Maximal commutative subalgebras of functions on spaces dual to Lie algebras

The problem of searching the maximal commutative sets of polynomial functions on the dual space to the semidirect sum of a Lie algebra and a vector space is studied. It is proved that if the first component of the semi-direct sum is a compact algebra, then the set of functions can be described explicitly. This result is applied to some particular Lie algebras.     

The effect of substituents on the helical twisting power of aldol condensation products of menthone

The helical twisting powers of the E-isomers of aldol condensation products of menthone and aromatic aldehydes are higher than those of the Z-isomers. In order to find out which chiral centre of these menthone derivatives is responsible for the value of the helical twisting in both isomers, the E-isomers of aldol condensation products of 3-methylcyclohexanone and 2-isopropylcyclohexanone were prepared and photoisomerized to form Z-isomers. The physical properties of these species were determined. It was concluded that the strong helical twisting power of the E-isomers of the derivatives of menthone is caused by the chiral carbon atom containing the methyl group in the ring. The relatively low helical twisting power of the Z-isomers and the composition of the E-Z isomers in the photostationary state are determined mainly by the other chiral centre containing the isopropyl group.     

A simple method for determination of the reflection coefficient at the internal surfaces of turbid slabs

The total reflectance of a slab turbid material is measured with an integrating sphere. Each slab was measured with a glossy and diffusing (etched) rear surface, both with and without a fully reflecting pill placed behind it. Formulae derived show that the results, together with the refractive index, permit calculation of the reflectance of the parity diffuse radiation at the internal rear surface. The method is applied to human dental enamel.     

Metabolites of the pathogenic fungusVerticillium dahliae. XI. Primary structure of the polypeptide moiety of the phytotoxic pigment PKZh-1

The sequence of the 27 amino acid residues composing the polypeptide moiety of the phytotoxic metabolite PKZh-1 of the fungusV. dahliae has been determined on the basis of the structures of tryptic and chymotryptic peptides. It has been established that the linkage of the polypeptide with 2,5,7-trihydroxy-1,4-naphthoquinone (flaviolin), which is the chromophoric moiety of PKZh-1, is effected through an ester bond formed by the carboxy group of the C-terminal amino acid and one of the hydroxy groups of flaviolin.