Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 729
Acceleration of summation over segments using the fast Hough transformation pyramid
Статья научная
In this paper, we propose an algorithm for fast approximate calculation of the sums over arbitrary segments given by a pair of pixels in the image. Using the results of intermediate calculations of the fast Hough transform, the proposed algorithm allows to calculate the sum over arbitrary line segment with a logarithmic complexity depending on the linear size of the original image (also called fast discrete Radon transform or Brady transform). In this approach, the key element of the algorithm is the search for the dyadic straight line passing through two given pixels. We propose an algorithm for solving this problem that does not degrade the general asymptotics. We prove the correctness of the algorithm and describe a generalization of this approach to the three-dimensional case for segments of straight lines and of planes.
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Acoustic waves propagation in heated water with vapor bubbles
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The problems of wave propagation in bubbly media are of great interest for researchers for nearly half a century due to the wide distribution of these systems in nature and their intense use in modern technology. It is known that the attenuation intensity of sound disturbances in the gas-liquid media is mainly determined by the thermophysical characteristics of the gas in bubbles. It turns out that these effects are significantly observable with increasing of steam concentration due to system temperature get higher. In this paper, we consider the propagation of small perturbations in a liquid with bubbles filled with vapor and gas insoluble in the liquid phase in an one-dimensional and one-velocity approximation. In order to take into account interfacial heat and mass transfer, we use the heat and diffusion equations inside the bubble and the heat equation in the fluid around the bubble. A dispersion equation was written from the existence condition of the solution in the form of a damped traveling wave, taking into account the effects of acoustic unloading of bubbles, and numerical calculations were carried out for water with vapor-gas bubbles. We investigate the features of the reflection of harmonic waves from the interface of "pure'' liquid and liquid with vapor-gas bubbles. Also, we carry out a numerical analysis of the effect of the initial volume gas content ag0 with two initial bubble sizes a0=10-6 m and 10-3 m. Finally, we study the effect of disturbance frequencies and temperature of the media on the attenuation coefficient of sound.
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Active parametric identification of Gaussian linear discrete system based on experiment design
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The application of methods of theory of experiment design for the identification of dynamic systems allows the researcher to gain more qualitative mathematical model compared with the traditional methods of passive identification. In this paper, the authors summarize results and offer the algorithms of active identification of the Gaussian linear discrete systems based on the design inputs and initial states. We consider Gaussian linear discrete systems described by state space models, under the assumption that unknown parameters are included in the matrices of the state, control, disturbance, measurement, covariance matrices of system noise and measurement. The original software for active identification of Gaussian linear discrete systems based on the design inputs and initial states are developed. Parameter estimation is carried out using the maximum likelihood method involving the direct and dual procedures for synthesizing A- and D- optimal experiment design. The example of the model structure for the control system of submarine shows the effectiveness and appropriateness of procedures for active parametric identification.
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Adaptive estimation of a moving object trajectory using sequential hypothesis testing
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The present paper addresses the problem of adaptive estimation of a moving object trajectory and detection of changes in the motion mode. It is supposed that an object moves along a complex trajectory and at known discrete-time instants it may change its motion to one of three possible modes: a uniform straight line motion or a uniform anticlockwise/clockwise circular motion. We propose a new algorithm for adaptive trajectory estimation that combines a hybrid linear stochastic model of an object trajectory with a bank of competitive Kalman filters and a decision rule based on a sequential hypothesis testing. A detailed description of the decision rule and pseudocode of the proposed algorithm are given. The software implementation of the algorithm is made in Matlab. A numerical example of adaptive estimation of the motion of an object along a complex trajectory consisting of nine different pieces is considered. We have conducted computational experiments with different levels of noise in the measurements. The results confirm the effectiveness of the proposed algorithm.
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Algorithm and software development to allocate locomotives for transportation of freight trains
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We suggest a mathematical model to allocate locomotives for transportation of freight trains. The aim of the optimization in this model is to minimize the number of locomotives used for the transportation of the trains by choosing routes of the trains and locomotives. It is supposed that the trains can be transported only at defined time intervals (so-called train paths); every locomotive has possible routes called railway hauls. We take into account the necessity of periodic maintenance. We use graph theory and integer optimization to formulate the problem. We suggest mathematical definitions of a railway haul, a train path, a train route, and a locomotive route. An heuristic search algorithm to find an approximate solution of the problem is suggested. The main idea of the algorithm is maximal usage of locomotives that started earlier than other ones. The algorithm contains three stages. A solution of the previous stage is improved at each following stage. We use transfers of the locomotives to improve the current solution. We describe software development to optimize the model. We solve the problem using the historical data of Moscow railway.
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Статья научная
The article is devoted to the construction of algorithm for solving inverse spectral problems generated by Sturm-Liouville differential operators of an arbitrary even order. The goal of solving inverse spectral problems is to recover operators from their spectral characteristics and spectral characteristics of auxiliary problems. In the scientific literature, we can not find examples of the numerical solution of inverse spectral problems for the Sturm-Liouville operator of higher than the second order. However, their solution is caused by the need to construct mathematical models of many processes arising in science and technology. Therefore, the development of computationally efficient algorithm for the numerical solution of inverse spectral problems generated by the Sturm-Liouville operators of an arbitrary even order is of great scientific interest. In this article, we use linear formulas obtained earlier in order to find the eigenvalues of discrete semi-bounded operators and develop algorithm for solving inverse spectral problems for Sturm-Liouville operators of an arbitrary even order. The results of the performed computational experiments show that the use of the algorithm developed in the article makes it possible to recover the values of the potentials in the Sturm-Liouville operators of any necessary even order.
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Статья научная
The weighted finite element method allows to find an approximate solution to a boundary value problem with a singularity faster in 106 times than the classical finite element method for a given error equal to 10-3. In this case, it is required to apply the necessary control parameters in the weighted finite element method. The body of optimal parameters is determined on the basis of carrying out and analysing a series of numerical experiments. In this paper we propose an algorithm for processing the results of calculations and determining the body of optimal parameters for the Dirichlet problem and the Lamé system in a domain with one reentrant corner on the boundary taking values from π to 2π.
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Algorithm for verifying the measurements
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This paper describes the Kramers-Kronig relation for verifying the obtained values of S-parameters for different operation conditions of a transmission line. We obtain and prove lemmas for S-parameters for operation conditions of the line under short-circuit, open-circuit, and matched load. We give a comparison of theoretical and experimental values, which confirm the correctness of the obtained relations and conclusions.
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Algorithm of effective transportation work for cargo traffic
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We suggest a mathematical model that describes railway network. This model is applied to the problem of allocation locomotive for transportation of freight trains. The aim of the optimization is to minimize the size of active locomotive fleet by choosing trains and locomotives routes. An alternative formulation of the optimization problem is proposed with the usage of a heuristic objective function, which makes it possible to construct an effective decision algorithm. A new deterministic algorithm for suboptimal control is described. This algorithm is a modification of the previously proposed, based on the construction of routes tree for each locomotive and, subsequently, the choice of such a route, in which the maximum value of the given objective function is reached. Numerical experiments were carried out on the example of the historical data of the Moscow Railway. The analysis and comparison of the results are given.
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Algorithm of polynomial factorization and its implementation in Maple
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In the work we propose an algorithm for a Wiener-Hopf factorization of scalar polynomials. The algorithm based on notions of indices and essential polynomials allows to find the factorization factors of the polynomial with the guaranteed accuracy. The method uses computations with finite Toeplitz matrices and permits to obtain coefficients of both factorization factors simultaneously. Computation aspects of the algorithm are considered. An a priory estimate for the condition number of the used Toeplitz matrices is found. Formulas for computation of the Laurent coefficients with the given accuracy for functions that analytical and non-vanishing in an annular neighborhood of the unit circle are obtained. Stability of the factorization factors is studied. Upper bounds for the accuracy of the factorization factors are established. All estimates are effective. The proposed algorithm is implemented in Maple computer system as module "PolynomialFactorization". Numerical experiments with the module show a good agreement with the theoretical studies.
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The Avalos-Triggiani problem for a system of wave equations and a linear Oskolkov system of non-zero order is investigated. The mathematical model contains a linear Oskolkov system describing the flow of an incompressible viscoelastic Kelvin-Voigt fluid of non-zero order, and a wave vector equation corresponding to some structure immersed in the fluid. Based on the method proposed by the authors of this problem, the existence of a unique solution to the Avalos-Triggiani problem for the indicated systems is proved.
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Статья научная
In this paper we consider a problem of two bodies bonded through a thin adhesive layer (a third material) of thickness δ. Leting δ go to zero, one obtains a boundary value transmission problem set on a fixed domain. We then give new results for the study of this problem in the framework of Hölder spaces: an explicit representation of the solution and necessary and sufficient conditions at the interface for its optimal regularity are obtained using the semigroups theory and the real interpolation spaces.
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An inference algorithm for monotone Boolean functions associated with undirected graphs
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Boolean functions are a modelling tool useful in many applications; monotone Boolean functions make up an important class of these functions. For instance, monotone Boolean functions can be used for describing the structure of the feasible subsystems of an infeasible system of constraints, because feasibility is a monotone feature. In this paper we consider monotone Boolean functions (MBFs), associated with undirected graphs, whose upper zeros are defined as binary tuples for which the corresponding subgraph of the original undirected graphs is either the empty graph, or it has no edges. For this class of MBFs, we present the settings of problems which are related to the search for upper zeros and maximal upper zeros of these functions. The notion of k-vertices and (k,m)-vertices in a graph is introduced. It is shown that for any k-vertices of the original graph there exists a maximal upper zero of an MBF associated with the graph, in which the component xi corresponding to this k-vertex takes the value . Based on this statement, we construct an algorithm of searching for a maximal upper zero, for the class of MBFs under consideration, which allows one to find, under certain conditions, the solution to the problem of searching for a maximal upper zero, or to substantially reduce the dimension of the original problem. The proposed algorithm was extended for the case of (k,m)-vertices. This extended algorithm allows one to fix a bound on the deviation of an upper zero of the MBF from the maximal upper zeros, in the sense of the number of units in these tuples. The algorithm has the complexity O(n2p), where n is a number of vertices and p is a number of edges of the original graph.
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An integral method for the numerical solution of nonlinear singular boundary value problems
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We discuss the numerical treatment of a nonlinear singular second order boundary value problem in ordinary differential equations, posed on an unbounded domain, which represents the density profile equation for the description of the formation of microscopic bubbles in a non-homogeneous fluid. Due to the fact that the nonlinear differential equation has a singularity at the origin and the boundary value problem is posed on an unbounded domain, the proposed approaches are complex and require a considerable computational effort. This is the motivation for our present study, where we describe an alternative approach, based on the reduction of the original problem to an integro-differential equation. In this way, we obtain a Volterra integro-differential equation with a singular kernel. The numerical integration of such equations is not straightforward, due to the singularity. However, in this paper we show that this equation may be accurately solved by simple product integration methods, such as the implicit Euler method and a second order method, based on the trapezoidal rule. We illustrate the proposed methods with some numerical examples.
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Analysis of biharmonic and harmonic models by the methods of iterative extensions
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The article describes the results of recent years on the analysis of biharmonic and harmonic models by the methods of iterative extensions. In mechanics, hydrodynamics and heat engineering, various stationary physical systems are modeled using boundary value problems for inhomogeneous Sophie Germain and Poisson equations. Deflection of plates, flows during fluid flows are described using the biharmonic model, i.e. boundary value problem for the inhomogeneous Sophie Germain equation. Deflection of membranes, stationary temperature distributions near the plates are described using the harmonic model, i.e. boundary value problem for the inhomogeneous Poisson equation. With the help of the developed methods of iterative extensions, efficient algorithms for solving the problems under consideration are obtained.
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Analysis of socio-economic system processes performance with the help of eigenstate models
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Analysis of the performance of business processes for socio-economic systems is considered. The analysis of the business processes efficiency is based on constructing on of a "perfect image" of their behavior. To extract the components that correspond to the "perfect image" of behavior, we propose the usage of eigenstate method, which allows to represent behavior of socio-economic system as a sum of independent components (eigenstates). The basic relationships of eigenstate method are considered. Construction of the socio-economic system models using the eigenstate method consists in calculation and selection of key eigenstates oriented towards formulated success factors. The selected eigenstates are used to form a "reference" model of the socio-economic system. The high performance of socio-economic system is evaluated with the help of comparison of model and actual values of socio-economic system variables. The eigenstate method efficiency is demonstrated by the example of analysis of sustainable development of the Chelyabinsk city. The sustainable development indicators of processes of the Chelyabinsk city are obtained.
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The paper considers a recurrent regularizing algorithm for joint estimation of distortions of a M-ary quadrature amplitude modulation (M-QAM) signal obtained in a direct conversion receiver path. The algorithm is synthesized using a modified least squares method in the form of Tikhonov's functional under conditions of a priori uncertainty about the laws of noise distribution. The resulting procedure can work both on the test sequence and on information symbols after the detection procedure. We analyze the influence of the Lagrange multiplier on the accuracy of the estimation procedure and on the complexity of the algorithm. It is shown that, with the same accuracy, the regularizing algorithm requires significantly fewer iterations than the procedure without the Lagrange multiplier, and therefore has a lower computational complexity.
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Статья научная
In the three-dimensional statement, we consider the Brinkman equation together with the equation of heterogeneous heat transfer for an unidirectional flow of the Newtonian fluid under laminar regime through horizontal porous channel having a constant rectangular cross-section with known thermal flows at the boundary and small values of the Darcy numbers. Due to the linearity of the formulated system of model equations, we obtain analytical solution of the system using the Laplace and Fourier integral transformation. The obtained solution allows to estimate the length of the input hydrodynamic section, the coefficient of hydraulic resistance, and the local Nusselt numbers. The results obtained for the hydrodynamic subproblem with a large porosity and thermal subproblem with a stationary temperature field agree with the classical data.
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Статья научная
Of concern is an initial-boundary value problem for the modified Boussinesq equation (IMBq equation) is considered. The equation is often used to describe the propagation of waves in shallow water under the condition of mass conservation in the layer and taking into account capillary effects. In addition, it is used in the study of shock waves. The modified Boussinesq equation belongs to the Sobolev type equations. Earlier, using the theory of relatively p-bounded operators, the theorem of existence and uniqueness of the solution to the initial-boundary value problem was proved. In this paper, we will prove that the solution constructed by the Galerkin method using the system orthornormal eigenfunctions of the homogeneous Dirichlet problem for the Laplace operator converges *-weakly to an precise solution. Based on the compactness method and Gronwall's inequality, the existence and uniqueness of solutions to the Cauchy-Dirichlet and the Showalter-Sidorov-Dirichlet problems for the modified Boussinesq equation are proved.
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