Mathematics Commons^™

Modeling The Spread Of Alfalfa Stem Nematodes: Insights Into Their Dynamics And Control, Scott G. Jordan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Alfalfa is a major cash crop in the western United States, where fields that are infested with the alfalfa stem nematode (Ditylenchus dipsaci) can be found. With no nematicides available to control alfalfa stem nematode spread, growers can use nematode resistant varieties of alfalfa to manage nematode populations in a field. A deterministic, discrete-time, host-parasite model is presented that describes the spread of alfalfa stem nematodes on resistant hosts that was fit to experimental data obtained in Weber County, Utah. Numerical results obtained from simulations with the model are used to compare how varying levels of resistance can affect …

Nonassociative Right Hoops, Peter Jipsen, Michael Kinyon

Mathematics, Physics, and Computer Science Faculty Articles and Research

The class of nonassociative right hoops, or narhoops for short, is defined as a subclass of right-residuated magmas, and is shown to be a variety. These algebras generalize both right quasigroups and right hoops, and we characterize the subvarieties in which the operation x ^^ y = (x/y)y is associative and/or commutative. Narhoops with a left unit are proved to be integral if and only if ^ is commutative, and their congruences are determined by the equivalence class of the left unit. We also prove that the four identities defining narhoops are independent.

Candy Sharing And Chip Firing Games On Graphs, Joseph Degaetani

Theses, Dissertations and Culminating Projects

The Candy Game begins with a finite number of players sitting in a circle, each with an initial amount of candy. At each time step, each player passes half of their pile to the player on their left (with odd sized stacks receiving an extra piece of candy). The original question was whether every initial distribution of candy results in every player holding the same number of pieces after a finite number of turns. For arbitrary initial distributions, we prove asymptotically tight bounds on the final amount of candy. The diffusion chip firing game assigns integral chip amounts to each …

The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, Michael Kumaresan

Dissertations, Theses, and Capstone Projects

We study the Cauchy problem for the advection-diffusion equation when the diffusive parameter is vanishingly small. We consider two cases - when the underlying flow is a shear flow, and when the underlying flow is generated by a Hamiltonian. For the former, we examine the problem on a bounded domain in two spatial variables with Dirichlet boundary conditions. After quantizing the system via the Fourier transform in the first spatial variable, we establish the enhanced-dissipation effect for each mode. For the latter, we allow for non-degenerate critical points and represent the orbits by points on a Reeb graph, with vertices …

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …

Start A Math Teacher Circle: Connect K-12 Teachers With Engaging, Approachable, And Meaningful Mathematical Problems, Tom Clark, Mike Janssen, Amanda Harsy, Dave Klanderman, Mandi Maxwell, Sharon Robbert

Faculty Work Comprehensive List

Many K-12 math teachers are not ready to teach from a conceptual and inquiry-oriented perspective because they have an algorithmic understanding of mathematics. One solution is to create a math teacher circle (MTC), which provides conceptual and inquiry-based learning activities and builds professionalism among the teachers. In this paper, we describe the origins of two such MTCs, highlighting the process of identifying leadership team members, submitting the grant proposal for seed money, and hosting launch events, intensive summer workshops, and monthly meetings during the academic year. We also share opportunities for professional development for college and university faculty, including research …

The Local Theory For Regular Systems In The Context Of T-Bonded Sets, Mikhail M. Bouniaev, Nikolay Dolbilin

School of Mathematical & Statistical Sciences Faculty Publications

The main goal of the local theory for crystals developed in the last quarter of the 20th Century by a geometry group of Delone (Delaunay) at the Steklov Mathematical Institute is to find and prove the correct statements rigorously explaining why the crystalline structure follows from the pair-wise identity of local arrangements around each atom. Originally, the local theory for regular and multiregular systems was developed with the assumption that all point sets under consideration are (r,R)" role="presentation">(r,R) -systems or, in other words, Delone sets of type (r,R)" role="presentation">(r,R) in d-dimensional Euclidean space. In this paper, we will …

The Average Measure Of A K-Dimensional Simplex In An N-Cube, John A. Carter

Graduate Theses/Dissertations

Within an n-dimensional unit cube, a number of k-dimensional simplices can be formed whose vertices are the vertices of the n-cube. In this thesis, we analyze the average measure of a k-simplex in the n-cube. We develop exact equations for the average measure when k = 1, 2, and 3. Then we generate data for these cases and conjecture that their averages appear to approach n^k/2 times some constant. Using the convergence of Bernstein polynomials and a k-simplex Bernstein generalization, we prove the conjecture is true for the 1-simplex and 2-simplex cases. We then develop a generalized formula for …

The Capacitated Transfer Point Covering Problem (Tpcp): Expanding Delivery Network Coverage With Minimal Resources, Jeffrey Allen Mcdougall

Theses and Dissertations

Retail delivery services have begun using unmanned systems in attempts to reduce the time from a customer’s order to when the product arrives at its intended destination. Utilizing these systems are beneficial to both the customer and retailer, however they create problems for the dispatchers making decisions about the delivery. Promised delivery times are now quick enough that orders cannot be grouped and dispatched at predetermined or cyclic departure times. The limited range of emerging delivery vehicles, specifically unmanned aerial systems, creates gaps in last mile retail distribution networks and excludes significant numbers of potential customers. Distributers must use a …

Coincidence Of Bargaining Solutions And Rationalizability In Epistemic Games, Todd Stambaugh

Dissertations, Theses, and Capstone Projects

Chapter 1: In 1950, John Nash proposed the Bargaining Problem, for which a solution is a function that assigns to each space of possible utility assignments a single point in the space, in some sense representing the ’fair’ deal for the agents involved. Nash provided a solution of his own, and several others have been presented since then, including a notable solution by Ehud Kalai and Meir Smorodinsky. In chapter 1, a complete account is given for the conditions under which the two solutions will coincide for two player bargaining scenarios.

Chapter 2: In the same year, Nash …

Divergence Of Cat(0) Cube Complexes And Coxeter Groups, Ivan Levcovitz

Dissertations, Theses, and Capstone Projects

We provide geometric conditions on a pair of hyperplanes of a CAT(0) cube complex that imply divergence bounds for the cube complex. As an application, we characterize right-angled Coxeter groups with quadratic divergence and show right-angled Coxeter groups cannot exhibit a divergence function between quadratic and cubic. This generalizes a theorem of Dani-Thomas that addressed the class of 2-dimensional right-angled Coxeter groups. This characterization also has a direct application to the theory of random right-angled Coxeter groups. As another application of the divergence bounds obtained for cube complexes, we provide an inductive graph theoretic criterion on a right-angled Coxeter group's …

The Distribution Of Totally Positive Integers In Totally Real Number Fields, Tianyi Mao

Dissertations, Theses, and Capstone Projects

Hecke studies the distribution of fractional parts of quadratic irrationals with Fourier expansion of Dirichlet series. This method is generalized by Behnke and Ash-Friedberg, to study the distribution of the number of totally positive integers of given trace in a general totally real number field of any degree. When the number field is quadratic, Beck also proved a mean value result using the continued fraction expansions of quadratic irrationals. We generalize Beck’s result to higher moments. When the field is cubic, we show that the asymptotic behavior of a weighted Diophantine sum is related to the structure of the unit …

On Some Geometry Of Graphs, Zachary S. Mcguirk

Dissertations, Theses, and Capstone Projects

In this thesis we study the intrinsic geometry of graphs via the constants that appear in discretized partial differential equations associated to those graphs. By studying the behavior of a discretized version of Bochner's inequality for smooth manifolds at the cone point for a cone over the set of vertices of a graph, a lower bound for the internal energy of the underlying graph is obtained. This gives a new lower bound for the size of the first non-trivial eigenvalue of the graph Laplacian in terms of the curvature constant that appears at the cone point and the size of …

Geometry And Analysis Of Some Euler-Arnold Equations, Jae Min Lee

Dissertations, Theses, and Capstone Projects

In 1966, Arnold showed that the Euler equation for an ideal fluid can arise as the geodesic flow on the group of volume preserving diffeomorphisms with respect to the right invariant kinetic energy metric. This geometric interpretation was rigorously established by Ebin and Marsden in 1970 using infinite dimensional Riemannian geometry and Sobolev space techniques. Many other nonlinear evolution PDEs in mathematical physics turned out to fit in this universal approach, and this opened a vast research on the geometry and analysis of the Euler-Arnold equations, i.e., geodesic equations on a Lie group endowed with one-sided invariant metrics. In this …

A Logistic Regression Analysis Of First-Time College Students’ Completion Rates At The University Of Southern Mississippi, Jesse Homer Robinson

Honors Theses

The demand for employees with a college degree is steadily on the rise in a plethora of competitive job markets throughout the United States. This increase in demand has aided in the increasing college enrollment rates throughout the country. However, unlike enrollment trends, the rate of college completion has not had the same fortunate rise.

The goal of this study is to research and compare differences among those first-time college students who completed college within four years, six years, or did not complete. The primary source for data in this study was the Office of Institutional Research at USM. Both …

Particular Solutions Of Products Of Helmholtz-Type Equations Using The Matern Function, Xiao-Yan Liu, Ching-Shyang Chen, Wen Li, Ming Li

Faculty Publications

We derive closed-form particular solutions for Helmholtz-type partial differential equations. These are derived explicitly using the Matern basis functions. The derivation of such particular solutions is further extended to the cases of products of Helmholtz-type operators in two and three dimensions. The main idea of the paper is to link the derivation of the particular solutions to the known fundamental solutions of certain differential operators. The newly derived particular solutions are used, in the context of the method of particular solutions, to solve boundary value problems governed by a certain class of products of Helmholtz-type equations. The leave-one-out cross validation …

The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

Honors Projects

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …

On Rugina’S System Of Thought, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This article investigates Rugina's orientation table and gives particular examples for several of its seven models. Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in Rugina's orientation table in systems which are s percent stable and 100 ÿ s percent unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. Classical logic and modern logic are united in Rugina's integrated logic, and then generalized in neutrosophic logic.

Non-Commutative Zero-Knowledge Protocols, Bailey Stewart

Departmental Honors & Graduate Capstone Projects

We examine zero-knowledge protocols working in non-commutative structures. Specifically, we will discuss the advantages and disadvantages of using invertible elements and elements that have a square root. An adaptation of the zero-knowledge protocol will be presented for working in symmetric groups and monoids of endomorphisms and matrices. Additionally, the security behind these zero-knowledge protocols will be discussed as well as showing different scenarios where invertible elements and elements with squares are vulnerable to attacks.

An Analysis Of Efficiency Measures Of The S/V Zodiac, Henry Darron

Departmental Honors & Graduate Capstone Projects

This paper concerns forecasting the performance of the S/V Zodiac, a two-masted schooner operating as a public and private charter vessel out of Bellingham, Washington. Two aspects of performance are discussed, namely the business cycle of the Zodiac and the operating efficiency of the Zodiac. For the business cycle, it is found that the best model for the business cycle is the one-year-ahead plan developed for the vessel in or around November each year. As for the operating efficiency, an original model is developed from techniques used for forecasting power outputs of wind farms and individual wind turbines. …

Jacobian Elliptic Kummer Surfaces And Special Function Identities, Elise Griffin, Andreas Malmendier

Mathematics and Statistics Faculty Publications

We derive formulas for the construction of all inequivalent Jacobian elliptic fibrations on the Kummer surface of two non-isogeneous elliptic curves from extremal rational elliptic surfaces by rational base transformations and quadratic twists. We then show that each such decomposition yields a description of the Picard-Fuchs system satisfied by the periods of the holomorphic two-form as either a tensor product of two Gauss' hypergeometric differential equations, an Appell hypergeometric system, or a GKZ differential system. As the answer must be independent of the fibration used, identities relating differential systems are obtained. They include a new identity relating Appell's hypergeometric system …

An Optimized Route For Q100'S Bert And Kristin To Visit All Jersey Mike's Subs In Atlanta For Charity

Symposium of Student Scholars

The Bert Show is a popular morning show on Atlanta’s Q100 radio station. They host a non-profit organization that provides a “magical, all-expenses-paid, five-day journey to Walt Disney World for children with chronic and terminal illnesses and their families” called “Bert’s Big Adventure.” On March 28^th, 2018, thirty-seven locations of Jersey Mike’s are participating in the their Jersey Mike’s Day of Giving to support Bert’s Big Adventure. The goal is to have two popular radio show hosts visit each of these locations for some photos and presence to draw in more customers! But how do we get two …

Non-Commutative Massey-Omura Encryption With Symmetric Groups, Shannon Haley

Departmental Honors & Graduate Capstone Projects

We introduce two non-commutative variations on the original Massey-Omura encryption system using conjugations in the symmetric group S_n. Patented in 1986, the original system was based on the cyclic group F^* of units in a finite field F. In place of the abelian group F^*, we will work in the non-abelian group S_nusing disjoint permutations as well as maximal abelian subgroups in order to potentially create a more secure system. Introducing the non-abelian group S_n presents the need to create a keyspace of commuting permutations and abelian subgroups of sufficient size. …

Abstraction And Infinity (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Abstraction and Infinity by Paolo Mancosu, Oxford University Press, 2017. 222 pp. ISBN: 9780198746829.

Forcing Number, Maximum Nullity, And Minimum Rank Theorems Concerning The Generalized Petersen Graph And Related Observations, Hobert J. Holbrook, R. Duane Skaggs

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Mathematical Surfaces And 3d Printing, Haily A. Slone, R. Duane Skaggs

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashuwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

In this paper, we explore the notion of simplicity. We use definitions of simplicity proposed by philosophers, scientists, and economists. In an age when the rapidly growing human population faces an equally rapidly declining energy/material resources, there is an urgent need to consider various notions of simplicity, collective and individual, which we believe to be a sensible path to restore our planet to a reasonable state of health. Following the logic of mathematicians and physicists, we suggest that simplicity can be related to sustainability. Our efforts must therefore not be spent so much in pursuit of growth but in achieving …

Measuring A Rifle’S Recoil Using Wireless Dynamics Sensor System, Seth Baker, Ignacio Birriel

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Efficient Reduced Bias Genetic Algorithm For Generic Community Detection Objectives, Aditya Karnam Gururaj Rao

Theses

The problem of community structure identification has been an extensively investigated area for biology, physics, social sciences, and computer science in recent years for studying the properties of networks representing complex relationships. Most traditional methods, such as K-means and hierarchical clustering, are based on the assumption that communities have spherical configurations. Lately, Genetic Algorithms (GA) are being utilized for efficient community detection without imposing sphericity. GAs are machine learning methods which mimic natural selection and scale with the complexity of the network. However, traditional GA approaches employ a representation method that dramatically increases the solution space to be searched by …

Effect Of A Pre-Dinner Walnut Snack On Nutrient Intake Among University Students, Michelle E. Lacasse, Mackenzie J. Weis, Lauren S. Devaan, Gabrielle L. Schnellman, Elizabeth M. Gile, Molly D. Ahmann, Ted Wilson, Tisha L. Hooks

Undergraduate Research Celebration 2018

No abstract provided.