Mathematics Commons^™

Situating Sotl Within The Disciplines: Mathematics In The United States As A Case Study, Jacqueline Dewar, Curtis Bennett

Mathematics, Statistics and Data Science Faculty Works

After two decades of work, many in the SoTL community are pondering the future of the SoTL movement. Will it sustain its influence? Will it continue to attract new participants? What role should the disciplines play? From the perspective of mathematics, this paper examines efforts by the Carnegie Academy and individuals within the mathematical community to build disciplinary support for the scholarship of teaching and learning. The authors, both mathematicians and Carnegie scholars, restrict their observations to the efforts undertaken in the United States during the last decade and examine the situation in mathematics in greater depth than has heretofore …

On The Construction Of Explicit Solutions To The Matrix Equation X2ax = Axa, Ed Mosteig, Aihua Li

Mathematics, Statistics and Data Science Faculty Works

In a previous article by Aihua Li and Duane Randall, the existence of solutions to certain matrix equations is demonstrated via nonconstructive methods. A recurring example appears in that work, namely the matrix equation AXA=X2AX, where A is a fixed, square matrix with real entries and X is an unknown square matrix. In this paper, the solution space is explicitly constructed for all 2×2 complex matrices using Gr ̈obner basis techniques. When A is a 2×2 matrix, the equation AXA=X2AXis equivalent to a system of four polynomial equations. The solution space then is the variety defined by the polynomials involved. …

Derived Categories And The Analytic Approach To General Reciprocity Laws. Part Iii, Michael Berg

Mathematics, Statistics and Data Science Faculty Works

Building on the scaffolding constructed in the first two articles in this series, we now proceed to the geometric phase of our sheaf (-complex) theoretic quasidualization of Kubota's formalism for n-Hilbert reciprocity. Employing recent work by Bridgeland on stability conditions, we extend our yoga of t-structures situated above diagrams of specifically designed derived categories to arrangements of metric spaces or complex manifolds. This prepares the way for proving n-Hilbert reciprocity by means of singularity analysis.

Epimorphisms And Boundary Slopes Of 2–Bridge Knots, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

In this article we study a partial ordering on knots in S³ where K₁≥K₂ if there is an epimorphism from the knot group of K₁ onto the knot group of K₂ which preserves peripheral structure. If K₁ is a 2–bridge knot and K₁≥K₂, then it is known that K₂ must also be 2–bridge. Furthermore, Ohtsuki, Riley and Sakuma give a construction which, for a given 2–bridge knot K_p∕q, produces infinitely many 2–bridge knots K_p′/q′ with K_p′∕q′≥K_p∕q. After characterizing all 2–bridge knots …

Spark-Induced Sparks As A Mechanism Of Intracellular Calcium Alternans In Cardiac Myocytes, Robert J. Rovetti, Xiaohua Cui, Alan Garfinkel, James N. Weiss, Zhilin Qu

Mathematics, Statistics and Data Science Faculty Works

Rationale: Intracellular calcium (Ca) alternans has been widely studied in cardiac myocytes and tissue, yet the underlying mechanism remains controversial.

Objective: In this study, we used computational modeling and simulation to study how randomly occurring Ca sparks interact collectively to result in whole-cell Ca alternans.

Methods and Results: We developed a spatially-distributed intracellular Ca cycling model in which Ca release units (CRUs) are locally coupled by Ca diffusion throughout the myoplasm and sarcoplasmic reticulum (SR) network. Ca sparks occur randomly in the CRU network when periodically paced with a clamped voltage waveform, but Ca alternans develops as the pacing speeds …

Investigating Mathematical Literacy Through Teacher Language, Alyson Lischka

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Communication about mathematical concepts using appropriate terminology is a standard established by the National Council of Teachers of Mathematics. However, international test results show that United States’ students are lagging in mathematical literacy. This case study analyzes the ways in which instructors use language to help students move toward conceptual understanding of mathematical vocabulary. Three mathematics education professors at a mid-size four year institution were observed teaching math classes to students enrolled in elementary or secondary certification programs. Collected data included: audio-recorded observations and field notes, lesson artifacts such as quizzes and handouts, and audio-recorded interviews with each participant. Findings …

Evolving Models: A Density-Based Approach To Modeling Sexual Dimorphism And Adaptive Speciation, Audrey Smith

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

In this paper, we begin by extending existing deterministic and individual-based ecological models for sexual dimorphism and adaptive speciation into density-based mathematical models describing the density or number of individuals with various trait values, or phenotypes. These density-based models describe the dynamics of a population of males and females using both clonal and sexual reproduction. Each generation, the populations are subject to mating, mutation, and ecological dynamics including infraspecific competition and carrying capacity of the environment. By avoiding individual-based models, we are able to avoid simulations and instead achieve repeatable results.

Implementing these models numerically, we are able to show …

Numerical Solution Of The Five-Moment Ideal Two-Fluid Equations In One Dimension, Marcus Scott

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

Plasmas are frequently treated as a single conducting fluid and modeled using the equations of magnetohydrodynamics. However, this regime works better for low-frequency plasmas. High-frequency plasmas may be modeled using the principles of kinetic theory. For plasmas with frequencies between these two extremes, a two-fluid approach can yield better results. In 2006, Ammar Hakim mathematically modeled a plasma with a set of equations called the five-moment ideal two-fluid equations. An attempt is made reproduce those results. A derivation of this set of equations by taking moments of the Boltzmann equation is presented. Electric and magnetic fields contribute to the source …

Assessment Of Utah Bankruptcies By Census Tracts: A Spatial Statistical Approach, Kenneth Pena

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

There are two questions raised when looking at the spatial pattern of the rate of bankruptcies in Utah: (i) are there similarities between the bankruptcy data in adjacent census tracts and (ii) can local cluster and outliers be identified within the data? Specifically, are there similar rates of bankruptcies in bordering census tracts and are there any localized areas of interest where we find extremely high or extremely low rates of bankruptcies? This study uses spatial statistics to perform tests for spatial autocorrelation to address these two questions. It also looks at commonalities in the clusters and differences in the …

Weighted Inverse Weibull And Beta-Inverse Weibull Distribution, Jing Xiong Kersey

College of Graduate Studies: Theses & Dissertations

The weighted inverse Weibull distribution and the beta-inverse Weibull distribution are considered. Theoretical properties of the inverse Weibull model, weighted inverse Weibull distribution including the hazard function, reverse hazard function, moments, moment generating function, coefficient of variation, coefficient of skewness, coefficient of kurtosis, Fisher information and Shanon entropy are studied. The estimation for the parameters of the length-biased inverse Weibull distribution via maximum likelihood estimation and method of moment estimation techniques are presented, as well as a test for the detection of length-biasedness in the inverse Weibull model. Furthermore, the beta-inverse Weibull distribution which is a weighted distribution is presented, …

Using Mathematics As A Gateway To Literacy For English Language Learners, Krista Hemphill

Honors Program Theses

One teaching approach that alleviates language barriers involves teachers using what students know and can do to develop students‟ understanding of and ability in another area. Thus, 2 teachers can promote ELLs‟ literacy development by integrating knowledge and skills ELLs have from another subject area into their literacy instruction. Specifically, teachers can integrate mathematics into literacy instruction because research suggests that ELLs often understand and successfully carry out mathematical tasks. For example, Gunning (2003) points out that ELLs tend to perform well on mathematical computations. The universality of mathematical symbols seems to promote ELLs‟ understanding of mathematics instruction although lessons …

Numerical Computations For Pde Models Of Rocket Exhaust Flow In Soil, Brian Brennan

Electronic Theses and Dissertations

We study numerical methods for solving the nonlinear porous medium and Navier-Lame problems. When coupled together, these equations model the flow of exhaust through a porous medium, soil, and the effects that the pressure has on the soil in terms of spatial displacement. For the porous medium equation we use the Crank-Nicolson time stepping method with a spectral discretization in space. Since the Navier-Lame equation is a boundary value problem, it is solved using a finite element method where the spatial domain is represented by a triangulation of discrete points. The two problems are coupled by using approximations of solutions …

Initial-Value Technique For Singularly Perturbed Two Point Boundary Value Problems Via Cubic Spline, Luis G. Negron

Electronic Theses and Dissertations

A recent method for solving singular perturbation problems is examined. It is designed for the applied mathematician or engineer who needs a convenient, useful tool that requires little preparation and can be readily implemented using little more than an industry-standard software package for spreadsheets. In this paper, we shall examine singularly perturbed two point boundary value problems with the boundary layer at one end point. An initial-value technique is used for its solution by replacing the problem with an asymptotically equivalent first order problem, which is, in turn, solved as an initial value problem by using cubic splines. Numerical examples …

Detection And Approximation Of Function Of Two Variables In High Dimensions, Minzhe Pan

Electronic Theses and Dissertations

This thesis originates from the deterministic algorithm of DeVore, Petrova, and Wojtaszcsyk for the detection and approximation of functions of one variable in high dimensions. We propose a deterministic algorithm for the detection and approximation of function of two variables in high dimensions.

Inverse Limits With Upper Semi-Continuous Set Valued Bonding Functions: An Example, Christopher David Jacobsen

Masters Theses

"While there is a wealth of information pertaining to inverse limits with single valued bonding maps, comparatively little is known about inverse limits with upper semi-continuous set valued bonding functions. In order to add somewhat to the communal knowledge on the subject, this paper provides an example of an inverse limit with a single upper semi-continuous set valued bonding function. It is then shown that the space is a continuum, and its structure is examined via its arc components and through various of its properties, such as dimension and decomposability"--Abstract, page iii.

Warped Product Semi-Slant Submanifolds In Kenmotsu Manifolds, Mehmet Atçeken

Turkish Journal of Mathematics

In this paper, we research the existence or non-existence of warped product semi-slant submanifolds in Kenmotsu manifolds. Consequently, we see that there are no proper warped product semi-slant submanifolds in Kenmotsu manifolds such that totally geodesic and totally umbilical submanifolds of warped product are proper semi-slant and invariant (or anti-invariant), respectively.

On Weakly M-Supplemented Primary Subgroups Of Finite Groups, Long Miao, Wolfgang Lempken

Turkish Journal of Mathematics

A subgroup H of a group G is said to be weakly M-supplemented in G if there exists a subgroup B of G provided that (1) G=HB, and (2) if H_1/H_G is a maximal subgroup of H/H_G, then H_1B=BH_1

Statistical Convergence Of Max-Product Approximating Operators, Oktay Duman

Turkish Journal of Mathematics

In this study, using the notion of statistical convergence, we obtain various statistical approximation theorems for a general sequence of max-product approximating operators, including Shepard type operators, although its classical limit fails. We also compute the corresponding statistical rates of the approximation.

Transversal Lightlike Submanifolds Of Indefinite Sasakian Manifolds, Cumali̇ Yildirim, Bayram Şahi̇n

Turkish Journal of Mathematics

We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical transversal lightlike submanifolds.

Chaos In Product Maps, Nedi̇m Deği̇rmenci̇, Şahi̇n Koçak

Turkish Journal of Mathematics

We discuss how chaos conditions on maps carry over to their products. First we give a counterexample showing that the pro\-duct of two chaotic maps (in the sense of Devaney) need not be chaotic. We then remark that if two maps (or even one of them) exhibit sensitive dependence on initial conditions, so does their product; likewise, if two maps possess dense periodic points, so does their product. On the other side, the product of two topologically transitive maps need not be topologically transitive. We then give sufficient conditions under which the product of two chaotic maps is chaotic in …

Characterizations Of Slant Helices In Euclidean 3-Space, Levent Kula, Nejat Ekmekci̇, Yusuf Yayli, Kazim İlarslan

Turkish Journal of Mathematics

In this paper we investigate the relations between a general helix and a slant helix. Moreover, we obtain some differential equations which they are characterizations for a space curve to be a slant helix. Also, we obtain the slant helix equations and its Frenet aparatus.

Finite Subquandles Of Sphere, Nüli̇fer Özdemi̇r, Hüseyi̇n Azcan

Turkish Journal of Mathematics

In this work finite subquandles of sphere are classified by using classification of subgroups of orthogonal group O(3). For any subquandle Q of sphere there is a subgroup G_Q of O(3) associated with Q. It is shown that if Q is a finite (infinite) subquandle, then G_Q is a finite (infinite) subgroup. Finite subquandles of sphere are obtained from actions of finite subgroups of SO(3) on sphere. It is proved that the finite subquandles Q_1 and Q_2 of sphere whose all elements are not on the same great circle are isomorphic if and only if the subgroups G_{Q_1} and G_{Q_2} …

On The Codifferential Of The Kähler Form And Cosymplectic Metrics On Maximal Flag Manifolds, Marlio Paredes, Sofia Pinzon

Turkish Journal of Mathematics

Using moving frames we obtain a formula to calculate the codifferential of the Kähler form on a maximal flag manifold. We use this formula to obtain some differential type conditions so that a metric on the classical maximal flag manifold be cosymplectic.

Traveling Wavefronts In A Single Species Model With Nonlocal Diffusion And Age-Structure, Xue-Shi Li, Guo Lin

Turkish Journal of Mathematics

This paper is concerned with the existence of monotone traveling wavefronts in a single species model with nonlocal diffusion and age-structure. We first apply upper and lower solution technique to prove the result if the wave speed is larger than a threshold depending only on the basic parameters. When the wave speed equals to the threshold, we show the conclusion by passing to a limit function.

Notes On Null Curves In Minkowski Spaces, Makoto Sakaki

Turkish Journal of Mathematics

We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the 4-dimensional Minkowski space. Also we characterize pseudo-spherical null curves in the n-dimensional Minkowski space in terms of the curvature functions.

The Linear Functionals On Fundamental Locally Multiplicative Topological Algebras, E. Ansari-Piri

Turkish Journal of Mathematics

In this paper we study the dual space of fundamental locally multiplicative topological algebras and prove some results for linear and multiplicative linear functionals on these algebras. An investigation on locally compactness of the carrier space of these algebras is the last part of this note.

Heteroclinic Solutions To An Asymptotically Autonomous Second-Order Equation, Gregory S. Spradlin

Mathematics - Daytona Beach

We study the differential equation ẍ(t) = a(t)V '(x(t)), where V is a double-well potential with minima at x = ±1 and a(t) →l > 0 as |t| → 1. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the differential equation with x(t) → -1 as t → -1 and x(t) → 1 as t → ∞. The assumptions allow l - a(t) to change sign for arbitrarily large values of |t|, and do not restrict the decay rate of |l -a(t)| as |t| → ∞ © 2010 Texas State University - …

On Baryon Number Non-Conservation In Two-Dimensional O(2n+1) Qcd, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We construct a classical dynamical system whose phase space is a certain infinite dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O(2N + 1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.

Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene

Publications and Research

The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series. However, we only described the method standard wavelet series and …

Women And Math Performance: The Effects Of Stereotype Threat, Math Identity, And Gender Identity, Felicia W. Chu

Seton Hall University Dissertations and Theses (ETDs)

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