Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered {\pi}-ton contribution to optical conductivity, and quite generically constitute dominant vertex corrections in low-dimensional correlated electron systems. Here we study arguably simplest version of these $\pi$-tons based on semi-analytical random phase approximation (RPA) ladder transversal...

The complete subtree (CS) method is widely accepted for the broadcast encryption. A new method for assigning keys in the CS method is proposed in this paper. The essential idea behind the proposed method is to use two trapdoor permutations. Using the trapdoor information, the key management center computes and assigns a key to each terminal so that the terminal can derive all information necess...

Let P1, P2 be graph properties. A vertex (P1,P2)-partition of a graph G is a partition {V1, V2} of V (G) such that for i = 1, 2 the induced subgraph G[Vi] has the property Pi. A property R = P1◦P2 is defined to be the set of all graphs having a vertex (P1,P2)-partition. A graph G ∈ P1◦P2 is said to be uniquely (P1,P2)-partitionable if G has exactly one vertex (P1,P2)-partition. In this note, we...

In this paper, we always assume that H is an N-dimensional complex Hilbert space. Let L(H) be the set of all linear operators from H to H . A state ρ of some quantum system, described by H , is a positive semi-definite operator of trace one, in particular, for each unit vector |ψ〉 ∈ H , the operator ρ = |ψ〉〈ψ| is said to be a pure state. The set of all states onH is denoted by D(H). If X,Y ∈ L(...