ZurL 2-Bestapproximation eines konvexen Körpers durch einen bewegten konvexen Körper

LetK andL be convex bodies of then-dimensional Euclidean spaceE ⁿ . The -distance ofK andL is defined by , whereh _k andh _L denote the support functions ofK andL restricted to the unit sphereS ^n–1 E ⁿ . We consider the problem of best approximation ofL by the images k ofK under proper rigid motions :E ⁿ E ⁿ . A motion that minimizes ²(K L) is called optimal for (K, L) in the sense of the metric ². The results in the general case (n2 arbitrary) base on the fact that the Steiner points of K andL coincide if is optimal for (K, L). Forn=2 we obtain a relationship between convex convolution bodies and the underlying approximation problem.     

Diastereoselective [4+2] annulation of vinyl carbodiimides with N-alkyl imines. Asymmetric synthetic access to the batzelladine alkaloids

A diastereoselective [4+2] annulation of vinyl carbodiimides with chiral N-alkyl imines has been developed to access the stereochemically rich tricyclic core of the batzelladine alkaloids. Its application to the asymmetric synthesis of batzelladine D permitted the use of long-range, directed hydrogenation and stereoselective intramolecular iodoamination as additional key steps to establish the remaining stereocenters within the natural product with excellent stereocontrol.     

VISUAL PIGMENTS—10. SPECTROSCOPY AND PHOTOPHYSICAL DYNAMICS OF RETINOL AND RETINYL ETHER

Abstract— The absorption and emission spectra, lifetimes and quantum yields of all-trans retinol have been examined as a function of solvent and temperature. In addition, the spectroscopy of retinyl ether and 2 other polyene alcohols have been determined. Based on the results obtained, we conclude that the singlet excited state of retinol and retinyl cther is of a forbidden character and of the type loosely called ¹A^-_g. Retinol forms a dimer in an alkane solvent when cooling from 298 to 77 K. A general structure for the dimer is proposed.     

Luteone,a twenty three carbon terpenoid from the dorid nudi branch Cadlina luteomarginata

The structure of luteone ($\text{1}$), a twenty three carbon terpenoid, has been solved by performing a single crystal x-ray analysis on a 3,4-dinitrophenylhydrazone derivative.