2021 Issue №1

Studies of intelligent control in a dynamic environment and the work of an operator have revealed serious differences between the mental image of an operational and technological control object and its display in automated sys­tems used by the operator, which prevents him from working and performing actions in his mind, and contributes to the occurrence of data interpretation errors. The processing of heterogeneous information by logical-symbolic meth­ods has been studied and the results are widely used in practice. However, the questions of the right-handed, visual-figurative reasoning of the operator re­main unexplored. Such reasoning provides intuitive decision-making based on the demonstrated image of the problem situation and the proposed options for understanding it,. This paper presents the results of the study of the subject of operational and technological management in the regional power system, the features of his work, thinking and his surrounding reality.

We reconsider the composite string model introduced 30 years ago to study the vacuum energy. The model consists of a scalar field, describing the transversal vibrations of a string consisting of piecewise constant sections with different tensions and mass densities, keeping the speed of light constant across the section. We consider the spectrum using transfer matrices and Chebyshev polynomials to get a closed formula for the eigenfrequencies. We calculate vacuum and free energy as well as the entropy of this system in two approaches, one using contour integration and another one using a Hurwitz zeta function. The latter results in a representation in terms of finite sums over polynomials. Several limiting cases are considered as well, for instance, the high-temperature expansion, which is expressed in terms of the heat kernel coefficients. The vacuum energy has no ultraviolet divergences, and the corresponding heat kernel coefficient  is zero due to the constancy of the speed of light. This is in parallel to a similar situation in macroscopic elect­ro­dynamics.

We study an optimization problem for a portfolio with a risk-free, a li­quid, and an illiquid risky asset. The illiquid risky asset is sold in an exogenous random moment with a prescribed liquidation time distribution. We assume that the investor chooses an exponential utility function. Study of op­timization problems with three assets including an illiquid asset leads to three-dimensional nonlinear Hamilton — Jacobi — Bellman (HJB) equations.

It is well known that the exponential utility function is connected with the HARA utility function through a limiting procedure if the parameter of the HARA utility function is going to infinity. We show that the optimization problem with the exponential utility function is not connected to the optimization problem with the HARA utility by the limiting procedure and we obtain essentially different results. We provide the Lie group analysis of the corresponding HJB equation.

For the main three-dimensional PDE with the exponential utility function, we obtain the complete set of the nonequivalent Lie group invariant reductions to two-dimensional PDEs according to an optimal system of subalgebras of the admitted Lie algebra. We prove that in just one case the invariant reduction is consistent with the boundary condition. This reduction represents a significant simplification of the original problem.

The paper considers the design of the transmitting antenna system in­tended for use in the technique of radio-frequency methods of substance re­search and justifies its advantages. It is advisable to use the device when stud­ying objects located outside the receiving and transmitting circuits. At the same time, the operating frequencies for which it is designed, occupy a wide spectrum, covering the ranges from myriameter to decameter waves, which implies a high uniformity of the radiated power. The use of the proposed de­sign will improve the methods used for contactless search for connections of a certain type.