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  • A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem

    Creator:
    Rockwell, Daniel Luke
    Abstract:
    The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the...
    Resource Type:
    Dissertation
    Full Text:
    , and New Demonstrations of, the Borel Normal Number Theorem Abstract approved: Robert M. Burton The

  • 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:
    determining the number of zeros of Eisenstein series which is the focus of this dissertation. Since Ek(τ) is

  • 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:
    number α is a measure of how arithmetically compli- cated α is. We say α is totally p-adic if the

  • Role of IL-8 and TIMP-2 on term canine trophoblast migration, invasion, and proliferation

    Creator:
    Gullaba, Justine Marie
    Abstract:
    Placental pathologies are not uncommon in dogs. For example, in primiparous bitches, the reported incidence of subinvolution of placental sites is 21% - 100%. Despite years of research in multiple species, the mechanisms regulating late gestation trophoblast behavior in the dog remain unexamined. Therefore, the objective of this study was...
    Resource Type:
    Masters Thesis
    Full Text:
    : Role of IL-8 and TIMP-2 on Term Canine Trophoblast Migration, Invasion, and Proliferation

  • Weak-supervision Time-series Analysis

    Creator:
    You, Zeyu
    Abstract:
    Efficient time-series analysis can impact multiple application domains such as motif discovery in gene analysis or music data, extracting spectro-temporal patterns in acoustic scene analysis, or annotating and classifying electrical bio-signals (such as ECG, EEG, and EMG) for medical applications. Time-series analysis involves a variety of tasks. To predict future...
    Resource Type:
    Dissertation
    Full Text:
    12, 2019. Title: Weak-supervision Time-series Analysis Abstract approved: Raviv Raich E�cient

  • OSU theses and dissertations : 1978-1982

    Creator:
    Leasher, Evelyn M.
    Abstract:
    The bibliographic series contains a listing of all theses and dissertations accepted by the University from 1932 to date.
    Resource Type:
    Book
    Full Text:
    6, OSU Theses & Dissertations 1943 - 1959 Bibliographic Series Number 8, OSU Theses & Dissertations

  • Bilinear stochastic processes and time series

    Creator:
    Tang, Zhigiang
    Abstract:
    In engineering, biology, ecology, medicine, economics and social science, some processes are essentially bilinear, and some could be approximated accurately by bilinear processes under certain conditions. In this thesis the bilinear stochastic process and bilinear time series are discussed. Bilinear models essentially are nonlinear; the superposition rule is not valid....
    Resource Type:
    Dissertation
    Full Text:
    Bilinear stochastic processes and time series AN

  • Class Number One Problems

    Creator:
    Bunnell, Elijah
    Abstract:
    In this paper we examine some of the developments concerning the Gauss class number problems and build a solid understanding of the class number. First we will develop some background knowledge necessary to understand the problem, specifically the theory of quadratic forms and quadratic fields and how the class number...
    Resource Type:
    Capstone Project
    Full Text:
    Gauss’ class number one discriminants by 4 we get {-4, -8, -12, -16, -28}. Now, disregarding the non

  • Mahler's order functions and algebraic approximation of p-adic numbers

    Creator:
    Dietel, Brian Christopher
    Abstract:
    If P is an integer polynomial denote the degree of P by ∂(P) and let H(P) be the maximum of the absolute value of the coefficients of P. Define Λ(P)=2[superscript ∂(P)]H(P) and for a fixed prime p let C[subscript p] denote the completion of the algebraic closure of the p-adic...
    Resource Type:
    Dissertation
    Full Text:
    consider how well a given transcendental number can be approximated by algebraic numbers, or if there

  • Arithmetic dynamical questions with local rationality conditions

    Creator:
    Noytaptim, Chatchai
    Abstract:
    We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...
    Resource Type:
    Dissertation
    Full Text:
    algebraic number is totally real (respectively, totally p-adic) if its minimal polynomial over Q splits