Submitted by Lara Oliveira (lara@ufersa.edu.br) on 2017-07-17T23:03:01Z No. of bitstreams: 1 ClaudioMMA_DISSERT.pdf: 1868632 bytes, checksum: 181427139e69d7b9f1645804fede5b2c (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-18T15:07:00Z (GMT) No. of bitstreams: 1 ClaudioMMA_DISSERT.pdf: 1868632 bytes, checksum: 181427139e69d7b9f1645804fede5b2c (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-18T15:07:15Z (GMT) No. of bitstreams: 1 ClaudioMMA_DISSERT.pdf: 1868632 bytes, checksum: 181427139e69d7b9f1645804fede5b2c (MD5) / Made available in DSpace on 2017-07-18T15:07:33Z (GMT). No. of bitstreams: 1 ClaudioMMA_DISSERT.pdf: 1868632 bytes, checksum: 181427139e69d7b9f1645804fede5b2c (MD5) Previous issue date: 2013-08-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / With the aid of the mathematical the man uses representations that are able to explain and interpret phenomena in studies, with this, the use of mathematics with language symbolic leads representation of the problem situation in mathematical terms, which in turn, this model can be understood as a set of symbols and relationships that represent a situation, phenomenon, or a real object to be studied. Therefore, this paper presents a mathematical modeling of quarter suspension system of an automobile in order to obtain a transfer function and then put the system in a state space representation. The second part deals with the problems of stabilization in continuous-time linear systems using static output feedback. The second part deals with the problems of stabilization in continuous-time linear systems using static output feedback. The results presented have as their starting point the concept of subspaces (C,A,B)-invariant algebraically characterized by a pair of coupled Sylvester equations, whose solution can be obtained for systems that verify the condition Kimura, in two stages using the algorithm and Lewis Syrmos. In the case of normal systems as studied in this work will be used the technique of the stabilization for two systems satisfying the condition Kimura, will be simulations of this car passing by two external disturbances, and controller gains employees will be obtained by the methods of allocation poles and coupled Sylvester equations, and finishes the work by making a bond regarding the responses of two arrays of feedback gains / Com o auxilio da matemática o homem utiliza representações que são capazes de explicar e interpretar fenômenos em estudos, com isso, o uso da matemática como linguagem simbólica conduz a uma representação da situação problema em termos matemáticos, que por sua vez, este modelo pode ser entendido como um conjunto de símbolos e relações que representa uma situação, um fenômeno, ou um objeto real a ser estudado. Diante disso, o presente trabalho apresenta a modelagem matemática de um quarto do sistema de suspensão de um automóvel, a fim de obter uma função de transferência para em seguida colocar o sistema em uma representação no espaço de estados. Serão tratados também os problemas de estabilização em sistemas lineares contínuos no tempo usando realimentação estática de saídas. Os resultados apresentados têm como ponto de partida o conceito de subespaços (C, A,B)-invariantes caracterizados algebricamente através de um par de equações acopladas de Sylvester, cuja solução pode ser obtida, para sistemas que verificam a condição de Kimura, em duas etapas utilizando o algoritmo de Syrmos e Lewis. No caso de sistemas normais como é estudado neste trabalho será usado à técnica de estabilização para dois sistemas satisfazendo a condição de Kimura será feitas simulações deste automóvel passando por duas perturbações externas, e os ganhos dos controladores empregados serão obtidos através dos métodos de alocação de polos e das equações acopladas de Sylvester, e finaliza o trabalho fazendo um elo em relação a respostas das duas matrizes de ganhos de realimentação / 2017-07-17

This thesis examines concrete poetry in England and Scotland from 1962 to 1975. Through the 1950s-70s, international concrete poetry evolved away from constructivist influenced, “classical” ideals of minimalism and iconic visual effect towards principles owing more to Dadaism and Futurism: spontaneity, maximalism, sonority and an emphasis on intermedial expression. Against this backdrop, using close textual analysis supported by primary research, I engage with four poets whose work collectively exemplifies the wide range of values which concrete poetry represented in England and Scotland during the period in question. A movement away from classical ideals can be tracked across the oeuvres of Finlay, Morgan, Houédard and Cobbing; but many aspects of their work cannot be accounted for by this general rubric. Finlay saw concrete poetry as a means of casting off Scottish literary tradition, but also of embodying an immutable vision of aesthetic and ethical order, using a marriage of the visual and linguistic to emphasise links between disparate ideas and things. However, his restless reconfiguration of poetry’s visual-physical aspects ultimately resulted in a re-separation of word and image which, together with an increasing historical-mindedness, ended his attachment to the style. Morgan, by contrast, used concrete poetry to redefine rather than repel Scottish literary culture, and was a more context-focused poet, using concrete grammar – whose sonic possibilities he exploited more than Finlay – to depict specific communicative scenarios, and thus to register ethical and political imperatives, often reflecting Scottish nationalist ideals. The emphasis on semantics common to Morgan and Finlay’s work, reflecting relative fidelity to classical principles, is overridden in Houédard’s concrete poetry, which came to employ a grammar of abstract visual motifs in which linguistic meaning was subsumed, related as much to apophatic theology as to classical concrete. For Cobbing too, concrete became a means of evading language, in his case to access a transcendent realm of “intermedial” poetry equally related to language’s sonic and visual dimensions, and influenced by various contemporary artforms, and by counter-cultural ideals. However, Cobbing’s emphasis on performing poems, and the reintegration of semantics into his work throughout this period, led by the early 1970s to an alternative poetic ideal of relativity.

We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and performance of the resulting methods with existing Sylvester solvers. The algorithms proposed here are easy to parallelize. We report on the parallelization of those algorithms and demonstrate their high efficiency and scalability using experimental results obtained on a cluster of Intel Pentium Xeon processors.

Power networks are sophisticated dynamical systems whose stable operation is essential to modern society. We study the swing equation for networks and its linearization (LSEN) as a tool for modeling power systems. Nowadays, phasor measurement units (PMUs) are used across power networks to measure the magnitude and phase angle of electric signals. Given the abundant data that PMUs can produce, we study applications of the dynamic mode decomposition (DMD) and Loewner framework to power systems. The matrices that define the LSEN model have a particular structure that is not recovered by DMD. We thus propose a novel variant of DMD, called structure-preserving DMD (SPDMD), that imposes the LSEN structure upon the recovered system. Since the solution of the LSEN can potentially exhibit interesting transient dynamics, we study the transient growth for the exponential matrix related to the LSEN. We follow Godunov's approach to get upper bounds for the transient growth and also analyze the relationship of such bounds with classical bounds based on the spectrum, numerical range, and pseudospectra. We show how Godunov's bounds can be optimized to bound the solution operator at a given time. The Loewner framework provides a tool for identifying a dynamical system from tangential measurements. The singular values of Loewner matrices guide the discovery of the true order of the underlying system. However, these singular values can exhibit rapid decay when the interpolation points are far from the poles of the system. We establish a range of bounds for this decay of singular values and apply this analysis to power systems. / Doctor of Philosophy / Power networks are sophisticated dynamical systems whose stable operation is essential to modern society. We study a mathematical model called the LSEN to understand and recover the dynamics of power networks. The LSEN model defines some matrices that have special structures dictated by the application. We propose a novel method to recover matrices with this desired structure from data. We also study some properties of the solution of the LSEN model related to the exponential of a matrix, connecting classical results with the particular approach that we follow. In the system identification context, we also study bounds on the singular values of Loewner matrices to understand the interplay between the data (measurements of the system) and mathematical artifacts (poles of the system).

Cette thèse porte sur des méthode de résolution d'équations matricielles appliquées à la résolution numérique d'équations aux dérivées partielles ou des problèmes de contrôle linéaire. On s'intéressen en premier lieu à des équations matricielles linéaires. Après avoir donné un aperçu des méthodes classiques employées pour les équations de Sylvester et de Lyapunov, on s'intéresse au cas d'équations linéaires générales de la forme M(X)=C, où M est un opérateur linéaire matriciel. On expose la méthode de GMRES globale qui s'avère particulièrement utile dans le cas où M(X) ne peut s'exprimer comme un polynôme du premier degré en X à coefficients matriciels, ce qui est le cas dans certains problèmes de résolution numérique d'équations aux dérivées partielles. Nous proposons une approche, noté LR-BA-ADI consistant à utiliser un préconditionnement de type ADI qui transforme l'équation de Sylvester en une équation de Stein que nous résolvons par une méthode de Krylox par blocs. Enfin, nous proposons une méthode de type Newton-Krylov par blocs avec préconditionnement ADI pour les équations de Riccati issues de problèmes de contrôle linéaire quadratique. Cette méthode est dérivée de la méthode LR-BA-ADI. Des résultats de convergence et de majoration de l'erreur sont donnés. Dans la seconde partie de ce travail, nous appliquons les méthodes exposées dans la première partie de ce travail à des problèmes d'équations aux dérivées partielles. Nous nous intéressons d'abord à la résolution numérique d'équations couplées de type Burgers évolutives en dimension 2. Ensuite, nous nous intéressons au cas où le domaine borné est choisi quelconque. Nous établissons des résultats théoriques de l'existence de tels interpolants faisant appel à des techniques d'algèbre linéaire. / This thesis deals with some matrix equations involved in numerical resolution of partial differential equations and linear control. We first consider some numerical resolution techniques of linear matrix equation. In the second part of this thesis, we apply these resolution techniques to problems related to partial differential equations.

Given a full-range simply-invariant shift-invariant subspace <i>M</i> of the vector-valued <i>L²</i> space on the unit circle, the classical Beurling-Lax-Halmos (BLH) theorem obtains a unitary operator-valued function <i>W</i> so that <i>M</i> may be represented as the image of of the Hardy space <i>H²</i> on the disc under multiplication by <i>W</i>. The work of Ball-Helton later extended this result to find a single function representing a so-called dual shift-invariant pair of subspaces <i>(M,M^Ã)</i> which together form a direct-sum decomposition of <i>L²</i>. In the case where the pair <i>(M,M^Ã)</i> are finite-dimensional perturbations of the Hardy space <i>H²</i> and its orthogonal complement, Ball-Gohberg-Rodman obtained a transfer function realization for the representing function <i>W</i>; this realization was parameterized in terms of zero-pole data computed from the pair <i>(M,M^Ã)</i>. Later work by Ball-Raney extended this analysis to the case of nonrational functions <i>W</i> where the zero-pole data is taken in an infinite-dimensional operator theoretic sense. The current work obtains analogues of these various results for arbitrary dual shift-invariant pairs <i>(M,M^Ã)</i> of the <i>L²</i> spaces on the real line; here, shift-invariance refers to invariance under the translation group. These new results rely on recent advances in the understanding of continuous-time infinite-dimensional input-state-output linear systems which have been codified in the book by Staffans. / Ph. D.

In this thesis we study the computation of the greatest common divisor of two polynomials. Firstly, properties of Sylvester matrices are considered as well as their role in computation. We then note, that this approach can be naturally generalized for several polynomials. In the penultimate section, Bézout matrices are studied as an analogy to the Sylvester ones, providing necessary comparison. Extension for more than polynomials is presented here as well. Algorithms corresponding to the individual approaches are presented as well. Finally, the algorithms are implemented in MATLAB and are compared in numerical experiments. Powered by TCPDF (www.tcpdf.org)

Thesis (M.A.)--University of the Witwatersrand, Faculty of Humanities, History of Arts, 2013 / This report examines the collecting practices of the private collector of South African art, situated in South Africa, and considers the way in which the act of collecting influences both the contemporary market and the construction of the art historical canon. The report questions the contribution made to the South African art world by collecting practices and considers what is involved in the collecting of fine art. I discuss the collector in relation to Sylvester Ogbechie’s (2010) notion of cultural brokerage; I examine notions of both public and private through the writings of Michael Warner (2002); and I consider what makes into one a collector, with reference to Thomas G. Tanselle’s (1998) text A Rationale of Collecting, while engaging several other sources. The report continues with a comparison between international collectors, with a focus on the ways in which they contribute to what becomes and remains relevant, as well as discussing some local collectors. I conclude with an examination of the way in which auction houses have played a seminal role in the establishment of the canon in South Africa, and the role of the collector in relation to this system. In summary, this paper examines the ways in which the private collector of South African art has a great influence on what is perceived as relevant to the canon, to culture and to art history.

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