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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 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 ...
Classical and impulse stochastic control on the optimization of the dividends for the terminal bankruptcy model and its application
(University of Missouri--Columbia, 2010)
In this dissertation, I discuss the optimization of dividends of reinsurance companies with the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, meanwhile ...
Coefficient theorems of Birancon-Skoda type
(University of Missouri--Columbia, 2011)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The original Briancon-Skoda theorem, proved for the ring of convergent power series over the field $mathbb{C}$ of complex numbers, was later generalized ...
Statistical and stochastic results for three dimensional fluids
(University of Missouri--Columbia, 2012)
In part I, we show that the longitudinal correlation function for homogeneous and isotropic turbulence remains negative in an interval of time, up to Galerkin approximation. Part II covers the existence and uniqueness of ...
Counterexamples to Strichartz Type Inequalities
(University of Missouri--Columbia, 2013)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The study of Strichartz s inequality is very important in the theory of nonlinear Shrodinger equations. The inequalities do not hold for all choice of ...
Generalized local Tb theorem and applications
(University of Missouri--Columbia, 2012)
The Tb theorem, like its predecessor, the T1 Theorem, is an L2 boundedness criterion, originally established by McIntosh and Meyer, and by David, Journé and Semmes in the context of singular integrals, but later extended ...
Topics in Littlewood-Paley theory and BMO
(University of Missouri--Columbia, 2012)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In this thesis we discuss some important results in Littlewood-Paley theory and the space of Bounded-Mean Oscillation functions, henceforth called ...
The Evans function, the Weyl-Titchmarsh function, and the Birman-Schwinger operators
(University of Missouri--Columbia, 2012)
We focus on the spectral stability of travelling wave solutions of partial differential equations. First, we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an ...
Almost everywhere convergence for modified Bochner Riesz means at the critical index for [rho] [greater than or equal to] 2
(University of Missouri--Columbia, 2010)
The Fourier transform is a mathematical operation that can be used with its inverse to rewrite a function as a sum of waves. It has been a useful mathematical tool for many applied sciences. Sometimes Fourier inversion is ...
Finite point configurations and projection theorems in vector spaces over finite fields
(University of Missouri--Columbia, 2010)
We study a variety of combinatorial distance and dot product related problems in vector spaces over finite fields. First, we focus on the generation of the Special Linear Group whose elements belong to a finite field with ...
A transition matrix for two bases of the integral cohomology of the Hilbert scheme of points in the projective plane
(University of Missouri--Columbia, 2010)
This work is devoted to comparing two integral bases for the integral cohomology of the Hilbert scheme of points in the projective plane. Let X be a smooth complex projective surface. One of the more interesting moduli ...
Measures on Hilbert spaces and applications to hydrodynamics
(University of Missouri--Columbia, 2010)
Homogeneous and isotropic statistical solutions of the Navier-Stokes equations are produced. These are shown to be approximated by Galyerkin statistical solutions on finite dimensional subspaces. Homogeneous and isotropic ...
Minimal resolutions for a class of Gorenstein determinantal ideals
(University of Missouri--Columbia, 2010)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let X = {x[subscript ij]} [subscript mxn] be a matrix with entries in a noetherian commutative ring R. I[subscript t](X) denotes the determinantal ...
On the periodicity of the first Betti number of the semigroup ring under translations
(University of Missouri--Columbia, 2010)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Any curve C in any dimension can be described by a parameterization. In particular in the plane, that is dimension 2, the coordinates x and y are both ...
Geometric combinatorics in discrete settings
(University of Missouri--Columbia, 2011)
This thesis is a compilation of work in which the author studies geometric configurations in finite fields and the integers modulo q. The results of this dissertation are threefold. First, we prove a finite field analog ...
Minimal homogeneous resolutions, almost complete intersections and Gorenstein Artin algebras
(University of Missouri--Columbia, 2011)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This work is devoted to the study of the structures of the graded resolutions of codimension three almost complete intersections and the unimodality ...
Endpoint solvability results for divergence form, complex elliptic equations
(University of Missouri--Columbia, 2011)
We consider divergence form elliptic equations Lu := ∇ • (A∇u) = 0 in the half space ℝn+1+ := {(x,t)∈ ℝn x (0,∞)}, whose coeffi cient matrix A is complex elliptic, bounded and measurable. In addition, we suppose that A ...
Geometric and nonlinear limit theorems in probability theory
(University of Missouri--Columbia, 2012)
The concentration of measure phenomenon is a nonlinear equivalent of the law of large numbers that deals with real valued Lipschitz functions and includes linear functionals such as the sample mean. In the first part of ...
Topics in non-locally convex functional analysis and geometrical analysis with applications to boundary value problems
(University of Missouri--Columbia, 2012)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation is comprised of two parts. The first part, consisting of chapters 2-13, deals with issues pertaining to non-locally functional analysis. ...