The article presents an example of finishing treatment for aluminum alloys with the use of vibration machining, with loose abrasive media in a closed tumbler. For the analysis of selected properties of the surface layer prepared flat samples of aluminum alloy PA6/2017 in the state after recrystallization. The samples in the first stage were subjected to a treatment of deburring using ceramic media. In a second step polishing process performed with a strengthening metal media. In addition, for comparative purposes was considered. only the case of metal polishing. The prepared samples were subjected to hardness tests and a tangential tensile test. As a result of finishing with vibratory machining, it was possible to remove burrs, flash, rounding sharp edges, smoothing and lightening the surface of objects made. The basic parameters of the surface geometry were obtained using the Talysurf CCI Lite - Taylor Hobson optical profiler. As a result of the tests it can be stated that the greatest reduction of surface roughness and mass loss occurs in the first minutes of the process. Mechanical tests have shown that the most advantageous high values of tensile strength and hardness are obtained with two-stage vibration treatment, - combination of deburring and polishing. Moreover the use of metal media resulted in the strengthening of the surface by pressure deburring with metal media.

We study the exact and approximate controllabilities of the Langevin equation describing the Brownian motion of particles with a white noise. The Langevin equation is shown to describe also the bacterial run-and-tumble motion. Applying the Green’s function approach to the Green’s function representation of the Langevin equation, we obtain necessary and sufficient conditions for exact controllability in the form of a finite-dimensional problem of moments. For the approximate controllability, we obtain only sufficient conditions. The sets of resolving controls are characterized in both cases. The theoretical derivations are supported by a numerical analysis.