Artículos científicos

URI permanente para esta colecciónhttp://10.0.96.45:4000/handle/11056/14723

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50 metros al este del antiguo Higuerón: formas culturales de abordar la localización espacial con potencialidades etnomatemáticas
(Bolema: Boletim de Educação Matemática, 2021) Gavarrete Villaverde, María Elena; Albanese, Veronica
Desde la Etnomatemática se plantea la importancia de tener en consideración aspectos propios de la cultura de los estudiantes, para acercarlos al aprendizaje de conceptos matemáticos que están en uso durante las prácticas cotidianas. Para ello es necesario, primero, analizar en profundidad tales elementos de la cultura para identificar relaciones con la matemática escolar y después formar adecuadamente a los docentes. Presentamos entonces, aquí, el análisis etnomatemático del signo cultural costarricense de las direcciones a la tica como un signo idiosincrático para la localización espacial de las direcciones postales o de las indicaciones para determinar un lugar. Utilizamos las perspectivas teóricas ética local, émica global, y dialógica glocal como principales herramientas teóricas y metodológicas para realizar el análisis. Finalmente, problematizamos este signo cultural para la acción pedagógica describiendo algunas actividades que se han llevado a cabo para la formación de docentes en Costa Rica.
A Microscopic Model for a One Parameter Class of Fractional Laplacians with Dirichlet Boundary Conditions
(Springer Science and Business Media Deutschland GmbH, 2021) Bernardin, Cèdric; Gonçalves, Patrícia; Jiménez-Oviedo, Byron
We prove the hydrodynamic limit for the symmetric exclusion process with long jumps given by a mean zero probability transition rate with infinite variance and in contact with infinitely many reservoirs with density α at the left of the system and β at the right of the system. The strength of the reservoirs is ruled by κN−θ > 0. Here N is the size of the system, κ > 0 and θ ∈ R. Our results are valid for θ ≤ 0. For θ = 0, we obtain a collection of fractional reaction–diffusion equations indexed by the parameter κ and with Dirichlet boundary conditions. Their solutions also depend on κ. For θ < 0, the hydrodynamic equation corresponds to a reaction equation with Dirichlet boundary conditions. The case θ > 0 is still open. For that reason we also analyze the convergence of the unique weak solution of the equation in the case θ = 0 when we send the parameter κ to zero. Indeed, we conjecture that the limiting profile when κ → 0 is the one that we should obtain when taking small values of θ > 0
A mixed virtual element method for a pseudostress-based formulation of linear elasticity
(Elsevier B.V., 2019) Cáceres, Ernesto; Gatica, Gabriel N.; Sequeira, Filander
In this paper we introduce and analyze a mixed virtual element method (mixed-VEM) for a pseudostress-displacement formulation of the linear elasticity problem with non homogeneous Dirichlet boundary conditions. We follow a previous work by some of the authors, and employ a mixed formulation that does not require symmetric tensor spaces in the finite element discretization. More precisely, the main unknowns here are given by the pseudostress and the displacement, whereas other physical quantities such as the stress, the strain tensor of small deformations, and the rotation, are computed through simple postprocessing formulae in terms of the pseudostress variable. We first recall the corresponding variational formulation, and then summarize the main mixed-VEM ingredients that are required for our discrete analysis. In particular, we utilize a well known local projector onto a suitable polynomial subspace to define a calculable version of our discrete bilinear form, whose continuous version requires information of the variables on the interior of each element. Next, we show that the global discrete bilinear form satisfies the hypotheses required by the Babuška–Brezzi theory. In this way, we conclude the well-posedness of our mixed-VEM scheme and derive the associated a priori error estimates for the virtual solutions as well as for the fully computable projections of them. Furthermore, we also introduce a second element-by-element postprocessing formula for the pseudostress, which yields an optimally convergent approximation of this unknown with respect to the broken H(div)-norm. In addition, this postprocessing formula can also be applied to the postprocessed stress tensor. Finally, several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence are presented.
A mixed virtual element method for quasi-Newtonian stokes flows
(SIAM, 2018) CACERES, ERNESTO; Gatica, Gabriel; Sequeira, Filander
In this paper we introduce and analyze a virtual element method (VEM) for an augmented mixed variational formulation of a class of nonlinear Stokes models arising in quasi-Newtonian fluids. While the original unknowns are given by the pseudostress, the velocity, and the pressure, the latter is eliminated by using the incompressibility condition, and in order to handle the nonlinearity involved, the velocity gradient is set as an auxiliary one. In this way, and adding a redundant term arising from the constitutive equation relating the psdeudostress and the velocity, an augmented formulation showing a saddle point structure is obtained, whose well-posedness has been established previously by using known results from nonlinear functional analysis. Then, following the basic principles and ideas of the mixed- VEM approach, we introduce a Galerkin scheme employing generic virtual element subspaces and projectors satisfying suitable abstract conditions and derive the corresponding solvability analysis, along with the associated a priori error estimates for the virtual element solution as well as for the fully computable projection of it. Next, we provide two specific choices of subspaces and local projectors verifying the required hypotheses, one of them yielding an optimally convergent mixed- VEM for the fully nonlinear problem studied here, and the other one providing a new approach for the linear version of it, that is, for the Stokes problem. In addition, we are able to apply a second element-by-element postprocessing formula for the pseudostress, which yields an optimally convergent approximation of it with respect to the broken H(div)-norm. Finally, several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence are reported. © 2018 Society for Industrial and Applied Mathematics.
A mixed virtual element method for the boussinesq problem on polygonal meshes
(Global Science Press, 2021) Gatica, Gabriel; Munar Benitez, Edgar Mauricio; Sequeira, Filander
In this work we introduce and analyze a mixed virtual element method (mixed-VEM) for the two-dimensional stationary Boussinesq problem. The continuous formulation is based on the introduction of a pseudostress tensor depending nonlinearly on the velocity, which allows to obtain an equivalent model in which the main unknowns are given by the aforementioned pseudostress tensor, the velocity and the temperature, whereas the pressure is computed via a postprocessing formula. In addition, an augmented approach together with a fixed point strategy is used to analyze the well-posedness of the resulting continuous formulation. Regarding the discrete problem, we follow the approach employed in a previous work dealing with the Navier-Stokes equations, and couple it with a VEM for the convection-diffiusion equation modelling the temperature. More precisely, we use a mixed-VEM for the scheme associated with the uid equations in such a way that the pseudostress and the velocity are approximated on virtual element subspaces of H(div) and H1, respectively, whereas a VEM is proposed to approximate the temperature on a virtual element subspace of H1. In this way, we make use of the L2-orthogonal projectors onto suitable polynomial spaces, which allows the explicit integration of the terms that appear in the bilinear and trilinear forms involved in the scheme for the uid equations. On the other hand, in order to manipulate the bilinear form associated to the heat equations, we define a suitable projector onto a space of polynomials to deal with the fact that the diffiusion tensor, which represents the thermal conductivity, is variable. Next, the corresponding solvability analysis is performed using again appropriate fixed-point arguments. Further, Strang-type estimates are applied to derive the a priori error estimates for the components of the virtual element solution as well as for the fully computable projections of them and the postprocessed pressure. The corresponding rates of convergence are also established. Finally, several numerical examples illustrating the performance of the mixed-VEM scheme and confirming these theoretical rates are presented.
A mixed virtual element method for the Brinkman problem
(Mathematical Models and Methods in Applied Sciences vol.27 no.4 707-743 2017, 2017) Cáceres, Ernesto; Gatica, G.N.; Sequeira, Filander
In this paper, we introduce and analyze a mixed virtual element method (mixed-VEM) for the two-dimensional Brinkman model of porous media flow with non-homogeneous Dirichlet boundary conditions. More precisely, we employ a dual-mixed formulation in which the only unknown is given by the pseudostress, whereas the velocity and pressure are computed via postprocessing formulae. We first recall the corresponding variational formulation, and then summarize the main mixed-VEM ingredients that are required for our discrete analysis. In particular, in order to define a calculable discrete bilinear form, whose continuous version involves deviatoric tensors, we propose two well-known alternatives for the local projector onto a suitable polynomial subspace, which allows the explicit integration of these terms. Next, we show that the global discrete bilinear form satisfies the hypotheses required by the Lax–Milgram lemma. In this way, we conclude the well-posedness of our mixed-VEM scheme and derive the associated a priori error estimates for the virtual solution as well as for the fully computable projection of it. Furthermore, we also introduce a second element-by-element postprocessing formula for the pseudostress, which yields an optimally convergent approximation of this unknown with respect to the broken ℍ(div)-norm. Finally, several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence are presented.
A Monte Carlo Study of the Photon Spectrum due to the Different Materials Used in the Construction of Flattening Filters of LINAC
(Hindawi, 2017-07-10) Estepa Jiménez, Juan Sebastián; Díaz Lagos, Mercedes; Martínez Ovalle, Segundo Agustín
Different types the spectrum of photons were studied; they were emitted from the flattening filter of a LINAC Varian 2100 C/D that operates at 15 MV. The simplified geometry of the LINAC head was calculated using the MCNPX code based on the studies of the materials of the flattening filter, namely, SST, W, Pb, Fe, Ta, Al, and Cu. These materials were replaced in the flattening filter to calculate the photon spectra at the output of this device to obtain the spectrum that makes an impact with the patient. The different spectra obtained were analyzed and compared to the emission from the original spectra configuration of the LINAC, which uses material W. In the study, different combinations of materials were considered in order to establish differences between the use of different materials and the original material, with the objective of establishing advantages and disadvantages from a clinical standpoint.
A posteriori error analysis of a mixed virtual element method for a nonlinear Brinkman model of porous media flow
(Elsevier Ltd, 2020-06-25) Munar, Mauricio; Sequeira, Filander
In this paper we present an a posteriori error analysis of a mixed-VEM discretization for a nonlinear Brinkman model of porous media flow, which has been proposed by the authors in a previous work. Therein, the system is formulated in terms of a pseudostress tensor and the velocity gradient, whereas the velocity and the pressure of the fluid are computed via postprocessing formulas. Furthermore, the well-posedness of the associated augmented formulation along with a priori error bounds for the discrete scheme also were established. We now propose reliable and efficient residualbased a posteriori error estimates for a computable approximation of the virtual solution associated to the aforementioned problem. The resulting error estimator is fully computable from the degrees of freedom of the solutions and applies on very general polygonal meshes. For the analysis we make use of a global inf–sup condition, Helmholtz decomposition, local approximation properties of interpolation operators and inverse inequalities together with localization arguments based on bubble functions. Finally, we provide some numerical results confirming the properties of our estimator and illustrating the good performance of the associated adaptive algorithm
A priori and a posteriori error analyses of a pseudostress-based mixed formulation for linear elasticity
(Computers and Mathematics with Applications vol.71 no.2 585-614 2016, 2016-01-02) Gatica, Gabriel N.; Gatica, Luis F.; Sequeira, Filánder A.
In this paper we present the a priori and a posteriori error analyses of a non-standard mixed finite element method for the linear elasticity problem with non-homogeneous Dirichlet boundary conditions. More precisely, the approach introduced here is based on a simplified interpretation of the pseudostress-displacement formulation originally proposed in Arnold and Falk (1988), which does not require symmetric tensor spaces in the finite element discretization. In addition, physical quantities such as the stress, the strain tensor of small deformations, and the rotation, are computed through a simple postprocessing in terms of the pseudostress variable. Furthermore, we also introduce a second element-by-element postprocessing formula for the stress, which yields an optimally convergent approximation of this unknown with respect to the broken ℍ(div)-norm. We apply the classical Babuška-Brezzi theory to prove that the corresponding continuous and discrete schemes are well-posed. In particular, Raviart-Thomas spaces of order k≥0 for the pseudostress and piecewise polynomials of degree ≤k for the displacement can be utilized. Moreover, we remark that in the 3D case the number of unknowns behaves approximately as 9 times the number of elements (tetrahedra) of the triangulation when k=0. This factor increases to 12.5 when one uses the classical PEERS. Next, we derive a reliable and efficient residual-based a posteriori error estimator for the mixed finite element scheme. Finally, several numerical results illustrating the performance of the method, confirming the theoretical properties of the estimator, and showing the expected behaviour of the associated adaptive algorithm, are provided.
A Priori and a Posteriori Error Analyses of an Augmented HDG Method for a Class of Quasi-Newtonian Stokes Flows
(Springer, 2016-12) Gatica, Gabriel; Sequeira, Filander
In a recent work we developed a new hybridizable discontinuous Galerkin (HDG) method for a class of nonlinear Stokes models arising in quasi-Newtonian fluids. The approach there uses the incompressibility condition to eliminate the pressure, sets the gradient of the velocity as an auxiliary unknown, and enriches the original formulation with convenient redundant equations, thus giving rise to an augmented scheme. However, the corresponding analysis, which makes use of a fixed point strategy that depends on a suitably chosen parameter, yields optimal rates of convergence for only two of the six resulting unknowns, whereas the reported numerical results, showing higher orders than predicted, support the conjecture that the a priori error estimates are not sharp. In the present paper, the main features of the aforementioned augmented formulation are maintained, but after introducing slight modifications of the finite element subspaces for the pseudostress and velocity, we are able to significantly improve our previous analyses and results. More precisely, on one hand we realize here that it suffices to choose the stabilization tensor as the identity times the meshsize, and hence neither fixed-point arguments nor related parameters are needed anymore to establish the well-posedness of the discrete scheme, and on the other hand we now prove optimally convergent approximations for all the unknowns. Furthermore, we develop a reliable and efficient residual-based a posteriori error estimator, and propose the associated adaptive algorithm for our HDG approximation of the nonlinear model problem. Finally, several numerical results illustrating the performance of the method, confirming the theoretical properties of the estimator, and showing the expected behaviour of the adaptive refinements, are presented. © 2016, Springer Science+Business Media New York
A priori and a posteriori error analyses of an HDG method for the Brinkman problem
(Elsevier, 2018-01-15) Gatica, Luis; Sequeira, Filánder
In this paper we introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for the linear Brinkman model of porous media flow in two and three dimensions and with non-homogeneous Dirichlet boundary conditions. We consider a fully-mixed formulation in which the main unknowns are given by the pseudostress, the velocity and the trace of the velocity, whereas the pressure is easily recovered through a simple postprocessing. We show that the corresponding continuous and discrete schemes are well-posed. In particular, we use the projection-based error analysis in order to derive a priori error estimates. Furthermore, we develop a reliable and efficient residual-based a posteriori error estimator, and propose the associated adaptive algorithm for our HDG approximation. Finally, several numerical results illustrating the performance of the method, confirming the theoretical properties of the estimator and showing the expected behavior of the adaptive refinements are presented. © 2017 Elsevier Ltd
A RTk - P-k approximation for linear elasticity yielding a broken H(div) convergent postprocessed stress
(Universidad Nacional, Costa Rica, 2015) Gatica, Gabriel N.; Gatica, Luis F.; Sequeira, Filander
We present a non-standard mixed finite element method for the linear elasticity problem in R-n with non-homogeneous Dirichlet boundary conditions. More precisely, our approach is based on a simplified interpretation of the pseudostress displacement formulation originally proposed in Arnold and Falk (1988), which does not require symmetric tensor spaces in the finite element discretization. We apply the classical Babuska-Brezzi theory to prove that the corresponding continuous and discrete schemes are well-posed. In particular, Raviart-Thomas spaces of order k >= 0 for the pseudostress and piecewise polynomials of degree <= k for the displacement can be utilized. In addition, complementing the results in the aforementioned reference, we introduce a new postprocessing formula for the stress recovering the optimally convergent approximation of the broken H(div)-norm. Numerical results confirm our theoretical findings. (C) 2015 Elsevier Ltd. All rights reserved.
Abandono temprano en estudiantes universitarios: un estudio de cohorte sobre sus posibles causas
(Universidad Nacional, Costa Rica, 2021-01-31) Rodriguez Pineda, Magaly; Zamora Araya, José Andrey
El objetivo principal de esta investigación es conocer las razones por las cuales un estudiante de primer ingreso se puede convertir en un desertor temprano; se estudia el caso particular de la Universidad Nacional. Se usó un enfoque cuantitativo de tipo exploratorio, no experimental y correlacional. Los participantes fueron 158 estudiantes de la cohorte 2014, que no reportaron matrícula en el primer ciclo del 2015, a los que se les aplicó un cuestionario con 25 preguntas. Por medio de un análisis factorial exploratorio, se logró determinar que las variables asociadas con el abandono escolar respondían a factores de tipo (1) académico y de ambiente estudiantil, representado por las notas; (2) motivacional, en el que destacan variables como el estado de ánimo, duración de la carrera, falta de orientación, entre otras; (3) económico-familiar, asociado con la falta de beca, problemas familiares o cambio del estado conyugal; y (4) vocacional, relacionado con variables como falta de interés y percepción de poca utilidad de la carrera seleccionada como primera opción. Además, la deserción fue mayor en estudiantes del estrato 3, es decir, aquellos provenientes de colegios con menores oportunidades educativas y de los sectores sociales más vulnerables.
Abelian covers of alternating groups
(Archiv der Mathematik 107 135-150, 2016-07-07) Barrantes, Daniel; Hill, Nick; Ramírez, Jeremías
Let G = A n , a finite alternating group. We study the commuting graph of G and establish, for all possible values of n barring 13, 14, 17, and 19 whether or not the independence number is equal to the clique-covering number.
Acciones y desafíos en la formación de docentes de matemáticas en el contexto de la pandemia en la Universidad Nacional - Costa Rica
(Universidad Nacional (Costa Rica), 2021) Morales-López, Yuri; Alpízar Vargas, Marianela; Gavarrete Villaverde, María Elena
A raíz de la pandemia de Covid-19, muchas de las actividades que se realizan en la formación de docentes de matemáticas sufrieron afectaciones. En la Escuela de Matemática de la Universidad Nacional en Costa Rica se han abordado los retos generados y se han propuesto soluciones para mitigar, en la medida de lo posible, tal afectación. En esta escuela se ha trabajado en la continuidad de los cursos y en el vínculo con el contexto laboral, en el seguimiento de los trabajos finales de graduación (investigaciones ejecutadas por los estudiantes) y en los proyectos de investigación inscritos de manera formal en dicha universidad en el marco de la educación matemática. Se muestran en las siguientes páginas los principales factores que tomaron parte en este proceso de adaptación y cómo se han plantado y ejecutado las acciones de contingencia; además, se muestran algunas lecciones aprendidas y que podrían ser de interés para la comunidad educativa nacional e internacional.
Las actitudes hacia la matemática, el desarrollo social, el nivel educativo de la madre y la autoeficacia como factores asociados al rendimiento académico en matemática
(Universidad Nacional (Costa Rica), 2020-01) Zamora Araya, José Andrey
El documento trata sobre la problemática del bajo rendimiento académico en matemática (RAM) y, como objetivo principal, analiza de qué manera se relaciona este con las actitudes hacia la materia, la autoeficacia percibida, el desarrollo social y el nivel educativo. Participaron 197 estudiantes de 7.o, 8.o y 9.o grado de colegio con edades entre los 13 y 16 años. El estudio es de tipo correlacional y se utilizaron las técnicas de análisis factorial exploratorio y regresión múltiple, para determinar la asociación entre los constructos. Tales tácticas confirman la importancia de que los estudiantes tengan seguridad en sí mismos cuando realizan tareas matemáticas, lo que se refleja en los coeficientes significativos para las dimensiones de confianza (p = 0.001) y experiencia de maestría (p < 0.001), pero no así el nivel educativo de la madre. También, se obtuvieron resultados inesperados con respecto al desarrollo social y algunas dimensiones de la escala de actitudes hacia la matemática; sin embargo, se reafirma lo fundamental de estos constructos y la autoeficacia en el RAM, por lo que se recomienda ampliar la investigación sobre dichas variables
Administración de proyectos con Excel usando PERT/CPM
(Universidad Nacional (Costa Rica), 2002) Azofeifa Zamora, Carlos E.
Se presenta la técnica PERT/CPM de la ciencia administrativa, que ayuda a comprobar y controlar aquellos proyectos que involucran muchas tareas interrelacionadas, mediante la resolución de un problema de la administración de proyectos con la ayuda de la hoja electrónica Excel, además, se realiza un análisis de sus beneficios. También se aplica la técnica PERT/Costos en el control de los costos del proyecto, Nassir Sapag Chain (2001) es una guía especial en este tema.
Alfabetización, razonamiento y pensamiento estadísticos: competencias específicas que requieren promoverse en el aula
(Red de Investigadores Educativos Chihuahua AC, 2021-09) Aguilar Fernández, Eduardo; Zamora Araya, José Andrey; Guillén Oviedo, Helen Susana
El objetivo principal del ensayo consiste en analizar cómo el enfoque por competencias puede contribuir al cumplimiento de los fines de la educación estadística. Se realiza una revisión sobre el concepto de competencias, sus tipos y enfoque. Posteriormente se analiza la relación entre el enfoque por competencias y la educación estadística, de tal manera que la incorporación de la alfabetización, razonamiento y pensamiento estadístico se consideren como competencias por desarrollar. Asimismo se brindan definiciones de competencias matemáticas y estadísticas, enfatizando en que son diferentes pero complementarias. Finalmente se rescatan las recomendaciones del informe de la Guidelines for Assessment and Instruction in Statistics Education (GAISE) para la enseñanza de la estadística y sugerencias de cómo podrían implementarse las competencias estadísticas en las aulas bajo un enfoque por competencias.
Algunos métodos para la solución de problemas de la física-matemática
(Universidad Nacional (Costa Rica), 1994) Quintero, R.; Bonatti, J.
En este trabajo, se exponen algunos métodos para la solución de problemas de frontera, en regiones donde esta frontera es desconocida y se encuentra en movimiento (problema tipo Stefan). Como ejemplo se resuelve analíticamente el problema de congelamiento de un suelo húmedo. Brevemente se exponen algunos conceptos y resultados de la teoría de funciones generalizadas pertinentes a esta investigación, procediendo luego, al planteo del citado problema del congelamiento de un suelo húmedo como un problema generalizado de Cauchy y a su correspondiente solución. Se expone también un método numérico de solución.
Análisis de Correspondencia para estudiar la relación entre algunas variables medidas a partir de la Encuesta Nacional de Opinión Pública del año 2006 (ENOPU-06)
(Universidad de Costa Rica, 2011) Aguilar Fernández, Eduardo
Este estudio tiene como finalidad establecer relaciones entre distintas variables educativas y de salud de la ENOPU-06. Para ello se estudia la relación entre las variables nivel educativo y centro de salud que visitó la última vez, nivel de ingreso del hogar y región donde vive, edad y establecimiento de salud que visitó la última vez. Para estudio de la relación entre las variables se aplicó la técnica de Análisis de Correspondencia. Los resultados muestran que las personas de mayor edad buscan atención médica más local y que las personas de edades intermedias fueron las más dadas a buscar atención médica. Las personas de la región metropolitana parecen tener un ingreso que les permite satisfacer sus necesidades. Además, las personas con mayor nivel de preparación académica tienden a buscar los centros hospitalarios que cuentan con mayor cantidad de servicios especializados

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