Mathematics Commons^™

Asymptotics Of Carleman Polynomials For Level Curves Of The Inverse Of A Shifted Joukowsky Transformation, Michael Carr Northington

Electronic Theses and Dissertations

Let L be a level curve of the inverse of the shifted Joukowsky transformation w [special characters omitted] w − 1 + (w − 1) –1, that is, [special characters omitted]In this thesis we investigate the asymptotic properties of the sequence of polynomials that are orthonormal over the interior domain of L with respect to the area measure. We establish strong asymptotic formulas describing the behavior of these polynomials (as their degree increases) at every point of the complex plane.

Iteratively Reweighted Least Squares Minimization With Prior Information A New Approach, Dmitriy Popov

Electronic Theses and Dissertations

Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard 1 l -minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to further reduce the number of measurements required to recover the solution with specified accuracy. Although Miosso et al. obtained a number of …

Prediction Of Survival Of Early Stages Lung Cancer Patients Based On Er Beta Cellular Expressions And Epidemiological Data, Evgeny Martinenko

Electronic Theses and Dissertations

We attempted a mathematical model for expected prognosis of lung cancer patients based on a multivariate analysis of the values of ER-interacting proteins (ERbeta) and a membrane bound, glycosylated phosphoprotein MUC1), and patients clinical data recorded at the time of initial surgery. We demonstrate that, even with the limited sample size available to use, combination of clinical and biochemical data (in particular, associated with ERbeta and MUC1) allows to predict survival of lung cancer patients with about 80% accuracy while prediction on the basis of clinical data only gives about 70% accuracy. The present work can be viewed as a …

Zero Divisor Graphs And Poset Decomposition, Bette Catherine Putnam

Electronic Theses and Dissertations

A graph is associated to any commutative ring R where the vertices are the non-zero zero divisors of R with two vertices adjacent if x · y = 0. The zero-divisor graph has also been studied for various algebraic stuctures such as semigroups and partially ordered sets. In this paper, we will discuss some known results on zero-divisor graphs of posets as well as the concept of compactness as it relates to zero-divisor graphs. We will dicuss equivalence class graphs defined on the elements of various algebraic structures and also the reduced graph defined on the vertices of a compact …

Price Discovery In The U.S. Bond Market Trading Strategies And The Cost Of Liquidity, Haimei Shao

Electronic Theses and Dissertations

The world bond market is nearly twice as large as the equity market. The goal of this dissertation is to study the dynamics of bond price. Among the liquidity risk, interest rate risk and default risk, this dissertation will focus on the liquidity risk and trading strategy. Under the mathematical frame of stochastic control, we model price setting in U.S. bond markets where dealers have multiple instruments to smooth inventory imbalances. The difficulty in obtaining the optimal trading strategy is that the optimal strategy and value function depend on each other, and the corresponding HJB equation is nonlinear. To solve …

Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems, Todd Blanton Smith

Electronic Theses and Dissertations

In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in …

A Predictive Model For Secondary Rna Structure Using Graph Theory And A Neural Network., Denise Renee Koessler

Electronic Theses and Dissertations

In this work we use a graph-theoretic representation of secondary RNA structure found in the database RAG: RNA-As-Graphs. We model the bonding of two RNA secondary structures to form a larger structure with a graph operation called merge. The resulting data from each tree merge operation is summarized and represented by a vector. We use these vectors as input values for a neural network and train the network to recognize a tree as RNA-like or not based on the merge data vector.

The network correctly assigned a high probability of RNA-likeness to trees identified as RNA-like in the RAG database, …

Total Domination Dot Critical And Dot Stable Graphs., Stephanie Anne Marie Mcmahon

Electronic Theses and Dissertations

Two vertices are said to be identifed if they are combined to form one vertex whose neighborhood is the union of their neighborhoods. A graph is total domination dot-critical if identifying any pair of adjacent vertices decreases the total domination number. On the other hand, a graph is total domination dot-stable if identifying any pair of adjacent vertices leaves the total domination number unchanged. Identifying any pair of vertices cannot increase the total domination number. Further we show it can decrease the total domination number by at most two. Among other results, we characterize total domination dot-critical trees with total …

Lifting Module Maps Between Different Noncommutative Domain Algebras, Jonathan Von Stroh

Electronic Theses and Dissertations

The classical Carathéodory interpolation problem is the following: let n be a natural number, a₀, a₁, . . . , a_N be complex numbers, and D the unit disk. When does there exist an analytic function F : D → C and complex numbers a_N+1, a_N+2, . . . such that F(z) = a₀ + a₁z + a₂z² + . . . + a_Nz^N + a_N+1z^N+1 + . . . and ||F||_∞ < 1? In 1967, Sarason used operator theory techniques to give an elegant solution to the Carathéodory interpolation problem. In 1968, Sz.-Nagy and Foias extended Sarason's approach into a commutant lifting theorem. Both the theorem and the technique of the proof have become standard tools in control theory. In particular, the commutant lifting theorem approach lends itself to a wide range of generalizations. This thesis concerns one such generalization.

Arias presented generalizations of the original …

Bicircular Matroids With Circuits Of At Most Two Sizes, Torina Deachune Lewis

Electronic Theses and Dissertations

Young in his paper titled, Matroid Designs in 1973, reports that Murty in his paper titled, Equicardinal Matroids and Finite Geometries in 1968, was the first to study matroids with all hyperplanes having the same size. Murty called such a matroid an ``Equicardinal Matroid''. Young renamed such a matroid a ``Matroid Design''. Further work on determining properties of these matroids was done by Edmonds, Murty, and Young in their papers published in 1972, 1973, and 1970 respectively. These authors were able to connect the problem of determining the matroid designs with specified parameters with results on balanced incomplete block designs. …

Numerical Computations For Pde Models Of Rocket Exhaust Flow In Soil, Brian Brennan

Electronic Theses and Dissertations

We study numerical methods for solving the nonlinear porous medium and Navier-Lame problems. When coupled together, these equations model the flow of exhaust through a porous medium, soil, and the effects that the pressure has on the soil in terms of spatial displacement. For the porous medium equation we use the Crank-Nicolson time stepping method with a spectral discretization in space. Since the Navier-Lame equation is a boundary value problem, it is solved using a finite element method where the spatial domain is represented by a triangulation of discrete points. The two problems are coupled by using approximations of solutions …

Initial-Value Technique For Singularly Perturbed Two Point Boundary Value Problems Via Cubic Spline, Luis G. Negron

Electronic Theses and Dissertations

A recent method for solving singular perturbation problems is examined. It is designed for the applied mathematician or engineer who needs a convenient, useful tool that requires little preparation and can be readily implemented using little more than an industry-standard software package for spreadsheets. In this paper, we shall examine singularly perturbed two point boundary value problems with the boundary layer at one end point. An initial-value technique is used for its solution by replacing the problem with an asymptotically equivalent first order problem, which is, in turn, solved as an initial value problem by using cubic splines. Numerical examples …

Detection And Approximation Of Function Of Two Variables In High Dimensions, Minzhe Pan

Electronic Theses and Dissertations

This thesis originates from the deterministic algorithm of DeVore, Petrova, and Wojtaszcsyk for the detection and approximation of functions of one variable in high dimensions. We propose a deterministic algorithm for the detection and approximation of function of two variables in high dimensions.

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.

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.

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.

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 …

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.

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( …

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 …

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.

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 …

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 …

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 …

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) …

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 …

Restrained And Other Domination Parameters In Complementary Prisms., Wyatt Jules Desormeaux

Electronic Theses and Dissertations

In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or …

Double Domination Of Complementary Prisms., Lamont D. Vaughan

Electronic Theses and Dissertations

The complementary prism of a graph G is obtained from a copy of G and its complement G̅ by adding a perfect matching between the corresponding vertices of G and G̅. For any graph G, a set D ⊆ V (G) is a double dominating set (DDS) if that set dominates every vertex of G twice. The double domination number, denoted γ_×2(G), is the cardinality of a minimum double dominating set of G. We have proven results on graphs of small order, specific families and lower bounds on γ_{×2 …}