[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 ...

Consider a two-dimensional body of water with constant density which lies below a vacuum. The ocean bed is assumed to be impenetrable, while the boundary which separates the uid and the vacuum is assumed to be a free ...

the introduction of that theory to pure mathematics has proved to have great utility for studying four-dimensional manifolds, particularly for classifying such spaces. A foliation is a geometric space that is broken down into disjoint lower dimension spaces, each...

The first topic of this dissertation is concerned with the L^2 boundedness of a maximal Fourier integral operator which arises by transferring the spherical maximal operator on the sphere S^n to a Euclidean space of the ...

This dissertation provides new results in two areas. The first part concerns the particular properties that are inherited by a sequence of rank-1 projections from the inducing sequence of unit-norm vectors. The second part ...

In this dissertation, we provide results which characterize when a class of partial differential equations can be solved. These partial differential equations arise in the study of the Porous Media Equation, which can model ...

in optical diffraction theory and radio wave propagation. This decay condition, which has become known as Sommerfeld's radiation condition, has been subsequently adapted to various other operators of interest in mathematics, engineering, and physics. Examples...

A fundamental problem in Riemannian Geometry and related areas is to determine whether two diffeomorphic compact Riemannian manifolds (M, [subscript g][subscript M]) and (N, [subscript g][subscript N]) are isometric; that ...

Generalizing the ideas in [LQ] and using virtual Hodge polynomials as well as torus actions, we compute the Euler characteristics of some moduli spaces of 1-dimensional closed subschemes when the ambient smooth projective ...

The Erd̋os distance problem asks for the minimum number of distinct distances determined by large finite point sets in the plane. The aim of this work is to investigate how the classical techniques employed in the study ...

[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 ...

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 ...

We study how large a set of points needs to be in a vector space over a finite field in order for the points to determine all of a certain type of geometric structure. In addition we show that there are key differences ...

The concept of Constant Proportion Portfolio Insurance (CPPI) in terms of jump-diffusion, as well as the associated mean-variance hedging problem, has been studied. Three types of risk related to: the probability of loss, ...

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 ...

[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. ...

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 ...

of the Busemann-Petty problem. We are interested in comparing classes of [kappa]-intersection bodies. In the first chapter we present the result that was published in J. Schlieper, A note on [kappa]-intersection bodies, Proceedings American. Mathematical Society...

In this dissertation, we will examine two distinct areas of frame theory. The first will be the area of outer products. In particular, we will examine the spanning and independence properties of the collection [see abstract ...