Mathematics Commons^™

On Spectra Of Composition Operators, Valentin Matache

Mathematics Faculty Publications

In this paper we consider composition operators Cφ on the Hilbert Hardy space over the unit disc, induced by analytic selfmaps φ. We use the fact that the operator C∗φCφ is asymptotically Toeplitz to obtain information on the essential spectrum and spectrum of Cϕ, which we are able to describe in select cases (including the case of some hypercyclic composition operators or that of composition operators with the property that the asymptotic symbol of C∗φCφ is constant a.e.). One of our tools is the Nikodym derivative of the pull-back measure induced by φ. An alternative formula for the essential norm …

Free Split Bands, Francis Pastijn, Justin Albert

Mathematics, Statistics and Computer Science Faculty Research and Publications

We solve the word problem for the free objects in the variety consisting of bands with a semilattice transversal. It follows that every free band can be embedded into a band with a semilattice transversal.

Extremal H-Colorings Of Graphs With Fixed Minimum Degree, John Engbers

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, a homomorphism from G to H, or H-coloring of G, is a map from the vertices of G to the vertices of H that preserves adjacency. When H is composed of an edge with one looped endvertex, an H-coloring of G corresponds to an independent set in G. Galvin showed that, for sufficiently large n, the complete bipartite graph Κ is the n-vertex graph with minimum degree δ that has the largest number of independent sets. In this article, we begin the project of generalizing this result …

E-Super Vertex Magic Labelling Of Graphs And Some Open Problems, G. Marimuthu, B. Suganya, S. Kalaivani, M. Balakrishnan

Applications and Applied Mathematics: An International Journal (AAM)

Let G be a finite graph with p vertices and q edges. A vertex magic total labelling is a bijection from the union of the vertex set and the edge set to the consecutive integers 1, 2, 3, . . . , p + q with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k for some constant k. Such a labelling is E-super, if the labels of the edge set is the set {1, 2, 3, . . …

Nonlocally Maximal Hyperbolic Sets For Flows, Taylor Michael Petty

Theses and Dissertations

In 2004, Fisher constructed a map on a 2-disc that admitted a hyperbolic set not contained in any locally maximal hyperbolic set. Furthermore, it was shown that this was an open property, and that it was embeddable into any smooth manifold of dimension greater than one. In the present work we show that analogous results hold for flows. Specifically, on any smooth manifold with dimension greater than or equal to three there exists an open set of flows such that each flow in the open set contains a hyperbolic set that is not contained in a locally maximal one.

Practical Applications Of An Integrally Christian Approach To Teaching Mathematics, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Descriptions of various frameworks and approaches to integrating Christian faith in the mathematics classroom are explored, as well as examples and techniques. In particular, a subject-centered approach is advocated in contrast to the traditional teacher-centered approach or, more recently, the student-centered approach.

Progenitors Related To Simple Groups, Elissa Marie Valencia

Electronic Theses, Projects, and Dissertations

This thesis contains methods of finding new presentations of finite groups, particularly nonabelian simple groups. We have presented several progenitors such as 2^{*8}:Z_4 wr Z_2, 3^{*3}:_m L(2,7), 2^{*4}:[2:2^2], 2^{*11}:D_{11} and many more on which we've found the mathieu group M12 and 2*[M21:2^2] among their homomorphic images. We give the full monomial automorphism groups of Aut(3^{*2}), Aut(3^{*3}), and Aut(5^{*2}). Included is a proof showing that the full monomial automorphism group of Aut(m^{*n}) is isomorphic to U(m) wr S_n. In addition we have constructed the Cayley Diagrams of PGL(2,7), [3 x A_5]:2, 3:[A_6:2], and 2 x [(3 x L(2,11)):2] using the process …

Algebra 1 Students’ Ability To Relate The Definition Of A Function To Its Representations, Sarah A. Thomson

Electronic Theses, Projects, and Dissertations

One hundred high school Algebra students from a southern California school participated in this study to provide information on students’ ability to relate the definition of function to its representations. The goals of the study were (1) to explore the extent to which students are able to distinguish between representations of functions/non-functions; (2) to compare students’ ability to distinguish between familiar/unfamiliar representations of functions/non-functions; (3) to explore the extent to which students are able to apply the definition of function to verify function representations; and (4) to explore the extent to which students are able to provide an adequate definition …

Symmetric Presentations Of Non-Abelian Simple Groups, Leonard B. Lamp

Electronic Theses, Projects, and Dissertations

The goal of this thesis is to show constructions of some of the sporadic groups such as the Mathieu group, M₁₂, J₁, Projective Special Linear groups, PSL(2,8), and PSL(2,11), Unitary group U(3,3) and many other non-abelian simple groups. Our purpose is to find all simple non-abelian groups as homomorphic images of permutation or monomial progenitors, as well grasping a deep understanding of group theory and extension theory to determine groups up to isomorphisms. The progenitor, developed by Robert T. Curtis, is a semi-direct product of the following form: P≅2*ⁿ: N = {πw | π …

Homomorphic Images And Related Topics, Kevin J. Baccari

Electronic Theses, Projects, and Dissertations

We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m^*n and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2^*n: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M₁₁ and M₁₁, as well as …

Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence

Mathematics Faculty Publications and Presentations

We give the Castelnuovo–Mumford regularity of arrangements of (n−2)-planes in Pⁿ whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen–Macaulay.

Symmetric Presentations And Generation, Dustin J. Grindstaff

Electronic Theses, Projects, and Dissertations

The aim of this thesis is to generate original symmetric presentations for finite non-abelian simple groups. We will discuss many permutation progenitors, including but not limited to 2^*14 : D₂₈, 2^∗9 : 3^•(3²), 3^∗9 : 3^•(3²), 2^∗21 : (7X3) : 2 as well as monomial progenitors, including 7^∗5 :_m A₅, 3^∗5 :_m S₅. We have included their homomorphic images which include the Mathieu group M₁₂, 2^•J_{2 …}

Comparison Of Robotics, Functional Electrical Stimulation, And Motor Learning Methods For Treatment Of Persistent Upper Extremity Dysfunction After Stroke: A Randomized Controlled Trial, Jessica Mccabe, Michelle Monkiewicz, John P. Holcomb, Svetlana Pundik, Janis J. Daly

Mathematics and Statistics Faculty Publications

Objective

To compare response to upper-limb treatment using robotics plus motor learning (ML) versus functional electrical stimulation (FES) plus ML versus ML alone, according to a measure of complex functional everyday tasks for chronic, severely impaired stroke survivors.

Design

Single-blind, randomized trial.

Setting

Medical center.

Participants

Enrolled subjects (N=39) were >1 year post single stroke (attrition rate=10%; 35 completed the study).

Interventions

All groups received treatment 5d/wk for 5h/d (60 sessions), with unique treatment as follows: ML alone (n=11) (5h/d partial- and whole-task practice of complex functional tasks), robotics plus ML (n=12) (3.5h/d of ML and 1.5h/d of shoulder/elbow robotics), …

Edge Colorings Of Graphs And Their Applications, Daniel Johnston

Dissertations

Edge colorings have appeared in a variety of contexts in graph theory. In this work, we study problems occurring in three separate settings of edge colorings.

For more than a quarter century, edge colorings have been studied that induce vertex colorings in some manner. One research topic we investigate concerns edge colorings belonging to this class of problems. By a twin edge coloring of a graph G is meant a proper edge coloring of G whose colors come from the integers modulo k that induce a proper vertex coloring in which the color of a vertex is the sum of …

Octahedral Extensions And Proofs Of Two Conjectures Of Wong, Kevin Ronald Childers

Theses and Dissertations

Consider a non-Galois cubic extension K/Q ramified at a single prime p > 3. We show that if K is a subfield of an S_4-extension L/Q ramified only at p, we can determine the Artin conductor of the projective representation associated to L/Q, which is based on whether or not K/Q is totally real. We also show that the number of S_4-extensions of this type with K as a subfield is of the form 2^n - 1 for some n >= 0. If K/Q is totally real, n > 1. This proves two conjectures of Siman Wong.

Topics Pertaining To The Group Matrix: K-Characters And Random Walks, Randall Dean Reese

Theses and Dissertations

Linear characters of finite groups can be extended to take k operands. The basics of such a k-fold extension are detailed. We then examine a proposition by Johnson and Sehgal pertaining to these k-characters and disprove its converse. Probabilistic models can be applied to random walks on the Cayley groups of finite order. We examine random walks on dihedral groups which converge after a finite number of steps to the random walk induced by the uniform distribution. We present both sufficient and necessary conditions for such convergence and analyze aspects of algebraic geometry related to this subject.

Analysis Of Multiple Collision-Based Periodic Orbits In Dimension Higher Than One, Skyler C. Simmons

Theses and Dissertations

We exhibit multiple periodic, collision-based orbits of the Newtonian n-body problem. Many of these orbits feature regularizable collisions between the masses. We demonstrate existence of the periodic orbits after performing the appropriate regularization. Stability, including linear stability, for the orbits is then computed using a technique due to Roberts. We point out other interesting features of the orbits as appropriate. When applicable, the results are extended to a broader family of orbits with similar behavior.

Elliptic Curves, Trinity Mecklenburg

Electronic Theses, Projects, and Dissertations

The main focus of this paper is the study of elliptic curves, non-singular projective curves of genus 1. Under a geometric operation, the rational points E(Q) of an elliptic curve E form a group, which is a finitely-generated abelian group by Mordell’s theorem. Thus, this group can be expressed as the finite direct sum of copies of Z and finite cyclic groups. The number of finite copies of Z is called the rank of E(Q).

From John Tate and Joseph Silverman we have a formula to compute the rank of curves of the form …

Unique Prime Factorization Of Ideals In The Ring Of Algebraic Integers Of An Imaginary Quadratic Number Field, Nolberto Rezola

Electronic Theses, Projects, and Dissertations

The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order …

Methods For Two-Sample Comparisons From Censored Time-To-Event Data, Nubyra Ahmed

Dissertations

In the analysis of censored survival data, it is frequently of interest to determine the efficacy of a treatment or new method over a control or existing method. For this purpose, one may report estimates of the two survival functions or, more specifically, their difference, accompanied by simultaneous confidence bands (SCBs). Alternatively, or in addition, one may conduct hypothesis testing for the difference of the two survival functions.

The first project exploits two bootstrap methods to develop new Wald-type SCBs for the difference of survival functions. The censored data bootstrap is employed to obtain nonparametric SCBs for the difference of …