Mathematics Commons^™

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 …

The Wright Message, 2015-2016, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Alumni and Friends
-- Dr. Edward Rathmell retires from UNI
-- 2015 Hari Shankar Lecture
-- Around Wright Hall
-- Congratulations to....
-- Faculty Highlights
-- Student News
-- 2015-2016 Tenure-Stream Faculty
-- Alumni Spotlight: Clayton Edwards & Mary Theilen
-- Department Interviews: Adrienne Stanley, Joel Haack, , Benjamin Castle & Suzanne Shontz
-- UNI Students Travel to Korea
-- Trijitzsky Scholarship Winner Emily Wardenburg
-- Student Spotlights: Amber Irlmeier, Britney Bockstahler, Derek Hofland & Julia Robinson
-- PAEMST Award Winner Allysen Lovstuen
-- Donor Spotlight: Alan and Barbara Hubbard
-- News fro KME
-- …

Iteration Modeled By Playlists: An Unexpected Occurrence Of The Triangular Numbers, Catherine M. Miller, Douglas J. Shaw

Faculty Publications

Our world is changing rapidly; one example is the growth of smart technologies that have become part of our lives. Smart playlists are the source for a mathematics problem that can be approached in a variety of ways. A playlist is a set of songs that can be played separately from the albums on digital music players. The device (mp 3 player, Ipod®, etc.) can create a smart playlist based on criteria inputted by the user.

Some Combinatorial Applications Of Sage, An Open Source Program, Jessica Ruth Chowning

Masters Theses

"In this thesis, we consider the usefulness of Sage, an online and open-source program, in analyzing permutation puzzles such as the Rubik's cube and a specific combinatorial structure called the projective plane. Many programs exist to expedite calculations in research and provide previously-unavailable solutions; some require purchase, while others, such as Sage, are available for free online. Sage is asked to handle a small permutation puzzle called Swap, and then we explore how it calculates solutions for a Rubik's cube. We then discuss projective planes, Sage's library of functions for dealing with projective planes, and how they relate to the …

Day Of The Week Effect In Returns And Volatility Of The S&P 500 Sector Indices, Juan Liu

Masters Theses

"Previous studies have shown that returns associated with the stock market or foreign exchange's futures show variations across the day of the week. On such study, that employs a modified GARCH model for estimation, shows that returns associated with the S&P 500 stock index is highest on Wednesday and lowest returns on Monday. The same study shows that volatility is highest on Fridays and lowest on Wednesdays. In this study we investigate if this day-of-the-week effect on returns and volatility is present in the different sectors that constitute the S&P 500 index. The data set used provides daily returns from …

Volterra Difference Equations, Nasrin Sultana

Doctoral Dissertations

"This dissertation consists of five papers in which discrete Volterra equations of different types and orders are studied and results regarding the behavior of their solutions are established. The first paper presents some fundamental results about subexponential sequences. It also illustrates the subexponential solutions of scalar linear Volterra sum-difference equations are asymptotically stable. The exact value of the rate of convergence of asymptotically stable solutions is found by determining the asymptotic behavior of the transient renewal equations. The study of subexponential solutions is also continued in the second and third articles. The second paper investigates the same equation using the …

Essays On Unit Root Testing In Time Series, Xiao Zhong

Doctoral Dissertations

"Unit root tests are frequently employed by applied time series analysts to determine if the underlying model that generates an empirical process has a component that can be well-described by a random walk. More specifically, when the time series can be modeled using an autoregressive moving average (ARMA) process, such tests aim to determine if the autoregressive (AR) polynomial has one or more unit roots. The effect of economic shocks do not diminish with time when there is one or more unit roots in the AR polynomial, whereas the contribution of shocks decay geometrically when all the roots are outside …

Spherically Symmetric Finsler Metrics With Scalar Flag Curvature, Weidong Song, Fen Zhou

Turkish Journal of Mathematics

In this paper, we study spherically symmetric Finsler metrics F= y \phi( x ,\frac{}{ y }), where x \in B^n(r) \subset R^n, y \in T_xB^n(r)\{0} and \phi:[0,r)\times R \rightarrow R. By investigating a PDE equivalent to these metrics being locally projectively flat, we manufacture projectively flat spherically symmetric Finsler metrics in terms of error functions and, using Shen's result, we give its flag curvature.

The Ext-Strongly Gorenstein Projective Modules, Jie Ren

Turkish Journal of Mathematics

In this paper, we introduce and study Ext-strongly Gorenstein projective modules. We prove that the class of Ext-strongly Gorenstein projective modules is projective resolving. Moreover, we consider Ext-strongly Gorenstein projective precovers.

On Ampleness And Pseudo-Anosov Homeomorphisms In The Free Group, Rizos Sklinos

Turkish Journal of Mathematics

We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first-order theory of non-Abelian free groups, T_{fg}, is n-ample for any n \in \omega. This result adds to the work of Pillay, which proved that T_{fg} is non-CM-trivial. The sequence witnessing ampleness is a sequence of primitive elements in F_{\omega}. Our result provides an alternative proof to the main result of a recent preprint by Ould Houcine and Tent.

On P-Schemes With The Same Degrees Of Thin Radical And Thin Residue, Fatemeh Raei Barandagh, Amir Rahnamai Barghi

Turkish Journal of Mathematics

Let p and n>1 be a prime number and an integer, respectively. In this paper, first we show that any p-scheme whose thin radical and thin residue are equal is isomorphic to a fission of the wreath product of 2 thin schemes. In addition, we characterize association p-schemes whose thin radical and thin residue each have degree equal to p. We also characterize association p-schemes on p^n points whose thin radical and thin residue each have degree equal to p^{n-1}, and whose basis relations each have valency 1 or p^{n-1}. Moreover, we show that such schemes are Schurian.

A Decomposition Of Transferable Utility Games: Structure Of Transferable Utility Games, Ayşe Mutlu Derya

Turkish Journal of Mathematics

We define a decomposition of transferable utility games based on shifting the worth of the grand coalition so that the associated game has a nonempty core. We classify the set of all transferable utility games based on that decomposition and analyze their structure. Using the decomposition and the notion of minimal balanced collections, we give a set of necessary and sufficient conditions for a transferable utility game to have a singleton core.

Some Remarks On Distributional Chaos For Bounded Linear Operators, Lvlin Luo, Bingzhe Hou

Turkish Journal of Mathematics

The aim of this paper is to study distributional chaos for bounded linear operators. We show that distributional chaos of type k \in {1,2} is an invariant of topological conjugacy between two bounded linear operators. We give a necessary condition for distributional chaos of type 2 where it is possible to distinguish distributional chaos and Li--Yorke chaos. Following this condition, we compare distributional chaos with other well-studied notions of chaos for backward weighted shift operators and give an alternative proof to the one where strong mixing does not imply distributional chaos of type 2 (Martínez-Giménez F, Oprocha P, Peris A. …

The Fundamental Theorems Of Algebroid Functions On Annuli, Yang Tan, Qingcai Zhang

Turkish Journal of Mathematics

An extension of Nevanlinna value distribution theory for algebroid functions on annuli is proposed. The main characteristics are one-parameter and possess the same properties as in the classical case. Analogs of the Cartan theorem, the first fundamental theorem, the second fundamental theorem, deficient values, and the uniqueness of algebroid functions on annuli are proved.

Finite Groups With Three Conjugacy Class Sizes Of Primary And Biprimary Elements, Changguo Shao, Qinhui Jiang

Turkish Journal of Mathematics

We determine the structure of finite $\pi(m)$-separable groups if the set of conjugacy class sizes of primary and biprimary elements is $\{1, m, mn\}$, where $m$ and $n$ are two coprime integers.

Regular Poles For The P-Adic Group $Gsp_4$-Ii, Yusuf Danişman

Turkish Journal of Mathematics

We compute the regular poles of the L-factors of the admissible and irreducible representations of the group $GSp_4$, which admit a nonsplit Bessel functional and have a Jacquet module length of 3 with respect to the unipotent radical of the Siegel parabolic, over a non-Archimedean local field of odd characteristic. We also compute the $L$-factors of the generic representations of $GSp_4$.

Od-Characterization Of Some Alternating Groups, Shitian Liu

Turkish Journal of Mathematics

Let $G$ be a finite group. Moghaddamfar et al. defined prime graph $\Gamma(G)$ of group $G$ as follows. The vertices of $\Gamma(G)$ are the primes dividing the order of $G$ and two distinct vertices $p,q$ are joined by an edge, denoted by $p\sim q$, if there is an element in $G$ of order $pq$. Assume $ G =p_{1}^{\alpha_{1}}\cdots p_{k}^{\alpha_{k}}$ with $P_{1}$ <$\cdots$&\lt;$p_{k}$ and nature numbers $\alpha_{i}$ with $i=1,2,\cdots,k$. For $p\in\pi(G)$, let the degree of $p$ be $\deg(p)= \{q\in\pi(G)\mid q\sim p\} $, and $D(G)=(\deg(p_{1}), \deg(p_{2}), \cdots, \deg(p_{k}))$. Denote by $\pi(G)$ the set of prime divisor of $ G $. Let $GK(G)$ be the graph with vertex set $\pi(G)$ such that two primes $p$ and $q$ in $\pi(G)$ are joined by an edge if $G$ has an element of order $p\cdot q$. We set $s(G)$ to denote the number of connected components of the prime graph $GK(G)$. Some authors proved some groups are $OD$-characterizable with $s(G)\geq2$. Then for $s(G)=1$, what is the influence of $OD$ on the structure of groups? We knew that the alternating groups $A_{p+3}$, where $7\neq p\in\pi(100!)$, $A_{130}$ and $A_{140}$ are $OD$-characterizable. Therefore, we naturally ask the following question: if $s(G)=1$, then is there a group $OD$-characterizable? In this note, we give a characterization of $A_{p+3}$ except $A_{10}$ with $s(A_{p+3})=1$, by $OD$, which gives a positive answer to Moghaddamfar and Rahbariyan's conjecture.

Characterizing Rational Groups Whose Irreducible Characters Vanish Only On Involutions, Saeed Jafari, Hesam Sharifi

Turkish Journal of Mathematics

A rational group is a finite group whose irreducible complex characters are rational valued. The aim of this paper is to classify rational groups $G$ for which every nonlinear irreducible character vanishes only on involutions.

Groups With The Given Set Of The Lengths Of Conjugacy Classes, Neda Ahanjideh

Turkish Journal of Mathematics

We study the structures of some finite groups such that the conjugacy class size of every noncentral element of them is divisible by a prime $p$.

The Prime Tournaments $T$ With $\Mid\! W_{5}(T) \!\Mid = \Mid\! T \!\Mid -2$, Houmem Belkhechine, Imed Boudabbous, Kaouthar Hzami

Turkish Journal of Mathematics

We consider a tournament $T=(V, A)$. For $X\subseteq V$, the subtournament of $T$ induced by $X$ is $T[X] = (X, A \cap (X \times X))$. A module of $T$ is a subset $X$ of $V$ such that for $a, b\in X$ and $ x\in V\setminus X$, $(a,x)\in A$ if and only if $(b,x)\in A$. The trivial modules of $T$ are $\emptyset$, $\{x\}(x\in V)$, and $V$. A tournament is prime if all its modules are trivial. For $n\geq 2$, $W_{2n+1}$ denotes the unique prime tournament defined on $\{0,\dots,2n\}$ such that $W_{2n+1}[\{0,\dots,2n-1\}]$ is the usual total order. Given a prime tournament $T$, …