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Physical Sciences and Mathematics Commons™

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1994

Claremont Colleges

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Articles 1 - 30 of 43

Full-Text Articles in Physical Sciences and Mathematics

Portable, High-Bandwidth Frequency-Domain Photon Migration Instrument For Tissue Spectroscopy, Steen J. Madsen, Eric R. Anderson, Richard C. Haskell, Bruce J. Tromberg Dec 1994

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.

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Multiple Solutions For A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio Nov 1994

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.

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Rapid Relaxation Of An Axisymmetric Vortex, Andrew J. Bernoff, Joseph F. Lingevitch Nov 1994

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 (Re1/3) 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 Re1/3 time scale due to a shear/diffusion …

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Multiple Solutions For A Semilinear Dirichlet Problem, Alfonso Castro, Jorge Cossio Nov 1994

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.

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Low-Frequency Line Shapes In Guided Acoustic-Wave Brillouin Scattering, Benjamin I. Greene, Peter N. Saeta Oct 1994

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.

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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 Oct 1994

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 …

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Lattice-Ordered Algebras That Are Subdirect Products Of Valuation Domains, Melvin Henriksen, Suzanne Larson, Jorge Martinez, R. G. Woods Sep 1994

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 …

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Letter From The Editor, Issue 10, 1994, Alvin White Aug 1994

Letter From The Editor, Issue 10, 1994, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

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Applied Mathematics Should Be Taught Mixed, Gary I. Brown Aug 1994

Applied Mathematics Should Be Taught Mixed, Gary I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

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Female Voices In Mathematics: A New Course, Shobha Gulati Aug 1994

Female Voices In Mathematics: A New Course, Shobha Gulati

Humanistic Mathematics Network Journal

No abstract provided.

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Poetry, Helen Lewy Aug 1994

Poetry, Helen Lewy

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics In Literature And Poetry, Joanne S. Growney Aug 1994

Mathematics In Literature And Poetry, Joanne S. Growney

Humanistic Mathematics Network Journal

No abstract provided.

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Math: It's Not Just A Four Letter Word, Susan Byerly Aug 1994

Math: It's Not Just A Four Letter Word, Susan Byerly

Humanistic Mathematics Network Journal

No abstract provided.

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Nctm Standards, Second Edition: A Review And Commentary On Zalman Usiskin's Address, Harald M. Ness Aug 1994

Nctm Standards, Second Edition: A Review And Commentary On Zalman Usiskin's Address, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

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What Changes Should Be Made For The Second Edition Of The Nctm Standards?, Zalman Usiskin Aug 1994

What Changes Should Be Made For The Second Edition Of The Nctm Standards?, Zalman Usiskin

Humanistic Mathematics Network Journal

No abstract provided.

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Epsilon And Delta: A Little Love Story, Bonnie Shulman Aug 1994

Epsilon And Delta: A Little Love Story, Bonnie Shulman

Humanistic Mathematics Network Journal

No abstract provided.

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Humacrostic, Stephen I. Brown Aug 1994

Humacrostic, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

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Subpicosecond Thomson Scattering Measurements Of Optically Ionized Helium Plasmas, T. E. Glover, Thomas D. Donnelly, E. A. Lipman, A. Sullivan, R. W. Falcone Jul 1994

Subpicosecond Thomson Scattering Measurements Of Optically Ionized Helium Plasmas, T. E. Glover, Thomas D. Donnelly, E. A. Lipman, A. Sullivan, R. W. Falcone

All HMC Faculty Publications and Research

We present the first subpicosecond time-resolved temperature measurements of plasmas produced by high-intensity optical ionization. Thomson scattering is used to measure electron and ion temperatures of helium plasmas created by 125 fs, 800 nm laser pulses focused to an intensity of 2 × 1017 W/cm2. We find that the electron temperature is accurately predicted by a tunneling ionization model. The measured ion temperature is consistent with direct heating by the laser pulse.

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Radially Symmetric Solutions To A Dirichlet Problem Involving Critical Exponents, Alfonso Castro, Alexandra Kurepa Jun 1994

Radially Symmetric Solutions To A Dirichlet Problem Involving Critical Exponents, Alfonso Castro, Alexandra Kurepa

All HMC Faculty Publications and Research

In this paper we answer, for N = 3,4, the question raised in [1] on the number of radially symmetric solutions to the boundary value problem -Δu(x) = λu(x) + u(x)|u(x)|^{4/(N-2)}, x ε B: = x ε RN:{|x| < 1}, u(x)=0, x ε ∂B, where Δ is the Laplacean operator and λ>0. Indeed, we prove that if N = 3,4, then for any λ>0 this problem has only finitely many radial solutions. For N = 3,4,5 we show that, for each λ>0, the set of radially symmetric solutions is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

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Tabletop X-Ray Lasers, D. C. Eder, P. Amendt, L. B. Dasilva, R. A. London, B. J. Macgowan, D. L. Matthews, B. M. Penetrante, M. D. Rosen, S. C. Silks, Thomas D. Donnelly, R. W. Falcone, G. L. Strobel May 1994

Tabletop X-Ray Lasers, D. C. Eder, P. Amendt, L. B. Dasilva, R. A. London, B. J. Macgowan, D. L. Matthews, B. M. Penetrante, M. D. Rosen, S. C. Silks, Thomas D. Donnelly, R. W. Falcone, G. L. Strobel

All HMC Faculty Publications and Research

Details of schemes for two tabletop size x‐ray lasers that require a high‐intensity short‐pulse driving laser are discussed. The first is based on rapid recombination following optical‐field ionization. Analytical and numerical calculations of the output properties are presented. Propagation in the confocal geometry is discussed and a solution for x‐ray lasing in Li‐like N at 247 Å is described. Since the calculated gain coefficient depends strongly on the electron temperature, the methods of calculating electron heating following field ionization are discussed. Recent experiments aimed at demonstrating lasing in H‐like Li at 135 Å are discussed along with modeling results. The …

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X-Rays From Microstructured Targets Heated By Femtosecond Lasers, S. P. Gordon, Thomas D. Donnelly, A. Sullivan, H. Hamster, R. W. Falcone Apr 1994

X-Rays From Microstructured Targets Heated By Femtosecond Lasers, S. P. Gordon, Thomas D. Donnelly, A. Sullivan, H. Hamster, R. W. Falcone

All HMC Faculty Publications and Research

We have demonstrated efficient conversion of ultrashort-pulse laser energy to x rays with energies above 1 keV, using laser-produced plasmas generated on a variety of microstructured surfaces. Lithographically produced grating targets generated 0.1 mJ of kilo-electron-volt x rays, and porous gold and aluminum targets emitted 1 mJ. This represents an improvement of a factor of 100 over flat targets. The K-shell emission spectrum of porous aluminum was composed primarily of heliumlike spectral lines.

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Letter From The Editor, Issue 9, 1994, Alvin White Feb 1994

Letter From The Editor, Issue 9, 1994, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

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Writing Mathematics, E. G. Bernard Feb 1994

Writing Mathematics, E. G. Bernard

Humanistic Mathematics Network Journal

No abstract provided.

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Letter To The Editor, Ken Ross Feb 1994

Letter To The Editor, Ken Ross

Humanistic Mathematics Network Journal

No abstract provided.

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The Language Of Mathematics: A Quantitative Course For A General Audience, Stephanie F. Singer Feb 1994

The Language Of Mathematics: A Quantitative Course For A General Audience, Stephanie F. Singer

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics And The Arts: Taking Their Resemblances Seriously, Frederick Reiner Feb 1994

Mathematics And The Arts: Taking Their Resemblances Seriously, Frederick Reiner

Humanistic Mathematics Network Journal

No abstract provided.

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Students' Understanding Of Functions In Calculus Courses, G. S. Monk Feb 1994

Students' Understanding Of Functions In Calculus Courses, G. S. Monk

Humanistic Mathematics Network Journal

No abstract provided.

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Poems, Lee Goldstein Feb 1994

Poems, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

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Back Matter, Issue 9, 1994 Feb 1994

Back Matter, Issue 9, 1994

Humanistic Mathematics Network Journal

No abstract provided.

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Philosophy Of Mathematics, Mathematics Education, And Philosophy Of Mathematics Education, Yuxin Zheng Feb 1994

Philosophy Of Mathematics, Mathematics Education, And Philosophy Of Mathematics Education, Yuxin Zheng

Humanistic Mathematics Network Journal

No abstract provided.

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