Abstract:
The cluster M67 (= NGC 2682) in Cancer is a rich stellar cluster, usually classified as an open cluster. Using our own observations with the 0.4 m telescope, we show that M67 is a tight group of about 1200 stars. The actual radius of the cluster is about 3.1 pc and the average mass of a star in the system is about . We also show that the ratio of the mean kinetic energy of the cluster to its mean gravitational potential energy , while the value predicted by the virial theorem is equal to . So the system is a gravitationally bound. This value of is considered as an evidence of quasi-stability of the cluster and allows us to use the Chandrasekhar-Spitzer relaxation time for M67 Myr as a characteristic dynamical relaxation time of the system. As the cluster is almost twice older its half-life time , it is argued that M67 was in the past (about 4 Gyr ago, close to its forma-tion) a relatively small ( stars) globular cluster, but got “open cluster” shape due to the dynamical evapora-tion of the majority of its stars.

Abstract:
The reaction of collective oscillations excited in the interaction between aperiodically growing Jeans-type gravity perturbations and stars of a rapidly rotating disk of flat galaxies is considered. An equation is derived which describes the change in the main body of equilibrium distribution of stars in the framework of the nonresonant weakly nonlinear theory. Certain applications of the theory to the problem of relaxation of the Milky Way at radii where two-body relaxation is not effective are explored. The theory, as applied to the Solar neighborhood, accounts for observed features, such as the shape for the velocity ellipsoid of stars and the increase in star random velocities with age.

Abstract:
Linear theory is used to determine the stability of the self-gravitating, rapidly (and nonuniformly) rotating, two-dimensional, and collisional particulate disk against small-amplitude gravity perturbations. A gas-kinetic theory approach is used by exploring the combined system of the Boltzmann and the Poisson equations. The effects of physical collisions between particles are taken into account by using in the Boltzmann kinetic equation a Krook model integral of collisions modified to allow collisions to be inelastic. It is shown that as a direct result of the classical Jeans instability and a secular dissipative-type instability of small-amplitude gravity disturbances (e.g. those produced by a spontaneous perturbation and/or a companion system) the disk is subdivided into numerous irregular ringlets, with size and spacing of the order of the Jeans length (= (4-6) mean epicyclic radius). The present research is aimed above all at explaining the origin of various structures in highly flattened, rapidly rotating systems of mutually gravitating particles. In particular, it is suggested that forthcoming Cassini spacecraft high-resolution images may reveal this kind of hyperfine of the order of 100 m structure in the main rings A, B, and C of the Saturnian ring system.

Abstract:
An improved linear stability theory of small-amplitude oscillations of a self-gravitating, infinitesimally thin gaseous disk of spiral galaxies has been developed. It was shown that in the differentially rotating disks for nonaxisymmetric perturbations Toomre's modified hydrodynamical simulations to test the validity of the modified local criterion.

Abstract:
The time evolution of models for an isolated disk of highly flattened galaxies of stars is investigated by direct integration of the Newtonian equations of motion of N=30,000 identical stars over a time span of many galactic rotations. Certain astronomical implications of the simulations to actual disk-shaped (i.e. rapidly rotating) galaxies are explored as well.

Abstract:
The kinetic theory is used to study the evolution of the self-gravitating disk of planetesimals. The effects of frequent collisions between planetesimals are taken into account by using a Krook integral in the Boltzmann kinetic equation. It is shown that as a result of an aperiodic collision-dissipative instability of small gravity disturbances the disk is subdivided into numerous dense fragments. These can eventually condense into the planetary sequence.

Abstract:
The time evolution of initially balanced, rapidly rotating models for an isolated disk of highly flattened galaxies of stars is calculated. The method of direct integration of the Newtonian equations of motion of stars over a time span of many galactic rotations is applied. Use of modern concurrent supercomputers has enabled us to make long simulation runs using a sufficiently large number of particles N=30,000. One of the goals of the present simulation is to test the validities of a modified local criterion for stability of Jeans-type gravity perturbations (e.g. those produced by a barlike structure, a spontaneous perturbation and/or a companion galaxy) in a self-gravitating, infinitesimally thin and collisionless disk. In addition to the local criterion we are interested in how model particles diffuse in velocity. This is of considerable interest in the kinetic theory of stellar disks. Certain astronomical implications of the simulations to actual disk-shaped (i.e. rapidly rotating) galaxies are explored. The weakly nonlinear, or quasi-linear kinetic theory of the Jeans instability in disk galaxies of stars is described as well.

Abstract:
Motivated by the previously reported high orbital decay rate of the planet WASP-43b, eight newly transit light curves are obtained and presented. Together with other data in literature, we perform a self-consistent timing analysis with data covering a timescale of 1849 epochs. The results give an orbital decay rate dP/dt = -0.02890795\pm 0.00772547 sec/year, which is one order smaller than previous values. This slow decay rate corresponds to a normally assumed theoretical value of stellar tidal dissipation factor. In addition, through the frequency analysis, the transit timing variations presented here are unlikely to be periodic, but could be signals of a slow orbital decay.

Abstract:
It is widely believed that electron dynamics in the shock front is essentially collisionless and determined by the quasistationary magnetic and electric fields in the shock. In thick shocks the electron motion is adiabatic: the magnetic moment is conserved throughout the shock and v2^ ∝ B. In very thin shocks with large cross-shock potential (the last feature is typical for shocks with strong electron heating), electrons may become demagnetized (the magnetic moment is no longer conserved) and their motion may become nonadiabatic. We consider the case of substantial demagnetization in the shock profile with the small-scale internal structure. The dependence of electron dynamics and downstream distributions on the angle between the shock normal and upstream magnetic field and on the upstream electron temperature is analyzed. We show that demagnetization becomes significantly stronger with the increase of obliquity (decrease of the angle) which is related to the more substantial influence of the inhomogeneous parallel electric field. We also show that the demagnetization is stronger for lower upstream electron temperatures and becomes less noticeable for higher temperatures, in agreement with observations. We also show that demagnetization results, in general, in non-gyrotropic down-stream distributions. Key words. Interplanetary physics (interplanetary shocks; planetary bow shocks)

Abstract:
Application of the computer image analysis for improving microbial viability assessment by plate count and fluorescence microscopy was investigated. Yeast cells were used as a model microorganism. The application of the improved methods for the viability assessment of yeast cells after preservation by freezing and freeze-drying was demonstrated.