Download or read book Autonomous Categories written by M. Barr and published by Springer. This book was released on 2006-11-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Combinatorics written by W. D. Wallis and published by Springer. This book was released on 2006-11-15 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Invariant Theory written by T.A. Springer and published by Springer. This book was released on 2006-11-14 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lie Algebras and Lie Groups written by Jean-Pierre Serre and published by Springer. This book was released on 2009-02-07 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I.I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, . This part has been written with the help of F. Raggi and J. Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x, y) under this map by [x, y) then the condition becomes for all x e k. [x, x)=0 2). (lx, II], z]+ny, z), x) + ([z, xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/, x).

Download or read book Regularly Varying Functions written by E. Seneta and published by Springer. This book was released on 2006-11-14 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Axiom of Choice written by Horst Herrlich and published by Springer. This book was released on 2006-07-21 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. It is shunned by some, used indiscriminately by others. This treatise shows paradigmatically that disasters happen without AC and they happen with AC. Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.

Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment 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. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Download or read book Simple Singularities and Simple Algebraic Groups written by P. Slodowy and published by Springer. This book was released on 2006-11-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spherical Harmonics written by Claus Müller and published by Springer. This book was released on 2006-11-14 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer. This book was released on 2011-03-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Download or read book Algebraic Spaces written by Donald Knutson and published by Springer. This book was released on 2006-11-15 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reversible Systems written by Mikhail B. Sevryuk and published by Springer. This book was released on 2006-11-14 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Theory of Lie Superalgebras written by M. Scheunert and published by Springer. This book was released on 2006-11-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sequences Discrepancies and Applications written by Michael Drmota and published by Springer. This book was released on 2006-11-14 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.

Download or read book Diophantine Approximation written by W.M. Schmidt and published by Springer. This book was released on 2009-02-05 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

Download or read book Orlicz Spaces and Modular Spaces written by J. Musielak and published by Springer. This book was released on 2006-11-14 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Moment Weight Inequality and the Hilbert Mumford Criterion written by Valentina Georgoulas and published by Springer Nature. This book was released on 2022-01-01 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to geometric invariant theory from a differential geometric viewpoint. It is inspired by certain infinite-dimensional analogues of geometric invariant theory that arise naturally in several different areas of geometry. The central ingredients are the moment-weight inequality relating the Mumford numerical invariants to the norm of the moment map, the negative gradient flow of the moment map squared, and the Kempf--Ness function. The exposition is essentially self-contained, except for an appeal to the Lojasiewicz gradient inequality. A broad variety of examples illustrate the theory, and five appendices cover essential topics that go beyond the basic concepts of differential geometry. The comprehensive bibliography will be a valuable resource for researchers. The book is addressed to graduate students and researchers interested in geometric invariant theory and related subjects. It will be easily accessible to readers with a basic understanding of differential geometry and does not require any knowledge of algebraic geometry.