2005, XIV, 308 p., Hardcover
ISBN: 0-387-23200-1
About this book
The theory of singular perturbations has evolved as a response to
the need to find approximate solutions (in an analytical form) to
complex problems. Typically, such problems are expressed in terms
of differential equations which contain at least one small
parameter, and they can arise in many fields: fluid mechanics,
particle physics, and combustion processes, to name but three.
Table of contents
Foreword.- Preface.- Mathematical Preliminaries.- Introductory
Applications.- Further Applications.- The Method of Multiple
Scales.- Some Worked Examples arising from Physical Problems.-
Appendix.- Answers and Hints.- References.- Subject Index.
2005, XX, 444 p., Hardcover
ISBN: 0-387-23195-1
About this book
Inverse Problems is a monograph which contains a self-contained
presentation of the theory of several major inverse problems and
the closely related results from the theory of ill-posed problems.
The book is aimed at a large audience which include graduate
students and researchers in mathematical, physical, and
engineering sciences and in the area of numerical analysis.
Table of contents
Introduction.- Methods of soliving ill-posed problems.- One-dimensional
inverse scattering and spectral problems.- Inverse obstacle
scattering.- Stability of the solution to 3D Inverse scattering
problems with fixed-energy data.- Non-uniqueness and uniqueness
results.- Inverse problems of potential theory and other inverse
source problems.- Non-overdetermined inverse problems.- Low-frequency
inversions.- Wave scattering by small bodies of arbitrary shapes.-
The Pompeiu problem.- Bilbliographical Notes.- References.- Index.
Series: Developments in Mathematics, Vol. 12
2005, X, 168 p., Hardcover
ISBN: 0-387-23533-7
About this book
The theme of this book are the interactions between group theory
and algebra/geometry/number theory, showing ubiquity and power of
the basic principle of Galois theory. The book presents recent
developments in a major line of work about covers of the
projective line (and other curves), their fields of definition
and parameter spaces, and associated questions about arithmetic
fundamental groups. This is intimately tied up with the Inverse
Problem of Galois Theory, and uses methods of algebraic geometry,
group theory and number theory.
Table of contents
Preface.- Supplementary Thoughts on Symplectic Groups.-
Automorphisms of the Modular Curve.- Reducing the Fontaine-Mazur
Conjecture to Group Theory.- Relating Two Genus 0 Problems of
John Thompson.- Relatively Projective Groups as Absolute Galois
Groups.- Invariants of Binary Forms.- Some Classical Views on the
Parameters of GT.- The Image of a Hurwitz Space under the Moduli
Map.- Very Simply Presentation: Variations on a Theme of Clifford.
Series: Grundlehren der mathematischen Wissenschaften, Vol.
249
2005, XII, 444 p. 5 illus., Hardcover
ISBN: 0-387-22026-7
About this textbook
From the reviews of the First Edition:
"This excellent book is based on several sets of lecture
notes written over a decade and has its origin in a one-semester
course given by the author at the ETH, Zurich, in the spring of
1970. The author's aim was to present some of the best features
of Markov processes and, in particular, of Brownian motion with a
minimum of prerequisites and technicalities. The reader who
becomes acquainted with the volume cannot but agree with the
reviewer that the author was very successful in accomplishing
this goalcThe volume is very useful for people who wish to
learn Markov processes but it seems to the reviewer that it is
also of great interest to specialists in this area who could
derive much stimulus from it. One can be convinced that it will
receive wide circulation." (Mathematical Reviews)
This new edition contains 9 new chapters which include new
exercises, references, and multiple corrections throughout the
original text.
Table of contents
Preface.- Part I: Markov Process. Basic Properties. Hunt Process.
Brownian Motion. Potential Developments. Bibliography.- Part II:
Generalities. Markov Chains: A Fireside Chat. Ray Processes.
Application to Markov Chains. Time Reversal. h-Transforms. Death
and Transfiguration: A Fireside Chat. Processes in Duality. The
Basis of Duality: A Fireside Chat. References. Index.
Series: Lecture Notes in Mathematics, Vol. 1861
2005, XIV, 177 p., Softcover
ISBN: 3-540-24064-0
About this book
This volume compiles three series of lectures on applications of
the theory of Hamiltonian systems, contributed by some of the
specialists in the field. The aim is to describe the state of the
art for some interesting problems, such as the Hamiltonian theory
for infinite-dimensional Hamiltonian systems, including KAM
theory, the recent extensions of the theory of adiabatic
invariants, and the phenomena related to stability over
exponentially long times of Nekhoroshev's theory. The books may
serve as an excellent basis for young researchers, who will find
here a complete and accurate exposition of recent original
results and many hints for further investigation.
Table of contents
A. Giorgilli: Preface.- G. Benettin: Physical Applications of
Nekhoroshev Theorem and Exponential Estimates.- J. Henrard: The
Adiabatic Invariant Theory and Applications.- S. Kuksin: Lectures
on Hamiltonian Methods in Nonlinear PDEs.
Series: Springer Monographs in Mathematics,
2005, XII, 539 p. 165 illus., Hardcover
ISBN: 3-540-23158-7
About this book
Convex Polyhedra is one of the classics in geometry. There simply
is no other book with so many of the aspects of the theory of 3-dimensional
convex polyhedra in a comparable way, and in anywhere near its
detail and completeness. It is the definitive source of the
classical field of convex polyhedra and contains the available
answers to the question of the data uniquely determining a convex
polyhedron. This question concerns all data pertinent to a
polyhedron, e.g. the lengths of edges, areas of faces, etc. This
vital and clearly written book includes the basics of convex
polyhedra and collects the most general existence theorems for
convex polyhedra that are proved by a new and unified method. It
is a wonderful source of ideas for students.
The English edition includes numerous comments as well as added
material and a comprehensive bibliography by V.A. Zalgaller to
bring the work up to date. Moreover, related papers by L.A.Shor
and Yu.A.Volkov have been added as supplements to this book.
Table of contents