Artículos (Análisis Funcional)No Descriptionhttps://hdl.handle.net/10784/43952024-06-17T23:18:23Z2024-06-17T23:18:23Z41Wavelet-Petrov-Galerkin Method for the Numerical Solution of the KdV EquationVillegas Gutiérrez, Jairo AlbertoCastaño B., JorgeDuarte V., JulioFierro Y., Esperhttps://hdl.handle.net/10784/74102021-09-24T21:44:19Z2012-01-01T00:00:00Zdc.title: Wavelet-Petrov-Galerkin Method for the Numerical Solution of the KdV Equation
dc.contributor.author: Villegas Gutiérrez, Jairo Alberto; Castaño B., Jorge; Duarte V., Julio; Fierro Y., Esper
dc.description.abstract: 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).; 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).
2012-01-01T00:00:00ZA q-exponential statistical Banach manifoldQuiceno Echavarría, Héctor RománLoaiza Ossa, Gabriel Ignaciohttps://hdl.handle.net/10784/52452021-09-24T21:44:19Z2013-02-01T00:00:00Zdc.title: A q-exponential statistical Banach manifold
dc.contributor.author: Quiceno Echavarría, Héctor Román; Loaiza Ossa, Gabriel Ignacio
dc.description.abstract: 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; 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
2013-02-01T00:00:00ZA Riemannian geometry in the q-Exponential Banach manifold induced by q-DivergencesLoaiza Ossa, Gabriel IgnacioQuiceno Echavarría, Héctor Románhttps://hdl.handle.net/10784/52442021-09-24T21:44:19Z2013-01-01T00:00:00Zdc.title: A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences
dc.contributor.author: Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román
dc.description.abstract: 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; 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
2013-01-01T00:00:00ZLimits of quotients of bivariate real analytic functionsMolina, SergioCadavid Moreno, Carlos AlbertoVélez Caicedo, Juan Diegohttps://hdl.handle.net/10784/50662021-09-24T21:44:18Z2013-03-01T00:00:00Zdc.title: Limits of quotients of bivariate real analytic functions
dc.contributor.author: Molina, Sergio; Cadavid Moreno, Carlos Alberto; Vélez Caicedo, Juan Diego
dc.description.abstract: 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; 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
2013-03-01T00:00:00Z