The Liouville-Bratu-Gelfand Problem for Radial Operators

We determine precise existence and multiplicity results for radial solutions of the Liouville-Bratu-Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.     

The Synthesis of L-aminosugar and the studies of L-pyranoses on the ring III of pyranmycins

The synthesis of a novel class of aminoglycoside, pyranmycin, and a convenient method for the preparation of 6-amino-L-idopyranosides were reported. One of the members in the reported pyranmycin families, TC010, has prominent activity against Escherichia coli, Staphylococcus aureus, and Bacillus megaterium. We also discovered that the (4)C(1) chair conformation on ring III of pyranmycin is essential for the antibacterial activity. [reaction: see text]     

STOPPING RULES AND THE CONTROL OF STOCK POLLUTANTS

A stock pollutant is defined as a residual waste that might accumulate over time. This paper examines some of the important distinctions between degradable and nondegradable stock pollutants and between nondegradable stock pollutants with known versus uncertain environmental cost. The latter case is examined using the more recent literature on stochastic control with Brownian motion. The presence of irreversibility and uncertainty is known to lead to more conservative investment rules and places a value on the preservation of options. In the case of a nondegradable stock pollutant with Brownian environmental cost, options are preserved by stopping accumulation at a lower level than in the corresponding certainty-equivalent problem. The model presented in this paper permits the derivation of closed-form stopping rules. For a simple numerical problem, the optimal nondegradable stock with Brownian environmental cost was 20 to 45 percent lower than the optimal level with known environmental cost. The empirical study of an actual nondegradable stock pollutant will require time series data on private and social cost in order to estimate drift and variance parameters which will influence the actual extent to which the optimal stock is less than the certainty-equivalent stock.     

EOM/Propagator ionization potentials: Extension of the excitation operator manifold

The excitation operator manifold required for the calculation of vertical IPs in the EOM/propagator formalism is extended to include products of five spin orbital field operators (refered to as the h₅ basis). Spin symmetry adaptation is used for all the operators of this manifold. Using a direct diagonalization technique introduced previously the effect of inclusion of the h₅ basis on calculated IPs is illustrated for various levels of approximation to the electron density by numerical applications to ethylene and water. The fourth-order terms thus introduced are shown to have greater magnitude than previously included third-order terms, in agreement with earlier work.     

The structure of gascardic acid from an x-ray diffraction study

The complete structure of the unique tricyclic sesterterpene gascardic acid is proposed based on a single crystal x-ray diffraction analysis of the dicyclohexylammonium salt.     

A digital integrator for controlled-potential coulometry

Accurate electrolysis current integration is required in controlled-potential coulometry. Analog integrators have been shown to deviate from ideal response by as much as —0.1%. A digital integrator was designed to optimize the linearity of the voltage-to-frequency converter used, minimize the effects of temperature, eliminate integration errors caused by small polarity changes and signal noise, and allow interchangeability with an analog integrator in a state-of-the-art coulometer widely used throughout the nuclear field for controlled-potential coulometry. Evaluation of the digital integrator, calibrated versus the Faraday, showed bias-free determinations of plutonium with a relative standard deviation of approximately 0.02%. The integrator was designed specifically for use in the controlled-potential coulometric determination of plutonium, but many of the features incorporated can be adopted to digital integrators for other uses where accurate integration over long periods of time is required.