We describe a new modular method for the calculation of wave propagation in stratified media based on the direct use of reflection and transmission coefficients. Within this reflection from the left, transmission, and reflection from the right (LTR) method we define addition and multiplication operators that enable the theoretical construction of any multilayered structures from substructures. ...

There are infinitely many hyperbolic transforms of complex abelian surfaces. The corresponding universal covers change from the complex plane to the unit ball, from flat to hyperbolic metrics. Looking back to Jacobi’s periodic functions we were able to construct 2-dimensional abelian functions transformable to automorphic forms on the ball. In this article we prove explicit dimension formulas f...

For pure gravity in AdS3, Witten has given a recipe for the construction of holomorphically factorizable partition functions of pure gravity theories with central charge c = 24k. The partition function was found to be a polynomial in the modular invariant j-function. We show that the partition function can be obtained instead as a modular sum which has a more physical interpretation as a sum ov...

Modular approaches to design and use of ontologies are essential to the success of the Semantic web enterprise. We describe P-OWL (Package-based OWL) which extends OWL, a widely used ontology language that supports modular design, adaptation, use, and reuse of ontologies. P-OWL localizes the semantics of entities and relationships in OWL to modules called packages. P-OWL and the associated tool...

If L is a finite lattice, we show that there is a natural topological lattice structure on the geometric realization of its order complex ∆(L) (definition recalled below). Lattice-theoretically, the resulting object is a subdirect product of copies of L. We note properties of this construction and of some variants, and pose several questions. For M3 the 5-element nondistributive modular lattice...