The simple analytical formula for description of the scattering of ultrashort laser pulse with the shape of the Meyer wavelet by atomic system is obtained. The dependence of the scattered pulse shape as a function of the system spectral width is discussed.Signal, arb.u. Comparison of a short pulse and its approximation with the five Meyer wavelets: a is exact signal, b is approximation of the signal

The article deals with the effectiveness of reducing the level of force interaction of the rail vehicle wheels with rails in curved sections of the track through the use of mechatronic position control systems for wheel pairs in the rail gauge in the horizontal plane. The approaches to the creation of such a mechatronic system operating on the principles of fuzzy logic are described. To determine the angles of attack of wheels on the rails, it was proposed to use the acoustic emission indicators of the contact of the wheel with the rail. To determine the direction of curvature of the rail track, it is advisable to use data from navigation systems. The study of the dynamics of the rail vehicle during the passage of a curved section of the track in real time was carried out using the Matlab/Simulink software package. The proposed mechatronic control system for the position of the wheel sets in the horizontal plane allows to ensure their optimal installation under various driving conditions in the rail gauge. This makes it possible to minimize the angles of attack of the wheels and reduce the forces of the horizontal interaction of the wheels with the rails.

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The scalar problem for a plane wave pulse spreading behind the diaphragm is solved. The calculation is carried out on the base ofthe non-stationary Kirchhoff-Sommerfeld integral and the expansion ofpulse in terms ofwavelet. The round and square diaphragm are considered. The pulse propagation under the condition offocusing is calculated The Greenfunction of the problemfor the round diaphragm with and without nonabberativefocusing is constructed