## No 1 (2018)

ON A LINEAR NEUTRAL-TYPE EQUATION IN A DEGENERATE CASE

#### Abstract

For the linear neutral-type equation, , t Î [ a , b ], solvability conditions for the Cauchy problem are obtained. It is allowed that the coefficient, m (·), can be zero on a positive-measure set of [ a , b ] (the degenerate case).

**Applied Mathematics and Control Sciences**. 2018;(1):7-12

ON relationship between THE FUNDAMENTAL SOLUTION AND THE CAUCHY FUNCTION FOR neutral functional differential equationS

#### Abstract

We consider a linear autonomous neutral functional differential equation. We obtain formulas relating the fundamental solution and the Cauchy function for this equation. On the basis of the formulas the asymptotic behavior of solutions of the equation is studied.

**Applied Mathematics and Control Sciences**. 2018;(1):13-25

MODELLING OF PROCESS OF PRESSING OF AXISYMMETRIC HARDWARE TAKING INTO ACCOUNT TECHNOLOGICAL PARAMETERS

#### Abstract

In work modeling of processes of pressing of axisymmetric hardware at production of bars and pipes is considered. Modeling is carried out in the conditions of the optimum scheme of a tension - mainly in the conditions of uneven three-axis compression. When developing model of technological operations the cross amount of preparation is chosen, proceeding from minimum admissible extract providing optimum mechanical properties of a product and their uniformity on the section and length. Thus the saved-up practical data taking into account key parameters of process of pressing - pressing speeds (speed of the movement of a punch of a press) and the expiration speed (the size defining high-speed conditions at the exit from a matrix point) are used.

**Applied Mathematics and Control Sciences**. 2018;(1):29-43

IDENTIFICATION OF DYNAMIC OBJECT OF CONTROL ACCORDING TO THE EXPERIMENTAL DATA ON THE EXAMPLE OF THE PRESSURIZED WATER REACTOR

#### Abstract

The pressurized water reactor is describes in this article, the example of which demonstrates the possibility of identifying the parameters of a complex dynamic control object using by the modified algorithm, well-proven in the study of input variables such as pressure, steam balance, the distance to the lattice, mass velocities and one output variable, such as heat flux. This paper presents the relationship between the input and output variables such as the mass velocity at the reactor inlet and the heat flux at the reactor outlet. The modified algorithm is compared with the Chadaev-Ilyushin algorithm, since the algorithm for identification of the dynamic control object developed by them allowed to calculate the values of the multiple correlation coefficient and standard deviation with high accuracy. The article shows that the modified algorithm for identification of a dynamic control object allows to filter out the lines with poor parameter estimates and calculate the multiple correlation coefficient and mean square deviation even more accurately than the Chadaev-Ilyushin algorithm allowed to do.

**Applied Mathematics and Control Sciences**. 2018;(1):47-70

Operational enterprise resource planning wich using by the knowledge base and the fuzzy prefernces

#### Abstract

Advanced manufacture scheduling process on the state of goods and accumulated knowledge about the resources is considered. A mathematical formulation of the operational planning problem is suggested, which uses main limitations on available resources and the fuzzy nature of the quality criteria on the plans being formed. To use the previous planning experience, the specialization function of workers and work center is introduced, which formulated as the task of adaptive search based on the knowledge base.

**Applied Mathematics and Control Sciences**. 2018;(1):73-88

THEORETICAL AND EXPERIMENTAL STUDY OF THE STRATEGIC BEHAVIOR OF THE MANAGERS OF THE OF SHOPPING CENTERS

#### Abstract

A management problem of shopping centers and a necessity to consider the strategic behavior of managers are discuss. Here is an optimal agent’s strategy, where his rival’s strategy and environmental conditions know. A game example is show in very simple presentations, where the participants are simply two agents that differ in a reflection level. It is indicate that a theoretically predicted behavior of management entities of shopping centers and the importance of experimental study of people’s strategic behavior are possible to determine mathematically by conducting a set of business games.

**Applied Mathematics and Control Sciences**. 2018;(1):91-107

Using symmetric and asymmetric filters in evaluation of underwriting cycles length

#### Abstract

The paper analyses methods for evaluation of underwriting cycle’s length and their usage in the developed decision support system for formation of effective insurance company strategy. Baxter and King along with symmetric and asymmetric Cristiano and Fitzgerald band-pass filters are applied to extract medium-term cyclical component in loss ratio time series of property, CTP, and property and liability insurance. Then, using second order autoregression model we get real underwriting cycle’s length.

**Applied Mathematics and Control Sciences**. 2018;(1):111-124

OPTIMIZATION OF THE FULL VALUE OF CONTRACTS WITH SUPPLIERS BASED ON ECONOMIC-MATHEMATICAL MODELING

#### Abstract

The paper states the problem of evaluation of total minimum contract value including transaction costs of an industrial enterprise when distributing an order among several suppliers. We present the model, where transaction costs on opportunism reduction are the control parameter. Numerical experiments were carried out. The paper states the optimization problem for determination of minimum total value of contracts, considering transaction costs of an industrial enterprise in case of diversification the order among several suppliers. Transaction costs are divided into three groups: the costs of information search about the supplier including qualifying selection of the suppliers; negotiation costs with the supplier and costs of supplier opportunism reduction. We present the model where the total contract value consists of the value of the delivered goods, transaction costs and losses in case of non-delivery of goods. The model also takes into account probable losses from both passive and active opportunism. A number of numerical experiments was carried out. That allowed to establish the existence of a minimum for the target function and showed the stability of the model for changes of input parameters.

**Applied Mathematics and Control Sciences**. 2018;(1):125-137