Numerical solutions of boundary value problems for K-surfaces in R3

A K-surface is a surface whose Gauss curvature K is a positive constant. In this article, we will consider K-surfaces that are defined by a nonlinear boundary value problem. In this setting, existence follows from some recent results on nonlinear second-order elliptic partial differential equations. The analytical techniques used to establish these results motivate effective numerical methods for computing K-surfaces. In theory, the solvability of the boundary value problem reduces to the existence of a subsolution. In an analogous way, we find that if an approximate numerical subsolution can be determined, then the corresponding K-surface can be computed. We will consider two boundary value problems. In the first problem, the K-surface is a graph over a plane. In the second, the K-surface is a radial graph over a sphere. From certain geometrical considerations, it follows that there is a maximum Gauss curvature K_max for these problems. Using a continuation method, we estimate K_max and determine numerically the unique one-parameter family of K-surfaces that exist for K E (0,K_max). This is the first time that this numerical method has been applied to the nonlinear partial differential equations for a K -surface. Sharp estimates for K_max are not available analytically, except in special situations such as a surface of revolution, where the parametrization can be obtained explicitly in terms of elliptic functions. We find that our numerical estimates for K_max are in close agreement with the expected values in these cases. © 1996 John Wiley & Sons, Inc.     

Polyethylene-based polyurethane copolymers and block copolymers

Low molecular weight hydroxy terminated polyethylene (HTPE) containing on average an ethyl group every 16–18 carbon atoms, and a hydroxy functionality of 2.6, has been used to prepare polyurethane copolymers and block copolymers which have good solvent resistance. The polymers show somewhat complicated thermal behavior, including T_g's at around −40°C due to the HTPE and diffuse endotherms between 40 and 60°C. The simple copolymers, containing only the polyol and a diisocyanate, show infrared evidence for two phases in the case where CHDI (trans-1,4-diisocyanatocyclohexane) was used, and poorer phase separation where other diisocyanates were used. Dynamic mechanical spectra show very broad tan delta transitions for the copolymers in the range of -9 to −23°C. All the polymers exhibit another transition in the G” curve above room temperature. SAXS reveals a microphase separated structure at 30°C for the simple copolymers which increases in spacing, then disappears in the 60–70°C range. With cooling, the microphase separated structure reappears readily for the CHDI-based copolymer, while its reappearance shows a hysteresis resulting from rate effects for the other copolymers.     

Determination of DiazaCon in quail feed and quail serum by ion pair reversed-phase chromatography.

Liquid chromatographic (LC) methods were developed for quantitating the potential avian contraceptive DiazaCon in quail feed and serum. DiazaCon was extracted from ground quail feed with basic n-butyl chloride. The n-butyl chloride extract was evaporated to dryness. The DiazaCon residues were dissolved in an aqueous methanolic ion pairing solution and quantitated by LC at 206 nm. Avian sera was combined with an equal volume of a pH 4 aqueous solution of ion pairing reagent and filtered to remove interfering proteins. DiazaCon was quantitated by LC. Mean recoveries for 500 and 2000 ppm fortified feed were 89.1 and 91.0%, respectively. The mean recovery for sera fortified at 5 levels ranging from 35 to 2000 ppm was 84.9%. Method limits of detection were approximately 14 and 13 ppm for feed and sera, respectively.     

Occurrence of 1,4-dioxane in cosmetic raw materials and finished cosmetic products.

Surveys of cosmetic raw materials and finished products for the presence of the carcinogen 1,4-dioxane have been conducted by the U.S. Food and Drug Administration since 1979. Analytical methods are described for the determination of 1,4-dioxane in ethoxylated cosmetic raw materials and cosmetic finished products. 1,4-Dioxane was isolated by azeotropic atmospheric distillation and determined by gas chromatography using n-butanol as an internal standard. A solid-phase extraction procedure based on a previously published method for the determination of 1,4-dioxane in cosmetic finished products was also used. 1,4-Dioxane was found in ethoxylated raw materials at levels up to 1410 ppm, and at levels up to 279 ppm in cosmetic finished products. Levels of 1,4-dioxane in excess of 85 ppm in children's shampoos indicate that continued monitoring of raw materials and finished products is warranted.     

Tabular electrical conductivity for aluminium

A new Sesame-type table for the electrical conductivity of aluminium is described. The table is based on density functional theory calculations and ranges from 10⁻³ to 1 times solid density (2.7 g/cm³), and from 10⁻² to 10³ eV in temperature. The table is compared with other those of simulations and to experiments and is generally in good agreement. The high-temperature, classical limit of the conductivity is recovered for the highest temperatures and lowest densities. The table is critically evaluated, and directions for improvements are discussed.     

Atmospheric chemistry of cyclohexanone: UV spectrum and kinetics of reaction with chlorine atoms

Absolute and relative rate techniques were used to study the reactivity of Cl atoms with cyclohexanone in 6 Torr of argon or 800–950 Torr of N₂ at 295 ± 2 K. The absolute rate experiments gave k(Cl + cyclohexanone) = (1.88 ± 0.38) × 10^?10, whereas the relative rate experiments gave k(Cl + cyclohexanone) = (1.66 ± 0.26) × 10^?10 cm³ molecule^?1 s^?1. Cyclohexanone has a broad UV absorption band with a maximum cross section of (4.0 ± 0.3) × 10^?20 cm² molecule^?1 near 285 nm. The results are discussed with respect to the literature data. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 223–229, 2008     

Limitations and factors affecting the lactam reduction approach to the synthesis of anthramycin analogs

The limitations and factors affecting the hydride reduction of pyrrolo [1,4]benzodiazepine-5,10-diones to anthramycin-type analogs have been explored.