Structure of 2-(2,6-dimethoxyphenyl)-2,5- dimethylbicyclo[3.2.1]octane-6,8-dione

C18H2204, orthorhombic, P212~21, a = 7.343 (4), b = 11.251 (4), c = 19.357 (4)A, Z = 4, Dr, ' = 1.20, D e = 1.254 g cm -3, F(000) = 648, p(MoKa) = 0.94 cm -~. X-ray intensity data were collected on a Nonius CAD-4 diffractometer and the structure was solved by direct methods. Full-matrix least-squares refinement gave R = 0.052 (R w = 0.045) for 1053 observed reflections. The stereochemical configuration at C(2) has been shown to be 2-exo-methyl-2-endo-(2,6-dimethoxyphenyl), i.e. (3) in contrast to the structure (2) assigned earlier based on its ~H NMR data.

Renormalisation of the Fayet-Illiopoulos term in supersymmetric spontaneously broken U( 1) gauge theories

It is shown that the Fayet-Illiopoulos D term in N= 1 supersymmetric spontaneously broken U( 1) gauge theories may get one-loop corrections, even when trace U( 1) charges are zero. However, these corrections are only logarithmically divergent and hence do not affect the naturalness of the theory.

Analysis of drop formation at conical tips : 1. Theory

The phenomenon of drop formation at conical tips under near zero flow conditions has been investigated using a theoretical approach. The analysis permits the prediction of drop profile and drop volume, until the onset of instability. A semiempirical approach based on the similarity of drop shapes has been adopted to predict the detaching drop volumes at conical tips. The effects of base diameter of the cone, cone angle, interfacial tension, and the densities of the drop and the surrounding fluid on the maximum and detached drop volumes are predicted.