# Revista de Matemáticas 12(1 y 2)

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Ítem Modelo Multifractal Aplicado al Riego(2012-03-02 00:00:00) Mercado Escalante, José Roberto; Aldama R., Álvaro Alberto; Íñiguez C., Mauro; Mejía G., Miguel ÁngelMás... We define the binomial multifractal distribution as an expression of a law of small numbers. We studied a form of evaluation or design of a distribution system in an irrigation district by determining its conduction capacity with the desired flexibility knowing the following parameters: flow, frequency, and irrigation time. The method consists of the approximation of the binomial distribution through the Gaussian, an inverse relation of probability, two estimations of Gaussian parameters, and the application of the multifractal distribution. We present the mathematical reformulation of Boltzmann relation in the statistical mechanics, which gives origin to the multifractal model. In particular, we illustrate its application in the problems of irrigation, pointing out that it is also possible to apply it to multifractal models: variogram, exponential, gamma, and Gaussian.Más... Ítem Program Implementation of the Rating Methods of Preference Ranking(2012-03-02 00:00:00) Torres, Kelly; Sadovski, Alexey; Steidley, Carl W.Más... Tide charts, based upon harmonic analysis, is the general method of choice for predicting water levels. In the shallow waters of the Gulf of Mexico, however, tide charts are woefully inadequate for the prediction of water levels. We have developed a number of models for the prediction of water levels. In this paper we summarize these methods and discuss the development of an axiomatic tool that we use to measure the quality of predictions of water levels in the estuaries and shallow waters of the Gulf of Mexico. This quality measure is based upon the preference rankings of National Ocean Service criteria by experts in the field.Más... Ítem Comparison of Gap Interpolation Methodologies for water Level time Series using perl/pdl(2012-03-02 00:00:00) Mostella, Aimee; Sadovski, Alexey; Duff, Scott; Michaud, Patrick; Tissot, Philippe E. Tissot; Steidley, Carl W.Más... Extensive time series of measurements are often essential to evaluate long term changes and averages such as tidal datums and sea level rises. As such, gaps in time series data restrict the type and extent of modeling and research which may be accomplished. The Texas A&M University Corpus Christi Division of Nearshore Research (TAMUCC-DNR) has developed and compared various methods based on forward and backward linear regression to interpolate gaps in time series of water level data. We have developed a software system that retrieves actual and harmonic water level data based upon user provided parameters. The actual water level data is searched for missing data points and the location of these gaps are recorded. Forward and backward linear regression are applied in relation to the location of missing data or gaps in the remaining data. After this process is complete, one of three combinations of the forward and backward regression is used to fit the results. Finally, the harmonic component is added back into the newly supplemented time series and the results are graphed. The software created to implement this process of linear regression is written in Perl along with a Perl module called PDL (Perl Data Language). Generally, this process has demonstrated excellent results in filling gaps in our water level time series. The program was tested on existing data under three typesof typical weather conditions: calm summers, frontal passages and extreme weather conditions, such as hurricanes. The parameters varied in order to test the accuracy of the methodology included the number of coefficients utilized in the linear regression processes as well as the size of the gaps to be filled. Results are presented for the different weather conditions and the different gap size and coefficient combinations.Más... Ítem Artificial Neural Network Predictions of Water Levels in a Gulf of Mexico Shallow Embayment(2012-03-01 00:00:00) Bowles, Zack; Tissot, Philippe E. Tissot; Michaud, Patrick; Sadovski, AlexeyMás... Tide tables are the method of choice for water level predictions in most coastal regions. However, for many locations along the coast of the Gulf of Mexico, tide tables do not meet United States National Ocean Service (NOS) standards. Wind forcing has been recognized as the main variable not included. The performance of the tide tables is particularly poor in shallow embayments. Recent research has shown that Artificial Neural Network (ANN) models including input variables such as previous water levels, tidal forecasts, wind speed, wind direction, wind forecasts and barometricpressure can greatly improve over the tide charts for locations including open coast and deep embayments. In this paper, the ANN modeling technique is applied to a shallow embayment, the station of Rockport, located near Corpus Christi, Texas. The ANN model performance is compared against the NOS tide charts and the persistence model for the years 1997 to 2001. The performance is assessed using NOS criteria including Central Frequency (CF of 15 cm), Maximum Duration of Positive Outliers (MDPO), and Maximum Duration of Negative Outliers (MDNO). Over the study period, the performances of the three models (tide table, persistence, ANN) are respectively CF’s of 85%, 95.8% and 96.9%, MDPOs of 16, 14 and 5.9 hours, and MDNOs of 72.8 hours, 0.6 and 9.5 hours.Más... Ítem Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood(2012-03-02 00:00:00) Mahdi, Smail; Cenac, MyrteneMás... We derive here estimators for the parameters of the Gumbel distribution using three estimating methods, namely, the probability weighted moments, the moment and the maximum likelihood methods. Furthermore, we compare the performance of these estimators using simulations. Both integer and non-integer orders are considered in the probability weighted moments method. Overall, the results show that the probability weighted moments method outperforms the other methods in the estimation of both $\alpha$ and $\epsilon$ parameters.Más... Ítem Term Structure of Interest Rates(2012-03-02 00:00:00) Stradi, Benito A.Más... The risk free rate on bonds is a very important quantity that allows calculation of premium values on bonds. This quantity of stochastic nature has been modeled with different degrees of sophistication. This paper reviews the major models utilized in the estimation of the risk free rate and gives an example of the behavior generated by one of these models.Más... Ítem Scattering of e Polarized Whispering-Gallery mode from Concave Boundary(2012-03-01 00:00:00) Anyutin, Alexander P.; Stasevich, V.I.Más... In this work we present numerical results for the 2D problem of scattering E polarised whispering-gallery mode from concave convex perfectly conducting boundary. The results were obtained by applying the developed method of currants integral equations (CIE) [6,7] for high frequency domain when the size of the scatterer match is greater than the wave length. We have applied the described procedure in order to find numerical solutions of scattering whispering-gallery mode by concave finite convex boundary as a part of a circular cylinder or part of parabolic cylinder. As incident wave we have considered cylindrical waves from line source and Gauss beam [6] with different effective width. It is shown that we have a complicated process of focusing and oscillating of the beam’s reflected field, both cylindrical and Gauss beam incident fields. The distortions of reflected field depend on shape of the boundary and parameters of the incident fields.Más... Ítem Un Algoritmo Evolutivo para Resolver el Problema de Coloración Robusta(2012-03-22 00:00:00) Lara Velázquez, Pedro; Gutiérrez Andrade, Miguel Ángel; Ramírez Rodríguez, Javier; López Bracho, RafaelMás... Let G and \bar{G} be two complementary graphs. Given a penalty function defined over the edges of \bar{G}, it is said that the rigidity of a k-coloring of G is the summation ofthe penalties of the edges of G that join vertices whose endpoint are equally colored. Based on this previous definition, the Robust Coloring Problem is set when searching the valid k-coloring of minimum rigidity. Yáñez and Ramírez proved that this is an NP-hard problem. In this work we present an evolutive algorithm based in the scatter search technique, which obtains optimal solutions for those instances for which an optimal solution is known, and obtains the best known solutions compared to other heuristics, such as: simulated annealing, tabu search and partial enumeration.Más... Ítem Una propuesta de Modelamiento para los Sistemas de Recompensa(2012-03-01 00:00:00) de los Cobos Silva, Sergio Gerardo; Brunet Icart, Ignasi; Pérez Salvador, Blanca Rosa; González Santoyo, Federico; Flores Romero, BeatrizMás... One of the most important subjects of interest, in nearly any human activity, is the perception of salary. It could even be said that the decision of following a career depends deeply on the perspective that the individual may have about the future income. In this work we propose a general model for its computation. We define an employee’s reward system as a function that depends on monetary and non monetary parameters; hence, the reward system can be stated as a multiobjective system to be optimized. In the article we present a rationale of the proposed reward system, as a general model of solution, and we present come examples.Más... Ítem Un Modelo Matemático para la bola de Fútbol(2012-03-01 00:00:00) Escalante, René; Pacheco, FranciscoMás... This work refers to the analysis, study and resolution of the mathematical problem involved in the design and construction of the cover of a ball, such as the ones used in sports, in order to achieve a ball with optimal roundness and sphericity factors.The design of well distributed ball structures has grown in importance in the last years, most of all in the field of sports, such as soccer. The current trend is directed mainly towards finding a fast ball that will give more dynamism to the game. In order to achieve a greater velocity of the ball during its movement it is important that it has not only an adequate distribution of panels, that give it a greater sphericity, but also that it has a structure that allows for a good distribution of the existing tension between the panels. Starting from an initial design, we define a process of readjustment of the panels in the ball cover, which will lead us to obtain optimal sphericity factors. Then, through a “twisting” process, we can add area to the surface without altering the sphericity factors, and solving the Missing Area Problem (or MAP). Finally, by redefining the final form of the panels, we propose tessellate strategies that will optimize the ball’s spherical structure.Más... Ítem Indentificación de Fases de la Diabetes Espontánea de un Biomodelo Murino mediante Análisis Multidimensional de Datos(2012-03-02 00:00:00) Moscoloni, Nora; Montenegro, Silvana M.; Navone, Hugo D.; Picena, Juan Carlos; Martínez, Stella M.; Tarrés, M. CristinaMás... Biomodels used in the study of diabetes allow to evaluate genetic and environmental factors. Our aim was to characterize individuals of eSS, a genetically diabetic line of rats. We applied multivariate analysis, using the values obtained during the performance of oral glucose tolerance tests, presence of glucosuria, together with other physiological and environmental characteristics totalling 9 variables. Previously, an assignation of missing values of glucosuria was carried out through an artificial neural network classifier. To characterize individuals, principal componentes analysis was carried out. On describing data structure in a graphical representation of factorial coordinates, the first axe separated individuals according to glycemias, age and weight and the second opposed biomass in early ages to litter size. The cluster analysis defined a typology based on five classes. When these results were correlated with clinical classification, it was possible to separate eSS males from the youngest rats with low body weight, aglucosuric, with normal fasting glycemia but impaired glucose tolerance, up to diabetic individuals, older, with higher biomass and glucosuric. This methodology allows to identify stages in the progression of the diabetic syndromeMás... Ítem The Combinatorial ANT System for Dynamic Combinatorial Optimization Problems(2012-03-22 00:00:00) Aguilar, JoseMás... In this paper is presented a distributed algorithm based on Ant System concepts,called Combinatorial Ant System, to solve dynamic combinatorial optimization problems. Our approach consists of mapping the solution space of the dynamic combinatorial optimization problem in the space where the ants will walk, and defining the transition probability and the pheromone update formula of the Ant System according to the objective function of the optimization problem. We test our approach on a telecommunication problem.Más... Ítem One-Sided Confidence Interval Estimation for Weibull Shape and Scale Parameters(2012-03-02 00:00:00) Mahdi, SmailMás... In this paper, we consider the problem of one-sided conditional and unconditional interval estimation for the scale and shape parameters in a two-parameter Weibull model. The statistical inference is based upon the pivots advocated in Bain and Engelhardt, the likelihood ratio method and Birnbaum statistic. Simulation results illustrating the performance of these interval estimating methods are discussed and displayed. Empirical point estimate results obtained with the maximum likelihood, generalized moment and generalized probability weighted moment methods are alsopresented.Más... Ítem ¿Como Trabajan las Calculadoras?(2012-03-22 00:00:00) Edwards, Bruce H.Más... What happens when you press the sine key on your calculator? How does a calculator quickly produce the values of trigonometric functions? For instance, how does the TI-89 calculate sin 1.0? You might be surprised to know that the calculator does not use series or polynomial approximation, but rather a simple algorithm called the CORDIC method. In fact, the CORDIC method is used for almost all function evaluations (trigonometric, logarithmic, exponential, hyperbolic, inverse functions, etc.), and even multiplication and division. In this paper we will present the main ideas of the CORDIC method along with some elementary examples.Más... Ítem Interval Mathematics Applied to Critical Point Transitions(2012-03-02 00:00:00) Stradi, Benito A.Más... The determination of critical points of mixtures is important for both practical and theoretical reasons in the modeling of phase behavior, especially at high pressure. The equations that describe the behavior of complex mixtures near critical points are highly nonlinear and with multiplicity of solutions to the critical point equations. Interval arithmetic can be used to reliably locate all the critical points of a given mixture. The method also verifies the nonexistence of a critical point if a mixture of a given composition does not have one. This study uses an interval Newton/Generalized Bisection algorithm that provides a mathematical and computational guarantee that all mixture critical points are located. The technique is illustrated using several example problems. These problems involve cubic equation of state models; however, the technique is general purpose and can be applied in connection with other nonlinear problems.Más... Ítem Supplemental data acquisition tools for modeling environmental systems(2009-02-20 00:00:00) Steidley, Carl W.; Bachnak, Rafic; Sadovski, AlexeyMás... The goal of our on-going research is to develop effective and reliable tools formodeling the environmental systems of the Gulf of Mexico. For example, our on-goingresearch into methodologies for the prediction of water levels in the shallow watersof the bays and estuaries along the Texas Gulf coast. Our modeling approaches arebased on the real-time data collected by the Texas Coastal Ocean Observation Network(TCOON). TCOON is managed by the Division of Nearshore Research (DNR) incooperation with the Department of Computing and Mathematical Sciences (CAMS)both of Texas A& M University-Corpus Christi. TCOON consists of approximately50 data gathering stations located along the Texas Gulf coast from the Louisiana toMexico borders.In addition to a short description of our major data acquisition system for ourresearch efforts, this paper presents design issues, development issues, and test resultsencountered in the production of two supplemental data acquisition systems as wellas several of our environmental systems modeling efforts at Texas A&M UniversityCorpus Christi.Keywords: Data acquisition, environmental modeling, robotics.Más... Ítem El Análisis de la Variación Estacional en Medicina(2012-03-08 00:00:00) Marrero, OsvaldoMás... This is a survey of recent methods for the analysis of seasonal variation in medical research. These methods are effective even when the data show small amplitude and the sample size is small, two characteristics that are often present when one analyzes medical data for seasonal variation. The methods deal with both cases: one group and multiple groups. Also, these methods can be used to analyze different types of seasonal variation. Real-data examples are used to illustrate the application of these techniques.Más...