On bilinear invariant differential operators acting on tensor fields on the symplectic manifold

Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$, in other words, $T(V)$ is the space of tensor fields of type $V$ on $M$ on which the group \Diff (M) of diffeomorphisms of $M$ naturally acts. Elsewhere, the author classified the \Diff (M)-invariant differential operators $D: T(V_{1})\otimes T(V_{2})\longrightarrow T(V_{3})$ for irreducible fibers with lowest weight. Here the result is generalized to bilinear operators invariant with respect to the group \Diff_{\omega}(M) of symplectomorphisms of the symplectic manifold $(M, \omega)$. We classify all first order invariant operators; the list of other operators is conjectural. Among the new operators we mention a 2nd order one which determins an ``algebra'' structure on the space of metrics (symmetric forms) on $M$

Once More About the Possibility of Determining the Local Electron Concentration by the Dispersion Method with the Help of AES and on New Ionization Maxima in the Ionosphere

Reliability of ionospheric density measurements by satellites using dispersion metho

Mirror instability in a plasma with cold gyrating dust particles

In this work linear stability analysis of a magnetized dusty plasma with an anisotropic dust component having transversal motions much stronger than motions parallel to the external magnetic field, and isotropic light plasma components is described. Such a situation presumably establishes in a shock compressed space dusty plasma downstream the shock front. Oblique low-frequency magneto-hydrodynamic waves ($\omega\ll \omega_{cd}$, $\omega_{cd}$ being the dust cyclotron frequency) are shown to be undergone to the mirror instability. Consequences for nonthermal dust destruction behind shock fronts in the interstellar medium are discussed.Comment: 13 pages, 5 figs, accepted to Phys. Pasma

Irreducible modules over finite simple Lie conformal superalgebras of type K

We construct all finite irreducible modules over Lie conformal superalgebras of type KComment: Accepted for publication in J. Math. Phys