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.     

Dynamics and kinematics of simple neural systems

The dynamics of simple neural systems is of interest to both biologists and physicists. One of the possible roles of such systems is the production of rhythmic patterns, and their alterations (modification of behavior, processing of sensory information, adaptation, control). In this paper, the neural systems are considered as a subject of modeling by the dynamical systems approach. In particular, we analyze how a stable, ordinary behavior of a small neural system can be described by simple finite automata models, and how more complicated dynamical systems modeling can be used. The approach is illustrated by biological and numerical examples: experiments with and numerical simulations of the stomatogastric central pattern generators network of the California spiny lobster. (c) 1996 American Institute of Physics.