Synthesis of (−)-Dihydroraputindole D by Enantioselective Benzoylation of a 1,3-Diol Intermediate

The enantioselective synthesis of (−)-dihydroraputindole D is reported. The key step is the desymmetrizing benzoylation of a prochiral 1,3-diol employing Trost′s ProPhenol catalyst system, which has been applied for the first time to a cyclic molecule carrying geminal hydroxymethyl groups. The cyclopenta[f]indoline system was assembled by Au(I)-catalyzed cyclization of an alkynylated indoline precursor. (−)-Dihydroraputindole D was obtained in 17 steps and 8% overall yield starting from dihydroxyacetone. In combination with quantum chemical calculations of the ECD spectra, our synthesis allowed us to determine the absolute configuration (5S,7R) of the natural product (+)-raputindole D from the Rutaceous plant Raputia simulans.     

Syndioselective propylene polymerizations by ansa-zirconocenium catalyst

The effect of reaction conditions, including catalyst concentration, temperature, and immobilization on support, have been investigated for syndioselective propylene polymerization by the “bare” zirconocenium ion generated from 1,1-diphenyl-methylidene(1-η⁵-cyclopentadienyl)(9-η⁵-fluorenyl)zirconium-dichloride precursor (2). Neither variation of the catalyst concentration nor immobilization of 2 on silica support affect the syndiospecificity of polymerization. The stereoregularity of the syndiotactic polypropylene, as judged from the melting transition temperature and homosteric r-pentad population by ¹³C-NMR, were found to be proportional to polymer molecular weight. These behaviors are compared with a typical isoselective catalyst ethylenebis(4,5,6,7-tetrahydroindenyl) Zr precursor (4). They are in close resemblance in the case of the S-enantiomeric complex of 4, but the racemic mixture of 4 is markedly inferior. The origins of stereo- and regio-errors are discussed. © 1996 John Wiley & Sons, Inc.     

A perturbation method applied to the buckling of a compressed elastica

We consider the problem of carrying out an asymptotic analysis for the phenomenon of bifurcation which occurs at critical values of an axial force applied to an elastic column. In the present setting a discontinuous coefficient precludes the possibility of carrying out the usual asymptotic analysis. The problem is overcome via a nonlinear change of independent variables.     

Approximate Wannier functions

We present a method for constructing approximate Wannier functions from finite sets of Bloch functions specified at special points in the Brillouin zone.     

Brief Review

Computational Linear Algebra with Models (Second Edition), by Gareth Williams. Allen and Bacon, Inc., 1978, 480+ xv pp. Linear Algebra with Applications, by Jeanne Agnew and Robert C. Knapp, Brooks/Cole Pub. Co., Monterey, California, 1978, 465+x pp.