Revista de Matemáticas 22(1)

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  • Ítem
    Algunas soluciones exactas para la ecuación unidimensional de fokker-planck usando simetrías de lie
    (2015-01-01 00:00:00) Ortíz Álvarez, Hugo Hernán; Jiménez García, Francy Nelly; Posso Agudelo, Abel Enrique
    La ecuación de Fokker Planck aparece en el estudio de fenómenos de difusión, procesos estocásticos y mecánica clásica y cuantica. Un caso particular de esta ecuación, ut − uxx − xux − u = 0, es analizada empleando el método de los grupos de Lie. De la condición de invariación fue posible obtener los generadores infinitesimales ó vectores de la ecuación identificando los correspondientes grupos de simetría. Se obtuvieron soluciones exactas para cada uno de estos generadores y se construyeron nuevas soluciones aplicando propiedades de simetría.
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    Times of analgesic efficacy of two drugs in the treatment of patients with renal-ureteral colic compared by survival models
    (2015-01-01 00:00:00) Reyes Velázquez, Luis; Ulín Montejo, Fidel; Pérez Chavez, Jorge Alejandro; Salinas Hernández, Rosa María; Torres López, Jorge Elías
    Renourethral colic is a very painful clinical situation that requires a quick diagnosis and treatment. A study was done with patients who were administered two types of analgesics, and whose pain was measured through a visual analogue scale. Censored data results were obtained, considering the time when the pain disappeared as the random variable. Maximum likelihood and survival analysis give useful methods to estimate the distribution and parametric functions for this variable. This study will allow a more effective, timely, lower cost and suitable medical treatment for patients.
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    Cognitive rhythms and evolutionary algorithms in university timetables scheduling
    (2015-03-18 15:16:40) Castrillón, Omar Danilo
    The main purpose of this research is to design a methodology based on evolutionary algorithms to university timetable scheduling. This methodology will consider the students’ cognitive rhythms, which establish that teaching certain subjects in specific time intervals is much better than other techniques. This project takes place in three phases. First of all, there is a description of the different techniques used to solve this problem. Then, a new methodology based on cognitive rhythms and evolutionary algorithms is proposed, and finally, different methodologies are compared to determine the best. It is concluded that evolutionary algorithms are more efficient than other techniques in the university timetable scheduling. Future lines of research will determine the impact of these techniques within the students’ learning process.
  • Ítem
    (2015-01-01 00:00:00) Chávez Bosquez, Oscar; Pozos Parra, Pilar; Gómez Ramos, José Luis
    The aspiration criterion is an imperative element in the Tabu Search, with aspiration-by-default and the aspiration-by-objective the mainly used criteria in the literature. In this paper a new aspiration criterion is proposed in order to implement a probabilistic function when evaluating an element classified as tabu which improves the current solution, the proposal is called Tabu Search with Probabilistic Aspiration Criterion (BT- CAP). The test case used to evaluate the performance of the Probabilistic Aspiration Criterion proposed consists on the 20 instances of the problem described in the First International Timetabling Competition. The results are compared with 2 additional variants of the Tabu Search Algorithm: Tabu Search with Default Aspiration Criterion (BT-CAD) and Tabu Search with Objective Aspiration Criterion (BT-CAO). Wilcoxon test was applied to the generated results, and it was proved with 99 % confidence that BT-CAP algorithm gets better solutions than the two other variants of the Tabu Search algorithm.
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    (2015-01-01 00:00:00) Grigorieva, Ellina V.; Khailov, Evgenii N.
    In this paper we consider a monopoly producing a consumer good of high demand. Its market price depends on the volume of the produced goods described by the Cobb-Douglas production function. A production-sales activity of the firm is modeled by a nonlinear differential equation with two bounded controls: the share of the profit obtained from sales that the company reinvests into expanding own production, and the amount of short-term loans taken from a bank for the same purpose. The problem of maximizing discounted total profit on a given time interval is stated and solved. In order to find the optimal production and sales strategies for the company, the Pontryagin maximum principle is used. In order to investigate the arising two-point boundary value problem for the maximum principle, an analysis of the corresponding Hamiltonian system is applied. Based on a qualitative analysis of this system, we found that depending on the initial conditions and parameters of the model, both, singular and bang- bang controls can be optimal. Economic analysis of the optimal solutions is discussed.
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    Selective methodology of population dynamics for optimizing a multiobjective environment of job shop production
    (2015-03-18 15:16:40) Ruiz, Santiago; Castrillón, Omar Danilo; Sarache, William Ariel
    This paper develops a methodology based on population genetics to improve the performance of two or more variables in job shop production systems. The methodology applies a genetic algorithm with special features in the individual selection when they pass from generation to generation. In comparison with the FIFO method, the proposed methodology showed better results in the variables makespan, idle time and energy cost. When compared with NSGA II, the methodology did not showed relevant differences in makespan and idle time; however better performance was obtained in energy cost and, especially, in the number of required iterations to get the optimal makespan.
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    An adaptive wavelet-galerkin method for parabolic partial differentia equations
    (2015-01-01 00:00:00) Vampa, Victoria; Martín, María T.
    In this paper an Adaptive Wavelet-Galerkin method for the solution of parabolic partial differential equations modeling physical problems with different spatial and temporal scales is developed. A semi-implicit time difference scheme is applied and B-spline multiresolution structure on the interval is used. As in many cases these solutions are known to present localized sharp gradients, local error estimators are designed and an efficient adaptive strategy to choose the appropriate scale for each time is developed. Finally, experiments were performed to illustrate the applicability and efficiency of the proposed method.
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    Special software for computing the special functions of wave catastrophes
    (2015-01-01 00:00:00) Kryukovsky, Andrey S.; Lukin, Dmitry S.; Rogachev, Sergey V.
    The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and interoperability.
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    Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
    (2015-01-01 00:00:00) Cabuzel, Catherine; Pietrus, Alain; Burnet, Steeve
    This paper deals with the study of an iterative method for solving a variational inclusion of the form 0 ∈ f (x)+F (x) where f is a locally Lipschitz subanalytic function and F is a set-valued map from Rn to the closed subsets of Rn. To this inclusion, we firstly associate a Newton then secondly an Inexact Newton type sequence and with some semistability and hemistability properties of the solution x∗ of the previous inclusion, we prove the existence of a sequence which is locally superlinearly convergent.
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    Infinitely oscillating wavelets and a efficient implementation algorithm based the FFT
    (2015-01-01 00:00:00) Fabio, Marcela; Serrano, Eduardo P.
    In this work we present the design of an orthogonal wavelet, infinitely oscillating, located in time with decay 1/|t|n and limited-band. Its appli- cation leads to the signal decomposition in waves of instantaneous, well defined frequency. We also present the implementation algorithm for the analysis and synthesis based on the Fast Fourier Transform (FFT) with the same complexity as Mallat’s algorithm.
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    Fourier coefficientes computation in two variables, a distributional version
    (2015-01-01 00:00:00) Ulata R., Carlos Manuel
    The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.