LSD and AMAZE: the mass-metallicity relation at z>3

We present the first results on galaxy metallicity evolution at z>3 from two projects, LSD (Lyman-break galaxies Stellar populations and Dynamics) and AMAZE (Assessing the Mass Abundance redshift Evolution). These projects use deep near-infrared spectroscopic observations of a sample of ~40 LBGs to estimate the gas-phase metallicity from the emission lines. We derive the mass-metallicity relation at z$>$3 and compare it with the same relation at lower redshift. Strong evolution from z=0 and z=2 to z=3 is observed, and this finding puts strong constrains on the models of galaxy evolution. These preliminary results show that the effective oxygen yields does not increase with stellar mass, implying that the simple outflow model does not apply at z>3.Comment: 5 pages, to appear in the IAUS 255 conference proceedings: "Low-Metallicity Star Formation: from the First Stars to Dwarf Galaxies", L.K. Hunt, S. Madden and R. Schneider ed

Comparison Principles for subelliptic equations of Monge-Ampere type

We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group

The Hubble Deep Field Reveals a Supernova at z~0.95

We report the discovery of a variable object in the Hubble Deep Field North (HDF-N) which has brightened, during the 8.5 days sampled by the data, by more than 0.9 mag in I and about 0.7 mag in V, remaining stable in B. Subsequent observations of the HDF-N show that two years later this object has dimmed back to about its original brightness in I. The colors of this object, its brightness, its time behavior in the various filters and the evolution of its morphology are consistent with being a Type Ib supernova in a faint galaxy at z~0.95.Comment: 5 pages including 2 figures. Accepted for publication in MNRA

Regularity of Nash payoffs of Markovian nonzero-sum stochastic differential games

In this paper we deal with the problem of existence of a smooth solution of the Hamilton-Jacobi-Bellman-Isaacs (HJBI for short) system of equations associated with nonzero-sum stochastic differential games. We consider the problem in unbounded domains either in the case of continuous generators or for discontinuous ones. In each case we show the existence of a smooth solution of the system. As a consequence, we show that the game has smooth Nash payoffs which are given by means of the solution of the HJBI system and the stochastic process which governs the dynamic of the controlled system.Comment: To appear in "Stochastic

Observational clues to the progenitors of Type-Ia supernovae

Type-Ia supernovae (SNe Ia) are important distance indicators, element factories, cosmic-ray accelerators, kinetic-energy sources in galaxy evolution, and endpoints of stellar binary evolution. It has long been clear that a SN Ia must be the runaway thermonuclear explosion of a degenerate carbon-oxygen stellar core, most likely a white dwarf (WD). However, the specific progenitor systems of SNe Ia, and the processes that lead to their ignition, have not been identified. Two broad classes of progenitor binary systems have long been considered: single-degenerate (SD), in which a WD gains mass from a non-degenerate star; and double-degenerate (DD), involving the merger of two WDs. New theoretical work has enriched these possibilities with some interesting updates and variants. We review the significant recent observational progress in addressing the progenitor problem. We consider clues that have emerged from the observed properties of the various proposed progenitor populations, from studies of their sites, pre- and post-explosion, from analysis of the explosions themselves, and from the measurement of event rates. The recent nearby and well-studied event, SN 2011fe, has been particularly revealing. The observational results are not yet conclusive, and sometimes prone to competing theoretical interpretations. Nevertheless, it appears that DD progenitors, long considered the underdog option, could be behind some, if not all, SNe Ia. We point to some directions that may lead to future progress.Comment: to appear in Annual Reviews of Astronomy and Astrophysics, 2014. For near-final published version see http://www.annualreviews.org/doi/abs/10.1146/annurev-astro-082812-14103