A Generalization Of The Difference Of Slopes Test To Poisson Regression With Three-Way Interaction, 2016 Marshall University
A Generalization Of The Difference Of Slopes Test To Poisson Regression With Three-Way Interaction, Melinda Bierhals
Theses, Dissertations and Capstones
Linear regression models involving interaction can use the difference of slopes test to compare slopes for various situations. We will be generalizing this process to develop a procedure to compare rates in a Poisson regression model, allowing us to consider unbounded count data as opposed to continuous data. We will apply this process to an educational data set from a sample of students located in two different Los Angeles high schools. Our model will include a three-way interaction and address the following questions:
• Does language ability impact the relationship between math ability and attendance in the same way for …
Arithmetic Local Constants For Abelian Varieties With Extra Endomorphisms, 2016 College of Saint Benedict/Saint John's University
Arithmetic Local Constants For Abelian Varieties With Extra Endomorphisms, Sunil Chetty
Mathematics Faculty Publications
This work generalizes the theory of arithmetic local constants, introduced by Mazur and Rubin, to better address abelian varieties with a larger endomorphism ring than ℤ. We then study the growth of the p∞- Selmer rank of our abelian variety, and we address the problem of extending the results of Mazur and Rubin to dihedral towers k ⊂ K ⊂ F in which [F : K] is not a p-power extension.
Generalized Eulerian Numbers And Multiplex Juggling Sequences, 2016 College of Saint Benedict/Saint John's University
Generalized Eulerian Numbers And Multiplex Juggling Sequences, Esther M. Banaian
All College Thesis Program, 2016-2019
We consider generalizations of both juggling sequences and non-attacking rook placements. We demonstrate the important connection between these objects, and also propose a generalization of the Eulerian numbers. These generalizations give rise to several interesting counting problems, which we explore.
Nonexistence Of Nonquadratic Kerdock Sets In Six Variables, 2016 University of Richmond
Nonexistence Of Nonquadratic Kerdock Sets In Six Variables, John Clikeman
Honors Theses
Kerdock sets are maximally sized sets of boolean functions such that the sum of any two functions in the set is bent. This paper modifies the methodology of a paper by Phelps (2015) to the problem of finding Kerdock sets in six variables containing non-quadratic elements. Using a computer search, we demonstrate that no Kerdock sets exist containing non-quadratic six- variable bent functions, and that the largest bent set containing such functions has size 8.
Partitioning Groups With Difference Sets, 2016 University of Richmond
Partitioning Groups With Difference Sets, Rebecca Funke
Honors Theses
This thesis explores the use of difference sets to partition algebraic groups. Difference sets are a tool belonging to both group theory and combinatorics that provide symmetric properties that can be map into over mathematical fields such as design theory or coding theory. In my work, I will be taking algebraic groups and partitioning them into a subgroup and multiple McFarland difference sets. This partitioning can then be mapped to an association scheme. This bridge between difference sets and association schemes have important contributions to coding theory.
A New Class Of Generalized Power Lindley Distribution With Applications To Lifetime Data, 2016 Georgia Southern University
A New Class Of Generalized Power Lindley Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Tiantian Yang, Boikanyo Makubate
Department of Mathematical Sciences Faculty Publications
In this paper, a new class of generalized distribution called the Kumaraswamy Power Lindley (KPL) distribution is proposed and studied. This class of distributions contains the Kumaraswamy Lindley (KL), exponentiated power Lindley (EPL), power Lindley (PL), generalized or exponentiated Lindley (GL), and Lindley (L) distributions as special cases. Series expansion of the density is obtained. Statistical properties of this class of distributions, including hazard function, reverse hazard function, monotonicity property, shapes, moments, reliability, quantile function, mean deviations, Bonferroni and Lorenz curves, entropy and Fisher information are derived. Method of maximum likelihood is used to estimate the parameters of this new …
An Analysis Of Charles Fefferman's Proof Of The Fundamental Theorem Of Algebra, 2016 Eastern Michigan University
An Analysis Of Charles Fefferman's Proof Of The Fundamental Theorem Of Algebra, Kyle O. Linford
Senior Honors Theses and Projects
Many peoples' first exploration into more rigorous and formalized mathematics is with their early explorations in algebra. Much of their time and effort is dedicated to finding roots of polynomials-a challenge that becomes more increasingly difficult as the degree of the polynomials increases, especially if no real number roots exist. The Fundamental Theorem of Algebra is used to show that there exists a root, particularly a complex root, for any nth degree polynomial. After struggling to prove this statement for over 3 centuries, Carl Friedrich Gauss offered the first fairly complete proof of the theorem in 1799. Further proofs of …
Classifying Coloring Graphs, 2016 University of Richmond
Classifying Coloring Graphs, Julie Beier, Janet Fierson, Ruth Haas, Heather M. Russell, Kara Shavo
Department of Math & Statistics Faculty Publications
Given a graph G, its k-coloring graph is the graph whose vertex set is the proper k-colorings of the vertices of G with two k-colorings adjacent if they differ at exactly one vertex. In this paper, we consider the question: Which graphs can be coloring graphs? In other words, given a graph H, do there exist G and k such that H is the k-coloring graph of G? We will answer this question for several classes of graphs and discuss important obstructions to being a coloring graph involving order, girth, and induced subgraphs.
Concrete Examples Of H(B) Spaces, 2016 University of Richmond
Concrete Examples Of H(B) Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Department of Math & Statistics Faculty Publications
In this paper we give an explicit description of de Branges-Rovnyak spaces H(b) when b is of the form qr, where q is a rational outer function in the closed unit ball of H∞ and r is a positive number.
An Inner-Outer Factorization In ℓp With Applications To Arma Processes, 2016 University of Richmond
An Inner-Outer Factorization In ℓp With Applications To Arma Processes, Raymond Cheng, William T. Ross
Department of Math & Statistics Faculty Publications
The following inner-outer type factorization is obtained for the sequence space ℓp: if the complex sequence F = (F0, F1,F2,...) decays geometrically, then for an p sufficiently close to 2 there exists J and G in ℓp such that F = J * G; J is orthogonal in the Birkhoff-James sense to all of its forward shifts SJ, S2J, S3J, ...; J and F generate the same S-invariant subspace of ℓp; and G is a cyclic vector for S on ℓ …
Real Complex Functions, 2016 University of Richmond
Real Complex Functions, Stephan Ramon Garcia, Javad Mashreghi, William T. Ross
Department of Math & Statistics Faculty Publications
We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to operator theory.
Introduction To Model Spaces And Their Operators, 2016 University of Richmond
Introduction To Model Spaces And Their Operators, William T. Ross, Stephan Ramon Garcia, Javad Mashreghi
Bookshelf
The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.
The Prominence Of Affect In Creativity: Expanding The Conception Of Creativity In Mathematical Problem Solving, 2016 Hope College
The Prominence Of Affect In Creativity: Expanding The Conception Of Creativity In Mathematical Problem Solving, Eric L. Mann, Scott A. Chamberlin, Amy K. Graefe
Faculty Publications
Constructs such as fluency, flexibility, originality, and elaboration have been accepted as integral components of creativity. In this chapter, the authors discuss affect (Leder GC, Pehkonen E, Törner G (eds), Beliefs: a hidden variable in mathematics education? Kluwer Academic Publishers, Dordrecht, 2002; McLeod DB, J Res Math Educ 25:637–647, 1994; McLeod DB, Adams VM, Affect and mathematical problem solving: a new perspective. Springer, New York, 1989) as it relates to the production of creative outcomes in mathematical problem solving episodes. The saliency of affect in creativity cannot be underestimated, as problem solvers require an appropriate state of mind in order …
Sphere Representations, Stacked Polytopes, And The Colin De Verdière Number Of A Graph, 2016 American Mathematical Society
Sphere Representations, Stacked Polytopes, And The Colin De Verdière Number Of A Graph, Lon Mitchell, Lynne Yengulalp
Mathematics Faculty Publications
We prove that a k-tree can be viewed as a subgraph of a special type of (k + 1)- tree that corresponds to a stacked polytope and that these “stacked” (k + 1)-trees admit representations by orthogonal spheres in R k+1. As a result, we derive lower bounds for Colin de Verdi`ere’s µ of complements of partial k-trees and prove that µ(G) + µ(G) > |G| − 2 for all chordal G.
Existence Of Periodic Solutions For A Quantum Volterra Equation, 2016 University of Dayton
Existence Of Periodic Solutions For A Quantum Volterra Equation, Muhammad Islam, Jeffrey T. Neugebauer
Mathematics Faculty Publications
The objective of this paper is to study the periodicity properties of functions that arise in quantum calculus, which has been emerging as an important branch of mathematics due to its various applications in physics and other related fields. The paper has two components. First, a relation between two existing periodicity notions is established. Second, the existence of periodic solutions of a q-Volterra integral equation, which is a general integral form of a first order q-difference equation, is obtained. At the end, some examples are provided. These examples show the effectiveness of the relation between the two periodicity notions that …
Necessary And Sufficient Conditions For Stability Of Volterra Integro-Dynamic Equation Systems On Time Scales, 2016 University of Dayton
Necessary And Sufficient Conditions For Stability Of Volterra Integro-Dynamic Equation Systems On Time Scales, Youssef Raffoul
Mathematics Faculty Publications
In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.
Stochastic Models Of Evidence Accumulation In Changing Environments, 2016 University of Dayton
Stochastic Models Of Evidence Accumulation In Changing Environments, Alan Veliz-Cuba, Zachary P. Kilpatrick, Krešimir Josić
Mathematics Faculty Publications
Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information …
Almost Automorphic Solutions Of Delayed Neutral Dynamic Systems On Hybrid Domains, 2016 Izmir University
Almost Automorphic Solutions Of Delayed Neutral Dynamic Systems On Hybrid Domains, Murat Adıvar, Halis Can Koyuncuoğlu, Youssef Raffoul
Mathematics Faculty Publications
We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for an almost periodic solutions of the system.
Positive Solutions For A Singular Fourth Order Nonlocal Boundary Value Problem, 2016 Baylor University
Positive Solutions For A Singular Fourth Order Nonlocal Boundary Value Problem, John M. Davis, Paul W. Eloe, John R. Graef, Johnny Henderson
Mathematics Faculty Publications
Positive solutions are obtained for the fourth order nonlocal boundary value problem, u(4)=f(x,u), 0 < x < 1, u(0) = u''(0) = u'(1) = u''(1) - u''(2/3)=0, where f(x,u) is singular at x = 0, x=1, y=0, and may be singular at y=∞. The solutions are shown to exist at fixed points for an operator that is decreasing with respect to a cone.
Serre Weights And Wild Ramification In Two-Dimensional Galois Representations, 2016 University of Warwick
Serre Weights And Wild Ramification In Two-Dimensional Galois Representations, Lassina Dembélé, Fred Diamond, David P. Roberts
Mathematics Publications
A generalization of Serre’s Conjecture asserts that if F is a totally real field, then certain characteristic p representations of Galois groups over F arise from Hilbert modular forms. Moreover, it predicts the set of weights of such forms in terms of the local behaviour of the Galois representation at primes over p. This characterization of the weights, which is formulated using p-adic Hodge theory, is known under mild technical hypotheses if p > 2. In this paper we give, under the assumption that p is unramified in F, a conjectural alternative description for the set of weights. …