• 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)
    In the first part of this work, under minimal assumptions, we characterize the Fredholm property and compute the Fredholm index of abstract differential operators -d/dt + A([dot]) acting on spaces of functions R [arrow] ...
  • 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 ...
  • An extension of Green's theorem with application 

    Judd, Kristin N. (University of Missouri--Columbia, 2008)
    The main result of this thesis is a generalization of Green's Theorem. Green' s Theorem states: If Omega is an open subset of R[logical and]2 containing a compact subset K with smooth boundary. Let P and Q be two real ...
  • The implicit function theorem for Lipschitz functions and applications 

    Wuertz, Michael (University of Missouri--Columbia, 2008)
    The subject matter of this thesis is the classical Implicit Function Theorem and its generalizations. Dictated by practical applications, it is of interest to relax the hypothesis of the standard Implicit Function Theorem ...
  • 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 ...
  • Surface to surface changes of variables and applications 

    Brewster, Kevin, 1982- (University of Missouri--Columbia, 2008)
    The present thesis addresses a number of basic problems in relation to integration over surfaces in the Euclidean space, such as how the surface measure and unit normal changes under a smooth diffeomorphism how the integration ...
  • 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 ...