This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.
Abrasive Water Jet Perforation and Multi-Stage Fracturing gives petroleum engineers, well completion managers and fracturing specialists a critical guide to understanding all the details of the technology including materials, tools, design methods and field applications. The exploitation and development of unconventional oil and gas resources has continued to gain importance, and multi-stage fracturing with abrasive water jets has emerged as one of the top three principal methods to recover unconventional oil and gas, yet there is no one collective reference to explain the fundamentals, operations and influence this method can deliver. The book introduces current challenges and gives solutions for the problems encountered. Packed with references and real-world examples, the book equips engineers and specialists with a necessary reservoir stimulation tool to better understand today's fracturing technology. - Provides understanding of the fundamentals, design and application of water jet perforation - Examines the pressure boosting assembly in all phases including initiation, hydraulic isolation and production stage - Evaluates production analysis, pump pressure predictions and the latest design software - Introduces current challenges and gives solutions for the problems encountered
Special Distillation Processes, Second Edition focuses on the latest developments in the field, such as separation methods that may prove useful for solving problems encountered during research. Topics include extraction, membrane and adsorption distillation involving the separation principle, process design and experimental techniques. The relationship between processes and techniques are also presented. Comprehensive and easy-to-read, this book provides key information needed to understand processes. It will be a valuable reference source for chemical engineers and students wishing to branch out in chemical engineering. - Provides the only comprehensive book available on special distillation processes - Contains a thorough introduction to recent developments in the field - Presents a valuable reference for students, academics and engineers in chemical engineering
The phonological history of Chinese can be traced back to two main traditions: one starting with the Qieyun of 601, and the other starting with the Zhongyuan Yinyun of 1324. The former marks the beginning of Middle Chinese, and the latter marks the beginning of Old Mandarin. Both of these systems, as well as reconstructed Old Chinese, should be understood as ideal phonological standards and composite in nature. Until modern times, phonological standards were never based strictly on the phonology of a single dialect. This book provides the first study written in English, of the phonological history of Chinese. It provides information about the standard phonological systems for each of the language's major historical periods, drawing on a range of historical materials such as dictionaries, rhyming tables and poetry, and is the reference book for understanding the key developments in the Chinese sound system.
This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.
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