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Erdős distance problem in the hyperbolic half-plane
(University of Missouri--Columbia, 2009)
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 ...
Approximate isometries and distortion energy functionals
(University of Missouri--Columbia, 2009)
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 ...
Explorations of geometric combinatorics in vector spaces over finite fields
(University of Missouri--Columbia, 2008)
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 ...
Applications of fourier analysis to intersection bodies
(University of Missouri--Columbia, 2008)
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...
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 ...
Box approximation and related techniques in spectral theory
(University of Missouri--Columbia, 2008)
This dissertation is concerned with various aspects of the spectral theory of differential and pseudodifferential operators. It consists of two chapters. The first chapter presents a study of a family of spectral shift ...
Transference and Szego's theorem for measure preserving representations
(University of Missouri--Columbia, 2007)
of the logarithm, for functions in generalized Hardy spaces Hp([gamma],[mu]). The latter are defined in terms of strongly continuous, measure preserving representations in Lp([gamma],[mu]), where ([gamma],[mu]) is a locally compact measure space. In a similar...
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 ...
Oscillators : resonances and excitations
(University of Missouri--Columbia, 2009)
This thesis is a compilation of work done in the field of oscillators. One topic is an investigation into impact oscillators and their properties. The second topic is concerned with excitation of oscillators. The thesis begins with mathematical...
Mathematical problems from cryobiology
(University of Missouri--Columbia, 2009)
Cryobiology is the study of life anddeath at low temperatures and provides a fascinating setting for applied mathematics. The interdisciplinary nature of cryobiology mirrors the diversity of applications ranging from animal agriculture to laboratory...
Elliptic curves and their applications in cryptography
(University of Missouri--Columbia, 2009)
In 1985, Koblitz and Miller proposed elliptic curves to be used for public key cryptosystems. This present thesis examines the role of elliptic curves on cryptography and basic problems involving implementation and security of some elliptic curve...
Asymptotic unconditionality in Banach spaces
(University of Missouri--Columbia, 2009)
We show that a separable real Banach space embeds almost isometrically in a space [Upsilon] with a shrinking 1-unconditional basis if and only if lim [subscript n] [subscript arrow] [subscript infinity] [norms] [chi] [group ...
Complex and almost-complex structures on six dimensional manifolds
(University of Missouri--Columbia, 2006)
We investigate the properties of hypothetical exotic complex structures on three dimensional complex projective space CP³. This is motivated by the long standing question in differential geometry of whether or not the six ...
Uniqueness theorems for non-symmetric convex bodies
(University of Missouri--Columbia, 2009)
determined by the Gaussian covariogram. The Gaussian covariogram of a body K is a function that yields the standard Gaussian measure of the intersection of K with its translates.--From public.pdf....
Extension theorems in vector spaces over finite fields
(University of Missouri--Columbia, 2008)
We study the L[superscript p] - L[superscript r] boundedness of the extension operator associated with algebraic varieties such as nondegenerate quadratic surfaces, paraboloids, and cones in vector spaces over finite fields. ...
Seiberg-Witten invariants on 3-manifolds with an orientation reversing involution
(University of Missouri--Columbia, 2009)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This work is devoted to the study of Seiberg-Witten theory for three dimensional manifolds in the presence of involutions. G. Tian and S.Wang explored ...
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 ...
Incorporation of directionally dependent diffusion with polymer composite flow theory
(University of Missouri--Columbia, 2006)
The extensive industrial use of short-fiber reinforced polymer composites demands an accurate understanding of fiber orientation kinematics. There is a growing concern in recent literature with the popular Folgar and Tucker ...
A free boundary gas dynamic model as a two-body field theory problem
(University of Missouri--Columbia, 2009)
Motivated by the two-body problem in the classical field theories of electrodynamics and gravitation, in which finite propagation speeds lead to radiation reaction and runaway solutions, we develop a free boundary problem ...