Series: Lecture Notes in Mathematics , Vol. 1910
2007, VIII, 332 p., Softcover
ISBN: 978-3-540-72052-2
About this book
This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) during the years 2004-2005 follows the long tradition of the previous volumes that reflect the general trends of the Theory and are a source of inspiration for research. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis, ranging from classical topics in the geometry of convex bodies, to inequalities involving volumes of such bodies or, more generally, log-concave measures, to the study of sections or projections of convex bodies. In many of the papers Probability Theory plays an important role; in some limit laws for measures associated with convex bodies, resembling Central Limit Theorems, are derive and in others probabilistic tools are used extensively. There are also papers on related subjects, including a survey on the behavior of the largest eigenvalue of random matrices and some topics in Number Theory.
Table of contents
Series: Lecture Notes in Mathematics , Vol. 1911
Subseries: Fondazione C.I.M.E., Firenze ,
2007, Approx. 365 p., 29 illus., Softcover
ISBN: 978-3-540-72186-4
About this book
The present Cime volume includes 4 lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan’s notes start with an extensive review of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts. Williams’ lectures describe the stability of multidimensional viscous shocks. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, and necessary and sufficient conditions for nonlinear stability.
Table of contents
P. Marcati: Preface.- A. Bressan: BV Solutions to Hyperbolic Systems by Vanishing Viscosity.- D. Serre: Discrete Shock Profiles: Existence and Stability.- M. Williams: Stability of Multidimensional Viscous Shocks.- K. Zumbrun: Planar Stability Criteria for Viscous Shock Waves of Systems with Real Viscosity.- A. Bressan: Tutorial on Center Manifold Theorem.
Series: Mathematics and Visualization
2007, Approx. 230 p., Hardcover
ISBN: 978-3-540-70822-3
About this book
Enabling insight into large and complex datasets is a prevalent theme in visualization research for which different approaches are pursued.
Topology-based methods are built on the idea of abstracting characteristic structures such as the topological skeleton from the data and to construct the visualizations accordingly. There are currently new demands for and renewed interest in topology-based visualization solutions. This book presents 13 peer-reviewed papers as written results from the 2005 workshop "Topology-Based Methods in Visualization" that was initiated to enable additional stimulation in this field. It contains a longer chapter dedicated to a survey of the state-of-the-art, as well as a great deal of original work by leading experts that has not been published before, spanning both theory and applications. It captures key concepts and novel ideas and serves as an overview of current trends in topology-based visualization research.
Table of contents
Series: Universitext
2007, Approx. 215 p., Softcover
ISBN: 978-0-387-71938-2
About this textbook
Introductory Probability is a pleasure to read and provides a fine answer to the question: How do you construct Brownian motion from scratch, given that you are a competent analyst?
There are at least two ways to develop probability theory. The more familiar path is to treat it as its own discipline, and work from intuitive examples such as coin flips and conundrums such as the Monty Hall problem. An alternative is to first develop measure theory and analysis, and then add interpretation. Bhattacharya and Waymire take the second path. To illustrate the authors' frame of reference, consider the two definitions they give of conditional expectation. The first is as a projection of L2 spaces. The authors rely on the reader to be familiar with Hilbert space operators and at a glance, the connection to probability may not be not apparent. Subsequently, there is a discusssion of Bayes's rule and other relevant probabilistic concepts that lead to a definition of conditional expectation as an adjustment of random outcomes from a finer to a coarser information set.
Table of contents
Random Maps, Distribution, and Mathematical Expectation.- Independence, Conditional Expectation.- Martingales and Stopping Times.- Classical Zero-One Laws, Laws of Large Numbers and Large Deviations.- Weak Convergence of Probability Measures.- Fourier Series, Fourier Transform, and Characteristic Functions.- Classical Central Limit Theorems.- Laplace Transforms and Tauberian Theorem.- Random Series of Independent Summands.- Kolmogorov's Extension Theorem and Brownian Motion.- Brownian Motion: The LIL and Some Fine-Scale Properties.- Skorokhod Embedding and Donsker's Invariance Principle.- A Historical Note on Brownian Motion.- References.- Index.- Symbol Index.
Series: Universitext
Originally published by Academic Press, 1979
2007, Approx. 460 p., Softcover
ISBN: 978-0-387-24527-0
About this textbook
Learning homological algebra is a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and, often, this involves yet another language: spectral sequences. This book gives a treatment of homological algebra which motivates the subject in terms of its origins in algebraic topology.
In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author also included material about homotopical algebra, alias K-theory, contrasting it with homological algebra.
Table of contents
Introduction * Hom and X * Projectives, Injectives, and Flats * Specific Rings * Extensions of Groups * Homology * Ext * Tor * Son of Specific Rings * The Return of Cohomolgy of Groups * Spectral Sequences * References * Index