Mathematics Commons^™

Knörrer Periodicity And Bott Periodicity, Michael K. Brown

Department of Mathematics: Dissertations, Theses, and Student Research

The main goal of this dissertation is to explain a precise sense in which Knörrer periodicity in commutative algebra is a manifestation of Bott periodicity in topological K-theory. In Chapter 2, we motivate this project with a proof of the existence of an 8-periodic version of Knörrer periodicity for hypersurfaces defined over the real numbers. The 2- and 8-periodic versions of Knörrer periodicity for complex and real hypersurfaces, respectively, mirror the 2- and 8-periodic versions of Bott periodicity in KU- and KO-theory. In Chapter 3, we introduce the main tool we need to demonstrate the compatibility between Knörrer …

Extremal Results For The Number Of Matchings And Independent Sets, Lauren Keough

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation answers several questions in extremal graph theory, each concerning the maximum or minimum number of certain substructures a graph can have, given that it must satisfy certain properties. In recent years there has been increased interest in such problems, which are extremal problems for "counting" parameters of graphs. The results in this dissertation focus on graphs that have n vertices and e edges and 3-uniform hypergraphs that have n vertices and e edges.

We first observe in the preliminaries chapter that for graphs with a fixed number of vertices and edges there is a threshold graph attaining the …

Invariant Basis Number And Basis Types For C*-Algebras, Philip M. Gipson

Department of Mathematics: Dissertations, Theses, and Student Research

We develop the property of Invariant Basis Number (IBN) in the context of C*-algebras and their Hilbert modules. A complete K-theoretic characterization of C*- algebras with IBN is given. A scheme for classifying C*-algebras which do not have IBN is given and we prove that all such classes are realized. We investigate the invariance of IBN, or lack thereof, under common C*-algebraic construction and perturbation techniques. Finally, applications of Invariant Basis Number to the study of C*-dynamical systems and the classification program are investigated.

Adviser: David Pitts

Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, Brittney Keel

Department of Mathematics: Dissertations, Theses, and Student Research

The exact evolutionary history of any set of biological sequences is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this dissertation we propose a game-theoretic approach to clustering biological sequences and analyzing their evolutionary histories. In this context we use the term evolution as a broad descriptor for the entire set of mechanisms driving the inherited characteristics of a population. The key assumption in our development is that evolution tries to accommodate the competing forces of selection, of which the conservation force seeks to …

Incorporating Relaxivities To More Accurately Reconstruct Mr Images, Muge Karaman, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

To develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step.

Materials and methods

In magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T₂^⁎, T₁, and a phase determined by magnetic field inhomogeneity (∆B) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted …

Time Integration Methods Of Fundamental Solutions And Approximate Fundamental Solutions For Nonlinear Elliptic Partial Differential Equations, Corey Leon Jones

Dissertations

A time-dependent method is coupled with the Method of Approximate Particular Solutions (MAPS) of Delta-shaped basis functions, the Method of Fundamental Solutions (MFS), and the Method of Approximate Fundamental Solutions (MAFS) to solve a second order nonlinear elliptic partial differential equation (PDE) on regular and irregular shaped domains. The nonlinear PDE boundary value problem is first transformed into a time-dependent quasilinear problem by introducing a fictitious time. Forward Euler integration is then used to ultimately convert the problem into a sequence of time-dependent linear nonhomogeneous modified Helmholtz boundary value problems on which the superposition principle is applied to split the …

Phantom Maps, Decomposability, And Spaces Meeting Particular Finiteness Conditions, James Schwass

Dissertations

The purpose of this dissertation is to extend principles for detecting the existence of essential phantom maps into spaces meeting particular finiteness conditions. Zabrodsky shows that a space Y having the homotopy type of a finite CW complex is the target of essential phantom maps if and only if Y has a nontrivial rational homology group. We show this observation holds on the collection of finite generalized CW complexes. Similarly, Iriye shows a finite-type, simply connected suspension space is the target of essential phantom maps if and only if it has a nontrivial rational homology group. We show this observation …

On Color Fixing Groups Associated With Colored Symmetrical Tilings, April Lynne D. Say-Awen, Ma. Louise Antonette N. De Las Peñas, Teofina A. Rapanut

Mathematics Faculty Publications

In this paper, we contribute to the study of colored symmetrical tilings by giving formulas for their associated color fixing groups. In the second part of the paper we provide an application of the results in describing symmetry groups of nanostructures.

Schwarzschild Spacetime And Friedmann-Lemaitre-Robertson-Walker Cosmology, Zachary Cohen

Honors Scholar Theses

The advent of General Relativity via Einstein's field equations revolutionized our understanding of gravity in our solar system and universe. The idea of General Relativity posits that gravity is entirely due to the geometry of the universe -- that is, the mass distribution throughout the universe results in the "curving" of spacetime, which gives us the physics we see on a large scale. In the framework of General Relativity, we find that the universe behaves differently than was predicted in the model of gravitation developed by Newton. We will derive the general relativistic model for a simple system near a …

Revised Model For Antibiotic Resistance In A Hospital, Ruhang Pei

Electronic Theses and Dissertations

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

Exploring Ways Of Identifying Outliers In Spatial Point Patterns, Jie Liu

Electronic Theses and Dissertations

This work discusses alternative methods to detect outliers in spatial point patterns.

Outliers are defined based on location only and also with respect to associated variables. Throughout the thesis we discuss five case studies, three of them come from experiments with spiders and bees, and the other two are data from earthquakes in a certain region. One of the main conclusions is that when detecting outliers from the point of view of location we need to take into consideration both the degree of clustering of the events and the context of the study. When detecting outliers from the point of …

The Pricing Of Asian Options In High Volatile Markets: A Pde Approach, Nabil Kamal Riziq Al Farra

Theses

Financial derivatives are very important tools in risk management since they decrease uncertainty. Moreover, if used effectively, they can grow the income and save the cost. There are many types of financial derivatives, for instance: futures/forwards, options, and swaps. The present thesis deals with the pricing problem for Asian options. The main aim of the thesis is to generalize the Asian option pricing Partial Differential Equation (PDE) in order to handle post-crash markets where the volatility is high. In other words, we seek to extend the work on the Asian option pricing PDE under the well-known Black-Scholes model to a …

Quaternary Affine-Invariant Codes, Badria H Omar Salih

Theses

This thesis concerned with extended cyclic codes. The objective of this thesis is to give a full description of binary and quaternary affine-invariant codes of small dimensions. Extended cyclic codes are studied using group ring methods. Affine-invariant codes are described by their defining sets. Results are presented by enumeration of defining sets. Full description of affine-invariant codes is given for small dimensions

Families Of Weighted Sum Formulas For Multiple Zeta Values, Li Guo, Peng Lei, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper, we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.

The Apprentices' Tower Of Hanoi, Cory Bh Ball

Electronic Theses and Dissertations

The Apprentices' Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented.

Managing The Spread Of Alfalfa Stem Nematodes Ditylenchus Dipsaci: The Relationship Between Crop Rotation And Pest Re-Emergence, Scott Jordan

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow end-users to design better management programs and farming practices. This is of particular importance given that there are no nematicides available against alfalfa stem nematode and control strategies largely rely on crop rotation to non-host crops or by planting resistant varieties. I present a basic host-parasite model that describes the spread of the alfalfa stem nematode on alfalfa crops. With this …

Survival Analysis For Truncated Data And Competing Risks, Michael Steelman

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this project is to consider the problems of left truncation and competing risks in analyzing censored survival data, and to compare and contrast various approaches for handling these problems. The motivation for this work comes from an analysis of data from the Cache County Memory Study. Study investigators were interested in the association between early-life psychologically stressful events (e.g., parental or sibling death, or parental divorce, among others) and late-life risk of Alzheimer's disease (AD). While conventional methods for censored survival data can be applied, the presence of left truncation and competing risks (i.e., other adverse events …

Comparing Linear Mixed Models To Meta-Regression Analysis In The Greenville Air Quality Study, Lynsie M. Daley

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The effect of air quality on public health is an important issue in need of better understanding. There are many stakeholders, especially in Utah and Cache Valley, where the poor air quality as measured by PM 2.5 levels and consequent inversions can sometimes be the very worst in the nation. This project focuses on comparing two statistical methods used to analyze an important air quality data set from the Greenville Air Quality Study, focusing on a lung function response variable. A linear mixed model, with a random factor for subject, gives slope estimates and their significance for predictor variables of …

Modeling Seed Dispersal And Population Migration Given A Distribution Of Seed Handling Times And Variable Dispersal Motility: Case Study For Pinyon And Juniper In Utah, Ram C. Neupane

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The spread of fruiting tree species is strongly determined by the behavior and range of fruit-eating animals, particularly birds. Birds either consume and digest seeds or carry and cache them at some distance from the source tree. These carried and settled seeds provide some form of distribution which generates tree spread to the new location. Firstly, we modal seed dispersal by birds and introduce it in a dispersal model to estimate seed distribution. Using this distribution, we create a population model to estimate the speed at which juniper and pinyon forest boundaries move.

Secondly, we introduce a fact that bird …

Modeling Deformations Of Solids At The Continuum Scale, Paxton Turner

Honors Capstones

No abstract provided.