In this article we review recent developments on Morita equivalence of star products and their Picard groups. We point out the relations between noncommutative field theories and deformed vector bundles which give the Morita equivalence bimodules.

We describe how to obtain the imprimitivity bimodules of the noncommutative torus from a “principal bundle” construction, where the total space is a quasi-associative deformation of a 3-dimensional Heisenberg manifold.

By using properties of dualizing parametrization functions, Lagrangian functions and the epigraph technique, some sufficient and necessary conditions of the stable strong duality and strong total duality for a class of DC optimization problems are established.

We define and study a lift of the Boardman-Vogt tensor product of operads to bimodules over operads. Introduction Let Op denote the category of symmetric operads in the monoidal category S of simplicial sets. The Boardman-Vogt tensor product [3] −⊗− : Op× Op→ Op, which endows the category Op with a symmetric monoidal structure, codifies interchanging algebraic structures. For all P,Q ∈ Op, a (P...

A hypergraph F is a set family defined on vertex set V . The dual of F is the set of minimal subsetsH of V such that F∩H 6= ∅ for any F ∈ F . The computation of the dual is equivalent to many problems, such as minimal hitting set enumeration of a subset family, minimal set cover enumeration, and the enumeration of hypergraph transversals. Although many algorithms have been proposed for solving ...

In this first part of a study of ordered operator spaces, we develop the basic theory of 'ordered C*-bimodules'. A crucial role is played by 'open central tripotents', a JB*-triple variant of Akemann's notion of open projection.