Series on University Mathematics - Vol. 1
by S S Chern (University of California,
Berkeley), W H Chen (Beijing University)
& K S Lam (California State Polytechnic University)
This book is a translation of an authoritative introductory text
based on a lecture series delivered by the renowned differential
geometer, Professor S S Chern in Beijing University in 1980. The
original Chinese text, authored by Professor Chern and Professor
Wei-Huan Chen, was a unique contribution to the mathematics
literature, combining simplicity and economy of approach with
depth of contents.
The present translation is aimed at a wide audience, including
(but not limited to) advanced undergraduate and graduate students
in mathematics, as well as physicists interested in the diverse
applications of differential geometry to physics.
In addition to a thorough treatment of the fundamentals of
manifold theory, exterior algebra, the exterior calculus,
connections on fiber
bundles, Riemannian geometry, Lie groups and moving frames, and
complex manifolds (with a succinct introduction to the theory of
Chern classes), and an appendix onthe relationship between
differential geometry and theoretical physics, this book includes
a new chapter on Finsler geometry and a new appendix on the
history andrecent developments of differential geometry, the
latter prepared specially for this edition by Professor Chern to
bring the text into perspectives.
Contents:
Differentiable Manifolds
Multilinear Algebra
Exterior Differential Calculus
Connections
Riemannian Geometry
Lie Groups and Moving Frames
Complex Manifolds
Finsler Geometry
Historical Notes
Differential Geometry and Theoretical Physics
Readership: Undergraduates, graduates and researchers in pure
mathematics and mathematical physics.
368pp
Pub. date: Nov 1999
ISBN 981-02-3494-5
ISBN 981-02-4182-8(pbk)
edited by A Degasperis & G
Gaeta (Universit・di Roma "La Sapienza")
The second workshop on "Symmetry and
Perturbation Theory" served as a forum for discussing the
relations between symmetry and perturbationtheory, and this put
in contact rather different communities.
The extension of the rigorous results of perturbation theory
established for ODE's to thecase of nonlinear evolution PDE's was
also discussed: here a number of results are known, particularly
in connection with (perturbation of) integrablesystems, but there
is no general frame as solidly established as in the
finite-dimensional case. In aiming at such an
infinite-dimensional extension, forwhich standard analytical
tools essential in the ODE case are not available, it is natural
to look primarily at geometrical and topological methods, and
first of all at those based on exploiting the symmetry properties
of the systems under study (both the unperturbed and the
perturbed ones); moreover, symmetry considerations are in
several ways basic to our understanding of integrability, i.e.
finally of the unperturbed systems on whose understanding the
whole of perturbation theory has unavoidablyto rely.
This volume contains tutorial, regular and contributed papers.
The tutorial papers give students and newcomers to the field a
rapid introduction to some active themes ofresearch and recent
results in symmetry and perturbation theory.
Contents:
Nonlinear Symmetries and Normal Forms (G Cicogna & G Gaeta)
Asymptotic Integrability (A Degasperis & M Procesi)
Families of Relative Equilibria in Hamiltonian Systems with
Dissipation (G Derks)
On Averaging Methods for Partial Differential Equations (F
Verhulst)
The Geometrical Description of Hyperelliptically Separable
Systems (S Abenda & Y Fedorov)
Smooth Seminormal Forms of Symmetric and Reversible Systems (P
Bonckaert)
Convergent Normal Forms, Bifurcations and Symmetries (G Cicogna)
Perturbing a Symmetric Resonance: The Magnetic Spherical Pendulum
(J Montaldi)
Symmetry Reductions and Periodic Orbits in the Planar 3-Body
Problem (L Sbano)
Simultaneous Normal Forms of Commuting Maps and Vector Fields (M
Yoshino)
Interlaced Branching Equations and Invariance in the Theory of
Nonlinear Equations (N A Sidorov & V R Abdullin)
and other papers
Readership: Researchers and students in mathematics, physics and
mechanics.
336pp
Pub. date: Jan 2000
ISBN 981-02-4166-6
edited by S Elaydi (Trinity
University, San Antonio, USA), F Allan, M Saleh (Birzeit
University, Palestine),
A Elkhader (Northern State University, Aberdeen, USA) & T
Mughrabi (Al-Quds University, Palestine)
This volume covers topics ranging from pure and
applied mathematics to pedagogical issues in mathematics. There
are papers in mathematical biology, differential equations,
difference equations, dynamical systems, orthogonal polynomials,
topology, calculus reform, algebra, and numerical analysis. Most
of the papers include new, interesting results that are at the
cutting edge of the respective subjects. However, there are some
papers of an expository nature.
Contents:
On the Existence and Non-Uniqueness of Nonhomogeneous Blasuis
Problem (F Allan & R M Abu-Sarris)
On Monotonicity of Green Operator for Singular Boundary Value
Problem (M J Alves)
Numerical Solution of the Two-Point Boundary Value Problems
Arising in Modeling Viscoelastic Flows (B S Attili)
On Direct Sums of Modules which Satisfy Generalizations of
Injectivity (J Clark)
The Stieltjes Matrix Moment Problem and de Branges Spaces
Associated with Them (Yu M Dyukarev)
On Some Open Problems in Difference Equations (S Elaydi)
Direct Limits of Effect Algebras (E D Habil)
An Extremal Problem for Generalized Jacobi Polynomials (M E H
Ismail)
A Semilinear Hyperbolic System (H Smith)
Subharmonic Bifurcation at Multiple Resonances (A Vanderbauwhede)
Module and Comodule Categories ・A Survey (R Wisbauer)
and other papers
Readership: Researchers and graduate students in mathematics,
mathematics education and sciences.
300pp (approx.)
Pub. date: Scheduled Spring 2000
ISBN 981-02-4220-4
Proceedings of the Conference
"Kadanoff-Baym Equations: Progress and Perspectives for
Many-Body Physics"
Rostock, Germany 20 - 24 September 1999
Equilibrium and nonequilibrium properties of correlated many-body
systems are of growing interest in many fields of physics,
including condensed matter, dense plasmas, nuclear matter and
particles. The most powerful and general method which applies
equally to all these areas is given by quantum field theory .
Written by the leading experts and understandable to
non-specialists, this book provides an overview on the basic
ideas and concepts of the method of nonequilibrium Green's
functions. It is complemented by modern applications of the
method to a variety of topics, such as optics and transport in
dense plasmas and semiconductors; correlations, bound states and
coherence; strong field effects and short-pulse lasers; nuclear
matter and QCD.
Contents:
General Problems
Coulomb Systems
Nuclear Matter, Correlations
Numerical Concepts Index.
Authors include: Gordon Bayan, Pawel Danielewicz, Don DuBois,
Hartmut Haug, Klaus Henneberger, Antti-Pekka Jauho, Jn Kuoll,
Dietrich Kremp, Pavel Lipavsky and Paul C Martin.
Readership: Graduate students and researchers interested in the
theoretical description of quantum many-body systems in
nonequilibrium.
500pp (approx.)
Pub. date: Scheduled Spring 2000
ISBN 981-02-4218-2
This volume contains articles by leading
mathematicians and physicists in different directions, such as
geometry, probability, variational problems, dynamical
systems,mathematical economics, quantum field theory, string
theory and cosmology.
Readership: Mathematicians and physicists.
350pp (approx.)
Pub. date: Scheduled Spring 2000
ISBN 981-02-4223-9
Series on Advances in Mathematics for Applied Sciences
edited by P Ciarlini (CNR, Roma, Italy), A B
Forbes (National Physical Laboratory, Teddington, UK), F Pavese
(CNR, Torino, Italy) & D Richter (Physikalisck-Technische
Bundesanstat, Berlin)
Advances in metrology depend on improvements in scientific and
technical knowledge and in instrumentation quality, as well as
better use of advanced mathematical tools and development of new
ones. In this volume, scientists from both the mathematical and
the metrological fields exchange their experiences. Industrial
sectors, such as instrumentation and software, are likely to
benefit from this exchange, since metrology has a high impact on
the overall quality of industrial products, and applied
mathematics is becoming more and more important in industrial
processes.
This book is of interest to people in universities, research
centers and industries who are involved in measurements and need
advanced mathematical tools to solve their problems, and to those
developing such mathematical tools.
Readership: Researchers in metrological institutes, universities
(measurement science and industries (quality systems,
calibration, certification).
380pp (approx.)
Pub. date: Scheduled Spring 2000
ISBN 981-02-4216-6
Proceedings of the Conference in Honor of
Gerard Rauzy on His 60th Birthday
Luminy-Marseille, France 6 - 10 July 1998
This book focuses on the interactions between discrete and
geometric dynamical systems, and between dynamical systems and
theoretical physics and computer science.
Accordingly, the contributions revolve around two main topics:
(1) interaction between geometric and symbolic systems, with
emphasis on tiling problems for quasicrystals, substitutions and
their multidimensional generalizations, geodesic and horocycle
flow, adic systems; (2) dynamical systems: geometry and chaos,
with special interest in smooth ergodic theory, statistical and
multifractal properties of chaotic systems, stability and
turbulence in extended complex systems.
Readership: Graduates and researchers in chaos and dynamical
systems.
300pp (approx.)
Pub. date: Scheduled Spring 2000
ISBN 981-02-4217-4
Series in Real Analysis - Vol. 7
by Jaroslav Kurzweil (Mathematical Institute,
Academy of Sciences of the Czech Republic)
Henstock-Kurzweil (HK) integration, which is based on integral
sums, can be obtained by an inconspicuous change in the
definition of Riemann integration.
It is an extension of Lebesgue integration and there exists an
HK-integrable function f such that its absolute value |f| is not
HK-integrable. In this book HK integration is treated only on
compact one-dimensional intervals.
The set of convergent sequences of HK-integrable functions is
singled out by an elementary convergence theorem. The concept of
convergent sequences is transferred to the set P of primitives of
HK-integrable functions; these convergent sequences of functions
from P are called E-convergent. The main results: there exists a
topology
U on P such that (1) (P,U) is a topological vector space, (2)
(P,U) is complete, and (3) every E-convergent sequence is
convergent in (P,U). On the other hand, there is no topology U
fulfilling (2), (3) and (P,U) being a locally convex space.
Contents:
Integrable Functions and Their Primitives
Gauges and Borel Measurability
Convergence
An Abstract Setting
Abstract Setting with D Countable
Locally Convex Topologies Tolerant to Q-Convergence
Topological Vector Spaces Tolerant to Q-Convergence
P as a Complete Topological Vector Space
Open Problems
Readership: Graduate students and mathematicians.
120pp (approx.)
Pub. date: Scheduled Spring 2000
ISBN 981-02-4207-7