN
ap-1275	11	9	asymptotics	asymptotic	NOUN
ap-1275	11	10	for	for	ADP
ap-1275	11	11	the	the	DET
ap-1275	11	12	sequence	sequence	NOUN
ap-1275	11	13	of	of	ADP
ap-1275	11	14	polynomials	polynomial	NOUN
ap-1275	11	15	{	{	PUNCT
ap-1275	11	16	pn(z	pn(z	NOUN
ap-1275	11	17	)	)	PUNCT
ap-1275	11	18	}	}	PUNCT
ap-1275	11	19	.	.	PUNCT
ap-1275	12	1	2.1	2.1	NUM
ap-1275	12	2	two	two	NUM
ap-1275	12	3	asymptotic	asymptotic	ADJ
ap-1275	12	4	measures	measure	NOUN
ap-1275	12	5	given	give	VERB
ap-1275	12	6	a	a	DET
ap-1275	12	7	polynomial	polynomial	ADJ
ap-1275	12	8	family	family	NOUN
ap-1275	12	9	{	{	PUNCT
ap-1275	12	10	pn(z	pn(z	PROPN
ap-1275	12	11	)	)	PUNCT
ap-1275	12	12	}	}	PUNCT
ap-1275	12	13	where	where	SCONJ
ap-1275	12	14	deg	deg	PROPN
ap-1275	12	15	pn(z	pn(z	PUNCT
ap-1275	12	16	)	)	PUNCT
ap-1275	12	17	=	=	SYM
ap-1275	13	1	n	n	X
ap-1275	13	2	we	we	PRON
ap-1275	13	3	define	define	VERB
ap-1275	13	4	two	two	NUM
ap-1275	13	5	basic	basic	ADJ
ap-1275	13	6	measures	measure	NOUN
ap-1275	13	7	:	:	PUNCT
ap-1275	13	8	(	(	PUNCT
ap-1275	13	9	i	i	NOUN
ap-1275	13	10	)	)	PUNCT
ap-1275	13	11	asymptotic	asymptotic	ADJ
ap-1275	13	12	root	root	NOUN
ap-1275	13	13	-	-	PUNCT
ap-1275	13	14	counting	count	VERB
ap-1275	13	15	measure	measure	NOUN
ap-1275	13	16	μ	μ	NOUN
ap-1275	13	17	;	;	PUNCT
ap-1275	13	18	(	(	PUNCT
ap-1275	13	19	ii	ii	NOUN
ap-1275	13	20	)	)	PUNCT
ap-1275	13	21	asymptotic	asymptotic	ADJ
ap-1275	13	22	ratio	ratio	NOUN
ap-1275	13	23	measure	measure	NOUN
ap-1275	13	24	ν	ν	PROPN
ap-1275	13	25	.	.	PUNCT
ap-1275	13	26	definition	definition	NOUN
ap-1275	13	27	2	2	NUM
ap-1275	13	28	associate	associate	NOUN
ap-1275	13	29	to	to	ADP
ap-1275	13	30	each	each	PRON
ap-1275	13	31	pn(x	pn(x	NOUN
ap-1275	13	32	)	)	PUNCT
ap-1275	13	33	a	a	DET
ap-1275	13	34	finite	finite	ADJ
ap-1275	13	35	probability	probability	NOUN
ap-1275	13	36	measure	measure	NOUN
ap-1275	13	37	μn	μn	INTJ
ap-1275	13	38	by	by	ADP
ap-1275	13	39	placing	place	VERB
ap-1275	13	40	the	the	DET
ap-1275	13	41	mass	mass	NOUN
ap-1275	13	42	1	1	NUM
ap-1275	13	43	n	n	NOUN
ap-1275	13	44	at	at	ADP
ap-1275	13	45	every	every	DET
ap-1275	13	46	root	root	NOUN
ap-1275	13	47	of	of	ADP
ap-1275	13	48	pn(x	pn(x	NOUN
ap-1275	13	49	)	)	PUNCT
ap-1275	13	50	.	.	PUNCT
ap-1275	14	1	(	(	PUNCT
ap-1275	14	2	if	if	SCONJ
ap-1275	14	3	some	some	DET
ap-1275	14	4	root	root	NOUN
ap-1275	14	5	is	be	AUX
ap-1275	14	6	multiple	multiple	ADJ
ap-1275	14	7	we	we	PRON
ap-1275	14	8	place	place	VERB
ap-1275	14	9	at	at	ADP
ap-1275	14	10	this	this	DET
ap-1275	14	11	point	point	NOUN
ap-1275	14	12	the	the	DET
ap-1275	14	13	mass	mass	NOUN
ap-1275	14	14	equal	equal	ADJ
ap-1275	14	15	to	to	ADP
ap-1275	14	16	its	its	PRON
ap-1275	14	17	multiplicity	multiplicity	NOUN
ap-1275	14	18	divided	divide	VERB
ap-1275	14	19	by	by	ADP
ap-1275	14	20	n.	n.	NOUN
ap-1275	14	21	)	)	PUNCT
ap-1275	14	22	the	the	DET
ap-1275	14	23	limit	limit	NOUN
ap-1275	14	24	μ	μ	NOUN
ap-1275	14	25	=	=	PROPN
ap-1275	14	26	lim	lim	PROPN
ap-1275	14	27	n	n	PROPN
ap-1275	14	28	μn	μn	PROPN
ap-1275	15	1	(	(	PUNCT
ap-1275	15	2	if	if	SCONJ
ap-1275	15	3	it	it	PRON
ap-1275	15	4	exists	exist	VERB
ap-1275	15	5	in	in	ADP
ap-1275	15	6	the	the	DET
ap-1275	15	7	sense	sense	NOUN
ap-1275	15	8	of	of	ADP
ap-1275	15	9	weak	weak	ADJ
ap-1275	15	10	convergence	convergence	NOUN
ap-1275	15	11	)	)	PUNCT
ap-1275	15	12	will	will	AUX
ap-1275	15	13	be	be	AUX
ap-1275	15	14	called	call	VERB
ap-1275	15	15	the	the	DET
ap-1275	15	16	asymptotic	asymptotic	ADJ
ap-1275	15	17	root	root	NOUN
ap-1275	15	18	-	-	PUNCT
ap-1275	15	19	counting	count	VERB
ap-1275	15	20	measure	measure	NOUN
ap-1275	15	21	of	of	ADP
ap-1275	15	22	{	{	PUNCT
ap-1275	15	23	pn(z	pn(z	NOUN
ap-1275	15	24	)	)	PUNCT
ap-1275	15	25	}	}	PUNCT
ap-1275	15	26	.	.	PUNCT
ap-1275	16	1	definition	definition	NOUN
ap-1275	16	2	3	3	NUM
ap-1275	16	3	consider	consider	VERB
ap-1275	16	4	the	the	DET
ap-1275	16	5	ratio	ratio	NOUN
ap-1275	16	6	qn(z	qn(z	NUM
ap-1275	16	7	)	)	PUNCT
ap-1275	16	8	=	=	SYM
ap-1275	16	9	pn−1(z	pn−1(z	NOUN
ap-1275	16	10	)	)	PUNCT
ap-1275	16	11	pn(z	pn(z	PUNCT
ap-1275	16	12	)	)	PUNCT
ap-1275	16	13	.	.	PUNCT
ap-1275	17	1	(	(	PUNCT
ap-1275	17	2	assume	assume	VERB
ap-1275	17	3	for	for	ADP
ap-1275	17	4	simplicity	simplicity	NOUN
ap-1275	17	5	that	that	SCONJ
ap-1275	17	6	pn(z	pn(z	PUNCT
ap-1275	17	7	)	)	PUNCT
ap-1275	17	8	has	have	VERB
ap-1275	17	9	no	no	DET
ap-1275	17	10	multiple	multiple	ADJ
ap-1275	17	11	roots	root	NOUN
ap-1275	17	12	and	and	CCONJ
ap-1275	17	13	expand	expand	VERB
ap-1275	17	14	qn(z	qn(z	NOUN
ap-1275	17	15	)	)	PUNCT
ap-1275	18	1	=	=	PUNCT
ap-1275	19	1	n∑	n∑	PROPN
ap-1275	19	2	i=1	i=1	PROPN
ap-1275	19	3	κi	κi	PROPN
ap-1275	19	4	,	,	PUNCT
ap-1275	19	5	n	n	PROPN
ap-1275	19	6	z	z	NOUN
ap-1275	19	7	−	−	PROPN
ap-1275	19	8	zi	zi	PROPN
ap-1275	19	9	,	,	PUNCT
ap-1275	19	10	n	n	PROPN
ap-1275	19	11	.	.	PUNCT
ap-1275	19	12	)	)	PUNCT
ap-1275	19	13	associate	associate	NOUN
ap-1275	19	14	to	to	ADP
ap-1275	19	15	qn(z	qn(z	NUM
ap-1275	19	16	)	)	PUNCT
ap-1275	19	17	the	the	DET
ap-1275	19	18	finite	finite	ADJ
ap-1275	19	19	complex	complex	NOUN
ap-1275	19	20	-	-	PUNCT
ap-1275	19	21	valued	value	VERB
ap-1275	19	22	measure	measure	NOUN
ap-1275	19	23	by	by	ADP
ap-1275	19	24	placing	place	VERB
ap-1275	19	25	κi	κi	NOUN
ap-1275	19	26	,	,	PUNCT
ap-1275	19	27	n	n	CCONJ
ap-1275	19	28	at	at	ADP
ap-1275	19	29	zi	zi	NOUN
ap-1275	19	30	,	,	PUNCT
ap-1275	19	31	n.	n.	NOUN
ap-1275	19	32	define	define	VERB
ap-1275	19	33	the	the	DET
ap-1275	19	34	asymptotic	asymptotic	ADJ
ap-1275	19	35	ratio	ratio	NOUN
ap-1275	19	36	measure	measure	NOUN
ap-1275	19	37	of	of	ADP
ap-1275	19	38	the	the	DET
ap-1275	19	39	sequence	sequence	NOUN
ap-1275	19	40	{	{	PUNCT
ap-1275	19	41	pn(z	pn(z	PROPN
ap-1275	19	42	)	)	PUNCT
ap-1275	19	43	}	}	PUNCT
ap-1275	19	44	as	as	ADP
ap-1275	19	45	ν	ν	PROPN
ap-1275	19	46	=	=	PROPN
ap-1275	19	47	lim	lim	PROPN
ap-1275	19	48	n→∞	n→∞	PRON
ap-1275	20	1	νn	νn	PROPN
ap-1275	20	2	.	.	NOUN
ap-1275	20	3	observation	observation	NOUN
ap-1275	20	4	.	.	PUNCT
ap-1275	21	1	supports	support	NOUN
ap-1275	21	2	of	of	ADP
ap-1275	21	3	μ	μ	PROPN
ap-1275	21	4	and	and	CCONJ
ap-1275	21	5	ν	ν	NOUN
ap-1275	21	6	coincide	coincide	NOUN
ap-1275	21	7	but	but	CCONJ
ap-1275	21	8	ν	ν	NOUN
ap-1275	21	9	is	be	AUX
ap-1275	21	10	often	often	ADV
ap-1275	21	11	complex	complex	ADV
ap-1275	21	12	-	-	PUNCT
ap-1275	21	13	valued	value	VERB
ap-1275	21	14	.	.	PUNCT
ap-1275	22	1	2.2	2.2	NUM
ap-1275	22	2	examples	example	NOUN
ap-1275	22	3	below	below	ADV
ap-1275	22	4	we	we	PRON
ap-1275	22	5	show	show	VERB
ap-1275	22	6	the	the	DET
ap-1275	22	7	root	root	NOUN
ap-1275	22	8	distribution	distribution	NOUN
ap-1275	22	9	for	for	ADP
ap-1275	22	10	p55(z	p55(z	NOUN
ap-1275	22	11	)	)	PUNCT
ap-1275	22	12	for	for	ADP
ap-1275	22	13	4	4	NUM
ap-1275	22	14	different	different	ADJ
ap-1275	22	15	exactly	exactly	ADV
ap-1275	22	16	solvable	solvable	ADJ
ap-1275	22	17	operators	operator	NOUN
ap-1275	22	18	t1	t1	NOUN
ap-1275	22	19	=	=	PUNCT
ap-1275	23	1	z(z	z(z	NOUN
ap-1275	23	2	−	−	NOUN
ap-1275	24	1	1)(z	1)(z	NUM
ap-1275	24	2	−	−	PROPN
ap-1275	24	3	i	i	PRON
ap-1275	24	4	)	)	PUNCT
ap-1275	24	5	d3	d3	VERB
ap-1275	24	6	dz3	dz3	PROPN
ap-1275	24	7	;	;	PUNCT
ap-1275	24	8	t2	t2	NOUN
ap-1275	24	9	=	=	SYM
ap-1275	24	10	(	(	PUNCT
ap-1275	24	11	z	z	NOUN
ap-1275	24	12	−	−	NOUN
ap-1275	24	13	i)(z	i)(z	PUNCT
ap-1275	25	1	+	+	CCONJ
ap-1275	25	2	i)(z	i)(z	NOUN
ap-1275	25	3	−	−	PROPN
ap-1275	25	4	2	2	NUM
ap-1275	25	5	+	+	CCONJ
ap-1275	25	6	3i)(z	3i)(z	NUM
ap-1275	25	7	−	−	NOUN
ap-1275	25	8	3−	3−	NUM
ap-1275	25	9	2i	2i	NUM
ap-1275	25	10	)	)	PUNCT
ap-1275	25	11	d4	d4	PROPN
ap-1275	25	12	dz4	dz4	NOUN
ap-1275	25	13	;	;	PUNCT
ap-1275	25	14	t3	t3	PROPN
ap-1275	25	15	=	=	PUNCT
ap-1275	25	16	(	(	PUNCT
ap-1275	25	17	z	z	NOUN
ap-1275	25	18	−	−	NOUN
ap-1275	25	19	i)(z	i)(z	PUNCT
ap-1275	26	1	+	+	CCONJ
ap-1275	26	2	i)(z	i)(z	NOUN
ap-1275	26	3	−	−	PROPN
ap-1275	26	4	2	2	NUM
ap-1275	26	5	+	+	CCONJ
ap-1275	26	6	3i)(z	3i)(z	NUM
ap-1275	26	7	−	−	NOUN
ap-1275	26	8	3−	3−	NUM
ap-1275	26	9	2i	2i	NUM
ap-1275	26	10	)	)	PUNCT
ap-1275	26	11	(	(	PUNCT
ap-1275	26	12	z	z	NOUN
ap-1275	26	13	+	+	NOUN
ap-1275	26	14	3	3	X
ap-1275	26	15	)	)	PUNCT
ap-1275	26	16	d5	d5	NOUN
ap-1275	26	17	dz5	dz5	NOUN
ap-1275	26	18	;	;	PUNCT
ap-1275	26	19	t4	t4	PROPN
ap-1275	26	20	=	=	PROPN
ap-1275	26	21	(	(	PUNCT
ap-1275	26	22	z2	z2	PROPN
ap-1275	26	23	+	+	CCONJ
ap-1275	26	24	1)(z	1)(z	NUM
ap-1275	26	25	−	−	PROPN
ap-1275	26	26	2	2	NUM
ap-1275	26	27	+	+	CCONJ
ap-1275	26	28	3i)(z	3i)(z	NUM
ap-1275	26	29	−	−	NOUN
ap-1275	26	30	3−	3−	NUM
ap-1275	26	31	2i)(z	2i)(z	NUM
ap-1275	26	32	+	+	CCONJ
ap-1275	26	33	3	3	X
ap-1275	26	34	)	)	PUNCT
ap-1275	26	35	(	(	PUNCT
ap-1275	26	36	z	z	NOUN
ap-1275	26	37	+	+	NOUN
ap-1275	26	38	1	1	NUM
ap-1275	26	39	+	+	CCONJ
ap-1275	26	40	i	i	NOUN
ap-1275	26	41	)	)	PUNCT
ap-1275	26	42	d6	d6	VERB
ap-1275	26	43	dz6	dz6	NOUN
ap-1275	26	44	of	of	ADP
ap-1275	26	45	the	the	DET
ap-1275	26	46	form	form	NOUN
ap-1275	26	47	q(z	q(z	PROPN
ap-1275	26	48	)	)	PUNCT
ap-1275	26	49	dk	dk	PROPN
ap-1275	26	50	dzk	dzk	NOUN
ap-1275	26	51	where	where	SCONJ
ap-1275	26	52	q(z	q(z	PROPN
ap-1275	26	53	)	)	PUNCT
ap-1275	26	54	is	be	AUX
ap-1275	26	55	a	a	DET
ap-1275	26	56	monic	monic	ADJ
ap-1275	26	57	polynomial	polynomial	NOUN
ap-1275	26	58	of	of	ADP
ap-1275	26	59	degree	degree	NOUN
ap-1275	27	1	k	k	PROPN
ap-1275	28	1	+	+	NOUN
ap-1275	28	2	1	1	NUM
ap-1275	28	3	.	.	X
ap-1275	28	4	77	77	NUM
ap-1275	28	5	acta	acta	PROPN
ap-1275	28	6	polytechnica	polytechnica	PROPN
ap-1275	28	7	vol	vol	NOUN
ap-1275	28	8	.	.	PROPN
ap-1275	29	1	50	50	NUM
ap-1275	29	2	no	no	NOUN
ap-1275	29	3	.	.	PUNCT
ap-1275	30	1	5/2010	5/2010	NUM
ap-1275	30	2	0	0	NUM
ap-1275	30	3	0.2	0.2	NUM
ap-1275	30	4	0.4	0.4	NUM
ap-1275	30	5	0.6	0.6	NUM
ap-1275	30	6	0.8	0.8	NUM
ap-1275	30	7	1	1	NUM
ap-1275	30	8	0	0	NUM
ap-1275	30	9	0.2	0.2	NUM
ap-1275	30	10	0.4	0.4	NUM
ap-1275	30	11	0.6	0.6	NUM
ap-1275	30	12	0.8	0.8	NUM
ap-1275	30	13	1	1	NUM
ap-1275	30	14	0	0	NUM
ap-1275	30	15	0.5	0.5	NUM
ap-1275	30	16	1	1	NUM
ap-1275	30	17	1.5	1.5	NUM
ap-1275	30	18	2	2	NUM
ap-1275	30	19	2.5	2.5	NUM
ap-1275	30	20	3	3	NUM
ap-1275	30	21	-3	-3	INTJ
ap-1275	30	22	-2	-2	INTJ
ap-1275	30	23	-1	-1	SYM
ap-1275	30	24	0	0	NUM
ap-1275	30	25	1	1	NUM
ap-1275	30	26	2	2	NUM
ap-1275	30	27	-3	-3	INTJ
ap-1275	30	28	-2	-2	NOUN
ap-1275	30	29	-1	-1	SYM
ap-1275	30	30	0	0	NUM
ap-1275	31	1	1	1	NUM
ap-1275	31	2	2	2	NUM
ap-1275	31	3	3	3	NUM
ap-1275	31	4	-3	-3	INTJ
ap-1275	31	5	-2	-2	NOUN
ap-1275	31	6	-1	-1	SYM
ap-1275	31	7	0	0	NUM
ap-1275	31	8	1	1	NUM
ap-1275	31	9	2	2	NUM
ap-1275	31	10	-3	-3	INTJ
ap-1275	31	11	-2	-2	NOUN
ap-1275	31	12	-1	-1	SYM
ap-1275	31	13	0	0	NUM
ap-1275	31	14	1	1	NUM
ap-1275	31	15	2	2	NUM
ap-1275	31	16	3	3	NUM
ap-1275	31	17	-3	-3	INTJ
ap-1275	31	18	-2	-2	NOUN
ap-1275	31	19	-1	-1	SYM
ap-1275	31	20	0	0	NUM
ap-1275	31	21	1	1	NUM
ap-1275	31	22	2	2	NUM
ap-1275	31	23	fig	fig	NOUN
ap-1275	31	24	.	.	PUNCT
ap-1275	32	1	1	1	NUM
ap-1275	32	2	:	:	PUNCT
ap-1275	32	3	roots	root	NOUN
ap-1275	32	4	of	of	ADP
ap-1275	32	5	p55(z	p55(z	NOUN
ap-1275	32	6	)	)	PUNCT
ap-1275	32	7	for	for	ADP
ap-1275	32	8	the	the	DET
ap-1275	32	9	above	above	PROPN
ap-1275	32	10	t	t	PROPN
ap-1275	32	11	’s	’s	PART
ap-1275	32	12	explanations	explanation	NOUN
ap-1275	32	13	to	to	ADP
ap-1275	32	14	fig	fig	VERB
ap-1275	32	15	.	.	PUNCT
ap-1275	33	1	1	1	X
ap-1275	33	2	.	.	X
ap-1275	34	1	the	the	DET
ap-1275	34	2	larger	large	ADJ
ap-1275	34	3	dots	dot	NOUN
ap-1275	34	4	show	show	VERB
ap-1275	34	5	the	the	DET
ap-1275	34	6	roots	root	NOUN
ap-1275	34	7	of	of	ADP
ap-1275	34	8	the	the	DET
ap-1275	34	9	corresponding	corresponding	ADJ
ap-1275	34	10	q(z	q(z	PROPN
ap-1275	34	11	)	)	PUNCT
ap-1275	34	12	and	and	CCONJ
ap-1275	34	13	the	the	DET
ap-1275	34	14	smaller	small	ADJ
ap-1275	34	15	dots	dot	NOUN
ap-1275	34	16	are	be	AUX
ap-1275	34	17	the	the	DET
ap-1275	34	18	fifty	fifty	NUM
ap-1275	34	19	five	five	NUM
ap-1275	34	20	roots	root	NOUN
ap-1275	34	21	of	of	ADP
ap-1275	34	22	the	the	DET
ap-1275	34	23	corresponding	corresponding	ADJ
ap-1275	34	24	p55(z	p55(z	NOUN
ap-1275	34	25	)	)	PUNCT
ap-1275	34	26	.	.	PUNCT
ap-1275	35	1	2.3	2.3	NUM
ap-1275	35	2	classical	classical	ADJ
ap-1275	35	3	prototypes	prototype	NOUN
ap-1275	35	4	theorem	theorem	VERB
ap-1275	35	5	1	1	NUM
ap-1275	35	6	(	(	PUNCT
ap-1275	35	7	g.	g.	PROPN
ap-1275	35	8	szegö	szegö	PROPN
ap-1275	35	9	)	)	PUNCT
ap-1275	35	10	if	if	SCONJ
ap-1275	35	11	{	{	PUNCT
ap-1275	35	12	pn(z	pn(z	NOUN
ap-1275	35	13	)	)	PUNCT
ap-1275	35	14	}	}	PUNCT
ap-1275	35	15	is	be	AUX
ap-1275	35	16	a	a	DET
ap-1275	35	17	family	family	NOUN
ap-1275	35	18	of	of	ADP
ap-1275	35	19	polynomials	polynomial	NOUN
ap-1275	35	20	orthogonal	orthogonal	ADJ
ap-1275	35	21	w.r.t	w.r.t	VERB
ap-1275	35	22	a	a	DET
ap-1275	35	23	positive	positive	ADJ
ap-1275	35	24	weight	weight	NOUN
ap-1275	35	25	w(z	w(z	NOUN
ap-1275	35	26	)	)	PUNCT
ap-1275	35	27	supported	support	VERB
ap-1275	35	28	on	on	ADP
ap-1275	35	29	[	[	X
ap-1275	35	30	−1	−1	NOUN
ap-1275	35	31	,	,	PUNCT
ap-1275	35	32	1	1	NUM
ap-1275	35	33	]	]	PUNCT
ap-1275	35	34	such	such	ADJ
ap-1275	35	35	that	that	SCONJ
ap-1275	35	36	∫	∫	PROPN
ap-1275	35	37	1	1	NUM
ap-1275	35	38	−1	−1	NOUN
ap-1275	35	39	lnw(z	lnw(z	PROPN
ap-1275	35	40	)	)	PUNCT
ap-1275	35	41	dz	dz	X
ap-1275	35	42	<	<	X
ap-1275	35	43	∞	∞	PROPN
ap-1275	35	44	then	then	ADV
ap-1275	35	45	the	the	DET
ap-1275	35	46	asymptotic	asymptotic	ADJ
ap-1275	35	47	root	root	NOUN
ap-1275	35	48	-	-	PUNCT
ap-1275	35	49	counting	count	VERB
ap-1275	35	50	measure	measure	NOUN
ap-1275	35	51	has	have	VERB
ap-1275	35	52	the	the	DET
ap-1275	35	53	density	density	NOUN
ap-1275	35	54	1	1	NUM
ap-1275	35	55	π	π	NOUN
ap-1275	35	56	√	√	PROPN
ap-1275	35	57	1−	1−	NUM
ap-1275	35	58	z2	z2	PROPN
ap-1275	35	59	,	,	PUNCT
ap-1275	35	60	x	x	PUNCT
ap-1275	35	61	∈	∈	PROPN
ap-1275	36	1	[	[	X
ap-1275	36	2	−1	−1	NOUN
ap-1275	36	3	,	,	PUNCT
ap-1275	36	4	1	1	NUM
ap-1275	36	5	]	]	PUNCT
ap-1275	36	6	.	.	PUNCT
ap-1275	37	1	theorem	theorem	ADJ
ap-1275	37	2	2	2	NUM
ap-1275	37	3	(	(	PUNCT
ap-1275	37	4	g.	g.	PROPN
ap-1275	37	5	szegö	szegö	PROPN
ap-1275	37	6	)	)	PUNCT
ap-1275	37	7	if	if	SCONJ
ap-1275	37	8	{	{	PUNCT
ap-1275	37	9	pn(z	pn(z	NOUN
ap-1275	37	10	)	)	PUNCT
ap-1275	37	11	}	}	PUNCT
ap-1275	37	12	is	be	AUX
ap-1275	37	13	a	a	DET
ap-1275	37	14	family	family	NOUN
ap-1275	37	15	of	of	ADP
ap-1275	37	16	polynomials	polynomial	NOUN
ap-1275	37	17	orthogonal	orthogonal	ADJ
ap-1275	37	18	w.r.t	w.r.t	VERB
ap-1275	37	19	a	a	DET
ap-1275	37	20	weight	weight	NOUN
ap-1275	37	21	w(z	w(z	NOUN
ap-1275	37	22	)	)	PUNCT
ap-1275	37	23	supported	support	VERB
ap-1275	37	24	on	on	ADP
ap-1275	37	25	[	[	X
ap-1275	37	26	−1	−1	NOUN
ap-1275	37	27	,	,	PUNCT
ap-1275	37	28	1	1	NUM
ap-1275	37	29	]	]	PUNCT
ap-1275	37	30	such	such	ADJ
ap-1275	37	31	that	that	SCONJ
ap-1275	37	32	∫	∫	PROPN
ap-1275	37	33	1	1	NUM
ap-1275	37	34	−1	−1	NOUN
ap-1275	37	35	lnw(z	lnw(z	NOUN
ap-1275	37	36	)	)	PUNCT
ap-1275	37	37	dz√	dz√	PROPN
ap-1275	37	38	1−	1−	NUM
ap-1275	37	39	z2	z2	PROPN
ap-1275	37	40	>	>	PUNCT
ap-1275	38	1	−∞	−∞	X
ap-1275	38	2	then	then	ADV
ap-1275	38	3	the	the	DET
ap-1275	38	4	asymptotic	asymptotic	ADJ
ap-1275	38	5	ratio	ratio	NOUN
ap-1275	38	6	measure	measure	NOUN
ap-1275	38	7	has	have	VERB
ap-1275	38	8	the	the	DET
ap-1275	38	9	density	density	NOUN
ap-1275	38	10	2	2	NUM
ap-1275	38	11	√	√	PROPN
ap-1275	38	12	1−	1−	NUM
ap-1275	38	13	z2	z2	PROPN
ap-1275	38	14	π	π	PROPN
ap-1275	38	15	,	,	PUNCT
ap-1275	38	16	z	z	PROPN
ap-1275	38	17	∈	∈	PROPN
ap-1275	39	1	[	[	X
ap-1275	39	2	−1	−1	NOUN
ap-1275	39	3	,	,	PUNCT
ap-1275	39	4	1	1	NUM
ap-1275	39	5	]	]	PUNCT
ap-1275	39	6	.	.	PUNCT
ap-1275	40	1	3	3	NUM
ap-1275	40	2	first	first	ADJ
ap-1275	40	3	results	result	VERB
ap-1275	40	4	3.1	3.1	NUM
ap-1275	40	5	non	non	ADJ
ap-1275	40	6	-	-	ADJ
ap-1275	40	7	degenerate	degenerate	ADJ
ap-1275	40	8	exactly	exactly	ADV
ap-1275	40	9	solvable	solvable	ADJ
ap-1275	40	10	operators	operator	NOUN
ap-1275	40	11	the	the	DET
ap-1275	40	12	next	next	ADJ
ap-1275	40	13	subsection	subsection	NOUN
ap-1275	40	14	is	be	AUX
ap-1275	40	15	based	base	VERB
ap-1275	40	16	on	on	ADP
ap-1275	40	17	[	[	X
ap-1275	40	18	10	10	NUM
ap-1275	40	19	,	,	PUNCT
ap-1275	40	20	2	2	NUM
ap-1275	40	21	]	]	PUNCT
ap-1275	40	22	.	.	PUNCT
ap-1275	41	1	definition	definition	NOUN
ap-1275	41	2	4	4	NUM
ap-1275	41	3	the	the	DET
ap-1275	41	4	cauchy	cauchy	ADJ
ap-1275	41	5	transform	transform	NOUN
ap-1275	41	6	of	of	ADP
ap-1275	41	7	a	a	DET
ap-1275	41	8	(	(	PUNCT
ap-1275	41	9	complex	complex	ADV
ap-1275	41	10	-	-	PUNCT
ap-1275	41	11	valued	value	VERB
ap-1275	41	12	)	)	PUNCT
ap-1275	41	13	measure	measure	NOUN
ap-1275	41	14	ρ	ρ	PROPN
ap-1275	41	15	satisfying	satisfy	VERB
ap-1275	41	16	∫	∫	PROPN
ap-1275	41	17	c	c	PROPN
ap-1275	41	18	dρ(ξ	dρ(ξ	NOUN
ap-1275	41	19	)	)	PUNCT
ap-1275	41	20	<	<	X
ap-1275	41	21	∞	∞	PROPN
ap-1275	41	22	is	be	AUX
ap-1275	41	23	given	give	VERB
ap-1275	41	24	by	by	ADP
ap-1275	41	25	cρ(z	cρ(z	PUNCT
ap-1275	41	26	)	)	PUNCT
ap-1275	41	27	=	=	SYM
ap-1275	42	1	∫	∫	PROPN
ap-1275	42	2	c	c	PROPN
ap-1275	42	3	dρ(ξ	dρ(ξ	VERB
ap-1275	42	4	)	)	PUNCT
ap-1275	43	1	z	z	NOUN
ap-1275	43	2	−	−	PROPN
ap-1275	43	3	ξ	ξ	PROPN
ap-1275	43	4	.	.	PUNCT
ap-1275	44	1	example	example	NOUN
ap-1275	44	2	.	.	PUNCT
ap-1275	45	1	if	if	SCONJ
ap-1275	45	2	ρ(z	ρ(z	NUM
ap-1275	45	3	)	)	PUNCT
ap-1275	45	4	=	=	SYM
ap-1275	45	5	1	1	NUM
ap-1275	45	6	π	π	SYM
ap-1275	45	7	√	√	PROPN
ap-1275	45	8	1−	1−	NUM
ap-1275	45	9	z2	z2	PROPN
ap-1275	45	10	,	,	PUNCT
ap-1275	45	11	z	z	NOUN
ap-1275	45	12	∈	∈	PROPN
ap-1275	46	1	[	[	X
ap-1275	46	2	−1	−1	NOUN
ap-1275	46	3	,	,	PUNCT
ap-1275	46	4	1	1	NUM
ap-1275	46	5	]	]	PUNCT
ap-1275	46	6	then	then	ADV
ap-1275	46	7	cμ	cμ	PROPN
ap-1275	46	8	=	=	SYM
ap-1275	46	9	1√	1√	PROPN
ap-1275	46	10	z2	z2	PROPN
ap-1275	46	11	−	−	PROPN
ap-1275	46	12	1	1	NUM
ap-1275	46	13	in	in	ADP
ap-1275	46	14	c	c	NOUN
ap-1275	46	15	\	\	PUNCT
ap-1275	47	1	[	[	X
ap-1275	47	2	−1	−1	NOUN
ap-1275	47	3	,	,	PUNCT
ap-1275	47	4	1	1	NUM
ap-1275	47	5	]	]	PUNCT
ap-1275	47	6	and	and	CCONJ
ap-1275	47	7	cν	cν	X
ap-1275	47	8	=	=	SYM
ap-1275	47	9	2	2	NUM
ap-1275	47	10	z	z	NOUN
ap-1275	47	11	+	+	CCONJ
ap-1275	47	12	√	√	PROPN
ap-1275	47	13	z2	z2	NOUN
ap-1275	47	14	−	−	NOUN
ap-1275	47	15	1	1	NUM
ap-1275	47	16	in	in	ADP
ap-1275	47	17	c	c	NOUN
ap-1275	47	18	\	\	PUNCT
ap-1275	48	1	[	[	X
ap-1275	48	2	−1	−1	NOUN
ap-1275	48	3	,	,	PUNCT
ap-1275	48	4	1	1	NUM
ap-1275	48	5	]	]	PUNCT
ap-1275	48	6	.	.	PUNCT
ap-1275	49	1	definition	definition	NOUN
ap-1275	49	2	5	5	NUM
ap-1275	49	3	an	an	DET
ap-1275	49	4	exactly	exactly	ADV
ap-1275	49	5	solvable	solvable	ADJ
ap-1275	49	6	operator	operator	NOUN
ap-1275	49	7	t	t	NOUN
ap-1275	49	8	=	=	SYM
ap-1275	49	9	k∑	k∑	PROPN
ap-1275	49	10	i=1	i=1	PROPN
ap-1275	49	11	qi(z	qi(z	X
ap-1275	49	12	)	)	PUNCT
ap-1275	49	13	di	di	X
ap-1275	49	14	dzi	dzi	PROPN
ap-1275	49	15	is	be	AUX
ap-1275	49	16	called	call	VERB
ap-1275	49	17	non	non	ADJ
ap-1275	49	18	-	-	ADJ
ap-1275	49	19	degenerate	degenerate	ADJ
ap-1275	49	20	if	if	SCONJ
ap-1275	49	21	degqk(z	degqk(z	NUM
ap-1275	49	22	)	)	PUNCT
ap-1275	49	23	=	=	PUNCT
ap-1275	49	24	k.	k.	NOUN
ap-1275	49	25	proposition	proposition	PROPN
ap-1275	49	26	1	1	NUM
ap-1275	49	27	assuming	assume	VERB
ap-1275	49	28	that	that	SCONJ
ap-1275	49	29	ψ(z	ψ(z	PROPN
ap-1275	49	30	)	)	PUNCT
ap-1275	49	31	=	=	SYM
ap-1275	49	32	lim	lim	PROPN
ap-1275	49	33	n→∞	n→∞	NUM
ap-1275	49	34	p′n(z	p′n(z	PROPN
ap-1275	49	35	)	)	PUNCT
ap-1275	49	36	npn(z	npn(z	PROPN
ap-1275	49	37	)	)	PUNCT
ap-1275	49	38	exists	exist	VERB
ap-1275	49	39	in	in	ADP
ap-1275	49	40	some	some	DET
ap-1275	49	41	open	open	ADJ
ap-1275	49	42	neighborhood	neighborhood	NOUN
ap-1275	49	43	ω	ω	NOUN
ap-1275	49	44	of	of	ADP
ap-1275	49	45	c	c	PROPN
ap-1275	49	46	one	one	PRON
ap-1275	49	47	gets	get	VERB
ap-1275	49	48	that	that	DET
ap-1275	49	49	ψ(z	ψ(z	NOUN
ap-1275	49	50	)	)	PUNCT
ap-1275	49	51	satisfies	satisfie	NOUN
ap-1275	49	52	in	in	ADP
ap-1275	49	53	ω	ω	NUM
ap-1275	49	54	the	the	DET
ap-1275	49	55	algebraic	algebraic	ADJ
ap-1275	49	56	equation	equation	NOUN
ap-1275	49	57	qk(z)ψk(z	qk(z)ψk(z	PROPN
ap-1275	49	58	)	)	PUNCT
ap-1275	50	1	=	=	SYM
ap-1275	50	2	1	1	X
ap-1275	50	3	.	.	X
ap-1275	50	4	theorem	theorem	NOUN
ap-1275	50	5	3	3	NUM
ap-1275	50	6	(	(	PUNCT
ap-1275	50	7	h.	h.	PROPN
ap-1275	50	8	rullg̊ard	rullg̊ard	PROPN
ap-1275	50	9	)	)	PUNCT
ap-1275	50	10	let	let	VERB
ap-1275	50	11	qk(z	qk(z	PUNCT
ap-1275	50	12	)	)	PUNCT
ap-1275	51	1	be	be	AUX
ap-1275	51	2	a	a	DET
ap-1275	51	3	monic	monic	ADJ
ap-1275	51	4	degree	degree	NOUN
ap-1275	51	5	k	k	PROPN
ap-1275	51	6	polynomial	polynomial	PROPN
ap-1275	51	7	.	.	PUNCT
ap-1275	52	1	then	then	ADV
ap-1275	52	2	there	there	PRON
ap-1275	52	3	exists	exist	VERB
ap-1275	52	4	a	a	DET
ap-1275	52	5	unique	unique	ADJ
ap-1275	52	6	probability	probability	NOUN
ap-1275	52	7	measure	measure	NOUN
ap-1275	52	8	μq	μq	SCONJ
ap-1275	52	9	such	such	ADJ
ap-1275	52	10	that	that	DET
ap-1275	52	11	1	1	NUM
ap-1275	52	12	)	)	PUNCT
ap-1275	52	13	suppμq	suppμq	NOUN
ap-1275	52	14	is	be	AUX
ap-1275	52	15	compact	compact	ADJ
ap-1275	52	16	;	;	PUNCT
ap-1275	52	17	2	2	X
ap-1275	52	18	)	)	PUNCT
ap-1275	52	19	its	its	PRON
ap-1275	52	20	cauchy	cauchy	NOUN
ap-1275	52	21	transform	transform	NOUN
ap-1275	52	22	cμ	cμ	NOUN
ap-1275	52	23	satisfies	satisfy	VERB
ap-1275	52	24	the	the	DET
ap-1275	52	25	equation	equation	NOUN
ap-1275	52	26	qk(z)ck	qk(z)ck	PROPN
ap-1275	52	27	μ(z	μ(z	PROPN
ap-1275	52	28	)	)	PUNCT
ap-1275	53	1	=	=	SYM
ap-1275	53	2	1	1	NUM
ap-1275	53	3	almost	almost	ADV
ap-1275	53	4	everywhere	everywhere	ADV
ap-1275	53	5	in	in	ADP
ap-1275	53	6	c.	c.	PROPN
ap-1275	53	7	78	78	NUM
ap-1275	53	8	acta	acta	PROPN
ap-1275	53	9	polytechnica	polytechnica	PROPN
ap-1275	53	10	vol	vol	NOUN
ap-1275	53	11	.	.	PROPN
ap-1275	54	1	50	50	NUM
ap-1275	54	2	no	no	NOUN
ap-1275	54	3	.	.	PUNCT
ap-1275	55	1	5/2010	5/2010	NUM
ap-1275	55	2	0	0	NUM
ap-1275	55	3	0.5	0.5	NUM
ap-1275	55	4	1	1	NUM
ap-1275	55	5	1.5	1.5	NUM
ap-1275	55	6	2	2	NUM
ap-1275	55	7	2.5	2.5	NUM
ap-1275	55	8	3	3	NUM
ap-1275	55	9	0	0	NUM
ap-1275	55	10	0.2	0.2	NUM
ap-1275	55	11	0.4	0.4	NUM
ap-1275	55	12	0.6	0.6	NUM
ap-1275	55	13	0.8	0.8	NUM
ap-1275	55	14	1	1	NUM
ap-1275	55	15	0	0	NUM
ap-1275	55	16	0.2	0.2	NUM
ap-1275	55	17	0.4	0.4	NUM
ap-1275	55	18	0.6	0.6	NUM
ap-1275	55	19	0.8	0.8	NUM
ap-1275	55	20	1	1	NUM
ap-1275	55	21	1.2	1.2	NUM
ap-1275	55	22	-1.5	-1.5	NUM
ap-1275	55	23	-1	-1	PUNCT
ap-1275	55	24	-0.5	-0.5	X
ap-1275	55	25	0	0	NUM
ap-1275	55	26	0.5	0.5	NUM
ap-1275	55	27	1	1	NUM
ap-1275	55	28	fig	fig	NOUN
ap-1275	55	29	.	.	PUNCT
ap-1275	56	1	2	2	NUM
ap-1275	56	2	:	:	PUNCT
ap-1275	56	3	the	the	DET
ap-1275	56	4	measure	measure	NOUN
ap-1275	56	5	μq	μq	VERB
ap-1275	56	6	before	before	ADV
ap-1275	56	7	and	and	CCONJ
ap-1275	56	8	after	after	ADP
ap-1275	56	9	the	the	DET
ap-1275	56	10	straightening	straighten	VERB
ap-1275	56	11	transformation	transformation	NOUN
ap-1275	56	12	in	in	ADP
ap-1275	56	13	the	the	DET
ap-1275	56	14	case	case	NOUN
ap-1275	56	15	q(z	q(z	PROPN
ap-1275	56	16	)	)	PUNCT
ap-1275	56	17	=	=	PUNCT
ap-1275	57	1	(	(	PUNCT
ap-1275	57	2	z	z	NOUN
ap-1275	57	3	−	−	PROPN
ap-1275	57	4	1)(z	1)(z	NUM
ap-1275	57	5	−	−	PROPN
ap-1275	57	6	3)(z	3)(z	NUM
ap-1275	57	7	−	−	PROPN
ap-1275	57	8	i	i	PROPN
ap-1275	57	9	)	)	PUNCT
ap-1275	57	10	theorem	theorem	VERB
ap-1275	57	11	4	4	NUM
ap-1275	57	12	(	(	PUNCT
ap-1275	57	13	main	main	ADJ
ap-1275	57	14	result	result	NOUN
ap-1275	57	15	,	,	PUNCT
ap-1275	57	16	see	see	VERB
ap-1275	57	17	fig	fig	NOUN
ap-1275	57	18	.	.	PUNCT
ap-1275	58	1	2	2	NUM
ap-1275	58	2	)	)	PUNCT
ap-1275	58	3	in	in	ADP
ap-1275	58	4	the	the	DET
ap-1275	58	5	above	above	ADJ
ap-1275	58	6	notation	notation	NOUN
ap-1275	58	7	1	1	NUM
ap-1275	58	8	)	)	PUNCT
ap-1275	58	9	suppμq	suppμq	NOUN
ap-1275	58	10	is	be	AUX
ap-1275	58	11	a	a	DET
ap-1275	58	12	curvilinear	curvilinear	ADJ
ap-1275	58	13	tree	tree	NOUN
ap-1275	58	14	which	which	PRON
ap-1275	58	15	is	be	AUX
ap-1275	58	16	straightened	straighten	VERB
ap-1275	58	17	out	out	ADP
ap-1275	58	18	by	by	ADP
ap-1275	58	19	the	the	DET
ap-1275	58	20	analytic	analytic	ADJ
ap-1275	58	21	mapping	mapping	NOUN
ap-1275	58	22	ξ(z	ξ(z	NOUN
ap-1275	58	23	)	)	PUNCT
ap-1275	59	1	=	=	SYM
ap-1275	60	1	∫	∫	PROPN
ap-1275	60	2	z	z	PROPN
ap-1275	61	1	a	a	DET
ap-1275	61	2	dz	dz	PROPN
ap-1275	61	3	k	k	X
ap-1275	61	4	√	√	PROPN
ap-1275	61	5	qk(z	qk(z	NUM
ap-1275	61	6	)	)	PUNCT
ap-1275	61	7	.	.	PUNCT
ap-1275	62	1	2	2	X
ap-1275	62	2	)	)	PUNCT
ap-1275	62	3	suppμq	suppμq	NOUN
ap-1275	62	4	contains	contain	VERB
ap-1275	62	5	all	all	DET
ap-1275	62	6	the	the	DET
ap-1275	62	7	zeros	zero	NOUN
ap-1275	62	8	of	of	ADP
ap-1275	62	9	qk(z	qk(z	PROPN
ap-1275	62	10	)	)	PUNCT
ap-1275	62	11	and	and	CCONJ
ap-1275	62	12	is	be	AUX
ap-1275	62	13	contained	contain	VERB
ap-1275	62	14	in	in	ADP
ap-1275	62	15	the	the	DET
ap-1275	62	16	convex	convex	NOUN
ap-1275	62	17	hull	hull	NOUN
ap-1275	62	18	of	of	ADP
ap-1275	62	19	those	those	PRON
ap-1275	62	20	.	.	PUNCT
ap-1275	63	1	3	3	X
ap-1275	63	2	)	)	PUNCT
ap-1275	63	3	there	there	PRON
ap-1275	63	4	is	be	VERB
ap-1275	63	5	a	a	DET
ap-1275	63	6	natural	natural	ADJ
ap-1275	63	7	formula	formula	NOUN
ap-1275	63	8	for	for	ADP
ap-1275	63	9	the	the	DET
ap-1275	63	10	angles	angle	NOUN
ap-1275	63	11	between	between	ADP
ap-1275	63	12	the	the	DET
ap-1275	63	13	branches	branch	NOUN
ap-1275	63	14	,	,	PUNCT
ap-1275	63	15	and	and	CCONJ
ap-1275	63	16	the	the	DET
ap-1275	63	17	masses	masse	NOUN
ap-1275	63	18	of	of	ADP
ap-1275	63	19	the	the	DET
ap-1275	63	20	branches	branch	NOUN
ap-1275	63	21	satisfy	satisfy	PROPN
ap-1275	63	22	kirchhoff	kirchhoff	PROPN
ap-1275	63	23	law	law	PROPN
ap-1275	63	24	.	.	PUNCT
ap-1275	64	1	below	below	ADP
ap-1275	64	2	we	we	PRON
ap-1275	64	3	show	show	VERB
ap-1275	64	4	an	an	DET
ap-1275	64	5	example	example	NOUN
ap-1275	64	6	of	of	ADP
ap-1275	64	7	such	such	DET
ap-1275	64	8	a	a	DET
ap-1275	64	9	measure	measure	NOUN
ap-1275	64	10	in	in	ADP
ap-1275	64	11	a	a	DET
ap-1275	64	12	proper	proper	ADJ
ap-1275	64	13	scale	scale	NOUN
ap-1275	64	14	and	and	CCONJ
ap-1275	64	15	with	with	ADP
ap-1275	64	16	all	all	DET
ap-1275	64	17	angles	angle	NOUN
ap-1275	64	18	between	between	ADP
ap-1275	64	19	its	its	PRON
ap-1275	64	20	vertices	vertex	NOUN
ap-1275	64	21	marked	mark	VERB
ap-1275	64	22	,	,	PUNCT
ap-1275	64	23	see	see	VERB
ap-1275	64	24	fig	fig	NOUN
ap-1275	64	25	.	.	PUNCT
ap-1275	65	1	3	3	NUM
ap-1275	65	2	.	.	NOUN
ap-1275	65	3	0	0	NUM
ap-1275	66	1	0.5	0.5	NUM
ap-1275	66	2	1	1	NUM
ap-1275	66	3	1.5	1.5	NUM
ap-1275	66	4	-1.5	-1.5	NUM
ap-1275	66	5	-1	-1	PUNCT
ap-1275	66	6	-0.5	-0.5	X
ap-1275	66	7	0	0	NUM
ap-1275	66	8	60	60	NUM
ap-1275	66	9	150	150	NUM
ap-1275	66	10	150	150	NUM
ap-1275	66	11	120	120	NUM
ap-1275	66	12	150	150	NUM
ap-1275	66	13	90	90	NUM
ap-1275	66	14	150	150	NUM
ap-1275	66	15	150	150	NUM
ap-1275	66	16	120	120	NUM
ap-1275	66	17	90	90	NUM
ap-1275	66	18	150	150	NUM
ap-1275	66	19	60	60	NUM
ap-1275	66	20	fig	fig	NOUN
ap-1275	66	21	.	.	PUNCT
ap-1275	67	1	3	3	NUM
ap-1275	67	2	:	:	PUNCT
ap-1275	67	3	example	example	NOUN
ap-1275	67	4	of	of	ADP
ap-1275	67	5	μq	μq	PRON
ap-1275	67	6	with	with	ADP
ap-1275	67	7	angles	angle	NOUN
ap-1275	67	8	problem	problem	NOUN
ap-1275	67	9	1	1	NUM
ap-1275	67	10	is	be	AUX
ap-1275	67	11	it	it	PRON
ap-1275	67	12	true	true	ADJ
ap-1275	67	13	that	that	SCONJ
ap-1275	67	14	the	the	DET
ap-1275	67	15	support	support	NOUN
ap-1275	67	16	of	of	ADP
ap-1275	67	17	the	the	DET
ap-1275	67	18	measure	measure	NOUN
ap-1275	67	19	μq	μq	PRON
ap-1275	67	20	is	be	AUX
ap-1275	67	21	a	a	DET
ap-1275	67	22	subset	subset	NOUN
ap-1275	67	23	of	of	ADP
ap-1275	67	24	the	the	DET
ap-1275	67	25	stokes	stoke	NOUN
ap-1275	67	26	lines	line	NOUN
ap-1275	67	27	of	of	ADP
ap-1275	67	28	the	the	DET
ap-1275	67	29	corresponding	correspond	VERB
ap-1275	67	30	operator	operator	NOUN
ap-1275	67	31	q	q	NOUN
ap-1275	67	32	dk	dk	PROPN
ap-1275	67	33	dzk	dzk	NOUN
ap-1275	67	34	?	?	PUNCT
ap-1275	68	1	some	some	DET
ap-1275	68	2	partial	partial	ADJ
ap-1275	68	3	results	result	NOUN
ap-1275	68	4	in	in	ADP
ap-1275	68	5	this	this	DET
ap-1275	68	6	direction	direction	NOUN
ap-1275	68	7	can	can	AUX
ap-1275	68	8	be	be	AUX
ap-1275	68	9	found	find	VERB
ap-1275	68	10	in	in	ADP
ap-1275	68	11	[	[	X
ap-1275	68	12	12	12	NUM
ap-1275	68	13	]	]	PUNCT
ap-1275	68	14	.	.	PUNCT
ap-1275	69	1	3.2	3.2	NUM
ap-1275	69	2	degenerate	degenerate	ADJ
ap-1275	69	3	exactly	exactly	ADV
ap-1275	69	4	solvable	solvable	ADJ
ap-1275	69	5	operators	operator	NOUN
ap-1275	69	6	this	this	DET
ap-1275	69	7	subsection	subsection	NOUN
ap-1275	69	8	is	be	AUX
ap-1275	69	9	based	base	VERB
ap-1275	69	10	on	on	ADP
ap-1275	69	11	[	[	X
ap-1275	69	12	1	1	NUM
ap-1275	69	13	]	]	PUNCT
ap-1275	69	14	.	.	PUNCT
ap-1275	70	1	definition	definition	NOUN
ap-1275	70	2	6	6	NUM
ap-1275	70	3	an	an	DET
ap-1275	70	4	exactly	exactly	ADV
ap-1275	70	5	solvable	solvable	ADJ
ap-1275	70	6	t	t	NOUN
ap-1275	70	7	of	of	ADP
ap-1275	70	8	order	order	NOUN
ap-1275	70	9	k	k	X
ap-1275	70	10	is	be	AUX
ap-1275	70	11	called	call	VERB
ap-1275	70	12	degenerate	degenerate	ADJ
ap-1275	70	13	iff	iff	PROPN
ap-1275	70	14	degqk	degqk	PROPN
ap-1275	70	15	<	<	X
ap-1275	70	16	k.	k.	PROPN
ap-1275	70	17	classical	classical	ADJ
ap-1275	70	18	examples	example	NOUN
ap-1275	70	19	:	:	PUNCT
ap-1275	71	1	t	t	X
ap-1275	71	2	=	=	SYM
ap-1275	71	3	z	z	PROPN
ap-1275	71	4	d2	d2	PROPN
ap-1275	71	5	dz2	dz2	NOUN
ap-1275	71	6	+	+	CCONJ
ap-1275	71	7	(	(	PUNCT
ap-1275	71	8	az	az	PROPN
ap-1275	71	9	+	+	PROPN
ap-1275	71	10	b	b	X
ap-1275	71	11	)	)	PUNCT
ap-1275	71	12	d	d	NOUN
ap-1275	71	13	dz	dz	PROPN
ap-1275	71	14	,	,	PUNCT
ap-1275	71	15	t	t	NOUN
ap-1275	71	16	=	=	SYM
ap-1275	71	17	d2	d2	PROPN
ap-1275	71	18	dz2	dz2	NOUN
ap-1275	71	19	+	+	CCONJ
ap-1275	71	20	(	(	PUNCT
ap-1275	71	21	az	az	PROPN
ap-1275	71	22	+	+	PROPN
ap-1275	71	23	b	b	X
ap-1275	71	24	)	)	PUNCT
ap-1275	71	25	d	d	NOUN
ap-1275	71	26	dz	dz	PROPN
ap-1275	71	27	leading	lead	VERB
ap-1275	71	28	to	to	ADP
ap-1275	71	29	laguerre	laguerre	PROPN
ap-1275	71	30	resp	resp	NOUN
ap-1275	71	31	.	.	PUNCT
ap-1275	72	1	hermite	hermite	ADJ
ap-1275	72	2	polynomials	polynomial	NOUN
ap-1275	72	3	.	.	PUNCT
ap-1275	73	1	proposition	proposition	NOUN
ap-1275	73	2	2	2	NUM
ap-1275	73	3	the	the	DET
ap-1275	73	4	union	union	NOUN
ap-1275	73	5	of	of	ADP
ap-1275	73	6	all	all	DET
ap-1275	73	7	roots	root	NOUN
ap-1275	73	8	of	of	ADP
ap-1275	73	9	all	all	DET
ap-1275	73	10	polynomial	polynomial	ADJ
ap-1275	73	11	eigenfunctions	eigenfunction	NOUN
ap-1275	73	12	of	of	ADP
ap-1275	73	13	an	an	DET
ap-1275	73	14	exactly	exactly	ADV
ap-1275	73	15	solvable	solvable	ADJ
ap-1275	73	16	t	t	NOUN
ap-1275	73	17	is	be	AUX
ap-1275	73	18	unbounded	unbounded	ADJ
ap-1275	73	19	if	if	SCONJ
ap-1275	74	1	and	and	CCONJ
ap-1275	74	2	only	only	ADV
ap-1275	74	3	if	if	SCONJ
ap-1275	74	4	t	t	PROPN
ap-1275	74	5	is	be	AUX
ap-1275	74	6	degenerate	degenerate	ADJ
ap-1275	74	7	.	.	PUNCT
ap-1275	75	1	problem	problem	NOUN
ap-1275	75	2	2	2	NUM
ap-1275	75	3	given	give	VERB
ap-1275	75	4	a	a	DET
ap-1275	75	5	degenerate	degenerate	ADJ
ap-1275	75	6	t	t	NOUN
ap-1275	75	7	with	with	ADP
ap-1275	75	8	the	the	DET
ap-1275	75	9	family	family	NOUN
ap-1275	75	10	of	of	ADP
ap-1275	75	11	eigenpolynomials	eigenpolynomial	NOUN
ap-1275	75	12	{	{	PUNCT
ap-1275	75	13	pn(z	pn(z	NOUN
ap-1275	75	14	)	)	PUNCT
ap-1275	75	15	}	}	PUNCT
ap-1275	75	16	how	how	SCONJ
ap-1275	75	17	fast	fast	ADV
ap-1275	75	18	does	do	AUX
ap-1275	75	19	the	the	DET
ap-1275	75	20	maximum	maximum	PROPN
ap-1275	75	21	rn	rn	PROPN
ap-1275	75	22	of	of	ADP
ap-1275	75	23	the	the	DET
ap-1275	75	24	modulus	modulus	NOUN
ap-1275	75	25	of	of	ADP
ap-1275	75	26	roots	root	NOUN
ap-1275	75	27	of	of	ADP
ap-1275	75	28	pn(z	pn(z	NOUN
ap-1275	75	29	)	)	PUNCT
ap-1275	75	30	grow	grow	VERB
ap-1275	75	31	?	?	PUNCT
ap-1275	76	1	conjecture	conjecture	NOUN
ap-1275	76	2	1	1	NUM
ap-1275	76	3	given	give	VERB
ap-1275	76	4	a	a	DET
ap-1275	76	5	degenerate	degenerate	ADJ
ap-1275	76	6	t	t	NOUN
ap-1275	76	7	=	=	SYM
ap-1275	76	8	k∑	k∑	PROPN
ap-1275	77	1	j=1	j=1	NOUN
ap-1275	77	2	qj(z	qj(z	NOUN
ap-1275	77	3	)	)	PUNCT
ap-1275	77	4	dj	dj	NOUN
ap-1275	77	5	dzj	dzj	VERB
ap-1275	77	6	denote	denote	NOUN
ap-1275	77	7	by	by	ADP
ap-1275	77	8	j0	j0	PROPN
ap-1275	77	9	the	the	DET
ap-1275	77	10	largest	large	ADJ
ap-1275	77	11	j	j	NOUN
ap-1275	77	12	for	for	ADP
ap-1275	77	13	which	which	PRON
ap-1275	77	14	degqj(z	degqj(z	NOUN
ap-1275	77	15	)	)	PUNCT
ap-1275	77	16	=	=	PUNCT
ap-1275	78	1	j.	j.	PROPN
ap-1275	78	2	then	then	ADV
ap-1275	78	3	lim	lim	PROPN
ap-1275	78	4	n→∞	n→∞	PROPN
ap-1275	79	1	rn	rn	PROPN
ap-1275	79	2	nd	nd	NOUN
ap-1275	79	3	=	=	NOUN
ap-1275	79	4	ct	ct	NUM
ap-1275	79	5	where	where	SCONJ
ap-1275	79	6	ct	ct	PROPN
ap-1275	79	7	>	>	X
ap-1275	79	8	0	0	NUM
ap-1275	79	9	is	be	AUX
ap-1275	79	10	a	a	DET
ap-1275	79	11	positive	positive	ADJ
ap-1275	79	12	constant	constant	NOUN
ap-1275	79	13	and	and	CCONJ
ap-1275	79	14	d	d	NOUN
ap-1275	79	15	:	:	PUNCT
ap-1275	79	16	=	=	SYM
ap-1275	79	17	max	max	PROPN
ap-1275	79	18	j∈[j0	j∈[j0	PROPN
ap-1275	79	19	+	+	PROPN
ap-1275	79	20	1,k	1,k	PROPN
ap-1275	79	21	]	]	X
ap-1275	79	22	(	(	PUNCT
ap-1275	79	23	j	j	PROPN
ap-1275	79	24	−	−	PROPN
ap-1275	79	25	j0	j0	PROPN
ap-1275	79	26	j	j	PROPN
ap-1275	79	27	−	−	PROPN
ap-1275	79	28	degqj	degqj	PROPN
ap-1275	79	29	)	)	PUNCT
ap-1275	79	30	.	.	PUNCT
ap-1275	80	1	corollary	corollary	ADJ
ap-1275	80	2	1	1	NUM
ap-1275	80	3	(	(	PUNCT
ap-1275	80	4	of	of	ADP
ap-1275	80	5	the	the	DET
ap-1275	80	6	latter	latter	ADJ
ap-1275	80	7	conjecture	conjecture	NOUN
ap-1275	80	8	)	)	PUNCT
ap-1275	80	9	the	the	DET
ap-1275	80	10	cauchy	cauchy	PROPN
ap-1275	80	11	transform	transform	VERB
ap-1275	80	12	c(z	c(z	NOUN
ap-1275	80	13	)	)	PUNCT
ap-1275	80	14	of	of	ADP
ap-1275	80	15	the	the	DET
ap-1275	80	16	asymptotic	asymptotic	ADJ
ap-1275	80	17	root	root	NOUN
ap-1275	80	18	measure	measure	NOUN
ap-1275	80	19	μ	μ	PROPN
ap-1275	80	20	of	of	ADP
ap-1275	80	21	the	the	DET
ap-1275	80	22	scaled	scale	VERB
ap-1275	80	23	eigenpolynomial	eigenpolynomial	ADJ
ap-1275	80	24	qn(z	qn(z	NUM
ap-1275	80	25	)	)	PUNCT
ap-1275	81	1	=	=	SYM
ap-1275	81	2	pn(n	pn(n	NOUN
ap-1275	81	3	dz	dz	PROPN
ap-1275	81	4	)	)	PUNCT
ap-1275	81	5	of	of	ADP
ap-1275	81	6	a	a	DET
ap-1275	81	7	degenerate	degenerate	ADJ
ap-1275	81	8	t	t	NOUN
ap-1275	81	9	satisfies	satisfy	VERB
ap-1275	81	10	the	the	DET
ap-1275	81	11	following	follow	VERB
ap-1275	81	12	algebraic	algebraic	ADJ
ap-1275	81	13	equation	equation	NOUN
ap-1275	81	14	for	for	ADP
ap-1275	81	15	almost	almost	ADV
ap-1275	81	16	all	all	PRON
ap-1275	81	17	complex	complex	ADJ
ap-1275	81	18	z	z	NOUN
ap-1275	81	19	:	:	PUNCT
ap-1275	81	20	zj0cj0(z	zj0cj0(z	NUM
ap-1275	81	21	)	)	PUNCT
ap-1275	82	1	+	+	CCONJ
ap-1275	82	2	∑	∑	ADP
ap-1275	82	3	j∈a	j∈a	PROPN
ap-1275	82	4	αj	αj	PROPN
ap-1275	82	5	,	,	PUNCT
ap-1275	82	6	degqj	degqj	PROPN
ap-1275	82	7	z	z	PROPN
ap-1275	82	8	degqj	degqj	PROPN
ap-1275	82	9	cj(z	cj(z	PROPN
ap-1275	82	10	)	)	PUNCT
ap-1275	82	11	=	=	SYM
ap-1275	82	12	1	1	NUM
ap-1275	82	13	,	,	PUNCT
ap-1275	82	14	where	where	SCONJ
ap-1275	82	15	a	a	PRON
ap-1275	82	16	is	be	AUX
ap-1275	82	17	the	the	DET
ap-1275	82	18	set	set	NOUN
ap-1275	82	19	consisting	consist	VERB
ap-1275	82	20	of	of	ADP
ap-1275	82	21	all	all	DET
ap-1275	82	22	j	j	NOUN
ap-1275	82	23	for	for	ADP
ap-1275	82	24	which	which	PRON
ap-1275	82	25	the	the	DET
ap-1275	82	26	maximum	maximum	ADJ
ap-1275	82	27	d	d	NOUN
ap-1275	82	28	:	:	PUNCT
ap-1275	82	29	=	=	SYM
ap-1275	82	30	max	max	PROPN
ap-1275	82	31	j∈[j0	j∈[j0	PROPN
ap-1275	82	32	+	+	PROPN
ap-1275	82	33	1,k	1,k	PROPN
ap-1275	82	34	]	]	X
ap-1275	82	35	(	(	PUNCT
ap-1275	82	36	j	j	PROPN
ap-1275	82	37	−	−	PROPN
ap-1275	82	38	j0	j0	PROPN
ap-1275	82	39	j	j	PROPN
ap-1275	82	40	−	−	PROPN
ap-1275	82	41	degqj	degqj	PROPN
ap-1275	82	42	)	)	PUNCT
ap-1275	82	43	is	be	AUX
ap-1275	82	44	attained	attain	VERB
ap-1275	82	45	,	,	PUNCT
ap-1275	82	46	i.e.	i.e.	X
ap-1275	82	47	a	a	X
ap-1275	82	48	=	=	SYM
ap-1275	82	49	{	{	PUNCT
ap-1275	82	50	j	j	NOUN
ap-1275	82	51	:	:	PUNCT
ap-1275	82	52	(	(	PUNCT
ap-1275	82	53	j	j	X
ap-1275	82	54	−	−	NOUN
ap-1275	82	55	j0)/(j	j0)/(j	PRON
ap-1275	82	56	−	−	PROPN
ap-1275	82	57	degqj	degqj	NOUN
ap-1275	82	58	)	)	PUNCT
ap-1275	82	59	=	=	PUNCT
ap-1275	83	1	d	d	X
ap-1275	83	2	}	}	PUNCT
ap-1275	83	3	.	.	PUNCT
ap-1275	84	1	79	79	NUM
ap-1275	84	2	acta	acta	PROPN
ap-1275	84	3	polytechnica	polytechnica	PROPN
ap-1275	84	4	vol	vol	NOUN
ap-1275	84	5	.	.	PROPN
ap-1275	85	1	50	50	NUM
ap-1275	85	2	no	no	NOUN
ap-1275	85	3	.	.	PUNCT
ap-1275	86	1	5/2010	5/2010	NUM
ap-1275	86	2	-1	-1	PUNCT
ap-1275	86	3	-0.5	-0.5	X
ap-1275	86	4	0	0	NUM
ap-1275	86	5	0.5	0.5	NUM
ap-1275	86	6	1	1	NUM
ap-1275	86	7	-1	-1	SYM
ap-1275	86	8	-0.5	-0.5	X
ap-1275	86	9	0	0	NUM
ap-1275	86	10	0.5	0.5	NUM
ap-1275	86	11	1	1	NUM
ap-1275	86	12	-0.6	-0.6	NOUN
ap-1275	86	13	-0.4	-0.4	X
ap-1275	86	14	-0.2	-0.2	PROPN
ap-1275	86	15	0	0	NUM
ap-1275	86	16	0.2	0.2	NUM
ap-1275	86	17	0.4	0.4	NUM
ap-1275	86	18	0.6	0.6	NUM
ap-1275	86	19	-1	-1	PUNCT
ap-1275	86	20	-0.5	-0.5	X
ap-1275	86	21	0	0	NUM
ap-1275	86	22	0.5	0.5	NUM
ap-1275	86	23	1	1	NUM
ap-1275	86	24	fig	fig	NOUN
ap-1275	86	25	.	.	PUNCT
ap-1275	87	1	4	4	NUM
ap-1275	87	2	:	:	PUNCT
ap-1275	87	3	examples	example	NOUN
ap-1275	87	4	of	of	ADP
ap-1275	87	5	the	the	DET
ap-1275	87	6	root	root	NOUN
ap-1275	87	7	distributions	distribution	NOUN
ap-1275	87	8	of	of	ADP
ap-1275	87	9	scaled	scale	VERB
ap-1275	87	10	eigenpolynomials	eigenpolynomial	NOUN
ap-1275	87	11	to	to	PART
ap-1275	87	12	degenerate	degenerate	VERB
ap-1275	87	13	exactly	exactly	ADV
ap-1275	87	14	solvable	solvable	ADJ
ap-1275	87	15	operators	operator	NOUN
ap-1275	87	16	the	the	DET
ap-1275	87	17	latter	latter	ADJ
ap-1275	87	18	equation	equation	NOUN
ap-1275	87	19	for	for	ADP
ap-1275	87	20	the	the	DET
ap-1275	87	21	cauchy	cauchy	ADJ
ap-1275	87	22	transform	transform	NOUN
ap-1275	87	23	(	(	PUNCT
ap-1275	87	24	if	if	SCONJ
ap-1275	87	25	true	true	ADJ
ap-1275	87	26	)	)	PUNCT
ap-1275	87	27	leads	lead	VERB
ap-1275	87	28	to	to	ADP
ap-1275	87	29	very	very	ADV
ap-1275	87	30	detailed	detailed	ADJ
ap-1275	87	31	information	information	NOUN
ap-1275	87	32	about	about	ADP
ap-1275	87	33	the	the	DET
ap-1275	87	34	support	support	NOUN
ap-1275	87	35	of	of	ADP
ap-1275	87	36	the	the	DET
ap-1275	87	37	asymptotic	asymptotic	ADJ
ap-1275	87	38	root	root	NOUN
ap-1275	87	39	-	-	PUNCT
ap-1275	87	40	counting	count	VERB
ap-1275	87	41	measure	measure	NOUN
ap-1275	87	42	for	for	ADP
ap-1275	87	43	the	the	DET
ap-1275	87	44	sequence	sequence	NOUN
ap-1275	87	45	of	of	ADP
ap-1275	87	46	scaled	scale	VERB
ap-1275	87	47	eigenpolynomials	eigenpolynomial	NOUN
ap-1275	87	48	.	.	PUNCT
ap-1275	88	1	we	we	PRON
ap-1275	88	2	illustrate	illustrate	VERB
ap-1275	88	3	this	this	PRON
ap-1275	88	4	in	in	ADP
ap-1275	88	5	fig	fig	NOUN
ap-1275	88	6	.	.	PUNCT
ap-1275	89	1	4	4	NUM
ap-1275	89	2	.	.	SYM
ap-1275	89	3	4	4	NUM
ap-1275	89	4	homogenized	homogenize	VERB
ap-1275	89	5	spectral	spectral	ADJ
ap-1275	89	6	problem	problem	NOUN
ap-1275	89	7	for	for	ADP
ap-1275	89	8	non	non	ADJ
ap-1275	89	9	-	-	ADJ
ap-1275	89	10	degenerate	degenerate	ADJ
ap-1275	89	11	t	t	NOUN
ap-1275	89	12	this	this	DET
ap-1275	89	13	section	section	NOUN
ap-1275	89	14	is	be	AUX
ap-1275	89	15	based	base	VERB
ap-1275	89	16	on	on	ADP
ap-1275	89	17	[	[	X
ap-1275	89	18	6	6	NUM
ap-1275	89	19	]	]	PUNCT
ap-1275	89	20	.	.	PUNCT
ap-1275	90	1	an	an	DET
ap-1275	90	2	observant	observant	ADJ
ap-1275	90	3	reader	reader	NOUN
ap-1275	90	4	has	have	AUX
ap-1275	90	5	noticed	notice	VERB
ap-1275	90	6	that	that	SCONJ
ap-1275	90	7	so	so	ADV
ap-1275	90	8	far	far	ADV
ap-1275	90	9	only	only	ADV
ap-1275	90	10	the	the	DET
ap-1275	90	11	leading	lead	VERB
ap-1275	90	12	coefficient	coefficient	NOUN
ap-1275	90	13	of	of	ADP
ap-1275	90	14	an	an	DET
ap-1275	90	15	exactly	exactly	ADV
ap-1275	90	16	solvable	solvable	ADJ
ap-1275	90	17	operator	operator	NOUN
ap-1275	90	18	effected	effect	VERB
ap-1275	90	19	the	the	DET
ap-1275	90	20	asymptotic	asymptotic	ADJ
ap-1275	90	21	root	root	NOUN
ap-1275	90	22	-	-	PUNCT
ap-1275	90	23	counting	count	VERB
ap-1275	90	24	measure	measure	NOUN
ap-1275	90	25	,	,	PUNCT
ap-1275	90	26	which	which	PRON
ap-1275	90	27	makes	make	VERB
ap-1275	90	28	the	the	DET
ap-1275	90	29	situation	situation	NOUN
ap-1275	90	30	somewhat	somewhat	ADV
ap-1275	90	31	unsatisfactory	unsatisfactory	ADJ
ap-1275	90	32	.	.	PUNCT
ap-1275	91	1	to	to	PART
ap-1275	91	2	make	make	VERB
ap-1275	91	3	the	the	DET
ap-1275	91	4	whole	whole	ADJ
ap-1275	91	5	symbol	symbol	NOUN
ap-1275	91	6	of	of	ADP
ap-1275	91	7	an	an	DET
ap-1275	91	8	operator	operator	NOUN
ap-1275	91	9	important	important	ADJ
ap-1275	91	10	we	we	PRON
ap-1275	91	11	consider	consider	VERB
ap-1275	91	12	(	(	PUNCT
ap-1275	91	13	following	follow	VERB
ap-1275	91	14	the	the	DET
ap-1275	91	15	classical	classical	ADJ
ap-1275	91	16	pattern	pattern	NOUN
ap-1275	91	17	of	of	ADP
ap-1275	91	18	e.g.	e.g.	ADV
ap-1275	91	19	w.	w.	PROPN
ap-1275	91	20	wasow	wasow	PROPN
ap-1275	91	21	,	,	PUNCT
ap-1275	91	22	m.	m.	NOUN
ap-1275	91	23	fedoryuk	fedoryuk	NOUN
ap-1275	91	24	)	)	PUNCT
ap-1275	91	25	the	the	DET
ap-1275	91	26	homogenized	homogenized	ADJ
ap-1275	91	27	spectral	spectral	ADJ
ap-1275	91	28	problem	problem	NOUN
ap-1275	91	29	of	of	ADP
ap-1275	91	30	the	the	DET
ap-1275	91	31	form	form	NOUN
ap-1275	91	32	tλ	tλ	ADP
ap-1275	91	33	=	=	PUNCT
ap-1275	91	34	k∑	k∑	NOUN
ap-1275	92	1	i=0	i=0	PROPN
ap-1275	92	2	qi(z)λ	qi(z)λ	PROPN
ap-1275	92	3	k−i	k−i	VERB
ap-1275	92	4	di	di	X
ap-1275	92	5	dzi	dzi	PROPN
ap-1275	92	6	,	,	PUNCT
ap-1275	92	7	where	where	SCONJ
ap-1275	92	8	each	each	DET
ap-1275	92	9	qi(x	qi(x	NUM
ap-1275	92	10	)	)	PUNCT
ap-1275	92	11	=	=	VERB
ap-1275	93	1	aiiz	aiiz	PROPN
ap-1275	93	2	i+	i+	NUM
ap-1275	93	3	ai	ai	PROPN
ap-1275	93	4	,	,	PUNCT
ap-1275	93	5	i−1z	i−1z	ADJ
ap-1275	93	6	i−1	i−1	PROPN
ap-1275	93	7	+	+	PROPN
ap-1275	93	8	.	.	PUNCT
ap-1275	93	9	.	.	PUNCT
ap-1275	94	1	.	.	PUNCT
ap-1275	95	1	is	be	AUX
ap-1275	95	2	a	a	DET
ap-1275	95	3	polynomial	polynomial	ADJ
ap-1275	95	4	of	of	ADP
ap-1275	95	5	degree	degree	NOUN
ap-1275	95	6	i.	i.	NOUN
ap-1275	95	7	definition	definition	NOUN
ap-1275	95	8	7	7	NUM
ap-1275	95	9	a	a	DET
ap-1275	95	10	non	non	ADJ
ap-1275	95	11	-	-	ADJ
ap-1275	95	12	degenerate	degenerate	ADJ
ap-1275	95	13	t	t	PROPN
ap-1275	95	14	is	be	AUX
ap-1275	95	15	called	call	VERB
ap-1275	95	16	of	of	ADP
ap-1275	95	17	general	general	ADJ
ap-1275	95	18	type	type	NOUN
ap-1275	95	19	iff	iff	PROPN
ap-1275	95	20	degqk(z	degqk(z	NOUN
ap-1275	95	21	)	)	PUNCT
ap-1275	96	1	=	=	SYM
ap-1275	96	2	k	k	PROPN
ap-1275	96	3	and	and	CCONJ
ap-1275	96	4	k∑	k∑	VERB
ap-1275	96	5	i=0	i=0	PROPN
ap-1275	96	6	aiiλ	aiiλ	ADJ
ap-1275	96	7	k−i	k−i	NOUN
ap-1275	96	8	=	=	SYM
ap-1275	96	9	0	0	PROPN
ap-1275	96	10	has	have	VERB
ap-1275	96	11	k	k	PROPN
ap-1275	96	12	distinct	distinct	ADJ
ap-1275	96	13	zeros	zero	NOUN
ap-1275	96	14	.	.	PUNCT
ap-1275	97	1	proposition	proposition	NOUN
ap-1275	97	2	3	3	NUM
ap-1275	97	3	if	if	SCONJ
ap-1275	97	4	t	t	PROPN
ap-1275	97	5	is	be	AUX
ap-1275	97	6	of	of	ADP
ap-1275	97	7	general	general	ADJ
ap-1275	97	8	type	type	NOUN
ap-1275	97	9	then	then	ADV
ap-1275	97	10	1	1	NUM
ap-1275	97	11	)	)	PUNCT
ap-1275	97	12	for	for	ADP
ap-1275	97	13	all	all	PRON
ap-1275	97	14	sufficiently	sufficiently	ADV
ap-1275	97	15	large	large	ADJ
ap-1275	97	16	n	n	CCONJ
ap-1275	97	17	there	there	ADV
ap-1275	97	18	exist	exist	VERB
ap-1275	97	19	exactly	exactly	ADV
ap-1275	97	20	k	k	PROPN
ap-1275	97	21	distinct	distinct	ADJ
ap-1275	97	22	values	value	NOUN
ap-1275	97	23	λn	λn	PROPN
ap-1275	97	24	,	,	PUNCT
ap-1275	97	25	j	j	PROPN
ap-1275	97	26	,	,	PUNCT
ap-1275	97	27	j	j	PROPN
ap-1275	97	28	=	=	NOUN
ap-1275	97	29	1	1	NUM
ap-1275	97	30	,	,	PUNCT
ap-1275	97	31	.	.	PUNCT
ap-1275	97	32	.	.	PUNCT
ap-1275	98	1	.	.	PUNCT
ap-1275	99	1	,	,	PUNCT
ap-1275	99	2	k	k	PROPN
ap-1275	99	3	of	of	ADP
ap-1275	99	4	the	the	DET
ap-1275	99	5	spectral	spectral	ADJ
ap-1275	99	6	parameter	parameter	NOUN
ap-1275	99	7	λ	λ	PROPN
ap-1275	99	8	such	such	ADJ
ap-1275	99	9	that	that	SCONJ
ap-1275	99	10	the	the	DET
ap-1275	99	11	operator	operator	NOUN
ap-1275	99	12	tλ	tλ	AUX
ap-1275	99	13	has	have	VERB
ap-1275	99	14	a	a	DET
ap-1275	99	15	polynomial	polynomial	ADJ
ap-1275	99	16	eigenfunction	eigenfunction	NOUN
ap-1275	99	17	pn	pn	NOUN
ap-1275	99	18	,	,	PUNCT
ap-1275	99	19	j(z	j(z	PROPN
ap-1275	99	20	)	)	PUNCT
ap-1275	99	21	of	of	ADP
ap-1275	99	22	degree	degree	NOUN
ap-1275	99	23	n.	n.	NOUN
ap-1275	99	24	2	2	NUM
ap-1275	99	25	)	)	PUNCT
ap-1275	99	26	asymptotically	asymptotically	ADV
ap-1275	99	27	λn	λn	NOUN
ap-1275	99	28	,	,	PUNCT
ap-1275	99	29	j	j	X
ap-1275	99	30	∼	∼	NOUN
ap-1275	99	31	nλj	nλj	ADV
ap-1275	99	32	where	where	SCONJ
ap-1275	99	33	λ1	λ1	ADJ
ap-1275	99	34	,	,	PUNCT
ap-1275	99	35	.	.	PUNCT
ap-1275	99	36	.	.	PUNCT
ap-1275	100	1	.	.	PUNCT
ap-1275	101	1	,	,	PUNCT
ap-1275	101	2	λk	λk	X
ap-1275	101	3	is	be	AUX
ap-1275	101	4	the	the	DET
ap-1275	101	5	set	set	NOUN
ap-1275	101	6	of	of	ADP
ap-1275	101	7	roots	root	NOUN
ap-1275	101	8	of	of	ADP
ap-1275	101	9	the	the	DET
ap-1275	101	10	algebraic	algebraic	ADJ
ap-1275	101	11	equation	equation	NOUN
ap-1275	101	12	k∑	k∑	PROPN
ap-1275	102	1	i=0	i=0	AUX
ap-1275	102	2	ai	ai	VERB
ap-1275	102	3	,	,	PUNCT
ap-1275	102	4	ix	ix	ADP
ap-1275	102	5	k−i	k−i	NOUN
ap-1275	102	6	=	=	NOUN
ap-1275	102	7	0	0	X
ap-1275	102	8	.	.	PUNCT
ap-1275	102	9	conjecture	conjecture	VERB
ap-1275	102	10	2	2	NUM
ap-1275	102	11	if	if	SCONJ
ap-1275	102	12	t	t	PROPN
ap-1275	102	13	is	be	AUX
ap-1275	102	14	of	of	ADP
ap-1275	102	15	general	general	ADJ
ap-1275	102	16	type	type	NOUN
ap-1275	102	17	and	and	CCONJ
ap-1275	102	18	all	all	DET
ap-1275	102	19	λ1	λ1	ADJ
ap-1275	102	20	,	,	PUNCT
ap-1275	102	21	.	.	PUNCT
ap-1275	102	22	.	.	PUNCT
ap-1275	103	1	.	.	PUNCT
ap-1275	104	1	,	,	PUNCT
ap-1275	104	2	λk	λk	X
ap-1275	104	3	have	have	VERB
ap-1275	104	4	distinct	distinct	ADJ
ap-1275	104	5	arguments	argument	NOUN
ap-1275	104	6	then	then	ADV
ap-1275	104	7	for	for	ADP
ap-1275	104	8	each	each	DET
ap-1275	104	9	j	j	PROPN
ap-1275	104	10	=	=	SYM
ap-1275	104	11	1	1	NUM
ap-1275	104	12	,	,	PUNCT
ap-1275	104	13	.	.	PUNCT
ap-1275	104	14	.	.	PUNCT
ap-1275	105	1	.	.	PUNCT
ap-1275	106	1	,	,	PUNCT
ap-1275	106	2	k	k	PROPN
ap-1275	106	3	∃	∃	PROPN
ap-1275	106	4	!	!	PROPN
ap-1275	106	5	probability	probability	NOUN
ap-1275	106	6	measure	measure	NOUN
ap-1275	106	7	μj	μj	NOUN
ap-1275	106	8	with	with	ADP
ap-1275	106	9	compact	compact	ADJ
ap-1275	106	10	support	support	NOUN
ap-1275	106	11	whose	whose	DET
ap-1275	106	12	cauchy	cauchy	NOUN
ap-1275	106	13	transform	transform	NOUN
ap-1275	106	14	cj(z	cj(z	NOUN
ap-1275	106	15	)	)	PUNCT
ap-1275	106	16	satisfies	satisfie	NOUN
ap-1275	106	17	almost	almost	ADV
ap-1275	106	18	everywhere	everywhere	ADV
ap-1275	106	19	in	in	ADP
ap-1275	106	20	c	c	PROPN
ap-1275	106	21	k∑	k∑	PROPN
ap-1275	106	22	i=1	i=1	PROPN
ap-1275	106	23	qi(z)(λjcj(z	qi(z)(λjcj(z	PROPN
ap-1275	106	24	)	)	PUNCT
ap-1275	106	25	)	)	PUNCT
ap-1275	107	1	i	i	PRON
ap-1275	107	2	=	=	NOUN
ap-1275	108	1	0	0	X
ap-1275	108	2	.	.	PUNCT
ap-1275	108	3	conjecture	conjecture	VERB
ap-1275	108	4	3	3	NUM
ap-1275	108	5	cj(z	cj(z	NOUN
ap-1275	108	6	)	)	PUNCT
ap-1275	109	1	=	=	SYM
ap-1275	109	2	lim	lim	PROPN
ap-1275	109	3	n→∞	n→∞	NUM
ap-1275	109	4	p′n	p′n	PROPN
ap-1275	109	5	,	,	PUNCT
ap-1275	109	6	j(z	j(z	PROPN
ap-1275	109	7	)	)	PUNCT
ap-1275	109	8	λn	λn	NOUN
ap-1275	109	9	,	,	PUNCT
ap-1275	109	10	jpn	jpn	PROPN
ap-1275	109	11	,	,	PUNCT
ap-1275	109	12	j(z	j(z	PROPN
ap-1275	109	13	)	)	PUNCT
ap-1275	109	14	outside	outside	ADP
ap-1275	109	15	the	the	DET
ap-1275	109	16	support	support	NOUN
ap-1275	109	17	of	of	ADP
ap-1275	109	18	μj	μj	NUM
ap-1275	109	19	which	which	PRON
ap-1275	109	20	is	be	AUX
ap-1275	109	21	the	the	DET
ap-1275	109	22	union	union	NOUN
ap-1275	109	23	of	of	ADP
ap-1275	109	24	finitely	finitely	ADV
ap-1275	109	25	many	many	ADJ
ap-1275	109	26	segments	segment	NOUN
ap-1275	109	27	of	of	ADP
ap-1275	109	28	analytic	analytic	ADJ
ap-1275	109	29	curves	curve	NOUN
ap-1275	109	30	forming	form	VERB
ap-1275	109	31	a	a	DET
ap-1275	109	32	curvilinear	curvilinear	ADJ
ap-1275	109	33	tree	tree	NOUN
ap-1275	109	34	.	.	PUNCT
ap-1275	110	1	observation	observation	NOUN
ap-1275	110	2	.	.	PUNCT
ap-1275	111	1	near	near	ADP
ap-1275	111	2	∞	∞	PROPN
ap-1275	111	3	∈	∈	PROPN
ap-1275	111	4	cp1	cp1	NOUN
ap-1275	111	5	the	the	DET
ap-1275	111	6	cauchy	cauchy	NOUN
ap-1275	111	7	transforms	transform	VERB
ap-1275	111	8	λ1c1(z	λ1c1(z	NOUN
ap-1275	111	9	)	)	PUNCT
ap-1275	111	10	,	,	PUNCT
ap-1275	111	11	.	.	PUNCT
ap-1275	111	12	.	.	PUNCT
ap-1275	112	1	.	.	PUNCT
ap-1275	113	1	,	,	PUNCT
ap-1275	113	2	λkck(z	λkck(z	PROPN
ap-1275	113	3	)	)	PUNCT
ap-1275	113	4	are	be	AUX
ap-1275	113	5	independent	independent	ADJ
ap-1275	113	6	sections	section	NOUN
ap-1275	113	7	of	of	ADP
ap-1275	113	8	the	the	DET
ap-1275	113	9	symbol	symbol	NOUN
ap-1275	113	10	equation	equation	NOUN
ap-1275	113	11	of	of	ADP
ap-1275	113	12	tλ	tλ	AUX
ap-1275	113	13	considered	consider	VERB
ap-1275	113	14	as	as	ADP
ap-1275	113	15	a	a	DET
ap-1275	113	16	branched	branched	ADJ
ap-1275	113	17	cover	cover	NOUN
ap-1275	113	18	over	over	ADP
ap-1275	113	19	cp	cp	PROPN
ap-1275	113	20	1	1	NUM
ap-1275	113	21	.	.	PUNCT
ap-1275	113	22	problem	problem	NOUN
ap-1275	113	23	3	3	NUM
ap-1275	113	24	find	find	VERB
ap-1275	113	25	an	an	DET
ap-1275	113	26	explicit	explicit	ADJ
ap-1275	113	27	description	description	NOUN
ap-1275	113	28	of	of	ADP
ap-1275	113	29	(	(	PUNCT
ap-1275	113	30	the	the	DET
ap-1275	113	31	support	support	NOUN
ap-1275	113	32	)	)	PUNCT
ap-1275	113	33	of	of	ADP
ap-1275	113	34	the	the	DET
ap-1275	113	35	measures	measure	NOUN
ap-1275	113	36	μi	μi	X
ap-1275	113	37	.	.	PUNCT
ap-1275	114	1	is	be	AUX
ap-1275	114	2	there	there	PRON
ap-1275	114	3	any	any	DET
ap-1275	114	4	relation	relation	NOUN
ap-1275	114	5	of	of	ADP
ap-1275	114	6	these	these	DET
ap-1275	114	7	measures	measure	NOUN
ap-1275	114	8	to	to	ADP
ap-1275	114	9	the	the	DET
ap-1275	114	10	periods	period	NOUN
ap-1275	114	11	of	of	ADP
ap-1275	114	12	the	the	DET
ap-1275	114	13	plane	plane	NOUN
ap-1275	114	14	curve	curve	NOUN
ap-1275	114	15	k∑	k∑	VERB
ap-1275	115	1	i=1	i=1	PRON
ap-1275	116	1	qi(z)y	qi(z)y	VERB
ap-1275	116	2	i	i	NOUN
ap-1275	116	3	=	=	NOUN
ap-1275	116	4	0	0	X
ap-1275	116	5	?	?	SYM
ap-1275	116	6	5	5	NUM
ap-1275	116	7	heine	heine	NOUN
ap-1275	116	8	-	-	PUNCT
ap-1275	116	9	stieltjes	stieltjes	PROPN
ap-1275	116	10	theory	theory	NOUN
ap-1275	116	11	this	this	DET
ap-1275	116	12	section	section	NOUN
ap-1275	116	13	is	be	AUX
ap-1275	116	14	based	base	VERB
ap-1275	116	15	on	on	ADP
ap-1275	116	16	[	[	X
ap-1275	116	17	11	11	NUM
ap-1275	116	18	]	]	PUNCT
ap-1275	116	19	.	.	PUNCT
ap-1275	117	1	take	take	VERB
ap-1275	117	2	an	an	DET
ap-1275	117	3	arbitrary	arbitrary	ADJ
ap-1275	117	4	univariate	univariate	ADJ
ap-1275	117	5	linear	linear	ADJ
ap-1275	117	6	differential	differential	NOUN
ap-1275	117	7	operator	operator	NOUN
ap-1275	117	8	t	t	PROPN
ap-1275	117	9	=	=	SYM
ap-1275	117	10	k∑	k∑	PROPN
ap-1275	117	11	i=0	i=0	PROPN
ap-1275	117	12	qi(z	qi(z	X
ap-1275	117	13	)	)	PUNCT
ap-1275	117	14	di	di	X
ap-1275	117	15	dzi	dzi	PROPN
ap-1275	117	16	with	with	ADP
ap-1275	117	17	polynomial	polynomial	ADJ
ap-1275	117	18	coefficients	coefficient	NOUN
ap-1275	117	19	and	and	CCONJ
ap-1275	117	20	set	set	VERB
ap-1275	117	21	r	r	NOUN
ap-1275	117	22	=	=	SYM
ap-1275	117	23	max	max	PROPN
ap-1275	118	1	i	i	PRON
ap-1275	118	2	(	(	PUNCT
ap-1275	118	3	degqi(z)−	degqi(z)−	PROPN
ap-1275	118	4	i	i	PROPN
ap-1275	118	5	)	)	PUNCT
ap-1275	118	6	.	.	PUNCT
ap-1275	119	1	definition	definition	NOUN
ap-1275	119	2	8	8	NUM
ap-1275	119	3	if	if	SCONJ
ap-1275	119	4	r	r	NOUN
ap-1275	119	5	≥	≥	NOUN
ap-1275	119	6	0	0	NUM
ap-1275	119	7	,	,	PUNCT
ap-1275	119	8	degqk(z	degqk(z	NUM
ap-1275	119	9	)	)	PUNCT
ap-1275	119	10	=	=	PUNCT
ap-1275	119	11	k+	k+	NOUN
ap-1275	119	12	r	r	NOUN
ap-1275	119	13	and	and	CCONJ
ap-1275	119	14	qk(z	qk(z	NUM
ap-1275	119	15	)	)	PUNCT
ap-1275	119	16	has	have	VERB
ap-1275	119	17	at	at	ADV
ap-1275	119	18	least	least	ADJ
ap-1275	119	19	two	two	NUM
ap-1275	119	20	distinct	distinct	ADJ
ap-1275	119	21	roots	root	NOUN
ap-1275	119	22	we	we	PRON
ap-1275	119	23	call	call	VERB
ap-1275	119	24	t	t	PROPN
ap-1275	119	25	a	a	DET
ap-1275	119	26	general	general	ADJ
ap-1275	119	27	lame	lame	ADJ
ap-1275	119	28	-	-	PUNCT
ap-1275	119	29	type	type	NOUN
ap-1275	119	30	operator	operator	NOUN
ap-1275	119	31	.	.	PUNCT
ap-1275	120	1	80	80	NUM
ap-1275	120	2	acta	acta	PROPN
ap-1275	120	3	polytechnica	polytechnica	PROPN
ap-1275	120	4	vol	vol	NOUN
ap-1275	120	5	.	.	PROPN
ap-1275	121	1	50	50	NUM
ap-1275	121	2	no	no	NOUN
ap-1275	121	3	.	.	PUNCT
ap-1275	122	1	5/2010	5/2010	NUM
ap-1275	122	2	0	0	NUM
ap-1275	122	3	1	1	NUM
ap-1275	122	4	2	2	NUM
ap-1275	122	5	3	3	NUM
ap-1275	122	6	4	4	NUM
ap-1275	122	7	5	5	NUM
ap-1275	122	8	6	6	NUM
ap-1275	122	9	0	0	NUM
ap-1275	122	10	1	1	NUM
ap-1275	122	11	2	2	NUM
ap-1275	122	12	3	3	NUM
ap-1275	122	13	4	4	NUM
ap-1275	122	14	0	0	NUM
ap-1275	122	15	1	1	NUM
ap-1275	122	16	2	2	NUM
ap-1275	122	17	3	3	NUM
ap-1275	122	18	4	4	NUM
ap-1275	122	19	0	0	NUM
ap-1275	122	20	1	1	NUM
ap-1275	122	21	2	2	NUM
ap-1275	122	22	3	3	NUM
ap-1275	122	23	4	4	NUM
ap-1275	122	24	0	0	NUM
ap-1275	122	25	1	1	NUM
ap-1275	122	26	2	2	NUM
ap-1275	122	27	3	3	NUM
ap-1275	122	28	4	4	NUM
ap-1275	122	29	-1	-1	SYM
ap-1275	122	30	0	0	NUM
ap-1275	122	31	1	1	NUM
ap-1275	122	32	2	2	NUM
ap-1275	122	33	3	3	NUM
ap-1275	122	34	4	4	NUM
ap-1275	122	35	0	0	NUM
ap-1275	122	36	1	1	NUM
ap-1275	122	37	2	2	NUM
ap-1275	122	38	3	3	NUM
ap-1275	122	39	4	4	NUM
ap-1275	122	40	5	5	NUM
ap-1275	122	41	6	6	NUM
ap-1275	122	42	-1	-1	SYM
ap-1275	122	43	0	0	NUM
ap-1275	122	44	1	1	NUM
ap-1275	122	45	2	2	NUM
ap-1275	122	46	3	3	NUM
ap-1275	122	47	4	4	NUM
ap-1275	122	48	fig	fig	NOUN
ap-1275	122	49	.	.	PUNCT
ap-1275	123	1	5	5	NUM
ap-1275	123	2	:	:	SYM
ap-1275	123	3	three	three	NUM
ap-1275	123	4	root	root	NOUN
ap-1275	123	5	-	-	PUNCT
ap-1275	123	6	counting	count	VERB
ap-1275	123	7	measures	measure	NOUN
ap-1275	123	8	and	and	CCONJ
ap-1275	123	9	their	their	PRON
ap-1275	123	10	union	union	NOUN
ap-1275	123	11	for	for	ADP
ap-1275	123	12	a	a	DET
ap-1275	123	13	homogenized	homogenized	ADJ
ap-1275	123	14	spectral	spectral	ADJ
ap-1275	123	15	problem	problem	NOUN
ap-1275	123	16	with	with	ADP
ap-1275	123	17	an	an	DET
ap-1275	123	18	operator	operator	NOUN
ap-1275	123	19	of	of	ADP
ap-1275	123	20	order	order	NOUN
ap-1275	124	1	3	3	NUM
ap-1275	124	2	0	0	NUM
ap-1275	124	3	0.5	0.5	NUM
ap-1275	124	4	1	1	NUM
ap-1275	124	5	1.5	1.5	NUM
ap-1275	124	6	2	2	NUM
ap-1275	124	7	2.5	2.5	NUM
ap-1275	124	8	3	3	NUM
ap-1275	124	9	-3	-3	INTJ
ap-1275	124	10	-2	-2	INTJ
ap-1275	124	11	-1	-1	SYM
ap-1275	124	12	0	0	NUM
ap-1275	124	13	1	1	NUM
ap-1275	124	14	2	2	NUM
ap-1275	124	15	0	0	NUM
ap-1275	124	16	0.5	0.5	NUM
ap-1275	124	17	1	1	NUM
ap-1275	124	18	1.5	1.5	NUM
ap-1275	124	19	2	2	NUM
ap-1275	124	20	2.5	2.5	NUM
ap-1275	124	21	3	3	NUM
ap-1275	124	22	-3	-3	INTJ
ap-1275	124	23	-2	-2	INTJ
ap-1275	124	24	-1	-1	SYM
ap-1275	124	25	0	0	NUM
ap-1275	124	26	1	1	NUM
ap-1275	124	27	2	2	NUM
ap-1275	124	28	fig	fig	NOUN
ap-1275	124	29	.	.	PUNCT
ap-1275	125	1	6	6	NUM
ap-1275	125	2	:	:	PUNCT
ap-1275	125	3	examples	example	NOUN
ap-1275	125	4	of	of	ADP
ap-1275	125	5	μq	μq	PRON
ap-1275	125	6	’s	’s	NOUN
ap-1275	125	7	for	for	ADP
ap-1275	125	8	t	t	NOUN
ap-1275	125	9	=	=	SYM
ap-1275	125	10	(	(	PUNCT
ap-1275	125	11	z2	z2	PROPN
ap-1275	125	12	+	+	CCONJ
ap-1275	125	13	1)(z	1)(z	NUM
ap-1275	125	14	+	+	NOUN
ap-1275	125	15	2i	2i	NUM
ap-1275	125	16	−	−	NOUN
ap-1275	125	17	3)(z	3)(z	NUM
ap-1275	125	18	−	−	NOUN
ap-1275	125	19	3i	3i	NOUN
ap-1275	125	20	−	−	NOUN
ap-1275	125	21	2	2	NUM
ap-1275	125	22	)	)	PUNCT
ap-1275	125	23	d3	d3	NOUN
ap-1275	125	24	dz3	dz3	ADV
ap-1275	125	25	consider	consider	VERB
ap-1275	125	26	the	the	DET
ap-1275	125	27	following	follow	VERB
ap-1275	125	28	multi	multi	ADJ
ap-1275	125	29	-	-	ADJ
ap-1275	125	30	parameter	parameter	ADJ
ap-1275	125	31	spectral	spectral	ADJ
ap-1275	125	32	problem	problem	NOUN
ap-1275	125	33	.	.	PUNCT
ap-1275	126	1	for	for	ADP
ap-1275	126	2	a	a	DET
ap-1275	126	3	given	give	VERB
ap-1275	126	4	non	non	ADJ
ap-1275	126	5	-	-	ADJ
ap-1275	126	6	negative	negative	ADJ
ap-1275	126	7	integer	integer	NOUN
ap-1275	126	8	n	n	PRON
ap-1275	126	9	find	find	VERB
ap-1275	126	10	all	all	DET
ap-1275	126	11	polynomials	polynomial	NOUN
ap-1275	126	12	v	v	ADP
ap-1275	126	13	(	(	PUNCT
ap-1275	126	14	z	z	NOUN
ap-1275	126	15	)	)	PUNCT
ap-1275	126	16	of	of	ADP
ap-1275	126	17	degree	degree	NOUN
ap-1275	126	18	at	at	ADP
ap-1275	126	19	most	most	ADJ
ap-1275	126	20	r	r	NOUN
ap-1275	126	21	such	such	ADJ
ap-1275	126	22	that	that	SCONJ
ap-1275	126	23	the	the	DET
ap-1275	126	24	equation	equation	NOUN
ap-1275	126	25	t	t	X
ap-1275	126	26	(	(	PUNCT
ap-1275	126	27	p(z	p(z	NOUN
ap-1275	126	28	)	)	PUNCT
ap-1275	126	29	)	)	PUNCT
ap-1275	127	1	+	+	CCONJ
ap-1275	127	2	v	v	X
ap-1275	127	3	(	(	PUNCT
ap-1275	127	4	z)p(z	z)p(z	NUM
ap-1275	127	5	)	)	PUNCT
ap-1275	127	6	=	=	SYM
ap-1275	127	7	0	0	NUM
ap-1275	127	8	,	,	PUNCT
ap-1275	127	9	has	have	VERB
ap-1275	127	10	a	a	DET
ap-1275	127	11	polynomial	polynomial	ADJ
ap-1275	127	12	solution	solution	NOUN
ap-1275	127	13	p(z	p(z	NOUN
ap-1275	127	14	)	)	PUNCT
ap-1275	127	15	of	of	ADP
ap-1275	127	16	degree	degree	NOUN
ap-1275	127	17	n.	n.	NOUN
ap-1275	127	18	(	(	PUNCT
ap-1275	127	19	classically	classically	ADV
ap-1275	127	20	,	,	PUNCT
ap-1275	127	21	p(z	p(z	PROPN
ap-1275	127	22	)	)	PUNCT
ap-1275	127	23	is	be	AUX
ap-1275	127	24	called	call	VERB
ap-1275	127	25	a	a	DET
ap-1275	127	26	stieltjes	stieltjes	NOUN
ap-1275	127	27	polynomial	polynomial	ADJ
ap-1275	127	28	and	and	CCONJ
ap-1275	127	29	v	v	ADJ
ap-1275	127	30	(	(	PUNCT
ap-1275	127	31	z	z	NOUN
ap-1275	127	32	)	)	PUNCT
ap-1275	127	33	is	be	AUX
ap-1275	127	34	called	call	VERB
ap-1275	127	35	a	a	DET
ap-1275	127	36	van	van	PROPN
ap-1275	127	37	vleck	vleck	NOUN
ap-1275	127	38	polynomial	polynomial	NOUN
ap-1275	127	39	.	.	PUNCT
ap-1275	127	40	)	)	PUNCT
ap-1275	128	1	proposition	proposition	NOUN
ap-1275	128	2	4	4	NUM
ap-1275	128	3	under	under	ADP
ap-1275	128	4	the	the	DET
ap-1275	128	5	above	above	ADJ
ap-1275	128	6	assumptions	assumption	NOUN
ap-1275	128	7	for	for	ADP
ap-1275	128	8	any	any	DET
ap-1275	128	9	sufficiently	sufficiently	ADV
ap-1275	128	10	large	large	ADJ
ap-1275	128	11	n	n	CCONJ
ap-1275	128	12	there	there	ADV
ap-1275	128	13	exist	exist	VERB
ap-1275	128	14	exactly	exactly	ADV
ap-1275	128	15	(	(	PUNCT
ap-1275	128	16	n+	n+	ADP
ap-1275	128	17	r	r	NOUN
ap-1275	128	18	r	r	NOUN
ap-1275	128	19	)	)	PUNCT
ap-1275	128	20	degree	degree	NOUN
ap-1275	128	21	n	n	DET
ap-1275	128	22	stieltjes	stieltjes	NOUN
ap-1275	128	23	polynomials	polynomial	VERB
ap-1275	128	24	pn	pn	PROPN
ap-1275	128	25	,	,	PUNCT
ap-1275	128	26	j(z	j(z	PROPN
ap-1275	128	27	)	)	PUNCT
ap-1275	128	28	and	and	CCONJ
ap-1275	128	29	corresponding	correspond	VERB
ap-1275	128	30	van	van	PROPN
ap-1275	128	31	vleck	vleck	PROPN
ap-1275	128	32	polynomials	polynomial	NOUN
ap-1275	128	33	vn	vn	PROPN
ap-1275	128	34	,	,	PUNCT
ap-1275	128	35	j(z	j(z	PROPN
ap-1275	128	36	)	)	PUNCT
ap-1275	128	37	.	.	PUNCT
ap-1275	129	1	proposition	proposition	NOUN
ap-1275	129	2	5	5	NUM
ap-1275	129	3	if	if	SCONJ
ap-1275	129	4	a	a	DET
ap-1275	129	5	sequence	sequence	NOUN
ap-1275	129	6	{	{	PUNCT
ap-1275	129	7	ṽn	ṽn	NOUN
ap-1275	129	8	,	,	PUNCT
ap-1275	129	9	jn(z	jn(z	NOUN
ap-1275	129	10	)	)	PUNCT
ap-1275	129	11	}	}	PUNCT
ap-1275	129	12	,	,	PUNCT
ap-1275	129	13	n	n	NOUN
ap-1275	129	14	=	=	SYM
ap-1275	129	15	1	1	NUM
ap-1275	129	16	,	,	PUNCT
ap-1275	129	17	.	.	PUNCT
ap-1275	129	18	.	.	PUNCT
ap-1275	130	1	.	.	PUNCT
ap-1275	131	1	,	,	PUNCT
ap-1275	131	2	of	of	ADP
ap-1275	131	3	scaled	scale	VERB
ap-1275	131	4	van	van	PROPN
ap-1275	131	5	vleck	vleck	NOUN
ap-1275	131	6	polynomials	polynomial	VERB
ap-1275	131	7	converges	converge	NOUN
ap-1275	131	8	to	to	ADP
ap-1275	131	9	some	some	DET
ap-1275	131	10	polynomial	polynomial	ADJ
ap-1275	131	11	ṽ	ṽ	PROPN
ap-1275	131	12	(	(	PUNCT
ap-1275	131	13	z	z	NOUN
ap-1275	131	14	)	)	PUNCT
ap-1275	131	15	then	then	ADV
ap-1275	131	16	the	the	DET
ap-1275	131	17	sequence	sequence	NOUN
ap-1275	131	18	of	of	ADP
ap-1275	131	19	finite	finite	ADJ
ap-1275	131	20	measures	measure	NOUN
ap-1275	131	21	μn	μn	PROPN
ap-1275	131	22	,	,	PUNCT
ap-1275	131	23	j	j	PROPN
ap-1275	131	24	of	of	ADP
ap-1275	131	25	the	the	DET
ap-1275	131	26	corresponding	corresponding	ADJ
ap-1275	131	27	family	family	NOUN
ap-1275	131	28	of	of	ADP
ap-1275	131	29	eigenpolynomials	eigenpolynomial	NOUN
ap-1275	131	30	{	{	PUNCT
ap-1275	131	31	pn	pn	NOUN
ap-1275	131	32	,	,	PUNCT
ap-1275	131	33	jn(z	jn(z	NOUN
ap-1275	131	34	)	)	PUNCT
ap-1275	131	35	}	}	PUNCT
ap-1275	131	36	converges	converge	VERB
ap-1275	131	37	to	to	ADP
ap-1275	131	38	a	a	DET
ap-1275	131	39	measure	measure	NOUN
ap-1275	131	40	μ	μ	PROPN
ap-1275	131	41	ṽ	ṽ	PROPN
ap-1275	131	42	satisfying	satisfy	VERB
ap-1275	131	43	the	the	DET
ap-1275	131	44	properties	property	NOUN
ap-1275	131	45	:	:	PUNCT
ap-1275	131	46	a	a	X
ap-1275	131	47	)	)	PUNCT
ap-1275	131	48	suppμ	suppμ	PROPN
ap-1275	131	49	ṽ	ṽ	PROPN
ap-1275	131	50	is	be	AUX
ap-1275	131	51	a	a	DET
ap-1275	131	52	forest	forest	NOUN
ap-1275	131	53	of	of	ADP
ap-1275	131	54	curvilinear	curvilinear	ADJ
ap-1275	131	55	trees	tree	NOUN
ap-1275	131	56	;	;	PUNCT
ap-1275	131	57	b	b	X
ap-1275	131	58	)	)	PUNCT
ap-1275	131	59	the	the	DET
ap-1275	131	60	union	union	NOUN
ap-1275	131	61	of	of	ADP
ap-1275	131	62	the	the	DET
ap-1275	131	63	leaves	leave	NOUN
ap-1275	131	64	of	of	ADP
ap-1275	131	65	suppμ	suppμ	PROPN
ap-1275	131	66	ṽ	ṽ	PROPN
ap-1275	131	67	coincides	coincide	VERB
ap-1275	131	68	with	with	ADP
ap-1275	131	69	the	the	DET
ap-1275	131	70	union	union	NOUN
ap-1275	131	71	of	of	ADP
ap-1275	131	72	all	all	DET
ap-1275	131	73	zeros	zero	NOUN
ap-1275	131	74	of	of	ADP
ap-1275	131	75	qk(z	qk(z	PROPN
ap-1275	131	76	)	)	PUNCT
ap-1275	131	77	and	and	CCONJ
ap-1275	131	78	those	those	PRON
ap-1275	131	79	of	of	ADP
ap-1275	131	80	ṽ	ṽ	PROPN
ap-1275	131	81	(	(	PUNCT
ap-1275	131	82	z	z	NOUN
ap-1275	131	83	)	)	PUNCT
ap-1275	131	84	.	.	PUNCT
ap-1275	132	1	c	c	X
ap-1275	132	2	)	)	PUNCT
ap-1275	132	3	suppμ	suppμ	PROPN
ap-1275	132	4	ṽ	ṽ	PROPN
ap-1275	132	5	is	be	AUX
ap-1275	132	6	straightened	straighten	VERB
ap-1275	132	7	out	out	ADP
ap-1275	132	8	by	by	ADP
ap-1275	132	9	the	the	DET
ap-1275	132	10	transformation	transformation	NOUN
ap-1275	132	11	given	give	VERB
ap-1275	132	12	by	by	ADP
ap-1275	132	13	∫	∫	PROPN
ap-1275	132	14	z	z	PROPN
ap-1275	132	15	a	a	DET
ap-1275	132	16	ṽ	ṽ	PROPN
ap-1275	132	17	(	(	PUNCT
ap-1275	132	18	z)dz	z)dz	PROPN
ap-1275	132	19	qk(z	qk(z	NUM
ap-1275	132	20	)	)	PUNCT
ap-1275	132	21	.	.	PUNCT
ap-1275	133	1	explanations	explanation	NOUN
ap-1275	133	2	to	to	ADP
ap-1275	133	3	fig	fig	NOUN
ap-1275	133	4	.	.	PUNCT
ap-1275	134	1	6	6	NUM
ap-1275	134	2	and	and	CCONJ
ap-1275	134	3	7	7	NUM
ap-1275	134	4	.	.	PUNCT
ap-1275	135	1	in	in	ADP
ap-1275	135	2	fig	fig	NOUN
ap-1275	135	3	.	.	PUNCT
ap-1275	136	1	6	6	NUM
ap-1275	136	2	we	we	PRON
ap-1275	136	3	give	give	VERB
ap-1275	136	4	two	two	NUM
ap-1275	136	5	examples	example	NOUN
ap-1275	136	6	of	of	ADP
ap-1275	136	7	different	different	ADJ
ap-1275	136	8	van	van	PROPN
ap-1275	136	9	vleck	vleck	NOUN
ap-1275	136	10	polynomials	polynomial	VERB
ap-1275	136	11	v	v	ADP
ap-1275	136	12	(	(	PUNCT
ap-1275	136	13	z	z	NOUN
ap-1275	136	14	)	)	PUNCT
ap-1275	136	15	and	and	CCONJ
ap-1275	136	16	the	the	DET
ap-1275	136	17	corresponding	corresponding	ADJ
ap-1275	136	18	stieltjes	stieltjes	NOUN
ap-1275	136	19	polynomials	polynomial	NOUN
ap-1275	136	20	p(z	p(z	PROPN
ap-1275	136	21	)	)	PUNCT
ap-1275	136	22	.	.	PUNCT
ap-1275	137	1	the	the	DET
ap-1275	137	2	average	average	ADJ
ap-1275	137	3	size	size	NOUN
ap-1275	137	4	dots	dot	NOUN
ap-1275	137	5	are	be	AUX
ap-1275	137	6	the	the	DET
ap-1275	137	7	4	4	NUM
ap-1275	137	8	roots	root	NOUN
ap-1275	137	9	of	of	ADP
ap-1275	137	10	the	the	DET
ap-1275	137	11	polynomial	polynomial	ADJ
ap-1275	137	12	q(z	q(z	PROPN
ap-1275	137	13	)	)	PUNCT
ap-1275	137	14	=	=	PUNCT
ap-1275	137	15	(	(	PUNCT
ap-1275	137	16	z2	z2	PROPN
ap-1275	137	17	+	+	CCONJ
ap-1275	137	18	1)(z	1)(z	NUM
ap-1275	137	19	+	+	NOUN
ap-1275	137	20	2i	2i	NUM
ap-1275	137	21	−	−	NOUN
ap-1275	137	22	3)(z	3)(z	NUM
ap-1275	137	23	−	−	NOUN
ap-1275	137	24	3i	3i	NOUN
ap-1275	137	25	−	−	NOUN
ap-1275	137	26	2	2	NUM
ap-1275	137	27	)	)	PUNCT
ap-1275	137	28	,	,	PUNCT
ap-1275	137	29	the	the	DET
ap-1275	137	30	81	81	NUM
ap-1275	137	31	acta	acta	PROPN
ap-1275	137	32	polytechnica	polytechnica	PROPN
ap-1275	137	33	vol	vol	NOUN
ap-1275	137	34	.	.	PROPN
ap-1275	138	1	50	50	NUM
ap-1275	138	2	no	no	NOUN
ap-1275	138	3	.	.	PUNCT
ap-1275	139	1	5/2010	5/2010	NUM
ap-1275	139	2	unique	unique	ADJ
ap-1275	139	3	large	large	ADJ
ap-1275	139	4	dot	dot	NOUN
ap-1275	139	5	is	be	AUX
ap-1275	139	6	the	the	DET
ap-1275	139	7	only	only	ADJ
ap-1275	139	8	root	root	NOUN
ap-1275	139	9	of	of	ADP
ap-1275	139	10	v	v	NOUN
ap-1275	139	11	(	(	PUNCT
ap-1275	139	12	z	z	NOUN
ap-1275	139	13	)	)	PUNCT
ap-1275	139	14	(	(	PUNCT
ap-1275	139	15	which	which	PRON
ap-1275	139	16	is	be	AUX
ap-1275	139	17	linear	linear	ADJ
ap-1275	139	18	in	in	ADP
ap-1275	139	19	this	this	DET
ap-1275	139	20	case	case	NOUN
ap-1275	139	21	)	)	PUNCT
ap-1275	139	22	.	.	PUNCT
ap-1275	140	1	small	small	ADJ
ap-1275	140	2	dots	dot	NOUN
ap-1275	140	3	show	show	VERB
ap-1275	140	4	the	the	DET
ap-1275	140	5	roots	root	NOUN
ap-1275	140	6	of	of	ADP
ap-1275	140	7	p(z	p(z	NOUN
ap-1275	140	8	)	)	PUNCT
ap-1275	140	9	.	.	PUNCT
ap-1275	141	1	in	in	ADP
ap-1275	141	2	fig	fig	NOUN
ap-1275	141	3	.	.	PUNCT
ap-1275	142	1	7	7	NUM
ap-1275	142	2	we	we	PRON
ap-1275	142	3	show	show	VERB
ap-1275	142	4	the	the	DET
ap-1275	142	5	union	union	NOUN
ap-1275	142	6	of	of	ADP
ap-1275	142	7	all	all	DET
ap-1275	142	8	roots	root	NOUN
ap-1275	142	9	of	of	ADP
ap-1275	142	10	p(z	p(z	NOUN
ap-1275	142	11	)	)	PUNCT
ap-1275	142	12	of	of	ADP
ap-1275	142	13	degree	degree	NOUN
ap-1275	142	14	25	25	NUM
ap-1275	142	15	for	for	ADP
ap-1275	142	16	the	the	DET
ap-1275	142	17	same	same	ADJ
ap-1275	142	18	problem	problem	NOUN
ap-1275	142	19	.	.	PUNCT
ap-1275	143	1	0	0	NUM
ap-1275	143	2	0.5	0.5	NUM
ap-1275	143	3	1	1	NUM
ap-1275	143	4	1.5	1.5	NUM
ap-1275	143	5	2	2	NUM
ap-1275	143	6	2.5	2.5	NUM
ap-1275	143	7	3	3	NUM
ap-1275	143	8	-3	-3	INTJ
ap-1275	143	9	-2	-2	INTJ
ap-1275	143	10	-1	-1	SYM
ap-1275	143	11	0	0	NUM
ap-1275	143	12	1	1	NUM
ap-1275	143	13	2	2	NUM
ap-1275	143	14	fig	fig	NOUN
ap-1275	143	15	.	.	PUNCT
ap-1275	144	1	7	7	NUM
ap-1275	144	2	:	:	PUNCT
ap-1275	144	3	union	union	NOUN
ap-1275	144	4	of	of	ADP
ap-1275	144	5	μq	μq	PROPN
ap-1275	144	6	’s	’s	NOUN
ap-1275	144	7	for	for	ADP
ap-1275	144	8	the	the	DET
ap-1275	144	9	above	above	ADJ
ap-1275	144	10	t	t	PROPN
ap-1275	144	11	6	6	NUM
ap-1275	144	12	schrödinger	schrödinger	NOUN
ap-1275	144	13	operator	operator	NOUN
ap-1275	144	14	with	with	ADP
ap-1275	144	15	polynomial	polynomial	ADJ
ap-1275	144	16	potential	potential	NOUN
ap-1275	144	17	this	this	DET
ap-1275	144	18	section	section	NOUN
ap-1275	144	19	is	be	AUX
ap-1275	144	20	based	base	VERB
ap-1275	144	21	on	on	ADP
ap-1275	144	22	[	[	X
ap-1275	144	23	7	7	NUM
ap-1275	144	24	,	,	PUNCT
ap-1275	144	25	8	8	NUM
ap-1275	144	26	]	]	PUNCT
ap-1275	144	27	.	.	PUNCT
ap-1275	145	1	consider	consider	VERB
ap-1275	145	2	the	the	DET
ap-1275	145	3	operator	operator	NOUN
ap-1275	145	4	h	h	NOUN
ap-1275	145	5	=	=	PUNCT
ap-1275	146	1	−	−	PROPN
ap-1275	146	2	d2	d2	PROPN
ap-1275	146	3	dz2	dz2	NOUN
ap-1275	146	4	+	+	CCONJ
ap-1275	146	5	p	p	X
ap-1275	146	6	(	(	PUNCT
ap-1275	146	7	z	z	NOUN
ap-1275	146	8	)	)	PUNCT
ap-1275	146	9	where	where	SCONJ
ap-1275	146	10	p	p	NOUN
ap-1275	146	11	(	(	PUNCT
ap-1275	146	12	z	z	NOUN
ap-1275	146	13	)	)	PUNCT
ap-1275	146	14	=	=	SYM
ap-1275	147	1	z2l	z2l	PUNCT
ap-1275	148	1	+	+	CCONJ
ap-1275	148	2	2l−1∑	2l−1∑	NUM
ap-1275	148	3	i=0	i=0	PROPN
ap-1275	148	4	aiz	aiz	X
ap-1275	149	1	i	i	PRON
ap-1275	149	2	is	be	AUX
ap-1275	149	3	a	a	DET
ap-1275	149	4	monic	monic	ADJ
ap-1275	149	5	polynomial	polynomial	NOUN
ap-1275	149	6	of	of	ADP
ap-1275	149	7	even	even	ADJ
ap-1275	149	8	degree	degree	NOUN
ap-1275	149	9	with	with	ADP
ap-1275	149	10	real	real	ADJ
ap-1275	149	11	coefficients	coefficient	NOUN
ap-1275	149	12	.	.	PUNCT
ap-1275	150	1	it	it	PRON
ap-1275	150	2	is	be	AUX
ap-1275	150	3	well	well	ADV
ap-1275	150	4	-	-	PUNCT
ap-1275	150	5	known	know	VERB
ap-1275	150	6	that	that	SCONJ
ap-1275	150	7	the	the	DET
ap-1275	150	8	classical	classical	ADJ
ap-1275	150	9	spectral	spectral	ADJ
ap-1275	150	10	problem	problem	NOUN
ap-1275	150	11	h(y	h(y	ADV
ap-1275	150	12	)	)	PUNCT
ap-1275	150	13	=	=	SYM
ap-1275	150	14	λy	λy	X
ap-1275	150	15	(	(	PUNCT
ap-1275	150	16	1	1	NUM
ap-1275	150	17	)	)	PUNCT
ap-1275	150	18	where	where	SCONJ
ap-1275	150	19	y	y	PROPN
ap-1275	150	20	belongs	belong	VERB
ap-1275	150	21	to	to	ADP
ap-1275	150	22	l2(r	l2(r	PROPN
ap-1275	150	23	)	)	PUNCT
ap-1275	150	24	has	have	VERB
ap-1275	150	25	a	a	DET
ap-1275	150	26	discrete	discrete	ADJ
ap-1275	150	27	and	and	CCONJ
ap-1275	150	28	simple	simple	ADJ
ap-1275	150	29	spectrum	spectrum	NOUN
ap-1275	150	30	0	0	PUNCT
ap-1275	150	31	<	<	X
ap-1275	150	32	λ0	λ0	NOUN
ap-1275	150	33	<	<	X
ap-1275	150	34	λ1	λ1	ADJ
ap-1275	150	35	<	<	X
ap-1275	150	36	λ2	λ2	NOUN
ap-1275	150	37	<	<	X
ap-1275	150	38	.	.	PUNCT
ap-1275	150	39	.	.	PUNCT
ap-1275	150	40	.	.	PUNCT
ap-1275	151	1	<	<	X
ap-1275	152	1	λn	λn	X
ap-1275	152	2	<	<	X
ap-1275	152	3	.	.	PUNCT
ap-1275	152	4	.	.	PUNCT
ap-1275	152	5	.	.	PUNCT
ap-1275	153	1	denote	denote	VERB
ap-1275	153	2	by	by	ADP
ap-1275	153	3	φ0(z	φ0(z	NOUN
ap-1275	153	4	)	)	PUNCT
ap-1275	153	5	,	,	PUNCT
ap-1275	153	6	φ1(z	φ1(z	PROPN
ap-1275	153	7	)	)	PUNCT
ap-1275	153	8	,	,	PUNCT
ap-1275	153	9	.	.	PUNCT
ap-1275	153	10	.	.	PUNCT
ap-1275	154	1	.	.	PUNCT
ap-1275	155	1	,	,	PUNCT
ap-1275	155	2	φn(z	φn(z	PROPN
ap-1275	155	3	)	)	PUNCT
ap-1275	155	4	,	,	PUNCT
ap-1275	155	5	.	.	PUNCT
ap-1275	156	1	.	.	PUNCT
ap-1275	156	2	.	.	PUNCT
ap-1275	157	1	the	the	DET
ap-1275	157	2	sequence	sequence	NOUN
ap-1275	157	3	of	of	ADP
ap-1275	157	4	the	the	DET
ap-1275	157	5	corresponding	corresponding	ADJ
ap-1275	157	6	eigenfunctions	eigenfunction	NOUN
ap-1275	157	7	.	.	PUNCT
ap-1275	158	1	these	these	DET
ap-1275	158	2	eigenfunctions	eigenfunction	NOUN
ap-1275	158	3	are	be	AUX
ap-1275	158	4	real	real	ADJ
ap-1275	158	5	entire	entire	ADJ
ap-1275	158	6	functions	function	NOUN
ap-1275	158	7	of	of	ADP
ap-1275	158	8	order	order	NOUN
ap-1275	158	9	l+	l+	X
ap-1275	158	10	1	1	NUM
ap-1275	158	11	and	and	CCONJ
ap-1275	158	12	φn(z	φn(z	NUM
ap-1275	158	13	)	)	PUNCT
ap-1275	159	1	has	have	VERB
ap-1275	159	2	exactly	exactly	ADV
ap-1275	159	3	n	n	PRON
ap-1275	159	4	real	real	ADJ
ap-1275	159	5	zeros	zero	NOUN
ap-1275	159	6	.	.	PUNCT
ap-1275	160	1	set	set	NOUN
ap-1275	160	2	ψn(z	ψn(z	PUNCT
ap-1275	160	3	)	)	PUNCT
ap-1275	161	1	=	=	SYM
ap-1275	161	2	φn	φn	PROPN
ap-1275	161	3	(	(	PUNCT
ap-1275	161	4	2l	2l	NUM
ap-1275	161	5	√	√	NUM
ap-1275	161	6	λnz	λnz	NOUN
ap-1275	161	7	)	)	PUNCT
ap-1275	161	8	which	which	PRON
ap-1275	161	9	we	we	PRON
ap-1275	161	10	call	call	VERB
ap-1275	161	11	the	the	DET
ap-1275	161	12	scaled	scale	VERB
ap-1275	161	13	n	n	CCONJ
ap-1275	161	14	-	-	PUNCT
ap-1275	161	15	th	th	VERB
ap-1275	161	16	eigenfunction	eigenfunction	NOUN
ap-1275	161	17	.	.	PUNCT
ap-1275	162	1	the	the	DET
ap-1275	162	2	stokes	stokes	PROPN
ap-1275	162	3	graph	graph	NOUN
ap-1275	162	4	of	of	ADP
ap-1275	162	5	any	any	DET
ap-1275	162	6	complex	complex	ADJ
ap-1275	162	7	polynomial	polynomial	ADJ
ap-1275	162	8	p	p	NOUN
ap-1275	162	9	(	(	PUNCT
ap-1275	162	10	z	z	NOUN
ap-1275	162	11	)	)	PUNCT
ap-1275	162	12	is	be	AUX
ap-1275	162	13	the	the	DET
ap-1275	162	14	following	follow	VERB
ap-1275	162	15	object	object	NOUN
ap-1275	162	16	.	.	PUNCT
ap-1275	163	1	each	each	DET
ap-1275	163	2	root	root	NOUN
ap-1275	163	3	of	of	ADP
ap-1275	163	4	p	p	NOUN
ap-1275	163	5	(	(	PUNCT
ap-1275	163	6	z	z	NOUN
ap-1275	163	7	)	)	PUNCT
ap-1275	163	8	is	be	AUX
ap-1275	163	9	called	call	VERB
ap-1275	163	10	a	a	DET
ap-1275	163	11	turning	turning	NOUN
ap-1275	163	12	point	point	NOUN
ap-1275	163	13	.	.	PUNCT
ap-1275	164	1	a	a	DET
ap-1275	164	2	(	(	PUNCT
ap-1275	164	3	local	local	ADJ
ap-1275	164	4	)	)	PUNCT
ap-1275	164	5	stokes	stoke	NOUN
ap-1275	164	6	line	line	NOUN
ap-1275	164	7	of	of	ADP
ap-1275	164	8	p	p	NOUN
ap-1275	164	9	(	(	PUNCT
ap-1275	164	10	z	z	NOUN
ap-1275	164	11	)	)	PUNCT
ap-1275	164	12	is	be	AUX
ap-1275	164	13	a	a	DET
ap-1275	164	14	maximal	maximal	ADJ
ap-1275	164	15	segment	segment	NOUN
ap-1275	164	16	of	of	ADP
ap-1275	164	17	the	the	DET
ap-1275	164	18	real	real	ADJ
ap-1275	164	19	analytic	analytic	ADJ
ap-1275	164	20	curve	curve	NOUN
ap-1275	164	21	containing	contain	VERB
ap-1275	164	22	at	at	ADP
ap-1275	164	23	most	most	ADV
ap-1275	164	24	two	two	NUM
ap-1275	164	25	turning	turning	NOUN
ap-1275	164	26	points	point	NOUN
ap-1275	164	27	(	(	PUNCT
ap-1275	164	28	finite	finite	NOUN
ap-1275	164	29	or	or	CCONJ
ap-1275	164	30	infinite	infinite	NOUN
ap-1275	164	31	)	)	PUNCT
ap-1275	164	32	which	which	PRON
ap-1275	164	33	solves	solve	VERB
ap-1275	164	34	the	the	DET
ap-1275	164	35	equation	equation	NOUN
ap-1275	164	36	:	:	PUNCT
ap-1275	164	37	�	�	PROPN
ap-1275	164	38	ξz0(z	ξz0(z	NUM
ap-1275	164	39	)	)	PUNCT
ap-1275	165	1	=	=	SYM
ap-1275	165	2	0	0	NUM
ap-1275	166	1	where	where	SCONJ
ap-1275	166	2	(	(	PUNCT
ap-1275	166	3	2	2	NUM
ap-1275	166	4	)	)	PUNCT
ap-1275	166	5	ξz0(z	ξz0(z	NUM
ap-1275	166	6	)	)	PUNCT
ap-1275	166	7	=	=	SYM
ap-1275	167	1	∫	∫	PROPN
ap-1275	167	2	z	z	PROPN
ap-1275	167	3	z0	z0	PROPN
ap-1275	167	4	√	√	PROPN
ap-1275	167	5	p	p	NOUN
ap-1275	167	6	(	(	PUNCT
ap-1275	167	7	u	u	NOUN
ap-1275	167	8	)	)	PUNCT
ap-1275	167	9	du	du	PROPN
ap-1275	167	10	=	=	SYM
ap-1275	167	11	0	0	PROPN
ap-1275	167	12	,	,	PUNCT
ap-1275	167	13	with	with	ADP
ap-1275	167	14	respect	respect	NOUN
ap-1275	167	15	to	to	ADP
ap-1275	167	16	z	z	NOUN
ap-1275	167	17	,	,	PUNCT
ap-1275	167	18	where	where	SCONJ
ap-1275	167	19	z0	z0	PROPN
ap-1275	167	20	is	be	AUX
ap-1275	167	21	one	one	NUM
ap-1275	167	22	of	of	ADP
ap-1275	167	23	the	the	DET
ap-1275	167	24	turning	turning	NOUN
ap-1275	167	25	points	point	NOUN
ap-1275	167	26	of	of	ADP
ap-1275	167	27	p	p	NOUN
ap-1275	167	28	(	(	PUNCT
ap-1275	167	29	z	z	NOUN
ap-1275	167	30	)	)	PUNCT
ap-1275	167	31	.	.	PUNCT
ap-1275	168	1	the	the	DET
ap-1275	168	2	stokes	stoke	NOUN
ap-1275	168	3	graph	graph	NOUN
ap-1275	168	4	stp	stp	PROPN
ap-1275	168	5	of	of	ADP
ap-1275	168	6	the	the	DET
ap-1275	168	7	polynomial	polynomial	ADJ
ap-1275	168	8	p	p	X
ap-1275	168	9	(	(	PUNCT
ap-1275	168	10	z	z	NOUN
ap-1275	168	11	)	)	PUNCT
ap-1275	168	12	is	be	AUX
ap-1275	168	13	the	the	DET
ap-1275	168	14	union	union	NOUN
ap-1275	168	15	of	of	ADP
ap-1275	168	16	all	all	PRON
ap-1275	168	17	its	its	PRON
ap-1275	168	18	local	local	ADJ
ap-1275	168	19	stokes	stoke	NOUN
ap-1275	168	20	curves	curve	NOUN
ap-1275	168	21	.	.	PUNCT
ap-1275	169	1	a	a	DET
ap-1275	169	2	local	local	ADJ
ap-1275	169	3	stokes	stoke	NOUN
ap-1275	169	4	line	line	NOUN
ap-1275	169	5	connecting	connect	VERB
ap-1275	169	6	two	two	NUM
ap-1275	169	7	finite	finite	ADJ
ap-1275	169	8	turning	turning	NOUN
ap-1275	169	9	points	point	NOUN
ap-1275	169	10	,	,	PUNCT
ap-1275	169	11	i.e.	i.e.	X
ap-1275	169	12	two	two	NUM
ap-1275	169	13	roots	root	NOUN
ap-1275	169	14	of	of	ADP
ap-1275	169	15	p	p	NOUN
ap-1275	169	16	(	(	PUNCT
ap-1275	169	17	z	z	NOUN
ap-1275	169	18	)	)	PUNCT
ap-1275	169	19	is	be	AUX
ap-1275	169	20	called	call	VERB
ap-1275	169	21	short	short	ADJ
ap-1275	169	22	.	.	PUNCT
ap-1275	170	1	(	(	PUNCT
ap-1275	170	2	the	the	DET
ap-1275	170	3	stokes	stokes	PROPN
ap-1275	170	4	graph	graph	PROPN
ap-1275	170	5	st	st	PROPN
ap-1275	170	6	(	(	PUNCT
ap-1275	170	7	p	p	NOUN
ap-1275	170	8	)	)	PUNCT
ap-1275	170	9	of	of	ADP
ap-1275	170	10	a	a	DET
ap-1275	170	11	generic	generic	ADJ
ap-1275	170	12	p	p	NOUN
ap-1275	170	13	(	(	PUNCT
ap-1275	170	14	z	z	NOUN
ap-1275	170	15	)	)	PUNCT
ap-1275	170	16	has	have	VERB
ap-1275	170	17	no	no	DET
ap-1275	170	18	short	short	ADJ
ap-1275	170	19	stokes	stoke	NOUN
ap-1275	170	20	lines	line	NOUN
ap-1275	170	21	.	.	PUNCT
ap-1275	170	22	)	)	PUNCT
ap-1275	171	1	proposition	proposition	NOUN
ap-1275	171	2	6	6	NUM
ap-1275	171	3	for	for	ADP
ap-1275	171	4	a	a	DET
ap-1275	171	5	given	give	VERB
ap-1275	171	6	positive	positive	ADJ
ap-1275	171	7	integer	integer	NOUN
ap-1275	171	8	l	l	NOUN
ap-1275	171	9	the	the	DET
ap-1275	171	10	stokes	stokes	PROPN
ap-1275	171	11	graph	graph	PROPN
ap-1275	171	12	st	st	PROPN
ap-1275	171	13	(	(	PUNCT
ap-1275	171	14	z2l	z2l	PROPN
ap-1275	171	15	−	−	PROPN
ap-1275	171	16	1	1	NUM
ap-1275	171	17	)	)	PUNCT
ap-1275	171	18	consists	consist	VERB
ap-1275	171	19	of	of	ADP
ap-1275	171	20	1	1	NUM
ap-1275	171	21	)	)	PUNCT
ap-1275	171	22	l	l	NOUN
ap-1275	171	23	short	short	ADJ
ap-1275	171	24	stokes	stoke	NOUN
ap-1275	171	25	lines	line	NOUN
ap-1275	171	26	for	for	ADP
ap-1275	171	27	l	l	NOUN
ap-1275	171	28	odd	odd	ADJ
ap-1275	171	29	and	and	CCONJ
ap-1275	171	30	l	l	NOUN
ap-1275	171	31	−	−	PROPN
ap-1275	171	32	1	1	NUM
ap-1275	171	33	short	short	ADJ
ap-1275	171	34	stokes	stoke	NOUN
ap-1275	171	35	lines	line	NOUN
ap-1275	171	36	for	for	ADP
ap-1275	171	37	l	l	NOUN
ap-1275	171	38	even	even	ADV
ap-1275	171	39	connecting	connect	VERB
ap-1275	171	40	all	all	DET
ap-1275	171	41	pairs	pair	NOUN
ap-1275	171	42	of	of	ADP
ap-1275	171	43	the	the	DET
ap-1275	171	44	roots	root	NOUN
ap-1275	171	45	of	of	ADP
ap-1275	171	46	z2l	z2l	PROPN
ap-1275	171	47	−	−	PROPN
ap-1275	171	48	1	1	NUM
ap-1275	171	49	which	which	PRON
ap-1275	171	50	are	be	AUX
ap-1275	171	51	symmetric	symmetric	ADJ
ap-1275	171	52	w.r.t	w.r.t	NOUN
ap-1275	171	53	the	the	DET
ap-1275	171	54	imaginary	imaginary	ADJ
ap-1275	171	55	axis	axis	NOUN
ap-1275	171	56	;	;	PUNCT
ap-1275	171	57	2	2	X
ap-1275	171	58	)	)	PUNCT
ap-1275	171	59	for	for	ADP
ap-1275	171	60	l	l	NOUN
ap-1275	171	61	odd	odd	ADJ
ap-1275	171	62	each	each	DET
ap-1275	171	63	root	root	NOUN
ap-1275	171	64	of	of	ADP
ap-1275	171	65	z2l	z2l	PROPN
ap-1275	171	66	−	−	PROPN
ap-1275	171	67	1	1	NUM
ap-1275	171	68	is	be	AUX
ap-1275	171	69	connected	connect	VERB
ap-1275	171	70	by	by	ADP
ap-1275	171	71	2	2	NUM
ap-1275	171	72	infinite	infinite	ADJ
ap-1275	171	73	stokes	stoke	NOUN
ap-1275	171	74	lines	line	NOUN
ap-1275	171	75	to	to	ADP
ap-1275	171	76	∞.	∞.	PROPN
ap-1275	171	77	more	more	ADV
ap-1275	171	78	exactly	exactly	ADV
ap-1275	171	79	,	,	PUNCT
ap-1275	171	80	the	the	DET
ap-1275	171	81	2	2	NUM
ap-1275	171	82	infinite	infinite	ADJ
ap-1275	171	83	stokes	stoke	NOUN
ap-1275	171	84	lines	line	NOUN
ap-1275	171	85	passing	pass	VERB
ap-1275	171	86	through	through	ADP
ap-1275	171	87	the	the	DET
ap-1275	171	88	root	root	NOUN
ap-1275	171	89	e	e	PROPN
ap-1275	171	90	πik	πik	PROPN
ap-1275	171	91	l	l	PROPN
ap-1275	171	92	,	,	PUNCT
ap-1275	171	93	k	k	PROPN
ap-1275	171	94	=	=	PUNCT
ap-1275	171	95	0	0	PROPN
ap-1275	171	96	,	,	PUNCT
ap-1275	171	97	.	.	PUNCT
ap-1275	171	98	.	.	PUNCT
ap-1275	172	1	.	.	PUNCT
ap-1275	173	1	,	,	PUNCT
ap-1275	173	2	2l	2l	NOUN
ap-1275	173	3	−	−	NOUN
ap-1275	173	4	1	1	NUM
ap-1275	173	5	are	be	AUX
ap-1275	173	6	tangent	tangent	NOUN
ap-1275	173	7	at	at	ADP
ap-1275	173	8	∞	∞	PROPN
ap-1275	173	9	to	to	ADP
ap-1275	173	10	the	the	DET
ap-1275	173	11	stokes	stokes	PROPN
ap-1275	173	12	rays	ray	NOUN
ap-1275	173	13	having	have	VERB
ap-1275	173	14	the	the	DET
ap-1275	173	15	nearest	near	ADJ
ap-1275	173	16	slope	slope	NOUN
ap-1275	173	17	to	to	ADP
ap-1275	173	18	πik	πik	PROPN
ap-1275	173	19	l	l	PROPN
ap-1275	173	20	;	;	PUNCT
ap-1275	173	21	3	3	X
ap-1275	173	22	)	)	PUNCT
ap-1275	173	23	for	for	ADP
ap-1275	173	24	l	l	NOUN
ap-1275	173	25	even	even	ADV
ap-1275	173	26	each	each	DET
ap-1275	173	27	root	root	NOUN
ap-1275	173	28	of	of	ADP
ap-1275	173	29	z2l	z2l	PROPN
ap-1275	173	30	−	−	PROPN
ap-1275	173	31	1	1	NUM
ap-1275	173	32	except	except	SCONJ
ap-1275	173	33	for	for	ADP
ap-1275	173	34	±i	±i	PRON
ap-1275	173	35	is	be	AUX
ap-1275	173	36	connected	connect	VERB
ap-1275	173	37	to	to	ADP
ap-1275	173	38	∞	∞	NUM
ap-1275	173	39	by	by	ADP
ap-1275	173	40	2	2	NUM
ap-1275	173	41	infinite	infinite	ADJ
ap-1275	173	42	stokes	stoke	NOUN
ap-1275	173	43	lines	line	NOUN
ap-1275	173	44	with	with	ADP
ap-1275	173	45	the	the	DET
ap-1275	173	46	same	same	ADJ
ap-1275	173	47	property	property	NOUN
ap-1275	173	48	as	as	ADP
ap-1275	173	49	above	above	ADV
ap-1275	173	50	.	.	PUNCT
ap-1275	174	1	the	the	DET
ap-1275	174	2	roots	root	NOUN
ap-1275	174	3	±i	±i	ADV
ap-1275	174	4	have	have	VERB
ap-1275	174	5	3	3	NUM
ap-1275	174	6	infinite	infinite	ADJ
ap-1275	174	7	stokes	stoke	NOUN
ap-1275	174	8	lines	line	NOUN
ap-1275	174	9	each	each	PRON
ap-1275	174	10	.	.	PUNCT
ap-1275	175	1	theorem	theorem	VERB
ap-1275	175	2	5	5	NUM
ap-1275	175	3	for	for	ADP
ap-1275	175	4	any	any	DET
ap-1275	175	5	monic	monic	ADJ
ap-1275	175	6	polynomial	polynomial	ADJ
ap-1275	175	7	pc(z	pc(z	NOUN
ap-1275	175	8	)	)	PUNCT
ap-1275	175	9	of	of	ADP
ap-1275	175	10	even	even	ADV
ap-1275	175	11	degree	degree	VERB
ap-1275	175	12	the	the	DET
ap-1275	175	13	sequence	sequence	NOUN
ap-1275	175	14	of	of	ADP
ap-1275	175	15	meromorphic	meromorphic	ADJ
ap-1275	175	16	functions	function	NOUN
ap-1275	175	17	{	{	PUNCT
ap-1275	175	18	cn(z	cn(z	NOUN
ap-1275	175	19	)	)	PUNCT
ap-1275	175	20	}	}	PUNCT
ap-1275	176	1	=	=	SYM
ap-1275	176	2	{	{	PUNCT
ap-1275	176	3	ψ′	ψ′	NUM
ap-1275	176	4	n(z	n(z	NOUN
ap-1275	176	5	)	)	PUNCT
ap-1275	176	6	nψn(z	nψn(z	PROPN
ap-1275	176	7	)	)	PUNCT
ap-1275	176	8	}	}	PUNCT
ap-1275	176	9	converges	converge	VERB
ap-1275	176	10	to	to	ADP
ap-1275	176	11	c(z	c(z	NUM
ap-1275	176	12	)	)	PUNCT
ap-1275	176	13	=	=	PUNCT
ap-1275	177	1	−kl	−kl	PROPN
ap-1275	178	1	√	√	PROPN
ap-1275	178	2	z2l	z2l	SYM
ap-1275	178	3	−	−	PROPN
ap-1275	178	4	1	1	NUM
ap-1275	178	5	uniformly	uniformly	ADV
ap-1275	178	6	on	on	ADP
ap-1275	178	7	any	any	DET
ap-1275	178	8	compact	compact	ADJ
ap-1275	178	9	set	set	NOUN
ap-1275	178	10	lying	lie	VERB
ap-1275	178	11	in	in	ADP
ap-1275	178	12	the	the	DET
ap-1275	178	13	domain	domain	NOUN
ap-1275	178	14	c	c	PROPN
ap-1275	178	15	\ucl	\ucl	PROPN
ap-1275	178	16	,	,	PUNCT
ap-1275	178	17	where	where	SCONJ
ap-1275	178	18	kl	kl	PROPN
ap-1275	178	19	=	=	PUNCT
ap-1275	178	20	√	√	PROPN
ap-1275	178	21	πγ	πγ	PROPN
ap-1275	178	22	(	(	PUNCT
ap-1275	178	23	3l+1	3l+1	PROPN
ap-1275	178	24	2l	2l	NUM
ap-1275	178	25	)	)	PUNCT
ap-1275	178	26	γ	γ	PROPN
ap-1275	178	27	(	(	PUNCT
ap-1275	178	28	2l+1	2l+1	NOUN
ap-1275	178	29	2l	2l	NUM
ap-1275	178	30	)	)	PUNCT
ap-1275	178	31	.	.	PUNCT
ap-1275	179	1	(	(	PUNCT
ap-1275	179	2	here	here	ADV
ap-1275	179	3	by	by	ADP
ap-1275	179	4	−	−	PROPN
ap-1275	179	5	√	√	PROPN
ap-1275	179	6	z2l	z2l	SYM
ap-1275	179	7	−	−	NOUN
ap-1275	179	8	1	1	NUM
ap-1275	180	1	we	we	PRON
ap-1275	180	2	mean	mean	VERB
ap-1275	180	3	the	the	DET
ap-1275	180	4	branch	branch	NOUN
ap-1275	180	5	which	which	PRON
ap-1275	180	6	is	be	AUX
ap-1275	180	7	negative	negative	ADJ
ap-1275	180	8	for	for	ADP
ap-1275	180	9	positive	positive	ADJ
ap-1275	180	10	z	z	NOUN
ap-1275	180	11	>	>	X
ap-1275	180	12	1	1	X
ap-1275	180	13	.	.	PUNCT
ap-1275	180	14	also	also	ADV
ap-1275	180	15	ucl	ucl	PROPN
ap-1275	180	16	is	be	AUX
ap-1275	180	17	a	a	DET
ap-1275	180	18	certain	certain	ADJ
ap-1275	180	19	subset	subset	NOUN
ap-1275	180	20	of	of	ADP
ap-1275	180	21	local	local	ADJ
ap-1275	180	22	stokes	stoke	NOUN
ap-1275	180	23	lines	line	NOUN
ap-1275	180	24	marked	mark	VERB
ap-1275	180	25	by	by	ADP
ap-1275	180	26	bold	bold	ADJ
ap-1275	180	27	on	on	ADP
ap-1275	180	28	fig	fig	NOUN
ap-1275	180	29	.	.	PUNCT
ap-1275	181	1	8	8	NUM
ap-1275	181	2	.	.	PUNCT
ap-1275	181	3	)	)	PUNCT
ap-1275	181	4	�	�	PROPN
ap-1275	181	5	�	�	PROPN
ap-1275	181	6	�	�	PROPN
ap-1275	181	7	�	�	PROPN
ap-1275	181	8	�	�	PROPN
ap-1275	181	9	�	�	PROPN
ap-1275	181	10	fig	fig	NOUN
ap-1275	181	11	.	.	PUNCT
ap-1275	182	1	8	8	NUM
ap-1275	182	2	:	:	PUNCT
ap-1275	182	3	stokes	stoke	VERB
ap-1275	182	4	lines	line	NOUN
ap-1275	182	5	of	of	ADP
ap-1275	182	6	z2l	z2l	PROPN
ap-1275	182	7	−	−	PROPN
ap-1275	182	8	1	1	NUM
ap-1275	182	9	for	for	ADP
ap-1275	182	10	l	l	NOUN
ap-1275	182	11	=	=	SYM
ap-1275	182	12	1	1	NUM
ap-1275	182	13	,	,	PUNCT
ap-1275	182	14	2	2	NUM
ap-1275	182	15	,	,	PUNCT
ap-1275	182	16	3	3	NUM
ap-1275	182	17	82	82	NUM
ap-1275	182	18	acta	acta	PROPN
ap-1275	182	19	polytechnica	polytechnica	PROPN
ap-1275	182	20	vol	vol	NOUN
ap-1275	182	21	.	.	PROPN
ap-1275	183	1	50	50	NUM
ap-1275	183	2	no	no	NOUN
ap-1275	183	3	.	.	PUNCT
ap-1275	184	1	5/2010	5/2010	NUM
ap-1275	184	2	7	7	NUM
ap-1275	184	3	finite	finite	NOUN
ap-1275	184	4	recurrences	recurrence	NOUN
ap-1275	184	5	this	this	DET
ap-1275	184	6	section	section	NOUN
ap-1275	184	7	is	be	AUX
ap-1275	184	8	based	base	VERB
ap-1275	184	9	on	on	ADP
ap-1275	184	10	[	[	X
ap-1275	184	11	4	4	NUM
ap-1275	184	12	]	]	PUNCT
ap-1275	184	13	.	.	PUNCT
ap-1275	184	14	consider	consider	VERB
ap-1275	184	15	a	a	DET
ap-1275	184	16	finite	finite	ADJ
ap-1275	184	17	recurrence	recurrence	NOUN
ap-1275	184	18	of	of	ADP
ap-1275	184	19	length	length	NOUN
ap-1275	184	20	(	(	PUNCT
ap-1275	184	21	k	k	NOUN
ap-1275	184	22	+	+	PROPN
ap-1275	184	23	1	1	X
ap-1275	184	24	)	)	PUNCT
ap-1275	184	25	given	give	VERB
ap-1275	184	26	by	by	ADP
ap-1275	184	27	pn+1(z	pn+1(z	PROPN
ap-1275	184	28	)	)	PUNCT
ap-1275	184	29	=	=	SYM
ap-1275	184	30	q1(z)pn(z	q1(z)pn(z	NUM
ap-1275	184	31	)	)	PUNCT
ap-1275	185	1	+	+	CCONJ
ap-1275	185	2	.	.	PUNCT
ap-1275	185	3	.	.	PUNCT
ap-1275	186	1	.+qk(z)pn−k+1(z	.+qk(z)pn−k+1(z	NOUN
ap-1275	186	2	)	)	PUNCT
ap-1275	186	3	,	,	PUNCT
ap-1275	186	4	with	with	ADP
ap-1275	186	5	polynomial	polynomial	ADJ
ap-1275	186	6	or	or	CCONJ
ap-1275	186	7	rational	rational	ADJ
ap-1275	186	8	coefficients	coefficient	NOUN
ap-1275	186	9	{	{	PUNCT
ap-1275	186	10	q1(z	q1(z	PROPN
ap-1275	186	11	)	)	PUNCT
ap-1275	186	12	,	,	PUNCT
ap-1275	186	13	.	.	PUNCT
ap-1275	186	14	.	.	PUNCT
ap-1275	187	1	.	.	PUNCT
ap-1275	188	1	,	,	PUNCT
ap-1275	188	2	qk(z	qk(z	ADV
ap-1275	188	3	)	)	PUNCT
ap-1275	188	4	}	}	PUNCT
ap-1275	188	5	uniquely	uniquely	ADV
ap-1275	188	6	determined	determine	VERB
ap-1275	188	7	by	by	ADP
ap-1275	188	8	the	the	DET
ap-1275	188	9	initial	initial	ADJ
ap-1275	188	10	k	k	NOUN
ap-1275	188	11	-	-	NOUN
ap-1275	188	12	tuple	tuple	ADJ
ap-1275	188	13	{	{	PUNCT
ap-1275	188	14	p0(z	p0(z	NUM
ap-1275	188	15	)	)	PUNCT
ap-1275	188	16	,	,	PUNCT
ap-1275	188	17	.	.	PUNCT
ap-1275	188	18	.	.	PUNCT
ap-1275	189	1	.	.	PUNCT
ap-1275	190	1	,	,	PUNCT
ap-1275	190	2	pk(z	pk(z	NUM
ap-1275	190	3	)	)	PUNCT
ap-1275	190	4	}	}	PUNCT
ap-1275	190	5	.	.	PUNCT
ap-1275	191	1	theorem	theorem	NOUN
ap-1275	191	2	6	6	NUM
ap-1275	191	3	there	there	ADV
ap-1275	191	4	exists	exist	VERB
ap-1275	191	5	a	a	DET
ap-1275	191	6	finite	finite	NOUN
ap-1275	191	7	subset	subset	NOUN
ap-1275	191	8	θ	θ	X
ap-1275	191	9	⊂	⊂	PROPN
ap-1275	191	10	c	c	X
ap-1275	192	1	depending	depend	VERB
ap-1275	192	2	on	on	ADP
ap-1275	192	3	the	the	DET
ap-1275	192	4	initial	initial	ADJ
ap-1275	192	5	k	k	NOUN
ap-1275	192	6	-	-	NOUN
ap-1275	192	7	tuple	tuple	NOUN
ap-1275	192	8	and	and	CCONJ
ap-1275	192	9	a	a	DET
ap-1275	192	10	curve	curve	NOUN
ap-1275	192	11	σ	σ	NOUN
ap-1275	192	12	depending	depend	VERB
ap-1275	192	13	on	on	ADP
ap-1275	192	14	the	the	DET
ap-1275	192	15	recurrence	recurrence	NOUN
ap-1275	192	16	such	such	ADJ
ap-1275	192	17	that	that	SCONJ
ap-1275	192	18	the	the	DET
ap-1275	192	19	asymptotic	asymptotic	ADJ
ap-1275	192	20	ratio	ratio	NOUN
ap-1275	192	21	ψ(z	ψ(z	PROPN
ap-1275	192	22	)	)	PUNCT
ap-1275	192	23	=	=	PROPN
ap-1275	192	24	lim	lim	PROPN
ap-1275	192	25	n→∞	n→∞	NUM
ap-1275	192	26	pn+1(z	pn+1(z	PROPN
ap-1275	192	27	)	)	PUNCT
ap-1275	192	28	pn(z	pn(z	PUNCT
ap-1275	192	29	)	)	PUNCT
ap-1275	192	30	exists	exist	VERB
ap-1275	192	31	and	and	CCONJ
ap-1275	192	32	satisfies	satisfy	VERB
ap-1275	192	33	the	the	DET
ap-1275	192	34	symbol	symbol	NOUN
ap-1275	192	35	equation	equation	NOUN
ap-1275	192	36	ψk(z	ψk(z	PUNCT
ap-1275	192	37	)	)	PUNCT
ap-1275	192	38	=	=	SYM
ap-1275	192	39	q1(z)ψk−1(z	q1(z)ψk−1(z	NOUN
ap-1275	192	40	)	)	PUNCT
ap-1275	192	41	+	+	CCONJ
ap-1275	192	42	.	.	PUNCT
ap-1275	192	43	.	.	PUNCT
ap-1275	193	1	.+qk(z	.+qk(z	PROPN
ap-1275	193	2	)	)	PUNCT
ap-1275	194	1	(	(	PUNCT
ap-1275	194	2	∗	∗	NOUN
ap-1275	194	3	)	)	PUNCT
ap-1275	194	4	in	in	ADP
ap-1275	194	5	c	c	NOUN
ap-1275	194	6	\	\	PROPN
ap-1275	194	7	(	(	PUNCT
ap-1275	194	8	σ	σ	PROPN
ap-1275	194	9	∪	∪	X
ap-1275	194	10	θ	θ	PROPN
ap-1275	194	11	)	)	PUNCT
ap-1275	194	12	.	.	PUNCT
ap-1275	195	1	here	here	ADV
ap-1275	195	2	σ	σ	PROPN
ap-1275	195	3	is	be	AUX
ap-1275	195	4	the	the	DET
ap-1275	195	5	so	so	ADV
ap-1275	195	6	-	-	PUNCT
ap-1275	195	7	called	call	VERB
ap-1275	195	8	stokes	stoke	NOUN
ap-1275	195	9	discriminant	discriminant	NOUN
ap-1275	195	10	of	of	ADP
ap-1275	195	11	(	(	PUNCT
ap-1275	195	12	∗	∗	NOUN
ap-1275	195	13	)	)	PUNCT
ap-1275	195	14	which	which	PRON
ap-1275	195	15	is	be	AUX
ap-1275	195	16	the	the	DET
ap-1275	195	17	set	set	NOUN
ap-1275	195	18	of	of	ADP
ap-1275	195	19	all	all	DET
ap-1275	195	20	z	z	NOUN
ap-1275	195	21	for	for	ADP
ap-1275	195	22	which	which	PRON
ap-1275	195	23	the	the	DET
ap-1275	195	24	equation	equation	NOUN
ap-1275	195	25	(	(	PUNCT
ap-1275	195	26	∗	∗	NOUN
ap-1275	195	27	)	)	PUNCT
ap-1275	195	28	has	have	VERB
ap-1275	195	29	at	at	ADP
ap-1275	195	30	most	most	ADV
ap-1275	195	31	two	two	NUM
ap-1275	195	32	roots	root	NOUN
ap-1275	195	33	with	with	ADP
ap-1275	195	34	the	the	DET
ap-1275	195	35	same	same	ADJ
ap-1275	195	36	and	and	CCONJ
ap-1275	195	37	maximal	maximal	ADJ
ap-1275	195	38	absolute	absolute	ADJ
ap-1275	195	39	value	value	NOUN
ap-1275	195	40	.	.	PUNCT
ap-1275	196	1	-3	-3	INTJ
ap-1275	197	1	-2	-2	INTJ
ap-1275	198	1	-1	-1	SYM
ap-1275	198	2	0	0	NUM
ap-1275	198	3	1	1	NUM
ap-1275	198	4	-3	-3	INTJ
ap-1275	198	5	-2	-2	INTJ
ap-1275	198	6	-1	-1	SYM
ap-1275	198	7	0	0	NUM
ap-1275	198	8	1	1	NUM
ap-1275	198	9	2	2	NUM
ap-1275	198	10	fig	fig	NOUN
ap-1275	198	11	.	.	PUNCT
ap-1275	199	1	9	9	NUM
ap-1275	199	2	:	:	PUNCT
ap-1275	199	3	zeros	zero	NOUN
ap-1275	199	4	of	of	ADP
ap-1275	199	5	p31(z	p31(z	NOUN
ap-1275	199	6	)	)	PUNCT
ap-1275	199	7	satisfying	satisfy	VERB
ap-1275	199	8	the	the	DET
ap-1275	199	9	recurrence	recurrence	NOUN
ap-1275	199	10	relation	relation	NOUN
ap-1275	199	11	(	(	PUNCT
ap-1275	199	12	z+1)pn(z	z+1)pn(z	NUM
ap-1275	199	13	)	)	PUNCT
ap-1275	199	14	=	=	PUNCT
ap-1275	200	1	(	(	PUNCT
ap-1275	200	2	z	z	NOUN
ap-1275	200	3	2	2	NUM
ap-1275	200	4	+	+	NOUN
ap-1275	200	5	1)pn−1(z	1)pn−1(z	NUM
ap-1275	200	6	)	)	PUNCT
ap-1275	201	1	+	+	CCONJ
ap-1275	201	2	(	(	PUNCT
ap-1275	201	3	z	z	NOUN
ap-1275	201	4	−	−	PROPN
ap-1275	201	5	5i)pn−2(z	5i)pn−2(z	NUM
ap-1275	201	6	)	)	PUNCT
ap-1275	202	1	+	+	CCONJ
ap-1275	202	2	(	(	PUNCT
ap-1275	202	3	z	z	NOUN
ap-1275	202	4	3−	3−	NUM
ap-1275	202	5	1−	1−	NUM
ap-1275	202	6	i)pn−3(z	i)pn−3(z	NOUN
ap-1275	202	7	)	)	PUNCT
ap-1275	202	8	acknowledgement	acknowledgement	NOUN
ap-1275	202	9	i	i	PRON
ap-1275	202	10	want	want	VERB
ap-1275	202	11	to	to	PART
ap-1275	202	12	thank	thank	VERB
ap-1275	202	13	my	my	PRON
ap-1275	202	14	coauthors	coauthor	NOUN
ap-1275	202	15	t.	t.	PROPN
ap-1275	202	16	bergkvist	bergkvist	NOUN
ap-1275	202	17	,	,	PUNCT
ap-1275	202	18	j.	j.	PROPN
ap-1275	202	19	borcea	borcea	PROPN
ap-1275	202	20	,	,	PUNCT
ap-1275	202	21	r.	r.	PROPN
ap-1275	202	22	bøgvad	bøgvad	PROPN
ap-1275	202	23	,	,	PUNCT
ap-1275	202	24	a.	a.	NOUN
ap-1275	202	25	eremenko	eremenko	PROPN
ap-1275	202	26	,	,	PUNCT
ap-1275	202	27	a.	a.	NOUN
ap-1275	202	28	gabrielov	gabrielov	PROPN
ap-1275	202	29	,	,	PUNCT
ap-1275	202	30	g.	g.	PROPN
ap-1275	202	31	masson	masson	PROPN
ap-1275	202	32	,	,	PUNCT
ap-1275	202	33	h.	h.	PROPN
ap-1275	202	34	rullg̊ard	rullg̊ard	PROPN
ap-1275	202	35	for	for	ADP
ap-1275	202	36	the	the	DET
ap-1275	202	37	pleasure	pleasure	NOUN
ap-1275	202	38	of	of	ADP
ap-1275	202	39	working	work	VERB
ap-1275	202	40	with	with	ADP
ap-1275	202	41	them	they	PRON
ap-1275	202	42	and	and	CCONJ
ap-1275	202	43	for	for	ADP
ap-1275	202	44	the	the	DET
ap-1275	202	45	numerous	numerous	ADJ
ap-1275	202	46	insights	insight	NOUN
ap-1275	202	47	and	and	CCONJ
ap-1275	202	48	results	result	NOUN
ap-1275	202	49	we	we	PRON
ap-1275	202	50	obtained	obtain	VERB
ap-1275	202	51	together	together	ADV
ap-1275	202	52	.	.	PUNCT
ap-1275	203	1	i	i	PRON
ap-1275	203	2	want	want	VERB
ap-1275	203	3	to	to	PART
ap-1275	203	4	thank	thank	VERB
ap-1275	203	5	the	the	DET
ap-1275	203	6	organizers	organizer	NOUN
ap-1275	203	7	of	of	ADP
ap-1275	203	8	the	the	DET
ap-1275	203	9	miniconference	miniconference	NOUN
ap-1275	203	10	‘	'	PUNCT
ap-1275	203	11	analytic	analytic	ADJ
ap-1275	203	12	and	and	CCONJ
ap-1275	203	13	algebraic	algebraic	ADJ
ap-1275	203	14	methods	method	NOUN
ap-1275	203	15	in	in	ADP
ap-1275	203	16	quantum	quantum	ADJ
ap-1275	203	17	mechanics	mechanic	NOUN
ap-1275	203	18	,	,	PUNCT
ap-1275	203	19	v	v	NOUN
ap-1275	203	20	’	'	PUNCT
ap-1275	203	21	for	for	ADP
ap-1275	203	22	the	the	DET
ap-1275	203	23	financial	financial	ADJ
ap-1275	203	24	support	support	NOUN
ap-1275	203	25	and	and	CCONJ
ap-1275	203	26	a	a	DET
ap-1275	203	27	great	great	ADJ
ap-1275	203	28	pleasure	pleasure	NOUN
ap-1275	203	29	of	of	ADP
ap-1275	203	30	visiting	visit	VERB
ap-1275	203	31	prague	prague	NOUN
ap-1275	203	32	in	in	ADP
ap-1275	203	33	may	may	PROPN
ap-1275	203	34	2009	2009	NUM
ap-1275	203	35	,	,	PUNCT
ap-1275	203	36	where	where	SCONJ
ap-1275	203	37	these	these	DET
ap-1275	203	38	results	result	NOUN
ap-1275	203	39	were	be	AUX
ap-1275	203	40	presented	present	VERB
ap-1275	203	41	.	.	PUNCT
ap-1275	204	1	references	reference	NOUN
ap-1275	204	2	[	[	X
ap-1275	204	3	1	1	NUM
ap-1275	204	4	]	]	X
ap-1275	204	5	bergkvist	bergkvist	NOUN
ap-1275	204	6	,	,	PUNCT
ap-1275	204	7	t.	t.	PROPN
ap-1275	204	8	:	:	PUNCT
ap-1275	204	9	on	on	ADP
ap-1275	204	10	asymptotics	asymptotic	NOUN
ap-1275	204	11	of	of	ADP
ap-1275	204	12	polynomial	polynomial	ADJ
ap-1275	204	13	eigenfunctions	eigenfunction	NOUN
ap-1275	204	14	for	for	ADP
ap-1275	204	15	exactly	exactly	ADV
ap-1275	204	16	-	-	PUNCT
ap-1275	204	17	solvable	solvable	ADJ
ap-1275	204	18	differential	differential	NOUN
ap-1275	204	19	operators	operator	NOUN
ap-1275	204	20	,	,	PUNCT
ap-1275	204	21	j.	j.	PROPN
ap-1275	204	22	approx	approx	PROPN
ap-1275	204	23	.	.	PUNCT
ap-1275	205	1	theory	theory	NOUN
ap-1275	205	2	149(2	149(2	NUM
ap-1275	205	3	)	)	PUNCT
ap-1275	205	4	,	,	PUNCT
ap-1275	205	5	(	(	PUNCT
ap-1275	205	6	2007	2007	NUM
ap-1275	205	7	)	)	PUNCT
ap-1275	205	8	,	,	PUNCT
ap-1275	205	9	151–187	151–187	NUM
ap-1275	205	10	.	.	PUNCT
ap-1275	206	1	[	[	X
ap-1275	206	2	2	2	NUM
ap-1275	206	3	]	]	X
ap-1275	206	4	berqkvist	berqkvist	NOUN
ap-1275	206	5	,	,	PUNCT
ap-1275	206	6	t.	t.	PROPN
ap-1275	206	7	,	,	PUNCT
ap-1275	206	8	rullg̊ard	rullg̊ard	NOUN
ap-1275	206	9	,	,	PUNCT
ap-1275	206	10	h.	h.	PROPN
ap-1275	206	11	:	:	PUNCT
ap-1275	206	12	on	on	ADP
ap-1275	206	13	polynomial	polynomial	ADJ
ap-1275	206	14	eigenfunctions	eigenfunction	NOUN
ap-1275	206	15	for	for	ADP
ap-1275	206	16	a	a	DET
ap-1275	206	17	class	class	NOUN
ap-1275	206	18	of	of	ADP
ap-1275	206	19	differential	differential	ADJ
ap-1275	206	20	operators	operator	NOUN
ap-1275	206	21	,	,	PUNCT
ap-1275	206	22	math	math	NOUN
ap-1275	206	23	.	.	PUNCT
ap-1275	207	1	res	re	NOUN
ap-1275	207	2	.	.	PUNCT
ap-1275	208	1	lett	lett	PROPN
ap-1275	208	2	.	.	PROPN
ap-1275	208	3	,	,	PUNCT
ap-1275	208	4	9	9	NUM
ap-1275	208	5	(	(	PUNCT
ap-1275	208	6	2002	2002	NUM
ap-1275	208	7	)	)	PUNCT
ap-1275	208	8	,	,	PUNCT
ap-1275	208	9	153–171	153–171	NUM
ap-1275	208	10	.	.	PUNCT
ap-1275	209	1	[	[	X
ap-1275	209	2	3	3	NUM
ap-1275	209	3	]	]	X
ap-1275	209	4	berqkvist	berqkvist	NOUN
ap-1275	209	5	,	,	PUNCT
ap-1275	209	6	t.	t.	PROPN
ap-1275	209	7	,	,	PUNCT
ap-1275	209	8	rullg̊ard	rullg̊ard	NOUN
ap-1275	209	9	,	,	PUNCT
ap-1275	209	10	h.	h.	PROPN
ap-1275	209	11	,	,	PUNCT
ap-1275	209	12	shapiro	shapiro	PROPN
ap-1275	209	13	,	,	PUNCT
ap-1275	209	14	b.	b.	PROPN
ap-1275	209	15	:	:	PUNCT
ap-1275	209	16	on	on	ADP
ap-1275	209	17	bochner	bochner	NOUN
ap-1275	209	18	-	-	PUNCT
ap-1275	209	19	krall	krall	NOUN
ap-1275	209	20	orthogonal	orthogonal	ADJ
ap-1275	209	21	polynomial	polynomial	ADJ
ap-1275	209	22	systems	system	NOUN
ap-1275	209	23	,	,	PUNCT
ap-1275	209	24	math	math	NOUN
ap-1275	209	25	.	.	PUNCT
ap-1275	210	1	scand	scand	PROPN
ap-1275	210	2	.	.	PROPN
ap-1275	210	3	,	,	PUNCT
ap-1275	210	4	94	94	NUM
ap-1275	210	5	(	(	PUNCT
ap-1275	210	6	2004	2004	NUM
ap-1275	210	7	)	)	PUNCT
ap-1275	210	8	,	,	PUNCT
ap-1275	210	9	148–154	148–154	NUM
ap-1275	210	10	.	.	PUNCT
ap-1275	211	1	[	[	X
ap-1275	211	2	4	4	NUM
ap-1275	211	3	]	]	X
ap-1275	211	4	borcea	borcea	PROPN
ap-1275	211	5	,	,	PUNCT
ap-1275	211	6	j.	j.	PROPN
ap-1275	211	7	,	,	PUNCT
ap-1275	211	8	bøgvad	bøgvad	PROPN
ap-1275	211	9	,	,	PUNCT
ap-1275	211	10	r.	r.	PROPN
ap-1275	211	11	,	,	PUNCT
ap-1275	211	12	shapiro	shapiro	PROPN
ap-1275	211	13	,	,	PUNCT
ap-1275	211	14	b.	b.	PROPN
ap-1275	211	15	:	:	PUNCT
ap-1275	211	16	on	on	ADP
ap-1275	211	17	rational	rational	ADJ
ap-1275	211	18	approximation	approximation	NOUN
ap-1275	211	19	of	of	ADP
ap-1275	211	20	algebraic	algebraic	ADJ
ap-1275	211	21	functions	function	NOUN
ap-1275	211	22	,	,	PUNCT
ap-1275	211	23	adv	adv	PROPN
ap-1275	211	24	.	.	PUNCT
ap-1275	211	25	math	math	NOUN
ap-1275	211	26	.	.	PUNCT
ap-1275	212	1	204	204	NUM
ap-1275	212	2	(	(	PUNCT
ap-1275	212	3	2006	2006	NUM
ap-1275	212	4	)	)	PUNCT
ap-1275	212	5	,	,	PUNCT
ap-1275	212	6	448–480	448–480	NUM
ap-1275	212	7	.	.	PUNCT
ap-1275	213	1	[	[	X
ap-1275	213	2	5	5	NUM
ap-1275	213	3	]	]	X
ap-1275	213	4	borcea	borcea	NOUN
ap-1275	213	5	,	,	PUNCT
ap-1275	213	6	j.	j.	PROPN
ap-1275	213	7	,	,	PUNCT
ap-1275	213	8	shapiro	shapiro	PROPN
ap-1275	213	9	,	,	PUNCT
ap-1275	213	10	b.	b.	PROPN
ap-1275	213	11	:	:	PUNCT
ap-1275	213	12	root	root	NOUN
ap-1275	213	13	asymptotics	asymptotic	NOUN
ap-1275	213	14	of	of	ADP
ap-1275	213	15	spectral	spectral	ADJ
ap-1275	213	16	polynomials	polynomial	NOUN
ap-1275	213	17	for	for	ADP
ap-1275	213	18	the	the	DET
ap-1275	213	19	lamé	lamé	NOUN
ap-1275	213	20	operator	operator	NOUN
ap-1275	213	21	,	,	PUNCT
ap-1275	213	22	comm	comm	NOUN
ap-1275	213	23	.	.	PUNCT
ap-1275	214	1	math	math	NOUN
ap-1275	214	2	.	.	PUNCT
ap-1275	215	1	phys	phy	NOUN
ap-1275	215	2	,	,	PUNCT
ap-1275	215	3	282	282	NUM
ap-1275	215	4	(	(	PUNCT
ap-1275	215	5	2008	2008	NUM
ap-1275	215	6	)	)	PUNCT
ap-1275	215	7	,	,	PUNCT
ap-1275	215	8	323–337	323–337	NUM
ap-1275	215	9	.	.	PUNCT
ap-1275	216	1	[	[	X
ap-1275	216	2	6	6	NUM
ap-1275	216	3	]	]	PUNCT
ap-1275	216	4	borcea	borcea	PROPN
ap-1275	216	5	,	,	PUNCT
ap-1275	216	6	j.	j.	PROPN
ap-1275	216	7	,	,	PUNCT
ap-1275	216	8	bøgvad	bøgvad	PROPN
ap-1275	216	9	,	,	PUNCT
ap-1275	216	10	r.	r.	PROPN
ap-1275	216	11	,	,	PUNCT
ap-1275	216	12	shapiro	shapiro	PROPN
ap-1275	216	13	,	,	PUNCT
ap-1275	216	14	b.	b.	PROPN
ap-1275	216	15	:	:	PUNCT
ap-1275	216	16	homogenized	homogenize	VERB
ap-1275	216	17	spectral	spectral	ADJ
ap-1275	216	18	pencils	pencil	NOUN
ap-1275	216	19	for	for	ADP
ap-1275	216	20	exactly	exactly	ADV
ap-1275	216	21	solvable	solvable	ADJ
ap-1275	216	22	operators	operator	NOUN
ap-1275	216	23	:	:	PUNCT
ap-1275	216	24	asymptotics	asymptotic	NOUN
ap-1275	216	25	of	of	ADP
ap-1275	216	26	polynomial	polynomial	ADJ
ap-1275	216	27	eigenfunctions	eigenfunction	NOUN
ap-1275	216	28	,	,	PUNCT
ap-1275	216	29	publ	publ	PROPN
ap-1275	216	30	.	.	PUNCT
ap-1275	217	1	rims	rims	PROPN
ap-1275	217	2	,	,	PUNCT
ap-1275	217	3	45	45	NUM
ap-1275	217	4	(	(	PUNCT
ap-1275	217	5	2009	2009	NUM
ap-1275	217	6	)	)	PUNCT
ap-1275	217	7	,	,	PUNCT
ap-1275	217	8	525–568	525–568	NUM
ap-1275	217	9	.	.	PUNCT
ap-1275	218	1	[	[	X
ap-1275	218	2	7	7	NUM
ap-1275	218	3	]	]	X
ap-1275	218	4	gabrielov	gabrielov	PROPN
ap-1275	218	5	,	,	PUNCT
ap-1275	218	6	a.	a.	NOUN
ap-1275	218	7	,	,	PUNCT
ap-1275	218	8	eremenko	eremenko	PROPN
ap-1275	218	9	,	,	PUNCT
ap-1275	218	10	a.	a.	PROPN
ap-1275	218	11	,	,	PUNCT
ap-1275	218	12	shapiro	shapiro	PROPN
ap-1275	218	13	,	,	PUNCT
ap-1275	218	14	b.	b.	PROPN
ap-1275	218	15	:	:	PUNCT
ap-1275	218	16	zeros	zero	NOUN
ap-1275	218	17	of	of	ADP
ap-1275	218	18	eigenfunctions	eigenfunction	NOUN
ap-1275	218	19	of	of	ADP
ap-1275	218	20	some	some	DET
ap-1275	218	21	anharmonic	anharmonic	ADJ
ap-1275	218	22	oscillators	oscillator	NOUN
ap-1275	218	23	,	,	PUNCT
ap-1275	218	24	annales	annales	X
ap-1275	218	25	de	de	X
ap-1275	218	26	l’institut	l’institut	X
ap-1275	218	27	fourier	fourier	NOUN
ap-1275	218	28	,	,	PUNCT
ap-1275	218	29	58(2	58(2	NUM
ap-1275	218	30	)	)	PUNCT
ap-1275	218	31	(	(	PUNCT
ap-1275	218	32	2008	2008	NUM
ap-1275	218	33	)	)	PUNCT
ap-1275	218	34	,	,	PUNCT
ap-1275	218	35	603–624	603–624	NUM
ap-1275	218	36	.	.	PUNCT
ap-1275	219	1	[	[	X
ap-1275	219	2	8	8	NUM
ap-1275	219	3	]	]	X
ap-1275	219	4	gabrielov	gabrielov	PROPN
ap-1275	219	5	,	,	PUNCT
ap-1275	219	6	a.	a.	NOUN
ap-1275	219	7	,	,	PUNCT
ap-1275	219	8	eremenko	eremenko	PROPN
ap-1275	219	9	,	,	PUNCT
ap-1275	219	10	a.	a.	PROPN
ap-1275	219	11	,	,	PUNCT
ap-1275	219	12	shapiro	shapiro	PROPN
ap-1275	219	13	,	,	PUNCT
ap-1275	219	14	b.	b.	PROPN
ap-1275	219	15	:	:	PUNCT
ap-1275	219	16	high	high	ADJ
ap-1275	219	17	energy	energy	NOUN
ap-1275	219	18	eigenfunctions	eigenfunction	NOUN
ap-1275	219	19	of	of	ADP
ap-1275	219	20	one	one	NUM
ap-1275	219	21	-	-	PUNCT
ap-1275	219	22	dimensional	dimensional	ADJ
ap-1275	219	23	schrödinger	schrödinger	NOUN
ap-1275	219	24	operators	operator	NOUN
ap-1275	219	25	with	with	ADP
ap-1275	219	26	polynomial	polynomial	ADJ
ap-1275	219	27	potentials	potential	NOUN
ap-1275	219	28	,	,	PUNCT
ap-1275	219	29	comput	comput	NOUN
ap-1275	219	30	.	.	PUNCT
ap-1275	220	1	methods	method	NOUN
ap-1275	220	2	funct	funct	VERB
ap-1275	220	3	.	.	PUNCT
ap-1275	221	1	theory	theory	NOUN
ap-1275	221	2	,	,	PUNCT
ap-1275	221	3	8(2	8(2	NUM
ap-1275	221	4	)	)	PUNCT
ap-1275	221	5	(	(	PUNCT
ap-1275	221	6	2008	2008	NUM
ap-1275	221	7	)	)	PUNCT
ap-1275	221	8	,	,	PUNCT
ap-1275	222	1	513–529	513–529	NUM
ap-1275	222	2	.	.	PUNCT
ap-1275	223	1	[	[	X
ap-1275	223	2	9	9	NUM
ap-1275	223	3	]	]	SYM
ap-1275	223	4	holst	holst	NOUN
ap-1275	223	5	,	,	PUNCT
ap-1275	223	6	t.	t.	PROPN
ap-1275	223	7	,	,	PUNCT
ap-1275	223	8	shapiro	shapiro	PROPN
ap-1275	223	9	,	,	PUNCT
ap-1275	223	10	b.	b.	PROPN
ap-1275	223	11	:	:	PUNCT
ap-1275	223	12	on	on	ADP
ap-1275	223	13	higher	high	ADJ
ap-1275	223	14	heine	heine	PROPN
ap-1275	223	15	-	-	PUNCT
ap-1275	223	16	stieltjes	stieltjes	NOUN
ap-1275	223	17	polynomials	polynomial	NOUN
ap-1275	223	18	,	,	PUNCT
ap-1275	223	19	to	to	PART
ap-1275	223	20	appear	appear	VERB
ap-1275	223	21	in	in	ADP
ap-1275	223	22	isr	isr	PROPN
ap-1275	223	23	.	.	PUNCT
ap-1275	224	1	j.	j.	PROPN
ap-1275	224	2	math	math	PROPN
ap-1275	224	3	.	.	PUNCT
ap-1275	225	1	[	[	X
ap-1275	225	2	10	10	NUM
ap-1275	225	3	]	]	X
ap-1275	225	4	masson	masson	PROPN
ap-1275	225	5	,	,	PUNCT
ap-1275	225	6	g.	g.	PROPN
ap-1275	225	7	,	,	PUNCT
ap-1275	225	8	shapiro	shapiro	PROPN
ap-1275	225	9	,	,	PUNCT
ap-1275	225	10	b.	b.	PROPN
ap-1275	225	11	:	:	PUNCT
ap-1275	225	12	on	on	ADP
ap-1275	225	13	polynomial	polynomial	ADJ
ap-1275	225	14	eigenfunctions	eigenfunction	NOUN
ap-1275	225	15	of	of	ADP
ap-1275	225	16	a	a	DET
ap-1275	225	17	hypergeometric	hypergeometric	ADJ
ap-1275	225	18	-	-	PUNCT
ap-1275	225	19	type	type	NOUN
ap-1275	225	20	operator	operator	NOUN
ap-1275	225	21	,	,	PUNCT
ap-1275	225	22	exper	exper	PROPN
ap-1275	225	23	.	.	PUNCT
ap-1275	225	24	math	math	PROPN
ap-1275	225	25	.	.	PUNCT
ap-1275	226	1	,	,	PUNCT
ap-1275	226	2	10	10	NUM
ap-1275	226	3	(	(	PUNCT
ap-1275	226	4	2001	2001	NUM
ap-1275	226	5	)	)	PUNCT
ap-1275	226	6	,	,	PUNCT
ap-1275	226	7	609–618	609–618	NUM
ap-1275	226	8	.	.	PUNCT
ap-1275	227	1	[	[	X
ap-1275	227	2	11	11	NUM
ap-1275	227	3	]	]	X
ap-1275	227	4	shapiro	shapiro	PROPN
ap-1275	227	5	,	,	PUNCT
ap-1275	227	6	b.	b.	PROPN
ap-1275	227	7	:	:	PUNCT
ap-1275	227	8	algebro	algebro	ADJ
ap-1275	227	9	-	-	PUNCT
ap-1275	227	10	geometric	geometric	ADJ
ap-1275	227	11	aspects	aspect	NOUN
ap-1275	227	12	of	of	ADP
ap-1275	227	13	heinestieltjes	heinestieltjes	PROPN
ap-1275	227	14	theory	theory	NOUN
ap-1275	227	15	,	,	PUNCT
ap-1275	227	16	submitted	submit	VERB
ap-1275	227	17	.	.	PUNCT
ap-1275	228	1	[	[	X
ap-1275	228	2	12	12	NUM
ap-1275	228	3	]	]	X
ap-1275	228	4	shapiro	shapiro	PROPN
ap-1275	228	5	,	,	PUNCT
ap-1275	228	6	b.	b.	PROPN
ap-1275	228	7	,	,	PUNCT
ap-1275	228	8	takemura	takemura	VERB
ap-1275	228	9	,	,	PUNCT
ap-1275	228	10	k.	k.	PROPN
ap-1275	228	11	,	,	PUNCT
ap-1275	228	12	tater	tater	NOUN
ap-1275	228	13	,	,	PUNCT
ap-1275	228	14	m.	m.	NOUN
ap-1275	228	15	:	:	PUNCT
ap-1275	228	16	on	on	ADP
ap-1275	228	17	spectral	spectral	ADJ
ap-1275	228	18	polynomials	polynomial	NOUN
ap-1275	228	19	of	of	ADP
ap-1275	228	20	the	the	DET
ap-1275	228	21	heun	heun	PROPN
ap-1275	228	22	equation	equation	NOUN
ap-1275	228	23	.	.	PUNCT
ap-1275	229	1	ii	ii	PROPN
ap-1275	229	2	,	,	PUNCT
ap-1275	229	3	submitted	submit	VERB
ap-1275	229	4	.	.	PUNCT
ap-1275	230	1	prof	prof	PROPN
ap-1275	230	2	.	.	PUNCT
ap-1275	231	1	boris	boris	PROPN
ap-1275	231	2	shapiro	shapiro	PROPN
ap-1275	231	3	e	e	PROPN
ap-1275	231	4	-	-	NOUN
ap-1275	231	5	mail	mail	NOUN
ap-1275	231	6	:	:	PUNCT
ap-1275	231	7	shapiro@math.su.se	shapiro@math.su.se	ADJ
ap-1275	231	8	department	department	NOUN
ap-1275	231	9	of	of	ADP
ap-1275	231	10	mathematics	mathematics	PROPN
ap-1275	231	11	stockholm	stockholm	PROPN
ap-1275	231	12	university	university	PROPN
ap-1275	231	13	se-106	se-106	PROPN
ap-1275	231	14	91	91	NUM
ap-1275	231	15	,	,	PUNCT
ap-1275	231	16	stockholm	stockholm	PROPN
ap-1275	231	17	,	,	PUNCT
ap-1275	231	18	sweden	sweden	PROPN
ap-1275	231	19	83	83	NUM