Análisis Funcional y Aplicaciones

URI permanente para esta comunidad

https://hdl.handle.net/10784/4394

Sostiene una actividad investigativa que promueve el trabajo colaborativo, multidisciplinario e interinstitucional, el cual propende por conocer y resolver las problemáticas de los sectores estratégicos del país, entre ellos, el sector de energía y el sector de hidrocarburos. Naturalmente, promueve decididamente las matemáticas y, dentro de ellas, el Análisis Funcional constituye una de las áreas de mayor importancia, dado que contiene los elementos básicos y principales, para otras áreas de aplicación como la optimización y las ecuaciones diferenciales, entre otras.
Coordinador: María Eugenia Puerta Yepes
Email: mpuerta@eafit.edu.co
Categoría: B
Area: Ciencias y Humanidades

Noticias

Líneas de investigación
- Aplicaciones de espacios de Orlicz y estructuras matemáticas deformadas
- Aplicaciones de las ecuaciones de difusión en geometría y topología
- Optimización
- Solución numérica de ecuaciones diferenciales

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Mostrando 1 - 9 de 9

A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
(Springer, 2013) Quiceno, H. R.; Loaiza, Gabriel; Universidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones; Gabriel Loaiza (gloaiza@eafit.edu.co)
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.
Computational methods for solving multi-objective uncertain optimization problems
(Universidad EAFIT, 2011-05-12) Puerta Yepes, María Eugenia; Cano Cadavid, Andrés Felipe; María. E Puerta Yepes (mpuerta@eafit.edu.co); Andrés Felipe Cano Cadavid (acanocad@gmail.com)
In recent years, there has been an increasing interest in the multi-objective uncertain optimization, discussed in the framework of the interval-valued optimization, as a consequence theoretical developments have achieved significant results as theorems analogous to the conditions of Karush Kunt Tucker, but computational developments are still incipient. This paper makes an extension of Strength Pareto Evolutionary Algorithm 2 - SPEA2 - and Multi-objective Particle Swarm Optimization - MOPSO -, which ones are traditionally used in multi-objective optimization, these are modified to the case of multi-objective uncertain optimization, where the model uses the interval-valued optimization as shown by Wu [?, ?, ?], these new algorithms have arithmetic advantage in the image set of the objective function. At the end, numerical examples are shown where they applied the algorithms implemented.
Duality in Multi-Objective Optimization Under Uncertainty
(Universidad EAFIT, 2014-02-20) Puerta Yepes, María Eugenia; Gaviria, C.; Fernández Gutiérrez, Juan Pablo; María E. Puerta (mpuerta@eafit.edu.co)
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
Optimization problem with interval-valued random functions
(Universidad EAFIT, 2012-12-10) Puerta Yepes, María Eugenia
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
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
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. Departamento de Ciencias; 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. Loading... Geometric Science of InformationGeometric Science of Information Look Inside Chapter Metrics Downloads1K Provided by Bookmetrix Other actions Export citation About this Book Reprints and Permissions Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn
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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