Uniform approximation of analytic functions by polynomials in domains with a boundary of bounded rotation and without zero exterior angles

One obtains direct theorems of the constructive function theory for domains on the indicated type. In the neighborhood of the points where the exterior angle is equal to 2π, one obtains a new effect in the approximation by polynomials, related to the possibly different properties of the boundary of the domain along the different sides from a similar point. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 65, pp. 199–202, 1976.     

On one new effect of the Einsteinian theory of gravitation

It is shown by using the equation of geodesic deviation that a small test particle, placed in the centre of inertia of a terrestrial spherical satellite, will vibrate if a small initial momentum dⁱ/dsbe given to this particle at a certain moment of the satellite's proper time S=0. These vibrations may be in the satellite's orbital plane and the plane perpendicular to it with the frequencies determined by the formulae (14) and (16). The difference between the periods of these vibrations determined by the formula (20) is one new effect of the Einsteinian theory of gravitation (GTR). The shifting of the point of intersection on the lines of these vibrations corresponds to this difference of periods (20). This shifting, taking place in the time of several complete periods, will be of a distance 10^–6–10^–7 cm if plausible assumptions about the quantities of the test particle velocities and amplitudes are made.     

Computer simulation of perturbation of a shock wave in nitrogen by optical radiation

The possibility of a displacement of the front of a shock wave formed in a 1D nitrogen flow to the low gas pressure region (in front of the shock wave) upon absorption of the laser pulse energy in the region of the shock wave front is demonstrated using computer simulation based on the finite difference technique. The low-pressure region formed in the region of the initially high pressure under the action of a light pulse moves in the direction opposite to the direction of propagation of the shock wave front. Analysis is carried out for a typical experimental situation corresponding to the growth of carbon-nitride nanofilms.     

Group-Theoretical Classification of Aristotypes of Cation and Anion Orders in Perovskites

Crystallography Reports - A group-theoretical classification of cation and anion orders of crystals with a perovskite structure is presented. Aristotypes are idealized structures (phases), from...