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A new heterocyclic compound, C(2)-symmetric bis-sulfoxide 1, has been found to be an efficient chiral auxiliary for asymmetric desymmetrization of cyclic meso-1,2-diols via diastereoselective acetal fission. Both (R,R)- and (S,S)-1 are readily synthesized with high optical purity via asymmetric oxidation of 1, 5-benzodithiepan-3-one (2). After acetalization of meso-1,2-diols 6a-e and a mono-TMS ether 6f with this chiral auxiliary 1, the resulting acetals 7a-f were subjected to base-promoted acetal fission upon treatment with potassium hexamethyldisilazide (KHMDS) followed by acetylation or benzylation to give the desymmetrized diol derivatives 8a-f with high diastereoselectivity. The chiral auxiliary 1 is readily removed by acid-promoted hydrolysis and can be recovered without a loss in enantiomeric excess.

A new definition is given for the ``ideal random function'' (derivative of the Wiener function), which separates out infinite factors by fullest exploitation of the possibilities of the Dirac delta function. By allowing all integrals to be written formally as sums, this facilitates the definition and manipulation of the Wiener-Hermite functionals, especially for vector random processes of multiple argument. Expansion of a random function in Wiener-Hermite functionals is discussed. An expression is derived for the expectation value of the product of any number of Wiener-Hermite functionals; this is all that is needed in principle to obtain full statistical information from the Wiener-Hermite functional expansion of a random function. The method is illustrated by the calculation of the first correction to the flatness factor (measure of Gaussianity) of a nearly-Gaussian random function.

The behavior of a quantized meson field in a classical gravitational field is examined. Physical quantities such as the expectation value for the number of created mesons are represented in terms of a formal Green's function. They are computed explicitly for the case of a special space-independent gravitational field. The inadequacy of standard iteration procedures is discussed in an Appendix.