Poul G. Hjorth (University of Southern Denmark, Odense, Denmark),
Carsten Lunde Petersen (University of Roskilde, Denmark), Editors
Dynamics on the Riemann Sphere
A Bodil Branner Festschrift
ISBN 3-03719-011-6
January 2006, 226 pages, hardcover, 16.5 cm x 23.5 cm.
Dynamics on the Riemann Sphere presents a collection of original
research articles by leading experts in the area of holomorphic
dynamics. These papers arose from the symposium Dynamics in the
Complex Plane, held on the occasion of the 60th birthday of Bodil
Branner. Topics covered range from Lattes maps to cubic
polynomials over rational maps with Sierpinsky Carpets and
Gaskets as Julia sets, as well as rational and entire
transcendental maps with Herman rings.
Contributors include Artur Avila (Paris VI, France), Arnault
Cheritat (Toulouse, France), Robert L. Devaney (Boston, USA),
Adrien Douady (Orsay, France), Nuria Fagella (Barcelona, Spain),
Christian Henriksen (Lyngby, Denmark), Wolf Jung (Aachen, Germany),
Tomoki Kawahira (Kyoto, Japan), Tan Lei (Cergy Pontoise, France),
Mikhail Lyubich (Stony Brook, USA), Carsten Lunde Petersen (Roskilde,
Denmark), John Milnor (Stony Brook, USA), Pascale
Alber, Yakov, Ryazantseva, Irina
Nonlinear Ill-posed Problems of Monotone Type
2006, XIII, 410 p., Hardcover
ISBN: 1-4020-4395-3
About this book
Interest in regularization methods for ill-posed nonlinear
operator equations and variational inequalities of monotone type
in Hilbert and Banach spaces has grown rapidly over recent years.
Results in the field over the last three decades, previously only
available in journal articles, are comprehensively explored with
particular attention given to applications of regularization
methods as well as to practical methods used in computational
analysis.
Written for:
Specialists in nonlinear functional analysis, operator theory,
optimisation and optimal problems and their applications;
specialists in the field of solving ill-posed problems in
science, economics and engineering
Table of contents
Preface.- Introduction into the theory of monotone and accretive
operators.- Regularization of operator equations.-
Parameterization of regularization methods.- Regularization of
variational inequalities.- Applications of the regularization
methods.- Special topics on regularization methods.- Appendix.-
Bibliography.- Index.
Xu, Yichao
Theory of Complex Homogeneous Bounded Domains
Series: Mathematics and Its Applications, Vol. 569
2005, X, 427 p., Hardcover
ISBN: 1-4020-2132-1
About this book
Theory of Complex Homogeneous Bounded Domains studies the
classification and function theory of complex homogeneous bounded
domains systematically for the first time. In the book, the
Siegel domains are discussed in detail. Proofs are given for 1:
every homogeneous bounded domain is holomorphically isomorphic to
a homogeneous Siegel domain, and 2: every homogeneous Siegel
domain is affine isomorphic to a normal Siegel domain. Using the
normal Siegel domains to realize the homogeneous bounded domains,
we can obtain more property of the geometry and the function
theory on homogeneous bounded domains.
Table of contents
1. Siegel Domains and sub chapters, 2. Homogeneous Siegel Domains
and sub chapters, 3. Normal Siegel Domains and sub chapters, 4.
Other Realizations and sub chapters, 5. Automorphism Group and
sub chapters, 6. Classification of Square Domains and sub
chapters , 7. Symmetric Bounded Domains and sub chapters , 8.
Szego Kernel and Poisson Kernel and sub chapters, 9. Homogeneous
Bounded Domains and sub chapters, References, Index
Michel Le Bellac
Universite de Nice, Sophia Antipolis
Quantum Physics
Hardback (ISBN-13: 9780521852777 | ISBN-10: 0521852773)
March 2006 | 714 pages | 247 x 174 mm
Courses: Every physics undergraduate will take at least one, and
often two, courses in quantum mechanics. Further courses will be
taken at masters level. Quantum Mechanics Quantum Physics
Levels: ADVANCED UNDERGRADUATE AND GRADUATE
Quantum physics allows us to understand the nature of the
physical phenomena which govern the behavior of solids, semi-conductors,
lasers, atoms, nuclei, subnuclear particles and light. In Quantum
Physics, Le Bellac provides a thoroughly modern approach to this
fundamental theory. Throughout the book, Le Bellac teaches the
fundamentals of quantum physics using an original approach which
relies primarily on an algebraic treatment and on the systematic
use of symmetry principles. In addition to the standard topics
such as one-dimensional potentials, angular momentum and
scattering theory, the reader is introduced to more recent
developments at an early stage. These include a detailed account
of entangled states and their applications, the optical Bloch
equations, the theory of laser cooling and of magneto-optical
traps, vacuum Rabi oscillations, and an introduction to open
quantum systems. This is a textbook for a modern course on
quantum physics, written for advanced undergraduate and graduate
students.
* Completely original and contemporary approach, using algebra
and symmetry principles
* Introduces recent developments at an early stage, including
many topics that cannot be found in standard textbooks.
* Contains 130 physically relevant exercises
Contents1. Introduction; 2. Mathematics of quantum mechanics I:
finite dimension; 3. Polarization: photons and spin 1/2
particles; 4. Postulates of quantum mechanics; 5. Systems with a
finite number of levels; 6. Entangled states; 7. Mathematics of
quantum mechanics II: infinite dimension; 8. Symmetries in
quantum physics; 9. Wave mechanics; 10. Angular momentum; 11. The
harmonic oscillator; 12. Elementary scattering theory; 13.
Identical particles; 14. Atomic physics; 15. Open quantum
systems; Appendices; References.
Thierry Dauxois / Ecole Normale Superieure, Lyon
Michel Peyrard / Ecole Normale Superieure, Lyon
Physics of Solitons
Hardback (ISBN-13: 9780521854214 | ISBN-10: 0521854210)
March 2006 | 432 pages | 247 x 174 mm
Solitons are waves with exceptional stability properties which
appear in many areas of physics. The basic properties of solitons
are introduced here using examples from macroscopic physics (e.g.
blood pressure pulses and fibre optical communications). The book
then presents the main theoretical methods before discussing
applications from solid state or atomic physics such as
dislocations, excitations in spin chains, conducting polymers,
ferroelectrics and Bose-Einstein condensates. Examples are also
taken from biological physics and include energy transfer in
proteins and DNA fluctuations. Throughout the book the authors
emphasize a new approach to modelling nonlinearities in physics.
Instead of a perturbative approach, nonlinearities are treated
intrinsically and the analysis based on the soliton equations
introduced in this book. Based on the authors' graduate course,
this textbook gives an instructive view of the physics of
solitons for students with a basic knowledge of general physics,
and classical and quantum mechanics.
* Physical aspects of solitons explained
* All statements are justified from basic physical principles
* Includes numerous applications that have not previously been
presented
Contents
Introduction; Part I. Different Classes of Solitons: 1. The
Korteweg-de Vries equation; 2. Sine-Gordon equation; 3. The
nonlinear Schrodinger equation; 4. Modelling: waves in a plasma;
Part II. Mathematical Methods for the Study of Solitons: 5.
Linearisation around a soliton; 6. Collective-coordinate method;
7. The inverse-scattering transform; Part III. Examples in Solid
State and Atomic Physics: 8. The Fermi-Pasta-Ulam problem; 9. A
simple model for dislocations; 10. Ferroelectric domain walls; 11.
Incommensurate phases; 12. Solitons in magnetic systems; 13.
Conducting polymers; 14. Solitons in Bose-Einstein condensates;
Part IV. Nonlinear Excitations in Biological Molecules: 15.
Energy localisation in proteins; 16. Nonlinear dynamics of DNA;
Conclusion: Physical solitons: do they exist?; Part V. Appendices:
A. Hydrodynamic waves; B. Mechanics of a continuous medium; C.
Coherent states of an harmonic oscillator; Table of portraits;
Bibliography; Index.