On complementability of certain generalized hypercenters in Artinian modules

We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.     

Arc Discharge in a Channel with Transparent Walls at Intense Flow Rates of a Plasma Forming Gas

The arc discharge was studied in a transparent channel at an intense flow rate of nitrogen, hydrogen, air, carbon dioxide in the current range 100–1500 A. The internal diameter of the porous channel varied from 10 to 34 mm, the length - from 50 to 150 mm, the air and nitrogen flow rates - from 0.05 to 1.5 kg/s, hydrogen - from 0.005 to 0.05 kg/s. The electric field strength in the arc channel reached a value of 300 V/cm for N₂ and 500 V/cm for H₂. The effect of plasma thermochemical non-equilibrium was discovered.     

Chernoff efficiency of the sign and Wilcoxon tests for testing the symmetry hypothesis

The local Chernoff efficiency of the sign and Wilcoxon statistics are derived for the testing of symmetry on the basis of the analysis of the probabilities of large deviations of these statistics under the hypothesis and the alternative.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 101–107, 1989.     

On the function of action on a manifold of ground state solutions

The functions of action and energy are introduced on a manifold of ground states of the Euclidian scalar field functional of action. The differential identity connecting these two functions is proved.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 3, pp. 438–449, December, 1995.     

Determination of formic and acetic acids in air by piezoelectric microweighing

The quantitative and kinetic parameters of sorption of formic and acetic acids on thin films of various modifiers of piezoelectric quartz resonator electrodes are determined. Parameters of film formation on the electrodes (application procedure and thickness) are optimized. Methods for joint and separate determination of formic and acetic acids in air by piezoelectric microweighing with single- and double-sensor devices are developed.     

Measurement of the elastic moduli of dense layers of oriented carbon nanotubes by a scanning force microscope

A technique is developed for measuring the modulus of elasticity of a material with a Nanoscan scanning force microscope on the basis of measuring the dependence of probe vibration frequency on the penetration depth of the needle into the specimen. This technique makes it possible to study materials with elastic moduli from 50 to 1000 GPa. The Young moduli of dense films of carbon nanotubes oriented at angles of 45° and 90° to the quartz substrate are measured. From their ratio, the Young modulus in the direction perpendicular to the tubes and the anisotropy of the elastic moduli are determined. A comparison of these values with the corresponding values obtained for a nanotube film deposited on a silicon substrate is carried out. On the basis of this comparison, a conclusion is made concerning the interaction between single-layer nanotubes and between nanotubes in a mixture of single-layer and multilayer ones.     

Formation of an icosahedral structure during crystallization of nickel nanoclusters

The crystallization of nickel nanoclusters is investigated using a molecular dynamics simulation with tight-binding potentials. The formation of a cluster structure depends on the cooling conditions. Slow cooling results in the formation of a face-centered cubic structure, whereas fast cooling, according to the data obtained in 40% of the simulation experiments, leads to the formation of an icosahedral structure. The molecular dynamics simulation experiments demonstrate the possibility of controlling the formation of a structure of nickel nanoclusters during crystallization.