On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Weak and strong disjunction in possibilistic ASP

Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules. The resulting framework allows to combine both non-monotonic reasoning and reasoning under uncertainty in a single framework. While PASP has been well-studied for possibilistic definite and possibilistic normal programs, we argue that the current semantics of possibilistic disjunctive programs are not entirely satisfactory. The problem is twofold. First, the treatment of negation-as-failure in existing approaches follows an all-or-nothing scheme that is hard to match with the graded notion of proof underlying PASP. Second, we advocate that the notion of disjunction can be interpreted in several ways. In particular, in addition to the view of ordinary ASP where disjunctions are used to induce a non-deterministic choice, the possibilistic setting naturally leads to a more epistemic view of disjunction. In this paper, we propose a semantics for possibilistic disjunctive programs, discussing both views on disjunction. Extending our earlier work, we interpret such programs as sets of constraints on possibility distributions, whose least specific solutions correspond to answer sets.

Temperature-dependent gap edge in strong-coupling superconductors determined using the Eliashberg-Nambu formalism

Using the theory of Eliashberg and Nambu for strong-coupling superconductors, we have calculated the gap function for a model superconductor and a selection of real superconductors includong the elements Al, Sn, Tl, Nb, In, Pb and Hg and one alloy, Bi2Tl. We have determined thetemperature-dependent gap edge in each and found that in materials with weak electron-phonon ($\lambda 1.20$), not only is the gap edge double valued but it also departs significantly from the BCS form and develops a shoulderlike structure which may, in some cases, denote a gap edge exceeding the $T = 0$ value. These computational results support the insights obtained by Leavens in an analytic consideration of the general problem. Both the shoulder and double value arise from a common origin seated in the form of the gap function in strong coupled materials at finite temperatures. From the calculated gap function, we can determine the densities of states in the materials and the form of the tunneling current-voltage characteristics for junctions with these materials as electroddes. By way of illustration, results are shown for the contrasting cases of Sn ($\lambda=0.74$) and Hg ($\lambad=1.63$). The reported results are distinct in several ways from BCS predictions and provide an incentive determinative experimental studies with techniques such as tunneling and far infrared absorption.

A high C/O ratio and weak thermal inversion in the atmosphere of exoplanet WASP-12b

The carbon-to-oxygen ratio (C/O) in a planet provides critical information about its primordial origins and subsequent evolution. A primordial C/O greater than 0.8 causes a carbide-dominated interior, as opposed to the silicate-dominated composition found on Earth; the atmosphere can also differ from those in the Solar System. The solar C/O is 0.54 (ref. 3). Here we report an analysis of dayside multi-wavelength photometry of the transiting hot-Jupiter WASP-12b (ref. 6) that reveals C/O>=1 in its atmosphere. The atmosphere is abundant in CO. It is depleted in water vapour and enhanced in methane, each by more than two orders of magnitude compared to a solar-abundance chemical-equilibrium model at the expected temperatures. We also find that the extremely irradiated atmosphere (T>2,500K) of WASP-12b lacks a prominent thermal inversion (or stratosphere) and has very efficient day-night energy circulation. The absence of a strong thermal inversion is in stark contrast to theoretical predictions for the most highly irradiated hot-Jupiter atmospheres.

SN 2011A: A low-luminosity interacting transient with a double plateau and strong sodium absorpton

We present optical photometry and spectroscopy of the optical transient SN 2011A. Our data span 140 days after discovery including BVRI u′g′r′i′z′ photometry and 11 epochs of optical spectroscopy. Originally classified as a type IIn supernova (SN IIn) due to the presence of narrow Hα emission, this object shows exceptional characteristics. First, the light curve shows a double plateau, a property only observed before in the impostor SN 1997bs. Second, SN 2011A has a very low luminosity (M_V=-15.72), placing it between normal luminous SNe IIn and SN impostors. Third, SN 2011A shows low velocity and high equivalent width absorption close to the sodium doublet, which increases with time and is most likely of circumstellar origin. This evolution is also accompanied by a change in line profile; when the absorption becomes stronger, a P Cygni profile appears. We discuss SN 2011A in the context of interacting SNe IIn and SN impostors, which appears to confirm the uniqueness of this transient. While we favor an impostor origin for SN 2011A, we highlight the difficulty in differentiating between terminal and non-terminal interacting transients.

Strong parallel magnetic field effects on the hydrogen molecular ion

Equilibrium distances, binding energies and dissociation energies for the ground and low-lying states of the hydrogen molecular ion in a strong magnetic field parallel to the internuclear axis are calculated and refined, by using the two- dimensional pseudospectral method. High-precision results are presented for the binding energies over a wider field regime than already given in the literature (Kravchenko and Liberman 1997 Phys. Rev. A 55 2701). The present work removes a long- standing discrepancy for the R-eq value in the 1sigma(u) state at a field strength of 1.0 x 10(6) T. The dissociation energies of the antibonding 1pi(g) state induced by magnetic fields are determined accurately. We have also observed that the antibonding 1pi(g) potential energy curve develops a minimum if the field is sufficiently strong. Some unreliable results in the literature are pointed out and discussed. A way to efficiently treat vibrational processes and coupling between the nuclear and the electronic motions in magnetic fields is also suggested within a three-dimensional pseudospectral scheme.

Ionization energies of beryllium in strong magnetic fields: a frozen core approximation

An effective frozen core approximation has been developed and applied to the calculation of energy levels and ionization energies of the beryllium atom in magnetic field strengths up to 2.35 x 10(5) T. Systematic improvement over the existing results for the beryllium ground and low-lying states has been accomplished by taking into account most of the correlation effects in the four-electron system. To our knowledge, this is the first calculation of the electronic properties of the beryllium atom in a strong magnetic field carried out using a configuration interaction approximation and thus allowing a treatment beyond that of Hartree-Fock. Differing roles played by strong magnetic fields in intrashell correlation within different states are observed. In addition, possible ways to gain further improvement in the energies of the states of interest are proposed and discussed briefly.