Maps preserving the spectrum of certain products of operators

Let H be a complex Hilbert space, B(H) and S(H) be the spaces of all bounded operators and all self-adjoint operators on H, respectively. We give the concrete forms of the maps on B(H) and also S(H) which preserve the spectrum of certain products of operators.Comment: 11 page

Operators on Weak Hypervector Spaces

Let X and Y be weak hypervector spaces and Lw (X,Y ) be the set of all weak linear operators from X into Y . We prove some algebraic properties of Lw (X,Y )

On the Narumi-Katayama Index of Composite Graphs

The Narumi-Katayama index of a graph G, denoted by N K(G), is equal to the product of degrees of vertices of G. In this paper we investigate its behavior under several binary operations on graphs. We present explicit formulas for its values for composite graphs in terms of its values for operands and some auxiliary invariants. We demonstrate applications of our results to several chemically relevant classes of graphs and show how the Narumi-Katayama index can be used as a measure of graph irregularity. (doi: 10.5562/cca2329

Chaotic biogeography algorithm for size and shape optimization of truss structures with frequency constraints

Size and shape optimization of truss structures with natural frequency constraints is inherently nonlinear dynamic optimization problem with  several local optima. Therefore theoptimization method should be sagacious enough to avoid being trapped in local optima and in this way to reduce premature convergence. To address this problem, we develop a Chaotic Biogeography-Based Optimization (CBBO) algorithm which combines the chaos theory and the biogeography-based optimization (BBO) to achieve an ecient optimization method. In this method, new chaotic migration and mutation operators are proposed to enhance the exploration ability of BBO. The performance of the method is demonstrated through five benchmark design examples with size and shape variables associated by multiply frequency constraints. The results show the eciency and robustness of proposed method and in most cases, CBBO finds a relatively lighter structural weight than those previously reported results in the literature