Asterisque 296 (2004), xxviii+270 pages
Resume :
Cet ouvrage en deux volumes rassemble les actes du colloque Analyse complexe, systemes dynamiques, sommabilite des series divergentes et theories galoisiennes organise a Toulouse du 22 au 26 septembre 2003 a l'occasion du soixantieme anniversaire de Jean-Pierre Ramis.
En introduction, le premier volume propose deux textes de souvenirs et trois textes de synthese des travaux de J.-P. Ramis en analyse complexe, en theorie des equations differentielles lineaires et en theorie des equations differentielles non-lineaires. Suivent des textes essentiellement consacres aux theories galoisiennes, a l'arithmetique et a l'integrabilite: analogies entre theories differentielles et theories arithmetiques, equations aux q-differences classiques ou p-adiques, probleme de Riemann-Hilbert et renormalisation, b-fonctions, problemes de descente, modules de Krichever, lieu d'integrabilite, theorie de Drach et equation de Painleve VI.
Le deuxieme volume rassemble des textes plutot lies a des questions d'analyse et de geometrie: stabilite de Lyapounov, analyse asymptotique et dynamique pour des pinceaux de trajectoires, analyse WKB et geometrie de Stokes, equations de Painleve I et II, formes normales des singularites de type n?ud-col, tores invariants d'equations aux derivees partielles.
Mots clefs : Algebre differentielle; monodromie p-adique; equations differentielles, equations aux differences, equations aux q-differences dans le champ complexe; modules de Krichever; descente; pinceaux de feuilletages; courbure; D-modules holonomes; b-fonctions; integrabilite; geometrie non commutative (a la Connes); renormalisation; algebres de Hopf; theories de Galois; correspondance de Riemann-Hilbert; deformations isomonodromiques
Abstract:
Complex analysis, dynamical systems, summability of divergent series and Galois theories (I), Volume in honor of Jean-Pierre Ramis
These two bound volumes present the proceedings of the conference Complex Analysis, Dynamical Systems, Summability of Divergent Series and Galois Theories held in Toulouse from September to September 2003, on the occasion of J.-P. Ramis' birthday.
The first volume opens with two texts composed of recollections and three texts on J.-P. Ramis' works on Complex Analysis and Ordinary Differential Equations Theory, both linear and non-linear. This introduction is followed by papers concerned with Galois Theories, Arithmetic or Integrability: analogies between differential and arithmetical theories, q-difference equations, classical or p-adic, the Riemann-Hilbert problem and renormalisation, b-functions, descent problems, Krichever modules, the set of integrability, Drach theory and the VI Painleve equation.
The second volume contains papers dealing with analytical or geometrical aspects: Lyapunov stability, asymptotic and dynamical analysis for pencils of trajectories, monodromy in moduli spaces, WKB analysis and Stokes geometry, first and second Painleve equations, normal forms for saddle-node type singularities, invariant tori for PDEs.
Key words: Differential algebra, p-adic monodromy; differential equations, difference equations, q-difference equations in the complex domain; Krichever modules; descent; pencils of foliations; curvature; holonomic D-modules; b-functions; integrability; noncommutative geometry (in the sense of Connes); renormalization; Hopf algebras; Galois theories; Riemann-Hilbert correspondence; isomonodromic deformations
ISBN : 2-85629-167-8
Asterisque 297 (2004), xxii+232 pages
Resume :
Cet ouvrage en deux volumes rassemble les actes du colloque Analyse complexe, systemes dynamiques, sommabilite des series divergentes et theories galoisiennes organise a Toulouse du 22 au 26 septembre 2003 a l'occasion du soixantieme anniversaire de Jean-Pierre Ramis.
En introduction, le premier volume propose deux textes de souvenirs et trois textes de synthese des travaux de J.-P. Ramis en analyse complexe, en theorie des equations differentielles lineaires et en theorie des equations differentielles non-lineaires. Suivent des textes essentiellement consacres aux theories galoisiennes, a l'arithmetique et a l'integrabilite: analogies entre theories differentielles et theories arithmetiques, equations aux q-differences classiques ou p-adiques, probleme de Riemann-Hilbert et renormalisation, b-fonctions, problemes de descente, modules de Krichever, lieu d'integrabilite, theorie de Drach et equation de Painleve VI.
Le deuxieme volume rassemble des textes plutot lies a des questions d'analyse et de geometrie: stabilite de Lyapounov, analyse asymptotique et dynamique pour des pinceaux de trajectoires, analyse WKB et geometrie de Stokes, equations de Painleve I et II, formes normales des singularites de type n?ud-col, tores invariants d'equations aux derivees partielles.
Mots clefs : Feuilletages analytiques singuliers reels ou complexes, separabilite, enlacement, formes normales d'un n?ud-col; tores invariants associes a des EDP; connexions et equations differentielles dans le champ complexe, monodromie, asymptotique, analyse WKB, geometrie de Stokes, equations de Painleve ou de type Painleve, espaces de modules; applications symplectiques, stabilite de Lyapounov, diffusion d'Arnold
Abstract:
Complex analysis, dynamical systems, summability of divergent series and Galois theories (II), Volume in honnor of Jean-Pierre Ramis
These two bound volumes present the proceedings of the conference Complex Analysis, Dynamical Systems, Summability of Divergent Series and Galois Theories held in Toulouse from September to September 2003, on the occasion of J.-P. Ramis' birthday.
The first volume opens with two texts composed of recollections and three texts on J.-P. Ramis' works on Complex Analysis and Ordinary Differential Equations Theory, both linear and non-linear. This introduction is followed by papers concerned with Galois Theories, Arithmetic or Integrability: analogies between differential and arithmetical theories, q-difference equations, classical or p-adic, the Riemann-Hilbert problem and renormalisation, b-functions, descent problems, Krichever modules, the set of integrability, Drach theory and the VI Painleve equation.
The second volume contains papers dealing with analytical or geometrical aspects: Lyapunov stability, asymptotic and dynamical analysis for pencils of trajectories, monodromy in moduli spaces, WKB analysis and Stokes geometry, first and second Painleve equations, normal forms for saddle-node type singularities, invariant tori for PDEs.
Key words: Real or complex singular analytic foliations, separability, linking, normal form of a saddle-node; invariant tori associated with PDEs; connections and differential equations in the complex domain, monodromy, asymptotics, WKB analysis, Stokes geometry, Painleve or Painleve type equations, moduli spaces; symplectic maps, Lyapunov stability, Arnold diffusion
ISBN : 2-85629-168-6
Expected publication date is August 19, 2005
Description
Mathematicians are expected to publish their work: in journals, conference proceedings, and books. It is vital to advancing their careers. Later, some are asked to become editors. However, most mathematicians are trained to do mathematics, not to publish it.
But here, finally, for graduate students and researchers interested in publishing their work, Steven G. Krantz, the respected author of several "how-to" guides in mathematics, shares his experience as an author, editor, editorial board member, and independent publisher. This new volume is an informative, comprehensive guidebook to publishing mathematics. Krantz describes both the general setting of mathematical publishing and the specifics about all the various publishing situations mathematicians may encounter.
As with his other books, Krantz's style is engaging and frank. He gives advice on how to get your book published, how to get organized as an editor, what to do when things go wrong, and much more. He describes the people, the language (including a glossary), and the process of publishing both books and journals.
Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published more than 130 research articles and 45 books. He has worked as an editor of several book series, research journals, and for the Notices of the AMS. He is also the founder of the Journal of Geometric Analysis.
Other titles available from the AMS by Steven G. Krantz are How to Teach Mathematics, A Primer of Mathematical Writing, A Mathematician's Survival Guide, and Techniques of Problem Solving.
Contents
Introductory thoughts
Why publish?
What do I publish?
Different types of publishing
Publishing an article or paper
Journal publishing
How to write an article or paper
Publication of a book
Your magnum opus
How to write a book
Publishing personnel
The people in publishing
The role of book editors
The nitty gritty of editing
Parts of the publishing process
The manuscript
What happens to your book at the publishing house
Legal matters
Copyright and author rights
Details of the book contract
Closing thoughts
Putting the scholarly life into perspective
Copy editor's/proofreader's marks
Use of copy editor's marks
Specialized mathematics symbols
Alternative mathematical notations
\TEX, PostscriptR, AcrobatR, and related internet sites (plus tips on now to ftp)
The AMS consent to publish agreement
The AMS guidelines for journal editors
Glossary
References
Index
Details:
Publication Year: 2005
ISBN: 0-8218-3699-4
Paging: approximately 320 pp.
Binding: Softcover
Expected publication date is August 19, 2005
Description
Collected here are papers that were presented at or inspired by the DIMACS workshop, Algebraic Coding Theory and Information Theory (Rutgers University, Piscataway, NJ). Among the topics discussed are universal data compression, graph theoretical ideas in the construction of codes and lattices, decoding algorithms, and computation of capacity in various communications schemes. The book is suitable for graduate students and researchers interested in coding and information theory.
Contents
G. Caire, S. Shamai, A. Shokrollahi, and S. Verdu -- Fountain codes for lossless data compression
G. I. Shamir -- Applications of coding theory to universal lossless source coding performance bounds
K. W. Shum and I. F. Blake -- Expander graphs and codes
A. Barg and G. Zemor -- Multilevel expander codes
M. R. Sadeghi and D. Panario -- Low density parity check lattices based on construction $D^\prime$ and cycle-free Tanner graphs
J. S. Yedidia -- Sparse factor graph representations of Reed-Solomon and related codes
M. El-Khamy and R. J. McEliece -- Interpolation multiplicity assignment algorithms for algebraic soft-decision decoding of Reed-Solomon codes
S. Litsyn and A. Shpunt -- On the capacity of two-dimensional weight-constrained memories
G. Kramer and S. A. Savari -- On networks of two-way channels
R. G. Cavalcante, H. Lazari, J. d. D. Lima, and R. Palazzo, Jr. -- A new approach to the design of digital communication systems
Details:
Series: DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume: 68
Publication Year: 2005
ISBN: 0-8218-3626-9
Paging: 176 pp.
Binding: Hardcover
Expected publication date is July 14, 2005
Description
Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem of his famous lecture at the international congress in Paris. Thus, as the nineteenth century came to a close and the twentieth century began, Cantor's work was finally receiving its due and Hilbert had made one of Cantor's most important conjectures his number one problem. It was time for the second generation of Cantorians to emerge.
Foremost among this group were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory. He is recognized as the era's leading Cantorian.
Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets. This volume contains translations of these papers with accompanying introductory essays. They are highly accessible, historically significant works, important not only for set theory, but also for model theory, analysis and algebra.
This book is suitable for graduate students and researchers interested in set theory and the history of mathematics.
Also available from the AMS by Felix Hausdorff are the classic work, Grundzuge der Mengenlehre, and its English translation, Set Theory, as Volume 69 and Volume 119 in the AMS Chelsea Publishing series.
Contents
J. M. Plotkin -- Selected Hausdorff bibliography
J. Plotkin -- Introduction to "About a certain kind of ordered sets"
F. Hausdorff -- About a certain kind of ordered sets [H 1901b]
J. M. Plotkin -- Introduction to "The concept of power in set theory"
F. Hausdorff -- The concept of power in set theory [H 1904a]
J. Plotkin -- Introduction to "Investigations into order types, I, II, III"
F. Hausdorff -- Investigations into order types [H 1906b]
J. Plotkin -- Introduction to "Investigations into order types IV, V"
F. Hausdorff -- Investigations into order types [H 1907a]
J. Plotkin -- Introduction to "About dense order types"
F. Hausdorff -- About dense order types [H 1907b]
J. Plotkin -- Introduction to "The fundamentals of a theory of ordered sets"
F. Hausdorff -- The fundamentals of a theory of ordered sets [H 1908]
J. Plotkin -- Introduction to "Graduation by final behavior"
F. Hausdorff -- Graduation by final behavior [H 1909a]
F. Hausdorff -- Appendix. Sums of $\aleph_1$ sets [H 1936b]
Bibliography
Details:
Series: History of Mathematics,Volume: 25
Publication Year: 2005
ISBN: 0-8218-3788-5
Paging: 322 pp.
Binding: Softcover