Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2004

Discipline
Institution
Keyword
Publication
Publication Type
File Type

Articles 181 - 210 of 319

Full-Text Articles in Mathematics

Pokémon® Cards And The Shortest Common Superstring, Mark Stamp, Austin Stamp Jan 2004

Pokémon® Cards And The Shortest Common Superstring, Mark Stamp, Austin Stamp

Faculty Publications, Computer Science

Evidence is presented that certain sequences of Pokémon cards are determined by selecting consecutive elements from a longer sequence. We then consider the problem of recovering the shortest common superstring (SCS), i.e., the shortest string that contains each of the Pokémon card sequences as a consecutive substring. The SCS problem arises in many applications, most notably in DNA sequencing.

Go to article

Various Steiner Systems, Valentin Jean Racataian Jan 2004

Various Steiner Systems, Valentin Jean Racataian

Theses Digitization Project

This project deals with the automorphism group G of a Steiner system S (3, 4, 10). S₁₀, the symmetrical group of degree 10, acts transitively on T, the set of all Steiner systems with parameters 3, 4, 10. The purpose of this project is to study the action of S₁₀ on cosets of G. This will be achieved by means of a graph of S₁₀ on T x T. The orbits of S₁₀ on T x T are in one-one correspondence with the orbits of G, the stabilizer of an S [e] T on T.

Go to article

The Use Of Divergent Series In History, Alina Birca Jan 2004

The Use Of Divergent Series In History, Alina Birca

Theses Digitization Project

In this thesis the author presents a history of non-convergent series which, in the past, played an important role in mathematics. Euler's formula, Stirling's series and Poincare's theory are examined to show the development of asymptotic series, a subdivision of divergent series.

Go to article

The Riemann Zeta Function, Ernesto Oscar Reyes Jan 2004

The Riemann Zeta Function, Ernesto Oscar Reyes

Theses Digitization Project

The Riemann Zeta Function has a deep connection with the distribution of primes. This expository thesis will explain the techniques used in proving the properties of the Rieman Zeta Function, its analytic continuation to the complex plane, and the functional equation that the the Riemann Zeta Function satisfies.

Go to article

Homomorphic Images Of Semi-Direct Products, Lamies Joureus Nazzal Jan 2004

Homomorphic Images Of Semi-Direct Products, Lamies Joureus Nazzal

Theses Digitization Project

The main purpose of this thesis is to describe methods of constructing computer-free proofs of existence of finite groups and give useful techniques to perform double coset enumeration of groups with symmetric presentations over their control groups.

Go to article

Symmetric Representations Of Elements Of Finite Groups, Abeir Mikhail Kasouha Jan 2004

Symmetric Representations Of Elements Of Finite Groups, Abeir Mikhail Kasouha

Theses Digitization Project

This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.

Go to article

Macmahon's Master Theorem And Infinite Dimensional Matrix Inversion, Vivian Lola Wong Jan 2004

Macmahon's Master Theorem And Infinite Dimensional Matrix Inversion, Vivian Lola Wong

Electronic Theses and Dissertations

MacMahon's Master Theorem is an important result in the theory of algebraic combinatorics. It gives a precise connection between coefficients of certain power series defined by linear relations. We give a complete proof of MacMahon's Master Theorem based on MacMahon's original 1960 proof. We also study a specific infinite dimensional matrix inverse due to C. Krattenthaler.

Go to article

Fifth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics Jan 2004

Fifth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Go to article

Curvature And The Shape Of The Universe, Chikako Mese Jan 2004

Curvature And The Shape Of The Universe, Chikako Mese

Undergraduate Mathematics Day: Past Content

We may have an intuitive idea of what it means for surfaces to be curved, but what does it mean for higher dimensional spaces to be curved? In this talk, we will try to quantify curvature on a surface and try to extend this notion to three dimensional spaces. We will show that with an understanding of curvature, we can make sense of a universe which is finite but without boundary.

Go to article

An Algorithm To Recognise Small Seifert Fiber Spaces, J. Hyam Rubinstein Jan 2004

An Algorithm To Recognise Small Seifert Fiber Spaces, J. Hyam Rubinstein

Turkish Journal of Mathematics

The homeomorphism problem is, given two compact n-manifolds, is there an algorithm to decide if the manifolds are homeomorphic or not. The homeomorphism problem has been solved for many important classes of 3-manifolds - especially those with embedded 2-sided incompressible surfaces (cf [12], [15], [16]), which are called Haken manifolds. It is also well-known that the homeomorphism problem is easily solvable for two 3-manifolds which admit geometries in the sense of Thurston [36], [31]. Hence the recognition problem, to decide if a 3-manifold has a geometric structure, is a significant problem. The recognition problem has been solved for all geometric …

Go to article

Radical Submodules And Uniform Dimension Of Modules, Patrick F. Smith Jan 2004

Radical Submodules And Uniform Dimension Of Modules, Patrick F. Smith

Turkish Journal of Mathematics

We investigate the relations between a radical submodule N of a module M being a finite intersection of prime submodules of M and the factor module M/N having finite uniform dimension. It is proved that if N is a radical submodule of a module M over a ring R such that M/N has finite uniform dimension, then N is a finite intersection of prime submodules. The converse is false in general but is true if the ring R is fully left bounded left Goldie and the module M is finitely generated. It is further proved that, in general, if a …

Go to article

The Independence Of Characters On Nonabelian Groups, David E. Grow, Kathryn E. Hare Jan 2004

The Independence Of Characters On Nonabelian Groups, David E. Grow, Kathryn E. Hare

Mathematics and Statistics Faculty Research & Creative Works

We show that there are characters of compact, connected, nonabelian groups that approximate random choices of signs. The work was motivated by Kronecker's theorem on the independence of exponential functions and has applications to thin sets.

Go to article

Neural Networks Satisfying Stone-Weiestrass Theorem And Approximating, Pinal Thakkar Jan 2004

Neural Networks Satisfying Stone-Weiestrass Theorem And Approximating, Pinal Thakkar

Electronic Theses and Dissertations

Neural networks are an attempt to build computer networks called artificial neurons, which imitate the activities of the human brain. Its origin dates back to 1943 when neurophysiologist Warren Me Cello and logician Walter Pits produced the first artificial neuron. Since then there has been tremendous development of neural networks and their applications to pattern and optical character recognition, speech processing, time series prediction, image processing and scattered data approximation. Since it has been shown that neural nets can approximate all but pathological functions, Neil Cotter considered neural network architecture based on Stone-Weierstrass Theorem. Using exponential functions, polynomials, rational functions …

Go to article

Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan Jan 2004

Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan

Articles and Preprints

In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the non-anticipating nature of the SDDE, the use of anticipating calculus methods appears to be novel.

Go to article

A Survey Of Results Involving Transforms And Convolutions In Function Space, David Skough, David Storvick Jan 2004

A Survey Of Results Involving Transforms And Convolutions In Function Space, David Skough, David Storvick

Department of Mathematics: Faculty Publications

In this paper we survey various results involving Fourier-Wiener transforms, Fourier-Feynman transforms, integral transforms and convolution products of functionals over function space that have been established since Cameron and Martin first introduced Fourier-Wiener transforms in 1945.

Go to article

Inspiring Students To Study And Learn Mathematics Using Technology, Ma. Louise Antonette N. De Las Peñas, Wei-Chi Yang Jan 2004

Inspiring Students To Study And Learn Mathematics Using Technology, Ma. Louise Antonette N. De Las Peñas, Wei-Chi Yang

Mathematics Faculty Publications

In this paper, we focus on the advantages of studying mathematics from analytical, graphical and geometric perspectives. Using Casio’s ClassPad 300 ([1]), we present activities on problems involving abstract concepts and real life applications. These activities viewed from the analytical, graphical, tabular and geometric points of view, promote creative ways to facilitate the learning of mathematics that inspire students with varying levels of ability. Consequently, students develop a profound appreciation and a deeper understanding of mathematics.

Go to article

Mathematical Magic, Arthur T. Benjamin Jan 2004

Mathematical Magic, Arthur T. Benjamin

All HMC Faculty Publications and Research

In this paper, we present simple strategies for performing mathematical calculations that appear magical to most audiences. Specifically, we explain how to square large numbers, memorize pi to 100 places and determine the day of the week of any given date.

Go to article

Essential P-Spaces: A Generalization Of Door Spaces, Emad Abu Osba, Melvin Henriksen Jan 2004

Essential P-Spaces: A Generalization Of Door Spaces, Emad Abu Osba, Melvin Henriksen

All HMC Faculty Publications and Research

An element f of a commutative ring A with identity element is called a von Neumann regular element if there is a g in A such that f2g=f. A point p of a (Tychonoff) space X is called a P-point if each f in the ring C(X) of continuous real-valued functions is constant on a neighborhood of p. It is well-known that the ring C(X) is von Neumann regular ring iff each of its elements is a von Neumann regular element; in which case X is called a P-space. If all but at most one point of X …

Go to article

Radon Transforms And The Finite General Linear Groups, Michael E. Orrison Jan 2004

Radon Transforms And The Finite General Linear Groups, Michael E. Orrison

All HMC Faculty Publications and Research

Using a class sum and a collection of related Radon transforms, we present a proof G. James’s Kernel Intersection Theorem for the complex unipotent representations of the finite general linear groups. The approachis analogous to that used by F. Scarabotti for a proof of James’s Kernel Intersection Theorem for the symmetric group. In the process, we also show that a single class sum may be used to distinguish between distinct irreducible unipotent representations.

Go to article

Is Mathematics Education Taking A Step Backward?, Frances Kuwahara Chinn Jan 2004

Is Mathematics Education Taking A Step Backward?, Frances Kuwahara Chinn

Humanistic Mathematics Network Journal

This paper considers the recent history of mathematics teaching.

Go to article

Tesselland: A Mathematical Oddment, Martin Glover Jan 2004

Tesselland: A Mathematical Oddment, Martin Glover

Humanistic Mathematics Network Journal

No abstract provided.

Go to article

Bridging To Infinity, Mike Pinter Jan 2004

Bridging To Infinity, Mike Pinter

Humanistic Mathematics Network Journal

The author's own experiences as a mathematics student and teacher have influenced how he thinks about the infinite. Author Madeleine L'Engle has also shaped his thinking with her writing. The author offers some thoughts that connect some of L'Engle's writing with his experience.

Go to article

Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips Jan 2004

Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips

Humanistic Mathematics Network Journal

No abstract provided.

Go to article

Humanistic Mathematics: Personal Evaluation And Excavations, Stephen I. Brown Jan 2004

Humanistic Mathematics: Personal Evaluation And Excavations, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

Go to article

A Brief Look At Mathematics And Theology, Philip J. Davis Jan 2004

A Brief Look At Mathematics And Theology, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

Go to article

Innumeracy And Its Perils, Numeracy And Its Promises, Ramakrishnan Menon Jan 2004

Innumeracy And Its Perils, Numeracy And Its Promises, Ramakrishnan Menon

Humanistic Mathematics Network Journal

No abstract provided.

Go to article

Book Review: Fermat's Enigma By Simon Singh, Matthew Becker Jan 2004

Book Review: Fermat's Enigma By Simon Singh, Matthew Becker

Humanistic Mathematics Network Journal

No abstract provided.

Go to article

Are You A Quantitative Or Qualitative Runner?: 5.13 Miles And Rosemary-Lilac Shampoo, Shelly Sheats Harkness Jan 2004

Are You A Quantitative Or Qualitative Runner?: 5.13 Miles And Rosemary-Lilac Shampoo, Shelly Sheats Harkness

Humanistic Mathematics Network Journal

No abstract provided.

Go to article

Evaluation Of Multiple Models To Distinguish Closely Related Forms Of Disease Using Dna Microarray Data: An Application To Multiple Myeloma, Johanna S. Hardin, Michael Waddell, C. David Page, Fenghuang Zhan, Bart Barlogie, John Shaughnessy, John J. Crowley Jan 2004

Evaluation Of Multiple Models To Distinguish Closely Related Forms Of Disease Using Dna Microarray Data: An Application To Multiple Myeloma, Johanna S. Hardin, Michael Waddell, C. David Page, Fenghuang Zhan, Bart Barlogie, John Shaughnessy, John J. Crowley

Pomona Faculty Publications and Research

Motivation: Standard laboratory classification of the plasma cell dyscrasia monoclonal gammopathy of undetermined significance (MGUS) and the overt plasma cell neoplasm multiple myeloma (MM) is quite accurate, yet, for the most part, biologically uninformative. Most, if not all, cancers are caused by inherited or acquired genetic mutations that manifest themselves in altered gene expression patterns in the clonally related cancer cells. Microarray technology allows for qualitative and quantitative measurements of the expression levels of thousands of genes simultaneously, and it has now been used both to classify cancers that are morphologically indistinguishable and to predict response to therapy. It is …

Go to article

On The Space Of Oriented Affine Lines In R-3, Brendan Guilfoyle, Wilhelm Klingenberg Jan 2004

On The Space Of Oriented Affine Lines In R-3, Brendan Guilfoyle, Wilhelm Klingenberg

Preprints

We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean R 3 and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in R 3 , as we illustrate with a number of explicit examples

Go to article

First Prev Next Last