Vol 17, No 3 (2013)

We summarize the first twenty five years of scientific publishing “Computer Optics”, analyze its creating pre-conditions and history, and its development by the example of breakthrough articles on the diffractive optics, information optical technologies, image processing. We describe the progress of editorial team and the future development of journal.

The problem for the equation of the mixed elliptic-hyperbolic type with nonlocal boundary conditions is viewed. This problem is reduced to the inverse problem for elliptichyperbolic equation with unknown right-hand parts. The criterion of the uniqueness is established. The explicit solution is constructed as the sum of orthogonal trigonometric series of the one-dimensional spectral problem eigenfunctions. The argumentation of the series convergence under some restrictions is given. The stability of the solution by the boundary functions is proved.

We consider the Mikusinski operational calculus based on the convolution algebra of distributions $D^{+}$ and $D^{-}$. We state and prove the basic theorems, and give examples of Mikusinski operational calculus using, which demonstrate its additional possibilities, such as extension of solutions to the domain of negative argument values, removing the growth limits of right-hand functions and obtaining the new methods for solving the nonhomogeneous equations with discontinuous right part.

The method for calculation of cylindrical sample rheological deformation and fracture in creep conditions for three types of stress state: tension, pure torsion, the combined effect of tensile load and torque is offered. The procedure is based on the theory of creep and creep rupture strength of energy type. Calculations are performed for all three types of stress state for solid and hollow cylinder tests from aluminum alloy D16T at 250 ℃. Comparison of the calculated data with the corresponding test data for each type of stress state is conducted. It shows the agreement between the calculated and experimental values. The intensification of creep and decreasing of creep rupture strength factors after the application of torque to the specimen under the axial tension are established. The substantial redistribution of axial and shear stresses along the radius depending on the time is observed. The estimates of errors of deviation of calculated data from the experimental values are given.

The mathematical model of evaporation of multicomponent liquids is developed for open systems with consideration of mass-transfer substances in a liquid phase. Feature of the given model is the mathematical description of one-dimensional evaporation of the multicomponent liquid mixes containing poorly volatile solvent and n of diluted substances. Exact analytical solution of the boundary value problem based on Green’s functions method is received by reduction of the differential equations system with moving boundary of the $n$ diluted substances to the $n$ differential equations with fixed boundary.

The distributions of reflection and admission coefficients of a different wave-length radiation by the biological tissues were experimentally studied. A physical basis of the methods of approach to an optimum selection of the laser sources and the conditions of its practical application to solution of the fundamental and applied problems of the medical-and-biological investigations was given.

The experimental results of the macroscopic spherical particles penetration in the halfinfinite aluminium and steel targets have been analyzed. It is shown, that for particles, having sizes about 50–100 µm and velocities in the range 1000–3000 m/s, the hydrodynamical penetration model is not applicable. Under such conditions the penetration procedure is determined by the processes, taking place immediately in front of the particles surface. It fundamentally differs from models, suiting for describing the damage of target metal under the influence of large mechanical bodies. The specific penetration model for macroscopic particles, having small size have been formulated. The special properties of this mechanism which distinguish it from the common approach are shown.

The boundary value problem for mixed type equation with nonlocal initial conditions in integral form is considered. The main result states that the nonlocal problem is equivalent to the classical boundary value problem for a loaded equation. This fact helps to prove the uniqueness and, under extra restrictions, the existence of a generalized solution of the problem.