Mathematics Commons^™

Algebraic And Combinatorial Properties Of Schur Rings Over Cyclic Groups, Andrew F. Misseldine

Theses and Dissertations

In this dissertation, we explore the nature of Schur rings over finite cyclic groups, both algebraically and combinatorially. We provide a survey of many fundamental properties and constructions of Schur rings over arbitrary finite groups. After specializing to the case of cyclic groups, we provide an extensive treatment of the idempotents of Schur rings and a description for the complete set of primitive idempotents. We also use Galois theory to provide a classification theorem of Schur rings over cyclic groups similar to a theorem of Leung and Man and use this classification to provide a formula for the number of …

Involutive Translation Surfaces And Panov Planes, Charles Johnson

All Dissertations

This dissertation is concerned with the study of Panov planes and involutive translation surfaces, motivated by questions encountered in trying to understand certain self-similar billiard trajectories in the periodic variant of the Ehrenfest wind-tree model. In particular, we outline a new approach for studying billiard trajectories in certain types of infinite billiard tables by using Panov planes. After describing how this is done in the special case of the wind-tree model, we generalize our construction to show that there are typically several Panov planes that may be associated to an involutive translation surface. The first three chapters of the dissertation …

Modeling Dengue Transmission And Vaccination, Abhishek Pandey

All Dissertations

Dengue is one of the most rapidly spreading mosquito-borne viral diseases in the world and inflicts significant health, economic and social burdens on populations. In this dissertation, I studied different aspects of modeling of dengue and vector-borne diseases in general. Among various dengue models that have appeared in literature, some explicitly model the mosquito population, while others model them implicitly. In spite of extensive use of both modeling approaches, little guidance exists for which type of model should be preferred. I developed a Bayesian approach that uses a Markov chain Monte Carlo (MCMC) method to fit disease models to epidemiological …

Family-Wise Error Rate Control In Quantitative Trait Loci (Qtl) Mapping And Gene Ontology Graphs With Remarks On Family Selection, Garrett Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypotheses are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene …

Modeling Asset Volatility Using Various Resources, Isaac G. Blackhurst

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

Volatility is of central interest in modern financial econometrics. This thesis evaluates three different methods of measuring volatility.

High Cognitive Test Item Development And Implementation, Ashley Salisbury

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

In secondary math classrooms there has been a movement toward discovery and problem solving based instruction. This type of instruction requires teachers to teach on what is often considered a higher level of cognition and allows students to discover more ideas and concepts on their own as opposed to traditional lecture style. Teachers with well thought-out examples, questions, and activities provide students with tools to solve problems on their own requiring students to make mathematical discoveries and connections. These skills not only benefit students in their math class but are analytical skills students can use throughout their lives.

With this …

The Optimal Release Of Sterile Males In Pest Management, Sergio Ramirez

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

With an application of the sterile insect technique, it is our goal to know the optimal rate of production of sterile males in order to control an insect pest invasion and protect crops. Starting with a fundametal relationship between costs of production and feeding rates, we construct an objective functional. We then use the relationships between the dierent stages of female reproduction to build the state equations. Once, we have dened the optimal control problem, we use the simulated annealing algorithm to determine the amount of sterile males to be released at each discrete time event. Multiple calculations are made …

Topological Pressure And Fractal Dimensions For Bi-Lipschitz Mappings, Hugo E. Olvera

Theses and Dissertations - UTB/UTPA

In this thesis, first we have defined the topological pressure P(t) and then using Banach limit we have determined a unique Borel probability measure µh supported by the invariant set E of a system of bi-Lipschitz mappings where h is the unique zero of the pressure function. Using the topological pressure and the measure µh, under certain condition on bi-Lipschitz constants, we have shown that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension of the set E are all equal to h. Moreover, it is shown that the h-dimensional Hausdorff measure and the …

Results On Edge-Colored Graphs And Pancyclicity, James Carraher

Department of Mathematics: Dissertations, Theses, and Student Research

This thesis focuses on determining when a graph with additional structure contains certain subgraphs, particularly circuits, cycles, or trees. The specific problems and presented results include a blend of many fundamental graph theory concepts such as edge-coloring, routing problems, decomposition problems, and containing cycles of various lengths. The three primary chapters in this thesis address the problems of finding eulerian circuits with additional restrictions, decomposing the edge-colored complete graph K_n into rainbow spanning trees, and showing a 4-connected claw-free and N(3,2,1)-free graph is pancyclic.

Adviser: Stephen G. Hartke

Lattice Methods For The Valuation Of Options With Regime Switching, Atul Sancheti

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, we have developed two numerical methods for evaluating option prices under the regime switching model of stock price processes: the Finite Difference lattice method and the Monte Carlo lattice method.

The Finite Difference lattice method is based on the explicit finite difference scheme for parabolic problems. The Monte Carlo lattice method is based on the simulation of the Markov chain. The advantage of these methods is their flexibility to compute the option prices for any given stock price at any given time. Numerical examples are presented to examine these methods. It has been shown that the proposed …

N-Dimensional Quasipolar Coordinates - Theory And Application, Tan Mai Nguyen

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, various generalizations to the n-dimension of the polar coordinates and spherical coordinates are introduced and compared with each other and the existent ones in the literature. The proof of the Jacobian of these coordinates is very often wrongfully claimed. Currently, prior to our proof, there are only two complete proofs of the Jacobian of these coordinates known to us. A friendlier definition of these coordinates is introduced and an original, direct, short, and elementary proof of the Jacobian of these coordinates is given. A method, which we call a perturbative (not perturbation) method, is introduced so that …

On The Effect Of Temperature And Pressure Gradient On The Flow Of Non-Homogeneous Fluids, Joseph Anthony Fiordilino

Theses, Dissertations and Culminating Projects

not available

Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus

Electronic Theses and Dissertations

The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or …

Physiologically-Based Pharmacokinetic Model For Ertapenem, Whitney Forbes

Electronic Theses and Dissertations

Ertapenem is a carbapenem used to treat a wide range of bacterial infections. What sets ertapenem apart from other carbapenems is its longer half-life which implies it need only be administered once daily. We developed a physiologically-based pharmacokinetic model for the distribution of ertapenem within the body. In the model, parameters such as human body weight and height, age, organ volumes, blood flow rates, and partition coefficients of particular tissues are used to examine the absorption, distribution, metabolism, and excretion of ertapenem. The total and free blood concentrations found were then compared to experimental data. We then examined the sensitivity …

The Triangle Inequality And The Dual Gromov-Hausdorff Propinquity, Frédéric Latrémolière

Mathematics Preprint Series

he dual Gromov-Hausdorff propinquity is a generalization of the Gromov-Hausdorff distance to the class of Leibniz quantum compact metric spaces, designed to be well-behaved with respect to C*-algebraic structures. In this paper, we present a variant of the dual propinquity for which the triangle inequality is established without the recourse to the notion of journeys, or finite paths of tunnels. Since the triangle inequality has been a challenge to establish within the setting of Leibniz quantum compact metric spaces for quite some time, and since journeys can be a complicated tool, this new form of the dual propinquity is a …

Dao Selected For Economics Research Fellowship, Hannah Dhue

News and Events (Discontinued Series)

No abstract provided.

Simultaneous Approximation Of A Multivariate Function And Its Derivatives By Multilinear Splines, Ryan Anderson, Yuliya Babenko, Tetiana Leskevych

Faculty Articles

Abstract: In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We obtain the exact uniform approximation error on classes of functions with moduli of continuity bounded above by certain majorants. [Copyright &y& Elsevier]

2014 Sonia Kovalevsky Math For Girls Day Program, Association For Women In Mathematics, Lincoln University Of Missouri, Kjlu Radio Station, Ameren Ue Callaway Plant Win- Women In Nuclear

Math for Girls Day Documents

9th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program on April 25, 2014.

2014 Sonia Kovalevsky Math For Girls Day Registration Form, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

Registration form for 9th Annual Lincoln University Sonia Kovalevsky Math for Girls Day on April 25, 2014.

2014 Sonia Kovalevsky Math For Girls Day Evaluation Forms, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

Presenter, student and teacher evaluation forms for the 9th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 25, 2014.

Combinatorial And Algebraic Coding Techniques For Flash Memory Storage, Kathryn A. Haymaker

Department of Mathematics: Dissertations, Theses, and Student Research

Error-correcting codes are used to achieve reliable and efficient transmission when storing or sending information across a noisy channel. This thesis investigates a mathematical approach to coding techniques for storage devices such as flash memory storage, although many of the resulting codes and coding schemes can be applied in other contexts. The main contributions of this work include the design of efficient codes and decoding algorithms using discrete structures such as graphs and finite geometries, and developing a variety of strategies for adapting codes to a multi-level setting.

Information storage devices are prone to errors over time, and the frequency …

Quasigroup Structures Arising From Partial Latin Squares, William Cocke, Dr. Rodney Forcade

Journal of Undergraduate Research

Latin squares represent one of the oldest elements of modern algebra, despite being over- shadowed by the structurally superior subclass of nite groups. Every nite group generates a Latin square, an n by n grid wherein n distinct element appear exactly once in each row and column. This grid is a Latin square

Generalizations Of The Inverse Weibull And Related Distributions With Applications, Broderick O. Oluyede, Tao Yang

Mathematical Sciences: Faculty Publications

In this paper, the generalized inverse Weibull distribution including the exponentiated or proportional reverse hazard and Kumaraswamy generalized inverse Weibull distributionsare presented. Properties of these distributions including the behavior of the hazard and reverse hazard functions, moments, coefficients of variation, skewness, andkurtosis, entropy, Fisher information matrix are studied. Estimates of the model parameters via method of maximum likelihood (ML), and method of moments (MOM) are presented for complete and censored data. Numerical examples are also presented.

The Security Of Simplified Data Encryption Standard, Brandon Barker

College of Arts and Sciences Presentations

The Data Encryption Standard (DES) is the most widely used symmetric key cryptosystem in the commercial world. DES was published in 1975 by the National Bureau of Standards, and since then it and its variants have been commonly used. DES is utilized in many modern industries and products including the Blackberry, electronic financial transactions, and access cards to corporate offices. An efficient but secure cryptosystem is challenging to produce and even after it has been deemed “secure” new attacks and vulnerabilities are often discovered. By investigating the algebraic structure of a simplified version of DES we are able to analyze …

A Simplified Aes With Field Characteristic 7, Suzanne Craig

College of Arts and Sciences Presentations

Today the greatest challenge to the cyber world is security. Technology rapidly changes, making old methods obsolete and requiring new developments and advancements in information security. Cryptography, the science of preparing coded or protected communications, designs systems which make messages intelligible only to the person possessing a key. There are two types of key-based cryptosystems: symmetric key and asymmetric cryptosystem. Symmetric key encryption is a cryptographic technique that uses a shared secret key to encrypt and decrypt data. Symmetric encryption algorithms are very efficient in processing large amounts of information. There are two types of symmetric encryption algorithms: stream ciphers …

Packing Tree Factors In Random And Pseudo-Random Graphs, Deepak Bal, Alan Frieze, Michael Krivelevich, Po Shen Loh

Department of Mathematics Faculty Scholarship and Creative Works

For a fixed graph H with t vertices, an H-factor of a graph G with n vertices, where t divides n, is a collection of vertex disjoint (not necessarily induced) copies of H in G covering all vertices of G. We prove that for a fixed tree T on t vertices and ε > 0, the random graph Gn,p, with n a multiple of t, with high probability contains a family of edge-disjoint T-factors covering all but an ε-fraction of its edges, as long as ε4np ≫ log2 n. Assuming stronger divisibility conditions, the edge probability can be taken down to …

New Pod Error Expressions, Error Bounds, And Asymptotic Results For Reduced Order Model Of Parabolic Pdes, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The derivations of existing error bounds for reduced order models of time varying partialdi erential equations (PDEs) constructed using proper orthogonal decomposition (POD) haverelied on bounding the error between the POD data and various POD projections of that data.Furthermore, the asymptotic behavior of the model reduction error bounds depends on theasymptotic behavior of the POD data approximation error bounds. We consider time varyingdata taking values in two di erent Hilbert spacesHandV, withVH, and prove exactexpressions for the POD data approximation errors considering four di erent POD projectionsand the two di erent Hilbert space error norms. Furthermore, the exact error expressions …

A Short Journey Through The Riemann Integral, Jesse Keyton

2014-2016 Undergraduate

An introductory-level theory of integration was studied, focusing primarily on the well-known Riemann integral and ending with the Lebesgue integral. An examination of the Riemann integral's basic properties and necessary conditions shows that this integral is not very strong. This conclusion leads to Lebesgue's necessary and sufficient condition for Riemann integrability, perhaps where the Riemann integral ends and the Lebesgue integral begins: a function defined on a closed integral [a, b] is Riemann integrable if and only if the function is discontinuous on a set of measure zero. The proof of this uses that the infinite union …

Arithmagons, Jose Franco

Mathematics Colloquium Series

Arithmagons are polygonal graphs whose vertices and edges are numbered by natural numbers in such a way that the product of the labels of two adjacent vertices equals the label on the edge that connects them. During the talk, Franco will briefly explore the conditions for solvability. The remainder of the talk will focus on counting the number of arithmagons that can be constructed so that the multiplication of all the values on the edges equals a fixed natural number.

Localized Quantum States, Francois Ziegler

Mathematical Sciences: Faculty Publications

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any "large enough" subgroup G of Aut(L). This definition has two major drawbacks: when G=Aut(L) there are no known examples; and when G is a Lie subgroup the notion is, as we shall see, far from selective enough. In this paper we introduce the concept of a quantum state *localized at Y*, where Y is a coadjoint orbit of a …