No 3 (2019)

QUASI SINGULAR CONTROL IN ONE WITH VARIABLE STRUCTURE OPTIMAL CONTROL PROBLEM DESCRIBEDBY THE QOURSAT - DARBOUX SYSTEM
Mansimov K.B., Suleimanova S.S.

Abstract

We study one optimal control problem with a variable structure described by the Goursat - Darboux system. Under the assumption that the control region is convex, the necessary optimality condition is proved in the form of a linearized maximum condition. The case of degeneration of the linearized maximum condition is considered (a quasi-special case). The necessary optimality conditions for quasi-singular controls are established.
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):9-39
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LINEAR REPRESENTATION OF THE STABILITY AREAS OF SOME CLASSES OF DIFFERENCE EQUATIONS
Kandakov A.A.

Abstract

The work is devoted to obtaining new stability domains for linear autonomous difference equations, as well as a demonstration of the use of the lined-structure property of D -decompositions in solving this problem. It is proposed to study D -decompositions in the form of a set of plane cross-sections consisting of lines. Using the proposed method, one of the known results is obtained and a new area is found. The prospects of transferring the approach to the study of wider classes of equations are indicated.
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):40-53
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MATHEMATICAL MODEL OF ARTIFICIAL ELECTRICAL CAPACITY FOR REDUCING THE PEAK LOAD OF MANOVER HEAT
Popov I.P.

Abstract

The possibility of equipping a shunting diesel locomotive with an inert-capacitive energy storage device is being considered, which will smooth the load on the power plant and thereby reduce its power and mass and dimensions. The relatively frequent change in the operating mode of a shunting locomotive determines the efficiency and feasibility of equipping it with an energy storage device. In addition to smoothing the load on the power plant, the drive will allow energy to be recovered during braking, thereby increasing the energy efficiency of the shunting diesel locomotive. The theoretical background for creating an inert-capacitive energy storage device, which is technically designed as a DC machine with a super flywheel, is presented. The use of flywheels on shunting diesel locomotives is justified by virtue of not rigid requirements for the total weight. Another advantage of the locomotive is the presence of an electromechanical transmission, which minimizes the development for it of the considered inert-capacitive drive
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):57-64
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THE NUMERICAL CHARACTERISTICS OF THE KINETICALLY MODELLED SIMPLE NONSTATIONARY RANDOM PROCESS
Selianinov A.A., Osipenko M.A., Baranova A.A., Vikhareva E.V., Khrenkov A.N.

Abstract

The simple nonstationary random process with the sufficiently smooth realizations is considered. On the basis of kinetic modelling, the governing parameter of the process is represented for the each realization as the function of time and parameters of the kinetic equation. According to the realizations, these parameters represent the system of random quantities. As a result, the nonstationary random process is represented by the usual function of system of limited number of random quantities. For the purpose of reliability, the numerical characteristics of this process are determined by two approximate methods: linearization of function and analysis using the hypothesis of the normal distribution of the system of random quantities. The proposed lemma along with the hypothesis of the normal distribution of the system of random quantities gives the analytical expressions for the numerical characteristics up to the correlation functions for the process and for its rate. It is noted that just the expression for the expectation value contains the variances of the random quantities. In this connection, the variance restrictions are obtained. It is shown that for the both approaches the numerical characteristics converge as the variances decrease. The suggested method is illustrated with the repeatability of the process of the biological destruction of some medicine.
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):65-83
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DEVELOPMENT OF AN INTEGRATED METHOD OF CALCULATION OF THE STRESSED-DEFORMED STATE OF THE COMPOSITION SHELL IN THE PROCESS OF MANUFACTURE
Sakhabutdinova L.R., Smetannikov O.I., Il'inykh G.V.

Abstract

The paper discusses the key stages of developing an integrated methodology for predicting the stress-strain state of a sand-polymer mandrel-plastic shell system during heat treatment with the adaptation of experimentally determined viscoelastic characteristics of components in the CAE ANSYS Mechanical APDL package. The first stage solves the problem of determining the effective viscoelastic characteristics for the shell. Viscoelastic characteristics are determined on the basis of the developed complex experimental calculation method based on the solution of boundary quasistatic problems of thermomechanics on a representative volume at two scale levels. The results obtained in this work, based on experimental data and developed numerical methods for determining the thermo-viscoelastic characteristics of composites, make it possible to estimate the contribution of stress relaxation in the mandrel and the shell to the evolution of the stress-strain state in the process of manufacturing the shell. Also, the developed technique makes it possible to predict the appearance of technological defects and determine the stages of heat treatment at which these defects occur.
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):84-99
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DETERMINATION OF REPRESENTATIVE IMAGE SIZE FOR ESTIMATION OF STRUCTURAL CHARACTERISTICS OF MATER
Batin S.E.

Abstract

Estimation of image representativity is under consideration. The determination is needed to substantiate reliability of macro properties estimation based on structure parameters. Statement of the problem is presented. Original approach based on the Monte Carlo simulation is suggested. Results for synthetic ellipsoidal structure are received. The method allows to solve the problem.
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):103-115
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ON ONE CONTROL PROBLEM OF THE PROCESS OF GAMMA IRRADIATION OF THE POLYETHYLENE
Oniskiv V.D., Stolbov V.I., Khatiamov R.K.

Abstract

Solved a particular problem of optimization of process of radiation of gamma quanta of polyethylene with the aim of obtaining heat-shrinkable tubing with the shape memory effect. The problem of optimizing the placement of ionizing radiation sources in an industrial installation is presented. Some results of optimization, which have practical application and allow to significantly reduce the exposure time, are presented.
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):119-130
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OPERATIONAL EVALUATION OF THE PROBABILITY OF PERFORMANCE OF THE ORDER IN THE CONDITION OF UNCERTAINTY OF CONSUMER DEMAND
Tolstobrov D.A.

Abstract

Modern software allows industrial enterprises to rationalize the use of employees' working hours, to reduce labor intensity and material consumption of manufactured products, but the factor of consumer demand uncertainty forces us to focus on a probabilistic model when forming a portfolio of orders. The paper considers the method of operational forecasting of production costs and the probability of execution of the application by an enterprise operating in the market of perfect competition in the conditions of clients filing applications with an incomplete amount of information. The author's approach to the operational assessment of production costs is based on the ABC method and the rules of cutting design "Muller and son". It allows the calculation step of the request to edit a group of multidimensional products according to customer's requirements, the result is the ratio of the balance between expected customer price and pledged the company profitability. It allows at the stage of calculating the application to edit a group of multidimensional products according to customer requirements, as a result, a balance is reached between the price expected by the client and the profitability laid by the enterprise. According to this method, for calculating a non-standard request, a multidimensional product is represented as a group of rectangular parallelepiped shapes. Costs for each material layer used in the product are considered separately in the calculation process. The study of the nature of the relationship between the consumption rates of sheet material, the dimensions of a multidimensional product and the useful width of the roll made it possible to establish their proportions leading to peak values of the consumption of material. To exclude additional material costs, a method has been developed and tested to find the optimal material consumption taking into account the probability of order fulfillment. Application of these recommendations will allow industrial enterprises to increase the value of products and the enterprise for each participant of relations; will be the basis for the growth of competitiveness of domestic products.
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):133-157
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STATISTICAL ASSESSMENT OF THE BONDS DEFAULT RISK BY EXAMPLE PJSC “SOLOMENSKII LESOZAVOD”
Duplyakin V.M., Boldyrev M.A.

Abstract

The application of the previously proposed methodology for the formation of models for quantitative assessment of the risk of default of companies’ securities, taking into account the characteristics of the financial condition of issuing companies in the reporting and previous periods, is considered. The methodology includes a three-stage selection of working variables using statistical hypothesis testing (Student t-test and Fisher test are applied), correlation and one-way regression analysis. The probability of multicollinearity of variables in a developed model is also monitored. The logit-model and probit-model for assessing the risk of default of Russian companies by bonds, developed using the proposed methodology, are presented. A sample of 96 Russian companies that placed bonds on the stock market was used, 48 of which did not fulfill financial obligations on securities was used for developing the models. The results of a comparative analysis of the reliability of the constructed models and well-known models of other Russian and foreign authors, applied to assessing the risk of default of Russian companies on bonds, are also presented. When conducting a comparative analysis of the reliability of the models, the Student t-test, the Mann-Whitney test, the Kruskal-Wallis test and the Wilcoxon test, as well as the modeling efficiency index, are used. An example of applying the logit-model and probit-model to assessing the risk of default of PJSC "Solomenskiy lesozavod" on bonds is demonstrated.
Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences. 2019;(3):161-179
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