The network design problems can be generalized in a natural way by considering a related problem relative to a given partition of the nodes of the graph into node sets (clusters), while the feasibility constraints are expressed in terms of the clusters. Several applications of the generalized network design problems arise in fields of telecommunications, facility and locations, transportation, ...

This is the first of two interconnected parts: Part I contains the geometric theory of generalized modular forms and their connections with the cooperation algebra for elliptic cohomology, E``∗E``, while Part II is devoted to the more algebraic theory associated with Hecke algebras and stable operations in elliptic cohomology. We investigate the structure of the stable operation algebra E``∗E``...

We present a characterization, in terms of torsion-free generalized connections, for the integrability various structures (generalized almost complex structures, hypercomplex Hermitian and hyper-Hermitian structures) defined on Courant algebroids. develop new, self-contained, approach theory Dirac generating operators regular algebroids with scalar product neutral signature. As an application w...

In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK, . These dual extensions are constructed by embedding a given L/K in an inner Galois extension N/K. The Appendix shows that such an embedding can alwa...