2009, Approx. 315 p., Softcover
ISBN: 978-3-540-85205-6
Due: March 19, 2009
This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. While infinite-dimensional groups often exhibit very peculiar features, this book describes unifying geometric ideas of the theory and gives numerous illustrations and examples, ranging from the classification of the Virasoro coadjoint orbits to knot theory, from optimal mass transport to moduli spaces of flat connections on surfaces.
The text includes many exercises and open questions, and it is accessible to both students and researchers in Lie theory, geometry, and Hamiltonian systems.
Mathematicians, theoretical physicists
Preface.- Introduction.- I Preliminaries.- II Infinite-dimensional Lie
Groups: Their Geometry, Orbits and Dynamical Systems.- III Applications
of Groups: Topological and Holomorphic Gauge Theories.- Appendices.- A1
Root Systems.- A2 Compact Lie Groups.- A3 Krichever-Novikov Algebras.-
A4 Kahler Structures on the Virasoro and Loop Group Coadjoint Orbits.-
A5 Metrics and Diameters of the Group of Hamiltonian Diffeomorphisms.-
A6 Semi-Direct Extensions of the Diffeomorphism Group and Gas Dynamics.-
A7 The Drinfeld-Sokolov Reduction.- A8 Surjectivity of the Exponential
Map on Pseudo-Differential Symbols.- A9 Torus Actions on the Moduli Space
of Flat Connections.- Bibliography.- Index
Series: Universitext
2009, XXI, 336 p. 85 illus., Softcover
ISBN: 978-3-540-92928-4
Due: March 12, 2009
Covers on an introductory level the very important issue of computational aspects of derivative pricing
People with a solid background of stochastics, numerics, and derivative pricing will gain an immediate profit
This book is very easy to read and one can gain a quick snapshot of computational issues arising in financial mathematics. Researchers or students of the mathematical sciences with an interest in finance will find this book a very helpful and gentle guide to the world of financial engineering. SIAM review (46, 2004).
The fourth edition is thoroughly revised and extended. Major revisions concern topics like calibration, Monte Carlo Methods, American options, exotic options and Algorithms for Bermuda Options.
New figures, more exercises, more background material make this guide to the world of financial engineering a real must-to-have for everyone working in FE.
Students (Master and PhD) interested in computational aspects of mathematical finance; practitioners
Series: Publications of the Scuola Normale Superiore
Subseries: Theses (Scuola Normale Superiore) , Vol. 12
2009, Approx. 150 p., Softcover
ISBN: 978-88-7642-340-6
Due: February 2009
The aim of this book is to provide a self-contained introduction and an up-to-date survey on many aspects of the theory of transport equations and ordinary differential equations with non-smooth velocity fields. The interest in this topic is motivated by important issues in nonlinear PDEs, in particular conservation laws and fluid mechanics. A fascinating feature of this research area, which is currently of concern in mathematics, is the interplay between PDE techniques and geometric measure theory techniques.
Several masterpieces appear in the related literature, balancing completely rigorous proofs with more heuristic arguments. A consistent part of the book is based on results obtained by the author in collaboration with other mathematicians. After a short introduction to the classical smooth theory, the book is divided into two parts. The first part focuses on the PDE aspect of the problem, presenting some general tools of this analysis, many well-posedness results, an abstract characterization of the well-posedness, and some examples showing the sharpness of the assumptions made. The second part, instead, deals with the ODE aspect of the problem, respectively by an abstract connection with the PDE, and by some direct and simple (but powerful) a priori estimates.
Researchers and PhD students with interests in PDEs and in geometric measure theory
Series: Universitext
2009, Approx. 555 p. 112 illus., 2 in color., Softcover
ISBN: 978-3-540-93982-5
Due: March 5, 2009
All needed notions are developed within the book with the exception of fundamentals, which are presented in introductory lectures; no other knowledge is assumed
Provides a more in-depth introduction to the subject than other existing books in this area
Over 400 exercises including hints for solutions are included
The idea of this book is to give an extensive description of the classical complex analysis, here ''classical'' means roughly that sheaf theoretical and cohomological methods are omitted.
The first four chapters cover the essential core of complex analysis presenting their fundamental results. After this standard material, the authors step forward to elliptic functions and to elliptic modular functions including a taste of all most beautiful results of this field. The book is rounded by applications to analytic number theory including distinguished pearls of this fascinating subject as for instance the Prime Number Theorem. Great importance is attached to completeness, all needed notions are developed, only minimal prerequisites (elementary facts of calculus and algebra) are required.
More than 400 exercises including hints for solutions and many figures make this an attractive, indispensable book for students who would like to have a sound introduction to classical complex analysis.
For the second edition the authors have revised the text carefully.
Students in mathematics and physics
Differential Calculus in the Complex Plane C.- Integral Calculus in the Complex Plane.- Sequences and Series of Analytic Functions, the Residue Theorem.- Construction of Analytic Functions.- Elliptic Functions.- Elliptic Modular Forms.- Analytic Number Theory.- Solutions to the Exercises.- References.- Index
Series: Studies in Fuzziness and Soft Computing , Vol. 243
2009, Approx. 590 p., Hardcover
ISBN: 978-3-540-93801-9
Due: March 2009
For more than four decades of its existence, the scientific "Fuzzy Group" has grown from a few engineers, working either alone or in small groups to a large scientific community. From the perspective of the history of science, it is quite normal over the course of time for such research programs to adapt themselves to the phenomena of branching out and differentiation into special projects and penetrating other disciplines. This applies not only to the distribution of research projects, the number of researchers, and the benefits of various research funding programs but also in the high profile of the subject in widely diverse fields of science, technology and business.
For more than forty years fuzzy logic and fuzzy mathematics have been continuously developed, resulting in important theoretical expansions of this mathematical theory of unsharp amounts or logic of unsharp statements, which have often very quickly led to new application systems. At the same time, the areas of artificial neural networks and of evolutionary and genetic algorithms emerged as independent research disciplines and beginning in the 1980s new developments arose that were hardly foreseeable: the theory of fuzzy sets and systems was combined with these new scientific theories and methods and the use of "hybrid systems" became more and more common in all types of applications.
In our new century, the theory of fuzzy sets and systems is in the core of "Soft Computing" and "Computational Intelligence" and has become a normal scientific theory in the fields of exact sciences and engineering and it is well on its way to becoming normal in the soft sciences as well. This book is a collection of the views of numerous scholars in different parts of the world who are involved in various research projects concerning fuzziness in science, technology, economic systems, social sciences, logics and philosophy. This volume demonstrates that there are many different views of the theory of fuzzy sets and systems and of their interpretation and applications in diverse areas of our cultural and social life.