The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between ma...
ISBN:
(数字)9789814365123
ISBN:
(纸本)9789814365116
The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.
Over the last half century we have witnessed tremendous progress in the production of high-quality photons by electrons in accelerators. This dramatic evolution has seen four generations of accelerators as photon sour...
ISBN:
(数字)9789814340397
ISBN:
(纸本)9789814340380
Over the last half century we have witnessed tremendous progress in the production of high-quality photons by electrons in accelerators. This dramatic evolution has seen four generations of accelerators as photon sources. The 1st generation used the electron storage rings built primarily for high-energy physics experiments, and the synchrotron radiation from the bending magnets was used parasitically. The 2nd generation involved rings dedicated to synchrotron radiation applications, with the radiation again from the bending magnets. The 3rd generation, currently the workhorse of these photon sources, is dedicated advanced storage rings that employ not only bending magnets but also insertion devices (wigglers and undulators) as the source of the radiation. The 4th generation, which is now entering operation, is photon sources based on the free electron laser (FEL), an invention made in the early *** generation yielded growths in brightness and time resolution that were unimaginable just a few years earlier. In particular, the progression from the 3rd to 4th generation is a true revolution; the peak brilliance of coherent soft and hard x-rays has increased by 7-10 orders of magnitude, and the image resolution has reached the angstrom (1 #65533; = 10-10 meters) and femto-second (1 fs = 10-15 second) scales. These impressive capabilities have fostered fundamental scientific advances and led to an explosion of numerous possibilities in many important research areas including material science, chemistry, molecular biology and the life sciences. Even more remarkably, this field of photon source invention and development shows no signs of slowing down. Studies have already been started on the next generation of x-ray sources, which would have a time resolution in the atto-second (1 as = 10-18 second) regime, comparable to the time of electron motion inside atoms. It can be fully expected that these photon sources will stand out among the most powerful future science
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitat...
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ISBN:
(数字)9781118111130
ISBN:
(纸本)9780470647288
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.
In the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of mathematics in Tianjin of May 200...
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ISBN:
(数字)9789814327848
ISBN:
(纸本)9789814327831
In the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on lectures in the following areas of nonlinear analysis: critical point theory, Hamiltonian dynamics, partial differential equations and systems, KAM theory, bifurcation theory, symplectic geometry, geometrical analysis, and celestial mechanics. Combinations of topological, analytical (especially variational), geometrical, and algebraic methods in these researches play important roles. In this proceedings, introductory materials on new theories and surveys on traditional topics are also given. Further perspectives and open problems on hopeful research topics in related areas are described and proposed. Researchers, graduate and postgraduate students from a wide range of areas in mathematics and physics will find contents in this proceedings are helpful.
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