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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 ...
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 ...