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  • On the distribution of orbits in affine varieties

    Creator:
    Petsche, Clayton
    Abstract:
    Given an affine variety X, a morphism ϕ:X→X, a point α∈X, and a Zariski-closed subset V of X, we show that the forward ϕ-orbit of α meets V in at most finitely many infinite arithmetic progressions, and the remaining points lie in a set of Banach density zero. This may...
    Resource Type:
    Article
    Full Text:
    Se p 20 14 On the distribution of orbits in affine varieties Clayton Petsche Abstract. Given an

  • Critically Separable Rational Maps in Families

    Creator:
    Petsche, Clayton
    Abstract:
    Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...
    Resource Type:
    Article

  • On Small Heights of Totally p-adic Numbers

    Creator:
    Stacy, Emerald T.
    Abstract:
    The height of an algebraic number A is a measure of how arithmetically complicated A is. We say A is totally p-adic if the minimal polynomial of A splits completely over the field of p-adic numbers. In this paper, we investigate what can be said about the smallest nonzero height...
    Resource Type:
    Dissertation
    Full Text:
    Heights of Totally p-adic Numbers. Abstract approved: Clayton J. Petsche The height of an algebraic

  • Fourier Analysis and Equidistribution on the p-adic Integers

    Creator:
    Somasunderam, Naveen
    Abstract:
    In this dissertation, we use Fourier-analytic methods to study questions of equidistribution on the compact abelian group Zp of p-adic integers. In particu- lar, we prove a LeVeque-type Fourier analytic upper bound on the discrepancy of sequences. We establish p-adic analogues of the classical Dirichlet and Fejér kernels on R/Z,...
    Resource Type:
    Dissertation
    Full Text:
    Analysis and Equidistribution on the p-adic Integers Abstract approved: Clayton J. Petsche In this

  • Subalgebras of the Split Octonions

    Creator:
    Bentz, Lida
    Abstract:
    We classify the subalgebras of the split octonions, paying particular attention to the null subalgebras and their extensions.
    Resource Type:
    Capstone Project

  • Classifying Octonionic-Linear Operators

    Creator:
    Putnam, Alexander
    Abstract:
    The goal of this paper is to classify linear operators with octonionic coefficients and octonionic variables. While building up to the octonions we also classify linear operators over the quaternions and show how to relate the linear operators over the quaternions and octonions to matrices. We also construct a basis...
    Resource Type:
    Capstone Project

  • A dynamical pairing between two rational maps

    Creator:
    Petsche, Clayton, Szpiro, Lucien, and Tucker, Thomas J.
    Abstract:
    Given two rational maps φ and ψ on Ρ¹ of degree at least two, we study a symmetric, nonnegative real-valued pairing〈φ, ψ〉which is closely related to the canonical height functions hφ and hψ associated to these maps. Our main results show a strong connection between the value of〈φ, ψ〉and the...
    Resource Type:
    Article
    Full Text:
    on November 10, 2011 A DYNAMICAL PAIRING BETWEEN TWO RATIONAL MAPS CLAYTON PETSCHE, LUCIEN SZPIRO

  • Efficient, secure and covert channel capacity bounded protocols for multilevel security cross-domain environments - an experimental system

    Creator:
    Nandakumar Thampi, Archana
    Abstract:
    The communication in MLS cross-domain environments faces many challenges. The three most important challenges are efficient key management, privacy preserving and covert channel. We propose an Efficient, Secure and Covert Channel Capacity Bounded Protocol which has three algorithms that addresses these challenges: The Efficient Attribute-based Fine-Grained Authentication (EAFA) algorithm, Anonymous...
    Resource Type:
    Masters Thesis
    Full Text:
    Dr. Bella Bose, Dr. Mike Rosulek and Dr. Clayton Petsche for reviewing my work and serving on my

  • Zeros of Certain Combinations of Products of Eisenstein Series

    Creator:
    Klangwang, Jetjaroen
    Abstract:
    In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower...
    Resource Type:
    Dissertation
    Full Text:
    past four years. I also would like to give special thanks to my dissertation committee, Clayton

  • Structural Results and Approximation Algorithms in Minor-free Graphs

    Creator:
    Le, Hung V.
    Abstract:
    Planarity has been successfully exploited to design faster and more accurate approximation algorithms for many graph optimization problems. The celebrated theorem of Kuratowski completely characterizes planar graphs as those excluding K_5 and K_{3,3} as minors. Kuratowski's theorem allows one to generalize planar graphs to H-minor-free graphs: those that exclude a...
    Resource Type:
    Dissertation
    Full Text:
    thank Christian Wulff-Nilse, Amir Nayyeri , Mike Rosulek, Eugene Zhang and Clayton Petsche for serving