DOCUMENTS MATHEMATIQUES Tome : 18
Rational points on curves over finite fields
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Annee : 2020
Format : Papier
Langue de l'ouvrage :
Anglais
Class. Math. : 11G20 ; 14G15; 14G05
Nb. de pages : x+187
ISBN : 978-2-85629-923-4
ISSN : 1629-4939
In 1985, Jean-Pierre Serre gave a series of lectures at Harvard University on the number of points on curves over finite fields. Based on notes taken at that time by F. Q. Gouvea, the present revised and completed document provides an insightful introduction to this beautiful topic and to most of the ideas that have been developed in this area during the last 30 years.
Finite fields, curves, rational points; class field theory; asymptotic result; genus 2; genus 3; bounds; explicit formulas
Memoires de la Societe Mathematique de France, Volume: 166
2020; 94 pp; Softcover
MSC: Primary 35; 82;
Print ISBN: 978-2-85629-928-9
Product Code: SMFMEM/166
Expected publication date February 20, 2021
Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let VV denote an electric potential driven by a voltage drop between the conducting surfaces of the wire. The authors consider the operator Ah=?h2??+iVAh=?h2??+iV in the semi-classical limit h??0h??0 and obtain both the asymptotic behavior of the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. They extend here previous results obtained for potentials for which the set where the current (or ??V??V) is normal to the boundary is discrete, in contrast with the present case where VV is constant along the conducting surfaces.
Graduate students and research mathematicians.
This book represents material suitable for a two semester graduate course in analysis. Based on courses given by the author since 2007, it is targeted towards graduate students preparing for a research career in mathematics. After reviewing what a typical student would have learned in single variable and multivariable calculus courses, the first chapter presents familiar material from a mature mathematical perspective. The second chapter surveys measure theory and highlights the essential theorems that have now become ubiquitous in mathematics. The third chapter on Fourier transforms derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. The fourth chapter reviews complex analysis giving a synthetic, rigorous development of the calculus of residues and its applications to a wide array of problems. The final chapter is an introduction to algebraic topology and is included to show the symbiosis between algebra and analysis.
IMSC Lecture Notes Series/4
2020; 350 pp; Softcover, 9789386279842, Rs.700.00
Published: 8 January 2021
Publisher: International Press of Boston, Inc.
Paperback
230 pages
This volume presents lively and engaging articles from the lecturers and the participants of the 25th and 26th Gokova Geometry-Topology Conferences, held on the shores of Gokova Bay, Turkey, in May/June of 2018 and May/June of 2019.
The 25th and 26th Gokova Geometry-Topology Conferences were sponsored by the National Science Foundation, by the Turkish Mathematical Society, and by the European Research Council.
Dedicated by the editors to the memory of Sir Michael Atiyah.
This volume is part of the Gokova Geometry-Topology Conferences book series.
Includes state-of-the-art methods for estimating change in the presence of measurement error
It covers the entire process from data collection to analysis
It is multi-disciplinary with methods and examples from multiple fields such as: survey methodology, sociology, psychology, health, statistics, and official statistics
Longitudinal data is essential for understanding how the world around us changes. Most theories in the social sciences and elsewhere have a focus on change, be it of individuals, of countries, of organizations, or of systems, and this is reflected in the myriad of longitudinal data that are being collected using large panel surveys. This type of data collection has been made easier in the age of Big Data and with the rise of social media. Yet our measurements of the world are often imperfect, and longitudinal data is vulnerable to measurement errors which can lead to flawed and misleading conclusions.
Measurement Error in Longitudinal Data tackles the important issue of how to investigate change in the context of imperfect data. It compiles the latest advances in estimating change in the presence of measurement error from several fields and covers the entire process, from the best ways of collecting longitudinal data, to statistical models to estimate change under uncertainty, to examples of researchers applying these methods in the real world.
This book introduces the essential issues of longitudinal data collection, such as memory effects, panel conditioning (or mere measurement effects), the use of administrative data, and the collection of multi-mode longitudinal data. It also presents some of the most important models used in this area, including quasi-simplex models, latent growth models, latent Markov chains, and equivalence/DIF testing. Finally, the use of vignettes in the context of longitudinal data and estimation methods for multilevel models of change in the presence of measurement error are also discussed.
Hardback
Published: 18 March 2021 (Estimated)
464 Pages
234x156mm
ISBN: 9780198859987