Physical Sciences and Mathematics Commons^™

Lump Solutions And Riemann-Hilbert Approach To Soliton Equations, Sumayah A. Batwa

USF Tampa Graduate Theses and Dissertations

In the first part of this dissertation we introduce two matrix iso-spectral problems, a Kaup-Newell type and a generalization of the Dirac spectral problem, associated with the three-dimensional real Lie algebras sl(2;R) and so(3;R), respectively. Through zero curvature equations, we furnish two soliton hierarchies. Hamiltonian structures for the resulting hierarchies are formulated by adopting

the trace identity. In addition, we prove that each of the soliton hierarchies has a bi-Hamiltonian structure which leads to the integrability in the Liouville sense. The motivation of the first part is to construct soliton hierarchies with infinitely many commuting symmetries and conservation laws.

The …

Groups Generated By Automata Arising From Transformations Of The Boundaries Of Rooted Trees, Elsayed Ahmed

USF Tampa Graduate Theses and Dissertations

In this dissertation we study groups of automorphisms of rooted trees arising from the transformations of the boundaries of these trees. The boundary of every regular rooted tree can be endowed with various algebraic structures. The transformations of these algebraic structures under certain conditions induce endomorphisms or automorphisms of the tree itself that can be described using the language of Mealy automata. This connection can be used to study boundarytransformations using the propertiesof the induced endomorphisms, or vice versa.

We concentrate on two ways to interpret the boundary of the rooted d-regular tree. In the first approach discussed in detail …

Quantitative Literacy And Civic Virtue, William Briggs

Numeracy

Mathematics educators are occasionally called upon to justify the existence or the offering of quantitative literacy courses. This paper argues that effective quantitative literacy courses have different goals than algebra courses and are legitimate alternatives to algebra courses for non-STEM students. Furthermore, quantitative literacy courses affirm the historic relationship between citizenship and education. In today’s world of proliferating news sources, social media, and fake news, quantitative literacy has become an essential component of the long-held ideal of civic virtue.

Hamiltonian Structures And Riemann-Hilbert Problems Of Integrable Systems, Xiang Gu

USF Tampa Graduate Theses and Dissertations

We begin this dissertation by presenting a brief introduction to the theory of solitons and integrability (plus some classical methods applied in this field) in Chapter 1, mainly using the Korteweg-de Vries equation as a typical model. At the end of this Chapter a mathematical framework of notations and terminologies is established for the whole dissertation.

In Chapter 2, we first introduce two specific matrix spectral problems (with 3 potentials) associated with matrix Lie algebras $\mbox{sl}(2;\mathbb{R})$ and $\mbox{so}(3;\mathbb{R})$, respectively; and then we engender two soliton hierarchies. The computation and analysis of their Hamiltonian structures based on the trace identity affirms …

Generalizations Of Quandles And Their Cohomologies, Matthew J. Green

USF Tampa Graduate Theses and Dissertations

Quandles are distributive algebraic structures originally introduced independently by David Joyce and Sergei Matveev in 1979, motivated by the study of knots. In this dissertation, we discuss a number of generalizations of the notion of quandles. In the first part of this dissertation we discuss biquandles, in the context of augmented biquandles, a representation of biquandles in terms of actions of a set by an augmentation group. Using this representation we are able to develop a homology and cohomology theory for these structures.

We then introduce an n-ary generalization of the notion of quandles. We discuss a number of properties …

Developing A Model To Predict Prevalence Of Compulsive Behavior In Individuals With Ocd, Lindsay D. Fields

USF Tampa Graduate Theses and Dissertations

The most common method of diagnosing Obsessive-Compulsive Disorder is the Yale-Brown Obsessive Compulsive Scale, which measures the severity of symptoms without regard to compulsions. However, this scale is limited to only considering the quantifiable time and energy lost to compulsions. Conversely, current systems of brain imaging arrest mobility and thus make it virtually impossible to observe compulsions at all, focusing instead on neurological responses to external stimuli. There is little research which merges both approaches, to consider the neuro-physiological effects of obsessions as well as the physical response through compulsions. As such, this research is focused on developing a model …

A Hybrid Dynamic Modeling Of Time-To-Event Processes And Applications, Emmanuel A. Appiah

USF Tampa Graduate Theses and Dissertations

In the survival and reliability data analysis, parametric and nonparametric methods are used to estimate the hazard/risk rate and survival functions. A parametric approach is based on the assumption that the underlying survival distribution belongs to some specific family of closed form distributions (normal, Weibull, exponential, etc.). On the other hand, a nonparametric approach is centered around the best-fitting member of a class of survival distribution functions. Moreover, the Kaplan-Meier and Nelson-Aalen type nonparametric approach do not assume either distribution class or closed-form distributions. Historically, well-known time-to-event processes are death of living specie in populations and failure of component in …

Orthogonal Polynomials With Respect To The Measure Supported Over The Whole Complex Plane, Meng Yang

USF Tampa Graduate Theses and Dissertations

In chapter 1, we present some background knowledge about random matrices, Coulomb gas, orthogonal polynomials, asymptotics of planar orthogonal polynomials and the Riemann-Hilbert problem. In chapter 2, we consider the monic orthogonal polynomials, $\{P_{n,N}(z)\}_{n=0,1,\cdots},$ that satisfy the orthogonality condition,

\begin{equation}\nonumber \int_\mathbb{C}P_{n,N}(z)\overline{P_{m,N}(z)}e^{-N Q(z)}dA(z)=h_{n,N}\delta_{nm} \quad(n,m=0,1,2,\cdots), \end{equation}

where $h_{n,N}$ is a (positive) norming constant and the external potential is given by

$$Q(z)=|z|^2+ \frac{2c}{N}\log \frac{1}{|z-a|},\quad c>-1,\quad a>0.$$

The orthogonal polynomial is related to the interacting Coulomb particles with charge $+1$ for each, in the presence of an extra particle with charge $+c$ at $a.$ For $N$ large and a fixed ``c'' this …

Non-Equilibrium Phase Transitions In Interacting Diffusions, Wael Al-Sawai

USF Tampa Graduate Theses and Dissertations

The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific …

Review Of Painting By Numbers By Jason Makansi, Thomas J. Pfaff

Numeracy

Makansi, Jason. 2016. Painting By Numbers: How to Sharpen Your BS Detector and Smoke Out the "Experts." (Tucson, AZ: Layla Dog Press, 2016). 196 pp. ISBN 978-0-9984259-0-0.

In Painting by Numbers Jason Makansi adds another book to the quantitative literacy bookshelf, with a book focusing on models. The book offers twelve commandments to aid the reader in assess quantitative models. The second section of the book offers examples to apply the models. Increasing quantitative literacy is crucial and generally, the more books the better. Unfortunately, this book is too superficial, often misses key ideas, and can easily lead a person …

Life, The Universe, And Numeracy: Review Of A Numerate Life By John Allen Paulos (2015), Kira H. Hamman

Numeracy

John Allen Paulos. 2015. A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours (Buffalo, NY: Prometheus Books) 200 pp. ISBN: 978-1633881181

John Allen Paulos, author of Innumeracy and many other books addressing quantitative literacy and numeracy in society, tackles autobiography in this quirky "anti-memoir."

A Few Reflections On A Numerate Life, John Allen Paulos

Numeracy

John Allen Paulos. 2015. A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours (Amherst, NY: Prometheus Books). 200 pp. ISBN 978-1633881181.

This piece briefly introduces and excerpts A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours, written by John Allen Paulos and published by Prometheus Books. The book shares observations on life—many biographical—from the perspective of a numerate mathematician. The excerpt uses basic statistical reasoning to explore why we should expect that being odd is a most normal experience.

Math Course For Liberal Arts Majors: A Pilot With Embedded Remediation, Eileen B. Perez, Hansun To, Mary Fowler, Linda Larrivee

Numeracy

This study was designed to determine if embedded remediation is significant in accelerating the pathway to completion of a college-level math course for students needing remediation. The project studied the impact on student success in a quantitative literacy course at a Massachusetts four-year state university with remedial material embedded. The course satisfies the university’s general education math requirement for students with liberal arts majors who are not required to complete college algebra or calculus-based courses. The paper begins with a presentation of the issues with remedial mathematics and its impact on students’ graduation and persistence. Next, the paper covers the …

Organic Agricultural Analysis: Efficiency Of Common Practices, Bradley Biega

Undergraduate Journal of Mathematical Modeling: One + Two

To analyze the efficiency of common watering practices in an organic agriculture setting we use Sweetwater Organic Farm’s conventional methods for irrigation and land allotment as well as some algebra and calculus technique. Sweetwater’s operation is limited to their largest growing field. A mathematical model is built to determine the current efficiency of the rotary head sprinkler system. Then the efficiency of this system is compared to a new drip line system. Several variables like soil porosity, absorption rates, and areas where no plants are located, are taken into consideration. Our results show that the current irrigation in place wastes …

Using The Entropy Rate Balance To Determine The Heat Transfer And Work In An Internally Reversible, Polytropic, Steady State Flow Process, Savannah Griffin

Undergraduate Journal of Mathematical Modeling: One + Two

The entropy rate equation for internally reversible steady state flow process has been used to calculate the heat transfer and work in an internally reversible, polytropic, steady state flow process.

Polycrystalline Silicon Solar Module Power Max, Jaynil Patel

Undergraduate Journal of Mathematical Modeling: One + Two

In recent years solar energy has started to make its impact in the sunshine state. The solar panels are made up of photovoltaic cells, which convert the sun’s rays into electricity. One of the ways to improve solar panel efficiency is to increase the power output of a solar collector. The maximum power is calculated by determining the maximum power for voltage and the current. This is done by adding the maximum values for the equation for power and then using differentiation. After the maximum values are found for each hour of the day from sunset to noon, each individual …

Model Function Of Women’S 1500m World Record Improvement Over Time, Annie Allmark

Undergraduate Journal of Mathematical Modeling: One + Two

We give an example of simple modeling of the known sport results that can be used for athletes’ self-improvement and estimation of future achievements.

This project compares the women’s 1500-meter world record times to the time elapsed between when they were run. The function of time which describes this comparison is found through graphing the data and interpreting the graphs. Then the obtained model function is compared to the real time data. The conclusions drawn from the result include that the calculated function of time lacks in accuracy as time elapsed increases, but the model could be used to estimate …

Optimization Of A Water Gas Shift Reaction, Ali Albuloushi

Undergraduate Journal of Mathematical Modeling: One + Two

The optimum flow rate of steam (H₂0) to the reactor for the purpose of producing hydrogen gas for sale is determined.

Tsunami Waves, Samantha Pennino

Undergraduate Journal of Mathematical Modeling: One + Two

Predicting the travel time of tsunami waves is imperative to the safety and well-being of possibly affected communities since tsunami waves can happen incredibly fast. So, knowing how long an area is until a tsunami approaches dramatically helps with mitigation strategies. As an example we calculate the travel time of a tsunami wave to Somalia and Sri-Lanka that flowed an earthquake in 2004 in the Indian ocean off the coast of Sumatra. This is done by using the velocity from the shallow wave equation of the waves and piecewise integration.

Geochemical Modeling Of Fractional Magma Crystallization, Luke Varner

Undergraduate Journal of Mathematical Modeling: One + Two

Modern day geologists use many different modeling programs such as Geospatial Information Systems in addition to R (programming language) for a wide array of applications such as: projecting collected data for mapping, visualization, and trend prediction. Computational power for these modeling programs is derived from Calculus, Probability, and Statistics. The purpose of this paper is to provide a site-specific geochemical analysis of an igneous rock formation composed of two specific compositions allowing for the predictions of rock formation derived from the resultant geochemical model.

Design Of Nozzle For High-Powered Solid Rocket Propellant, Jackson Stephenson

Undergraduate Journal of Mathematical Modeling: One + Two

This paper presents a preliminary nozzle design for a high-altitude rocket to be built by SOAR, the Society of Aeronautics and Rocketry. The equations and methods used for analysis came from professional sources via text or informational videos. The equations in focus will look at the temperature/pressure/area-Mach relationships for isentropic flow, pressure expansions in selected materials, and finding other characteristic properties using safe chemical property assumptions using CEARUN. The equations were used under the assumption of an isentropic flow under sea level conditions. If the design and the projected results look promising, they will be implemented soon for machining and …

Trend Analysis And Completion Prediction Of The Section Project, Ronald Jones

Undergraduate Journal of Mathematical Modeling: One + Two

Creating an accurate prediction of the completion timeline of a software development project is complicated and error prone. Developers will gain a natural intuition as to how long a task should take then. However, this prediction can end up being wrong in many cases due to many factors. This paper will attempt to determine a formula which allows a more accurate prediction to be created.

Creating an accurate prediction of the completion timeline of a software development project is complicated and error prone. Developers will gain a natural intuition as to how long a task should take then. However, this …

Comparing Two Flywheel-Piston Linkages, Anthony Sanchez

Undergraduate Journal of Mathematical Modeling: One + Two

The main idea of this paper is to compare two different ways of linking a flywheel to a piston: the Scotch Yoke linkage and the Eccentric linkage. The Scotch Yoke linkage is a way to convert the linear motion of a piston into rotational motion by using a flywheel, or vice versa. The Eccentric mechanism, on the other hand, consists of a circular wheel that is fixed to a rotating axle that makes it rotate. We compare two methods by expressing both motions as functions of three variables (R, L and θ) and use these functions to …

Minimizing Container Weight, Ibrahim Alomran

Undergraduate Journal of Mathematical Modeling: One + Two

Increased globalization has resulted in increased competition in the shipping industry. Since large carriers control over 70% of the total shipping industry, small carriers are left with only 30% of the market share to compete for. Ultimately, profit margins for small carriers have become very minimal. There is, therefore, need to develop a strategy that will aid in optimizing the profits of carriers. The goal of this paper is to develop a model that will help determine the minimum weight for a particular container design. The validity of the model is important in the sense that minimum container weight will …

Elapsed Time Of Vehicle Acceleration, Jensen Mctighe

Undergraduate Journal of Mathematical Modeling: One + Two

Newton’s Second Law states that force is equal to the mass of an object multiplied by its acceleration. More specifically, force is the mass times the instantaneous change in velocity over time of an object. By rearranging this equation, it can be determined that the time elapsed of the acceleration of an object is equal to the integral of the inverse value of the force relative to change in velocity (dv). In the context of real world application, this method can be used to calculate the time taken for a vehicle to accelerate from its minimum to maximum speed, given …