Physical Sciences and Mathematics Commons^™

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 …

On Dedekind’S “Über Die Permutationen Des Körpers Aller Algebraischen Zahlen", Joseph Jp Arsenault Jr

Electronic Theses and Dissertations

We provide an analytic read-through of Richard Dedekind's 1901 article “Über die Permutationen des Körpers aller algebraischen Zahlen," describing the principal results concerning infinite Galois theory from both Dedekind's point of view and a modern perspective, noting an apparently uncorrected error in the supplement to the article in the Collected Works. As there is no published English-language translation of the article, we provide an annotated original translation.

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.

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 …

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.

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.

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. …

Propagation Failure In Discrete Inhomogeneous Medium Using A Caricature Of The Cubic, Elizabeth Lydon

Electronic Theses and Dissertations

Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent …

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 …

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, …

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 …

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 𝖱𝖫𝑛 � 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 …

The Least Prime Number That Splits Completely In S3-Sextic Number Fields, Zhenchao Ge

Electronic Theses and Dissertations

In number theory, an integer n is quadratic residue modulo an odd prime p if n is congruent to a perfect square modulo p. Otherwise, n is is called a quadratic nonresidue. Bounding the least prime quadratic residue and the least quadratic nonresidue are two very classical problems in number theory. These classical problems can be generalized to any number field K by asking for bounds the least for prime that splits completely or does not split completely, respectively, in the ring of integers of K. The goal of this thesis is to bound the least prime that splits completely …

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 …

Tiling With Polyominoes, Polycubes, And Rectangles, Michael Saxton

Electronic Theses and Dissertations

In this paper we study the hierarchical structure of the 2-d polyominoes. We introduce a new infinite family of polyominoes which we prove tiles a strip. We discuss applications of algebra to tiling. We discuss the algorithmic decidability of tiling the infinite plane Z x Z given a finite set of polyominoes. We will then discuss tiling with rectangles. We will then get some new, and some analogous results concerning the possible hierarchical structure for the 3-d polycubes.

Calibration Of Option Pricing In Reproducing Kernel Hilbert Space, Lei Ge

Electronic Theses and Dissertations

A parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be ill-posed. We propose a regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows us to embrace both the financial and time factors of the options. …

Analysis And Simulation For Homogeneous And Heterogeneous Sir Models, Joseph Wilda

Electronic Theses and Dissertations

In mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous Susceptible-Infectious-Removed (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement between populations is incorporated into a heterogeneous SIR model with nonlinear incidence. The analysis of the combined effects of the spatial heterogeneity and nonlinear incidence on the disease dynamics of our model is presented …

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 …

Improved Full-Newton-Step Infeasible Interior-Point Method For Linear Complementarity Problems, Mustafa Ozen

Electronic Theses and Dissertations

In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity …

Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra

Electronic Theses and Dissertations

We examine the automorphism group of configurations of rational curves on $K3$ surfaces. We use the properties of finite automorphisms of $\PP^1$ to examine what restrictions a given elliptic fibration imposes on the possible finite order non-symplectic automorphisms of the $K3$ surface. We also examine the fixed loci of these automorphisms, and construct an explicit fibration to demonstrate the process.

Graphs Of Classroom Networks, Rebecca Holliday

Electronic Theses and Dissertations

In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism …

Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman

Electronic Theses and Dissertations

In this thesis, we examine two topics. In the first part, we consider Leech tree which is a tree of order n with positive integer edge weights such that the weighted distances between pairs of vertices are exactly from 1 to n choose 2. Only five Leech trees are known and some non-existence results have been presented through the years. Variations of Leech trees such as the minimal distinct distance trees and modular Leech trees have been considered in recent years. In this thesis, such Leech-type questions on distances between leaves are studied as well as some other labeling questions …

Combinatorial Game Theory: An Introduction To Tree Topplers, John S. Ryals Jr.

Electronic Theses and Dissertations

The purpose of this thesis is to introduce a new game, Tree Topplers, into the field of Combinatorial Game Theory. Before covering the actual material, a brief background of Combinatorial Game Theory is presented, including how to assign advantage values to combinatorial games, as well as information on another, related game known as Domineering. Please note that this document contains color images so please keep that in mind when printing.