Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 739
Статья научная
In this paper we prove some new results on Sturm - Liouville abstract problems of the second order differential equations of elliptic type in a new non-commutative framework. We study the case when the second member belongs to a Sobolov space. Existence, uniqueness and optimal regularity of the strict solution are proved. This paper is naturally the continuation of the ones studied by Cheggag et al in the commutative case. We also give an example to which our theory applies.
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Supercomputer simulation of oil spills in the Azov Sea
Статья научная
We present the research on microbiological destruction of oil pollution in shallow water. In order to conduct the research, we use a multiprocessor computer system with distributed memory. The research takes into account the oil fractional composition as well as hydrodynamic and chemical-biological features of water. In order to simulate the dynamics of hydrocarbon microbiological degradation in the Azov Sea, we propose the complex of interrelated precision models. For model discretization, we use the space splitting schemes taking into account the partial filling cells of computational domain. Therefore, the computational accuracy significantly increases, while the computational time decreases. On supercomputer, we implement an experimental software for predictive modelling the ecological situation under oil and other pollution conditioned by natural and industrial challenges in shallow water.
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Synthesis of surface h-polarized currents on an unclosed cylindrical surface
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The article describes the inverse problem of diffraction of electromagnetic waves, finding surface H-polarized currents on an unclosed cylindrical surface according to a given radiation pattern. The work is based on modelling an operator equation with a small parameter. The operator is represented as the sum of a positive-definite, continuously invertible operator and a compact positive operator. The positive-definite operator exactly coincides with the main operator of the corresponding direct problem of diffraction of electromagnetic waves. Due to this fact, the solution to the simulated equation satisfies the necessary boundary conditions. And this is the novelty and difference of the approach developed in this work from the methods known in the scientific literature. We develop a theory of an operator equation with a small parameter and a numerical method based on Chebyshev polynomials with weights that take into account the behavior at the boundary. The efficiency of the numerical method is shown.
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System analysis of classification of prime knots and links in thickened surfaces of genus 1 and 2
Статья научная
In this paper, we present a system analysis of approaches to classification of prime knots and links in thickened surfaces of genus 1 and 2 obtained by the author in collaboration with S.V. Matveev and V.V. Tarkaev in 2012 - 2020. The algorithm of the classification forms structure of the present paper. The results of classification are considered within system analysis of the main ideas of key steps of the algorithm. First, we construct prime projections. To this end, we define a prime link projection, enumerate graphs of special type which embedding in the surface can be a prime projection, enumerate projections in the surface, and show that all obtained projections are prime and not equivalent using some invariants of projections. Second, we construct prime links. To this end, we define a prime link, construct a preliminary set of diagrams, use invariants of links to form equivalence classes of the obtained diagrams and show that the resulting diagrams are not equivalent, and prove primality of the obtained links. At that, at each step, the used methods and the introduced objects are characterized from viewpoints of two cases (genus 1 and 2), and we distinguish properties that are common for both cases or characteristics of only one of two cases. Note consolidated tables, which systematize the classified projections with respect to their properties: generative graph, genus, number of components and crossings, existence and absence of bigon that simplifies the further work with the proposed classification of projections and links.
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Table recognition technology in tax documents of the Russian Federation
Статья научная
This paper investigates the problem of cell recognition in the image of a table using the example of the Russian tax document (2-NDFL). Despite the simple structure of the tables, the printing method is based on a flexible template. The flexibility of the form is observed in the modifications of textual information and in the table area. The flexibility of tables lies in the modification of the number and size of columns. A structural method was proposed for table detection. The input data are the detected horizontal and vertical segments. Segments were searched by the Smart Document Reader system. Implementing and testing the method were also carried out in the Smart Document Reader system. In addition to detecting the area where tables can be placed, the following objectives were achieved: searching for table cells, naming table cells, and validating the table area. Validation of the table area was performed for separate tables and for table sets. The application of table aggregate descriptions showed the high reliability of linking table sets.
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The Barenblatt-Zheltov-Kochina model on the segment with Wentzell boundary conditions
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In terms of the theory of relative p-bounded operators, we study the Barenblatt-Zheltov-Kochina model, which describes dynamics of pressure of a filtered fluid in a fractured-porous medium with general Wentzell boundary conditions. In particular, we consider spectrum of one-dimensional Laplace operator on the segment [0, 1] with general Wentzell boundary conditions. We examine the relative spectrum in one-dimensional Barenblatt-Zheltov-Kochina equation, and construct the resolving group in the Cauchy-Wentzell problem with general Wentzell boundary conditions. In the paper, these problems are solved under the assumption that the initial space is a contraction of the space L2(0, 1).
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The Cauchy problem for the Sobolev type equation of higher order
Статья научная
Of concern is the semilinear mathematical model of ion-acoustic waves in plasma. It is studied via the solvability of the Cauchy problem for an abstract complete semilinear Sobolev type equation of higher order. The theory of relatively polynomially bounded operator pencils, the theory of differentiable Banach manifolds, and the phase space method are used. Projectors splitting spaces into direct sums and an equation into a system of two equivalent equations are constructed. One of the equations determines the phase space of the initial equation, and its solution is a function with values from the eigenspace of the operator at the highest time derivative. The solution of the second equation is the function with values from the image of the projector. Thus, the sufficient conditions were obtained for the solvability of the problem under study. As an application, we consider the fourth-order equation with a singular operator at the highest time derivative, which is in the base of mathematical model of ion-acoustic waves in plasma. Reducing the model problem to an abstract one, we obtain sufficient conditions for the existence of a unique solution.
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The Lyapunov stability of the Cauchy-Dirichlet problem for the generalized Hoff equation
Статья научная
We consider the initial boundary value problem with homogeneous Dirichlet boundary conditions for the generalized Hoff equation in a bounded domain. This equation models the dynamics of buckling of a double-tee girder under constant load and belongs to a large class of Sobolev type semilinear equations (We can isolate the linear and non-linear parts of the operator acting on the original function). The paper addresses the stability of zero solution of this problem. There are two methods in the theory of stability: the first one is the study of stability by linear approximation and the second one is the study of stability by Lyapunov function. We use the second Lyapunov''s method adapted to the case of incomplete normed spaces. The main result of this paper is a theorem on the stability and asymptotic stability of zero solution to this problem.
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The Pyt'ev-Chulichkov method for constructing a measurement in the Shestakov-Sviridyuk model
Статья научная
One of the approaches to solution of the problem on restoring a distorted input signal by the recorded output data of the sensor is the problem on optimal dynamic measurement, i.e. the Shestakov-Sviridyuk model. This model is the basis of the theory of optimal dynamic measurements and consists of the problem on minimizing the difference between the values of a virtual observation obtained using a computational model and experimental data, which are usually distorted by some noise. We consider the Shestakov-Sviridyuk model of optimal dynamic measurement in the presence of various types of noises. In the article, the main attention is paid to the preliminary stage of the study of the problem on optimal dynamic measurement. Namely, we consider the Pyt'ev-Chulichkov method of constructing observation data, i.e. transformation of the experimental data to make them free from noise in the form of ``white noise" understood as the Nelson-Gliklikh derivative of the multidimensional Wiener process. In order to use this method, a priori information about the properties of the functions describing the observation is used.
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The blow-up solutions to nonlinear fractional differential Caputo-system
Статья научная
In this paper, we establish the finite time blow-up of solutions to nonlinear differential systems governed by Caputo fractional differential equation. Then, we derive sufficient conditions on parameters with positive given data. Moreover, for this purpose under some assumptions, we prove the non existence of global solutions to the considered class of nonlinear fractional differential Caputo-system subject to the initial condition. To prove our main result, we apply the test function method, Riemann-Liouville integral, Caputo derivative operator and some general analysis tools. Our result is new and generalizes the existing one.
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The contribution of Angelo Favini in twenty years of joint research (1996 - 2016)
Персоналии
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We study conditions for the loss of stability in a plastic deformation of a layer of weaker material in a sheet specimen. The layer is not collinear with the exterior forces acting in the sheet plane, which are orthogonal to each other and have opposite signs. The parameters of the problem are: the angle between the layer and the direction of exterior forces; the ratio of stresses due to exterior forces; the ratio of strengths of the layer material and the main material of the sheet specimen; the strengthening law of the layer material; the ratio of thicknesses of the layer and the specimen. Basing on Swift's plastic instability criterion for a deformation of the layer material, we obtain an algorithm for calculating critical stress in the layer and critical exterior loading in dependence on the indicated parameters. When contact strengthening of the layer is absent, our results have explicit analytic expressions. We find conditions under which the layer does not lower the strength of the specimen. We find conditions for the stressed state of the layer to be a pure shear and study this case.
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Статья научная
Krasnoyarsk Subsidiary of Kutateladze Institute of Thermophysics SB RAS and the Department of Thermophysics of the Siberian Federal University are developing a freely distributable "SigmaFW" software package for numerical simulation of the hydrodynamics, heat and mass transfer problems. It is assumed that the software package will be used in scientific and educational institutions as well as industrial enterprises in Russian Federation. Mathematical models realized in the software package describe steady and unsteady laminar and turbulent single - and multicomponent flow taking into account the dispersed phase, the conjugate and radiative heat transfer, and homogeneous gas-phase chemical reactions. The "SigmaFW" contains the necessary tools for building numerical domains, carrying out multi-threaded calculation, and visual analysis of the results. The article describes the three main blocks of software package: the grid generator, calculation module and analysis of the results. In additition, a number of test and application tasks are presented to demonstrate the capabilities of the software.
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The elements of the operator convexity in the construction of the programmed iteration method
Статья научная
The problem of retention studied here can be regarded (in the case of bounded control interval) as a variant of the approach problem within the given constraints in the phase space and the target set given by the hyperplane of the space positions corresponding to the terminal moment of the process (the retention problem on the infinite horizon also fits the problem stated in the work). The main difference of the problem from the previously considered formulation is the possibility of variation of the spaces of system trajectories and disturbance realizations depending on the initial moment of control. It is shown that the unsolvability set of the retention problem is the operator convex hull of the empty set constructed on the base of programmed absorption operator. Under some additional coherence conditions (on the spaces of system trajectories and disturbance realizations corresponding to different initial moments) the set of successful solvability is constructed as the limit of the iterative procedure in the space of sets, elements of which are positions of the game; in this case the structure of resolving quasistrategy is also given.
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The existence of a unique solution to a mixed control problem for Sobolev-type equations
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This article studies a mixed control problem for Sobolev-type equations in the case of a relatively radial operator. We use the Showalter-Sidorov initial condition. The difference in the statement of our problem from those studied previously by other researchers amounts to the form of the quality functional, which, in the authors' opinion, is more adequate to model applications in economics and technology. We prove an existence and uniqueness theorem for the solution to this problem.
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Статья научная
This paper describes a method of use of equations in M.F. Shul'gin's form in Lagrangian variables for steady motion stability and stabilization problems of systems with geometric constraints. These equations of motion are free from Lagrange multipliers; we substantiate their advantage for solving stability and stabilization problems. Depended coordinates corresponding to zero solutions of characteristic equation are allocated in the disturbed equations of motion. These variables are necessarily present in systems with geometric constraints for any control method. It is suggested to present equations of motion in Routh variables for finding stabilizing control coefficients; Lagrangian variables are more useful for constructing an estimation system of object state. In addition to previous results, we evaluate the ability to reduce the dimension of measured output signal obtained in conformity with the chosen modelling method. Suppose the state of system is under observations and the dimension of measurement vector is as little as possible. Stabilizing linear control law is fulfilled as feedback by the estimation of state. We can determine uniquely the coefficients of linear control law and estimation system can be determined uniquely by solving of the corresponding linear-quadratic problems for the separated controllable subsystems using the method of N.N. Krasovsky. The valid conclusion about asymptotical stability of the original equations is deduced using the previously proved theorem. This theorem is based on the nonlinear stability theory methods and analysis of limitations imposed by the geometric constraints on the initial disturbances.
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The mathematical modelling of the production of construction mixtures with prescribed properties
Статья научная
We propose a method for the mathematical modelling of the preparation of construction mixes with prescribed properties. The method rests on the optimal control theory for Leontieff-type systems. Leontieff-type equations originally arose as generalizations of the well-known input-output model of economics taking supplies into account. Then they were used with success in dynamical measurements, therefore giving rise to the theory of optimal measurements. In the introduction we describe the ideology of the proposed model. As an illustration, we use an example of preparing of simple concrete mixes. In the first section we model the production process of similar construction mixtures (for instance, concrete mixtures) depending on investments. As a result, we determine the price of a unit of the product. In the second section we lay the foundation for the forthcoming construction of numerical algorithms and software, as well as conduction of simulations. Apart from that, we explain the prescribed properties of construction mixes being optimal with respect to expenses.
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The multipoint initial-final value condition for the Navier - Stokes linear model
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The Navier - Stokes system models the dynamics of a viscous incompressible fluid. The problem of existence of solutions of the Cauchy - Dirichlet problem for this system is included in the list of the most serious problems of this century. In this paper it is proposed to consider the multipoint initial-final conditions instead of the Cauchy conditions. It should be noted that nowadays the study of solvabilityof initial-final value problems is a new and actively developing direction of the Sobolev type equations theory. The main result of the paper is the proof of unique solvability of the stated problem for the system of Navier - Stokes equations.
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