Mathematics Commons^™

On Some Results On Ip-Graphs, Roghayeh Hafezieh, Moohammadali Iranmanesh

Turkish Journal of Mathematics

The IP-graph of a naturally valenced association scheme and some of its properties have been studied recently. In this paper we introduce the bipartite version of this graph for a naturally valenced association scheme (X,S), denoted by BIP(S). We also investigate some of its properties.

On The Centroid Of Prime Semirings, Hasret Yazarli, Mehmet Ali̇ Öztürk

Turkish Journal of Mathematics

We define and study the extended centroid of a prime semiring. We show that the extended centroid is a semifield and give some properties of the centroid of a right multiplicatively cancellable prime semiring.

Math Department Newsletter, 2012-2013 (Year In Review), Mathematics Department

Mathematics Newsletter

No abstract provided.

Horizon Content Knowledge In The Work Of Teaching: A Focus On Planning, Nick Wasserman, Julianna Connelly Stockton

Mathematics Faculty Publications

Horizon content knowledge, one component of Ball et al.’s mathematical knowledge for teaching framework (e.g., Ball, Thames, & Phelps, 2008), has yet to reach adequate clarity and consensus in the field. Recently, various scholars have worked to further conceptualize and describe the mathematical horizon (e.g., Jakobsen, Thames & Ribeiro, 2013; Figueiras et al., 2011; Zazkis & Mamolo, 2011). In this communication, we identify some limitations in the ways such knowledge has thus far been described and offer an additional form of potential impact of horizon content knowledge on the work of teaching.

Eigenfunction Expansions Associated With The One-Dimensional Schrödinger Operator, Daphne Gilbert

Articles

We consider the form of eigenfunction expansions associated with the time-independent Schrödinger operator on the line, under the assumption that the limit point case holds at both of the infinite endpoints. It is well known that in this situation the multiplicity of the operator may be one or two, depending on properties of the potential function. Moreover, for values of the spectral parameter in the upper half complex plane, there exist Weyl solutions associated with the restrictions of the operator to the negative and positive half-lines respectively, together with corresponding Titchmarsh-Weyl functions.

Second Order Approximations In Sequential Point Estimation Of The Probability Of Zero In Poisson Distribution, Eisa Mahmoudi, Mohammad Hatami Kamin

Turkish Journal of Mathematics

In the analysis of the count data, the Poisson model becomes overtly restrictive in the case of over-dispersed or under-dispersed data. When count data are under-dispersed, specific models such as generalized linear models (GLM) are proposed. Other examples are the zero-inflated Poisson model (ZIP) and zero-truncated Poisson model (ZTP), which have been used in literature to deal with an excess or absence of zeros in count data. Thus having a knowledge of the probability of zeros and its estimation in Poisson distribution can be significant and useful. Some estimation problems with unknown parameter cannot attain minimum risk where the sample …

The Wright Message, 2013-2014, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- Around Wright Hall
-- New Faculty: C. Adam Feldhaus
-- 2013 - 2014 Tenure-Stream Faculty
-- Faculty Spotlight: Syed Kirmani
-- UNI on the March
-- The Litwiller Bequest: A Gift that Keeps on Giving
-- Retiring Faculty Member: Glenn Nelson
-- The Center for Teaching and Learning Mathematics
-- David & Lois Kail: Donor Spotlight
-- Addresses by Mathematics Faculty
-- Department of Mathematics Goes Digital
-- Alumni Spotlight: Slade Hovick & Sarah Miesner
-- Student Spotlight: Jesse Moeller, Katherine Pearce, & Adam Feller
-- The 2013 Math Shindig …

Two-Step Arithmetic Word Problems, Enrique Castro-Martínez, Antonio Frías-Zorilla

The Mathematics Enthusiast

This study uses the perspective of schemes to analyze characteristics of arithmetic word problems that can influence the process of translation from the verbal statement to an arithmetical representation. One characteristic that we have detected in the two-step word problems is the presence of one or two connections (nodes) in schemes that represent them, and this paper explores whether the number of nodes affects the activation of the associated schemas. With students from the 5th and 6th grades of elementary school (11 and 12 years of age), we analyze the written productions and would stress that the number of connections …

Trajectory Of A Problem: A Study In Teacher Training, Alain Kuzniak, Bernard Parzysz, Laurent Vivier

The Mathematics Enthusiast

Problems are frequently used in mathematics to introduce and convey new notions and skills. Hence, teachers transform and adjust those problems to their students' level. The present study focuses on this transformation process on the particular case of a geometric problem posed by two teacher educators in one French Institute for Teacher Training. The whole process is described as a trajectory of the problem through various institutions from training center to secondary school and back. Before presenting the notion of trajectory of the problem, some elements about a general theoretical frame which refers to didactics of mathematics are presented.

Primary School Teacher’S Noticing Of Students’ Mathematical Thinking In Problem Solving, Ceneida Fernández, Salvador Llinares, Julia Valls

The Mathematics Enthusiast

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

Tme Volume 10, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

On Discrete Analytic Functions: Products, Rational Functions, And Reproducing Kernels, Daniel Alpay, Palle Jorgensen, Ron Seager, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis.

Two-Coloring Cycles In Complete Graphs, Claire Djang

Honors Papers

Inspired by an investigation of Ramsey theory, this paper aims to clarify in further detail a number of results regarding the existence of monochromatic cycles in complete graphs whose edges are colored red or blue. The second half focuses on a proof given by Gyula Károlyi and Vera Rosta for the solution of all R(Cn,Ck).

Intersection Number Of Plane Curves, Margaret E. Nichols

Honors Papers

In algebraic geometry, seemingly geometric problems can be solved using algebraic techniques. Some of the most basic geometric objects we can study are polynomial curves in the plane. In this paper we focus on the intersections of two curves. We address both the number of times two curves intersect at a given point, counting multiplicity (whatever that means), and the total number of intersections of the curves, again counting multiplicity. The former is known as the intersection number of the curves at the point. This concept, although geometrically motivated, can be described in algebraic terms; it is this relationship which …

The Jormungand Climate Model, Christopher V. Rackauckas

Honors Papers

The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the …

Group Developed Weighing Matrices, K. T. Arasu, Jeffrey R. Hollon

Mathematics and Statistics Faculty Publications

A weighing matrix is a square matrix whose entries are 1, 0 or −1, such that the matrix times its transpose is some integer multiple of the identity matrix. We examine the case where these matrices are said to be devel- oped by an abelian group. Through a combination of extending previous results and by giving explicit constructions we will answer the question of existence for 318 such matrices of order and weight both below 100. At the end, we are left with 98 open cases out of a possible 1,022. Further, some of the new results provide insight into …

Recent Progress On Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason’s seminal paper [88] from 2007.

Some Remarks On Arslan’S 2011 Paper, Gholamhossein Hamedani, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

It is shown that the main theorem of Arslan’s paper (Theorem 2, 2011), as stated, is incorrect. Under additional conditions, we present a short proof of the corrected version of the theorem. We also give a proof of a theorem of Rao and Shanbhag (1991), employed by Arslan, without the use of the Kolmogorov Consistency Theorem.

Probability Inequalities For The Sum Of Random Variables When Sampling Without Replacement, Jeremy Becnel, Kent Riggs, Dean Young

Faculty Publications

Exponential-type upper bounds are formulated for the probability that the maximum of the partial sample sums of discrete random variables having finite equispaced support exceeds or differs from the population mean by a specified positive constant. The new inequalities extend the work of Serfling (1974). An example of the results are given to demonstrate their efficacy.

Generalized Derivations Of Prime Rings On Multilinear Polynomials With Annihilator Conditions, Nurcan Argaç, Çağri Demi̇r

Turkish Journal of Mathematics

Let K be a commutative ring with unity, R be a prime K-algebra with characteristic not 2, U be the right Utumi quotient ring of R, C the extended centroid of R, I a nonzero right ideal of R and a a fixed element of R. Let g be a generalized derivation of R and f(X_1,..., X_n) a multilinear polynomial over K. If ag(f(x_1,...,x_n))f(x_1,...,x_n)=0 for all x_1,...,x_n \in I, then one of the following holds: (1) aI=ag(I)=0; (2) g(x)=bx+[c,x] for all x\in R, where b,c\in U. In this case either [c,I]I=0=abI or aI=0=a(b+c)I; (3) [f(X_1,...,X_n),X_{n+1}]X_{n+2} is an identity for I.

On The Nilpotent Graph Of A Ring, Mohammad Javad Nikmehr, Soheila Khojasteh

Turkish Journal of Mathematics

Let R be a ring with unity. The nilpotent graph of R, denoted by \Gamma_N(R), is a graph with vertex set Z_N(R)^* = {0 \neq x \in R \mid xy \in N(R) for some 0 \neq y \in R}; and two distinct vertices x and y are adjacent if and only if xy \in N(R), where N(R) is the set of all nilpotent elements of R. Recently, it has been proved that if R is a left Artinian ring, then diam(\Gamma_N(R)) \leq 3. In this paper, we present a new proof for the above result, where R is a finite …

Complex Symplectic Geometry With Applications To Vector Differential Operators, Chuan Fu Yang

Turkish Journal of Mathematics

Let l(y) be a formally self-adjoint vector-valued differential expression of order n on an interval (a, \infty)(-\infty \leq a < \infty) with complex matrix-valued function coefficients and finite equal deficiency indices. In this paper, applying complex symplectic algebra, we give a reformulation for self-adjoint domains of the minimal operator associated with l(y) and classify them.

Global Existence, Decay And Blow Up Solutions For Coupled Nonlinear Wave Equations With Damping And Source Terms, Erhan Pi̇şki̇n, Necat Polat

Turkish Journal of Mathematics

We study the initial-boundary value problem for a system of nonlinear wave equations with nonlinear damping and source terms, in a bounded domain. The decay estimates of the energy function are established by using Nakao's inequality. The nonexistence of global solutions is discussed under some conditions on the given parameters.

L^P Solutions Of Infinite Time Interval Bsdes And The Corresponding G-Expectations And G-Martingales, Zhaojun Zong

Turkish Journal of Mathematics

In this paper we study the existence and uniqueness theorem for L^p (1

Boolean Partition Algebras, Joseph Anthony Van Name

USF Tampa Graduate Theses and Dissertations

A Boolean partition algebra is a pair $(B,F)$ where $B$ is a Boolean

algebra and $F$ is a filter on the semilattice of partitions of $B$ where $\bigcup F=B\setminus\{0\}$. In this dissertation, we shall investigate the algebraic theory of Boolean partition algebras and their connection with uniform spaces. In particular, we shall show that the category of complete non-Archimedean uniform spaces

is equivalent to a subcategory of the category of Boolean partition algebras, and notions such as supercompleteness

of non-Archimedean uniform spaces can be formulated in terms of Boolean partition algebras.

Analytic Functions With Real Boundary Values In Smirnov Classes EP, Lisa De Castro

USF Tampa Graduate Theses and Dissertations

This thesis concerns the classes of analytic functions on bounded, n-connected domains known as the Smirnov classes E^p, where p > 0. Functions in these classes satisfy a certain growth condition and have a relationship to the more well known classes of functions known as the Hardy classes H^p. In this thesis I will show how the geometry of a given domain will determine the existence of non-constant analytic functions in Smirnov classes that possess real boundary values. This is a phenomenon that does not occur among functions in the Hardy classes.

The preliminary and background information …

Topological Degree And Variational Inequality Theories For Pseudomonotone Perturbations Of Maximal Monotone Operators, Teffera Mekonnen Asfaw

USF Tampa Graduate Theses and Dissertations

Let X be a real reflexive locally uniformly convex

Banach space with locally uniformly convex dual space X^*

. Let G be a

bounded open subset of X. Let T:X⊃ D(T)⇒ 2X^*

be maximal

monotone and S: X ⇒ 2X^*

be bounded

pseudomonotone and such that 0 notin cl((T+S)(D(T)∩partG)). Chapter 1 gives general introduction and mathematical prerequisites. In

Chapter 2 we develop a homotopy invariance and uniqueness results for the degree theory constructed by Zhang and Chen for multivalued (S₊) perturbations of

maximal monotone operators. Chapter 3 is devoted to the construction of a new …

Modeling State Transitions With Automata, Egor Dolzhenko

USF Tampa Graduate Theses and Dissertations

Models based on various types of automata are ubiquitous in modern science. These models allow reasoning about deep theoretical questions and provide a basis for the development of efficient algorithms to solve related computational problems. This work discusses several types of automata used in such models, including cellular automata and mandatory results automata.

The first part of this work is dedicated to cellular automata. These automata form an important class of discrete dynamical systems widely used to model physical, biological, and chemical processes. Here we discuss a way to study the dynamics of one-dimensional cellular automata through the theory of …

A Study Of Permutation Polynomials Over Finite Fields, Neranga Fernando

USF Tampa Graduate Theses and Dissertations

Let p be a prime and q = p^k. The polynomial g_n,q isin F_p[x] defined by the functional equation Sigma_{a isin Fq} (x+a)ⁿ = g_n,q(x^q- x) gives rise to many permutation polynomials over finite fields. We are interested in triples (n,e;q) for which g_n,q is a permutation polynomial of F_q^e. In Chapters 2, 3, and 4 of this dissertation, we present many new families of permutation polynomials in the form of g_n,q. The permutation behavior of g_n,q is becoming increasingly more …

Mathematical Self-Efficacy: Addressing The Declining Interest In Engineering Careers, Eileen Goold

Conference Papers

This paper presents the findings of a study investigating whether there is a relationship between students’ experiences with school mathematics and their choice of engineering as a career. The study was inspired by the observation that there is a lacuna in the scholarly literature concerning the nature of mathematics’ role, if any, as a significant cause of the declining number of students entering professional engineering courses. The population of interest in this study comprises professional engineers practising in Ireland. Engineers’ experiences of school mathematics, factors that contributed to their engagement with school mathematics and the impact of their feelings about …