Series: Lecture Notes in Mathematics , Vol. 1965
2009, Approx. 335 p., Softcover
ISBN: 978-1-84882-189-7
Due: January 2009
Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years.
Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings.
Carefully referenced and full of recent, incisive findings and interesting open-questions, this volume will prove useful for graduate students of mathematical analysis and will be a key-read for mathematicians with an interest in applications of geometric properties of Banach spaces, as well as specialists in nonlinear operator theory.
Series: Surveys and Tutorials in the Applied Mathematical Sciences , Vol. 5
2009, Approx. 200 p., Softcover
ISBN: 978-0-387-87682-5
Due: May 2009
The aim of the book is to give a user friendly tutorial of an interdisciplinary research topic (fronts in random media) to senior undergraduates and beginning graduate students with basic knowledge of partial differential equations (PDE) and probability.
The approach taken is semi-formal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigorous theorems with details found in references of the bibliography. As the topic concerns both differential equations and probability, yet probability is traditionally a technical subject with heavy measure theoretical treatment, the book strives to develop a simplistic approach so students can grasp the essentials of fronts and random media and their applications in a self-contained tutorial.
The scope of the book goes from wave properties of scalar deterministic PDEs (Burgers, Hamilton-Jacobi, reaction-diffusion etc) to the asymptotic analysis of their stochastic versions. The readers get to appreciate new random phenomena step by step.
Preface.- Fronts in Homogeneous Media.- Fronts in Periodic Media.- Fronts in Random Burgers Equations.- Stochastic Homogenization of Hamilton-Jacobi and Fronts.- KPP Fronts in Random Media.
Series: Theoretical and Mathematical Physics
2008, XVIII, 666 p., Hardcover
ISBN: 978-1-4020-8869-8
The second edition of this course-tested book provides a detailed and in-depth discussion of the foundations of quantum theory as well as its applications to various systems. The exposition is self-contained; in the first part the reader finds the mathematical background in chapters about functional analysis, operators on Hilbert spaces and their spectral theory, as well as operator sets and algebras. This material is used in the second part to a systematic explanation of the foundations, in particular, states and observables, properties of canonical variables, time evolution, symmetries and various axiomatic approaches. In the third part, specific physical systems and situations are discussed. Two chapters analyze Schrodinger operators and scattering, two others added in the second edition are devoted to new important topics, quantum waveguides and quantum graphs.
Some praise for the previous edition:
"I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone...." John R. Taylor, Professor of Physics and Presidential Teaching Scholar, University of Colorado at Boulder
Originally published in the series: Springer Tracts in Modern Physics
2009, XII, 282 p., Softcover
ISBN: 978-3-540-87850-6
Due: December 4, 2008
The book gives an overview of path integral quantization and stochastic quantization of classical mechanics and field theory. The non-Abelian gauge field, the gravitational field, and the path integral representation of quantum statistical mechanics and stochastic quantization are described.
Path Integral Representation of Quantum Mechanics.- Path Integral Representation of Quantum Field Theory.- Path Integral Quantization of Gauge Field Theory.- Path Integral Quantization of Gravitational Field.- Path Integral Representation of Quantum Statistical Mechanics.- Stochastic Quantization.- Appendix.- List of References