A compact spherical tokamak MEPhIST (MEPhI Spherical Tokamak) aimed at educational, demonstration and research purposes is under development at Institute of Laser and Plasma technologies (LaPlas) at NRNU MEPhI. The main purposes are training in the field of controlled thermonuclear fusion for Russian installations (T-15MD, T11-M and others) and the international ITER reactor, as well as solving innovative problems in the field of fusion technologies. An important feature of this project is the most possible digitalization of the installation in order to provide a remote access for students of other universities specializing in the field of fusion technologies with magnetic plasma confinement. With the successful implementation of the project to create a reliable tokamak, this installation will be used to solve a number of urgent scientific and technological problems: acceleration of lithium technologies development, studies of plasma confinement in a spherical tokamak, development of high-frequency (RF) technologies (microwave preionization and steady-state RF current drive) and to develop in situ methods for analyzing plasma-surface interaction. At this stage, the design of the educational, demonstration and research tokamak MEPhIST has been carried out, the concepts of diagnostic systems and additional heating of the plasma have been developed, the production of a vacuum chamber and elements of an electromagnetic system has been started.

   In this study, we consider the problem of multiple recycling of uranium in the fuel cycle of thermal neutron reactors. The general approach to reusing recovered uranium extracted from spent fuel is related to its enrichment by the target fissile isotope ²³⁵U in cascades of gas centrifuges. However, the reprocessed uranium enrichment has difficulties related to ^{232, 236}U isotopes presence and a higher concentration of ²³⁴U comparing to natural uranium. The low-enriched uranium product should meet the requirements on these even-numbered isotopes owing to radiation and neutron-physical characteristics. These conditions lead to obstacles for the complete return of the material to the cycle using the known enrichment schemes. This necessitates the search for new regeneration enrichment schemes that can solve this problem. In this paper, we propose a new configuration based on the modified double cascade of gas centrifuges, which allows consuming the whole amount of reprocessed uranium during the enrichment process. It is preferable to use the proposed cascade scheme when we deal with multiple uranium recycling, starting from the second recycle round. It corresponds to sustainable fuel recovery for a fleet of thermal neutron reactors.

   This paper presents the results of production and radiographic examination of micro-samples of curium-244 compounds with ion, cobalt and carbon, prepared by high temperature condensation of metal curium vapor onto corresponding substrates. The effect of carbon in the Cm–Co and Cm–Fe systems was studied. In the Cm–C system carbides Cm₂C₃ and Cm₃С with a cubic lattice were detected, which were isostructural with regard to carbides Am₂C₃ and Sm₃С. The absence of mutual solubility of system components at room temperature was established. The effect of high alpha-activity of ²⁴⁴Cm nuclide on the crystal structure of the compounds obtained was demonstrated.

   The qualitative features of the numerical integration of two-point boundary-value problems of boundary-layer type by using nonlocal transformations are described. Such transformations, sometimes also called Sundman-type transformations, are defined by using an auxiliary differential equation and allow one to “stretch” the boundary-layer region (after which any adequate numerical methods with a fixed stepsize can be applied). Multiparameter nonlinear singularly perturbed boundary-value problems with a small parameter having exact solutions in elementary functions are presented, which can be used to test various numerical methods on non-uniform grids. Particular attention is paid to the study of the most difficult boundary-value problems for numerical analysis, which have non-monotonic solutions or degenerate solutions at the boundary of the boundary-layer. A comparison of numerical and exact solutions shows the high efficiency of the nonlocal transformation method for numerical integration of boundary-value problems with a boundary layer.

   The AFES program (automatic finding exact solutions) designed to find exact solutions of polinomial ordinary differential equations has been described. The simplest equations method has been used to find exact solutions. The method consists in constructing exact solutions of differential equations using a general solution of a lower order differential equation. In order to choose the form of the exact solution, it is necessary to determine the pole order of the solution of the original equation and the pole order of the solution of the simplest equation. The program for automatically constructing Newton polygons ACNP (automatic construction of Newton polygons) has been used. The Riccati equation and the equation for the elliptic Weierstrass function have been considered as simple equations. In order to test the program, examples of constructing exact solutions of various nonlinear differential equations are given. The AFES program is written in the Maple computer algebra system. The algorithm of the program and examples of its application are given. The AFES program has several advantages over wellknown programs for finding exact solutions of differential equations. In particular, constructed exact solutions are different and they cannot be transformed to each other.

   Based on the definition of an additional sought-for function (ASF) and additional boundary conditions (ABC), a highly accurate solution of the heat transfer problem in a turbulent boundary layer for boundary conditions of the first kind was obtained. The relation characterizing the change of the thermal boundary layer thickness that depends on longitudinal variables is taken as an additional sought-for function. The use of this function makes it possible to reduce the partial differential equation to the ordinary differential equation. Additional boundary conditions are accepted in such a form that their satisfying is equal to satisfying an equation at the boundary points. Empirical formulas of the velocity profile and its thickness in the turbulent dynamic boundary layer were used to obtain the solution of the problem for the thermal turbulent layer. Based on the results one can conclude that the thickness of the laminar thermal boundary layer is almost twice the thickness of the turbulent one.

   This paper presents the simulation of airflow around a set of typical obstructions (three-dimensional cube and hemisphere, as well as a two-dimensional hill) by means of ANSYS FLUENT package within the framework of the standard (k–ε) turbulence model. The obstructions represent the buildings and typical landforms in the area of nuclear power plant emissions. To ensure the convergence of the results, we used a non-uniform spatial grid on the computational domain, which thickened near the obstruction surface and the outer boundaries. The size and position of the obstruction were chosen to best match the conditions of the published experiments. The result of modeling the velocity and direction of the air flow as a whole reveals a good agreement with the experimental data in wind tunnels in the areas in front of the obstacle, above it, as well as in its aerodynamic shadow. Characteristic zones of accelerated flow, vortices and reverse flow are reliably reproduced. The length of the turbulence zone of the leeward side of the cube is the maximum in comparison with the hill and hemisphere. Unlike the latter, the cube also forms a turbulent zone with the separation of the flow over the upper plane of the roof. Differences with experiments are observed only in local areas of strong turbulence in the aerodynamic shadow of an obstacle near the ground surface. All this opens the possibility of a full-fledged simulation of the diffusion of nuclear power plant emissions, taking into account the terrain features of the site of a particular station and its main building in order to refine the personnel and public exposure.

   Qualification tests were interpreted as specific case of semi–natural experiment where laboratory plant takes part of environment physical model with studied object. In this situation virtualization represents transfer from physical to mathematical models and allows virtual qualification, i. e. qualification test implementation in form of numerical experiment. Virtualization permits performing extrapolation of laboratory results to normal exploitation conditions and recalculation of these conditions to qualification experiment parameters. Virtualization effectiveness demonstrated at math models optimization, qualification experiments correction and their results forecasting, at criteria models application for qualification experiments adequate parameterization on exploitation characteristics. Models of internal combustion engine were created for investigation of tribological and chimmotolologcal factors influence on engine dynamics end effectiveness. They are based on balance relation and differ with method of cylinder pressure imitation only. Friction influence was based on Gersy–Streebeck curve approximation and its use for friction coefficient calculation in dependence of Sommerfeld’s number. Basing on anti–wear properties investigation criteria model of volume wear was developed and used for wear evaluation at specified conditions. It was proposed to use this model for wear forecast at extreme conditions and forming of corresponding qualification normative. For oils density approximation model – oriented identification was proposed to use. Toward this end, modified algorithm was built which is based on law of corresponding states. In contrast to usual algorithm based on correlation tables use modified algorithm uses density presentation in form of power function of oil pressure and temperature. It was shown that for light oils modified algorithm provides better precision in comparison with usual one.

   The research proposes the neural network methods to include a textual dependency tree structure in classification tasks of Russian texts. Author profiling task of gender identification was chosen to test the models, and two corpora used in experiments: based on a crowdsource, and in-person polling. The first approach is based on a long short-term memory (LSTM) layers, and developed graph embedding algorithm. The second one is based on a graph convolution network and LSTM. Two syntactic parsers were used to obtain dependency trees from the texts. Input data was represented in different forms: morphological binary vectors, FastText vectors, and their combination. The developed models result was compared to the state-of-the-art, that is neural network model based on a convolutional and LSTM layers. Finally, we demonstrate that including textual dependency tree structure to input feature space improves f1-score of gender classification task on 4 % for the RusPersonality dataset, and 7 % for the crowdsource dataset in average. The developed models resulting f1-score is 84% and 83 %, respectively.