Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case x¨=f(x,t)\ddot{x}=f(x,t)

In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with 1+1/2 degree of freedom. In particular, we analyze the non-integrability of some important families of differential equations such as Painlev\'e II, Sitnikov and Hill-Schr\"odinger equation. We emphasize in Painlev\'e II, showing its non-integrability through three different Hamiltonian systems, and also in Sitnikov in which two different version including numerical results are shown. The main tool to study the non-integrability of these kind of Hamiltonian systems is Morales-Ramis theory. This paper is a very slight improvement of the talk with the almost-same title delivered by the author in SIAM Conference on Applications of Dynamical Systems 2007.Comment: 15 pages without figures (19 pages and 6 figures in the published version

Optical observations of very low ionization HII regions in the large Magellanic cloud

Several very low ionization isolated HII regions were detected on a prism-objective plate of the Large Magellanic Cloud. Most of the objects show a very weak (OIII) lambda 5007 emission line and, on the other hand the (OII) lambda 6584 doublets are very intense. This kind of objects seem to be ideal in order to determine accurate N and O abundance, avoiding the use of large ionization correction factors in the N abundance determination. Spectrophotometric observations of these regions were carried out with the 4 m telescope and the 2-D Frutti spectrograph at Cerro Tololo, and with the 1.52 m and the Image Dissector Scanner (IDS) at La Silla, ESO. The wavelength range lambda lambda 3700 to 7000 A was covered. Calibrated fluxes of the emission lines detected were measured, and from these data preliminary results of physical conditions of the gas as well as some ionic abundances were derived. Comparisons of the observations with ionization structure models show that the effective temperatures of the ionizing stars are less than 35,000 K. Possible abundances gradients across the large megallanic cloud are discussed

The Earth Mantle-Core Effect in Matter-Induced Asymmetries for Atmospheric Neutrino Oscillations

Earth medium effects in the three-neutrino oscillations of atmospheric neutrinos are observable under appropriate conditions. This paper generalizes the study of the medium effects and the possibility of their observation in the atmospheric neutrino oscillations from the case of neutrinos traversing only the Earth mantle, where the density is essentially constant, to the case of atmospheric neutrinos crossing also the Earth core. In the latter case new resonance-like effects become apparent. We calculate the CPT-odd asymmetry for the survival probability of muon neutrinos and the observable muon-charge asymmetry, taking into account the different atmospheric neutrino fluxes, and show the dependence of these asymmetries on the sign of $\Delta m^{2}_{3 1}$ and on the magnitude of the mixing angle $\theta_{13}$. A magnetized detector with a sufficiently good neutrino momentum resolution is required for the observation of the muon-charge asymmetry generated by the Earth mantle-core effect.Comment: 14 pages, 5 figure

Vanishing chiral couplings in the large-N_C resonance theory

The construction of a resonance theory involving hadrons requires implementing the information from higher scales into the couplings of the effective Lagrangian. We consider the large-Nc chiral resonance theory incorporating scalars and pseudoscalars, and we find that, by imposing LO short-distance constraints on form factors of QCD currents constructed within this theory, the chiral low-energy constants satisfy resonance saturation at NLO in the 1/Nc expansion.Comment: 5 pages, 2 figures. Version published in Physical Review D. Some equations to facilitate the discussion have been adde