Loday, J.-L., CNRS et Universite Louis Pasteur, Strasbourg, France Frabetti, A., University of Lausanne, Switzerland Chapoton, F., Universite Pierre et Marie Curie, Paris, France Goichot, F., Universite de Valenciennes et du Hainaut Cambresis, Valencienneas, France
Dialgebras and Related Operads
2001. IV, 132 pp. Softcover
3-540-42194-7
The main object of study of these four papers is the notion of associative dialgebras which are algebras equipped with two associative operations satisfying some more relations of the associative type. This notion is studied from a) the homological point of view: construction of the (co)homology theory with trivial coefficients and general coefficients, b) the operadic point of view: determination of the dual operad, that is the dendriform dialgebras which are strongly related with the planar binary trees, c) the algebraic point of view: Hopf structure and Milnor-Moore type theorem.
Keywords: operads, planar trees, dialgebras, Koszul duality, Hopf algebras MathematicsSubject Classification : 05C05, 16A24, 16W30, 17Axx, 17D99, 18D50, 18D60 ,55Uxx
Contents: J.-L. Loday: Dialgebras.-
A. Frabetti: Dialgebras (co)homology with coefficients.-
F. Chapoton: Un endofoncteur de la categorie des operades.-
F. Goichot: Une theorie de Milnor-Moore pour les algebres de Leibniz.
Series: Lecture Notes in Mathematics. VOL. 1763
Cannas da Silva, A., Instituto Superior Tecnico, Lisboa, Portugal
Lectures on Symplectic Geometry
2001. XII, 217 pp. Softcover
3-540-42195-5
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text covers symplectomorphisms, local forms, contact manifold, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moments maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster.
Contents: Symplectic Manifolds.- Symplectic Forms. Symplectic Form on the Cotangent Bundle. Symplectomorphisms.- Lagrangian Submanifolds. Generating Functions. Recurrence. Local Forms.- Preparation for the Local Theory. Moser Theorems. Darbox-Moser-Winstein Theory. Weinstein Tubular Neighborhood Theorem. Contact Manifolds.- Contact Forms. Contact Dynamics. Compatible Almost Complex Structures.- Almost Complex Structures. Compatible Triples. Dolbeault Theory. Kaehler Manifolds.- Complex Manifolds. Kaehler Forms. Compact Kaehler Manifolds. Hamiltonian Mechanics.- Hamiltonian Vector Fields. Variational Principles. Legendre Transform. Moment Maps.- Actions. Hamiltonian Actions. Symplectic Reduction.- The Marsden-Weinstein-Meyer Theorem. Reduction. Moment Maps Revisited.- Moment Map in Gauge Theory. Existence and Uniqueness of Moment Maps. Convexity. Symplectic Toric Manifolds.- Classification of Symplectic Toric Manifolds. Delzant Construction. Duistermaat-Heckman Theorems.
Series: Lecture Notes in Mathematics. VOL. 1764
Hiriart-Urruty, J.-B., Universite Paul Sabatier,
Toulouse, France Lemarechal, C., INRIA, Montbonnot, France
Fundamentals of Convex Analysis
2001. X, 257 pp. Softcover
3-540-42205-6
This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306). It presents an introduction to the basic concepts in convex analysis and a study of convex minimization problems (with an emphasis on numerical algorithms). The "backbone" of both volumes was extracted, some material deleted which was deemed too advanced for an introduction, or too closely attached to numerical algorithms. Some exercises were included and finally the index has been considerably enriched.
The main motivation of the authors was to "light the entrance" of the monument Convex Analysis. This book is not a reference book to be kept on the shelf by experts who already know the building and can find their way through it; it is far more a book for the purpose of learning and teaching
Series: Grundlehren Text Editions
Everitt, B.S., Institute of Psychiatry, London, UK
Rabe-Hesketh, S., Institute of Psychiatry, London, UK
Analyzing Medical Data Using S-PLUS
2001. Approx. 495 pp. Hardcover
0-387-98862-9
Each chapter consists of basic statistical theory, simple examples of S-PLUS code, plus more complex examples of S-PLUS code, and exercises. All data sets are taken from genuine medical investigations and will be available on a web site. The examples in the book contain extensive graphical analysis to highlight one of the prime features of S-PLUS. Written with few details of S-PLUS and less technical descriptions, the book concentrates solely on medical data sets, demonstrating the flexibility of S-PLUS and its huge advantages, particularly for applied medical statisticians.
Contents: Introduction to Medical Statistics.-
Introduction to S-PLUS.-
Simple Data Description and Inference.-
Boxplots, Scatterplots, Histograms.-
Correlation, Simple Linear Regression and Simple Anova.-
Basic Epidemiology, Odds Ratio, Chi-squared Tests, Cross Tabulations.-
Simple Analyses of Longitudinal Data.-
Multiple Regression/ Robust Regression.-
Logistic Regression.-
Generalized Linear Model.-
More on the Analysis of Longitudinal Data Including Non-linear Models.-
Generalized Additive Models.-
Tree Regression Models.-
Survival Analysis.-
Time Series Analysis.-
Principal Components and Factor Analysis.-
Cluster Analysis.-
Discriminant Function and Canonical Correlation Analysis.-
Bootstrap/Jackknife.-
Spatial Statistics.
Series: Statistics for Biology and Health.
Bromley, D.A., Yale University, New Haven, CT, USA
A Century of Physics
2001. Approx. 130 pp. 117 figs., 67 in color. Hardcover
0-387-95247-0
In this amazing tour d'horizon, D. Allan Bromley uses the occasion of the centenary of the American Physical Society to reflect upon the growth of physics over the past 100 years, its fragmentation into numerous subdisciplines, the impact physics has had upon modern technology, and the re-emergence of the fundamental unity of the discipline in recent years. Hundreds of historical illustrations accompany the text. Bromley conveys much of the excitement and wonder that research in physics generated in the 20th century and asks what new things are in store in the next century. He covers such topics as relativity and quantum mechanics, the Manhattan project, superconductivity, transistors and the revolution brought about by solid-state electronics, protein folding, the uses of nuclear and atomic physics in biology and medicine, plate tectonics, the expansion of the universe and the Big Bang, and gravitational radiation. Bromley, the Sterling Professor of the Sciences and Dean of Yale University, served as Assistant to the President for Science and Technology Policy 1989-1993 and was president of the American Physical Society in 1997. One of the World's leading nuclear scientists, he was founder and director of Yale's nuclear structure laboratory and has received numerous medals and awards, including the National Medal of Science.
Contents: Form the Contents: Part 1: An Historical Overview, 1900-1949: What is Physics?- The Early 20th Century.- Activities in the Cambridge Cavendish Laboratory.- The Development of Quantum Mechanics.- 1932-Annus Mirabilis.- The Discovery of Nuclear Fission.- The Manhattan Project.- The MIT Radiation Laboratory.- The Merger of Natural Philosophy and Invention.- Physics in the 1930's.- The Immediate Post-War Period; Part 2: The Explosive Growth of Post-War Physics, 1950-1999.- Materials Science.- Superconductivity.- Bukckyballs and Nanotubes.- Surface Science.- Fluid Physics.- Self-Similarity.- Development of the Transistor.
Saranen, J., University of Oulu, Finland
Vainikko, G., Helsinki University of Technology, Espoo, Finland
Periodic Integral and Pseudodifferential Equations
with Numerical Approximation
2001. XI, 452 pp. Hardcover
3-540-41878-4
Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
Keywords: Periodic pseudodifferential equations, periodic integral equations, boundary integral equations, fully discrete methods, fast solvers
Series: Springer Monographs in Mathematics.