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2002

Mathematics

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Articles 31 - 60 of 264

Full-Text Articles in Physical Sciences and Mathematics

A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga Sep 2002

A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga

Mathematics Research Reports

Superconvergence of order O(h1+rho), for some rho is greater than 0, is established for gradients recovered using Polynomial Preserving Recovery technique when the mesh is mildly structured. Consequently this technique can be used in building a posteriori error estimator that is asymptotically exact.

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Using Composition Techniques To Improve Classroom Instruction And Students’ Understanding Of Proof, Christopher D. Goff Sep 2002

Using Composition Techniques To Improve Classroom Instruction And Students’ Understanding Of Proof, Christopher D. Goff

College of the Pacific Faculty Articles

This paper describes an effort to incorporate standard composition exercises into a sophomore-level discrete mathematics class. It provides an example of how peer review can be integrated with a mathematical curriculum through the writing of proofs.

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Writing Mathematics-A Nut And A Bolt Of Style, Frank A. Farris Sep 2002

Writing Mathematics-A Nut And A Bolt Of Style, Frank A. Farris

Mathematics and Computer Science

As editor of Mathematics Magazine, I see a lot of manuscripts. Some of them are written with a charming sense of style, but many of them leave me thinking that the author's only concern was to set out the mathematics clearly. This is a fine place to start, but the tradition of the Magazine is to offer things that people will enjoy reading, and this requires more than clarity. Let me explain an important step authors can take in order to make their work more attractive.

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Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty Sep 2002

Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty

Mathematics and Statistics Faculty Publications

Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic to the plane, projective plane, or torus. We will also state and prove old and new results of the type that the dual matroid of G is the matroid of the topological dual G*.

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The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt Sep 2002

The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt

All HMC Faculty Publications and Research

We determine precise existence and multiplicity results for radial solutions of the Liouville–Bratu–Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.

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Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman Sep 2002

Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman

All HMC Faculty Publications and Research

We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.

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Infinitely Many Nonradial Solutions To A Superlinear Dirichlet Problem, Hugo Aduén, Alfonso Castro Sep 2002

Infinitely Many Nonradial Solutions To A Superlinear Dirichlet Problem, Hugo Aduén, Alfonso Castro

All HMC Faculty Publications and Research

In this article we provide sufficient conditions for a superlinear Dirichlet problem to have infinitely many nonradial solutions. Our hypotheses do not require the nonlinearity to be an odd function. For the sake of simplicity in the calculations we carry out details of proofs in a ball. However, the proofs go through for any annulus.

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The Fourier Transform And Some Applications, Christopher Zion Sep 2002

The Fourier Transform And Some Applications, Christopher Zion

Masters Theses & Specialist Projects

none

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Tilings Of Low-Genus Surfaces By Quadrilaterals, John Gregoire, Isabel Averil Aug 2002

Tilings Of Low-Genus Surfaces By Quadrilaterals, John Gregoire, Isabel Averil

Mathematical Sciences Technical Reports (MSTR)

In contribution to the classification of all tilings of low-genus surfaces, the kaleidoscopic and non-kaleidoscopic tilings by quadrilaterals are given up to genus 12. As part of their classification, the algebraic structure of the conformal tiling groups and the geometric structure of the tiles are specified. In addition, several infinite classes of tilings and tiling groups are presented.

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Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang Aug 2002

Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang

Mathematics Research Reports

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under general quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h1+rho) for rho = min(alpha, 1) when the mesh is distorted O(h1+alpha) (alpha > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

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Optimal Path Planning And The Fast Marching Method, J. J. Clark Aug 2002

Optimal Path Planning And The Fast Marching Method, J. J. Clark

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The problem of determining an optimal path for an object moving through some obstacle space presents several nontrivial subproblems. The foremost being the computational complexity that is involved and how to best deal with the associated large data volume. For example, a non-symmetric object moving in three dimensions possesses six degrees of freedom. This can lead to a computational grid that may easily be on the order of 1012. Furthermore, for every point in the computational domain, several complex calculations must be performed. These include performing tests to determine if the object and obstacles intersect, and numerically solving …

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Separable Preference Orders, Jonathan K. Hodge Aug 2002

Separable Preference Orders, Jonathan K. Hodge

Dissertations

Whenever a decision-maker must express simultaneously his or her preferences on several possibly related issues, the existence of interdependence among these preferences can lead to collective decisions that are unsatisfactory or even paradoxical. Intuitively, an individual’s preferences are said to be separable on a subset of issues if they do not depend on the choice of alternatives for issues outside the subset. Here we explore from a mathematical standpoint the properties of separable and nonseparable preference orders. We begin by formulating a general model of multidimensional preferences and we formally introduce the notions of separability and noninfluentiality. We study the …

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On The Quantum Moduli Space Of M-Theory Compactifications, Tamar Friedmann Jul 2002

On The Quantum Moduli Space Of M-Theory Compactifications, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We study the moduli space of M-theories compactified on G2 manifolds which are asymptotic to a cone over quotients of S3 × S3. We show that the moduli space is composed of several components, each of which interpolates smoothly among various classical limits corresponding to low energy gauge theories with a given number of massless U (1) factors. Each component smoothly interpolates among supersymmetric gauge theories with different gauge groups.

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Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys Jul 2002

Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys

Mathematics and Statistics Department Faculty Publication Series

In this note we study simple modules for a reduced enveloping algebra Ux (g) in the critical case when X E 2 g^x is “nilpotent”. Some dimension formulas computed by Jantzen suggest modified versions of Weyl’s dimension formula, based on certain reflecting hyperplanes for the affine Weyl group which might be associated to Kazhdan–Lusztig cells.

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A Restricted Partition Function Modulo 3, Naomi Utgof Jul 2002

A Restricted Partition Function Modulo 3, Naomi Utgof

Mathematical Sciences Technical Reports (MSTR)

The ordinary partition function p(n) counts the number of representations of a positive integer n as the sum of positive integers. We denote by p3(n) the number of partitions of n with no parts divisible by 3: We demonstrate congruence relations for arithmetic sequences qn+(2q2-2)/24 where q is a prime other than 3 congruent to 3 (mod 4): We also prove a result when q = 5 and make a conjecture about a generalization .

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Central Twisted Transformation Groups And Group C*-Algebras Of Central Group Extensions, Siegfried Echterhoff, Dana P. Williams Jul 2002

Central Twisted Transformation Groups And Group C*-Algebras Of Central Group Extensions, Siegfried Echterhoff, Dana P. Williams

Dartmouth Scholarship

We examine the structure of central twisted transformation group C∗-algebras C0(X) ⋊id,u G, and apply our results to the group C ∗-algebras of central group extensions. Our methods require that we study Moore’s cohomology group H2 (G, C(X,T)), and, in particular, we prove an inflation result for pointwise trivial cocyles which may be of use elsewhere.

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Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang Jul 2002

Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang

Mathematics Research Reports

Some recovery type error estimators for linear finite element method are analyzed under O(h1+alpha) (alpha greater than 0) regular grids. Superconvergence is established for recovered gradients by three different methods when solving general non-self-adjoint second-order elliptic equations. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.

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Nearly Balanced And Resolvable Block Designs, Brian Henry Reck Jul 2002

Nearly Balanced And Resolvable Block Designs, Brian Henry Reck

Mathematics & Statistics Theses & Dissertations

One of the fundamental principles of experimental design is the separation of heterogeneous experimental units into subsets of more homogeneous units or blocks in order to isolate identifiable, unwanted, but unavoidable, variation in measurements made from the units. Given v treatments to compare, and having available b blocks of k experimental units each, the thoughtful statistician asks, “What is the optimal allocation of the treatments to the units?” This is the basic block design problem. Let nij be the number of times treatment i is used in block j and let N be the v x b matrix N …

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On The Minimum Ropelength Of Knots And Links, Jason Cantarella, Robert B. Kusner, John M. Sullivan Jun 2002

On The Minimum Ropelength Of Knots And Links, Jason Cantarella, Robert B. Kusner, John M. Sullivan

Robert Kusner

The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are C 1,1 curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.

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Computational Geometry Column 43, Joseph O'Rourke Jun 2002

Computational Geometry Column 43, Joseph O'Rourke

Computer Science: Faculty Publications

The concept of pointed pseudo-triangulations is defined and a few of its applications described.

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Global Stability Of Cycles: Lotka-Volterra Competition Model With Stocking, Saber Elaydi, Abdul-Aziz Yakubu Jun 2002

Global Stability Of Cycles: Lotka-Volterra Competition Model With Stocking, Saber Elaydi, Abdul-Aziz Yakubu

Mathematics Faculty Research

In this article, we prove that in connected metric spaces k - cycles are not globally attracting (where k>2). We apply this result to a two species discrete-time Lotka-Volterra competion model with stocking. In particular, we show that an k-cycle cannot be the ultimate life-history of evolution of all population sizes. This solves Yakubu's conjecture but the question on the structure of the boundary of the basins of attraction of the locally stable n-cycles is still open.

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From The Editor, Issue 26, 2002, Alvin White Jun 2002

From The Editor, Issue 26, 2002, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

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History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego Jun 2002

History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego

Humanistic Mathematics Network Journal

The main goal of this essay is to discuss, informally, an intuitive approach to the history of mathematics as an academic discipline. The initial point of departure includes the analysis of some traditional definitions of the concept of 'history' taken from standard dictionaries. This concise dissection attempts to suggest the complexity of the discipline.

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Comments On Zal Usiskin's Article In The Humanistic Mathematics Network Journal For May, 2001, Robert Stein Jun 2002

Comments On Zal Usiskin's Article In The Humanistic Mathematics Network Journal For May, 2001, Robert Stein

Humanistic Mathematics Network Journal

No abstract provided.

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Humanizing Mathematics: The Humanistic Impression In The Course For Mathematics Teaching, Ada Katsap Jun 2002

Humanizing Mathematics: The Humanistic Impression In The Course For Mathematics Teaching, Ada Katsap

Humanistic Mathematics Network Journal

No abstract provided.

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Loopy, George W. Hart Jun 2002

Loopy, George W. Hart

Humanistic Mathematics Network Journal

No abstract provided.

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A Brief Look At Mathematics And Theology, Philip J. Davis Jun 2002

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

Humanistic Mathematics Network Journal

No abstract provided.

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Pat's Prologues: Introductions To The First Two Airings Of Math Medley, A Radio Talk Show, Patricia Clark Kenschaft Jun 2002

Pat's Prologues: Introductions To The First Two Airings Of Math Medley, A Radio Talk Show, Patricia Clark Kenschaft

Humanistic Mathematics Network Journal

No abstract provided.

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Notes On Formal Constructivism, D. Joyner, P. Lejarraga Jun 2002

Notes On Formal Constructivism, D. Joyner, P. Lejarraga

Humanistic Mathematics Network Journal

Our aim is to sketch some ideas related to how we (as in, we two) think we (as in, we humans) think. "That theory is useless. It isn't even wrong." - Wolfgang Pauli. Our hope in this paper is to provide a theory, admittedly somewhat vague, of how we think about mathematics. We also hope our ideas do not cause the reader to be reminded of Pauli's quote above. These notes were motivated by the interesting book by Changeaux and Connes.

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Calculus, Sarah Glaz Jun 2002

Calculus, Sarah Glaz

Humanistic Mathematics Network Journal

No abstract provided.

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