Series: Universitext
2015, X, 314 p.
Softcover
ISBN 978-3-319-16052-8
Due: June 14, 2015
Prefers ideas to calculations
Explains the ideas without parsimony of words
Based on 35 years of teaching at Paris University
Blends mathematics skilfully with didactical and historical considerations
Volume III sets out classical Cauchy theory. It is much more geared towards its innumerable applications than towards a more or less complete theory of analytic functions. Cauchy-type curvilinear integrals are then shown to generalize to any number of real variables (differential forms, Stokes-type formulas). The fundamentals of the theory of manifolds are then presented, mainly to provide the reader with a "canonical'' language and with some important theorems (change of variables in integration, differential equations). A final chapter shows how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject that is rarely addressed in the general literature though it only requires elementary techniques.
Besides the Lebesgue integral, Volume IV will set out a piece of specialized mathematics towards which the entire content of the previous volumes will converge: Jacobi, Riemann, Dedekind series and infinite products, elliptic functions, classical theory of modular functions and its modern version using the structure of the Lie algebra of SL(2,R).
Content Level ≫ Graduate
Keywords ≫ Cauchy theory - Riemann surface of an algebraic function - complex Mellin and Fourier transforms - differential forms and Stokes formula - differential manifolds
Related subjects ≫ Analysis
Series: Progress in Mathematical Physics, Vol. 68
2015, Approx. 180 p.
Hardcover
ISBN 978-3-319-14315-6
Due: September 7, 2015
Renowned scientists, including a 2012 Physics Nobel laureate, present their view on Bohr’s foundational contributions and his legacy in present-day quantum physics
Relates Bohr’s seminal work both to that of Einstein, Schrodinger, Bell and Feynman and to that of Kant
Based on educational lectures given at the Institut Henri Poincare in Paris for the centennial of Bohr's atom model
This fourteenth volume in the Poincare Seminar Series is devoted to Niels Bohr, his foundational contributions to understanding atomic structure and quantum theory and their continuing importance today. This book contains the following chapters: - Tomas Bohr, Keeping Things Open; - Olivier Darrigol, Bohr's Trilogy of 1913; -John Heilbron, The Mind that Created the Bohr Atom; - Serge Haroche & Jean-Michel Raimond, Bohr's Legacy in Cavity QED; - Alain Aspect, From Einstein, Bohr, Schrodinger to Bell and Feynman: a New Quantum Revolution?; - Antoine Browaeys, Interacting Cold Rydberg Atoms: A Toy Many-Body System; - Michel Bitbol & Stefano Osnaghi, Bohr´s Complementarity and Kant´s Epistemology. Dating from their origin in lectures to a broad scientific audience these seven chapters are of high educational value.
This volume is of general interest to physicists, mathematicians and historians.
?Foreword.- Keeping Things Open, Tomas Bohr.- Bohr's Trilogy of 1913, Olivier Darrigol.- The Mind that Created the Bohr atom, John Heilbron.- Bohr's Legacy in Cavity QED, Serge Haroche & Jean-Michel Raimond.- From Einstein, Bohr, Schrodinger to Bell and Feynman: A New Quantum Revolution?, Alain Aspect.- Interacting Cold Rydberg Atoms: A Toy Many-Body System, Antoine Browaeys.- Bohr's Complementarity and Kant's Epistemology, Michel Bitbol & Stefano Osnaghi.
Series: Progress in Probability
2015, Approx. 300 p.
Hardcover
ISBN 978-3-0348-0908-5
Due: August 14, 2015
This book presents an up-to-date picture of research on stochastic analysis and highlights recent developments in the form of lecture notes contributed by leading international experts. The topics include the influence of stochastic perturbations on differential and partial differential equations, the modeling of stochastic perturbations by Levy processes and the numerical aspects of the approximation of such equations, stochastic integration and stochastic calculus in abstract function spaces, stochastic partial differential equations arising from measure-valued diffusions, and reflection problems for multidimensional Brownian motion.
Based on a course given at the Ecole Polytechnique Federale’s Bernoulli Center in Lausanne, Switzerland, from January to June 2012, these lecture notes offer a valuable resource not only for specialists, but also for other researchers and PhD students in the fields of probability, analysis and mathematical physics.
Preface.- List of participants.- S. Albeverio and S. Mazzucchi: An introduction to infinite dimensional oscillatory and probabilistic integrals.- M. Arnaudon and A.B. Cruzeiro: Stochastic Lagrangian flows and the Navier-Stokes equations.- V. Bally: Integration by parts formulas and regularity of probability laws.- V. Barbu: Stochastic porous media equations.- H. Bessaih: Stochastic incompressible Euler equations in a two-dimensional domain.- Z. Brzezniak and M.Ondrejat: Stochastic geometric wave equations.- K. Burdzy: Reflections on reflections.- F. Flandoli: A stochastic view over the open problem of well-posed ness for the 3D Navier-Stokes equations.- A. Kohatsu-Higa: A short course on weak approximations for Levy driven SDE's.- C. Mueller: Stochastic PDE from the point of view of particle systems and duality.- J. van Neerven, M. Veraar and L. Weis: Stochastic integration in Banach spaces ? a survey.- S. Peszat: Stochastic partial differential equations with Levy noise (a few aspects).- J.C. Zambrini: The research program of stochastic deformation (with a view toward geometric mechanics).
Series: Springer Monographs in Mathematics
2015, Approx. 685 p.
Hardcover
ISBN 978-3-319-16359-8
Due: June 14, 2015
Provides the first comprehensive treatment of valuation theory for finite-dimensional division algebras
Showcases an innovative new approach to valuation theory via associated graded structures
Includes various division algebra constructions with special features, like noncrossed products and indecomposable algebras
This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of noncrossed products and Platonov's solution of the Tannaka-Artin problem.
This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased.
The intended audience consists of graduate students and research mathematicians.
Valuations on Division Rings.- Graded Algebra.- Value Functions.- Existence and Fundamental Properties of Gauges.- Graded and Valued Field Extensions.- Brauer Groups.- Total Ramifcation.- Division Algebras over Henselian Fields.- Subfields and Splitting Fields of Division Algebras.- Indecomposable Division Algebras.- Computation of SK1(D).- The Essential Dimension of Central Simple Algebras.
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
978-1-46-658484-6
March 9th 2015
Available for pre-order
Since the publication of the first edition over 30 years ago, the literature related to Pareto distributions has flourished to encompass computer-based inference methods. Pareto Distributions, Second Edition provides broad, up-to-date coverage of the Pareto model and its extensions. This edition expands several chapters to accommodate recent results and reflect the increased use of more computer-intensive inference procedures.
New material on multivariate inequality
Recent ways of handling the problems of inference for Pareto models and their generalizations and extensions
New discussions of bivariate and multivariate income and survival models
This book continues to provide researchers with a useful resource for understanding the statistical aspects of Pareto and Pareto-like distributions. It covers income models and properties of Pareto distributions, measures of inequality for studying income distributions, inference procedures for Pareto distributions, and various multivariate Pareto distributions existing in the literature.