Estimation of the Overall Tax Burden on the Economy in Ukraine

The estimation of the tax burden is important, since, on the one hand, its results reflect the tax system efficiency, and, on the other hands, the level of income redistribution in the national economy. The estimation of the general tax burden level on the national economy of Ukraine should be realized through the development of forecast scenarios, based on economic and mathematical modelling. The economists have not yet sufficiently worked out the problems of the predictive assessment of the tax system efficiency through the introduction of a scenario approach, economic-mathematical modelling and extrapolation of dynamics series. It is necessary to evaluate and to develop scenarios for forecasting the level of the overall tax burden on the national economy of Ukraine. The modelling of the influence of GDP dynamics on the volume of tax revenues and a unified social tax is implemented. The method of calculating the level of the overall tax burden on the national economy is proposed. The scenarios for forecasting the total tax burden on the Ukrainian economy have been developed. It is proved that in Ukraine, by the end of 2017, one third of the revenues in the national economy is redistributed through the fiscal system, while in 2004 the tax burden made only a quarter of GDP. Thus, it is established, that over the next 5 years, the overall tax burden on the national economy will increase (growth may range from +0.9 to +4 %)

Application Of Nonlinear Models For A Well-defined Description Of The Dynamics Of Rotors In Magnetic Bearings

A research report has been submitted. It deals with implementing a method for a mathematical description of the nonlinear dynamics of rotors in magnetic bearings of different types (passive and active). The method is based on Lagrange-Maxwell differential equations in a form similar to that of Routh equations in mechanics. The mathematical models account for such nonlinearities as the nonlinear dependencies of magnetic forces on gaps in passive and active magnetic bearings and on currents in the windings of electromagnets; nonlinearities related to the inductances in coils; the geometric link between the electromagnets in one AMB and the link between all AMBs in one rotor, which results in relatedness of processes in orthogonal directions, and other factors. The suggested approach made it possible to detect and investigate different phenomena in nonlinear rotor dynamics. The method adequacy has been confirmed experimentally on a laboratory setup, which is a prototype of a complete combined magnetic-electromagnetic suspension in small-size rotor machinery. Different variants of linearizing the equations of motion have been considered. They provide for both linearization of restoring magnetic or electromagnetic forces in passive and active magnetic bearings, and exclusion of nonlinear motion equation terms. Calculation results for several linearization variants have been obtained. An appraisal of results identified the drawbacks of linearized mathematical models and allowed drawing a conclusion on the necessity of applying nonlinear models for a well-defined description of the dynamics of rotor systems with magnetic bearings

Radiative nonrecoil nuclear finite size corrections of order α(Zα)5\alpha(Z \alpha)^5 to the Lamb shift in light muonic atoms

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $\alpha(Z \alpha)^5$ to the Lamb shift in muonic hydrogen and helium. To construct the interaction potential of particles, which gives the necessary contributions to the energy spectrum, we use the method of projection operators to states with a definite spin. Separate analytic expressions for the contributions of the muon self-energy, the muon vertex operator and the amplitude with spanning photon are obtained. We present also numerical results for these contributions using modern experimental data on the electromagnetic form factors of light nuclei.Comment: 8 pages, 1 Figur

Hyperfine structure of S-states in muonic deuterium

On the basis of quasipotential method in quantum electrodynamics we calculate corrections of order $\alpha^5$ and $\alpha^6$ to hyperfine structure of S-wave energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $\Delta E^{hfs}(1S)=50.2814$ meV (1S state) and $\Delta E^{hfs}(2S)=6.2804$ meV (2S state) represent reliable estimate for a comparison with forthcoming experimental data of CREMA collaboration. The hyperfine structure interval $\Delta_{12}=8\Delta E^{hfs}(2S)-\Delta E^{hfs}(1S)=-0.0379$ meV can be used for precision check of quantum electrodynamics predictions for muonic deterium.Comment: 18 pages, 7 figure

Heavy Quark Fragmentation into Baryons in a Quark-Diquark Model

In the framework of the nonrelativistic QCD and a quark-diquark model of baryons we have obtained the fragmentation functions for heavy quark to split into spin-1/2 and spin-3/2 double heavy baryons. It was predicted the production rates as well as the shape of the energy spectra for the $cc-$ and $bc-$baryons in the region of $Z^o$ peak at LEP collider.Comment: LaTeX, 9 pages, 2 figure

Electrostatic gyroscope drift caused by rotor asphericity

Calculating drift of electrostatic gyroscopes due to rotor asphericit