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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 ...
The implicit function theorem for Lipschitz functions and applications
(University of Missouri--Columbia, 2008)
The subject matter of this thesis is the classical Implicit Function Theorem and its generalizations. Dictated by practical applications, it is of interest to relax the hypothesis of the standard Implicit Function Theorem ...
Surface to surface changes of variables and applications
(University of Missouri--Columbia, 2008)
The present thesis addresses a number of basic problems in relation to integration over surfaces in the Euclidean space, such as how the surface measure and unit normal changes under a smooth diffeomorphism how the integration ...
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 ...
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 ...
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 ...
Existence and construction of real-valued equiangular tight frames
(University of Missouri--Columbia, 2009)
This paper presents results on real-valued equiangular tight frames (ETFs) and related topics. Some geometric theorems are developed, and aspects of frame theory are used to gain insight into ETFs. We develop a projection ...
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 ...
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 ...
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 ...
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 ...
Parabolic layer potentials and initial boundary value problems in Lipschitz cylinders with data in Besov spaces
(University of Missouri--Columbia, 2006)
We adapt the method of boundary layer potentials to the Poisson problem for the heat operator [partial differential]t [delta] in a bounded Lipschitz cylinder, with Dirichlet and Neumann boundary conditions. When the lateral ...
Directional time-frequency analysis with applications
(University of Missouri--Columbia, 2006)
The purpose of this dissertation is to introduce a new directionally-sensitive time frequency representation of a function. It is shown that we may break up a function (or signal) into individual time-frequency-direction ...
Applications of the fourier transform to convex geometry
(University of Missouri--Columbia, 2006)
The thesis is devoted to the study of various problems arising from Convex Geometry and Geometric Functional Analysis using tools of Fourier Analysis. In chapters two through four we consider the Busemann-Petty problem and ...
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 ...
Trace formulae in finite von Neumann algebras
(University of Missouri--Columbia, 2007)
The dissertation is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for ...
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 ...
Volatility estimation and price prediction using a hidden Markov model with empirical study
(University of Missouri--Columbia, 2007)
This work provides a solid development of a hidden Markov model (HMM) from the economic insight to the mathematic formulation. In this model, we assume both drift and volatility of the security return process are driven ...
Uniqueness theorems for non-symmetric convex bodies
(University of Missouri--Columbia, 2009)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This dissertation involves the determination of convex bodies and the comparison of sections of convex bodies. Uniqueness of convex bodies via derivatives ...