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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 ...
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 ...
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 ...
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 ...
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 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 ...
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 ...
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 ...
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 ...
Stability estimates for semigroups and partly parabolic reaction diffusion equations
(University of Missouri--Columbia, 2013)
The purpose of my dissertation is the application of the methods of abstract theory of strongly continuous operator semigroups (and of evolution semigroups in particular) to study of the spectral properties of a class of ...
Limit of many molecules dynamics with rigorous macroscopic results
(University of Missouri--Columbia, 2013)
The thesis builds on recent ideas that combine work by C.B. Morrey (1955) and D.W. Jepsen & D. ter Haar (1962) with more recent analytic techniques: measure disintegration, PDEs for measures, etc. (M.I. Vishik & A.V. ...
Results in analytic and algebraic number theory
(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 = ...
Groupoids and semigroupoids
(University of Missouri--Columbia, 2013)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The theory of semigroupoids and groupoids makes the transition between arbitrary sets and groups. The usefulness of developing theory stems from various ...
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 ...
Nonlinear equations with natural growth terms
(University of Missouri--Columbia, 2011)
This thesis concerns the study of a class of second order quasilinear elliptic differential operators. For 1 < p < ∞, the model equation we consider is: (1) L(u) = -Δpu - σ∣u∣p-2u. Here the potential is a function (or ...
Fusion frame constructions and frame partitions
(University of Missouri--Columbia, 2013)
Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Despite ...
On projective morphisms of varieties with nef anticanonical divisor
(University of Missouri--Columbia, 2012)
We shall study and discuss some important properties of the projective varieties with nef anticanonical bundles and nef tangent bundles. And we shall review some background and history about the subject. Then we shall use ...
Stochastically perturbed Navier-Stokes system on the rotating sphere
(University of Missouri--Columbia, 2013)
We show the existence and uniqueness of an invariant measure for the kick-forced Navier-Stokes system on the 2-dimensional sphere, first without deterministic force and then with a time-independent deterministic force. The ...
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 ...