Revista de Matemáticas 8(2)

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  • Ítem
    A method for analyzing turbulence models
    (2009-02-19 00:00:00) Grebene, V. N.; Ilyushin, B. B.
    In this article we introduce a concept based on the differential constraints methodto examine the closure procedure in Turbulence Models. We show how this conceptmay be applied to study the problem of interaction and mixing between two semiinfinitehomogeneous turbulent flow fields of different scales.Keywords:  ResumenTurbulence models, closure procedure, differential constraints, invariant sets,third-order closure model, selfsimilar solution, asymptotic behavior.
  • Ítem
    Teoría de nudos geométricos e isotopía poligonal
    (2009-02-19 00:00:00) Calvo Soto, Jorge Alberto
    The space of n-sided polygons embedded in euclidean three-space consists of a smoothmanifold in which points correspond to piecewise linear or “geometric” knots, while pathscorrespond to isotopies which preserve the geometric structure of these knots. The topologyof these spaces for the case n = 6 and n = 7 is described. In both of these cases, each knotspace consists of five components, but contains only three (when n = 6) or four (when n = 7)topological knot types. Therefore “geometric knot equivalence” is strictly stronger thantopological equivalence. This point is demonstrated by the hexagonal trefoils and heptagonalfigure-eight knots, which, unlike their topological counterparts, are not reversible. Extendingthese results to the cases n 8 will also be discussed.Keywords:  polygonal knots, space polygons, knot spaces, knot invariants.
  • Ítem
    Modeling genetic algorithms with interacting particle systems
    (2009-02-19 00:00:00) Del Moral, P.; Kallel, L.; Rowe, J.
    We present in this work a natural Interacting Particle System (IPS) approach formodeling and studying the asymptotic behavior of Genetic Algorithms (GAs). In thismodel, a population is seen as a distribution (or measure) on the search space, and theGenetic Algorithm as a measure valued dynamical system. This model allows one toapply recent convergence results from the IPS literature for studying the convergenceof genetic algorithms when the size of the population tends to infinity.We first review a number of approaches to Genetic Algorithms modeling and relatedconvergence results. We then describe a general and abstract discrete timeInteracting Particle System model for GAs, and we propose a brief review of some recentasymptotic results about the convergence of the N-IPS approximating model (offinite N-sized-population GAs) towards the IPS model (of infinite population GAs),including law of large number theorems, IL p-mean and exponential bounds as well aslarge deviations principles.Finally, the impact of modeling Genetic Algorithms with our interacting particlesystem approach is detailed on different classes of generic genetic algorithms includingmutation, cross-over and proportionate selection. We explore the connections betweenFeynman-Kac distribution flows and the simple genetic algorithm. This Feynman-Kacrepresentation of the infinite population model is then used to develop asymptoticstability and uniform convergence results with respect to the time parameter.Keywords:  Genetic algorithms, Interacting particle systems, asymptotical convergence,Feynman-Kac formula, measure valued processes.
  • Ítem
    Estabilizacíon del modelo poblacional de may a través de controles direccionales
    (2009-02-19 00:00:00) Delgado Andrade, Víctor
    The May population model consider a satiate parameter over the predators andhas an unstable equilibrium state surrounded by a limit cycle. This work gives acontrol strategy driven to disturb the model in such way that the equilibrium statebecome locally asymptotically stable. The way to perform this objective is to considera directional feedback control over the linearization of the model.Keywords:  stability, linearization, directional feedback control, linearly equivalent systems.
  • Ítem
    Some properties and inequalities related to the kth inverse moment of a positive binomial variate
    (2009-02-19 00:00:00) Arias López, Rodrigo; Garrido, José
     We present some known properties of bk(n, p) the kth inverse moment of a positive binomial variate. Additional properties of this function and new bounds are derived. Keywords:  Probability, statistics, life contingencies, Bernstein polynomials.