# Revista de Matemáticas 20(2)

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Ítem Dice, sticks, pixels and bits: didactic alternatives to explore the methodology of Monte Carlo in a ludic tone(2013-08-29 00:00:00) Navone, Hugo D.; Scancich, Miriam; Zorzi, Alejandra F.Más... This paper presents didactic strategies in a ludic tone to explore the methodology of Monte Carlo and analizes the implementations that have been performed in several educational scenarios. These proposals allow us to put into action concepts of probability and statistics in an amusing and attractive way by conducting cooperative “experiments-games” that are based on the use of real and virtual objects. Each strategy is aimed to teachers of high school and teacher training institutes, and also for early stages at University level, in order to be modified, recreated, and enhanced according to the specific areas of application.Más... Ítem Challenges for statistics teaching and teacher’s training in Mexico(2013-08-29 00:00:00) Hernández González, Sergio; Ruiz Hernández, Blanca; Pinto Sosa, Jesús E.; Albert Huerta, J. ArmandoMás... This work will cover the problems that are found in teacher training and professional development in Probability and Statistics in higher education in Mexico. It will be approached through four focuses: a) the characterization and training of teachers that drive the development and implementation of curriculum reforms in the teaching of Statistics; b) challenges of teachers in the instruction of university-level Statistics; c) new curricular reforms with respect to the instruction of Statistics that propose the development of a learning based in projects through the use of appropriate statistical software, and d) educational innovation as a body of knowledge in development, by which the shaping of networks consisting of professors who favor the emergence of real innovation is brought about. Starting from these perspectives, the challenges confronted in the teaching and training of Statistics professors will be proposed.Más... Ítem Comparative analysis of the orbital structure for non–cuspy and cuspy triaxial models of galaxies using different expansions of the gravitational potential(2013-08-29 00:00:00) Navone, Hugo D.; Zorzi, Alejandra F.Más... One way to create models of elliptical galaxies is to start from a system of particles with a suitable distribution and to follow its evolution with an N-body code until it reaches equilibrium. In previous works we used the code of L.A. Aguilar to generate non-cuspy and cuspy models, the latter giving a better representation of elliptical galaxies. However, the method proposed by Hernquist and Ostriker is more suitable for the cases with central cusps, because it uses an expansion of the potential in radial functions that already reflects the cuspy character. Here we consider two models, one non-cuspy and another cuspy, obtained with the method of Aguilar and whose potentials we now fit with the Hernquist and Ostriker expansion. We obtained the corresponding variational equations and we used them to determine the Lyapunov exponents of orbits already investigated with the method of Aguilar and to separate the chaotic ones. We classified the regular orbits through the analysis of their orbital frequencies. Here we present a comparison of the results obtained with the two methods for both types of orbits.Más... Ítem Algoritmo de búsqueda tabú para una variante del problema de coloración(2013-08-29 00:00:00) Aboytes Ojeda, Mario; Laureano Cruces, Ana Lilia; Ramírez Rodríguez, JavierMás... El problema de coloración robusta generalizado (PCRG) resuelve problemas de horarios que consideran restricciones especiales. Al ser una generalización del problema de coloración robusta, que es a su vez una generalización del problema de coloración, el PCRG es entonces un problema NP-Completo, por lo que es necesario utilizar métodos aproximados para encontrar buenas soluciones en un tiempo de cómputo razonable. En este trabajo se presenta un algoritmo de búsqueda tabú para programar casos de 30 a 180 horas por semana, para algunos de ellos encuentra la solución óptima, en otros casos, la solución obtenida supera a la mejor solución conocida. También se presentan ejemplos de mayor tamaño a los conocidos, obteniendo resultados muy competitivos, lo que se puede verificar por la ausencia de conflicto entre clases.Más... Ítem Simulation models generator. Applications in scheduling(2013-08-29 00:00:00) Castrillón, Omar Danilo; Giraldo, Jaime Alberto; Sarache, William ArielMás... The aim of this study is to disseminate the academic community a prototype computer that automatically generates simulation models of a given industrial production system, in order to facilitate the learning of some deterministic and stochastic scheduling. The basic architecture of the prototype computer developed in terms of presentation layers, processing and storage. Through the processing layer generates a prototype simulation model which is stored in the storage layer and subsequently can be run in order to test various models of production scheduling system. Scheduling theory has led to alternatives to generate the best solutions to problems of production scheduling and intends to develop this software to test some of these alternatives by computer simulation. Among the benefits that simulation brings is the ability to assess the impact that decisionsRev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 20(2): 231–241, July 2013 generador de modelos de simulacion 233 will, in order to have an approach to reality to evaluate decisions in order to take more assertive. To test prototype was used as the modeling example of a production system with 9 machines and 5 works as a job shop configuration, testing stops processing times and stochastic machine to measure rates of use of machines and time average jobs in the system, as measures of system performance. This test shows the goodness of the prototype, to save the user the simulation model buildingMás... Ítem General guidelines solution for linear programming with fuzzy coefficients(2013-08-29 00:00:00) de los Cobos Silva, Sergio Gerardo; Terceño Gómez, Antonio; Gutiérrez Andrade, Miguel ÁngelMás... This work introduce to the Possibilistic Programming and the Fuzzy Programming as paradigms that allow to resolve problems of linear programming when the coefficients of the model or the restrictions on the same are presented as fuzzy numbers, rather than exact numbers (crisp). This work presents some examples based on [1].Más... Ítem An optimization algorithm inspired by musical composition in constrained optimization problems(2013-08-29 00:00:00) Mora Gutiérrez, Roman Anselmo; Rincón García, Eric Alfredo; Ramírez Rodríguez, Javier; Ponsich, Antonin; Herrera Alcántara, Oscar; Lara Velázquez, PedroMás... Many real-world problems can be expressed as an instance of the constrained nonlinear optimization problem (CNOP). This problem has a set of constraints specifies the feasible solution space. In the last years several algorithms have been proposed and developed for tackling CNOP. In this paper, we present a cultural algorithm for constrained optimization, which is an adaptation of “Musical Composition Method” or MCM, which was proposed in [33] by Mora et al. We evaluated and analyzed the performance of MCM on five test cases benchmark of the CNOP. Numerical results were compared to evolutionary algorithm based on homomorphous mapping [23], Artificial Immune System [9] and anti-culture population algorithm [39]. The experimental results demonstrate that MCM significantly improves the global performances of the other tested metaheuristics on same of benchmark functions.Más... Ítem Sea level rise and the geoid: factor analysis approach(2013-08-29 00:00:00) Sadovski, Alexey; Song, Hongzhi; Jeffress, GaryMás... Sea levels are rising around the world, and this is a particular concern along most of the coasts of the United States. A 1989 EPA report shows that sea levels rose 5-6 inches more than the global average along the Mid-Atlantic and Gulf Coasts in the last century. The main reason for this is coastal land subsidence. This sea level rise is considered more as relative sea level rise than global sea level rise. Thus, instead of studying sea level rise globally, this paper describes a statistical approach by using factor analysis of regional sea level rates of change. Unlike physical models and semi-empirical models that attempt to approach how much and how fast sea levels are changing, this methodology allows for a discussion of the factor(s) that statistically affects sea level rates of change, and seeks patterns to explain spatial correlations.Más... Ítem Symmetry orbits and their data-analytic properties(2013-08-29 00:00:00) Viana, Marlos A.G.Más... The concept of data indexed by finite symmetry orbits is reviewed within the data-analytic framework of symmetry studies. Data decompositions are discussed in terms of canonical projections and Plancherel’s formulas, and interpreted in terms of orbit invariants.Más... Ítem A new method for the analysis of images: the square wave method(2013-08-29 00:00:00) Skliar, Osvaldo; Oviedo Blanco, Guillermo; Monge, Ricardo E.; Medina, Víctor; Gapper, SherryMás... The Square Wave Method (SWM) – previously applied to the analysis of signals – has been generalized here, quite naturally and directly, for the analysis of images. Each image to be analyzed is subjected to a process of digitization so that it can be considered to be made up of pixels. A numeric value or “level” ranging from 0 to 255 (on a gray scale going from black to white) corresponds to each pixel. The analysis process described causes each image analyzed to be “decomposed” into a set of “components”. Each component consists of a certain train of square waves. The SWM makes it possible to determine these trains of square waves unambiguously. Each row and each column of the image analyzed can be obtained once again by adding all the trains of square waves corresponding to a particular row or to a particular column. In this article the entities analyzed were actually sub-images of a certain digitized image. Given that any sub-image of any image is also an image, it was feasible to apply the SWM for the analysis of all the sub-images.Más... Ítem Sensibility concept for the discrete case in the cost sharing problem(2013-08-29 00:00:00) Hernández Lamoneda, Luis; Macías Ponce, Julio Cesar; Sánchez Sánchez, FranciscoMás... Suppose that a vector is produced jointly. We will consider the problem of dividing the cost of production among a group of components. In this paper we characterized a solution through two axioms, s-sensibility and separability. The sensibility is a concept related to the variations of a solution due to slight changes of the cost function and the separability is standard. We study the discrete cost sharing problem. We provide a axiomatic solution.Más... Ítem Analysis of optimal control problems for the process of wastewater biological treatment(2013-08-29 00:00:00) Grigorieva, Ellina V.; Bondarenko, Natalia V.; Khailov, Evgenii N.; Korobeinikov, AndreiMás... We consider a three-dimensional deterministic control model of the process of aerobic wastewater biotreatment. For this model, we formulate and solve two optimal control problems, each of which has a corresponding minimizing functional. For the first problem, the functional is a weighted sum of the pollutant concentration at the end of a fixed time interval and the cumulative biomass con- centration over the interval. For the second problem, the functional is a weighted sum of the pollutant concentration at the end of the time interval and the cumulative oxygen and biomass concentra- tions over the interval. In order to solve these problems, we apply the Pontryagin Maximum Principle. The switching functions are analytically investigated and uniquely determine the type of the op- timal controls for the considered problems. Their properties allow the simplification of the optimal control problems to that of finite- dimensional constrained minimization. Numerical solutions of the optimal control problems are also provided.Más...