The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in Ch-Kl], is based on a double null foliation of spacetime instead of the mixed...

Across the centuries, the development and growth of mathematical concepts have been strongly stimulated by the needs of mechanics. Vector algebra was developed to describe the equilibrium of force systems and originated from Stevin's experiments (1548-1620). Vector analysis was then introduced to study velocity fields and force fields. Classical dynamics required the differential calculus developed by Newton (1687). Nevertheless, the concept of particle acceleration was the starting point for introducing a structured spacetime. Instantaneous velocity involved the set of particle positions in...

This book on the theory of three-dimensional spinors and their applications fills an important gap in the literature. It gives an introductory treatment of spinors.

From the reviews:

"Gathers much of what can be done with 3-D spinors in an easy-to-read, self-contained form designed for applications that will supplement many available spinor treatments. The book...should be appealing to graduate students and researchers in relativity and mathematical physics." --MATHEMATICAL REVIEWS

* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems

* All the necessary classical material is initially presented

* Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics

This new volume in the Poincare Seminar Series, describing recent developments at the interface between physics and biology, is directed towards a broad audience of physicists, biologists, and mathematicians. Both the theoretical and experimental aspects are covered, and particular care is devoted to the pedagogical nature of the presentations. The first survey article, by Jean-Francois Joanny and Jacques Prost, describes the theoretical advances made in the study of "active gels," with applications to liquid crystals and cell motility. Jasper van der Gucht and Cecile Sykes then report on...

* Develops new tools to efficiently describe different branches of physics within one mathematical framework

* Gives a clear geometric expression of the symmetry of physical laws

* Useful for researchers and graduate students interested in the many physical applications of bounded symmetric domains

* Will also benefit a wider audience of mathematicians, physicists, and graduate students working in relativity, geometry, and Lie theory

Parabolic equations in this framework have been largely ignored and are the primary focus of this work.; This book will appeal to mathematicians and physicists in PDEs who are interested in boundary and initial value problems, and may be used as a supplementary text by graduate students.

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

In this book we display the fundamental structure underlying classical electro dynamics, i. e., the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More over, they should be familiar with linear algebra and elementary analysis, in cluding vector...