Menu

Publications

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

Editor-in-Chief

**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

Partners

**Summaries of the Issue**

### OPTICAL ENGINEERING

Organic-inorganic light-absorbing composites for near infrared part of spectrum

Sergei K. Evstropiev, Valery M. Volynkin, Bulyga Dmitry V. , Ostrovskii Vyacheslav A., Makarov Konstantin N. , Dukelskii Konstantin V., Polishchuk Grigoriy S. 529

Synthesis and study on structure and properties of organic-inorganic composites based on epoxy resin, CuO and Fe3O4 absorbing light in infrared part of spectrum was performed. The composites synthesis was performed by introduction of CuO and Fe3O4 micropowders into liquid epoxy composition with subsequent homogenization of the mixture and polymerization. The study on structure and properties of organic-inorganic composites was performed by methods of optical microscopy, infrared and visible spectroscopy, study on microhardness. According to the IR spectroscopy data, introduction of oxide particles leads to decrease in epoxy polymer degree of calcification. The composites containing Fe3O4 show relatively low light reflection until 4.2 % in the spectral range of 1000–1100 nm that corresponds to the theoretical estimation data. Incorporation of CuO and Fe3O4 micropowders into the epoxy polymer leads to an increase in microhardness from 120 to 160 MPa. Obtained experimental data can serve as the base for development of IR-absorbing organic-inorganic composites for laser technology.

Study of pyroelectric effect and creation of modified design of phase modulator based on lithium niobate

Shulepova Alena V., Vladimir A. Shulepov , Vladimir E. Strigalev 538

The study explores the phenomenon of the pyroelectric effect and demonstrates its influence on the emergence of an additional phase shift of the passing light wave in waveguide structures of photonic integrated circuits formed on a lithium niobate crystal X-cut substrate. Measurements were carried out using interferometric methods in a Mach-Zehnder fiber-optic interferometer configuration with radiation modulation in the reference arm allowing for continuous phase measurement in the arm with the sample under study. The calculation of the temporal parameters of each element of the experimental setup was performed to determine the relaxation times of pyroelectric charges. An analysis of the contribution of pyroelectric phase drift, its magnitude, and the temporal characteristics of charge relaxation causing the drift was conducted. A model was proposed and the design of a phase modulator based on a lithium niobate crystal with additional back Z-oriented plates located on the modulator electrodes was investigated. The proposed solution method is capable of compensating for the pyroelectric field and, as a result, reducing parasitic phase shift.

### PHOTONICS AND OPTOINFORMATIСS

Contrast change of the test object image in single-pixel and focal-plane array imaging through a scattering medium

Egor N. Oparin, Lappo-Danilevskaia Anastasiia K., Chernykh Aleksey V. , Tsypkin Anton N. 548

In recent years, the single-pixel imaging technique which uses a detector without spatial resolution and spatially modulated illumination patterns to reconstruct an object image has been finding its application for imaging objects in visibility obstructing conditions such as smoke or fog. The unifying feature of the studies published so far is the proof of workability of the methods proposed by the authors to improve the quality of single-pixel imaging images at their chosen scattering medium parameters without revealing the limits of applicability. This work experimentally demonstrates the influence of the number of scattering particles in the medium on the contrast of single-pixel images, and also compares the results with images obtained with a CCD camera, which allows not only to compare imaging methods under varying conditions, but also to evaluate the influence of losses introduced by the presence of a scattering medium on the contrast of single-pixel images. This work uses the classical experimental scheme of single-pixel imaging in which the single-pixel detector and focusing lens were replaced by a CCD camera to obtain images for comparison. A cuvette containing milk solution of different concentrations was placed between the object and the detector. For each concentration, an image of the object was reconstructed using the single-pixel imaging method and then recorded on the CCD camera until the concentration of the scattering agent was reached at which no image could be obtained by either method. The contrast was then calculated for each image obtained. It is shown that the single-pixel imaging method for milk concentrations up to 1/150 has an average contrast of 0.21, which does not decrease as the scattering increases. At the same time for CCD camera the contrast in the absence of scattering is 0.70, and with increasing milk concentration monotonically decreases to 0.07. The main feature of images obtained by single-pixel imaging through scattering media is the preservation of contrast as the concentration of the scattering medium increases indicating that the relationships between all the recorded on a single-pixel detector intensities used in the construction of the correlation function are preserved. A single-pixel image ceases to be reconstructed only when information about the object does not reach the detector due to multiple scattering and absorption produced by a milk solution. The considered features show the prospect of using single-pixel imaging for the construction of remote sensing systems with pattern recognition, as they allow obtaining similar images at different scattering coefficients of the scattering medium.

### AUTOMATIC CONTROL AND ROBOTICS

Synthesis of adaptive observer for nonlinear nonstationary systems

Nguyen Khac Tung, Vlasov Sergey M., Pyrkin Anton Alexandrovich, Kalinin Konstantin Yu., Nguyen Minh Hung , Nguyen Van Vuong, Bui Van Huan 554

A new method for the synthesis of adaptive state observation for a class of nonlinear non-stationary systems is proposed. This task is important and fundamental in control theory and is related to both the control problem and the task of monitoring the efficiency of the system operation. The solution to the problem is based on the generalized observer parameter estimation method to obtain the regression equation necessary for estimating the state and parameters of the system. Further, the dynamic regressor expansion and blending method dynamic regressor extension and mixing method is applied to identify the unknown system parameters. The paper proposes a method for estimating the state vector for a nonlinear non-stationary system in which the unknown parameters depend on the state vector under external disturbances. The results obtained are rigorously proved using mathematical theory. Simulation in Matlab/Simulink is performed to demonstrate the effectiveness of the developed algorithm. The mathematical model of the considered objects is a nonlinear system of equations with variable parameters. Compared to previous methods, the method proposed in this paper is more general, especially in a system where the unknown parameters depend on the state vector with nonlinear functions. However, the problem is currently solved only for discrete systems. In the future, it may be possible to extend it to continuous systems.

### MATERIAL SCIENCE AND NANOTECHNOLOGIES

Automation of search for optimal values of the ethylene oligomerization process parameters

Antipina Evgenia V., Mustafina Svetlana A., Antipin Andrey F. 563

A mathematical description of the process of ethylene oligomerization on a NiO/B2O3-Al2O3 catalyst in a liquid heptane solvent is given. Problems of optimal process control are formulated. The temperature and time of the process are taken as control parameters. An algorithm is proposed for solving the problem of optimal control of the industrially significant catalytic process of ethylene oligomerization. The search for solutions to the formulated problems is carried out using a genetic algorithm with real coding. For each of the problems under consideration, a method is proposed for representing a mathematical analogue of a population on the basis of which a solution is searched. A step-by-step algorithm for determining the optimal parameters for the ethylene oligomerization process is presented. A special feature of the algorithm is the simultaneous search for the values of a continuous control parameter (temperature) and a discrete control parameter (process time). A program (application) has been developed to determine the optimal values of process parameters. The application allows the user to select an optimal control problem, set the values of the genetic algorithm parameters to find a solution, and visualize the results obtained. A computational experiment was carried out for the process of ethylene oligomerization. The optimal duration of the process under isothermal conditions was calculated, at which the highest concentration of C4 hydrocarbons is achieved. The optimal temperature conditions and duration of the ethylene oligomerization process were determined to ensure the maximum concentration of C6 hydrocarbons. The conducted numerical experiments demonstrated lower resource consumption compared to the methods of uniform search and variations in the control space. The proposed algorithm can be used to study the patterns of catalytic processes without resorting to laboratory experiments associated with additional material and time costs.

Electroluminescence of new coordination compounds of europium ions with β-diketones, acetic and butyric acids

Osadchenko Anna V., Ambrozevich Sergey A., Zakharchuk Ivan A. , Andrey A. Vashchenko, Daibagya Daniil S. , Ryzhov Alexandr V. , Pevtsov Dmitry N., Pevtsov Nikolai V., Selyukov Alexandr S. 571

In this work, organic light-emitting LEDs based on Eu3+ coordination compounds with β-diketones and acetic and butyric acids were created and studied. At the moment, an active search is underway for new materials to create optoelectronic devices with high luminescent characteristics. One of these characteristics is high color purity and it can be achieved through the use of materials with narrow-band luminescence, for example, compounds based on Eu3+ ions. Complexes based on Eu3+ with 1,1,1-trifluoro4-phenyl-2,4-butanedione and acetic Eu(Cl)(Btfa)(CH3COO) (compound 1), butyric Eu(Btfa)2(CH3(CH2)3COO) (compound 2) acids were synthesized. The LEDs of the synthesized compounds were manufactured using a combined technique including the method of centrifugation and the method of thermal spraying in vacuum. The characteristics of the LEDs were measured by optical spectroscopy. To study the optical properties of the complexes, the powder was placed between two quartz substrates. Photoluminescence spectra were recorded using a SDL-1 spectrometer, an LED with a wavelength of 365 nm and a photoelectronic multiplier operating in linear mode. Electroluminescence spectra were obtained using the Ocean Optics Maya 2000 PRO spectrometer. A linear structure characteristic of Eu3+ ions was observed in the photoluminescence spectrum of the studied complexes. In the electroluminescence spectrum, radiation characteristic of Eu3+ ions is also observed, in addition to it, an additional wide band with a maximum at a wavelength of 390 nm and a half-height width of 61 nm is observed in the short-wavelength region. The operating voltage of the LED was 10 V. A characteristic “cold” white glow was observed for the studied LEDs. In the spectra of photos- and electroluminescence the following main transitions were found for the studied complexes: 5D0 → 7F0 (maxima at wavelengths λ1 = λ2 = 580 nm for compounds 1 and 2), 5D0 → 7F1 (split band, with maxima at wavelengths λ1 = 587 nm, λ2 = 593 nm, λ3 = 600 nm for the compound 1 and λ1 = 592 nm, λ2 = 599 nm for compound 2), 5D0 → 7F2 (split band, with maxima at wavelengths λ1 = 614 nm, λ2 = 619 nm, λ3 = 623 nm for compound 1 and λ1 = 614 nm, λ2 = 618 nm, λ3 = 620 nm for junction 2), 5D0 → 7F3 (split band, with maxima at wavelengths λ1 = 648 nm, λ2 = 652 nm, λ3 = 655 nm for junction 1 and λ1 = 652 nm, λ2 = 655 nm for compound 2). The wide band observed in the electroluminescence spectrum arises due to the contribution of the hole transport layer, due to the through flow of charge carriers through the active radiating layer, which leads to recombination in the PVK OLED layer. An analysis of the volt-ampere characteristics of the manufactured devices showed that they are characterized by two main conduction modes: the first corresponds to a limitation of the current by a spatial charge (0–7 V), the second is a limitation due to the processes of capture of charge carriers (7–23 V). The results of this work can be used in the production of industrial lighting.

### COMPUTER SCIENCE

Method for generating multimedia files for the tasks of facial biometrics and its applications

Kaziyeva Nazym M., Kukharev Georgy A., Kalybek S. Maulenov 578

The methods of constructing compact multimedia files based on a color image of a face, biometric data and documentary information about the person to whom this face belongs are considered. The essence of the proposed method consists in generating a color QR code based on facial characteristics and embedding the code into the face image. The formation of a color QR code is performed by replacing three slices of the Least Significant Bit of the original image. Mathematical descriptions, pseudocodes and graphic illustrations are presented to understand the idea of the method, the proposed solutions, and the algorithm implementing the method of embedding a color QR code in a face image. The developed new method of embedding color QR codes in face images is implemented programmatically and is the basis for the formation of multimedia files. The method can be recommended for the tasks of facial biometrics and its applications.

Advanced methods for knowledge injection in large language models

Nikita I. Kulin, Muravyov Sergey B. 588

Transformer-based language models have revolutionized Natural Language Processing tasks, with advancements in language modeling techniques. Current transformer architectures utilize attention mechanisms to model text dependencies effectively. Studies have shown that these models embed syntactic structures and knowledge, explaining their performance in tasks involving syntactic and semantic elements. However, transformer-based models are prone to hallucination where incorporated knowledge is not utilized effectively. To address this, methods are emerging to mitigate hallucination and integrate external knowledge sources like knowledge graphs (e.g., Freebase, WordNet, ConceptNet, ATOMIC). Knowledge graphs represent real-world knowledge through entities and relationships offering a potential injection point to enhance model performance in inference tasks. Various injection approaches, including input, architectural, and output injections, aim to incorporate knowledge from graphs into transformer models. Input injections modify data preprocessing, architectural injections add layers for knowledge integration, and output injections adjust error functions to correct knowledge incorporation during training. Despite ongoing research, a universal solution to hallucination remains elusive, and a standardized benchmark for comparing injection methods is lacking. This study investigates knowledge graphs as one of the methods to mitigate hallucination and their possible integration into Large Language Models. Comparative experiments across General Language Understanding Evaluation benchmark tasks demonstrated that ERNIE 3.0 and XLNet outperform other injection methods with the average scores of 91.1 % and 90.1 %.

Predicting gene-disease associations using a heterogeneous graph neural network

Sidorenko Denis A. , Shalyto Anatoly A. 594

The research presents the development of a heterogeneous graph neural network model for predicting gene-disease using existing genomic and medical data. The novelty of the approach is in integrating the principles of graph neural networks and heterogeneous information networks for efficient processing of structured data and consideration of complex genepathology interactions. The solution proposed is a heterogeneous graph neural network which utilizes a heterogeneous graph structure for representing genes, diseases, and their relationships. The performance of the developed model was evaluated on the DisGeNET, LASTFM, YELP datasets. On these datasets, a comparison was made with current SOTA models. The comparison results demonstrated that the proposed model outperforms other models in terms of Average Precision (AP), F1-measure (F1@S), Hit@k, Area Under Receiver Operating Characteristic curve (AUROC) in predicting “gene-disease” associations. The model developed serves as a tool for bioinformatics analysis and can aid researchers and doctors in studying genetic diseases. This could expedite the discovery of new drug targets and the advancement of personalized medicine.

### MODELING AND SIMULATION

Computer simulation of the interaction between a shock wave and a wall shielded by an inhomogeneous gas suspension layer

Dmitry V. Sadin 602

In modern technologies of pneumatic transport, fluidization, and polymer spraying, gas-dispersed media are widely used. Of particular interest, from the point of view of dynamic loading of structures, are shock-wave processes in gas-dispersed mixtures in the vicinity of the walls. The use of computer modeling methods makes it possible to reduce time and material costs for improving designs and optimizing technological process parameters. A hybrid large-particle method of second order approximation with a nonlinear correction, Superbee at the Eulerian stage and VanLeer at the Lagrangian stage, was used for the calculations. The algorithm is implemented as multi-threaded solver code, with processing of graphical results in a separate parallel process. A detailed numerical simulation of the characteristic stages of the interaction of a shock wave with a wall shielded by a layer of finely dispersed gas suspension with a cylindrical region of increased particle density was carried out. The beginning of the process (before the interaction of a plane shock wave passing into the layer of gas suspension with inhomogeneity) is one-dimensional in nature. Further development of the physical picture is associated with a significant restructuring of the flow. The shock wave enveloping the cylindrical boundary of the inhomogeneity converges to the plane of symmetry with the formation of a focusing effect. Due to baroclinic instability (mismatch of pressure and density gradients), a vortex zone is formed on the surface of the highdensity boundary. As shown by a detailed analysis of the calculation results, the most significant (more than an order of magnitude relative to the initial state) surges in pressure and density of the gas suspension are caused by the interactions of a focused shock wave that has passed into the inhomogeneity, and then an incident reflected composite shock wave pulse. The results obtained have theoretical and applied significance. New physical effects of shock wave reflection from a wall shielded by a layer of gas suspension with a cylindrical region of increased density of the dispersed fraction have been revealed. The reasons for the sequence of bursts in pressure and density of the mixture, which can lead to ignition and detonation of the combustible dispersed phase, are determined. The developed numerical algorithm and computer modeling technique can form the basis for the analysis of shock wave phenomena in the vicinity of the walls of structures and the justification of rational parameters of technological gas-powder technologies.

Flexible and tractable modeling of multivariate data using composite Bayesian networks

Irina Yu. Deeva, Shakhkyan Karine A. , Kaminsky Yury K. 608

The article presents a new approach to modeling nonlinear dependencies called composite Bayesian networks. The main emphasis is on integrating machine learning models into Bayesian networks while maintaining their fundamental principles. The novelty of the approach is that it allows us to solve the problem of data inconsistency with traditional assumptions about dependencies. The presented method consists in selecting a variety of machine learning models at the stage of training composite Bayesian networks. This allows you to flexibly customize the nature of the dependencies in accordance with the requirements and dictated characteristics of the modeled object. The software implementation is made in the form of a specialized framework that describes all the necessary functionality. The results of experiments to evaluate the effectiveness of modeling dependencies between features are presented. Data for the experiments was taken from the bnlearn repository for benchmarks and from the UCI repository for real data. The performance of composite Bayesian networks was validated by comparing the likelihood and F1 score with classical Bayesian networks trained with the Hill-Climbing algorithm, demonstrating high accuracy in representing multivariate distributions. The improvement in benchmarks is insignificant since they contain linear dependencies that are well modeled by the classical algorithm. An average 30 % improvement in likelihood was obtained on real UCI datasets. The obtained data can be applied in areas that require modeling complex dependencies between features, for example, in machine learning, statistics, data analysis, as well as in specific subject areas.

Method for obtaining two-component composite materials with a given thermal conductivity

Zarichnyak Yury P. , Vyacheslav P. Khodunkov 615

A method for obtaining two-component composite materials is proposed which differs from known methods in that as a result of the implementation of the method any value of the thermal conductivity of the composite being created can be achieved, if taken from the range of thermal conductivity of the initial components. The method consists in mixing substantially heterogeneous solid components in a given proportion, their subsequent pressing, and sintering. The proportion of the components is previously calculated based on the required value of the thermal conductivity of the mixture. To estimate the expected thermal conductivity of the composite and find the required proportion of components, it is proposed to use the structure model with chaotically arranged components developed by the authors of the article. It is shown that in order to achieve the goal, the thermal conductivity of a two-component mixture can be successfully modeled by a structure with chaotically arranged components, where an eight-element cubic cell proposed by the authors of the work is used as an elementary cell. At the same time, the accuracy of setting the required thermal conductivity value is at least 90 %. The implementation of the method is shown by the example of obtaining a copper-alund composite with a given thermal conductivity value λ = 110 W/(m·K) which, according to the calculation presented in the example, corresponds to a percentage ratio of components 74/26 (copper/alund). The developed method makes it possible to obtain two-component composites with a given thermal conductivity in a wide range from several units to several hundred W/(m·K). An almost unlimited range of substances in a solid powdery state can be used as components. It is possible to implement a continuous scale of thermal conductivity of solids. When using refractory substances, this scale can be extended to a temperature of 2000–2500 °C. The method is intended for use in metrology, metallurgy, nuclear technology, aviation and heavy industry, shipbuilding.

Computer simulation of heat and mass transfer processes during water vapor condensation from natural gas combustion products on smooth cylindrical tubes

Bryzgunov Pavel A. , Rogalev Andrey N. , Kindra Vladimir O., Komarov Ivan I., Zlyvko Olga V. 620

The results of numerical simulation of heat and mass transfer processes during the condensation of water vapor from natural gas combustion products on bundles of smooth horizontal cylindrical tubes are presented. An empirical mathematical model of condensation of water vapor from a gas-steam mixture with a high content of non-condensable gases has been developed based on experimental data. The proposed mathematical model includes jointly solvable equations of thermal energy, momentum and mass conservation, while the equation of conservation of mass takes into account the species transport due to convection, molecular and turbulent diffusion. The phase change is taken into account in the source terms of the mass conservation equation; both condensation in the volume as the mixture passes through the dew point and local surface condensation on the cooling tubes are taken into account. To describe condensation in the volume, the return to saturation temperature model is used, and for surface condensation an algebraic empirical model was developed based on the analysis of experimental data. The advantage of the chosen approach is that there is no need to calculate the hydrodynamics of droplets and condensate films as a separate continuous one due to the influence of these factors on heat and mass transfer in the experimental coefficients, which significantly reduces the computational complexity of the problem and allows engineering calculations to be carried out in a coupled formulation. The structure of the developed mathematical model ensures easy integration with common commercial and freely available CFD codes. Based on experimental data, the coefficient of the developed condensation model was determined. It is shown that when adjusting the coefficient using one base point, the model ensures agreement with experimental data for other modes with a deviation not exceeding the experimental error. Using a verified model, a section of a condensation heat exchanger for gas turbine unit exhaust gases with a staggered bundle of smooth pipes in a coupled formulation was simulated, and the numerical value of increasing cooling water heat perception due to the utilization of latent heat of condensation was determined. The obtained modeling data and the developed model of condensation of water vapor from natural gas combustion products can be used in the calculations and design of condensing heat exchangers as well as condensing boilers.

Instability of a rectangular CCCC-nanoplate

Mikhail V. Sukhoterin, Sosnovskaya Anna A. 629

The spectrum of critical loads and equilibrium forms of a CCCC-nanoplate (C — clamped edge) at various values of a non–local nanoparameter has been studied. The symmetric solution is represented by two hyperbolo-trigonometric series in two coordinates which obeyed the basic differential equation of the physical state of Eringen. The boundary conditions for the absence of deflections and angles of rotation of the pinched faces were precisely satisfied. As a result, a homogeneous infinite system of linear algebraic equations with respect to unknown coefficients of these series is obtained containing a relative compressive load as the main parameter. After the conversion, the system began to contain only one sequence of coefficients. An iterative process of searching for a non-trivial solution in combination with the method of iterating over the load value is constructed. For each value of the nonlocal parameter, the first four critical loads for symmetric forms of supercritical equilibrium are found and their 3D images are obtained. It was found that critical loads decreased with an increase in the nonlocal parameter. The influence of the number of members held in rows and the number of iterations on the accuracy of the results is investigated. The results obtained can be used in the design of various nanoscale smart structures.

Using genetic algorithms to solve the problem of finding the optimal composition of the reaction mixture

Miftakhov Eldar N. , Kashnikova Anastasia P., Ivanov Dmitry V. 637

A heuristic approach to optimization of complex physicochemical processes in the form of a genetic algorithm for solving problems is presented. In comparison with other evolutionary methods, the genetic algorithm allows working with large search spaces and complex evaluation functions, which is especially important in the study of multifactor physicochemical systems. Due to the relatively high need for computing resources when working with large and complex search spaces, optimization of existing calculation organization schemes has a positive effect on the accuracy of the calculated results. The paper presents a modified genetic algorithm that minimizes the number of iterations to achieve a given accuracy when solving the problem of finding the optimal composition of the initial reaction mixture. For a complex physicochemical process, an optimization problem is formulated which consists in finding the composition of the initial reaction mixture that promotes maximization (or minimization) of a given target parameter. The optimality criterion is determined by the type of the problem being solved and, when organizing calculations, is focused on the maximum yield of the target product. The main steps of implementing the genetic algorithm include creating an initial set of solutions and subsequent iterative evaluation of their quality for subsequent combination and modification until optimal values are achieved using mechanisms similar to biological evolution. To improve the efficiency of the method and reduce the number of iterations, a modification of the genetic algorithm is proposed which boils down to a dynamic estimate of the “mutation” parameter, depending on the diversity of individuals in the formed population of solutions. In a series of computational experiments, an analysis was made of the influence of the genetic algorithm parameters on the accuracy and efficiency of solving the problem using the example of studying the kinetics of the Michaelis-Menten enzymatic reaction. The results of calculations to determine the optimal composition of the reaction mixture showed that the dynamic determination of the “mutation” parameter contributes to an increase in the accuracy of the problem solution and a multiple decrease in the relative error value reaching 0.77 % when performing 200 iterations and 0.21 % when performing 400 iterations. The presented modified approach to solving the optimization problem is not limited by the type and content of the studied physicochemical process. The calculations performed showed a high degree of influence of the “mutation” parameter on the accuracy and efficiency of the problem solution, and dynamic control of the value of this parameter allowed increasing the speed of the genetic algorithm and reduce the number of iterations to achieve an optimal solution of a given accuracy. This is especially relevant in the study of multifactorial systems when the influence of parameters is non-trivial.

Configurable combustion models of combustion chamber of microturbine engine with possibility of connecting various physico-chemical processes

Bulat Pavel V, Vokin Leonid O. , Konstantin N. Volkov, Nikitenko Alexander B. , Prodan Nikolai V., Maksim E. Renev 645

Mathematical and numerical models of the combustion of a fuel mixture in the combustion chamber of a microturbine engine have been developed. Complexity of the models can vary, which gives developers a fairly convenient calculation and design tool. Models allow to take into account the required design tasks by considering and not taking into account various physical processes, and create an optimal complexity model for each specific case. The development of the required configuration begins with the consideration of a simple model of the global kerosene in air combustion reaction without conjugate heat exchange with solids. Step by step, models of extended kinetics, swirling flow, radiation, heat exchange with walls, and the presence of lubricant oil in kerosene are added to the calculation methodology. The results of calculating the wall temperature and combustion completeness were compared with those of JetCat P100-RX and P550-PRO turbojet engines, the integral characteristics of which are well known. In the course of the performed computational and experimental studies, a comparison of the run-off spots on the walls of the combustion chamber with the calculated temperature distributions was performed. A good agreement of the results was obtained for the complete mathematical model. The effect of better cooling of the combustion chamber and increasing the completeness of combustion by twisting the flow behind the compressor is revealed. The effect of the addition of oil to kerosene on an increase in specific fuel consumption by 1–4 % has been determined. The significance of the results obtained lies in the possibility of applying the proposed calculation methodology in engineering practice. The considered modifications of the model represent an important stage in the creation and verification of a mathematical model of in-chamber processes.

Multilevel splitting for rare events estimation in permutation tests

Sukhov Vladimir D. , Korotkevich Gennady V., Sergushichev Alexey A. 654

Permutation tests are widely employed in statistical analysis, especially when the assumptions of parametric tests are violated, or the data distribution is unknown. However, classical permutation tests encounter challenges when attempting to estimate the probabilities of rare events with high relative accuracy, leading to difficulties in applying corrections for multiple hypothesis testing. In this study, we propose an original method for estimating arbitrarily small P-values in permutation tests, which is based on multilevel splitting for Monte Carlo method. The proposed method involves splitting the original permutation space into non-overlapping levels based on the statistic values. This approach allows the problem of estimating the original probability of a rare event to be reduced to estimating ordinary conditional probabilities for each level. Utilizing such an approach enables efficient estimation of the desired P-values while maintaining a balance between computation time and the level of relative error. The efficacy of the method is demonstrated in its application to the task of estimating arbitrary P-values in the two-sample Kolmogorov-Smirnov test. Comparing the method results with true P-values has shown practical convergence of the method. Moreover, examples of the superiority of the proposed method over alternative asymptotic approaches have been provided. Thus, the proposed method shows significant potential for application across a broad spectrum of scientific fields, such as systems biology, immunology, and others. Furthermore, the method can be adapted for use in various statistical analysis scenarios that require handling probabilities of rare events in permutation tests.

### BRIEF PAPERS

Method of muscle tissue segmentation in computed tomography images based on preprocessed three-channel images

Teplyakova Anastasia R., Shershnev Roman V. , Starkov Sergey O. 661

The results of a study of a preprocessing influence method based on the formation of three-channel images on the accuracy of muscle tissue segmentation models on the computed tomography scans corresponding to the levels of the vertebrae of the thoracic and lumbar spine are presented. Ten models have been trained and tested on the Sparsely Annotated Region and Organ Segmentation dataset. The values of the Dice similarity coefficient and the Intersection over Union in the ranges of 0.9353–0.9421 and 0.8737–0.8885 were obtained. The use of a three-channel approach to the formation of input data increased the accuracy of models of four of the five architectures considered. Trained models can be used to quickly and accurately annotate muscle tissue during the diagnostic process.

Model of adsorption on epitaxial graphene: analytical results

Davydov Sergei Yu., Lebedev Alexander A 665

The atom/graphene/substrate system is considered and a scheme for obtaining analytical expressions for the adatom occupation numbers is proposed. The possibility of the presence of a gap in the electronic spectrum of graphene was taken into account. Simple and transition metals and semiconductors were considered as substrates, and simple theoretical models were used to describe their densities of states.