Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование

Все статьи: 748

Real sectorial operators

Real sectorial operators

Yagi A.

Статья научная

Sectorial operators that act in complex Banach spaces and map real subspaces into themselves should be called real sectorial operators. These operators have already been used implicitly in the study of various diffusion equations. Meanwhile, in the Lojasiewicz - Simon theory which provides longtime convergence of solutions to stationary solutions, the real valued Lyapunov functions play an important role. In order to make general methods for studying longtime convergence problems on the basis of the Lojasiewicz - Simon theory, it may therefore be meaningful to give an explicit definition for these real sectorial operators and to show their basic properties that are inherited from those of complex sectorial operators.

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Recent results on the Cahn - Hilliard equation with dynamic boundary conditions

Recent results on the Cahn - Hilliard equation with dynamic boundary conditions

Colli P., Gilardi G., Sprekels J.

Статья научная

The pure or viscous Cahn - Hilliard equation with possibly singular potentials and dynamic boundary conditions is considered and the well-posedness of the related initial value problem is discussed. Then, a boundary control problem for the viscous Cahn - Hilliard system is studied and first order necessary conditions for optimality are shown. Moreover, the same boundary control problem is addressed for the pure Cahn - Hilliard system, by investigating it and passing to the limit in the analogous results for the viscous Cahn - Hilliard system as the viscosity coefficient tends to zero.

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Recovering of the heat transfer coefficient from the temperature measurements

Recovering of the heat transfer coefficient from the temperature measurements

Shergin S.N., Pyatkov S.G.

Статья научная

An inverse analysis is used to recover the heat transfer coefficient in heat conduction problems from boundary measurement of the temperature. The numerical scheme is based on the finite element method in the space variables, the method of finite differences in time, and a special iteration scheme to determine the heat transfer coefficients on each time step. The heat transfer coefficients is sought in the form of a finite segment of a series with unknown Fourier coefficients depending on time. The algorithm for solving the problem relies on theoretical results stating that this problem is well-posed and can be reduced to an operator equation with a contraction. The results of numerical experiments confirm theoretical arguments that this problem is indeed well-posed. The obtained results reveal the accuracy, efficiency, and robustness of the proposed algorithm. It is stable under random perturbations of the data.

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Regularity results and solution semigroups for retarded functional differential equations

Regularity results and solution semigroups for retarded functional differential equations

Favini A., Tanabe H.

Статья научная

We show that the solutions of the retarded functional differential equations in a Banach space, whose existence and uniqueness are established in paper of A. Favini and H. Tanabe, have some further regularity properties if the initial data and the inhomogeneous term satisfy some smootheness assumptions. Some results on the solution semigroups analogous to the one of G. Di Blasio, K. Kunisch and E. Sinestrari and to the one of E. Sinestrari are also obtained.

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Relay races along a pair of selectable routes

Relay races along a pair of selectable routes

Larkin E.V., Bogomolov A.V., Privalov A.N., Dobrovolsky N.N.

Статья научная

Case of two teams competition, which should overcome the distance divided onto stages, is considered. In the case under consideration, every stage has its own number of routes, which the participants of the team may select to overcome. It is shown, that competition bears the character of the relay race, and two-parallel semi-Markov process is the natural approach to modelling of the situation. From all possible routes two were selected. The conception of switching space, which display all possible switching trajectories is proposed. The formula for calculation of switching trajectories number is acquired. It is shown, that ordinary semi-Markov process with the use of the recursive procedure may be obtained from the complex two-parallel semi-Markov process, which describes the wandering through selected routes. The formulae for realization of the recursion are proposed. Conception of distributed forfeit is proposed. It is shown, that forfeit depends on difference of stages, teams overcome at current time, and routes, on which participants solved to overcome stage. The formula for estimation of total forfeit, which one team pays to other team is obtained. It is shown, that the sum of forfeit may be used as the optimization criterion in the game strategy optimization task.

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Research of default risk level of Russian energy

Research of default risk level of Russian energy

Mokhov V.G., Chebotareva G.S.

Краткое сообщение

The liberalization of the electricity market intensifies the competition for investors in the Russian energy market, for which the financial stability of energy companies is an important criterion. The paper presents the mathematical modelling of integrated assessment of the default risk level of Russian energy companies, taking into account their specific characteristics: type of the energy business, form of ownership, and regional specific. The research is based on the industry approach to the diagnostics of default risk level of energy companies. The approach includes the logit-model and assessment of the coefficients significance. The complexity of this model is conditioned by the study of external and internal financial and economic indicators, as well as qualitative criteria based on the introduction of dummy-variables. Four groups of default risk level of Russian energy companies are proposed. The use of mathematical modelling tools increases the accuracy of assessing the financial insolvency of energy companies in comparison with the traditional methods. Therefore, the proposed approach is novel, relevant, and practically significant. Research veracity is confirmed by the practical implementation. We recommend the use of the proposed methodology in assessment of the current state and development strategy of Russian energy companies, as well as by investors and analysts to make financial decisions.

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Research of the Optimal Control Problem for One Mathematical Model of the Sobolev Type

Research of the Optimal Control Problem for One Mathematical Model of the Sobolev Type

K.V. Perevozchikova, N.A. Manakova

Статья научная

The article is devoted to the study of optimal control for one mathematical model of the Sobolev type, which is based on the model equation, which describes various processes (for example, deformation processes, processes occurring in semiconductors, wave processes, etc.) depending on the parameters and can belong either to the class of degenerate (for  > 0) equations or to the class of nondegenerate (for  < 0) equations. The article is the first attempt to study the control problem for mathematical semilinear models of the Sobolev type in the absence of the property of non-negative definiteness of the operator at the time derivative, i.e. the construction of a singular optimality system in accordance with the singular situation caused by the instability of the model. Conditions for the existence of a control-state pair are presented, and conditions for the existence of an optimal control are found.

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Resource allocation in cloud computing via optimal control to queuing systems

Resource allocation in cloud computing via optimal control to queuing systems

Madankan A., Delavarkhalafi A., Karbassi S.M., Adibnia F.

Статья научная

We consider resource allocation problem in the cloud computing. We use queuing model to model the process of entering into the cloud and to schedule and to serve incoming jobs. In this paper, the main problem is to allocate resources in the queuing systems as a general optimization problem for controlled Markov process with finite state space. For this purpose, we study a model of cloud computing where the arrival jobs follow a stochastic process. We reduce this problem to a routing problem. In the case of minimizing, cost is given as a mixture of an average queue length and number of lost jobs. We use dynamic programming approach. Finally, we obtain the explicit form of the optimal control by the Bellman equation.

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Semilinear Sobolev type mathematical models

Semilinear Sobolev type mathematical models

Zamyshlyaeva A.A., Bychkov E.V.

Статья научная

The article contains a review of the results obtained in the scientific school of Georgy Sviridyuk in the field of semilinear Sobolev type mathematical models. The paper presents results on solvability of the Cauchy and Showalter-Sidorov problems for semilinear Sobolev type equations of the first, the second and higher orders, as well as examples of non-classical models of mathematical physics, such as the generalized Oskolkov model of nonlinear filtering, propagation of ion-acoustic waves in plasma, propagation waves in shallow water, which are studied by reduction to one of the above abstract problems. Methods for studying the semilinear Sobolev type equations are based on the theory of relatively -bounded operators for equations of the first order and the theory of relatively polynomially bounded operator pencils for equations of the second and higher orders in the variable . The paper uses the phase space method, which consists in reducing a singular equation to a regular one defined on some subspace of the original space, to prove existence and uniqueness theorems, and the Galerkin method to construct an approximate solution.

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Sequential application of the hierarchy analysis method and associative training of a neural network in examination problems

Sequential application of the hierarchy analysis method and associative training of a neural network in examination problems

Avsentiev O.S., Meshcheryakova T.V., Navoev V.V.

Краткое сообщение

We propose development of examination methodology based on a sequential application of the MAI method (i.e., the hierarchy analysis method) and associative training of neural networks. The proposed method is an alternative to the usual methods to solve a direct examination problem. We present a methodological approach to the examination problem. The approach allows to save information about all objects and consider their indicators in total. Therefore, there is the soft maximum principle (softmax), based on the model of expert evaluations mixing. This approach allows different interpretations of the examination results, which save quality unchanged overall picture of the examination object indicators ratio, and to get more reliable examination results, especially in cases where the objects characteristics are very different.

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Sergey Grigorievich Pyatkov (on 65th birthday)

Sergey Grigorievich Pyatkov (on 65th birthday)

Abasheeva N.L., Zagrebina S.A., Zamyshlyaeva A.A., Keller A.V., Kozhanov A.I., Sviridyuk G.A., Kabanikhin S.I., Safonov E.I., Soldatov A.P., Slavskii V.V.

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Simulation of Processes to Protect Information of Informatization Objects Against Leakage Through Technical Channels Using an Apparatus of Petri - Markov Nets

Simulation of Processes to Protect Information of Informatization Objects Against Leakage Through Technical Channels Using an Apparatus of Petri - Markov Nets

O.S. Avsentiev, A.O. Avsentiev, A.G. Krugov, Yu.K. Yazov

Статья научная

We propose an approach to simulation of information protection processes at informatization objects in the dynamics of realizing threats of its leakage through technical channels using the apparatus of composite Petri–Markov nets. We investigate the interrelationships of the processes of transferring information at the object of informatization, its interception by a violator from outside this object through technical channels and protection against interception. Analytical expressions are obtained for calculating the probabilistic-temporal characteristics of simulated processes in order to assess the possibility of a violator implementing threats of information leakage at objects of informatization; protection of this information through the use of preventive measures aimed at blocking or anticipating the actions of the violator to implement these threats

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Simulation of concurrent games

Simulation of concurrent games

Ivutin A.N., Larkin E.V.

Статья научная

Concurrent games, in which participants run some distance in real physical time, are investigated. Petri - Markov models of paired and multiple competitions are formed. For paired competition formula for density function of time of waiting by winner the moment of completion of distance by loser is obtained. A concept of distributed forfeit, which amount is defined as a share of sum, which the winner gets from the loser in current moment of time is introduced. With use of concepts of distributed forfeit and waiting time the formula for common forfeit, which winner gets from loser, is obtained. The result, received for a paired competition, was spread out onto multiple concurrent games. Evaluation of common wins and loses in multiple concurrent game is presented as a recursive procedure, in which participants complete the distance one after another, and winners, who had finished the distance get forfeits from participants, who still did not finish it. The formula for evaluation of common winning in concurrent game with given composition of participants is obtained. The result is illustrated with numerical example.

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Simulation of relay-races

Simulation of relay-races

Larkin E.V., Kotov V.V., Ivutin A.N., Privalov A.N.

Статья научная

It is shown that multistage concurrent games, or relay-races, are widely used in practice. It is proposed to model relay-races in the state space, in which discrete co-ordinates are the mathematical analogue of stages, which participants pass in the current time, and basic principle of modelling of residence of participant in space states is the M-parallel semi-Markov process. With use of the proposed formalisms formulae for evaluation of stochastic and time characteristics of relay-races evolution are obtained. For arbitrary realization of switching trajectory the recurrent procedure of evolution with evaluation of stochastic and time characteristics of realization under investigation is worked out. Conception of distributed forfeit, which depends on difference of stages of participants compete in pairs is introduced. Dependence for evaluation of total forfeit for every participant is obtained.

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SkifCh: эффективный коммуникационный интерфейс

SkifCh: эффективный коммуникационный интерфейс

Климов Юрий Андреевич, Орлов Антон Юрьевич, Шворин Артем Борисович

Статья научная

В работе описывается SkifCh - низкоуровневый интерфейс передачи сообщений. Данный интерфейс эффективно поддерживается на уровне сетевого оборудования, которое, в свою очередь, может быть реализовано в ПЛИС (как сделано в суперкомпьютере СКИФ-Аврора) или в специализированных микросхемах. Интерфейс SkifCh может быть использован для высокоэффективных сетевых обменов непосредственно из прикладных программ, а также для реализации коммуникационных библиотек более высокого уровня. На данный момент поверх интерфейса SkifCh реализованы системы MPI, SHMEM, GASNet и ARMCI. В работе также приведено сравнение эффективности использования SkifCh и MPI на суперкомпьютере СКИФ-Аврора.

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Smooth approximation of the quantile function derivatives

Smooth approximation of the quantile function derivatives

Sobol V.R., Torishnyy R.O.

Краткое сообщение

In this paper, a smooth approximation of the second-order derivatives of quantile function is provided. The convergence of approximations of the first and second order derivatives of quantile function is studied in cases when there exists a deterministic equivalent for the corresponding stochastic programming problem. The quantile function is one of common criteria in stochastic programming problems. The first-order derivative of quantile function can be represented as a ratio of partial derivatives of probability function. Using smooth approximation of probability function and its derivatives we obtain approximations of these derivatives in the form of volume integrals. Approximation of the second-order derivative is obtained directly as derivative of the first-order derivative. A numerical example is provided to evaluate the accuracy of the presented approximations.

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Sobolev type equations in spaces of differential forms on Riemannian manifolds without boundary

Sobolev type equations in spaces of differential forms on Riemannian manifolds without boundary

Shafranov D.E.

Статья научная

The article contains a review of the results obtained by the author both independently and in collaboration with other members of the Chelyabinsk scientific school founded by G.A. Sviridyuk and devoted to Sobolev-type equations in specific spaces, namely the spaces of differential forms defined on some Riemannian manifold without boundary. Sobolev type equations are nonclassical equations of mathematical physics and are characterized by an irreversible operator at the highest derivative. In our spaces, we need to use special generalizations of operators to the space of differential forms, in particular, the Laplace operator is replaced by its generalization, the Laplace-Beltrami operator. We consider specific interpretations of equations with the relatively bounded operators: linear Barenblatt-Zheltov-Kochina, linear and semilinear Hoff, linear Oskolkov ones. For these equations, we investigate the solvability of the Cauchy, Showalter-Sidorov and initial-final value problems in different cases. Depending on the choice of the type of equation (linear or semi-linear), we use the corresponding modification of the phase space method. In the spaces of differential forms, in order to use this method based on domain splitting and the actions of the corresponding operators, the basis is the Hodge-Kodaira theorem on the splitting of the domain of the Laplace-Beltrami operator.

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Software for the mobile robot spatial orientation system

Software for the mobile robot spatial orientation system

Bazhenov E.I., Mokrushin S.A., Okhapkin S.I.

Краткое сообщение

Ensuring the orientation of the mobile robot in space requires solving the problem of its precise positioning. For this purpose, it is proposed to include an additional measuring complex in the control system of the mobile robot. The complex is designed to determine the orientation of the robot in space by the values of the angles of course, roll and pitch. The analysis of the mobile robot positioning solutions allows to justify the feasibility of using inertial navigation systems based on microelectromechanical sensors to obtain navigation information about the orientation of the mobile robot in space. The key element of the developed functional scheme of the mobile robot control system is the software of the mobile robot spatial orientation system. The software implements separate sections of the code that determine the orientation in space using inertial sensors in parallel to the main algorithm of the mobile robot. The result of the developed software is a string containing up-to-date information about the three orientation angles of the robot: the string is sent to the server to form control actions to correct the spatial orientation of the mobile robot. To improve the accuracy of determining the robot orientation in space based on the values of the angles of course, roll and pitch, the developed software eliminates the systematic error of microelectromechanical sensors and corrects the magnetometer readings taking into account the displacement of the magnetic field along its three axes. The developed software of the mobile robot spatial orientation system provides a significant increase in the positioning accuracy of the mobile robot designed for use in a room with an area of 30 to 200 m with a known layout and a priori set starting point.

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Software set of intellectual support and security of LMS MAI Class.Net

Software set of intellectual support and security of LMS MAI Class.Net

Naumov A.V., Mkhitaryan G.A., Rybalko A.A.

Статья научная

The article discusses integration of mathematical methods and security components in a learning management system (LMS). The discussed methods provide a statistical analysis of user data in process of online training in mathematical disciplines and adapting the content of the system for different users. The software package allows automatic calculation of questions complexity and user ratings by using statistical data. This helps the system administrator to detect users which use illegal hints or help from others. A procedure is designed for content selection for a variety of tests and control activities, with restrictions and without a time limit for the test. Two probabilistic models were used during development of mathematical methods: the Rasch model to describe the probability of users' answer correctness and Van der Linden model to describe the time it took for a user to respond to the question. The software package contains special optimization procedures that estimate the parameters of these models based on the accumulated statistics across all users. Apart from discussing efficiency of LMS usage with the above mentioned methods, the article also discusses general security architecture of the LMS, a set of technologies used for developing system security with specific implementation examples.

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Solitary wave effects of Woods-Saxon potential in Schrodinger equation with 3D cubic nonlinearity

Solitary wave effects of Woods-Saxon potential in Schrodinger equation with 3D cubic nonlinearity

Inc M., Iqbal M.S., Ali A.H., Manzoor Z., Ashraf F.

Статья научная

In this research article, we apply the generalized projective Riccati equation method to construct traveling wave solutions of the d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential. The generalized projective Riccati equation method is a powerful and effective mathematical tool for obtaining exact solutions of nonlinear partial differential equations, and it allows us to derive a variety of traveling wave solutions of the 3d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential. These solutions contain periodic wave solutions, bright and dark soliton solutions. The study of many physical systems, such as Bose-Einstein condensates and nonlinear optics, that give rise to the nonlinear Schrödinger equation. We provide a detailed description of the generalized projective Riccati equation method in the paper, and demonstrate its usefulness in solving the nonlinear Schrödinger equation with Woods-Saxon potential. We present various graphical representations of the obtained solutions using MATLAB software, and analyze their characteristics. Our results provide new insights into the behavior of the d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential, and have potential applications in numerous fields of physics, as well as nonlinear optics and condensed matter physics.

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