The retarded solution of the scalar wave equation by means of Green's functions

A formula is obtained for the retarded solution of the scalar wave equation in a curved space-time, with boundary conditions appropriate to the case of asymptotic flatness. By means of a conformal transformation, the retarded solution is evaluated in the slow-motion expansion. It is shown that it is necessary to impose further asymptotic restrictions on the source for the usual iterative method to give the correct retarded solution to the given degree of approximation. The weak field case is briefly considered, with the same result.     

Organometallic intermediates : V. Further reactions of cyclopropenones with nickel carbonyl

The reactions of cycloheptacyclopropenone and diphenylcyclopropenone with nickel carbonyl under anhydrous conditions have been investigated and structures deduced for the resulting products.     

A new aromaticity index and its application to five-membered ring heterocycles

A new index of aromatic character has been devised based upon a statistical evaluation of the deviations in peripheral bond orders. The latter can be derived readily from experimentally determined bond lengths. The utility of this index is exemplified by its application to five-membered ring heterocycles and their mesoionic derivatives.     

Configuration-dependent friction coefficients and elastic dumbbell rheology

The kinetic theory of nonlinear elastic dumbbells, with bead friction coefficients that depend linearly on the interbead distance, is used to obtain the elongational viscosity and the dumbbell stretching as a function of elongation rate. The results are obtained by solving numerically the “diffusion equation” for the configurational distribution function. No S-shaped curves were found for the elongational viscosity or for the mean-square end-to-end distance. Previous investigators did report S-shaped curves and related “hysteresis” effects. However, their results were based on using mathematical approximations that now appear to be inappropriate.     

1-Substituted 1,3-Dihydroisothianaphthen-2,2-dioxides: Preparation and Use as ortho-Quinodimethane Precursors in Intramolecular Cycloadditions. Preliminary communication

1,3-Dihydroisothianaphthen-2,2-dioxide (1) was readily converted to the 1-substituted sulfones 3 by deprotonation and subsequent electrophilic attack (Scheme 3 and Table). The appropriate 1-alkenyl- and 1-alkenoyl-sulfones 3 on heating at 213° to 240° underwent SO₂-extrusion to give, via the non-isolated (E)-quinodimethanes II (Scheme 1), polycyclic products such as 4, 6 and 7 in good yields (Schemes 4 and 5). On the other hand, thermolysis of the 1-alkenoyl-1-thioether sulfones 9 furnished mainly the isochromenes 10 (Scheme 6).     

An alternative synthesis of 3-amino-1,2,3,4-tetrahydrocarbazoles

3-Amino-1,2,3,4-tetrahydrocarbazoles are easily prepared from the readily available 3-hydroxy-1,2,3,4-tetrahydrocarbazoles by conversion of the latter to the p-toluene- or methanesulfonate ester, followed by nu-cleophilic displacement with azide ion. The resulting 3-azido-1,2,3,4-tetrahydrocarbazoles are then catalytically hydrogenated to their 3-amino counterparts.