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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 ...
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 ...
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 ...
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 ...
On the spectra of Schrödinger and Jacobi operators with complex-valued quasi-periodic algebro-geometric coefficients
(University of Missouri--Columbia, 2005)
In this thesis we characterize the spectrum of one-dimensional Schrödinger operators. H = -d2/dx2+V in L2(R; dx) with quasi-periodic complex-valued algebro geometric, potentials V (i.e., potentials V which satisfy one ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
The absolute functional calculus for sectorial operators
(University of Missouri--Columbia, 2005)
We introduce the absolute functional calculus for sectorial operators. This notion is stronger than the common holomorphic functional calculus. We are able to improve a key theorem related to the maximal regularity problem ...
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 ...
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 ...
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 ...
Potential theory and harmonic analysis methods for quasilinear and Hessian equations
(University of Missouri--Columbia, 2006)
The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems:-[delta]pu = uq + [mu], Fk[-u] ...