The penetration of cylindrical strikers with a flat end through ice barriers on the normal to the front surface of the barriers. The possibility of using induction sections to fix the time strikers in the study of the penetration through a fresh ice barrier in the range of initial velocities from 800 to 1500 m/s. Diagrams of motion (depth versus time) and the size of the cavities have been experimentally obtained by pulsed radiography. According to the results of the tests and analysis of the results, the influence of the ice temperature on its strength, resistance coefficient, and the size of the cavity have been determined.

   Some features of the core loading formation for the MIR.M1 research reactor during preparation of experiments to study the behavior of fuel rods for water-cooled reactors in accidents with loss of a coolant are discussed. The main structural and physical features of the reactor, as well as main directions of its use, are briefly presented. It has been shown that the preparation of the same type of experiments with the same initial requirements to ensure the test conditions in the MIR.M1 reactor core is a difficult task, depending on the initial conditions for loading the working and loop channels, poisoning of beryllium blocks of the core. For successful implementation of experiments, it is necessary to take into account numerous factors associated with both structural and operational features of the reactor. In this case, the final state of the reactor at the beginning of the experiment and upon reaching the target parameters of the test rig in a loop channel can be completely different. It has been shown that described approaches to the reactor core loading formation make it possible to safely conduct complex dynamic experiments simulating the emergency operation of the tested nuclear fuel rods. Some results of these experiments important for the discussed problem have been presented.

   The family of nonlinear Schrödinger equations describes a number of physical phenomena. The simulation and analysis of the propagation of highly dispersive optical pulses with allowance for several non-linearity types are currently of great interest. The dispersion is determined by the order of the governing equation. In this work, we consider the sixth order equation with cubic, quintic, and septic nonlinearities is analyzed. The search for solitary waves propagating in a nonlinear medium plays an important role in the study of the propagation of optical pulses. To solve this problem, the method based on the search for solitary wave solutions is used. At the first step, the substitution of travelling wave variables reduces the initial equation to the system of two differential equations corresponding to the real and imaginary parts of the initial equation. Restrictions on the parameters have been obtained from the equation corresponding to the imaginary part. The pole order of the equation corresponding to the real part has been determined. A nonzero pole order makes it possible to find solitary wave solutions at the next step. These solutions have been constructed and plots of solutions at different parameters have been analyzed.

   New methods for constructing exact solutions of nonlinear mathematical physics equations with delay have been proposed with the use of special solutions of simpler auxiliary equations of mathematical physics without delay. The capabilities of the proposed methods are illustrated on nonlinear reaction–diffusion and wave equations with delay and variable coefficients, which contain three-to-seven arbitrary functions depending on the spatial variable or the unknown. New generalized traveling wave solutions and functional separable solutions are obtained in the implicit form. Examples of exact solutions of more complex nonlinear equations with variable delay, which arbitrarily depends on time, are also given. The considered equations and their exact solutions can be used to formulate test problems intended to verify the adequacy and evaluate the accuracy of numerical and approximate analytical methods for solving the corresponding non-linear initial-boundary value problems with delay.

   The generalized Kuramoto–Sivashinsky equation is used to describe a lot of nonlinear physical processes. In this work, dynamical regimes described by the traveling wave reduction of the generalized Kuramoto–Sivashinsky equation are examined. The main goal of this work is to study how the dispersive term suppresses chaotic regimes in the system. The traveling wave reduction of the Kuramoto–Sivashinsky equation is written in the normal form. The divergence of the vector field this system has been calculated. The parameters for which the studied system is dissipative have been determined. The bifurcation diagram is plotted for three different nonlinearity degrees of the generalized Kuramoto–Sivashinsky equation. The dispersion term coefficient is chosen as the bifurcation parameter. The largest Lyapunov exponent is plotted as a function of the dispersion parameter for the three studied cases. The Benettin algorithm is employed to compute largest Lyapunov exponents. It has been found that a chaotic regime is observed in the system at some values of the dispersion parameter. Routes to chaos are described. Phase portraits for some of the dynamical regimes are presented.

   Functional iterative processes f_k(x) = f(f_k-1(x)), k = 2, 3, where the initial function belongs to the class of non-degenerate linear fractional functions are considered. The aim of this work is to study all types of iterative processes that arise when the parameters are varied. To solve the appearing recurrence relations, matrix methods and complex numbers are used. Formulas for the coefficients of the k_th iteration for any k depending on the coefficients of the initial function are obtained in the general form. Two invariants of iterative processes are defined. It is shown that cycles of the length n > 2 can exist only for complex conjugate eigenvalues of the coefficient matrix of a linear-fractional function. All initial functions that generate cycles of an arbitrary given length are found and explicit expressions are obtained for the coefficients of any element of the cycle in terms of the coefficients of the initial function. An example of a cycle of the maximum length n = 6, where all the coefficients of each iteration are integers, is given. For non-cyclic processes, the behavior of the k_th iteration is studied for k →  and limit functions are determined in the cases of convergence. Non-cyclic iterative processes are divided into converging (real eigenvalues) and diverging (complex conjugate values that do not satisfy cyclic conditions). Converging iterations have a constant function as their limit function.

   A heuristic mathematical model of cataract evolution has been proposed on the basis of a simplified physiological model. The process is presented as a non-stationary Neumann problem for the Poisson equation. Its initial conditions are the solution of the stationary problem corresponding to a healthy eye. According to the crystalline lens degradation concept, the feeding agent is being transported inside the boundary and naturally consumed. Its lack results in opacification of the crystalline lens tissue. The crystalline lens is considered as a biconvex lens-like body constrained within intersecting spheres of different radii. The Green’s function for the area has been built by the reflection method. A finite number of reflections occur if the spheres are orthogonal; this circumstance, together with the height and thickness of the crystalline lens, uniquely determines the geometry of the problem. The model describes the nuclear, subcapsular, and cortical cataract. The behavior of solutions in each case is discussed. The physiological meaning of an arbitrary constant in the Neumann problem solution is interpreted. A necessity to reach some agreement with respect to the threshold value of the feeding agent concentration that enables one to distinguish between healthy and unhealthy regimes of the eye functioning is emphasized. Extended names of cataract types are offered with adding the etymological feature to the morphological one: diffuse–nuclear, sclerotic–subcapsular, and sclerotic–cortical, respectively.

   The radial distribution of the temperature in a fuel element of a nuclear reactor has been studied taking into account the boundary conditions of the third kind in five regions with different characteristics. The problem with zero derivative of the temperature on the left boundary of the solution domain has been considered separately as a special case of a boundary condition of the third kind. The numerical simulation has shown that a constant radial distribution of the temperature in the fuel element is established quite quickly. For this reason, stationary heat conduction equations are considered in each of the five regions, and a general solution is obtained for each region. For the case of zero derivative of the temperature on the left boundary, an analytical form of the stationary temperature distribution in all regions is obtained. It has been found that the numerical solution converges quite rapidly to the analytical solution. In addition, the distribution of the concentration of radionuclides is studied taking into account radioactive transformations. The radioactive decay chain of ¹³¹Sn has been considered as an example. The results of the numerical simulation are presented in the form of plots of the concentration distribution along the radius of the fuel rod. The main result is a program that allows the numerical simulation of the temperature distribution and concentration of radionuclides under various boundary conditions and for different values of the parameters of the fuel element that can be set by the user of the program.

   The TCAD simulation of noise pulses caused by the action of single ionizing particles on the elements of a chain of two-phase CMOS inverters with a C-element on a two-input inverter with the third state has been reported. A noise pulse on one of the inputs of the C-element is blocked, and the C-element stores the last output logical state on the capacitor of the output. The elements are modeled using the 65-nm CMOS bulk technology. Transient processes accompanying the collection of charge from tracks directed along the normal to the crystal surface, with the input points both in the drain area of transistors and at a distance of 0.3–0.65 μm from them have been analyzed. In the case of a track passing through a transistor drain or nearby, interference occurs only on one output of a two-phase inverter and can affect only one input of the next inverter or C-element. The C-element transits to a highly resistive state at the output to store its logical state regardless of the completion of transients in the inverter circuit. The duration of storage is 10–20 ns. The C-element switching delay is 25–40 ps.

   Sensitive elements of current sensors for three-phase circuits based on delay lines on surface acoustic waves, where the impedance connected to a reflective counter-pin converter depends on the current in the conducting bus, have been studied. The impedance is a series-connected inductor with a ferrite core and a capacitor. The inductance changes under the influence of the magnetic field created by the current, and the capacitance depends on the voltage induced in the winding wound on a magnetic wire located around a current-conducting wire or bus. It has been shown that it is better to use closed magnetic circuits without a permanent magnet, but with a winding wound on it, the voltage from which is fed through diodes to varicaps or to an additional winding located on a ferrimagnetic core of a magnetically sensitive inductance. In this case, the positive and negative half-waves of the alternating current are measured independently, which allows us to estimate nonlinear distortions in the power grid and more accurately evaluate the power consumption. The use of a varicap circuit as a capacitor can significantly increase the sensitivity and accuracy of current measurement. The use of sparse counter-pin converters allows significantly reducing the operating frequency band, which makes it possible to measure currents simultaneously in three phases in the range of permitted frequencies of 2400–2483 MHz. In general, the use of sensors of the new design will expand the dynamic range of measured currents.

   To consider the system of two or more cointegration equations with the same variables, it appears necessary to reveal whether the cointegration relationship has the standard properties of reflexivity, symmetry, and transitivity. In this work, the transitivity property of the cointegration relationship is analyzed. The theoretical substantiation for the transitivity of cointegration is presented. The computational experiment with the use of the Engle–Granger test to check the transitivity property of the cointegration relationship is carried out. It has shown that statistical tests do not necessarily confirm the theoretical calculations: the Engle–Granger test rejects the null hypothesis for the (Z; Y) and (Y; X) pairs in favor of cointegration, but does not necessarily reject it for the (Z; X) pair. A possible interpretation of this result has been proposed: low power and high probability of type II error of the Dickey–Fuller test underlying the Engle–Granger test. A new methodology for identifying cointegrated asset pairs has been proposed: to test the regression residuals obtained with the Engle–Granger test for stationarity using the KPSS test and combine the results of these tests. The results of the backtests of the proposed methodology on the Moscow Exchange 2017 data are presented. According to the results of the backtests, the average annual return on the proposed methodology for identifying cointegrated pairs of shares was 19.67 %. Compared to identifying cointegrated pairs of shares using the Engle–Granger test, the average annual return increased by 7.05 %.

   A method for interpretation of results of identification age style imitation in the text based on a gated recurrent unit (GRU) with an additional network layer to map the activity of the hidden layer for each word in the text has been proposed. At the same time, the special corpus has been collected for the task of age imitation identification. The corpus contains three types of texts: texts written in the author’s natural style, texts with imitation of a younger person style, and texts with imitation of an older person style. The texts have been presented in a segmented form, as words and sentences, and their morphological analysis and lemmatization have been performed using the UDPipe program. The network topology includes: an internal bidirectional GRU layer of 32 neurons providing activity for each word of the document, which is an input of a fully-connected layer with the ReLU activation function and size of 32, which connected to another fully-connected layer with the hyperbolic tangent activation function and 3 neurons (just as the number of age imitation classes). An additional interpretive layer returns the coefficients determining the class to which the text belongs. The analysis of the experiments has revealed that the characteristic features for determining the age imitation type in the text are the beginning and greeting used by a person in the text.