On the Finiteness of the Number of Elliptic Fields with Given Degrees of $$S$$ -Units and Periodic Expansion of $$\sqrt f $$

Doklady Mathematics - For a field k of characteristic 0, up to a natural equivalence relation, it is proved that the number of nontrivial elliptic fields $$k(x)(\sqrt f )$$ with a periodic...     

Analysis of a set of nonlinear dynamics trajectories: Stability of difference equations

For a set of difference equations generated by discretization of the set of differential equations with Hukuhara derivative a principle of comparison with matrix Lyapunov function is specified and sufficient stability conditions of certain type are established. The analysis is carried out in terms of a matrix Lyapunov function of special structure. For an essentially nonlinear multiconnected switched difference system, conditions are obtained providing the asymptotic stability of its zero solution for any switching law. An example is presented to demonstrate efficiency of the proposed approaches.     

Thermalization of the flow of sputtered target atoms during ion-plasma deposition of films

The boundary of the zone in which sputtered atoms are thermalized in the substrate–target drift space during the ion-plasma magnetron deposition of films is determined theoretically and experimentally. A comparison of the thicknesses of films deposited on the front and back sides of substrates situated at different distances from the target makes it possible to divide the flow of atoms sputtered toward substrates into direct and diffusion flows and to determine the dimensions of the spatial zone in which sputtered atoms are thermalized. The experimental data are in quantitative agreement with the results of a statistical simulation of the thermalization process of atomic particles during the ion-plasma deposition. This simulation enables optimization of the technology of defect-free growth of films with uniform thickness on substrates with complex 3D configuration.     

Generation of 1-aryl-3-methoxycarbonylnitrilimines and their reaction with halogen-containing unsaturated compounds

Thermal decomposition of 1-(4-methoxyphenyl)- and 1-(4-fluorophenyl)hepta(methoxycarbonyl)-3a,7a-dihydroindazoles at 135 °C in the presence of allyl or propargyl halides leads to the elimination of hexamethyl benzenehexacarboxylate and the formation of the corresponding pyrazolines or pyrazoles as the products of 1,3-dipolar cycloaddition of 1-aryl-3-methoxycarbonylnitrilimines to the multiple bonds of the substrates used. In the case of vinyl halides, the products of the target reactions are either obtained in low yields or nonexistent, with a side conversions taking place instead. Thus, for example, in the case of 1,1-dichloro-4-methylpenta-1,3-diene, besides hexamethyl benzenehexacarboxylate, 3,5,5-trichloro-2-methylpent-4-en-2-ol and arylchlorohydrazones MeO₂CC(Cl)=N-NHAr were unexpectedly isolated as the main products, as well.     

Time-of-flight neutron spectrometer for micro sample studies under high pressure

Abstract

A new neutron spectrometer for investigations of elastic and inelastic neutron scattering on polycrystal microsamples under high pressure in diamond and sapphire anvils cells is described. The spectrometer is operating at the IBR-2 pulsed reactor at JINR. The time-of-flight method and ring-shaped multicounter detector are used to register the scattered neutrons. Parameters and methodical peculiarities of the device and the examples of experimental studies are given.     

Kinetics of the electrochemical oxidation of 1,1-bis-hydroperoxy-4-methylcyclohexane on platinum

The electrochemical synthesis of 3,12-dimethyl-7,8,15,16-tetraoxadispiro[5.2.5.2]hexadecane (1,2,4,5-tetraoxane) from 1,1-bis-hydroperoxy-4-methylcyclohexane on platinum electrode in a cell with separated and unseparated cathode and anode space in an aprotic solvent is conducted. The kinetics of electrochemical oxidation of 1,1-bis(hydroperoxy)-4-methylcyclohexane is studied. The current yield of the reaction is determined.