Mathematics Commons^™

On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies

Mathematical Sciences: Faculty Publications

We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we determine the possible fixed loci and show that when the Picard lattice is fixed, K3 surfaces come in mirror pairs.

R0 Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, J. Jacobsen, M. A. Lewis

Department of Mathematics: Faculty Publications

Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem im- pacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R₀ for advection-diffusion-reaction equations and on related measures. We apply the measures to popula- tion persistence in rivers under various flow regimes. This …

The Distribution Of Individual Stock Returns In A Modified Black-Scholes Option Pricing Model, Daniel Lee Richey

College of Graduate Studies: Theses & Dissertations

Author's abstract: There have been many attempts to find a model that can accurately price options. These models are built on many assumptions, including which probability distribution stock returns follow. In this paper, we test several distributions to see which best fit the log returns of 20 different companies over a period between November 1, 2006 to October 31, 2011. If a "best" distribution is found, a modified Black-Scholes model will be defined by modifying the Weiner process. We use Monte Carlo simulations to generate estimated prices under specified parameters, and compare these prices to those simulated by the model …

Applications Of Compressive Sensing To Surveillance Problems, Christopher Huff

Electronic Theses and Dissertations

In many surveillance scenarios, one concern that arises is how to construct an imager that is capable of capturing the scene with high fidelity. This could be problematic for two reasons: first, the optics and electronics in the camera may have difficulty in dealing with so much information; secondly, bandwidth constraints, may pose difficulty in transmitting information from the imager to the user efficiently for reconstruction or realization. In this thesis, we will discuss a mathematical framework that is capable of skirting the two aforementioned issues. This framework is rooted in a technique commonly referred to as compressive sensing. We …

Heat Equation, Wyatt Sherlock

A with Honors Projects

This document describes the process of deriving the heat equation from known thermodynamic laws followed by an analytic solution. Towards the end of the document, the heat equation is discussed in terms of practical engineering problems.

Volume 04, Matt Szemborski, Phillip Van Ness, Sarah Croughwell, Sarah Mayfield, Alyssa Strackbein, Marley Kimmel, Stephanie Skipp, Jamie Yurasits, Katherine Taggart, Alex Leonhart, Kristen Rawls, Andrew Armes, Amanda Haymens, Allison Paqlowski, Erica May, Stephanie Lane, Luke Acree, Cassandra L. Wilson, Stephanie Pishock, Erica Hopson, K. Juston Osborne, Katheryn Grayson, Kyle Fowlkes, Jessica Cox, Kaity Byrum, John-Harwood Scott, Ashley Johnson, Samantha Hockman, Emily Staskiel, Nancy Macdonald, R. Kruger Bressin, Benjamin P. Bilodeau, Andrea Irby, Kristin Macquarrie, Sarah Bietsch, Elizabeth Bednar

Incite: The Journal of Undergraduate Scholarship

Please note that part of pages 92-95 are redacted, in the digital copy, due to a misprint of the original printed article.

Introduction from Dean Dr. Charles Ross

The Internal Other: Transculturation and Postcolonial Magical Realism in Rushdie’s Midnight’s Children by Matt Szemborski

Photography by Phillip Van Ness

Photography “Waterfall” by Sarah Croughwell

Romancing the Bite: Statistical Analysis of Young Adult Vampire Novels by Sarah Mayfield

Photography by Alyssa Strackbein

Photography by Marley Kimmel

Wine and Society in the Viceroyalty of Peru by Stephanie Skipp

Analysis of Claud Monet’s Impression, Sunrise by Jamie Yurasits

Exploring Meaning: The Lindisfarne Gospels by …

Berry-Esseen Bounds For Nonlinear Statistics, And Asymptotic Relative Efficiency Between Correlation Statistics, Raymond E. Molzon

Dissertations, Master's Theses and Master's Reports - Open

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall …

Estimating Population Exposure To Fine Particulate Matter In The Conterminous U.S. Using Shape Function-Based Spatiotemporal Interpolation Method: A County Level Analysis, Lixin Li, Xingyou Zhang, James B. Holt, Jie Tian, Reinhard Piltner

Mathematical Sciences: Faculty Publications

This paper investigates spatiotemporal interpolation methods for the application of air pollution assessment. The air pollutant of interest in this paper is fine particulate matter PM_2.5. The choice of the time scale is investigated when applying the shape function-based method. It is found that the measurement scale of the time dimension has an impact on the quality of interpolation results. Based upon the result of 10-fold cross validation, the most effective time scale out of four experimental ones was selected for the PM_2.5 interpolation. The paper also estimates the population exposure to the ambient air pollution of …

Infeasible Full-Newton-Step Interior-Point Method For The Linear Complementarity Problems, Antré Marquel Drummer

College of Graduate Studies: Theses & Dissertations

In this tesis, we present a new Infeasible Interior-Point Method (IPM) for monotone Linear Complementarity Problem (LPC). The advantage of the method is that it uses full Newton-steps, thus, avoiding the calculation of the step size at each iteration. However, by suitable choice of parameters the iterates are forced to stay in the neighborhood of the central path, hence, still guaranteeing the global convergence of the method under strict feasibility assumption. The number of iterations necessary to find -approximate solution of the problem matches the best known iteration bounds for these types of methods. The preliminary implementation of the method …

Homogeneous Symplectic Manifolds Of The Galilei Group, Michael S. Davis

College of Graduate Studies: Theses & Dissertations

In this thesis we classify all symplectic manifolds admitting a transitive, 2-form preserving action of the Galilei group G. Using the moment map and a theorem of Kirillov-Kostant-Souriau, we reduce the problem to that of classifying the coadjoint orbits of a central extension of G discovered by Bargmann. We then develop a systematic inductive technique to construct a cross section of the coadjoint action. The resulting symplectic orbits are interpreted as the manifolds of classical motions of elementary particles with or without spin, mass, and color.

White Noise Based Stochastic Calculus Associated With A Class Of Gaussian Processes, Daniel Alpay, Haim Attia, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.

An Interpolation Problem For Functions With Values In A Commutative Ring, Daniel Alpay, Haim Attia

Mathematics, Physics, and Computer Science Faculty Articles and Research

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we study an interpolation problem in this setting. A key tool is the principle of permanence of algebraic identities.

Stochastic Processes Induced By Singular Operators, Daniel Alpay, Palle Jorgensen

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure σ on Rn. The case when σ is assumed absolutely continuous with respect to Lebesgue measure was stud- ied earlier in the literature, when n = 1. Our focus here is on showing how different equivalence classes (defined from relative absolute continuity for pairs of measures) translate into concrete spectral decompositions of the corresponding stochastic processes under study. The measures σ we consider are typically purely singular. Our proofs rely on the theory of (singular) unbounded operators in …

Bicomplex Numbers And Their Elementary Functions, M. E. Luna-Elizarrarás, M. Shapiro, Daniele C. Struppa, Adrian Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we introduce the algebra of bicomplex numbers as a generalization of the field of complex numbers. We describe how to define elementary functions in such an algebra (polynomials, exponential functions, and trigonometric functions) as well as their inverse functions (roots, logarithms, inverse trigonometric functions). Our goal is to show that a function theory on bicomplex numbers is, in some sense, a better generalization of the theory of holomorphic functions of one variable, than the classical theory of holomorphic functions in two complex variables.

Groupoids, Imaginaries And Internal Covers, Ehud Hrushovski

Turkish Journal of Mathematics

Let T be a first-order theory. A correspondence is established between internal covers of models of T and definable groupoids within T. We also consider amalgamations of independent diagrams of algebraically closed substructures, and find strong relation between covers, uniqueness for 3-amalgamation, existence of 4-amalgamation, imaginaries of T^\si, and definable groupoids. As a corollary, we describe the imaginary elements of families of finite-dimensional vector spaces over pseudo-finite fields.

On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values, Youming Wang

Turkish Journal of Mathematics

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain D \subseteq C and n be a positive integer. Let a, b be two finite complex constants such that a \neq 0. If n \geq 3 and f + a(f')^n and g + a(g')^n share b in D for every pair of functions f, g \in F, then F is normal in D. And some examples are provided to show the result is sharp.

Invariant Subspaces Of Weakly Compact-Friendly Operators, Mert Çağlar, Remzi̇ Tunç Misirlioğlu

Turkish Journal of Mathematics

We prove that if a non-zero weakly compact-friendly operator B on a Banach lattice with topologically full center is locally quasi-nilpotent, then the super right-commutant [B\rangle of B has a non-trivial closed invariant ideal. An example of a weakly compact-friendly operator which is not compact-friendly is also provided.

Extended Cross Product In A 3-Dimensional Almost Contact Metric Manifold With Applications To Curve Theory, Çeti̇n Camci

Turkish Journal of Mathematics

In this work, we define a new cross product in 3-dimensional almost contact metric manifold and we study the theory of curves using this new cross product in this manifold. Besides, in the works of Baikousis, Blair [1] and Cho et al. [4], we observe that some theorems are incomplete and excessively generalized are thus their alternative proofs presented.

Invariants Of Symmetric Algebras Associated To Graphs, Maurizio Imbesi, Monica La Barbiera

Turkish Journal of Mathematics

In this work we deal with the symmetric algebra of monomial ideals that arise from graphs, the edge ideals. The notion of s-sequence is explored for such ideals in order to compute standard algebraic invariants of their symmetric algebra in terms of the corresponding invariants of special quotients of the polynomial ring related to the graphs.

Value Distribution Of Meromorphic Functions And Their Differences, Ranran Zhang, Zongxuan Chen

Turkish Journal of Mathematics

Let f(z) be a transcendental meromorphic function. Results are proved concerning the value distribution of the n'th forward difference \Delta^nf(z), in terms of Borel exceptional values of f(z). The results may be partly viewed as discrete analogues of a classical theorem of Hayman dealing with the possible relationships between Picard exceptional values of f(z) and its derivatives.