Physical Sciences and Mathematics Commons^™

Banach Spaces On Infinitely Branching Trees, Annette B. Locke

Electronic Theses and Dissertations

An example of a Banach space, X_∞, with a nonseparable dual such that l₁ does not imbed in X_∞ is investigated. Not every weakly null sequence has a subsequence equivalent to the usual basis of c₀, but c₀ imbeds in many subspaces of X_∞. The space l₁ does imbed in X_∞^∗, the dual space of X_∞, yet weakly converging sequences in X_∞^∗ need not converge in norm.

Independent Domination In Complementary Prisms., Joel Agustin Gongora

Electronic Theses and Dissertations

Let G be a graph and G̅ be the complement of G. The complementary prism GG̅ of G is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. For example, if G is a 5-cycle, then GG̅ is the Petersen graph. In this paper we investigate independent domination in complementary prisms.

The Last Of The Mixed Triple Systems., Ernest Jum

Electronic Theses and Dissertations

In this thesis, we consider the decomposition of the complete mixed graph on v vertices denoted M_v, into every possible mixed graph on three vertices which has (like M_v) twice as many arcs as edges. Direct constructions are given in most cases. Decompositions of theλ-fold complete mixed graph λM_v, are also studied.

Structure And Properties Of Maximal Outerplanar Graphs., Benjamin Allgeier

Electronic Theses and Dissertations

Outerplanar graphs are planar graphs that have a plane embedding in which each vertex lies on the boundary of the exterior region. An outerplanar graph is maximal outerplanar if the graph obtained by adding an edge is not outerplanar. Maximal outerplanar graphs are also known as triangulations of polygons. The spine of a maximal outerplanar graph G is the dual graph of G without the vertex that corresponds to the exterior region. In this thesis we study metric properties involving geodesic intervals, geodetic sets, Steiner sets, different concepts of boundary, and also relationships between the independence numbers and domination numbers …

Decompositions Of Mixed Graphs With Partial Orientations Of The P4., Adam M. Meadows

Electronic Theses and Dissertations

A decomposition D of a graph H by a graph G is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. A mixed graph on V vertices is an ordered pair (V,C), where V is a set of vertices, |V| = v, and C is a set of ordered and unordered pairs, denoted (x, y) and [x, y] respectively, of elements of V [8]. An ordered pair (x …

Locating-Domination In Complementary Prisms., Kristin Renee Stone Holmes

Electronic Theses and Dissertations

Let G = (V (G), E(G)) be a graph and G̅ be the complement of G. The complementary prism of G, denoted GG̅, is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. A set D ⊆ V (G) is a locating-dominating set of G if for every u ∈ V (G)D, its neighborhood N(u)⋂D is nonempty and distinct from N( …

Cyclic, F-Cyclic, And Bicyclic Decompositions Of The Complete Graph Into The 4-Cycle With A Pendant Edge., Daniel Shelton Cantrell

Electronic Theses and Dissertations

In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of:

(1) a single cycle of length v,

(2) f fixed points and a cycle of length v − f, or

(3) two disjoint cycles.

The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of K_v.

Efficient Cone Beam Reconstruction For The Distorted Circle And Line Trajectory, Souleymane Konate

Electronic Theses and Dissertations

We propose an exact filtered backprojection algorithm for inversion of the cone beam data in the case when the trajectory is composed of a distorted circle and a line segment. The length of the scan is determined by the region of interest , and it is independent of the size of the object. With few geometric restrictions on the curve, we show that we have an exact reconstruction. Numerical experiments demonstrate good image quality.

Optimal Dual Frames For Erasures And Discrete Gabor Frames, Jerry Lopez

Electronic Theses and Dissertations

Since their discovery in the early 1950's, frames have emerged as an important tool in areas such as signal processing, image processing, data compression and sampling theory, just to name a few. Our purpose of this dissertation is to investigate dual frames and the ability to find dual frames which are optimal when coping with the problem of erasures in data transmission. In addition, we study a special class of frames which exhibit algebraic structure, discrete Gabor frames. Much work has been done in the study of discrete Gabor frames in Rn, but very little is known about the l2(Z) …

The Sheffer B-Type 1 Orthogonal Polynomial Sequences, Daniel Galiffa

Electronic Theses and Dissertations

In 1939, I.M. Sheffer proved that every polynomial sequence belongs to one and only one type. Sheffer extensively developed properties of the B-Type 0 polynomial sequences and determined which sets are also orthogonal. He subsequently generalized his classification method to the case of arbitrary B-Type k by constructing the generalized generating function A(t)exp[xH1(t) + · · · + xk+1Hk(t)] = ∑∞n=0 Pn(x)tn, with Hi(t) = hi,iti + hi,i+1t i+1 + · · · , h1,1 ≠ 0. Although extensive research has been done on characterizing polynomial sequences, no analysis has yet been completed on sets of type one or higher …

Almost Regular Graphs And Edge Face Colorings Of Plane Graphs, Lisa Macon

Electronic Theses and Dissertations

Regular graphs are graphs in which all vertices have the same degree. Many properties of these graphs are known. Such graphs play an important role in modeling network configurations where equipment limitations impose a restriction on the maximum number of links emanating from a node. These limitations do not enforce strict regularity, and it becomes interesting to investigate nonregular graphs that are in some sense close to regular. This dissertation explores a particular class of almost regular graphs in detail and defines generalizations on this class. A linear-time algorithm for the creation of arbitrarily large graphs of the discussed class …

Weighted Lp-Stability For Localized Infinite Matrices, Qiling Shi

Electronic Theses and Dissertations

This dissertation originates from a classical result that the lp-stability of the convolution operator associated with a summable sequence are equivalent to each other for different p . This dissertation is motivated by the recent result by C. E. Shin and Q. Sun (Journal ofFunctional Analysis, 256(2009), 2417-2439), where the lp-stability of infinite matrices in the Gohberg-Baskakov-Sjostrand class are proved to be equivalent to each other for different p. In the dissertation, for an infinite matrix having certain off-diagonal decay, its weighted lp-stability for different p are proved to be equivalent to each other and hence a result by Shin …

Analytical And Numerical Solutions Of Differentialequations Arising In Fluid Flow And Heat Transfer Problems, Erik Sweet

Electronic Theses and Dissertations

The solutions of nonlinear ordinary or partial differential equations are important in the study of fluid flow and heat transfer. In this thesis we apply the Homotopy Analysis Method (HAM) and obtain solutions for several fluid flow and heat transfer problems. In chapter 1, a brief introduction to the history of homotopies and embeddings, along with some examples, are given. The application of homotopies and an introduction to the solutions procedure of differential equations (used in the thesis) are provided. In the chapters that follow, we apply HAM to a variety of problems to highlight its use and versatility in …

Permutation Patterns, Reduced Decompositions With Few Repetitions And The Bruhat Order, Daniel Alan Daly

Electronic Theses and Dissertations

This thesis is concerned with problems involving permutations. The main focus is on connections between permutation patterns and reduced decompositions with few repetitions. Connections between permutation patterns and reduced decompositions were first studied various mathematicians including Stanley, Billey and Tenner. In particular, they studied pattern avoidance conditions on reduced decompositions with no repeated elements. This thesis classifies the pattern avoidance and containment conditions on reduced decompositions with one and two elements repeated. This classification is then used to obtain new enumeration results for pattern classes related to the reduced decompositions and introduces the technique of counting pattern classes via reduced …

Standing Waves Of Spatially Discrete Fitzhugh-Nagumo Equations, Joseph Segal

Electronic Theses and Dissertations

We study a system of spatially discrete FitzHugh-Nagumo equations, which are nonlinear differential-difference equations on an infinite one-dimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for all 1-pulse solutions. We determine the range of parameter values that allow for the existence of standing waves. We use numerical methods to demonstrate the stability of …