Closed geodesics on the space of stable two-monopoles

We show that the Atiyah-Hitchin metric on the space of stable two-monopoles admits closed geodesics.This research was supported in part by the National Science Foundation under grant DMS-87-02502     

Effect of moisture on supercritical fluid extraction of polynuclear aromatic hydrocarbons and phenols from soil using an automated extractor

An automated supercritical fluid extraction system was evaluated with polynuclear aromatic hydrocarbons and phenols to demonstrate extraction efficiency, collection efficiency, and sample cross contamination. Results showed that 75/25 glass beads/octadecyl silica provided the highest collection efficiency for these classes of compounds. Also, the automated SFE system was used to study the effect of different percentages of water (w/w) in soil on extraction efficiency of fortified PAH and phenols at different temperatures and pressures. Results showed that the presence of (available) water in soil (>10%) does, increase extraction efficiency of higher molecular weight PAH at higher temperature. Also it was demonstrated that temperature rather than pressure had a marked effect on extraction efficiency. The extraction efficiency of phenols from soil which contained 5% of water, using pure supercritical CO₂, was higher than those obtained from dry soil or soil containing 1 % water. Extraction of phenols from soil did not show a dependence on pressure or temperature.     

Constrained interpolation and smoothing

Numerical and theoretical questions related to constrained interpolation and smoothing are treated. The prototype problem is that of finding the smoothest convex interpolant to given univariate data. Recent results have shown that this convex programming problem with infinite constraints can be recast as a finite parametric nonlinear system whose solution is closely related to the second derivative of the desired interpolating function. This paper focuses on the analysis of numerical techniques for solving the nonlinear system and on the theoretical issues that arise when certain extensions of the problem are considered. In particular, we show that two standard iteration techniques, the Jacobi and Gauss-Seidel methods, are globally convergent when applied to this problem. In addition we use the problem structure to develop an efficient implementation of Newton's method and observe consistent quadratic convergence. We also develop a theory for the existence, uniqueness, and representation of solutions to the convex interpolation problem with nonzero lower bounds on the second derivative (strict convexity). Finally, a smoothing spline analogue to the convex interpolation problem is studied with reference to the computation of convex approximations to noisy data.     

Application of the three-temperatue theory of gaseous ion transport

The three-temperature theory of gaseous ion transport is generalized to allow arbitrary choices for the parallel and perpendicular ion temperatures and the velocity displacement. A truncation-parametrization sheme is proposed which simplifies the numerical computation. Results obtained in this way compare favorably with exact and Monte Carlo results available for special cases. Finally, the theory is used to test a proposed interaction potential for Cs⁺-Ar by comparison of calculated and measured mobility and diffusion coefficients.     

An elementary proof of the Petersson-Knopp theorem on Dedekind sums

A brief and elementary proof of Petersson and Knopp's recent theorem on Dedekind sums is given. The proof is based on a result of Subrahmanyam.