Tao Qian - Böcker

The Sōushén hòujì 搜神後記 (Latter Notes on Collected Spirit Phenomena), attributed to the celebrated poet Táo Qián 陶潛 (365-427), is a compilation of anecdotes and stories known as zhìguài 志怪 ('records of the anomalous') that document strange and unusual phenomena the author observed in his lifetime. Intended to serve as a sequel to Gān Băo's 干寳 (d. 336) Sōushénjì 搜神記 (Collected Spirit Phenomena), the original text was lost but was reconstructed in the late Míng dynasty. This volume presents an annotated translation of the entire Míng version of the Sōushén hòujì as well as of an additional set of surviving stories that were identified and restored to the text by the modern scholar Lĭ Jiànguó 李劍國. The book also includes a history of the Sōushén hòujì text, an examination of its linguistic style and characteristics, a discussion of the historical nature of its contents and how it fits into the zhìguài genre, providing a window onto medieval Chinese society and culture, and a brief overview of recent zhìguài scholarship to guide readers who hope to continue their exploration of the genre.

On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations ·2 ·2 1 Z =] = - , ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra structure for three dimensional visual space with in particular the possibility of representing all spatial rotations by algebra multiplications and since 1835 he started looking for generalized complex numbers (hypercomplex numbers) of the form a + bi + cj. It hence took him a long time to accept that a fourth dimension was necessary and that commutativity couldn't be kept and he wondered about a possible real life meaning of this fourth dimension which he identified with the scalar part qo as opposed to the vector part ql i + q2j + q3k which represents a point in space.

This book collects lectures given by the plenary speakers at the 10th International ISAAC Congress, held in Macau, China in 2015. The contributions, authored by eminent specialists, present some of the most exciting recent developments in mathematical analysis, probability theory, and related applications. Topics include: partial differential equations in mathematical physics, Fourier analysis, probability and Brownian motion, numerical analysis, and reproducing kernels. The volume also presents a lecture on the visual exploration of complex functions using the domain coloring technique. Thanks to the accessible style used, readers only need a basic command of calculus.

By structuring the content according to the various mathematical topics, the volume offers specialists and non-specialists alike an excellent source of information on the state-of-the-art in Mathematical Analysis and its interdisciplinary applications.

The contributions, authored by eminent specialists, present some of the most exciting recent developments in mathematical analysis, probability theory, and related applications. Topics include: partial differential equations in mathematical physics, Fourier analysis, probability and Brownian motion, numerical analysis, and reproducing kernels.

The study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool lies in the heart of Clifford analysis. The focus is on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. At the present time, the study of Clifford algebra and Clifford analysis has grown into a major research field. There are two sources of papers in this collection. One is from a satellite conference to the ICM 2002 in Beijing, held August 15-18 at the University of Macau; and the other stems from invited contributions by top-notch experts in the field. All articles were strictly refereed and contain unpublished new results. Some of them are incorporated with comprehensive surveys in the particular areas that the authors work in.

This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics.Key topics:Approximation and Fourier AnalysisConstruction of Wavelets and Frame TheoryFractal and Multifractal TheoryWavelets in Numerical AnalysisTime-Frequency AnalysisAdaptive Representation of Nonlinear and Non-stationary SignalsApplications, particularly in image processingThrough the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.

The main purpose of this book is to provide a detailed and comprehensive survey of the theory of singular integrals and Fourier multipliers on Lipschitz curves and surfaces, an area that has been developed since the 1980s.