Series: Astrophysics and Space Science Library, Vol. 313
2004, X, 191 p., Hardcover
ISBN: 1-4020-3039-8
About this book
The field of Order and Chaos had a remarkable expansion in the
last 50 years. The main reason was the use of computers, and the
development of new theoretical methods that we call now 'the
theory of chaos'. The author describes this fascinating period in
a relaxed and sometimes humorous autobiographical way. He relates
his interactions with many people in dynamical astronomy and he
quotes several anecdotes from these interactions. He refers also
to his experiences when he served in various international
positions, such as general secretary of the IAU and chairman of
the journal Astronomy and Astrophysics. In recent years the
theory of chaos has been extended to new areas, like relativity,
cosmology and quantum mechanics and it continues expanding in
almost all branches of physics. The book describes many important
ideas in this field in a simple way. It refers also to problems
of more general interest, like writing papers and giving lectures
and the interaction of authors and referees. Finally it gives
some useful prospects for the future of dynamical astronomy and
related fields.
Table of contents
1. Years of study.- 2. Thesis.- 3. First Trips Abroad.- 4.
Appointment as a Professor.- 5. The Third Integral.- 6. To the
United States (Through Moscow).- 7. Yale.- 8. Chandrasekhar.- 9.
Princeton - New York.- 10. First IAU Symposium in Dynamical
Astronomy.- 11. IAU Commission 33.- 12. Applications of the Third
Integral.- 12.1. Celestial Mechanics. 12.2. Galactic Dynamics. 12.3.
The Fermi-Pasta-Ulam Problem. 12.4. The Stormer Problem. 12.5.
Solitons. 12.6. Other Applications. 12.7. The Breakdown of the
Third Integral. 13. Resonance Overlap.- 14. The Junta Period and
the IAU.- 15. Second Sabbatical in the USA. The Density Wave
Theory.- 16. A Visit to Israel.- 17. First IAU regional meeting.-
18. Contacts in Italy.- 19. Service in the IAU.- 20. IAU
secretariat.- 21. Visits to the USSR.- 22. Topological methods in
Galactic Dynamics.- 23. The IAU General Assembly in Grenoble.- 24.
A Sabbatical at ESO.- 25. Astronomy and Astrophysics.- 26.
Travelling in Western Europe.- 27. Destruction of the Integrals.-
28. Systems of three Degrees of Freedom.- 29. Bifurcations.- 30.
The IAU General Assembly in Greece.- 31. Brouwer Prize.- 32.
Visits to ESO.- 33. Termination of Spirals and Bars.- 34. Further
Travel.- 35. Order and Chaos.- 36. Relativity and Cosmology.- 37.
Quantum Mechanics vs. Classical Mechanics.- 38. University of
Florida.- 39. Integrable Models.- 40. Escapes.- 41. Potentials
without Escapes.- 42. Chaos and Randomness.- 43. Homoclinic and
Heteroclinic Tangles.- 44. Honorary Degree from the University of
Chicago.- 45. Dynamical Spectra.- 46. Destruction of Islands of
Stability.- 47. Stickiness.- 48. Collaborators in Greece.- 49.
Collaborators Abroad.- 50. Our Faculty.- 51. NATO.- 52.
Motivation.- 53. Papers and Referees.- 54. Lectures.- 55. Academy
of Athens.- 56. Prospects for the Future
Series: Developments in Mathematics, Vol. 13
2005, XVI, 496 p., Hardcover
ISBN: 0-387-24231-7
About this book
This book, dedicated to Mizan Rahman, is made up of a collection
of articles on various aspects of q-series and special functions.
It also includes an article by Askey, Ismail, and Koelink on
Rahman’s mathematical contributions and how they influenced the
recent upsurge in the subject.
Table of contents
Preface.- Dedication.- Mizan Rahman, His Mathematics and Literary
Writings.- q-Bessel Functions.- a-Gaussian Polynomials.- On a
Generalized Gamma Convolution Related to the q-Calculus.-
Ramanujan and Cranks.- The Saalschutz Chain Reactions and
Multiple q-Series Transformations.- Painleve Equations and
Associated Polynomials.- Zeta Functions of Heisenberg Graphs over
Finite Rings.- q-Analogues of Some Multivariable Biorthogonal
Polynomials.- Multivariable Askey-Wilson Polynomials.- Continuous
Hahn Functions.- Series and Integrals.- Little q-Jacobi Functions.-
A Second Addition Formula for Continuous q-Ultraspherical
Polynomials.- A Bilateral Series Involving Basic Hypergeometric
Functions.- Hilbert Space Asymptotics for Orthogonal Polynomials.-
Generalizations of Jacobi’s Triple Product Identity.- Summable
Sums.- Askey-Wilson Functions and Quantum Groups.- Expansions in
q-Polynomials.- Strong Nonnegative Linearization of Orthogonal
Polynomials.- Remarks on Some Basic Hypergeometric Series.
2005, Approx. 400 p. 96 illus., Hardcover
ISBN: 0-387-24347-X
About this book
Graph Theory, Combinatorics and Algorithms: Interdisciplinary
Applications focuses on discrete mathematics and combinatorial
algorithms interacting with real world problems in computer
science, operations research, applied mathematics and engineering.
Its 11 chapters written by experts in their respective fields,
and covers a wide spectrum of high-interest problems across these
discipline domains. Among the contributing authors are Richard
Karp of UC Berkeley and Robert Tarjan of Princeton; both are at
the pinnacle of research scholarship in Graph Theory and
Combinatorics. The chapters from the contributing authors focus
on "real world" applications, all of which will be of
considerable interest across the areas of Operations Research,
Computer Science, Applied Mathematics, and Engineering. These
problems include Internet congestion control, high-speed
communication networks, multi-object auctions, resource
allocation, software testing, data structures, etc. In sum, this
is a book focused on major, contemporary problems, written by the
top research scholars in the field, using cutting-edge
mathematical and computational techniques.
Table of contents
Optimization Problems Related to Internet Congestion Control.-
Problems in Data Structures and Algorithms.- Algorithmic Graph
Theory and its Applications.- Decompositions and Forcing
Relations in Graphs and Other Combinatorial Structures.- The
Local Ratio Technique and its Application to Scheduling and
Resource Allocation Problems.- Domination Analysis of
Combinatorial Optimization Algorithms and Problems.- On-Multi-Object
Auctions and Matching Theory: Algorithmic Aspects.- Strategies
for Searching Graphs.- Recent Trends in Arc Routing.- Software
and Hardware Testing Using Combinatorial Covering Suites.-
Incidences.
2005, X, 160 p., Hardcover
ISBN: 3-540-23433-0
Due: March 2, 2005
About this textbook
The wavelets transform is a mathematical technique in the field
of image compression and digital signal analysis.
The author aims at providing the reader with a working
understanding of wavelets. In numerous examples, he discusses the
potentials and limits of the tool in industrial applications.
The book is completed by the author`s own Matlab codes.
It is very well suited for electrical engineering students and
engineers in industry.
Table of contents
Series: Springer Monographs in Mathematics,
2005, VIII, 222 p., Hardcover
ISBN: 3-540-24518-9
About this book
The fundamental question of characterizing continuity and
boundedness of Gaussian processes goes back to Kolmogorov. After
essential contributions by R. Dudley and X. Fernique, it was
solved by the author in 1985. This advance was followed by a
great improvement of our understanding of the boundedness of
other fundamental classes of processes (empirical processes,
infinitely divisible processes, etc.) This challenging body of
work has now been considerably simplified through the notion of
"generic chaining", a completely natural variation on
the ideas of Kolmogorov. The entirely new presentation adopted
here takes the reader from the first principles to the edge of
current knowledge, and to the wonderful open problems that remain
in this domain.