The paper reports on developing a method for selective detection of molecular iodine isotopologues of ¹²⁷I₂, ¹²⁷I¹²⁹I and ¹²⁹I₂ in gaseous media typical for nuclear fuel cycle enterprises and atmosphere. The method proposed relates to the methods of laser–fluorescence spectroscopy and consists in the analysis of fluorescence spectra of molecular iodine isotopologues mixture. The method provides for the registration of fluorescence intensities at pre–calculated wavelengths. Copper vapor lasers emitting at wavelengths of 510.6 and 578.2 nm are proposed as a source of fluorescence excitation. The method allows for highly sensitive online monitoring of molecular iodine isotopologues (including radioactive ¹²⁹I₂) in technological environments that are formed as the result of processing of spent nuclear fuel, in radiochemical enterprises gas emissions, and in atmospheric air.

This work investigates the three-spin system ¹⁴NV-¹³C, which includes the electronic spin of the NV center and the nuclear spins of the ¹³C and ¹⁴N atoms. In this system, a twofold degeneracy of the energy levels is observed in zero magnetic field (Kramers' degeneracy) due to the time-reversal symmetry of the spin Hamiltonian. To study the influence of magnetic and electric fields on the energy levels of the system, optically detected magnetic resonance (ODMR) spectra of this hybrid quantum system were simulated within the framework of the spin Hamiltonian method under the simultaneous influence of magnetic and electric or intracrystalline fields. The constructed model agrees well with the experimental ODMR spectrum of a single ¹⁴NV-¹³C complex localized in an ultrapure diamond sample using a confocal microscope. Based on the ODMR spectrum splitting in zero magnetic field and quantum chemical modeling data, it was determined that the ¹³C atom is located in the third coordination sphere of the NV center. The corresponding hyperfine interaction tensor between the electronic spin of the NV center and the nuclear spin of the ¹³C isotope was used in the model. As a result, numerical calculations showed that the degeneracy is lifted only by the magnetic field, regardless of the presence of any electric (crystalline) field, making this quantum system promising for magnetometry.

Classical and non-classical symmetries of algebraic equations and systems of algebraic equations are considered. Transformations that preserve the form of some algebraic equations, as well as transformations that reduce the order of these equations, are described. It is shown that individual algebraic equations with hidden symmetries can be reduced to classical symmetric systems of algebraic equations by introducing a new additional variable. It has been established that symmetric systems of algebraic equations of mixed type, consisting of symmetric and antisymmetric polynomials, can be converted to simpler systems. A method is presented for solving non-classical symmetric systems of two algebraic equations that change places when the unknowns are rearranged. Algebraic equations containing the second iteration of a given polynomial are studied, which are reduced to non-classical symmetric systems of equations. Examples are given of solving specific algebraic equations and systems of such equations that admit explicit and hidden symmetries. In particular, nontrivial algebraic equations of the sixth and ninth degrees are considered, containing free parameters that admit solutions in radicals. Irrational equations are described, which, by introducing two new variables, are reduced to symmetric systems of algebraic equations.

Numerical modeling of non-stationary radiation transfer process in the kinetic model is a very labor-intensive task. The complexity is caused by the large dimension of the problem and, additionally, for radiant energy transfer problems – by strong nonlinearity. For deterministic approaches based on discretization of the particle flight direction, it is necessary to solve a system of hyperbolic equations of large dimension. Accordingly, it is desirable that the schemes used for numerical modeling are economical both in terms of memory use and calculation time and show acceptable results for a wide range of Courant numbers. In the case of radiant transfer, the situation is aggravated by the strong nonlinearity of the problem being solved, which leads to a significant change in the properties of the medium at time steps. This imposes increased requirements for the monotonicity of the schemes with a change in optical thickness. According to Godunov's theorem, among two-layer linear schemes in time, there are no monotonic schemes of a higher approximation order. One of the directions of solving this problem is the development of NFC (Nonlinear Flux Correction) schemes of end-to-end counting, in which an increased order of accuracy on smooth solutions and monotonicity are achieved due to nonlinear correction of flows. The numerical solution is monotonized using a special algorithm in the vicinity of large gradients of the exact solution. The paper provides a brief overview and characteristics of the finite-difference scheme developed and successfully used for many years at RFNC-VNIITF to solve radiation transfer problems. The TVD (Total Variation Diminishing) methodology is used to monotonize the scheme.

In the paper, in the case of two independent spatial variables, a complete system of equations is considered Navier-Stokes, whose solutions describe the movements of a compressible viscous heat-conducting gas. For it, the Cauchy problem with continuous initial data is posed squared on the xOy plane. After a corresponding continuation of these data on the second square, the solution of the Cauchy problem is presented in the form of corresponding trigonometric series for spatial variables. The coefficients of the series are the desired functions of time. An infinite system of ordinary differential equations with corresponding initial conditions is given for these coefficients. Finite segments of trigonometric sums are constructed, approximating the solutions of the Cauchy problem under consideration.

The article examines the problem of using decision trees and their ensembles (decision forests) in the problem of classifying credit institutions as objects of economic security. Although decision trees and their ensembles have been successfully used in the banking sector, decision trees and their ensembles have not previously been used for automated identification of unreliable credit institutions. The classification of credit institutions was carried out on the basis of bank reporting form No. 101. As a result of the analysis, key performance indicators of credit institutions were identified, namely «Profit», «Accounts with the Bank of Russia», «Securities». Taking into account these indicators, the classification accuracy of 85 % was obtained for the CART model. For the Random Forest, Adaboost, and Xgboost models, all 23 financial statement measures (Form 101) were used, and the accuracy achieved was 83, 80, and 80 %, respectively. an urgent scientific and practical problem has been solved - mathematical models have been developed that make it possible to identify high-risk credit organizations and predict the risks of revocation of their licenses. During their application, a list of potentially unreliable credit institutions was identified, to which it is recommended that government authorities pay close attention.

Nonlinear transport equations with proportional delay, allowing exact solutions, are considered. More than thirty equations with proportional delay and a constant transfer coefficient, or with a transfer coefficient of power-law, exponential or logarithmic form depending on the desired function, have been described. The kinetic functions of all equations under consideration contain free parameters and in most cases also contain arbitrary functions. Exact additive, multiplicative, generalized and functional separable solutions, as well as traveling-wave and self-similar solutions are obtained. Most exact solutions contain free parameters. Over twenty more complex nonlinear transport equations with arbitrary arguments, allowing exact solutions, are also presented. The equations considered and their exact solutions can be used in the formulation of test problems to assess the accuracy of numerical methods

The development of information and communication technologies has led to a significant change in the life of society in the field of information consumption formation. With the spread of the Internet, various means of information dissemination began to appear, such as social networks that support text, visual and audio formats. The society has the opportunity to publish and create content, which in turn affects the information environment, which has already become the arena of information confrontation not only between states and organizations, but also individuals. Methods of automatic content generation based on generative algorithms that can create objects of such formats as images, video, audio and text play a special role in the information confrontation today. The article discusses the possibilities of using generative algorithms in information warfare. The main difficulty in substantiating the totality of topics of generative algorithms and information warfare is the novelty of such a tool as a generative adversarial network, the lack of a regulatory framework in the Russian Federation, as well as confirmed cases of the use of generative algorithms in information warfare.

Chromium coating can increase the corrosion resistance of a fuel rod cladding made of EP823-Sh steel in a liquid lead environment at temperatures up to 650 °C. It is advisable to block the diffusion interaction of the chromium coating and steel during the entire period of operation of the fuel rod. Studies of samples after high-temperature tests showed the presence of a coating-steel interaction layer. At a temperature of 420 °C and a holding time of 1000 hours, the coating retained adhesion, and no interaction between the coating and steel was observed. When tested at 540 °C and 650 °C and a holding time of 1000 hours, an interaction layer of uneven thickness within the range of 150-600 nm appears at the coating-steel interface. This layer has a complex composition and blocks further mutual diffusion of the steel components and coating into each other. EP823-Sh steel contains molybdenum and tungsten about 1 wt.% and they accelerate coating-steel interactions. An analysis of the interaction in the coating-steel system revealed the promise of using chromium as a protective coating for the inner surface of the fuel rod cladding made of EP823-Sh steel.