Series: Progress in Nonlinear Differential Equations and Their Applications , Vol. 75
2008, Approx. 440 p., Hardcover
ISBN: 978-3-7643-8481-4
About this book
This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The purpose of the volume is to bring the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.
It treats the nonlinear aspects of the theory of differential equations, of the calculus of variations, dynamical systems, as well as topics related to chaotic systems and their relations with physical problems. The reader will find both some surveys of the more recent developments in several topics related with differential equations, chaos and variational problems, as well as new contributions in active and important areas of research as Young measures, optimal control, differential and delay-differential equations and inclusions.
Written for:
Graduates and researchers in differential equations, dynamical systems, calculus of variations, control theory, physical systems
Keywords:
chaos
differential equation
nonlinear
variational problem
Table of contents
Preface.- 34 contributions by highly distinguished researchers.
Series: Trends in Mathematics
2008, Approx. 280 p., Hardcover
ISBN: 978-3-7643-8536-1
About this book
The articles in this book give comprehensive introductions through a series of texts starting at an elementary level and ending with a discussion of current research. The main subjects studied are vector bundles and coherent sheaves, principal bundles and sheaves, as well as their moduli; current generalizations of geometric invariant theory; Drinfeld's shtukas and their stacks; interactions between intersection theory and commutative algebra; Thom polynomials.
Written for:
Graduate and postgraduate students; researchers in algebraic geometry, algebraic topology, commutative algebra, and singularity theory
Keywords:
algebraic cycle
cohomology theory
modulus
sheave
shtuka
Table of contents
Preface.- Life and Work of J.M. Hoene-Wronski.- Exotic Fine Moduli Spaces of Coherent Sheaves.- Principal Bundles over Projective Varieties.- Zero Schemes of Sections of Vector Bundles.- Moduli Spaces of Coherent Sheaves on Multiples Curves.- Stacks of Shtukas.- Geometric Invariant Theory Relative to a Base Curve.- Thom Polynomials of Invariant Cones.- Torsion-free Sheaves and Their Moduli.- Applications of Algebraic Cycles to Affine Algebraic Geometry.
Series: Cambridge Monographs on Mathematical Physics
Paperback (ISBN-13: 9780521715966)
Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.
? General introduction to the conceptual and technical problems of quantum gravity ? Complete up-do-date introduction to loop quantum gravity ? In-depth discussion of the modification of the notions of space and time required by the new physics
Contents
Preface; Acknowledgements; Terminology and notation; Part I. Relativistic Foundations: 1. General ideas and heuristic picture; 2. General relativity; 3. Mechanics; 4. Hamiltonian general relativity; 5. Quantum mechanics; Part II. Loop Quantum Gravity: 6. Quantum space; 7. Dynamics and matter; 8. Applications; 9. Quantum spacetime: spinfoams; 10. Conclusion; Part III. Appendices: References; Index.
Series: Cambridge Studies in Advanced Mathematics (No. 109)
Hardback (ISBN-13: 9780521865852)
This text on contact topology is the first comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem G4=0 via the classification of tight contact structures on the 3--sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3--manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3--dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
? First text to give a comprehensive introduction to contact geometry, with thorough discussion of all basic methods of the subject ? Accessible to those new to this area, with an extensive introductory chapter on the historical roots of contact geometry, plus many detailed examples and figures ? Proofs of many folklore results and expositions of all fundamental results in the subject, including a full exposition of Eliashberg’s classification of overtwisted contact structure ? Long introductory chapter on the historical roots of contact geometry and its connection with physics, Riemannian geometry, and geometric topology ? Proofs of many folklore results and detailed expositions of all fundamental results in the subject ? Detailed exposition of Eliashberg’s classification of overtwisted contact structure
Contents
Foreword; 1. Facets of Contact Geometry; 2. Contact Manifolds; 3. Knots in Contact 3-Manifolds; 4. Contact Structures on 3-Manifolds; 5. Symplectic Fillings and Convexity; 6. Contact Surgery; 7. Further Constructions of Contact Manifolds; 8. Contact Structures on 5-Manifolds; Appendix A: The generalised Poincare lemma; Appendix B: Time-dependent vector fields; References; List of Notations; Author Index; Subject Index.
Volume 11 NATO Science for Peace and Security Series: Information and Communication Security
July 2007, 248 pp., hardcover
ISBN: 978-1-58603-749-9 NEW
This volume aims to assess the state-of-the-art in the field of Quantum Communication and Security and to identify new research challenges. The papers in this book concentrate mainly on quantum cryptography (both technical and experimental aspects and pure theory), general problems of theoretical quantum information and its realizations (laboratories and applied physics), and finally the related topics concerning quantum theory itself ? the most fundamental questions.
This publication is divided into four chapters:
Quantum Cryptography
Theory of Quantum Information
Production of Entangled States, Experimental Techniques
Quantum Communication and Computation