Slope inequalities for irregular cyclic covering fibrations

Let $f:S\to B$ be a finite cyclic covering fibration of a fibered surface. We study the lower bound of slope $\lambda_{f}$ when the relative irregularity $q_{f}$ is positive.Comment: 24page

The Simulation of the Inelastic Impact

The coefficient of normal restitution (COR) in an oblique impact is theoretically studied. Using a two-dimensional lattice models for an elastic disk and an elastic wall, we investigate the dependency of COR on an incident angle and demonstrate that COR can exceed one and have a peak against an incident angle in our simulation. Finally, we explain these phenomena based upon the phenomenological theory of elasticity.Comment: 2 pages, 3 figures, submitted as the proceedings of the international conference on slow dynamics in complex systems(Sendai, Nov.3-8, 2003