Ефимова Т.Л. «Решение задачи о свободных колебаниях прямоугольных пластин из градиентных материалов» Доповiдi нацiональноi академii наук Украiни, № 8, с. 54-58 (2011)

A problem of natural vibrations of rectangular plates made from functionally gradient materials is studied on the base of classical theory. The mechanic parameters vary along the coordinate x. Using the methods of spline-approximation and collocation, the problem is solved by the steady-state numerical method of discrete orthogonalization with incremental search.

Мостовой В.С., Мостовой С.В. «Оптимальные оценки нелинейных параметров в моделях сейсмоакустического мониторинга» Доповiдi нацiональноi академii наук Украiни, № 8, с. 103-107 (2011)

In the problem of optimal estimation of model parameters using risk criteria, we propose an approach to the separation of linear parameters from nonlinear ones. In the problem of finding a global minimum of risk criteria, our approach leads to a decrease of the dimension of the space of free variables up to the dimension of the space of nonlinear parameters. This allows one to obtain a simpler minimization problem, which can be solved more efficiently via Monte-Carlo methods. Such an improvement is very significant in the estimation of models of the object "aging" at the investigation of geophysical objects, models of which typically have high dimensionality. We illustrate the proposed method with the processing and analysis of data obtained during the field observations in the regime of monitoring.