Mathematics Commons^™

On Hall Magnetohydrodynamics: X-Type Neutral Point And Parker Problem, Kyle Reger

Electronic Theses and Dissertations

The framework for the Hall magnetohydrodynamic (MHD) model for plasma physics is built up from kinetic theory and used to analytically solve problems of interest in the field. The Hall MHD model describes fast magnetic reconnection processes in space and laboratory plasmas. Specifically, the magnetic reconnection process at an X-type neutral point, where current sheets form and store enormous amounts of magnetic energy which is later released as magnetic storms when the sheets break up, is investigated. The phenomena of magnetic flux pile-up driving the merging of antiparallel magnetic fields at an ion stagnation-point flow in a thin current sheet, …

Improving Student Learning In Undergraduate Mathematics, Gabrielle Rejniak

Electronic Theses and Dissertations

The goal of this study was to investigate ways of improving student learning, par- ticularly conceptual understanding, in undergraduate mathematics courses. This study focused on two areas: course design and animation. The methods of study were the following: Assessing the improvement of student conceptual understanding as a result of team project-based learning, individual inquiry-based learning and the modi ed empo- rium model; and Assessing the impact of animated videos on student learning with the emphasis on concepts. For the first part of our study (impact of course design on student conceptual understanding) we began by comparing the following three groups …

Assessing Impulsive-Analytic Disposition: The Likelihood-To-Act Survey And Other Instruments, Kien H. Lim, Amy E. Wagler

Departmental Papers (Math)

The likelihood-to-act (LtA) survey is a 32-item instrument that measures impulsive and analytic dispositions in solving math problems. In this research report, we compare it to other instruments related to the impulsive-analytic construct such as Frederick’s Cognitive Reflection Test (CRT) and the Barratt Impulsive Scale in terms of mean scores, Cronbach alpha values, and correlation values. Both LtA-Impulsive and LtA-Analytic subscales have acceptable reliabilities of 0.79 and 0.83 respectively. The LtA-Analytic and LtA-Difference (analytic-impulsive difference) correlated well with other the Need for Cognition subscale and CRT scores. The correlations involving LtA-Impulsive subscale were unexpected and call for further investigation.

Impulsive-Analytic Disposition In Mathematical Problem Solving: A Survey And A Mathematics Test, Kien H. Lim, Amy E. Wagler

Departmental Papers (Math)

The Likelihood-to-Act (LtA) survey and a mathematics test were used in this study to assess students’ impulsive-analytic disposition in the context of mathematical problem solving. The results obtained from these two instruments were compared to those obtained using two widely-used scales: Need for Cognition (NFC) and Barratt Impulsivity Scale (BIS). The exhibited correlations of the LtA scores with the NFC, BIS, and a math test provide evidence of the criterion validity of the analytic LtA items, and suggests further revision of the impulsive LtA items to improve the overall measurement validity of the LtA scale. Students LtA scores were found …

The Hammer-And-Nail Phenomenon In Mathematics Education, Kien H. Lim

Departmental Papers (Math)

"For a person with a hammer, everything looks like a nail" is a proverb that can be used to highlight the phenomenon that students tend to rely on familiar ideas as opposed to taking time to think about and analyse a problem. Presented in this theoretical paper is the usefulness of the hammer-and-nail metaphor, other related theoretical constructs, pedagogical causes of student impulsive behaviours, and pedagogical suggestions for addressing them.

Nonresonance On The Boundary And Strong Solutions Of Elliptic Equations With Nonlinear Boundary Conditions, Nsoki Mavinga, M. N. Nkashama

Mathematics & Statistics Faculty Works

We deal with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions by imposing asymptotic nonresonance conditions of nonuniform type with respect to the Steklov spectrum on the boundary nonlinearity. Unlike some recent approaches in the literature for problems with nonlinear boundary conditions, we cast the problem in terms of nonlinear compact perturbations of the identity on appropriate trace spaces in order to prove the existence of strong solutions. The proofs are based on a priori estimates for possible solutions to a homotopy on suitable trace spaces and topological degree arguments.

Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part I, Carol Jacoby, Katrin Leistner, Peter Loth, Lutz Strungmann

Mathematics Faculty Publications

We consider the class of abelian groups possessing partial decomposition bases in L^δ_∞ω for δ an ordinal. This class contains the class of Warfield groups which are direct summands of simply presented groups or, alternatively, are abelian groups possessing a nice decomposition basis with simply presented cokernel. We prove a classification theorem using numerical invariants that are deduced from the classical Ulm-Kaplansky and Warfield invariants. This extends earlier work by Barwise-Eklof, Göbel and the authors.

Capability Of 2 Gait Measures For Detecting Response To Gait Training In Stroke Survivors: Gait Assessment And Intervention Tool And The Tinetti Gait Scale, Janice Zimbelman, Janis J. Daly, Kristen L. Roenigk, Kristi Butler, Richard Burdsall, John P. Holcomb Jr.

Mathematics and Statistics Faculty Publications

Zimbelman J, Daly JJ, Roenigk KL, Butler K, Burdsall R, Holcomb JP. Capability of 2 gait measures for detecting response to gait training in stroke survivors: Gait Assessment and Intervention Tool and the Tinetti Gait Scale. Objective:To characterize the performance of 2 observational gait measures, the Tinetti Gait Scale (TGS) and the Gait Assessment and Intervention Tool (G.A.I.T.), in identifying improvement in gait in response to gait training. Design: In secondary analysis from a larger study of multimodal gait training for stroke survivors, we measured gait at pre-, mid-, and posttreatment according to G.A.I.T. and TGS, assessing their capability to …

A Kinetic Model For Semidilute Bacterial Suspensions, Shawn D. Ryan, Leonid Berlyand, Brian M. Haines, D. A. Karpeev

Mathematics and Statistics Faculty Publications

Suspensions of self-propelled microscopic particles, such as swimming bacteria, exhibit collective motion leading to remarkable experimentally observable macroscopic properties. Rigorous mathematical analysis of this emergent behavior can provide significant insight into the mechanisms behind these experimental observations; however, there are many theoretical questions remaining unanswered. In this paper, we study a coupled PDE/ODE system first introduced in the physics literature and used to investigate numerically the effective viscosity of a bacterial suspension. We then examine the kinetic theory associated with the coupled system, which is designed to capture the long-time behavior of a Stokesian suspension of point force dipoles (infinitesimal …

A Locking-Free Hp Dpg Method For Linear Elasticity With Symmetric Stresses, Jamie Bramwell, Leszek Demkowicz, Jay Gopalakrishnan, Weifeng Qiu

Mathematics and Statistics Faculty Publications and Presentations

We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov- Galerkin (DPG) framework. In this framework, both the stress and the displacement ap- proximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.

Mixed Finite Element Approximation Of The Vector Laplacian With Dirichlet Boundary Conditions, Douglas N. Arnold, Richard S. Falk, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

We consider the finite element solution of the vector Laplace equation on a domain in two dimensions. For various choices of boundary conditions, it is known that a mixed finite element method, in which the rotation of the solution is introduced as a second unknown, is advantageous, and appropriate choices of mixed finite element spaces lead to a stable, optimally convergent discretization. However, the theory that leads to these conclusions does not apply to the case of Dirichlet boundary conditions, in which both components of the solution vanish on the boundary. We show, by computational example, that indeed such mixed …

A Class Of Discontinuous Petrov–Galerkin Methods. Part Iii: Adaptivity, Leszek Demkowicz, Jay Gopalakrishnan, Antti H. Niemi

Mathematics and Statistics Faculty Publications and Presentations

We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: for 1D and for 2D problems. The adaptive process is fully automatic and starts …

Integrable Models For Shallow Water With Energy Dependent Spectral Problems, Rossen Ivanov, Tony Lyons

Articles

We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependence on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup–Boussinesq equation. We formulate the inverse problem as a Riemann–Hilbert problem with a Z₂ reduction group. The soliton solutions are explicitly obtained.

Product Of Graded Submodules, Ameer Jaber

Turkish Journal of Mathematics

Let \Delta be an abelian group. By considering the notion multiplication of \Delta-graded modules (see [7]) over a commutative \Delta-graded ring with unity, we introduce the notion of product of two \Delta-graded submodules which we use to characterize the \Delta-graded prime submodules of a multiplication \Delta-graded module. Finally we proved a graded version of Nakayama lemma for multiplication \Delta-graded modules.

Banach Limit And Some New Spaces Of Double Sequences, Mohammad Mursaleen, Syed Abdul Mohiuddine

Turkish Journal of Mathematics

In this paper, we define and study the Banach limit for double sequences and introduce some new spaces related to the concept of almost and strong almost convergence for double sequences. We characterize these spaces through some sublinear functionals and we also establish some inclusion relations.

On Some New Inequalities For Convex Functions, Mevlüt Tunç

Turkish Journal of Mathematics

In the present paper we establish some new integral inequalities analogous to the well known Hadamard's inequality by using a fairly elementary analysis.

The Wright Message, 2012-2013, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- Department Head
-- Around Wright Hall
-- 2012 - 2013 Tenure-Stream Faculty
-- New Faculty
-- Retiring Faculty: Larry Leutzinger
-- In Memory of Bonnie Litwiller
-- John & Marla Peterson: Making an Impact
-- The 2012 Hari Shankar Lecture
-- Internal UNI Awards
-- Projects and Grants
-- Student Spotlight: Melinda McDowell & Duncan Wright
-- Recent winners of the Purple and Old Gold Award
-- Alumni Spotlight: Karla Digmann, Kamilla Svajgl, & Suzanne Shontz
-- Math Day 2012
-- Squigonometry
-- Student Organizations
-- News from KME
-- …

Permutation Notations For The Exceptional Weyl Group F4, Patricia Cahn, Ruth Haas, Aloysius G. Helminck, Juan Li, Jeremy Schwartz

Mathematics Sciences: Faculty Publications

This paper describes a permutation notation for the Weyl groups of type F4 and G2. The image in the permutation group is presented as well as an analysis of the structure of the group. This description enables faster computations in these Weyl groups which will prove useful for a variety of applications.

A New Qcd Effect: The Shrinking Radius Of Hadrons, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We propose an extended schematic model for hadrons in which quarks as well as diquarks serve as building blocks. The outcome is a reclassification of the hadron spectrum in which there are no radially excited hadrons: all mesons and baryons previously believed to be radial excitations are orbitally excited states involving diquarks. Also, there are no exotic hadrons: all hadrons previously believed to be exotic are states involving diquarks and are an integral part of the model. We discuss the implications of this result for a new understanding of confinement and its relation to asymptotic freedom, as well as its …

An Epidemiological Model Of Rift Valley Fever With Spatial Dynamics, Tianchan Niu, Holly D. Gaff, Yiannis E. Papelis, David M. Hartley

Biological Sciences Faculty Publications

As a category A agent in the Center for Disease Control bioterrorism list, Rift Valley fever (RVF) is considered a major threat to the United States (USA). Should the pathogen be intentionally or unintentionally introduced to the continental USA, there is tremendous potential for economic damages due to loss of livestock, trade restrictions, and subsequent food supply chain disruptions. We have incorporated the effects of space into a mathematical model of RVF in order to study the dynamics of the pathogen spread as affected by the movement of humans, livestock, and mosquitoes. The model accounts for the horizontal transmission of …