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Mathematics

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1999

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Articles 31 - 60 of 139

Full-Text Articles in Physical Sciences and Mathematics

Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li Aug 1999

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.

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Dynamics And Asymptotic Behavior Of The Solutions Of A Nonlinear Differential Equation, Robert Palmer Aug 1999

Dynamics And Asymptotic Behavior Of The Solutions Of A Nonlinear Differential Equation, Robert Palmer

Masters Theses & Specialist Projects

Initial value problems of the form dx/dt= t xP, x(a) = β are examined, first when p = 2. Applying Euler's method, a numerical approximation technique, when p = 2 for certain initial conditions produces a numerical solution which resembles a bifurcation diagram very similar to that produced by the logistic map. Comparisons of such numerical solutions to the logistic map are made, and a partial explanation of such numerical solutions is given. Then, the exact solution of the initial value problem with p = 2, for which the software package Mathematica 3.0 determines an explicit formula, is analyzed to …

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A Stochastic Analog To The Richardson's Arms Race Model, John Fricks Aug 1999

A Stochastic Analog To The Richardson's Arms Race Model, John Fricks

Masters Theses & Specialist Projects

In this thesis, a stochastic version of the Richardson's arms race model is developed through the method of birth-death processes. The expected value of the model is explored and shown to be analogous to the original deterministic arms race model. The numerical method of randomization is then expanded and applied to the stochastic model. A comparison is then made between outcomes of the deterministic and stochastic models.

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An Ellam Scheme For Advection-Diffusion Equations In Two Dimensions, Hong Wang, Helge K. Dahle, Richard E. Ewing, Magne S. Espedal, Robert Sharpley, Shushuang Man Jul 1999

An Ellam Scheme For Advection-Diffusion Equations In Two Dimensions, Hong Wang, Helge K. Dahle, Richard E. Ewing, Magne S. Espedal, Robert Sharpley, Shushuang Man

Faculty Publications

We develop an Eulerian--Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to …

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P-Cross-Section Bodies, Richard J. Gardner, Apostolos Giannopoulos Jul 1999

P-Cross-Section Bodies, Richard J. Gardner, Apostolos Giannopoulos

Mathematics Faculty Publications

If K is a convex body in En, its cross-section body CK has a radial function in any direction u is ∈ Sn-1 equal to the maximal volume of hyperplane sections of K orthogonal to u. A generalization called the p-cross-section body CpK of K, where p > -1, is introduced. The radial function of CpK in any direction u ∈ Sn-1 is the pth mean of the volumes of hyperplane sections of K orthogonal to u through points in K. It is shown that C …

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Why The Player Never Wins In The Long Run At La Blackjack, Arthur T. Benjamin, Michael Lauzon '00, Christopher Moore '00 Jul 1999

Why The Player Never Wins In The Long Run At La Blackjack, Arthur T. Benjamin, Michael Lauzon '00, Christopher Moore '00

All HMC Faculty Publications and Research

No abstract provided in this article.

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Resolutions Of Subsets Of Finite Sets Of Points In Projective Space, Steven P. Diaz, Anthony V. Geramita, Juan C. Migliore Jun 1999

Resolutions Of Subsets Of Finite Sets Of Points In Projective Space, Steven P. Diaz, Anthony V. Geramita, Juan C. Migliore

Mathematics - All Scholarship

Given a finite set, X, of points in projective space for which the Hilbert function is known, a standard result says that there exists a subset of this finite set whose Hilbert function is "as big as possible'' inside X. Given a finite set of points in projective space for which the minimal free resolution of its homogeneous ideal is known, what can be said about possible resolutions of ideals of subsets of this finite set? We first give a maximal rank type description of the most generic possible resolution of a subset. Then we show that this generic resolution …

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Zero-Parity Stabbing Information, Joseph O'Rourke, Irena Pashchenko Jun 1999

Zero-Parity Stabbing Information, Joseph O'Rourke, Irena Pashchenko

Computer Science: Faculty Publications

Everett et al. [EHN96, EHN97] introduced several varieties of stabbing information for the lines determined by pairs of vertices of a simple polygon P, and established their relationships to vertex visibility and other combinatorial data. In the same spirit, we define the “zero-parity (ZP) stabbing information” to be a natural weakening of their “weak stabbing information,” retaining only the distinction among {zero, odd, even > 0} in the number of polygon edges stabbed. Whereas the weak stabbing information’s relation to visibility remains an open problem, we completely settle the analogous questions for zero parity information, with three results: (1) ZP information …

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The Stable Manifold Theorem For Stochastic Systems With Memory (Probability Seminar, Université Henri Poincaré Nancy 1), Salah-Eldin A. Mohammed Jun 1999

The Stable Manifold Theorem For Stochastic Systems With Memory (Probability Seminar, Université Henri Poincaré Nancy 1), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

We state and prove a Local Stable Manifold Theorem for nonlinear stochastic differential systems with finite memory (viz. stochastic functional differential equations (sfde's)). We introduce the notion of hyperbolicity for stationary solutions of sfde's. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary solution. The stable and unstable manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses infinite-dimensional multiplicative ergodic theory techniques and interpolation arguments.

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On-Off Intermittency In Stochastically Driven Electrohydrodynamic Convection In Nematics, Thomas John, Ralf Stannarius, Ulrich Behn Jun 1999

On-Off Intermittency In Stochastically Driven Electrohydrodynamic Convection In Nematics, Thomas John, Ralf Stannarius, Ulrich Behn

Mathematics - All Scholarship

We report on-off intermittency in electroconvection of nematic liquid crystals driven by a dichotomous stochastic electric voltage. With increasing voltage amplitude we observe laminar phases of undistorted director state interrupted by shorter bursts of spatially regular stripes. Near a critical value of the amplitude the distribution of the duration of laminar phases is governed over several decades by a power law with exponent -3/2. The experimental findings agree with simulations of the linearized electrohydrodynamic equations near the sample stability threshold.

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Tilings Which Split A Mirror, Jim Belk Jun 1999

Tilings Which Split A Mirror, Jim Belk

Mathematical Sciences Technical Reports (MSTR)

We consider the mirror of a reflection which consists of its subset of fixed points. We investigate a number of conditions on the tiling that guarantee that the surface splits at a mirror.

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The Weierstrass–Enneper System For Constant Mean Curvature Surfaces And The Completely Integrable Sigma Model, Paul Bracken, A. M. Grundland, L. Martina Jun 1999

The Weierstrass–Enneper System For Constant Mean Curvature Surfaces And The Completely Integrable Sigma Model, Paul Bracken, A. M. Grundland, L. Martina

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The integrability of a system which describes constant mean curvature surfaces by means of the adapted Weierstrass–Enneper inducing formula is studied. This is carried out by using a specific transformation which reduces the initial system to the completely integrable two-dimensional Euclidean nonlinear sigma model. Through the use of the apparatus of differential forms and Cartan theory of systems in involution, it is demonstrated that the general analytic solutions of both systems possess the same degree of freedom. Furthermore, a new linear spectral problem equivalent to the initial Weierstrass–Enneper system is derived via the method of differential constraints. A new procedure …

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The Deconstruction Of Mathematics, David J. Stucki May 1999

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.

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Teaching Linear Algebra And Abstract Algebra With Two Way Video And Audio, Edward Reinke May 1999

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.

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Lewis Carroll: Author, Mathematician, And Christian, David L. Neuhouser May 1999

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.

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Book Review - The Language Of Mathematics: Making The Invisible Visible By Kieth Devlin, Charles R. Hampton May 1999

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

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Book Review: Virtual Gods: The Seduction Of Power And Pleasure In Cyberspace, Jonathan R. Senning May 1999

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.

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Tracking The Trochoid On Safari, Andrew Simoson May 1999

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.

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Revolutions In Mathematics (Book Review), Kevin Vander Meulen May 1999

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.

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A Mathematician At The Science And Theology Book Club, Greg Crow May 1999

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.

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Book Review, David J. Stucki May 1999

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.

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

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

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

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

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

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

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

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

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

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

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

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

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Σary, Moorhead State University, Mathematics Department May 1999

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

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Small Extensions Of Witt Rings, Robert W. Fitzgerald May 1999

Small Extensions Of Witt Rings, Robert W. Fitzgerald

Articles and Preprints

We consider certain Witt ring extensions S of a noetherian Witt ring R obtained by adding one new generator. The conditions on the new generator are those known to hold when R is the Witt ring of a Field F, S is the Witt ring of a Field K and K/F is an odd degree extension. We show that if R is of elementary type then so is S.

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The Decomposition Theorem For Two-Dimensional Shifts Of Finite Type, Aimee S. A. Johnson, K. M. Madden May 1999

The Decomposition Theorem For Two-Dimensional Shifts Of Finite Type, Aimee S. A. Johnson, K. M. Madden

Mathematics & Statistics Faculty Works

A one-dimensional shift of finite type can be described as the collection of bi-infinite "walks" along an edge graph. The Decomposition Theorem states that every conjugacy between two shifts of finite type can be broken down into a finite sequence of splittings and amalgamations of their edge graphs. When dealing with two-dimensional shifts of finite type, the appropriate edge graph description is not as clear; we turn to Nasu's notion of a "textile system" for such a description and show that all two-dimensional shifts of finite type can be so described. We then define textile splittings and amalgamations and prove …

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Connectivity Of Cycle Matroids And Bicircular Matroids, Zhi-Hong Chen, Kuang Ying-Qiang, Hong-Jian Lai May 1999

Connectivity Of Cycle Matroids And Bicircular Matroids, Zhi-Hong Chen, Kuang Ying-Qiang, Hong-Jian Lai

Scholarship and Professional Work - LAS

A unified approach to prove former connectivity results of Tutte, Cunningham, Inukai and Weinberg, Oxley and Wagner.

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Particle Simulation In Contact Mechanics Of A Bouncing Elastic Ball, Donald Greenspan May 1999

Particle Simulation In Contact Mechanics Of A Bouncing Elastic Ball, Donald Greenspan

Mathematics Technical Papers

An elastic ball is simulated by considering lumped mass molecular sets called particles. Particles are allowed to interact only locally in a fashion similar to that employed in molecular mechanics. Under local and gravity forces an n-body problem results when initial data are prescribed. By scaling the forces, the resulting n-body problem is solved numerically using only a scientific personal computer. A variety of examples of bouncing balls are described and discussed.

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