• Erdős distance problem in the hyperbolic half-plane 

    Senger, Steven, 1982- (University of Missouri--Columbia, 2009)
    The Erd̋os distance problem asks for the minimum number of distinct distances determined by large finite point sets in the plane. The aim of this work is to investigate how the classical techniques employed in the study ...
  • 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 ...
  • Groupoids and semigroupoids 

    Vasko, Maria (University of Missouri--Columbia, 2013)
    The theory of semigroupoids and groupoids makes the transition between arbitrary sets and groups. The usefulness of developing theory stems from various applications where a group structure is lacking, yet there exists ...
  • 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 ...
  • Incorporation of directionally dependent diffusion with polymer composite flow theory 

    Jack, David Abram, 1977- (University of Missouri--Columbia, 2006)
    The extensive industrial use of short-fiber reinforced polymer composites demands an accurate understanding of fiber orientation kinematics. There is a growing concern in recent literature with the popular Folgar and Tucker ...
  • A priori estimates for solutions of elliptic partial differential equations on surfaces 

    Steenblock, Heidi, 1984- (University of Missouri--Columbia, 2009)
    Let S be an (n-1)-dimensional bounded surface of class C² in R[real number] [superscript n] and let [set theory][subscript s] be the Laplace-Beltrami operator on S. In this thesis, under suitable geometric assumptions, we ...
  • Quasi-metric geometry: smoothness and convergence results 

    Brigham, Dan, 1987- (University of Missouri--Columbia, 2011)
    This thesis has two distinct yet related parts, the first pertaining to geometry on quasi-metric spaces with emphasis on the Hausdorff outer-measure, the natural extension of the Gromov-Pompeiu-Hausdorff distance to ...
  • Results in analytic and algebraic number theory 

    Yeager, Aaron (University of Missouri--Columbia, 2012)
    The thesis begins with proving some theorems about Gauss sums and Jacobi sums. Using theorems the first chapter ends with a proof that if p is a prime such that p ≡ 1 (mod 4), then there are integers a and b such that p ...
  • 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 ...
  • Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles 

    Alvarado, Ryan (University of Missouri--Columbia, 2011)
    The present thesis consists of two main parts. In the first part, we prove that a function defined on a closed subset of a geometrically doubling quasi-metric space which satisfies a Hölder-type condition may be extended ...
  • Topics in Littlewood-Paley theory and BMO 

    Thompson, Brian (University of Missouri--Columbia, 2012)
    In this thesis we discuss some important results in Littlewood-Paley theory and the space of Bounded-Mean Oscillation functions, henceforth called BMO. Littlewood-Paley Theory has its roots in the Littlewood-Paley Theorem, ...