Browsing Auburn Theses and Dissertations by Department "Mathematics and Statistics"
Now showing items 21-40 of 316
Atomic Characterization of L_1 And The Lorentz-Bochner Space L^X(p,1) for With Some Applications
(2016-12-09)
In the 1950s, G. G Lorentz introduced the spaces $\Lambda(\alpha)$ and $M(\alpha)$, for $0<\alpha<1$ and showed that the dual of $\Lambda(\alpha)$ is equivalent to $M(\alpha)$ in his paper titled 'Some New Functional ...
Avoiding k-Rainbow Graphs in Edge Colorings of Kn and other Families of Graphs
(2024-04-26)
A simple graph, G, avoids a k-rainbow edge coloring if any color appears on at least k + 1 edges of G. For any positive integer k, the k-Anti-Ramsey Number, ARk(G,H), is the maximum number of colors in an edge coloring of ...
Bayesian Inference for Longitudinal Data with Envelope Models
(2025-12-12)
Longitudinal studies play a crucial role in biomedical research, such as monitoring chronic
diseases like osteoarthritis. Repeated measures over time enable the tracking of disease pro-
gression and treatment effects. ...
Bell Numbers of Graphs
(2012-05-04)
Let G be a simple graph with vertex set V (G). Let F be a family of graphs such that K1 ∈ F. Denote by B(G; F) the number of unordered partitions of V(G) such that each part induces a member of F. We call B(G; F) the Bell ...
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 and Uncertainty Quantification of Multivariate Functional D
(2025-12-12)
Functional data—data observed continuously over time, space, or other domains—arise in numerous modern applications such as biomedical signal analysis, handwriting and speech recognition, and remote sensing. With advances ...
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 ...
Combinatorial Methods for Undergraduate Mathematics Curriculum Analysis & Design
(2025-05-06)
Student retention is a significant issue in Research in Undergraduate Mathematics Education (RUME), and freshman calculus is notorious for “weeding out” students from STEM majors. Since the late 1980s, various attempts ...
A Combined Study of Autonomous and Nonautonomous Systems for Zoonotic Diseases
(2025-12-08)
Zoonotic diseases transmitted naturally between humans and animals pose a major and persistent threat to global health security. Recent outbreaks such as avian influenza, Ebola, SARS, and COVID-19 have highlighted the ...
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. ...