Desde principios del siglo pasado se propuso una generalización de la función exponencial natural; una deformación de la misma. Con el desarrollo de la estadística de Tsallis, a partir de la generalización del concepto de entropía dada en 1998, en la década de los noventa se hace teoría sobre funciones exponenciales y logarítmicas deformadas. Sólo a partir del presente siglo, se plantean investigaciones donde se hacen desarrollos teóricos y aplicaciones de dichas funciones. Precisamente, se presentan las funciones, sus propiedades, algunas aplicaciones en teoría matemática y en diferentes contextos como en física o ciencias sociales.
La representación de funciones puede ser útil en diferentes áreas, por ejemplo, las series de Fourier son utilizadas para convertir señales discretas en señales continuas, esto es de gran utilidad en el área de telecomunicaciones para convertir las señales digitales en analógicas, por ejemplo las señales que recibe un celular cuando una persona está hablando simplemente son los coeficientes de la serie de Fourier, para poder ver televisión digital en televisores analógicos se convierte la señal digital, la cual es una señal discreta de ceros y unos, a través de la representación de esta señal por medio de la serie de Fourier, en una señal analógica, la cual es continua (senos y cosenos). Representar señales por medio de la Wavelet de Haar también podría ser de interés ya que lo que hace es lo contrario de la serie de Fourier, es decir, convierte una señal continua en una señal discreta. Hacer un análisis del error de la representación de funciones es de bastante interés, ya que se puede cuantificar la pérdida de información en el proceso de conversión, para tomar medidas al respecto.
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En estas notas que constituyen las memorias del curso práctica investigativa II, se muestra parte del potencial investigativo subyacente en la consideración de dichas funciones. Precisamente se presentan las funciones, sus propiedades, algunas aplicaciones en teoría matemática y en diferentes contextos como en física o en ciencias sociales.
A Wong-Zakai type numerical method for the strong solution of stochastic differential equations is introduced and developed. The main feature of the method is that it takes advantage of the well developed techniques for solution of ordinary differential equations. Focus is given to the evaluation of the numerical performance of the method.
En este documento presentamos un análisis de los tiempos de cómputo y la calidad de las soluciones obtenidas al resolver sistemas de ecuaciones tridiagonales y pentadiagonales con métodos directos e iterativos. Para problemas de gran dimensión, se obtienen mejores soluciones con los métodos iterativos, mientras que para los problemas con dimensión menor a 50 X 50 pueden obtenerse mejores soluciones con los métodos directos.
Ordinary differential equations (ODEs) are a common tool for modelling physical systems. Such models represent idealized versions of real systems, as they are purely deterministic. Stochastic differential equations (SDEs) are the instrument for building more realistic models, as they include the random elements. SDEs are used in many areas of applications, including investment finance, economics, insurance, signal processing and filtering, several fields of biology and physics, population dynamics and genetics.
Esta investigación construye y analiza un modelo de cadena de suministro de semiconductores en la cual la demanda del cliente responda a la disponibilidad del producto, basado en un largo y profundo estudio del campo de la cadena de suministro de Intel, el modelo captura los flujos de material de producción y de la respuesta de los clientes al porcentaje de disponibilidad o nivel de servicio del fabricante.
In this paper, the design, experimentation, and analysis of a metaheuristic algorithm to solve the k-TRP is performed. The k-TRP is a variant of the traveling salesman problem (TSP) in which the cost-based classical objective function becomes the weighted sum of completion times at sites and k agents or vehicles cover one of k routes. The k-TRP is an optimization problem where k dealers, needs to schedule their visitation order to a set of customers, taking into account that each customer has a level of priority. In our implementation those priorities correspond to their demands. A solution is given by a schedule of the visits for each agent k, trying to end the set of least costly routes.
Este trabajo constituye un reporte sobre las capacidades matemáticas con las que ingresaron los estudiantes nuevos al semestre 2015-1 y que realizaron el curso de Iniciación al Cálculo.
Inicialmente se describe la metodología seguida y comentarios sobre el porqué de la dirección que se le dio al proyecto. Se presentarán gráficos y tablas estadísticas sobre el desempeño de los estudiantes que presentaron el curso, discriminando por género, carrera, escuela, tipo de beca, y tipo de talleres abordados. En las últimas secciones se hará la discusión de resultados y las conclusiones.
We present a methodology through exemplication to perform parameter estimation subject to possible factors of uncertainty. The underlying optimization problem is posed in the framework of the theory of interval-valued optimization. The implementation of numerical procedures required to achieve effcient solutions implied the use of the ℓ1 norm instead of usual ℓ2 regression. Finally, an implementation using real data was performed, demonstrating the ability of interval analysis to encapsulate uncertainty while facing non-trivial parameter estimation problems.
A process quality is the ability it has to produce goods according to item specifications and it is measured through process capability indices. Real data associated to production processes do not always fit into a normal distribution, even though most industries assume normal behavior. Real process data are flexible and are influenced by various external factors requiring considering process capability indices for asymmetric distributions, or giving wrong information otherwise and preventing industry of performing what is really needed. Skewed Normal distribution is an excellent tool to fit real process data into capability indices since it can contemplate three associated behaviors regarding asymmetric distributions. A flowchart is added to explain indices calculation and the methodology is implemented in R programming language.
In this work we present the methodology and results coming from the application of the finite element method on an advection-diffusion problem modelling the air quality of a given area defined mathematically by a partial differential equation under certain domains and boundary and initial conditions. Through the consideration of certain conditions on the problem it was possible to build a discretization of the reduced and general equation using the finite difference method as a comparation base to analyze the effectivity of the main method. Finally, the concentration curves and the evolution surface representing it are presented in order to scrutinize in the obtained numerical results.
This paper proposes a new betting strategy using three different variations of the Kelly criterion, it is shown an elicitation procedure based on betting odds to find the hyperparameters of the prior distributions that are used to predict the outcomes of the premier league for the two different seasons using the Categorical-Dirichlet with the addition of historical information. Our results show that betting according to our elicitation gives a better performance compared with others proposed methodologies in the literature, specifically we show a pro t of 98% betting in a total of 380 matches in a two-year period.
The Burr type XII distribution plays an important role in a variety of applied mathematics contexts (Watkins, 1999). One of them is the process capability analysis (Ahmad et al., 2009) and the estimation of the distribution parameters is essential for its applications. The estimation with tabulated values is a common method. This paper implement three heuristics to find good solutions for the estimation of the parameters: Particle Swarm Optimization, Median-oriented Particle Swarm Optimization and Artificial Bee Colony. A comparison between the solution given by these methods and other proposed in literature is presented. Finally, the heuristic methods are implemented to estimate the Process Capability Index.
In this work we present the methodology and results coming from the application of the Wavelet-Galerkin method on a second order linear ordinary differential equation with constant coefficients. The classical scaling and mother wavelet functions are used to find a proper approximation for the studied case. Through this article several algorithms are displayed in order to make a posterior implementation of the method. Finally, the approximate curve and errors for a particular case are analyzed using the proposed methodology to show the method potential and behavior.
We propose a model selection procedure when facing high multicollinearity levels applied to the inference over a treatment effect. We show different Frequentist and Bayesian approaches applied to a model selection procedure based on a post double estimation procedure. Our simulation results have evidence in favor of Bayesian procedures when the number of observations is not much higher than the number of possible controls. Finally, we perform a post double MC3 procedure on real data regarding the impact of legalized abort on crimes rates.
The selection of a time series model is a well-studied problem, because of its importance in forecasting problems. Different model selection criteria have been used, and recently, studies use them combined to find an adaptation of the criteria to reach accuracy. This paper implement some multivariate statistic techniques to find a new adaptation of a weighted criterion for model selection of time series.
This work Proposes a mathematical programming model to support planning decisions centered around the harvest of flowers minimizing the amount of resources used and the waste generated from the harvest. The constraints of the model seek to fulfill the demands of flowers, respect workers' schedules and performance, availability of the flowers, and productivity of the flower plants according to its time in the cycle of harvest.