Mathematics Commons^™

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 …

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 …

Very Cost Effective Domination In Graphs, Tony K. Rodriguez

Electronic Theses and Dissertations

A set S of vertices in a graph G=(V,E) is a dominating set if every vertex in V\S is adjacent to at least one vertex in S, and the minimum cardinality of a dominating set of G is the domination number of G. A vertex v in a dominating set S is said to be very cost effective if it is adjacent to more vertices in V\S than to vertices in S. A dominating set S is very cost effective if every vertex in S is very cost effective. The minimum cardinality of a very cost effective dominating set of …

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 …

Multiplicity Results Of Periodic Solutions For Two Classes Of Nonlinear Problems, Kazuya Hata

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We investigate the existences and qualitative properties of periodic solutions of the following two classes of nonlinear differential equations:

I) (Special) Relativistic Pendulum Equations (RPEs);

II) (2-coupled) Gross-Pitaevskii Equations (GPEs).

The pendulum equation describes the motion of a pendulum. According to Special Relativity, which was published by A. Einstein in 1905, causality is more fundamental than constant time-space, thus time will flow slower and space will distort to keep causality if the speed of motion is near the speed of light. In such high speed situations, the pendulum equation needs to be revised due to Special Relativity. The revised equation …

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 …

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 …

Traditional Lecture Versus An Activity Approach For Teaching Statistics: A Comparison Of Outcomes, Jennifer L. Loveland

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many educational researchers have proposed teaching statistics with less lecture and more active learning methods. However, there are only a few comparative studies that have taught one section of statistics with lectures and one section with activity-based methods; of those studies, the results are contradictory. To address the need for more research on the actual effectiveness of active learning methods in introductory statistics, this research study was undertaken.

An introductory, university level course was divided into two sections. One section was taught entirely with traditional lecture. The other section was taught using active learning methods and a minimal amount of …

Observability In Traffic Modeling: Eulerian And Lagrangian Coordinates, Sergio Contreras

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traditionally, one of the ways traffic flow has been studied is by using the kinematic wave model. This model is studied in the Eulerian framework. Recently, the kinematic wave model has been transformed into Lagrangian coordinates. This model of traffic flow together with the concept of observability for linear time invariant discrete time systems is applied to study the observability of four sections of a freeway in both Eulerian and Lagrangian coordinates. A system with densities in four sections of a freeway is designed, and the observability of the system is studied with different situations for sensors. When the system …

Hamiltonicity, Pancyclicity, And Cycle Extendability In Graphs, Deborah C. Arangno

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A significant portion of Graph Theory is devoted to determining the characteristics which guarantee the existence of long cycles.

Long cycles have roles in applications to civil engineering, chemistry, and communications, among many others, but the problem, in and of itself, of determining whether a graph has a cycle of some fixed and typically large length is one of the most important problems of both pure Mathematics and Computer Science.

A cycle containing all the vertices of the graph is called a Hamiltonian cycle, and a graph which possesses such a cycle is said to be Hamiltonian. If …

Statistical Modeling, Exploration, And Visualization Of Snow Water Equivalent Data, James Beguah Odei

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Due to a continual increase in the demand for water as well as an ongoing regional drought, there is an imminent need to monitor and forecast water resources in the Western United States. In particular, water resources in the Intermountain West rely heavily on snow water storage. Thus, the need to improve seasonal forecasts of snowpack and considering new techniques would allow water resources to be more effectively managed throughout the entire water-year. Many available models used in forecasting snow water equivalent (SWE) measurements require delicate calibrations.

In contrast to the physical SWE models most commonly used for forecasting, we …

Network Applications And The Utah Homeless Network, Michael A. Snyder

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Graph theory is the foundation on which social network analysis (SNA) is built. With the flood of "big data," graph theoretical concepts and their linear algebraic counterparts are essential tools for analysis in the burgeoning field of network data analysis, in which SNA is a subset. Here we begin with an overview of SNA. We then discuss the common descriptive measures taken on network data as well as proposing new measures specific to homeless networks. We also define a new data structure which we call the location sequence matrix. This data structure makes certain computational network analyses particularly easy. …

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 …

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.