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A class of Gorenstein Artin algebras of embedding dimension four
(University of Missouri--Columbia, 2007)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let R be a polynomial ring in n variables and I be a homogeneous ideal in R. Such an ideal I is called Gorenstein if the quotient R/I has a free ...
On the Morgan-Shalen compactification of the SL(2,C) character varieties of surface groups
(1998)
A gauge theoretic description of the Morgan-Shalen compactification of the SL(2, C)
character variety of the fundamental group of a hyperbolic surface is given in terms of a natural compactification of the moduli space ...
Ubiquity of simplices in subsets of vector spaces over finite fields
(2007)
We prove that a sufficiently large subset of the $d$-dimensional vector space over a finite field with $q$ elements, $ {\Bbb F}_q^d$, contains a copy of every $k$-simplex. Fourier analytic methods, Kloosterman sums, and ...
Sums and products in finite fields: an integral geometric viewpoint
(2007)
We prove that if $A \subset {\Bbb F}_q$ is such that $$|A|>q^{{1/2}+\frac{1}{2d}},$$ then $${\Bbb F}_q^{*} \subset dA^2=A^2+...+A^2 d \text{times},$$ where $$A^2=\{a \cdot a': a,a' \in A\},$$ and where ${\Bbb F}_q^{*}$ ...
How often is a permutation an n'th power?
(1997)
We give a short argument that for any fixed n, the probability that a permutation on m letters is an n'th power is asymptotically C m^{phi(n)/n - 1}.
Transference and Szego's theorem for measure preserving representations
(University of Missouri--Columbia, 2007)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] We prove analogues of the classical Szeg̈o's theorem concerning approximation by polynomials on the unit circle, and Jensen's inequality involving the ...
F-rational rings and the integral closure of ideals
(2000)
The history of the Briançon-Skoda theorem and its ensuing avatars in commutative algebra has been well-documented in many papers. A theorem proved by Briançon and Skoda for convergent power series over the complex numbers ...
The vanishing of Tor_1^R(R^+,k) implies that R is regular
(2003)
Let (R,m,k) be an excellent local ring of positive prime characteristic. We show that if Tor_1^R(R^+,k) = 0 then R is regular. This improves a result of Schoutens, in which the additional hypothesis that R was an isolated ...
Decomposition of analytic measures on groups and measure spaces
(2011)
This paper provides a new approach to proving generalizations of the F.&M. Riesz Theorem, for example, the result of Helson and Lowdenslager, the result of Forelli (and de Leeuw and Glicksberg), and more recent results of ...
Tidal dynamics in Kerr spacetime
(Institute of Physics, 2006)
The motion of free nearby test particles relative to a stable equatorial circular
geodesic orbit about a Kerr source is investigated. It is shown that the nonlinear
generalized Jacobi equation can be transformed in this ...
Quasi-metric geometry : smoothness and convergence results
(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 ...
On some classes of non-analytic functions of a complex variable
(University of Missouri--Columbia, 1909)
The fact, namely, that the analytic functions are a very limited and special class, with the additional fact that there seems to be no reason a priori why many of the theorems concerning analytic functions cannot be extended ...
Boundary value problems for the Stokes system in arbitrary Lipschitz domains
(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 ...
Algebraic resolution of formal ideals along a valuation
(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 ...
Dichotomy theorems for evolution equations
(University of Missouri--Columbia, 2008)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In the first part of this work, under minimal assumptions, we characterize the Fredholm property and compute the Fredholm index of abstract differential ...
Toroidalization of locally toroidal morphisms
(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 ...
An extension of Green's theorem with application
(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 ...
On the theory of integer sequences
(University of Missouri--Columbia, 2010)
We explore certain sequences of integers which appear in the number theory. We start by exploring properties of Beatty sequences. We concentrate on looking at the sum of primes from a Beatty sequence and properties of ...
Topics in geometric analysis with applications to partial differential equations
(University of Missouri--Columbia, 2009)
The main aim of the current thesis is to investigate the mathematical tools and methods used to study problems which bridge between analysis and geometry. Such an undertaking is particularly useful in situations in which ...
On the ionization of a Keplerian binary system by periodic gravitational radiation
(American Institute of Physics, 1996)
The gravitational ionization of a Keplerian binary system via normally incident periodic gravitational radiation of definite helicity is discussed. The periodic orbits of the planar tidal equation are investigated on the ...