Long-term changes in the numbers of the barbastelle Barbastella barbastellus in Poland
A b s t r a c t . In order to identify population trends in Barbastella barbastellus in Poland we summarised results of long-term winter bat counts conducted between 1985 and 2004 in seven of the most important hibernacula of the species. The results show an upward trend in four of the sites while in the remaining four no trend was found. The numbers of barbastelles in Poland seem stable or even increasing. In Central Europe the species is not threatened as seriously as it is in Western Europe.
We study multiple orthogonal polynomials of Meixner-Pollaczek type with respect to a symmetric system of two orthogonality measures. Our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem. We also provide a Rodrigues formula and closed expressions for the recurrence coefficients. The proof of the main result follows from a connection with the eigenvalues of block Toeplitz matrices, for which we provide some general results of independent interest. ::: The motivation for this paper is the study of a model in statistical mechanics, the so-called six-vertex model with domain wall boundary conditions, in a particular regime known as the free fermion line. We show how the multiple Meixner-Pollaczek polynomials arise in an inhomogeneous version of this model.