Scielo RSS <![CDATA[Revista de la Unión Matemática Argentina]]> http://www.scielo.org.ar/rss.php?pid=0041-693220080001&lang=es vol. 49 num. 1 lang. es <![CDATA[SciELO Logo]]> http://www.scielo.org.ar/img/en/fbpelogp.gif http://www.scielo.org.ar <![CDATA[Mischa Cotlar, in memoriam: 1913 - 2007]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100001&lng=es&nrm=iso&tlng=es <![CDATA[Bifurcation theory applied to the analysis of power systems]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100002&lng=es&nrm=iso&tlng=es In this paper, several nonlinear phenomena found in the study of power system networks are described in the context of bifurcation theory. Toward this end, a widely studied 3-bus power system model is considered. The mechanisms leading to static and dynamic bifurcations of equilibria as well as a cascade of period doubling bifurcations of periodic orbits are investigated. It is shown that the cascade verifies the Feigenbaum's universal theory. Finally, a two parameter bifurcation analysis reveals the presence of a Bogdanov-Takens codimension-two bifurcation acting as an organizing center for the dynamics. In addition, evidence on the existence of a complex global phenomena involving homoclinic orbits and a period doubling cascade is included. <![CDATA[Finite element approximation of the vibration problem for a Timoshenko curved rod]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100003&lng=es&nrm=iso&tlng=es The aim of this paper is to analyze a mixed finite element method for computing the vibration modes of a Timoshenko curved rod with arbitrary geometry. Optimal order error estimates are proved for displacements and rotations of the vibration modes, as well as a double order of convergence for the vibration frequencies. These estimates are essentially independent of the thickness of the rod, which leads to the conclusion that the method is locking free. A numerical test is reported in order to assess the performance of the method. <![CDATA[Iterated Aluthge transforms: a brief survey]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100004&lng=es&nrm=iso&tlng=es Given an r &times; r complex matrix T, if <IMG SRC="/img/revistas/ruma/v49n1/1a047x.png" WIDTH=72 HEIGHT=19>is the polar decomposition of T, then the Aluthge transform is defined by <IMG SRC="/img/revistas/ruma/v49n1/1a049x.png" WIDTH=172 HEIGHT=22> Let <IMG SRC="/img/revistas/ruma/v49n1/1a0410x.png" WIDTH=47 HEIGHT=19>denote the n-times iterated Aluthge transform of T, i.e. <IMG SRC="/img/revistas/ruma/v49n1/1a0412x.png" WIDTH=86 HEIGHT=19>and <IMG SRC="/img/revistas/ruma/v49n1/1a0413x.png" WIDTH=168 HEIGHT=19>, <IMG SRC="/img/revistas/ruma/v49n1/1a0414x.png" WIDTH=46 HEIGHT=14>. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence <IMG SRC="/img/revistas/ruma/v49n1/1a0415x.png" WIDTH=93 HEIGHT=19>converges for every r &times; r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. <![CDATA[Regular Optimal Control Problems with Quadratic Final Penalties]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100005&lng=es&nrm=iso&tlng=es Given an r &times; r complex matrix T, if <IMG SRC="/img/revistas/ruma/v49n1/1a047x.png" WIDTH=72 HEIGHT=19>is the polar decomposition of T, then the Aluthge transform is defined by <IMG SRC="/img/revistas/ruma/v49n1/1a049x.png" WIDTH=172 HEIGHT=22> Let <IMG SRC="/img/revistas/ruma/v49n1/1a0410x.png" WIDTH=47 HEIGHT=19>denote the n-times iterated Aluthge transform of T, i.e. <IMG SRC="/img/revistas/ruma/v49n1/1a0412x.png" WIDTH=86 HEIGHT=19>and <IMG SRC="/img/revistas/ruma/v49n1/1a0413x.png" WIDTH=168 HEIGHT=19>, <IMG SRC="/img/revistas/ruma/v49n1/1a0414x.png" WIDTH=46 HEIGHT=14>. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence <IMG SRC="/img/revistas/ruma/v49n1/1a0415x.png" WIDTH=93 HEIGHT=19>converges for every r &times; r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. <![CDATA[Some aspects of the history of applied mathematics in Argentina]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100006&lng=es&nrm=iso&tlng=es In this paper we shall briefly describe some aspects of the history, evolution and problems of applied mathematics in Argentina. <![CDATA[Poisson-Lie T-duality and integrable systems]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100007&lng=es&nrm=iso&tlng=es We describe a hamiltonian approach to Poisson-Lie T-duality based on the geometry of the underlying phases spaces of the dual sigma and WZW models. Duality is fully characterized by the existence of a hamiltonian action of a Drinfeld double Lie group on the cotangent bundle of its factors and the associated equivariant momentum maps. The duality transformations are explicitly constructed in terms of these actions. It is shown that compatible integrable dynamics arise in a general collective form. <![CDATA[The Duality Between Algebraic Posets and Bialgebraic Frames: A Lattice Theoretic Perspective]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100008&lng=es&nrm=iso&tlng=es This paper sets two goals. The first is to present algebraists with a purely order-theoretic derivation of the adjunction between the category DCPO of DCPOs (directed complete posets) and the category Frm of frames. This adjunction restricts to several Stone-type dualities which are well-known and of considerable interest to computer scientists. The second goal is to describe the object classes of these subdualities in terms familiar to algebraists, thereby making a large body of literature about them more accessible. <![CDATA[On the Notion of Bandlimitedness and its Generalizations]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100009&lng=es&nrm=iso&tlng=es In this survey article we introduce the Paley-Wiener space of bandlimited functions <IMG SRC="/img/revistas/ruma/v49n1/1a090x.png" WIDTH=45 HEIGHT=16>and review some of its generalizations. Some of these generalizations are new and will be presented without proof because the proofs will be published somewhere else. Guided by the role that the differentiation operator plays in some of the characterizations of the Paley-Wiener space, we construct a subspace of vectors <IMG SRC="/img/revistas/ruma/v49n1/1a091x.png" WIDTH=67 HEIGHT=19>in a Hilbert space <IMG SRC="/img/revistas/ruma/v49n1/1a092x.png" WIDTH=15 HEIGHT=12>using a self-adjoint operator <IMG SRC="/img/revistas/ruma/v49n1/1a093x.png" WIDTH=18 HEIGHT=12>We then show that the space <IMG SRC="/img/revistas/ruma/v49n1/1a094x.png" WIDTH=67 HEIGHT=19>has similar properties to those of the space <IMG SRC="/img/revistas/ruma/v49n1/1a095x.png" WIDTH=43 HEIGHT=15> The paper is concluded with an application to show how to apply the abstract results to integral transforms associated with singular Sturm-Liouville problems. <![CDATA[Saturated neighbourhood models of Monotonic Modal Logics]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100010&lng=es&nrm=iso&tlng=es In this paper we shall introduce the notions of point-closed, point-compact, and m-saturated monotonic neighbourhood models. We will give some characterizations, and we will prove that the ultrafilter extension and the valuation extension of a model are m-saturated. <![CDATA[The <IMG SRC="/img/revistas/ruma/v49n1/1a110x.png" WIDTH=14 HEIGHT=14>-homology of representations]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000100011&lng=es&nrm=iso&tlng=es The <IMG SRC="/img/revistas/ruma/v49n1/1a111x.png" WIDTH=10 HEIGHT=10>-homology groups of a <IMG SRC="/img/revistas/ruma/v49n1/1a112x.png" WIDTH=9 HEIGHT=12>-module provide a natural and fruitful extension of the concept of highest weight to the representation theory of a noncompact reductive Lie group. In this article we give an introduction to the <IMG SRC="/img/revistas/ruma/v49n1/1a113x.png" WIDTH=10 HEIGHT=10>-homology groups and a survey of some developments, with a particular emphasis on results pertaining to the problem of caculating <IMG SRC="/img/revistas/ruma/v49n1/1a114x.png" WIDTH=10 HEIGHT=9>-homology groups.