Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.

Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

An eigenvalue problem for the biharmonic operator on Z(2)-symmetric regions

In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set Of Z(2)-symmetric regions of R-n, n >= 2, with a suitable topology. To accomplish this, we combine Baire`s lemma, a generalised version of the transversality theorem, due to Henry [Perturbation of the boundary in boundary value problems of PDEs, London Mathematical Society Lecture Note Series 318 (Cambridge University Press, 2005)], and the method of rapidly oscillating functions developed in [A. L. Pereira and M. C. Pereira, Mat. Contemp. 27 (2004) 225-241].

Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

Estudo e implementação de um controlador preditivo generalizado bilinear compensado adaptativo

The present work presents the study and implementation of an adaptive bilinear compensated generalized predictive controller. This work uses conventional techniques of predictive control and includes techniques of adaptive control for better results. In order to solve control problems frequently found in the chemical industry, bilinear models are considered to represent the dynamics of the studied systems. Bilinear models are simpler than general nonlinear model, however it can to represent the intrinsic not-linearities of industrial processes. The linearization of the model, by the approach to time step quasilinear , is used to allow the application of the equations of the generalized predictive controller (GPC). Such linearization, however, generates an error of prediction, which is minimized through a compensation term. The term in study is implemented in an adaptive form, due to the nonlinear relationship between the input signal and the prediction error.Simulation results show the efficiency of adaptive predictive bilinear controller in comparison with the conventional.

Controle ótimo H∞ de sistemas não-lineares com modelos fuzzy takagi-sugeno

Neste trabalho é proposta uma metodologia de rastreamento de sinais e rejeição de distúrbios aplicada a sistemas não-lineares. Para o projeto do sistema de rastreamento, projeta-se os controladores fuzzy M(a) e N(a) que minimizam o limitante superior da norma H∞ entre o sinal de referência r(t) e o sinal de erro de rastreamento e(t), sendo e(t) a diferença entre a entrada de referência e a saída do sistema z(t). No método de rejeição de distúrbio utiliza-se a realimentação dinâmica da saída através de um controlador fuzzy Kc(a) que minimiza o limitante superior da norma H∞ entre o sinal de entrada exógena w(t) e o sinal de saída z(t). O procedimento de projeto proposto considera as não-linearidades da planta através dos modelos fuzzy Takagi-Sugeno. Os métodos são equacionados utilizando-se inequações matriciais lineares (LMIs), que quando factíveis, podem ser facilmente solucionados por algoritmos de convergência polinomial. Por fim, um exemplo ilustra a viabilidade da metodologia proposta.

Beta: uma ferramenta para geração de testes de unidade a partir de especificações B

Formal methods and software testing are tools to obtain and control software quality. When used together, they provide mechanisms for software specification, verification and error detection. Even though formal methods allow software to be mathematically verified, they are not enough to assure that a system is free of faults, thus, software testing techniques are necessary to complement the process of verification and validation of a system. Model Based Testing techniques allow tests to be generated from other software artifacts such as specifications and abstract models. Using formal specifications as basis for test creation, we can generate better quality tests, because these specifications are usually precise and free of ambiguity. Fernanda Souza (2009) proposed a method to define test cases from B Method specifications. This method used information from the machine s invariant and the operation s precondition to define positive and negative test cases for an operation, using equivalent class partitioning and boundary value analysis based techniques. However, the method proposed in 2009 was not automated and had conceptual deficiencies like, for instance, it did not fit in a well defined coverage criteria classification. We started our work with a case study that applied the method in an example of B specification from the industry. Based in this case study we ve obtained subsidies to improve it. In our work we evolved the proposed method, rewriting it and adding characteristics to make it compatible with a test classification used by the community. We also improved the method to support specifications structured in different components, to use information from the operation s behavior on the test case generation process and to use new coverage criterias. Besides, we have implemented a tool to automate the method and we have submitted it to more complex case studies

Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An application of the Adomian's decomposition method to the analysis of MHD duct flows

A new approach is proposed in this work for the treatment of boundary value problems through the Adomian's decomposition method. Although frequently claimed as accurate and having fast convergence rates, the original formulation of Adomian's method does not allow the treatment of homogeneous boundary conditions along closed boundaries. The technique here presented overcomes this difficulty, and is applied to the analysis of magnetohydrodynamic duct flows. Results are in good agreement with finite element method calculations and analytical solutions for square ducts. Therefore, new possibilities appear for the application of Adomian's method in electromagnetics.

A comparative study between two relaxed LMI-based fuzzy control designs

A comparative study, with theoretical analysis and digital simulations, of two conditions based on LMI for the quadratic stability of nonlinear continuous-time dynamic systems, described by Takagi-Sugeno fuzzy models, are presented. This paper shows that the methods proposed by Teixeira et. al. in 2003 provide better or at least the same results of a recent method presented in the literature. © 2005 IEEE.

Low caloric value of ethanol itself increases alveolar bone loss in ligature-induced periodontitis in male rats

This study aimed at morphometrically evaluating the influence of variable caloric values of ethanol consumption on alveolar bone loss in periodontitis in male rats. Thirty-six male rats were randomized into four groups of nine rats each, as follows: Test group A (low) - rats were fed an ethanol-containing liquid diet (ethanol representing 22% of total caloric value); Control group A - rats were fed a pair-fed control diet (ethanol replaced by isocaloric amounts of carbohydrate); Test group B (high) - rats were fed an ethanol-containing liquid diet (ethanol representing 36% of total caloric value); Control group B - rats were fed a pair-fed control diet for Test B. Following anesthesia, cotton ligatures were placed around the cervix of the right upper second molar. At eight weeks, the maxillary bones were removed and alveolar bone loss was analyzed by measuring the distance between the cementoenamel junction and the alveolar bone crest at buccal and palatal sites of the upper second molar. The unligated groups showed no significant differences between the bone loss values observed for the low and high caloric values of ethanol (p > 0.05). In the ligated groups, the rats receiving low caloric values of ethanol showed significantly greater bone loss compared to the isocaloric rats (p < 0.05); however, the rats receiving high caloric values of ethanol showed no significant differences compared to the controls. Analysis of the results demonstrated that, in male rats, ethanol itself affected ligature-induced bone loss when representing a low value in the total caloric value.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.