Parametrizing Equivalence Classes of Invariant Star Products

Let (M,,) be a symplectic manifold endowed with a symplectic connection . Let Symp(M,) be the group of symplectic transformations of (M,) and Aff(M,) be the group of affine transformations of the affine manifold (M, ). In this Letter, we show that, for any subgroup G of Symp(M,) Aff(M,), the set of G-equivalence classes of G-invariant star products on (M,) is canonically parametrized by the set of sequences of elements belonging to the second de Rham cohomology space of the G-invariant de Rham complex on M.     

4-phenyl-4H-pyrazolo[3,4-c] furazans. The reactions of 3,4-dacylfuroxans with phenylhydrazine and with aniline

Three different 3,4-diaeylfuroxans (1) are shown to give 3-substituted-l-phenyl-4,5-dioximino-2-pyrazolines (2) upon reaction with phenylhydrazine. The compounds 2 were dehydrated to 6-sul)stituted-4-phenyl-4H-pyrazolo[3,4-c]furazans. ( 3 ) and thermally converted to 3-substituted 5-imino-4-oximino-1-phenyl-2-pyrazolines ( 6 ). The compounds 1 react with aniline to give 3-anilino-4-acylfurazans ( 10 ).     

The bromination of isatoic anhydride

Bromination of isatoic anhydride in acetic acid gives N-dibromoacetyl-3,5-dibromoanthranilic acid. Three new anthranils are described.