# Revista de Matemáticas 19(2)

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Ítem A note on $k$-finite objects in a boolean topos with the natural numbers object(2012-07-01 00:00:00) Acuña Ortega, OsvaldoMás... We prove that every $k$-finite object in a boolean topos with nat-ural number object is internally the quotient of a natural number object.Keywords: Topoi, $k$-finite objects, natural numbers.Mathematics Subject Classification: 03G30, 18B25.Más... Ítem Application of a cognitive model of emotional appraisal to the board evaluation function of a program that plays chess(2012-07-01 00:00:00) Laureano Cruces, Ana Lilia; Hernández González, Diego Enrique; Mora Torres, Martha; Ramírez Rodríguez, JavierMás... This paper describes the analysis and design of a cognitive emotional assesment model. This model is based on the goals looked for a chess player during a game. The model affects the output of the board evaluation function of a computational agent which plays chess, giving more weight to aspects related to the most urgent goals, according to the context. Thus, it perceives environment changes, and consequently changes its choice of the next play. The aim is that the computational agent incorporates into the decision making process, the emotional state and choose the plays based on that state. For that purpose were used tools of cognitive psychology and soft computing in order to simulate emotion, and affect the agent’s behavior computer.Keywords: computer chess; mental models; emotive elicitation; synthetic emotions; evaluation function; fuzzy cognitive mapsMathematics Subject Classification: 68T20, 68T37.Más... Ítem Variants of the mixed postman problem solvable using linear programming(2012-07-01 00:00:00) Zaragoza Martínez, Francisco Javier; López Bracho, RafaelMás... Given a connected mixed graph with costs on its edges and arcs, the mixed postman problem consists of finding a minimum cost closed tour of the mixed graph traversing all of its edges and arcs. It is well-known that this problem is NP-hard. However, under certain conditions, the problem can be solved in polynomial time using linear programming, in other words, the corresponding polyhedra are integral. Some of these conditions are: the mixed graph is series parallel or the mixed graph is even. Also, we show that if we add the constraint that each edge is traversed exactly once then the problem can be solved in polynomial time if the set of arcs forms a forest.Keywords: Mixed graph, postman problem, linear programming.Mathematics Subject Classification: 05C45, 90C35.Más... Ítem New geometrical compactness measures for zones design(2012-07-01 00:00:00) Rincón García, Eric Alfredo; Gutiérrez Andrade, Miguel Ángel; de los Cobos Silva, Sergio Gerardo; Lara Velázquez, PedroMás... The design of compact zones has been studied because of its influence in the creation of zones with regular forms, which are easier to analyze, to investigate or to administer. This paper propose a new method to measure compactness,by means of the transformation of the original geographical spaces, into figures formed with square cells, which are used to measure the similarity between the original zone and an ideal zone with straight forms. The proposed method was applied to design electoral zones, which must satisfy constraints of compactness, contiguity and population balance, in a topographical configuration that favors the creation of twisted and diffuse shapes. The results show that the new method favors the creation of zones with straight forms, without an important effect to the population balance, which are considered zones of high quality.Keywords: Redistricting, compactness, simulated annealing, GIS.Mathematics Subject Classification: 90C59, 90C29, 68T20.Más... Ítem Lagrangean relaxation for the geographical partitioning problem(2012-07-01 00:00:00) Díaz García, Juan Antonio; Bernabé Loranca, María Beatriz; Luna Reyes, Dolores Edwiges; Olivares Benítez, Elías; Martínez Flores, José LuisMás... Among methodologies used in territory clustering, stand location-allocation and set partitioning models, to group small geographic areas, usually called “basic units” into a given number of larger groups called “territories”. The territory clustering problem is modeled as a p-median problem. A Lagrangean relaxation is used to obtain lower bounds to the optimal solution of the problem and a procedure is used to obtain upper bounds. In order to evaluate the performance of the proposed procedure, instances of two Mexico cities are used. The results obtained with the proposed method are compared to partitioning methods from the literature. According to the obtained results for the considered instances using different number of groups, optimal or near optimal solution are obtained with a reasonable amount of computer effort.Keywords: partitioning, Lagrangean relaxation, heuristics.Mathematics Subject Classification: 90C59, 62H30, 91C20.Más... Ítem Time-frequency methods based on the wavelet transform(2012-07-01 00:00:00) Serrano, Eduardo P.; Fabio, Marcela; Figliola, AlejandraMás... The information contained in an analog signal is reveled by its numerical representation. The Fourier pair, in two complementary representations, expounds time and frequency structures. However, to detect and characterize those events which combine both structures in diverse and complex patterns, it is necessary to implement more refined methods joint with appropriate time-frequency representations.Among various options, the wavelet transform provides an efficient tool time-scale. Their extensions lead to appropriate representations coexisting in the same analytical context. Make it possible implement flexible strategies, well adapted to the characteristics of the signal.Keywords: time-frequency representations, wavelet transform, multiresolution analysis, wavelet packets, instantaneous frequency.Mathematics Subject Classification: 42C40, 44A05.Más... Ítem Implementation of LDG method for 3D unstructured meshes(2012-07-01 00:00:00) Sequeira Chavarría, Filander A.; Castillo, Paul E.Más... This paper describes an implementation of the Local Discontinuous Galerkin method (LDG) applied to elliptic problems in 3D. The implementation of the major operators is discussed. In particular the use of higher-order approximations and unstructured meshes. Efficient data structures that allow fast assembly of the linear system in the mixed formulation are described in detail.Keywords: Discontinuous finite element methods, high-order approximations, unstructured meshes, object-oriented programming.Mathematics Subject Classification: 65K05, 65N30, 65N55.Más... Ítem Asymptotical analysis and Padé approximation in problems on diffusion-controlled cracks propagation(2012-07-01 00:00:00) Balueva, Alla V.; Germanovich, Leonid N.Más... In this work, we consider the diffusion-controlled axisymmetric fracture in an infinite space, and half-space. An important example of diffusion-controlled fracture growth is given by hydrogen induced cracking. In metals, hydrogen is typically dissolved in the proton form. When protons reach the crack surface, they recombine with electrons and form molecular hydrogen in the crack cavity. Then, the fracture can propagate even in the absence of any external loading, that is, only under the excessive pressure of gas hydrogen accumulated inside the crack.Our results show that in the long-time asymptotic approximation (based on the quasi-static solution), the diffusion-controlled delamination propagates with constant velocity. We determine a maximum critical concentration that limits the use of the quasi-static solution. A transient solution, representing a short time asymptotic approximation, is used when the concentration of gas exceeds the critical concentration. We then match these two end-member cases by using the method of Padé approximations and present closed-form solutions for both internal and near-surface diffusion-controlled crack propagation at different time scales.Keywords: diffusion, crack propagation, asymptotic analysis, Padé approximation.Mathematics Subject Classification: 74A45, 74N25, 41A21.Más...