Electronic Theses and Dissertations

# Browsing Auburn Theses and Dissertations by Department "Mathematics and Statistics"

Now showing items 1-20 of 257

### 3-Cycle Systems and Structure within Graph Decompositions ﻿

(2014-07-24)
An $H$-decomposition of a graph $G$ is a partition of the edge set $E(G)$ such that each element of the partition induces a subgraph isomorphic to $H$. A packing or cover of $\lambda K_n$ (with triples) is an ordered pair ...

### 4-cycles systems of line graphs of complete multipartite graphs ﻿

(2008-08-15)
Here we investigate the necessary and sufficient conditions for the existence of 4 - cycle systems of the line graphs of complete multipartite graphs.

### 5-cycle systems ﻿

(2014-04-25)
A k-cycle system of a multigraph G is an ordered pair (V,C) where V is the vertex set of G and C is a set of k-cycles, the edges of which partition the edges of G. A k-cycle system of lambda K_v is known as a lambda-fold ...

### A-Stability For Two Species Competition Diffusion Systems ﻿

(2006-08-15)
My dissertation research focuses on establishing the structural stability of the attractor ($\mathcal{A}$-stability) via Morse-Smale property for diffusive two-species competition systems \label{abst ...

### Adjoint Orbits of Borel Subgroup on Maximal Nilpotent Subalgebra of Types A and C. ﻿

(2021-11-18)  ETD File Embargoed
We describe the adjoint orbits of a Borel subgroup on a maximal nilpotent algebra of Types A and C. In Chapter 1, we provide a historical background and motivation behind the study. We highlight the important works in ...

### Advanced Statistical Learning Approaches to Healthcare ﻿

(2019-06-03)  ETD File Embargoed
In this dissertation, we propose a novel statistical modeling methodology that effectively analyzes and extracts information from large datasets. Two real datasets were employed to validate the proposed methodology: breast ...

### Almost Resolvable Maximum Packings of Complete Bipartite Graphs with 4-Cycles ﻿

(2012-07-17)
A packing of a complete bipartite graph K(m,n) with 4-cycles is a decomposition of K(m,n) into a collection C of edge-disjoint 4-cycles and a set of unused edges L referred to as the leave. If C is as large as possible ...

### Amalgamations and Detachments of Graphs and Hypergraphs ﻿

(2012-07-09)
A \textit{detachment} of a graph $H$ is a graph obtained from $H$ by splitting some or all of its vertices into more than one vertex. If $g$ is a function from $V(H)$ into $\mathbb {N}$, then a \textit{$g$-detachment} of ...

### Analysis and finite element approximation for nonlinear problems in poroelasticity and bioconvection ﻿

(2013-04-23)
This dissertation is concerned with nonlinear systems of partial differential equation with solution dependent physical coefficients satisfying the Nemytskii assumption. Such equations arise from two important application ...

### Analysis and Optimal control of deterministic Vector-Borne diseases model ﻿

(2018-07-18)
In this dissertation, two systems of deterministic differential equations are introduced to study the transmission of vector-borne diseases between a host and a vector. The total population of the host and the vector are ...

### An Analysis of Item Response Theory ﻿

(2019-07-02)
This paper examines a field of psychological and educational measurement testing theory called Item Response Theory. The paper delves into the basics of the theory, its theoretical and statistical background, and discusses ...

### Analysis of stochastic vector-host epidemic models ﻿

(2017-07-25)
In this dissertation, deterministic and stochastic mathematical models are proposed to study vector-host epidemic models with direct transmission. The total population of the host and the vector is divided into different ...

### The Application of Complex Numbers and Quaternions in Navigation ﻿

(2020-11-30)
Complex numbers and quaternions have a wide array of applications. This paper beginsby briefly going over the history of complex numbers and quaternions, bringing up little knownfacts on main discoverers. Then, we ...

### Applications of Stationary Sets in Set Theoretic Topology ﻿

(2010-11-10)
The notion of a stationary subset of a regular cardinal, a set which intersects any closed unbounded subset of that cardinal, is a useful tool in investigating certain properties of topological spaces. In this paper we ...

### Applications of Stochastic Gradient Descent for Optimization of Complex Systems with Uncertainty ﻿

(2021-07-27)
The Stochastic Gradient Descent (SGD) method in all its variations has gained popularity with the recent progress in Machine learning. In this dissertation we implement and analyze two modifications of the SGD method. In ...

### Asymptotic Dynamics of Competition Systems with Immigration and/or Time Periodic Dependence ﻿

(2015-05-08)
This dissertation is devoted to the study of the asymptotic dynamics, in particular, coexistence states and convergence of nonnegative solutions to the competition systems with immigration and time periodic dependence. ...

### Asymptotic Results in Noncompact Semisimple Lie Groups ﻿

(2013-04-22)
This dissertation is a collection of results on analysis on real noncompact semisimple Lie groups. Specifically, we examine the convergence patterns of sequences arising from the special group decompositions that exist ...

### 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 ...

### 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 ...