Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including non-abelian duality, non-commutative geometry, and the classification of simple $C*$-algebras. The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of $C*$-algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising. The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.
A modern treatment of this complex mathematical topic for students beginning research in operator algebras as well as mathematical physicists. Topics include the algebra of compact operators, sheaves, cohomology, the Brauer group and group actions, and the imprimivity theorem. The authors assume a knowledge of C*-algebras, the Gelfand-Naimark Theorem, continuous functional calculus, positivity, and the GNS- construction. Annotation copyrighted by Book News, Inc., Portland, OR
A modern treatment of this complex mathematical topic for students beginning research in operator algebras as well as mathematical physicists. Topics include the algebra of compact operators, sheaves, cohomology, the Brauer group and group actions, and the imprimivity theorem. The authors assume a knowledge of C*-algebras, the Gelfand-Naimark Theorem, continuous functional calculus, positivity, and the GNS- construction. Annotation copyrighted by Book News, Inc., Portland, OR
Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including non-abelian duality, non-commutative geometry, and the classification of simple $C*$-algebras. The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of $C*$-algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising. The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.
There are few more beautiful places than Scotland's winter mountains. But even when most of the snow has melted, isolated patches can linger well into summer and beyond. In The Vanishing Ice, Iain Cameron chronicles these remarkable and little-seen relics of the Ice Age, describing how they have fascinated travellers and writers for hundreds of years, and reflecting on the impact of climate change. Iain was nine years old when snow patches first captured his imagination, and they have been inextricably bound with his life ever since. He developed his expertise through correspondence (and close friendship) with research ecologist Dr Adam Watson, and is today Britain's foremost authority on this weather phenomenon. Iain takes us on a tour of Britain which includes the Scottish Highlands, the Southern Uplands, the Lake District and Snowdonia, seeking elusive patches of snow in wild and often inaccessible locations. His adventures include a perilous climb in the Cairngorms with comedian Ed Byrne, and glorious days spent out on the hills with Andrew Cotter and his very good dogs, Olive and Mabel. Based on sound scientific evidence and personal observations, accompanied by stunning photography and wrapped in Iain's shining passion for the British landscape, The Vanishing Ice is a eulogy to snow, the mountains and the great outdoors.
Cool BritanniaSnowier times in 1580-1930 than sinceGlobal warming and climate change have become headline news in recent years. Climate, however, has always changed. Thick ice covered most of Britain in the last Ice Age, and prehistoric man thrived during a warm climate after the ice melted. In a later warm period the Vikings farmed in Greenland, but then came the cold of the Little Ice Age for several centuries up to the mid 1800s. Climatologists in the 1900s noted some old writings that told of more snow in northern Europe then, including Britain. For this authoritative new book, the most experienced observer of British snow patches has combined forces with the keenest recent enthusiast who has stimulated many new voluntary observers. A factual review, it gives more evidence of a colder snowier Britain in the 1580s to early 1900s than since 1930. The most comprehensive historical account yet published for snow patches on British hills, it also collates for the lowlands much evidence that was previously unpublished or in obscure, little-known sources. The authors recount a few past extraordinary cases of severe snow affecting British folk, even in lowland southern England. Their verbatim quotations from early writers give a remarkably live impression, so that readers feel they are out in the cold with these pioneers of long ago. The modern scientific evidence is clear that the cool centuries described by the authors for Britain also affected the rest of Europe and indeed all other continents across the globe. Hence this book will be of interest to many readers far beyond Britannia.AuthorsAdam Watson, BSc, PhD, DSc, DUniv, raised in lowland Aberdeenshire, is a retired research ecologist aged 80. He began lifelong interests on winter snow in 1937, snow patches in 1938, the Cairngorms in 1939. A mountaineer and ski-mountaineer since boyhood, he has experienced Scotland, Iceland, Norway, Sweden, mainland Canada, Newfoundland, Baffin Island, Finland, Switzerland, Italy, Vancouver Island and Alaska. His main research was and is on population biology, behaviour and habitat of northern birds and mammals. In retirement he has contributed 16 scientific publications on snow patches since 1994. He is a Fellow of the Arctic Institute of North America, Centre for Ecology and Hydrology, Royal Meteorological Society, Royal Society of Edinburgh, and Society of Biology. Since 1954 he has been a member of the Scottish Mountaineering Club and since 1968 author of the Club's District Guide to the Cairngorms.Iain Cameron, 37, was brought up in lowland Renfrewshire, and works as an environmental, safety and health manager. Since 2007 he has been a co-author with Adam Watson on the annual snow-patch paper published by the Royal Meteorological Society in their scientific journal Weather. Although living in south-east England, he spends many weekends each summer and autumn in the Scottish Highlands, doing detailed fieldwork on snow patches. During preparation of this book, he inspected works by early authors at the British Library, and visited sites in lowland England where early writers reported extraordinary summer snow patches. Since 2008 he has stimulated and coordinated many new voluntary observers of snow patches across Britain. Through them, he contributed the first comprehensive note on snow patches in England and Wales in summer 2010, published in Weather.
This is your invitation to the front row. Spanning over seven decades and 300 shows, this beautiful book tells the story of the high fashion catwalk. Through this inspirational collection of fashion show invites and tales from fashion week, curator and fashion writer Iain R Webb opens a window into the world’s most exclusive fashion houses. Whether it’s dreamy romance at Givenchy, cutting-edge modernity at Alexander McQueen, floral drama at Valentino, vintage-inspired fun at Kenzo or heartfelt emotion at Yves Saint Laurent’s final haute couture show, the unique themes and styles that have graced the runway in the past 50 years are gloriously curated and described in The Fashion Show. From understated presentation to melodramatic performance, this stylish archive is your passport to the international fashion collections.
In The Endless Tide, Iain R. Thomson turns his attention to the Hebrides, and the collection of stories that permeate the area. Meeting a vast cast of characters, he ranges from personal anecdotes of country life to political and scientific issues, looking at agricultural politics and ecological debates. North Scotland's brutal Viking origins and the mysterious Pagan practices of its past are explored, yet The Endless Tide's reach extends far beyond this, touching on world events since pre-Biblical times. Varied and compelling, humorous and poetic, space and freedom pour from the pages. Mixing his own personal story with Scotland's history, Iain Thomson presents a myriad of ideas, snapshots and autobiographical accounts which conjure up the vital past and continuing force of the elusive Highland spirit. The Endless Tide is a sweeping, imaginative, provocative work which functions on a micro- and macro-level, examining the continual cycle of humanity, and Scotland's part in the process.
Through his unique blend of Scottish good humour, real-life experience, and funny stories of mishaps and misadventures, Iain M. MacLeod draws the reader into his vibrant life from childhood to the present, a life not defined by Cerebral Palsy, which he has had since the age of three. Racing from one adventure to the next on wheels galore, from his tricycle as a small child to his first wheelchair and first car, and many more adapted cars after that, Iain has travelled throughout his native Scotland as well as to America and Europe, all with the desire to go as fast as possible and accomplish everything he can.
Although overshadowed by his contemporaries Adam Smith and David Hume, the Scottish philosopher Adam Ferguson strongly influenced eighteenth-century currents of political thought. A major reassessment of this neglected figure, Adam Ferguson in the Scottish Enlightenment: The Roman Past and Europe’s Future sheds new light on Ferguson as a serious critic, rather than an advocate, of the Enlightenment belief in liberal progress. Unlike the philosophes who looked upon Europe’s growing prosperity and saw confirmation of a utopian future, Ferguson saw something else: a reminder of Rome’s lesson that egalitarian democracy could become a self-undermining path to dictatorship. Ferguson viewed the intrinsic power struggle between civil and military authorities as the central dilemma of modern constitutional governments. He believed that the key to understanding the forces that propel nations toward tyranny lay in analysis of ancient Roman history. It was the alliance between popular and militaristic factions within the Roman republic, Ferguson believed, which ultimately precipitated its downfall. Democratic forces, intended as a means of liberation from tyranny, could all too easily become the engine of political oppression—a fear that proved prescient when the French Revolution spawned the expansionist wars of Napoleon. As Iain McDaniel makes clear, Ferguson’s skepticism about the ability of constitutional states to weather pervasive conditions of warfare and emergency has particular relevance for twenty-first-century geopolitics. This revelatory study will resonate with debates over the troubling tendency of powerful democracies to curtail civil liberties and pursue imperial ambitions.
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