Solving one extreme problem in a class of locally single-leaf functions

Центральное место в теории конформных отображений занимает решение экстремальных задач на классах однолистных отображений. В известных классах нормированных голоморфных функций $S$ и $C$ решение «проблемы коэффициентов» связано с получением точных оценок модулей тейлоровских коэффициентов элементов классов. Аналогичные задачи ставятся для классов локально однолистных отображений. В.Г.Шеретов ввел в рассмотрение классы локально конформных отображений, генерируемых с помощью интегральных структурных формул из элементов классов $S$ и $C$. В статье решена задача о точной оценке модуля тейлоровского коэффициента в этом классе. The central place in the theory of conformal maps is occupied by the solution of extreme problems on classes of single-leaf maps. In the known classes of normalized holomorphic functions S and C, the solution of the "coefficient problem" is associated with obtaining accurate estimates of the modules of the Taylor coefficients of class elements. Similar problems are posed for classes of locally single-leaf mappings. V.G.Sheretov introduced classes of locally conformal mappings generated using integral structural formulas from elements of classes S and C. The article solves the problem of an accurate estimation of the modulus of the Taylor coefficient in this class.

Synthesis of Optimal Information and Energy Schemes of Measuring and Converting Devices

The synthesis of information and energy schemes is posed as an extreme problem, the purpose of which is a weighted directed graph of the minimum length from the input value to the output value of the device. The nodes of the graph are the physical effects included in the given database, and the branches are the input and output values of the effects. Nodes and branches are mathematically defined by diagonal multidimensional matrices, whose elements are determined by the dimensions of the quantities in the selected system of physical coordinates with a given number of basic units of measurement. The weight or resource intensity of the graph elements is determined by the norm of the corresponding matrices. The resulting circuit is suitable for use in technical documentation to explain the operating principle of the device, as well as for patent protection.In the enhanced formulation of the extreme problem, restrictions are introduced on the numerical values of the input and output values of the effect and its dynamic properties in the form of the transfer function of the effect. In this case, the size of the transfer matrices of nodes and branches is expanded by one. As a result, the transfer matrix of the effect contains information not only about the dynamic properties of the effect, but also about the dimensions of the physical quantities at its input and output.In a detailed example, the case of searching for the operating principle of a measuring-converting device of a pressure sensor with an electric current output is considered. To simplify the geometric representation of graph vectors on a plane, the problem is considered for a two-dimensional system of physical quantities with basic units of length and time. The calculation of the resource capacity is carried out according to the scheme of dimensional simulation, in which the phase variables of the differential equation enter with their physical dimensions. According to the numerical value of the resource capacity, you can compare different versions of the implementation of the operating physical principle of the device.

Approximation of the Constant in a Markov-Type Inequality on a Simplex Using Meta-Heuristics

Markov-type inequalities are often used in numerical solutions of differential equations, and their constants improve error bounds. In this paper, the upper approximation of the constant in a Markov-type inequality on a simplex is considered. To determine the constant, the minimal polynomial and pluripotential theories were employed. They include a complex equilibrium measure that solves the extreme problem by minimizing the energy integral. Consequently, examples of polynomials of the second degree are introduced. Then, a challenging bilevel optimization problem that uses the polynomials for the approximation was formulated. Finally, three popular meta-heuristics were applied to the problem, and their results were investigated.

Extreme problem for a mosaic system of points

In the geometric theory of functions of a complex variable, the well-known direction is related to the estimates of the products of the inner radii of pairwise nonoverlapping domains. This direction is called extreme problems in classes of pairwise nonoverlapping domains. One of the problems of this type is considered in the present work.

Radicalisation: A Social Psychological Perspective (Part I)

Terrorism, being a long-standing phenomenon and a threat that has existed for at least two millennia, is still an extreme problem in the life of society. Understanding how a person comes to commit terrorist acts requires consideration of the process of radicalisation. The aim of our literature review is to analyse the process of radicalisation.Security and counter-terrorism are one of the priority areas of scientific development in Russia. This direction has different facets of analysis. From a psychological point of view, the development of measures of influence should be based on knowledge of how a person joins groups and organizations of a terrorist nature, what are the psychological mechanisms of radicalization, as well as an understanding of the laws of deradicalization. Our analytical review within the framework of social psychological knowledge has allowed us to overcome a kind of gap existing in the literature, namely, to acquaint the Russian readers with a promising explanatory model of the process of radicalisation - the uncertainty — identity theory, proposed by Hogg. This model explains why and how people join groups with extremist and radical beliefs, as well as why they prefer acts of violence, acting on behalf of these groups.

Application of a Volterra quadratic polynomial to modeling elements of heat engineering devices

This paper considers integral models built to describe dynamic processes in a 135 MW power unit condenser. For this purpose, we use a quadratic segment of the Volterra integral power series. The first set of models was built with a perturbation of the cooling water flow, and the second one with a perturbation of the steam flow. For all sets of models, changes in pressure and temperature in the condenser, as well as temperature changes in LHP-1, were considered as a response to perturbation. For models built with perturbation of the cooling water flow velocity, we considered an extreme problem of finding optimal amplitudes of the input perturbations. The results of calculations proved to be sufficiently accurate.

VARIABLE METHOD OF SYNTHESIS OF THE ELEMENTAL SIGNAL WITH MINIMUM ENERGY OUTSIDE OF WORKING FREQUENCY

It is shown in the paper that the synthesis of a signal of the optimum form is an extreme problem, the variational nature of which allows for its solution to apply the ideas and methods of functional analysis. Variational calculus was applied to study the extreme properties of the functional. An expression describing the form of the elementary signal of finite duration with minimum energy outside the working frequency band was obtained.