The usual quantizer based on an n-dimensional lattice Λ maps a point x ∈ Rn to a closest lattice point. Suppose Λ is the intersection of lattices Λ1, . . . ,Λr. Then one may instead combine the information obtained by simultaneously quantizing x with respect to each of the Λi. This corresponds to decomposing Rn into a honeycomb of cells which are the intersections of the Voronoi cells for the Λ...

We discuss the worldvolume description of intersecting D-branes, including the metric on the moduli space of deformations. We impose a choice of static gauge that treats all the branes on an equal footing and describes the intersection of D-branes as an embedded special Lagrangian three-surface. Some explicit solutions to these equations are given and their interpretation in terms of a superpot...

Suppose mu and v are arcs whose union is an arc alpha and whose intersection is an arc beta. Suppose further that mu and v, respectively, lie in the boundaries of the disks M and N. It is shown that either alpha lies on the boundary of a disk or mu and v, respectively, lie in the boundaries of disks M' and N' which meet only in the arc beta. The construction is basic to recent results exploring...