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Now showing items 21-40 of 41
Sections of complex convex bodies
(University of Missouri--Columbia, 2008)
The main idea of the Fourier analytic approach to sections of convex bodies is to express different parameters of a body in terms of the Fourier transform and then apply methods of Fourier analysis to solve geometric ...
Applications of fourier analysis to intersection bodies
(University of Missouri--Columbia, 2008)
The concept of an intersection body is central for the dual Brunn-Minkowski theory and has played an important role in the solution of the Busemann-Petty problem. A more general concept of [kappa]-intersection bodies is ...
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 ...
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 ...
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 ...
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 ...
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 ...
Boundary value problems for the Stokes system in arbitrary Lipschitz domains
(University of Missouri--Columbia, 2008)
The goal of this work is to treat the main boundary value problems for the Stokes system, i.e., (i) the Dirichlet problem with Lp-data and nontangential maximal function estimates, (ii) the Neumann problem with Lp-data and ...
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 ...
Transference and Szego's theorem for measure preserving representations
(University of Missouri--Columbia, 2007)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] We prove analogues of the classical Szeg̈o's theorem concerning approximation by polynomials on the unit circle, and Jensen's inequality involving the ...
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 ...
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 ...
The poisson problem on Lipschitz domains
(University of Missouri--Columbia, 2005)
The aim of this work is to describe the sharp ranges of indices, for which the Poisson problem for Laplacian with Dirichlet or Neumann boundary conditions is well-posed on the scales of Besov and Triebel-Lizorkin spaces ...
A priori estimates for solutions of elliptic partial differential equations on surfaces
(University of Missouri--Columbia, 2009)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let S be an ([lowercase nu ? 1)-dimensional bounded surface of class C[superscript 2] in [double-struck R][superscript n] and let [uppercase delta]S ...
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 ...
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 ...
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 ...
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. ...