On Hopf's Lemma and the Strong Maximum Principle

In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum Principle and we give a condition which is at once necessary for the validity of Hopf's Lemma and sufficient for the validity of the Strong Maximum Principle.Comment: 27 pages,4 figure

Anisotropy probe of galactic and extra-galactic Dark Matter annihilations

We study the flux and the angular power spectrum of gamma-rays produced by Dark Matter (DM) annihilations in the Milky Way (MW) and in extra-galactic halos. The annihilation signal receives contributions from: a) the smooth MW halo, b) resolved and unresolved substructures in the MW, c) external DM halos at all redshifts, including d) their substructures. Adopting a self-consistent description of local and extra-galactic substructures, we show that the annihilation flux from substructures in the MW dominates over all the other components for angles larger than O(1) degrees from the Galactic Center, unless an extreme prescription is adopted for the substructures concentration. We also compute the angular power spectrum of gamma-ray anisotropies and find that, for an optimistic choice of the particle physics parameters, an interesting signature of DM annihilations could soon be discovered by the Fermi LAT satellite at low multipoles, l<100, where the dominant contribution comes from MW substructures with mass M>10^4 solar masses. For the substructures models we have adopted, we find that the contribution of extra-galactic annihilations is instead negligible at all scales.Comment: 14 pages, 7 figure

UB CCD photometry of the old, metal rich, open clusters NGC 6791, NGC 6819 and NGC 7142

We report on a UV-oriented imaging survey in the fields of the old, metal-rich open clusters, NGC 6791, NGC 6819 and NGC 7142. These three clusters represent both very near and ideal stellar aggregates to match the distinctive properties of the evolved stellar populations, as in elliptical galaxies and bulges of spirals. The CMD of the three clusters is analyzed in detail, with special emphasis to the hot stellar component. We report, in this regard, one new extreme horizontal-branch star candidate in NGC 6791. For NGC 6819 and 7142, the stellar luminosity function points to a looser radial distribution of faint lower Main Sequence stars, either as a consequence of cluster dynamical interaction with the Galaxy or as an effect of an increasing fraction of binary stars toward the cluster core, as actually observed in NGC 6791 too.Comment: 12 pages with 15 Figures & 5 Tables. To appear in the Astronomical Journa

A critical appraisal of ATLAS9 and NextGen 5 model atmospheres

The fitting atmosphere parameters (Teff, g, and [Fe/H]) for over 300 stars in the Gunn & Striker and Jacoby et al. catalogs have been obtained relying on the Kurucz (1992) ATLAS9 and Hauschildt et al (1999) NextGen5 synthesis models. The output results are compared, and a critical appraisal of both theoretical codes is performed.Comment: 2 pages, 2 figures; proceedings of "New Quests in Stellar Astrophysics: The link between Stars and Cosmology", 26-30 March, 2001, Puerto Vallarta, Mexico, eds. M. Chavez, A. Bressan, A. Buzzoni & D. Mayya, to be published by the Kluwer Academic Publisher

The locus of points of the Hilbert scheme with bounded regularity

In this paper we consider the Hilbert scheme $Hilb_{p(t)}^n$ parameterizing subschemes of $P^n$ with Hilbert polynomial $p(t)$, and we investigate its locus containing points corresponding to schemes with regularity lower than or equal to a fixed integer $r'$. This locus is an open subscheme of $Hilb_{p(t)}^n$ and, for every $s\geq r'$, we describe it as a locally closed subscheme of the Grasmannian $Gr_{p(s)}^{N(s)}$ given by a set of equations of degree $\leq \mathrm{deg}(p(t))+2$ and linear inequalities in the coordinates of the Pl\"ucker embedding.Comment: v2: new proofs relying on the functorial definition of the Hilbert scheme. v3: Sections reorganized, new self-contained proof of the representability of the Hilbert functor with bounded regularity (Section 6

Test of the gravitational redshift with stable clocks in eccentric orbits: application to Galileo satellites 5 and 6

The Einstein Equivalence Principle (EEP) is one of the foundations of the theory of General Relativity and several alternative theories of gravitation predict violations of the EEP. Experimental constraints on this fundamental principle of nature are therefore of paramount importance. The EEP can be split in three sub-principles: the Universality of Free Fall (UFF), the Local Lorentz Invariance (LLI) and the Local Position Invariance (LPI). In this paper we propose to use stable clocks in eccentric orbits to perform a test of the gravitational redshift, a consequence of the LPI. The best test to date was performed with the Gravity Probe A (GP-A) experiment in 1976 with an uncertainty of $1.4\times10^{-4}$. Our proposal considers the opportunity of using Galileo satellites 5 and 6 to improve on the GP-A test uncertainty. We show that considering realistic noise and systematic effects, and thanks to a highly eccentric orbit, it is possible to improve on the GP-A limit to an uncertainty around $(3-4)\times 10^{-5}$ after one year of integration of Galileo 5 and 6 data.Comment: 13 pages, 5 figures, accepted in Classical and Quantum Gravity as a Fast Track Communicatio