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The Quantization of Gravity
A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point...
Regularity of Free Boundaries in Obstacle-Type Problems
The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.
The Einstein Equations and the Large Scale Behavior of Gravitational Fields
The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
The Principle of the Fermionic Projector
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionicprojector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differen...
Extrinsic Geometric Flows
Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give an extensive introduction to a few of the most prominent extrinsic flows, namely, the curve shortening flow, the mean curvature flow, the Gauß curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type. The authors highlight techniques and behaviors that frequently arise in the study of these (and other) flows. To illustrate the broad applicability of the techniques developed, they also consider general classes of fully nonlinear curvature flows. The bo...
Dictionary of American Family Names
Where did your surname come from? Do you know how many people in the United States share it? What does it tell you about your lineage? From the editor of the highly acclaimed Dictionary of Surnames comes the most extensive compilation of surnames in America. The result of 10 years of research and 30 consulting editors, this massive undertaking documents 70,000 surnames of Americans across the country. A reference source like no other, it surveys each surname giving its meaning, nationality, alternate spellings, common forenames associated with it, and the frequency of each surname and forename. The Dictionary of American Family Names is a fascinating journey throughout the multicultural United States, offering a detailed look at the meaning and frequency of surnames throughout the country. For students studying family genealogy, others interested in finding out more about their own lineage, or lexicographers, the Dictionary is an ideal place to begin research.
Mac OS X For Unix Geeks
If you're a developer or system administrator lured to Mac OS X because of its Unix roots, you'll quickly discover that performing Unix tasks on a Mac is different than what you're accustomed to. Mac OS X for Unix Geeks serves as a bridge between Apple's Darwin OS and the more traditional Unix systems. This clear, concise guide gives you a tour of Mac OS X's Unix shell in both Leopard and Tiger, and helps you find the facilities that replace or correspond to standard Unix utilities. You'll learn how to perform common Unix tasks in Mac OS X, such as using Directory Services instead of the standard Unix /etc/passwd and /etc/group, and you'll be able to compile code, link to libraries, and port...
National Union Catalog
Includes entries for maps and atlases.
Mac OS X Tiger for Unix Geeks
If you're one of the many Unix developers drawn to Mac OS X for its Unix core, you'll find yourself in surprisingly unfamiliar territory. Unix and Mac OS X are kissing cousins, but there are enough pitfalls and minefields in going from one to another that even a Unix guru can stumble, and most guides to Mac OS X are written for Mac aficionados. For a Unix developer, approaching Tiger from the Mac side is a bit like learning Russian by reading the Russian side of a Russian-English dictionary. Fortunately, O'Reilly has been the Unix authority for over 25 years, and in Mac OS X Tiger for Unix Geeks, that depth of understanding shows.This is the book for Mac command-line fans. Completely revised...
