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Blaschke rolling theorem in its original form dealt with the problem of finding sufficient conditions for a ball [italic]D1 to roll freely inside a compact convex set [italic]D2 with a non-empty interior. The paper is divided into two parts. Part I is primarily concerned with producing conditions of a local nature sufficient to ensure an arbitrary open convex set [italic]B1 is a subset of another arbitrary open convex set [italic]B2. Part I sets up the machinery for Part II, where necessary and sufficient conditions of a local nature are found for the general free rolling problem.
In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Newmann founded the field of continuous geometry. For students and researchers interested in ring theory or projective geometries, von Neumann discusses his findings and their applications.
This comprehensive volume presents indispensable and up-to-date information on viroids and viroid diseases. It provides a single source of information on the properties of viroids, the economic impact of viroid diseases, and methods for their detection and control. It examines the diseases associated with different plant species, the geographic distribution and epidemiology of viroids, diseases of possible viroid etiology, and the future applications of viroids. Viroids examines the biology of viroids, molecular characteristics, localization and movement, replication, pathogenesis, viroids and gene silencing, classification, viroid-like satellite RNAs, detection of viroids using bioamplification hosts, biological indexing, polyacrylamide gel electrophoresis, molecular hybridisation and polymerase chain reaction. The book looks at the geographical distribution and epidemiology of viroids in North America, Australasia, China, Japan, Europe, the Middle East, Africa, South America, and at the global level. It covers the control of viroids including quarantine of imported germplasm, availability of viroid-tested propagation materials, thermotherapy, tissue culture, and other conventional strategies as well as biotechnological control approaches. Special topics such as ribozyme reaction of viroids and economic advantages of viroid infection are also included. Other chapters summarise the current state of knowledge concerning viroid diseases of the crop in question and aspects of the natural history of viroids in horticulture. Among the crops covered are potato, tomato, tobacco, cucumber, pome fruits, stone fruits, avocado, citrus, grapevines, hop, chrysanthemum, coleus, columnea, and coconut palm. The four eminent editors of this watershed volume have assembled an international group of more than 70 scientists who have substantial experience with viroids and viroid diseases. They have produced a cohesive and comprehensive work that can be used by students, researchers, extension agents, and regulators. It may also be of a great value to science managers, policy makers, and industries in formulating policies and products to obtain viroid-free plants and control viroid diseases. The information on plant quarantine and certification programs will help anyone concerned with the safe movement of plant material across international boundaries or within a single country.
First published during the Eisenhower administration, researchers have long depended on America Votes for its consistent and detailed presentation of election data from across disparate state election offices. America Votes (AV) is published biennially, and contains an introduction and election coverage by the author, which captures new trends analysis, and is predominantly composed of election result tables. Organized by state, this edition of AV is a valuable resource that includes official, state-certified special, primary, and general election returns for the House, Senate, and gubernatorial elections of 2021 and 2022.
This is a scholarly and informative account of the origin and settlement of the counties of Albemarle, Augusta, Caroline, Essex, Gloucester, Goochland, Hanover, King William, King and Queen, Louisa, New Kent, and Orange, and of the people and events associated with their history. Woven throughout the narrative are descriptions of homes and homeowners, lands and landowners, and choice and enthralling tidbits of lore and legend, not to mention biographical sketches of notable countians and lists of civil and military officers, histories of churches and other institutions, and much, much more.
Digital technology has transformed the entire photographic workflow--and Adobe™ Lightroom, the latest application from the creators of Photoshop�, is at the forefront of the revolution. With this in-depth guide, photographers can make the most of the cutting-edge software and understand the entire image-making process. It’s filled with expert tips and techniques, and comprehensively covers both professional essentials (setting up photo libraries, white balance) and advanced topics like studio branding. You’ll learn how to have a photo shoot, whittle it down to the best shots, and fine-tune their tone, balance, and exposure. Zoom in, zoom out, crop, and undo, all without altering the original. Put the file on CD or the web for clients or friends, then make picture-perfect prints, in color, mono, or sepia. The possibilities are amazing!
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