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Italian Domination On Ladders And Related Products, Bradley Gardner
Italian Domination On Ladders And Related Products, Bradley Gardner
Electronic Theses and Dissertations
An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete graph $K_2$. We will find the value of the Italian domination …
Topological Properties Of A 3-Rung Möbius Ladder, Rebecca Woods
Topological Properties Of A 3-Rung Möbius Ladder, Rebecca Woods
Electronic Theses and Dissertations
In this work, we discuss the properties of the 3-rung Möbius ladder on the torus. We also prove ℤ2 is an orientation preserving topological symmetry group of the 3-rung Möbius ladder with sides and rungs distinct, embedded in the torus.
Three Examples Of Mondoromy Groups, Alice A. Wise
Three Examples Of Mondoromy Groups, Alice A. Wise
Electronic Theses and Dissertations
This thesis illustrates the notion of the Monodromy group of a global analytic function through three examples. One is a relatively simple finite example; the others are more complicated infinite cases, one abelian and one non-abelian, which show connections to other parts of mathematics.
The Hilbert-Huang Transform: A Theoretical Framework And Applications To Leak Identification In Pressurized Space Modules, Kenneth R. Bundy
The Hilbert-Huang Transform: A Theoretical Framework And Applications To Leak Identification In Pressurized Space Modules, Kenneth R. Bundy
Electronic Theses and Dissertations
Any manned space mission must provide breathable air to its crew. For this reason, air leaks in spacecraft pose a danger to the mission and any astronauts on board. The purpose of this work is twofold: the first is to address the issue of air pressure loss from leaks in spacecraft. Air leaks present a danger to spacecraft crew, and so a method of finding air leaks when they occur is needed. Most leak detection systems localize the leak in some way. Instead, we address the identification of air leaks in a pressurized space module, we aim to determine the …
Rediscovering The Interpersonal: Models Of Networked Communication In New Media Performance, Alicia Champlin
Rediscovering The Interpersonal: Models Of Networked Communication In New Media Performance, Alicia Champlin
Electronic Theses and Dissertations
This paper examines the themes of human perception and participation within the contemporary paradigm and relates the hallmarks of the major paradigm shift which occurred in the mid-20th century from a structural view of the world to a systems view. In this context, the author’s creative practice is described, outlining a methodology for working with the communication networks and interpersonal feedback loops that help to define our relationships to each other and to media since that paradigm shift. This research is framed within a larger field of inquiry into the impact of contemporary New Media Art as we experience it. …
The 2-Domination Number Of A Caterpillar, Presley Chukwukere
The 2-Domination Number Of A Caterpillar, Presley Chukwukere
Electronic Theses and Dissertations
A set D of vertices in a graph G is a 2-dominating set of G if every vertex in V − D has at least two neighbors in D. The 2-domination number of a graph G, denoted by γ2(G), is the minimum cardinality of a 2- dominating set of G. In this thesis, we discuss the 2-domination number of a special family of trees, called caterpillars. A caterpillar is a graph denoted by Pk(x1, x2, ..., xk), where xi is the number of leaves attached to the ith vertex …
Wald Confidence Intervals For A Single Poisson Parameter And Binomial Misclassification Parameter When The Data Is Subject To Misclassification, Nishantha Janith Chandrasena Poddiwala Hewage
Wald Confidence Intervals For A Single Poisson Parameter And Binomial Misclassification Parameter When The Data Is Subject To Misclassification, Nishantha Janith Chandrasena Poddiwala Hewage
Electronic Theses and Dissertations
This thesis is based on a Poisson model that uses both error-free data and error-prone data subject to misclassification in the form of false-negative and false-positive counts. We present maximum likelihood estimators (MLEs), Fisher's Information, and Wald statistics for Poisson rate parameter and the two misclassification parameters. Next, we invert the Wald statistics to get asymptotic confidence intervals for Poisson rate parameter and false-negative rate parameter. The coverage and width properties for various sample size and parameter configurations are studied via a simulation study. Finally, we apply the MLEs and confidence intervals to one real data set and another realistic …
The Expected Number Of Patterns In A Random Generated Permutation On [N] = {1,2,...,N}, Evelyn Fokuoh
The Expected Number Of Patterns In A Random Generated Permutation On [N] = {1,2,...,N}, Evelyn Fokuoh
Electronic Theses and Dissertations
Previous work by Flaxman (2004) and Biers-Ariel et al. (2018) focused on the number of distinct words embedded in a string of words of length n. In this thesis, we will extend this work to permutations, focusing on the maximum number of distinct permutations contained in a permutation on [n] = {1,2,...,n} and on the expected number of distinct permutations contained in a random permutation on [n]. We further considered the problem where repetition of subsequences are as a result of the occurrence of (Type A and/or Type B) replications. Our method of enumerating the Type A replications causes double …
Surface Entropy Of Shifts Of Finite Type, Dennis Pace
Surface Entropy Of Shifts Of Finite Type, Dennis Pace
Electronic Theses and Dissertations
Let χ be the class of 1-D and 2-D subshifts. This thesis defines a new function, HS : χ x R → [0,∞] which we call the surface entropy of a shift. This definition is inspired by the topological entropy of a subshift and we compare and contrast several structural properties of surface entropy to entropy. We demonstrate that much like entropy, the finiteness of surface entropy is a conjugacy invariant and is a tool in the classification of subshifts. We develop a tiling algorithm related to continued fractions which allows us to prove a continuity result about surface …
T-De Vries Algebra, Nawal Alznad
T-De Vries Algebra, Nawal Alznad
Electronic Theses and Dissertations
The main point of this dissertation is to introduce the action on de Vries algebra by a topological monoid and we denoted the resulting category by dVT. In order to reach our goal, we started with introducing new proofs for some well known results in the category of flows. Then, we studied the Generalized Smirnov's Theorem for flows. After we studied the new category (dVT), we were able to provide a new way to construct the Čech-stone flow compactification of a given flow. Finally, we developed the co-free T-de Vries algebra for a special case.
Factorization In Integral Domains., Ryan H. Gipson
Factorization In Integral Domains., Ryan H. Gipson
Electronic Theses and Dissertations
We investigate the atomicity and the AP property of the semigroup rings F[X; M], where F is a field, X is a variable and M is a submonoid of the additive monoid of nonnegative rational numbers. In this endeavor, we introduce the following notions: essential generators of M and elements of height (0, 0, 0, . . .) within a cancellative torsion-free monoid Γ. By considering the latter, we are able to determine the irreducibility of certain binomials of the form Xπ − 1, where π is of height (0, 0, 0, . . .), in the monoid domain. Finally, …
Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates
Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates
Electronic Theses and Dissertations
Ever since Shor's algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I …
Developing Optimization Techniques For Logistical Tendering Using Reverse Combinatorial Auctions, Jennifer Kiser
Developing Optimization Techniques For Logistical Tendering Using Reverse Combinatorial Auctions, Jennifer Kiser
Electronic Theses and Dissertations
In business-to-business logistical sourcing events, companies regularly use a bidding process known as tendering in the procurement of transportation services from third-party providers. Usually in the form of an auction involving a single buyer and one or more sellers, the buyer must make decisions regarding with which suppliers to partner and how to distribute the transportation lanes and volume among its suppliers; this is equivalent to solving the optimization problem commonly referred to as the Winner Determination Problem. In order to take into account the complexities inherent to the procurement problem, such as considering a supplier’s network, economies of scope, …
Developmental Mathematics: A Quantitative Investigation Of Instructor Classification As Related To Student Success, Brittany A. Fish
Developmental Mathematics: A Quantitative Investigation Of Instructor Classification As Related To Student Success, Brittany A. Fish
Electronic Theses and Dissertations
The purpose of this quantitative study was to examine what type of predictive power exists between an instructor’s employment classification, student gender, student race, and first-generation status on a student’s academic success in developmental mathematics, as measured by final semester grades at a regionally comprehensive state university in Texas between fall 2013 and spring 2017. Data were collected from the institution under study and the sample population included 1932 unique student observations. The data collected in this study were analyzed through a binary logistic regression model to determine whether an instructor’s employment classification, student gender, student race, and first-generation status …
Re-Evaluating Performance Measurement: New Mathematical Methods To Address Common Performance Measurement Challenges, Jordan David Benis
Re-Evaluating Performance Measurement: New Mathematical Methods To Address Common Performance Measurement Challenges, Jordan David Benis
Electronic Theses and Dissertations
Performance Measurement is an essential discipline for any business. Robust and reliable performance metrics for people, processes, and technologies enable a business to identify and address deficiencies to improve performance and profitability. The complexity of modern operating environments presents real challenges to developing equitable and accurate performance metrics. This thesis explores and develops two new methods to address common challenges encountered in businesses across the world. The first method addresses the challenge of estimating the relative complexity of various tasks by utilizing the Pearson Correlation Coefficient to identify potentially over weighted and under weighted tasks. The second method addresses the …
A Study Of Topological Invariants In The Braid Group B2, Andrew Sweeney
A Study Of Topological Invariants In The Braid Group B2, Andrew Sweeney
Electronic Theses and Dissertations
The Jones polynomial is a special topological invariant in the field of Knot Theory. Created by Vaughn Jones, in the year 1984, it is used to study when links in space are topologically different and when they are topologically equivalent. This thesis discusses the Jones polynomial in depth as well as determines a general form for the closure of any braid in the braid group B2 where the closure is a knot. This derivation is facilitated by the help of the Temperley-Lieb algebra as well as with tools from the field of Abstract Algebra. In general, the Artin braid group …
Vector Partitions, Jennifer French
Vector Partitions, Jennifer French
Electronic Theses and Dissertations
Integer partitions have been studied by many mathematicians over hundreds of years. Many identities exist between integer partitions, such as Euler’s discovery that every number has the same amount of partitions into distinct parts as into odd parts. These identities can be proven using methods such as conjugation or generating functions. Over the years, mathematicians have worked to expand partition identities to vectors. In 1963, M. S. Cheema proved that every vector has the same number of partitions into distinct vectors as into vectors with at least one component odd. This parallels Euler’s result for integer partitions. The primary purpose …
Italian Domination In Complementary Prisms, Haley D. Russell
Italian Domination In Complementary Prisms, Haley D. Russell
Electronic Theses and Dissertations
Let $G$ be any graph and let $\overline{G}$ be its complement. The complementary prism of $G$ is formed from the disjoint union of a graph $G$ and its complement $\overline{G}$ by adding the edges of a perfect matching between the corresponding vertices of $G$ and $\overline{G}$. An Italian dominating function on a graph $G$ is a function such that $f \, : \, V \to \{ 0,1,2 \}$ and for each vertex $v \in V$ for which $f(v)=0$, it holds that $\sum_{u \in N(v)} f(u) \geq 2$. The weight of an Italian dominating function is the value $f(V)=\sum_{u \in V(G)}f(u)$. …
Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch
Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch
Electronic Theses and Dissertations
The performance and stability of the Particle Swarm Optimization algorithm depends on parameters that are typically tuned manually or adapted based on knowledge from empirical parameter studies. Such parameter selection is ineffectual when faced with a broad range of problem types, which often hinders the adoption of PSO to real world problems. This dissertation develops a dynamic self-optimization approach for the respective parameters (inertia weight, social and cognition). The effects of self-adaption for the optimal balance between superior performance (convergence) and the robustness (divergence) of the algorithm with regard to both simple and complex benchmark functions is investigated. This work …
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Electronic Theses and Dissertations
Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …
Analytical And Numerical Investigations Of The Kudryashov Generalized Kdv Equation, William Hilton
Analytical And Numerical Investigations Of The Kudryashov Generalized Kdv Equation, William Hilton
Electronic Theses and Dissertations
This thesis concerns an analytical and numerical study of the Kudryashov Generalized Korteweg-de Vries (KG KdV) equation. Using a refined perturbation expansion of the Fermi-Pasta-Ulam (FPU) equations of motion, the KG KdV equation, which arises at sixth order, and general higher order KdV equations are derived. Special solutions of the KG KdV equation are derived using the tanh method. A pseudospectral integrator, which can handle stiff equations, is developed for the higher order KdV equations. The numerical experiments indicate that although the higher order equations exhibit complex dynamics, they fail to reach energy equipartition on the time scale considered.
Quasi-Gorenstein Modules, Alexander York
Quasi-Gorenstein Modules, Alexander York
Electronic Theses and Dissertations
This thesis will study the various roles that quasi-Gorenstein modules and their properties play in the study of homological dimensions and linkage of modules. To that effect we begin by studying these modules in their own right. An R-module M of grade g will be quasi-Gorenstein if ExtiR(M, R) = 0 for i 6= g and there is an isomorphism M ∼= ExtgR(M, R). Such modules have many nice properties which we will explore throughout this thesis. We will show they help extend a characterization of diagonalizable matrices over principal ideal domains to more general rings. We will use their …
Weierstrass Vertices And Divisor Theory Of Graphs, Ajani Ruwandhika Chulangi De Vas Gunasekara
Weierstrass Vertices And Divisor Theory Of Graphs, Ajani Ruwandhika Chulangi De Vas Gunasekara
Electronic Theses and Dissertations
Chip-firing games and divisor theory on finite, connected, undirected and unweighted graphs have been studied as analogs of divisor theory on Riemann Surfaces. As part of this theory, a version of the one-dimensional Riemann-Roch theorem was introduced for graphs by Matt Baker in 2007. Properties of algebraic curves that have been studied can be applied to study graphs by means of the divisor theory of graphs. In this research, we investigate the property of a vertex of a graph having the Weierstrass property in analogy to the theory of Weierstrass points on algebraic curves. The weight of the Weierstrass vertices …
The Impact Of Data Sovereignty On American Indian Self-Determination: A Framework Proof Of Concept Using Data Science, Joseph Carver Robertson
The Impact Of Data Sovereignty On American Indian Self-Determination: A Framework Proof Of Concept Using Data Science, Joseph Carver Robertson
Electronic Theses and Dissertations
The Data Sovereignty Initiative is a collection of ideas that was designed to create SMART solutions for tribal communities. This concept was to develop a horizontal governance framework to create a strategic act of sovereignty using data science. The core concept of this idea was to present data sovereignty as a way for tribal communities to take ownership of data in order to affect policy and strategic decisions that are data driven in nature. The case studies in this manuscript were developed around statistical theories of spatial statistics, exploratory data analysis, and machine learning. And although these case studies are …
Statistical Algorithms And Bioinformatics Tools Development For Computational Analysis Of High-Throughput Transcriptomic Data, Adam Mcdermaid
Statistical Algorithms And Bioinformatics Tools Development For Computational Analysis Of High-Throughput Transcriptomic Data, Adam Mcdermaid
Electronic Theses and Dissertations
Next-Generation Sequencing technologies allow for a substantial increase in the amount of data available for various biological studies. In order to effectively and efficiently analyze this data, computational approaches combining mathematics, statistics, computer science, and biology are implemented. Even with the substantial efforts devoted to development of these approaches, numerous issues and pitfalls remain. One of these issues is mapping uncertainty, in which read alignment results are biased due to the inherent difficulties associated with accurately aligning RNA-Sequencing reads. GeneQC is an alignment quality control tool that provides insight into the severity of mapping uncertainty in each annotated gene from …
Categories Of Residuated Lattices, Daniel Wesley Fussner
Categories Of Residuated Lattices, Daniel Wesley Fussner
Electronic Theses and Dissertations
We present dual variants of two algebraic constructions of certain classes of residuated lattices: The Galatos-Raftery construction of Sugihara monoids and their bounded expansions, and the Aguzzoli-Flaminio-Ugolini quadruples construction of srDL-algebras. Our dual presentation of these constructions is facilitated by both new algebraic results, and new duality-theoretic tools. On the algebraic front, we provide a complete description of implications among nontrivial distribution properties in the context of lattice-ordered structures equipped with a residuated binary operation. We also offer some new results about forbidden configurations in lattices endowed with an order-reversing involution. On the duality-theoretic front, we present new results on …
Generalized Characteristics Of A Generic Polytope, Tommy Naugle
Generalized Characteristics Of A Generic Polytope, Tommy Naugle
Electronic Theses and Dissertations
For a smooth hypersurface S ⊂ R 2n given by the level set of a Hamiltonian function H, a symplectic form ω on R2n induces a vector field XH which flows tangent to S. By the nondegeneracy of ω, there exists a distinguished line bundle LS whose characteristics are the integral curves of XH. When S is the boundary of a smooth convex domain K˜ ⊂ R 2n, then the least action among closed characteristics of LS is equal to the Ekeland-Hofer-Zehnder capacity, a symplectic invariant. From a result due to Artstein-Avidan and Ostrover, there exists a continuous extension of …
Sparse Trees With A Given Degree Sequence, Ao Shen
Sparse Trees With A Given Degree Sequence, Ao Shen
Electronic Theses and Dissertations
In this thesis, we consider the properties of sparse trees and summarized a certain class of trees under some constraint (including with a given degree sequence, with given number of leaves, with given maximum degree, etc.) which have maximum Wiener index and the minimum number of subtrees at the same time. Wiener index is one of the most important topological indices in chemical graph theory. Steiner k�� Wiener index can be regarded as the generalization of Wiener index, when k = 2, Steiner Wiener index is the same as Wiener index. Steiner k�� Wiener index of a tree T is …
In Quest Of Bernstein Inequalities Rational Functions, Askey-Wilson Operator, And Summation Identities For Entire Functions, Rajitha Puwakgolle Gedara
In Quest Of Bernstein Inequalities Rational Functions, Askey-Wilson Operator, And Summation Identities For Entire Functions, Rajitha Puwakgolle Gedara
Electronic Theses and Dissertations
The title of the dissertation gives an indication of the material involved with the connecting thread throughout being the classical Bernstein inequality (and its variants), which provides an estimate to the size of the derivative of a given polynomial on a prescribed set in the complex plane, relative to the size of the polynomial itself on the same set. Chapters 1 and 2 lay the foundation for the dissertation. In Chapter 1, we introduce the notations and terminology that will be used throughout. Also a brief historical recount is given on the origin of the Bernstein inequality, which dated back …
Bases In Spaces Of Regular Multilinear Operators And Homogeneous Polynomials On Banach Lattices, Khazhak Varazdat Navoyan
Bases In Spaces Of Regular Multilinear Operators And Homogeneous Polynomials On Banach Lattices, Khazhak Varazdat Navoyan
Electronic Theses and Dissertations
For Banach lattices E1,…, Em and F with 1-unconditional bases, we show that the monomial sequence forms a 1-unconditional basis of Lr(E1,…, Em;F), the Banach lattice of all regular m-linear operators from E1×···× Em to F, if and only if each basis of E1,…,Em is shrinking and every positive m-linear operator from E 1×···×Em to F is weakly sequentially continuous. As a consequence, we obtain necessary and sufficient conditions for which the m-fold Fremlin projective tensor product E1⊗ |π|··· ⊗|π|E m (resp. the m-fold positive injective tensor product E1⊗|ϵ|··· ⊗ |ϵ|Em) has a shrinking basis or a boundedly complete basis. …