On the Theory of Quantum Oscillations of the Elastic Moduli in Layered Conductors

In this paper we study theoretically how the local geometry of the Fermi surface (FS) of a layered conductor can affect quantum oscillations in the thermodynamic observables. We introduce a concrete model of the FS of a layered conductor. The model permits us to analyze the characteristic features of quantum oscillatory phenomena in these materials which occure due to local anomalies of the Gaussian curvature of the FS. Our analysis takes into account strong interaction among quasiparticles and we study the effect of this interaction within the framework of Fermi-liquid theory. We show that the Fermi-liquid interaction strongly affects the density of states of quasiparticles (DOS) on the FS. As a result DOS can have singularities near the peaks of its oscillations in a strong magnetic field. These singularities can be significantly strengthened when the FS of the layered conductor is locally flattened. This can lead to magnetic and lattice instabilities of a special kind which are considered in the final part of the work.Comment: 11 pages, 2 figures, minor changes in the title are made, published versio

On the central limit theorem for homogeneous discrete-time nonlinear Markov chains

The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are characterized by complex limit behavior and ergodic properties, for which the usual criteria for Markov processes are not sufficient. Being a subclass of nonlinear Markov processes, nonlinear Markov chains have inherited these features. In this paper, conditions for the fulfillment of the central limit theorem for homogeneous nonlinear Markov chains in discrete time and with a discrete finite state space are studied. Also, a brief review of known results on the ergodic properties of nonlinear Markov chains is included. The obtained result complements the existing results in this area and may be useful for further applications in statistics.Comment: in Russian languag

Overgroups of elementary block-diagonal subgroups in even unitary groups over quasi-finite rings

Shchegolev A. Overgroups of elementary block-diagonal subgroups in even unitary groups over quasi-finite rings. Bielefeld: University of Bielefeld; 2015

High-Precision U-Pb Zircon Age Calibration of the Global Carboniferous Time Scale and Milankovitch Band Cyclicity in the Donets Basin, Eastern Ukraine

High-precision ID-TIMS U-Pb zircon ages for 12 interstratified tuffs and tonsteins are used to radiometrically calibrate the detailed lithostratigraphic, cyclostratigraphic, and biostratigraphic framework of the Carboniferous Donets Basin of eastern Europe. Chemical abrasion of zircons, use of the internationally calibrated EARTHTIME mixed U-Pb isotope dilution tracer, and improved mass spectrometry guided by detailed error analysis have resulted in an age resolution o