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Exactly one hundred years ago, in 1895, G. de Vries, under the supervision of D. J. Korteweg, defended his thesis on what is now known as the Korteweg-de Vries Equation. They published a joint paper in 1895 in the Philosophical Magazine, entitled `On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave', and, for the next 60 years or so, no other relevant work seemed to have been done. In the 1960s, however, research on this and related equations exploded. There are now some 3100 papers in mathematics and physics that contain a mention of the phrase `Korteweg-de Vries equation' in their title or abstract, and there are thousands more in...
This unique volume provides a comprehensive overview of exactly solved models in statistical mechanics by looking at the scientific achievements of F Y Wu in this and related fields, which span four decades of his career. The book is organized into topics ranging from lattice models in condensed matter physics to graph theory in mathematics, and includes the author's pioneering contributions. Through insightful commentaries, the author presents an overview of each of the topics and an insider's look at how crucial developments emerged. With the inclusion of important pedagogical review articles by the author, Exactly Solved Models is an indispensable learning tool for graduate students, and an essential reference and source book for researchers in physics and mathematics as well as historians of science.
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
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Chance and Uncertainty is a subject with a broad span, in that there is no academic discipline or walk of life that is not beset by uncertainty and chance. However, the way these issues are handled varies widely between disciplines and from one individual to another. Between the authors in this volume there is some overlap but much more eclectic variety. Altogether there are five contributions from natural science and mathematics, six from the social and behavioural sciences, and one from the medical field. The entire range of approaches to uncertainty and chance appears to be represented. All the contributors agree on the relevance of these concepts to their discipline or profession, but the level of abstraction of the contributions varies widely. This is not only a matter of discipline but also, within some disciplines, a question of personal approach. All contributors and editors are scholars of the Universiteit van Amsterdam.