Dedieu, Jean-Pierre
Points Fixes, Zeros et la Methode de Newton
Collection: Mathematiques et Applications, Vol. 54
2006, XII, 198 p. 7 illus., Broche
ISBN: 3-540-30995-0
A propos de ce livre
Cet ouvrage est consacre aux points fixes d'applications
differentiables, aux zeros de systemes non-lineaires et a la
methode de Newton. Il s'adresse a des etudiants de mastere ou
preparant l'agregation de mathematique et a des chercheurs
confirmes. La premiere partie est consacree a la methode des
approximations successives et confronte un point de vue ≪systemes
dynamiques≫ (theoremes de Grobman-Hartman, de la variete stable)
a des exemples issus de l'analyse numerique. La seconde partie de
cet ouvrage expose la methode de Newton et ses developpements les
plus recents (theorie alpha de Smale, systemes sous ou sur-determines).
Elle presente une nouvelle approche de ce sujet et un ensemble de
resultats originaux publies pour la premiere fois dans un ouvrage
de langue francaise.
This is an advanced text on fixed points, zeros of nonlinear
systems and the Newton method. Its first part, devoted to fixed
points, includes the Grobman-Hartman and the stable manifold
theorems. The second part describes the Newton method from a
modern point of view: Smale's alpha theory, underdetermined and
overdetermined systems of equations. These results are
illustrated by various examples from numerical analysis.
Sommaire
Miguel, M.C.; Rubi, J.M. (Eds.)
Jamming, Yielding, and Irreversible Deformation in Condensed
Matter
Series: Lecture Notes in Physics, Vol. 688
2006, XIII, 211 p. 88 illus., Hardcover
ISBN: 3-540-30028-7
About this book
This collection of ten tutorial reviews by leading researchers in
the field introduces and renews recent advances on irreversible
deformation phenomena in solid state and soft condensed matter
physics. The focus in applications is on amorphous materials,
crystalline solids under stress and, more generally, elastic
manifolds driven by external processes. This book addresses in
particular nonspecialists and graduate students wishing to enter
the field.
Table of contents
Introduction.- Yielding and Jamming of Dense Suspensions.-
Thermal Noise Properties of Two Aging Materials.- Jamming in
Dense Granular Media.- Rheological Aspects of the Solid-Liquid
Transition in Jammed Systems.- Dynamics of Disordered Elastic
Systems.- Edge Contamination Effects in the Dynamics of Vortex
Matter in Superconductors: Memory Effects and Excess Flux-Flow
Noise.- Out-of-Equilibrium Relaxation of a Time-Dependent
Effective Temperature.- Depinning and Plasticity of Driven
Disordered Lattices.- Mixing, Ergodicity and the Fluctuation-Dissipation
Theorem in Complex Systems.- Jamming and Yielding of Dislocations:
From Crystal Plasticity to Superconducting Vortex Flow.
Abdullaev, Sadrilla S.
Construction of Mappings for Hamiltonian Systems and Their
Applications
Series: Lecture Notes in Physics, Vol. 691
2006, XIV, 379 p. 135 illus., 4 in colour., Hardcover
ISBN: 3-540-30915-2
About this book
Based on the method of canonical transformation of variables and
the classical perturbation theory, this innovative book treats
the systematic theory of symplectic mappings for Hamiltonian
systems and its application to the study of the dynamics and
chaos of various physical problems described by Hamiltonian
systems. It develops a new, mathematically-rigorous method to
construct symplectic mappings which replaces the dynamics of
continuous Hamiltonian systems by the discrete ones. Applications
of the mapping methods encompass the chaos theory in non-twist
and non-smooth dynamical systems, the structure and chaotic
transport in the stochastic layer, the magnetic field lines in
magnetically confinement devices of plasmas, ray dynamics in
waveguides, etc. The book is intended for postgraduate students
and researches, physicists and astronomers working in the areas
of plasma physics, hydrodynamics, celestial mechanics, dynamical
astronomy, and accelerator physics. It should also be useful for
applied mathematicians involved in analytical and numerical
studies of dynamical systems.
Table of contents
Basics of Hamiltonian Mechanics.- Perturbation Theory for Nearly
Integrable Systems.- Mappings for Perturbed Systems.- Method of
Canonical Transformation for Constructing Mappings.- Mappings
near Separatrix. Theory.- Mappings near Separatrix. Examples.-
The KAM theory. Chaos. Nontwist and nonsmooth Maps.- Rescaling
Invariance of Hamiltonian Systems near Saddle Points.- Chaotic
Transport in Stochastic Layers.- Magnetic Field Lines in Fusion
Plasmas.- Mapping of field Lines in Ergodic Divertor Tokamaks.-
Mappings of Magnetic field Lines in Poloidal Divertor Tokamaks.-
Miscellaneous.- The Second Order Generating Function.- Asymptotic
Estimations of the Integral K(h) and L(h) Near Separatrix.- Proof
of Rescaling Invariance of the Equations of Motion.- Relation
between v and O.- Asymptotic Estimation of the Integral Smm,(10.49).-
Sample Program for Implementing a Mapping Procedure.- References.-
Index.
Bjorner, D.
Software Engineering 2
Specification of Systems and Languages
Series: Texts in Theoretical Computer Science. An EATCS Series
Volume package: Software Engineering
2006, XXIV, 780 p. 151 illus., Hardcover
ISBN: 3-540-21150-0
About this textbook
The art, craft, discipline, logic, practice and science of
developing large-scale software products needs a professional
base. The textbooks in this three-volume set combine informal,
engineeringly sound approaches with the rigor of formal,
mathematics-based approaches.
This volume covers the basic principles and techniques of
specifying systems and languages. It deals with modelling the
semiotics (pragmatics, semantics and syntax of systems and
languages), modelling spatial and simple temporal phenomena, and
such specialized topics as modularity (incl. UML class diagrams),
Petri nets, live sequence charts, statecharts, and temporal
logics, including the duration calculus. Finally, the book
presents techniques for interpreter and compiler development of
functional, imperative, modular and parallel programming
languages.
This book is targeted at late undergraduate to early graduate
university students, and researchers of programming methodologies.
Vol. 1 of this series is a prerequisite text.
Table of contents
Ross Brady
Universal Logic
The classical logic of Frege and Russell dominated formal logic in the 20th century. But a new type of weak relevant logic may prove itself to be better equipped to present new solutions to persisting paradoxes.
Universal Logic conceptualizes a new weak quantified relevant
logic where the main inference connective is understood as
`meaning containment'. This logic is intended to analyze naive
set/class theories. The volume begins with an overview of
classical logic and relevant logic, and discusses the limitations
of both types of logic in analyzing certain paradoxes. A summary
on the history of logic segues into the author's introduction of
his new logic modeled on the properties of set-theoretic
containment. This book is the first to demonstrate how the main
set-theoretic and semantic paradoxes can be solved in a
systematic way, which is conceptualized independently of the
paradoxes themselves.
Ross Brady is a senior lecturer in philosophy at La Trobe
University in Australia.
9/1/2005
ISBN (Paperback): 1575862565
ISBN (Cloth): 1575862557