This book examines and systematises the theoretical dimensions of paradiplomacy - the role of subnational governments in international relations.Throughout the world, subnational governments play an active role in international relations by participating in international trade, cultural missions and diplomatic relations with foreign powers. These governments, including states in the USA and landers in Germany, can sometimes even challenge the official foreign policy of their nation...

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian inte...

Expanding on the concept of the authors’ previous book “Electroweak Processes in External Electromagnetic Fields,” this new book systematically describes the investigation methods for the effects of external active media, both strong electromagnetic fields and hot dense plasma, in quantum processes. Solving the solar neutrino puzzle in a unique experiment conducted with the help of the heavy-water detector at the Sudbery Neutrino Observatory, along with another neutrino experiments, brings...

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of fa...

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this bo...

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a g...

The 'Enigma of Gravity' gives an insight into the origin and nature of an architectural phenomenon of the universe, namel gravity, the book starts by asking the fundamental questions, what is light, matter, space, time and energy and using classical physics seeks the relationships between these fundamental physical phenomenon and the cause of gravity. Is is possible to travel faster than light? Can gravity, space and time be manipulated? What is the physical nature of Einstein's curved spa...

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solv...

Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory.Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific in...

This second edition of the successful textbook, Modern Physics: An Introductory Text, preserves the unique blend of readability, scientific rigour and authenticity that made its predecessor so indispensible a text for non-physics science majors. As in the first edition, it sets out to present 20th century physics in a form accessible and useful to students of the life sciences, medicine, agricultural, earth and environmental sciences. It is also valuable as a first reader and source text f...

Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathe...

Quantum mechanics is widely recognized as the basic law which governs all of nature, including all materials and devices. It has always been essential to the understanding of material properties, and as devices become smaller it is also essential for studying their behavior. Nevertheless, only a small fraction of graduate engineers and materials scientists take a course giving a systematic presentation of the subject. The courses for physics students tend to focus on the fundamentals and f...