Diffusive Shock Acceleration of Cosmic Rays -- Quasi-thermal and Non-thermal Particle Distributions

A well-known paradigm about the origin of Galactic cosmic rays (CRs) is that these high-energy particles are accelerated in the process of diffusive shock acceleration (DSA) at collisionless shocks (at least up to the so-called "knee"energy of $10^{15}$ eV). Knowing the details of injection of electrons, protons and heavier nuclei into the DSA, their initial and the resulting spectrum, is extremely important in many "practical" applications of the CR astrophysics, e.g. in modelling of the gamma or synchrotron radio emission of astrophysical sources. In this contribution I we will give an overview of the DSA theory and the results of observations and kinetic Particle-In-Cell (PIC) simulations that support the basic theoretical concepts. PIC simulations of quasi-parallel collisionless shocks show that thermal and supra-thermal proton distribution functions at the shock can be represented by a single quasi-thermal distribution - the $\kappa$-distribution that is commonly observed in out-of-equilibrium space plasmas. Farther downstream, index $\kappa$ increases and the low-energy spectrum tends to Maxwell distribution. On the other hand, higher-energy particles continue through the acceleration process and the non-thermal particle spectrum takes a characteristic power-law form predicted by the linear DSA theory. In the end, I will show what modification of the spectra is expected in the non-linear DSA, when CR back-reaction to the shock is taken into account.Comment: 13 pages, 5 figures, 11th International Conference of the Balkan Physical Union (BPU11), 28 August - 1 September 2022, Belgrade, Serbi

Radial Dependence of Extinction in Parent Galaxies of Supernovae

The problem of extinction is the most important issue to be dealt with in the process of obtaining true absolute magnitudes of core-collapse supernovae (SNe). The plane-parallel model which gives absorption dependent on galaxy inclination, widely used in the past, was shown not to describe extinction adequately. We try to apply an alternative model which introduces radial ependence of extinction. A certain trend of dimmer SNe with decreasing radius from the center of a galaxy was found, for a chosen sample of stripped-envelope SNe.Comment: 4 pages, 1 table, 2 figures, 6th SCSLSA Pro

Croatian Accession to the European Union: Economic and Legal Challenges

This paper analyses the EU tax system and its main components qua conditions for the accession of the Croatia to the European Union as well as the current degree of adjustment of Croatian taxation regulations with the corresponding regulations in the EU. As a result of this analysis, proposals for further procedures on the part of the creators of taxation policy in Croatia are made. After the tax reforms started in the 1990s, after the achievement of independence, the Croatian tax system was comparable with the tax systems of EU member countries. All the essential taxes correspond conceptually to the same kinds of taxes in EU countries. However, there is still space for further adjustment, above all in connection with value added tax, and it is desirable that this should be carried out as soon as possible. However, adjustments in the area of profit tax and adjustments of some rates of excise duties should be put off until the moment when they will have to be done for the sake of joining the Union, because the maintenance of the current situation, which is not in line with the provisions of European regulations, but nevertheless not in contravention of general rules regulating the area of taxation, is in the interests of Croatia. In the area of the taxation of income no adjustment or coordination is needed, for members are allowed to settle the taxation of income in their countries independently, as long as the fundamental principles of the single market are not threatened (the free movement of goods, people, services and capital).European Union, Croatia, taxes, profit tax, income tax, value added tax,excise duties, adjustment, harmonisation