Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 739
Oskolkov models and Sobolev-type equations
Статья научная
This article is a review of the works carried out by the author together with her students and devoted to the study of various Oskolkov models. Their distinctive feature is the use of the semigroup approach, which is the basis of the phase space method used widely in the theory of Sobolev-type equations. Various models of an incompressible viscoelastic fluid described by the Oskolkov equations are presented. The degenerate problem of magnetohydrodynamics, the problem of thermal convection, and the Taylor problem are considered as examples. The solvability of the corresponding initial-boundary value problems is investigated within the framework of the theory of Sobolev-type equations based on the theory for -sectorial operators and degenerate semigroups of operators. An existence theorem is proved for a unique solution, which is a quasi-stationary semitrajectory, and a description of the extended phase space is obtained. The foundations of the theory of solvability of Sobolev-type equations were laid by Professor G.A. Sviridyuk. Then this theory, together with various applications, was successfully developed by his followers.
Бесплатно
Статья научная
One of the most interesting and relevant approaches for solving optimization problems are parallel algorithms that work simultaneously with a large number of tasks. The paper presents a new parallel algorithm for NACO that is a hybrid algorithm that consists of the Ant Colony Optimization method combined with the Neighbour Joining method to get accurate and efficient results when solving the Traveling Salesman Problem. Through carrying out comprehensive experiments using a wide variety of real dataset sizes and the multi-core system, the practical results show that the developed program outperforms NACO in terms of execution time and consumed storage space. Availability and implementation: source codes in MATLAB 2017 are publicly available at Internet[i].
Бесплатно
Статья научная
For the analysis of huge problems which are very sensitive to the rounding errors, the software providing rational calculations is developed. Software uses MPI interface for communication in the distributed computational environment. Improved efficiency of such software my be achieved by using heterogeneous computation systems. Local arithmetic operations with long numbers may be done in parallel mode with a lot of processes per one operation. This work introduces the research of increasing of the scalability of basic arithmetic operations.Abilities of the massive parallelism for the heterogeneous computation systems for the efficiency improving are shown. Redundant numerical system with a constant time of the addition operation is introduced. It allows to design well scaled algorithms for all basic arithmetic operations with integer numbers. Scalability of the basic integer arithmetic algorithms is easy applied to rational arithmetic.
Бесплатно
Parallel delivery operations modelling
Краткое сообщение
Some delivery organization scheme is considered. The key point is the principle of routes parallelization using several carriers at the same time and these auxiliary carriers can be based on the main carrier. An example of such a delivery system is a van carrying several autonomous carriers, which in turn can carry out simultaneous so-called parallel deliveries. Delivery routes are determined based on the coordinates of customers, the determination of acceptable starting points for auxiliary carriers, the technical and energy limitations of the main and auxiliary carriers, and the minimization of the amount of time spent on delivery operations. The developed algorithm for solving the problem on routing of delivery using primary and secondary carriers allows to reduce delivery time and resources. The algorithm is implemented in Python using the libraries for processing and visualization of trajectories and other space-time data, packages for extracting, modelling, analyzing and visualizing street networks on the example of the Yekaterinburg city.
Бесплатно
Parameter identification and control in heat transfer processes
Статья научная
The article is devoted to the study of some mathematical models describing heat transfer processes. We examine an inverse problem of recovering a control parameter providing a prescribed temperature distribution at a given point of the spatial domain. The parameter is a lower order coefficient depending on time in a parabolic equation. This nonlinear problem is reduced to an operator equation whose solvability is established with the help of a priori estimates and the fixed point theorem. Existence and uniqueness theorems of solutions to this problem are stated and proved. Stability estimates are exposed. The main result is the global (in time) existence of solutions under some natural conditions of the data. The proofs rely on the maximum principle. The main functional spaces used are the Sobolev spaces.
Бесплатно
Parameters identification algorithm for the SUSUPLUME air pollution propagation model
Краткое сообщение
The article presents the method of identifying the parameters of a dynamic dispersion calculation model SUSUPLUME. It is supposed that the model parameters contain not only the characteristics of the atmosphere and the pollutant, but also information about the influence of other particular conditions such as terrain, building, background, etc. The model parameters are configured based on instrumental measurements of concentrations of pollutants in the atmospheric air in the surface layer (2 meters above ground level). Three identification strategies are considered: identification of parameters by all measurements, identification of parameters by measurements of a given source and identification of parameters using another approved model. A method for weighing these strategies is proposed in the issue. The article also provides objective functions for optimization criteria, an acceptable set of parameters, an algorithm for solving an optimization problem, a decision tree of a feasible set and a global optimization algorithm.
Бесплатно
Parametric identification based on the adaptive unscented Kalman filter
Статья научная
The detailed adaptive unscented Kalman filter algorithm is provided. Step-by-step schemes of filtering algorithms used for the software development are given. Nonlinear filtering algorithm efficiency is investigated with considering an example of a nonlinear continuous-discrete model. The statistic estimator based on the continuous-discrete adaptive unscented Kalman filter with noise is proposed for the nonlinear system parameters estimation. The solution to the problem of solar radiation parameters estimation based on the maximum likelihood method and the adaptive unscented Kalman filter is shown. The obtained results lead to significant improvement of satellite trajectory prediction quality.
Бесплатно
Performance bounds and suboptimal policies for multi-class queue
Статья научная
In this paper, we consider a general class of a queuing system with multiple job types and flexible service facility. We use a stochastic control policy to determine the performance loss in multi-class M/M/1 queue. The considered system is originally a Markov decision processes (MDP). The author showed how to compute performance bounds for the stochastic control policy of MDP with an average cost criteria. In practice, many authors used heuristic control policies due to some hardness in computing and running mathematically optimal policies. The authors found bounds on performance in order to an optimal policy where the goal of this job is to compute the difference of optimality and a specific policy. In other words, this study shows that, the optimal bounds of the average queue length for any non-idling policies can be found by a factor of service rates.
Бесплатно
Статья научная
In this note we consider the population the model of which, derived on the basis of ethnographical accounts, includes a projection matrix with both positive and negative entries. Interpreting the eventually negative trajectories as representing the collapse of the population, we use some classical tools from convex analysis to determine a cone containing the initial conditions that give rise to the persistence of both the population and its social structure.
Бесплатно
Positive solutions to Sobolev type equations with relatively p-sectorial operators
Статья научная
The article describes sufficient conditions for the existence of positive solutions to both the Cauchy problem and the Showalter-Sidorov problem for an abstract linear Sobolev type equation. A distinctive feature of such equations is the phenomenon of non-existence and non-uniqueness of solutions. The research is based on the theory of positive semigroups of operators and the theory of degenerate holomorphic semigroups of operators. The merger of these theories leads to a new theory of degenerate positive holomorphic semigroups of operators. In spaces of sequences, which are analogues of Sobolev function spaces, the constructed abstract theory is used to study a mathematical model. The results can be used to study economic and engineering problems.
Бесплатно
Статья научная
Prediction of a new object state at a lack of the known characteristics and estimates of quality indicators of a number of studied objects (a set of reference data) often leads to the problem of multicollinearity of basic data. We propose the following three ways to overcome this problem relating to the sphere of data mining: use a ridge regression, train with the teacher a two-layer neural network, consecutive adapt a single-layer neural network. Also, we compare characteristics of the proposed ways. In the ridge regression method, the introduction of a regularizing term into the LMS equation gives an approximate solution with a sufficient degree of accuracy. A disadvantage of use of the two-layer neural network "feed-forward backprop" and the procedure of training with the teacher "train" is that adjusted weights of the neural network take chaotic (and even negative) values that contradicts a common practice of examination. The following features are revealed: considerable dispersion of weights and shifts of a neural network, ambiguity of the solution due to the choice of random initial conditions, strong dependence on a training algorithm. In order to overcome this shortcoming, we propose a transition to consecutive adaptation of a single-layer neural network with fixing shifts of neurons at zero level.
Бесплатно
Probabilistic solutions to the problem of rational consumer choice with random income
Статья научная
Probabilistic solutions are used when the amount of decision-makers is large. Each of them chooses the optimal solution independently of the others by solving his optimization problem. In this case, the optimal solution constructed by a randomly selected person (e.g. a consumer of goods) can be considered as a random vector. In particular, probabilistic solutions arise naturally in the rational consumer choice problem if income is assumed to be random. The problem of the utility function maximization at a time when the income of a randomly selected consumer is described as a random variable is considered as the stochastic optimization problem. The properties and distribution of the probabilistic solution of the consumer choice problem for various types of the utility function and income distribution are studied.
Бесплатно
Procedure for constructing soft models of complex systems by time series
Статья научная
The problem of creating models of complex systems for assessing their state is considered. The analysis of approaches to construction of diagnostic models is given and their features are marked. For a complex system with a hierarchical structure, a procedure for constructing the models to assess its state using a scalar time series is proposed. In this case, each hierarchical level is described by a lumped-parameter differential equation. The procedure is based on the concept of soft modelling. The efficiency of the proposed procedure is demonstrated by the example of constructing a model for assessing the state of a complex heart rhythm regulation system.
Бесплатно
Quantitative estimates on Jacobians for hybrid inverse problems
Статья научная
We consider σ-harmonic mappings, that is mappings U whose components ui solve a divergence structure elliptic equation div(σui)=0, for i=1,...,n. We investigate whether, with suitably prescribed Dirichlet data, the Jacobian determinant can be bounded away from zero. Results of this sort are required in the treatment of the so-called hybrid inverse problems, and also in the field of homogenization studying bounds for the effective properties of composite materials.
Бесплатно
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.
Бесплатно
Recent results on the Cahn - Hilliard equation with dynamic boundary conditions
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.
Бесплатно
Recovering of the heat transfer coefficient from the temperature measurements
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.
Бесплатно
Regularity results and solution semigroups for retarded functional differential equations
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.
Бесплатно
Relay races along a pair of selectable routes
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.
Бесплатно
