## No 2 (2018)

FIRST AND SECOND ORDER NECESSARY OPTIMALITY CONDITIONS IN ONE STEP CONTROL PROBLEM OF DISCRETE TWO-PARAMETRIC SYSTEMS

#### Abstract

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.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):7-29

ON A SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS INTEGRABLE IN QUADRATURES

#### Abstract

We consider a system of two nonlinear differential equations, for which we found an approach allowing to represent a solution in the form of quadratures. The obtained results are applied to the investigation of two mathematical models. One of them describes labor market conditions in the case of closed mono-branch economy. The other model has hydrodynamic origin.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):30-39

SCALAR AND VECTOR DIVISION AND DERIVATIVES VECTORS

#### Abstract

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.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):43-55

ON ONE METHOD OF SOLVING THE THREE-DIMENSIONAL PROBLEM OF PHYSICALLY NON-LINEAR DEFORMATION OF TRANSVERSAL-ISOTROPIC MULTI-VARIABLE BODIES

#### Abstract

The method for solving the three-dimensional problem of elastic-plastic deformation of transversely isotropic multiply connected bodies by the finite element method (FEM) is presented in the article. The process of solving the problem consists of: determining the effective parameters of a transversely isotropic medium; construction of the finite element mesh of the body configuration, including the determination by the front method of the local minimum value of the width of the tape of non-zero coefficients of equation systems; constructing the coefficients of the stiffness matrix and the components of the node load vector of the equation of state of an individual finite element according to the theory of small elastic-plastic deformations for a transversely isotropic medium; the formation of a resolving symmetric-tape system of equations by summing the coefficients of the equations of state of all finite elements; solution of the system of symmetric-tape system of equations by means of the square root method; calculation of the elastic-plastic stress-strain state of the body by performing the iterative process of the method of elastic solutions AA Ilyushin. For each stage of solving the problem, effective computational algorithms have been developed that make it possible to reduce the number of computational operations by modifying existing methods of solving and taking into account the structure of the matrix coefficients. As an example, the solution of the problem of deformation of a transversally isotropic body in the form of a rectangle with a circular notch in the center is given.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):56-75

Optimization of production of construction materials assortment based on system engineering methods

#### Abstract

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.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):79-94

Quality management of educational programs for students with corrective actions based on the negentropic approach

#### Abstract

The quality management algorithm of educational programs on the basis of a negentropic approach and learning curves is proposed. The mathematical model and algorithms of complex estimation of level of formation of competences of the student and adjusting educational programs to improve the quality of their implementation to the required level is presented.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):97-108

INTELLIGENT TECHNOLOGIES OF DEVELOPMENT DECISIONS MAKING IN RESIDENTIAL CIVIL ENGINEERING

#### Abstract

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.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):109-119

TIME OPTIMIZATION MATHEMATICAL MODEL OF THE REAL INVESTMENTS PORTFOLIO

#### Abstract

The effective using of investment resources which directed to finance the real sector of the economy is the basis for stable economic development. This work is devoted to the method of the real investments portfolio optimizing, which taking into account the cash flows dynamics. The article presents algorithms describing step-by-step actions in the situation of spatial and temporal optimization. The time optimization features are described in detail. Mathematical models that serve as the basis for solving the optimization problem are described too. The maximum NPV was chosen as criterion for the objective function. The linear optimization method is used in this paper.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):123-129

THE SIMULATION OF OPTIMAL FINANCING OF THE INVESTMENT PROJECTS PORTFOLIO BASED ON THE MECHANISM OF MINIMUM OPTIMUM DEVIATIONS

#### Abstract

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.

**Прикладная математика и вопросы управления / Applied Mathematics and Control Sciences**. 2018;(2):130-143