# Revista de Matemáticas 19(1)

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Ítem Ttsunami. An Interesting Mathematical Problem(2012-03-12 00:00:00) González González, Rodrigo; Ortiz Figueroa, Modesto; Montoya Rodríguez, José MiguelMás... We present some key aspects regarding the mathematics and the computational tool that support the complex description of the physical process tsunami from two specific approaches. In particular, it addresses analytically a simple hydroelastic model for the problem of tsunami wave generation, which provides results in the rupture area. Moreover, the propagation of tsunami waves in the ocean and the impact along the coastline is analyzed numerically using the hydrodynamic approach, presenting in particular a direct application to the prediction of tsunamis in Mexico caused by potential earthquakes in the Mesoamerican trench through the design of a “Tsunami Toolbox” to simulate tsunamis caused by earthquakes in the subduction zone on the western coast of Mexico.Más... Ítem On the Cramér–Von Mises Statistic(2012-03-11 00:00:00) Martínez Camblor, Pablo; Carleos, Carlos; Corral, NorbertoMás... Probably, one of the most useful criterions in order to compare distribution functions is the one introduced by the researchers Harald Cramér and Richard Edler von Mises which is known as Cramérvon Mises criterion $(C_M)$. It has been applied on a vast variety of problems. In this work, the theory of empirical processes is applied in order to obtain the asymptotic distribution for the generalization to the k-sample problem of $(C_M)$ proposed by Kiefer. The quality of this approximation is also studied and some indications about how to obtain an approximation to the final P-value are also included.Más... Ítem Regularidad local del Mercado de índices para la crisis económica de 2008(2012-03-08 00:00:00) Figliola, Alejandra; Rosenblatt, Mariel; Serrano, Eduardo P.Más... There is evidence that signals from financial markets, such as stock indices, interest rates or commodities, have a multifractal nature. In recent years, many efforts have been made to relate the inefficiency of markets with the multifractal characteristics of this corresponding signals. These characteristics are summarized in the knowledge of the spectrum of singularities or multifractal spectrum that relates to the set of singular points of the signal with its corresponding Hausdorff dimension. The novel approach proposed in this paper, to study the dynamics of financial markets, is to analyze the evolution of the set of singular points or Hölder exponents of the series of exchanges, measured daily. We examined the “logarithmic returns” of stock indices from 9 countries in developed markets and 12 belonging to emerging markets from February 2006 to March 2009.The analysis reveals that the temporal variation of the local Hölder exponent point reflects the evolution of the crisis and identifies the historical events which have occurred during this phenomenon, from the minimum values of the Hölder exponent.Más... Ítem Small data existence for the Boltzmann Equation in $L^{1}$(2012-03-11 00:00:00) Galeano Andrades, Rafael; Ortega Palencia, Pedro; Vásquez Ávila, María OfeliaMás... An existence theorem for the Boltzmann Equation with force term and small initial data is proved in an $L^{1}$ settingMás... Ítem Influence Factors in Private Investment in El Salvador(2012-03-12 00:00:00) Palacios, René; Funes, NerysMás... According to many empirical studies, one aspect that determines the foundations of economic cycles in the short and medium term is the investment of capital goods since it belongs to an aggregate demand and explains the changes in phase and scope of the productive cycle in the economy. Here we establish factors that are determinant of the private investment in El Salvador. This study was prepared based on historic economic records from the period 1958-2008 and using dynamic regression techniques of time series. The methodology implemented is the following: A univariate analysis is undertaken of each series, with the goal of adequately identifying a proper ARIMA model that corresponds and adjusts to the dynamic regression model for the private investment. The objective of this study is to contribute to the establishment to the economic policies for El Salvador and to offer orientation for the modeling of phenomena in which time series are involved.Más... Ítem Joint Kalman–Haar Algorithm Applied to Signal Processing(2012-03-08 00:00:00) Viegener, Alejandro; Sirne, Ricardo O.; Sirne, Ricardo O.; Serrano, Eduardo P.; Serrano, Eduardo P.; Fabio, Marcela; Fabio, Marcela; D'Attellis, Carlos E.; D'Attellis, Carlos E.Más... Under the analysis of signals disturbed by noise, in this paper we propose a working methodology aimed to seize the best estimate of combining Kalman filtering with the characterization that is achieved by applying a multiresolution analysis (MRA) using wavelets. From the standpoint of Kalman filtering this combined procedure is quasi-optimal, but the change to be made allows the simultaneous implementation of a scheme of wavelet denoising; with this decreases the computational cost of applying both procedures separately. Our proposal is to process the signal by successive non-overlapping intervals, combining the process for calculating the optimal filter with a MRA using the Haar wavelet. The method takes advantage of the combined use of both tools (Kalman-Haar) and is free from edge problems related to the signal segmentation.Más... Ítem Co-occurrence Matrix and fractal dimension for image segmentation(2012-03-08 00:00:00) Marón, Beatriz S.Más... One of the most important tasks in image processing problem and machine vision is object recognition, and the success of many proposed methods relies on a suitable choice of algorithm for the segmentation of an image. This paper focuses on how to apply texture operators based on the concept of fractal dimension and cooccurence matrix, to the problem of object recognition and a new method based on fractal dimension is introduced. Several images, in which the result of the segmentation can be shown, are used to illustrate the use of each method and a comparative study of each operator is made.Más... Ítem Estimation of General Equilibium Model in Dynamic Economies using Markov Chain Monte Carlo Methods(2012-03-08 00:00:00) Estévez, Gloria; Infante, Saba; Sáez, FranciscoMás... This paper describes a general procedure to do Bayesian inference based on the likelihood evaluation of the stochastic general equilibrium models (MEGE) through Markov Chain Monte Carlo methods (MCMC). The proposed methodology involves log linearizing the model, transformed into state space form, then use the Kalman filter to evaluate the likelihood function and finally apply the Metropolis Hastings algorithm to estimate the posterior distribution parameters. Technique is illustrated using the stochastic growth of basic model, considering quarterly data on the Venezuelan economy between the first quarter of (1984) through the third quarter of (2004). The empirical analysis made allows us to conclude that the algorithms used to estimate the model parameters work efficiently and low computational cost, the estimates obtained are consistent, that is, estimates of the predictions adequately reflect the behavior of the product, employment, consumption and investment per capita in the country. The graphs of the estimated histograms show bimodal and skewed distributions.Más... Ítem K-finite decidable objects and finite cardinals in an arbitrary topos(2012-03-08 00:00:00) Acuña Ortega, OsvaldoMás... In an elemetary topos $\varepsilo$, we prove that the class of K-finite decidable objects is the same to the class of finite cardinals in E if and only if every K-finite decidable object X such that $X \longrightarrow 1$ is epic, then $1 \longrightarrow X $ is split epic.Más...