Mathematics Commons^™

The Wright Message, 2016-2017, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Alumni and Friends
-- A Tribute for Karen Sabey
-- The 2016 Hari Shankar Lecture
-- Faculty Spotlight
-- Around Wright Hall
-- Alumni Spotlight
-- CTLM News
-- Interview with Allysen Lovstuen
-- Students Spotlight
-- Donor Spotlight
-- Contributions to an Account - Recognition
-- Department Funds

1. Measuring Speed, Ruth Dover

More on Derivatives

Tables of values to measure rates.

Series 05, Ruth Dover

Series

Popular Maclaurin series and using substitution to create new series.

1. Coffee, Ruth Dover

Differential Equations

Newton’s Law of Cooling.

Series 06, Ruth Dover

Series

More manipulation of series – substitution, differentiation, and integration.

Series 02, Ruth Dover

Series

Repeats Series01 with the function y = arctanx.

Alternating Series 1, Ruth Dover

Series

Partial sums of alternating series.

Taylor Review, Ruth Dover

Series

Assorted problems.

Approximations 2, Ruth Dover

Integrals

Drawing rectangles and calculating Riemann sums.

Series 09, Ruth Dover

Series

Practice using series to evaluate limits and definite integrals.

Limits3, Ruth Dover

Limits

Algebraic techniques for functions with holes.

Rate Of Change 1, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

4. Integral Test For Series, Ruth Dover

Series

Relating Riemann sums and series – requiring a lot of teacher help!

Approximations 1, Ruth Dover

Integrals

Measuring distance and accumulation.

Real-Time Translation Of American Sign Language Using Wearable Technology, Jackson Taylor

Honors Theses

The goal of this work is to implement a real-time system using wearable technology for translating American Sign Language (ASL) gestures into audible form. This system could be used to facilitate conversations between individuals who do and do not communicate using ASL. We use as our source of input the Myo armband, an affordable commercially-available wearable technology equipped with on-board accelerometer, gyroscope, and electromyography sensors. We investigate the performance of two different classification algorithms in this context: linear discriminant analysis and k-Nearest Neighbors (k-NN) using various distance metrics. Using the k-NN classifier and windowed dynamic time …

Drawing Dna Sequence Networks, Julia Olivieri

Honors Papers

We explore methods for drawing a graph of DNA sequences on a digital canvas such that the Euclidean distances between sequences on the canvas suggest the distances between the sequences as calculated from pairwise sequence alignment. We use data from three plant taxa, the genus Castilleja as well as the families Caryophyllaceae and Cactaceae, to test our methods. We discuss different possible measures of the cost of a drawing, and analyze heuristic approaches to the problem including random assignment, greedy assignment, the iterated hill-climber, and simulated annealing. We find that our hill-climbing method tends to return superior drawings. Our simulated …

Development Of A Novel Fe Based Heterogeneous Catalyst For Co2 Conversion, Scott Bamonte

Discovery Day (formerly Post & Beyond)

Greenhouse gas emission has been a growing problem on the earth because of global warming and pollution of our air. The primary objective of this project is to develop a novel Fe based heterogeneous catalyst to enhance the catalytic conversion of CO2 by H2 for the synthesis of value added chemicals such as CO, methanol and fuels. We are focusing on iron for this catalyst because iron is one of the most abundant elements in the world and is very cheap making it optimal for catalyst use. The Fe-based solution we developed can be tuned to be either acidic or …

The Von Neumann Inequality For 3 × 3 Matrices, Greg Knese

Mathematics Faculty Research

This note details how recent work of Kosiński on the three point Pick interpolation problem on the polydisc can be used to prove the von Neumann inequality for d-tuples of commuting 3 x 3 contractive matrices.

Canonical Agler Decompositions And Transfer Function Realizations, Kelly Bickel, Greg Knese

Mathematics Faculty Research

A seminal result of Agler proves that the natural de Branges-Rovnyak kernel function associated to a bounded analytic function on the bidisk can be decomposed into two shift-invariant pieces. Agler's decomposition is non-constructive—a problem remedied by work of Ball-Sadosky-Vinnikov, which uses scattering systems to produce Agler decompositions through concrete Hilbert space geometry. This method, while constructive, so far has not revealed the rich structure shown to be present for special classes of functions--inner and rational inner functions. In this paper, we show that most of the important structure present in these special cases extends to general bounded analytic functions. We …

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.

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.

The Reversibility Problem For A Family Of Two-Dimensional Cellular Automata, Mehmet Emi̇n Köroğlu, İrfan Şi̇ap, Hasan Akin

Turkish Journal of Mathematics

In this paper the reversibility problem of a family of two-dimensional cellular automata is completely resolved. It is well known that the reversibility problem is a very difficult one in general. In order to determine whether a cellular automaton is reversible or not the reversibility of its rule matrix is studied via linear algebraic tools. However, in this particular study the authors consider a novel approach. By observing the algebraic structures of rule matrices that represent these families and associating them with polynomials in two variables in a quotient ring, the solution to the reversibility problem is simplified greatly. Hence, …

Analyzing Unique-Matching Games Using Elementary Mathematics, Calvin Jongsma, Tom Clark

Faculty Work Comprehensive List

We present here an analysis of the game of Spot It! that can be used as background information for the purpose of leading a math circle around the game. The presentation here follows the progression of solving the puzzle for simple cases first and culminating in the solution of the original game.

Challenges In Developing Applications For Aging Populations, Drew Marie Williams, Md O. Gani, Ivor D. Addo, Akm Jahangir Alam Majumder, Chandana Tamma, Mong-Te Wang, Chih-Hung Chang, Sheikh Iqbal Ahamed, Cheng-Chung Chu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Elderly individuals can greatly benefit from the use of computer applications, which can assist in monitoring health conditions, staying in contact with friends and family, and even learning new things. However, developing accessible applications for an elderly user can be a daunting task for developers. Since the advent of the personal computer, the benefits and challenges of developing applications for older adults have been a hot topic of discussion. In this chapter, the authors discuss the various challenges developers who wish to create applications for the elderly computer user face, including age-related impairments, generational differences in computer use, and the …

Nuclear Space Facts, Strange And Plain, Jeremy Becnel, Ambar Sengupta

Faculty Publications

We present a scenic but practical guide through nuclear spaces and their dual spaces, examining useful, unexpected, and often unfamiliar results both for nuclear spaces and their strong and weak duals.

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.

Induced Subgraph Saturated Graphs, Craig M. Tennenhouse

Theory & Applications of Graphs

A graph G is said to be H-saturated if G contains no subgraph isomorphic to H but the addition of any edge between non-adjacent vertices in G creates one. While induced subgraphs are often studied in the extremal case with regard to the removal of edges, we extend saturation to induced subgraphs. We say that G is induced H-saturated if G contains no induced subgraph isomorphic to H and the addition of any edge to G results in an induced copy of H. We demonstrate constructively that there are non-trivial examples of saturated graphs for …

On Minimum Spanning Subgraphs Of Graphs With Proper Connection Number 2, Zhenming Bi, Gary Chartrand, Garry L. Johns, Ping Zhang

Theory & Applications of Graphs

An edge coloring of a connected graph G is a proper-path coloring if every two vertices of G are connected by a properly colored path. The minimum number of colors required of a proper-path coloring of G is called the proper connection number pc(G) of G. For a connected graph G with proper connection number 2, the minimum size of a connected spanning subgraph H of G with pc(H) = 2 is denoted by μ(G). It is shown that if s and t are integers such that t ≥ s + 2 ≥ 5 …

Generalized Bertrand Curves With Spacelike $\Left(1,3\Right) $-Normal Plane In Minkowski Space-Time, Ali̇ Uçum, Osman Keçi̇li̇oğlu, Kazim İlarslan

Turkish Journal of Mathematics

In this paper, we reconsider the $(1,3)$-Bertrand curves with respect to the casual characters of a $\left( 1,3\right) $-normal plane that is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of $(1,3)$-Bertrand curves to the spacelike $\left( 1,3\right) $-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with spacelike $\left( 1,3\right) $-normal plane to be $(1,3)$-Bertrand curves and we give the related examples for these curves.

Anti-Invariant Riemannian Submersions From Kenmotsu Manifolds Onto Riemannian Manifolds, Ayşe Beri̇, İrem Küpeli̇ Erken, Cengi̇zhan Murathan

Turkish Journal of Mathematics

The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved the nonexistence of (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that the characteristic vector field $\xi $ is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic vector field $\xi $ …