|
|
 Âûïóñê 84
- Rusev V. On some asymptotic expansion of solution of renewal equation
In this paper, the renewal equation is studied. It is the Volterra integral convolution equation of the second kind with a difference kernel. This equation is considered both for the renewal density and for its primitive, the renewal function. The renewal function is essential in the theory of technical systems reliability not only as a descriptive characteristic, but also for operational strategies optimization in the preventive maintenance management, assuming the implementation of the recurrent recovery flows model. A certain analytical method is suggested for obtaining an asymptotic representation of the recovery equation solution for the special class of distributions under some given conditions. The validity of the stated expansion was checked for the exponential distribution, which is basic in the reliability mathematical theory. To show that the class of the described distributions is not an empty set, as an example, the two-parameter Weibull-Gnedenko distribution was considered, which is a natural generalization of the exponential distribution. The apparatus of series theory and the generating moment function method are used. The last is a Laplace transform of non-negative continuous random variable density distributions. The Chebyshev-Markov-Stieltjes moment problem is also highlighted. It means the possibility of the unique distribution restoration by the sequence of its moments. This problem is significant for the mentioned expansion. The expression for the renewal equation solution in the case of the renewal density has the form of Gram-Charlier’s type series in terms of probability moments.
- Breer V. Threshold models of warfare
Modified models of the conduct of hostilities by Lanchester - Osipov are studied, in which three variants of the psychological characteristics of agents are taken into account: surrender, evasion of the struggle against its possible resumption, and conformal desertion. For the first two options, the threshold model of Schelling's limited partnership is used; for the latter, the threshold model of Granovetter's conformal behavior. So, the agent has a threshold in relation to the proportion of “ours” deserting from the battlefield. If this fraction is greater than the threshold, then the agent also joins the runaways (here the threshold corresponds to the level of his discipline). For modification, the distribution functions of the thresholds of conformity of agents were used. The two-parameter beta function with the distribution density x1-a(1-x)1-b. is selected as the distribution function. This is due to the fact that its parameters allow meaningful interpretation of such characteristics as the ratio of "cowards" and "brave men" of the fighting parties. So, the more a, the more “cowardly” agents in the group. The more b, the more “bold” agents in the group. In each of the models, the ODE system was numerically solved for a certain threshold distribution function, the dynamics of the number of agents participating in the battle were plotted, and the results were analyzed.
- Turzynsky M. On study of stability of one class of stationary solutions for gas dynamics equations on a rotating plane
We consider a two-dimensional system of equations of an ideal polytropic gas on a rotating plane, which arises in the dynamics of the atmosphere. The problem is very difficult in the general case, however, it admits solutions with a linear profile of velocity (corresponding to motion with uniform deformation), which can be found by solving a quadratically nonlinear system of ordinary differential equations. The system has two families of equilibria: the first family is one-parametric (corresponds to a vortex) and the second one is two-parametric (corresponds to a shift flow), the latter is always unstable. The stability of equilibria means the stability of stationary solutions of the original system in the class of perturbations with linear profile of velocity. The article considers a one-parametric family of equilibria, which corresponds to a stationary vortex motion, the parameter is responsible for the vortex intensity and changes over the real axis. Intervals of the parameter where equilibrium is unstable and where it is stable in the sense of Lyapunov were found earlier. However, they did not cover the entire real axis. For the remaining parameter values, the matrix of linearization has three pairs of purely imaginary complex conjugate eigenvalues, therefore the study of stability by conventional methods is difficult. We investigate the matter in Lagrangian coordinates. Estimates that provide intervals of guaranteed stability are constructed. The stability issue is completely resolved for a gas with one, two, and three degrees of freedom.
- Livatkin P. Finite-frequency identification of a delay via sliding phase lag
This article proposes a phase sliding improvement of finite-frequency identification algorithm for a linear stable plant with time-delay in presence of unknown-but-bounded external disturbances (with unknown stochastic characteristics). Finite-frequency identification algorithm feeds to the plant's input a testing signal, that consist of a single harmonic or a sum of them. Phase sliding improvement allows to identify two unknown values, such as coefficients of the plant’s transfer function or time-delay value for the successful identification and more than one harmonic if it is needed to increase accuracy or identify a long time-delay value. There are two ideas in the article. Firstly, phase sliding for each harmonic may be opposite for phase deviation, caused by plant's time-delay. Time-delay, phase sliding and harmonic's frequency are analytically related. Secondly, plant's transfer function will be the same for different combinations of harmonics if they are opposite to plant's time-delay. For a definite solution of the delay identification problem the upper bound of the time-delay value is required. The article describes how to select theoretically optimal harmonics, providing time-delay identification without known upper bound. There are three algorithms for the detection equality of phase-slided and time-delayed values, which differ one from each other computational complexity and sensitivity to external disturbances.
- Ougolnitsky G., Gorbaneva O., Usov A. et al. Theory of sustainable management in active systems
The theory of sustainable management in active systems is presented as one of the directions of development of the theory of active systems. The paper reviews this branch of research. A concept of extended active system as a hierarchically controlled dynamic system is proposed. The control methods with consideration of the requirements of homeostasis are formalized. The methods and algorithms of solution of the respective differential game theoretic control problems are developed. The information-analytical decision support systems are described. A dynamic generalization of the incentive control mechanisms in organizational systems is given. The models of sustainable management in environmental-economic, territorial, education systems are built and investigated. Static models of coordination of interests in resource allocation are studied. An approach to the modeling of corruption in hierarchical control systems is implemented. The principal mathematical models that form a base of the theory of sustainable management in active systems are described briefly.
- Dobronets B., Popova O. Computational aspects of digital economy
The article discusses the main computational problems in the digital economy, primarily related to the processing and analysis of big data, the organization of computational processes and improving the accuracy of numerical procedures. The approach is based on the application of new methods of data aggregation based on computational probabilistic analysis, the use of probabilistic extensions and numerical operations on piecewise polynomial functions. One of the most important tasks of numerical modeling of big data is the calculation of functional dependencies. It is proposed to use functional regression on empirical distributions to identify dependencies in big data. New methods for modeling functional dependencies based on spline approximations are considered. To study and improve the accuracy of calculations, an approach based on the Runge rule and Richardson extrapolation is used. To organize the computing process, a recursive-parallel scheme is used, based on the properties of probabilistic extensions. This approach provides a technique for fast and reliable calculations in the conditions of large volumes of data for various types of uncertainty. As an example, the problem of assessing investment risks is considered. The probability density functions of factors such as net present value (NPV) and internal rate of return (IRR) are calculated.
- Sidelnikov Y. Development and the realization of approach to the correct description of the expert. creative method. P. 2. Realization of approach based on example of the brainstorm
An informational verbal model of such a creative method as a brain attack was developed in this article. The implementation of this model is based on the previously proposed approach to the correct description of an arbitrary variety of expert method. The paper suggests the grounds for using models of potential options for creative methods. The developed model of brain attack allows you to analyze, compare and improve existing types of brain attacks. The model allows you to select such a variety that will function more effectively than others by adapting the parameters of the brain attack to the conditions and limitations of the task. In the framework of this approach, in particular, a postulate was proposed characterizing the possibility of comparing objects of the same type, including expert methods. Twenty-two types of brain attacks were found, briefly described, and analyzed that satisfy the necessary requirements for their membership in the aggregate. The article identifies the characteristics and indicators that characterize the possible varieties of these brain attacks. The paper proposes the interpretation of the normative information model of the creative expert method as a tuple, including an ordered set of parameters and indicators characterizing this method. The article substantiates the need for the simultaneous solution of six problems, with the general task of modeling an arbitrary variety of brain attack. Thus, a syncretic model consisting of six models is considered. The article suggests possible directions for further development of the approach to the correct description of an arbitrary expert method.
- Kozhevnikov A. Features of application of system approach at assessment of degree of efficiency of management process in health sector
The features of system approach application for efficiency assessment of management process in a health sector are presented in the article. The indexes of problems existence describing the research object and the mathematical express analysis used for processing of statistical data and also for sociological information are the basis of this approach. The procedure presented in this article and indexes calculation method of problems existence allows to range the obtained data by risk factors influence on management process. It also allows authorities to form plans and decisions about management of the revealed problems. The stated material promotes achievement of the required result without complication of the procedure of processing and the analysis of information. Formation of conclusions and recommendations is based on provisions of the theory of system analysis, the theory of management of organizational systems, methods of statistical data analysis. The example of application of the specified technique in the course of the comparative analysis of activity of private medical institutions and municipalities is given. Assessment of a condition of a health care system of Novokuznetsk is received.
- Krygin A. Evaluation of the Weibull distribution parameters for small volume of the sample in the problems of optimization of planning repair works on engineering networks
In the previously developed economic and statistical methodology for assessing the state of the engineering network section and information support when deciding to extend its service life, there are serious requirements for the initial data. One of the conditions for the correct operation of the methodology is the presence of complete statistics of damage and repairs carried out, starting from the moment the site is commissioned. However, for many sites such statistics are available only for the last few years. In order to expand the scope for cases of incomplete damage statistics, a separate study was carried out to estimate the Weibull distribution parameters with a small sample size using the example of heat supply network sections. This work is devoted to the results of the study. Three classes of sites were identified: with fairly complete damage statistics, with a small amount of statistics, and without statistics. For each class, an algorithm was proposed for estimating the necessary parameters for the Weibull distribution, which were further used in the methodology for estimating the state of a site, and a criterion was determined by which a site could be assigned to a particular class.
|
|
