We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S. Zakrzewski classification correspond to twisted deformations of Abelian and Jordanian types
. A part of twists corresponding to the r-matrices of Zakrzewski classification are given in explicit form.
Cosmic ray propagation is diffusive because of pitch angle scattering by waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence with $tilde B/langle Brangle sim 1$ is present on top of the mean field gradient, the diffusion becomes asymmetric. As an example, we consider the vertical transport of cosmic rays in our Galaxy propagating away from a point-like source. We solve this diffusion problem analytically using a one-dimensional Markov chain analysis. We obtained that the cosmic ray density markedly differs from the standard diffusion prediction and has a sizable effect on their distribution throughout the galaxy. The equation for the continuous limit is also derived, which shows limitations of the convection-diffusion equation.
We suggest and verify a new photometric method enabling derivation of relative thickness of a galactic disk from two-dimensional surface-brightness distribution of the galaxy in the plane of the sky. The method is applied to images of 45 early-type (S0-Sb) galaxies with known radial exponential or double-exponential (with a flatter outer profile) surface-brightness distributions. The data in the r-band have been retrieved from the SDSS archive. Statistics of the estimated relative thicknesses of the stellar disks of early-type disk galaxies shows the following features. The disks of lenticular and early-type spiral galaxies have similar thicknesses. The presence of a bar results in only a slight marginal increase of the thickness. However, we have found a substantial difference between the thicknesses of the disks with a single-scaled exponential brightness profile and the disks that represent the inner segments of the Type III (antitruncated) profiles. The disks are significantly thicker in the former subsample than in the latter one. This may provide evidence for a surface-brightness distribution of a single-scaled exponential disk to be formed due to viscosity effects acting over the entire period of star formation in the disk.
We present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for multipoint potentials in two and three dimensions. For single point potentials in 3D such formulas were obtained in an old unpublished work of L.D. Faddeev. For single point potentials in 2D such formulas were given recently by the authors in arXiv:1110.3157 .
By means of panoramic spectroscopy at the SAO RAS BTA telescope, we investigated the properties of stellar populations in the central regions of five early-type galaxies -- the NGC 524 group members. The evolution of the central regions of galaxies looks synchronized: the average age of stars in the bulges of all the five galaxies lies in the range of 3--6 Gyr. Four of the five galaxies revealed synchronized bursts of star formation in the nuclei 1--2 Gyr ago. The only galaxy, in which the ages of stellar population in the nucleus and in the bulge coincide (i.e. the nuclear burst of star formation did not take place) is NGC 502, the farthest from the center of the group of all the galaxies studied.
Members of the NGC 524 group of galaxies are studied using data obtained on the 6m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences, with the SCORPIO reducer in an imaging mode. Surface photometry has been carried out and parameters of the large-scale galactic components - disks and bulges - have been determined for the six largest galaxies of the group. A lower than expected percentage of bars and high percentage of ring structures were found. Integrated B-V colours for a hundred of dwarf galaxies in the vicinity (within 30 kpc) of the six largest galaxies of the group have been measured. A considerable number of blue irregular galaxies with ongoing star formation is found among dwarf satellites of the lenticular galaxies of the group. The luminosity function for the dwarf galaxies of the group suggests that the total mass of the group is not very high, and that the X-ray emitting gas observed around NGC 524 relates to the central galaxy and not to the group as a whole.
To estimate influence of the dark energy on the Keplerian orbits, we solve the general relativistic equations of motion of a test particle in the field of a point-like mass embedded in the cosmological background formed by the Lambda-term with realistic cosmological Robertson-Walker asymptotics at infinity. It is found that under certain relations between three crucial parameters of the problem--the initial radius of the orbit, Schwarzschild and de Sitter radii--the specific secular perturbation caused by the Lambda-term becomes significant, i.e. can reach the rate of the standard Hubble flow. This fact is interesting both by itself and may have important consequences for the long-term dynamics of planets and stellar binary systems.
By studying the stellar population properties along the radius in 15 nearby S0 galaxies, I have found that the outer stellar disks are mostly old, with the SSP-equivalent ages of 8-15 Gyr, being often older than the bulges. This fact puts into doubt a currently accepted paradigm that S0 galaxies have formed at z=0.4 by quenching star formation in spiral galaxies.
The results of photometric decomposition of surface brightness distributions in 85 early-type unbarred galaxies are presented. The SDSS r-images are analysed. Double-tiered exponential disks are found in all galaxies which are studied; the statistics of the disk parameters is derived.
We discussed twisted quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S.Zakrzewski classification can be presented as a sum of subordinated r-matrices of Abelian and Jordanian types. Corresponding twists describing quantum deformations are obtained in explicit form. This work is an extended version of the paper url{arXiv:0704.0081v1 [math.QA]}.
