Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-02-17Bitstream added on 2014-06-13T20:28:18Z : No. of bitstreams: 1 porto_d_me_sjrp.pdf: 388104 bytes, checksum: ef6b41d53662a13bad28fcc9baed7ad9 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo deste trabalho é o estudo do sistema de controle impulsivo de [Wolenski e Zabi´c 2007] para o caso em que o sistema é dado por uma igualdade e modificado pela adição de dois controles abstratos. Tal estudo foi feito utilizando duas abordagens. Na primeira, reparametrizamos o sistema inicial a partir da função distribuição relacionada à medida atômica e, através da discretização de Euler do sistema reparametrizado, obtemos uma sequência de soluções que converge no gráfico para a solução do sistema original, sob algumas hipóteses. Na segunda abordagem, definimos um novo sistema associado a uma sequência de medidas absolutamente contínuas que converge no gráfico para a medida atômica. A partir desse novo sistema, obtemos uma sequência de soluções com a propriedade de convergência no gráfico da solução do sistema original / The aim of this work is to study the impulsive control system of [ Wolenski e Zabic 2007] to the case where system is given by an equality and modified by addition of two abstract controls. The study was done using two approaches. At first, we've reparameterized the initial system from distribution function related to atomic measure and, through Euler's discretization of reparameterized system, we've obtained a sequence of solutions which graph converge to the solution of original system, under some hypothesis. In the second approach, we've defined a new system associated with a sequence of absolutely continuous measures which graph converge to atomic measure. From this new system, we've obtained a sequence of solutions with the graph convergence prop erty of the solution of the original system

Thesis (M.S.)--Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

Honors thesis (B.A.)-Ithaca College Dept. of Mathematics, 2008. / Title from abstract page. "April 15, 2008." includes abstract Includes bibliographical references (leaf 33). Also available in print form in the Ithaca College Archives.

<P> In this thesis, we mainly study geodesics on various two dimensional surfaces. All the background material needed throughout the thesis is provided, including an explanation of the theory of geodesics. We will calculate geodesics using two numerical methods: Euler's method and Runge-Kutta method of fourth order. Using Maple, we will test the accuracy of the numerical methods on a test case surface, the Poincare half plane. Later, we proceed to investigate several interesting surfaces by numerically calculating geodesics. From the investigated surfaces, we will draw similarities between the human cerebral cortex and certain surfaces. The human cerebral cortex is the most intensely studied part of the brain and it is believe that their exists a relation between the function and structure of the cortex. Geodesic analysis can possibly be an essential tool in better understanding the cortical surface as it is in many disciplines of science to understand the nature of physical based problems. </P> / Thesis / Master of Science (MSc)

In chapter 1, we focus on the noncharacteristic boundary layers for the parabolic regularization of quasi-linear hyperbolic problems, where the viscosity matrix is positive definite, with the zero Dirichlet boundary conditions. We adapt the method developed by Grenier and Gues [?] where the center-stable manifold theorem is used to prove the existence and exponential decay property of the leading boundary layer profile under suitable conditions on the boundary x = 0. With this boundary condition we prove the well-posedness of the initial boundary value problem of the inviscid flow. Then we prove the stability of the boundary layer by an energy estimate, where exponential decay property of the boundary layer profile plays an important role. Finally, we can specify the limit of the viscous solutions to the corresponding inviscid solution. / In chapter 2, we consider the noncharacteristic one-dimensional compressible full Navier-Stokes equations for the ideal gas with outflow boundary condition on the velocity and suitable initial conditions, which make all the three characteristics to the corresponding Euler equations negative up to some local time, especially on the boundary. By the aymptotic analysis, we derive an algebraic-differential equation for the leading boundary layer functions. The center-stable manifold theorem helps to prove the existence and exponential decay property of the leading boundary layer function. The outflow boundary condition makes it possible to estimate the normal derivatives. Combining this with the tangential derivative estimate, we can recover the H1 estimate of the error term. Thus we establish the stability of the boundary layers which satisfy an algebraic-differential equation in this case. With this stability result, we obtain the relation between the solutions to Navier-Stokes and Euler equations. / In chapter 3, we concentrate on the existence and nonlinear stability of the totally characteristic boundary layer for the quasi-linear equations with positive definite viscosity matrix under the assumption that the boundary matrix vanishes identically on the boundary x = 0. We carry out a weighted estimate to the boundary layer equations---Prandtl type equations to get the regularity and the far field behavior of the solutions. This allows us to perform a weighted energy estimate for the error equation to prove the stability of the boundary layers. The stability result finally implies the asymptotic limit of the viscous solutions. / In this thesis we study three kinds of asymptotic limiting behavior of the solutions to the initial boundary value problem of one-dimensional quasilinear equations with viscosity by carrying out the boundary layer analysis. / Wang, Jing. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 71-01, Section: B, page: 0407. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 107-112). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese.

Communication networks are vulnerable to natural as well as man-made disasters. The geographical layout of the network influences the impact of these disasters. It is therefore, necessary to identify areas that could be most affected by a disaster and redesign those parts of the network so that the impact of a disaster has least effect on them. In this work, we assume that disasters which have a circular impact on the network. The work presents two new algorithms, namely the WHF-PG algorithm and the WHF-NPG algorithm, designed to solve the problem of finding the locations of disasters that would have the maximum disruptive effect on the communication infrastructure in terms of capacity.

Not available / text

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Orientador: Geraldo Nunes Silva / Banca: Orizon Pereira Ferreira / Banca: Fernando Manuel F. Lobo Pereira / Resumo: O objetivo deste trabalho é o estudo do sistema de controle impulsivo de [Wolenski e šZabi'c 2007] para o caso em que o sistema é dado por uma igualdade e modificado pela adição de dois controles abstratos. Tal estudo foi feito utilizando duas abordagens. Na primeira, reparametrizamos o sistema inicial a partir da função distribuição relacionada à medida atômica e, através da discretização de Euler do sistema reparametrizado, obtemos uma sequência de soluções que converge no gráfico para a solução do sistema original, sob algumas hipóteses. Na segunda abordagem, definimos um novo sistema associado a uma sequência de medidas absolutamente contínuas que converge no gráfico para a medida atômica. A partir desse novo sistema, obtemos uma sequência de soluções com a propriedade de convergência no gráfico da solução do sistema original / Abstract: The aim of this work is to study the impulsive control system of [ Wolenski e šZabic 2007] to the case where system is given by an equality and modified by addition of two abstract controls. The study was done using two approaches. At first, we've reparameterized the initial system from distribution function related to atomic measure and, through Euler's discretization of reparameterized system, we've obtained a sequence of solutions which graph converge to the solution of original system, under some hypothesis. In the second approach, we've defined a new system associated with a sequence of absolutely continuous measures which graph converge to atomic measure. From this new system, we've obtained a sequence of solutions with the graph convergence prop erty of the solution of the original system / Mestre

Orientador: Renata Zotin Gomes de Oliveira / Banca: Suzinei Aparecida Siqueira Marconato / Banca: Maria Beatriz Ferreira Leite / Resumo: O principal objetivo deste trabalho é o estudo da teoria do Cálculo de Variações com ênfase na Equação de Euler, que trata de uma condição necessária para uma função ser extremo de um funcional. Existe uma grande variedade de problemas, mas neste trabalho trataremos de problemas com fronteiras fixas, tempo final livre, estado final livre, funcional dependente de mais de uma função e problemas com alguns tipos de restrições. Dois problemas do Cálculo de uma variável e um exemplo de controle ótimo são estudados para ilustrar a aplicabilidade do Cálculo Variacional / Abstract: The main purpose of this work is the study of the theory of the Calculus of Variations, with emphasis on the Euler equation, that is a necessary condition for a function to be an extreme of a functional. There are a large variety of problems but we will consider the problem of xed boundary, free nal time, free nal state, functionals that contain several independent functions and problems with some constraints. Two problems of the Calculus of one variable and an example of optimal control problem are studied to illustrate the applicability of Variational Calculus / Mestre