Mathematics Commons^™

Vessiot: A Maple Package For Varational And Tensor Calculus In Multiple Coordinate Frames, Charles E. Miller

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Maple V package Vessiot is an extensive set of procedures for performing computations in variational and tensor calculus. Vessiot is an extension of a previous package, Helmholtz, which was written by Cinnamon Hillyard for performing operations in the calculus of variations. The original set of commands included standard operators on differential forms, Euler-Lagrange operators, the Lie bracket operator, Lie derivatives, and homotopy operators. These capabilities are preserved in Vessiot, and enhanced so as to function in a multiple coordinate frame context. In addition, a substantial number of general tensor operations have been added to the package. These include standard …

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

Mathematics Technical Papers - Archive

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.

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.

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 …

Construction And Analysis Of A Family Of Numerical Methods For Hyperbolic Conservation Laws With Stiff Source Terms, Cinnamon Hillyard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Numerical schemes for the partial differential equations used to characterize stiffly forced conservation laws are constructed and analyzed. Partial differential equations of this form are found in many physical applications including modeling gas dynamics, fluid flow, and combustion. Many difficulties arise when trying to approximate solutions to stiffly forced conservation laws numerically. Some of these numerical difficulties are investigated.

A new class of numerical schemes is developed to overcome some of these problems. The numerical schemes are constructed using an infinite sequence of conservation laws.

Restrictions are given on the schemes that guarantee they maintain a uniform bound and satisfy …

A Short Proof That ‘Proper = Unit’, Kenneth P. Bogart, Douglas B. West

Dartmouth Scholarship

A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.

Designing An Integrated Environment For Artificial Intelligence, Andrew B. Ritger '99

Honors Projects

The SHELLEY RESEARCH GROUP (part of the Illinois Wesleyan Intelligence Network on Knowledge -IWINK) has been in existence for several years, and has benefited immensely from various student contributors who have added such components as robotic arm control, cross platform networking, an artificially intelligent tic-tac-toe player, and an interactive teaching tool demonstrating the functionality of artificial neural networks. What is lacking, however, amidst these undergraduate contributions to the SHELLEY Project, is an effective means of integrating existing components into a single cohesive functional unit, let alone any easy means of making further contributions within a simple unified context. The focus …

Shout With The Largest Mob : Toward A Model For Primitive Communication In Mobile Automata, Rebecca A. Weber

Honors Theses

We consider the problem of simulating communication between independent, autonomous agents, or machines, using only local rules with no global control over the agents' behavior. First, we construct an algorithm by which the machines will avoid collisions with each other and with boundaries or obstacles. Noting that collision avoidance alone will not result in higher-level behavior, and with the goal of creating agents which would self-organize, we begin to develop a signalling system by which agents can communicate. This leads to a new method for modeling agent motion in the plane. Throughout, we are motivated by possible linkages between our …

An Examination Of Codewords With Optimal Merit Factor, Michael W. Cammarano, Anthony G. Kirilusha

Department of Math & Statistics Technical Report Series

We examine the codewords with best possible merit factor (minimum sum of squares of periodic autocorrelations) for a variety of lengths. Many different approaches were tried in an attempt to find construction methods for such codewords, or for codewords with good but non-optimal merit factors.

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 …}

Automorphic Subsets Of The N-Dimensional Cube Are Translations Of Cwatsets, Matthew Lepinski

Mathematical Sciences Technical Reports (MSTR)

It is known that automorphic subsets are generalizations of cwatsets. In this paper we show that an automorphic subset is the translation of some cwatset, and therefore that each automorphic subset is internally isomorphic to a cwatset.

The Best Way To Knock 'M Down, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

"Knock 'm Down" is a game of dice that is so easy to learn that it is being played in classrooms around the world. Although this game has been effective at developing students' intuition about probability [Fendel et al. 1997; Hunt 1998], we will show that lurking underneath this deceptively simple game are many surprising and highly unintuitive results.

Unevening The Odds Of "Even Up", Arthur T. Benjamin, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

A Numerical Solution Of Low-Energy Neutron Boltzmann Equation, Martha Sue Clowdsley

Mathematics & Statistics Theses & Dissertations

A multigroup method using a straight ahead approximation is created to calculate low energy neutron fluence due to the elastic scattering of evaporation neutrons produced in interactions of high energy particles with target nuclei. This multigroup method is added to NASA Langley Research Center's HZETRN particle transport code. This new code is used to calculate the energy spectra of the neutron fluence in several different materials. The multigroup method is found to be an efficient way of calculating low energy neutron fluence in multiple atom materials as well as single atom materials. Comparisons to results produced by Monte Carlo methods …

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.

Ossa's Theorem And Adams Covers, Robert R. Bruner

Mathematics Faculty Research Publications

We show that Ossa’s theorem splitting ku ∧ BV for elementary abelian groups V follows from general facts about ku ∧ BZ/2 and Adams covers. For completeness, we also provide the analogous results for ko ∧ BV .

The Classroom Encounter, Reuben Hersh

Humanistic Mathematics Network Journal

No abstract provided.

Letter To The New York Times, Arthur B. Powell, Miriam L. Yevick

Humanistic Mathematics Network Journal

No abstract provided.

To My Students, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Cantor’S Coat, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Fiction, Pat Mower

Humanistic Mathematics Network Journal

No abstract provided.

A Day In The Life Of Diophantus (C. 251 A.D.), Rebecca Pekrul

Humanistic Mathematics Network Journal

No abstract provided.

Limericks On The "Century Of Genius", Thomas J. Lipp

Humanistic Mathematics Network Journal

No abstract provided.

Book Announcement: Women, Art And Geometry In Southern Africa, By Paulus Gerdes

Humanistic Mathematics Network Journal

No abstract provided.

The Moral Significance Of Indetectable Effects, Sven Ove Hansson

RISK: Health, Safety & Environment (1990-2002)

A reassessment of Parfit's fifth "mistake in moral mathematics."

Mathematicians Can Be Wrong, Tony Dunlop, Ken Kaminsky

Humanistic Mathematics Network Journal

No abstract provided.

News Extra: Ancient Document Discovered"Could Be The Greatest Of All Time If Validated" Says Professor, Shawn Dolezilek

Humanistic Mathematics Network Journal

No abstract provided.

Book Reviews: Einstein, A Life, By Denis Brian, And The Silver Horse-Shoe, By Javad Tarjemanov, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

"Numbers Man", Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

Spirograph® Math, Karin M. Deck

Humanistic Mathematics Network Journal

No abstract provided.