Mathematics Commons^™

Kernel Based Quadrature On Spheres And Other Homogeneous Spaces, E. Fuselier, T. Hangelbroek, F. J. Narcowich, J. D. Ward, G. B. Wright

Mathematics Faculty Publications and Presentations

Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate independent quadrature (or cubature) formulas associated with certain classes of positive definite and conditionally positive definite kernels that are invariant under the group action of the homogeneous manifold. In particular, we show that these formulas are accurate—optimally so in many cases—and stable under an increasing number of nodes and in the presence of noise, provided the set X of quadrature nodes is quasi-uniform. …

Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde

Mathematics Faculty Research

Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diffusion coefficient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, sufficient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure …

Algebraic Properties Of Generalized Rijndael-Like Ciphers, L. Babinkostova, Kevin W. Bombardier, Matthew M. Cole, Thomas A. Morrell, Cory B. Scott

Mathematics Faculty Publications and Presentations

We provide conditions under which the set of Rijndael-like functions considered as permutations of the state space and based on operations of the finite field GF(p^k) (p ≥ 2) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen generalized Rijnadael like ciphers. In R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field GF(2^k) is equal to the alternating group on the state space. In [39], this paper we provide conditions under which …

An Introductory Look At Deterministic Chaos, Kenneth Coiteux

Mathematics Undergraduate Theses

This is a brief introduction to deterministic chaos. We will be studying the logistic map and the 'double-humped' logistic map.

The Behavior Of Midsets When Repeatedly Taking The Midset Of Two Lines In L1 Geometry, Joshua M. Fitzhugh, David L. Farnsworth

Articles

We study the outcome of taking midsets of two lines in ℓ1 geometry.We establish the algorithm for repeatedly finding these midsets and characterize the limiting midsets.We discuss the issue of angle measurement in Minkowski geometries, especially with respect to the limiting midsets.

The Study Of Middle School Mathematics And Science Teachers' Practices, Perceptions, And Attitudes Related To Mathematics And Science Integration, Eliza Leszczynski

Theses, Dissertations and Culminating Projects

The purpose of this qualitative study was to investigate the nature of mathematics and science connections made by sixth and seventh grade mathematics and science teachers in their classrooms. This study also examined the extent to which these connections represented mathematics and science integration and described the teachers’ perceptions of and attitudes about mathematics and science integration. The primary data sources included classroom observations and teacher interviews.

Findings suggested that teacher practices in making mathematics and science connections in the classroom incorporated many of the characteristics of integrated instruction presented in the literature. Teacher attitudes toward integration were found to …

Tracking In Middle School Mathematics, Alexis Geisler

Mathematics Graduate Theses

This paper is a review of research pertaining to the issue of tracking in middle and high school mathematics. More focus is given to middle school because this is usually where tracking begins in mathematics. It supports research on the rationale behind detracking our schools and moving towards heterogeneous classrooms. Research behind the psychological effects of tracking is also provided, along with how tracking can segregate our school systems. There is a variety of research on the effect of tracking in mathematics. One of the most prevalent issues is how tracking is detrimental to the low tracked students. It not …

Categorical Data Analysis Of First-Year Programs And Its Effect On Retention Of Lsu First-Year Students, Morgan Matchett

Honors Capstones

No abstract provided.

Introduction Of Advanced Math Concepts Through A Geometry Project, Emelie Mativi

Honors Capstones

No abstract provided.

A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson

Undergraduate Honors Thesis Collection

The idea for this thesis originated from my fascination with the studies of both music and mathematics throughout my entire life. As a triple major in Middle/Secondary Math Education, Mathematics, and Music, I have learned more than I thought possible of music and math. In proposing this thesis, I desired to use my knowledge of arithmetic and aesthetics to research how music and mathematics are intertwined. I am confident that the following three chapters have allowed me to develop as an academic in both music and mathematics. This thesis serves as a presentation of the connections of music and math …

Calculator Usage In Secondary Level Classrooms: The Ongoing Debate, Nicole Plummer

Honors College Theses

With technology becoming more prevalent every day, it is imperative that students gain enough experience with different technological tools in order to be successful in the “real-world”. This thesis will discuss the debate and overall support for an increased usage of calculators as tools in the secondary level classroom. When the idea of calculators in the classroom first came to life, many educators were very apprehensive and quite hesitant of this change. Unfortunately, more than 40 years later, there is still hesitation for their usage; and rightfully so. While there are plenty of advantages of calculator use in the classroom, …

Modeling Magnetic Separation Of Oil Spill Clean Up To Enhance Virtual Laboratory Learning In The Classroom, Kofi James

Theses, Dissertations and Culminating Projects

This thesis links an applied mathematics study of oil spill cleanup to a mathematics education study of the efficacy of virtual laboratory activities in physical and mathematical sciences. Oil spills will be investigated using a multi-phase Navier-Stokes Direct Numerical Simulation (DNS) code for magnetic fluids, also known as ferrofluids. Simulations model cases that are not possible to study in a laboratory experiment or in the real world. Simulation results show that scaling up this process involves fluid mechanical obstacles and that real world effects, such as seawater contamination, will also impact cleanup effectiveness. A physics laboratory classroom curriculum based on …

Partial Colorings Of Graphs, Matthew Jakubowski

Theses, Dissertations and Culminating Projects

Recently, there has been great interest in counting the number of homomorphisms from a graph G into a fixed image graph H. For this thesis, we let H be a complete graph on three vertices with exactly one looped vertex. Homomorphisms from a graph G to this H correspond to partial proper two-colorings of the vertices of G. We are mainly interested in finding which graphs maximize the number of partial two-colorings given a graph with n vertices and m edges. The general result is given for all graphs with m < n -1 as well as basic enumerative results for some very common graphs.

Geometrical Prediction Models Of Visceral Adipose Tissue, Robert Cowell Moore

Theses, Dissertations and Culminating Projects

Objective: Trunk shape is a known predictor of amounts of visceral adipose tissue (VAT). The amount of total adipose tissue in the abdomen also predicts visceral adipose tissue mass but it is unknown how much of VAT can be attributed to abdominal shape versus size. Using two new measures derived from external measures such as hip circumference and waist circumference, we investigated how shape and adiposity along with demographic covariates are related to amounts of visceral adipose tissue. These new measures are known as Trunk Shape and Trunk Size. These measures were then used to develop models that predicted the …

Quantitative Literacy And High School Mathematics : The Evolution Of A Collaboratively Constructed Course And Its Impact On Students' Attitudes And Numeracy, Mark Francis Russo

Theses, Dissertations and Culminating Projects

This study describes a practitioner action research project in which I co-constructed a high school mathematics elective course with my students. The focus of the course was on developing students’ quantitative literacy. I examined the impact of the coconstruction process on the evolution of the course, analyzed how the course influenced students’ quantitative literacy and attitudes about mathematics, and reflected on some of the lessons I learned about making mathematics more relevant for my students. This study fills a gap in the literature by describing the impact of a quantitative literacy course at the high school level and by documenting …

Gpu Accelerated Approach To Numerical Linear Algebra And Matrix Analysis With Cfd Applications, Adam Phillips

HIM 1990-2015

A GPU accelerated approach to numerical linear algebra and matrix analysis with CFD applications is presented. The works objectives are to (1) develop stable and efficient algorithms utilizing multiple NVIDIA GPUs with CUDA to accelerate common matrix computations, (2) optimize these algorithms through CPU/GPU memory allocation, GPU kernel development, CPU/GPU communication, data transfer and bandwidth control to (3) develop parallel CFD applications for Navier Stokes and Lattice Boltzmann analysis methods. Special consideration will be given to performing the linear algebra algorithms under certain matrix types (banded, dense, diagonal, sparse, symmetric and triangular). Benchmarks are performed for all analyses with baseline …

Stochastic Order Relations Among Parallel Systems From Weibull Distributions, Nuria Torrado, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

In this article, we focus on stochastic orders to compare the magnitudes of two parallel systems from Weibull distributions when one set of scale parameters majorizes the other. The new results obtained here extend some of those proved by Dykstra et al. (1997) and Joo and Mi (2010) from exponential to Weibull distributions. Also, we present some results for parallel systems from multiple-outlier Weibull models.

Observability In Traffic Modeling: Eulerian And Lagrangian Coordinates, Sergio Contreras

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traditionally, one of the ways traffic flow has been studied is by using the kinematic wave model. This model is studied in the Eulerian framework. Recently, the kinematic wave model has been transformed into Lagrangian coordinates. This model of traffic flow together with the concept of observability for linear time invariant discrete time systems is applied to study the observability of four sections of a freeway in both Eulerian and Lagrangian coordinates. A system with densities in four sections of a freeway is designed, and the observability of the system is studied with different situations for sensors. When the system …

Polynomial Factoring Algorithms And Their Computational Complexity, Nicholas Cavanna

Honors Scholar Theses

Finite fields, and the polynomial rings over them, have many neat algebraic properties and identities that are very convenient to work with. In this paper we will start by exploring said properties with the goal in mind of being able to use said properties to efficiently irreducibly factorize polynomials over these fields, an important action in the fields of discrete mathematics and computer science. Necessarily, we must also introduce the concept of an algorithm’s speed as well as particularly speeds of basic modular and integral arithmetic opera- tions. Outlining these concepts will have laid the groundwork for us to introduce …

High Frequency Data: Modeling Durations Via The Acd And Log Acd Models, Lilian Cheung

Honors Scholar Theses

This thesis proposes a method of finding initial parameter estimates in the Log ACD₁ model for use in recursive estimation. The recursive estimating equations method is applied to the Log ACD₁ model to find recursive estimates for the unknown parameters in the model. A literature review is provided on the ACD and Log ACD models, and on the theory of estimating equations. Monte Carlo simulations indicate that the proposed method of finding initial parameter estimates is viable. The parameter estimation process is demonstrated by fitting an ACD model and a Log ACD model to a set of IBM …

Very Cost Effective Domination In Graphs, Tony K. Rodriguez

Electronic Theses and Dissertations

A set S of vertices in a graph G=(V,E) is a dominating set if every vertex in V\S is adjacent to at least one vertex in S, and the minimum cardinality of a dominating set of G is the domination number of G. A vertex v in a dominating set S is said to be very cost effective if it is adjacent to more vertices in V\S than to vertices in S. A dominating set S is very cost effective if every vertex in S is very cost effective. The minimum cardinality of a very cost effective dominating set of …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Restrictions On The Coefficients, Brett A. Shields Mr.

Electronic Theses and Dissertations

In this thesis, we put restrictions on the coefficients of polynomials and give bounds concerning the number of zeros in a specific region. Our results generalize a number of previously known theorems, as well as implying many new corollaries with hypotheses concerning monotonicity of the modulus, real, as well as real and imaginary parts of the coefficients separately. We worked with Enestr\"{o}m-Kakeya type hypotheses, yet we were only concerned with the number of zeros of the polynomial. We considered putting the same type of restrictions on the coefficients of three different types of polynomials: polynomials with a monotonicity``flip" at some …

Identifying Codes And Domination In The Product Of Graphs, Kirsti Wash

All Dissertations

An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code in a graph $G$ is denoted $\gid(G)$. We consider identifying codes of the direct product $K_n \times K_m$. In particular, we answer a question of Klav\v{z}ar and show the exact value of $\gid(K_n \times K_m)$. It was recently shown by Gravier, Moncel and Semri that for the Cartesian product of two same-sized cliques $\gid(K_n \Box K_n) = \lfloor{\frac{3n}{2}\rfloor}$. Letting $m \ge …

A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal

Undergraduate Honors Theses

In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans …

Network Applications And The Utah Homeless Network, Michael A. Snyder

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Graph theory is the foundation on which social network analysis (SNA) is built. With the flood of "big data," graph theoretical concepts and their linear algebraic counterparts are essential tools for analysis in the burgeoning field of network data analysis, in which SNA is a subset. Here we begin with an overview of SNA. We then discuss the common descriptive measures taken on network data as well as proposing new measures specific to homeless networks. We also define a new data structure which we call the location sequence matrix. This data structure makes certain computational network analyses particularly easy. …

Traditional Lecture Versus An Activity Approach For Teaching Statistics: A Comparison Of Outcomes, Jennifer L. Loveland

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many educational researchers have proposed teaching statistics with less lecture and more active learning methods. However, there are only a few comparative studies that have taught one section of statistics with lectures and one section with activity-based methods; of those studies, the results are contradictory. To address the need for more research on the actual effectiveness of active learning methods in introductory statistics, this research study was undertaken.

An introductory, university level course was divided into two sections. One section was taught entirely with traditional lecture. The other section was taught using active learning methods and a minimal amount of …

Hamiltonicity, Pancyclicity, And Cycle Extendability In Graphs, Deborah C. Arangno

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A significant portion of Graph Theory is devoted to determining the characteristics which guarantee the existence of long cycles.

Long cycles have roles in applications to civil engineering, chemistry, and communications, among many others, but the problem, in and of itself, of determining whether a graph has a cycle of some fixed and typically large length is one of the most important problems of both pure Mathematics and Computer Science.

A cycle containing all the vertices of the graph is called a Hamiltonian cycle, and a graph which possesses such a cycle is said to be Hamiltonian. If …

Statistical Modeling, Exploration, And Visualization Of Snow Water Equivalent Data, James Beguah Odei

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Due to a continual increase in the demand for water as well as an ongoing regional drought, there is an imminent need to monitor and forecast water resources in the Western United States. In particular, water resources in the Intermountain West rely heavily on snow water storage. Thus, the need to improve seasonal forecasts of snowpack and considering new techniques would allow water resources to be more effectively managed throughout the entire water-year. Many available models used in forecasting snow water equivalent (SWE) measurements require delicate calibrations.

In contrast to the physical SWE models most commonly used for forecasting, we …

Multiplicity Results Of Periodic Solutions For Two Classes Of Nonlinear Problems, Kazuya Hata

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We investigate the existences and qualitative properties of periodic solutions of the following two classes of nonlinear differential equations:

I) (Special) Relativistic Pendulum Equations (RPEs);

II) (2-coupled) Gross-Pitaevskii Equations (GPEs).

The pendulum equation describes the motion of a pendulum. According to Special Relativity, which was published by A. Einstein in 1905, causality is more fundamental than constant time-space, thus time will flow slower and space will distort to keep causality if the speed of motion is near the speed of light. In such high speed situations, the pendulum equation needs to be revised due to Special Relativity. The revised equation …