Browsing by Department "Mathematics and Statistics"
Now showing items 21-40 of 280
Bounded Complete Embedding Graphs
(2015-07-21)
In the study of graph embeddings, there is particular interest in small embeddings and in bounds on the minimum number of vertices that must be added in order to achieve an embedding of a particular design. We introduce ...
A Brief Exploration of the Sorgenfrey Line and the Lexicographic Order
(2006-05-15)
The author will compare properties of the usual topology on the real line with the properties of the Sorgenfrey Line. After that she will look at properties of the Lexiographic Order on the reals cross [0,1]. The main ...
A Brief Survey of Hyperspaces and a Construction of a Whitney Map
(2009-08-03)
This paper is a brief survey of hyperspaces of topological spaces. In particular, the hyperspace of all nonempty compact subsets of a space and the hyperspace of all nonempty subcontinua of a space with the Vietoris topology. ...
C-wild knots
(2013-04-16)
Here we give a definition of infinite connected sum of tame knots and define a C-wild knot
to be an infinite connected sum of tame knots whose wild points form a Cantor set. We further
give a classification of C-wild ...
C4-Factorizations with Two Associate Classes
(2010-04-29)
Let $K = K(a,p;\lambda_{1},\lambda_{2})$ be the multigraph with: the number of vertices in each part equal to $a$; the number of parts equal to $p$; the number of edges joining any two vertices of the same part equal to ...
Choice numbers, Ohba numbers and Hall numbers of some complete k-partite graphs
(2009-07-15)
The choice numbers of some complete k−partite graphs are found, after we resolved
a dispute regarding the choice number of K(4, 2, . . . , 2) when k is odd. Estimates of the
choice numbers and the Ohba numbers of K(m, ...
The Chromatic Number of the Euclidean Plane
(2009-08-03)
We discuss the chromatic number of the plane problem. We provide a detailed history
of its origins, along with some of the recent progress.
Classification Using A Functional Partial Least Squares Logistic Regression Method
(2016-04-12)
Statistical analysis of functional data has been explored extensively over the last decade
and functional partial least squares regression has emerged as a popular choice for classification problems. In partial least ...
Coefficient Space Properties and a Schur Algebra Generalization
(2005-12-15)
Let K be an infinite field and Gamma = GL_(n)(K). If we linearly extend the natural action of Gamma on the set E of n-dimensional column vectors over K to the group algebra KGamma, then E becomes a KGamma-module. We then ...
Color Trades on Graphs
(2022-08-03)
Edge-colorings of graphs have a rich history and are widely studied. Trade spectra of
graphs are relatively new and ripe for study. The color-trade-spectrum of a graph G is defined
to be the set of all t for which there ...
Colorful Results on Euclidean Distance Graphs and Their Chromatic Numbers
(2012-05-03)
In this work we study Euclidean distance graphs whose vertex set is the n-dimensional rational space. In particular, we deal with the chromatic numbers (and some related parameters) of such graphs when n = 2 or n = 3. A ...
Compactifications of indecomposable topological spaces
(2017-04-20)
A continuum is a compact and connected topological space. A continuum that is not the union of any two of its proper subcontinua is said to be indecomposable. We examine topological spaces which are closely related to ...
A Comparison of Two Proofs of Yamamoto's Theorem Relating Eigenvalue Moduli and Singular Values of a Matrix
(2006-12-15)
We examine two proofs of Yamamoto’s theorem regarding the asymptotic relationship
between singular values and eigenvalue moduli of a matrix. The first proof is by T.
Yamamoto in 1967 and makes use of compound matrices. ...
Competition Graphs
(2012-04-18)
Competition graphs were originally created in 1968 by Biologist Joel Cohen. In this paper we discuss four things. First, the use of linear algebra is considered with connection to competition graphs. Second, we generalize ...
The Complete Solution of the Intersection Problem for Maximum Packings of K_n with Triples
(2018-07-03)
In the late 1980's the intersection problem for maximum packings of K_n with triples was solved by Hoffman, Lindner, and Quattrocchi. Their combined results showed that for any n = i mod(6) such that i in { 0, 2, 4, 5} the ...
Completeness Properties in Function Spaces with the Compact-Open Topology
(2014-05-01)
It is an open problem to characterize those spaces X for which the compact-open topology C_k(X) has various completeness properties. It is conjectured that C_k(X) is Baire if and only if X has the moving off property. ...
Computational Design of Random Rough Surfaces in Thin-film Solar Cells by Stochastic Gradient Methods
(2021-07-21)
We present an efficient numerical algorithm to solve for the optimal random structure in
maximizing the absorptance for thin-film solar cells. Random rough texture can increase the
absorbing efficiency of solar cells by ...
Concerning a Problem of K. Kuratowski
(2006-05-15)
Suppose (S,T) is a topological space and A is any subset of S. Then the functions f and g from the power set of S, P(S), into P(S) are defined as: f(A) is the closure of A and g(A) is the complement of A. In this thesis, ...
Constructing Cubic Splines on the Sphere
(2009-07-15)
A method to approximate functions defined on a sphere using Tensor Product cubic B-splines is presented here. The method is based on decomposing the sphere into six identical patches obtained by radially projecting the ...
Construction of Orthonormal Multivariate Wavelets
(2011-08-01)
The purpose of this paper is to explain the construction of orthonormal multivariate wavelets associated with a multiresolution analysis. This paper primarily uses the work of R. A. Zalik [10], where he outlines a method ...