Proper Holomorphic Maps from Domains in ?2 with Transverse Circle Action

The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space, where the domain is of finite type and admits a transverse circle action. The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action.     

Bin packing with divisible item sizes

We study a variety of NP-hard bin packing problems under a divisibility constraint that generalizes the often encountered situation in which all item sizes are powers of 2. For ordinary one-dimensional bin packing, we show that First Fit Decreasing produces optimal packings under this restriction, and that if in addition the largest item size divides the bin capacity, then even the less powerful First Fit algorithm is optimal. Similar results are obtained for two-dimensional bin packing and multiprocessor scheduling, along with several other simple variants. For more complicated problems, like vector packing and dynamic bin packing, the improvement is less substantial, and we indicate why.     

A two-dimensional bin-packing model of preemptive, FIFO storage allocation

An approximation algorithm for an NP-complete problem in dynamic storage allocation is studied. A preemptive regime is assumed. It is shown that in the worst-case the waiting times for FIFO allocation of requests are linear functions of the minimum achievable times.     

Existence and uniqueness results for semi-linear Dirichlet problems in annuli

Communicated by J. Serrin