Mathematics Commons^™

The Effectiveness Of Manipulatives In A High School Algebra Ii Class, Brooke Elizabeth Bruins

Online Theses and Dissertations

This study explores the use of manipulatives in high school Algebra II. The effectiveness of the Concrete-Representational-Abstract (CRA) Model is compared to explicit instruction. The participants in this study are students from six high school Algebra II classes -two honors classes, and four standard classes. One honors class and two standard classes were randomly selected as the treatment groups receiving CRA instruction. The other three classes learned through abstract explicit instruction. Each class learned two new mathematical concepts, domain and range of quadratic functions and transformations of quadratic functions, through the selected method of instruction. At the end of instruction, …

Subfunctors Of Extension Functors, Furuzan Ozbek

Theses and Dissertations--Mathematics

This dissertation examines subfunctors of Ext relative to covering (enveloping) classes and the theory of covering (enveloping) ideals. The notion of covers and envelopes by modules was introduced independently by Auslander-Smalø and Enochs and has proven to be beneficial for module theory as well as for representation theory. The first few chapters examine the subfunctors of Ext and their properties. It is showed how the class of precoverings give us subfunctors of Ext. Furthermore, the characterization of these subfunctors and some examples are given. In the latter chapters ideals, the subfunctors of Hom, are investigated. The definition of cover and …

Comparative Analysis Of Gps Data, Kiel Von Lindenberg

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to calculate the distance traveled during a bike ride around the University of South Florida using information gathered by a GPS (Global Positioning System) application on a smartphone. We calculate the route distance in two ways: from latitudes and longitudes using the haversine formula and 2) from velocities and times using the trapezoidal rule. These computed distances were compared to the distance given by the smartphone application.

Voltage Smoothing With A Capacitor, Martin Copello

Undergraduate Journal of Mathematical Modeling: One + Two

A rectifier is an electrical circuit that converts alternating current to direct current, e.g., a half wave rectifier removes lower valleys of the AC voltage wave. If a capacitor is placed in parallel with a half wave rectifier, the transition from voltage peak to peak is smoothed to closer resemble constant DC voltage. The objective of this project was to model the voltage changes of a half wave rectifier with a parallel capacitor. It was found that the smoothness of the voltage waves increased as the capacitance of the capacitor increased.

Calculating The Solar Energy Of A Flat Plate Collector, Ariane Rosario

Undergraduate Journal of Mathematical Modeling: One + Two

The amount of solar energy that could be obtained by a flat plate solar collector of one square meter dimension is calculated in three different locations: Tampa FL, Fairbanks AL, and Pontianak Indonesia, considering the varying sunset time for each day of the year. The results show that if the collectors are placed near the equator, more total energy could be obtained. In fact, by placing a solar collector in Pontianak, Indonesia 12.42% more solar energy can be obtained than by placing it in Tampa and 96.9% more solar energy than Alaska.

Florida Sinkholes And Grout Injection Stabilization, Charles Hunt Griffith Ii

Undergraduate Journal of Mathematical Modeling: One + Two

Florida has a major problem when it comes to sinkholes. These sinkholes can become very hazardous to people, homes, and to the landscape as a whole. Florida sits on a carbonate platform which is highly indicative of sinkholes. There are three main types of sinkholes which occur in Florida: dissolution, cover subsidence, and cover collapse. I will compare these types of sinkholes to the underlying formation beneath Florida to see if there is a connection between the types of sinkholes that occur. I will also create a 3D model of grout injection stabilization and calculate its volume to compare to …

Rocket Flight Path, Jamie Waters

Undergraduate Journal of Mathematical Modeling: One + Two

This project uses Newton’s Second Law of Motion, Euler’s method, basic physics, and basic calculus to model the flight path of a rocket. From this, one can find the height and velocity at any point from launch to the maximum altitude, or apogee. This can then be compared to the actual values to see if the method of estimation is a plausible. The rocket used for this project is modeled after Bullistic-1 which was launched by the Society of Aeronautics and Rocketry at the University of South Florida.

Fukushima: A Model Study, Melinda Kathryn Mckell

Undergraduate Journal of Mathematical Modeling: One + Two

This article investigates the radiation dispersion modeling system available to Japanese authorities during the response phase of the Fukushima Dai-Ichi incident.

Modeling Rocket Flight In The Low-Friction Approximation, Logan White

Undergraduate Journal of Mathematical Modeling: One + Two

In a realistic model for rocket dynamics, in the presence of atmospheric drag and altitude-dependent gravity, the exact kinematic equation cannot be integrated in closed form; even when neglecting friction, the exact solution is a combination of elliptic functions of Jacobi type, which are not easy to use in a computational sense. This project provides a precise analysis of the various terms in the full equation (such as gravity, drag, and exhaust momentum), and the numerical ranges for which various approximations are accurate to within 1%. The analysis leads to optimal approximations expressed through elementary functions, which can be implemented …

Survival Analysis - Breast Cancer, Minh Hoang Pham

Undergraduate Journal of Mathematical Modeling: One + Two

In this study we used the parametric survival approach to analyze the survival time of African American breast cancer patients. In research about the survival time of patients, the Cox Proportional Hazard model, a semi-parametric method, is primarily used, but this approach does not rely on the distributional assumptions. The parametric method is more consistent with a theoretical approach compared to a semi-parametric approach. We observe that the survival time of African American breast cancer patients follows the Weibull Probability Distribution. First, we fitted the model to represent the survival ability of the general population (African American women diagnosed with …

Decay Estimates On Trace Norms Of Localized Functions Of Schrödinger Operators, Aaron Saxton

Theses and Dissertations--Mathematics

In 1973, Combes and Thomas discovered a general technique for showing exponential decay of eigenfunctions. The technique involved proving the exponential decay of the resolvent of the Schrödinger operator localized between two distant regions. Since then, the technique has been been applied to several types of Schrödinger operators. This dissertation will show that the Combes--Thomas method works well with trace, Hilbert--Schmidt and other trace-type norms. The first result we prove shows exponential decay on trace-type norms of a resolvent of a Schrödinger operator localized between two distant regions. We build on this result by applying the Combes--Thomas method again to …

Representation Theory Of Totally Reflexive Modules Over Non-Gorenstein Rings, Denise Amanda Rangel

Mathematics Dissertations - Archive

In the late 1960's Auslander and Bridger published Stable Module Theory, in whichthe idea of totally reflexive modules first appeared. These modules have been studiedby many. However, a bulk of the information known about them is when they are overa Gorenstein ring, since in that case they are exactly the maximal Cohen-Macaulaymodules. Much is already known about maximal Cohen-Macaulay modules, that is,totally reflexive modules over a Gorenstein ring. Therefore, we investigate the existence and abundance of totally reflexive modules over non-Gorenstein rings.It is known that if there exist one non-trivial totally reflexive module over a non-Gorenstein ring, then there exists …

Safety Effect Of Missouri's Strategic Highway Safety Plan: Missouri's Blueprint For Safer Roadways, Mojtaba A. Mohammadi, V. A. Samaranayake, Ghulam H. Bham

Mathematics and Statistics Faculty Research & Creative Works

This study systematically evaluated the changes in motor vehicle crashes that occurred on the Missouri Interstate highway system following the implementation of the Missouri Strategic Highway Safety Plan (MSHSP) between 2004 and 2007. The MSHSP implemented crash injury reduction strategies in enforcement, education, engineering, and public policy. Empirical Bayesian methods were commonly used to evaluate the effects of any change in safety as a result of countermeasures. This paper presents a simple new approach to evaluating the effects of Missouri's safety plans on roadway crashes. For crash data associated with traffic and roadway characteristics, negative binomial regression models were developed …

An Isometric Dynamics For A Causal Set Approach To Discrete Quantum Gravity, S. Gudder

Mathematics Preprint Series

We consider a covariant causal set approach to discrete quantum gravity. We first review the microscopic picture of this approach. In this picture a universe grows one element at a time and its geometry is determined by a sequence of integers called the shell sequence. We next present the macroscopic picture which is described by a sequential growth process. We introduce a model in which the dynamics is governed by a quantum transition amplitude. The amplitude satisfies a stochastic and unitary condition and the resulting dynamics becomes isometric. We show that the dynamics preserves stochastic states. By “doubling down” on …

The Prevalence Of Antibodies Against Wheat And Milk Proteins In Blood Donors And Their Contribution To Neuroimmune Reactivities, Aristo Vojdani, Datis Kharrazian, Partha Sarathi Mukherjee

Mathematics Faculty Publications and Presentations

The aim of this study was to look for the presence of IgG, IgM, and IgA antibodies against two widely consumed foods, wheat and milk, in a relatively large number of specimens. As wheat, milk, and their antigens have been found to be involved in neuroimmune disorders, we measured the co-occurrence of their antibodies against various neural antigens. We assessed the reactivity of sera from 400 donors to wheat and milk proteins, GAD-65, cerebellar, MBP, and MOG. Statistical analysis showed significant clustering when certain wheat and milk protein antibodies were cross-referenced with neural antibodies. Approximately half of the sera with …

On Constructions Of Generalized Skein Modules, Uwe Kaiser

Mathematics Faculty Publications and Presentations

Jozef Przytycki introduced skein modules of 3-manifolds and skein deformation initiating algebraic topology based on knots. We discuss the generalized skein modules of Walker, defined by fields and local relations. Some results by Przytycki are proven in a more general setting of fields defined by decorated cell-complexes in manifolds. A construction of skein theory from embedded TQFT-functors is given, and the corresponding background is developed. The possible coloring of fields by elements of TQFT-modules is discussed for those generalized skein modules. Also an approach of defining skein modules from studying compressions of fields is described.

Performance Modeling And Optimization Techniques For Heterogeneous Computing, Supada Laosooksathit

Doctoral Dissertations

Since Graphics Processing Units (CPUs) have increasingly gained popularity amoung non-graphic and computational applications, known as General-Purpose computation on GPU (GPGPU), CPUs have been deployed in many clusters, including the world's fastest supercomputer. However, to make the most efficiency from a GPU system, one should consider both performance and reliability of the system.

This dissertation makes four major contributions. First, the two-level checkpoint/restart protocol that aims to reduce the checkpoint and recovery costs with a latency hiding strategy in a system between a CPU (Central Processing Unit) and a GPU is proposed. The experimental results and analysis reveals some benefits, …

Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene

Publications and Research

This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.

Elements Of Convergence Approach Theory, William D. Trott

College of Graduate Studies: Theses & Dissertations

We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

College of Graduate Studies: Theses & Dissertations

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.