Revista de Matemáticas 15(1)

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  • Ítem
    An approach to ladder operators for the two-dimensional harmonic oscillator
    (2009-02-25 00:00:00) López Bonilla, José; Cruz Beltrán, L.
    We show that elementary properties of associated Laguerre polynomials generatethe ladder operators for the harmonic oscillator radial wave function in two dimensions.Keywords: Harmonic oscillator, ladder operators, Laguerre polynomials.
  • Ítem
    Conformally invariant differential operators and bilinear functionals in six dimensions
    (2009-02-25 00:00:00) Ugalde Gómez, William Javier
    We review how to construct the Paneitz operator in dimension four and the correspondingoperator in dimension six, by constructing symmetric bilinear differentialfunctionals that are conformally invariant.Keywords: Conformal invariants, Paneitz operator, bilinear differential functionals.
  • Ítem
    La ecuación de Navier-Stokes y multifractales
    (2009-02-25 00:00:00) Mercado Escalante, José Roberto
    There is currently no general theorem on the existence and unicity of solutions tothe Navier-Stokes equation, which describes the flow of a viscous and incompressiblefluid. This is an open problem at the international level, known as the millenniumprize problem, for which the Clay Institute of France is offering one million dollarssince may 2000.The purpose of this article is to present a brief revision of the most importantaspects of the evolution and current status of the problem. Our contribution is theanalytical description of turbulence, fully developed, through the resolution rates andthe features of multifractal processes, as a collection of generalized Cantor processes.We present four models for the distribution of velocity variations. The first one isbased on the life times and risk functions for the interaction between the vortices andtheir later fragmentation in ever smaller and more numerous vortices. The secondone is based on potentiated Bernoulli tests, and we found the number of features,the spectrum, and the structure function. We found the relationship of the shapeparameters with the box dimension of the maximum spectrum as well as with thelocal dimensions and we described qualitatively the associated tree.The above-mentioned rates serve as support, not only for the description of athree-dimensional model of intermittent turbulence that generalizes the Kolmogorovparadigmatic result, but also for the energy transferred in each stage of the fractalizationprocess, and also for the number of characteristic exponents, which producesa higher level for Hausdorff’s dimension of the set of singularities of the solution.Keywords: Navier-Stokes, turbulence, intermittency, multifractals, velocity gradients.
  • Ítem
    Elaboración de una metodología para la evaluación de la vulnerabilidad sísmica
    (2009-02-25 00:00:00) Aldama Ojeda, Alejandro; Gómez Soberón, Consuelo; Guillén López, Briseida
    This work presents a methodology to assess the seismic vulnerability of a set ofstructures over a specific region. Using a simplified inference method we estimate theconditions of the structures in order to recommend either rehabilitation or a detailedanalysis. The procedure is based on the implementation of different sampling schemes to the region surveyed considered as the objective population. The estimated conditionfor sampled structures is compared with the condition observed in the objectivepopulation census, in order to show that the procedure is reliable and economic. Inaddition we present a method to evaluate and assign a vulnerability index (VI). Thenthis VI is used to design vulnerability maps. In addition we assume that the resultsyielded here will contribute to implement future seismic risk studies.Keywords: Seismic vulnerability, seismic risk, inference, sampling.
  • Ítem
    Estimación bayesiana en la familia Pareto generalizada
    (2009-02-25 00:00:00) Sánchez Gómez, Rubén
    The generalized Pareto family of distributions with scale parameter > 0 andk form, has been used for modeling surplus over a given threshold, even though theparametric estimation in this family has some problems. In this work we study theBayesian approach for estimating parameters and k when no a priori informationis available and we discuss the case when there is previous information. We presenta simulation study in order to analyze the performance of the Bayesian methodology,employing non informative a priori distributions and the methods available in theliterature. This study shows that the Bayesian estimation performs better than otherproposed methods, in terms of bias and aquare root of the mean quadratic error. Theestimation methodologies analized are applied to real data sets.Keywords: Generalized Pareto family, estimation methods, Monte Carlo study.
  • Ítem
    Generalización de dos métodos de detección de conglomerados. Aplicaciones en bioinformática.
    (2009-02-25 00:00:00) Rodríguez Corvea, Laureano; Casas Cardoso, Gladys M.; Grau Abalo, Ricardo; Pupo Meriño, Mario
    This paper presents a modification to the temporal disease clusters methods inorder to apply them to other sciences. Particular specifications are shown in Scanand temporal Grimson techniques. The original data are transformed in a binary sequence:the value “one” represents the interest category and value “zero” correspondsto all other cases. Computational transformations of the algorithms are implementedusing Mathematica Package. Besides some interesting bioinformatics applications arepresented.Keywords: Temporal disease clusters, Scan method, Grimson method, Bioinformaticsapplications.
  • Ítem
    Nautelia: sistema automatizado para el ruteo náutico meteorológico
    (2009-02-25 00:00:00) Cordero Hernández, Yovany; Fernández Castillo, Karelia; Baguer Díaz-Romañach, Marta L.; Calnick, Anneris; Borrajeros, Israel
    For the captain of a ship, it is very important to have a proposal of the routethat allows him to reach the desired destiny as soon as possible, taking into accountweather conditions. In order to find such a route a former estimation of meteorologicalvariables for every single day of the journey is needed, because those variables have adirect influence in the speed of the ship. This estimation is done using the weatherforecast, obtained from the Internet.To find a route fast enough one must transform the weather forecast data so thatit can be used afterwards for computing the speed. Besides, it is necessary to buildmodels that describe the influence of each one of the meteorological variables in thespeed of the ship for a certain place and time and estimate the journey time fora specific route, depending on the ships characteristics. Finally, the sailing time isoptimized, basically changing the initial route using optimization methods.Keywords: Nonlinear programming, interpolation, splines, ordinary differential equations,genetic algorithms.
  • Ítem
    Métodos de punto interior para optimización cuadrática convexa con matrices no definidas positivas
    (2009-02-25 00:00:00) Palencia F., Gonzalo; Hing C., Rosina; Rojas C., Mariledy; Medina S., Denysde
    In this article a modification of the recursive algorithm of Cholesky is obtainedthat allows the factorization of Semi Definite Positive Matrices, even though theseare not positive defined, without increasing the computational cost. Thanks to thisfactorization Convex Quadratic Programming Problems are transformed into SecondOrder Conical Problems, which are solved with the aid of the generalization of thePredictor-Corrector algorithm of Mehrotra for these problems. There are carried outnumeric experiments for validating the results.Keywords: convex quadratic programming, second-order cones, interior point methods.