Mathematics | Open Access Articles | Digital Commons Network™

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

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

Mathematics Research Reports

Superconvergence of order O(h^1+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

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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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

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(h^{1+rho) for rho = min(alpha, 1) when the mesh is distorted O(h^{1+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

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

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

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

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

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

Mathematics Research Reports

Some recovery type error estimators for linear finite element method are analyzed under O(h^{1+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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Parameter Identification For Semiconductor Diodes By Lbic Imaging, Weifu Fang, Kazufumi Ito, David A. Redfern

Mathematics and Statistics Faculty Publications

Laser-beam-induced-current (LBIC) imaging is a nondestructive technique used for the characterization of the electrical structure within a semiconductor. In this paper a model is formulated for this technique using the standard drift-diffusion model, and, subsequently, an approximate version and its dual are derived for the study of the inverse problem. The formulation is then applied to a cross-sectional model for n-on-p devices of finite depth to study in detail the relation between the LBIC images and the device parameters. Numerical methods are developed for the simulation of the LBIC image of a diode as well as for the identification of …

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

Humanistic Mathematics Network Journal

No abstract provided.

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

Humanistic Mathematics Network Journal

No abstract provided.

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

Humanistic Mathematics Network Journal

No abstract provided.

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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

Humanistic Mathematics Network Journal

No abstract provided.

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Equation Story, Whitney Perret

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

Humanistic Mathematics Network Journal

No abstract provided.

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Letters And Comments, Issue 26, 2002, Dick Tahta

Humanistic Mathematics Network Journal

No abstract provided.

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Mini-Course On Stochastic Systems With Memory (University Of Campinas), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

This is a mini-course consisting of three talks on the theme : ``Stochastic Systems with Memory", given at the Mathematics Institute, University of Campinas, Campinas, Brazil. My visit to Campinas was fully supported by a grant from FAPESP (of the State of Sao Paulo).

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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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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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Totally Magic Graphs, Geoffrey Exoo, Alan C. H. Ling, John P. Mcsorley, Nicholas C. Phillips, Walter D. Wallis

Articles and Preprints

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge is constant. In this paper we examine graphs possessing a labeling that is simultaneously …

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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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Loopy, George W. Hart

Humanistic Mathematics Network Journal

No abstract provided.

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

Humanistic Mathematics Network Journal

No abstract provided.

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Full-Text Articles in Mathematics

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

All HMC Faculty Publications and Research

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

All HMC Faculty Publications and Research

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

Mathematics Research Reports

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

College of the Pacific Faculty Articles

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

Mathematical Sciences Technical Reports (MSTR)

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

Mathematics Research Reports

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

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

Separable Preference Orders, Jonathan K. Hodge

Dissertations

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

Mathematics Sciences: Faculty Publications

A Restricted Partition Function Modulo 3, Naomi Utgof

Mathematical Sciences Technical Reports (MSTR)

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

Dartmouth Scholarship

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

Mathematics Research Reports

Parameter Identification For Semiconductor Diodes By Lbic Imaging, Weifu Fang, Kazufumi Ito, David A. Redfern

Mathematics and Statistics Faculty Publications

Nearly Balanced And Resolvable Block Designs, Brian Henry Reck

Mathematics & Statistics Theses & Dissertations

From The Editor, Issue 26, 2002, Alvin White

Humanistic Mathematics Network Journal

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

Humanistic Mathematics Network Journal

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

Humanistic Mathematics Network Journal

Portfolio Assessment In Liberal Arts Mathematics, Mike Kenyon

Humanistic Mathematics Network Journal

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

Humanistic Mathematics Network Journal

Equation Story, Whitney Perret

Humanistic Mathematics Network Journal

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

Letters And Comments, Issue 26, 2002, Dick Tahta

Humanistic Mathematics Network Journal

Mini-Course On Stochastic Systems With Memory (University Of Campinas), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

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

Mathematics Faculty Research

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

Humanistic Mathematics Network Journal

Totally Magic Graphs, Geoffrey Exoo, Alan C. H. Ling, John P. Mcsorley, Nicholas C. Phillips, Walter D. Wallis

Articles and Preprints

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

Humanistic Mathematics Network Journal

Loopy, George W. Hart

Humanistic Mathematics Network Journal

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

Humanistic Mathematics Network Journal

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

Humanistic Mathematics Network Journal