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9bility 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
considered for non-scalar fields. This report contains a generalizations of this method for the case of vector
and 2-tensor fields. The results of numerical simulations are presented.
This work was supported by the Russian Foundation for Basic Research (RFBR) and the German Science Foundation
(DFG) according to the joint German-Russian research project 19-51-12008.
References
1. Natterer F 1986. The Mathematics of Computerized Tomography (New York: John Wiley & Sons).
2. Defrise M and De Mol C 1983 A regularized iterative algorithm for limited-angle inverse Radon transform // Opt.
Acta: Int. J. Opt 30. 403-408.
Comparative analysis of the Gerchberg � Papoulis method in the problems of scalar and vector tomography
S. V. Maltseva 1, V. V. Pickalov 2
1Sobolev Institute of Mathematics SB RAS
2Khristianovich Institute of Theoretical and Applied Mechanics SB RAS
Email: maltsevasv@math.nsc.ru; pickalov@itam.nsc.ru
DOI 10.24412/cl-35065-2021-1-02-03
The paper discusses the methods of solving the inverse problems of a few-views and limited angle data of
two-dimensional tomography using iterative procedures in Fourier space. Partial absence of angular data can
be approximately compensated by extrapolation in the Gerchberg � Papoulis iterative method [1]. In particu-
lar, these algorithms should be complemented by a priori information and regularization procedures [2�3].
The computational experiment compare reconstruction errors of mathematical models of scalar and vector
problems.
This research was partially supported by the Russian Foundation for Basic Research, project RFBR-DFG No. 19-51-
12008.
References
1. Defrise M., De Mol C. A regularized iterative algorithm for limited-angle inverse Radon transform // Optica Acta.
1983. V. 30, N. 4. P. 403-408.
2. Maltseva S. V., Svetov I. E., and Louis A. K. An iterative algorithm for reconstructing a 2D vector field by its limited-
angle ray transform // J. of Physics: Conference Series. 2021. V. 1715, art. 12037.
3. Derevtsov E.Yu., Pickalov V.V. Reconstruction of vector fields and their singularities from ray transforms //
Numerical Analysis and Applications. 2011. V. 4, N. 1. P. 21-35.
The problem of identification an unknown substance by the radiographic method
V. G. Nazarov
Institute of Applied Mathematics FEB RAS
Email: naz@iam.dvo.ru
DOI 10.24412/cl-35065-2021-1-02-04
The paper considers the problem of partial identification of the chemical composition of unknown medi-
um by the method of multiple transillumination of this medium with X-ray radiation. Sample of unknown sub-
stance is assumed to be homogeneous in chemical composition, and the photon flux, collimated both in direc-
tion and in energy. A mathematical model is formulated for the identification problem. The proposed ap-
proach to solving the problem is based on the method of singular value decomposition of a matrix [1, 2]. At
the first stage of solving the problem is reduced to finding singular numbers and singular vectors for the series
systems of algebraic equations linear with respect to products of unknown quantities. Then, based on the re-
ceived data, a special function is built, called an indicator of the distinguishability of substances, which enables
