Mathematics Commons^™

A Sequence Of Polynomials For Approximating Arctangent, Herbert A. Medina

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

Editorial: Growth & Change, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Automated Geometric Theorem Proving: Wu's Method, Joran Elias

The Mathematics Enthusiast

Wu’s Method for proving geometric theorems is well known. We investigate the underlying algorithms involved, including the concepts of pseudodivision, Ritt’s Principle and Ritt’s Decomposition algorithm. A simple implementation for these algorithms in Maple is presented, which we then use to prove a few simple geometric theorems to illustrate the method.

Modeling Interdisciplinary Activities Involving Mathematics And Philosophy, Steffen M. Iversen

The Mathematics Enthusiast

In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series …

Mathematically Promising Students From The Space Age To The Information Age, Linda Jensen Sheffield

The Mathematics Enthusiast

On October 4, 1957, with the launch of Sputnik 1 by the Soviet Union, the world entered the Space Age and the United States became quite concerned that the Soviet Union had a head start in the space race. A year later, realizing that the support of gifted and talented mathematics and science students was critical to national security, the United States federal government passed the National Defense Education Act (NDEA), providing aid to education in the United States at all levels, primarily to stimulate the advancement of education in science, mathematics, and modern foreign languages. Also, during this time, …

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

Algorithmic Problems In Junior Contests In Latvia, Agnis Andžans, Inese Berzina, Dace Bonka

The Mathematics Enthusiast

Mathematical contests are of great importance for advanced education in Latvia today. Their content must be well-balanced and must correspond to the inner logic and recent trends of mathematics. A classification of algorithmic problems and characteristic examples are considered.

Tme's Worldwide Circulation Statistics

The Mathematics Enthusiast

No abstract provided.

Is Hollywood Good For Mathematics? (A Brief Discussion)., Christopher D. Goff

College of the Pacific Faculty Presentations

Mathematics has played a role in many recent films, such as Good Will Hunting, A Beautiful Mind, and Proof. But how exactly is mathematics being portrayed? What ramifications does this portrayal have on our ”students,” broadly defined? In Good Will Hunting, mathematics is Will’s ticket out of his lower-class life and into a prestigious existence. In A Beautiful Mind, mathematical talent and schizophrenia are identified, at least in part. In Proof, mathematics not only links a daughter to her late father, but it also provides a backdrop for much of the story’s conflict. In this discussion, we will begin by …

Simultaneous Transitional And Multiplicative Tiling And Wavelet Sets In R2, Eugen J. Ionascu

Faculty Bibliography

Simultaneous tiling for several different translational sets has been studied rather extensively, particularly in connection with the Steinhaus problem. The study of orthonormal wavelets in recent years, particularly for arbitrary dilation matrices, has led to the study of multiplicative tilings by the powers of a matrix. In this paper we consider the following simultaneous tiling problem: Given a lattice in Z ∈ Rd and a matrix A ∈ GL (d, R), does there exist a measurable set T such that both {T + α : α ∈ L} and {AnT : n ∈ Z} are tilings of Rd? This problem …

Vector Theory Of Spontaneous Lorentz Violation, Shu Hong Fung

Undergraduate Research Symposium (UGRS)

Classical electromagnetism predicts two massless propagating modes, which are known as the two polarizations of the photon. On the other hand, if the Lorentz symmetry of classical electromagnetism is spontaneously broken, the new theory will still have two massless Nambu-Goldstone modes resembling the photon. If the Lorentz symmetry is broken by a bumblebee potential that allows for excitations out of the minimum, then massive modes arise. Furthermore, in curved spacetime, such massive modes will be created through a process other than the usual Higgs mechanism because of the dependence of the bumblebee potential on both the vector field and the …

Spectral Analysis Of The Supreme Court, B Lawson, M Orrison, David Uminsky

Mathematics

Should you decide that spectral analysis is worth looking into (as we hope to convince you), then you will be happy to know that there are efficient algorithms for doing spectral analysis. Perhaps more interestingly, at least from a mathematical perspective, these algorithms involve an intriguing mixture of ideas and techniques from linear algebra, abstract algebra, numerical analysis, and graph theory.

The focus of this paper is the linear algebraic framework in which the spectral analysis of voting data like that above is carried out. As we will show, this framework can be used to pinpoint voting coalitions in small …

On Self-Adjoint And J-Self-Adjoint Dirac-Type Operators: A Case Study, Stephen L. Clark, Fritz Gesztesy

Mathematics and Statistics Faculty Research & Creative Works

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl-Titchmarsh half-line m-coefficients (and 2 × 2 matrix-valued M-matrices) in the non-self-adjoint context and derive some of their basic properties. We conclude with an illustrative example showing that crossing spectral arcs in the non-self-adjoint context imply the blowup of the norm of spectral projections in the limit where the crossing point …

Multiple Lebesgue Integration On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.

Singular Second-Order Multipoint Dynamic Boundary Value Problems With Mixed Derivatives, Hua Luo, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We study a certain singular second-order m-point boundary value problem on a time scale and establish the existence of a solution. The proof of our main result is based upon the Leray-Schauder continuation theorem.

Modeling Of Bioinspired Sensors For Flow Separation Detection For Micro Air Vehicles, Belinda A. Batten, John R. Singler, Benjamin T. Dickinson

Mathematics and Statistics Faculty Research & Creative Works

Autonomous micro air vehicle (MAV) flight faces inherent stability challenges. One challenge is controlling flow separation over the airfoil and an autonomous control system for MAV flight may be enhanced with closed loop separation control. In this work, we focus on modeling biologically inspired hair cell sensors for future flow control applications. We model the sensor output and present examples and numerical results.

Feedback Control Of Low Dimensional Models Of Transition To Turbulence, John A. Burns, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The problem of controlling or delaying transition to turbulence in shear flows has been the subject of numerous papers over the past twenty years. This period has seen the development of several low dimensional models for parallel shear flows in an attempt to explain the failure of classical linear hydrodynamic stability theory to correctly predict transition. In recent years, ideas from robust control theory have been employed to attack this problem. In this paper we use these models to develop a scenario for transition that employs both classical bifurcation theory and robust control theory. In addition, we present numerical results …

The Poweratlas: A Power And Sample Size Atlas For Microarray Experimental Design And Research, Grier P. Page, Jode W. Edwards, Gary L. Gadbury, Prashanth Yelisetti, Jelai Wang, Prinal Trivedi, David B. Allison

Mathematics and Statistics Faculty Research & Creative Works

Microarrays permit biologists to simultaneously measure the mRNA abundance of thousands of genes. An important issue facing investigators planning microarray experiments is how to estimate the sample size required for good statistical power. What is the projected sample size or number of replicate chips needed to address the multiple hypotheses with acceptable accuracy? Statistical methods exist for calculating power based upon a single hypothesis, using estimates of the variability in data from pilot studies. There is, however, a need for methods to estimate power and/or required sample sizes in situations where multiple hypotheses are being tested, such as in microarray …

The Emergence Of Large-Scale Coherent Structure Under Small-Scale Random Bombardments, Andrew Majda, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We provide mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small-scale random bombardments with small forcing and appropriate scaling assumptions. the analysis shows that the large-scale structure emerging out of the small-scale random forcing is not the one predicted by equilibrium statistical mechanics. But the error is very small, which explains earlier successful prediction of the large-scale structure based on equilibrium statistical mechanics. © 2005 Wiley Periodicals, Inc.

Dynamics Of Rotating Bose-Einstein Condensates And Its Efficient And Accurate Numerical Computation, Weizhu Bao, Qiang Du, Yanzhi Zhang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we study the dynamics of rotating Bose--Einstein condensates (BEC) based on the Gross--Pitaevskii equation (GPE) with an angular momentum rotation term and present an efficient and accurate algorithm for numerical simulations. We examine the conservation of the angular momentum expectation and the condensate width and analyze the dynamics of a stationary state with a shift in its center. By formulating the equation in either the two-dimensional polar coordinate system or the three-dimensional cylindrical coordinate system, the angular momentum rotation term becomes a term with constant coefficients. This allows us to develop an efficient time-splitting method which is …

The Hurwitz Zeta Function As A Convergent Series, Roman Dwilewicz, Jan Minac

Mathematics and Statistics Faculty Research & Creative Works

New series for the Hurwitz zeta function which converge on the whole plane, except s = 1, are developed. This is applied to obtain a remarkably simple evaluation of some special values of the function.

On Modeling Hiv Infection Of Cd4+ T Cells, Amy Comerford

Electronic Theses and Dissertations

We examine an early model for the interaction of HIV with CD4+ T cells in vivo and define possible parameters and effects of said parameters on the model. We then examine a newer, more simplified model for the interaction of HIV with CD4+ T cells that also considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The stability of both the disease free steady state and the endemically infected steady state are examined utilizing standard methods and the Routh-Hurwitz criteria. We show that if N, the number of infectious virions produced per …

Geometric Field Stability And Normal Field Curvature Of Solution Sets Of Ordinary Differential Equations In Two Variables, Leslie L. Kerns

Theses, Dissertations and Capstones

The classical linearization approach to stability theory determines whether or not a system is stable in the vicinity of its equilibrium points. This classical approach partly depends on the validity of the linear approximation. The definition of stability developed in this article takes a different approach and uses a curvature function to assess the relative locations of solutions within a field of solutions (the underlying solution set of the ODE). The present approach involves calculations that directly yield stability information, without having to enter into the often lengthy eigenvalue-eigenvector method. The present results both complement and are compatible with the …

Undergraduates' Use Of Mathematics Textbooks, Bret Benesh, Tim Boester, Aaron Weinberg, Eimilie Wiesner

Mathematics Faculty Publications

No abstract provided.

A Database Of Local Fields, John W. Jones, David P. Roberts

Mathematics Publications

We describe our online database of finite extensions of Q_p, and how it can be used to facilitate local analysis of number fields.

Higher Dimensional Enrichment, Stefan Forcey

Mathematical Sciences Faculty Research

Lyubashenko has described enriched 2–categories as categories enriched over V–Cat, the 2–category of categories enriched over a symmetric monoidal V. Here I generalize this to a k–fold monoidal V. The latter is defined as by Balteanu, Fiedorowicz, Schw¨anzl and Vogt but with the addition of making visible the coherent associators _i. The symmetric case can easily be recovered. The introduction of this paper proposes a recursive definition of V–n–categories and their morphisms. Then I consider the special case of V–2–categories and give the details of the proof that with their morphisms these form the structure of a 3–category.

Atomic Hardy Space Theory For Unbounded Singular Integrals, Ryan Berndt

Mathematics Faculty Scholarship

No abstract provided.

Review: Stability Of Bases And Frames Of Reproducing Kernels In Model Spaces, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Siegel’S Lemma With Additional Conditions, Lenny Fukshansky

CMC Faculty Publications and Research

Let K be a number field, and let W be a subspace of K-N, N >= 1. Let V-1,..., V-M be subspaces of KN of dimension less than dimension of W. We prove the existence of a point of small height in W\boolean OR(M)(i=1) V-i, providing an explicit upper bound on the height of such a point in terms of heights of W and V-1,..., V-M. Our main tool is a counting estimate we prove for the number of points of a subspace of K-N inside of an adelic cube. As corollaries to our main result we derive an explicit …

On Prime Generation Through Primitive Divisors Of Recurrence Sequences, Richard Russell

Electronic Theses and Dissertations

We examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. Mathematicians have speculated over many centuries that these sequences contain an infinite number of prime terms, however no proof has been given as such. We examine a less direct method of showing an infinitude of primes in each sequence by showing that the sequences contain an infinite number of terms with primitive divisors.