The Compton scattering effect of electromagnetic waves (photons) by free electrons has been known since the beginning of the 20th century. A photon moving towards a fast electron can be scattered in the opposite direction, significantly increasing its energy due to the loss of it by the electron. When the scattering electron is not free, but moves in a single crystal in the channeling mode, periodic harmonics of the potential of atomic planes or axes along which the channeled electron moves can serve as the scattered photon. In the so-called accompanying reference system moving at the velocity, equal to the longitudinal component of the channeled particle velocity, these harmonics can be considered as electromagnetic waves (equivalent photons) interacting with the electron making finite orbital or oscillatory motion in the averaged potential of the atomic axis or plane. The result of equivalent photon backscattering is a real photon, observable as a high-energy photon in the laboratory system. Due to the discreteness of the transversal motion energy spectrum of the channeled electron, the emitted photon spectrum will also be discrete. This work continues a series of our previous studies [3–5] of effects associated with electromagnetic processes during the passage of the fast charged particles through crystal structures within a mixed quantum–classical approach. The backscattering kinematics of photons and equivalent photons by the ultrarelativistic electrons has been analyzed in detail in the general case and in the channeling mode. The characteristic frequencies have been calculated and the intensity of the resulting radiation has been estimated.

   The analytical properties of solutions of three families of three-dimensional autonomous conservative systems with two or four quadratic nonlinearities are studied. The conservative systems of the first family have two quadratic nonlinearities and two linear components. The conservative systems of the second family have two quadratic nonlinearities, one linear component, and one constant term. The conservative systems of the third family have four quadratic nonlinearities. To analyze the solutions of the systems under consideration, the Painlevé test, the reduction of the systems to second- or third-order equations equivalent to them, and the comparison of the latter with the known nonlinear P-type equations are used. Three systems whose general solutions have the Painlevé property are separated. The solutions of one of these systems are expressed in terms of elementary functions, and the other two are expressed in terms of solutions of the first or second Painlevé equation. It is shown that there are some non-Painlevé -type systems, one of the components of which does not have any moving singular points. For each of the systems of the third family, exact one-parameter families of solutions are constructed. In addition, it is shown that one of the systems of the third family has a two-parameter family of meromorphic solutions. A common qualitative property of thesesystems, except for one, is the absence of chaos in them.

   The perturbed Chen–Li–Liu equation with an arbitrary refractive index describing the propagation of pulses in an optical fiber is considered. The traveling wave reduction is used to find a solution of this nonlinear partial differential equation. Separating the imaginary and real parts of the resulting equation and equating them to zero, a system of ordinary differential equations is constructed. The compatibility conditions of the system of ordinary differential equations are determined. Stationary points of the system of equations are found. Exact solutions of the mathematical model are obtained for n = 1 and 2 expressed in terms of the Jacobi and Weierstrass elliptic functions. It is shown that the solutions found in the case of an arbitrary refractive index have the form of periodic and solitary waves (optical solitons).

   A second order periodically perturbed ordinary differential equation, which is a traveling wave reduction of the Triki–Biswas equation, used to describe the propagation pulses in nonlinear optics has been considered. A stability analysis of the studied system of ordinary differential equations is carried out. It has been found that, depending on the control parameters, the considered system of equations can have three or five stationary points, which affects the structure of its stable and unstable manifolds. The Melnikov function of the system of equations under study is constructed for the case of three stationary points, where the stable and unstable manifolds of the unperturbed system of equations coincide with its homoclinic orbit. It has been found that homoclinic chaos always occurs in the system under consideration. To control it, a damping term has been added to the system. Constraints are found on the parameters of the new system at which homoclinic chaos is realized in it. Basins of attraction have been plotted. It has been found that they have a fractal structure when the damping parameter are less than the critical ones obtained by the Melnikov criterion. The results of the numerical analysis are in agreement with those obtained theoretically by the Melnikov method.

   In modern control systems, the quality indicators of the control process are divided into direct and indirect. Direct quality indicators include properties determined by the transient characteristics of the system. Indirect quality indicators include root, frequency and integral indicators. The possibility of applying quadratic integral quality criteria for automatic control systems has been considered in this work. The analysis is carried out for the possibility and expediency of using such a criterion in digital control systems built based on software and hardware complexes using the principles of optimal control. To perform this analysis, an automatic control system with a classical proportional-integral regulator is considered. The function of calculating the instantaneous and integral quadratic and root-mean-square criteria of the desired controlled parameter from the real signal at the output of the control object has been added to the algorithm of this system. The criteria have been calculated throughout the entire transition process, as well as at each period of the controller call. Then, the results obtained are compared. The possibility of applying integral quality criteria in digital control systems built on the basis of software–hardware complexes has been demonstrated.

   The development and implantation of a control system for the thyristor units of a boiling stand at the National Research Center Kurchatov Institute are described. The general purpose of the Boiling stand, the operation of thyristor units, and the experimental section heating are discussed. The design of the thyristor units of the boiling stand, the heating control system, the principles of constructing control systems in real time, and technological programming systems for their various hierarchical levels are studied. Particular attention is paid to the middle-level algorithmic programming system, which is the foundation for the main control algorithms of the boiling stand. Using the data obtained, control algorithms for the equipment of the boiling stand have been developed and implemented. Their application software operates in real time and makes it possible to control the heating of the experimental section in an optimal way, as well as to control the output currents of thyristor aggregates more accurately and efficiently. The experiments results of the implemented software after the experiments at various capacities and different operating modes of the boiling stand have been analyzed.

   Problems in detecting early (up to 27 weeks of pregnancy) risk signs of developing preeclampsia, which is a severe complication of pregnant women, are discussed using screening results for pregnant women in the Moscow region. Screening involves the measurement of the concentration of angio- and antiangiogenic proteins PlGF and sFlt-1 in the blood serum. These proteins are considered as preeclampsia markers in contemporary medicine. The PlGF protein stimulates the blood vessel growth in the mother’s placenta, whereas the sFLT-1 protein suppresses vascular growth. Patients are divided according to doctor’s diagnoses into three groups (classes): a control group (patients without preeclampsia), a group with a moderate complication form, and a group with a severe preeclampsia form. Integral distributions of patients on PlGF and sFLT-1 proteins are obtained. Calculated thresholds separating patient`s classes point to the possibility of detecting early preeclampsia signs. Then, the dynamics of the concentration of the PlGF and sFLT-1 proteins during the second trimester of pregnancy is investigated and is compared with the dynamics of their development for patients without preeclampsia. A prognostic rule is formulated indicating the risk of developing preeclampsia with an increase in the pregnancy period. The rule will help the treating doctor pay special attention to the treatment of patients at risk of complication.

   Earlier, we showed that when aggregating network traffic measurements, starting from a certain aggregation window, a stable distribution is formed, which is approximated with a high accuracy by a lognormal law. In addition, we observed a violation of this law during a hacker attack on a small local area network. The procedure for organizing a DDoS attack using measurements of Internet traffic, recorded in the trunk channel is discussed in this work. It has been found that when simulating a DDoS attack, no violation of the log-normal law is observed. Therefore, to verify the deviation from the lognormal law in a hacker attack on a net-work, it is necessary to organize a controlled DDoS attack on a specific network resource.

   The hypotheses about the parabolic form of the function of the price of the bitcoin cryptocurrency and the price of shares of the MMM financial pyramid are tested using the least squares method. The coefficients of these functions are found in an explicit form. The statistical significance of the constructed models is checked using the correlation, determination, and Fisher indices. The adequacy of the found regressions has been proved. A brief overview of operations with the bitcoin cryptocurrency and the history of the MMM financial pyramid is given. The monthly data in US dollars of the bitcoin price for 11 years and the price of MMM shares for 31 years taken from the website of the information portal of the stock market Investing.com have been analyzed. The monthly data of cryptocurrency quotes in US dollars for 2010–2021 are given in the tabular form together with plots illustrating the dynamics of prices for bitcoin and MMM shares. In addition to the actual data, the figures show parabolas found by the least squares method. To study the behavior of the price of cryptocurrency, almost the entire period of the existence of bitcoin, namely from 2010, is initially considered. The number of analyzed observations is 133. In the second stage of the study, the period has been shifted to 2017. The number of observations in this case is reduced to 57. The price of MMM shares from 1990 to 2021 is analyzed and the time series is built on 376 monthly data.

   The oxygen concentration distribution in argon inside the mockup channel and the furnace channel for sintering uranium-plutonium nitride fuel pellets at room temperature is modeled numerically and experimentally. The numerical modeling is performed within the CFD model of the furnace channel developed with Ansys Fluent software. The CFD model is tested and verified using previous experimental data on the distribution of oxygen concentrations in argon obtained on a specifically designed test bench for gas-dynamic studies of the furnace channel for sintering uranium–plutonium nitride fuel pellets. The study reports the calculated and experimental possibility in principle to implement a three-zone separation of gases in a furnace channel with specific nitrogen and argon concentrations required for sintering nuclear fuel pellets. The CFD model satisfactorily describes the gas-dynamic processes in the sintering furnace channel in the fuel pellet heating, sintering, and cooling zones. The best agreement between the calculated and experimental concentrations is reached in the central part of the channel (in the area of location of the fuel pellet boats). The calculated concentrations of oxygen in argon exceed the experimental ones almost everywhere, except for several points on the surface of the supporting plates with boat dummies near the oxygen supply unit. The difference between the calculated and experimental oxygen concentrations on the surface of the supporting plates with the boat dummies is in the range from 0.1 to 6.6 vol %. The CFD model can be used to select the parameters for the furnace channel to ensure compliance with the established requirements for the composition of gaseous media at operating temperatures.

   A software and hardware complex for measuring the concentration of gases is presented. It includes a physical prototype of a gas analyzer paired with a smartphone, software for the prototype and for the smartphone with Android OS, a website, a database, and scripts for exchanging information between the components of the complex. The principle of operation of the server for expanding the online functionality of the gas analyzer that measures the concentration of several gases (methane, propane, butane, carbon monoxide, hydrogen) is also described. The gas analyzer is paired with the Android smartphone. The smartphone is used to display information, to control the modes of displaying information on the screen, to determine the location of the user of the gas analyzer, and to send operational information to a remote server. The server is deployed on a RaspberryPiB+ computer with the FreeBSD operating system and the MySQ database. The server is designed to store the results of gas measurements and the coordinates of the place where the measurements were made. A website has also been developed where the user can view the measurement indicators in the form of graphs. The developed complex will allow the constant monitoring of the concentration of potentially dangerous substances. In addition, the complex will allow one to quickly respond to a possible emergency situation.