In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.

Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

in this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

In this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

Abstract We study the structure and compute stable rank of $C^{*}$ -algebras finite higher-rank graphs. completely determine -algebra when $k$ -graph either contains no cycle with an entrance or is cofinal. also exactly which finite, locally convex -graphs yield unital stably -algebras. give several examples to illustrate our results.

The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...