• Algebraic resolution of formal ideals along a valuation 

    El Hitti, Samar, 1979- (University of Missouri--Columbia, 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 

    Schlieper, Jared (University of Missouri--Columbia, 2008)
    The concept of an intersection body is central for the dual Brunn-Minkowski theory and has played an important role in the solution of the Busemann-Petty problem. A more general concept of [kappa]-intersection bodies is ...
  • Boundary value problems for the Stokes system in arbitrary Lipschitz domains 

    Wright, Matthew E., 1980- (University of Missouri--Columbia, 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 Lp-data and nontangential maximal function estimates, (ii) the Neumann problem with Lp-data and ...
  • Box approximation and related techniques in spectral theory 

    Borovyk, Vita, 1979- (University of Missouri--Columbia, 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 

    Pogan, Alexandru Alin, 1976- (University of Missouri--Columbia, 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 

    Hart, Derrick, 1980- (University of Missouri--Columbia, 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 

    Koh, Doowon, 1972- (University of Missouri--Columbia, 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 

    Zymonopoulou, Maria-Isavella, 1973- (University of Missouri--Columbia, 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 

    Hanumanthu, Krishna Chaithanya, 1981- (University of Missouri--Columbia, 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 ...