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.

The rigid kinetic energy (RKE) concept for deflective suspended mobile robot in energy workspace

In this paper, the research study on the rigid kinetic energy (RKE) concept for deflective suspended mobile robot in energy workspace is adopted. This method is applied to solve and address the rigid kinetic problem, to specify the significant of the deflective coefficient problem, to derive a mathematical formation of rigid kinetic energy, to determine the nature of energy environment and to develop an algorithm to drive the rigid mobile robot in the energy workspace. The experiment was conducted on Lenovo Laptop with Microsoft window 10 operating system and MOBOT software application.

Numerical study of the coefficient identification algorithm based on ensembles of adjoint problem solutions for a production-destruction model

A numerical algorithm for the solution of an inverse coefficient problem for nonstationary, nonlinear production-destruction type model is proposed and tested on an example of the Lorenz’63 system. With an ensemble of adjoint problem solutions, the inverse problem is transformed into a quasi-linear matrix problem and solved with Newton-type algorithm. Two different ways of the adjoint ensemble construction are compared. In the first one, a trigonometric basis is used. In the second one in situ measurements are taken into account. Local convergence properties of the algorithm are studied numerically to find out when the use of more data can lead to the degradation of the reconstruction results.