Browsing Electronic Theses by Author "Bachman, Dale J."
Now showing items 17 of 7

Characteristics of Counter Example Loops in the Collatz Conjecture
Allen, Thomas W., II (20120607)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 (20131115)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. (20140724)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 (20140725)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 (20120607)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 (20150727)The block monoid B(G) of a finite abelian group G is the set of zerosum 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 (20121018)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 ...