Series: International Series of Numerical Mathematics, Vol. 153
.2012, XX, 476 p.
Hardcover version ISBN 978-3-0348-0512-4
Due: September 30, 2012
Considerably extended second edition of a well-written monograph on modern theory of PDEs
Presents theory and applications in a concise, clear, elegant and rigorous way
Useful also to engineers, physicists, biologists and other scientists interested in nonlinear differential models
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook.
The 2nd edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and PhD students and researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems.
Preface.- Preface to the 2nd edition.- 1 Preliminary general material.- Part I Steady-state problems.- 2 Pseudomonotone or weakly continuous mappings.- 3 Accretive mappings.- 4 Potential problems: smooth case.- 5 Nonsmooth problems; variational inequalities.- 6. Systems of equations: particular examples.- Part II Evolution problems.- 7 Special auxiliary tools.- 8 Evolution by pseudomonotone or weakly continuous mappings.- 9 Evolution governed by accretive mappings.- 10 Evolution governed by certain set-valued mappings.- 11 Doubly-nonlinear problems.- 12 Systems of equations: particular examples.- References.- Index.
Series: Algebra and Applications
2013, 2013, XV, 435 p. 5 illus.
Hardcover
ISBN 978-1-4471-4392-5
Due: September 30, 2012
Covers the connection between algebraic K-theory and Bokstedt, Hsiang and Madsen's topological cyclic homology, and gives a proof of the fact that the difference between the theories are 'locally constant'
Provides an inroad to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework
Contains the proof of the integral Goodwillie ICM 1990 conjecture and explains the mathematical prerequisites needed to do this
Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bokstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are elocally constantf. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of enearbyf calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
Algebraic K-theory.- Gamma-spaces and S-algebras.- Reductions.- Topological Hochschild Homology.- The Trace K ¨ THH.- Topological Cyclic Homology.- The Comparison of K-theory and TC.
Series: Fields Institute Monographs, Vol. 30
2013, 2013, XIV, 204 p.
Hardcover
ISBN 978-1-4614-5057-3
Due: October 31, 2012
Presents a self-contained development of selected topics in the theory of uniform spaces using pseudometrics rather than the more common approach via entourages
Contains exercises and research problems and can be used as supplementary text in graduate and advanced undergraduate courses
Details the history of core concepts and links to key references to help the reader understand connections to related areas and explore other sources?
Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures -- a need that became more critical when uniform measures recently reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations.
Uniform measures are functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in topological measure theory, probability theory, and abstract harmonic analysis. They offer a natural framework for results about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups.
This book can serve as a reference for the theory of uniform measures. It includes a self-contained development of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It also includes several new results, and presents diverse results from many sources organized in a logical whole. The content is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis, and contains a number of exercises with hints to solutions as well as several open problems with suggestions for further research.
Preface.- 1. Prerequisites.- 2. Uniformities and Topologies.- 3. Induce Uniform Structures.- 4. Uniform Structures on Semigroups.- 5. Some Notable Classes of Uniform Spaces.- 6. Measures on Complete Metric Spaces.- 7. Uniform Measures.- 8. Uniform Measures as Measures.- 9. Instances of Uniform Measures.- 10. Direct Product and Convolution.- 11. Free Union Measures.- 12. Approximation of Probability Distributions.- 13. Measurable Functionals.- Excercise Hints.- Index of terms.- Index of symbols.- Cited authors.- References.
Series: Applied Mathematical Sciences, Vol. 93
3rd ed. 2013, 2013, X, 417 p. 8 illus., 4 in color.
Hardcover
ISBN 978-1-4614-4941-6
Due: October 31, 2012
This book has become the standard reference book in the field of inverse scattering theory
The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scattering theory.
Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle Scattering.- Acoustic Waves in an Inhomogeneous Medium.- Electromagnetic Waves in an Inhomogeneous Medium.- The Inverse Medium Problem.-References.- Index
Series: Springer Texts in Statistics, Vol. 120
2013, 2013, XIV, 576 p. 34 illus.
Hardcover
ISBN 978-1-4614-4817-4
Due: October 31, 2012
.Valuable information for graduate students and as reference for researchers?
Contains R code throughout the text and in sample problems
Includes an appendix covering derivative notation and formulas
This book is for students and researchers who have had a first year graduate level mathematical statistics course. It covers classical likelihood, Bayesian, and permutation inference; an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large number of examples and problems.
An important goal has been to make the topics accessible to a wide audience, with little overt reliance on measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimation and testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology.
Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods.
Roles of Modeling in Statistical Inference.- Likelihood Construction and Estimation.- Likelihood-Based Tests and Confidence Regions.- Bayesian Inference.- Large Sample Theory: The Basics.- Large Sample Results for Likelihood-Based Methods.- M-Estimation (Estimating Equations).- Hypothesis Tests under Misspecification and Relaxed Assumptions?.- Monte Carlo Simulation Studies?.- Jackknife.- Bootstrap.- Permutation and Rank Tests.- Appendix: Derivative Notation and Formulas.- References.- Author Index.- Example Index?.- R-code Index.- Subject Index.