23,539 research outputs found
Continuous dependence estimates for the ergodic problem of Bellman equation with an application to the rate of convergence for the homogenization problem
This paper is devoted to establish continuous dependence estimates for the
ergodic problem for Bellman operators (namely, estimates of (v_1-v_2) where v_1
and v_2 solve two equations with different coefficients). We shall obtain an
estimate of ||v_1-v_2||_\infty with an explicit dependence on the
L^\infty-distance between the coefficients and an explicit characterization of
the constants and also, under some regularity conditions, an estimate of
||v_1-v_2||_{C^2(\R^n)}.
Afterwards, the former result will be crucial in the estimate of the rate of
convergence for the homogenization of Bellman equations. In some regular cases,
we shall obtain the same rate of convergence established in the monographs
[11,26] for regular linear problems
On the puzzle of space weathering alteration of basaltic asteroids
The majority of basaltic asteroids are found in the inner main belt, although
a few have also been observed in the outer main belt and near-Earth space.
These asteroids -referred to as V-types- have surface compositions that
resemble that of the 530km sized asteroid Vesta. Besides the compositional
similarity, dynamical evidence also links many V-type asteroids to Vesta.
Moreover, Vesta is one of the few asteroids to have been identified as source
of specific classes of meteorites, the howardite, eucrite, diogenite
achondrites (HEDs). Despite the general consensus on the outlined scenario,
several questions remain unresolved. In particular, it is not clear if the
observed spectral diversity among Vesta, V-types and HEDs is due to space
weathering, as is thought to be the case for S-type asteroids. In this paper,
SDSS photometry is used to address the question of whether the spectral
diversity among candidate V-types and HEDs can be explained by space
weathering. We show that visible spectral slopes of V-types are systematically
redder with respect to HEDs, in a similar way to what is found for ordinary
chondrite meteorites and S-types. On the assumption that space weathering is
responsible for the slope mismatch, we estimated an upper limit for the
reddening timescale of about 0.5Ga. Nevertheless, the observed slope mismatch
between HEDs and V-types poses several puzzles to understanding its origin. The
implication of our findings is also discussed in the light of Dawn mission to
Vesta.Comment: Accepted by ApJ
Stellar populations in the Magellanic Clouds: looking through the dust
We present the first results of our study of stellar populations in the Large
and Small Magellanic Clouds based on multi-band WFPC2 observations of "random"
fields taken as part of the "pure parallel" programme carried out with the HST
as a service to the community.Comment: Two pages, one figure, to appear in the proceedings of IAU Symposium
241 "Stellar Populations as Building Blocks of Galaxies", eds. A. Vazdekis
and R. Peletie
A comparison among various notions of viscosity solutions for Hamilton-Jacobi equations on networks
Three definitions of viscosity solutions for Hamilton-Jacobi equations on
networks recently appeared in literature ([1,4,6]). Being motivated by various
applications, they appear to be considerably different. Aim of this note is to
establish their equivalence
Stationary Mean Field Games systems defined on networks
We consider a stationary Mean Field Games system defined on a network. In
this framework, the transition conditions at the vertices play a crucial role:
the ones here considered are based on the optimal control interpretation of the
problem. We prove separately the well-posedness for each of the two equations
composing the system. Finally, we prove existence and uniqueness of the
solution of the Mean Field Games system
Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations
Aim of this paper is to extend the continuous dependence estimates proved in
\cite{JK1} to quasi-monotone systems of fully nonlinear second-order parabolic
equations. As by-product of these estimates, we get an H\"older estimate for
bounded solutions of systems and a rate of convergence estimate for the
vanishing viscosity approximation. In the second part of the paper we employ
similar techniques to study the periodic homogenization of quasi-monotone
systems of fully nonlinear second-order uniformly parabolic equations. Finally,
some examples are discussed
The Luminosity Function of Omega Centauri
Deep HST-WFPC2 observations of the stellar population in the globular cluster
Omega Cen (NGC 5139) have been used to measure the luminosity function of main
sequence stars at the low-mass end. Two fields have been investigated, located
respectively ~4.6' and ~7' away from the cluster center, or near the half-light
radius of this cluster (~4.8'). The color-magnitude diagrams derived from these
data show the cluster main sequence extending to the detection limit at I ~ 24.
Information on both color and magnitude is used to build the luminosity
functions of main sequence stars in these fields and the two independent
determinations are found to agree very well with each other within the
observational uncertainty. Both functions show a peak in the stellar
distribution around M_I ~ 9 followed by a drop at fainter magnitudes well
before photometric incompleteness becomes significant, as is typical of other
globular clusters observed with the HST. This result is at variance with
previous claims that the luminosity function of Omega Cen stays flat at low
masses, but is in excellent agreement with recent near-IR NICMOS observations
of the same cluster.Comment: To appear in The Astronomical Journal. Contains 7 pages, 4 figures,
prepared with the AAS LaTeX macr
NGC2298: a globular cluster on its way to disruption
We have studied the stellar main sequence (MS) of the globular cluster
NGC2298 using deep HST/ACS observations in the F606W and F814W bands covering
an area of 3.4' x 3.4' around the cluster centre or about twice the cluster's
half-mass radius. The colour-magnitude diagram that we derive in this way
reveals a narrow and well defined MS extending down to the 10 sigma detection
limit at m_606~26.5, m_814~25, corresponding to stars of ~0.2 Msolar. The
luminosity function (LF) obtained with these data, once corrected for the
limited effects of photometric incompleteness, reveals a remarkable deficiency
of low-mass stars as well as a radial gradient, in that the LF becomes
progressively steeper with radius. Using the mass-luminosity relation
appropriate for the metallicity of NGC2298, we derive the cluster's global mass
function (GMF) by using a multi-mass Michie-King model. Over the range 0.8 -
0.2 Msolar, the number of stars per unit mass decreases following a power-law
distribution of the type dN/dm \propto m^(0.5), where, for comparison, typical
halo clusters have dN/dm \propto m^(-1.5). If the IMF of NGC2298 was similar to
that of other metal poor halo clusters, like e.g. NGC6397, the present GMF that
we obtain implies that this object must have lost of order 85% of its original
mass, at a rate much higher than that suggested by current models based on the
available cluster orbit. The latter may, therefore, need revision.Comment: 9 pages, 6 figures, accepted for publication in Astronomy and
Astrophysic
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