Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 26 num. 1 lang. es <![CDATA[SciELO Logo]]> <![CDATA[<b>ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION</b>]]> In Riemannian foliation, a transverse affine vector field preserves the curvature and its covariant derivatives. In this paper we solve the converse problem. Actually, we show that an infinitesimal automorphism of a Riemannian foliation which preserves the curvature and its covariant derivatives induces a transverse almost homothetic vector field. If in addition the manifold is closed and the foliation is irreducible harmonic , then a such infinitesimal automorphism induces a transverse killing vector field. <![CDATA[<b>UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES</b>]]> If λ is a sequence K-space and Σ x j is a series in a topological vector space X; the series is said to be λ-multiplier convergent if the series <img border=0 width=75 height=24 id="_x0000_i1026" src="../img/sumatoria.JPG">converges in X for every t = {tj} <img border=0 width=15 height=15 id="_x0000_i1027" src="../img/pertenece.JPG">λ. We show that if λ satisfies a gliding hump condition, called the signed strong gliding hump condition, then the series <img border=0 width=75 height=24 id="_x0000_i1028" src="../img/sumatoria.JPG">converge uniformly for t = {tj} belonging to bounded subsets of λ. A similar uniform convergence result is established for a multiplier convergent series version of the Hahn-Schur Theorem. <![CDATA[<b>ABOUT DECAY OF SOLUTION OF THE WAVE EQUATION WITH DISSIPATION</b>]]> In this work, we consider the problem of existence of global solutions for a scalar wave equation with dissipation. We also study the asymptotic behaviour in time of the solutions. The method used here is based in nonlinear techniques. <![CDATA[ON WREATH PRODUCT OF PERMUTATION GROUPS]]> This report is essentially an upgrade of the results of Audu (see [1] and [2]) on some finite permutation groups. It consists of the basic procedure for computing wreath product of groups. We also discussed the conditions under which the wreath products of permutation groups are faithful, transitive and primitive. Further, the centre of the stabilizer and the centre of wreath products was investigated, and finally, an illustration was supplied to support our findings <![CDATA[<b>ASYMPTOTICS FOR SECOND ORDER DELAYED DIFFERENTIAL EQUATIONS</b>]]> In this work we present a way to find asymptotic formulas for some solutions of second order linear differential equations with a retarded functional perturbation <![CDATA[MAXWELL REVISITED]]> This work explores what other mathematical possibilities were available to Maxwell for formulating his electromagnetic field model, by characterizing the family of mathematical models induced by the analytical equations describing electromagnetic phenomena prevailing at that time. The need for this research stems from the article "Inertial Relativity - A Functional Analysis Review", recently published in "Proyecciones", which claims and demonstrates the existence of an axiomatic conflict between the special and general theories of relativity on one side, and functional analysis on the other, making the reformulation of the relativistic theories, mandatory. As will be shown herein, such reformulation calls for a revision of Maxwell's electromagnetic field model. The conclusion is reached that -given the set of equations considered by Maxwell- not a unique, but an infinite number of mathematically correct reformulations to Ampere's law exists, resulting in an equally abundant number of potential models for the electromagnetic phenomena (including Maxwell's). Further experimentation is required in order to determine which is the physically correct model.