The asymptotic expansions (at small and large internuclear distances R) of the eigenvalues (potential curves) E(R) of the two-Coulomb-centre problem are obtained. The Dirac equation with an axially symmetrical potential, not allowing complete separation of variables, is solved analytically by the Wentzel-Kramers-Brillouin approach and boundary-layer method. In the framework of this scheme, the relativistic two-Coulomb-centre wavefunction is constructed. The first two terms of the asymptotic (at large internuclear distance) behaviour of the exchange interaction potential for an ion with an atom are calculated.

The system of remote monitoring of atmosphere is designed to obtain information about the state of atmosphere. The principle of the remote monitoring of atmosphere is based on registering and processing GLONASS/GPS radio signals. Modern networks of active reference stations allow us to solve both practical problems of geodesy, navigation, and purely scientific problems that are important in all geosciences. The paper investigates a spatiotemporal instability in the atmosphere, based on 845 temporal measurements of tropospheric delay over the territory covered by 20 active reference stations of the UA-EUPOS/ZAKPOS network. The method elaborated by the authors for the determination of tropospheric delay in the UA-EUPOS/ZAKPOS network in real time takes relief of the region into account. The results are very good, since mapping tropospheric delay can be made with an average RMSE of 1.5 mm. The method developed in this research can be used to improve the quality of weather forecasts and the prevention of natural disasters.

The problem of interaction of two quasimolecular electrons located at an arbitrary distance from each other and near different atoms (nuclei) is solved. The interaction is considered as a second-order effect of quantum electrodynamics in the coordinate representation. It is shown that consistent account of the natural condition of the interaction symmetry with respect to both electrons leads to the additional contribution to the relativistic interaction of the two quasimolecular electrons compared with both the standard Breit operator and the generalized Breit operator obtained previously [O. N. Gadomskii, Usp. Fiz. Nauk 170, 1145 (2000) [Phys. Usp. 43, 1071 (2000)]]. The generalized Breit-Pauli operator for interaction of two quasimolecular electrons located at an arbitrary distance from each other is obtained.

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