2002 VIII, 183 p. Softcover
3-540-44006-2
Moment Theory is not a new subject; however, in classical
treatments, the ill-posedness of the problem is not taken into
account - hence this monograph. Assuming a "true"
solution to be uniquely determined by a sequence of moments (given
as integrals) of which only finitely many are inaccurately given,
the authors describe and analyze several regularization methods
and derive stability estimates. Mathematically, the task often
consists in the reconstruction of an analytic or harmonic
function, as is natural from concrete applications discussed (e.g.
inverse heat conduction problems, Cauchy's problem for the
Laplace equation, gravimetry). The book can be used in a graduate
or upper undergraduate course in Inverse Problems, or as
supplementary reading for a course on Applied Partial
Differential Equations.
Keywords: Moment problems, inverse problems, potential theory,
reconstruction of analytic functions, regularization methods
Contents: Introduction.- Mathematical Preliminaries.-
Regularization of moment problems by trancated expansion and by
the Tikhonov method.- Backus-Gilbert regularization of a moment
problem.- The Hausdorff moment problem: regularization and error
estimates.- Analytic functions: reconstruction and Sinc
approximations.- Regularization of some inverse problems in
potential theory.- Regularization of some inverse problems in
heat conduction.- Epilogue.- References.- Index.
Series: Lecture Notes in Mathematics. Volume. 1792
Approx. 630 pp. 157 figs. Softcover
0-387-95448-1
Approx. 630 pp. 157 figs. Hardcover
0-387-95495-3
This book is an introductory graduate-level textbook on the
theory of smooth manifolds. Its goal is to familiarize students
with the tools they will need in order to use manifolds in
mathematical or scientific research - smooth structures, tangent
vectors and covectors, vector bundles, immersed and embedded
submanifolds, tensors, differential forms, de Rham cohomology,
vector fields, flows, foliations, Lie derivatives, Lie groups,
Lie algebras, and more. The approach is as concrete as possible,
with pictures and intuitive discussions of how one should think
geometrically about the abstract concepts, while making full use
of the powerful tools that modern mathematics has to offer. Along
the way, the book introduces students to some of the most
important examples of geometric structures that manifolds can
carry, such as Riemannian metrics, symplectic structures, and
foliations. The book is aimed at students who already have a
solid acquaintance with general topology, the fundamental group,
and covering spaces, as well as basic undergraduate linear
algebra and real analysis.
John M. Lee is Professor of Mathematics at the University of
Washington in Seattle, where he regularly teaches graduate
courses on the topology and geometry of manifolds. He was the
recipient of the American Mathematical Societys Centennial
Research Fellowship and he is the author of two previous Springer
books, Introduction to Topological Manifolds (2000) and
Riemannian Manifolds: An Introduction to Curvature (1997).
Contents: Preface.- Smooth Manifolds.- Smooth Maps.- Tangent
Vectors.- Vector Fields.- Vector Bundles.- The Cotangent Bundle.-
Submersions, Immersions, and Embeddings.- Submanifolds.-
Embedding and Approximation Theorems.- Lie Group Actions.-
Tensors.- Differential Forms.- Orientations.- Integration on
Manifolds.- De Rham Cohomology.- The De Rham Theorem.- Integral
Curves and Flows.- Lie Derivatives.- Integral Manifolds and
Foliations.- Lie Groups and Their Lie Algebras.- Appendix: Review
of Prerequisites.- References.- Index.
Series: Graduate Texts in Mathematics. Volume. 218
Approx. 290 pp. 32 figs. Hardcover
0-387-95320-5
This rather unique book is a guided tour through number theory.
While most introductions to number theory provide a systematic
and exhaustive treatment of the subject, the authors have chosen
instead to illustrate the many varied subjects by associating
recent discoveries, interesting methods, and unsolved problems.
In particular, we read about combinatorial problems in number
theory, a branch of mathematics co-founded and popularized by
Paul Erdos. Janos Suranyis vast teaching experience successfully
complements Paul Erdos'ability to initiate new directions of
research by suggesting new problems and approaches. This book
will surely arouse the interest of the student and the teacher
alike.
Until his death in 1996, Professor Paul Erdos was one of the most
prolific mathematicians ever, publishing close to 1,500 papers.
While his papers contributed to almost every area of mathematics,
his main research interest was in the area of combinatorics,
graph theory, and number theory. He is most famous for proposing
problems to the mathematical community which were exquisitely
simple to understand yet difficult to solve. He was awarded
numerous prestigious prizes including the Frank Nelson Cole prize
of the AMS.
Professor Janos Suranyi is a leading personality in Hungary, not
just within the mathematical community, but also in the planning
and conducting of different educational projects which have led
to a new secondary school curriculum. His activity has been
recognized by, amongst others, the Middle Cross of the Hungarian
Decoration and the Erdos Award of the World Federation of
National Mathematical Competitions.
Contents: Divisibility, the Fundamental Theorem of Number Theory.-
Congruences.- Rational and irrational numbers. Approximation of
numbers by rationals. (Diophantine approximation.).- Geometric
methods in number theory.- Properties of prime numbers.-
Sequences of integers.- Diophantine problems.- Arithmetic
functions.- Hints to more difficult exercises.- Index.
Series: Undergraduate Texts in Mathematics.
The International Conference on Modern
Mathematics and the International Symposium on Differential
Geometry, in honor of Professor Su Buchin on the centenary of his
birth, were held in September 2001 at Fudan University, Shanghai,
China. Around 100 mathematicians from China, France, Japan,
Singapore and the United States participated.
The proceedings cover a broad spectrum of advanced topics in
mathematics, especially in differential geometry, such as some
problems of common interest in harmonic maps, submanifolds, the
Yang?Mills field and the geometric theory of solitons.
Readership: Researchers and graduate students in mathematics.
300pp (approx.) Pub. date: Scheduled Spring 2003
ISBN 981-238-188-0
Advanced Series in Mathematical Physics - Vol.
26
The theory of soliton equations and integrable systems has
developed rapidly during the last 30 years with numerous
applications in mechanics and physics. For a long time, books in
this field have not been written but the flood of papers was
overwhelming: many hundreds, maybe thousands of them. All this
output followed one single work by Gardner, Green, Kruskal, and
Mizura on the Korteweg-de Vries equation (KdV), which had seemed
to be merely an unassuming equation of mathematical physics
describing waves in shallow water.
This branch of science is attractive because it is one which
revives the interest in the basic principles of mathematics, a
beautiful formula.
Contents:
Readership: Applied mathematicians and
mathematical physicists.
Review of the first edition:
"There is a bibliography of 112 items. This book is
pedagogically written and is highly recommended for its detailed
description of the resolvent method for soliton equations."
Mathematical Reviews
350pp (approx.) Pub. date: Scheduled Spring 2003
ISBN 981-238-173-2