Physical Sciences and Mathematics Commons^™

Missing Dimensions Of Mathematics Instruction, Walter Meyer

Humanistic Mathematics Network Journal

No abstract provided.

Writing Assignments In An Abstract Algebra Course, Krystina K. Leganza

Humanistic Mathematics Network Journal

No abstract provided.

Poetry, Monte J. Zerger

Humanistic Mathematics Network Journal

No abstract provided.

And This Is The Tale That Xeno Told, Sanda Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

Human Values And Science, Art & Mathematics, Cindy Cichy

Humanistic Mathematics Network Journal

No abstract provided.

Reaction To Human Values, Science, And Mathematics By Lillian R. And Hugh Gray Lieber, Jeanette Nelson

Humanistic Mathematics Network Journal

No abstract provided.

Math Puzzler, Paul J. Tobias

Humanistic Mathematics Network Journal

No abstract provided.

Letters From The Editor And Production Manager, Issue 11, 1995, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

In Memory Of Stavros Busenberg, Mario Martelli, Graeme Wake, Courtney Coleman, Melissa Aczon

Humanistic Mathematics Network Journal

No abstract provided.

Poetry, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

A New Start For College Mathematics; Or Mathematics' Greatest Hits, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

To Stephen W. Hawking, Lillia N. Apostolova

Humanistic Mathematics Network Journal

No abstract provided.

The Study Of Mathematics And Growth In The Spirit, Rosemary Schmalz

Humanistic Mathematics Network Journal

No abstract provided.

Some Notes On How Students Perceive Mathematics, Joan Countryman

Humanistic Mathematics Network Journal

No abstract provided.

What Is Mathematics?: An Answer To Our Liberal Arts Dilemma, Bruce Williamson

Humanistic Mathematics Network Journal

No abstract provided.

Theoretical Study Of Solvent Effects On The Electronic Coupling Element In Rigidly Linked Donor-Acceptor Systems, Robert J. Cave, Marshall D. Newton, Krishna Kumar, Matthew B. Zimmt

All HMC Faculty Publications and Research

The recently developed generalized Mulliken-Hush approach for the calculation of the electronic coupling matrix element for electron-transfer processes is applied to two rigidly linked donor-bridge-acceptor systems having dimethoxyanthracene as the donor and a dicarbomethoxycyclobutene unit as the acceptor. The dependence of the electronic coupling matrix element as a function of bridge type is examined with and without solvent molecules present. For clamp-shaped bridge structures solvent can have a dramatic effect on the electronic coupling matrix element. The behavior with variation of solvent is in good agreement with that observed experimentally for these systems.

Approximation Algorithms: Good Solutions To Hard Problems, Ran Libeskind-Hadas

All HMC Faculty Publications and Research

Consider a computer network represented by an undirected graph where the vertices represent computer nodes and the edges represent links between the nodes. Since some of the links in the network may become faulty, link testing devices are placed at some of the nodes. A tester at a particular node can test all links incident to that node. Since the testers are expensive, however, we wish to deploy the minimum number of these devices such that every link is incidient to at least one node containing a tester. In graph theoretic terms, a vertex cover is a subset of the …

Optical Measurements Of The Core Radius Of High-Δ Fibers With 1-Nm Resolution, Peter N. Saeta

All HMC Faculty Publications and Research

An optical technique for measuring the core radius of high-Δ optical fibers is described. Variations in the core radius of step-index fibers can be measured down to a scale of 1 nm.

Analysis Of A Recurrence Arising From A Construction For Nonblocking Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

Define f on the integers n > 1 by the recurrence f(n) = min( n, min_m|n( 2f(m) + 3f(n/m) ). The function f has f(n) = n as its upper envelope, attained for all prime n.

The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form f(n) ~ C(log n)^{1 + 1/γ} for certain constants γ and C, in the sense that for any ε > 0, the inequality f(n) ≤ (C + ε)(log n)^{1 + 1/γ} holds for infinitely many n, while f(n) ≤ (C + ε)(log …

Analysis Of A Recurrence Arising From A Construction For Non-Blocking Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

Define f on the integers $n > 1$ by the recurrence $f( n ) = \min \{ n,\min _{m|n} 2f( m ) + 3f( n/m ) \}$. The function f has $f( n ) = n$ as its upper envelope, attained for all prime n. The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form $f( n ) \sim C( \log n )^{1 + 1/\gamma } $ for certain constants $\gamma $ and C, in the sense that for any $\varepsilon > 0$, the inequality $f( n ) \leq ( …

Bones Of Puffinus Lherminieri Lesson (Aves: Procellaridae) And Two Other Vertebrates From Cueva Del Agua, Mona Isalnd, Puerto Rico (West Indies), Angel M. Nieves-Rivera, John M. Mylroie, Donald A. Mcfarlane

WM Keck Science Faculty Papers

From a dive in Cueva del Agua, Mona Island, Puerto Rico, twelve un-mineralized bones of Puffinus Lherminieri Lesson, one of Cyclura stejnegeri Stejneger, and one of Moormops blainvilii Leach were collected. The subfossil evidence confirms that P. Lherminieri was a common species on Mona Island. Cyclura stejnegeri and M. blainvilii probably became trapped and died in the pool chamber.

Optimal Klappenspiel, Arthur T. Benjamin, Derek Stanford '93

All HMC Faculty Publications and Research

The game Klappenspiel ("flipping game") is a traditional German game of flipping tiles according to dice rolls. In this paper, we derive the optimal strategy for this game by using dynamic programming. We show that the probability of winning using the optimal strategy is 0.30%.

Femtosecond Laser-Produced Plasma X-Rays From Periodically Modulated Surface Targets, J. C. Gautheir, S. Bastiani, P. Audebert, J. P. Geindre, K. Neuman, Thomas D. Donnelly, M. Hoffer, R. W. Falcone, R. Shepherd, D. Price, B. White

All HMC Faculty Publications and Research

We have studied theoretically and experimentally the x-ray production above 1 keV from femtosecond laser plasmas generated on periodically modulated surface targets. Laser energy coupling to plasma surface waves has been modeled using a numerical differential method. Almost total absorption of incident laser radiation is predicted for optimized interaction conditions. Silicon gratings have been irradiated by a 120fs Ti:sapphire laser at irradiances in excess of 10¹⁶ W/cm². X-ray intensities above 1.5 keV (K-shell lines) have been measured as a function of the incidence angle. Results show a distinct x-ray emission maximum for the first order diffraction …

Portable, High-Bandwidth Frequency-Domain Photon Migration Instrument For Tissue Spectroscopy, Steen J. Madsen, Eric R. Anderson, Richard C. Haskell, Bruce J. Tromberg

All HMC Faculty Publications and Research

We describe a novel frequency-domain photon migration instrument employing direct diode laser modulation and avalanche photodiode detection, which is capable of noninvasively determinating the optical properties of biological tissues in near real time. An infinite medium diffusion model was used to extract absorption and transport scattering coefficients from 300-kHz to 800-MHz photon-density wave phase data. Optical properties measured in tissue-simulating solutions at 670 nm agreed to within 10% of those expected.

Rapid Relaxation Of An Axisymmetric Vortex, Andrew J. Bernoff, Joseph F. Lingevitch

All HMC Faculty Publications and Research

In this paper it is argued that a two‐dimensional axisymmetric large Reynolds number (Re) monopole when perturbed will return to an axisymmetric state on a time scale (Re^1/3) that is much faster than the viscous evolution time scale (Re). It is shown that an arbitrary perturbation can be broken into three pieces; first, an axisymmetric piece corresponding to a slight radial redistribution of vorticity; second, a translational piece which corresponds to a small displacement of the center of the original vortex; and finally, a nonaxisymmetric perturbation which decays on the Re^1/3 time scale due to a shear/diffusion …

Multiple Solutions For A Semilinear Dirichlet Problem, Alfonso Castro, Jorge Cossio

All HMC Faculty Publications and Research

The authors prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Extensive use is made of Lyapunov–Schmidt reduction arguments, the mountain pass lemma, and characterizations of the local degree of critical points.

Multiple Solutions For A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio

All HMC Faculty Publications and Research

The authors prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Extensive use is made of Lyapunov-Schmidt reduction arguments, the mountain pass lemma, and characterizations of the local degree of critical points.

Boundary Conditions For The Diffusion Equation In Radiative Transfer, Richard C. Haskell, Lars O. Svaasand, Tsong-Tseh Tsay, Ti-Chen Feng, Matthew S. Mcadams, Bruce J. Tromberg

All HMC Faculty Publications and Research

Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for …

Low-Frequency Line Shapes In Guided Acoustic-Wave Brillouin Scattering, Benjamin I. Greene, Peter N. Saeta

All HMC Faculty Publications and Research

Guided acoustic‐wave Brillouin scattering (GAWBS) measurements were performed on 20‐cm lengths of optical fibers with particular attention focused on the lowest lying resonance. In 125‐μm‐diam silica fibers, this resonance was observed to occur at ~22 MHz and have a line shape which varied erratically from sample to sample. Significant line shape fluctuations were evident even between sequential samples from the same fiber spool. We speculate that the observed effects are attributable to 0.01-0.1 μm distributed geometric deviations from a perfect cylinder.

Lattice-Ordered Algebras That Are Subdirect Products Of Valuation Domains, Melvin Henriksen, Suzanne Larson, Jorge Martinez, R. G. Woods

All HMC Faculty Publications and Research

An f-ring (i.e., a lattice-ordered ring that is a subdirect product of totally ordered rings) A is called an SV-ring if A/P is a valuation domain for every prime ideal P of A. If M is a maximal ℓ-ideal of A , then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal ℓ-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A …