Mathematics Dissertations and Theses: Recent submissions
Now showing items 161-179 of 179
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Long time behavior and stability of special solutions of nonlinear partial differential equations.
(University of Kansas, 2011-04-21)In this dissertation, in the first part, I study the long-time behavior of the solutions of the Kuramoto-Sivashinsky equation and the Burgers-Sivashinsky equation. First, I work on a two-dimensional modified KS equation ... -
Shor's Algorithm and Grover's Algorithm in Quantum Computing
(University of Kansas, 2011-04-25)In this paper we will analyse two quantum algorithms that sparked interest in the potential of quantum computers. The first is Lov Grover's algorithm which may be used to conduct a type of database search. The second is ... -
Polynomials associated with graph coloring and orientations
(University of Kansas, 2011-04-26)We study colorings and orientations of graphs in two related contexts. Firstly, we generalize Stanley's chromatic symmetric function using the k-balanced colorings of Pretzel to create a new graph invariant. We show that ... -
NEW ESTIMATES IN HARMONIC ANALYSIS FOR MIXED LEBESGUE SPACES
(University of Kansas, 2010-07-16)Mixed Lebesgue spaces are a generalization of Lp spaces that occur naturally when considering functions that depend on quantities with different properties, such as space and time. We first present mixed Lebesgue versions ... -
Some topics on the fractional Brownian motion and stochastic partial differential equations
(University of Kansas, 2010-04-25)In this dissertation, we investigate some problems in fractional Brownian motion and stochastic partial differential partial differential equations driven by fractional Brownian motion and Hilbert space valued Wiener ... -
A Central Limit Theorem for Functionals of Gaussian Processes
(University of Kansas, 2009-12-10)The aim of this thesis is to study and show, as described in the works of Nualart, that a sequence of functionals of Gaussian processes that belongs to a Wiener chaos of fixed order converges in distribution to a standard ... -
Approximating Artinian Rings by Gorenstein Rings and 3-Standardness of the Maximal Ideal
(University of Kansas, 2009-07-23)We study two different problems in this dissertation. In the first part, we wish to understand how one can approximate an Artinian local ring by a Gorenstein Artin local ring. We make this notion precise in Chapter 2, by ... -
A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection.
(University of Kansas, 2009-06-11)The study focuses primarily on Vandermonde-like matrix systems. The idea is to express Vandermonde and Vandermonde-like matrix systems as the problems related to Krylov Matrices. The connection provides a different angle ... -
Linear and multilinear fractional operators: weighted inequalities, sharp bounds, and other properties
(University of Kansas, 2009-04-27)In this work we consider various fractional operators, including the classical fractional integral operators, related fractional maximal functions, multilinear fractional integral operators, and multisublinear fractional ... -
SOME NEW DEVELOPMENTS ON TWO SEPARATE TOPICS: STATISTICAL CROSS VALIDATION AND FLOODPLAIN MAPPING
(University of Kansas, 2008-08-06)This dissertation describes two unrelated threads of research. The first is a study of cross validation (CV), which is a data resampling method. CV is used for model ranking in model selection and for estimating expected ... -
A STRUCTURED METHOD FOR THE REAL QUADRATIC EIGENVALUE PROBLEM FOR SPECIFIC GYROSCOPIC SYSTEMS
(University of Kansas, 2008-12-15)This study examines a specific numerical approach that computes the eigenvalues (normal modes) of a Quadratic Eigenvalue Problem (QEP) of the form (&lambda^2 & middotI + &lambda · B + C)· x = 0 where B is constrained to a ... -
Some Properties of Realcompact Subspaces and Coarser Normal Spaces
(University of Kansas, 2009-04-23)In this work we obtain results in two areas of topology, normal condensations of products and size of realcompact subspaces of a space. In 2000 Swardson proved that every uncountable compact space has a realcompact subspace ... -
Coarser connected topologies and non-normality points
(University of Kansas, 2009-01-01)We investigate two topics, coarser connected topologies and non-normality points. The motivating question in the first topic is: When does a space have a coarser connected topology with a nice topological property? We will ... -
Forecasting Volatility in Stock Market Using GARCH Models
(University of Kansas, 2008-01-01)Forecasting volatility has held the attention of academics and practitioners all over the world. The objective for this master's thesis is to predict the volatility in stock market by using generalized autoregressive ... -
Homological Invariants of Monomial and Binomial Ideals
(University of Kansas, 2008-08-19)In this dissertation, we study numerical invariants of minimal graded free resolutions of homogeneous ideals in a polynomial ring R. Chapters 2, 3 and 4 deal with homological invariants of edge ideals of bipartite graphs. ... -
Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels
(University of Kansas, 2008-07-31)Important properties of ion channels can be described by a steady state Poisson-Nernst-Plank system for electrodiffusion. The solution to the PNP system gives a relation between the current and electric potential of the ... -
Analytical and Numerical Studies of One-Dimensional Poisson-Nernst-Planck Models for Ion Channels
(University of Kansas, 2008-08-01)We study the event of ion flow through ion channel proteins modeled with a one-dimensional Poisson-Nernst-Planck system in presence of two or three types of ions with permanently charges located inside the channel. A ... -
Some Problems in Stochastic Portfolio Theory
(University of Kansas, 2007-12-11)We consider some problems in the stochastic portfolio theory of equity markets. In the first part, we maximize the expected terminal value of a portfolio of equities. The optimal investment problem is then solved by the ... -
Maximum Queue Length of a Fluid Model with a Gaussian Input
(University of Kansas, 2007-12-11)A fractional Brownian queueing model, that is, a fluid model with an input of a fractional Brownian motion, was proposed in the 1990s to capture the self-similarity and long-range dependence observed in Internet traffic. ...