Applied Mathematics and Control Sciences

One step optimal control problem described by discrete two-parameter systems of the Fornazini - Markesini type is considered, assuming openness of the control domain. An analog of the Euler equation and a quadratic necessary optimality condition are established.

The work is devoted to the operations of differentiation in the space of vector fields and smooth functions. In mechanics, it is widely used derivative of a scalar function of the vector. To some extent, like it is determined by the derivative of the vector to another vector. However, formally interpreting the derivative as division differentials are entered in consideration of scalar and vector derived vector on another vector, which may have application to the solution of problems of mechanics. The definition of a derivative of a scalar vector field on another vector field. We prove a theorem on the representation of the scalar derivative in the form of a combination of partial derivatives. As a typical particular case is considered a scalar derivative in the radius vector, generating formalism linking it with the operator nabla. It is noted that in solving some problems in the mechanics to simplify the calculation coordinate system is chosen so that at least some vectors direction coincides with one of the coordinate axes. If it concerns the vector for derivation to be performed, in such cases, the formula for the three-dimensional case can not be used because some of this vector differentials are equal to zero. This circumstance makes it necessary to prove two theorems for the two-dimensional and one-dimensional case. The definition of a vector derivative of a vector field on another vector field. We prove a theorem on the representation of the derivative vector as a combination of partial derivatives. As a typical particular case considered vector derivative of the radius vector, generating formalism linking it with the operator nabla. We prove similar theorems for two-dimensional and one-dimensional case. We give examples of applications of these results to problems of mechanics.

In the production of building materials, uncertainty arises due to the fact that integrated production teams include workers of various specialties, different machines, objects of labor and the activities of all these elements are interrelated and structured poorly. The process of reinforcing structural links between the elements of the system and reducing the degree of uncertainty associated with the human factor is considered through the production of a reasonable assortment of building materials whose characteristics must satisfy the specific functional purpose and operating conditions required individually for each structure in the real estate object. The technological process in this work is considered from the position of two participants in the production process: the consumer and the manufacturer, who have different views on the quality of the final product. Therefore, the choice of the technological process for the production of assortment of building materials is proposed to be carried out on the basis of compositions of models of preferences of both participants.

Intelligent technologies of grounding the development decisions for conceptual design of residential properties are suggested. The concept of the real estate property defines a set of properties that should be possessed by property, e.g., location, infrastructure, engineering equipment, decoration, layout, etc. Are methods of modeling consumer preferences, allowing to form the shape of the future building, satisfying most of the needs and desires of the real estate market. The technology is demonstrated on the example of a ten ten-storied one driveway of a residential building, where the factors influencing the choice of consumers use location, structural features, technical equipment and decoration.

The article deals with the problem of planning the distribution of investments in innovative projects. The dynamic analysis of efficiency of projects of OJSC "MegaFon" for 2013-2016 by regression analysis of the resulting profit function of projects from investment, which calculated the potential profitability of projects to determine the actual allocation of investments. On the basis of the mechanism of minimum deviations of Optima, the method of optimal allocation of investment resources between projects is developed. With the optimal distribution of investments, the values of the potential profit of each project are calculated, the increase in the profit for each project every year confirms the effectiveness of the mechanism.