Physical Sciences and Mathematics Commons^™

Problems In Which Given Information Is Ignored, Howard Wachtel

Humanistic Mathematics Network Journal

A set of problems is presented and discussed for which there is a tendency for students to ignore part of the given information in the problem and to substitute some extraneous assumptions. Typical student reactions are also discussed.

Educating The Public About School Mathematics, Zalman Usiskin

Humanistic Mathematics Network Journal

No abstract provided.

Zero, Sheila A. Mcneill

Humanistic Mathematics Network Journal

No abstract provided.

Hamilton's Icosian Calculus And His Icosian Game, Katye O. Sowell

Humanistic Mathematics Network Journal

No abstract provided.

Representation, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

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

Humanistic Mathematics Network Journal

No abstract provided.

Journal Review: Third International Anthology On Paradoxism, Joanne Growney

Humanistic Mathematics Network Journal

No abstract provided.

Students And Their Learning From Reading, Chris Fenwick

Humanistic Mathematics Network Journal

My aim in this article is to summarize work I have done over the last three years, focusing on the issue of helping students learn from whatever mathematics text they read. Although these types of texts generally contain 3 modes of communication, namely technical English, the language of mathematics itself and diagrams, I will focus this article only on the technical English of such texts. The idea, then, that students can develop techniques and strategies for learning from what they read is generally known as “reading to learn.”

Funny Problems, Florentin Smarandache

Humanistic Mathematics Network Journal

No abstract provided.

A Note On The Decimal Numeral System, Shaharir Bin Mohamad Zain

Humanistic Mathematics Network Journal

No abstract provided.

Real Numbers, Math Lives, Arnold L. Trindade

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Constance (A Poem Dedicated To Constance Reid), Arthur T. Benjamin

All HMC Faculty Publications and Research

Mathematical Constance (A Poem Dedicated to Constance Reid)

I think that I shall never see

A constant lovelier than e,

Whose digits are too great too state,

They're 2.71828…

And e has such amazing features

It's loved by all (but mostly teachers).

With all of e's great properties

Most integrals are done with … ease.

Theorems are proved by fools like me

But only Euler could make an e.

I suppose, though, if I had to try

To choose another constant, I

Might offer i or phi or pi.

But none of those would satisfy.

Of all the …

On D0 Brane Polarization By Tidal Forces, Vatche Sahakian

All HMC Faculty Publications and Research

Gravitational tidal forces may induce polarization of D0-branes, in analogy to the same effects arising in the context of constant background gauge fields. Such phenomena can teach us about the correspondence between smooth curved spacetime and its underlying non-commutative structure. However, unlike polarization by gauge fields, the gravitational counterpart involves concerns regarding the classical stability of the corresponding polarized states. In this work, we study this issue with respect to the solutions presented in hepth0010237 and find that they are classically unstable. The instability however appears with intricate features with all but a few decay channels being lifted. Through a …

Large-Scale Synchrony In Weakly Interacting Automata, Eric J. Friedman, Adam S. Landsberg

WM Keck Science Faculty Papers

We study the behavior of two spatially distributed (sandpile) models which are weakly linked with one another. Using a Monte Carlo implementation of the renormalization-group and algebraic methods, we describe how large-scale correlations emerge between the two systems, leading to synchronized behavior.

Proof With Words: 2 + 11 - 1 = 12, Arthur T. Benjamin

All HMC Faculty Publications and Research

Proof with words: 2 + 11 – 1 = 12

TWo ELeVEn

Phase Modulation At 125 Khz In A Michelson Interferometer Using An Inexpensive Piezoelectric Stack Driven At Resonance, Barbara M. Hoeling, Andrew D. Fernandez, Richard C. Haskell, Daniel C. Petersen

All HMC Faculty Publications and Research

Fast phase modulation has been achieved in a Michelson interferometer by attaching a lightweight reference mirror to a piezoelectric stack and driving the stack at a resonance frequency of about 125 kHz. The electrical behavior of the piezo stack and the mechanical properties of the piezo-mirror arrangement are described. A displacement amplitude at resonance of about 350 nm was achieved using a standard function generator. Phase drift in the interferometer and piezo wobble were readily circumvented. This approach to phase modulation is less expensive by a factor of roughly 50 than one based on an electro-optic effect.

Spectral Equivalence Of Bosons And Fermions In One-Dimensional Harmonic Potentials, Michael Crescimanno, Adam S. Landsberg

WM Keck Science Faculty Papers

Recently, Schmidt and Schnack [Physica A 260, 479 (1998)], following earlier references, reiterate that the specific heat of N noninteracting bosons in a one-dimensional harmonic well equals that of N noninteracting fermions in the same potential. We show that this peculiar relationship between heat capacities results from a more dramatic equivalence between Bose and Fermi systems. Namely, we prove that the excitations of such Bose and Fermi systems are spectrally equivalent. Two complementary proofs of this equivalence are provided; one based on a combinatoric argument, the other from analysis of the underlying dynamical symmetry group.

Discrepancy Convergence For The Drunkard's Walk On The Sphere, Francis E. Su

All HMC Faculty Publications and Research

We analyze the drunkard's walk on the unit sphere with step size θ and show that the walk converges in order C/sin²(θ) steps in the discrepancy metric (C a constant). This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.

Particle Size Determination: An Undergraduate Lab In Mie Scattering, I. Weiner '01, M. Rust '01, Thomas D. Donnelly

All HMC Faculty Publications and Research

A technique for determining the size of microscopic spherical particles using light scattering is presented as an undergraduate physics lab. Scatterer size is determined from angular scattering distribution measurements of laser light scattered from a dilute suspension of latex spheres with diameters of 4.99±0.05 and 6.038±0.045 μm. Previous experiments of this type used approximate theoretical corrections and required the construction of specialized sample cells to minimize complicating effects. As a significant improvement to these, we generate angular scattering distributions from Mie theory and, using an accurate numerical procedure, correct these distributions for Snell’s law and foreshortening effects. Scatterer size …

A New Species Of Extinct Oryzomyine Rodent From The Quaternary Of Curaçao, Netherlands Antilles, Donald A. Mcfarlane, Adolphe O. Debrot

WM Keck Science Faculty Papers

An extinct new species of Oryzomyine rodent, known since 1936 from the cave of Grot van Hato on the island of Curaçao, is described from abundant new specimens collected from owl-pellet deposits at three localities on the island.

Proof Without Words: The Pigeonhole Principle, Ran Libeskind-Hadas

All HMC Faculty Publications and Research

This article contains one image and no text.

Multicast Communication In Circuit-Switched Optical Networks, Ran Libeskind-Hadas, Rami Melhem

All HMC Faculty Publications and Research

In this paper we examine the problem of multicast routing in Wavelength-division multiplexed (WDM) optical networks. In particular, we examine wavelength and routing assignment problems in circuit-switched WDM networks. We show that although the routing and wavelength assignment (RWA) problem is NP-complete in general, the wavelength assignment (WA) problem can be solevd in a polynomial time.

Optimal Token Allocations In Solitaire Knock 'M Down, Arthur Benjamin, Matthew T. Fluet, Mark L. Huber

All HMC Faculty Publications and Research

In the game Knock ’m Down, tokens are placed in N bins. At each step of the game, a bin is chosen at random according to a fixed probability distribution. If a token remains in that bin, it is removed. When all the tokens have been removed, the player is done. In the solitaire version of this game, the goal is to minimize the expected number of moves needed to remove all the tokens. Here we present necessary conditions on the number of tokens needed for each bin in an optimal solution, leading to an asymptotic solution. MR Subject Classifications: …

Transient Anomalous Diffusion In Poiseuille Flow, Marco Latini '01, Andrew J. Bernoff

All HMC Faculty Publications and Research

We revisit the classical problem of dispersion of a point discharge of tracer in laminar pipe Poiseuille flow. For a discharge at the centre of the pipe we show that in the limit of small non-dimensional diffusion, D, tracer dispersion can be divided into three regimes. For small times (t [double less-than sign] D^−1/3), diffusion dominates advection yielding a spherically symmetric Gaussian dispersion cloud. At large times (t [dbl greater-than sign] D⁻¹), the flow is in the classical Taylor regime, for which the tracer is homogenized transversely across the pipe and diffuses with …

Enumeration Of Equicolourable Trees, Nicholas Pippenger

All HMC Faculty Publications and Research

A tree, being a connected acyclic graph, can be bicolored in two ways, which differ from each other by exchange of the colors. We shall say that a tree is equicolorable if these bicolorings assign the two colors to equal numbers of vertices. Labelled equicolored trees have been enumerated several times in the literature, and from this result it is easy to enumerate labelled equicolorable trees. The result is that the probability that a randomly chosen n-vertex labelled tree is equicolorable is asymptotically just twice the probability that its vertices would be equicolored if they were assigned colors by …

A Mathematical Tumor Model With Immune Resistance And Drug Therapy: An Optimal Control Approach, Lisette G. De Pillis, Ami E. Radunskaya

All HMC Faculty Publications and Research

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy …

An Open Field, Char Miller

Pomona Faculty Publications and Research

It should have been during a similarly punishing and mercurial moment in late twentieth-century San Antonio, enveloped in a "furious storm of rain, of hail, or of snow," that I initially encountered Richard White's seminal historiographical essay. Such a convergence of art, life, and weather pattern might have defied reality, but it would have made for a fabulous narrative opening. That said, like the norther's rush, his article, which I read shortly after its publication in the August 1985 issue of the Pacific Historical Review, blew me away.

Holography, A Covariant C Function, And The Geometry Of The Renormalization Group, Vatche Sahakian

All HMC Faculty Publications and Research

We propose a covariant geometrical expression for the c function for theories which admit dual gravitational descriptions. We state a c theorem with respect to this quantity and prove it. We apply the expression to a class of geometries, from domain walls in gauged supergravities, to extremal and near extremal Dp-branes, and the AdS Schwarzschild black hole. In all cases, we find agreement with expectations.

The Phases Of 2d Ncos, Vatche Sahakian

All HMC Faculty Publications and Research

We study the phases of the (1+1)-dimensional Non-Commutative Open String theory on a circle. We find that the length scale of non-commutativity increases at strong coupling, the coupling in turn being dressed by a power of D-string charge. The system is stringy at around this length scale, with dynamics involving an interplay between the open and wrapped closed strings sectors. Above this energy scale and at strong coupling, and below it at weak coupling, the system acquires a less stringy character. The near horizon geometry of the configuration exhibits several intriguing features, such as a flip in the dilaton field …

Existence Of Many Positive Nonradial Solutions For A Superlinear Dirichlet Problem On Thin Annuli, Alfonso Castro, Marcel B. Finan

All HMC Faculty Publications and Research

We study the existence of many positive nonradial solutions of a superlinear Dirichlet problem in an annulus in R^N. Our strategy consists of finding the minimizer of the energy functional restricted to the Nehrai manifold of a subspace of functions with symmetries. The minimizer is a global critical point and therefore is a desired solution. Then we show that the minimal energy solutions in different symmetric classes have mutually different energies. The same approach has been used to prove the existence of many sign-changing nonradial solutions (see [5]).