An initial-value method for integral operators—IV. Complex-valued kernels of laser theory

A new technique is presented for the calculation of the eigenvalues and eigenfunctions of complex-valued symmetric kernels which occur in laser theory. The method combines some classical results of integral equations and complex variables with a recent technique for transforming Fredholm integral equations into a Cauchy system of differential equations. The procedure is flexible and accurate, whereas many of the classical techniques, such as Rayleigh-Ritz, yield results of doubtful accuracy for the kernels of laser theory.     

Temperature-dependent light scattering from magnetic excitons in TlCoF3

Raman spectra of antiferromagnetic thallium cobaltous fluoride have been obtained with 4579A argon ion laser excitation at temperatures from 4°K to T_N = 94 ± 2°K. The features observed consist of six Co²⁺ excitons ranging in energy from 325 to 1070 cm^-1, at two-magnon peak with low-temperature energy of 315 cm^-1, and a one-magnon feature whose 4°K energy is 37 cm^-1. The energy and linewidth of the one-magnon scattering has been measured from 4°K to about 0.8 T_N; it is found that the magnon becomes critically damped at about 0.8 T_N, in good agreement with our previous observations on RbCoF₃. The Co²⁺ excitons observed at 325, 380, 410, 730 (weak), 960, and 1070 cm^-1 agree in energy quite well with the KCoF₃ levels calculated by Buyers, Holden et al. as 340, 400, 467, 767, 967 and 1050 cm^-1.     

Determinants,Grassmanniannians and Elliptic Boundary Problems for the Dirac Operator

We study the relations between different determinants of the Dirac operator over a manifold with boundary considered as sections of a holomorphic line bundle over the Grassmannian of boundary conditions of Atiyah–Patodi–Singer type.     

Wulff clusters inR 2

We give the first existence and regularity results on the cheapest way to enclose and separate planar regions of prescribed areas, where cost is given by a general norm ϕ, thus generalizing the Wulff shape for enclosing a single region. As an example, we classify the cheapest way to enclose and separate two planar regions of prescribed areas for the ℓ¹ norm (“Manhattan metric”) into three distinct types, according to the relative size of the prescribed areas.     

C(10)-methylation of steroidal synthesis intermediate BCD-tricyclic 9-en-5-ones

A literature survey indicated that stereospecific non-reductive β-face methylation at C(10) of steroidal synthesis intermediate BCD-tricyclic 9-en-5-ones had never been effected. An attempt to define the factors controlling the β/α product ratio in such alkylations was made. The course of methylation is significantly affected by the temperature. In the best case, methylation of the sodium enolate of 17 β-t-butoxy-19-(3,5-dimethyl-4-isoxazolyl)-deA-androst-9-en-5-one ( 18 ) in tetrahydrofuran at ? 78° gave a β/α product ratio of > 5:1. The reaction mixture contained no unalkylated or dialkylated materials, indicating that enolate exchange probably did not occur at this temperature. The 10β-methylated product 23 , isolated in 78% yield, was converted to Δ⁹(ll)-dehydrotestosterone ( 29 ). Compounds 23 and 29 are potential intermediates for the synthesis of 11-oxygenated steroids.     

Cyanide und Halogene

Ohne Zusammenfassung     

Beiträge zur Chemie des Kautschuks,II.

Ohne ZusammenfassungMitteilung aus dem Untersuchungslaboratorium der Diamond Rubber Co.     

Rhenium(VII) catalysis of Prins cyclization reactions

The rhenium(VII) complex O3ReOSiPh3 is a particularly effective catalyst for Prins cyclizations using aromatic and alpha,beta-unsaturated aldehydes. The reaction conditions are mild, and the highly substituted 4-hydroxytetrahydropyran products are formed stereoselectively. Rhenium(VII) complexes appear to spontaneously form esters with alcohols and to directly activate electron-rich alcohols for solvolysis. Re2O7 and perrhenic acid are equally effective in catalyzing these cyclizations.     

Gas-phase stereoselective binding to Mn/salen catalysts

Gas-phase equilibrium measurements have been used to determine the stereoselectivity of binding the enantiomers of 1-phenylethanol to manganese/salen asymmetric epoxidation catalysts. There is significant selectivity in the gas-phase binding, and the results are compared to data from condensed-phase epoxidations. The study demonstrates the utility of a novel internal standard approach that allows for rapid, accurate measures of the stereoselectivity of gas-phase ligand binding. Moreover, the data suggest that gas-phase binding stereoselectivity could be a potential predictor of condensed-phase enantioselectivity.