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Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Modelsby Fritz Gesztesy; Helge Holden; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak
Cambridge University Press 2003; US$ 131.00The Korteweg-de Vries (KdV), the AKNS, the nonlinear Schrödinger, the sine-Gordon and the Camassa-Holm equations, and the Thirring system, are all completely integrable nonlinear PDEs permitting special classes of solutions. This is a detailed treatment of the class of algebro-geometric solutions and their representations in terms of Riemann theta functions. more...
Practical Applied Mathematicsby Sam Howison; C. G. Crighton (Deceased); M. J. Ablowitz; S. H. Davis; E. J. Hinch; A. Iserles; J. Ockendon; P. J. Olver
Cambridge University Press 2005; US$ 64.00Used either by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them. Topics include distributions, asymptotic methods and the basics of modelling. Applications range from piano tuning to egg incubation and traffic flow. more...
The Lévy Laplacianby M. N. Feller; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak; B. Simon
Cambridge University Press 2005; US$ 30.00The Lévy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well-developed in recent years and this book is the first systematic treatment. With an extensive bibliography, the work will be valued by those working in functional analysis, partial differential equations and probability theory. more...
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Springer 2006; US$ 160.00Aimed at undergraduates, graduate students, mathematicians, and physicists, this work offers a differential geometry approach to such physical theories as gauge theory. Sheaf theory and sheaf cohomology explain the machinery of classical differential geometry. Together they present Maxwell fields, Yang-Mills fields, and general relativity. more...
Lectures On Fuzzy And Fuzzy Susy Physicsby A P Balachandran; S Kürkçüoglu; S Vaidya
World Scientific 2007; US$ 62.40Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes provide a comprehensive introduction to the field. Starting with the construction of fuzzy spaces, using the concrete examples of the fuzzy sphere and fuzzy complex projective spaces, the book moves on to discuss the technology of star products on noncommutative R2d and on the fuzzy sphere. Scalar, spinor and gauge field theories as well as extended objects such as monopoles and nonlinear sigma modes are treated in considerable detail. A detailed treatment of the regularization of supersymmetry... more...
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Cambridge University Press 2008; US$ 128.00Detailed treatment of the class of algebro-geometric solutions and their representations in terms of Riemann theta functions. more...
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