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Propagation of high-power phase-modulated femtosecond laser pulses in air is numerically simulated. Spatial modulation of the initial pulse wavefront is carried out using a programmable phase plate consisting of segments arranged in a checkerboard pattern with a variable wave phase jump. The self-focusing, filamentation and post-filamentation channeling of radiation for phase-modulating masks with different phase shifts at the boundaries of neighboring segments are studied within the numerical solution of the nonlinear Schrödinger equation for the time-averaged electric field amplitude. The filamentation domain in air for certain pulse phase modulation types is shown to be significantly shifted (along the coordinate) and elongated compared to an unmodulated pulse. In addition, it is found that the use of phase modulation makes it possible to reduce the angular divergence of high-intensity light channels generated during the post-filamentation propagation stage. This provides a possibility of self-channeling of radiation at distances multiple of the Rayleigh length.

The results of analysis of aerosol of an aqueous solution of NaCl by femtosecond-pulse laser-induced breakdown spectroscopy (FS-LIBS) are considered. The results of estimating the impurity (Na) concentration by the analytical pair method using the additive method are presented. The radiation of the atomic nitrogen ion N⁺ at a wavelength of 500.515 nm from atmospheric nitrogen molecules in the filamentation region was taken as the internal standard line. A possibility of estimating the concentration of the both desired substances, the radiation of which is recorded, and the compound containing it is shown. The results are of interest for the development of femtosecond lidar sensing methods.

The results of the laser granulometry of nanosize fraction of precipitated aerosols and UV spectrometry of water washes from the surfaces of needle of different age of four species of forest-forming plant species are analyzed. The phenolic compounds efflorescence activity on the needle surfaces is assessed for the period of winter dormancy of plants. A possibility of the secondary organic aerosols geeration as a result of photoactivated reactions between phenolic compounds and a precipitated aerosol substance has been shown. The possibility of secondary organic aerosols entering the winter forest canopy under the radiometric photophoresis is discussed. It is assumed that secondary aerosols photophoresis in the field of IR from the snow cover surface (“snow” photophoresis) can significantly affect the vertical transfer of secondary organic aerosols in the winter coniferous forest canopy.

The dependence of the intensity of emission lines Ca (393.3, 396.8, 422.6 nm), Mg (383.6 nm), and Na (589 nm) on the laser pulse duration in the method of filament-induced breakdown spectroscopy is investigated. The filament was excited in seawater aerosols droplets of 0.8-2 mm in size by laser pulses of 70, 230, 500, and 900 fs in duration at a constant pulse energy of 3.0 mJ. It is shown that with an increase in the laser pulse duration, the intensity of the emission lines of the studied elements increased, with the exception of the magnesium line. Optimal values of the laser pulse duration for the excitation of Ca, Mg, and Na lines in a seawater aerosol are derived.

This paper is devoted to the substantiation of a multiplicative model of time series decomposition based on the axiomatic approach. In this model, the original time series is represented as a component-by-component product of the selected components. The components are described in the form of monomials. To determine the values of variable monomials, a function is minimized that measures deviations from the unit of all components of the product of the selected components from the values of the corresponding components of the original series. In the model under consideration, all the components of the original series and the selected components are positive numbers. Four requirements are formulated for methods of selecting components. It is proved that all these requirements are met if and only if the time series decomposition is performed by a multiplicative model. As an example, we consider a model for selecting trends and seasonal fluctuations from monthly series of efficient data.

Based on the previously developed kinetic model of the catalytic reaction of the synthesis of benzylalkyl ethers, two- and three-criteria optimization of the conditions was carried out. The problem of multicriteria optimization is formulated with the definition of variable parameters: reaction temperature, proportionality coefficient of the starting reagents, reaction time; optimality criteria: yield of a target and by-products; restrictions on variable parameters. The computational aspects of multicriteria optimization by a grid algorithm (sensing) are examined. The calculated front values (optimality criteria) and Pareto sets (variable parameters) determine the exhaustive values of the reaction conditions and allow the decision maker to choose the most optimal ones. This made it possible to give technological recommendations for the industrial implementation of the synthesis of a benzyl butyl ether in the presence of a metal complex catalyst with a maximum yield of target products and a minimum content of by-products.

In this paper, one construction of the original «Harten-Lax-van Leer» method using a piecewise-linear reconstruction of physical variables is described. The obtained numerical method makes possible to reproduce a low-dissipation solution at discontinuities. To verify the method, we used the classical problems with an analytical solution based on various configurations of shock waves, contact discontinuities, and rarefaction waves. On the Sod-like problem, the order of accuracy of the developed numerical method was studied, it was shown that the main suppression of the order of accuracy occurs when the rarefaction wave is reproduced. The numerical method was verified by means of a three-dimensional Sedov test of a point explosion, and on the problem of a supernova Ia type explosion with two symmetric ignition points, leading to the formation of a G1.9+0.3 like remnant.

This paper considers the problem of phases probability distribution function estimation for phase-shift-keying signals. The modulating sequence, and, accordingly, the values of the symbols phases, as well as the statistical characteristics of this sequence are unknown. The Fourier coefficients are calculated based on a limited sample for estimation of phases probability distribution function. In this case, the obtained Fourier coefficients are regularized. Application of multiparameter regularization for increasing the estimation accuracy are considered. The numerical simulation results are presented.

Resistance to HIV-1 disease developed by some exposed individuals has shown a promising sign in the fight against HIV-1 infection. Behavior change has also become one of the most important protection strategies against HIV-1 pandemic, but both of them have been widely neglected by mathematical modelers. In this paper, a new virus resistance HIV-1 mathematical model incorporating behavior change is formulated and analyzed rigorously for both partial and total abstinence cases. The calculated reproduction number is used to establish the local stability of the disease-free equilibrium points using the approach of Watmough and Driessche in both cases. Using appropriate demographic and epidemiological data for South Africa in the numerical simulation, the positive effect of behavior change in the midst of HIV-1 resistance is thoroughly examined, and this strategy is absolutely effective in dealing with the threat of HIV-1. This work also provides a better result than what is obtainable in the majority of the referenced related works.

In this work, we deal with a convex quadratic problem with inequality constraints. We use a logarithmic barrier method based on some new approximate functions. These functions have the advantage that they allow computing the displacement step easily and without consuming much time contrary to a line search method, which is time-consuming and expensive to identify the displacement step. We have developed an implementation with MATLAB and conducted numerical tests on some examples of considerable size. The obtained numerical results show the accuracy and efficiency of our approach.