Abstract:
High quality spectra to be produced by SUBARU 8 meter telescope will be extremely valuable for numerous astronomical projects. Here I concentrate on two classical types of weak broad line objects -- distant supernovae and white dwarfs -- with emphasis of their importance for fundamental physics, not only for astronomy. With regard to recent results of MACHO experiment and HST weak star counts I discuss one exotic possibility: invisible stars made of the so called ``mirror'' matter.

Abstract:
We point out that confusion sometimes arises when using a chemical potential in plasma with Coulomb interactions. The results of our consideration are applied to the discussion of nuclear reactions screening. Finally, we present a transparent derivation of the thermal conductivity coefficient of a degenerate electron gas.

Abstract:
The propagation of thermonuclear flame in presupernovae Ia is considered. Front parameters are obtained, some speculations on front stability are presented.

Abstract:
Ultraviolet light curves are calculated for several thermonuclear supernova models using a multifrequency radiation hydrodynamic code. It is found that Chandrasekhar-mass models produce very similar light curves both for detonation and deflagration. Sub-Chandrasekhar-mass models essentially differ from ``normal'' Chandrasekhar ones regarding behaviour of their UV fluxes. Differences in absolute brightness and in shape of light curves of thermonuclear supernovae could be detectable up to 300 Mpc with modern UV space telescopes.

Abstract:
A treatment of line opacity in expanding medium is most crucial for the light curve (LC) modeling of Type Ia supernovae (SNe Ia). Spectral lines are the main source of opacity inside SN Ia ejecta from ultraviolet through infrared range. Here we focus on the mean opacity for the energy equation. We solve the Boltzmann equation for photons in the comoving frame for a spherically-symmetrical flow. For rectangle line profiles we find an analytical expression for frequency averaged intensity and absorptive opacity. The results differ from previously known heuristic solutions. The LCs in the I-band are in better agreement with observations.

Abstract:
Motivated by a recent discovery of Supernova 2010gx and numerical results of Fryer et al.(2010), we simulate light curves for several type I supernova models, enshrouded by dense circumstellar shells, or "super-wind", rich in carbon and oxygen and having no hydrogen. We demonstrate that the most luminous events like SN2010gx can be explained by those models at moderate explosion energies (2-3) foe if the total mass of SN ejecta and a shell is (3-5) Msun and the radius of the shell is ~10^{16} cm.

Abstract:
An energy deposition of \sim 10^{50} ergs into the exterior 10^{-3} M_\sun layers of a red giant is calculated to produce an optical phenomenon similar to afterglows of gamma-ray bursts (GRB) recently observed. This model can be realized if a GRB is generated by some mechanism in a close binary system. In contrast to a ``hypernova'' scenario for GRB recently proposed by Paczy\'nski (1997), this model does not require a huge kinetic energy of the expanding shell to explain optical afterglows of GRB.

Abstract:
An expression for the Green function G(E;x_1,x_2) of the Schroedinger equation is obtained through the approximations of the path integral by n-fold multiple integrals. The approximations to Re{G(E;x,x)} on the real E-axis have peaks near the values of the energy levels E_{j}. The analytic and numerical examples for one-dimensional and multi-dimensional harmonic and anharmonic oscillators, and Poeschl-Teller potential wells, show that median values of these peaks for approximate G(E;0,0) corresponds with accuracy of order 10% to the exact values of even levels already in the lowest orders of approximation n=1 and n=2, i.e. when the path integral is replaced by a line or double integral. The weights of the peaks approximate the values of the squared modulus of the wave functions at x=0 with the same accuracy.

Abstract:
A mechanism of creation of stellar-like objects in the very early universe, from the QCD phase transition till BBN and somewhat later, is studied. It is argued that in the considered process primordial black holes with masses above a few solar masses up to super-heavy ones could be created. This may explain an early quasar creation with evolved chemistry in surrounding medium and the low mass cutoff of the observed black holes. It is also shown that dense primordial stars can be created at the considered epoch. Such stars could later become very early supernovae and in particular high redshift gamma-bursters. In a version of the model some of the created objects can consist of antimatter.

Abstract:
We present numerical models for supernova remnant evolution, using a new version of the hydrodynamical code SUPREMNA. We added cosmic ray diffusion equation to the code scheme, employing two-fluid approximation. We investigate the dynamics of the simulated supernova remnants with different values of cosmic ray acceleration efficiency and diffusion coefficient. We compare the numerical models with observational data of Tycho's and SN1006 supernova remnants. We find models which reproduce the observed locations of the blast wave, contact discontinuity, and reverse shock for the both remnants, thus allowing us to estimate the contribution of cosmic ray particles into total pressure and cosmic-ray energy losses in these supernova remnants. We derive that the energy losses due to cosmic rays escape in Tycho's supernova remnant are 10-20% of the kinetic energy flux and 20-50% in SN1006.