One of the key elements of modern fiber-optic systems is an optical switch. So, the next-generation all optical switching systems have been presented by authors of the paper [1, 2]. Those systems have been based on 4×4 and 8×8 switching elements and ones have high performance and low complexity. And here we offer the models and algorithms of the all-optical 8×8 and 64×64 switching systems with decentralized control for the first time. The presented models is based on the graph theory and they allow us to get so-call non-blocking conditions for the first time also. The analytical model for the complexity and diameter of the proposed schemes is presented for the first time. The characteristics of the offered systems are compared with well-known schemes too. And the calculation results showed a significant advantage of the presented systems in comparison with the well-known existing ones. Одним из ключевых элементов современных волоконно-оптических систем связи является оптический коммутатор. Ранее авторами были представлены полностью оптические коммутационные системы сетей связи нового поколения, в основе которых лежат коммутационные элементы 4х4 и 8х8, которые обладают высоким быстродействием и имеют низкую сложность. В данной работе впервые предлагаются модели и алгоритмы работы такого рода полностью оптических коммутационных систем 8х8 и 64х64. Представленные модели основаны на теории графов и позволяют получить условия неблокируемости. Аналитическая модель для расчета сложности и диаметра предлагаемых схем также представлены впервые. В работе проведено сравнение характеристик предлагаемых систем с широко известными схемами. Результаты показали существенное преимущество разработанных систем по сравнению с известными аналогами.

The paper provides an overview of spectral and modal analysis methods for studying the stability of electric power systems (EPSs) and their control. Consideration is given to theoretical grounds of the methods and to the experience of their application for detecting the heterogeneity of the systems’ structure, identifying the coherency of generators’ motion, simplifying the mathematical model of the dynamics of EPSs, assessing their small-signal stability, and selecting the control actions to ensure it. The analysis of sub-Gramians for studying the EPS stability and other new directions in the development of the modal approach are discussed.

The article proposes a software package containing effective implementation of models of the dangerous fire factors spread dynamics and people evacuation in premises. The dangerous fire factors spread model included in the package consist of fire and heat spread models. The first one is based on two-dimensional four-state probabilistic cellular automaton, the second one is based on simple graph theory apparatus and basics of thermodynamics. The people evacuation model implemented in the package is based on multi-agent systems approach, simple graph theory and basics of mechanics which include kinematics, conservation laws and collision theory. The package implementation process in the Java programming language is described, advantages of the chosen language are listed. The software package distinctive features and functional requirements are listed and explained, its inner module structure is described and illustrated, user interaction types are shown. The package allows to simulate and analyze critical situations that arise during a fire, calculate the dynamics of dangerous fire factors development and simulate people evacuation from the premises. The implemented models and the algorithm for their interconnection provide high model performance and accuracy.

The aim of this work is to propose a method for estimating the parameter of the continuous distribution tail based on the largest order statistics of a sample. We prove the consistency and asymptotic normality of the proposed estimator. Note especially that we do not assume the fulfillment of the conditions of the extreme value theorem.