Artículos (Análisis Funcional)

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    Wavelet-Petrov-Galerkin Method for the Numerical Solution of the KdV Equation
    (Hikari, 2012) Villegas Gutiérrez, Jairo Alberto; Castaño B., Jorge; Duarte V., Julio; Fierro Y., Esper; Universidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones; Universidad Surcolombiana. Departamento de Matemáticas. Neiva, Colombia; Villegas Gutiérrez, Jairo Alberto; Análisis Funcional y Aplicaciones
    The development of numerical techniques for obtaining approximate solutions of partial differential equations has very much increased in the last decades. Among these techniques are the finite element methods and finite difference. Recently, wavelet methods are applied to the numerical solution of partial differential equations, pioneer works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others. In this paper, we employ the Wavelet-Petrov-Galerkin method to obtain the numerical solution of the equation Korterweg-de Vries (KdV).
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    A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences
    (Springer Berlin Heidelberg, 2013) Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román; Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones; Gabriel Loaiza (gloaiza@eafit.edu.co); Héctor R. Quiceno (hquiceno@eafit.edu.co); Análisis Funcional y Aplicaciones
    For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built -- In this paper, the geometry induced on this manifold is characterized by q-divergence functionals -- This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections -- Moreover, the classical Amari´s α-connections appears as special case of the q−connections (q) -- The main result is the expected one, namely the zero curvature of the manifold
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    A q-exponential statistical Banach manifold
    (ELSEVIER, 2013-02) Quiceno Echavarría, Héctor Román; Loaiza Ossa, Gabriel Ignacio; department:Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones; Héctor R. Quiceno (hquiceno@eafit.edu.co); Gabriel Loaiza (gloaiza@eafit.edu.co); Análisis Funcional y Aplicaciones
    Letµbe a given probability measure andMµ the set ofµ-equivalent strictly positive probability densities -- In this paper we construct a Banach manifold on Mµ, modeled on the space L∞(p · µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis’s deformed exponential), where 0 < q < 1 is any real number -- This family is characterized by the fact that when q → 1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space -- The coordinate mappings of the manifold are given in terms of Csiszár’s Φ-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score function
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    Limits of quotients of bivariate real analytic functions
    (ELSEVIER, 2013-03) Molina, Sergio; Cadavid Moreno, Carlos Alberto; Vélez Caicedo, Juan Diego; Universidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones; Carlos Cadavid M.(ccadavid@eafit.edu.co); Análisis Funcional y Aplicaciones
    Necessary and sufficient conditions for the existence of limits of the form lim(x,y)→(a,b) f (x, y)/g(x, y) are given, under the hypothesis that f and g are real analytic functions near the point (a, b), and g has an isolated zero at (a, b) -- The given criterion uses a constructive version of Hensel’s Lemma which could be implemented in a computer algebra system in the case where f and g are polynomials with rational coefficients, or more generally, with coefficients in a real finite extension of the rationals -- A high level description of an algorithm for determining the existence of the limit as well as its computation is provided