No. 7 (2021)

In the paper we consider the solution of a computationally expensive problem such as calculation
of statistics probability distribution with the help of modern computer technologies. To reduce
computational complexity and to provide a sufficient level of criteria efficiency not less than
the specified threshold, we suggest to use Δ-exact approximations. To calculate exact approximations,
we use the method of second order, based on solution of a system of linear equations. Owing
to this method, it is possible to calculate exact approximations for the maximum values of sample
parameters for available computational resource. The most laborious part of the method of second
order is the procedure of sequential detection of the vectors of possible solutions and test if the
vectors belong to the set of solutions. The system solution set membership test for the vectors of
possible solutions is data independent, so the algorithm can be data-parallelized. We give the algorithm
complexity equation for calculation of exact approximations of statistics probability distributions.
Using this equation, we calculated the complexity of modern practical problems for the
samples with the parameters (N, n) of the alphabet power and the sample size: (256,1280),
(128,640), (128, 320), and (192,3200) for the accuracy of calculations =10-5. The computational
complexity is 9.68·1022-1.60·1052 operations, and its average value is about 4.55·1025 operations,
the number of tested vectors is 6.50·1023-1.39·1050, and the number of solutions is 4.67·1012-
5.60·1025, respectively. The total solution time for clock-round duration of calculations cannot
exceed 30 days or 2.592·106 sec. For the obtained complexity evaluation, we analysed abilities of
modern cluster computer systems based on general-purpose processors, graphic accelerators, and
FPGA-based reconfigurable computer systems. For each technology, we determined the number of
computational nodes needed for calculation of exact approximations with the specified parameters
during the specified time. We proved that it is impossible to obtain a solution for the required parameters
of exact approximations of statistics probability with the help of the reviewed modern
computer technologies. In conclusion, we claim that it is necessary to analyse the abilities of advanced
computer technologies based of quantum and photonic computers, and also hybrid computer
systems for calculation of exact approximations of statistics probability distributions with
the specified parameters during reasonable time.

The advantage of the promising method of passive radiosensor technical diagnostics
(PRTD) over the currently existing methods for determining the technical condition (vibrometry,
thermal control, JTAG-testing, optical control) are: no inertia, no processor time, no galvanic
contact with the object of study. In modern scientific literature, almost no attention is paid to numerical
models of electronic devices, including those based on bipolar transistors (BPT), which
describe the process of oscillatory redistribution of energy and radiation used in PRTD. Therefore,
the purpose of this study is to develop the PRTD method through the development, analysis
and comparison of circuit and electrodynamic models of oscillatory energy redistribution in the
BPT. The paper presents and analyzes simplified circuit and electrodynamic models of oscillatory
redistribution of energy in the BPT. The parameters of the models are calculated signal radio
profiles (SRP) are obtained for the electrical component of electromagnetic radiation created by
the radio-electronic unit itself, built on the BPT. Methods for adjusting the reference parameters
depending on the actual conditions for switching on the BPT are shown. It has been established
that the cross-correlation function of the SRP obtained as a result of circuit and electrodynamic
modeling is not lower than 0.93, which indicates a high similarity of the presented models. In
practice, the use of the developed models in the analysis of SRP obtained by recording the intrinsic
emissions of radio engineering components of electronic devices will allow us to determine the
operating mode of the BPT and its speed with a sufficiently high accuracy. This analysis can be
used in the PRTD, indicating a malfunction of the signal circuits, or degradation of the parameters
of the element itself in the early stages

The task of building a decision-making system within the framework of automated systems of
accident-free control of technological processes based on forecasting models is considered.
The analysis of models and methods of emergency forecasting is presented. The task of developing
a methodology for practical implementation of the system based on the integral criterion of accident-
free control, taking into account the time reserves to bring the process to a normal state
(emergency forecasting system) and the resource component (preventive maintenance system) is
formulated. The conclusion is made about the expediency of building decision-making systems and
automated control systems based on forecasting models, as the most promising approach to solving
the problem of accident-free control of technological processes. The principle of building a
decision-making system is based on the use of the integral criterion of accident-free management.
The block diagram of the algorithm for calculating the integral criterion of accident-free control is
presented. Hybrid methodology for practical realization of such systems on the basis of priority
regulation, which includes a standard regulator, is offered. The procedure of formation of priority
regulators according to the forecast data is described. A block diagram of the algorithm of the
priority regulator, which determines the critical parameter on the basis of sensitivity theory, is
presented. In case of a positive forecast on an accident, the critical parameter is selected by the
maximum of the sensitivity coefficient, and the minimum or maximum value of the parameter depending
on the sign of its rate of change is fed to the standard regulator from the matrix of critical
values as a set point. The structure of the decision-making system based on the concept of accident-
free control of technological processes is given. The station of accident-free control forms the
data for the decision-making module on the basis of the compositional model of emergency forecasting
and the integral criterion of accident-free control. Algorithm block diagram of the decision
making module for priority regulation is given.

Some civil aircraft assume two actuators simultaneously turning aside the flight control surface
(rudder, in some cases aileron or elevator). Thus resulting in onset of the force fighting (mutual
loading force). There are several ways to reduce the mutual loading force. One of them is to insert
specific force equalization algorithm in actuators steering. This article deals with effectiveness of
force equalization algorithm as well as its influence on system “2 active actuators - elevator”. Mathematic model of two actuators on elevator has been formed and tested by the developed testing method
that reproduces the most severe operation conditions. There are several nonlinearities which is
contained in mathematic model: sleeve-travel physical limits, nonlinear effects of fluid foil, rod-travel
physical limits and attachment rigidity. Force equalization algorithm comprises a pressure differential
feedback loop with PID regulator. The results show that force equalization algorithm is highly
efficient (mutual loading force has been reduced over than 90%) in mode test without external load.
However, in test mode with external load it is necessary to introduce a limitation on the magnitude of
the corrective signal so as decrease the rod drop to level specified in terms of reference. Algorithm
has no effect on stability margin of the system. In conclusion, results of this study could also be useful
to expand the test program for two actuators simultaneously turning aside the flight control surfaces
to further simplify the implementation of the force equalization algorithm.

Nowadays, researchers are developing technologies in the aviation industry related to the
electrification of aircraft functional systems. The braking system has a direct impact on the safety,
stability and functionality of the aircraft. Therefore, the motivation for replacing the hydraulic
system is accompanied by the results of comprehensive studies of the architectures of electric
braking systems, including the possibility of improving the quality of such systems through the
introduction of effective control. The work is devoted to the methodology of analytical synthesis of
the control algorithm for the electric braking system of the aircraft landing gear, as a multiconnected
control object, based on the theory of embedded systems. The mathematical model contains
a description of the electrical, mechanical and thermal processes of the system. The require ments for the quality of transients in terms of the angular velocity of the wheel and the temperature
on the surface of the frictional disc are set in the form of restrictions on the settling time and overshoot
and then transformed into the form of a reference model. The results of computer simulation
of the dynamics of the initial and linearized systems, as well as a system with a synthesized regulator
by the full vector of states are shown. The discussion about the robustness of the resulting solution
are presented and the results of computer simulation of a system with a "simplified" regulator
are shown.

The article describes about of the typical methods of air data parametric quorum control,
and an analysis of their capabilities to determine parametric failures that occur in the air data
system. To perform the calculations, the most common types of failures of the path of perception
and measurement of air pressure of the air signal system, causing catastrophic consequences,
were selected, the physical principles of their occurrence were described, the implementation of
which made it possible to build mathematical models of signal distortion. Based on the results of
modeling the operation of typical quorum control methods, and their response to failures artificially
introduced into the system, the advantages and disadvantages of the methods used are determined.
In order to eliminate the shortcomings found as a result of the analysis, an alternative
method for determining failures of the sensor group of the air data system is proposed by implementing
cross-checking of the parameters obtained from the pneumatic and vane sensor groups of
the system. For the proposed method, the results of modeling based on real flight data of a mainline
aircraft with parametric failures artificially introduced into them are presented. The possibility
of using the cross-checking algorithm in single-channel systems of air signals of small-sized
aircraft is evaluated. The statement of the research problem is formulated as follows: in order to
ensure the flight safety of an aircraft when using information in the control loop from a singlechannel
air data system, it is necessary to ensure the detection and exclusion of unreliable data
from the array of information issued by the system to consumers of information. At the same time,
the task of detecting and excluding data must be solved by the air data system itself, without using
additional data from other aircraft systems. Mathematical analysis, numerical modeling, determination
of correction factors and preparation of initial data were carried out in the MathCAD software
and mathematical complex. Analysis of the results of the studying implemented in the
MathCAD PMC cross-checking algorithm showed that the problem of determining the reliability
of information can be solved autonomously when it implemented a single-channel system of air
signals in an aircraft.

The aim of the research was to control the electrical network of a hybrid power supply system
for an autonomous underwater vehicle designed to travel over ultra-long distances over tens
of thousands of kilometers. To overcome ultra-long distances, the urgent task is to minimize the
specific consumption of electricity, provided that all consumers are provided with electricity. The
relevance of the work is determined by the novelty of using a hybrid power supply system in autonomous
unmanned underwater vehicles, consisting of heterogeneous sources of electricity operating
on different physical principles. Due to the lack of research to date, related to the control of
the hybrid power supply system, coordinated with the modes of motion of the vehicle in a wide range of speeds, the problem arose of developing control algorithms for the hybrid power supply
system. To solve the problem, the reasons for the change in current consumption during the
movement of the device were analyzed, the necessary conditions for connecting consumers to the
bus ducts were formed, including providing all consumers with electricity in full, excluding the
excess of the rated currents of each bus duct with consumption currents, minimizing electricity
losses when passing through the conductor and through the equipment. In this regard, the possible
configurations of the construction of the electrical network using conductors and equipment were
analyzed, and losses on the current conductors and on the equipment used were estimated. Based
on the results of the research, a graph of consumers' connections to the conductors was formed,
and to determine the way of connecting each consumer to the energy source through the power
grid, a connection path was determined that minimizes losses. The problem was formalized as
finding the shortest path in a graph, and Dijkstra's algorithm was used as a basis to solve it. Based
on the research results, algorithms were formed for the formation of ways to connect consumers to
electricity sources through the power grid and an algorithm for controlling the switching of keys
in the power grid when the consumption currents change. The developed algorithms were implemented
in software, and a numerical experiment was carried out using a simulation model. The
results of the experiment showed the correctness of the developed algorithms, and can be further
used for implementation in the devices under development for moving over ultra-long distances.

The aim of the research is to return the autonomous underwater vehicle to the route trajectory
as soon as possible after the observation in the event of failures in the actuators that ensure
the movement of the vehicle. The need to solve the problem is due to the fact that when the device
overcomes distances of several thousand kilometers, its position deviates from the route trajectory due to the accumulation of the error in the reckoning of coordinates by the onboard inertial navigation
system. As a result, the apparatus is forced to return to the route trajectory, during which a
failure may occur in the actuators that ensure the movement of the apparatus. Previously, the
problem was not considered in this formulation, and the approaches used in similar situations to
unmanned aerial vehicles turned out to be unsuitable. The most typical reasons that distinguish an
underwater vehicle from a drone are: the difference in the reasons for deviation from the route
trajectory (inertial system for the device and the wind for the drone), lack of navigation using signals
from satellite radio navigation systems and the inability to control its location when returning
to the route , low maneuverability of the device in comparison with the drone. To solve the problem
of ensuring the movement of the apparatus to the route trajectory in the event of a failure of
the executive device, which ensures the movement of the apparatus, it is proposed to choose an
alternative one from the number of redundant ones instead of the failed one. The choice of a backup
device is determined, first of all, by the moment created by the device for maneuvering the apparatus
along the course. At the same time, it is shown that, in view of the limitations on the ability
of the backup device to provide the apparatus with the required maneuver along the course, it is
also necessary to choose the trajectory of the apparatus when returning to the route trajectory.
For this, five possible return methods were analyzed, differing in the dynamics of the course
change, the length of the path, and the duration of maneuvering. Taking into account the smoothness
of the course change for each trajectory, the most suitable actuators were determined, capable
of ensuring the movement of the apparatus along the selected trajectory. The main criterion
when choosing a trajectory, along with taking into account the limitations, was to minimize the
distance traveled to the route trajectory in order to save the energy resource of the apparatus.
After the selection of the actuator and the trajectory of the apparatus for restoration on the route
trajectory, a sequence of calculations is presented to determine the parameters of the actuator at
each moment of time throughout the return of the apparatus to the route trajectory. The results of
the research made it possible to solve the problem of restoring the position of an autonomous underwater
vehicle on the route trajectory in the shortest possible time in the event of a failure in the
executive devices that ensure its movement.

The article presents some results of research aimed at the design of human-machine interfaces,
taking into account the multimodal nature of human perception, for use in the on-board
equipment of an aircraft. In particular, we are talking about the possibility of a wider use of audio
channels for input and output of information. The advantages of sound interfaces in relation to
visual and tactile ones are, first of all, in the absence of the need for directed attention of the pilot,
in the ability to create auditory objects in three-dimensional space and indicate the direction to
several different objects at the same time. In the experiments, the possibilities of spatial separation
of speech information flows in an aircraft intercom in situations where the level of interference
significantly exceeded the level of the target speech message were tested. The indicators of target
message recognition were evaluated in the presence of two types of sound interference: the sound of
another speech message and the noise of an aircraft engine. The results showed that spatial separation
of audio messages significantly improves the operator’s ability to recognize their content, regardless
of the type of interference. The maximum number of errors when recognizing a target message
corresponds to its spatial position in the same direction as the noise of the interference. At the
same time, message recognition is significantly better if it is pronounced in a female voice. The fact of
spatial asymmetry of correct recognitions was also revealed: messages arriving from the right are recognized better than in cases of their arrival from the left. The practical significance of the research
concerns the possibility of creating intercom with increased security against conflicts between
different information flows, as well as against the impact of external acoustic noise. The prospect is
seen in the use of three-dimensional audio interfaces not only as part of an intercom, but also for
navigation and aircraft control systems, as well as monitoring its state.

Under the conditions of operation's and rolling stock owner’s plurality on the Russian railway
network the following issues are in case: excessive freight-hauling and carrying capacity of
section, oncoming rerun of empty boxcar in one type, excessive mileage of empty boxcars, sectional
speed reduction and others. More effective cooperation of transit process members based on
logistics, market simulation of freight traffics, creation of math models with the use of digitalization
and intellectualization methods of control are necessary for solving mentioned issues. This
study is devoted to research matters of principles updating modelling multi-agent interaction in
the portside transport systems. Methods of statistical, morphological, regression and system analysis,
mathematical and analytical modelling compose the methodological basis of the research.
Research and modelling characteristics of freight and car traffic flow distribution under contexts
of multiagency of transport complex, wherein the author-developed economic and geographical
method to delimit stations’ «spheres of influence» is applied allow to create analytical models of
transportation process based on integrated assessment of transport and technological infrastructure
of the railway polygon and cost of transport services. Building of a digital geographical model
of rolling stock distribution according to types of transportation service for portside stations by
analytic curves of higher order is one of special characteristics. «Spheres of influence» of loading
stations obtained by methods of economic and geographical delimitation allows formulating a
range of preferential directions while distributing car traffic. Acquired territorial scene of distributing
car traffic is a basis for solution of multi-attribute problem of optimization of boxcar directions
regulation taking into account multi-operator market of rolling stock, digitalization and intellectualization
of the branch. In addition to solution of objectives of transport services market
regulation in terms of rolling stock distribution, the problems of technological, economic, fiscaland digital interaction on a basis of logistics in the multi-agent systems are continued to be crucial.
Model and methodological propositions formed in this context should ensure reduction of
transport and logistic costs with parallel improvement of quantitative, qualitative and temporary
indicators of integrated logistic supply chains realization.

One of the main factors that significantly complicate the understanding, translation and
analysis of texts obtained by automatic recognition of speech or images of texts is the presence of
distortions in the form of erroneous symbols, words and phrases. Until recently, there were no
effective software tools for correcting texts with significant distortions, although this task is relevant
both for Russian and other common languages in the context of the active use of recognition
systems in advanced augmented reality systems. The authors proposed a new multi-stage method
for correcting distorted texts, which significantly increases the accuracy of the correction (in
terms of the number of correctly corrected words in the text) and is based on the sequential detection
of errors and their correction. In this paper, we evaluate the accuracy and computational
complexity of the proposed method for correcting distorted texts at various levels of distortion, and
determine its place among other modern approaches to correction. The most typical errors of
recognition systems are: – replacing a word with a similar sound or graphic spelling; – replacing
several words with one; – replacing one word with several; – omission of words; – insertion or
deletion of short words (including prepositions and conjunctions). As a result of recognition, a
distorted text is obtained, which consists mainly of dictionary words, even in places of distortion.
With a large number of distortions, the texts become almost unreadable. Due to the fact that it is
problematic to select texts with a wide range of distortion levels in the required amount based on
the results of real machine recognition of speech and images of texts, software modeling of distortions
was used. A text distortion technique has been proposed and implemented that simulates the
results of recognition systems in a wide range of distortions; distorted texts have been prepared in
the required amount. Within the framework of the proposed multi-stage correction method, nondictionary
word forms and words are considered distorted if the probability of their occurrence in
the text in accordance with the chosen language model is less than a given threshold. For such
distorted words, a list of possible variants of words is built, which includes only those word forms
from the dictionary that are at a certain Levenshtein distance from the word under study. The corrected
text from the tables of word variants is obtained by searching for the most probable chain
of word forms. The correction method consists of several stages, at each stage only those fragments
of the text that remain distorted after the previous stage are corrected. According to the
results of the experiments on the correction of distorted texts, it was concluded that the proposed
correction method showed good results with an average value of F-measure >50 % in the distortion
range from 0 to 75 %. Linguistic experts confirmed the fruitfulness of the proposed approach
to correction and its preference over other modern approaches, fixing that with a level of distortion
of up to 50 % of words, the corrected text is read with much less effort than a distorted one,
and with a level of distortion of up to 70% of words, the corrected text also allows you to highlight
useful information about the content.

The main goal of this work is to create a parallel application that performs computations
using a multithreaded execution model, optimized to make the best utilization of all available
hardware resources. One of the main implementation requirements is to optimize application performance
on different computer architectures, and to enable parallel execution of the application
on various computing devices that are part of a heterogeneous computing system. The possibility
of applying various methods of software and algorithmic optimization on multiprocessor architectures
of different generations was investigated as well as the effectiveness of their use for highly
loaded multithreaded applications was estimated. The problem of quasi-optimal dynamic distribution
of computational tasks among all currently available computing devices of a heterogeneous
computing system was also solved. Currently, not only multiprocessor computing systems are used
to solve large computational problems, but also various types of distributed systems. Distributed
computing systems have a number of features: possible failures of nodes and communication
channels, unstable operating time of nodes, possible errors in calculations, heterogeneity of computing
nodes. By heterogeneity of computing nodes, we will understand not only the different computing
capacity and different architectures of central processors, but also the presence of other
devices on the node capable of performing calculations. Such devices include video cards and
mathematical coprocessors. A node of a distributed computing system will be called heterogeneous
if, in addition to one or more central processing units, it contains additional computing devices.
When solving a computational problem on a distributed system, it is necessary to maximize the
utilization of all available computing resources. To do this, it is necessary not only to distribute
computing subtasks to nodes in accordance with their computing capacity, but also to take into
account the features of additional computing devices. This work is devoted to the study of methods
for maximizing the resources utilization of heterogeneous nodes.

When research in the field of malware detection, the authors focus exclusively on detection
methods, ignoring how these methods could practically be implemented. On the other hand, there
are works that reveal some technical details of the implementation or optimization of the process
of analyzing the malware sample and collecting data on its work. However, it is necessary to combine
the results of the concepts of experimental systems and the implementation possibilities that
are available. The purpose of the work is description of the implementation of an automated malware
detection system based on the method proposed earlier by the authors, thus supplementing
the results of previous studies and putting into practice the proposed method for detecting and
clustering malware. As a result, the technical requirements for the developed system for detecting
malware is described, due to the previously proposed method of detection and clustering. A comparison
of existing behavioral analysis tools was made, Сuckoo Sandbox was chosen as the most
suitable one, its main advantage is the open source code, which made it possible to refine both its
client part and server part. In particular, the list of controlled system functions has been expanded,
the source module of the call has been determined, and the call context has been determined.
Also, based on the Сuckoo Sandbox, an extension has been developed that implements the method
proposed by the authors. The article also reveals the possibility of porting the described system to
work with samples of malware developed for various platforms. In particular, it is shown that the
proposed methods can be adapted to platforms such as .NET or Android, while the improvements
are technical, not fundamental. From a practical point of view, the system is a software package
for a security specialist and allows for the rapid detection of previously unknown threats and, at
the same time, through clustering, to identify a specific threat in order to implement the most appropriate
protection measures against this threat. In the proposed form, it can be used as part of
the enterprise infrastructure to ensure anti-virus security.

Quantum computing in general and quantum deep learning represent a promising field related
to the research of modern methods and algorithms of quantum computing used for the purpose
of teaching and developing new architectures of artificial neural networks. Recently, there
has been a trend that research conducted in the field of quantum deep learning is becoming increasingly
widespread among specialists. This can be explained by the fact that it has been established
that quantum circuits are capable of functioning like artificial neural networks, while
demonstrating the best results in solving several tasks, including, for example, the actual task of
classifying objects in an image or in a video stream. Thanks to the rapid development of quantum
computing in the field of deep learning, optimal solutions have been found for such urgent problems
as the vanishing gradient problem, finding a local minimum, improving the efficiency of
large-scale parametric machine learning algorithms, eliminating decoherence and quantum errors,
etc. Within the framework of this work, the process of functioning of a quantum variational
scheme is described, its main characteristics are established, and disadvantages are identified.
The key features of quantum computing, on which the process of implementing quantum deep
learning with the reinforcement of a convolutional neural network is based, are also analyzed. In
addition, quantum deep learning of a convolutional neural network has been carried out using a
variational quantum scheme, which leads to an increase in the performance of a convolutional
neural network in solving the problem of image processing, namely its classification, using a
quantum computing environment. The relevance of this article consists in the implementation of a
quantum deep learning algorithm with the reinforcement of a convolutional neural network for
image processing, as well as the great importance of the subject of this study for the future development
of quantum computing devices that can be used in artificial intelligence systems, etc.,
which corresponds to the priority direction of the development of domestic science.

Many computational tasks can be represented in the form of a sequential information graph.
In the general case, such an information graph cannot be reduced to a parallel form in order to
speed up the execution of its operations. But if the vertices of this graph have the properties of
associativity, distributivity, etc., such a graph can be transformed into a parallel-pipeline form.
These transformations can be performed not only on graphs containing elementary operations -
addition, multiplication, logical AND, etc. - but also over graphs containing macro operations.
One example of such graphs is the information graph for solving SLAEs by the sweep method
(Thomas's method). The article considers a solution for tridiagonal linear systems. The information
graph of the sweep method consists of two parts: the forward move, in which the transition
from the three-diagonal form to the two-diagonal form is performed, and the reverse move, in
which the values of the variables are directly calculated. Despite the fact that the operations that
make up the basic macro-operation of the sweep method have the property of associativity, a simple
transformation of the graph to a pyramidal form will not give the desired result. It is necessary
to transform the basic macro operations in a special way and change what data is received on
them. After that, it will be possible to bring the graph to a pyramidal form. For the reverse move, a
similar transformation of the graph and its constituent base subgraphs is applied. Since in order to
start computations in the reverse run, we need to complete the computations of the forward run,
we should switch from two specialized types of computational blocks to one universal one, and
build a universal computational structure on its basis.

Increasing models complexity objects and processes study, in different sphere of science and
technology, set up plenty issues to necessary to use high-performance computing systems. Arrays
matrix processing by cluster multiprocessor computing systems in conjunction special methods
aimed at organizing parallel computations, basically obtain computing performance system is
quite high. However, that computational efficiency is not observed for all types of matrices. Matrix
structure be in a position contain large amount of insignificant elements, large dimension and
unstructured portrait. Calculation execute for described kind of matrices on cluster multiprocessorcomputing system couldn't achieve close peak performance. Considering that processing methods
leave out the complex structure of the matrix being processed. As a result, the performance of the
system is significantly reduced. The development of cluster MCS methods doesn't allow for full
ensure high performance for class of problems processing of large sparse unstructured matrices.
Rigid architecture of processor commutation net doesn’t take into account the peculiarities of such
matrices, and lead to non-uniformity loading processor. To achieve performance close the peak
for tasks large sparse unstructured matrices processing necessary to use reconfigurable computing
systems. RCS architecture allows adapting computation structure to the problem solved. This
makes it possible to organize pipeline processing, such a way that computational resource RCS
used only for informational significant operations. In addition using generally accepted methods
for structural organization of high-performance computing for RCS, it is necessary to develop a
format for storing and transferring large sparse unstructured matrices, to determine the principles
of constructing basic matrix macro-operations and the possibility of organizing composite discrete-
event matrix functions for solving applied problems. Сconsequently method founding laid
allows organizing computations operands, which are large sparse unstructured matrices. The
application this method for organizing computations can significantly increase productivity, and
provide an increase in the efficiency of such a system.

When studying natural objects, the problem of modeling complex systems with a structure
that cannot be described by means of Euclidean geometry tools often arises, therefore, fractal
geometry and the corresponding mathematical apparatus are used to represent them. So the model
of radon transport in an inhomogeneous medium, using superdiffusion, displays real data more
accurately than the classical one. An increase in the concentration of radon in the air is one of the
signs of an approaching earthquake, which makes it necessary to simulate the propagation of this
radioactive inert gas in real time. Reconfigurable computing systems have great potential for solving
problems in real time, but the currently existing means for solving systems of linear equations
have low efficiency due to the irregular structure of matrices obtained by discretizing the radon
superdiffusion model using adaptive grids. The basic subgraph of the Jacobi method is transformed
as follows: the input data is vectorized, the structure of the frame in which the value of one
unknown is calculated is divided into several microframes, parallelizing the calculations in the
first microframe, where the sum of the products of the matrix coefficients and the values of the
unknowns from the previous iteration is performed. The results obtained are buffered for subsequent
delivery to the second microframe, where the final processing and output of the iteration
result takes place. The described approach allows to reduce equipment downtime when solving a
system of linear equations with sparse irregular matrices, and gives a speed gain by 5–15 times in
comparison with existing methods for solving linear system on reconfigurable computing systems.