This book brings together two different branches of mathematics: the theory of Painlev and the theory of surfaces. Self-contained introductions to both these fields are presented. It is shown how some classical problems in surface theory can be solved using the modern theory of Painlev equations. In particular, an essential part of the book is devoted to Bonnet surfaces, i.e. to surfaces possessing families of isometries preserving the mean curvature function. A global classification of Bonnet surfaces is given using both ingredients of the theory of Painlev equations: the theory of isomonodromic deformation and the Painlev property. The book is illustrated by plots of surfaces. It is intended to be used by mathematicians and graduate students interested in differential geometry and Painlev equations. Researchers working in one of these areas can become familiar with another relevant branch of mathematics.
THE SUNDAY TIMES HISTORY BOOK OF THE YEAR 2017 'A beautiful and thoughtful exploration of the role of the horse in creating our world' James Rebanks 'Scintillating, exhilarating ... you have never read a book like it ... a new way of considering history' Observer The relationship between horses and humans is an ancient, profound and complex one. For millennia horses provided the strength and speed that humans lacked. How we travelled, farmed and fought was dictated by the needs of this extraordinary animal. And then, suddenly, in the 20th century the links were broken and the millions of horses that shared our existence almost vanished, eking out a marginal existence on race-tracks and pony clubs. Farewell to the Horse is an engaging, brilliantly written and moving discussion of what horses once meant to us. Cities, farmland, entire industries were once shaped as much by the needs of horses as humans. The intervention of horses was fundamental in countless historical events. They were sculpted, painted, cherished, admired; they were thrashed, abused and exposed to terrible danger. From the Roman Empire to the Napoleonic Empire every world-conqueror needed to be shown on a horse. Tolstoy once reckoned that he had cumulatively spent some nine years of his life on horseback. Ulrich Raulff's book, a bestseller in Germany, is a superb monument to the endlessly various creature who has so often shared and shaped our fate.
The innate immune system comprises the cells and mechanisms that are the first line of defence against infection by other organisms. This book provides a comprehensive synopsis of eye diseases, their immunological mechanisms and the role of the immune cells and mediators. Beginning with an introduction to the role of the innate immune system, the following chapters discuss the different types of immune cells in the eye and their role in the etiopathogenesis of various diseases including glaucoma and age-related macular degeneration. Edited by Manfred Zierhut, recognised expert from the University of Tuebingen Germany, this book is presented in an easy to read format, enabling practitioners to understand even the most sophisticated eye disorders from an immunological perspective. Key points Comprehensive synopsis of the role of the innate immune system in eye diseases Covers different types of immune cells Edited by internationally recognised specialist in Germany
A surprising, lively, and erudite history of horse and man, for readers of The Invention of Nature and The Soul of an Octopus. Horses and humans share an ancient, profoundly complex relationship. Once our most indispensable companions, horses were for millennia essential in helping build our cities, farms, and industries. But during the twentieth century, in an increasingly mechanized society, they began to disappear from human history. In this esoteric and rich tribute, award-winning historian Ulrich Raulff chronicles the dramatic story of this most spectacular creature, thoroughly examining how they’ve been muses and brothers in arms, neglected and sacrificed in war yet memorialized in paintings, sculpture, and novels—and ultimately marginalized on racetracks and in pony clubs. Elegiac and absorbing, Farewell to the Horse paints a stunning panorama of a world shaped by hooves, and the imprint left on humankind. “A beautiful and thoughtful exploration. . . . Farewell to the Horse is a grown-up, but also lyrical and creative, history book, and I very much enjoyed it.”— James Rebanks, author of the New York Times bestseller The Shepherd’s Life
The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.
This book brings together two different branches of mathematics: the theory of Painlev and the theory of surfaces. Self-contained introductions to both these fields are presented. It is shown how some classical problems in surface theory can be solved using the modern theory of Painlev equations. In particular, an essential part of the book is devoted to Bonnet surfaces, i.e. to surfaces possessing families of isometries preserving the mean curvature function. A global classification of Bonnet surfaces is given using both ingredients of the theory of Painlev equations: the theory of isomonodromic deformation and the Painlev property. The book is illustrated by plots of surfaces. It is intended to be used by mathematicians and graduate students interested in differential geometry and Painlev equations. Researchers working in one of these areas can become familiar with another relevant branch of mathematics.
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