Mathematics Commons^™

Book Review: Math: Facing An American Phobia By Marilyn Burns, Stephen L. Brown

ACMS Conference Proceedings 1999

No abstract provided.

On The Solutions Of A Family Of Sextic Thue Equations, Alain Togbe

ACMS Conference Proceedings 1999

No abstract provided.

Preface (1999), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

Introduction (1999), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

Schedule (1999), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

Table Of Contents (1999), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

Solutions To A Nonlinear Drift-Diffusion Model Of Semiconductors, Weifu Fang, Kazufumi Ito

Mathematics and Statistics Faculty Publications

A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.

Integer Maxima In Power Envelopes Of Golay Codewords, Michael W. Cammarano, Meredith L. Walker

Department of Math & Statistics Technical Report Series

This paper examines the distribution of integer peaks amoung Golay cosets in Ζ_4. It will prove that the envelope power of at least one element of every Golay coset of Ζ₄ of length 2^m (for m-even) will have a maximum at exactly 2^m+1. Similarly it will be proven that one element of every Golay coset of Ζ₄ of length 2^m (for m-odd) will have a maximum at exactly 2^m+1. Observations and partial arguments will be made about why Golay cosets of Ζ₄ of length 2^{m …}

Anticommuting Derivations, Steen Pedersen

Mathematics and Statistics Faculty Publications

We show that the re are no non-trivial closable derivations of a C*-algebra anticommuting with an ergodic action of a compact group, supposing that the set of squares is dense in the group. We also show that the re are no non-trivial closable densely defined rank one derivations on any C*-algebra.

A Priori Lρ Error Estimates For Galerkin Approximations To Porous Medium And Fast Diffusion Equations, Dongming Wei, Lew Lefton

Mathematics Faculty Publications

Galerkin approximations to solutions of a Cauchy-Dirichlet prob-

lem governed by a generalized porous medium equation.

Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.

Can Mathematics Be Taught In A Christian Way?, Johan Deklerk

ACMS Journal 2004

Some people would argue that mathematics cannot be taught in a Christian way. Others would say it can be done, but that they are unsure how to do it, and therefore do not do it. Some methods mentioned from time to time will be briefly discussed in this address. The question will be asked whether these techniques bring one closer to a Christian perspective on mathematics. My view is that some of these methods are just not sufficient and that more should be done. More attention should be paid to the context in which a mathematical subject is imbedded. Attention …

Lewis Carroll: Author, Mathematician, And Christian, David L. Neuhouser

ACMS Journal 2004

Although a Christian, an author, and a mathematician, Charles Letwidge Dodgson (better known as Lewis Carroll) wrote very few works in which these three aspects of his person was present. The only examples of him merging these interests are in Sylvie and Bruno and Sylvie and Bruno Concluded. This paper will explore what motivated him to make these works and whether or not they were successful.

The Deconstruction Of Mathematics, David J. Stucki

ACMS Journal 2004

Mathematics, as an academic discipline, has stood for many years as the last bastion against a growing tide of intellectual relativism that has become all but ubiquitous. More recently, however, efforts have been made to "humanize" mathematics by advocating a social-constructivist approach to the philosophy of mathematics, both in practice and education. This paper is intended to serve as a critical response to one advocate of this approach, Reuben Hersh (What Is Mathematics, Really?, 1997), and in the process a defense of Platonism.

Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

A report of progress in linear and nonlinear partial differential equations, microlocal analysis, singular partial differential operators, spectral analysis and hyperfunction theory. The papers aretaken from a conference on partial differential equations and their applications, held in Wuhan.

Reconstructing Subsets Of Reals, A. J. Radcliffe, A. D. Scott

Department of Mathematics: Faculty Publications

We consider the problem of reconstructing a set of real numbers up to translation from the multiset of its subsets of fixed size, given up to translation. This is impossible in general: for instance almost all subsets of Z contain infinitely many translates of every finite subset of Z. We therefore restrict our attention to subsets of R which are locally finite; those which contain only finitely many translates of any given finite set of size at least 2. We prove that every locally finite subset of R is reconstructible from the multiset of its 3-subsets, given up to …

Algebraic Geometric Codes Over Rings, Judy L. Walker

Department of Mathematics: Faculty Publications

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980’s. Recently, there has been an increased interest in the study of linear codes over finite rings. In this paper, we combine these two approaches to coding theory by introducing the study of algebraic geometric codes over rings. In addition to defining these new codes, we prove several results about their properties.

A Unified Approach To Difference Sets With Gcd(V, N) > 1, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

The five known families of difference sets whose parameters (v, k, λ; n) satisfy the condition gcd(v,n) > 1 are the McFarland, Spence, Davis-Jedwab, Hadamard and Chen families. We survey recent work which uses recursive techniques to unify these difference set families, placing particular emphasis on examples. This unified approach has also proved useful for studying semi-regular relative difference sets and for constructing new symmetric designs.

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Mathematics Faculty Publications

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.

On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for .

A Structural Result Of Irreducible Inclusions Of Type Iii Lambda Factors, Lambda Is An Element Of (0,1), Phan Loi

Mathematics and Statistics Faculty Publications

Given an irreducible inclusion of factors with finite index N ⊂ M, where M is of type III_λ1/m, N of type III_λ1/n, 0 < λ < 1, and m,n are relatively prime positive integers, we will prove that if N ⊂ M satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with N ⊂ M. Relations between N ⊂ M and a certain G-kernel on subfactors are also discussed.

A Generalization Of Cayley Graphs For Finite Fields, Dawn M. Jones

Dissertations

A central question in the area of topological graph theory is to find the genus of a given graph. In particular, the genus parameter has been studied for Cayley graphs. A Cayley graph is a representation of a group and a fixed generating set for that group. A group is said to be planar if there is a generating set which produces a planar Cayley graph. We say that a group is toroidal if there is a generating set that produces a toroidal Cayley graph and if there are no generating sets which produce a planar Cayley graph. Characterizations for …

Maximally Disjoint Solutions Of The Set Covering Problem, David J. Rader, Peter L. Hammer

Mathematical Sciences Technical Reports (MSTR)

This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP­ complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, …

Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny

Mathematics and Statistics Faculty Publications

A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C^1+α(Ω₀) for all t > Ω, where Ω₀ is the initial vortex region that is assumed to be in C^1+α. Consequently, for any time t, the vortex region Ω_t is of C^1+α, and the vorticity is in C^α(Ω_t).

Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann

Dissertations

No abstract provided.

The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis

Department of Math & Statistics Technical Report Series

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?

This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …

Positive Solutions For A Concave Semipositone Dirichlet Problem, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article

Orthogonal Harmonic Analysis Of Fractal Measures, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis.

Relationships Among The First Variation, The Convolution Product, And The Fourier-Feynman Transform, Chull Park, David Skough, David Storvick

Department of Mathematics: Faculty Publications

In this paper we examine the various relationships that exist among the first variation, the Fourier- Feynman transform, and the convolution product for functionals on Wiener space that belong to a Banach algebra S.

On C^1 Robust Singular Transitive Sets For Three-Dimensional Flows, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

The main goal of this paper is to study robust invariant transitive sets containing singularities for C¹ flows on three-dimensional compact boundaryless manifolds:they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C¹-perturbations of the flow.

Résumé:

Le but de ce travail est d'étudier des ensembles invariants robustes ayant des singularités pour des flots C¹ sur des variétés tridimensionelles : ce sont des ensembles hyperboliques singuliers. << Robuste >> veut dire ici que cette propriété ne peut être détruite par des …