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This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments. This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.
Ayn Rand chose Leonard Peikoff to be her successor as the spokesman for Objectivism. And in this brilliantly reasoned, thought-provoking work we learn why, as he demonstrates how far America has been detoured from its original path and led down the same road that Germany followed to Nazism. Self-sacrifice, Oriental mysticism, racial "truth," the public good, doing one's duty—these are among the seductive catch-phrases that Leonard Peikoff dissects, examining the kind of philosophy they symbolize, the type of thinking that lured Germany to its doom and that he says is now prevalent in the United States. Here is a frightening look at where America may be heading, a clarion call for all who are concerned about preserving our right to individual freedom.
What if you woke up to a new life every day? A collision of universes leaves Abby living two lives at once - and sharing them with her own double. Two worlds. Two guys. Two selves. How will she stay in control?
Advances in microelectronic technology have made massively parallel computing a reality and triggered an outburst of research activity in parallel processing architectures and algorithms. Distributed memory multiprocessors - parallel computers that consist of microprocessors connected in a regular topology - are increasingly being used to solve large problems in many application areas. In order to use these computers for a specific application, existing algorithms need to be restructured for the architecture and new algorithms developed. The performance of a computation on a distributed memory multiprocessor is affected by the node and communication architecture, the interconnection network topology, the I/O subsystem, and the parallel algorithm and communication protocols. Each of these parametersis a complex problem, and solutions require an understanding of the interactions among them. This book is based on the papers presented at the NATO Advanced Study Institute held at Bilkent University, Turkey, in July 1991. The book is organized in five parts: Parallel computing structures and communication, Parallel numerical algorithms, Parallel programming, Fault tolerance, and Applications and algorithms.
This three-volume work presents a compendium of current and seminal papers on parallel/distributed processing offered at the 22nd International Conference on Parallel Processing, held August 16-20, 1993 in Chicago, Illinois. Topics include processor architectures; mapping algorithms to parallel systems, performance evaluations; fault diagnosis, recovery, and tolerance; cube networks; portable software; synchronization; compilers; hypercube computing; and image processing and graphics. Computer professionals in parallel processing, distributed systems, and software engineering will find this book essential to their complete computer reference library.
From the Americas to the European Union, Asia-Pacific and Africa, countries around the world are facing increased pressure to clarify the application of intellectual property exhaustion. This wide-ranging Research Handbook explores the questions that pose themselves as a result. Should exhaustion apply at the national, regional, or international level? Should parallel imports be considered lawful imports? Should copyright, patent, and trademark laws follow the same regime? Should countries attempt to harmonize their approaches? To what extent should living matters and self-replicating technologies be subject to the principle of exhaustion? To what extent have the rise of digital goods and the “Internet of things” redefined the concept of exhaustion in cyberspace? The Handbook offers insights to the challenges surrounding these questions and highlights how one answer does not fit all.