Applied Mathematics and Control Sciences

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.

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.

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.

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.