Mathematics Commons^™

Topological Speedups, Drew Daehnhardt Ash

Electronic Theses and Dissertations

Given a dynamical system T:X rightarrow X one can define a speedup of (X,T) as another dynamical system conjugate to S:X rightarrow X where S(x)=T^{p(x)}(x) for some function p:X rightarrowZ^{+}. In 1985 Arnoux, Ornstein, and Weiss showed that any aperiodic measure preserving system is isomorphic to a speedup of any ergodic measure preserving system. In this thesis we study speedups in the topological category. Specifically, we consider minimal homeomorphisms on Cantor spaces. Our main theorem gives conditions on when one such system is a speedup of another. Moreover, the main theorem serves as a topological analogue of the Arnoux, Ornstein, …

A Mathematical Model For Feral Cat Ecology With Application To Disease., Jeff Sharpe

Electronic Theses and Dissertations

We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to Lotka-Volterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of per-capita removal …

Structure-Preserving Finite Difference Methods For Linearly Damped Differential Equations, Ashish Bhatt

Electronic Theses and Dissertations

Differential equations (DEs) model a variety of physical phenomena in science and engineering. Many physical phenomena involve conservative or dissipative forces, which manifest themselves as qualitative properties of DEs that govern these phenomena. Since only a few and simplistic models are known to have exact solutions, approximate solution techniques, such as numerical integration, are used to reveal important insights about solution behavior and properties of these models. Numerical integrators generally result in undesirable quantitative and qualitative errors . Standard numerical integrators aim to reduce quantitative errors, whereas geometric (numerical) integrators aim to reduce or eliminate qualitative errors, as well, in …

On Randic Energy Of Graphs, Brittany Burns

Electronic Theses and Dissertations

In this research, we explore the subject of graph energy. We first discuss the connections between linear algebra and graph theory and review some important definitions and facts of these two fields. We introduce graph energy and provide some historical perspectives on the subject. Known results of graph energy are also mentioned and some relevant results are proven. We discuss some applications of graph energy in the physical sciences. Then, Randic energy is defined and results are given and proved for specific families of graphs. We focus on simple, connected graphs that are commonly studied in graph theory. Also, the …

Identifying Data Centers From Satellite Imagery, Adam Buskirk

Electronic Theses and Dissertations

We develop two different descriptors which can be utilized to describe satellite imagery. The first, the differential-magnitude and radius descriptor, describes a scene by computing the directional gradient of the scene with respect to a vector field whose solutions are circles around a pixel to be described, and then counts pixels in a descriptor matrix according to the magnitude of this gradient and the distance at which this magnitude occurs. The second, the radial Fourier descriptor, extracts from the scene a sequence of annuloid sectors, and uses this to approximate the behavior of the image on a circle around the …

Analysis Of Employment And Earnings Using Varying Coefficient Models To Assess Success Of Minorities And Women, Amanda Goedeker

Electronic Theses and Dissertations

The objective of this thesis is to examine the success of minorities (black, and Hispanic/Latino employees) and women in the United States workforce, defining success by employment percentage and earnings. The goal of this thesis is to study the impact gender, race, passage of time, and national economic status reflected in gross domestic product have on the success of minorities and women. In particular, this thesis considers the impact of these factors in Science, Technology, Engineering and Math (STEM) industries. Varying coefficient models are utilized in the analysis of data sets for national employment percentages and earnings.

Modeling Rogue Waves In Deep Water, Maria Strawn

Electronic Theses and Dissertations

The evolution of surface waves in deep water is governed by the nonlinear Schrodinger (NLS) equation. Spatially periodic breathers (SPBs) and rational solutions of the NLS equation are used as typical models for rogue waves since they exhibit many features of rogue waves. A major component of the dissertation is the stability of solutions of the NLS equation. We address the stability of the rational solutions of the NLS equation used to model rogue waves using squared eigenfunctions of the associated Lax Pair. This allows us to contrast to the existing results for SPBs. The stability of the constant amplitude …

Building Lax Integrable Variable-Coefficient Generalizations To Integrable Pdes And Exact Solutions To Nonlinear Pdes, Matthew Russo

Electronic Theses and Dissertations

This dissertation is composed of two parts. In Part I a technique based on extended Lax Pairs is first considered to derive variable-coefficient generalizations of various Lax-integrable NLPDE hierarchies recently introduced in the literature. It is demonstrated that the technique yields Lax- or S-integrable nonlinear partial differential equations (PDEs) with both time- and space-dependent coefficients which are thus more general than almost all cases considered earlier via other methods such as the Painleve Test, Bell Polynomials, and various similarity methods. However, this technique, although operationally effective, has the significant disadvantage that, for any integrable system with spatiotemporally varying coefficients, one …

Independent Domination Of Subcubic Graphs, Bruce Allan Priddy

Electronic Theses and Dissertations

Let G be a simple graph. The independent domination number i(G) is the minimum cardinality among all maximal independent sets of G. A graph is subcubic whenever the maximum degree is at most three. In this paper, we will show that the independent domination number of a connected subcubic graph of order n having minimum degree at least two is at most 3(n+1)/7, providing a sharp upper bound for subcubic connected graphs with minimum degree at least two.

On Topological Indices And Domination Numbers Of Graphs, Shaohui Wang

Electronic Theses and Dissertations

Topological indices and dominating problems are popular topics in Graph Theory. There are various topological indices such as degree-based topological indices, distance-based topological indices and counting related topological indices et al. These topological indices correlate certain physicochemical properties such as boiling point, stability of chemical compounds. The concepts of domination number and independent domination number, introduced from the mid-1860s, are very fundamental in Graph Theory. In this dissertation, we provide new theoretical results on these two topics. We study k-trees and cactus graphs with the sharp upper and lower bounds of the degree-based topological indices(Multiplicative Zagreb indices). The extremal cacti …

Interval Edge-Colorings Of Graphs, Austin Foster

Electronic Theses and Dissertations

A proper edge-coloring of a graph G by positive integers is called an interval edge-coloring if the colors assigned to the edges incident to any vertex in G are consecutive (i.e., those colors form an interval of integers). The notion of interval edge-colorings was first introduced by Asratian and Kamalian in 1987, motivated by the problem of finding compact school timetables. In 1992, Hansen described another scenario using interval edge-colorings to schedule parent-teacher conferences so that every person's conferences occur in consecutive slots. A solution exists if and only if the bipartite graph with vertices for parents and teachers, and …

Comparing The Variational Approximation And Exact Solutions Of The Straight Unstaggered And Twisted Staggered Discrete Solitons, Daniel Marulanda

Electronic Theses and Dissertations

Discrete nonlinear Schrödinger equations (DNSL) have been used to provide models of a variety of physical settings. An application of DNSL equations is provided by Bose-Einstein condensates which are trapped in deep optical-lattice potentials. These potentials effectively splits the condensate into a set of droplets held in local potential wells, which are linearly coupled across the potential barriers between them [3]. In previous works, DNLS systems have also been used for symmetric on-site-centered solitons [11]. A few works have constructed different discrete solitons via the variational approximation (VA) and have explored their regions for their solutions [11, 12]. Exact solutions …

Computational Study Of Traveling Wave Solutions And Global Stability Of Predator-Prey Models, Yi Zhu

Electronic Theses and Dissertations

In this thesis, we study two types of reaction-diffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology. The first part of this thesis is on propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will be studied. The first is autocatalytic chemical reaction of order $m$ without decay. The second is chemical reaction of order $m$ with a decay of order …

Weighted Low-Rank Approximation Of Matrices:Some Analytical And Numerical Aspects, Aritra Dutta

Electronic Theses and Dissertations

This dissertation addresses some analytical and numerical aspects of a problem of weighted low-rank approximation of matrices. We propose and solve two different versions of weighted low-rank approximation problems. We demonstrate, in addition, how these formulations can be efficiently used to solve some classic problems in computer vision. We also present the superior performance of our algorithms over the existing state-of-the-art unweighted and weighted low-rank approximation algorithms. Classical principal component analysis (PCA) is constrained to have equal weighting on the elements of the matrix, which might lead to a degraded design in some problems. To address this fundamental flaw in …

The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, Derek T. Bryant

Electronic Theses and Dissertations

In this thesis, we explore the effect of restricting the coefficients of polynomials on the bounds for the number of zeros in a given region. The results presented herein build on a body of work, culminating in the generalization of bounds among three classes of polynomials. The hypotheses of monotonicity on each class of polynomials were further subdivided into sections concerning r reversals among the moduli, real parts, and both real and imaginary parts of the coefficients.

Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai

Electronic Theses and Dissertations

Traditional approaches to predicting financial market dynamics tend to be linear and stationary, whereas financial time series data is increasingly nonlinear and non-stationary. Lately, advances in dynamical systems theory have enabled the extraction of complex dynamics from time series data. These developments include theory of time delay embedding and phase space reconstruction of dynamical systems from a scalar time series. In this thesis, a time delay embedding approach for predicting intraday stock or stock index movement is developed. The approach combines methods of nonlinear time series analysis with those of causality testing, theory of dynamical systems and machine learning (artificial …

On Properties Of RW-Regular Graphs, Franklina Samani

Electronic Theses and Dissertations

If every vertex in a graph G has the same degree, then the graph is called a regular graph. That is, if deg(v) = r for all vertices in the graph, then it is denoted as an r-regular graph. A graph G is said to be vertex-weighted if all of the vertices are assigned weights. A generalized definition for degree regularity for vertex-weighted graphs can be stated as follows: A vertex-weighted graph is said to be r_w-regular if the sum of the weights in the neighborhood of every vertex is r_w. If all vertices are assigned …

Dihedral-Like Constructions Of Automorphic Loops, Mouna Ramadan Aboras

Electronic Theses and Dissertations

In this dissertation we study dihedral-like constructions of automorphic loops. Automorphic loops are loops in which all inner mappings are automorphisms. We start by describing a generalization of the dihedral construction for groups. Namely, if (G , +) is an abelian group, m > 1 and α ∈2 Aut(G ), let Dih(m, G, α) on Z_m × G be defined by

(i, u )(j, v ) = (i + j , ((-1)^j u + v )α^ij ).

We prove that the resulting loop is automorphic if and only if m = 2 …

The Apprentices' Tower Of Hanoi, Cory Bh Ball

Electronic Theses and Dissertations

The Apprentices' Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented.

Distance-2 Domatic Numbers Of Graphs, Derek Kiser

Electronic Theses and Dissertations

The distance d(u, v) between two vertices u and v in a graph G equals the length of a shortest path from u to v. A set S of vertices is called a distance-2 dominating set if every vertex in V \S is within distance-2 of at least one vertex in S. The distance-2 domatic number is the maximum number of sets in a partition of the vertices of G into distance-2 dominating sets. We give bounds on the distance-2 domatic number of a graph and determine the distance-2 domatic number of selected classes of graphs.

A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

Electronic Theses and Dissertations

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2. …

Exploring Ways Of Identifying Outliers In Spatial Point Patterns, Jie Liu

Electronic Theses and Dissertations

This work discusses alternative methods to detect outliers in spatial point patterns.

Outliers are defined based on location only and also with respect to associated variables. Throughout the thesis we discuss five case studies, three of them come from experiments with spiders and bees, and the other two are data from earthquakes in a certain region. One of the main conclusions is that when detecting outliers from the point of view of location we need to take into consideration both the degree of clustering of the events and the context of the study. When detecting outliers from the point of …

Revised Model For Antibiotic Resistance In A Hospital, Ruhang Pei

Electronic Theses and Dissertations

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

The Finite Embeddability Property For Some Noncommutative Knotted Varieties Of Rl And Drl, Riquelmi Salvador Cardona Fuentes

Electronic Theses and Dissertations

Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus FL. We denote by ������ � the varieties of knotted residuated lattices. Examples of these knotted rules include integrality and contraction. The extension of �� by the rules corresponding to these two equations is …

On The Theory Of Zeta-Functions And L-Functions, Almuatazbellah Awan

Electronic Theses and Dissertations

In this thesis we provide a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet's L-function. We have also investigated some fundamental concepts related to these functions and their universality properties. In addition, we also discuss different formulations and approaches to the proof of the Prime Number Theorem and the Riemann Hypothesis. These two topics constitute the main theme of this thesis. For the Prime Number Theorem, we provide a thorough discussion that compares and contrasts …

Modeling Network Worm Outbreaks, Evan Foley

Electronic Theses and Dissertations

Due to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible, Infectious, Treatment, and Antidotal. We shall show that allocating resources into treating infectious computers leads to a reduced peak of infections across …

Diagonals Of Tensor Products Of Banach Lattices With Bases., Byunghoon Lee

Electronic Theses and Dissertations

In this dissertation, we investigate diagonals of tensor products of Banach lattices with bases. We first consider questions on the positive tensor products of l_p spaces. We characterize the main diagonals of the positive projective tensor product and the positive injective tensor product of l_p space. Then by using these two main diagonals, we characterize the reflexivity, the property of being Kantorovich - Banach spaces, and the property of being order continuous of n-fold positive projective and positive injective tensor products of l_p spaces. Next, we consider the diagonals of injective tensor product of Banach lattices with bases. Let E …

Complex Vector Lattices: Tensor Products And Multilinear Maps, Christopher Michael Schwanke

Electronic Theses and Dissertations

In this thesis, we study completions of Archimedean real vector lattices relative to any nonempty set of continuous positively homogeneous functions defined on Rn. Examples of such completions include square mean closed vector lattices and geometric mean closed vector lattices. These functional completions lead to a vector lattice complexification of any Archimedean real vector lattice. Unlike the vector space complexification of an Archimedean real vector lattice, the vector lattice complexification always results in an Archimedean complex vector lattice. For example, we prove that the vector space complexification of the Fremlin tensor product C(X)⊗C(Y) is not a complex vector lattice when …

Gini Covariance Matrix And Its Affine Equivariant Version, Lauren Anne Weatherall

Electronic Theses and Dissertations

Gini's mean difference (GMD) and its derivatives such as Gini index have been widely used as alternative measures of variability over one century in many research fields especially in finance, economics and social welfare. In this dissertation, we generalize the univariate GMD to the multivariate case and propose a new covariance matrix so called the Gini covariance matrix (GCM). The extension is natural, which is based on the covariance representation of GMD with the notion of multivariate spatial rank function. In order to gain the affine equivariance property for GCM, we utilize the transformation-retransformation (TR) technique and obtain TR version …

Integral Representations Of Positive Linear Functionals, Angela Siple

Electronic Theses and Dissertations

In this dissertation we obtain integral representations for positive linear functionals on commutative algebras with involution and semigroups with involution. We prove Bochner and Plancherel type theorems for representations of positive functionals and show that, under some conditions, the Bochner and Plancherel representations are equivalent. We also consider the extension of positive linear functionals on a Banach algebra into a space of pseudoquotients and give under conditions in which the space of pseudoquotients can be identified with all Radon measures on the structure space. In the final chapter we consider a system of integrated Cauchy functional equations on a semigroup, …