Feynman method for disentangling operators and a singular oscillator

The problem of the evolution of a singular quantum oscillator with a frequency exhibiting an arbitrary time dependence has been solved. The probabilities w _mn of transitions in the oscillator spectrum and generating functions have been calculated, and the sum rules for w _mn have been derived. The calculations are based on the Feynman disentangling method and the theory of representations of the SU(1, 1) group.     

Mathematical Modeling of the Consumer Loan Market in Russia under Sanctions

Doklady Mathematics - The article develops and investigates a new model for the formation of interest rates on consumer loans based on an analysis of commercial interests and the logic of behavior...     

Effect of Sulfur Compounds and Higher Homologues of Methane on Hydrogen Cyanide Production by the Andrussow Method

The influence of sulfur compounds, higher homologues of methane on the parameters ofoxidative ammonolysis of methane was studied.     

Relaxation of an electrooptical effect in colloids induced by a field of short pulses

The possibility of studying the size distribution of particles suspended in a liquid irradiated with short pulses of strong electric fields, which almost do not change the properties of the disperse system is considered. The particle size is varied from 10 to 1000 nm. Relaxation dependences of the optically anisotropy induced by such pulses are investigated. The relaxation curves of the induced electrooptical effect are shown to behave similarly to the relaxation curves of the effect in the system with completely oriented particles. For aqueous polydisperse systems of diamond, graphite, and palygorskit, whose particles significantly differ in shape and physicochemical properties, the relaxation dependences of the electrooptical effect induced by fields of different duration and amplitude are measured. The correlation coefficients between the relaxation dependences are calculated. If the field is sufficiently strong, the correlation coefficients remain close to unity for all the three systems studied irrespective of the duration of the field pulse. This indicates that these curves are similar and that short powerful pulses can be used for determining the size distribution of particles in nanodisperse systems.     

Control and monitoring of the trigger system of the DIRAC experiment

In experiments with a large amount of electronics, it is important to provide monitoring for operation, flexibility to changes of the system configuration, and convenience of its use by experimentalists who are not experts in electronics. This work describes the organization of the completely computer-controlled trigger system of the DIRAC experiment at CERN.     

Effect of electric field on light scattering by aqueous colloids of diamond and graphite

We present the results of our experimental investigation of light scattering by polydisperse colloids of diamond and graphite. The scattering is studied at a random orientation of particles and in an external radiofrequency electric field, which orients particles along the strength. The average dimensions of particles in both colloids are close to each other and comparable with the wavelength of the incident light. The shape of particles and the optical and electrooptical properties of diamond and graphite colloids are significantly different. We analyze the polarization components of scattered light energy when the light incident on the colloids is linearly polarized. We show that the quadrupole light scattering by isotropic diamond particles has the main effect on angular dependences of depolarization of scattered light. For light scattering by anisotropic graphite particles, the depolarization of scattered light is mainly determined by a particular feature of the dipole scattering of particles. It is shown that, in both colloids, the orientational order of particles considerably reduces the depolarization of light scattered by particles. We show that relative changes in the intensity and depolarization of scattered light, which depend on the scattering angle and polarization direction of light, as well as on the parameters of particles, can be used as a measure of electrooptical effects observed in colloids.