Applied Mathematics Commons^™

The 25 Greatest Mathematicians, Robert L. Brabenec

ACMS Conference Proceedings 1995

No abstract provided.

Introduction (1995), David L. Neuhouser

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Table Of Contents (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Schedule (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez

Mathematical Sciences Technical Reports (MSTR)

In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic …

Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny

Mathematics and Statistics Faculty Publications

A new approach to some free boundary problems of the type of jets and cavities for potential flows is introduced. Both potential and Stokes flows are considered. The variable domain problems are relaxed so that they become nonsmooth optimization problems on fixed domains for somewhat singular state equations. State equations are considered, and multivalued generalized gradients of the variational functionals are studied. The method is constructive.

Descartes And Problem-Solving, Judith V. Grabiner

Pitzer Faculty Publications and Research

What can Descartes' Geometry teach us about problem solving?

An Elementary Proof That Finite Groups Lack Unique Product Structures, Matthew Cushman

Mathematical Sciences Technical Reports (MSTR)

We provide an elementary proof that no nontrivial finite group has a unique m-element product structure for any m greater than or equal to 2.

Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury

Mathematics and Statistics Faculty Publications

In this paper we study principal points and self-consistent points of p-variate elliptical distributions. We also discuss implications of our results for the computation and estimation of principal points.

Computations For A Vibrating System Diagonalize The Variance, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

The transformations to diagonalize potential energy matrices for coupled harmonic oscillators will also diagonalize the variance when written in matrix form. After a brief review of a geometrical interpretation of the variance, the transformations are described and an example is given.

Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe

Mathematics Faculty Publications

Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.

Mathematical And Theological Beliefs: A Cognitive Science Perspective, Ron Benbow

ACMS Journal 2004

In recent years, research studies have shown that control decisions and processes, beliefs about the nature of mathematics, attitudes, and other affective variables have enormous impact on the mathematical performance of students. This paper gives an overview of the research on mathematical beliefs and reviews some work done in Christian education relating to theological beliefs. It then compares the two.

Mathematics From The Viewpoint Of Science In Context, Johan Deklerk

ACMS Journal 2004

This is the first of a series of papers presented over several years by deKlerk exploring the notion of how mathematics might be taught from a Christian perspective. In this paper, he introduces the notion of context as the basis for such an approach. He then discusses seven contexts a teacher can employ.

A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn

Mathematics Faculty Publications

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rⁿ into R that was strictly increasing with respect to the new order imposed on Rⁿ. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces …

Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller

Mathematics and Statistics Faculty Publications

No abstract provided.

Metode De Calcul În Analiza Matematică, Florentin Smarandache, C. Dumitrescu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Generalized Geynman Integrals: The 𝓛(L2, L2) Theory, Chull Park, David Skough

Department of Mathematics: Faculty Publications

In this paper we develop an 𝓛(L₂(R), L₂(R)) theory for the Feynman integral of functionals of general stochastic processes.

Perturbations Of Certain Reflexive Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

In this note we use cohomological techniques to prove that if there is a linear map between two CSL algebras which is close to the identity, then the two CSL algebras are similar. We use our result to show that if 2' is a purely atomic, hyperreflexive CSL with uniform infinite multiplicity which satisfies the 4-cycle interpolation condition, then there are constants d, C > 0 such that whenever L is another CSL such that d(Alg2' , AlgL) < d, then there is an invertible operator S such that S Alg2'S-1 = AlgL and IISII liS-III < 1 + Cd(AIg2' , AIgL).

Reconstruction Of Semiconductor Doping Profile From Lbic Image, Weifu Fang, Kazufumi Ito

Mathematics and Statistics Faculty Publications

In this paper, the authors study the reconstruction of a semiconductor doping profile or, equivalently, the equilibrium potential, from its LBIC (laser-beam-induced current) image. For the one-dimensional case, the authors first characterize the attainable class of current measurements, and from this they show the nonuniqueness of the inverse problem. Then the reconstruction of the equilibrium potential is reduced to finding two constants subject to some constraints. A reconstruction algorithm is established based on a least squares formulation of the problem. The case of noise-collapsed data is also discussed. For a special case of two-dimensional domain, the authors apply the one-dimensional …

Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we prove the existence of self-similar solutions to the anisotropic curve shortening equation.

Remarks On Automorphisms Of Subfactors, Phan Loi

Mathematics and Statistics Faculty Publications

We establish certain properties of automorphisms on an inclusion of AFD type II₁ factors with finite index and finite depth and discuss their applications to the classification problem of AFD type III subfactors, including a different proof of a result on subfactors with principal graph D_n.

Uniqueness Of Stable And Unstable Positive Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam

All HMC Faculty Publications and Research

Abstract not included in this article.

Hankel Transforms In Generalized Fock Spaces, John Schmeelk

Mathematics and Applied Mathematics Publications

A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq),where ϕ0∈ℂ and ϕq∈Lp(ℝq), q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of …

Reconstruction Of Multiple Cracks From Experimental, Electrostatic Boundary Measurements, Kurt M. Bryan, Valdis Liepa, Michael Vogelius

Mathematical Sciences Technical Reports (MSTR)

We demonstrate the viability of using Electrical Impedance Tomography (EIT) for the reconstruction of multiple macroscopic cracks in a conductive medium.

Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho

Mathematics and Statistics Faculty Publications

Controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied. By investigating the properties of certain exponential series, it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue. A sufficient condition for exact controllability is also obtained in terms of the Riesz basis properties of those exponential series.

Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We describe a class of measurable subsets Ω in R^d such that L²(Ω) has an orthogonal basis of frequencies e_λ(x) = e^i2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ R^d. We show that such spectral pairs (Ω, Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L²(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis of mu may be built instead from a natural representation of the Cuntz …

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk

Mathematical Sciences Technical Reports (MSTR)

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …

A Conjectured Paradigm Shift In 21st Century Mathematics Pedagogy, Paul Isihara

ACMS Conference Proceedings 1993

With greater and greater capacity for automated content delivery, the role of teachers may shift increasingly to providing the human touch in pedagogy such as love for students.

A New Look At An Old 3:16 An Acms Devotional, Russell W. Howell

ACMS Conference Proceedings 1993

This paper examines John 3:16 in the bible by examining the language and cultural backgrounds of the verse.

Knuth's (1, 2, 1) Unstacking, Paul J. Zwier

ACMS Conference Proceedings 1993

This presentation is dedicated to Donald Knuth who has proposed many interesting and challenging problems in the Problems Section of The American Mathematical Monthly. The problem considered ist hat proposed by Barry Hayes, Knuth, and Carlos Subi (E3267 [1988,456]). The published solution, due to Albert Nijenhuis, just recently appeared in the March 1993 Monthly, pages 292-294.

The problem is as follows. Suppose that we are given n piles of blocks; the i-th pile having ai blocks, i = 1, 2, …, n. Dismantle the piles by choosing a pile having 2 or more blocks, removing …