Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 26 num. 3 lang. en <![CDATA[SciELO Logo]]> <![CDATA[ON THE ALGEBRAIC DIMENSION OF BANACH SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS OR ARBITRARY RANK]]> Let K be a complete non-archimedean valued field of any rank, and let E be a K-Banach space with a countable topological base. We determine the algebraic dimension of E (2.3, 2.4, 3.1). <![CDATA[THE UNIFORM BOUNDEDNESS PRINCIPLE FOR ARBITRARY LOCALLY CONVEX SPACES]]> We establish uniform boundedness principle for pointwise bounded families of continuous linear operators between locally convex spaces which require no assumptions such as barrelledness on the domain space of the operators. We give applications of the result to separately continuous bilinear operators between locally convex spaces <![CDATA[QUASI - MACKEY TOPOLOGY]]> Let E1, E2 be Hausdorff locally convex spaces with E2 quasi-complete, and T : E1 → E2 a continuous linear map. Then T maps bounded sets of E1 into relatively weakly compact subsets of E2 if and only if T is continuous with quasi-Mackey topology on E1. If E1 has quasi-Mackey topology and E2 is quasi-complete, then a sequentially continuos linear map T : E1 → E2 is an unconditionally converging operator. <![CDATA[REGULARITY AND AMENABILITY OF THE SECOND DUAL OF WEIGHTED GROUP ALGEBRAS]]> For a wide variety of Banach algebras A (containing the group algebras L¹(G), M (G) and A(G)) the Arens regularity of A** is equivalent to that A, and the amenability of A** is equivalent to the amenability and regularity of A. In this paper, among other things, we show that this variety contains the weighted group algebras L¹(G, w) and M(G, w). <![CDATA[A NOTE ON KKT-INVEXITY IN NONSMOOTH CONTINUOUS-TIME OPTIMIZATION]]> We introduce the notion of KKT-invexity for nonsmooth continuoustime nonlinear optimization problems and prove that this notion is a necessary and sufficient condition for every KKT solution to be a global optimal solution. <![CDATA[THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS]]> Mixed linear models, also known as two-level hierarchical models, are commonly used in many applications. In this paper, we consider the marginal distribution that arises within a Bayesian framework, when the components of variance are integrated out of the joint posterior distribution. We provide analytical tools for describing the surface of the distribution of interest. The main theorem and its proof show how to determine the number of local maxima, and their approximate location and relative size. This information can be used by practitioners to assess the performance of Laplace-type integral approximations, to compute possibly disconnected highest posterior density regions, and to custom-design numerical algorithms. <![CDATA[A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS]]> The main objective of this work is to build, based on the Euclidean algorithm, a “matrix of algorithms” <img border=0 width=476 height=41 id="_x0000_i1032" src="../img/formula1.JPG"> Where <img border=0 width=196 height=28 id="_x0000_i1031" src="../img/formula2.JPG">is a fixed matrix on<img border=0 width=68 height=29 id="_x0000_i1030" src="../img/formula3.JPG">The function <img border=0 width=17 height=20 id="_x0000_i1029" src="../img/formula4.JPG">B is called the algorithmic matrix function. Here we show its properties and some applications to Cryptography and nonlinear Diophantine equations. The case n = m = 1 has particular interest. On this way we show equivalences between <img border=0 width=17 height=20 id="_x0000_i1028" src="../img/formula4.JPG">B and the Carl Friedrich Gauߒs congruence module p. <![CDATA[ON THE LOCAL HYPERCENTER OF A GROUP]]> We introduce a local hypercenter of an arbitrary group and study its basic properties. With this concept, it turns out that classical theorems of Baer, Mal’cev and McLain on locally nilpotent groups can be obtained as special cases of statements which are valid in any group. Furthermore, we investigate the connection between the local hypercenter of a group and the intersection of its maximal locally nilpotent subgroups.