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10ductor heterostructure AlGaAs/InGaAs/GaAs used as a sample. Self-consistent numerical solution of Poisson�s
equation for electrostatic potential V(z) and Schrodinger�s equation for energy levels Ei and their correspond-
ing wave functions .i lets us to define zone structure of the semiconductor [2, 3]. The obtained data on the
wave functions and the distribution of the charge carriers across the layered structure are used to solve the
Boltzmann kinetic equation and to determine the electron drift velocity. It describes the transfer of two-
dimensional electron gas in the layered heterostructure [4, 5]. The model of electron gas transfer takes into
account the electron scattering by optical and acoustic phonons, and scattering at the roughness of the het-
erointerface.
This work was supported by the Russian Science Foundation under Grant 19-11-00019.
References
1. Gulyaev D.V., Zhuravlev K.S., et al., Influence of the additional p+ doped layers on the properties of
AlGaAs/InGaAs/AlGaAs heterostructures for high power SHF transistors. 2016. J. Phys. D:Appl. Phys., V. 49, 095108.
2. Abgaryan, K.K., Reviznikov, D.L. Numerical simulation of the distribution of charge carrier in nanosized semiconductor
heterostructures with account for polarization effects. Comput. Math. and Math. Phys. 2016, V. 56, P. 161�172.
3. Harrison P., Valavanis A., Quantum Wells, Wires and Dots. Theoretical and Computational Physics of
Semiconduccter Nanostructures. Wiley, UK. 2016.
4. Fawcett W., Boardman A. D., and Swain S., Monte Carlo determination of electron transport properties in Gallium
Arsenide. 1970. J. Phys. Chem. Solids, Pergamon Press, V. 31, p. 1963-1990.
5. Ivashenko V. M. and Mitin V. V., Simulation of Kinetic Phenomena in Semiconductors. Monte Carlo Method, Kiev:
Naukova Dumka, 1990.
Numerical stochastic models of non-stationary time series of bioclimatic indices in West and East Siberia
N. A. Kargapolova1,2, V. A. Ogorodnikov1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: nkargapolova@gmail.com
DOI 10.24412/cl-35065-2021-1-00-79
The report presents the results of numerical modeling of time series of several bioclimatic indices used to
study the unfavorable weather conditions during the cold season. The considered stochastic models of uncon-
ditional and conditional time series reproduce the diurnal cyclicity of the real bioclimatic processes. For a
number of weather stations located in West and East Siberia the results of comparison of estimates of the oc-
currence probability, duration and other characteristics of adverse meteorological conditions characterized
with extreme behavior of the bioclimatic indicators are presented.
This study was carried out under state contract with ICMMG SB RAS (0251-2021-0002).
Application of kernel regression in nonlinear adaptation algorithms as applied to multidimensional objects
S. I. Kolesnikova
Saint-Petersburg State University of Aerospace Instrumentation
Email: skolesnikova@yandex.ru
DOI 10.24412/cl-35065-2021-1-00-80
The application of the time series smoothing algorithm based on the construction of nuclear regression [1]
in the problems of nonlinear synthesis of control for continuous and discrete multidimensional objects is con-
sidered.
The illustrative examples of application of the proposed algorithm (biochemistry, immunology, economics,
and other fields of knowledge) are provided along with their statistical results of numerical simulation.
The results obtained would be useful in designing a smart control system and for real-time decision mak-
ing support as it concerns the problems of stochastic control over a wide range of poorly formalized objects
from different applied areas.
There are grounds for believing that the synthetic use of two popular nonparametric forecasting
algorithms will lead to a more efficient forecasting algorithm, at least for solving a certain class of control prob-
lems [2, 3].
This work was (partially) supported by the Russian Foundation for Basic Research (grant 20-08-00747).
References
1. Nadaraya E. On Estimating Regression. TV and its applications. 1964. V. 9(1). P. 141-142.
2. Kolesnikova S. Stochastic discrete nonlinear control system for minimum dispersion of the output variable n
Advances in Intelligent Systems and Computing. 2019. V. 986. P. 325-31.
3. Kolesnikova S.I. A multiple-control system for nonlinear discrete object under uncertainty.Optimization Methods
and Software. 2019. Vol. 34. No. 3. P. 578-585. URL: https://doi.org/10.1080/10556788.2018.1472258.
Comparative analysis of various projective algorithms of the Monte Carlo method in problems of the theory
of particle transfer
A. S. Korda1, G. A. Mikhailov1, S. V. Rogasinsky1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: asc@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-81
A comparative analysis of various variants of the projective algorithm of the Monte Carlo method [1] for
estimating the particles flow through a layer of medium with scattering of the Henyi-Greenstein type is carried
out.
For detailed optimization of the algorithms, a test problem is used that allows an analytical iterative ap-
proximation of the solution.
This work was carried out under state contract with ICMMG SB RAS � 0251-2021-0002.
References
1. Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. M.: Nauka, 1987 (in Russian).
The Monte Carlo method as a tool for the development of the apparatus of applied mathematical statistics
and ensuring the correctness of statistical inferences in applications
B. Yu. Lemeshko, S. B. Lemeshko
Novosibirsk State Technical University
E-mail: Lemeshko@ami.nstu.ru
DOI 10.24412/cl-35065-2021-1-02-88
The apparatus of applied mathematical statistics formed to date includes a hard-to-see set of methods
used to estimate the parameters of various probabilistic models, and criteria for testing various statistical hy-
potheses, which make it possible to build models and check their adequacy.
