Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 739
Статья научная
The quasi-stationary problem for modelling the process of electrochemical cutting with a plate electrode-tool is formulated. The formulation of the problem is based on the use of a stepwise function of current efficiency from the current density. Thus three areas with various conditions are formed on the machined surface. The usual stationarity condition is used in the area of high current densities. In the area of low current densities the dissolution is absent and the initial form of the boundaries remains. In the intermediate zone, the current density at each point is equal to the critical value. The presence of boundary conditions on each section of the machined surface allows to formulate a boundary problem for the analytical function of the complex variable and to find the shape of the boundary at any moment, regardless of the background. The solutions of quasi-stationary and non-stationary problems are compared, and the range of existence of quasi-stationary solutions is found.
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Complex approach to assessment of investment attractiveness of power generating company
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Present approaches based on the qualitative analysis methods are not effective enough for a comprehensive evaluation of the investment attractiveness of the power generating company (PGC). It resolves the urgency of the complex deterministic method of accounting for aggregated risk. The article presents the diagnostics of power generating company risks' and the assessment of the actual aggregated risk as the integral indicator of investment attractiveness of the PGC. The proposed authors' approach to ranking the risk taking into account the level of hazard is based on the calculation of individual limits of risk states variation and risk relative value. The individual risk assessment is based on the Bayes method complemented by a two-step normalization to account for the specificity of PGC. The Merton - Vasicek method and basic principles of the economic capital theory are used in developing the method of the final evaluation of the PGC investment attractiveness. Research veracity is confirmed by the practical implementation. The research results are recommended for use in assessing the current level of the PGC investment attractiveness and development strategy of its increase.
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Computational experiment for a class of mathematical models of magnetohydrodynamics
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The first initial-boundary value problem for the system modelling the motion of the incompressible viscoelastic Kelvin - Voigt fluid in the magnetic field of the Earth is investigated considering that the fluid is under external influence. The problem is studied under the assumption that the fluid is under different external influences depending not only on the coordinates of the point in space but on time too. In the framework of the theory of semi-linear Sobolev type equations the theorem of existence and uniqueness of the solution of the stated problem is proved. The solution itself is a quasi-stationary semi-trajectory. The description of the problem's extended phase space is obtained. The results of the computainal experiment are presented.
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Computational experiment for one class of evolution mathematical models in quasi-Sobolev spaces
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In the article the mathematical model representing one class of evolution equations in quasi-Banach spaces is studied. A theorem on the unique solvability of the Cauchy problem is stated. The conditions for the phase space existence are presented. We also give the conditions for exponential dichotomies of solutions. Based on the theoretical results there was developed an algorithm for the numerical solution of the problem. The algorithm is implemented in Maple. The article includes description of the algorithm which is illustrated by variety of model examples showing the work of the developed program and represent the main properties of solutions.
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Computational experiment for one mathematical model of ion-acoustic waves
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In the article the mathematical model of ion-acoustic waves in a plasma in an external magnetic field is studied. This model can be reduced to a Cauchy problem for a Sobolev type equation of the fourth order with polynomially (A,p)-bounded operator pencil. Therefore abstract results on solvability of the Cauchy problem for such equation can be used. In the article a theorem on the unique solvability of the Cauchy - Dirichlet problem is mentioned. Based on the theoretical results there was developed an algorithm for the numerical solution of the problem, using a modified Galerkin method. The algorithm is implemented in Maple. The article includes description of this algorithm. It is illustrated by model examples showing the work of the developed program.
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We investigate of a special dam optimal location at the Volga river in the area of the Akhtuba left sleeve beginning (7 km to the south of the Volga Hydroelectric Power Station dam). We claim that a new water-retaining dam can resolve the key problem of the Volga-Akhtuba floodplain related to insufficient water amount during spring floodings due to the overregulation of the Lower Volga. Using a numerical integration of Saint-Vanant equations we study the water dynamics across the northern part of the Volga-Akhtuba floodplain taking into account its actual topography. As the result we found an amount of water VA passing to the Akhtuba during spring period for a given water flow through the Volga Hydroelectric Power Station (so-called hydrograph which characterises the water flow per unit of time). By varying the location of the water-retaining dam xd,yd we obtained various values of VA(xd,yd) as well as various flow spatial structure on the territory during the flood period. Gradient descent method provides the dam coordinated with the maximum value of VA. Such approach to the dam location choice let us find the best solution, that the value VA increases by a factor of 2. Our analysis demonstrates a good potential of the numerical simulations in the field of hydraulic works.
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Consistency and Lyapunov stability of linear singular time delay systems: a geometric approach
Статья научная
When we consider the control design of practical systems (chemical engineering systems, lossless transmission lines, large-scale electric network control, aircraft attitude control, flexible arm control of robots, etc.), time-delay often appears in many situations. Singular time delayed systems are the dynamic systems described by a mixture of algebraic and differential equations with retarded argument. This paper investigates the geometric description of initial conditions that generate smooth solutions to such problems and the construction of the Lyapunov stability theory to bound the rates of decay of such solutions. The new delay dependent conditions for asymptotic stability for the class of systems under consideration were derived. Moreover, the result is expressed in terms of only systems matrices that naturally occur in the model, therefore avoiding the need to introduce algebraic transformations into the statement of the main theorem.
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Constructing of OE-postman path for a planar graph
Статья научная
With automated preparation of the cutting process, the cutting plan can be represented as a flat graph. The purpose of this simulation is to determine the shortest path of the cutting tool, provided that the part cut from the sheet would not require additional cuts. The article deals with the task of building the path of the Chinese postman in a flat graph, which is a model of the cutting plan. An orderly coverage condition is imposed on this path (i.e., the cycle of traversed edges does not encompass those not yet traversed). Such a path will also be called an OE path. This limitation means the absence of additional cuts for parts. The article discusses the recursive algorithm for constructing such chains. It is proved that the algorithm has polynomial complexity. The developed software allows solving the problem for an arbitrary flat graph. The program has been tested for various types of flat graphs.
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Construction of approximate mathematical models on results of numerical experiments
Статья научная
A mathematical model of an artillery shot is represented as a system of non-stationary one- and two-dimensional differential equations of the multiphase gas dynamics and heat transfer. Conjunction Euler-Lagrange method is used for the numerical solution of gas-dynamic equations. The initial mathematical model is approximated by a system of ordinary differential equations using a vector of correction functions. Correction functions are found from solutions of multiobjective optimal control problem. Multiobjective optimization is carried out using a hybrid genetic algorithm. The resulting model is adequate and allows doing more processing series of calculations the main process parameters (projectile velocity and maximum pressure) depending on the input parameters. Comparative analysis of different approximators (linear multiple regression, support vector machines, multi-layer neural network, radial network, the method of fuzzy decision trees) showed that an acceptable accuracy 0,4-0,5 % is provided by only non-linear approximation methods, such as multi-layer and radial neural networks. Constructed approximate models are not require much computing time and can be implemented in the control systems.
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Continuous and generalized solutions of singular integro-differential equations in Banach spaces
Статья научная
Continuous and generalized solutions of singular equations in Banach spaces are studied. We apply Lyapunov-Schmidt’s ideas and the generalized Jordan sets techniques and reduce partial differential-operator equations with the Fredholm operator in the main expression to regular problems. In addition the left and right regularizators of singular operators in Banach spaces and fundamental operators in the theory of generalized solutions of singular equations are constructed.
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Статья научная
Delay differential-algebraic equations (DDAEs) can be used for modelling real-life phenomena that involve simultaneously time-delay effect and constraints. It is also known that solving delay DAEs is more complicated than solving non-delay ones because approximation of solutions in the past time is usually needed and discontinuity in higher derivatives of the solutions is typical. Recently, we have proposed and investigated linear multistep (LM) methods for strangeness-free DAEs (without delay). In this paper, we extend the use of LM methods to a class of structured strangeness-free DAEs with constant delay. For the approximation of solutions at delayed time we use polynomial interpolation. Convergence analysis for LM methods is presented. It is shown that, similarly to the non-delay case, the strict stability of the second characteristic polynomial associated with the methods is not required for the convergence if we discretize an appropriately reformulated DDAE instead of the original one. Numerical experiments are also given for illustration.
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This paper considers the parameter estimation problem for models of one-dimensional chaotic systems. The guaranteed algorithm is proposed in the context of set-membership approach, which assumes that only intervals of possible values are known for the uncertain variables in the model (initial condition, parameter and measurement errors). The algorithm recursively computes the interval estimates of the parameter at every time step. If the prior information is correct, found interval estimates always contain the true value of the parameter. For certain models of measurement errors the result of the algorithm is the exact value of the parameter (the final interval estimate contains a single point). The goal of this study is to derive conditions under which the guaranteed algorithm improves the interval estimate of the parameter.
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Convergence modelling in international integration associations
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The article considers mathematical tools for modelling economic policy as a whole, as well as convergence in the field of labor, foreign economic activity, monetary and debt policy. Convergence was estimated using the σ-convergence model, which characterizes the decrease in time spread in the levels of development of countries and regions, reflecting the negative relationship between economic growth rates and the initial level of development of countries and regions. The σ-convergence was estimated by the coefficient of variation and by the dispersion-based model. To assess β-convergence, we used the Barro and Sala-i-Martin models, as well as the Baumol, Solow-Svan, and Quadrado-Rour models. The use of this mathematical toolkit allows to explore the presence and speed of convergence before and after joining international integration associations. The proposed mathematical modelling tools are recommended to be used in order to analyze convergence processes, study the dynamics of convergence or divergence, and also to adjust the directions and methods of state and regional economic policies of countries included in the integration association.
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Cooperation in a conflict of persons under uncertainty
Статья научная
The paper considers a model of a conflict system with N active participants with their own interests when exposed to an uncertain factor. At the same time, decision-makers do not have any statistical information about the possible implementation of an uncertain factor i.e. they only know the many possible realizations of this factor - uncertainties. Under the assumption that the participants of to the conflict can coordinate their actions in the decision-making process the model is formalized as a cooperative N-person game without side payments and under uncertainty. In this paper, we introduce a new principle of coalitional equilibration (CE). The integration of individual and collective rationality (from theory of cooperative games without side payments) and this principle allows us to formalize the corresponding concept of CE for a conflict of N persons under uncertainty. At the same time, uncertainty is taken into account along with using the concept of the "analogue of maximin'' proposed earlier in the our works and the "strong guarantees'' constracted on its basis. Next, we establish sufficient conditions for existence of coalitional equilibrium, which are reduced to saddle point design for the Germeier convolution of guaranteed payoffs. Following the above-mentioned approach of E. Borel, J. von Neumann and J. Nash, we also prove existence of coalitional equilibrium in the class of mixed strategies under standard assumptions of mathematical game theory (compact uncertainties, compact strategy sets, and continuous payoff functions). At the end of the paper, some directions or further research are given.
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Статья научная
The paper considers two simple systems of differential-algebraic equations that appear in the study of chemical kinetics problems with partial equilibria: some of the variables are determined from the condition argmin for some system function state, which depends on all variables of the problem. For such a statement, we can write a differential-algebraic system of equations where the algebraic subproblem expresses the conditions for the minimality of the state function at each moment. It is convenient to use splitting methods in numerical solving, i.e. to solve dynamic and optimization subproblems separately. In this work, we investigate the applicability of differential-algebraic splitting using two simplified systems. The convergence and order of accuracy of the numerical method are determined. Different decomposition options are considered. Calculations show that the numerical solution of the split system of equations has the same order of accuracy as the numerical solution of the joint problem. The constraints are fulfilled with sufficient accuracy if the procedure of the numerical method ends with the solution of the optimization subproblem. The results obtained can be used in the numerical solving of more complex chemical kinetics problems.
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Статья научная
In this article, we give new results on the study of elliptic abstract second order differential equation with variable operators coefficients under the general Robin homogeneous boundary value conditions, in the framework of UMD spaces. Here, we do not assume the differentiability of the resolvent operators. However, we suppose that the family of variable operators verifies the Labbas-Terreni assumption inspired by the sum theory and similar to the Acquistapace-Terreni one. We use Dunford calculus, interpolation spaces and semigroup theory in order to obtain existence, uniqueness and maximal regularity results for the classical solution to the problem.
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Differential-algebraic equations with regular local matrix pencils
Статья научная
In the projector based framework, any regular linear DAE features several continuous time-varying characteristic subspaces that are independent of construction technicalities, among them the so-called sum-subspaces. As it is well-known, the local matrix pencils of a higher-index time-varying linear DAE do not reflect the global structure of the DAE in general. We show that, on the given interval, the local matrix pencils of the DAE are regular and reflect the global DAE structure if several of these characteristic subspaces are time-invariant. We discuss practicable methods to check the time-invariance of these subspaces. The corresponding class of DAEs is related to the class of DAEs formerly introduced and discussed by Yuri E. Boyarintsev.
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Discrete model of paired relay-race
Статья научная
The case of the active and passive team relay-race, in which an active team operates in accordance with rigid schedule and a passive team overcome the stage of its distance at randomly selected alternative routs during occasional time intervals is considered. Due to high complexity of classical relay-race analysis, method of simulation, based on representation of time intervals densities of passing stages routs with discrete distributions is proposed. It is shown, that after transformation of time intervals densities into discrete distributions the problem of a relay race analysis reduces to the task of analysis of two-team system with rigid schedules. The method of sampling of densities composition with estimation a sampling error, and recursive procedure of rigid schedule relay-race analysis with calculation of forfeit are worked out. It is shown, that forfeit depends on the difference of stages, teams overcome at current time and a strategy, which active team realizes during relay-race.
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Статья научная
We examine the stability issue in the inverse problem of determining a scalar potential appearing in the stationary Schrödinger equation in a bounded domain, from a partial elliptic Dirichlet-to-Neumann map. Namely, the Dirichlet data is imposed on the shadowed face of the boundary of the domain and the Neumann data is measured on its illuminated face. We establish a log log stability estimate for the L2-norm (resp. the H-1-norm) of Ht, for t>0, and bounded (resp. L2) potentials.
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Статья научная
The research work develops a Context aware Data Fusion with Ensemblebased Machine Learning Model (CDF-EMLM) for improving the health data treatment. This research work focuses on developing the improved context aware data fusion and efficient feature selection algorithm for improving the classification process for predicting the health care data. Initially, the data from Internet of Things (IoT) devices are gathered and pre-processed to make it clear for the fusion processing. In this work, dual filtering method is introduced for data pre-processing which attempts to label the unlabeled attributes in the data that are gathered, so that data fusion can be done accurately. And then the Dynamic Bayesain Network (DBN) is a good trade-off for tractability becoming a tool for CADF operations. Here the inference problem is handled using the Hidden Markov Model (HMM) in the DBN model. After that the Principal Component Analysis (PCA) is used for feature extraction as well as dimension reduction. The feature selection process is performed by using Enhanced Recursive Feature Elimination (ERFE) method for eliminating the irrelevant data in dataset. Finally, this data are learnt using the Ensemble based Machine Learning Model (EMLM) for data fusion performance checking.
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