Series: Universitext
2012, 2012, XVIII, 465 p. 11 illus.
Softcover, ISBN 978-1-4471-2806-9
Due: February 29, 2012
Complements Adamsf Sobolev Spaces in comprising a complete presentation of functional spaces but combined with abstract convex analysis
Gathers together results from functional analysis that make it easier to understand the nature and properties of the functions occurring in these equations, as well as the constraints they must obey to qualify as solutions
Provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing
Linear and non-linear elliptic boundary problems are a fundamental subject in analysis and the spaces of weakly differentiable functions (also called Sobolev spaces) are an essential tool for analysing the regularity of its solutions.
The complete theory of Sobolev spaces is covered whilst also explaining how abstract convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. Other kinds of functional spaces are also included, useful for treating variational problems such as the minimal surface problem.
Almost every result comes with a complete and detailed proof. In some cases, more than one proof is provided in order to highlight different aspects of the result. A range of exercises of varying levels of difficulty concludes each chapter with hints to solutions for many of them.
It is hoped that this book will provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on Schwartz spaces.
Preliminaries on ellipticity.- Notions from Topology and Functional Analysis.- Sobolev Spaces and Embedding Theorems.- Traces of Functions on Sobolev Spaces.- Fractional Sobolev Spaces.- Elliptic PDE: Variational Techniques.- Distributions with measures as derivatives.- Korn's Inequality in Lp.- Appendix on Regularity.
Poincare Seminar 2010
Series: Progress in Mathematical Physics, Vol. 63
2012, 2012, Approx. 250 p.
lHardcover, ISBN 978-3-0348-0358-8
Due: February 2012
Presents an interdisciplinary view of the concept of Time
Contains a contribution of the 2010 Fields medalist Cedric Villani in English and French
Addressed to both physicists and mathematicians
This eleventh volume in the Poincare Seminar Series describes recent research related to the mathematical, physical, experimental, or philosophical facets of the fascinating concept of Time. It contains the following chapters: - Thibault Damour, "Time and relativity"; - Cedric Villani, "(Ir)reversibility and entropy"; - Cedric Villani, "(Ir)reversilite et entropie"; - Christopher Jaryzinski, "Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale"; - Christophe Salomon, "Time's measurement in the 21st century"; - Huw Price, "Time's arrow and Eddington's challenge"; - Jos Uffink and Giovanni Valente, "Time's arrow and Landford's theorem". This book should be of broad general interest to both physicists and mathematicians.
ime and relativity, Thibault Damour.- (Ir)reversibility and entropy, Cedric Villani.- (Ir)reversilite et entropie, Cedric Villani.- Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale, Christopher Jaryzinski.- Time's measurement in the 21st century, Christophe Salomon.- Timefs arrow and Eddingtonfs challenge, Huw Price.- Timefs arrow and Landfrodfs theorem, Jos Uffink and Giovanni Valente.
Series: Use R!
2012, 2012, IX, 182 p. 112 illus., 24 in color.
Softcover, ISBN 978-1-4614-2298-3
Due: March 31, 2012
Leaders in the field instruct using graphs and color images
Provides valuable information on graphical modelling with R
Including instructions to better understand relevant software programs
Graphical models in their modern form have been around since the late 1970s and appear today in many areas of the sciences. Along with the ongoing developments of graphical models, a number of different graphical modeling software programs have been written over the years. In recent years many of these software developments have taken place within the R community, either in the form of new packages or by providing an R interface to existing software. This book attempts to give the reader a gentle introduction to graphical modeling using R and the main features of some of these packages. In addition, the book provides examples of how more advanced aspects of graphical modeling can be represented and handled within R. Topics covered in the seven chapters include graphical models for contingency tables, Gaussian and mixed graphical models, Bayesian networks and modeling high dimensional data.
Graphs and Conditional Independence.- Log-Linear Models.- Bayesian Networks.- Gaussian Graphical Models.- Mixed Interaction Models.- Graphical Models for Complex Stochastic Systems.- High dimensional modelling.- References.- Index.
Series: Universitext
2012, 2012, Approx. 290 p. 31 illus.
Softcover, ISBN 978-3-642-28089-4
Due: May 31, 201
Self-contained introduction to three main areas of current research
Primarily intended for graduate students as well as researchers and useful as a self-study guide
Concatenates material that was placed so far in different books
Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory.
The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.
Preface.- I Ergodic Theory.- 1.Basic Notions and Examples.- 2.Further Topics.- II Entropy and Pressure.- 3.Metric Entropy and Topological Entropy.- 4.Thermodynamic Formalism. III Hyperbolic Dynamics.- 5.Basic Notions and Examples.- 6.Invariant Manifolds and Markov Partitions.- IV Dimension Theory.- 7.Basic Notions and Examples.- 8.Dimension Theory of Hyperbolic Dynamics.- A Notions from Measure Theory.- Bibliography.- Index.
Series: Developments in Mathematics, Vol. 26
2012, 2012, XII, 288 p. 6 illus.
Hardcover, ISBN 978-1-4614-3190-9
Due: May 31, 2012
Features a unified geometric approach based on the modulus method that is effectively applied to solving the Beltrami equation problems
Presents recent developments in the theory of Beltrami equations, especially on degenerate and alternating Beltrami equations
Discusses new concepts refining the analysis of problems related to the Beltrami equation, as well as applications of new research tools.
Authors are well-known specialists in geometric function theory and elliptic differential equations
The Beltrami Equation: A Geometric Approach will be particularly useful to many specialists in modern geometric analysis, quasiconformal mappings and extensions, beginning researchers, and graduate students with a yearfs background in complex variables. This book covers the state-of-the art in the ongoing study of the Beltrami equation, the classical equation that has been studied for more than 100 years. Along with its rich history, the Beltrami equation plays a significant role in geometry, analysis, and physics.
The most important feature of this work concerns the unified geometric approach taken based on the modulus method that can be effectively applied to solving many problems in mathematical physics. Beautiful examples illustrate the relationship between mappings with bounded oscillation and those with finite oscillations.
1. Introduction.- 2. Preliminaries.- 3. The Classical Beltrami Equation ||Ê|| < 1.- 4. The Degenerate Case.- 5. BMO- and FMO-Quasiconformal Mappings.- 6. Ring Q-Homeomorphisms at Boundary Points.- 7. Strong Ring Solutions of Beltrami Equations.- 8. On the Dirichlet Problem for Beltrami Equations.- 9. On the Beltrami Equations with Two Characteristics.- 10. Alternating Beltrami Equation.- References.- Index.