W∞W_{\infty}--Geometry and Associated Continuous Toda System

We discuss an infinite--dimensional k\"ahlerian manifold associated with the area--preserving diffeomorphisms on two--dimensional torus, and, correspondingly, with a continuous limit of the $A_r$--Toda system. In particular, a continuous limit of the $A_r$--Grassmannians and a related Pl\"ucker type formula are introduced as relevant notions for $W_{\infty}$--geometry of the self--dual Einstein space with the rotational Killing vector.Comment: 6 pages, no figure report\# ETH-TH/93-2

Kinetic consistent algorithm for incompressible conductive fluid

A kinetic model based on the single-particle Boltzmann-like distribution function is used to describe magneto gas dynamic phenomena. Along with the original kinetic consistent gas dynamic model, a simplified version that is more convenient for numerical implementation is considered and justified. Numerical results for a number of problems are presented, especially for the incompressible conductive fluid