In the study of the fundamental theory and the characterizations of space curves, the related curves for which there exist corresponding relations between the curves are very interesting and important problems. The most fascinating examples of such curve are associated curves, the curves for which at the corresponding points of them one of the Frenet vectors of a curve coincides with the one of...

The secondary hydroxyl group involved in the oxidation, and the cis-vicinal secondary hydroxyl group, must have a D configuration jvith respect to t,he primary alcohol group adjacent to the site of oxidation. This specific mode of otida,tion facilitated the synthesis of several new ketoses. In a series of papers, Hudson and Richtmyer and their a.ssociates described the microbiological synthesis...