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Articles 1831 - 1860 of 2640

Full-Text Articles in Physical Sciences and Mathematics

The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp Jan 2003

The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp

All HMC Faculty Publications and Research

We consider the Dirichlet problem Δu + λu + |u|2*−2u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in RN, N≥4, and 2* = 2N/(N−2) is the critical Sobolev exponent. We show that if Ω is invariant under an orthogonal involution then, for λ>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.

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Breakdown Of The Slowly Varying Amplitude Approximation: Generation Of Backward Traveling Second Harmonic Light, J. Z. Sanborn '01, C. Hellings '02, Thomas D. Donnelly Jan 2003

Breakdown Of The Slowly Varying Amplitude Approximation: Generation Of Backward Traveling Second Harmonic Light, J. Z. Sanborn '01, C. Hellings '02, Thomas D. Donnelly

All HMC Faculty Publications and Research

By numerically solving the nonlinear field equations, we simulate second-harmonic generation by laser pulses within a nonlinear medium without making the usual slowly-varying-amplitude approximation, an approximation which may fail when laser pulses of moderate intensity or ultrashort duration are used to drive a nonlinear process. Under these conditions we show that a backward-traveling, second-harmonic wave is created, and that the magnitude of this wave is indicative of the breakdown of the slowly-varying-amplitude approximation. Conditions necessary for experimental detection of this wave are discussed.

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Holography With Ramond-Ramond Fluxes, Vatche Sahakian Jan 2003

Holography With Ramond-Ramond Fluxes, Vatche Sahakian

All HMC Faculty Publications and Research

Starting from the non-linear sigma model of the IIB string in the light-cone gauge, we analyze the role of RR fluxes in Holography. We find that the worldsheet theory of states with only left or right moving modes does not see the presence of RR fields threading a geometry. We use this significant simplification to compute part of the strong coupling spectrum of the two dimensional NCOS theory. We also reproduce the action of a closed string in a PP-wave background using this general formalism; and we argue for various strategies to find new systems where the closed string theory …

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Spaces X In Which All Prime Z-Ideals Of C(X) Are Minimal Or Maximal, Melvin Henriksen, Jorge Martinez, R. G. Woods Jan 2003

Spaces X In Which All Prime Z-Ideals Of C(X) Are Minimal Or Maximal, Melvin Henriksen, Jorge Martinez, R. G. Woods

All HMC Faculty Publications and Research

Quasi P-spaces are defined to be those Tychonoff spaces X such that each prime z-ideal of C(X) is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of P-spaces. The compact quasi P-spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi P-spaces is given. If X is a cozero-complemented space and every nowhere dense zeroset is a z-embedded P-space, then X is a quasi P-space. Conversely, if X is a quasi P-space and …

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Software Requirements Specification Of A University Class Scheduler, Sergiu M. Dascalu, Fredrick C. Harris Jr., Deanna Needell, Jeff A. Stuart, Tamara C. Thiel Jan 2003

Software Requirements Specification Of A University Class Scheduler, Sergiu M. Dascalu, Fredrick C. Harris Jr., Deanna Needell, Jeff A. Stuart, Tamara C. Thiel

CMC Faculty Publications and Research

The University Class Scheduler (UCS) presented in this paper is a novel scheduling tool intended to be used by universities to schedule classes into classrooms. In essence, UCS allows university administrators to enter relevant college and building information, schedule the input classes (courses) into input classrooms, and create web pages that provide detailed schedule information on a semester-by-semester basis. The UCS, which performs the scheduling of classes according to a number of user-selected parameters, can be easily adapted for applications outside the academic realm. This paper presents the main aspects of the University Class Scheduler’s UML-based specification, gives details of …

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On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su Dec 2002

On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su

All HMC Faculty Publications and Research

When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric.

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Two Quick Combinatorial Proofs, Arthur T. Benjamin, Michael E. Orrison Nov 2002

Two Quick Combinatorial Proofs, Arthur T. Benjamin, Michael E. Orrison

All HMC Faculty Publications and Research

Presentation of two simple combinatorial proofs.

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Bidding For Envy-Freeness: A Procedural Approach To N-Player Fair-Division Problems, Claus-Jochen Haake, Matthias G. Raith, Francis E. Su Oct 2002

Bidding For Envy-Freeness: A Procedural Approach To N-Player Fair-Division Problems, Claus-Jochen Haake, Matthias G. Raith, Francis E. Su

All HMC Faculty Publications and Research

We develop a procedure for implementing an efficient and envy-free allocation of m objects among n individuals with the possibility of monetary side-payments, assuming that players have quasi–linear utility functions. The procedure eliminates envy by compensating envious players. It is fully descriptive and says explicitly which compensations should be made, and in what order. Moreover, it is simple enough to be carried out without computer support. We formally characterize the properties of the procedure, show how it establishes envy-freeness with minimal resources, and demonstrate its application to a wide class of fair-division problems.

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A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su Oct 2002

A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su

All HMC Faculty Publications and Research

We prove the following conjecture of Atanassov (Studia Sci. Math. Hungar.32 (1996), 71–74). Let T be a triangulation of a d-dimensional polytope P with n vertices v1, v2,…,vn. Label the vertices of T by 1,2,…,n in such a way that a vertex of T belonging to the interior of a face F of P can only be labelled by j if vj is on F. Then there are at least n−d full dimensional simplices of T, each labelled with d+1 different labels. We …

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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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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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