6,920 research outputs found
Multivariate time-space harmonic polynomials: a symbolic approach
By means of a symbolic method, in this paper we introduce a new family of
multivariate polynomials such that multivariate L\'evy processes can be dealt
with as they were martingales. In the univariate case, this family of
polynomials is known as time-space harmonic polynomials. Then, simple
closed-form expressions of some multivariate classical families of polynomials
are given. The main advantage of this symbolic representation is the plainness
of the setting which reduces to few fundamental statements but also of its
implementation in any symbolic software. The role played by cumulants is
emphasized within the generalized Hermite polynomials. The new class of
multivariate L\'evy-Sheffer systems is introduced.Comment: In pres
On some applications of a symbolic representation of non-centered L\'evy processes
By using a symbolic technique known in the literature as the classical umbral
calculus, we characterize two classes of polynomials related to L\'evy
processes: the Kailath-Segall and the time-space harmonic polynomials. We
provide the Kailath-Segall formula in terms of cumulants and we recover simple
closed-forms for several families of polynomials with respect to not centered
L\'evy processes, such as the Hermite polynomials with the Brownian motion, the
Poisson-Charlier polynomials with the Poisson processes, the actuarial
polynomials with the Gamma processes, the first kind Meixner polynomials with
the Pascal processes, the Bernoulli, Euler and Krawtchuk polynomials with
suitable random walks
On the computation of classical, boolean and free cumulants
This paper introduces a simple and computationally efficient algorithm for
conversion formulae between moments and cumulants. The algorithm provides just
one formula for classical, boolean and free cumulants. This is realized by
using a suitable polynomial representation of Abel polynomials. The algorithm
relies on the classical umbral calculus, a symbolic language introduced by Rota
and Taylor in 1994, that is particularly suited to be implemented by using
software for symbolic computations. Here we give a MAPLE procedure. Comparisons
with existing procedures, especially for conversions between moments and free
cumulants, as well as examples of applications to some well-known distributions
(classical and free) end the paper.Comment: 14 pages. in press, Applied Mathematics and Computatio
Dust in active nuclei. II. Powder or gravel?
In a companion paper, Maiolino et al. (2000) presented various observational
evidences for "anomalous" dust properties in the circumnuclear region of AGNs
and, in particular, the reduced E(B-V)/N_H and Av/N_H ratios, the absence of
the silicate absorption feature in mid-IR spectra of Sy2s and the absence of
the carbon dip in UV spectra of reddened Sy1s. In this paper we discuss various
explanations for these facts.
The observational constraints favor a scenario where coagulation, catalyzed
by the high densities in the circumnuclear region, yields to the formation of
large grains. The resulting extinction curve is featureless, flatter than
Galactic and the E(B-V)/N_H and Av/N_H ratios are significantly reduced. These
results should warn about an unappropriate use of the standard Galactic
extinction curve and Av/N_H ratio when dealing with the extreme gas conditions
typical of the circumnuclear clouds of AGNs.
We also investigated alternative scenarios for the observed anomalous
properties of dust in AGNs. Some of these scenarios might explain some of the
observed properties for a few objects, but they generally fail to account for
all of the observational constraints obtained for the large sample of AGNs
studied in these works.Comment: 13 pages, 7 figures, accepted for publication in A&
Early star formation traced by the highest redshift quasars
The iron abundance relative to alpha-elements in the circumnuclear region of
quasars is regarded as a clock of the star formation history and, more
specifically, of the enrichment by SNIa. We investigate the iron abundance in a
sample of 22 quasars in the redshift range 3.0<z<6.4 by measuring their rest
frame UV FeII bump, which is shifted into the near-IR, and by comparing it with
the MgII 2798 flux. The observations were performed with a device that can
obtain near-IR spectra in the range 0.8-2.4 um in one shot, thereby enabling an
optimal removal of the continuum underlying the FeII bump. We detect iron in
all quasars including the highest redshift (z=6.4) quasar currently known. The
uniform observational technique and the wide redshift range allows a reliable
study of the trend of the FeII/MgII ratio with redshift. We find the FeII/MgII
ratio is nearly constant at all redshifts, although there is marginal evidence
for a higher FeII/MgII ratio in the quasars at z~6. If the FeII/MgII ratio
reflects the Fe/alpha abundance, this result suggests that the z~6 quasars have
already undergone a major episode of iron enrichment. We discuss the possible
implications of this finding for the star formation history at z>6. We also
detect a population of weak iron emitters at z~4.5, which are possibly hosted
in systems that evolved more slowly. Alternatively, the trend of the FeII/MgII
ratio at high redshift may reflect significantly different physical conditions
of the circumnuclear gas in such high redshift quasars.Comment: Replaced to match the accepted version (ApJL in press), 5 page
Near-infrared K-band Spectroscopic Investigation of Seyfert 2 Nuclei in the CfA and 12 Micron Samples
We present near-infrared K-band slit spectra of the nuclei of 25 Seyfert 2
galaxies in the CfA and 12 micron samples. The strength of the CO absorption
features at 2.3-2.4 micron produced by stars is measured in terms of a
spectroscopic CO index. A clear anti-correlation between the observed CO index
and the nuclear K-L color is present, suggesting that a featureless hot dust
continuum heated by an AGN contributes significantly to the observed K-band
fluxes in the nuclei of Seyfert 2 galaxies. After correction for this AGN
contribution, we estimate nuclear stellar K-band luminosities for all sources,
and CO indices for sources with modestly large observed CO indices. The
corrected CO indices for 10 (=40%) Seyfert 2 nuclei are found to be as high as
those observed in star-forming or elliptical (=spheroidal) galaxies. We combine
the K-band data with measurements of the L-band 3.3 micron polycyclic aromatic
hydrocarbon (PAH) emission feature, another powerful indicator for
star-formation, and find that the 3.3 micron PAH to K-band stellar luminosity
ratios are substantially smaller than those of starburst galaxies. Our results
suggest that the 3.3 micron PAH emission originates in the putative nuclear
starbursts in the dusty tori surrounding the AGNs, because of its high surface
brightness, whereas the K-band CO absorption features detected at the nuclei
are dominated by old bulge (=spheroid) stars, and thus may not be a powerful
indicator for the nuclear starbursts. We see no clear difference in the
strength of the CO absorption and PAH emission features between the CfA and 12
micron Seyfert 2s.Comment: 28 pages, 6 figures, accepted for publication in ApJ (10 October
2004, v614 issue
Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum
The classification of certain class of static solutions for the
Einstein-Gauss-Bonnet theory in vacuum is performed in dimensions. The
class of metrics under consideration is such that the spacelike section is a
warped product of the real line and an arbitrary base manifold. It is shown
that for a generic value of the Gauss-Bonnet coupling, the base manifold must
be necessarily Einstein, with an additional restriction on its Weyl tensor for
. The boundary admits a wider class of geometries only in the special case
when the Gauss-Bonnet coupling is such that the theory admits a unique
maximally symmetric solution. The additional freedom in the boundary metric
enlarges the class of allowed geometries in the bulk, which are classified
within three main branches, containing new black holes and wormholes in vacuum
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