Series: Classics in Mathematics
Originally published in: Ergebnisse der Mathematik und ihrer Grenzgebiete
Reprint of the 1st ed. Berlin Heidelberg New York 1987, 2008, X, 516 p., Softcover
ISBN: 978-3-540-74120-6
From the reviews:
"[...] an efficient reference book for many fundamental techniques of Riemannian geometry. [...] despite its length, the reader will have no difficulty in getting the feel of its contents and discovering excellent examples of all interaction of geometry with partial differential equations, topology, and Lie groups. Above all, the book provides a clear insight into the scope and diversity of problems posed by its title."
S.M. Salamon in MathSciNet 1988
"It seemed likely to anyone who read the previous book by the same author, namely "Manifolds all of whose geodesic are closed", that the present book would be one of the most important ever published on Riemannian geometry. This prophecy is indeed fulfilled."
T.J. Wilmore in Bulletin of the London Mathematical Society 1987
Table of contents
Introduction.- Basic Material.- Basic Material: Kahler Manifolds.- Relativity.- Riemannian Functionals.- Ricci Curvature as a Partial Differential Equation.- Einstein Manifolds and Topology.- Homogeneous Riemannian Manifolds.- Compact Homogeneous Kahler Manifolds.- Riemannian Submersions.- Holonomy Groups.- Kahler-Einstein Metrics and the Calabi Conjecture.- The Moduli Space of Einstein Structures.- Self-Duality.- Quaternion-Kahler-Manifolds.- A Report on the Non-Compact Case.- Generalizations of the Einstein Condition.- Appendix. Sobolev Spaces and Elliptic Operators.- Addendum.- Bibliography.- Notation Index.- Subject Index.
Series: Cornerstones
2008, XLVI, 1454 p.
ISBN: 978-0-8176-4533-5
About this set
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole, presenting the subject matter in a forward-looking way that takes into account its historical development.
Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry. The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with separate sections giving hints or complete solutions for most of the problems.
Series: Modern Birkhauser Classics
Softcover reprint of the 1997 ed., 2008, XX, 570 p. 17 illus., Softcover
ISBN: 978-0-8176-4754-4
About this book
An affordable new softcover edition of a bestselling text
Replete with exercises
Comprehensive bibliography contains over 530 references
For a broad audience of graduate students and researchers in mathematics, engineering, and optimal control
May be used as a textbook in a graduate course on optimal control theory
This book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton?Jacobi type and its interplay with Bellmanfs dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions.
The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.
Table of contents
Preface.- Basic notations.- Outline of the main ideas on a model problem.- Continuous viscosity solutions of Hamilton-Jacobi equations.- Optimal control problems with continuous value functions: unrestricted state space.- Optimal control problems with continuous value functions: restricted state space.- Discontinuous viscosity solutions and applications.- Approximation and perturbation problems.- Asymptotic problems.- Differential games.- Numerical solution of Dynamic Programming.- Non-linear H control by Pierpaolo Soravia.- Bibliography.- Index
Series: Applied Logic Series , Vol. 35
2008, Approx. 620 p., Hardcover
ISBN: 978-1-4020-6781-5
About this book
Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are provided for a combined logic to be sound and complete when the original component logics are known to be sound and complete.
The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). It also provides examples of potential applications in emergent fields like security protocols, quantum computing, networks and argumentation theory, besides discussing more classical applications like software specification, knowledge representation, computational linguistics and modular automated reasoning.
This monograph will be of interest to researchers and graduate students in mathematical logic, theory of computation and philosophical logic with no previous knowledge of the subject of combining and decomposing logics, but with a working knowledge of first-order logic. The book will also be relevant for people involved in research projects where logic is used as a tool and the need for working with several logics at the same time is mandatory (for instance, temporal, epistemic and probabilistic logics).
Table of contents
Preface.- 1. Introductory Overview.- 2. Splicing Logics: Syntactic Fibring.- 3. Splicing Logics: Semantic Fibring.- 4. Heterogenous Fibring.- 5. Fibring Non-Truth Functional Logics.- 6. Fibring First-Order Logics.- 7. Fibring Higher-Order Logics.- 8. Modulated Fibring.- 9. Splitting Logics.- 10. New Trends: Network Fibring.- 11. Summing-up and Outlook.- Bibliography.- Subject Index.- Table of Symbols.- List of Figures.
Series: Modern Birkhauser Classics
Softcover reprint of the 1996 ed., 2008, XIV, 258 p. 28 illus., Softcover
ISBN: 978-0-8176-4758-2
About this book
An affordable new softcover edition of a bestselling text
Collects important new results in the field of systems and control
Important issues concerning large-signal robustness and performance are raised for the first time
For graduate students, researchers, and practitioners in nonlinear control and design engineering
This book presents advances in the theory and design of robust nonlinear control systems. In the first part of the book, the authors provide a unified framework for state-space and Lyapunov techniques by combining concepts from set-valued analysis, Lyapunov stability theory, and game theory. Within this unified framework, the authors then develop a variety of control design methods suitable for systems described by low-order nonlinear ordinary differential equations. Emphasis is placed on global controller designs, that is, designs for the entire region of model validity. Because linear theory deals well with local system behavior (except for critical cases in which Jacobian linearization fails), the authors focus on achieving robustness and performance for large deviations from a given operation condition.
The purpose of the book is to summarize Lyapunov design techniques for nonlinear systems and to raise important issues concerning large-signal robustness and performance. The authors have been the first to address some of these issues, and they report their findings in this text. For example, they identify two potential sources of excessive control effort in Lyapunov design techniques and show how such effort can be greatly reduced.
The researcher who wishes to enter the field of robust nonlinear control could use this book as a source of new research topics. For those already active in the field, the book may serve as a reference to a recent body of significant work. Finally, the design engineer faced with a nonlinear control problem will benefit from the techniques presented here.
Table of contents
Introduction.- Set- Valued Maps.- Robust Control Lyapunov Functions.- Inverse Optimality.- Robust Backstepping.- Measurement Disturbances.- Dynamic Partial State Feedback.- Robust Nonlinear PI Control.- Local K-Continuity in metric spaces.- Bibliography.- Index