Chemical predisposition in synthesis: application to the preparation of the pyrrolidine natural products, plakoridines A and B

The pyrrolidine natural products, plakoridines A and B, as well as an array of unnatural analogues, have been prepared using a five-step synthetic sequence modelled on a biogenetic theory. The key transformation involves a ‘Mannich/Michael/internal-redox’ cascade, which proceeds in yields of 31-63%.     

Linear Combinations of Generalized Crank Nicolson Schemes

The combination of two or more generalized Crank Nicolson schemesin order to obtain second, third and fourth order accurate discretizationsin time is considered. Particular attention is given to thestability properties of the methods proposed.     

Boundary Techniques for the Multistep Formulation of the Optimized Lax-Wendroff Method for Non-linear Hyperbolic Systems in Two Space Dimensions

Gourlay & Morris (1970) presented a multistep formulationof a scheme proposed by Strang (1968) for the numerical solutionof non-linear hyperbolic systems. This formulation did not takeaccount of given boundary data and led to instability in certainproblems. This note presents boundary techniques for the incorporationof the given boundary data and in numerical experiments, itis shown that the instabilities, which arose in the problemsof Gourlay & Morris, are prohibited.     

Ring Homomorphisms and Finite Gorenstein Dimension

The local structure of homomorphisms of commutative noetherianrings is investigated from the point of view of dualizing complexes.A concept of finite Gorenstein dimension, which substantiallyweakens the notion of finite flat dimension, is introduced forhomomorphisms. It is shown to impose structural constraints,due to a remarkable equivalence of subcategories of the derivedcategory of all modules. An essential part of this study is the development of relativenotions of dualizing complexes and Bass numbers. It is provedthat the Bass numbers of local homomorphisms are rigid, extendinga known result for local rings. Quasi-Gorenstein homomorphismsare introduced as local homomorphisms that base-change a dualizingcomplex for the source ring into one for the target. They areshown to have the stability properties of the Gorenstein homomorphismthat they generalize. 1991 Mathematics Subject Classification:primary 13H10, 13D23, 14E40; secondary 13C15.     

A synthetic approach to the plakoridines modeled on a biogenetic theory

An expedient synthetic route to the fully substituted pyrrolidine ring system of the plakoridines is described using an approach modeled on a plausible biosynthetic pathway.