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9Here ZY and ZT � concentration and temperature components of the residual functional; yile and yilc, Tile and Tilc �
experimental and calculated values of component concentrations and temperatures, L � number of time
points in observed substances during the reaction, I � number of observed substances.
In the mathematical model, the temperature change is taken into account according to the values of the
thermodynamic characteristics of the reaction components [2].
References
1. R. Z. Zaynullin, K. F. Koledina, I. M. Gubaydullin, A. F. Akhmetov, and S. N. Koledin Kinetic Model of Catalytic
Gasoline Reforming with Consideration for Changes in the Reaction Volume and Thermodynamic Parameters // Kinetics
and Catalysis, 2020, V. 61, No. 4, pp. 613-622.
2. Irek Gubaydullin, Kamila Koledina, Sergey Koledin, Ravil Zaynaullin Catalytic Reforming Reactor Section
Optimization Based On A Mathematical Model Accounting The Reaction Volume Changes // OPCS 2019 IEEE p 58-63.
Determination of the bottom scattering coefficient discontinuity lines in multibeam ocean sounding
E. O. Kovalenko1,2, I. V. Prokhorov1,2
1Institute of Applied Mathematics FEB RAS
2Far-Eastern Federal University, Vladivostok
Email: prokhorov@iam.dvo.ru
DOI 10.24412/cl-35065-2021-1-01-99
In this report, the problems of acoustic sounding of the sea bottom with using side-scan multibeam sonar
are studied. Within the model based on radiative transfer equation and diffuse reflection conditions at the
boundary, the problem of determining the coefficient of bottom scattering from the data of a multi-beam re-
ceiving antenna [1, 2]. Unlike previous works of the authors, the problem of determining only the singular
support of the reflection coefficient is formulated, and not the reflection coefficient itself. Numerical method
for solving the inverse problem is developed. Results shows that it is be able to use in highly scattering envi-
ronments. Analysis of the quality of the bottom scattering coefficient discontinuity lines depending on scatter-
ing level in the ocean, range and number of sounding angles is done.
The reported study was funded by RFBR (project number 20-01-00173) and the Ministry of Education and Science of
the Russian Federation (Additional Agreement no. 075�02�2020�1482�1).
References
1. Prokhorov I.V., Sushchenko A.A. Studying the problem of acoustic sounding of the seabed using methods of
radiative transfer theory //Acoustical Physics. 2015. V. 61. No. 3. P. 368�375.
2. Kovalenko �.�., Prokhorov I. V. Determination of the coefficient of bottom scattering during multi-beam sounding
of the ocean // Far Eastern Mathematical J. 2019. V. 19. No. 2. P. 206�222.
Identification of agent-based mathematical model of COVID-19 propagation in Russian Federation regions,
UK and USA
O. I. Krivorotko1,2, M. I. Sosnovskaya2, N. Yu. Zyatkov1
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: krivorotko.olya@mail.ru
DOI 10.24412/cl-35065-2021-1-02-00
The agent-based mathematical model of COVID-19 propagation in fixed region is characterized by stochas-
tic nature of epidemiological process, demographic features of the region and epidemiological parameters (re-
production number, initial asymptomatic infectious individuals, test rate, etc.). The sensitivity-based identifia-
bility analysis based on the Bayesian approach is carried out to three types of data: daily confirmed, critical
and death cases of COVID-19 [1-2]. As a result, the set of more sensitivity parameters is investigated. The sce-
narios of COVID-19 propagation on Siberia [3], UK and USA are modelled and discussed.
This work was supported by the Russian Foundation for Basic Research (grant 21-51-10003).
References
1. Krivorotko O. I., Kabanikhin S. I., Sosnovskaya M. I., Andornaya D. V. Sensitivity and identifiability analysis of
COVID-19 pandemic models // Vavilov J. of Genetics and Breeding. 2021. V. 25, N. 1. P. 82-91.
2. Andrianakis I., Vernon I. R., McCreesh N., et al. Bayesian history matching of complex infectious disease models
using emulation: a tutorial and a case study on HIV in Uganda // PLOS Computational Biology. 2015. V. 11, N. 1:
e1003968.
3. Krivorotko O. I., Kabanikhin S. I., Zyatkov N. Yu., et al. Mathematical modeling and forecasting of COVID-19 in
Moscow and Novosibirsk region // Numerical Analysis and Applications. 2020. V. 13, N. 4. P. 332-348.
Non-destructive testing of the state of the insulating coating of the main pipeline according
to the UAV-magnetometry data
V. N. Krizsky1, S. V. Viktorov2, O. V. Kosarev1, Ya. A. Luntovskaya1
1Saint-Petersburg Mining University
2Bashkir State University, Ufa
Email: Krizskiy_VN@pers.spmi.ru
DOI 10.24412/cl-35065-2021-1-02-01
Monitoring the state of trunk pipelines is an urgent practically important task for trouble-free operation.
Determination of the transient resistance at the "pipe/soil" boundary according to magnetometry data using
unmanned aerial vehicles is the inverse problem of mathematical geophysics to determine the coefficient
function of the boundary condition of the third kind.
The paper considers mathematical models of direct [1, 2] and inverse problems, algorithms for their solu-
tion based on the search for the extremal of the regularizing A.N. Tikhonov�s functional. The results of compu-
tational experiments are discussed.
References
1. Krizsky V. N., Aleksandrov P. N., Kovalskii A. A., Victorov S. V. Mathematical Modeling of Electric Fields of Pipelines
Cathodic Protection Systems in Anisotropic Media // Science & Technologies: Oil and Oil Products Pipeline Transportation.
2020. V. 10, N. 1. P. 52-63. DOI: 10.28999/2541-9595-2020-10-1-52-63.
2. Krizsky V. N., Aleksandrov P. N., Kovalskii A. A., Victorov S. V. Mathematical Modelling of Electric and Magnetic
Fields of Main Pipelines Cathodic Protection in Electrically Anisotropic Media // E3S Web of Conferences. II International
Conference �Corrosion in the Oil & Gas Industry 2020�, 2021. V. 225. [Electron. resource]. URL: https://www.e3s-
conferences.org/articles/e3sconf/abs/2021/01/e3sconf_corrosion2020_04002/ e3sconf_corrosion2020_04002.html (the
date of access: 01.03.2021) DOI: 10.1051/e3sconf/202122504002.
The Gerchberg � Papoulis method in non-scalar tomography problems with limited data
S. V. Maltseva
Sobolev Institute of Mathematics SB RAS
Email: maltsevasv@math.nsc.ru
DOI 10.24412/cl-35065-2021-1-02-02
The problem of recovery a scalar field by limited data [1] has some difficulties. One of the methods for
solving this problem is the Gerchberg � Papoulis iterative method [2]. Problem with limited data may also be
