Now showing items 1-7 of 7

  • Characteristics of Counter Example Loops in the Collatz Conjecture 

    Allen, Thomas W., II (2012-06-07)
    This thesis was undertaken in order to obtain new results about the Collatz Conjecture: that (4; 2; 1) is the only loop created by the Collatz function. We look at some past results and generalize one of them. We discover ...
  • Diophantine monoids defined by a single linear equation 

    Brock, Trey (2013-11-15)
    This project focuses on factorization properties of submonoids of N(r); for some positive integer r; de ned as the solution sets of certain linear equations. In particular, the goal is to determine all irreducible elements ...
  • An extension of the compound poisson information criterion to at most two change points 

    Roach, Jacob S. (2014-07-24)
    In a data set, there could exist more than one set of parameters. Initially, the observed data could follow a distribution with one set of parameters and at a certain point the parameters of the distribution change. The ...
  • Factorization in rings of upper triangular Toeplitz matrices 

    McQueen, Ashlee (2014-07-25)
    Let D be a principal ideal domain and let Rm(D) be the ring of (m + 1) × (m + 1) upper triangular Toeplitz matrices with entries in D. Then Rm(D) is a commutative, Noetherian ring with identity, and hence is atomic. We ...
  • Irreducible divisor simplicial complexes 

    Hobson, Jake (2012-06-07)
    Recently there has been much research on irreducible divisor graphs | visual representations of the factorizations of elements in commutative rings. In this thesis we expand on this concept by introducing the irreducible ...
  • The Monotone Catenary Degree of Block Monoids 

    Card, Alexander (2015-07-27)
    The block monoid B(G) of a finite abelian group G is the set of zero-sum sequences g1 · · · gn such that !n i=1 gi = 0 with operation given by concatenation. A factorization z = α1 · · · · · αn of length |z| = n of α ...
  • Nth roots of matrices 

    Jarman, Eric (2012-10-18)
    This paper investigates the feasibility of finding any nth root, and by extension any rational power, for an arbitrary m x m square matrix. Root finding methods are investigated for real m x m matrices and complex m x ...