Coincidences in generalized Lucas sequences

For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)}$ in nonnegative integers $n,k,m,\ell$ with $k, \ell\geq 2$. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method. This paper is a continuation of the earlier work [4].Comment: 14 page

Thermal X-ray emission from shocked ejecta in Type Ia Supernova Remnants. Prospects for explosion mechanism identification

The explosion mechanism behind Type Ia supernovae is a matter of continuing debate. The diverse attempts to identify or at least constrain the physical processes involved in the explosion have been only partially successful so far. In this paper we propose to use the thermal X-ray emission from young supernova remnants originated in Type Ia events to extract relevant information concerning the explosions themselves. We have produced a grid of thermonuclear supernova models representative of the paradigms currently under debate: pure deflagrations, delayed detonations, pulsating delayed detonations and sub-Chandrasekhar explosions, using their density and chemical composition profiles to simulate the interaction with the surrounding ambient medium and the ensuing plasma heating, non-equilibrium ionization and thermal X-ray emission of the ejecta. Key observational parameters such as electron temperatures, emission measures and ionization time scales are presented and discussed. We find that not only is it possible to identify the explosion mechanism from the spectra of young Type Ia Supernova Remnants, it is in fact necessary to take the detailed ejecta structure into account if such spectra are to be modeled in a self-consistent way. Neither element line flux ratios nor element emission measures are good estimates of the true ratios of ejected masses, with differences of as much as two or three orders of magnitude for a given model. Comparison with observations of the Tycho SNR suggests a delayed detonation as the most probable explosion mechanism. Line strengths, line ratios, and the centroid of the Fe Kalpha line are reasonably well reproduced by a model of this kind.Comment: 11 pages, 8 figures (5 of them color), accepted for publication by the Ap

Insights on the physics of SNIa obtained from their gamma-ray emission

Type Ia supernovae are thought to be the outcome of the thermonuclear explosion of a carbon/oxygen white dwarf in a close binary system. Their optical light curve is powered by thermalized gamma-rays produced by the radioactive decay of $^{56}$Ni, the most abundant isotope present in the debris. Gamma-rays escaping the ejecta can be used as a diagnostic tool for studying the structure of the exploding star and the characteristics of the explosion. The fluxes of the $^{56}$Ni lines and the continuum obtained by INTEGRAL from SN2014J in M82, the first ever gamma-detected SNIa, around the time of the maximum of the optical light curve strongly suggest the presence of a plume of $^{56}$Ni in the outermost layers moving at high velocities. If this interpretation was correct, it could have important consequences on our current understanding of the physics of the explosion and on the nature of the systems that explode.Comment: Proceedings of the 11th INTEGRAL Conference Gamma-Ray AStrophysics in Multi-Wavelength Perspectiv

Wavelength de-multiplexing properties of a single aperture flanked by periodic arrays of indentations

In this paper we explore the transmission properties of single subwavelength apertures perforated in thin metallic films flanked by asymmetric configurations of periodic arrays of indentations. It is shown how the corrugation in the input side can be used to transmit selectively only two different wavelengths. Also, by tuning the geometrical parameters defining the corrugation of the output side, these two chosen wavelengths can emerge from the structure as two very narrow beams propagating at well-defined directions. This new ability of structured metals can be used as a base to build micron-sized wavelength de-multiplexers.Comment: Accepted for publication in Photonics and Nanostructure

Solving dynamic stochastic economic models by mathematical programming decomposition methods.

Discrete-time optimal control problems arise naturally in many economic problems. Despite the rapid growth in computing power and new developments in the literature, many economic problems are still quite challenging to solve. Economists are aware of the limitations of some of these approaches for solving these problems due to memory and computational requirements. However, many of the economic models present some special structure that can be exploited in an efficient manner. This paper introduces a decomposition methodology, based on a mathematical programming framework, to compute the equilibrium path in dynamic models by breaking the problem into a set of smaller independent subproblems. We study the performance of the method solving a set of dynamic stochastic economic models. The numerical results reveal that the proposed methodology is efficient in terms of computing time and accuracyDynamic stochastic economic model; Computation of equilibrium; Mathematical programming; Decomposition techniques;