Physical Sciences and Mathematics Commons^™

Generalized D-Kaup-Newell Integrable Systems And Their Integrable Couplings And Darboux Transformations, Morgan Ashley Mcanally

USF Tampa Graduate Theses and Dissertations

We present a new spectral problem, a generalization of the D-Kaup-Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The first major motivation of this dissertation is to present spectral problems that generate two soliton hierarchies with infinitely many commuting conservation laws and high-order symmetries, i.e., they are Liouville integrable.

We use the soliton hierarchies and a non-seimisimple matrix loop Lie algebra in order …

On Extending Hansel's Theorem To Hypergraphs, Gregory Sutton Churchill

USF Tampa Graduate Theses and Dissertations

For integers $n \geq k \geq 2$, let $V$ be an $n$-element set, and let $\binom{V}{k}$ denote the family of all $k$-element subsets of $V$. For disjoint subsets $A, B \subseteq V$, we say that $\{A, B\}$ {\it covers} an element $K \in \binom{V}{k}$ if $K \subseteq A \dot\cup B$ and $K \cap A \neq \emptyset \neq K \cap B$. We say that a collection $\cC$ of such pairs {\it covers} $\binom{V}{k}$ if every $K \in \binom{V}{k}$ is covered by at least one $\{A, B\} \in \cC$. When $k=2$, covers $\cC$ of $\binom{V}{2}$ were introduced in~1961 by R\'enyi~\cite{Renyi}, where they …

Rethinking The Numerate Citizen: Quantitative Literacy And Public Issues – Discussion, Kira H. Hamman

Numeracy

I dispute Erickson's claim in Numeracy 9(2), Article 4 (2016), that quantitative literacy is neither necessary nor appropriate for informed citizenship, and explore his suggestion that Hardwig's notion of epistemic dependence is more suited to the task.

Quantitative Literacy In The Affective Domain: Computational Geology Students’ Reactions To Devlin’S The Math Instinct, Victor J. Ricchezza, H. L. Vacher

Numeracy

Building on suggestions from alumni from a recent interview project, students in Computational Geology at the University of South Florida were tasked with reading a popular non-fiction book on mathematics and writing about the book and their feelings about math. The book, The Math Instinct by Keith Devlin, was chosen because we believed it would give the students something interesting to write about and not because we had any expectations in particular about what it might reveal about or do for their math anxiety. The nature of the responses received from the students led to the performance of a post-hoc …

Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton

Numeracy

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added …

Patterns In Words Related To Dna Rearrangements, Lukas Nabergall

USF Tampa Graduate Theses and Dissertations

Patterns, sequences of variables, have traditionally only been studied when morphic images of them appear as factors in words. In this thesis, we initiate a study of patterns in words that appear as subwords of words. We say that a pattern appears in a word if each pattern variable can be morphically mapped to a factor in the word. To gain insight into the complexity of, and similarities between, words, we define pattern indices and distances between two words relative a given set of patterns. The distance is defined as the minimum number of pattern insertions and/or removals that transform …

Lump, Complexiton And Algebro-Geometric Solutions To Soliton Equations, Yuan Zhou

USF Tampa Graduate Theses and Dissertations

In chapter 2, we study two Kaup-Newell-type matrix spectral problems, derive their soliton hierarchies within the zero curvature formulation, and furnish their bi-Hamiltonian structures by the trace identity to show that they are integrable in the Liouville sense. In chapter 5, we obtain the Riemann theta function representation of solutions for the first hierarchy of generalized Kaup-Newell systems.

In chapter 3, using Hirota bilinear forms, we discuss positive quadratic polynomial solutions to generalized bilinear equations, which generate lump or lump-type solutions to nonlinear evolution equations, and propose an algorithm for computing higher-order lump or lump-type solutions. In chapter 4, we …

Prevalence Of Typical Images In High School Geometry Textbooks, Megan N. Cannon

USF Tampa Graduate Theses and Dissertations

Visualization in mathematics can be discussed in many ways; it is a broad term that references physical visualization objects as well as the process in which we picture images and manipulate them in our minds. Research suggests that visualization can be a powerful tool in mathematics for intuitive understanding, providing and/or supporting proof and reasoning, and assisting in comprehension. The literature also reveals some difficulties related to the use of visualization, particularly how illustrations can mislead students if they are not comfortable seeing concepts represented in varied ways. However, despite the extensive research on the benefits and challenges of visualization …

Cybersecurity: Probabilistic Behavior Of Vulnerability And Life Cycle, Sasith Maduranga Rajasooriya

USF Tampa Graduate Theses and Dissertations

Analysis on Vulnerabilities and Vulnerability Life Cycle is at the core of Cybersecurity related studies. Vulnerability Life Cycle discussed by S. Frei and studies by several other scholars have noted the importance of this approach. Application of Statistical Methodologies in Cybersecurity related studies call for a greater deal of new information. Using currently available data from National Vulnerability Database this study develops and presents a set of useful Statistical tools to be applied in Cybersecurity related decision making processes.

In the present study, the concept of Vulnerability Space is defined as a probability space. Relevant theoretical analyses are conducted and …

Contributions To Quandle Theory: A Study Of F-Quandles, Extensions, And Cohomology, Indu Rasika U. Churchill

USF Tampa Graduate Theses and Dissertations

Quandles are distributive algebraic structures that were introduced by David Joyce [24] in his Ph.D. dissertation in 1979 and at the same time in separate work by Matveev [34]. Quandles can be used to construct invariants of the knots in the 3-dimensional space and knotted surfaces in 4-dimensional space. Quandles can also be studied on their own right as any non-associative algebraic structures.

In this dissertation, we introduce f-quandles which are a generalization of usual quandles. In the first part of this dissertation, we present the definitions of f-quandles together with examples, and properties. Also, we provide a …

Modeling In Finance And Insurance With Levy-It'o Driven Dynamic Processes Under Semi Markov-Type Switching Regimes And Time Domains, Patrick Armand Assonken Tonfack

USF Tampa Graduate Theses and Dissertations

Mathematical and statistical modeling have been at the forefront of many significant advances in many disciplines in both the academic and industry sectors. From behavioral sciences to hard core quantum mechanics in physics, mathematical modeling has made a compelling argument for its usefulness and its necessity in advancing the current state of knowledge in the 21rst century. In Finance and Insurance in particular, stochastic modeling has proven to be an effective approach in accomplishing a vast array of tasks: risk management, leveraging of investments, prediction, hedging, pricing, insurance, and so on. However, the magnitude of the damage incurred in recent …

Schreier Graphs Of Thompson's Group T, Allen Pennington

USF Tampa Graduate Theses and Dissertations

Thompson’s groups F, T, and V represent crucial examples of groups in geometric group theory that bridge it with other areas of mathematics such as logic, computer science, analysis, and geometry. One of the ways to study these groups is by understanding the geometric meaning of their actions. In this thesis we deal with Thompson’s group T that acts naturally on the unit circle S¹, that is identified with the segment [0, 1] with the end points glued together. The main result of this work is the explicit construction of the Schreier graph of T with …

Linear Extremal Problems In The Hardy Space HP For 0 < P < 1, Robert Christopher Connelly

USF Tampa Graduate Theses and Dissertations

In this thesis, we consider linear extremal problems in the H^p spaces. For many of these extremal problems, a unique solution can be guaranteed. We will examine some of the classical examples of extremal problems in these spaces. With this framework in place we will then consider a particular problem which does not always have a unique solution.

A Madison-Numeracy Citation Index (2008-2015): Implementing A Vision For A Quantitatively Literate World, Nathan D. Grawe, H. L. Vacher

Numeracy

This editorial recognizes the contributions made by Bernard Madison to the field of quantitative literacy with a bibliographic index of his papers, edited volumes, and works contained therein that were cited in the first eight volumes (2008-2015) of Numeracy. In total, 61 citing papers ("sources") cite 42 Madison works ("citations") a total of 218 times. The source and citation indexes provided in the appendix at the end of this editorial make it easy to see the direct contribution of Madison's work to the arguments and debates contained in the founding years of the journal. For those who are new …

Danger Of Snow In The Sunshine State, Dmitrii Karpenko

Undergraduate Journal of Mathematical Modeling: One + Two

The main purpose of the project is to investigate the maximum deflection of a rectangular 16 x 8 inches beam, supported on both ends under uniform loading stress under snow pressure in the event that Tampa experiences snowfall. The required information for the project is the material of the beam and its dimensions, measurement of the area of the roof that would accumulate snow, and calculations of the Moment of Inertia and Uniform Distributed Load for the beam. The maximum deflection of the beam can be calculated using the information above.

The outcome of the research shows that the roof …

Alternative Typing Learning Curves, Marcel Kreuzer

Undergraduate Journal of Mathematical Modeling: One + Two

Typing is a part of everyday life for many people. However some people have difficulty in doing it. For example, for people who are blind and those who have carpal tunnel or cerebral palsy, a standard keyboard would not be effective to type. Alternative options include voice recognition and keyless keyboards. We focus on orbiTouch keyboard which has no keys, only two knobs which allow a person to type. Which alternative way of typing would be most effective given a person’s condition is discussed.

Approximating Surface Area Of Fluctuating Lipid Leaflets Using Weighted Grid Tessellation, Ahnaf Siddiqui

Undergraduate Journal of Mathematical Modeling: One + Two

The surface area per lipid is an important quantity useful in characterizing lipid bilayer structure and dynamics. However, simply dividing the flat surface area covered by the number of lipids does not give a sufficient characterization of surface dynamics in cases where parts of the lipid leaflets have curvaceous trajectories in three dimensions. An algorithm is proposed for modeling surface area per lipid using a three-dimensional tessellated grid. In this way both the vertical, as well as the more commonly considered the horizontal, fluctuations of lipids are used to accurately determine the area covered. This algorithm can reveal differences in …

Analyzation Of The Resistor-Inductor-Capacitor Circuit, Martin D. Elton

Undergraduate Journal of Mathematical Modeling: One + Two

Starting with the basics of what a Resistor-Inductor-Capacitor circuit (RLC) is, i.e. its fundamental components, and ending with practical applications using advanced calculus to aid in predetermining the results and circuit design, this paper analyzes the RLC circuit via an advanced calculus based approach.

Efficacy Of Acute Normovolemic Hemodilution In The Setting Of Chronic Anemia, Andrew Vieira

Undergraduate Journal of Mathematical Modeling: One + Two

A theoretical model for calculating hematocrit as it relates to blood volume loss was used to test the theoretical impact of acute normovolemic hemodilution prior to surgery in a chronically anemic patient. The technique of hemodilution is intended to decrease red blood cell loss that occurs as the result of surgical intervention, however its impact may be decreased in an anemic patient. An equation to find change in hematocrit resulting from blood volume loss was elucidated via integration. This equation was then applied to a theoretical patient with 5 L of blood and a hematocrit of 32 percent which revealed …

Diagnosing Breast Cancer With A Neural Network, John Cullen

Undergraduate Journal of Mathematical Modeling: One + Two

Fine needle aspiration (FNA) is a minimally invasive biopsy technique that can be used to successfully diagnose types of cancer, including breast cancer. Immediately, it is difficult for a human to spot any trends in the cell level data gathered during a fine needle aspiration procedure. One way to predict the type of tumor a patient has, is to use a computer to develop a mathematical model based on known data. This project utilizes the Diagnostic Wisconsin Breast Cancer Database (DWBCDB) to create an accurate mathematical model that predicts the type of a patient’s tumor (Malignant or Benign). A neural …

The Solow Model And Standard Of Living, Eric Frey

Undergraduate Journal of Mathematical Modeling: One + Two

All across the world, living standards vary significantly. The Solow growth model, developed by Nobel Prize winning economist Robert Solow in 1956, is still one of the most commonly used models in economics to explain economic growth. This paper will outline the Solow growth model, and its assertion that increases in total factor productivity (TFP) can lead to limitless increases in the standard of living in a country. Much of the mathematical notation and explanation has been derived from Stephen Williamson of Washington University. Additionally, it will provide empirical examples illustrating the model’s ability to match real-world data.

Application Of Simple Harmonics Modeling A Shock, Kai Raymond

Undergraduate Journal of Mathematical Modeling: One + Two

This project entails modeling a spring-shock absorber system in order to evaluate the position of a mass when this system is acted upon by outside forces. We will restrict our attention to the linear case where it is assumed that Hooke’s law gives the force exerted by the spring, and the resistance of the system will be proportional to the velocity of the mass. We analyze the time and frequency domain of the absorber system and compute its impulse response.

The Forces Affecting A Sailboat, Kelly Stukbauer

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project is to determine the specific effects of the various forces acting on a sailboat. Through this project, a greater understanding of both the physics behind sailing, and the calculus behind that physics, shall be gained.

Optimization Of A Fuel Cell, Eduardo Gines

Undergraduate Journal of Mathematical Modeling: One + Two

Fuel cells are devices that generate energy from a chemical reaction that takes place inside the cell. The main parts of these devices are two electrodes and an electrolyte solution. The project consists of determining the area of the electrodes for the fuel cell at which the cell produces its maximum amount of power. This was done with the performance curve of the fuel cell which was in terms of voltage vs current density. The performance curve was turned into terms of power density vs current density, and through this curve the maximum power was determined by identifying the maximum …

Analysis Of Rainfall In Tampa, Amy Polen

Undergraduate Journal of Mathematical Modeling: One + Two

Rainfall for a region is very important to define, because it affects an ecosystem health, wildlife, and even human behavior. Using data obtained from National Oceanographic and Atmospheric Administration (NOAA) at the Tampa Bay International Airport and graphing it, the total rainfall for a year was estimated by both a rough trapezoidal Riemann’s sum approximation and a definite integral generated by polynomial regression. It was determined that both approximations gave an underestimate of the total rainfall that was measured, but the polynomial integral gave a reasonable estimate with a small percent error. It was seen through the graphical representation of …

Rudimentary Model Of Glucose Response To Stress, Nasha Rios-Guzman

Undergraduate Journal of Mathematical Modeling: One + Two

A simplistic multifactorial model was crafted to represent change in plasma glucose concentrations after increases in stress hormones above baseline. A sample application of the predictive use of this model was demonstrated, and a reflection on possible models in diabetic populations was described. The potential for use of this model in conjunction with current models is discussed, as well as the issues pertinent to such a basic model.