Physical Sciences and Mathematics Commons^™

Sperner's Lemma, The Brouwer Fixed Point Theorem, The Kakutani Fixed Point Theorem, And Their Applications In Social Sciences, Ayesha Maliwal

Electronic Theses and Dissertations

Can a cake be divided amongst people in such a manner that each individual is content with their share? In a game, is there a combination of strategies where no player is motivated to change their approach? Is there a price where the demand for goods is entirely met by the supply in the economy and there is no tendency for anything to change? In this paper, we will prove the existence of envy-free cake divisions, equilibrium game strategies and equilibrium prices in the economy, as well as discuss what brings them together under one heading.

This paper examines three …

Microstructural Analysis Of Thermoelastic Response, Nonlinear Creep, And Pervasive Cracking In Heterogeneous Materials, Alden C. Cook

Electronic Theses and Dissertations

This dissertation is concerned with the development of robust numerical solution procedures for the generalized micromechanical analysis of linear and nonlinear constitutive behavior in heterogeneous materials. Although the methods developed are applicable in many engineering, geological, and materials science fields, three main areas are explored in this work. First, a numerical methodology is presented for the thermomechanical analysis of heterogeneous materials with a special focus on real polycrystalline microstructures obtained using electron backscatter diffraction techniques. Asymptotic expansion homogenization and finite element analysis are employed for micromechanical analysis of polycrystalline materials. Effective thermoelastic properties of polycrystalline materials are determined and compared …

Embedding Of Hypercube Graphs On Orientable Surfaces, Prateek Kunwar

Electronic Theses and Dissertations

The purpose of this thesis is to study hypercube graphs and their embeddings on orientable surfaces. We use rotation systems to represent these embeddings. We prove some results about the effect of adjacent switches in rotation system and create a rotation system called the ABC rotation system and prove general results about it. Using this rotation system, we give a general theorem about the minimal embedding of $Q_{n}$. We also look at some interesting types of maximal embedding of $Q_{n}$, such as the Eulerian walk embedding and the "big-face embedding". We prove a theorem that gives a recursively constructive way …

Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

Electronic Theses and Dissertations

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used …

Multilevel Models For Longitudinal Data, Aastha Khatiwada

Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each …

An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

Electronic Theses and Dissertations

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R³, but also to the general case of finding minimal functionals on hypersurfaces in Rⁿ associated with an arbitrary metric.

The Complete Structure Of Linear And Nonlinear Deformations Of Frames On A Hilbert Space, Devanshu Agrawal

Electronic Theses and Dissertations

A frame is a possibly linearly dependent set of vectors in a Hilbert space that facilitates the decomposition and reconstruction of vectors. A Parseval frame is a frame that acts as its own dual frame. A Gabor frame comprises all translations and phase modulations of an appropriate window function. We show that the space of all frames on a Hilbert space indexed by a common measure space can be fibrated into orbits under the action of invertible linear deformations and that any maximal set of unitarily inequivalent Parseval frames is a complete set of representatives of the orbits. We show …

Neighborhood-Restricted Achromatic Colorings Of Graphs, James D. Chandler Sr.

Electronic Theses and Dissertations

A (closed) neighborhood-restricted 2-achromatic-coloring of a graph G is an assignment of colors to the vertices of G such that no more than two colors are assigned in any closed neighborhood. In other words, for every vertex v in G, the vertex v and its neighbors are in at most two different color classes. The 2-achromatic number is defined as the maximum number of colors in any 2-achromatic-coloring of G. We study the 2-achromatic number. In particular, we improve a known upper bound and characterize the extremal graphs for some other known bounds.

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …

Global Supply Sets In Graphs, Christian G. Moore

Electronic Theses and Dissertations

For a graph G=(V,E), a set S⊆V is a global supply set if every vertex v∈V\S has at least one neighbor, say u, in S such that u has at least as many neighbors in S as v has in V \S. The global supply number is the minimum cardinality of a global supply set, denoted γgs (G). We introduce global supply sets and determine the global supply number for selected families of graphs. Also, we give bounds on the global supply number for general graphs, trees, and grid graphs.

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 …

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 …

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.

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 …

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 …

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 …

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 …

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, …

Follower And Extender Sets In Symbolic Dynamics, Thomas Kelly French

Electronic Theses and Dissertations

Given a word w in the language of a one-dimensional shift space X, the follower set of w, denoted F_X(w), is the set of all right-infinite sequences which follow w in some point of X. Extender sets are a generalization of follower sets and are defined similarly. To a given shift space X, then, we may associate a follower set sequence {|F_X(n)|} which records the number of distinct follower sets in X corresponding to words of length n. Similarly, we may define an extender set sequence {|E …

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 …

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 …

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 …

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 …

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 …

Gorenstein Projective (Pre)Covers, Michael J. Fox

Electronic Theses and Dissertations

The existence of the Gorenstein projective precovers is one of the main open problems in Gorenstein Homological algebra. We give sufficient conditions in order for the class of Gorenstein projective complexes to be special precovering in the category of complexes of R-modules Ch(R). More precisely, we prove that if every complex in Ch(R) has a special Gorenstein flat cover, every Gorenstein projective complex is Gorenstein flat, and every Gorenstein flat complex has finite Goenstein projective dimension, then the class of Gorenstein projective complexes, GP(C), is special precovering in Ch(R).

A Partition Function Connected With The Göllnitz-Gordon Identities, Nicolas A. Smoot

Electronic Theses and Dissertations

Nearly a century ago, the mathematicians Hardy and Ramanujan established their celebrated circle method to give a remarkable asymptotic expression for the unrestricted partition function. Following later improvements by Rademacher, the method was utilized by Niven, Lehner, Iseki, and others to develop rapidly convergent series representations of various restricted partition functions. Following in this tradition, we use the circle method to develop formulas for counting the restricted classes of partitions that arise in the Gollnitz-Gordon identities. We then show that our results are strongly supported by numerical tests. As a side note, we also derive and compare the asymptotic behavior …

Combinatorial Optimization Of Subsequence Patterns In Words, Matthew R. Just

Electronic Theses and Dissertations

Packing patterns in words concerns finding a word with the maximum number of a prescribed pattern. The majority of the work done thus far is on packing patterns into permutations. In 2002, Albert, Atkinson, Handley, Holton and Stromquist showed that there always exists a layered permutation containing the maximum number of a layered pattern among all permutations of length n. Consequently, the packing density for all but two (up to equivalence) permutation patterns up to length 4 can be obtained. In this thesis we consider the analogous question for colored patterns and permutations. By introducing the concept of colored blocks …

Gallai-Ramsey Number Of An 8-Cycle, Jonathan Gregory

Electronic Theses and Dissertations

Given a graph G and a positive integer k, define the Gallai-Ramsey number to be the minimum number of vertices n such that any k-edge-coloring of Kn contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this work, we establish the Gallai-Ramsey number of an 8-cycle for all positive integers.

Gorenstein Projective Precovers In The Category Of Modules, Katelyn Coggins

Electronic Theses and Dissertations

It was recently proved that if R is a coherent ring such that R is also left n-perfect, then the class of Gorenstein projective modules, GP, is precovering. We will prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring R such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes that of right coherent and left n-perfect rings.