An exact self-similar solution for an expanding ball of radiation

We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The matter satisfies the usual energy and thermodynamic conditions. The energy density and temperature are related by the Stefan-Boltzmann law. The solution admits a homothetic Killing vector in $5D$, which induces the existence of self-similar symmetry in 4D, where the line element as well as the dimensionless matter quantities are invariant under a simple "scaling" group.Comment: New version expanded and improved. To appear in Int. J. Mod. Phys.

On the notion of «quality culture» in relation to higher Professional pedagogical education

Приведена позиция автора в отношении понятий «качество высшего профессионально-педагогического образования», «культура качества высшего профессионально-педагогического образования»«Quality of education» and «culture of quality» are considered in relation to the training of teachers of vocational educatio

Evaluatsiya result of engineering training of teachers of vocational training

“Evaluation of the result of engineering training”, “quality assurance” and “culture of quality” are considered in relation to the training of teachers of vocational educationПриведена позиция автора относительно понятий «эвалюация результата инженерной подготовки», «культура качества» и «гарантии качества» применительно к высшему профессионально-педагогическому образовани

ABOUT STANDARDS AND RECOMMENDATIONS ENQA (ESG 2015) IN VOCATIONAL PEDAGOGICAL EDUCATION

Автором статьи стандарты и рекомендации для гарантии качества в Европейском пространстве высшего образования рассмотрены в контексте отечественной системы подготовки педагогов профессионального обученияIn the article European standards and guidelines (ESG) the European Association for Quality Assurance in Higher Education (ENQA) are considered in relation to the training of teachers of vocational educatio

The Non-Relativistic Evolution of GRBs 980703 and 970508: Beaming-Independent Calorimetry

We use the Sedov-Taylor self-similar solution to model the radio emission from the gamma-ray bursts (GRBs) 980703 and 970508, when the blastwave has decelerated to non-relativistic velocities. This approach allows us to infer the energy independent of jet collimation. We find that for GRB 980703 the kinetic energy at the time of the transition to non-relativistic evolution, t_NR ~ 40 d, is E_ST ~ (1-6)e51 erg. For GRB 970508 we find E_ST ~ 3e51 erg at t_NR ~ 100 d, nearly an order of magnitude higher than the energy derived in Frail, Waxman and Kulkarni (2000). This is due primarily to revised cosmological parameters and partly to the maximum likelihood fit we use here. Taking into account radiative losses prior to t_NR, the inferred energies agree well with those derived from the early, relativistic evolution of the afterglow. Thus, the analysis presented here provides a robust, geometry-independent confirmation that the energy scale of cosmological GRBs is about 5e51 erg, and additionally shows that the central engine in these two bursts did not produce a significant amount of energy in mildly relativistic ejecta at late time. Furthermore, a comparison to the prompt energy release reveals a wide dispersion in the gamma-ray efficiency, strengthening our growing understanding that E_gamma is a not a reliable proxy for the total energy.Comment: Submitted to ApJ; 13 pages, 6 figures, 1 table; high-resolution figures can be found at: http://www.astro.caltech.edu/~ejb/NR