Browsing 2008 Dissertations (MU) by Thesis Department "Mathematics (MU)"
Now showing items 19 of 9

Algebraic resolution of formal ideals along a valuation
(University of MissouriColumbia, 2008)Let X be a possibly singular complete algebraic variety, defined over a field [kappa] of characteristic zero. X is nonsingular at [rho] [element of] X if OX,[rho] is a regular local ring. The problem of resolution of ... 
Applications of fourier analysis to intersection bodies
(University of MissouriColumbia, 2008)The concept of an intersection body is central for the dual BrunnMinkowski theory and has played an important role in the solution of the BusemannPetty problem. A more general concept of [kappa]intersection bodies is ... 
Boundary value problems for the Stokes system in arbitrary Lipschitz domains
(University of MissouriColumbia, 2008)The goal of this work is to treat the main boundary value problems for the Stokes system, i.e., (i) the Dirichlet problem with Lpdata and nontangential maximal function estimates, (ii) the Neumann problem with Lpdata and ... 
Box approximation and related techniques in spectral theory
(University of MissouriColumbia, 2008)This dissertation is concerned with various aspects of the spectral theory of differential and pseudodifferential operators. It consists of two chapters. The first chapter presents a study of a family of spectral shift ... 
Dichotomy theorems for evolution equations
(University of MissouriColumbia, 2008)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In the first part of this work, under minimal assumptions, we characterize the Fredholm property and compute the Fredholm index of abstract differential ... 
Explorations of geometric combinatorics in vector spaces over finite fields
(University of MissouriColumbia, 2008)We study how large a set of points needs to be in a vector space over a finite field in order for the points to determine all of a certain type of geometric structure. In addition we show that there are key differences ... 
Extension theorems in vector spaces over finite fields
(University of MissouriColumbia, 2008)We study the L[superscript p]  L[superscript r] boundedness of the extension operator associated with algebraic varieties such as nondegenerate quadratic surfaces, paraboloids, and cones in vector spaces over finite fields. ... 
Sections of complex convex bodies
(University of MissouriColumbia, 2008)The main idea of the Fourier analytic approach to sections of convex bodies is to express different parameters of a body in terms of the Fourier transform and then apply methods of Fourier analysis to solve geometric ... 
Toroidalization of locally toroidal morphisms
(University of MissouriColumbia, 2008)Let X and Y be nonsingular varieties over an algebraically closed field [kappa] of characteristic zero. A toroidal structure on X is a simple normal crossing divisor DX on X. Suppose that DX and DY are toroidal structures ...