Global Lorentzian Geometry
Global Lorentzian Geometry

Author: John K. Beem

Publisher: Routledge

Published: 2017-09-29

Total Pages: 656

ISBN-13: 1351444719

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Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.

Global Lorentzian Geometry
Global Lorentzian Geometry

Author: John K. Beem

Publisher: Routledge

Published: 2017-09-29

Total Pages: 660

ISBN-13: 1351444700

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Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.

Global Optimization Using Interval Analysis
Global Optimization Using Interval Analysis

Author: Eldon Hansen

Publisher: CRC Press

Published: 2003-12-19

Total Pages: 528

ISBN-13: 9780203026922

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Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.

Analytical and Numerical Approaches to Mathematical Relativity
Analytical and Numerical Approaches to Mathematical Relativity

Author: Jörg Frauendiener

Publisher: Springer

Published: 2006-03-28

Total Pages: 288

ISBN-13: 354033484X

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General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

Hopf Algebras in Noncommutative Geometry and Physics
Hopf Algebras in Noncommutative Geometry and Physics

Author: Stefaan Caenepeel

Publisher: CRC Press

Published: 2019-05-07

Total Pages: 348

ISBN-13: 0429530072

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This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the

Handbook of Pseudo-Riemannian Geometry and Supersymmetry
Handbook of Pseudo-Riemannian Geometry and Supersymmetry

Author: Vicente Cortés

Publisher: European Mathematical Society

Published: 2010

Total Pages: 972

ISBN-13: 9783037190791

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The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kahler geometry or generalized geometry.

Semi-Riemannian Maps and Their Applications
Semi-Riemannian Maps and Their Applications

Author: Eduardo García-Río

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 203

ISBN-13: 9401729794

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A major flaw in semi-Riemannian geometry is a shortage of suitable types of maps between semi-Riemannian manifolds that will compare their geometric properties. Here, a class of such maps called semi-Riemannian maps is introduced. The main purpose of this book is to present results in semi-Riemannian geometry obtained by the existence of such a map between semi-Riemannian manifolds, as well as to encourage the reader to explore these maps. The first three chapters are devoted to the development of fundamental concepts and formulas in semi-Riemannian geometry which are used throughout the work. In Chapters 4 and 5 semi-Riemannian maps and such maps with respect to a semi-Riemannian foliation are studied. Chapter 6 studies the maps from a semi-Riemannian manifold to 1-dimensional semi- Euclidean space. In Chapter 7 some splitting theorems are obtained by using the existence of a semi-Riemannian map. Audience: This volume will be of interest to mathematicians and physicists whose work involves differential geometry, global analysis, or relativity and gravitation.

Products of Random Variables
Products of Random Variables

Author: Janos Galambos

Publisher: CRC Press

Published: 2004-07-20

Total Pages: 338

ISBN-13: 1482276631

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Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory. It uses entirely probabilistic arguments in actualizing the potential of the asymptotic theory of products of independent random variab

Multivalued Linear Operators
Multivalued Linear Operators

Author: Ronald Cross

Publisher: CRC Press

Published: 1998-07-09

Total Pages: 356

ISBN-13: 9780824702199

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Constructs a theoretical framework for the study of linear relations and provides underlying concepts, rules, formulae, theorems and techniques. The book compares the inversion, adjoints, completion and closure of various classes of linear operators. It highlights compact and precompact relations.