In the 20th century, many mathematicians
in Russia made great
contributions to the field of mathematics.
This invaluable book,
which presents the main achievements of Russian
mathematicians in
that century, is the first most comprehensive
book on Russian
mathematicians. It has been produced as a
gesture of respect and
appreciation for those mathematicians and
it will serve as a good
reference and an inspiration for future mathematicians.
It
presents differences in mathematical styles
and focuses on Soviet
mathematicians who often discussed "what
to do" rather
than "how to do it". Thus, the
book will be valued
beyond historical documentation.
The editor, Professor Yakov Sinai, a distinguished
Russian
mathematician, has taken pains to select
leading Russian
mathematicians Esuch as Lyapunov, Luzin,
Egorov, Kolmogorov,
Pontryagin, Vinogradov, Sobolev, Petrovski
and Krein Eand their
most important works. One can, for example,
find works of
Lyapunov, which parallel those of PoincarE
and works of Luzin,
whose analysis plays a very important role
in the history of
Russian mathematics; Kolmogorov has established
the foundations
of probability based on analysis. The editor
has tried to provide
some parity and, at the same time, included
papers that are of
interest even today.
The original works of the great mathematicians
will prove to be
enjoyable to readers and useful to the many
researchers who are
preserving the interest in how mathematics
was done in the former
Soviet Union.
Contents:
Lyapunov (A New Case of Integrability of
Differential Equations
of Motion of a Solid Body in Liquid)
Luzin (Sur l'absolue convergence des series
trigonometriques)
Egorov (Mathematics and Religion in Moscow,
by C E Ford)
Smirnov (Sur les polynomes orthogonaux a
une veriable complexe)
Bernstein (Sur la meilleure approximation
sur tout l'axe reel des
fonctions continues par des fonctions entieres
de degre fini)
Urysohn
Chebotarev
Vinogradov (Representation of an Odd Number
as the Sum of Three
Primes)
Aleksandrov (Sur la notion de dimension des
ensembles fermes)
Menshov
Gelfond (Sur le septierie probleme de Hilbert)
Khinchin (Three Pearls of Number Theory)
Kolmogorov (Local Structure of Turbulence
in an Incompressible
Viscous Fluid at Very Large Reynolds Numbers)
Pontryagin (Homotopic Classification of an
(n+2)-Dimensional
Spheres into an n-Dimensional Spheres)
Gelfand (On Identities for Eigenvalues of
a Second Order
Differential Operators)
Sobolev (On a Theorem of Functional Analysis)
Petrovsky (On Problem of some PDE's)
Krein (On Extreme Points of Regularly Convex
Sets)
Liusternik (Topology and Variational Problem)
Rokhlin (Proof of Gudkov's Hypothesis)
Novikov (Periodic Groups)
Bogoliubov (Mathematical Problems of Quantum
Field Theory)
Aleksadrov (Neue ungleichungen fur die mischvolumen
konvexer
korper)
Kantorovich (A New Method of Solving of Some
Classes of Extremal
Problems)
Malcev (Free Topological Algebras)
Linnik (An Application of the Theory of Matrices
and of
Lobatschevskian Geometry to the Theory of
Dirichlet's Real
Characters)
Markov (The Theory of Algorithms)
Lavrentev (On the Theory of Quasi-Conformal
Mapping of Three-Dimensional
Domains)
Tikhonov (Ueber die Erweiteung von Raumen)
Delone (Sur le nombre de representations
d'un nombre par une
forme eubique a discriminent negatif)
Keldysh (On the Completeness of the Eigenfunctions
of Some
Classes of Non-Self Adjoint Linear Operators)
Fadeeev
and other articles
Readership: General mathematicians.
800pp (approx.) Pub. date: Scheduled Fall
2003
ISBN 981-02-4390-1
ISBN 981-238-385-9(pbk)
World Scientific Series on Nonlinear Science,
Series A - Vol.
45
This book presents the theoretical frame
for studying lumped
nonsmooth dynamical systems: the mathematical
methods are
recalled, and adapted numerical methods are
introduced (differential
inclusions, maximal monotone operators, Filippov
theory, Aizerman
theory, etc.). Tools available for the analysis
of classical
smooth nonlinear dynamics (stability analysis,
the Melnikov
method, bifurcation scenarios, numerical
integrators, solvers,
etc.) are extended to the nonsmooth frame.
Many models and
applications arising from mechanical engineering,
electrical
circuits, material behavior and civil engineering
are
investigated to illustrate theoretical and
computational
developments.
Contents:
Introduction to Discontinuous ODEs
Mathematical Background for Multivalued Formulations
Properties of Numerical Schemes
Stick?Slip Oscillator with Two Degrees of
Freedom
Piecewise Linear Approximations
Chua's Circuit with Discontinuities
One DOF Mechanical System with Friction
A Mechanical System with 7 DOF
Triple Pendulum with Impacts
Analytical Prediction of Stick?Slip Chaos
and other topics
Readership: Upper-level undergraduates, graduate
students,
researchers and practitioners in engineering
mechanics, civil
engineering, biomechanics, and nonlinear
sciences and
applications.
564pp Pub. date: Jul 2003
ISBN 981-238-459-6
The Sixth International Workshop on Complex
Structures and
Vector Fields was a continuation of the previous
five workshops (1992,
1994, 1996, 1998, 2000) on similar research
projects. This series
of workshops aims at higher achievements
in studies of new
research subjects. The present volume will
meet with the
satisfaction of many readers.
Contents:
Real Analytic Almost Complex Manifolds (L
N Apostolova)
Involutive Distributions of Codimension One
in Kaehler Manifolds
(G Ganchev)
Three Theorems on Isotropic Immersions (S
Maeda)
On the Meilikhson Theorem (M S Marinov)
Curvature Tensors on Almost Contact Manifolds
with B-Metric (G
Nakova)
Complex Structures and the Quark Confinement
(I B Pestov)
Curvature Operators in the Relativity (V
Videv & Y Tsankov)
On Integrability of Almost Quaternionic Manifolds
(A Yamada)
and other papers
Readership: Graduate students and researchers
in complex
analysis, differential geometry and mathematical
physics.
248pp Pub. date: Jun 2003
ISBN 981-238-452-9
About the Author
Born in Shandong, China, in 1927, Zhe-Xian
Wan graduated from
Tsinghua University, Beijing, in 1948 and
became a teacher at the
same university. In 1950 he joined the Chinese
Academy of
Sciences, and in 1978 he was appointed Research
Professor at the
Academy. He is also a member of the Chinese
Academy of Sciences.
Professor Wan's main research interests are
algebra (pure and
applied), combinatorics and coding theory.
In addition to nearly
130 papers, he has published 18 books in
these areas, including
Classical Groups (jointly with L K Hua),
Lie Algebras, Algebra
and Coding, Introduction to Kac-Moody Algebras,
Geometry of
Classical Groups over Finite Fields, Geometry
of Matrices and
Quaternary Codes.
This is a textbook for graduate and upper
level undergraduate
students in mathematics, computer science,
communication
engineering and other fields. The explicit
construction of finite
fields and the computation in finite fields
are emphasised. In
particular, the construction of irreducible
polynomials and the
normal basis of finite fields are included.
The essentials of
Galois rings are also presented. This invaluable
book has been
written in a friendly style, so that lecturers
can easily use it
as a text and students can use it for self-study.
A great number
of exercises have been incorporated.
Contents:
Sets and Integers
Groups
Fields and Rings
Polynomials
Residue Class Rings
Structure of Finite Fields
Further Properties of Finite Fields
Bases
Factoring Polynomials over Finite Fields
Irreducible Polynomials over Finite Fields
Quadratic Forms over Finite Fields
More Group Theory and Ring Theory
Hensel's Lemma and Hensel Lift
Galois Rings
Readership: Upper level undergraduates, graduate
students and
lecturers in algebra.
350pp (approx.) Pub. date: Scheduled Fall
2003
ISBN 981-238-504-5
ISBN 981-238-570-3(pbk)