Experimental results for the extinction coefficient of exfoliated vermiculite determined by the FT-IR technique in the wavelength range from 1.33 to 27 μm are reported. The samples for the experiments have been prepared by dissolving particles of exfoliated vermiculite in IR transparent salt KBr of four different fractions (less than 60 μm, from 60 to 100 μm, from 100 to 150 μm and from 150 to 200 μm) and three mass concentrations (approximately 0.1, 0.2, and 0.3 %). The spectral scattering coefficient has been determined by the statistical modeling method of incident radiation scattering by particle (angle and point of incidence are set randomly by a uniform distribution and a particle linear size is set randomly by a normal distribution in fraction limits), which can be presented as one of three geometrical bodies: cylinder, sphere and rectangular parallelepiped, and using classical optics formulas. The spectral absorption coefficient obtained in our previous study has been refined from the experimental extinction coefficient. The Planck integral values of these coefficients and the Rosseland absorption coefficient have been calculated. Extinction coefficients have been theoretically evaluated to compare three proposed particle models on the best accordance with the results of jointly experiment and modeling.

   An approach to the computer solution of the problem of separating interference lines overlapping in a wide range of diffraction angles from an X-ray diffraction pattern of cellulose nitrate is presented. The results of calculations showed that the diffraction pattern of cellulose nitrate (CuK_α radiation) in the range of angles 2θ = 19°–26° includes three strong interference lines of cellulose nitrate. Three broad interference lines of cellulose nitrate located in a narrow range of diffraction angles 2θ = 19°–26° overlap and create a “single peak.” An analysis of the calculated results has shown that the effective sizes of the regions of coherent scattering of cellulose nitrate along different crystallographic directions vary from 0.5 to 3.0 nm and are comparable with the sizes of building blocks of nanomaterials. The nanosize of the coherent scattering regions leads to a significant smearing of the interference lines. This blurring of cellulose nitrate interference lines is typical of nanomaterials. The blurring of the interference lines of cellulose nitrate and, as a consequence, the general view of the diffraction pattern of cellulose nitrate is due to the small size of the coherent scattering regions of the test substance. It is shown that the degree of crystallinity of the studied samples of nitrocellulose cannot be less than 30%. The calculated degrees of crystallinity are 82 and 83 % for the two studied samples of nitrocellulose.

   The possibility of using the log files of the Proteus Plus medical device (IBA) is investigated in order to identify an unintentional error in the proton energy value, which, in turn, determines the depth of the Bragg peak in the phantom substance/patient tissue. An unintentional change in the energy of the proton beam has been detected by the displacement of its position in space in the transport system. The beam position has been measured by a strip ionization chamber and has been recorded in the log file of the proton therapy machine. The possibility of detecting such an error using log files has been checked by the controlled perturbation of the beam energy. The described technique has shown the possibility of detecting unintentional errors in the proton beam energy using the log files of the medical device for specific test treatment plans and proton energies. In addition, the parameters measured with the strip ionization chamber and used in the calculation of unintentional error showed stability over time.

   The electron microscopy method is actively applied in texture analysis to study the properties and characteristics of polycrystalline materials. To reconstruct the orientation distribution function from the experimentally obtained pole figures, methods of approximation of the normal distributions on SO(3) are used. One of these methods is the specialized Monte Carlo method. The modeling algorithm is specified by the following values: parameters of a given distribution (coordinates of the center and 6 parameters of an analogue of the covariance matrix), the number of n convolutions of infinitesimal rotations satisfying the central limit theorem (CLT) on the rotation group of the three-dimensional Euclidean space SO(3) and the sample size N from the obtained approximations. The result of the calculations is obtained in the form of rotation matrices, from which the Euler angles can be uniquely determined. The accuracy of approximations of the class of sequences for which the central limit theorem is valid (CLT sequences) has been studied on the three-dimensional rotation group SO(3) depending on the parameters. The dependence of the central normal distribution on the sharpness parameter ε (analogue of the standard deviation) has been studied. Orientations for the central normal distribution have been simulated by the specialized Monte Carlo method. An analytical estimate has been obtained of the accuracy of the approximations of the method of CLT sequences depending on the sharpness parameter in the sense of weak convergence.

   The urgent problem of protecting information that may become available through network communication channels from hacker attacks is considered. This task is associated with the storage and transmission of information in the management systems of individual enterprises and industries, in particular the electronics industry. To create a system for protecting information from threats, material costs are required, the value of which increases with the level of information protection. A mathematical scheme is proposed to determine such an optimal level of material costs in the information protection system, which ensures the minimum total costs for the information protection system and losses from remaining potential threats after the information protection system is implemented. A new robust scheme is presented to provide a stable solution to the problem of optimizing the cost of an information security system under conditions of uncertainty in the values of losses from hacker attacks. The scheme is based on a robust smoothing method and an iterative scheme for finding a harmonized component, in which the Tukey robust function is used to construct the objective function of the optimization problem. The presented robust scheme makes it possible to find a stable solution to the problem of minimizing material costs, including in conditions of abnormal emissions of the levels of hacker attacks.

   We have studied a 65-nm bulk CMOS triple majority gate based on the NAND logic with a topological structure in which all the transistors of the output 3NAND gate are one-by-one inserted into groups of transistors of the same type of three input NAND gates mutually separated by shallow trench insulation. The study involves the classification and analysis of error pulses that occur at the output of the majority gate when collecting charge from tracks of single ionizing particles both before and after switching the element at the inputs. The study carried out by means of 3D TCAD using tracks with a normal direction to the chip surface and a linear energy transfer of 60 MeV cm²/mg by a particle to a track. Four types of error pulses formed at the output of the majority element are established, which are based on the transition of the element to a nonstationary state when collecting charge from tracks of single particles. These are two types of error pulses formed before switching the element at the inputs of their 0 state to the 1 state. These is an error pulse with the nonstationary state duration, when the duration from the time of the track formation is farther to the time of switching the signals at the inputs from the 0 state to the 1 state compared to the duration of the nonstationary state, and an error pulse of ahead switching of the element before switching the inputs. In addition, there are two more types of error pulses generated at the output of the majority element after switching the inputs from the 1 state to the 0 state, namely, an error pulse with an additional delay in switching the element and an error pulse with the duration of the nonstationary state after switching the element.

   The theory of solving ultrahyperbolic differential equations is poorly developed, since it is believed that the problems associated with their solution do not occur in practice. However, it was found that in quantitative texture analysis, the pole figures measured experimentally by X-ray or neutron methods, depending on the choice of the crystallographic direction in R³, satisfy the ultrahyperbolic equation 2 × 2. Solutions of ultrahyperbolic differential equations combine the properties of both hyperbolic and elliptic equations. The direct application of solutions of ultrahyperbolic differential equations to the description of pole figures contains an additional complexity, which consists in the fact that a pole figure is the sum of solutions of two equations that depend on different independent variables. This is due to a special approach to the crystallographic directions in the X-ray experiment. In this paper, we analytically and numerically investigate the class of solutions of the ultrahyperbolic equations 2 × 2, and calculate some pole figures for them. The solutions found can be used as model functions for calculating experimental pole figures in quantitative texture analysis.

   The Lakshmanan–Porsezian–Daniel equation, which is used to describe pulse propagation through optical fibers apart from the nonlinear Schrödiger equation, is considered. Assuming that the Lakshmanan–Porsezian–Daniel equation holds a solution in the form of a monochromatic wave with an envelope as a function of the travelling wave variable, this partial differential equation is reduced to the overdetermined system of two ordinary differential equations for the envelope of the monochromatic wave. The method to obtain consistency of the ordinary differential equation system, which is different from assuming that coefficients of one of the equations are zero, is presented. Using the consistency condition obtained, two periodic solutions for the envelope of the monochromatic wave are derived from the ordinary differential equation system. These solutions are expressed in terms of the Jacobi elliptic functions and contain two and three arbitrary constants, respectively. The existence criteria for these solutions are presented. It is shown that one of the presented solutions degenerates to a soliton solution for a particular value of one of the arbitrary constants.

   It is an urgent task for the extractive industries to estimate the time of depletion of mineral reserves and the rate of their production. The difference in mining conditions and methods for extracting minerals leads to a significant spread in their cost and, consequently, different production intensities depending on the demand price, production cost, and other market characteristics. A model is proposed in the form of a non-linear differential equation of the second-order to predict the dynamics of the depletion of non-renewable minerals (uranium, iron, nickel, copper, and others), considering different production costs in different fields. The initial (known) parameters of the model are the explored residual volume of the fossil resource, the current market price of this fossil recoverable by traditional methods, the annual volume of resource extraction, and the production cost in the initial forecasting period. It presents the results of numerical modeling of the production of a certain conditional resource for the model function of the distribution of cost, demand prices for the resource, and the intensity of production from the expected income of mining companies, taking into account the influence of historical prices. It is shown that the intensity of production and the rate of depletion of the field significantly depends on the surges in the cost and the nature of the influence of historical prices.

   The influence of a number of economic factors on the average nominal and real wages is considered using the least squares method. The functions of the assumed dependences are found explicitly, and the statistical significance of the constructed models is checked. The data of nominal and real wages from 2000 to 2020 are considered in connection with the average export prices for crude oil, the average labor productivity in the economy of the Russian Federation as a whole. The weak interrelation of these factors is proved. In addition, for the same period, data on real wages depending on the physical volume of gross domestic product are analyzed, linear regression coefficients between these indicators have been determined, and the statistical significance of the constructed equation has been proven.

   The strategy of formation of highly qualified technical personnel for the nuclear industry is discussed. The necessity of a high level of training of schoolchildren in physics for successful mastering of professional competencies of engineering specialties is noted. The importance of early professional orientation of schoolchildren for the formation of stable motivation to obtain higher education in a technical university is emphasized. The necessity of carrying out work on the early professional orientation of schoolchildren to the engineering and technical professions of the nuclear industry on the basis of universities that train specialists for nuclear industry enterprises is indicated. Career guidance activities conducted at the Department of Physics, aimed at attracting schoolchildren to the nuclear industry are described. A comparative analysis of active and passive forms of organization of professional orientation of schoolchildren at the Department of Physics is carried out. The successful experience of implementing a career guidance project within the framework of the children’s summer scientific and technical school “Young Nuclear Scientists” is highlighted. The important role of physics departments of branch universities in the early professional orientation of potential applicants is noted.