Sujet
L'utilisation de l'algebre de Clifford en physique mathematique
et dans les sciences de l'ingenieur a connu un essor rapide ces
dernieres annees. Alors que les developpements recents ont
privilegie l'approche geometrique, l'auteur s'interesse quant a
lui a l'approche algebrique, qui peut etre introduite comme un
produit tensoriel d'algebres de quaternions et qui fournit un
calcul unifie, relativiste pour une grande partie de la physique.
Originalite
Cet ouvrage propose une introduction pedagogique a ce nouveau
calcul, a partir du groupe des quaternions, avec des applications
principalement dans les domaines de la relativite restreinte, de
l'electromagnetisme classique et de la relativite generale.
Public
Cet ouvrage s'adresse aux etudiants et chercheurs en physique et
en sciences de l'ingenieur, interesses par l'utilisation de ce
nouveau calcul de Clifford quaternionien.
Contenu
Introduction - Quaternions - Groupe de rotation - Quaternions
complexes - Algebre de Clifford - Groupes de symetrie -
Relativite restreinte - Electromagnetisme classique - Relativite
generale - Conclusions - Solutions - Bibliographie - Index.
ISBN: 2-88074-606-X
2004
184 pages
16x24cm
broche.
*
Sujet
Cet ouvrage constitue une introduction a la theorie des champs
quantiques tres differente des habituels exposes le plus souvent
formels. Apres avoir defini pas a pas les concepts mathematiques
necessaires au developpement de cette theorie, quelques exemples
classiques sont traites en detail. L'espace de Fock est ensuite
expose sans recours a des coordonnees particulieres. Cette
formulation generale permet alors d'introduire correctement les
champs quantiques des phonons et les photons. L'ouvrage se clot
par un expose de la theorie de la diffusion. Les problemes
exposes, avec leurs corriges, constituent d'utiles complements au
texte.
Originalite
Ouvrage particulierement clair et didactique, illustre de
nombreux exemples et exercices corriges, et redige par l'un des
specialistes francophones en la matiere.
Public
Etudiants, professeurs, chercheurs et ingenieurs en physique et
mecanique quantique.
Contenu
Avant-propos. Theorie des champs: Introduction - Problemes -
Principe de Cartan - Problemes - Champ de Maxwell - Problemes -
Champ de Schrodinger-Pauli - Problemes - Champ de Dirac -
Problemes - Electrodynamique - Problemes - References.
Problemes a N corps: Introduction - Problemes - Formalisme -
Problemes - Chaine quantique - Problemes - Champ transverse de
Maxwell - Problemes - References.
Diffusion: Introduction - Problemes - Matrice S - Problemes -
References. Corriges des problemes. Index.
ISBN: 2-88074-611-6
2005
104 pages
15x21cm
thermocolle.
The book is the first to give a comprehensive overview of the
techniques and tools currently being used in the study of
combinatorial problems in Coxeter groups. It is self-contained,
and accessible even to advanced undergraduate students of
mathematics.
The primary purpose of the book is to highlight approximations to
the difficult isomorphism problem in Coxeter groups. A number of
theorems relating to this problem are stated and proven. Most of
the results addressed here concern conditions which can be seen
as varying degrees of uniqueness of representations of Coxeter
groups. Throughout the investigation, the readers are introduced
to a large number of tools in the theory of Coxeter groups, drawn
from dozens of recent articles by prominent researchers in
geometric and combinatorial group theory, among other fields. As
the central problem of the book may in fact be solved soon, the
book aims to go further, providing the readers with many
techniques that can be used to answer more general questions. The
readers are challenged to practice those techniques by solving
exercises, a list of which concludes each chapter.
Contents:
Preliminaries on Coxeter Groups
Further Properties of Coxeter Groups
Rigidity
In the Beginning: Some Early Results
Even Coxeter Groups
More General Groups
Refinements and Generalizations: Automorphisms and Artin Groups
Readership: Graduate students in group theory and linear algebra,
mathematicians.
192pp Pub. date: Mar 2005
ISBN 1-86094-554-6
The Ginzburg?Landau equation as a mathematical model of
superconductors has become an extremely useful tool in many areas
of physics where vortices carrying a topological charge appear.
The remarkable progress in the mathematical understanding of this
equation involves a combined use of mathematical tools from many
branches of mathematics. The Ginzburg?Landau model has been an
amazing source of new problems and new ideas in analysis,
geometry and topology. This collection will meet the urgent needs
of the specialists, scholars and graduate students working in
this area or related areas.
Contents:
Bifurcation Problems for Ginzburg?Landau Equations and
Applications to Bose Einstein Condensates (A Aftalion)
Vortex Analysis of the Ginzburg?Landau Model of Superconductivity
(E Sandier)
On Singular Perturbation Problems Involving a “Circular-Well”
Potential (I Shafrir)
Existence Results on Ginzburg?Landau Equations (F Zhou)
A Survey on Ginzburg?Landau Vortices of Superconducting Thin
Films (S Ding)
On the Hydro-Dynamic Limit of Ginzburg?Landau Wave Vortices (F
Lin & P Zhang)
Singular Sets of the Landau?Lifshitz System (X-G Liu)
Analysis of Ginzburg?Landau Models for Type I Superconductivity (F
Yi)
Ferromagnets and Landau?Lifshitz Equation (J Zhai)
Readership: Specialists, scholars and graduate students in
applied mathematics, applied science and related areas.
210pp (approx.) Pub. date: Scheduled Summer 2005
ISBN 981-256-203-6
This book furthers new and exciting developments in
experimental designs, multivariate analysis, biostatistics, model
selection and related subjects. It features articles contributed
by many prominent and active figures in their fields. These
articles cover a wide array of important issues in modern
statistical theory, methods and their applications. Distinctive
features of the collections of articles are their coherence and
advance in knowledge discoveries.
Contents:
Multivariate Analysis
Experimental Design
Advances in Biostatistics
Advance in Statistics
Readership: Researchers and graduate students in multivariate
analysis, experimental designs and quasi-Monte Carlo methods.
468pp Pub. date: Mar 2005
ISBN 981-256-120-X