The theory, which utilizes an exponential enhancement of the first-order mean spherical approximation (FMSA) for the radial distribution functions of the hard-core plus square-well fluid, is adopted to study the properties of the simplest model of the core-softened fluids, i.e., the hard spheres with a square-shoulder interaction. The results for structure and thermodynamic properties are reported and compared against both the Monte Carlo simulation data as well as with those obtained within the conventional FMSA theory. We found that in the region of low densities and low temperatures, where the conventional FMSA theory fails, the exponential-based FMSA theory besides being qualitatively correct also provides with a notable quantitative improvement of the theoretical description.

Chain of kinetic equations for non-equilibrium single, double and s-particle distribution functions of particles is obtained taking into account nonlinear hydrodynamic fluctuations. Non-equilibrium distribution function of non-linear hydrodynamic fluctuations satisfies a generalized Fokker-Planck equation. The method of non-equilibrium statistical operator by Zubarev is applied. A way of calculating of the structural distribution function of hydrodynamic collective variables and their hydrodynamic velocities (above Gaussian approximation) contained in the generalized Fokker-Planck equation for the non-equilibrium distribution function of hydrodynamic collective variables is proposed.

A chain of kinetic equations for non-equilibrium one-particle, two-particle and s-particle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev non-equilibrium statistical operator with projection is used. Nonlinear hydrodynamic fluctuations are described with non-equilibrium distribution function of collective variables that satisfies generalized Fokker-Planck equation. On the basis of the method of collective variables, a scheme of calculation of non-equilibrium structural distribution function of collective variables and their hydrodynamic speeds (above Gaussian approximation) contained in the generalized Fokker-Planck equation for the non-equilibrium distribution function of collective variables is proposed. Contributions of short-and long-range interactions between particles are separated, so that the short-range interactions (for example, the model of hard spheres) are described in the coordinate space, while the long-range interactions -in the space of collective variables. Short-ranged component is regarded as basic, and corresponds to the BBGKY chain of equations for the model of hard spheres.

The security verification method using a transform random phase mask as an optical mark bonded to a document or other product is proposed. This mask consists of separated and shifted fragments of a reference phase mask. If the the transformed and the reference masks are entered into an optical correlator, the autocorrelation peaks series is produced on the correlator output. The distances between peaks and the peak intensities were used to produce the feature vector. Identification ofthe document or other product takes place ifthe feature vector and the reference feature vector coincide. The procedure of the transformed mask generation and the process of the peaks' producing in an conventional joint traisform correlator were considered. The advantages of ixansformed mask applications in optical correlators are discussed. The joint transform correlator experimental setup containing the spatial light modulator PRJZ was designed and the optimal conditions to produce the autocorrelation peaks were found.