Revista de Matemáticas 21(1)

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  • Ítem
    Artificial bee colony and particle swarm optimization for the estimation of nonlinear regression parameters
    (2014-04-03 19:29:59) de los Cobos Silva, Sergio Gerardo; Gutiérrez Andrade, Miguel Ángel; Rincón García, Eric Alfredo; Lara Velázquez, Pedro; Aguilar Cornejo, Manuel
    This paper shows the comparison results of ABC (Artificial Bee Colony) and PSO (Particle Swarm Optimization) heuristic tech- niques that were used to estimate parameters for nonlinear regression models. The algorithms were tested on 27 data bases from the NIST collection (2001), 8 of these are considered to have high difficulty, 11 medium difficulty and 8 low difficulty. Experimental results are presented.     
  • Ítem
    Location of police cars for public surveillance using two multicriteria models
    (2014-04-03 19:29:59) García G., María J.; Hernández, Gilberto; Hernández R., José G.
    The criminal boom in some Latin-American cities obliges the increment of patrols and policemen. Sadly they do not there sufficient vehicles to locate in all the places candidates. In the location of patrols, there are many parameters to consider, becoming a multicriteria problem. Two multi-criteria technical simpler to use are Multiattribute Model with Multiplicative factors (MMwMf) and Matrix Of Weighing (MOW). The MMwMf making decisions, considering the criteria that characterize the situation and the attributes, that define these criteria. By the other side the MOW, only they take into account criteria. The user friendliness of these two kinds of models, has inspired the objective of this work: Creating a pair of model multicriterion, that in independent form they permit to locate patrols in a determined population: A Multiattribute Model with Multiplicative factors (MMwMf) and a Matrix Of Weighing (MOW). 
  • Ítem
    The traveling salesman problem: a deterministic algorithm using tabu search
    (2014-04-03 19:29:59) López, Erasmo; Salas Huertas, Oscar; Murillo Fernández, Álex
    We implement an algorithm corresponding to the Taboo Search method, called EraDeterministic, experimenting with the basic algorithm that ex- plores the search space and incorporating the diversification as strategy to explore new regions. The algorithm is developed in the programming environment Visual Basic 6.0 and the implementation is aimed at finding close solutions to the optimum of the problem NP−complete of the Sym- metric Traveling Salesman (STS). To test the functionality, the model is compared with some instances of the Travel Salesman Problem Library (TSPLIB), some random instances and applied to three real-life situations. Finally, we present a section with comments and conclusions, that guide us on possible future developments that demonstrate the benefits and the efficiency of the implementation. 
  • Ítem
    Interstatis: the statis method for interval valued data
    (2014-04-03 19:29:59) Corrales, David; Rodríguez Rojas, Oldemar
    The STATIS method, proposed by L’Hermier des Plantes and Escoufier, is used to analyze multiple data tables in which is very common that each of the tables have information concerning the same set of individuals. The differences and similitudes between said tables are analyzed by means of a structure called the compromise. In this paper we present a new algorithm for applying the STATIS method when the input consists of interval data. This proposal is based on Moore’s interval arithmetic and the Centers Method for Principal Component Analysis with interval data, proposed by Cazes el al. [5]. In addition to presenting the INTERSTATIS method in an algorithmic way, an execution example is shown, alongside the interpretation of its results. 
  • Ítem
    GNM-NIPALS: general nonmetric-nonlinear estimation by iterative partial least squares
    (2014-04-03 19:29:59) Aluja, Tomás; González, Víctor Manuel
    This paper develops GNM-NIPALS as an extension of the NM-PLS methods, which allows to quantify the qualitative variables of mixed data, by means of the reconstitution function using the first k principal com- ponents, maximizing the inertia in the plane k subspace associated with the PCA of the quantified matrix. It generalizes the NM-NIPALS algo- rithm in the sense that the latter only uses the first principal component in the quantification of qualitative variables. From the maximization and positivity of the correlation ratio between each qualitative variable and the reconstituted function, we have that the accumulated inertia on the k- dimensional subspace associated to the quantification function of the same range is greater than or equal to the one generated on subspaces of equal dimension, but with quantification functions of different range. With the k principal components associated to the quantified matrix, a saturated in- ertia analysis is performed to evaluate if a dimension k∗< k still exists, from which the accumulated inertia on the axes of equal or superior order is already explained, in which case the definitive quantification function is of lesser range (k∗). 
  • Ítem
    On the design of membranes with increasing fundamental frequency
    (2014-04-03 19:29:59) González De Paz, Raúl B.
      By means of a relaxation approach, we study the shape design of a stiff inclusion with given area in a membrane in order to maximize its fun- damental frequency. As an eigenvalue control problem, the fundamental frequency is a concave function of the control, which is not described by the membrane shape, but by an element in a function space. First order optimality conditions allow to describe the optimal shape by means of a free boundary value problem. 
  • Ítem
    Funciones regulares en el plano y operadores de Nemytskii
    (2014-01-01 00:00:00) Aziz, Wadie
    En este artículo mostramos que el espacio de las llamadas funciones regularizadas definidas sobre algún rectángulo del plano es un espacio de Banach. Más aún, bajo las hipótesis adecuadas damos condición necesaria y suficiente para el operador de Nemytskii aplique el espacio de funciones regularizadas sobre el mismo. 
  • Ítem
    Construction and study of local linearization adaptive codes for ordinary differential equations
    (2014-04-03 19:29:59) Sotolongo Aguiar, Alina; Jiménez Sobrino, Juan Carlos
    The aim of this work is to construct adaptive integrators for ordinary differential equations based on the Local Linearization method. Different orders of the involved Padé approximation are considered and their effect on the adaptive integrators is studied. 
  • Ítem
    K-finite objects and decidability
    (2014-01-01 00:00:00) Acuña Ortega, Osvaldo
    We study the k-finite and decidable objects in an elementary topos. We prove some results concerning k-finite and decidable objects.