The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required.In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other.The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant.Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a 'Thousand Expert' Professorship at the Huazhong University of Science and Technology in Wuhan.
This book describes the emergence of new meanings in two languages, English and Chinese. Drawing on a corpus methodology, it presents metaphors as a basic instrument of thinking and cognition studies from a conceptual metaphor perspective, probing the compositional potentiality of “light” in English and Chinese, and highlighting the generative mechanism for word composition through metaphorization. The monograph includes detailed discussions of linguistic corpus construction, linguistic manifestations of metaphorization, the main motivation for the formation of metaphorical meanings, and socio-cultural influence in different languages. It expands the scope of previous studies and shows how conceptual metaphor studies can benefit from the use of a corpus methodology by providing not just a description, but an explanation, of how word composition develops. This book will be of interest to students and researchers interested in metaphor and intercultural studies, as well as cognitive linguistics, corpus linguistics and contrastive studies in English and Chinese.
This study explores the field of EFL (English as a foreign language) classroom learning within a formal learning institution. Drawing on theories and methods from various disciplines, this book explores the question which has been frustrating language teachers: why do so many students remain reticent and anxious in language class? Based on a large-scale survey and a more focused case study, the book argues persuasively that reticence and anxiety in formal EFL classrooms are important factors in determining the outcome of language learning. By means of a triangulated research method, this book examines various aspects of reticence and anxiety in EFL classroom learning situations. The author analyses causes and consequences, differences in terms of gender and proficiency level, and coping strategies.
This book introduces readers to nearly 600 common weeds. In addition to essential information, each chapter includes photos for a specific type of weed to show its morphology in different growth periods, such as seedling, root, flower, fruit, and mature plant. The book also discusses control measures, including agricultural, chemical, physical, biological, and comprehensive methods. The Volume2 mainly focuses on fern and 216 species of weeds of magnoliids or dicotyledoneae. With the development of society and economics, weeds have become a recurring problem. In particular, the exotic, invasive, and quarantine weeds have spread dramatically and rapidly. On the other hand, many people, even those who are engaged in weed control, do not (or cannot) distinguish between weeds. Thus there is significant demand for illustrations of weed morphologies, as well as information on their control measures. This book offers a valuable, practical guide for all those working in the fields of crop cultivation, plant protection and quarantine management.
The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required.In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other.The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant.Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a 'Thousand Expert' Professorship at the Huazhong University of Science and Technology in Wuhan.
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