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Articles 22531 - 22560 of 27436

Full-Text Articles in Physical Sciences and Mathematics

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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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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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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Aphorisms, Lee Goldstein Jun 2002

Aphorisms, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: My Dance Is Mathematics By Joanne Growney, Sally Lipsey Jun 2002

Book Review: My Dance Is Mathematics By Joanne Growney, Sally Lipsey

Humanistic Mathematics Network Journal

No abstract provided.

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When Is A Math Problem Really "Real"?, Michael E. Goldberg Jun 2002

When Is A Math Problem Really "Real"?, Michael E. Goldberg

Humanistic Mathematics Network Journal

No abstract provided.

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"Magic In A Box", Lacie Juris Jun 2002

"Magic In A Box", Lacie Juris

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: The Teaching Gap By James W. Stigler And James Hiebert, Michael L. Brown Jun 2002

Book Review: The Teaching Gap By James W. Stigler And James Hiebert, Michael L. Brown

Humanistic Mathematics Network Journal

No abstract provided.

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Portfolio Assessment In Liberal Arts Mathematics, Mike Kenyon Jun 2002

Portfolio Assessment In Liberal Arts Mathematics, Mike Kenyon

Humanistic Mathematics Network Journal

This paper describes my efforts to incorporate problem-solving portfolios into my liberal arts mathematics course. I begin with a description of the components of the portfolios and the factors I consider in evaluating them. I then address some of the more significant obstacles I have encountered as well as what I consider to be among the major benefits. A selection from one student’s portfolio is appended.

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Marcy's Dots: A Problem On National Test Revisited, Patricia Baggett, Andrzej Ehrenfeucht Jun 2002

Marcy's Dots: A Problem On National Test Revisited, Patricia Baggett, Andrzej Ehrenfeucht

Humanistic Mathematics Network Journal

No abstract provided.

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Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis Jun 2002

Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis

Humanistic Mathematics Network Journal

This paper describes a divisibility rule for any prime number as an engaging problem-solving activity for preservice secondary school mathematics teachers.

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Equation Story, Whitney Perret Jun 2002

Equation Story, Whitney Perret

Humanistic Mathematics Network Journal

No abstract provided.

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Special Section: On The Publication Of The 26th Issue Of The Humanistic Mathematics Network Journal, Sandra Z. Keith Jun 2002

Special Section: On The Publication Of The 26th Issue Of The Humanistic Mathematics Network Journal, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

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Does A Mathematical/Scientific Worldview Lead To A Clearer Or More Distorted View Of Reality?: Purposive Musings Inspired From Readings In The Urantia Book, The Cosmic Family, Volume I, And Elsewhere, Jeru Jun 2002

Does A Mathematical/Scientific Worldview Lead To A Clearer Or More Distorted View Of Reality?: Purposive Musings Inspired From Readings In The Urantia Book, The Cosmic Family, Volume I, And Elsewhere, Jeru

Humanistic Mathematics Network Journal

No abstract provided.

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Teaching As Though Students Mattered: A Biography Of Alvin White As Told To Sandra Keith, Alvin White, Sandra Z. Keith Jun 2002

Teaching As Though Students Mattered: A Biography Of Alvin White As Told To Sandra Keith, Alvin White, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

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