Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area. The book begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree?Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn?Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy. The book is written for advanced undergraduate and beginning graduate students, specifically those with mathematical backgrounds but without a priori knowledge of quantum mechanics, and can be used for self-study by researchers, instructors, and other scientists. The book can also serve as a starting point to learn about many-body perturbation theory, a topic at the frontier of the study of interacting electrons.
The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the Kohn-Sham map.
Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area. The book begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree?Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn?Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy. The book is written for advanced undergraduate and beginning graduate students, specifically those with mathematical backgrounds but without a priori knowledge of quantum mechanics, and can be used for self-study by researchers, instructors, and other scientists. The book can also serve as a starting point to learn about many-body perturbation theory, a topic at the frontier of the study of interacting electrons.
The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the Kohn-Sham map.
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
This book mainly focuses on ecological approaches for preventing and controlling non-point source (NPS) pollution on the basis of forestry measures. In addition to the effects of ecological control, it introduces readers to the characteristics of NPS pollution in Taihu Lake watershed, water eutrophication evaluation methods, and potential countermeasures. Given the crucial role of surface runoff and soil erosion in producing water pollution, the book presents forestry measures to combat them, such as the creation of public welfare forests, urban forestry, planting techniques for hedgerows on slope land, the establishment of shelter belts, nitrogen and phosphorus absorption by hydrophytes, and sustainable management for wetlands. Moreover, the results are supplemented by a wealth of numerical calculations, tables, figures and photographs. The book offers a valuable guide for researchers, educators and professionals working in the areas of water environment, water security and ecological construction. Prof. Jianfeng Zhang works at the Institute of Subtropical Forestry, Chinese Academy of Forestry, Fuyang, China.
In recent years there has been a significant increase of interest in continuous-time Principal-Agent models, or contract theory, and their applications. Continuous-time models provide a powerful and elegant framework for solving stochastic optimization problems of finding the optimal contracts between two parties, under various assumptions on the information they have access to, and the effect they have on the underlying "profit/loss" values. This monograph surveys recent results of the theory in a systematic way, using the approach of the so-called Stochastic Maximum Principle, in models driven by Brownian Motion. Optimal contracts are characterized via a system of Forward-Backward Stochastic Differential Equations. In a number of interesting special cases these can be solved explicitly, enabling derivation of many qualitative economic conclusions.
For the nearly three decades of coexistence between economic liberalization and political authoritarianism, China remains as an anomaly to the liberal mantra of our time. This book explores a segment of the China Paradox, the state-society interaction channeled by the Residents Committee. Being the largest urban neighborhood organization, the committee deserves study because of its controversial status between ordinary residents it claims to represent and the authoritarian state. The committee enters the discourse as a directly congruent example of the same paradox that the whole China displays, when it is endowed with important, yet tension-changed statutory functions ranging from social control to service provision and neighborhood self-governance. How, and under what conditions, does the committee carry out its functions? What can be learned about changing state-society relations from the dynamics of neighborhood politics in China? This book draws its analytical framework on the theoretical models of state penetration, civil disobedience, corporatism, and synergy, as well as on the practices of American, Cuban, and Japanese neighborhood organizations and the Chinese Rural Villagers Committee. Four distinctive Residents Committees in Tianjin City are studied in detail, and their functions are identified and explained primarily through their structural connections with the lowest state organ in cities, the street office, and residents (including other neighborhood organizations and activists). The book reveals multiple possibilities of Chinese social/political transformation. Among them emerges a promising trend of state-society cooperation, which is realigning and accommodating political authoritarianism and economic openness into a seemingly sustainable pattern of development at the urban grassroots. Referred to as an "amphibian" organization spanning public-private division, the committee highlights the limits of the state-society antithesis in the study of political transformation. The observed patterns of neighborhood politics also raise caution against the universal applicability of the liberal norm of civil society to countries like China with distinctive conditions from which the original norm is present and constructed.
This book analyzes the theory of ecological engineering of human settlements and provides case studies on the improvement of degraded lands and vegetation restoration, especially focusing on saline-alkali land, abandoned land, water source areas, and the impact of green belts on noise and air quality on the highways. In addition, it discusses the issue of biodiversity conservation strategies in rural landscape construction and demonstrates experiment measurement and field survey methods. The results obtained are supplemented by numerical calculations, presented in the form of tables and figures. As the first monograph on this subject, the book provides a wealth of ideas and resources for researchers, professionals and practitioners in the field of human settlements.
This is the first book of a two-volume book set which introduces software defined chips. In this book, it introduces the conceptual evolution of software defined chips from the development of integrated circuits and computing architectures. Technical principles, characteristics and key issues of software defined chips are systematically analyzed. The hardware architecture design methods are described involving architecture design primitives, hardware design spaces and agile design methods. From the perspective of the compilation system, the complete process from high-level language to configuration contexts is introduced in detail. This book is suitable for scientists and researchers in the areas of electrical and electronic engineering and computer science. Postgraduate students, practitioners and professionals in related areas are also potentially interested in the topic of this book.
This book is the second volume of a two-volume book set which introduces software-defined chips. In this book, the programming model of the software-defined chips is analyzed by tracing the coevolution of modern general-purpose processors and programming models. The enhancement in hardware security and reliability of the software-defined chips are described from the perspective of dynamic and partial reconfiguration. The challenges and prospective trends of software-defined chips are also discussed. Current applications in the fields of artificial intelligence, cryptography, 5G communications, etc., are presented in detail. Potential applications in the future, including post-quantum cryptography, evolutionary computing, etc., are also discussed. This book is suitable for scientists and researchers in the areas of electrical and electronic engineering and computer science. Postgraduate students, practitioners and professionals in related areas are also potentially interested in the topic of this book.
This book introduces the research background and significance of carbon emissions in the tunnel industry and systematically reviewed the research progresses of carbon emission researches for tunnels, LCA (life cycle assessment) research framework, and uncertainty research progress. The authors propose a novel modular carbon emission calculation method for highway tunnel construction and expounds on the modular LCA system boundary theory of tunnel construction. This method does not require abundant knowledge of LCA modeling, which is convenient for general engineering and technical personnel to calculate the carbon emission level of tunnel construction. The calculation formulas for input and carbon emissions of each module are provided. It also analyzes the parameter uncertainty, model uncertainty, and scenario uncertainty of the carbon emissions from tunnel construction by the Monte Carlo method. Further, this book proposes the fitting model of carbon emissions of unit engineering quantity in tunnel construction, which benefits to simplify the calculation of carbon emissions.This book is mainly aimed at engineering and technical personnel in the construction industry, especially tunnel and underground engineering, including tunnel design engineers; tunnel construction engineers, experts, and scholars; tunnel owners; management departments.
With the rapid development of artificial intelligence and the emergence of various new sensors, autonomous driving has grown in popularity in recent years. The implementation of autonomous driving requires new sources of sensory data, such as cameras, radars, and lidars, and the algorithm processing requires a high degree of parallel computing. In this regard, traditional CPUs have insufficient computing power, while DSPs are good at image processing but lack sufficient performance for deep learning. Although GPUs are good at training, they are too “power-hungry,” which can affect vehicle performance. Therefore, this book looks to the future, arguing that custom ASICs are bound to become mainstream. With the goal of ICs design for autonomous driving, this book discusses the theory and engineering practice of designing future-oriented autonomous driving SoC chips. The content is divided into thirteen chapters, the first chapter mainly introduces readers to the current challenges and research directions in autonomous driving. Chapters 2–6 focus on algorithm design for perception and planning control. Chapters 7–10 address the optimization of deep learning models and the design of deep learning chips, while Chapters 11-12 cover automatic driving software architecture design. Chapter 13 discusses the 5G application on autonomous drving. This book is suitable for all undergraduates, graduate students, and engineering technicians who are interested in autonomous driving.
This book discusses the overall development and use of smart courts from the perspective of system-of-systems engineering (SoSE) and its methodology, analyzes the relationships between the components, structures, environments, and functions of various systems, and illustrates the basic approaches to system design, specification, integration, operation and management. As the general introductory book of the China Smart Court Development Series, this book provides an overview of the development of Chinese people's courts in the application of information technology over the past two decades and outlines the key areas of exploration in the Smart Court SoSe project centered on the development practices during the 13th Five-Year Plan period. It also forecasts the future development and evolution of the smart court information system. The key topics introduced in the book, including the overall design of complex information systems, integrated interconnection networks-based system integration, judicial big data quality control and analytics services, various types of AI-enabled judicial services, quality and efficiency-oriented operation and maintenance services for large-scale information systems, etc., all came from the basic research of information science and theories, as well as the systems engineering practices of the Smart Court SoSe project. They not only reflect the latest findings on systems engineering and architecture methods in China and overseas, but also reveal many innovative approaches to SoSE methods and paradigms, which can be used for the design and continued development of smart courts at a new and higher starting point. It is believed that they can also serve as good examples and reference points for the development in IT application and complex information systems engineering in other sectors.
The most recent advances in research on coastal saline soil rehabilitation and utilization based on forestry approach are discussed. The forestry approach is emphasized rather than physical or engineering measures to ameliorate saline soils, which is significant for coastal environmental improvement and land resources expansion. The monograph is a useful reference for researchers using techniques of ecology, forestry and agronomy. Prof. Jianfeng Zhang works at the Institute of Subtropical Forestry, Chinese Academy of Forestry. He has been working on afforestation in saline soils for over 20 years.
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