

2022 year, number 2
R.K. Gaydukov
National Research University В«Higher School of Economics», Moscow, Russia
Keywords: doubledeck structure, averaging, Prandtl equations with induced pressure, periodic perturbations, numerical modeling
Abstract >>
A viscous liquid flow along a semiinfinite plate with small periodic irregularities on the surface was considered for large Reynolds numbers. The flow near the plate is described by Prandtl equations with induced pressure which are nonclassical PDE, because they contain a limiting term. The main goal is to construct a numerical algorithm for solving these equations with periodic boundary conditions. The results of numerical modeling of the flow are presented.

V.I. Zorkal’tsev^{1,2}, M.N. Polkovskaya^{3}
^{1}Limnological Institute of the Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia ^{2}Baikal State University, Irkutsk, Russia ^{3}Irkutsk State Agrarian University named after A.A. Yezhevsky, P. Molodezhny, Russia
Keywords: time series decomposition, axiomatic approach to method selection, multiplicative model
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This paper is devoted to the substantiation of a multiplicative model of time series decomposition based on the axiomatic approach. In this model, the original time series is represented as a componentbycomponent product of the selected components. The components are described in the form of monomials. To determine the values of variable monomials, a function is minimized that measures deviations from the unit of all components of the product of the selected components from the values of the corresponding components of the original series. In the model under consideration, all the components of the original series and the selected components are positive numbers. Four requirements are formulated for methods of selecting components. It is proved that all these requirements are met if and only if the time series decomposition is performed by a multiplicative model. As an example, we consider a model for selecting trends and seasonal fluctuations from monthly series of efficient data.

K.F. Koledina^{1,2}, I.M. Gubaydullin^{1,2}, S.N. Koledin^{2}
^{1}Institute of Petrochemistry and Catalysis of RAS, Ufa, Russia ^{2}Ufa State Petroleum Technological University, Ufa, Russia
Keywords: multicriteria optimization, kinetic model, benzylalkyl ethers, molar ratios of initial reagents, Pareto approximation
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Based on the previously developed kinetic model of the catalytic reaction of the synthesis of benzylalkyl ethers, two and threecriteria optimization of the conditions was carried out. The problem of multicriteria optimization is formulated with the definition of variable parameters: reaction temperature, proportionality coefficient of the starting reagents, reaction time; optimality criteria: yield of a target and byproducts; restrictions on variable parameters. The computational aspects of multicriteria optimization by a grid algorithm (sensing) are examined. The calculated front values (optimality criteria) and Pareto sets (variable parameters) determine the exhaustive values of the reaction conditions and allow the decision maker to choose the most optimal ones. This made it possible to give technological recommendations for the industrial implementation of the synthesis of a benzyl butyl ether in the presence of a metal complex catalyst with a maximum yield of target products and a minimum content of byproducts.

I.M. Kulikov
Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
Keywords: numerical modeling, computational astrophysics, HLL solver
Abstract >>
In this paper, one construction of the original «HartenLaxvan Leer» method using a piecewiselinear reconstruction of physical variables is described. The obtained numerical method makes possible to reproduce a lowdissipation solution at discontinuities. To verify the method, we used the classical problems with an analytical solution based on various configurations of shock waves, contact discontinuities, and rarefaction waves. On the Sodlike problem, the order of accuracy of the developed numerical method was studied, it was shown that the main suppression of the order of accuracy occurs when the rarefaction wave is reproduced. The numerical method was verified by means of a threedimensional Sedov test of a point explosion, and on the problem of a supernova Ia type explosion with two symmetric ignition points, leading to the formation of a G1.9+0.3 like remnant.

M.L. Maslakov^{1,2}, V.V. Egorov^{1,2}
^{1}Russian Institute of Power Radiobuilding, St. Petersburg, Russia ^{2}Saint Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia
Keywords: angle estimation, phase, phase probability distribution function, Fourier series, regularization, multiparameter regularization
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This paper considers the problem of phases probability distribution function estimation for phaseshiftkeying signals. The modulating sequence, and, accordingly, the values of the symbols phases, as well as the statistical characteristics of this sequence are unknown. The Fourier coefficients are calculated based on a limited sample for estimation of phases probability distribution function. In this case, the obtained Fourier coefficients are regularized. Application of multiparameter regularization for increasing the estimation accuracy are considered. The numerical simulation results are presented.

Rabiu Musa, Robert Willie, Nabendra Parumasur
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
Keywords: South Africa, HIV1, resistance, behavior change, partial and total abstinence, demography
Abstract >>
Resistance to HIV1 disease developed by some exposed individuals has shown a promising sign in the fight against HIV1 infection. Behavior change has also become one of the most important protection strategies against HIV1 pandemic, but both of them have been widely neglected by mathematical modelers. In this paper, a new virus resistance HIV1 mathematical model incorporating behavior change is formulated and analyzed rigorously for both partial and total abstinence cases. The calculated reproduction number is used to establish the local stability of the diseasefree equilibrium points using the approach of Watmough and Driessche in both cases. Using appropriate demographic and epidemiological data for South Africa in the numerical simulation, the positive effect of behavior change in the midst of HIV1 resistance is thoroughly examined, and this strategy is absolutely effective in dealing with the threat of HIV1. This work also provides a better result than what is obtainable in the majority of the referenced related works.

Soraya Chaghoub^{1}, Djamel Benterki^{2}
^{1}School of Mathematical Science Institute of Mathematics, Nanjing Normal University, Nanjing, China ^{2}Laboratory of Fundamental and Numerical Mathematics, Setif, Algeria
Keywords: quadratic programming, linear programming, interior point methods, line search, approximate function
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In this work, we deal with a convex quadratic problem with inequality constraints. We use a logarithmic barrier method based on some new approximate functions. These functions have the advantage that they allow computing the displacement step easily and without consuming much time contrary to a line search method, which is timeconsuming and expensive to identify the displacement step. We have developed an implementation with MATLAB and conducted numerical tests on some examples of considerable size. The obtained numerical results show the accuracy and efficiency of our approach.

Rishikesh Yadav^{1}, Ramakanta Meher^{1}, Vishnu Narayan Mishra^{2}
^{1}Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology Surat, Gujarat,India ^{2}Department of Mathematics, Indira Gandhi National Tribal University, Madhya Pradesh, India
Keywords: rate of convergence, Lipschitz function, DitzianTotik modulus of smoothness, function of bounded variation
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The present article deals with approximation results by means of the Lipschitz maximal function, DitzianTotik modulus of smoothness, and Lipschitz type space having two parameters for the summationintegral type operators defined by Mishra and Yadav [22]. Further, we determine the rate of convergence in terms of the derivative of bounded variation. To estimate the quantitative results of the defined operators, we establish quantitative Voronovskaya type and Gruss type theorems. Moreover; examples are given with graphical representation to support the main results.

