Applied Mathematics Commons^™

The Fokker-Planck And Related Equations In Theoretical Population Dynamics, George Derise

Mathematics & Statistics Theses & Dissertations

The population growth of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population dynamics because population growth is basically a random event. There are a large number of chance factors influencing growth that might not be taken into account by deterministic models. The effect of other species (for example, in the chance meeting of a predator), population fluctuations due to weather changes that would alter food …

Bimodules Over Cartan Subalgebras, Richard Mercer

Mathematics and Statistics Faculty Publications

Given a Cartan subalgebra A of a non Neumann algebra M, the techniques of Feldman and Moore are used to analyze the partial isometries v in M such that v* Av is contained in A. Orthonormal bases for M consisting of such partial isometries are discussed, and convergence of the resulting generalized fourier series is shown to take place in the Bures A-topology. The Bures A-topology is shown to be equivalent to the strong topology on the unit ball of M. These ideas are applied to A-bimodules and to give a simplified and intuitive proof of the Spectral Theorem …

On The Equivalence Of The Operator Equations Xa + Bx = C And X - P(-B)Xp(A)(-1) = W In A Hilbert-Space, P A Polynomial, Tapas Mazumdar, David Miller

Mathematics and Statistics Faculty Publications

We consider the solution of (*) XA+BX = C for bounded operators A,B,C and X on a Hilbert space, A normal. We establish the existence of a polynomial p and a bounded operator W with the property that the unique solution X of (*) also solves X − p(−B)Xp(A)⁻¹ = W uniquely. A known iterative algorithm can be applied to the latter equation to solve (*).

Stability Of A Viscoelastic Burgers Flow, D. Glenn Lasseigne, W. E. Olmstead

Mathematics & Statistics Faculty Publications

The system of equations proposed by Burgers to model turbulent flow in a channel is extended to include viscoelastic affects. The stability and bifurcation properties are examined in the neighborhood of the critical Reynolds number. For highly elastic fluids, the bifurcated state is periodic with a shift in frequency.

Boundary Value Problems In Elasticity And Thermoelasticity, Stuart Davidson

Mathematics & Statistics Theses & Dissertations

In this dissertation the author solves a series of mixed boundary value problems arising from crack problems in elasticity and thermoelasticity. Using integral transform techniques and separation of variables appropriately, it is shown that the solutions can be found by solving a corresponding set of triple or dual integral equations in some instances, while in others the solutions of triple or dual series relations are required. These in turn reduce to various singular integral equations which are solved in closed form, in two cases, or by numerical methods. The stress intensity factors at the crack tips, the physical parameters of …

Graphs, Maneuvers, And Turnpikes, Arthur T. Benjamin

All HMC Faculty Publications and Research

We address the problem of moving a collection of objects from one subset of Z^m to another at minimum cost. We show that underfairly natural rules for movement assumptions, if the origin and destination are far enough apart, then a near optimal solution with special structure exists: Our trajectory from the originto the destination accrues almost all of its cost repeatingat most m different patterns of movement. Directions for related research are identified.

Remarks On Estimates For The Green Function, Jose Luis Menaldi

Mathematics Faculty Research Publications

No abstract provided.

Bivariate C1 Quadratic Finite Elements And Vertex Splines, Tian-Xiao He

Scholarship

No abstract provided.

Spatial Critical Points Of Solutions Of A One-Dimensional Nonlinear Parabolic Problem, Larry Turyn

Mathematics and Statistics Faculty Publications

The number of spatial critical points is nonincreasing in time, for positive, analytic solutions of a scalar, nonlinear, parabolic partial differential equation in one space dimension. While proving this, we answer the question: What happens to a critical point which loses simplicity?

Nonnegative Solutions For A Class Of Radially Symmetric Nonpositone Problems, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We consider the existence of radially symmetric non-negative solutions for the boundary value problem

\begin{displaymath}\begin{array}{*{20}{c}} { - \Delta u(x) = \lambda f(u(x))\qua... ...\\ {u(x) = 0\quad \left\Vert x \right\Vert = 1} \\ \end{array} \end{displaymath}

where $ \lambda > 0,f(0) < 0$ (non-positone), $ f' \geq 0$ and $ f$ is superlinear. We establish existence of non-negative solutions for $ \lambda $ small which extends some work of our previous paper on non-positone problems, where we considered the case $ N = 1$. Our work also proves a recent conjecture by Joel Smoller and Arthur Wasserman.

On The Dimension Of Bivariate Superspline Spaces, Tian-Xiao He

Scholarship

A bivariate piecewise polynomial function of total degree d on some grid partition △ that has rth order continuous partial derivatives everywhere may have higher-order partial derivatives at the vertices of the grid partition. In finite element considerations and in the construction of vertex splines, it happens that only those functions with continuous partial derivatives of order higher than r at the vertices are needed to give the same full approximation order as the entire space of piecewise polynomials. This is certainly the case for d > 4r + 1. Such piecewise polynomial functions are called supersplines. This …

Simulated Annealing On Np-Complete Problems, Russell W. Howell

ACMS Conference Proceedings 1989

The Random House Dictionary defines anneal as " ... to free (glass, metals, etc.) from internal stress by heating and gradually cooling." In the physical world, impurities are annealed out of a substance by heating it to a high temperature. As it is cooled, its molecular structure gradually settles into a stable "low-energy" configuration. It is important to cool the substance slowly, especially at lower temperatures, so that impurities do not get "frozen" into place. With careful cooling, a low-energy state can eventually be reached. This state may not be the one with the lowest potential energy, where the spins …

The Mathematical Intelligencer, Dmitrii Egorov: Mathematics And Theology In Russia, Charles E. Ford

ACMS Conference Proceedings 1989

This paper tells the story of Russian mathematician Dmitri Egorov, recounting his faith and contributions to the field of mathematics.

A Course On Mathematics And The Christian Faith, W. David Laverell, Carl J. Sinke

ACMS Conference Proceedings 1989

The January interim term at Calvin College provides an opportunity for developing and teaching courses outside a normal major program. As a result faculty members are frequently given the interim off to provide time for research and development of new courses. In 1987 we were given such a leave in order to pursue the questions of the relationship between mathematics and the Christian Faith. One result was our presentation at the 1987 Association of Christians in the Mathematical Sciences conference. Immediately thereafter we began to develop a specific interim course based on our studies. We offered the course during the …

The Bisexual Galton-Watson Branching Process, David M. Hull

ACMS Conference Proceedings 1989

I would like to present the bisexual Galton-Watson branching process. The word "bisexual" indicates that we will be considering a population of two sexes--which will be designated as the usual male and female. Here is a brief overview of what I would like to cover.

1. The bisexual process motivated: why is it needed?
2. The standard Galton-Watson branching process.
3. The state of affairs regarding two-sex models.
4. The nuts and bolts of the bisexual Galton-Watson branching process (parameters defined and how it works).
5. A review of published bisexual results to date.
6. What is to come?

Newton And Saccheri: Case Studies In The Interplay Of Mathematics And Religion, Tommy Leavelle

ACMS Conference Proceedings 1989

In the course of this paper I will try to present to you the basic facts and some of the subsequent assessments of the life and work of two mathematicians for whom the interplay of mathematics and religion was influential: Issac Newton and Girolamo Saccheri.

A Tutorial On Prolog, Russell C. Bjork

ACMS Conference Proceedings 1989

PROLOG is a programming language based on the use of mathematical logic—specifically the first order predicate calculus. The name is a contraction for “Programming in Logic”. PROLOG was developed in 1972 by Phillippe Roussel of the AI Group (Groupe d’Intelligence Artificielle) of the University of Marseille. Specifically, it is an outgrowth of research there on automatic theorem proving. PROLOG has been widely used by AI researchers in Europe and Japan. In fact, the Japanese have made it the basis for the software side of their “Fifth Generation” computer project. PROLOG is currently used in a wide variety of areas, not …

Augustine's Mathematical Realism, Paul J. Zwier

ACMS Conference Proceedings 1989

After a review of Philip Kitcher's argument against Mathematical Realism, this paper presents the case for Mathematical Realism by looking at the life and writings of Saint Augustine.

Beauty In Mathematics: Some Theological Implications, David L. Neuhouser

ACMS Conference Proceedings 1989

It may come as a surprise to some that science or mathematics could be considered beautiful, but many prominent sciences and mathematicians from around the world have made such claims. Furthermore, the beauty of mathematics and order of the universe inspired some of the greatest developments in science and mathematics. This paper examines the beauty of mathematics and what scientists and other individuals have said about the subject.

Using Writing In The Mathematics Classroom, Dr. Barbara J. Rose

ACMS Conference Proceedings 1989

No abstract provided.

Mathematics Between The Lines Of Ecclesiates, Donald A. Joesphson

ACMS Conference Proceedings 1989

No abstract provided.

Writing Across The Curriculum Using Statistics, Carlos A. Pereira

ACMS Conference Proceedings 1989

No abstract provided.

Written Assignments In College Freshman And Sophomore Mathematics Courses, Jean Alliman

ACMS Conference Proceedings 1989

No abstract provided.

Mathematical Modeling In The Classroom, Jefferson Hartzler

ACMS Conference Proceedings 1989

No abstract provided.

The Fourth Dimension And The Theology Of Edwin Abbot Abbott, Thomas F. Banchoff

ACMS Conference Proceedings 1989

No abstract provided.

Schedule (1989), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor

Introduction (1989), Gene B. Chase

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor

Table Of Contents (1989), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor

The Fourth Dimension And The Theology Of Edwin Abbott Abbott, Thomas Banchoff

ACMS Conference Proceedings 1989

This paper is a brief biography of Edwin Abbott Abbott, author of Flatland, and a sketch of the main ideas in the book. It also incorporates some personal reflections.

Homoclinic Bifurcations With Nonhyperbolic Equilibria, Bo Deng

Department of Mathematics: Faculty Publications

A general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbolic equilbrium points of ordinary differential equations. It consists of a special normal form called admissible variables, exponential expansion, strong A-lemma, and Lyapnunov- Schmidt reduction for the Poincare maps under Sil'nikov variables. The method is based on the Center Manifold Theory, the contraction mapping principle, and the Implicit Function Theorem.