Browsing by Department "Mathematics and Statistics"
Now showing items 41-60 of 282
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 ...
Constructive Aspects for the Generalized Orthogonal Group
(2010-04-28)
Our main result is a constructive proof of the Cartan-Dieudonn\'{e}-Scherk Theorem in the real or complex fields. The Cartan-Dieudonn\'{e}-Scherk Theorem states that for fields of characteristic other than two, every ...
Containment Relations and Line Graphs
(2023-08-07)
This dissertation studies several problems involving containment relations and line graphs. First, motivated by Reed and Seymour's 2004 result that Hadwiger's Conjecture holds for line graphs, we provide a partial result ...
Convergence Analysis and Numerical Simulation of Particle Swarm Optimization
(2017-04-21)
Nature, including mankind, loves to optimize and the world is far from being deterministic.
Thus, stochastic optimization is an important and active area of research in applied mathematics.
Inspired by the social behavior ...
Convexity of Generalized Numerical Ranges Associated with SU(n) and SO(n)
(2010-05-20)
We give a new proof of a result of Tam on the convexity of the generalized numerical
range associated with the classical Lie groups SO(n). We also provide a connection between
the result and the convexity of the classical ...
Countably Compact, Countably Tight, Non-Compact Spaces
(2011-07-28)
In this work, we will study several examples of countably compact, countably tight, non-compact spaces. After reviewing the important basic notions, we will examine a construction of several such spaces first given by Manes ...
Cycle Systems
(2012-01-18)
In this dissertation the author has found the necessary and sufficient conditions for obtaining a 6-cycle system of the Cartesian product of two complete graphs covering 2-paths in the corresponding bipartite graph. She ...
Decomposing Graphs With Two Associate Classes Into Paths Of Length 3 And The Intersection Problem Of Latin Rectangles
(2018-07-24)
In this thesis, the decomposition problem of graphs with two associate classes into paths
of length 3 is completely settled. The intersection problem for latin rectangles is completely
solved as well. In addition, an ...
Decomposition of Complete Tri-Partite Graphs into 5-Cycles
(2013-04-16)
E. S. Mahmoodian gave necessary conditions for when the edges of a complete tripartite graph can be partitioned so that each set in the partition induces a 5-cycle. Since then, he, N. J. Cavenagh, E. J. Billington, S. ...
Dedekind Domains and the P-rank of Ext
(2017-04-21)
We address what can be said of torsion-free finite rank modules $A$ and $B$ over a Dedekind domain $R$ when their Ext's are isomorphic, extending an answer to Fuchs' Problem 43 and its dual by Goeters. We obtain a result ...
Deep Learning, Neural Networks and Aerospace Applications
(2018-11-15)
The ability to rack an enemy missile while in-flight, whether to accurately predict the point of impact (POI), the point of origin (POO) or to destroy the missile in-flight, is greatly enhanced if the missile type and/or ...
Defining Chaos
(2017-07-26)
This thesis is a study of the paper "Defining chaos" by Brian Hunt and Edward Ott [1] with added details to make arguments easier to follow. They introduced a new entropy-based definition of chaos called expansion entropy. ...
Defining Chaos
(2017-07-18)
This thesis is a study of the paper “Defining Chaos” by Brian Hunt and Edward Ott [1] with added details to make arguments easier to follow. They introduced a new entropy based definition of chaos called expansion entropy. ...
Derivations of subalgebras of the Lie algebra of block upper triangular matrices
(2016-07-22)
This dissertation studies the derivations of some subalgebras of the Lie algebra of block
upper triangular matrices. Specifically, we study the derivations of the Lie algebra of strictly
block upper triangular matrices ...
Development of Striae Distensae - A Mechanochemical Model
(2007-05-15)
Striae distensae, otherwise known as stretch marks, are common skin lesions found
in a variety of clinical settings. They occur frequently during adolescence or pregnancy
when there is rapid tissue expansion, but may ...
Differential geometry on matrix groups
(2020-03-20)
In this dissertation, we study the differential geometry of the matrix groups. In literatures, many authors proposed to compute matrix means using the geodesic distance defined by an invariant Riemannian metrics on the ...
Discrete sets, free sequences and cardinal properties of topological spaces
(2009-07-01)
We study the influence of discrete sets and free sequences on cardinal properties of topological spaces. We focus mainly on the minimum number of discrete sets needed to cover a space X (denoted by dis(X)) and on reflection ...
Disjoint G-Designs and the Intersection Problem for Some Seven Edge Graphs
(2017-04-21)
A $G$-Design of order $n$ is a decomposition of the edges of $K_n$ (the complete graph on $n$ vertices) into subgraphs of $K_n$ isomorphic to $G$, called blocks, in which each edge of $K_n$ appears in exactly one block. ...
Disjoint Intersection Problem For Steiner Triple Systems
(2007-12-15)
Let (S, T_1) and (S, T_2) be two Steiner Triple systems on the set S of symbols with the set of triples T_1 and T_2 respectively. They are said to intersect in m blocks if |T_1 intersection T_2| = m. Further, if the blocks ...
A Distribution-Free Control Chart for Retrospective Location Analysis of Subgrouped Multivariate Data
(2011-09-08)
In multivariate quality control, a proper Phase I analysis is essential to the success of Phase II monitoring. Even self-starting methods, which seek to minimize the Phase I process, usually recommend a single retrospective ...