Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: volume integral equations; patch antenna; reonators; MoM. Includes bibliographical references (p. 103-106).

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains x, 227 p.; also includes graphics Includes bibliographical references (p. 224-227). Available online via OhioLINK's ETD Center

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 32-33).

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Seja Ω um domÃnio fixado em Rn com fronteira S de classe C2 e denote Ω′ = Rn Ω. Ambos Ω e Ω′ nÃo necessariamente conexos. Nessas condiÃÃes, pretendemos resolver os problemas de Dirichlet e Neumann. No intuito da resoluÃÃo dos problemas citados, faremos um estudo daTeoria de Fredholm (operadores compactos), bem como da transformada de Kelvin, harmonicidade no infinito e dos potenciais de camada. / Let Ω be a fixed domain in Rn with boundary S of class C2 and denote Ω′ = Rn Ω. Both Ω and Ω′ not necessarily connected. Under these conditions, we intend to solve the problems of Dirichlet and Neumann. In order to overcome the mentioned the problems, we will study the Fredholm theory (compact operators), the Kelvin transformed, harmonicity in the infinite and potential of the layer.

Let H be a separable Hilbert space. Suppose (Ω, F, Ft, P) is a complete stochastic basis with a right continuous filtration and {Wt,t ∈ R} is an H-valued cylindrical Brownian motion with respect to {Ω, F, Ft, P). U(t, s) denotes an almost strong evolution operator generated by a family of unbounded closed linear operators on H. Consider the semilinear stochastic integral equation [formula omitted] where • f is of monotone type, i.e., ft(.) = f(t, w,.) : H → H is semimonotone, demicon-tinuous, uniformly bounded, and for each x ∈ H, ft(x) is a stochastic process which satisfies certain measurability conditions. • gs(.) is a uniformly-Lipschitz predictable functional with values in the space of Hilbert-Schmidt operators on H. • Vt is a cadlag adapted process with values in H. • X₀ is a random variable. We obtain existence, uniqueness, boundedness of the solution of this equation. We show the solution of this equation changes continuously when one or all of X₀, f, g, and V are varied. We apply this result to find stationary solutions of certain equations, and to study the associated large deviation principles. Let {Zt,t ∈ R} be an H-valued semimartingale. We prove an Ito-type inequality and a Burkholder-type inequality for stochastic convolution [formula omitted]. These are the main tools for our study of the above stochastic integral equation. / Science, Faculty of / Mathematics, Department of / Graduate

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The Mullins-Sekerka problem, also called two-sided Hele-Shaw flow, arises in modeling a binary material with two stable concentration phases. A coarsening process occurs, and large particles grow while smaller particles eventually dissolve. Single particles become spherical. This process is described by evolving harmonic functions within the two phases with the moving interface driven by the jump in the normal derivatives of the harmonic functions at the interface. The harmonic functions are continuous across the interface, taking on values equal to the mean curvature of the interface. This dissertation reformulates the three-dimensional problem as one on the two-dimensional interface by using boundary integrals. A semi-implicit scheme to solve the free boundary problem numerically is implemented. Numerical analysis tasks include discretizing surfaces, overcoming node bunching, and dealing with topology change in a toroidal particle. A particle (node)-cluster technique is developed with the aim of alleviating excessive run time caused by filling the dense matrix used in solving a system of linear equations.

The solutions for a class of Neutral Functional Di erential Equations (NFDE) with weakly singular kernels are studied. Using singular expansion techniques, a representation of the solution of the NFDE is obtained by studing an associated Volterra Integral Equation. We study the Collocation Method as a projection method for the approximation of solutions for Volterra Integral Equations. Particulary, the possibility of achieving higher order ap- proximations is discussed. Special attention is given to the choice of the projection space and its relation to the smoothness of the approximated solution. Finally, we study the identification problem for a parameter appearing in the weakly singular operator of the NFDE. / Ph. D.