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Abstnft. The theory of the 3-mixing process for thermal collisions between Rydberg atoms and neutral particles has been developed in the impulse approximation using the formalism of spherical tensor operators and the WKB approximation. We have derived a simple formula far the cross section of inelastic nU -"U' transitions, which provides the dependence on the principal n and orbital I quantum numbers, relative velocity V and the energy defect A%,,. of the fine-structure splitting. The analytical results obtained are in good agreement with the available experimental data and numerical calculations.

In this paper we study the convergence of energy integrals, stress tensors and frequencies of free vibrations for non‐homogeneous and porous elastic bodies with a periodic structure of period ε as ε → 0. The results are based on the estimates for solutions of the boundary value problem of the elasticity system with rapidly oscillating periodic coefficients, obtained in [4], [11].

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We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to the null state in finite time, the absolute value of the distributed control function being bounded. In this case the memory kernel is a linear combination of exponentials.

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