Physical Sciences and Mathematics Commons^™

The Popular Image Of Mathematics, Paul Ernest

Humanistic Mathematics Network Journal

No abstract provided.

A Multicultural Matrix For Mathematics Education: Generic Ideas, Rheta N. Rubenstein

Humanistic Mathematics Network Journal

No abstract provided.

Complete Issue 8, 1993

Humanistic Mathematics Network Journal

No abstract provided.

Primary Relaxation Processes At The Band Edge Of Sio₂, Peter N. Saeta, Benjamin I. Greene

All HMC Faculty Publications and Research

The kinetics of photoinduced defect formation in high-purity silicas has been studied by femtosecond transient absorption spectroscopy in the visible and ultraviolet. Band edge two-photon excitation produces singlet excitons which decay in 0.25 ps into defects with the absorption spectra of nonbridging oxygen hole centers (≡Si-O⋅) and silicon E’ centers (≡Si⋅). We identify these defect pairs with the self-trapped triplet exciton and the 0.25 ps decay with the motion of the photoexcited oxygen atom. Similar results were obtained with both crystalline and amorphous silica samples.

Uniqueness And Stability Of Nonnegative Solutions For Semipositone Problems In A Ball, Ismael Ali, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We study the uniqueness and stability of nonnegative solutions for classes of nonlinear elliptic Dirichlet problems on a ball, when the nonlinearity is monotone, negative at the origin, and either concave or convex.

Properties Of Photon Density Waves In Multiple-Scattering Media, Bruce J. Tromberg, Lars O. Svaasand, Tsong-Tseh Tsay, Richard C. Haskell

All HMC Faculty Publications and Research

Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency (ω) and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a highfrequency dispersion regime where density wave phase velocity V_p has a ω dependence and (2) a low-frequency domain where V_p is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (Φ) and modulation (m) response to …

Tissue Characterization And Imaging Using Photon Density Waves, Lars O. Svaasand, Bruce J. Tromberg, Richard C. Haskell, Tsong-Tseh Tsay, Michael W. Berns

All HMC Faculty Publications and Research

The optical properties of brain tissues have been evaluated by measuring the phase velocity and attenuation of harmonically modulated light. The phase velocity for photon density waves at 650-nm wavelength has been found to be in the range of 5 to 12% of the corresponding velocity in a nonscattering medium, and the optical penetration depth was in the range 2.9 to 5.2 mm. These results are used to predict the resolution of optical imaging of deep tissue structures by diffusely propagating incoherent photons. The results indicate that structures of a few millimeters in linear dimension can be identified at 10 …

Optimal Leapfrogging, Joel Auslander, Arthur T. Benjamin, Daniel S. Wilkerson

All HMC Faculty Publications and Research

No abstract provided in this article.

A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Alkali Halide Dimers, Robert P. Dickey '93, David Maurice '91, Robert J. Cave, Richard J. Mawhorter

All HMC Faculty Publications and Research

Results are presented from ab initio calculations on the symmetrical alkali halide dimers made up of Li, Na, K, F, and Cl. We examine the sensitivity of representative monomer and dimer geometries to the variation of the basis set with and without polarization and diffuse functions. The geometries are then compared with available experimental results. We have also calculated vibrational frequencies at the restricted Hartree–Fock level and examined the changes in geometry brought about by correlation using second‐order Møller–Plesset perturbation theory. It is found that Hartree–Fock theory in a modest basis set with diffuse and polarization functions yields results comparable …

Amblyrhiza And The Vertebrate Paleontology Of Anguillean Caves, Donald A. Mcfarlane, Ross D. E. Macphee

WM Keck Science Faculty Papers

Recorded interest in the caves of Anguilla dates back to the second half of the nineteenth century. The earliest explorations were concerned with the locating phosphatic cave earths, and resulted in the mining of several sites. Incidental to this work, the bones of the largest island rodent ever discovered were collected from Aguillan caves. Whereas the phosphate mining operations were short-lived, the remains of the giant rodent Amblyrhiza have catalyzed a continued interest in the caves of Anguilla. The most recent series of explorations have provided the first adequate documentation of Amhlyrhiza fossil sites, and have started to yield radiometric …

Optimal Blackjack Strategy With "Lucky Bucks", Arthur T. Benjamin, Eric Huggins '91

All HMC Faculty Publications and Research

In the casino game blackjack or "21," mathematically determined best plays have been calculated by various mathematicians and gambling experts. These optimal playing strategies all assume that the casino pays even money on bets (excluding when the player has a "blackjack"). However, many casinos offer the player "lucky bucks" that pay the player either 3-to-2 or 2-to-1. In the usual game, the player's expected loss is under 1¢ per dollar bet. in this paper, we derive optimal strategies under luck-buck conditions, giving the player an expected gain of 26¢ or 55¢ per dollar bet.

Light-Scattering Technique For The Study Of Dynamic Thickness Fluctuations In Thin Liquid Films, Richard C. Haskell, Daniel C. Petersen, Mark W. Johnson

All HMC Faculty Publications and Research

The authors describe a light-scattering technique capable of probing the dynamics of thickness fluctuations in lipid bilayers. The technique, which they call reflectance fluctuation spectroscopy (RFS), is keenly sensitive to light scattered from the squeeze modes of motion in a thin liquid film, and insensitive to light scattered from the bend modes. A laser beam is focused to a small spot on the film, and the power in the specularly reflected beam is recorded in real time. Thickness fluctuations associated with the squeeze modes of motion give rise to fluctuations in the power of the specularly reflected light. The frequency …

Light-Scattering Technique For The Study Of Dynamic Thickness Fluctuations In Thin Liquid Films, Richard C. Haskell, Daniel C. Petersen, Mark W. Johnson

All HMC Faculty Publications and Research

The authors describe a light-scattering technique capable of probing the dynamics of thickness fluctuations in lipid bilayers. The technique, which they call reflectance fluctuation spectroscopy (RFS), is keenly sensitive to light scattered from the squeeze modes of motion in a thin liquid film, and insensitive to light scattered from the bend modes. A laser beam is focused to a small spot on the film, and the power in the specularly reflected beam is recorded in real time. Thickness fluctuations associated with the squeeze modes of motion give rise to fluctuations in the power of the specularly reflected light. The frequency …

Topologies And Cotopologies Generated By Sets Of Functions, Alan Dow, Melvin Henriksen, Ralph Kopperman, R. G. Woods

All HMC Faculty Publications and Research

Let L be either [0, 1] or {0, 1} with the usual order. We study topologies on a set X for which the cozero-sets of certain subfamilies H of L^x form a base, and the properties imposed on such topologies by hypothesizing various order-theoretic conditions on H. We thereby obtain useful generalizations of extremely disconnected spaces, basically disconnected spaces, and F-spaces. In particular we use these tools to study the space of minimal prime ideals of certain commutative rings.

A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio

All HMC Faculty Publications and Research

In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL^-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order …

An Elementary Approach To Some Analytic Asymptotics, Nicholas Pippenger

All HMC Faculty Publications and Research

Fredman and Knuth have treated certain recurrences, such as $M(0) = 1$ and\[M(n + 1) = \mathop {\min }\limits_{0 \leqslant k \leqslant n} (\alpha M(k) + \beta M(n - k)),\] where $\min (\alpha ,\beta ) > 1$, by means of auxiliary recurrences such as \[h(x) = \left\{ {\begin{array}{*{20}c} {0\qquad {\text{if}}0 \leqslant x < 1,} \\ {1 + h({x / \alpha }) + h({x / \beta }){\text{ if}}1 \leq x < \infty .} \\ \end{array} } \right.\] The asymptotic behavior of $h(x)$ as $x \to \infty $ with $\alpha $ and $\beta $ fixed depends on whether ${{\log \alpha } / {\log \alpha }}$ is rational or irrational.

The solution of Fredman and Knuth used analytic methods in both cases, and used in particular the Wiener–Ikehara Tauberian theorem in the irrational case. The author shows that a more explicit solution to these recurrences can be obtained by entirely elementary methods, based on a geometric interpretation of $h(x)$ …

What They Didn’T Tell Me About Calculus And The Computer, Melvin Henriksen

All HMC Faculty Publications and Research

My first attempt at using computers as an aid to teaching calculus began in 1966 and culminated with the publication in 1971 of Single Variahle Calculus, written jointly with Milton Lees. Everyone used a mainframe and punched cards and few knew how to program. Computer use was limited to supplementary exercises that could be done today with a hand-held programmable calculator. A constructive sequential approach to limits and elementary numerical analysis were emphasized. The absence of programming displeased computer scientists, but it was too avant garde for all but a tiny minority of teachers of calculus. Attempts by others …

Direct Picosecond Measurement Of Photoinduced Cooper Pair Breaking In Lead, John F. Federici, Benjamin I. Greene, Peter N. Saeta, Douglas R. Dykaar, F. Sharifi, R. C. Dynes

All HMC Faculty Publications and Research

We report on a direct kinetic measurement of Cooper-pair breaking in superconducting lead. A 100-fs pulse of visible light was used to excite a thin-film lead sample, while the Cooper-pair density was optically probed using an ultrashort pulse of broadband far-infrared radiation. Subsequent to the absorption of the visible light, a rapid (ps) change in the far-infrared optical transmission was observed, corresponding to the breaking of Cooper pairs and the collapse of the superconducting gap.

Geometrical Phases And Symmetries In Dissipative Systems, Adam S. Landsberg

WM Keck Science Faculty Papers

A geometrical phase is constructed for dissipative dynamical systems possessing continuous symmetries. It emerges as the natural analog of the holonomy associated with the adiabatic variation of parameters in quantum-mechanical and classical Hamiltonian systems. In continuous media, the physical manifestation of this phase is a spatial shift of a wave pattern, typically a translation or rotation. An illustration associated with pattern formation in fluids is provided.

Another Way Of Counting Nᴺ, Arthur T. Benjamin, Fritz Juhnke

All HMC Faculty Publications and Research

An original combinatorial proof of a combinatorial identity is presented.

Letter To Professor Joanne S. Growney, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

Poems Taken From "An Evening Of Mathematical Poetry"

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics As A Humanistic Discipline, Elena Anne Corie Marchisotto

Humanistic Mathematics Network Journal

No abstract provided.

Writing Humanistic Mathematics, Ruth Hubbard

Humanistic Mathematics Network Journal

No abstract provided.

The Profit Motive: The Bane Of Mathematics Education, Neal Koblitz

Humanistic Mathematics Network Journal

No abstract provided.

Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92

All HMC Faculty Publications and Research

No abstract provided in this article.

From The Editor, Issue 7, 1992, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Three Comments On Ethics, Saunders Maclane

Humanistic Mathematics Network Journal

No abstract provided.

Toward A Definition Of 'Humanistic Mathematics', Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical References In Literature, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.