Topological properties of regular generalized function algebras

We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 page

Regulating entanglement production in multitrap Bose-Einstein condensates

A system of traps is considered, each containing a large number of Bose-condensed atoms. This ensemble of traps is subject to the action of an external modulating field generating nonequilibrium nonground-state condensates. When the frequency of the modulating field is in resonance with the transition frequency between two different topological coherent modes, each trap becomes an analog of a finite-level resonant atom. Similarly to the case of atoms in an electromagnetic resonant field, one can create entanglement between atomic traps subject to a common resonant modulating field generating higher coherent modes in each of the traps. A method is suggested for regulating entanglement production in such a system of multitrap and multimode Bose-Einstein condensates coupled through a common resonant modulating field. Several regimes of evolutional entanglement production, regulated by manipulating the external field, are illustrated by numerical calculations.Comment: Latex file, 3 figure

Embeddings of 3-connected 3-regular planar graphs on surfaces of non-negative Euler characteristic

Whitney's theorem states that every 3-connected planar graph is uniquely embeddable on the sphere. On the other hand, it has many inequivalent embeddings on another surface. We shall characterize structures of a $3$-connected $3$-regular planar graph $G$ embedded on the projective-plane, the torus and the Klein bottle, and give a one-to-one correspondence between inequivalent embeddings of $G$ on each surface and some subgraphs of the dual of $G$ embedded on the sphere. These results enable us to give explicit bounds for the number of inequivalent embeddings of $G$ on each surface, and propose effective algorithms for enumerating and counting these embeddings.Comment: 19 pages, 12 figure