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This book summarizes the history and present status and applications of Josephson junctions. These devices are leading elements in superconducting electronics and provide state-of-the-art performance in detection of small magnetic fields and currents, in several digital computing methods, and in medical diagnostic devices and now provide voltage standards used worldwide. Astronomical infrared (IR) telescopes, including the South Pole Telescope, use these junctions in combinations called superconducting quantum interference devices (SQUIDs).

This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images.

At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16^th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century).

In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you...