Mathematics Commons^™

The Story Of A Service-Learning Project: Mathematics In The Park, Joyce O'Halloran

Humanistic Mathematics Network Journal

No abstract provided.

Training Elementary Teachers For The New Millennium, Dixie Metheny, David Davison

Humanistic Mathematics Network Journal

No abstract provided.

True Prime, Pat Mower

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Knowing And Teaching Elementary Mathematics By Liping Ma, Roger Howe

Humanistic Mathematics Network Journal

No abstract provided.

Senior Seminar: A Capstone Course In The Computer And Mathematical Sciences, Ken Oberhoff, Ron Barnes

Humanistic Mathematics Network Journal

This paper describes the evolution of a course developed to tie together many strands of activity encountered by students in the computer and mathematical sciences (CMS). The senior level course is required of all majors in our computer science, applied mathematics and statistics undergraduate degree programs. One of the primary purposes of the course is to refine writing and presentation skills needed for those who will later pursue individual research projects. Writing projects are organized around the theme of “Ethical Decision Making in the Computer and Mathematical Sciences”. Numerous case studies are investigated. Additional topics in the course include designing …

Weizmann Day’S “Math Night” Brings Parents To Their Knees

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Geometry From Africa: Mathematical And Educational Explorations By Paulus Gerdes, Claudia Zaslavsky

Humanistic Mathematics Network Journal

No abstract provided.

A Nonlinear Parabolic Equation Modelling Surfactant Diffusion, Xinfu Chen, Chaocheng Huang, Jennifer Zhao

Mathematics and Statistics Faculty Publications

An initial-boundary value problem for nonlinear parabolic equations modelling surfactant diffusions is investigated. The boundary conditions are of nonlinear adsorptive types, and the initial value has a single point jump. We study the well-posedness of the problem, the convergence of a numerical scheme, and the regularity as well as quantitative behaviour of solutions.

Torsion-Free Modules Over Reduced Witt Rings, Robert W. Fitzgerald

Articles and Preprints

We compute the genus class group of a torsion-free module over a reduced Witt ring of finite stability index. This is applied to modules locally isomorphic to odd degree extensions of formally real fields.

On Some Self-Organizing Models And Their Applications., Amitava Dutta Dr.

Doctoral Theses

Abstract: Self-organizing neural network models constitute the main theme of this thesis. Some well-known self-organizing models are surveyed and their properties are discussed. The application areas on which the thesis focuses are briefly described.This thesis deals with Artificial Neural Network models, in particular, Self- organizing (unsupervisnd) models. We develop here a few self-organizing neural net- work models to solve certain problems which are well studied in the areas of Image Processing and Computationel Geometry and have wide applications in shape eztrac- tion and optimization.1.1 Artificial neural networkThe study of Biological Neural Networks originally comes under biological sciences. They deal with …

Bounded Point Evaluations And Local Spectral Theory, Abdellatif Bourhim

Mathematics - All Scholarship

We study in this paper the concept of bounded point evaluations for cyclic operators. We give a negative answer to a question of L.R. Williams Dynamic Systems and Apllications 3(1994) 103-112. Furthermore, we generalize some results of Williams and give a simple proof of theorem 2.5 of L.R. Williams (The Local Spectra of Pure Quasinormal Operators J. Math. anal. Appl. 187(1994) 842-850) that non normal hyponormal weighted shifts have fat local spectra.

Biological Implications Of A Discrete Mathematical Model For Collagen Deposition And Alignment In Dermal Wound Repair, J. C. Dallon, J. A. Sherratt, P. K. Maini, M. W. Ferguson

Faculty Publications

We develop a novel mathematical model for collagen deposition and alignment during dermal wound healing. We focus on the interactions between fibroblasts, modelled as discrete entities, and a continuous extracellular matrix composed of collagen and a fibrin based blood clot. There are four basic interactions assumed in the model: fibroblasts orient the collagen matrix, fibroblasts produce and degrade collagen and fibrin and the matrix directs the fibroblasts and determines the speed of the cells. Several factors which influence the alignment of collagen are examined and related to current anti-scarring therapies using transforming growth factor " The most influential of these …

Optimal Token Allocations In Solitaire Knock'm Down, Arthur T. Benjamin, Mark L. Huber, Matthew T. Fluet '99

All HMC Faculty Publications and Research

In the game Knock 'm Down, tokens are placed in N bins. At each step of the game, a bin is chosen at random according to a fixed probability distribution. If a token remains in that bin, it is removed. When all the tokens have been removed, the player is done. In the solitaire version of this game, the goal is to minimize the expected number of moves needed to remove all the tokens. Here we present necessary conditions on the number of tokens needed for each bin in an optimal solution, leading to an asymptotic solution.

An Approximation To Miscible Fluid Flows In Porous Media With Point Sources And Sinks By An Eulerian-Lagrangian Localized Adjoint Method And Mixed Finite Element Methods, Hong Wang, Liang Dong, Richard E. Ewing, Stephen L. Lyons, Guan Qin

Faculty Publications

We develop an Eulerian–Lagrangian localized adjoint method (ELLAM)-mixed finite element method (MFEM) solution technique for accurate numerical simulation of coupled systems of partial differential equations (PDEs), which describe complex fluid flow processes in porous media. An ELLAM, which was shown previously to outperform many widely used methods in the context of linear convection-diffusion PDEs, is presented to solve the transport equation for concentration. Since accurate fluid velocities are crucial in numerical simulations, an MFEM is used to solve the pressure equation for the pressure and Darcy velocity. This minimizes the numerical difficulties occurring in standard methods for approximating velocities caused …

Computational Geometry Column 39, Joseph O'Rourke

Computer Science: Faculty Publications

The resolution of a decades-old open problem is described: polygonal chains cannot lock in the plane.

Oslo Summer Workshop On Stochastic Analysis, Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

Examples, Counterexamples, And Enumeration Results For Foldings And Unfoldings Between Polygons And Polytopes, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Joseph O'Rourke

Computer Science: Faculty Publications

We investigate how to make the surface of a convex polyhedron (a polytope) by folding up a polygon and gluing its perimeter shut, and the reverse process of cutting open a polytope and unfolding it to a polygon. We explore basic enumeration questions in both directions: Given a polygon, how many foldings are there? Given a polytope, how many unfoldings are there to simple polygons? Throughout we give special attention to convex polygons, and to regular polygons. We show that every convex polygon folds to an infinite number of distinct polytopes, but that their number of combinatorially distinct gluings is …

Modelling The Dynamics Of Abyssal Equator-Crossing Currents, P. F. Choboter, G. E. Swaters

Mathematics

No abstract provided.

A Comparative Analysis Of Japanese And U.S. Teaching Styles Of Mathematics, Timothy Michael Wurdock

Mathematics Graduate Theses

This study examines the effects of different international teaching styles on the performance of junior high school students. Japanese students ranked higher than U.S. students on international tests. The whole-class method and open-ended problems are techniques frequently used in Japanese classrooms. These techniques will be incorporated into the author’s curriculum to determine their effectiveness in teaching mathematics. Two eighth grade classes will be studied. The author will teach the experimental group using the whole-class method. The control group will be taught using the American method.

Stochastic Systems With Memory: Theory, Examples And Applications (Postgraduate Seminar, University Of Central Venezuela), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

An Efficient Method For Band Structure Calculations In 3d Photonic Crystals, David C. Dobson, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

A method for computing band structures for three-dimensional photonic crystals is described. The method combines a mixed finite element discretization on a uniform grid with a fast Fourier transform preconditioner and a preconditioned subspace iteration algorithm. Numerical examples illustrating the behavior of the method are presented.

The Structure Of Free Semigroup Algebras, Kenneth R. Davidson, Elias Katsoulis, David R. Pitts

Department of Mathematics: Faculty Publications

A free semigroup algebra is WOT-closed algebra generated by an n-tuple of isometries with pairwise orthogonal ranges. The interest in these algebras arises primarily from two of their interesting features. The first is that they provide useful information about unitary invariants of representations of the Cuntz-Toeplitz algebras. The second is that they form a class of nonself-adjoint operator algebras which are of interest in their own right. This class contains a distinguished representative, the "non-commutative Toeplitz algebra", which is generated by the left regular representation of the free semigroup on n letters and denoted . This paper provides a general …

Restricted Words By Adjacencies, Don Rawlings

Mathematics

A recurrence, a determinant formula, and generating functions are presented for enumerating words with restricted letters by adjacencies. The main theorem leads to refinements (with up to two additional parameters) of known results on compositions, polyominoes, and permutations. Among the examples considered are (1) the introduction of the ascent variation on compositions, (2) the enumeration of directed vertically convex polyominoes by upper descents, area, perimeter, relative height, and column number, (3) a tri-variate extension of MacMahon's determinant formula for permutations with prescribed descent set, and (4) a combinatorial setting for an entire sequence of bibasic Bessel functions.

The Possibility Of Impossible Pyramids, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes

Mathematics and Statistics Faculty Research & Creative Works

For continua X and Y it is shown that if the projection f : X x Y ->X has its induced mapping C(f) open, then X is C*-smooth. As a corollary, a characterization of dendrites in these terms is obtained.

The Poisson Variation Of Montmort's Matching Problem, Don Rawlings

Mathematics

No abstract provided.

Phased Tilings And Generalized Fibonacci Identities, Arthur T. Benjamin, Jennifer J. Quinn, Francis E. Su

All HMC Faculty Publications and Research

Fibonacci numbers arise in the solution of many combinatorial problems. They count the number of binary sequences with no consecutive zeros, the number of sequences of 1's and 2's which sum to a given number, and the number of independent sets of a path graph. Similar interpretations exist for Lucas numbers. Using these interpretations, it is possible to provide combinatorial proofs that shed light on many interesting Fibonacci and Lucas identities (see [1], [3]). In this paper we extend the combinatorial approach to understand relationships among generalized Fibonacci numbers.

Given G₀ and G₁ a generalized Fibonacci sequence G …

Euclidean Weights Of Codes From Elliptic Curves Over Rings, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

We 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 certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.

A code is a subset of Aⁿ, where A is a finite set (called the alphabet). Usually A is just the field of two elements and, in this case, one speaks of binary codes. Such codes are used in applications where one transmits information through noisy channels. By building redundancy into the code, transmitted …

Random Approaches To Fibonacci Identities, Arthur T. Benjamin, Gregory M. Levin, Karl Mahlburg '01, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

Some Applications Of The Ultrapower Theorem To The Theory Of Compacta, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques.