Physical Sciences and Mathematics Commons^™

From The Editor, 1996, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Mathematician, Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Monasticism And Mathematics, John F. Loase

Humanistic Mathematics Network Journal

No abstract provided.

Gresham's Law : Algorithm Drives Out Thought, Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Using Mathematics Courses In Support Of Humanities In A Liberal Arts Curriculum, M. S. Jagadish

Humanistic Mathematics Network Journal

No abstract provided.

Ode To Numbers, Pablo Neruda

Humanistic Mathematics Network Journal

No abstract provided.

Humanistic Mathematics And The Internet: The Ugly, The Bad, And The Good, Ruth Guthrie, Judy Guthrie

Humanistic Mathematics Network Journal

No abstract provided.

Mixing Calculus, History, And Writing For Liberal Arts Students, W. M. Priestley

Humanistic Mathematics Network Journal

No abstract provided.

On Mathematics In Poetry, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

Multicultural Mathematical Ideas: A New Course, Bernadette Anne Berken

Humanistic Mathematics Network Journal

No abstract provided.

A Prandial Dialogue On Abstract Algebra As An Introduction To The Discipline Of Mathematics For Liberal Arts Students, Margaret Holen

Humanistic Mathematics Network Journal

No abstract provided.

The Mathematical Quest For The Perfect Letter, Frank J. Swetz

Humanistic Mathematics Network Journal

No abstract provided.

Personal Reflections On Mathematics And Mathematics Education, Lynn E. Garner

Humanistic Mathematics Network Journal

No abstract provided.

Symmetry: A Link Between Mathematics And Life, Catherine A. Gorini

Humanistic Mathematics Network Journal

No abstract provided.

Life Math, Kathy Hayes

Humanistic Mathematics Network Journal

No abstract provided.

Socrates And The Nonslave-Boy, W. M. Priestley

Humanistic Mathematics Network Journal

No abstract provided.

X-Ette, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

Mentalism, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

The Interaction Of Intense Laser Pulses With Atomic Clusters, T. Ditmire, Thomas D. Donnelly, A. M. Rubenchik, R. W. Falcone, M. D. Perry

All HMC Faculty Publications and Research

We examine the interaction of intense, femtosecond laser radiation with the large (50–200 Å) clusters produced in pulsed gas jets. Both experiment and simulation show that the plasmas produced during these interactions exhibit electron temperatures far in excess of that predicted by above-threshold ionization theory for a low-density gas. Efficient heating of the clusters by the laser is followed by rapid expansion of the clusters and long-lived x-ray emission from hot, decaying, underdense plasma.

Oscillatory Doubly Diffusive Convection In A Finite Container, Adam S. Landsberg, Edgar Knobloch

WM Keck Science Faculty Papers

Oscillatory doubly diffusive convection in a large aspect ratio Hele-Shaw cell is considered. The partial differential equations are reduced via center-unstable manifold reduction to the normal form equations describing the interaction of even and odd parity standing waves near onset. These equations take the form of the equations for a Hopf bifurcation with approximate D4 symmetry, verifying the conclusions of the preceding paper [A.S. Landsberg and E. Knobloch, Phys. Rev. E 53, 3579 (1996)]. In particular, the amplitude equations differ in the limit of large aspect ratios from the usual Ginzburg-Landau description in having additional nonlinear terms with O(1) coefficients. …

Oscillatory Bifurcation With Broken Translation Symmetry, Adam S. Landsberg, Edgar Knobloch

WM Keck Science Faculty Papers

The effect of distant endwalls on the bifurcation to traveling waves is considered. Previous approaches have treated the problem by assuming that it is a weak perturbation of the translation invariant problem. When the problem is formulated instead in a finite box of length L and the limit L--> [infinity] is taken, one obtains amplitude equations that differ from the usual Ginzburg-Landau description by the presence of an additional nonlinear term. This formulation leads to a description in terms of the amplitudes of the primary box modes, which are odd and even parity standing waves. For large L, the equations …

High Order Harmonic Generation In Atom Clusters, Thomas D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, R. W. Falcone

All HMC Faculty Publications and Research

We report the generation of short-wavelength, high-order harmonics of intense laser radiation from atom clusters. Clusters containing about 10³ atoms are produced in a high-pressure gas jet. We show them to be a unique nonlinear medium. Compared with monomer gases they yield a higher appearance intensity for a given harmonic order, stronger nonlinear dependence of harmonic signal on laser intensity, higher-order harmonics, and reduced saturation of the harmonic signal at high laser intensity.

Determinants Of The Tournaments, Clifford A. Mccarthy '94, Arthur T. Benjamin

All HMC Faculty Publications and Research

No abstract provided in this article.

Radial Solutions To A Dirichlet Problem Involving Critical Exponents When N=6, Alfonso Castro, Alexandra Kurepa

All HMC Faculty Publications and Research

In this paper we show that, for each λ>0, the set of radially symmetric solutions to the boundary value problem

-Δu(x) = λu(x) + u(x)|u(x)|, x ε B := {x ε R⁶:|x|<1},

u(x) = 0, x ε ∂B

is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

Combinatorics And Campus Security, Arthur T. Benjamin

All HMC Faculty Publications and Research

One day I received electronic mail from our director of campus security [Gilbraith 1993]:

"I have a puzzle for you that has practical applications for me. I need to know how many different combinations there are for our combination locks. A lock has 5 buttons. In setting the combination you can use only 1button or as many as 5. Buttons may be pressed simultaneously and / or successively, but the same button cannot be used more than once in the same combination.

I had a student (obviously not a math major) email me that there are only 120 possibilities, but …

Intraocular Lens Case Designs, Donald S. Remer, Stephen S. Davis, Michael Bak '95, Ken Kalafus, Ilan Sabar, Khannan Suntharam, William Washington, Yu-Tung Wong

All HMC Faculty Publications and Research

IOLAB Corporation makes two types of intraocular lenses for the replacement of cataracts: one from polymethyl methacrylate (PMMA) and a newer one from silicone. IOLAB ships the lens to the doctor in a two-piece case made from polycarbonate. At a price of $0.53 per case, IOLAB spends about $270,000 per year on lens cases (based on 1994 purchases of 500,000 cases). IOLAB asked us to reduce the cost of the existing lens case and to design a new case to protect and fold the silicone lens. We designed three items.

The Steady Boundary Layer Due To A Fast Vortex, Andrew J. Bernoff, Harald J. H. M. Van Dongen, Seth Lichter

All HMC Faculty Publications and Research

A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex c_v is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (c_v→∞) and numerically …

Existence Results For Semipositone Systems, V. Anuradha, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We study existence of positive solutions to the coupled-system of boundary value problems of the form

-Δu(x) = λf(x,u,v); x ∈ Ω

-Δv(x) = λg(x,u,v); x ∈ Ω

u(x) = 0 = v(x); x ∈ ∂Ω

where λ > 0 is a parameter, Ω is a bounded domain in R^N; N ≥ 1 with a smooth boundary ∂Ω and f,g are C^1 function with at least one of f(x_0,0,0) or g(x_0,0,0) being negative for some x_0 ∈ Ω (semipositone). We establish our existence results using the method of sub-super solutions. We also discuss non-existence results for λ small.

Experimental And Theoretical Investigation Of Recombination Pumped X-Ray Lasers Driven By High-Intensity, Short Pulse Lasers, Thomas D. Donnelly, L. Da Silva, R. W. Lee, S. Mrowka, M. Hofer, R. W. Falcone

All HMC Faculty Publications and Research

We have experimentally investigated a recombination-pumped soft-x-ray laser on a Lyman-α transition (135 Å) of hydrogenlike lithium. Furthermore, we have modeled the dynamics of this system, including the effects of the multipeaked electron distribution function that is obtained from the sequential, optical-field ionization of an atom. We compare the predictions of our model and our experimental results.

Modular Spaces And K-Widths, Asuman Güven Aksoy, Grzegorz Lewicki

CMC Faculty Publications and Research

In this paper, we show that the ball measure of noncompactness of a modular space X_p is equal to the limit of its K -widths when p is a left continuous, s-convex modular function, without any ∆₂-condition. We also obtain a similar result for SF-spaces, when the SF-norm N is uniformly continuous.