Examinando por Autor "Loaiza, Gabriel"

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    Ítem
    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.
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    Ítem
    Lie algebra classification, conservation laws and invariant solutions for the kind generalization of the Duffing-type equation
    (Springer, 2024-06-10) Londoño, Oscar; García, Danilo; Loaiza, Gabriel; Acevedo, Yeisson; UNICAMP; Universidad EAFIT
    This paper makes significant contributions to the study of a generalized form of the Duffing-type equation. We derive the generating operators of the optimal system associated with this equation, enabling us to characterize an implicit solution. Additionally, we present a complete classification of group symmetries and obtain the Lagrangian for the equation. Our results include the classification of the Lie algebra and the optimal system, providing a thorough understanding of the equation’s underlying structure. These contributions serve to enhance the current body of knowledge on the Duffing-type equation and provide useful insights for future research in this area.