The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on $S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small, the pericenter shift is computed using the perturbation theory. We also present the results of the numerical analysis based on the analogy with the motion of rigid body.Comment: 29 pages, 7 figure

Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D Cosmological Models

A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat capacities in equilibrium. Furthermore, by using the method of Chapman and Enskog for a kinetic model of the Boltzmann equation the non-equilibrium energy-momentum tensor and the entropy production rate are determined for a universe described by a two-dimensional Robertson-Walker metric. The solutions of the gravitational field equations that consider the non-equilibrium energy-momentum tensor - associated with the coefficient of bulk viscosity - show that opposed to the four-dimensional case, the cosmic scale factor attains a maximum value at a finite time decreasing to a "big crunch" and that there exists a solution of the gravitational field equations corresponding to a "false vacuum". The evolution of the fields of pressure, energy density and entropy production rate with the time is also discussed.Comment: 23 pages, accepted in PR

Detectors of charged particles and low-energy gamma-quanta on the basis of Ticor single crystals

Scintillation characteristics have been studied for detectors of charged particles and low-energy gamma-quanta produced on the basis of Ticor single crystals.У роботі представлені результати досліджень сцинтиляційних характеристик детекторів заряджених часток і низькоенергетичних гамма-квантів на основі кристалів тікору.В работе представлены результаты исследований сцинтилляционных характеристик детекторов заряженных частиц и низкоэнергетических гамма-квантов на основе кристаллов тикора

Effective Functional Form of Regge Trajectories

We present theoretical arguments and strong phenomenological evidence that hadronic Regge trajectories are essentially nonlinear and can be well approximated, for phenomenological purposes, by a specific square-root form.Comment: 29 pages, LaTeX. Published versio

Use of agroecological soil monitoring data in designing adaptive landscape farming systems

The article analyzes the experience of using agroecological monitoring data in designing adaptive landscape systems of agriculture and soil protection in the Belgorod region. On the basis of data on soil acidity, design and estimate documentation for liming is developed. Materials on the content of soil organic matter are used in the design of measures to form a deficient balance of humus. Information on the availability of arable soils with mobile forms of phosphorus and potassium is necessary for calculating doses of mineral fertilizers. With low availability of mobile forms of sulphur and trace elements, recommendations are being developed for the use of fertilizers containing scarce elements. As a result of the implementation by agricultural producers of projects of adaptive landscape systems of agriculture and soil protection, in 2015-2018, compared to 2010-2014, the use of mineral fertilizers increased by 14.4 kg/ha, organic - by 3.3 tons/ha, lime production - by 38.1 thousand ha/year. As a result, arable land productivity increased by 1.01 thousand feed units