Mathematics Commons^™

A Study Of Topological Invariants In The Braid Group B2, Andrew Sweeney

Electronic Theses and Dissertations

The Jones polynomial is a special topological invariant in the field of Knot Theory. Created by Vaughn Jones, in the year 1984, it is used to study when links in space are topologically different and when they are topologically equivalent. This thesis discusses the Jones polynomial in depth as well as determines a general form for the closure of any braid in the braid group B2 where the closure is a knot. This derivation is facilitated by the help of the Temperley-Lieb algebra as well as with tools from the field of Abstract Algebra. In general, the Artin braid group …

Localization And Compactness Of Operators On Fock Spaces, Zhangjian Hu, Xiaofen Lv, Brett D. Wick

Mathematics Faculty Research

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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 …

Vector Partitions, Jennifer French

Electronic Theses and Dissertations

Integer partitions have been studied by many mathematicians over hundreds of years. Many identities exist between integer partitions, such as Euler’s discovery that every number has the same amount of partitions into distinct parts as into odd parts. These identities can be proven using methods such as conjugation or generating functions. Over the years, mathematicians have worked to expand partition identities to vectors. In 1963, M. S. Cheema proved that every vector has the same number of partitions into distinct vectors as into vectors with at least one component odd. This parallels Euler’s result for integer partitions. The primary purpose …

Italian Domination In Complementary Prisms, Haley D. Russell

Electronic Theses and Dissertations

Let $G$ be any graph and let $\overline{G}$ be its complement. The complementary prism of $G$ is formed from the disjoint union of a graph $G$ and its complement $\overline{G}$ by adding the edges of a perfect matching between the corresponding vertices of $G$ and $\overline{G}$. An Italian dominating function on a graph $G$ is a function such that $f \, : \, V \to \{ 0,1,2 \}$ and for each vertex $v \in V$ for which $f(v)=0$, it holds that $\sum_{u \in N(v)} f(u) \geq 2$. The weight of an Italian dominating function is the value $f(V)=\sum_{u \in V(G)}f(u)$. …

Covering Arrays For Equivalence Classes Of Words, Joshua Cassels, Anant Godbole

Undergraduate Honors Theses

Covering arrays for words of length t over a d letter alphabet are k × n arrays with entries from the alphabet so that for each choice of t columns, each of the d^t t-letter words appears at least once among the rows of the selected columns. We study two schemes in which all words are not considered to be different. In the first case, words are equivalent if they induce the same partition of a t element set. In the second case, words of the same weighted sum are equivalent. In both cases we produce logarithmic upper bounds …

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 …

Relations Between Theta Functions Of Genus One And Two From Geometry, Thomas Hill

Undergraduate Honors Capstone Projects

Genus-two curves with special symmetries are related to pairs of genus-one curves by two and three-sheeted ramified coverings. This classical work dates back to early 20th century and is known as Jacobi and Hermite reduction. Jacobians of genus-two curves can be used to construct complex two-dimensional complex projective manifolds known as Kummer surfaces. On the other hand, the defining coordinates and parameters of both elliptic curves and Kummer surfaces can be related to Riemann Theta functions and Siegel Theta functions, respectively. This result goes back to the seminal work of Mumford in the 1980s. We use the geometric relation between …

Mindset, Attitudes, And Success In Statistics, Matthew Isaac

Undergraduate Honors Capstone Projects

Students in many disciplines are required to take an introductory statistics course while pursuing a college education. Despite the utility of statistical methods in future research and career pursuits, many students have negative views of statistics. We are interested in how students' mindsets and attitudes towards statistics impact their performance in an undergraduate statistics course. We administered a survey to students in several undergraduate statistics courses at Utah State University. This survey included questions addressing mathematics experience, attitudes towards statistics, mindset, and course performance. We observed that the majority of students indicated the presence of a growth mindset and positive …

Three Environmental Fluid Dynamics Papers, Eden Furtak-Cole

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Three papers are presented, applying computational fluid dynamics methods to fluid flows in the geosciences. In the first paper, a numerical method is developed for single phase potential flow in the subsurface. For a class of monotonically advancing flows, the method provides a computational savings as compared to classical methods and can be applied to problems such as forced groundwater recharge. The second paper investigates the shear stress reducing action of an erosion control roughness array. Incompressible Naiver-Stokes simulations are performed for multiple wind angles to understand the changing aerodynamics of individual and grouped roughness elements. In the third paper, …

A Series Of Papers On Detecting Examinees Who Used A Flawed Answer Key, Marcus W. Scott

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One way that examinees can gain an unfair advantage on a test is by having prior access to the test questions and their answers, known as preknowledge. Determining which examinees had preknowledge can be a difficult task. Sometimes, the compromised test content that examinees use to get preknowledge has mistakes in the answer key. Examinees who had preknowledge can be identified by determining whether they used this flawed answer key. This research consisted of three papers aimed at helping testing programs detect examinees who used a flawed answer key.

The first paper developed three methods for detecting examinees who used …

Learning Logic: A Mixed Methods Study To Examine The Effects Of Context Ordering On Reasoning About Conditionals, Christina W. Lommatsch

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Logical statements are prevalent in mathematics, the sciences, law, and many areas of everyday life. The most common logical statements are conditionals, which have the form “If H..., then C...,” where “H” is a hypothesis (or condition) to be satisfied and “C” is a conclusion to follow. Reasoning about conditionals is a skill that is only superficially understood by most individuals and depends on four main conditional contexts (e.g., intuitive, abstract, symbolic, or counterintuitive). The purpose of this study was to test a theory about the effects of context ordering on reasoning about conditionals. To test the theory, the researcher …

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 …

Analysis Of 2016-17 Major League Soccer Season Data Using Poisson Regression With R, Ian D. Campbell

Undergraduate Theses and Capstone Projects

To the outside observer, soccer is chaotic with no given pattern or scheme to follow, a random conglomeration of passes and shots that go on for 90 minutes. Yet, what if there was a pattern to the chaos, or a way to describe the events that occur in the game quantifiably. Sports statistics is a critical part of baseball and a variety of other of today’s sports, but we see very little statistics and data analysis done on soccer. Of this research, there has been looks into the effect of possession time on the outcome of a game, the difference …

Adjunct Instructors’ Opportunities For Learning Through Engagement With A Research-Based Mathematics Curriculum, Zareen Gul Rahman

Theses, Dissertations and Culminating Projects

There is a growing need to retain students in STEM fields and majors in the U.S. Improving students’ experience in early mathematics courses like Precalculus can influence students’ decisions to remain in STEM fields. Teachers can play an important role in providing effective learning experiences to the students. Supporting teachers and providing professional development can help the teachers in facilitating student learning. When it comes to implementing research-based mathematics curricula, teachers are key players in making the curriculum come alive inside their classrooms. The challenges that teachers face when implementing a research-based mathematics curriculum can provide opportunities for their own …

The Auxiliary Space Preconditioner For The De Rham Complex, Jay Gopalakrishnan, Martin Neumüller, Panayot S. Vassilevski

Portland Institute for Computational Science Publications

We generalize the construction and analysis of auxiliary space preconditioners to the n-dimensional finite element subcomplex of the de Rham complex. These preconditioners are based on a generalization of a decomposition of Sobolev space functions into a regular part and a potential. A discrete version is easily established using the tools of finite element exterior calculus. We then discuss the four-dimensional de Rham complex in detail. By identifying forms in four dimensions (4D) with simple proxies, form operations are written out in terms of familiar algebraic operations on matrices, vectors, and scalars. This provides the basis for our implementation of …

Density Estimation Using Nonparametric Bayesian Methods, Yanyi Wang

Arts & Sciences Graduate Student Theses and Dissertations

In modern data analysis, nonparametric Bayesian methods have become increasingly popular. These methods can solve many important statistical inference problems, such as density estimation, regression and survival analysis. In this thesis, We utilize several nonparametric Bayesian methods for density estimation. In particular, we use mixtures of Dirichlet processes (MDP) and mixtures of Polya trees (MPT) priors to perform Bayesian density estimation based on simulated data. The target density is a mixture of normal distributions, which makes the estimation problem non-trivial. The performance of these methods with frequentist nonparametric kernel density estimators is assessed according to a mean-square error criterion. For …

Resistance To Peer Influence Moderates The Relationship Between Perceived (But Not Actual) Peer Norms And Binge Drinking In A College Student Social Network, Graham T. Diguiseppi, Matthew K. Meisel, Sara G. Balestrieri, Miles Q. Ott, Melissa J. Cox, Melissa A. Clark, Nancy P. Barnett

Statistical and Data Sciences: Faculty Publications

Introduction: Adolescent and young adult binge drinking is strongly associated with perceived social norms and the drinking behavior that occurs within peer networks. The extent to which an individual is influenced by the behavior of others may depend upon that individual’s resistance to peer influence (RPI).

Methods: Students in their first semester of college (N = 1323; 54.7% female, 57% White, 15.1% Hispanic) reported on their own binge drinking, and the perceived binge drinking of up to 10 important peers in the first-year class. Using network autocorrelation models, we investigated cross-sectional relationships between participant’s binge drinking frequency and the perceived …

Covering A Ball By Smaller Balls, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

We prove that, for any covering of a unit d-dimensional Euclidean ball by smaller balls, the sum of radii of the balls from the covering is greater than d. We also investigate the problem of finding lower and upper bounds for the sum of powers of radii of the balls covering a unit ball.

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 …