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

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

Some arithmetic functions of factorials in Lucas sequences

We prove that if {un}n≥ 0 is a nondegenerate Lucas sequence, then there are only finitely many effectively computable positive integers n such that |un|=f(m!), where f is either the sum-of-divisors function, or the sum-of-proper-divisors function, or the Euler phi function. We also give a theorem that holds for a more general class of integer sequences and illustrate our results through a few specific examples. This paper is motivated by a previous work of Iannucci and Luca who addressed the above problem with Catalan numbers and the sum-of-proper-divisors function

Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes

By using a theoretical formalism able to work in both real and k-spaces, the physical origin of the phenomenon of extraordinary transmission of light through quasi-periodic arrays of holes is revealed. Long-range order present in a quasiperiodic array selects the wavevector(s) of the surface electromagnetic mode(s) that allows an efficient transmission of light through subwavelength holes.Comment: 4 pages, 4 figure

On a generalization of the Pell sequence

The Pell sequence $(P_n)_{n=0}^{\infty}$ is the second order linear recurrence defined by $P_n=2P_{n-1}+P_{n-2}$ with initial conditions $P_0=0$ and $P_1=1$. In this paper, we investigate a generalization of the Pell sequence called the $k$-generalized Pell sequence which is generated by a recurrence relation of a higher order. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences. Some interesting identities involving the Fibonacci and generalized Pell numbers are also deduced

Identificación de tipologías estructurales con el Inventario Forestal Nacional: el caso de los robledales albares en la Cordillera Cantábrica

The objective of this work was the creation of a structural stand classification for sessile oak dominated forests in the Cantabrian Range (northern Spain) as a basic tool for typological inventories. A dichotomous classification system and discriminant classification equations of nine forest types were defined with an accuracy of more than 95% by evaluating the data of the second Spanish National Forest Inventory (SNFI). The presence of large old trees appears as one of the main characteristics of the Cantabrian sessile oak forests. The structure assessment method presented in this study, based on a dataset (SNFI) and free-access software, can be considered an important low-cost alternative to traditional quantitative inventory methods.El objeto de este trabajo ha sido la elaboración de una clasificación tipológica para robledales cantábricos (norte de España) como herramienta base de inventario tipológico. Tomando como base de datos el inventario forestal nacional español (IFN) y con una fiabilidad superior al 95% se elaboran una clave de clasificación dicotómica y ecuaciones discriminantes de clasificación para nueve tipos estructurales de masa. La presencia de viejos robles de grandes diámetros aparece como uno de los rasgos diferenciales de los robledales cantábricos. La metodología de evaluación de la estructura forestal elaborada en el presente estudio, basada en una base de datos de libre acceso (IFN) y en un software gratuito, puede ser entendida como una alternativa de bajo coste al inventario cuantitativo tradicional