• Cohomology of Finite Modules over Short Gorenstein Rings 

    Menning, Melissa Christine (2016)
    We study two formal power series in the indeterminate t that generalize the Poincar´e series of a module. In the context of a Gorenstein local ring whose maximal ideal m satisfies m³ = 0, we prove that these two power ...
  • The Dirichlet problem for elliptic and degenerate elliptic equations, and related results 

    Le, Phi Long (University of Missouri--Columbia, 2016)
    In this thesis, we first prove the solvability of Dirichlet problem with Lp data on the boundary for degenerate elliptic equations. Second, We obtain Lp bounds semi-groups and their gradients, and then we get Lp bounds for ...
  • The Effects of Math Recovery on the Low-Performing Mathematics Student 

    Rossiter, Robert F. (2012)
    This study examined the effectiveness of the course, Math Recovery, on a group of ninth-grade students enrolled in the course Algebra/Geometry I measured by course grades and subsequent tenth-grade MAP scores. In addition, ...
  • A foliated Seiberg-Witten theory 

    Renner, Andrew (University of Missouri--Columbia, 2016)
    This dissertation set out to investigate a generalization of Seiberg-Witten theory from four-dimensional manifolds to four-codimensional Riemannian foliations. Seiberg-Witten theory was originally born out of the String ...
  • Generalized Koszul Properties of Commutative Local Rings 

    Hoffmeier, Justin Cole (2014)
    We study several properties of commutative local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers ...
  • GIT-equivalence and semi-stable subcategories of quiver representations 

    Granger, Valerie (University of Missouri--Columbia, 2016)
    The main investigation in this thesis is to determine when two weights give rise to the same semi-stable subcategory in the case of representations of quivers. This question was answered via explicit construction by Ingalls, ...
  • Inertial Chow rings and a new asymptotic product 

    Coleman, Thomas (University of Missouri--Columbia, 2016)
  • Maximal Fourier integrals and multilinear multiplier operators 

    Nguyen, Hanh Van (University of Missouri--Columbia, 2016)
  • Some results in convex geometry 

    Spencer, Patrick (University of Missouri--Columbia, 2016)
    This thesis is divided into four parts. The first part is about proving that the unit ball of the Lorentz space is not an intersection body for dimension greater than or equal to 5 and q > 2. We go on to explain the ...
  • Stability of planar fronts for a class of reaction diffusion systems 

    Yang, Xinyao (University of Missouri--Columbia, 2016)
    The purpose of this thesis is to study stability of one-dimensional traveling waves and multidimensional planar fronts as well as space-independent steady states for a class of reaction diffusion systems that arise in ...
  • Subsequences of frames and their operators 

    Lynch, Richard G. (University of Missouri--Columbia, 2016)
  • Weak Hardy spaces and paraproducts 

    He, Danqing (University of Missouri--Columbia, 2016)
    The purpose of this dissertation is to provide a new square function characterization of weak Hardy spaces in the full range of exponents possible and use this characterization in applications on endpoint estimates for ...