Physical Sciences and Mathematics Commons^™

Positive Solutions For A Semilinear Elliptic Problem With Critical Exponent, Ismail Ali, Alfonso Castro

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No abstract provided in article.

The Structure Of Alkali Halide Dimers: A Critical Test Of Ionic Models And New Ab Initio Results, T. Törring, S. Biermann, J. Hoeft, Richard J. Mawhorter, Robert J. Cave, C. Szemenyei

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In semiempirical ionic models a number of adjustable parameters have to be fitted to experimental data of either monomer molecules or crystals. This leads to strong correlations between these constants and prevents a unique test and a clear physical interpretation of the fit parameters. Moreover, it is not clear whether these constants remain unchanged when the model is applied to dimers or larger clusters. It is shown that these correlations can be substantially reduced when reliable information about dimers is available from experiments or ab initio calculations. Starting with Dunham coefficients of the monomer potential determined from microwave measurements, we …

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

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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.

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

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No abstract provided in this article.

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

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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.

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

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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.

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

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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 …

Combinatorics And Campus Security, Arthur T. Benjamin

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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 …

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

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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

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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.

An Nmr Investigation Of The Effect Of Hydrogen Bonding On The Rates Of Rotation About The C-N Bonds In Urea And Thiourea, Karl A. Haushalter, Janice Lau, John D. Roberts

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The interaction between urea and tetrabutylammonium acetate was investigated in dimethylformamide/ dimethyl sulfoxide solutions using ¹H and 15^N NMR. The chemical-shift behavior of the urea protons is consistent with a urea-acetate hydrogen-bonded complex involving both carboxylate oxygens and the urea hydrogens trans to the carbonyl oxygen with K_assoc = 120 ± 10. Line shape analysis of the temperature-dependent ¹H NMR spectra show that ∆G^‡ for rotation about the C-N bond of urea changes only slightly from 11.0 ± 0.1 to 11.2 ± 0.1 kcal/mol on 1:1 molar addition of tetrabutylammonium acetate to a dilute solution of urea. A parallel investigation …

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

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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.

Meyer Jerison, 1922-1995, Leonard Gillman, Melvin Henriksen

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Memories and biography of mathematician Meyer Jerison (b. November 28, 1922 - d. March 19, 1995).