Methods for construction and synthesis of dynamic models of complex control systems are considered. Discrete simulation and synthesis technique for hierarchical control systems together with the model of the corresponding information system are presented.

Решена проблема эквивалентности обыкновенных дифференциальных уравнений первого порядка с управляющим параметром относительно преобразования обратной связи. Используется аппарат дифференциальной геометирии и геометрической теории дифференциальных уравнений.

Посвящение 60-летию И.С. Красильщика.

We present a comprehensive {traffic measurement and analysis concept}to cope with the rapid deployment of peer-to-peer multimedia applications and their overlay structures. It integrates four orthogonal dimensions:traffic measurements at the packet layer, data extraction, flow analysis and inspection of peer-to-peer overlays based on a hierarchical multi-layer modeling concept, a characterization of overlay structures by techniques and metrics of complex networks,and a statistical characterization of peer-to-peer traffic features.

In this survey we discuss heat kernel estimates of self-similar type on metric spaces with doubling measures. We characterize the tail functions from heat kernel estimates in both non-local and local cases. In the local case we also specify the domain of the energy form as a certain Besov space, and identify the walk dimension in terms of the critical Besov exponent. The techniques used include self-improvement of heat kernel upper bound and the maximum principle for weak solutions. All proofs are completely analytic