Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 31 num. 1 lang. pt <![CDATA[SciELO Logo]]> <![CDATA[<b>Compact Composition Operators on Bloch type Spaces</b>]]> In this paper we characterize continuity and compactness of composition operators Cø; mapping the á-Bloch space into the μ-Bloch space, where μ is a weight defined on the unit disk D, in term of certain expression that involve the n-power of the symbol ø. <![CDATA[<b>On the Gauss-Newton method for solving</b> <b>equations</b>]]> We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss- Newton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solution <![CDATA[<b>A simple remark on fields of definition </b>]]> Let K< L be an extension of fields, in characteristic zero, with L algebraically closed and let ¯K < L be the algebraic closure of K in L. Let X and Y be irreducible projective algebraic varieties, X defined over ¯K and Y defined over L, and let π : X →Y be a non-constant morphism, defined over L. If we assume that ¯K ≠ L, then one may wonder if Y is definable over ¯K. In the case that K = Q, L = C and that X and Y are smooth curves, a positive answer was obtained by Gonzalez-Diez. In this short note we provide simple conditions to have a positive answer to the above question. We also state a conjecture for a class of varieties of general type. <![CDATA[<b>Improving some sequences convergent to Euler-Mascheroni constant</b>]]> We obtain the very fast sequences convergent to Euler-Mascheroni constant. <![CDATA[<b>An upper bound on the largest signless Laplacian of an odd unicyclic graph</b>]]> We derive an upper bound on the largest signless Laplacian eigenvalue of an odd unicyclic graph. The bound is given in terms of the largest vertex degree and the largest height of the trees obtained removing the edges of the unique cycle in the graph. <![CDATA[<b>The signature in actions of semisimple Lie groups on pseudo-Riemannian manifolds</b>]]> We study the relationship between the signature of a semisimple Lie group and a pseudoRiemannian manifold on wich the group acts topologically transitively and isometrically. We also provide a description of the bi-invariant pseudo-Riemannian metrics on a semisimple Lie Group over R in terms of the complexification of the Lie algebra associated to the group, and then we utilize it to prove a remark of Gromov. <![CDATA[<b>Half-Sweep Geometric Mean Iterative Method for the Repeated Simpson Solution of Second Kind Linear Fredholm Integral Equations</b>]]> In previous studies, the effectiveness of the Half-Sweep Geometric Mean (HSGM) iterative method has been shown in solving first and second kind linear Fredholm integral equations using repeated trapezoidal (RT) discretization scheme. In this work, we investigate the efficiency of the HSGM method to solve dense linear system generated from the discretization of the second kind linear Fredholm integral equations by using repeated Simpson's ^ (RS1) scheme. The formulation and implementation ofthe proposed method are also presented. In addition, several numerical simulations and computational complexity analysis were also included to verify the efficiency of the proposed method. <![CDATA[<b>On an algorithm for finding derivations of Lie</b> <b>algebras </b>]]> Let g be an arbitrary finite dimensional Lie algebra over the field R. We give as an additional alternative a detailed overview of an algorithm for finding derivations of g since such procedures are often of interest.