The motion of relativistic electrons in the planar channeling mode in the accompanying reference system moving along the channel at a velocity equal to the longitudinal channel component of the electron velocity can be considered as an implementation of the one-dimensional atom model with parameters depending on both the kind and orientation of the crystal and the relativistic energy of the charged particle moving in the channel. The motion mode in the planar channel can remain stable even if the crystal and its planar channels of motion are curved if the bending angle is not too large. It is demonstrated that the energy quantization condition for one-dimensional channeled motion within the Bohr–Sommerfeld approach coincides with the calculated adiabatic invariant of this motion. Using the expression for the adiabatic invariant in planar channeling, the maximum bending angle of the single crystal at which stable motion in the channeling mode is still possible is estimated. It is noted that the maximum bending angle of a single crystal should not exceed the Lindhard critical channeling angle. Thus, the hypothetical possibility of using the bent single crystals to control the directions of propagation of the accelerated particles beams is limited to only small angles of deflection.

   The thermal conductivity of an exfoliated vermiculite layer of 0.7–2 and 4-8 mm fractions, which is represented as a gray heat-conducting absorbing (non-scattering) material enclosed between black walls, has been estimated at temperatures from 500 to 1300 K and normal atmospheric pressure. To simplify the problem, stationary conditions and a one-dimensional case are considered. The hypothesis of local thermodynamic equilibrium is accepted. Radiation is assumed to be incoherent, unpolarized, and concentrated between black walls. The change in the emissivity with increasing temperature is also taken into account. The resulting relative deviation of the estimated thermal conductivity coefficient from its experimental values in a wide temperature range is no more than 15 % and has a high correlation coefficient, which may mean that the described method of determining the thermal conductivity coefficient as a property of expanded vermiculite can be applicable. The technique can assumingly provide satisfactory results for some other heat-insulating materials with known parameters such as temperatures at boundaries and sample thickness.

   A generalized model of the Schrödinger equation is considered to describe the propagation of pulses in a nonlinear medium with saturation. The Cauchy problem for it is not solved by the inverse scattering transform; the solution of the equation is considered including the travelling wave. A system of differential equations for the imaginary and real parts has been derived in terms of the traveling wave variables. Optical solitons for describing the propagation of pulses are obtained in the form of implicit functions. Analytical solutions are expressed in terms of an exponential function. The solutions obtained for light and dark solitons in a saturating medium of the generalized nonlinear Schrödinger equation are solitary waves under certain restrictions on the model parameters. The solutions obtained are plotted.

   A system of Maxwell’s equations describing the propagation of electromagnetic waves is considered. For this system, differentiable initial conditions separated by spatial variables are set at the initial time. The resulting Cauchy problem has an explicit general solution, which is the corresponding linear combination of plane waves traveling at the speed of light propagating along all three spatial directions.

   Pulse propagation in an optical fiber with two refractive indices is numerically simulated within the mathematical model based on the nonlinear Schrödinger equation with periodic boundary conditions. Traveling wave variables are used in order to find an analytical solution. A system of two nonlinear ordinary differential equations for the real and imaginary parts is obtained. The exact solution of this system in the form of solitary waves is found by applying the generalized simplest equation method. The numerical solution of the problem is constructed using the pseudo-spectral method implemented in Python. The program code has been tested by comparing the numerical solution with the analytical one with the restrictions on the mathematical model parameters. The influence of the model parameters on the behavior of the numerical solution is analyzed for various values of the refractive index of the medium. The tables showing the dependence of the error on the parameter α are presented. The analytical and numerical solutions are plotted and analyzed for n = 1, 3, and 5.

   Proposed recommendations for target changes and the expected consequences of these changes, in particular, a possible increase in the stability of the compression flow, as well as a certain energy saving of external influence, are discussed in application to laser fusion targets used at the American NIF facility. The proposed changes are based on the analysis of the results of a quite long-term mathematical simulation of gas-dynamic flows arising from various types of focusing of a continuous medium into a decreasing volume. The mathematical theory of shockless strong compression of an ideal gas is the main result of this work.

   A feature selection method for training various machine learning algorithms is described. It is based on well-known feature selection methods and can be  used for data processing to solve the classification problem using machine learning algorithms. The method consists of several stages: calculation of the score of each feature using the existing feature shuffling method based on several scoring parameters of the machine learning model, processing the collected data array for division into two classes (relevant and irrelevant features) using the K-means clustering algorithm, removal of irrelevant features from the general dataset to train the SVM classifier, and assessment of the classification accuracy of the algorithm. A uniqueness of the method lies in the use of several scoring parameters at once to improve the accuracy and flexibility of the model, as well as in the use of an ensemble of machine learning algorithms to select the best features. A number of experiments have been carried out to determine the effectiveness of the method. As a set of input data for the classifier, electromyographic muscle activity signal readings have been collected by a specialized sensor, where each data set corresponds to a special gesture (class). During the processing, a number of features have been extracted from the signal and selected using the developed method to compile the input dataset for further training of the SVM classifier. The trained model has been used to interpret gestures into control commands for the robotic device in real time. The application of the technique provides a higher accuracy of gesture recognition compared to methods that involve only one scoring parameter of the machine learning model for feature selection.

   Different implementation principles of a multi-channel human-machine control interface for robotic complex or cyber-physical system are discussed. When an operator executes a command via the interface, type-I and type-II errors may occur during command recognition. The type I error occurs when the operator executes the command, but it is not recognized. The type II error occurs when the command is recognized although the operator does not execute it. In case of using several human-machine interaction channels, the problem of choosing the command to execute arises because of the presence of conflicting commands that can be recognized from different channels and in the same time require the same resources for execution. To solve this problem, two main principles have been determined. The first principle is to implement a decision-making system, which receives commands through control channels (interfaces), and makes a decision about the command to be  executed. The second principle is to choose and use only the most efficient control method. Examples of implementation of decision-making system and algorithm of choosing one control method are presented. To implement these algorithms, various criteria of interface efficiency are considered. Based on the generated confusion matrices, a number of experiments have been carried out to determine the number of errors in command recognition and to calculate type-I and type-II errors for each algorithm.

   In application to complicated production technology and control objects in modern industrial areas of engineering systems management, classical control methods have their well-known disadvantages in stabilization and performance. To overcome these disadvantages, the development and implementation of more efficient intelligent algorithms for process control systems (APCS) is required. In addition, increasing the efficiency of process control systems is one of the important tasks in modern areas of management. To achieve these goals, it is necessary to introduce new approaches to building real-time control systems, such as adaptive control and control methods based on artificial intelligence including fuzzy logic. Control systems based on fuzzy logic are most often used when information about control objects is insufficient and classical PID controllers cannot provide the required quality of control and regulation. Some NPP control objects belong to this type of control objects. Stages of developing a fuzzy algorithm, its implementation in a real-time system, and integrating it into a toolkit for designing process control systems (APCS) are considered. The algorithm includes the stages of fuzzification, rule base, and defuzzification. The fuzzy logic algorithm is implemented in the MikBASIC interpreter environment, which is the MWBridge real-time database technological programming system. Furthermore, the aim of this work is to develop a real-time fuzzy controller to control a gate valve in order to maintain the system output parameters in accordance with the specified values.

   It has been shown that zinc aluminate nanopowder can be obtained by the ion-exchange synthesis method, in which a pre-synthesized cation-exchange material is used as a matrix and ionite serves as an auxiliary phase. The sample obtained have been studied by X-ray phase analysis, differential thermal analysis, and scanning electron microscopy. According to the X-ray diffraction data, the ZnAl₂O₄ crystalline phase is formed, the beginning of which corresponds to an annealing temperature of 600 °C. The monophasic structure of zinc aluminate is formed at 1000 °C as a result of ion exchange synthesis. The main diffraction maxima for samples calcined at 700 °C and above indicate the formation of a spinel structure with the space group Fd3m. According to the electron microscopy data, the average crystallite size is 26 nm. The parameters of the spinel lattice are determined. Thermogravimetric analysis has shown the thermal stability of the material in the temperature range of 30–1000 °C. Scanning electron microscopy data have demonstrated that the proposed scheme of ion-exchange synthesis with a short heat treatment makes it possible to obtain particles with a size up to 100 nm with a high degree of homogenization of the target product and a uniform accumulation of chemical elements by weight. During prolonged heat treatment, the particles are prone to agglomeration.

   Impact power generators and discharge initiation systems have been studied in order to evaluate the efficiency of their use in electric discharge devices and, in particular, for electrohydraulic technologies. Three variants of generator discharge initiation—by high-voltage breakdown from a pre-charged capacitor bank, high-voltage breakdown from the auxiliary high-voltage winding of the generator, and exploding metal inserts—have been comparatively analyzed. It has been shown that a preliminary short circuit of the generator with an instantaneous change in the short circuit mode to the electric arc discharge mode causes a forced input of energy into the discharge channel. This method of discharging the generator is implemented using exploding conductors. The initiation of the discharge by exploding conductors makes it possible to abandon the high-voltage capacitor bank and the means of charging it, but requires mechanical replacement of the conductors, which affects the pulse repetition rate. A shock power generator with an additional high-voltage winding makes it possible to obtain a higher pulse repetition rate without a high-voltage capacitor bank and means of charging it. The initiation of a generator discharge by a high-voltage breakdown without a preliminary short circuit of the working winding of the generator is inferior in terms of the efficiency of excitation of pressure shock waves to initiation by exploding conductors.