Periodic Integral and Pseudodifferential Equations with Numerical Approximation

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Leonard Susskind, James Lindesay

"Over the last decade the physics of black holes has been revolutionized by developments that grew out of Jacob Bekenstein's realization that black holes have entropy. This revolution has culminated in a remarkable principle called "the holographic principle," which is now a major focus of attention in gravitational research, quantum field theory and elementary particle physics. Leonard Susskind, one of the co-inventors of the holographic principle as well as one of the founders of string theory, develops and explains these concepts."--BOOK JACKET.

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Tudor Ratiu

The papers in this volume are an outgrowth of some of the lectures and informal discussions that took place during the workshop on the geometry of Hamiltonian systems, held at the MSRI in Berkeley in June of 1989. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, numerical simulations and dynamical systems in general. The articles are of differing lengths and scopes; some are research announcements while others are surveys of particularly active areas of interest where the results can only be found in scattered research articles and preprints. In- cluded in the book is A.T. Fomenko's survey of the classification of integrable systems.

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Dietmar Hildenbrand

<p>The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics.</p><p><p>This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications.</p><p>The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.

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Martial H. Hebert, Charles Thorpe, Anthony Stentz

Intelligent Unmanned Ground Vehicles describes the technology developed and the results obtained by the Carnegie Mellon Robotics Institute in the course of the DARPA Unmanned Ground Vehicle (UGV) project. The goal of this work was to equip off-road vehicles with computer-controlled, unmanned driving capabilities. The book describes contributions in the area of mobility for UGVs including: tools for assembling complex autonomous mobility systems; on-road and off-road navigation; sensing techniques; and route planning algorithms. In addition to basic mobility technology, the book covers a number of integrated systems demonstrated in the field in realistic scenarios. The approaches presented in this book can be applied to a wide range of mobile robotics applications, from automated passenger cars to planetary exploration, and construction and agricultural machines. Intelligent Unmanned Ground Vehicles shows the progress that was achieved during this program, from brittle specially-built robots operating under highly constrained conditions, to groups of modified commercial vehicles operating in tough environments. One measure of progress is how much of this technology is being used in other applications. For example, much of the work in road-following, architectures and obstacle detection has been the basis for the Automated Highway Systems (AHS) prototypes currently under development. AHS will lead to commercial prototypes within a few years. The cross-country technology is also being used in the development of planetary rovers with a projected launch date within a few years. The architectural tools built under this program have been used in numerous applications, from an automated harvester to an autonomous excavator. The results reported in this work provide tools for further research development leading to practical, reliable and economical mobile robots.