Mathematics Commons^™

Self-Consistency Algorithms, Thaddeus Tarpey

Mathematics and Statistics Faculty Publications

The k-means algorithm and the principal curve algorithm are special cases of a self-consistency algorithm. A general self-consistency algorithm is described and results are provided describing the behavior of the algorithm for theoretical distributions, in particular elliptical distributions. The results are used to contrast the behavior of the algorithms when applied to a theoretical model and when applied to finite datasets from the model. The algorithm is also used to determine principal loops for the bivariate normal distribution.

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Mathematics and Statistics Faculty Publications

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

A Perturbation Of A Periodic Hamiltonian System, Gregory S. Spradlin

Publications

No abstract provided.

A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler

Mathematics Faculty Publications

This paper will provide the general construction of the continuous, orthogonal, compactly-supported multiwavelets associated with a class of continuous, orthogonal, compactly-supported scaling functions that contain piecewise linears on a uniform triangulation of $\R^2$. This class of scaling functions is a generalization of a set of scaling functions first constructed by Donovan, Geronimo, and Hardin. A specific set of scaling functions and associated multiwavelets with symmetry properties will be constructed.

Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.

Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder

Mathematics and Statistics Faculty Publications

In this paper, we examine a random version of the lattice point problem.

Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li

Mathematics and Statistics Faculty Publications

Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.

Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff

All HMC Faculty Publications and Research

Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. In this letter we describe a systematic technique for calculating such solutions and determining their linear stability. For the problem of axisymmetric van der Waals driven rupture (recently studied by Zhang and Lister), we identify the unique stable similarity solution for point rupture of a thin film and an alternative mode of singularity formation corresponding to annular “ring rupture.”

Codes Over Rings From Curves Of Higher Genus, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

We construct certain error-correcting codes over finite rings and estimate their parameters. These codes are constructed using plane curves and the estimates for their parameters rely on constructing “lifts” of these curves and then estimating the size of certain exponential sums.

THE purpose of this paper is to construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools; notably, an estimate for the dimension of trace codes over rings (generalizing work of van der Vlugt over fields and some results on lifts of affin curves from field of characteristic p …

Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald

Mathematics and Statistics Faculty Publications

Let D be a smoothly bounded domain in Euclidean space and let X_t be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from D of a particle driven by X_t, where the average is taken overall starting points in D.

Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Tracking The Trochoid On Safari, Andrew Simoson

ACMS Conference Proceedings 1999

While on sabbatical in Dar es Salaam in 1997–98, I was tasked to be the department’s seminar director and discovered that a dearth of speakers roam about in east Africa; so I opted to set up a lecture tour for myself to include Zambia, Zimbabwe, and Botswana as well as Tanzania—and spoke about the envelope of curves generated by a series of line segments obtained when two runners attached by an ideal bungee cord (the line segments) proceed about a circular track. Herein we describe life in east Africa and show that those envelopes are trochoids.

Revolutions In Mathematics (Book Review), Kevin Vander Meulen

ACMS Conference Proceedings 1999

A review of Revolutions in Mathematics, edited by Donald Gillies, Clarendon Press, Oxford 1992.

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

ACMS Conference Proceedings 1999

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 Conference Proceedings 1999

This paper is a criticism of Reuben Hersh's What is Mathematics, Really? and the humanist philosophy of mathematics.

Book Review, David J. Stucki

ACMS Conference Proceedings 1999

A book review of Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science by Alan Sokal and Jean Bricmont.

Book Review: Virtual Gods: The Seduction Of Power And Pleasure In Cyberspace, Jonathan R. Senning

ACMS Conference Proceedings 1999

This paper is a review of Virtual Gods: The Seduction of Power and Pleasure in Cyberspace, edited by Tal Brooke, Harvest House Publishers, 1997.

Teaching Linear Algebra And Abstract Algebra With Two Way Video And Audio, Edward Reinke

ACMS Conference Proceedings 1999

An outline of a presentation discussing teaching two different algebra courses long-distance as well as in a classroom.

A Mathematician At The Science And Theology Book Club, Greg Crow

ACMS Conference Proceedings 1999

This paper is a case study of the insights gained and the contributions made in a weekly Science and Theology Faculty Book Club. The contribution of other group members to the expansion of one’s general understanding of their fields is demonstrated in increased vocabulary, use of existing theoretical models, glimpses of the depth of their disciplines, and in the recognition of the need for humility. The mathematician may contribute by helping to clarify definitions, by applying basic ideas in their own and related fields, and only very rarely by bringing their own research to the table.

Book Review - The Language Of Mathematics: Making The Invisible Visible By Kieth Devlin, Charles R. Hampton

ACMS Conference Proceedings 1999

Charles R. Hampton reviews The Language of Mathematics: Making the Invisible Visible. By Kieth Devlin. W. H. Freeman and Company, 1998

Determinism, Chaos, And The Meaning Of Randomness, Or Quantum Theory And The Sovereignty Of God, John Wicks

ACMS Conference Proceedings 1999

No abstract provided.

Book Review: The Number Sense: How The Mind Creates Mathematics By Stanislas Dehaene, Mary Vanderschoot

ACMS Conference Proceedings 1999

No abstract provided.

Book Review: The Philosophy Of Mathematics By W.S. Anglin, Richard D. Rockwell

ACMS Conference Proceedings 1999

No abstract provided.

Noncommunicative Algebraic Geometry, Dennis S. Keeler

ACMS Conference Proceedings 1999

No abstract provided.

Willing The Will Of God, Harold Heie

ACMS Conference Proceedings 1999

No abstract provided.

Book Review: An Imaginary Tale: The Story Of √-1 By Paul J. Nahin, Michael O'Leary

ACMS Conference Proceedings 1999

No abstract provided.

Doubt And Uncertainty - A Book And Idea Review, Richard Laatsch

ACMS Conference Proceedings 1999

No abstract provided.

Hyperbolic Geometry And Poincare's Half-Plane Model, Robert Frank

ACMS Conference Proceedings 1999

No abstract provided.

Can Mathematics Be Taught In A Christian Way?, Johan H. De Klerk

ACMS Conference Proceedings 1999

No abstract provided.

Using Mathematica To Explore Abstract Algebra, Al Hibbard

ACMS Conference Proceedings 1999

No abstract provided.