2 resultados para Transformation matrices

em Instituto Politécnico do Porto, Portugal


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Ian McEwan‘s novel Saturday deals with the complex issues of conflict and transformation in the age of terrorism. The plot presents one internal dilemma and several interpersonal altercations that occur within a mere twenty-four hours: a) Perowne (the protagonist) vs. himself, in face of his ambivalent thoughts regarding British military participation in the war in the Middle East; b) The protagonist vs. Baxter, a ruffian from East End, in the context of a car accident; c) Perowne vs. a fellow anaesthetist, Jay Strauss, during a squash game; d) Perowne‘s daughter, Daisy vs. her grandfather, John Grammaticus, both poets and rivals; e) Perowne‘s family vs. Baxter, who intrudes the protagonist‘s house. In this paper, I exemplify, analyse and discuss how: a) Understanding the causes of what we call evil constitutes an important step towards mutual understanding; b) Both science and arts (which Perowne considers, at first, irrelevant) are important elements in the process of transformation; c) Both personal and interpersonal conflicts are intrinsic to human nature — but they also propitiate healthy changes in behaviour and opinion, through reflection. In order to do so, I resort to Saturday, and to the work of several specialists in the field of conflict management.

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Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.