Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.Comment: 13 page

Reverberation measurement of the inner radius of the dust torus in NGC 4151 during 2008-2013

We investigate the correlation between infrared (JHKL) and optical (B) fluxes of the variable nucleus of the Seyfert galaxy NGC 4151 using partially published data for the last 6 years (2008-2013.). Here we are using the same data as in Oknyansky et al. (2014), but include also optical (B) data from Guo et al. We find that the lag of flux in all the infrared bands is the same, 40 +- 6 days, to within the measurement accuracy. Variability in the J and K bands is not quite simultaneous, perhaps due to the differing contributions of the accretion disk in these bands. The lag found for the K band compared with the B band is not significantly different from earlier values obtained for the period 2000-2007. However, finding approximately the same lags in all IR bands for 2008-2013 differs from previous results at earlier epochs when the lag increased with increasing wavelength. Examples of almost the same lag in different IR bands are known for some other active nuclei. In the case of NGC 4151 it appears that the relative lags between the IR bands may be different in different years. The available data, unfortunately, do not allow us to investigate a possible change in the lags during the test interval. We discuss our results in the framework of the standard model where the variable infrared radiation is mainly due to thermal re-emission from the part of the dusty torus closest to the central source. There is also a contribution of some IR emission from the accretion disk, and this contribution increases with decreasing wavelength. Some cosmological applications of obtained results are discussed.Comment: 3 pages, 2 figures, 14-th Odessa International Astronomical Gamow Conference-School Astronomy and beyond: Astrophysics, Cosmology and Gravitation, Cosmomicrophysics, Radio-astronomy and Astrobiolog

Ground state instability in systems of strongly interacting fermions

We analyze stability of a fermion system with model repulsive pair interaction potential. The possibility for different types of restructuring of the Fermi ground state (at sufficiently great coupling constant) is related to the analytic properties of such potential. In particular, for the screened Coulomb law it is shown that the restructuring cannot be of the Fermi condensation type, known earlier for some exactly solvable models, and instead it belongs to the class of topological transitions (TT). For this model, a phase diagram has been built in the variables "screening parameter - coupling constant" which displays two kinds of TT: a 5/2-kind similar to the known Lifshitz transitions in metals, and a 2-kind characteristic for a uniform strongly interacting system.Comment: The article has 11 pages, in Latex 2e (from Lyx), 3 eps figures or a ps fil

Anomalous asymmetry of magnetoresistance in NbSe3_3 single crystals

A pronounced asymmetry of magnetoresistance with respect to the magnetic field direction is observed for NbSe$_3$ crystals placed in a magnetic field perpendicular to their conducting planes. It is shown that the effect persists in a wide temperature range and manifests itself starting from a certain magnetic induction value $B_0$, which at $T=4.2$ K corresponds to the transition to the quantum limit, i.to the state where the Landay level splitting exceeds the temperature.Comment: 4 pages, 6 figures, to be appeared in JETP Let

Color Effects Associated with the 1999 Microlensing Brightness Peaks in Gravitationally Lensed Quasar Q2237+0305

Photometry of the Q2237+0305gravitational lens in VRI spectral bands with the 1.5-m telescope of the high-altitude Maidanak observatory in 1995-2000 is presented. Monitoring of Q2237+0305 in July-October 2000, made at nearly daily basis, did not reveal rapid (night-to-night and intranight) variations of brightness of the components during this time period. Rather slow changes of magnitudes of the components were observed, such as 0.08 mag fading of B and C components and 0.05 mag brightening of D in R band during July 23 - October 7, 2000. By good luck three nights in 1999 were almost at the time of the strong brightness peak of image C, and approximately in the middle of the ascending slope of the image A brightness peak. The C component was the most blue one in the system in 1998 and 1999, having changed its (V-I) color from 0.56 mag to 0.12 mag since August 1997, while its brightness increased almost 1.2 mag during this time period. The A component behaved similarly between August 1998 and August 2000, having become 0.47 mag brighter in R, and at the same time, 0.15 mag bluer. A correlation between the color variations and variations of magnitudes of the components is demonstrated to be significant and reaches 0.75, with a regression line slope of 0.33. A color (V-I) vrs color (V-R) plot shows the components settled in a cluster, stretched along a line with a slope of 1.31. Both slopes are noticeably smaller than those expected if a standard galactic interstellar reddening law were responsible for the differences between the colors of images and their variations over time. We attribute the brightness and color changes to microlensing of the quasar's structure, which we conclude is more compact at shorter wavelengths, as predicted by most quasar models featuring an energizing central source.Comment: 14 pages, 7 figures, LaTeX, submitted to A&

The complex approach to the geochemical research of oil and organic substance with the purpose of planning of geological exploration work for oil and gas

The article is devoted to the first results obtained for the complex of geochemical studies of the crude oils and organic matter of Vyngayakhinskoye field rocks of the West-Siberian oil and gas province. The main objective of this paper is the determination of the genetic unity of or, on the contrary, in the difference of the crude oil produced at the field, dedicated to the various oil complexes. Authors investigated the correlation between organic matter the breeds and crude oils of various oil-and-gas complexes with a view to identifying areas of generation, directions, and the scope and stages of migration of hydrocarbons. The study, in the future, can be used in the development of recommendations for the planning of geological exploration works on oil and gas, as well as to develop the reserves already discovered oil and gas deposits

Second wind of the Dulong-Petit Law at a quantum critical point

Renewed interest in 3He physics has been stimulated by experimental observation of non-Fermi-liquid behavior of dense 3He films at low temperatures. Abnormal behavior of the specific heat C(T) of two-dimensional liquid 3He is demonstrated in the occurrence of a T-independent term in C(T). To uncover the origin of this phenomenon, we have considered the group velocity of transverse zero sound propagating in a strongly correlated Fermi liquid. For the first time, it is shown that if two-dimensional liquid 3He is located in the vicinity of the quantum critical point associated with a divergent quasiparticle effective mass, the group velocity depends strongly on temperature and vanishes as T is lowered toward zero. The predicted vigorous dependence of the group velocity can be detected in experimental measurements on liquid 3He films. We have demonstrated that the contribution to the specific heat coming from the boson part of the free energy due to the transverse zero-sound mode follows the Dulong-Petit Law. In the case of two-dimensional liquid 3He, the specific heat becomes independent of temperature at some characteristic temperature of a few mK.Comment: 5 pages, 1 figur

Spontaneous breaking of four-fold rotational symmetry in two-dimensional electronic systems explained as a continuous topological transition

The Fermi liquid approach is applied to the problem of spontaneous violation of the four-fold rotational point-group symmetry ($C_4$) in strongly correlated two-dimensional electronic systems on a square lattice. The symmetry breaking is traced to the existence of a topological phase transition. This continuous transition is triggered when the Fermi line, driven by the quasiparticle interactions, reaches the van Hove saddle points, where the group velocity vanishes and the density of states becomes singular. An unconventional Fermi liquid emerges beyond the implicated quantum critical point.Comment: 6 pages, 4 figure

Measurement of the K+→μ+νμγK^+\rightarrow{\mu^+}{\nu_{\mu}}{\gamma} decay form factors in the OKA experiment

A precise measurement of the vector and axial-vector form factors difference $F_V-F_A$ in the $K^+\rightarrow{\mu^+}{\nu_{\mu}}{\gamma}$ decay is presented. About 95K events of $K^+\rightarrow{\mu^+}{\nu_{\mu}}{\gamma}$ are selected in the OKA experiment. The result is $F_V-F_A=0.134\pm0.021(stat)\pm0.027(syst)$. Both errors are smaller than in the previous $F_V-F_A$ measurements.Comment: 9 pages, 8 figure

Cross-Sections of Large-Angle Hadron Production in Proton- and Pion-Nucleus Interactions III: Tantalum Nuclei and Beam Momenta from +/-3 Gev/c to +/-15 Gev/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% nuclear interaction length thick stationary tantalum target, of proton and pion beams with momentum from +/-3 GeV/c to +/-15 GeV/c. Results are given for secondary particles with production angles between 20 and 125 degrees. They are of particular relevance for the optimization of the design parameters of the proton driver of a neutrino factory.Comment: 68 pages, 12 figures, corrections in v2: added 'HARP -CDP group' to author name, corrected two typos in Table 4 (last two p values for 65-90 degrees were all 0.972