by Hon-Ming Ho. / "May 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 69-71). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Este trabalho descreve os métodos e os resultados encontrados a partir da implementação de métodos estáticos para análise da estabilidade de tensão em sistemas elétricos de potência. A determinação da margem de estabilidade de tensão foi feita através do cálculo do menor valor singular da matriz jacobiana associada às equações de fluxo de carga, comumente utilizado como índice estático de colapso de tensão. As não linearidades e descontinuidades relatadas nas referências estudadas e encontradas nos testes realizados, levaram-nos a propor o uso da razão entre o menor e o maior valores singulares da mesma matriz jacobiana, na expectativa de que este índice tivesse um comportamento menos instável do que o menor valor singular, o que não foi confirmado nos testes realizados. Identifica-se também as regiões do sistema elétrico mais afetadas pela instabilidade, o que é feito através da determinação da barra crítica do sistema e da classificação das barras de carga em ilhas de controle de tensão. A barra crítica é identificada através do cálculo do vetor tangente do sistema, conforme proposto nas referências citadas no trabalho. Como alternativa ao vetor tangente para a identificação da barra crítica, propôs-se usar o vetor singular à direita associado ao menor valor singular da matriz jacobiana. A comparação da capacidade de identificação da barra crítica por esses dois vetores mostrou uma clara vantagem do uso do vetor tangente. A rotina para identificação das ilhas de controle de tensão foi adaptada a partir de um método desenvolvido para a análise de coerência em barras de carga, e os resultados encontrados foram bastante satisfatórios. Os métodos implementados foram testados em diversas situações, com o objetivo de se analisar os efeitos dos modelos de carga ZIP com elevadas parcelas de impedância constante, dos limitadores de potência reativa dos geradores e da repartição do incremento da carga de potência ativa entre os geradores. / This work describes the methods and results got from the implementation of static methods for power systems voltage stability analisys. The power system voltage stability margin was predicted by the smallest load flow jacobian\'s singular value, commonly used as a prediction index to voltage stability. lt is investigated the use of ratio of the smallest single value by the biggest one as voltage colapse index, assuming that it\'s less unstable than the singular value itself, specialy near the collapse point. The results presented shown a clear advantage of using the smallest singular value instead of this singular value rate. The identification of the system\'s regions affected by the voltage drop is made by the tangent vector and by the voltage island identification method proposed on this work. Is compared the ability to identify system\'s critical bus by the tangent vector and right singular vetor of the smallest jacobian\'s singular value. In this case, tests results show the superiority of tangent vector. All the simulations presented are compared to allow the analysis of the voltage dependents load models (with high percentual of constant impedances), reactive limiters and generators load sharing efects over the smallest singular value, the rate of the smallest single value by the biggest one, voltage island classification and the critical bus identification.

W1,p estimate for the solutions of elliptic equations whose coefficient matrix can have large jump along the boundary of subdomains is obtained. The principal coefficients are supposed to be in the John-Nirenberg space with small BMO seminorms. The domain and subdomains are Reifenberg flat domains and moreover, it has been shown that the estimates are uniform with respect to the distance between the subdomains.

Film blowing is a highly complex industrial process used to manufacture thin plastic films for uses in a wide range of applications; for example, plastic bags. The mathematical modelling of this process involves the analysis of highly nonlinear differential equations describing the complex phenomena arising in the film blowing process, and requires a sophisticated mathematical approach. This dissertation applies an innovative combination of tools, namely analytic, numerical and heuristic mathematical techniques to the analysis of the film blowing process. The research undertaken examines, in particular, a two-point boundary value problem arising from the modelling of the radial profile of the polymer film. For even the simplest modelling of this process, namely the isothermal Newtonian model, the resulting differential equation is a highly nonlinear, second order one, with an extra degree of difficulty due to the presence of a small parameter multiplying the highest derivative. Thus, the problem falls into the category of a nonlinear singular perturbation problem. Analytic techniques are applied to the isothermal Newtonian blown film model to obtain a closed form explicit approximation to the film bubble radius. This is then used as a base approximation for an iterative numerical scheme to obtain an improved numerical solution of the problem. The process is extended to include temperature variations, varying viscosity (Power law model) and viscoelastic effects (Maxwell model). As before, closed form approximations are constructed for these models which are used to launch numerical schemes, whose solutions display good accuracy. The results compare well with results obtained by purely numerical solutions in the literature.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 1997. / Includes bibliographical references. Also available on the Internet.

No description available.

This work is devoted to the equation <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cint_%7BS%7D%0A%5Cfrac%7Bu(y)%20%5C,%20dS(y)%7D%7B%7Cx-y%7C%5E%7BN-1%7D%7D%20=%20f(x)%20%5Ctext%7B,%7D%20%5Cqquad%20%5Cqquad%20x%20%5Cin%20S%20%5Ctext%7B,%7D%0A%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20(1)%0A" /> where S is the graph of a Lipschitz function φ on RN with small Lipschitz constant, and dS is the Euclidian surface measure. The integral in the left-hand side is referred to as a simple layer potential and f is a given function. The main objective is to find a solution u to this equation along with estimates for solutions near points on S. Our analysis is carried out in local Lp-spaces and local Sobolev spaces, and the estimates are given in terms of seminorms. In Paper 1, we consider the case when S is a hyperplane. This gives rise to the classical Riesz potential operator of order one, and we prove uniqueness of solutions in the largest class of functions for which the potential in (1) is defined as an absolutely convergent integral. We also prove an existence result and derive an asymptotic formula for solutions near a point on the surface. Our analysis allows us to obtain optimal results concerning the class of right-hand sides for which a solution to (1) exists. We also apply our results to weighted Lp- and Sobolev spaces, showing that for certain weights, the operator in question is an isomorphism between these spaces. In Paper 2, we present a fixed point theorem for a locally convex space <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathscr%7BX%7D" />, where the topology is given by a family <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5C%7Bp(%20%5C,%20%5Ccdot%20%5C,%20;%20%5Calpha%20)%5C%7D_%7B%5Calpha%20%5Cin%20%5COmega%7D" /> of seminorms. We study the existence and uniqueness of fixed points for a mapping<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathscr%7BK%7D%20%5C,%20:%20%5C;%20%5Cmathscr%7BD_K%7D%20%5Crightarrow%20%5Cmathscr%7BD_K%7D" /> defined on a set <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathscr%7BD_K%7D%20%5Csubset%20%5Cmathscr%7BX%7D" />. It is assumed that there exists a linear and positive operator K, acting on functions defined on the index set Ω, such that for every <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?u,v%20%5Cin%20%5Cmathscr%7BD_K%7D" />,   <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?p(%5Cmathscr%7BK%7D(u)%20-%20%5Cmathscr%7BK%7D(v)%20%5C,%20;%20%5C,%20%5Calpha%20)%20%0A%5Cleq%20K(p(u-v%20%5C,%20;%20%5C,%20%5Ccdot%20%5C,%20))%20(%5Calpha)%20%5Ctext%7B,%7D%20%5Cqquad%20%5Cqquad%20%5Calpha%20%5Cin%20%5COmega%0A%5Ctext%7B.%7D%0A" /> Under some additional assumptions, one of which is the existence of a fixed point for the operator K + p(<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathscr%7BK%7D(0)" /> ; · ), we prove that there exists a fixed point of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathscr%7BK%7D" />. For a class of elements satisfying Kn (p(u ; · ))(α) → 0 as n → ∞, we show that fixed points are unique. This class includes, in particular, the solution we construct in the paper. We give several applications, proving existence and uniqueness of solutions for two types of first and second order nonlinear differential equations in Banach spaces. We also consider pseudodifferential equations with nonlinear terms. In Paper 3, we treat equation (1) in the case when S is a general Lipschitz surface and 1 &lt; p &lt; ∞. Our results are presented in terms of Λ(r), which is the Lipschitz constant of φ on the ball centered at the origin with radius 2r. Estimates of solutions to (1) are provided, which can be used to obtain knowledge about behaviour near a point on S in terms of seminorms. We also show that solutions to (1) are unique if they are subject to certain growth conditions. Examples are given when specific assumptions are placed on Λ. The main tool used for both existence and uniqueness is the fixed point theorem from Paper 2. In Paper 4, we collect some properties and estimates of Riesz potential operators, and also for the operator that was used in Paper 1 and Paper 3 to invert the Riesz potential of order one on RN, for the case when the density function is either radial or has mean value zero on spheres. It turns out that these properties define invariant subspaces of the respective domains of the operators in question.

Digital information och kommunikation genom digitala medier är ett växande område. E-post och andra kommunikationsmedel används dagligen över hela världen. Parallellt med att området växer så växer även intresset av att hålla informationen säker. Transmission via antenner är inom signalbehandling ett välkänt område. Transmission från en sändare till en mottagare genom fri rymd är ett vanligt exempel. I en tuff miljö som till exempel ett rum med reflektioner och oberoende elektriska apparater kommer det att finnas en hel del distorsion i systemet och signalen som överförs kan, på grund av systemets egenskaper och buller förvrängas.Systemidentifiering är ett annat välkänt begrepp inom signalbehandling. Denna avhandling fokuserar på systemidentifiering i en tuff miljö med okända system. En presentation ges av matematiska verktyg från den linjära algebran samt en tillämpning inom signalbehandling. Denna avhandling grundar sig främst på en matrisfaktorisering känd som Singular Value Decomposition (SVD). SVD’n används här för att lösa komplicerade matrisinverser och identifiera system.Denna avhandling utförs i samarbete med Combitech AB. Deras expertis inom signalbehandling var till stor hjälp när teorin praktiserades. Med hjälp av ett välkänt programmeringsspråk känt som LabView praktiserades de matematiska verktygen och kunde synkroniseras med diverse instrument som användes för att generera signaler och system. / Digital information transmission is a growing field. Emails, videos and so on are transmitting around the world on a daily basis. Along the growth of using digital devises there is in some cases a great interest of keeping this information secure. In the field of signal processing a general concept is antenna transmission. Free space between an antenna transmitter and a receiver is an example of a system. In a rough environment such as a room with reflections and independent electrical devices there will be a lot of distortion in the system and the signal that is transmitted might, due to the system characteristics and noise be distorted. System identification is another well-known concept in signal processing. This thesis will focus on system identification in a rough environment and unknown systems. It will introduce mathematical tools from the field of linear algebra and applying them in signal processing. Mainly this thesis focus on a specific matrix factorization called Singular Value Decomposition (SVD). This is used to solve complicated inverses and identifying systems. This thesis is formed and accomplished in collaboration with Combitech AB. Their expertise in the field of signal processing was of great help when putting the algorithm in practice. Using a well-known programming script called LabView the mathematical tools were synchronized with the instruments that were used to generate the systems and signals.

The Singular Value Decomposition is one of the most useful matrix factorizations in applied linear algebra, the Principal Component Analysis has been called one of the most valuable results of applied linear algebra. How and why principal component analysis is intimately related to the technique of singular value decomposition is shown. Their properties and applications are described. Assumptions behind this techniques as well as possible extensions to overcome these limitations are considered. This understanding leads to the real world applications, in particular, image processing of neurons. Noise reduction, and edge detection of neuron images are investigated.

We here developed a third-order accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. The method is an intuitively simple numerical scheme based on a boundary integral formulation. It involves smoothing the singular Green's functions in the integrands and finding correction terms to the resulting smooth integrals. The analytical method is based on the singular integral methods of J. Thomas Beale, while the scattering problem is motivated by the 2D work of Stephanos Venakides, Mansoor Haider, and Stephen Shipman. The 3D problem was done with boundary element methods by Andrew Barnes. We present a method that is both more straightforward and more accurate. In solving these problems, we have used the M\"{u}ller integral equation formulation of Maxwell's equations, since it is a Fredholm integral equation of the second kind and is well-posed. M\"{u}ller derived his equations for the case of a compact scatterer. We outline the derivation and adapt it to a periodic scatterer. The periodic Green's functions found in the integral equation contain singularities which make it difficult to evaluate them numerically with accuracy. These functions are also very time consuming to evaluate numerically. We use Ewald splitting to represent these functions in a way that can be computed rapidly.We present a method of smoothing the singularity of the Green's function while maintaining its periodicity. We do local analysis of the singularity in order to identify and eliminate the largest sources of error introduced by this smoothing. We prove that with our derived correction terms, we can replace the singular integrals with smooth integrals and only introduce a error that is third order in the grid spacing size. The derivation of the correction terms involves transforming to principal directions using concepts from differential geometry. The correction terms are necessarily invariant under this transformation and depend on geometric properties of the scatterer such as the mean curvature and the differential of the Gauss map. Able to evaluate the integrals to a higher order, we implement a \mbox{GMRES} algorithm to approximate solutions of the integral equation. From these solutions, M\"{u}ller's equations allow us to compute the scattered fields and transmission coefficients. We have also developed acceleration techniques that allow for more efficient computation.We provide results for various scatterers, including a test case for which exact solutions are known. The implemented method does indeed converge with third order accuracy. We present results for which the method successfully resolves Wood's anomaly resonances in transmission. / Dissertation