Polyhedral representations of discrete differential manifolds

Any discrete differential manifold $M$ (finite set endowed with an algebraic differential calculus) can be represented by appropriate polyhedron ${\cal P}(M)$. This representation demonstrates the adequacy of the calculus of discrete differential manifolds and links this approach with that based on finitary substitutes of continuous spaces introduced by R.D.Sorkin.Comment: LaTeX, 35 Kb, submitted to JM

Local Axisymmetric Instability Criterion in the Thin, Rotating, Multicomponent Disk

Purely gravitational perturbations are considered in a thin rotating disk composed of several gas and stellar components. The dispersion relation for the axisymmetric density waves propagating through the disk is found and the criterion for the local axisymmetric stability of the whole system is formulated. In the appropriate limit of two-component gas we confirm the findings of Jog & Solomon (1984) and extend consideration to the case when one component is collisionless. Gravitational stability of the Galactic disk in the Solar neighborhood based on the multicomponent instability condition is explored using recent measurements of the stellar composition and kinematics in the local Galactic disk obtained by Hipparcos satellite.Comment: 8 pages, 5 figures, 1 table, to be submitted to MNRA