L2-cohomology of negatively curved Kaehler manifolds of finite volume

We compute the space of $L^2$ harmonic forms (outside the middle degrees) on negatively curved Kaehler manifolds of finite volume

Partial Averaging Near a Resonance in Planetary Dynamics

Following the general numerical analysis of Melita and Woolfson (1996), I showed in a recent paper that a restricted, planar, circular planetary system consisting of Sun, Jupiter and Saturn would be captured in a near (2:1) resonance when one would allow for frictional dissipation due to interplanetary medium (Haghighipour, 1998). In order to analytically explain this resonance phenomenon, the method of partial averaging near a resonance was utilized and the dynamics of the first-order partially averaged system at resonance was studied. Although in this manner, the finding that resonance lock occurs for all initial relative positions of Jupiter and Saturn was confirmed, the first-order partially averaged system at resonance did not provide a complete picture of the evolutionary dynamics of the system and the similarity between the dynamical behavior of the averaged system and the main planetary system held only for short time intervals. To overcome these limitations, the method of partial averaging near a resonance is extended to the second order of perturbation in this paper and a complete picture of dynamical behavior of the system at resonance is presented. I show in this study that the dynamics of the second-order partially averaged system at resonance resembles the dynamical evolution of the main system during the resonance lock in general, and I present analytical explanations for the evolution of the orbital elements of the main system while captured in resonance.Comment: Plain TeX, 21 Pages, 6 Figures, Submitted to Celest.Mech.Dynamic.Astr

On the Growth of Dust Particles in a Non-Uniform Solar Nebula

A summary of the results of a numerical study of the growth of solid particles in the vicinity of an azimuthally symmetric density enhancement of a protostellar disk are presented. The effects of gas drag and pressure gradients on the rate of growth of dust particles and their settling on the midplane of the nebula are also discussed.Comment: 4 pages, 2 figures, in the proceedings of "The Search For Other Worlds." The 14th Annual October Astrophysics Conference in Maryland. Eds. D. Deming and S. Hol