Let B be the unit ball in a complex Banach space. Let S _k+1 ^*(B) be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k+1 of f(z)-z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S _k+1 ^*(B).

The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.

The authors study the coincidence theory for pairs of maps from the Torus to the Klein bottle. Reidemeister classes and the Nielsen number are computed, and it is shown that any given pair of maps satisfies the Wecken property. The 1-parameter Wecken property is studied and a partial negative answer is derived. That is for all pairs of coincidence free maps a countable family of pairs of maps in the homotopy class is constructed such that no two members may be joined by a coincidence free homotopy.

The authors prove two global existence results of strong solutions of the isen-tropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.

The authors establish a Cheeger-Müller type theorem for the complex valued analytic torsion introduced by Burghelea and Haller for flat vector bundles carrying nondegenerate symmetric bilinear forms. As a consequence, they prove the Burghelea-Haller conjecture in full generality, which gives an analytic interpretation of (the square of) the Turaev torsion.

Let G : Ω → Ω′ be a closed unital map between commutative, unital quantales. G induces a functor Ḡ from the category of Ω-categories to that of Ω′-categories. This paper is concerned with some basic properties of Ḡ. The main results are: (1) when Ω, Ω′ are integral, G : Ω → Ω′ and F : Ω′ → Ω are closed unital maps, $\bar F$ is a left adjoint of Ḡ if and only if F is a left adjoint of G; (2) Ḡ is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and (3) a sufficient condition is obtained for Ḡ to preserve completeness in the sense that ḠA is a complete Ω′-category whenever A is a complete Ω-category.