Approximate joint block diagonalization (AJBD) of a set of matrices has applications in blind source separation, e.g., when the signal mixtures contain mutually independent subspaces of dimension higher than one. The main message of this paper is that certain ordinary approximate joint diagonalization (AJD) methods (which were originally derived for degenerate" subspaces of dimension 1) can als...

A simple and accurate method to determine the pitch of a cholesteric substance is the observation of disclination lines in a Grandjean-Cano-wedge [1—3] . However, from the position of these lines nothing can be said about the sense of rotation of the cholesteric helix. The determination of the sense is often made by either an additional experiment [4] or by a special construction of the wedge a...

Topological indices are empirical features of graphs that characterize the topology graph and, for most part, independent. An important branch theory is chemical theory. In theory, atoms corresponds vertices and edges covalent bonds. A topological index a numeric number represents underline structure. this article, we examined properties prism octahedron network dimension <math xmlns="http://ww...

The metal halide ionic octahedron, [MX6] (M = cation, X anion), is considered to be the fundamental building block and functional unit of perovskites. By representing octahedron in perovskites as a super ion/atom, perovskite can described an extended network (ION) charge balanced by selected cations. This new perspective based on ION enables prediction different packing connectivity octahedra s...

In this paper, we show that every 4-connected maximal plane graph with m finite faces other than the octahedron can be drawn in the plane so that at least (m+3)/2 faces are acute triangles. Moreover, this bound is sharp. © 2005 Published by Elsevier B.V.