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This volume presents a collection of twenty-five of Heinz König's recent and most influential works. Connecting to his book of 1997 Measure and Integration , the author has developed a consistent new version of measure theory over the past years. For the first time, his publications are collected here in one single volume. Key features include: - A first-time, original and entirely uniform treatment of abstract and topological measure theory - The introduction of the inner ¢ and outer ¢ premeasures and their extension to unique maximal measures - A simplification of the procedure formerly described in Chapter II of the author's previous book - The creation of new envelopes  for the initial set function (to replace the traditional Carathéodory outer measures), which lead to much simpler and more explicit treatment - The formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits, which allows to obtain the Kolmogorov type projective limit theorem for even huge domains far beyond the countably determined ones - The incorporation of non-sequential and of inner regular versions, which leads to much more comprehensive results - Significant applications to stochastic processes. Measure and Integration: Publications 1997-2011  will appeal to both researchers and advanced graduate students in the fields of measure and integration and probabilistic measure theory.

Mathematical physics --- differentiaalvergelijkingen

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The basic idea, simple and revolutionary at the same time, to replace the concept of a point particle with a one-dimensional string, has opened up a whole new field of research. Even today, four decades later, its multifaceted consequences are still not fully conceivable. Up to now string theory has offered a new way to view particles as different excitations of the same fundamental object. It has celebrated success in discovering the graviton in its spectrum, and it has naturally led scientists to posit space-times with more than four dimensions which in turn has triggered numerous interesting developments in fields as varied as condensed matter physics and pure mathematics. This book collects pedagogical lectures by leading experts in string theory, introducing the non-specialist reader to some of the newest developments in the field. The carefully selected topics are at the cutting edge of research in string theory and include new developments in topological strings, AdS/CFT dualities, as well as newly emerging subfields such as doubled field theory and holography in the hydrodynamic regime. The contributions to this book have been selected and arranged in such a way as to form a self-contained, graduate level textbook.

Mathematical physics --- wiskunde

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This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.

Geometry, Differential. --- Mathematical physics.

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Mathematical physics --- wiskunde

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Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s

Density functionals. --- Mathematical physics.