To the fauna of some groups of superfamily Cucujoidea (Coleoptera) of forest-steppe of Middle Volga Region. Communication 1. The families Erotylidae, Endomychidae and Coccinellidae

Data about the fauna, ecology and distribution of species of the families Erotylidae, Endomychidae and Coccinellidae in the Middle Volga Region are presente

Spectral extension of the quantum group cotangent bundle

The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators -- the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SLq(n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. Relation between the two operators is given by a modular functional equation for Riemann theta function.Comment: 38 pages, no figure

On subspecific structure of Patrobus septentrionis Dejean, 1828 (Coleoptera: Carabidae)

Some aspects of the subspecific structure of Patrobus septentrionis Dejean, 1828 are analyzed, the subspecific status of Patrobus septentrionis australis Sahlberg, 1873, subsp. resurr. is resurrected, new subspecies, P. septentrionis volgensis Zamotajlov et Isaev subsp. n. (the Middle Volga region) and P. septentrionis sajanus Zamotajlov subsp. n. (mountains of South Siberia), are described