Abstract: A catalyst composition for organic a symmetric synthesis is provided, which comprises: (A) a lanthanoid element ion; (B) a binaphthol, and (C) a nitrogen and/or phosphorus compound such as lutidine-N-oxide, 1,3-dimethyl-2-imidazolldinone, hexamethyl-phosphortriamide, triphenylphosphine oxide, tri(2-methylphenyl)phosphine oxide or tri(4-methylphenyl )phosphine oxide. Asymmetric epoxidation of an enone is conducted by allowing an enone to react with an oxidizing agent in the presence of the catalyst composition or a catalyst solution containing the catalyst composition.

Abstract: A spline-coupling structure in which at least one of male and female members has a press-fit guide face provided at its end opposed to the other member before press-fitting of the members. The press-fit guide face includes a plurality of guide face portions smoothly interconnecting the end and bottom lands of the spline teeth of the one member to form axially outwardly expanded arcs, a plurality of second guide face portions smoothly interconnecting tooth addendums of the spline teeth and the end to form axially outwardly expanded arcs, and a plurality of third guide face portions smoothly interconnecting tooth flanks of the spline teeth and the second guide face portion to form axially outwardly expanded arcs. The first, second and third guide face portions are connected smoothly to one another.

Abstract: The present invention provides optically active esters of 7-substituted 3,5-difunctionalized 6-heptenoic acids represented by the following formula: ##STR1## wherein R is a substituted or unsubstituted aromatic group, a substituted or unsubstituted heteroaromatic group or a substituted vinyl group;Ar is a condensed aromatic group;X.sup.1 and Y.sup.1 are not the same and each is a hydrogen atom or a hydroxyl group; andX.sup.2 and Y.sup.2 are not the same and each is a hydrogen atom or a hydroxyl group or enantiomers thereof.

Abstract: The present invention provides optically active esters of 7-substituted 3,5-difunctionalized 6-heptenoic acids represented by the following formula: ##STR1## wherein R is a substituted or unsubstituted aromatic group, a substituted or unsubstituted heteroaromatic group or a substituted vinyl group;Ar is a condensed aromatic group;X.sup.1 and Y.sup.1 are not the same and each is a hydrogen atom or a hydroxyl group, or may be combined to represent an oxygen atom which forms a carbonyl group together with the carbon atom to which X.sup.1 and Y.sup.1 are attached; andX.sup.2 and Y.sup.2 are not the same and each is a hydrogen atom or a hydroxyl group, or may be combined to represent an oxygen atom which forms a carbonyl group together with the carbon atom to which X.sup.2 and Y.sup.2 are attached,or enantiomers thereof.The present invention further provides processes for preparing the above optically active esters and 7-substituted (3R, 5S, 6E)-3,5-dihydroxy-6-hepten-1,5-olides.