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

Ultra-relativistic electrostatic Bernstein waves

A new general form of the dispersion relation for electrostatic Bernstein waves in ultra-relativistic pair plasmas, characterized by a−1 = kBT/(mec2)  1, is derived in this paper. The parameter Sp = aΩ0/ωp, where Ω0 is the rest cyclotron frequency for electrons or positrons and ωp is the electron (or positron) plasma frequency, plays a crucial role in characterizing these waves. In particular, Sp has a restricted range for permitted wave solutions; this range is effectively unlimited for classical plasmas, but is significant for the ultra-relativistic case. The characterization of these waves is applied in particular to the presence of such plasmas in pulsar atmospheres

Lotka--Volterra Type Equations and their Explicit Integration

In the present note we give an explicit integration of some two--dimensionalised Lotka--Volterra type equations associated with simple Lie algebras, other than the familiar $A_n$ case, possessing a representation without branching. This allows us, in particular, to treat the first fundamental representations of $A_r$, $B_r$, $C_r$, and $G_2$ on the same footing.Comment: 3 pages LATEX fil