How Stable Are Epoxides? A Novel Synthesis of Epothilone B

Remarkable stability of the oxirane function is displayed over a number of synthetic operations in a novel synthesis of the antitumor compound epothilone B (see scheme). The cis-epoxide, generated very early by dihydroxylation of an (E)-olefin, was resistant to more than ten synthetic steps under a wide variety of reaction conditions. TBS=tert-butyldimethylsilyl.     

Benz[c]octalen

An expedient new synthesis of benzo[c]octalene starting from the Diels-Alder adduct of benzocyclobutadiene to 7,8-dimethylenecycloocta-1,3,5-triene is described. This octalene derivative, in solution, exists as an equilibrating mixture of the double bond isomers (2) and (3) whereas in its crystalline state only the isomer (2) is present.     

Reduktionsverfahren für Differenzengleichungen bei Randwertaufgaben II

Summary In a recent paper [11], two of the authors investigated a fast reduction method for solving difference equations which approximate certain boundary value problems for Poisson's equation. In this second paper, we prove the numerical stability of the reduction method, and also report on further developments of the method. For the general case, the provided bounds for the numerical errors behave roughly like the condition numberO(n ²) of the linear system; for more realistic model problems estimates of order less thanO(n) are obtained (n ^–1=h=mesh width). The number of operations required for the reduction method isO(n ² ), for the usual five-point difference formula, as well as for the common nine-point formula with discretization error of orderh ⁴.