Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves

By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.Comment: 31 pages; revise

Topological Radon transforms and degree formulas for dual varieties

First published in Proceedings of the American Mathematical Society in volume136 and number7 2008 published by the American Mathematical Societyjournal articl

Was Martian mantle wet? A possible consequence of rapid core formation

Degassing of H2O in the planetary interior possibly plays an important role in the evolution of surface environment as well as geologic activity on the terrestrial planets. Mars may be such a planet that well preserves the materials and the geologic features directly related to early evolution of H2O. H2O content in the interior of proto-Mars during accretion and also core formation were investigated. Geodetic data shows that Mars has a dense core. The existence of iron-rich core on Mars may be also supported by the depletion of siderophile elements in SNC meteorites assuming that these samples came from Mars. Isotope systematics of these meteorites indicate that the core formation occurred very early, probably concurrently with Mars formation. Considering the kinetics of metal segregation from silicate, the melting of silicate is likely to precede the core formation. Once the core formation occurs, substantial amount of gravitational energy is released and thus the planetary interior is heated. This energy may be large enough to keep the silicate material in partially molten state along with the accretional heating. Under such circumstances, the silicate melt probably migrates to the surface. Early crustal formation, therefore, is also likely to be associated with the core formation