VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines.
This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods) Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics) The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.
VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines.
By the spring of 1943, after the defeat at Stalingrad, the writing was on the wall. But while commanders close to the troops on Germany's various fronts were beginning to read it, those at the top were resolutely looking the other way. This seventh volume in the magisterial 10-volume series from the Militärgeschichtliches Forschungsamt [Research Institute for Military History] shows both Germany and her Japanese ally on the defensive, from 1943 into early 1945. It looks in depth at the strategic air war over the Reich and the mounting toll taken in the Battles of the Ruhr, Hamburg, and Berlin, and at the "Battle of the Radar Sets" so central to them all. The collapse of the Luftwaffe in its retaliatory role led to hopes being pinned on the revolutionary V-weapons, whose dramatic but ultimately fruitless achievements are chronicled. The Luftwaffe's weakness in defence is seen during the Normandy invasion, Operation overlord, an account of the planning, preparation and execution of which form the central part of this volume together with the landings in the south of France, the setback suffered at Arnhem, and the German counter-offensive in the Ardennes. The final part follows the fortunes of Germany's ally fighting in the Pacific, Burma, Thailand, and China, with American forces capturing islands ever closer to Japan's homeland, and culminates in her capitulation and the creation of a new postwar order in the Far East. The struggle between internal factions in the Japanese high command and imperial court is studied in detail, and highlights an interesting contrast with the intolerance of all dissent that typified the Nazi power structure. Based on meticulous research by MGFA's team of historians at Potsdam, this analysis of events is illustrated by a wealth of tables and maps covering aspects ranging from Germany's radar defence system and the targets of RAF Bomber Command and the US 8th Air Force, through the break-out from the Normandy beachhead, to the battles for Iwo Jima and Okinawa.
An examination of the transmission and spread of papal documents in the Latin West between the 4th and 9th centuries. These documents, which were collected from the 5th century onwards, became the basis of canon law. The second part of the volume discusses the prevalence of forged decress which were attributed to the earliest popes.
Contemporary biographies of Galilei emphasize, in several places, that he was a masterful draughtsman. In fact, Galilei studied at the art academy, which is where his friendship with Ludovico Cigoli developed, who later became the official court artist. The book focuses on this formative effect – it tracks Galilei’s trust in the epistemological strength of drawings. It also looks at Galilei’s activities in the world of art and his reflections on art theory, ending with an appreciation of his fame; after all, he was revered as a rebirth of Michelangelo. For the first time, this publication collects all aspects of the appreciation of Galilei as an artist, contemplating his art not only as another facet of his activities, but as an essential element of his research.
Westcott’s Plant Disease Handbook, 7th Edition, should be useful to anyone with a keen interest in gardening. The seventh edition uses the traditional convenient format of previous editions providing easy access to essential information quickly with special dictionary-type entries on plant hosts and on symptoms. It provides useful cross references, indexes, illustrative plates of 34 key diseases, and 40 black and white illustrations of other diseases. New and updated material includes: significant taxonomic changes in fungi, bacteria, viruses and nematodes, and recently discovered diseases and new hosts for previously known plant-pathogens.
For forty years, this widely acclaimed classic has remained unsurpassed as an introduction to art in the Western world, boasting the matchless credibility of the Janson name. This newest update features a more contemporary, more colorful design and vast array of extraordinarily produced illustrations that have become the Janson hallmark. A narrative voice makes this book a truly enjoyable read, and carefully reviewed and revised updates to this edition offer the utmost clarity in contributions based on recent scholarship. Extensive captions for the book’s incredible art program offer profound insight through the eyes of twentieth-century art historians speaking about specific pieces of art featured throughout. Significantly changed in this edition is the chapter on “The Late Renaissance,” in which Janson offers a new perspective on the subject, tracing in detail the religious art tied to the Catholic Reform movement, whose early history is little known to many readers of art history. Janson has also rearranged early Renaissance art according to genres instead of time sequence, and he has followed the reinterpretation of Etruscan art begun in recent years by German and English art historians. With a truly humanist approach, this book gives written and visual meaning to the captivating story of what artists have tried to express—and why—for more than 30,000 years.
The English translation of the three-volume Exegetisches Wrterbuch zum Neuen Testament, this monumental work by an ecumenical group of scholars is first of all a complete English dictionary of New Testament Greek. Going beyond that, however EDNT also serves as a guide to the usage of every New Testament word in its various contexts, and it makes a significant contribution to New Testament exegesis and theology. EDNT's thorough, lengthy discussions of more significant words and its grouping of words related by root and meaning (with alphabetical cross-references) distinguish it from simpler Greek-English lexicons. Advancing the discussion of the Theological Dictionary of the Old Testament, EDNT summarizes more recent treatments of numerous questions in New Testament study and takes into consideration newer viewpoints of linguistics.
A collection of fifteen essays, most of them published previously. Ch. 6 (pp. 109-118), "Jews and Christians in Antioch at the End of the Fourth Century" [appeared in "Christian-Jewish Relations through the Centuries" (2000)], contrasts the vitriolic anti-Jewish polemics of John Chrysostom in regard to Judaizing with the attitude of the "Apostolic Constitutions" (material on ecclesiastical law). The latter, instead of denigrating the Jews, borrowed from them aspects of Judaism that local Christians found attractive. Ch. 12 (pp. 207-221), "Who Was Apion?" [unpublished], focuses on Apion's "scholarship" and writing, i.e. activities other than his anti-Jewish polemics. However, notes that Apion's self-proclaimed originality included his invention of the libel of Jewish cannibalism.
Heavily represented sections of contemporary philosophy subscribe to the notion of "embodiment". However promising this pragmatic turn of events may be, it remains limited in that it interprets the world as a projection of the cognizing "I". By contrast, Image Acts focuses on the counterforce of the form of images. The book subdivides this sphere into three parts: imitation, substitution, and the pure effect of the form. All three parts are contemplated with examples from antiquity through to the present and the iconoclastic controversies of our times. From this reconstruction of the image act springs the element of a new philosophy of affordance.
It was a compliment to me to be asked to prepare the fourth edition of Westcott's Plant Disease Handbook, and the decision to accept the responsi bility for the fourth edition and now the fifth edition was not taken lightly. The task has been a formidable one. I have always had a great respect professionally for Dr. Cynthia Westcott. That respect has grown considerably with the completion of the two editions. I now fully realize the tremendous amount of effort expended by Dr. Westcott in developing the Handbook. A book such as this is never finished, since one is never sure that everything has been included that should be. I would quote and endorse the words of Dr. Westcott in her preface to the first edition: "It is easy enough to start a book on plant disease. It is impossible to finish it. " This revision of the Handbook retains the same general format contained in the previous editions. The chemicals and pesticides regulations have been updated; a few taxonomic changes have been made in the bacteria, fungi, and mistletoes; the changing picture in diseases caused by viruses and/or viruslike agents has been described. A few new host plants have been added, and many recently reported diseases as well as previously known diseases listed now on new hosts have been included. In addition, photographs have been replaced where possible, and the color photograph section has been retained.
The Trees and Shrubs manual is a reference manual on diseases which attack trees, shrubs, and vines. The manual identifies various types of diseases which are known to invade these plants located throughout North, Central, and South America. The recordings include diseases caused by fungi, bacteria, viruses, viroids, phytoplasmas, and nematodes. Causal disease agents are described and illustrated in some cases and diseases and disease control measures are also discussed. A manual such as this is never finished since new reports of diseases are continuously reported.
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