Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes

This paper is the first in a series of three, the aim of which is to lay the foundations of algebraic geometry over the free metabelian Lie algebra $F$. In the current paper we introduce the notion of a metabelian Lie $U$-algebra and establish connections between metabelian Lie $U$-algebras and special matrix Lie algebras. We define the $\Delta$-localisation of a metabelian Lie $U$-algebra $A$ and the direct module extension of the Fitting's radical of $A$ and show that these algebras lie in the universal closure of $A$.Comment: 34 page

Muons with E_th >= 1 Gev and Mass Composition in the Energy Range 10^{18}-10^{20} ev Observed by Yakutsk Eas Array

The ratio of the muon flux density to charged particle flux density at distances of 300 and 600 m from the shower axis (\rhom(300)/\rhos(300) and \rhom(600)/\rhos(600)) is measured. In addition, the energy dependence of \rhom(1000) is analysed for showers with energies above $10^{18}$ eV. A comparison between the experimental data and calculations performed with the QGSJET model is given for the cases of primary proton, iron nucleus and gamma- ray. We conclude that the showers with \E\ge3\times10^{18} eV can be formed by light nuclei with a pronounced fraction of protons and helium nuclei. It is not excluded however that a small part of showers with energies above $10^{19}$ eV could be initiated by primary gamma-rays.Comment: 19th European Cosmic Ray Symposium, Aug 30 - Sep 3 2004, Florence, Italy. 3 pages, 1 figure. Submitted for publication in International Journal of Modern Physics

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

Magnetoresistance of Highly Correlated Electron Liquid

The behavior in magnetic fields of a highly correlated electron liquid approaching the fermion condensation quantum phase transition from the disordered phase is considered. We show that at sufficiently high temperatures $T\geq T^*(x)$ the effective mass starts to depend on $T$, $M^*\propto T^{-1/2}$. This $T^{-1/2}$ dependence of the effective mass at elevated temperatures leads to the non-Fermi liquid behavior of the resistivity, $\rho(T)\propto T$ and at higher temperatures $\rho(T)\propto T^{3/2}$. The application of a magnetic field $B$ restores the common $T^2$ behavior of the resistivity. The effective mass depends on the magnetic field, $M^*(B)\propto B^{-2/3}$, being approximately independent of the temperature at $T\leq T^*(B)\propto B^{4/3}$. At $T\geq T^*(B)$, the $T^{-1/2}$ dependence of the effective mass is re-established. We demonstrate that this $B-T$ phase diagram has a strong impact on the magnetoresistance (MR) of the highly correlated electron liquid. The MR as a function of the temperature exhibits a transition from the negative values of MR at $T\to 0$ to the positive values at $T\propto B^{4/3}$. Thus, at $T\geq T^*(B)$, MR as a function of the temperature possesses a node at $T\propto B^{4/3}$.Comment: 7 pages, revtex, no figure

Theory of high-T_c superconductivity based on the fermion-condensation quantum phase transition

A theory of high temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap which can be as big as $\Delta_1\sim 0.1\epsilon_F$, with $\epsilon_F$ being the Fermi level. We show that the critical temperature $2T_c\simeq\Delta_1$. If there exists the pseudogap above $T_c$ then $2T^*\simeq\Delta_1$, and $T^*$ is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at $T_c$ is calculated. The transition from conventional superconductors to high-$T_c$ ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered.Comment: 6 pages, Revte

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

Hall coefficient in heavy fermion metals

Experimental studies of the antiferromagnetic (AF) heavy fermion metal $\rm YbRh_2Si_2$ in a magnetic field $B$ indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at $B\geq B_{c0}$ and induces the jump even though the change of the magnetic field at $B=B_{c0}$ is infinitesimal. We investigate this by using the model of heavy electron liquid with the fermion condensate. Within this model the jump takes place when the magnetic field reaches the critical value $B_{c0}$ at which the ordering temperature $T_N(B=B_{c0})$ of the AF transition vanishes. We show that at $B\to B_{c0}$, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At $T\to0$ and $B=B_{c0}$, the Gr\"uneisen ratio as a function of temperature $T$ diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy $S(T)\propto S_0+a\sqrt{T}+bT$ with $S_0$, $a$ and $b$ are temperature independent constants.Comment: 5 pages, 2 figure

K^+ -> pi^+pi^0e^+e^-: a novel short-distance probe

We study the decay K^+ -> pi^+ pi^0 e^+ e^-, currently under analysis by the NA62 Collaboration at CERN. In particular, we provide a detailed analysis of the Dalitz plot for the long-distance, gamma^*-mediated, contributions (Bremsstrahlung, direct emission and its interference). We also examine a set of asymmetries to isolate genuine short-distance effects. While we show that charge asymmetries are not required to test short distances, they provide the best environment for its detection. This constitutes by itself a strong motivation for NA62 to study K^- decays in the future. We therefore provide a detailed study of different charge asymmetries and the corresponding estimated signals. Whenever possible, we make contact with the related processes K^+ -> pi^+ pi^0 gamma and K_L -> pi^+ pi^- e^+ e^- and discuss the advantages of K^+ -> pi^+ pi^0 e^+ e^- over them.Comment: 25 pages, 6 figure

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&