We show that regular Bethe ansatz eigenvectors of the XXZ spin chain at roots of unityare highest weight vectors and generate irreducible representations of the sl2 loop algebra.Here the parameter q, which is related to the XXZ anisotropy ∆ through ∆ = (q+q−1)/2,is given by a root of unity, q2N = 1, for an integer N . First, for a regular Bethe stateat a root of unity, we sh...

The second reference state of the open XXZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz. In the quasi-classical limit, two sets of Bethe states give the complete eigenstates of the associated Gaudin model. PACS: 03.65.Fd; 04.20.Jb; 05.30.-d; 75.10.Jm

methanolic extracts of five native species of salvia from the labiatae family were evaluated for antioxidant activity in low-erucic acid rapeseed oil using the schaal oven test at 60°c, with deterioration monitored by determination of peroxide value, conjugated diene content and p-anisidine value. the activity of the salvia extracts was compared with that of tbhq, ascorbyl palmitate, and extrac...

It has recently been observed that the permanent of a non-negative matrix, i.e., of a matrix containing only nonnegative real entries, can very well be approximated by solving a certain Bethe free energy minimization problem with the help of the sum-product algorithm. We call the resulting approximation of the permanent the Bethe permanent. In this paper we give reasons why this approach to app...

. Note that there are three terms in the expression, one for each edge, one for each factor node, and one for each variable node in the factor graph. The following claim justifies the study of Bethe free energy. Claim 1. For any factor graph, the stationary points of the Bethe free energy correspond to the fixed points of the Belief Propagation algorithm and vice versa. That is, ∂GB ∂ν = 0 if a...

The recreational use of Salvia divinorum has received increased attention by media outlets and policy-makers in recent years. The vast absence of research to guide the dissemination of information has prompted this research note describing the use of this substance in a large public institution of higher education. The prevalence of Salvia divinorum is described in this context and a descriptio...