Browsing by Department "Mathematics and Statistics"
Now showing items 121-140 of 283
Inequalities Involving Generalized Matrix Functions
(2015-07-17)
Given a set \(F\) of functions that have their domain and codomain in common, if the codomain is ordered we may partially order \(F\) by choosing a subset \(S\) of their domain and saying that for \(f,g \in F\), \(f \leq ...
Integral closures
(2010-07-06)
The q^th-power algorithm from Leonard [3], [4], and Leonard and Pellikaan [1] is a
recent and efficient method of computing the integral closure of a ring in its field of fractions.
Previously, the q^th-power algorithm ...
Interior Backus Problem with Expanded Data
(2019-12-09)
We consider a special formulation of the Backus geomagnetic problem in two and higher dimension. Given a domain $\Omega \subset \mathbb{R}^n$, we seek to determine whether there exists a unique harmonic function $u$ ...
Intermittency properties of space-time fractional stochastic partial differential equations
(2019-07-11)
This dissertation focuses on the analyses of the non-linear time-fractional stochastic reaction-diffusion equations of the type
\begin{equation}\label{abstract-eq}
\partial^\beta_tu_t(x)=-\nu(-\Delta)^{\alpha/2} ...
The Intersection Problem for Latin Squares with Holes of Size 2 and 3
(2009-04-28)
In this dissertation we give complete solutions for the intersection problem of latin
squares with holes of size 2 and 3. For a pair of 2n x 2n latin squares with holes of size 2
to have k entries in common outside of ...
The Intersection Problem for Maximum Packings of the Complete Graph with 4-Cycles
(2020-05-11)
A maximum packing of K_n with 4-cycles may leave some edges of the graph unpacked. The size of the leave is determined by the congruence class of n modulo 8. When n ≡ 1 (mod 8) the packing coincides with a 4-cycle system ...
The Intersection Problem for Steiner Triple Systems
(2011-11-16)
In this thesis we give a new solution to the intersection problem for Steiner triple systems, using results that were not available when the original solution was given. In particular we show for each pair (n,k), where n ...
The Intersection Problem for Steiner Triple Systems
(2016-04-22)
A Steiner triple system of order n is a pair (S,T) where T is an edge disjoint partition
of the edge set of K_n (the complete undirected graph on n vertices with vertex set S) into triangles (or triples). It is by now ...
Intersection problem for the class of Reed-Muller codes.
(2009-07-28)
The intersection problem for Coding Theory can be stated as follows: given a family or class of
families of codes, find the spectrum of intersection numbers. The general strategy to attack
this kind of problem begins ...
Intersection Structures on Secants of Grassmannians
(2023-08-02)
Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to k-planes with the restriction that their intersection has a prescribed dimension. This thesis calculates dimensions of ...
Intersections of Graph Theory and Combinatorial Commutative Algebra
(2023-07-27)
In this dissertation, we explore three problems in the fields of graph theory and combinatorial commutative algebra, and their intersections. First, we prove a higher upper bound for the slow coloring number of a certain ...
An Introduction to Bernstein-Gel’fand-Gel’fand Correspondence
(2022-08-04)
This master's thesis serves as an introduction to the Bernstein-Gel'fand-Gel'fand correspondence first written in 1978. We shall cover some of the fundamental objects that the reader may not be familiar with, mainly tensor ...
The Inverse Domination Number Problem, DI-Pathological Graphs, and Fractional Analogues
(2010-04-20)
The conjecture that $\alpha(G) \geq \gamma'(G)$ is unproven where $\alpha(G)$ is the vertex independence number and $\gamma'(G)$ is the inverse domination number of a simple graph G. We have found the conjecture to be true ...
Inverse eigenvalue problem for Euclidean distance matrices
(2014-04-23)
This paper examines the inverse eigenvalue problem (IEP) for the particular class of Euclidean distance matrices. Studying the necessary and sufficient conditions for a matrix to be an element of the set of Euclidean ...
Inverse Limit Spaces
(2008-12-15)
This paper is a vast survey of inverse limit spaces. After defining an inverse limit on continuous bonding functions, we prove important theorems about inverse limits, provide examples, and explore various generalizations ...
Inverse source problem and inverse diffusion coefficient problem for parabolic equations with applications in geology
(2017-07-26)
This dissertation deals with inverse problems for parabolic partial differential equations with an integral constraint and their applications in geology. We employ analytical and numerical methods to analyze and approximate ...
Isoperimetric Properties of the Circle
(2022-05-03)
Jakob Steiner and Karl Weierstrass provided formal proofs of the isoperimetric property of the circle in the late 1830s. New mathematical tools, proof language, and concepts were needed to prove this rather obvious fact, ...
Iteration Methods for Approximation of Solutions of Nonlinear Equations in Banach Spaces
(2008-08-15)
The objective in this manuscript is to study some iterative methods used to approximate
solutions of nonlinear equations in Banach Spaces. In particular, we study a Halperntype
iterative scheme in relation to nonexpansive ...
Iterative processes generating dense point sets
(2006-05-15)
The central problem of the thesis is the question of denseness of
certain sets of points in the plane. All of the following results
are joint with A. Bezdek. We consider point sets P, not a subset
of a line, having the ...
k-star Decompositions of Lambda-Fold Complete Multipartite Graphs
(2007-08-15)
We examine the problem of k-star decompositions on lambda-fold complete multipartite
graphs. After a brief examination of the computational complexity issues involved, we
present complete proofs for necessary and sufficient ...