Revista de Matemáticas 16(1)

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  • Ítem
    Un procedimiento de fuerte reducción de las dimensiones del RCPS/Pi
    (2009-02-27 00:00:00) Álvarez Valdés Olaguíbel, Ramón; Crespo, Enric; Tamarit Goerlich, José Manuel; Villa Juliá, M. Fulgencia
    Recently, in the field of project scheduling problems the concept of partially renewableresources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewableresources allow us to model a large variety of situations that do not fit intoclassical models, but can be found in real problems in timetabling and labour scheduling.When modelling real problems, the problem of project scheduling with partiallyrenewable resources, as many other combinatorial problems, gets such large dimensionsthat it is quite difficult to apply solution procedures. In this paper, we describesome powerful preprocessing techniques that reduce significantly the dimension of theproblems and therefore improve the efficiency of any algorithm used for solving them.The paper shows the excellent results obtained by these techniques on a set of testinstance taken from the literature.Keywords: Project Scheduling, Preprocessing, Partially Renewable Resources.
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    Evaluación de un algoritmo de recocido simulado con superficies de respuestas
    (2009-02-27 00:00:00) Loranca, Maria Beatriz Bernábe; Espinosa Rosales, José E.; Ramírez Rodríguez, Javier
    The solution of the geographical clustering problem includes a combinatorial classificationof the geographical units. The aggregation proposed in this work requiresan objective function that minimizes the distance between the objects that will beclustered together, in order to achieve geo-graphical compactness (a desirable goal inproblems of geographical design). Because this problem is NP hard [10], it is usuallysolved with heuristic methodologies that can proportionate satisfactory so-lutions in areasonable amount of computational time, even for large problems. The main purposeof this research, it is to propose a Box-Behnken experimental design applied into theresponse’s surface, in order to evaluate the quality of the generated solutions. Thebalance and adequacy of Simulated Annealing’s parameters would help to control anddirect the heuristic method to obtain good solutions for the partitioning problem.Keywords: Geographical Clustering, Experimental Design, Response’s Surface, SimulatedAnnealing.
  • Ítem
    Shipment consolidation by terminals and vehicles
    (2009-02-27 00:00:00) González Ramírez, Rosa G.; Askin, Ronald G.; Smith, Neale R.; Villalobos, René
    This project designs and implements a new module in a logistics analysis tool called”Logistika” that was developed by some graduate students in ASU. Initially, Logistikaonly had available a “Plant location module”, but this work makes an extension toinclude a new module that is called “Shipments Consolidation module”. The objectiveof the module is to determine the best distribution strategy for products manufacturedin Mexico to customers located in US. The tool explores two consolidation strategies:by vehicles and terminals, so as to minimize the transportation and in transit inventorycosts incurred. It also considers that it is desired to locate a consolidation center inMexico for which the best location must be found.Keywords: Consolidation, Location, Cost minimization, routing.
  • Ítem
    The BPS preconditioner on Beowulf cluster
    (2009-02-27 00:00:00) Salas Huertas, Oscar; Marazzina, Daniele; Rovida, Sergio; Sacchi, Giovanni; Scacchi, Simone
    This work presents the implementation on a Linux Cluster of a parallel preconditionerfor the solution of the linear system resulting from the finite element discretizationof a 2D second order elliptic boundary value problem. The numerical method,proposed by Bramble, Pasciak and Schatz, is developed using Domain Decompositiontechniques, which are based on the splitting of the computational domain into subregionsof smaller size, enforcing suitable compatibility conditions. The Fortran codeis implemented using PETSc: a suite of data structures and routines devoted to thescientific parallel computing and based on the MPI standard for all message-passingcommunications. The main interest of the paper is to present an efficient and portablecode for the solution of large-scale linear systems and to investigate how the architecturalaspects of the cluster influence the performance of the considered algorithm. Weprovide an analysis of the execution times as well as of the scalability, using as testcase the classical Poisson equation with Dirichlet boundary conditions.Keywords: Domain Decomposition, Parallelization, Partial Differential Equation, Preconditioner,Beowulf Cluster.
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    A multistep fundamental solution scheme for modeling groundwater flow
    (2009-02-27 00:00:00) Guevara Jordan, Juan M.; Da Silva Rodrigues, Carmen M.
    A new numerical scheme for solving transient pressure in a confined aquifer ispresented. It is based on the fundamental solution method (FSM) and it combinesfree Green functions, superposition principle, and singular value decomposition (SVD)method to obtain an efficient computational algorithm to approximate unsteady pressurein general two dimensional groundwater problems. Its mathematical formulationavoids integral equations, is meshfree, and its new multistep approach provides veryaccurate approximation of full transient aquifer pressure along any period of time.The new scheme was validated with synthetic aquifers problems with constant andvariable well rates. Its applications to arbitrary shaped aquifer with multiple wellsis developed and analyzed. Numerical results gave evidence that the new schemeis a versatile tool and an alternative choice to boundary element methods to solvegroundwater problems.Keywords: multistep, meshless, fundamental solution method, free Green function, singularvalue decomposition.
  • Ítem
    Minimization of the first eigenvalue in problems involving the bi-laplacian
    (2009-02-27 00:00:00) Anedda, Claudia; Cuccu, Fabrizio; Porru, Giovanni
    This paper concerns the minimization of the first eigenvalue in problems involvingthe bi-Laplacian under either homogeneous Navier boundary conditions or homogeneousDirichlet boundary conditions. Physically, in case of N = 2, our equation modelsthe vibration of a non homogeneous plate  which is either hinged or clamped alongthe boundary. Given several materials (with different densities) of total extension ||,we investigate the location of these materials inside  so to minimize the first modein the vibration of the corresponding plate.Keywords: bi-Laplacian, first eigenvalue, minimization.
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    Las ecuaciones de Reynolds y la relación de clausura
    (2009-02-27 00:00:00) Mercado Escalante, José Roberto
    We posed the problem to obtain the closure relation for the Reynolds equations.And like secondary target, to obtain analytical expressions for the Reynolds stress.Showing its jump of discontinuity like expression of the rupture of the symmetry; theone is interpret by us as a jump in the index of occupation of the space. Our mainresult consists of which the Reynolds stress is expressed like the fractional derived onefrom the average velocity.Being the order of the derived one index of space occupation; what the Reynoldsequations transform into differential integral equations. We formulate a model of fractionalPrandtl where the squared root of the Reynolds stress depends of the fractionalderived one from the average velocity and the model of Prandtl is recovered when thefractional derived one tends to the whole of value. A regularizated transition appearsbetween velocity of the inertial sub-layer and the viscous and the constant of Nikuradseis obtained like the hydraulic equivalent of the Euler’s constant, who measuresthe reason of the two scales. We analyze the Reynolds equations for a flow betweentwo planes parallels, through an equation of stationary Fokker-Planck. The velocityprofile for the viscous sub-layer is obtained as much; like for the inertial sub-layer.The fluid displays a transition of second order that is pronounced, at level macro, asa jump of discontinuity of the Reynolds stress in as much parameter of order, withrupture of the symmetry; and at micro level, as a jump in the index of occupation ofthe space.Keywords: Reynolds equations and stress, boundary layer, viscous layer, Prandtl’smodel, fractional derivatives, inverse problem, Camassa-Holm equation, second-order transition,order parameter.
  • Ítem
    Predicción estacional del clima en Centroamérica mediante la reducción de escala dinámica. Parte II: aplicación del modelo MM5V3
    (2009-02-27 00:00:00) Rivera Fernández, Erick; Amador Astúa, Jorge Alberto
    In the first part of this work it was determined that general circulation model(GCM) ECHAM4.5 shows more ability than CCM3.6 to simulate key climate featuresof Central America. For such reason, output from ECHAM4.5 was used to perform adynamical downscaling experiment using the regional model MM5v3, in which a setof high-resolution simulations (of up to 30-km horizontal resolution) was generated forJanuary 2000.The results of the dynamical downscaling allow to conclude that MM5v3 is able tosuitably reproduce aspects of the Central American climate that GCMs cannot capturebecause of their coarse horizontal resolution, their limitations in representing both theregional topography and the mesoscale dynamical interactions. Comparison with dataderived from observations indicates that the MM5v3 simulates the region of maximumlow-level wind that is related to the Intra-Americas Seas Low Level Jet, although theregional model underestimates its intensity. Regarding the precipitation patterns, theyagree with those derived from the observations (drier areas in the Pacific, wetter areasin the Caribbean). Nevertheless, there is a generalized overestimation in the amountof simulated rain. The analysis of the standard deviation for a twelve-member sampleshows areas in which MM5v3 has greater dispersion or uncertainty (mainly to thesouth of Panama).Keywords: numerical models, seasonal climate prediction, dynamical downscaling, climate,climate variability.
  • Ítem
    Descripción de dos métodos de rellenado de datos ausentes en series de tiempo meteorológicas
    (2009-02-27 00:00:00) Alfaro Martínez, Eric J.; Soley Alfaro, Francisco Javier
    Se presentan dos metodolog´?as para el rellenado de datos ausentes, enfocadas haciasu uso en series de tiempo geof´?sicas. La primera se basa en la descomposici´on encomponentes principales de la matriz de correlaci´on de datos de una misma variableentre estaciones cercanas y en periodos de tiempo comunes. Este m´etodo multivariablepermite incorporar en los valores rellenados los fen´omenos de mayor escala a partirde la informaci´on de las estaciones cercanas. El segundo m´etodo es para ser utilizadocuando no hay estaciones cercanas y el rellenado se debe hacer con la informaci´on dela misma estaci´on. Consiste en ajustar un modelo autoregresivo a la serie de tiempo yutilizar ese modelo como estimador de los datos ausentes. Se evaluaron dos algoritmospara calcular los coeficientes autoregresivos: el estimador de Burg y el propuesto porUlrych y Clayton. El primero es apropiado para procesos estoc´asticos y el segundo paraseries determin´?sticas. Las dos metodolog´?as descritos en este trabajo son recursivas:se hace una primera estimaci´on a los datos ausentes corriendo el algoritmo ignorandolos datos ausentes si es posible ´o aproxim´andolos de forma grosera. El algoritmo secontin´ua ejecutando con los nuevos valores sustituyendo los valores estimados en lacorrida anterior. La ejecuci´on termina cuando la diferencia m´axima de los valoresestimados entre dos corridas sucesivas es menor que un valor fijado de antemano porel usuario. Los datos rellenados conservan la media y la desviaci´on est´andar originalde la serie de tiempo. Estos algoritmos se adaptaron y modificaron, por medio del usode Interfaces Gr´aficas con el usuario, para su uso en SCILAB, que es una plataforma similar a MATLAB pero de fuente abierta y que corre indistintamente en Windows yLinux. Ellos fueron elaborados como una actividad de extensi´on de la Universidad deCosta Rica.Palabras clave: datos faltantes, control de calidad, filtros auto regresivos, an´alisis decomponentes principales, aplicaciones de software libre.
  • Ítem
    Indices of regularity and indices of randomness for m-ary strings
    (2009-02-27 00:00:00) Skliar, Osvaldo; Monge, Ricardo E.; Oviedo Blanco, Guillermo; Medina, Víctor
    The notions “regularity index” and “randomness index” previously introduced forbinary strings (2-ary) have been modified slightly and generalized for m-ary strings(m = 2, 3, 4, . . .). These notions are complementary and the regular/random dichotomyhas been replaced by a gradation of values of regularity and of randomness.With this approach, the more regular an m-ary string, the less random it is, and viceversa. The distributions of frequencies of different length strings —2-ary and 3-arystrings— according to their indices of randomness, are shown by histograms.Keywords: regularity index, randomness index, m-ary strings.
  • Ítem
    El método Statis como alternativa para detectar "response shift" en estudios de calidad de vida relacionada con la salud
    (2009-02-27 00:00:00) Vicente Galindo, María Purificación; Galindo Villardón, María Purificación
    After evaluating problems in conceptualisation of Quality of Life outcomes andestablishing an operational definition of HRQoL, we focus the attention on the different dimensions of Response Shift and the theoretical Models to explaining it. We payspecial attention to Schwartz and Sprangers Model.If Gamma change is present, the construct under assessment is not stable forthe patient; so it has no sense to compare scores because if an individual changesconceptualization of QoL over the course of time, then answers to the same items bythe same individual may not be as comparable over time as originally thought. So, itis crucial to capture Response Shift before Alpha change is evaluated.The analytical approaches to assess Response Shift are discussed, paying specialattention to the statistical aspects. We found several shortcomings of Ahmavaara’sMethod for comparing factorial structures and we have developed some alternativesto capture Beta and Gamma components of Response Shift.Keywords: Health Related Quality of Life (HRQoL), Response Shift, Beta change,Gamma change, Dual Statis method.
  • Ítem
    Detection of unobserved heterogeneity with growth mixture models
    (2009-02-27 00:00:00) Reinecke, Jost; Mariotti, Luca
    Latent growth curve models as structural equation models are extensively discussedin various research fields (Duncan et al., 2006). Recent methodological and statisticalextension are focused on the consideration of unobserved heterogeneity in empiricaldata. Muth´en extended the classical structural equation approach by mixture components,i. e. categorical latent classes (Muth´en 2002, 2004, 2007).The paper will discuss applications of growth mixture models with data from oneof the first panel studies in Germany which explore deviant and delinquent behavior ofadolescents (Reinecke, 2006a, 2006b). Observed as well as unobserved heterogeneitywill be considered with growth mixture models using the program Mplus (Muth´en& Muth´en, 2006). Special attention is given to the distribution of the substantivedependent variables as a count measures (Poisson distribution, zero-inflated Poissondistribution, cf. Nagin, 1999). Different model specifications with respect to substantivequestions will also be emphasized.Keywords: Panel data, growth mixture models, heterogeneity, Poisson distribution.
  • Ítem
    Árboles de clasificación para el análisis de gráficos de control multivariantes
    (2009-02-27 00:00:00) Gámez Martínez, Matías; Alfaro Cortés, Esteban; Alfaro Navarro, José Luis; García Rubio, Noelia
    In statistical quality control, one of the most widely used tools are the controlcharts. The main problem of the multivariate control charts lies in that they onlyindicate that a change in the process has happened, but they do not show whichvariable or variables are the source of this change. In the specialized literature thereare many approaches to tackle this problem, although the most usual consists on thedecomposition of the T2 statistic. In this research, we propose an alternative methodthrough the application of classification trees. The results show that this methodconstitutes a good tool to help to interpret the multivariate control charts.Keywords: Statistic Process Control, T2 Hotelling, Classification trees.