On the kernel of a singular integral operator with non-carleman shift and conjugation

On the Hilbert space (L) over tilde (2)(T) the singular integral operator with non-Carleman shift and conjugation K = P+ +(aI + AC)P- is considered, where P-+/- are the Cauchy projectors, A = (m)Sigma(j=0) a(j)U(j), a, a(j), j = (1, m) over bar, are continuous functions on the unit circle T, U is the shift operator and C is the operator of complex conjugation. Some estimates for the dimension of the kernel of the operator K are obtained.Fundacao para a Ciencia e Tecnologia (Portugal) through Centro de Analise Funcional e Aplicacoes of Instituto Superior Tecnicoinfo:eu-repo/semantics/publishedVersio

Numerical Study of the Thermal Efficiency of a School Building with Complex Topology for Different Orientations

In this work a numerical model that simulates the thermal behavior of a building with complex topology and evaluates the indoor thermal and air quality, in transient conditions, is used for a school building thermal project. The program calculates the building surfaces solar radiation field, the building's temperatures, the internal environmental variables, and the occupant's comfort levels. Initially, after the numerical model is validated, the software is used to evaluate the school building's thermal response for four different orientations, either in winter or summer conditions. The work then aims to identify uncomfortable spaces in order to propose, as an example, several solutions that could be introduced for each orientation, that would improve the thermal comfort and air quality levels to which the occupants are subjected, and decrease the building's energy consumption levels. The information obtained from this study could be used to help a designer choose which thermal systems and solutions function best for a preferred school building orientation

Dynamic and interactive tools to support teaching and learning

The use of technological learning tools has been increasingly recognized as a useful tool to promote students’ motivation to deal with, and understand, mathematics concepts. Current digital technology allows students to work interactively with a large number and variety of graphics, complementing the theoretical results and often used paper and pencil calculations. The computer algebra system Mathematica is a very powerful software that allows the implementation of many interactive visual applications. The main goal of this work is to show how some new dynamic and interactive tools, created with Mathematica and available in the Computable Document Format (CDF), can be used as active learning tools to promote better student activity and engagement in the learning process. The CDF format allows anyone with a computer to use them, at no cost, even without an active Wolfram Mathematica license. Besides that, the presented tools are very intuitive to use which makes it suitable for less experienced users. Some tools applicable to several mathematics concepts taught in higher education will be presented. This kind of tools can be used either in a remote or classroom learning environment. The corresponding CDF files are made available as supplement of the online edition of this article.info:eu-repo/semantics/publishedVersio

Symbolic computation applied to the study of the kernel of special classes of paired singular integral operators

Operator theory has many applications in several main scientific research areas (structural mechan-ics, aeronautics, quantum mechanics, ecology, probability theory, electrical engineering, among others) and theimportance of its study is globally acknowledged. On the study of the operator’s kernel some progress has beenachieved for some specific classes of singular integral operators whose properties allow the use of particular strate-gies. However, the existing algorithms allow, in general, to study the dimension of the kernel of some classes ofsingular integral operators but are not designed to be implemented on a computer. The main goal of this paper is toshow how the symbolic and numeric capabilities of a computer algebra system can be used to study the kernel ofspecial classes of paired singular integral operators with essentially bounded coefficients defined on the unit circle.It is described how some factorization algorithms can be used to compute the dimension of the kernel of specialclasses of singular integral operators. The analytical algorithms [ADimKerPaired-Scalar], [AKerPaired-Scalar],and [ADimKerPaired-Matrix] are presented. The design of these new algorithms was focused on the possibility ofimplementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Forthe essentially bounded hermitian coefficients case, there exist some relations with Hankel operators. The papercontains some interesting and nontrivial examples obtained with the use of a computer algebra system.Fundação para a Ciência e Tecnologia (Portugal) through the Center for Functional Analysis, Linear Structures and Applicationsinfo:eu-repo/semantics/publishedVersio

Desenvolvimento de espécies arbóreas nativas no sub-bosque de reflorestamento.

Estudou-se a sobrevivência e o desenvolvimento de duas espécies florestais jovens Vochysia tucanorum (C.K. Spreng.) Mart. (Vochysiaceae) e Aloysia virgata (Ruiz et Pav.) A.L. Juss. (Verbenaceae) em área aberta e sombreada de um sub-bosque de uma monocultura florestal de Pinus nem área pertencente à Universidade Federal de São Carlos, SP, Brasil. As melhores condições do solo do sub-bosque de Pinus, principalmente maior acúmulo de matéria orgânica, possibilitaram um ambiente mais propício para o desenvolvimento inicial e sobrevivência de ambas as espécies florestais nativas. Este estudo contribui para investigar a possibilidade de usarem-se monoculturas florestais exóticas juntamente com espécies florestais nativas para a recomposição da Reserva Legal Florestal seguindo as recomendações para o Estado de São Paulo de acordo com o Decreto nº 53.939, sancionado no ano de 2009

Ecofisiologia de espécies arbóreas jovens de cerrado.

Avaliou-se o crescimento e o desempenho fotossintético de quatro espécies lenhosas sob condições contrastantes de irradiância. Todas as espécies apresentaram maior acúmulo de biomassa, altura, diâmetro do colo, área foliar total e maior capacidade fotossintética crescendo em área aberta. Os indivíduos sob sombra modificaram a partição de biomassa e o metabolismo do carbono da folha, apresentando maiores valores da razão da área foliar e menor valor da massa especifica foliar, respiração no escuro. Elevada concentração transitória de CO2 aumentou a capacidade fotossintética em área aberta e sob sombra. Essas modificações fisiológicas e morfológicas em ambas as espécies sob irradiâncias contrastantes proporcionaram informações sobre a ecologia da regeneração requisitadas para o estabelecimento de plantas jovens do Cerrado

Symbolic computation applied to cauchy type singular integrals

The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear transport theory, in the theory of diffraction of acoustic and electromagnetic waves, in the theory of scattering and of inverse scattering, among others. In our work, we use the computer algebra system Mathematica to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. The main goal of this paper is to present new operator theory algorithms related to Cauchy type singular integrals, defined in the unit circle. The design of these algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Several nontrivial examples computed with the algorithms are presented. The corresponding source code of the algorithms has been made available as a supplement to the online edition of this article.info:eu-repo/semantics/publishedVersio

Wolfram | Alpha: uma ferramenta de aprendizagem ativa em Cálculo I

O motor de conhecimento computacional Wolfram|Alpha, desenvolvido pela Wolfram Research, é uma ferramenta dinâmica e interativa, de acesso livre e manuseamento intuitivo, que explora tópicos de várias áreas do conhecimento. Estas características facilitam a sua utilização no ensino e propiciam a criação de um contexto de aprendizagem ativa em sala de aula. O Wolfram|Alpha foi utilizado, no ano letivo 2013/14, em aulas de Cálculo I, disciplina transversal a diversos cursos de ciências naturais na Universidade do Algarve, com o objetivo de consolidar conteúdos programáticos adquiridos durante o ensino secundário e de tornar mais interessante a aquisição de novos conceitos matemáticos nas áreas do Pré-Cálculo e do Cálculo Diferencial. Com o propósito de recolher e analisar as opiniões dos alunos sobre a importância da utilização do Wolfram|Alpha como instrumento de aprendizagem em Cálculo I foi elaborado um questionário e recolhidas as opiniões dos alunos matriculados na respectiva unidade curricular e que se submeteram à avaliação.info:eu-repo/semantics/publishedVersio