Mathematics Commons^™

Investigating The Mathematical Dispositions And Self-Efficacy For Teaching Mathematics Of Preservice Teachers, Jasmine M. Cruz

Theses and Dissertations

The study of the individual's beliefs and the role and influence they have on the individual's actions and behaviors, have long been examined and investigated by educators and psychologists. Moreover, researchers have overwhelmingly claimed and demonstrated that the beliefs held by teachers significantly influences their behavior and educational practices in the classroom. This thesis study investigates the mathematical disposition and self-efficacy for teaching mathematics of preservice teachers. The study's primary goals are to discover if there is a relationship or association between a teacher's mathematical disposition(MD) and his/her self-efficacy for teaching mathematics (SEFTM), and if there are significant differences between …

Problem Book On Higher Algebra And Number Theory, Ryanto Putra

Theses and Dissertations

This book is an attempt to provide relevant end-of-section exercises, together with their step-by-step solutions, to Dr. Zieschang's classic class notes Higher Algebra and Number Theory. It's written under the notion that active hands-on working on exercises is an important part of learning, whereby students would see the nuance and intricacies of a math concepts which they may miss from passive reading. The problems are selected here to provide background on the text, examples that illuminate the underlying theorems, as well as to fill in the gaps in the notes.

Mathematical Modeling Of Mers-Cov Nosocomial Epidemic, Adriana Quiroz

Theses and Dissertations

This thesis concerns about the analysis and modeling of spread of an infectious disease inside a hospital. We begin from the basic knowledge of the simple models: SIR and SEIR, to show an appropriate understanding of the epidemic dynamic process. We consider the Middle East Respiratory Syndrome Corona Virus (MERS-CoV), in Saudi Arabia, to introduce MERS-CoV SEIR ward model by developing different systems of equations in each ward (unit). We use the Next Generation Matrix method to calculate the basic reproduction number R0. Simulations of different scenarios are done using different combination of parameters.

To model MERS-CoV we established …

Disease Modeling Using Fractional Differential Equations And Estimation, Daniel P. Medina

Theses and Dissertations

Ordinary differential equations has been the most conventional approach when modeling spread of infectious diseases. Effective research has shown that using fractional-order differentiation can be a very useful and efficient extension for some mathematical models. In this thesis, fractional calculus is used to depict an SEIR model with a system of fractional-order differential equations. I also simulate the fractional-order SEIR using integer-order numerical methods. I also establish the estimation framework and show that it is accurately working.

Coupled Telegraph And Sir Model Of Information And Diseases, Jose De Jesus Galarza

Theses and Dissertations

In this work, the effect of information propagation on disease spread and vaccination uptake through networks is studied. In this model the information reaches different people at different distances from the center of information containing the health data. We use a pair of Telegraph equations to depict the vaccine and disease information propagation on a network embedded into a straight line. The Telegraph equation is coupled with an SIR (Susceptible-Infected-Recovered) model to examine the anticipated mutual influence. Numerical simulations and stability analysis were made to study the model. We show how the propagation of information about the disease impacts the …

On The Denesting Of Nested Square Roots, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is rewritten as a sum of fourth-order roots of rational numbers. The theory is illustrated with several solved examples.

A Refined Approach For Non-Negative Entire Solutions Of Δ U + Up = 0 With Subcritical Sobolev Growth, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

Let N≥2and 1uis a non-negative classical solution of the Lane–Emden equation, thenu≡0. The method of moving planes combined with the Kelvin transform provides an elegant proof of this theorem. A classical approach of Serrin and Zou, originally used for the Lane–Emden system, yields another proof but only in lower dimensions. Motivated by this, we further refine this approach to find an alternative proof of the Liouville type theorem in all dimensions.

Spectral Theory Of Operators On Manifolds, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Differential operators that are defined on a differentiable manifold can be used to study various properties of manifolds. The spectrum and eigenfunctions play a very significant role in this process. The objective of this chapter is to develop the heat equation method and to describe how it can be used to prove the Hodge Theorem. The Minakshisundaram-Pleijel parametrix and asymptotic expansion are then derived. The heat equation asymptotics can be used to give a development of the Gauss-Bonnet theorem for two-dimensional manifolds.

Electric Ion Dispersion As A New Type Of Mass Spectrometer, Michael R. Lindstrom, Iain Moyles, Kevin Ryczko

School of Mathematical & Statistical Sciences Faculty Publications

At the 2014 Fields-MPrime Industrial Problem Solving Workshop, PerkinElmer presented a design problem for mass spectrometry. Traditionally, mass spectrometry is done via three methods: using magnetic fields to deflect charged particles whereby different masses bend differently; using a time-of-flight procedure where particles of different mass arrive at different times at a target; and using an electric quadrupole that filters out all masses except for one very narrow band. The challenge posed in the problem was to come up with a new design for mass spectrometry that did not involve magnetic fields and where mass fractions could be measured in an …

An Introduction To Ricci Flow For Two-Dimensional Manifolds, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The study of diferentiable manifolds is a deep an extensive area of mathematics. A technique such as the study of the Ricci flow turns out to be a very useful tool in this regard. This flow is an evolution of a Riemannian metric driven by a parabolic type of partial differential equation. It has attracted great interest recently due to its important achievements in geometry such as Perelman's proof of the geometrization conjecture and Brendle-Schoen's proof of the differentiable sphere theorem. It is the purpose here to give a comprehensive introduction to the Ricci flow on manifolds of dimension two …

Using Technology To Determine Factorability Or Non-Factorability Of Quadratic Algebraic Trinomials, John E. T. Bernard, Olga Ramirez, Cristina Villalobos

School of Mathematical & Statistical Sciences Faculty Publications

This paper is aimed for mathematics educators who teach algebra, more specifically, the factoring of quadratic algebraic expressions, and who want to enhance student learning of this topic using technology in conjunction with the Middle Term Splitting Method (Donnell, 2010; MTSM 2016a; MTSM 2016b). We will use technology-based algebra and geometry connections to help determine factorability or nonfactorability of quadratic algebraic trinomials over the integers, over the real numbers, and over the complex numbers, both with clarity, certainty and with understanding by using two equations, one derived from the coefficients of the outer terms and the other from the middle …

An Intrinsic Characterization Of Bonnet Surfaces Based On A Closed Differential Ideal, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The structure equations for a two-dimensional manifold are introduced and two results based on the Codazzi equations pertinent to the study of isometric surfaces are obtained from them. Important theorems pertaining to isometric surfaces are stated and a theorem due to Bonnet is obtained. A transformation for the connection forms is developed. It is proved that the angle of deformation must be harmonic, and that the differentials of many of the important variables generate a closed differential ideal. This implies that a coordinate system exists in which many of the variables satisfy particular ordinary differential equations, and these results can …

Toral And Spherical Aluthge Transforms Of 2-Variable Weighted Shifts, Raul E. Curto, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We introduce two natural notions of Aluthge transforms (toral and spherical) for 2-variable weighted shifts and study their basic properties. Next, we study the class of spherically quasinormal 2-variable weighted shifts, which are the fixed points for the spherical Aluthge transform. Finally, we briefly discuss the relation between spherically quasinormal and spherically isometric 2-variable weighted shifts.

Numerical Simulations Of Shock Waves Reflection And Interaction, Ligang Sun

Theses and Dissertations

The main objective of this dissertation is to detect and study the phenomena of reflection of one shock wave and interaction of two shock waves using numerical methods. In theory, solutions of non-linear Euler equations of compressive inviscid gas dynamics in two dimensions can display various features including shock waves and rarefaction waves. To capture the shock waves properly, highly accurate numerical schemes are designed according to second order Lax-Wendroff method. In this thesis, three numerical experiments were designed to show the reflection and interaction phenomena. Firstly, one shock was formed due to the encounter of two high speed gas …

Variable Moving Average Transform Stitching Waves, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

A moving average transform in the plane with a variable size and shape window depending on the position and the ’time’ is studied. The main objective is to select the window parameters in such a way that the new transform converges smoothly to the identity transform at the boundary of a prescribed bounded plane region. A new approximation of solitary waves arising from Korteweg-de Vries equation is obtained based on results in the paper. Numerical implementation and examples are included.

Multilocality And Fusion Rules On The Generalized Structure Functions In Two-Dimensional And Three-Dimensional Navier-Stokes Turbulence, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator “multilocality.” The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of …

Quantum Dynamics, Entropy And Quantum Versions Of Maxwell’S Demon, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Several subjects which reside in the overlap area of quantum mechanics, statistical physics and thermodynamics are investigated in depth. This collection of subjects shares a common domain which is referred to as Maxwell’s demon. The classical version of this idea is introduced, and then, the contribution made by Szilard to the subject is presented. Several demons are considered, and it is shown that to best understand this area, quantum mechanics and the role information plays in it must be appreciated deeply.

Expert Elicitation On The Uncertainties Associated With Chronic Wasting Disease, Michael G. Tyshenko, Tamer Oraby, Shalu Darshan, Margit Westphal, Maxine C. Croteau, Willy Aspinall, Susie Elsaadany, Daniel Krewski, Neil Cashman

School of Mathematical & Statistical Sciences Faculty Publications

A high degree of uncertainty exists for chronic wasting disease (CWD) transmission factors in farmed and wild cervids. Evaluating the factors is important as it helps to inform future risk management strategies. Expert opinion is often used to assist decision making in a number of health, science, and technology domains where data may be sparse or missing. Using the "Classical Model" of elicitation, a group of experts was asked to estimate the most likely values for several risk factors affecting CWD transmission. The formalized expert elicitation helped structure the issues and hence provide a rational basis for estimating some transmission …

Existence And Behavior Of Positive Solutions To Elliptic System With Hardy Potential, Lei Wei, Xiyou Cheng, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this article, we study a class of elliptic systems with Hardy potentials. We analyze the possible behavior of radial solutions to the system when p; t > 1, q; s > 0 and λ; μ > (N - 2)2=4, and obtain the existence of positive solutions to the system with the Dirichlet boundary condition under certain conditions. When λ; μ > 0, p; t > 1 and q; s > 0, we show that any radial positive solution is decreasing in r.

Lie Symmetry To Second-Order Nonlinear Differential Equations And Its First Integrals, Pengfei Gu

Theses and Dissertations

There are many well-known techniques for obtaining exact solutions of differential equations, but most of them are merely special cases of a few powerful symmetry methods. In this paper, we focus our attention on a second-order nonlinear ordinary differential equation of special forms with arbitrary parameters, which is a combination of Liénard-type equation and equation with quadratic friction. With the help of Lie Symmetry methods, we identify several integrable cases of this equation. And for each case, we use the Lie Symmetry method to derive the associated determining system, and apply it further to find infinitesimal generators under …

A Comparative Study And Data Analysis For The Ultimate Fighting Championship, Victor Villalpando

Theses and Dissertations

Mixed Martial Arts is the fastest growing sport with many organizations worldwide. The biggest stage or biggest organization for Mixed Martial Arts is the Ultimate Fighting Championship (UFC). There are eight weight classes for men. The website: http://www.foxsports.com/ufc/stats provides data on fighters in all these categories. This data measures Striking Accuracy, Take downs, Reversals, Knockdowns, etc. in each category. It is interesting to understand and interpret all these numbers and study their relationships. Statistical tools like both parametric and nonparametric inference may give rise to such interpretations and provide explanations how the weight classes differ from one another. In this …

The Precarious Health Of Young Mexican American Men In South Texas, Cameron County Hispanic Cohort, 2004–2015, Gordon P. Watt, Kristina Vatcheva, Derek M. Griffith, Belinda M. Reininger, Laura Beretta, Michael Fallon, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

Introduction

Hispanic men have higher rates of illness and death from various chronic conditions than do non-Hispanic men. We aimed to characterize the health of Mexican American men living on the US–Mexico border in South Texas and elucidate indications of chronic disease in young men.

Methods

We sampled all male participants from the Cameron County Hispanic Cohort, an ongoing population-based cohort of Mexican Americans in Brownsville, Texas. We calculated descriptive statistics and stratified the sample into 3 age groups to estimate the prevalence of sociodemographic, behavioral, and clinical factors by age group and evaluated differences between age groups.

Results

Obesity …

Sparse Representation For The Isar Image Reconstruction, Mengqi Hu

Theses and Dissertations

In this paper, a sparse representation for the data form a multi-input multi-output based inverse synthetic aperture radar (ISAR) system is derived for two dimensions. The proposed sparse representation motivates the use a of a Convex Optimization directly that recovers the image without the loss information of the image with far less samples that that is required by Nyquist–Shannon sampling theorem, which increases the efficiency and decrease the cost of calculation in radar imaging.

Riemann-Hilbert Approach For The Fqxl Model: A Generalized Camassa-Holm Equation With Cubic And Quadratic Nonlinearity, Zhen Wang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, the inverse scattering transform associated with a Riemann-Hilbert problem is formulated for the FQXL model: a generalized Camassa-Holm equation mt = 12 k1[m(u2 − u2 x )]x + 1 2 k2(2mux + mxu), m = u − ux x, which was originally included in the work of Fokas [Physica D 87, 145 (1995)] and was recently shown to be integrable in the sense of Lax pair, bi-Hamilton structure, and conservation laws by Qiao, Xia, and Li [e-print arXiv:1205.2028v2 (2012)]. We have discussed the following properties: direct scattering problems and Jost solutions, asymptotical and analytical behavior of Jost …

From Exam To Education: The Math Exam/Education Resources, Carmen Bruni, Christina Koch, Bernhard Konrad, Michael R. Lindstrom, Iain Moyles, Will Thompson

School of Mathematical & Statistical Sciences Faculty Publications

The Math Exam/Education Resources (MER) is an open online learning resource hosted at The University of British Columbia (UBC), aimed at providing mathematics education resources for students and instructors at UBC. In this paper, there will be a discussion of the motivation for creating this resource on the MediaWiki platform, key features of the implementation that support student learning (including the evolution of the MER wiki from an exam database to a more-general learning resource), data on student use and response, potential for future development, and a brief description of how the project was implemented. Preliminary correlation data between wiki …

Compressive Sensing And Radar Imaging, John Montalbo

Theses and Dissertations

The field of remote sensing contains many unique and practical problems. Radar imaging, in all of its many forms, lies within this field of study. One problem is the need to acquire high-resolution images and store them on-board the system acquisition vessel . For some systems this could mean storing very high amounts of data, depending on the scene in question [3]. So a very natural goal is to store only what is absolutely necessary and nothing more. We investigate methods to compress signals into their most important components so that other parties can recover the original data completely or …

Existence Of Positive Solutions To Semilinear Elliptic Systems With Supercritical Growth, Congming Li, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

We establish the existence of positive entire solutions to cooperative systems of semilinear elliptic equations involving nonlinearities with critical and supercritical growth. Consequently, we obtain existence results to several well-known model examples such as systems of the Hénon, Lane–Emden, and stationary Schrödinger types. The main technique for generating our results relies on a topological approach for the shooting method combined with nonexistence results to closely related boundary value problems.

On Solutions For Linear And Nonlinear Schrödinger Equations With Variable Coefficients: A Computational Approach, Gabriel Amador, Kiara Colon, Nathalie Luna, Gerardo Mercado, Enrique Pereira, Erwin Suazo

School of Mathematical & Statistical Sciences Faculty Publications

In this work, after reviewing two different ways to solve Riccati systems, we are able to present an extensive list of families of integrable nonlinear Schrödinger (NLS) equations with variable coefficients. Using Riccati equations and similarity transformations, we are able to reduce them to the standard NLS models. Consequently, we can construct bright-, dark- and Peregrine-type soliton solutions for NLS with variable coefficients. As an important application of solutions for the Riccati equation with parameters, by means of computer algebra systems, it is shown that the parameters change the dynamics of the solutions. Finally, we test numerical approximations for the …

Opinion Formation About Childhood Immunization And Disease Spread On Networks, Shan Shan Zhao

Theses and Dissertations

People are physically and socially connected with each other. Those connections between people represent two, probably overlapping, networks: biological networks, through which physical contacts occur, or social network, through which information diffuse. In my thesis research, I am trying to answer that question in the context of pediatric disease spread on the biological network between households as well as within them and its relationship with information sharing on the social network of households (parents in that case) via "Information Cascades." I mainly focus on the Erdos-Renyi network model. In particular, I use two different but overlapping Erdos-Renyi networks for the …

Generalized Reciprocal Identities, Timothy Huber, Daniel Schultz

School of Mathematical & Statistical Sciences Faculty Publications

Included in Ramanujan’s Notebooks are two reciprocal identities. The first identity connects the Rogers-Ramanujan continued fraction with an eta quotient. The second identity is a level thirteen analogue. These are special cases of a more general class of relations between eta quotients and modular functions defined by product generalizations of the Rogers-Ramanujan continued fraction. Each identity is shown to be a relation between generators for a certain congruence subgroup. The degree, form, and symmetry of the identities is determined from behavior at cusps of the congruence subgroup whose field of functions the parameters generate. The reciprocal identities encode information about …