Applied Mathematics and Control Sciences

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.

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.

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.

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.