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Filtering by: Creator Tuori, Robert P. Remove constraint Creator: Tuori, Robert P. Degree Field Mathematics Remove constraint Degree Field: Mathematics

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  • 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:
    to the p-adic numbers. Koblitz [17] and Robert [29] are also standard references on the p-adic

  • Using p-adic valuations to decrease computational error

    Creator:
    Limmer, Douglas J.
    Abstract:
    The standard way of representing numbers on computers gives rise to errors which increase as computations progress. Using p-adic valuations can reduce error accumulation. Valuation theory tells us that p-adic and standard valuations cannot be directly compared. The p-adic valuation can, however, be used in an indirect way. This gives...
    Resource Type:
    Masters Thesis
    Full Text:
    degree of Master of Science in Mathematics presented on June 8, 1993. Title: Using p-adic Valuations to

  • Systems of incongruences in a proof on addition mod m

    Creator:
    Sologuren P., Santiago
    Resource Type:
    Masters Thesis
    Full Text:
    AN ABSTRACT OF THE THESIS OF Santiago Sologuren P. for the degree of Master of Science in

  • 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

  • Measure-equivalence of quadratic forms

    Creator:
    Limmer, Douglas J.
    Abstract:
    This paper examines the probability that a random polynomial of specific degree over a field has a specific number of distinct roots in that field. Probabilities are found for random quadratic polynomials with respect to various probability measures on the real numbers and p-adic numbers. In the process, some properties...
    Resource Type:
    Dissertation

  • Khinchin's theorem on the Schnirelmann density of sums of sets of integers

    Creator:
    Gregersen, Gordon Stanley
    Abstract:
    In 1932 A. Ya. Khinchin gave the first partial solution of the celebrated 1931 αβ Conjecture of L.G. Schnirelmann and E. Landau of the density of sums of sets on integers, which was completely proved in 1942 by H.B. Mann. Khinchin's theorem is proved along with theorems of P. Scherk...
    Resource Type:
    Masters Thesis
    Full Text:
    colnpletely proved in l94Z by H. B. Mann. Khinchin's theorern is proved along with theorerns of P. Scherk

  • Even order subgroups of finite dimensional division rings

    Creator:
    Greenfield, Gary Robert
    Abstract:
    Let K be a field, and G a finite group. G is said to be K-adequate if there exists a division ring D, finite dimensional over K, and with center K, such that G is contained in the multiplicative group of nonzero elements of D. In this dissertation we investigate...
    Resource Type:
    Dissertation
    Full Text:
    AN ABSTRACT OF THE THESIS OF Gary Robert Greenfield for the

  • The greatest integer part function

    Creator:
    Murray, Peter John
    Abstract:
    This thesis contains a collection of properties of the greatest integer part function which were obtained by an extensive literature search. A few original properties are stated and proved and some of the properties which were found unproved in the literature are proved.
    Resource Type:
    Masters Thesis
    Full Text:
    t'entiertr, rneaning integer, for exarnple P. G. Lejeune- Dirichlet (24;3L1, A. Legendre (30; 56), R

  • Summation formulas for the greatest integer part function

    Creator:
    Haertel, Raymond Delbert
    Abstract:
    This thesis contains a collection of summation formulas for the greatest integer part function. Proofs are supplied for original results and for those formulas which are stated without proof in the literature. References are given for formulas and proofs which appear in the literature.
    Resource Type:
    Masters Thesis
    Full Text:
    (3, p. 3 -8). A brief history of this function, along with a development of its basic theory and a

  • How the perceptron reacts on non-separable classification problems

    Creator:
    Venema, Rienk S.
    Abstract:
    Neural networks are models which have been developed to simulate the anatomy of the nervous system. The connection between the elements of these networks, the so called artificial neurons, is similar to the connection between the biological neurons. In developing neural networks people are trying to create systems which have...
    Resource Type:
    Masters Thesis
    Full Text:
    -Separable Classification Problems Abstract approved: Robert M. Burton Neural networks are models which