Mathematics Commons^™

Heavy Episodic Drinking On College Campuses: Does Changing The Legal Drinking Age Make A Difference?, Jawaid W. Rasul, Robert G. Rommel, Geoffrey M. Jacquez, Ben G. Fitzpatrick, Azmy S. Ackleh, Neal Simonsen, Richard Scribner

Mathematics, Statistics and Data Science Faculty Works

This article extends the compartmental model previously developed by Scribner et al. in the context of college drinking to a mathematical model of the consequences of lowering the legal drinking age. Method: Using data available from 32 U.S. campuses, the analyses separate underage and legal age drinking groups into an eight-compartment model with different alcohol availability (wetness) for the underage and legal age groups. The model evaluates the likelihood that underage students will incorrectly perceive normative drinking levels to be higher than they actually are (i.e., misperception) and adjust their drinking accordingly by varying the interaction between underage students in …

Finitely 1-Convex F-Rings, Suzanne Larson

Mathematics, Statistics and Data Science Faculty Works

This paper investigates f-rings that can be constructed in a finite number of steps where every step consists of taking the fibre product of two f-rings, both being either a 1-convex f-ring or a fibre product obtained in an earlier step of the construction. These are the f-rings that satisfy the algebraic property that rings of continuous functions possess when the underlying topological space is finitely an F-space (i.e. has a Stone-čech compactification that is a finite union of compact F-spaces). These f-rings are shown to be SV f-rings with bounded inversion and finite rank and, when constructed from semisimple …

Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Eric Flapan, Blake Mellor, Ramin Naimi

Mathematics, Statistics and Data Science Faculty Works

We determine for which m the complete graph K_m has an embedding in S³ whose topological symmetry group is isomorphic to one of the polyhedral groups A₄, A₅ or S₄.

3-D Computational Investigation Of Viscoelastic Biofilms Using Gpus, Paisa Seeluangsawat

Theses and Dissertations

A biofilm is a slimy colony of bacteria and the materials they secrete, collectively called “extracellular polymeric substances (EPS)”. The EPS consists mostly of bio-polymers, which cross link into a network that behave viscoelastically under deformation. We propose a single-fluid multi-component phase field model of biofilms that captures this behavior, then use numerical simulations on GPUs to investigate the biofilm’s growth and its hydrodynamics properties.

On The Use Of Log-Transformation Vs. Nonlinear Regression For Analyzing Biological Power-Laws, Xiao Xiao

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Power-law relationships are among the most well-studied functional relationships in biology . Recently the common practice of fitting power-laws using linear regression on log-transformed data (LR) has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations we demonstrate that the error distribution determines which method performs better, with LR better characterizing data with multiplicative lognormal error and NLR better characterizing data with additive normal error. Analysis of 471 biological power-laws shows that both …

On Diamond-Alpha Dynamic Equations And Inequalities, Nuriye Atasever

College of Graduate Studies: Theses & Dissertations

In view of the recently developed theory of calculus for dynamic equations on time scales (which unifies discrete and continuous systems), in this project we give some of the basics of the extension of the theory to the combined delta (forward) and nabla (backward) derivatives. In this set up the newly developed theory of diamond-alpha derivatives are analyzed through some equation and inequality properties. In particular Opial type Diamond-alpha dynamic Inequalities are discussed in this context and recently developed results and their improved versions are given in this work.

Near Minimum Energy Distributions On The Sphere Using Voronoi Cells, Benedictus Sitou Mensah

Masters Theses

In this thesis we investigate the use of Voronoi cells to estimate a minimum energy configuration on the sphere. We introduce the notion of a Voronoi cell and give examples of its uses in various areas of mathematics. We consider the icosahedral decomposition of the sphere and apply a minimal energy configuration on the planar equilateral triangle to obtain spherical coordinates of a near minimal energy configuration on the sphere.

Price Discovery In The U.S. Bond Market Trading Strategies And The Cost Of Liquidity, Haimei Shao

Electronic Theses and Dissertations

The world bond market is nearly twice as large as the equity market. The goal of this dissertation is to study the dynamics of bond price. Among the liquidity risk, interest rate risk and default risk, this dissertation will focus on the liquidity risk and trading strategy. Under the mathematical frame of stochastic control, we model price setting in U.S. bond markets where dealers have multiple instruments to smooth inventory imbalances. The difficulty in obtaining the optimal trading strategy is that the optimal strategy and value function depend on each other, and the corresponding HJB equation is nonlinear. To solve …

Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems, Todd Blanton Smith

Electronic Theses and Dissertations

In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in …

Applications Of Finite Geometries To Designs And Codes, David C. Clark

Dissertations, Master's Theses and Master's Reports - Open

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures.

A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will …

Cyclic Automorphic Graph Decompositions , Michael Li Misson

Dissertations, Master's Theses and Master's Reports - Open

Chapter 1 introduces the tools and mechanics necessary for this report. Basic definitions and topics of graph theory which pertain to the report and discussion of automorphic decompositions will be covered in brief detail. An automorphic decomposition D of a graph H by a graph G is a G-decomposition of H such that the intersection of graph (D) @H. H is called the automorhpic host, and G is the automorphic divisor. We seek to find classes of graphs that are automorphic divisors, specifically ones generated cyclically.

Chapter 2 discusses the previous work done mainly by Beeler. …

Question 1: A Million Monkeys, Er, Humans; Question 2: Deicing New York City, Larry Weinstein

Physics Faculty Publications

Question 1: A Million Monkeys, er, Humans: Americans now seem to communicate more by typing than by speaking. Many of us are also chained to our computers. How many characters (letters, numbers, symbols) do all Americans type or text every year?

Question 2: Deicing New York City: How much deicing compound does New York City use during and after a major snowstorm?

Graded Multiplication Modules And The Graded Ideal \Theta_G (M), Shahabaddin Ebrahimi Atani, Reza Ebrahimi Atani

Turkish Journal of Mathematics

Let G be a group and let R be a G-graded commutative ring. For a graded R-module M, the notion of the associated graded ideal \theta_g (M) of R is defined. It is proved that the graded ideal \theta_g (M) is important in the study of graded multiplication modules. Among various application given, the following results are proved: if M is a graded faithful multiplication module, then \theta_g (M) is an idempotent graded multiplication ideal of R such that \theta_g (\theta_g (M)) = \theta_g (M), and every graded representable multiplication R-module is finitely generated.

Coverings Of Lie Groupoids, İlhan İçen, M. Habi̇l Gürsoy, A. Fati̇h Özcan

Turkish Journal of Mathematics

In this work we constitute the category of coverings of the Lie fundamental groupoid associated with a connected smooth manifold. We show that this category is equivalent to the category of universal coverings of a connected smooth manifold. In addition, we prove the equivalence of the category of coverings of a Lie groupoid and the category of actions of this Lie groupoid on a connected smooth manifold. Also we present two side results related to actions of Lie groupoids on the manifolds and coverings of Lie groupoids.

A Fixed Point Theorem For A Compact And Connected Set In Hilbert Space, Hülya Duru

Turkish Journal of Mathematics

Let (H,) be a real Hilbert space and let K be a compact and connected subset of H. We show that every continuous mapping T:K \rightarrow K satisfying a mild condition has a fixed point.

Probabilities For Absolute Irreducibility Of Multivariate Polynomials By The Polytope Method, Fati̇h Koyuncu, Ferruh Özbudak

Turkish Journal of Mathematics

Motivated by the Dubickas's result in [1], which computes the probability of the irreducible polynomials by Eisenstein's criterion for some families of polynomials in Z[x], we calculate the probabilities which represent the ratio of absolutely irreducible multivariate polynomials by the polytope method in some families of polynomials over arbitrary fields.

On Generalized (\Alpha,\Beta)-Derivations Of Semiprime Rings, Faisal Ali, Muhammad Anwar Chaudhry

Turkish Journal of Mathematics

We investigate some properties of generalized (\alpha,\beta)-derivations on semiprime rings. Among some other results, we show that if g is a generalized (\alpha,\beta)-derivation, with associated (\alpha,\beta)-derivation \delta, on a semiprime ring R such that [g(x),\alpha(x)]=0 for all x\in R, then \delta(x)[y,z]=0 for all x,y,z\in R and \delta is central. We also show that if \alpha,\nu,\tau are endomorphisms and \beta,\mu are automorphisms of a semiprime ring R and if R has a generalized (\alpha,\beta)-derivation g, with associated (\alpha,\beta)-derivation \delta, such that g([\mu(x),w(y)])=[\nu(x),w(y)]_{\alpha,\tau}, where w:R\rightarrow R is commutativity preserving, then [y,z]\delta(w(p))=0 for all y,z,p\in R.

Combinatorial Results For Order-Preserving And Order-Decreasing Transformations, Gonca Ayik, Hayrullah Ayik, Meti̇n Koç

Turkish Journal of Mathematics

Let O_n and C_n be the semigroup of all order-preserving transformations and of all order-preserving and order-decreasing transformations on the finite set X_n={1,2,\ldots ,n}, respectively. Let \fix (\alpha )={x\in X_n:x\alpha =x} for any transformation \alpha. In this paper, for any Y\subseteq X_n, we find the cardinalities of the sets O_{n,Y}={\alpha\in O_n:\fix (\alpha)=Y} and C_{n,Y}={\alpha\in C_n: \fix (\alpha )=Y}. Moreover, we find the numbers of transformations of O_n and C_n with r fixed points.

Gpq Modules And Generalized Armendariz Modules, Liang Zhao, Xiaosheng Zhu

Turkish Journal of Mathematics

Let M_R be a right R-module. We introduce the concept of right generalized p.q.-Baer modules (or simply, right GPQ modules) to extend the notion of right p.q.-Baer modules. We study on the relationship between the GPQ property of a module M_R and various quasi-Armendariz properties. We prove that every right GPQ module is a quasi-Armendariz module. As a sequence, we obtain a general form of some known results considering the p.q.Baer property of a ring, some known results are extended. Moreover, we prove that for the formal triangular ring R constructed from a pair of rings S, T and a …

Generalized Derivations On Lie Ideals In Prime Rings, Öznur Gölbaşi, Emi̇ne Koç

Turkish Journal of Mathematics

Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.