Mathematics Commons^™

It Is Better To Be Upside Than Sharpe!, Daniele Dapuzzo

Theses and Dissertations

Based on the assumption that returns in Commercial Real Estate are normally distributed, the Sharpe Ratio has been the standard risk-adjusted performance measure for the past several years. Research has questioned whether this assumption can be reasonably made. The Upside Potential Ratio as a risk-adjusted performance measure is an alternative to measure performance on a risk-adjusted basis but its values differ from the Sharpe Ratio's only in the assumption of skewed returns. We will provide reasonable evidence that CRE returns should not be fitted with a normal distribution and present the Gaussian Mixture Model as our choice of distribution to …

Connections Between Project-Based Learning And Mathematics Instruction: Exploring Their Integration In Classroom Curricula, Zoe Nietert

Undergraduate Honors Thesis Projects

Project-based learning is poorly defined leading to confusion and inconsistent implementation in the classroom. To eliminate the use of project-based learning as educational jargon it is imperative to define the term. This project aims to define project-based learning in a manner that outlines its critical and variable attributes. From the established definition, a rubric is created to determine the quality of project-based learning materials, specifically in the context of math education. The purpose of the rubric is to create a tool to be used in future classrooms as a means of identifying classroom curricula that demonstrate both project-based learning and …

Asymptotics For Primitive Roots Producing Polynomials And Primitive Points On Elliptic Curves, Nelson Carella

Publications and Research

Let $x \geq 1$ be a large number, let $f(n) \in \mathbb{Z}[x]$ be a prime producing polynomial of degree $\deg(f)=m$, and let \(u\neq \pm 1,v^2\) be a fixed integer. Assuming the Bateman-Horn conjecture, an asymptotic counting function for the number of primes $p=f(n) \leq x$ with a fixed primitive root $u$ is derived in this note. This asymptotic result has the form $$\pi_f(x)=\# \{ p=f(n)\leq x:\ord_p(u)=p-1 \}=\left (c(u,f)+ O\left (1/\log x )\right ) \right )x^{1/m}/\log x$$, where $c(u,f)$ is a constant depending on the polynomial and the fixed integer. Furthermore, new results for the asymptotic order of elliptic primes with …

Extending Uniqueness Implies Existence Results To Fractional Differential Equations, Tyler Masthay

Honors Theses

In 1967, Andrzej Lasota and Zdzisław Opial proved that under sufficient conditions, uniqueness of solutions for boundary value problems for a second-order ordinary differential equation implies their existence. Lloyd Jackson and Keith Schrader then proved an extension of this result for boundary value problems of third order. In proving the third-order case, this compactness theorem is applied as a key part of the proof. It states that under sufficient conditions, uniform boundedness of a sequence of solutions on a compact domain implies existence of a subsequence which converges uniformly with respect to its zeroth, first, and second derivatives. We present …

Kadison's Pythagorean Theorem And Essential Codimension, Jireh Loreaux, Victor Kaftal

SIUE Faculty Research, Scholarship, and Creative Activity

Kadison’s Pythagorean theorem (Proc Natl Acad Sci USA, 99(7):4178–4184, 2002; Proc Natl Acad Sci USA 99(8):5217–5222, 2002) provides a characterization of the diagonals of projections with a subtle integrality condition. Arveson (Proc Natl Acad Sci USA 104(4):1152–1158, 2007), Kaftal, Ng, Zhang (J Funct Anal 257(8):2497–2529, 2009), and Argerami (Integral Equ Oper Theory 82(1):33–49, 2015) all provide different proofs of that integrality condition. In this paper we interpret the integrality condition in terms of the essential codimension of a pair of projections introduced by Brown et al. (Proceedings of a conference on operator theory, Lecture notes …

Volatility Analysis Of Us Equity And Federal Funds Markets Through The Recent Financial Crisis And Recovery Periods, Based On Release Of Fomc Meeting Statements And Minutes, Hanxiao Yue

Student Theses and Dissertations

The Federal Open Market Committee (FOMC) is the principal maker of monetary policy in the United States. The main instrument of monetary policy is the target federal funds rate, which is de facto the base interest rate of the US economy. The FOMC meets around eight times a year to discuss the economic outlook and decide on this metric. Throughout most of its history, the Fed has been opaque about how it decides on monetary policy, but in recent years it has adopted a more transparent disclosure policy. For each FOMC meeting, it currently releases a brief statement immediately after …

Math Education In The U.S.: A Discussion Of History, Principles, And Practice, Kim Canzoneri , '17

Senior Theses, Projects, and Awards

No abstract provided.

A Study Of Perceptions Of Math Mindset, Math Anxiety, And View Of Math By Young Adults, Tami L. Hocker

Doctor of Education (Ed.D)

This study’s purpose was to determine whether instruction in growth math mindset led to change in perceptions of 18-22-year-old at-risk students in math mindset, math anxiety, and view of math. The experimental curriculum was created by the researcher with the guidance of experts in mathematics and education and focused on the impact of brain growth and learning supported by positive math mindset. Young adult public charter high school at-risk students were surveyed before and after completion of the experimental intervention to measure their perceptions in the domains of Math Mindset, Math Anxiety, and View of Math. The results revealed significant …

Making And Breaking Mathematical Sense (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Making and Breaking Mathematical Sense by Roi Wagner. Princeton, NJ: Princeton University Press, 2017. 236 pp. ISBN: 9780691171715.

Cross Ratio, Peyton Burlingame

Paper and Posters Presentations

A question posed in the MAA Monthly is the following: “Given four points A, B, C, and D in order on a line in Euclidean space, under what conditions will there be a point P off the line such that the angles ???APB, ?BPC, and ?CPD have equal measure.” We will present a partial solution of this question using the cross ratio. The cross ratio plays a central role in projective geometry however can be proved using the Law of Sines. The elements of the proofs are comprised of calculus, algebra, and geometry.

Deriving A Provisional Tolerable Intake For Intravenous Exposure To Silver Nanoparticles Released From Medical Devices, Laura C. Savery, Rene Vinas, Amber M. Nagy, Prachi Pradeep, Stephen Merrill, Subhas G. Malghan, Peter L. Goering, Ronald P. Brown

Mathematics, Statistics and Computer Science Faculty Research and Publications

Silver nanoparticles (AgNP) are incorporated into medical devices for their anti-microbial characteristics. The potential exposure and toxicity of AgNPs is unknown due to varying physicochemical particle properties and lack of toxicological data. The aim of this safety assessment is to derive a provisional tolerable intake (pTI) value for AgNPs released from blood-contacting medical devices. A literature review of in vivo studies investigating critical health effects induced from intravenous (i. v.) exposure to AgNPs was evaluated by the Annapolis Accords principles and Toxicological Data Reliability Assessment Tool (ToxRTool). The point of departure (POD) was based on an i. v. 28-day …

The Existence Of Solutions For A Nonlinear, Fractional Self-Adjoint Difference Equation, Kevin Ahrendt

Department of Mathematics: Dissertations, Theses, and Student Research

In this work we will explore a fractional self-adjoint difference equation which involves a Caputo fractional difference. In particular, we will develop a Cauchy function for initial value problems and Green's functions for several different types of boundary value problems. We will use the properties of those Green's functions and the Contraction Mapping Theorem to find sufficient conditions for when a nonlinear boundary value problem has a unique solution. We will also investigate the existence of nonnegative solutions for a nonlinear self-adjoint difference that have particular long run behavior.

Adviser: Allan Peterson

Predoctoral Dental Students’ Perceptions Of Dental Implant Training: Effect Of Preclinical Simulation And Clinical Experience, Soni Prasad, Naveen K. Bansal

School of Dentistry Faculty Research and Publications

The aims of this study were to assess 1) differences in perceptions of dental implant training between dental students who received didactic training alone (control group) and those who received didactic plus simulation training (test group); 2) differences in response between students with and without clinical experience in implant dentistry; and 3) the interaction effect of simulation training and clinical experience on students’ satisfaction. A survey was distributed to the control group in 2014 and to the test group in 2015; both groups were at the same U.S. dental school. Data were collected on confidence levels with various implant restorative …

New Bounds For The K-Out-Of-N Type Probabilities And Their Applications, Ahmed M. Binmahfoudh

Theses and Dissertations

The contribution of the shape information of the underlying distribution in probability bounding problem is investigated and an efficient linear programming based bounding methodology, which takes advantage of the advanced optimization techniques, probability theory, and the state-of-the-art tools, to obtain robust and efficiently computable bounds for the probabilities that at least k and exactly k-out-of-n events occur is developed. The k-out-of-n type probability bounding problem is formulated as linear programs under the assumption that the probability distribution is unimodal. The dual feasible bases structures of the relaxed versions of linear programs involved are fully described. The bounds for the probability …

Pythagorean Approximations For Lego: Merging Educational Robot Construction With Programming And Data Analysis, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

Abstract. This paper can be used in two ways. It can provide reference information for incorporating diagonal elements (for bracing or gear meshing) in educational robots built from standard LEGO kits. Alternatively, it can be used as the basis for an assignment for high school or college students to recreate this information; in the process, students will exercise skills in both computer programming and data analysis. Using the paper in the second way can be an excellent integrative experience to add to an existing course; for example, the Exploring Computer Science high school curriculum concludes with the units “Introduction to …

Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, S.C. Mancas

Publications

A one-parameter family of Emden-Fowler equations defined by Lampariello’s parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

A Framework For Predicting Impacts On Ecosystem Services From (Sub)Organismal Responses To Chemicals, Valery E. Forbes, Chris J. Salice, Bjorn Birnir, Randy J.F. Bruins, Peter Calow, Virginie Ducrot, Nika Galic, Kristina Garber, Bret C. Harvey, Henriette Jager, Andrew Kanarek, Robert Pastorok, Steve F. Railsback, Richard Rebarber, Pernille Thorbek

Department of Mathematics: Faculty Publications

Protection of ecosystem services is increasingly emphasized as a risk-assessment goal, but there are wide gaps between current ecological risk-assessment endpoints and potential effects on services provided by ecosystems. The authors present a framework that links common ecotoxicological endpoints to chemical impacts on populations and communities and the ecosystem services that they provide. This framework builds on considerable advances in mechanistic effects models designed to span multiple levels of biological organization and account for various types of biological interactions and feedbacks. For illustration, the authors introduce 2 case studies that employ well-developed and validated mechanistic effects models: the inSTREAM individual-based …

Regime Switching In Cointegrated Time Series, Bradley David Zynda Ii

Undergraduate Honors Capstone Projects

Volatile commodities and markets can often be difficult to model and forecast given significant breaks in trends through time. To account such breaks, regime switching methods allow for models to accommodate abrupt changes in behavior of the data. However, the difficulty often arises in beginning the process of choosing a model and its associated parameters with which to represent the data and the objects of interest. To improve model selection for these volatile markets, this research examines time series with regime switching components and argues that a synthesis of vector error correction models with regime switching models with ameliorate financial …

Motor Preparation Rather Than Decision-Making Differentiates Parkinson’S Disease Patients With And Without Freezing Of Gait, John Butler, Conor Fearon, Isabelle Killane, Saskia M. Waechter, Richard B. Reilly, Timothy Lynch

Articles

Objective: Freezing of gait (FOG) is a brief, episodic phenomenon affecting over half of people with Parkinson’s disease (PD) and leads to significant morbidity. The pathophysiology of FOG remains poorly understood but is associated with deficits in cognitive function and motor preparation.

Method: We studied 20 people with PD (10 with FOG, 10 without FOG) and performed a timed response target detection task while electroencephalographic data were acquired. We analysed the data to detect and examine cortical markers of cognitive decision making (P3b or centroparietal positivity, CPP) and motor readiness potential. We analysed current source density (CSD) to increase spatial …

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 …