Computing combinatorial decompositions of rings

Using Buchberger's Gröbner basis theory, we obtain explicit algorithms for computing Stanley decompositions, Rees decompositions and Hironaka decompositions of commutative Noetherian rings. These decompositions are of considerable importance in combinatorics, in particular in the theory of Cohen-Macaulay complexes. We discuss several applications of our methods, including a new algorithm for finding primary and secondary invariants of finite group actions on polynomial rings.Research supported by the Institute for Mathematics and its Applications, Minneapolis, with funds provided by the National Science Foundation     

A high yield route to ethyl esters of car☐ylic acids

Diethyl trichloromethylphosphonate reacts with car?ylic acids to yield their ethyl esters, via transesterification; even the hindered mesitoic acid is esterified in high yield.     

A novel approach to molecular similarity

Summary We review briefly the general problem of assessing the similarity between one molecule and another. We propose a novel approach to the quantitative estimation of the similarity of two electron distributions. The procedure is based on momentum space concepts, and avoids many of the difficulties associated with the usual position space definitions. Results are presented for the model systems CH₃CH₂CH₃, CH₃OCH₃, CH₃SCH₃, H₂O and H₂S.     

Mass spectral fragmentation pattern of 3-methyl- and 3-phenyl-4-(N-methylarylhydrazono)isoxazol-5-ones

3-Methyl-4-(N-methylarylhydrazono)isoxazol-5-ones and 3-phenyl-4-(N-methylarylhydrazono)isoxazol-5-ones undergo considerable fragmentation on electron impact involving rupture of the isoxazolone ring and bonds in the N-methylarylhydrazono side chain.