987 resultados para abstract Cauchy problem
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Introdução: Entre as estratégias de ensino e aprendizagem utilizadas nas práticas pedagógicas, a Problem Based Learning (PBL) (Aprendizagem Baseada em Problemas) é utilizada desde 1960, em especial nos cursos de Medicina. Mesmo sendo uma estratégia valiosa, um dos seus obstáculos é a pouca prática dos alunos em atividades autodirigidas, pesquisa e construção coletiva do conhecimento. Objetivo: Rastrear elementos constitutivos da PBL através de dados colhidos em artigos pesquisados em sítios de divulgação científica; Avaliar, nos estudos selecionados, os aspectos positivos e negativos que estejam relacionados com a metodologia do Sistema PBL aplicada ao ensino médico no Brasil. Metodologia: Estudo bibliográfico de 13 textos utilizando um modelo de desconstrução, denominada Análise Textual Discursiva (ATD) que consiste em: transformação dos artigos em pedaços menores; análise textual; identificação de padrões convergentes e divergentes em relação a PBL; organização e síntese dos dados, culminando com a elaboração de estratégia adaptativa da PBL para o curso de Medicina. Resultados: Foram encontradas 116 citações que convergiam para referências positivos acerca da metodologia PBL e 40 citações que divergiam acerca dos pontos positivos. Os aspectos positivos como o desenvolvimento de atitudes e habilidades; desenvolvimento de competências anteriores ao curso; efeitos positivos depois de terminada a graduação, como autonomia de estudo e a articulação entre currículo e realidade profissional, representam pontos a serem reforçados na aula. Em contraponto, foi observado que dentre os negativos a não compreensão do papel do professor como tutor; necessidade de conteúdo formal tradicional pelos alunos e a expectativa que o professor retire as suas dúvidas são pontos a serem evitados. Conclusões: A metodologia PBL deverá servir como metodologia ativa para aproveitar ao máximo as habilidades que os alunos já apresentam, potencializando o aprendizado na educação médica em sala de aula. Palavras-Chave: PBL; curso de medicina; metodologia ativa; educação médica.
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A method for the exact solution of the Bragg-difrraction problem for a photorefractive grating in sillenite crystals based on Pauli matrices is proposed. For the two main optical configurations explicit analytical expressions are found for the diffraction efficiency and the polarization of the scattered wave. The exact solution is applied to a detailed analysis of a number of particular cases. For the known limiting cases there is agreement with the published results.
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We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional parabolic inverse Cauchy–Stefan problem, where boundary data and the initial condition are to be determined from the Cauchy data prescribed on a given moving interface. In [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan Problem, Appl. Math Model. 35 (2011), pp. 4367–4378], the inverse Stefan problem was considered, where only the boundary data is to be reconstructed on the fixed boundary. We extend the MFS proposed in Johansson et al. (2011) and show that the initial condition can also be simultaneously recovered, i.e. the MFS is appropriate for the inverse Cauchy-Stefan problem. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be efficiently obtained with small computational cost.
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We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.
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We consider the problem of reconstruction of the temperature from knowledge of the temperature and heat flux on a part of the boundary of a bounded planar domain containing corner points. An iterative method is proposed involving the solution of mixed boundary value problems for the heat equation (with time-dependent conductivity). These mixed problems are shown to be well-posed in a weighted Sobolev space.
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We extend the method of quasilinearization to differential equations in abstract normal cones. Under some assumptions, corresponding monotone iterations converge to the unique solution of our problem and this convergence is superlinear or semi–superlinear
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Résumé : Une définition opérationnelle de la dyslexie qui est adéquate et pertinente à l'éducation n'a pu être identifiée suite à une recension des écrits. Les études sur la dyslexie se retrouvent principalement dans trois champs: la neurologie, la neurolinguistique et la génétique. Les résultats de ces recherches cependant, se limitent au domaine médical et ont peu d'utilité pour une enseignante ou un enseignant. La classification de la dyslexie de surface et la dyslexie profonde est la plus appropriée lorsque la dyslexie est définie comme trouble de lecture dans le contexte de l'éducation. L'objectif de ce mémoire était de développer un cadre conceptuel théorique dans lequel les troubles de lecture chez les enfants dyslexiques sont dû à une difficulté en résolution de problèmes dans le traitement de l'information. La validation du cadre conceptuel a été exécutée à l'aide d'un expert en psychologie cognitive, un expert en dyslexie et une enseignante. La perspective de la résolution de problèmes provient du traitement de l'information en psychologie cognitive. Le cadre conceptuel s'adresse uniquement aux troubles de lectures qui sont manifestés par les enfants dyslexiques.||Abstract : An extensive literature review failed to uncover an adequate operational definition of dyslexia applicable to education. The predominant fields of research that have produced most of the studies on dyslexia are neurology, neurolinguistics and genetics. Their perspectives were shown to be more pertinent to medical experts than to teachers. The categorization of surface and deep dyslexia was shown to be the best description of dyslexia in an educational context. The purpose of the present thesis was to develop a theoretical conceptual framework which describes a link between dyslexia, a text-processing model and problem solving. This conceptual framework was validated by three experts specializing in a specific field (either cognitive psychology, dyslexia or teaching). The concept of problem solving was based on information-processing theories in cognitive psychology. This framework applies specifically to reading difficulties which are manifested by dyslexic children.
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Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.
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Abstract: This paper reports a lot-sizing and scheduling problem, which minimizes inventory and backlog costs on m parallel machines with sequence-dependent set-up times over t periods. Problem solutions are represented as product subsets ordered and/or unordered for each machine m at each period t. The optimal lot sizes are determined applying a linear program. A genetic algorithm searches either over ordered or over unordered subsets (which are implicitly ordered using a fast ATSP-type heuristic) to identify an overall optimal solution. Initial computational results are presented, comparing the speed and solution quality of the ordered and unordered genetic algorithm approaches.
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Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.
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Ecological science contributes to solving a broad range of environmental problems. However, lack of ecological literacy in practice often limits application of this knowledge. In this paper, we highlight a critical but often overlooked demand on ecological literacy: to enable professionals of various careers to apply scientific knowledge when faced with environmental problems. Current university courses on ecology often fail to persuade students that ecological science provides important tools for environmental problem solving. We propose problem-based learning to improve the understanding of ecological science and its usefulness for real-world environmental issues that professionals in careers as diverse as engineering, public health, architecture, social sciences, or management will address. Courses should set clear learning objectives for cognitive skills they expect students to acquire. Thus, professionals in different fields will be enabled to improve environmental decision-making processes and to participate effectively in multidisciplinary work groups charged with tackling environmental issues.