July 2003, ISBN 1-4020-7537-5, Hardbound
Book Series: NONCONVEX OPTIMIZATION AND ITS
APPLICATIONS : Volume
69
This book includes a self-contained theory
of inequality problems
and their applications to unilateral mechanics.
Fundamental
theoretical results and related methods of
analysis are discussed
on various examples and applications in mechanics.
The work can
be seen as a book of applied nonlinear analysis
entirely devoted
to the study of inequality problems, i.e.
variational
inequalities and hemivariational inequalities
in mathematical
models and their corresponding applications
to unilateral
mechanics. It contains a systematic investigation
of the
interplay between theoretical results and
concrete problems in
mechanics. It is the first textbook including
a comprehensive and
systematic study of both elliptic, parabolic
and hyperbolic
inequality models, dynamical unilateral systems
and unilateral
eigenvalues problems. The book is self-contained
and it offers,
for the first time, the possibility to learn
about inequality
models and to acquire the essence of the
theory in a relatively
short time.
Audience: The book is suitable for researchers,
and for doctoral
and post-doctoral courses.
July 2003, ISBN 1-4020-7538-3, Hardbound
Book Series: NONCONVEX OPTIMIZATION AND ITS
APPLICATIONS : Volume
70
This book includes a self-contained theory
of inequality problems
and their applications to unilateral mechanics.
Fundamental
theoretical results and related methods of
analysis are discussed
on various examples and applications in mechanics.
The work can
be seen as a book of applied nonlinear analysis
entirely devoted
to the study of inequality problems, i.e.
variational
inequalities and hemivariational inequalities
in mathematical
models and their corresponding applications
to unilateral
mechanics. It contains a systematic investigation
of the
interplay between theoretical results and
concrete problems in
mechanics. It is the first textbook including
a comprehensive and
systematic study of both elliptic, parabolic
and hyperbolic
inequality models, dynamical unilateral systems
and unilateral
eigenvalues problems. The book is self-contained
and it offers,
for the first time, the possibility to learn
about inequality
models and to acquire the essence of the
theory in a relatively
short time.
Audience: The book is suitable for researchers,
and for doctoral
and post-doctoral courses.
May 2003, ISBN 1-4020-1378-7, Hardbound
Book Series: MATHEMATICAL PHYSICS STUDIES
: Volume 24
This volume contains papers presented at
the first conference
held to honor the memory of, arguably, the
greatest mathematician
of the twentieth century, Jean Leray. Contributors
from all over
the world have submitted their work to be
included in this unique
collection, and it reflects the esteem in
which Jean Leray was,
and still is held. The book is divided into
five parts:
hyperbolic systems and equations; symplectic
mechanics and
geometry; sheaves and spectral sequences;
elliptic operators and
index theory; and mathematical physics. This
volume will appeal
to all those who acknowledge the value of
Jean Leray's work in
general, and students and researchers interested
in analysis,
topology and geometry, mathematical physics,
classical mechanics
and fluid mechanics and dynamics in particular.
Contents and Contributors
I: Hyperbolic systems and equations. Caractere
holonome d'une
solution elementaire; L. Boutet de Monvel.
Necessary conditions
for hyperbolicity of first order systems;
A. Bove, T. Nishitani.
On the Cauchy problem for hyperbolic operators
with non-regular
coefficients; F. Colombini, et al. Multiple
points of the
characteristic manifold of a diagonalizable
operator; H.
Deliquie, J. Vaillant. Large temps de vie
des solutions d'une
probleme de Caucht non lineaire; D. Gourdin,
M. Mechab. Un
remarque sur une prolongement analytique
de la solution du
probleme de Cauchy; Y. Hamada. Conormality
and lagrangian
properties along diffractive rays; P. Laubin.
Caracterisation des
operateurs differentiels hyperboliques; Y.
Ohya. A dependence
domain for a class of micro-differential
equations with
involutive double characteristics; Y. Okada,
N. Tose.
Ramification non abelienne; C. Wagschal.
II: Symplectic mechanics and geometry. Extension
du calcul
differentiel et application a la theorie
des groupes de Lie en
dimension infinie; P. Dazord. The cohomological
meaning of
Maslov's lagrangian path intersection index;
M.de Gosson, S.de
Gosson. A Kahler structure on the punctured
cotangent bundle of
the cayley projective plane; K. Furutani.
On mechanical systems
with a Lie group as configuration space;
C.-M. Marle. Dirac
fields on asymptotically simple space-times;
J.-P. Nicolas. An
embedding result for some general symbol
classes in the Weyl
calculus; J. Toft. The lagrangian in symplectic
mechanics; G.M.
Tuynman. Geometry of solution spaces of spaces
of Yang Mills
equations; J. Sniatycki.
III: Sheaves and spectral sequences. La th<eacuteorie
des
residus sur un espace analytique complexe;
V. Ancona, B. Gaveau.
Derivation of exact triples and Leray Koszul
spectral sequences;
B. Bendiffalah.
IV: Elliptic operators: Index theory. Le
noyau de la chaleur des
operateurs sous-elliptiques des groupes d'Heisenberg;
R. Beals,
et al. The geometry of Cauchy data spaces;
B. Booss-Bavbek, et al.
On theCauchy problem for Kirchhoff equations
of p-laplacian type;
K. Kajitani. A remark on surgery in index
theory of elliptic
operators; V.-E. Nazaikinskii, B.-Y. Sternin.
The Ĵ invariant
and elliptic operators in subspaces; A. Savin,
et al.
Regularisation of mixed boundary problems;
B.-W. Schulze, et al.
V: Mathematical Physics. Covariant method
for solution of
Cauchy's problem based on Lie group analysis
and Leray's form; N.
Ibragimov. Liouville forms, parallelisms
and Cartan connections;
P. Libermann. A Two-dimensional non-linear
shell model of
Koiter's type; P.-G. Ciarlet. A model of
the process of thinking
based on the dynamics of bundles of branches
and sets of bundles
on p-adic trees; A. Khrennikov. Global wave
maps on black holes;
Y. Choquet-Bruhat. Entanglement, parataxy,
and cosmology; E.
Binz, W. Schempp. Sur le controle des equations
de Navier Stokes;
J.-L. Lyons. Addresses.
June 2003, ISBN 1-4020-1416-3, Hardbound
June 2003, ISBN 1-4020-1417-1, Paperback
Book Series: NATO SCIENCE SERIES: II: Mathematics,
Physics and
Chemistry : Volume 109
Synchronization is a universal phenomenon
that is encountered in
nature, science and engineering. The book
presents a broad view
of modern theoretical and experimental approaches
to
synchronization, especially in complex and
chaotic systems, and
its applications in life sciences and engineering.
Contributors
include applied mathematicians, physicists,
biologists, and
specialists in communications and control
theory. The study of
synchronization is presented in its many
aspects: basic
mathematical theory, numerical simulation
of complex systems,
applications of methods in theoretical physics,
experimental
implementation, and applications in engineering
and life sciences.
July 2003, ISBN 1-4020-1462-7, Hardbound
Book Series: MATHEMATICS AND ITS APPLICATIONS
: Volume 559
Asymptotic Characteristics of Entire Functions
and Their
Applications in Mathematics and Biophysics
is the second edition
of the same book in Russian, revised and
enlarged. It is devoted
to asymptotical questions of the theory of
entire and
plurisubharmonic functions. The new and traditional
asymptotical
characteristics of entire functions of one
and many variables are
studied. Applications of these indices in
different fields of
complex analysis are considered, for example
Borel-Laplace
transformations and their modifications,
Mittag-Leffler function
and its natural generalizations, integral
methods of summation of
power series and Riemann surfaces.
In the second edition, a new appendix is
devoted to the
consideration of those questions for a class
of entire functions
of proximate order. A separate chapter is
devoted to applications
in biophysics, where the algorithms of mathematical
analysis of
homeostasis system behaviour, dynamics under
external influence
are investigated, which may be used in different
fields of
natural science and technique.
This book is of interest to research specialists
in theoretical
and applied mathematics, postgraduates and
students of
universities who are interested in complex
and real analysis and
its applications.
August 2003, ISBN 1-4020-1457-0, Hardbound
In the last century many problems which arose
in the science,
engineering and technology literature involved
nonlinear complex
phenomena. In many situations these natural
phenomena give rise
to (i). ordinary differential equations which
are singular in the
independent and/or dependent variables together
with initial and
boundary conditions, and (ii). Volterra and
Fredholm type
integral equations. As one might expect general
existence results
were difficult to establish for the problems
which arose. Indeed
until the early 1990's only very special
examples were examined
and these examples were usually tackled using
some special
device, which was usually only applicable
to the particular
problem under investigation. However in the
1990's new results in
inequality and fixed point theory were used
to present a very
general existence theory for singular problems.
This monograph
presents an up to date account of the literature
on singular
problems. One of our aims also is to present
recent theory on
singular differential and integral equations
to a new and wider
audience. The book presents a compact, thorough,
and self-contained
account for singular problems. An important
feature of this book
is that we illustrate how easily the theory
can be applied to
discuss many real world examples of current
interest.
Contents
1: Differential Equations Singular in the
Independent Variable. 1.1.
Introduction. 1.2. Preliminaries. 1.3. Initial
Value Problems. 1.4.
Boundary Value Problems. 1.5. Bernstein Nagumo
Theory. 1.6.
Method of Upper and Lower Solutions. 1.7.
Solutions in Weighted
Spaces. 1.8. Existence Results Without Growth
Restrictions. 1.9.
Nonresonant Problems. 1.10. Nonresonant Problems
of Limit Circle
Type. 1.11. Nonresonant Problems of Dirichlet
Type. 1.12.
Resonance Problems. 1.13. Infinite Interval
Problems I. 1.14.
Infinite Interval Problems II.
2: Differential Equations Singular in the
Dependent Variable. 2.1.
Introduction. 2.2. First Order Initial Value
Problems. 2.3.
Second Order Initial Value Problems. 2.4.
Positone Problems. 2.5.
Semipositone Problems. 2.6. Singular Problems.
2.7. An Alternate
Theory for Singular Problems. 2.8. Singular
Semipositone Type
Problems. 2.9. Multiplicity Results for Positone
Problems. 2.10.
General Problems with Sign Changing Nonlinearities.
2.11.
Problems with Nonlinear Boundary Data. 2.12.
Problems with Mixed
Boundary Data. 2.13. Problems with Nonlinear
Left Hand Side. 2.14.
Infinite Interval Problems I. 2.15. Infinite
Interval Problems II.
3: Singular Integral Equations. 3.1. Introduction.
3.2.
Nonsingular Integral Equations. 3.3. Singular
Integral Equations
with a Special Class of Kernels. 3.4. Singular
Integral Equations
with General Kernels. 3.5. A New Class of
Integral Equations. 3.6.
Singular and Nonsingular Volterra Integral
Equations. Problems.
References. Subject Index.