Asterisque 312 (2007), xvi+210 pages
Resume :
Seminaire ARGOS sur les intersections de correspondances modulaires
Ce volume consiste des exposes faits dans le cadre du seminaire de geometrie arithmetique de Bonn en 2003/2004. Il donne une exposition systematique de la theorie des intersections de correspondances modulaires. Le but principal est la formule de Gross-Keating du nombre d'intersection de correspondances modulaires arithmetiques. Autres sujets traites sont le theoreme de Hurwitz sur l'intersection de correspondances modulaires sur le corps des nombres complexes, et la relation des nombres d'intersection arithmetiques aux coefficients de Fourier des series de Siegel-Eisenstein.
On a aussi inclus des rappels sur les groupes formels a un parametre et leurs endomorphismes, et sur les formes quadratiques sur l'anneau des entiers p-adiques.
Mots clefs : Correspondances modulaires, endomorphismes de groupes formels, formes quadratiques sur l'anneau des entiers p-adiques, series de Siegel-Eisenstein
Abstract:
This volume contains the written account of the Bonn seminar on arithmetic geometry 2003/2004. It gives a coherent exposition of the theory of intersections of modular correspondences. The focus of the seminar is the formula for the intersection number of arithmetic modular correspondences due to Gross and Keating. Other topics treated are Hurwitz's theorem on the intersection of modular correspondences over the field of complex numbers, and the relation of the arithmetic intersection numbers to Fourier coefficients of Siegel-Eisenstein series.
Also included is background material on one-dimensional formal groups and their endomorphisms, and on quadratic forms over the ring of p-adic integers.
Key words: Modular correspondences, endomorphisms of formal groups, quadratic forms over the ring of p-adic integers, Siegel-Eisenstein series
ISBN : 978-2-85629-231-0
Asterisque 310 (2006), viii+559 pages
Resume :
Complexes de Selmer
Ce livre construit de nouvelles fondations pour la theorie d'Iwasawa, basees sur une etude systematique d'invariants cohomologiques (vivant dans des categories derivees) pour les grosses representations galoisiennes. On developpe un nouveau formalisme de dualite dont on deduit des accouplements de Cassels-Tate generalises et des hauteurs p-adiques generalisees. Une des applications est un resultat de parite pour les groupes de Selmer attaches aux formes modulaires de Hilbert.
Mots clefs : Theorie d'Iwasawa, groupes de Selmer, grosses representations galoisiennes
Abstract:
This book builds new foundations of Iwasawa theory, based on a systematic study of cohomological invariants of big Galois representations in the framework of derived categories. A new duality formalism is developed, which leads to generalized Cassels-Tate pairings and generalized p-adic height pairings. One of the applications is a parity result for Selmer groups associated to Hilbert modular forms.
Key words: Iwasawa theory, Selmer groups, big Galois representations
ISBN : 978-2-85629-227-3
hardcover
978-0-8018-8714-7 (1 ctn qty)
December 2007 584 pp. 7 halftones, 75 line drawings
Description
Few mathematical structures are used and applied as frequently as matrices. Applied mathematicians, engineers, and physicists rely heavily on matrices when number-crunching. In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
Author Information
Raf Vandebril is a researcher in the Department of Computer Science at the Katholieke Universiteit Leuven in Belgium. Marc Van Barel is a professor of computer science at the Katholieke Universiteit Leuven in Belgium. Nicola Mastronardi is a researcher at the Istituto per le Applicazioni del Calcolo, sez. Bari, National Research Council of Italy.
ISBN: 978-0-470-04608-1
Hardcover
208 pages
August 2007
A valuable new edition of the trusted, practical guide to managing data in clinical trials
Regardless of size, type, or complexity, accurate results for any clinical trial are ultimately determined by the quality of the collected data. Management of Data in Clinical Trials, Second Edition explores data management and trial organization as the keys to developing an accurate and reliable clinical trial. With a focus on the traditional aspects of data collection as well as recent advances in technology, this new edition provides a complete and accessible guide to the management structure of a clinical trial, from planning and development to design and analysis. Practical approaches that result in the collection of complete and timely data are also provided.
While maintaining a comprehensive overview of the knowledge and tools that are essential for the organization of a modern clinical trial, the author has expanded the topical coverage in the Second Edition to reflect the possible uses of recent advances in technology in the data collection process. In addition, the Second Edition discusses the impact of international regulations governing the conduct of clinical trials and provides guidelines on ensuring compliance with national requirements.
Newly featured topics include:
The growing availability of "off-the-shelf" solutions for clinical trials
Potential models for collaboration in the conduct of clinical trials between academia and the pharmaceutical industry
The increasing use of the Internet in the collection of data and management of trials
Regulatory requirements worldwide and compliance with the ICH Good Clinical Practice (GCP) Guidelines
Development of Standard Operating Procedures for the conduct of clinical trials
Complete with chapter summaries that reinforce key points as well as over one hundred examples, Management of Data in Clinical Trials, Second Edition is an ideal resource for practitioners in the clinical research community who are involved in the development of clinical trials, including data managers, research associates, data coordinators, physicians, and statisticians. This book also serves as an excellent supplemental text for courses in clinical trials at both the undergraduate and graduate levels.
The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, Weiner, and Feynman.
The basic properties of each are proved, their similarities and differences are pointed out, and the reason for their existence and their uses are given. There is plentiful historical information.
The audience for the book is advanced undergraduate mathematics majors, graduate students, and faculty members. Even experienced faculty members are unlikely to be aware of all of the integrals in the Garden of Integrals and the book provides an opportunity to see them and appreciate the richness of the idea of integral. Professor Burke's clear and well-motivated exposition makes this book a joy to read.
The book can serve as a reference, as a supplement to course that include the theory of integration, and a source of exercises in analysis. There is no other book like it.
ISBN:978-0-88385-337-5
304 pp., Hardbound, 2007
Series:Dolciani Mathematical Expositions