The subject of this monograph is to describe orbits of slowly chaotic motion. The study of geodesic flow on the unit torus is motivated by the irrational rotation sequence, where the most outstanding result is the Kronecker-Weyl equidistribution theorem and its time-quantitative enhancements, including superuniformity. Another important result is the Khinchin density theorem on superdensity, a best possible form of time-quantitative density. The purpose of this monograph is to extend these classical time-quantitative results to some non-integrable flat dynamical systems.The theory of dynamical systems is on the most part about the qualitative behavior of typical orbits and not about individual orbits. Thus, our study deviates from, and indeed is in complete contrast to, what is considered the mainstream research in dynamical systems. We establish non-trivial results concerning explicit individual orbits and describe their long-term behavior in a precise time-quantitative way. Our non-ergodic approach gives rise to a few new methods. These are based on a combination of ideas in combinatorics, number theory, geometry and linear algebra.Approximately half of this monograph is devoted to a time-quantitative study of two concrete simple non-integrable flat dynamical systems. The first concerns billiard in the L-shape region which is equivalent to geodesic flow on the L-surface. The second concerns geodesic flow on the surface of the unit cube. In each, we give a complete description of time-quantitative equidistribution for every geodesic with a quadratic irrational slope.
The subject of this monograph is to describe orbits of slowly chaotic motion. The study of geodesic flow on the unit torus is motivated by the irrational rotation sequence, where the most outstanding result is the Kronecker-Weyl equidistribution theorem and its time-quantitative enhancements, including superuniformity. Another important result is the Khinchin density theorem on superdensity, a best possible form of time-quantitative density. The purpose of this monograph is to extend these classical time-quantitative results to some non-integrable flat dynamical systems.The theory of dynamical systems is on the most part about the qualitative behavior of typical orbits and not about individual orbits. Thus, our study deviates from, and indeed is in complete contrast to, what is considered the mainstream research in dynamical systems. We establish non-trivial results concerning explicit individual orbits and describe their long-term behavior in a precise time-quantitative way. Our non-ergodic approach gives rise to a few new methods. These are based on a combination of ideas in combinatorics, number theory, geometry and linear algebra.Approximately half of this monograph is devoted to a time-quantitative study of two concrete simple non-integrable flat dynamical systems. The first concerns billiard in the L-shape region which is equivalent to geodesic flow on the L-surface. The second concerns geodesic flow on the surface of the unit cube. In each, we give a complete description of time-quantitative equidistribution for every geodesic with a quadratic irrational slope.
This book presents novel state estimation methods for several classes of networked multi-rate systems including state estimation methods for networked multi-rate systems with various complex networked-induced phenomena and communication protocols. The systems investigated include stochastic nonlinear systems, time-delay systems, linear repetitive processes, and artificial neural networks. The techniques used are mainly the Lyapunov stability theory, the optimal estimation theory, the lifting technique, and certain convex optimization method. Features Gives a systematic investigation of the state estimation of multi-rate systems Discusses results on state estimation problems under network-induced complexities Studies different kinds of multi-rate systems including multi-rate nonlinear systems, multi-rate neural networks, and multi-rate linear repetitive processes Explores network-enhanced complexities and communication protocols Includes case studies showing the applicability of developed estimation algorithms including practical examples like DC servo systems and continuous stirred tank reactor systems Analysis and Synthesis for Networked Multi-Rate Systems is aimed at graduate students and researchers in signal processing, control systems, and electrical engineering.
This book is devoted to quantify the role of the world's major economies in the international division from the perspective of global value chains and clarify the value cycle system between China and developed and developing economies. This book establishes a theoretical paradigm that conforms to the current world economic structure. That is, the world economic structure gradually shifts from a single-cycle model centered on developed countries to a more complex dual-circulation model. Furthermore, based on the analysis of the current world economic situation, it also analyzes the interaction between trade and investment and the synergistic effect of the Corridors under the Belt and Road Initiative. The first part of the book brings a better understanding of mutual relationships between trade and investment under the Belt and Road Initiative and broadens the research fields of relevant studies. Additionally, comprehensive and specific country research is particularly conducted in this book. By analyzing the economic indicators, reviewing social history and social-economic development, covering various countries along the Belt and Road, it provides deep exploration of the fields and approaches of the most potential cooperation under the purpose of "Peace, Development, Cooperation and Win-Win." Therefore, this part draws a broad map of economic and cultures in order to provide a reference and assistance for promoting the Belt and Road Initiative. Fulfilling this vision, this book hopes to deepen the understanding of economic development of each relevant economy to encourage the participation of economies in regional connectivity.
Ouyang Yi, an extremely ordinary young man, relied on his own efforts and help to start a place of leisure and entertainment, a massage parlor.At such a young age, he was able to lead a life of competition at a shopping mall. In order to expand his scale and gain market share, he had competed with the son of the mayor!He was struggling in business, but everything was still unknown.Unfortunately, his feelings had a new twist. The girlfriend he had been in love with for so many years had suddenly left and the one he was currently in love with had suddenly died.When his career and love were in crisis, he fell into a valley of despair. Where would he go in the future? He could only grope his way forward step by step.
Yun Er, a woman that has been living amongst the common people, was born with the fragrance of the country's Se Tian, and has the color to topple the world.He, Xuanyuan Yuanyi, was the monarch of a nation. Their fortuitous meeting had caused her life to change ...She originally thought that with Wuyou as her life partner, she would be able to live a happy and peaceful life.However, everything was still a dream. For the sake of power, he was willing to give up on himself.The shortest distance was between heaven and hell.Just as she was feeling hopeless and sad, she made a decision. She wanted to leave this place.This journey lasted for several years. With a shake, she managed to reclaim her identity.She was actually the princess of a king! Back to his old home, to see him again.The love of the past seemed to have departed, but under the arrangement of fate, what would happen between him and her?
The book aims to analyse and evaluate the strategic positioning of China’s participation in terms of firm-level performance in the generation of infrastructure capacity in African countries. Africa counts among its development challenges a major bottleneck of infrastructure capacity and shortage of investable capital. China’s long period of high growth generates the strengths to secure availability of energy from Africa by enhancing infrastructure provision for the region. To achieve this complementary macro-level development, beyond the traditional dimension of infrastructure provision (ODA), Chinese IMNEs become the vital players on the intersection of these processes. Thus this research makes practical and analytical contributions to international business studies and development issues by making concrete the analysis of bilateral development processes from a macro context to a micro level framework (e.g. focusing on ICT and construction sectors), then fitting this into the real world story. Infrastructure itself is a key element for potential investment and development processes. Therefore, how IMNEs achieve not only exist simply in a way of a commercial-oriented investment, but also in their implications for development and political related issues.
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