Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kähler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.
The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.
This is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and are familiar with basic facts from algebra, number theory and complex analysis. The goal is to present the fundamental concepts of representation theory, to describe the connection between them, and to explain some of their background. The focus is on groups which are of particular interest for applications in physics and number theory (e.g. Gell-Mann's eightfold way and theta functions, automorphic forms). The reader finds a large variety of examples which are presented in detail and from different points of view.
Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kähler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.
Combining algebraic groups and number theory, this volume gathers material from the representation theory of this group for the first time, doing so for both local (Archimedean and non-Archimedean) cases as well as for the global number field case.
This is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and are familiar with basic facts from algebra, number theory and complex analysis. The goal is to present the fundamental concepts of representation theory, to describe the connection between them, and to explain some of their background. The focus is on groups which are of particular interest for applications in physics and number theory (e.g. Gell-Mann's eightfold way and theta functions, automorphic forms). The reader finds a large variety of examples which are presented in detail and from different points of view.
Director F.W. Murnau's Nosferatu: A Symphony of Horror, made in 1921, right after the devastating Spanish Flu pandemic, has become the ultimate cult classic among horror film buffs around the world. For years there was much speculation about the production background, the filmmakers, and their star, the German actor Max Schreck. This book tells the complete story drawing on rare sources. This book tells the complete story, drawing on rare sources. The trail leads to a group of occultists with a plan to establish a leading film company that would produce a momentous series of horror movies. Along the way, the author touches upon other classic German fantasy silents, such as The Golem, The Cabinet of Dr. Caligari and Metropolis.
Mallorca is not only a primary holiday destination for sun-lovers, but also a true hiking paradise, with lovely valleys, wild, romantic gorges and countless panoramic summits, all in the serene hinterland, tucked away from the seasonally overcrowded coasts. The "other" Mallorca surprises the visitor with a well-developed network of trails, and offers a variety of tours for all demands and levels of difficulty, starting from simple beach walks, to adventurous cliff tours and challenging mountain hikes, up to a spectacular canyon crossing. Rolf Goetz, the author of this Rother hiking guide, is one of the best experts on the Spanish Islands, and, through his various publications, has already made an excellent name for himself. He presents hikers with a wide variety of entertaining tour suggestions, mainly emphasising the wild, chasm-filled Serra de Tramuntana in the Northwest, but also including other island regions. This handy little hiking book, which opens up one of the most popular island hiking destinations in the Mediterranean area, has 77 tour recommendations described in detail, generously illustrated by colour photos and colour map excerpts (scale 1:50,000 and 1:75,000). Thoroughly-researched introductory chapters with tips on interesting sights and a bus schedule complete this excellent guide, which no traveller should do without. Thus, this guide remains a reliable companion on all hikes on this diverse island.
The authors provide an excellent overview of conjugation effects in organic chemistry within and between Pi systems. Besides various aspects of aromaticity one finds detailed discussions of homo-, spiroand hyperconjugation as well as effects of through-space and throughbond interactions. These effects are presented on the basis of experimental results and are analyzed by the use of qualitative arguments of perturbation theory and from a comparison with results from high level ab initio calculations. This book is a must-have for bachelor students from the second year on, master and PhD students of chemistry. Also students in science such as physics, biology and medicine will benefit from the concepts described in the book. Furthermore, chemists in research and development will be grateful to find here an overview of conjugation effects allowing to understand the structures, the dynamics and the reactivity of molecules.
For over a century, the Middle East has weathered seemingly endless conflicts, ensnaring political players from around the world. And perhaps no nation has displayed a greater range of policies toward, and experiences in, the region than Germany, as this short and accessible volume demonstrates. Beginning with Kaiser Wilhelm’s intermittent support for Zionism, it follows the course of German-Mideast relations through two world wars and the rise of Adolf Hitler. As Steininger shows, the crimes of the Third Reich have inevitably shaped postwar German Mideast policy, with Germany emerging as one of Israel’s staunchest supporters while continuing to navigate the region’s complex international, religious, and energy politics.
This book presents a mathematical programming approach to the analysis of production frontiers and efficiency measurement. The authors construct a variety of production frontiers, and by measuring distances to them are able to develop a model of efficient producer behaviour and a taxonomy of possible types of departure from efficiency in various environments. Linear programming is used as an analytical and computational technique in order to accomplish this. The approach developed is then applied to modelling producer behaviour. By focusing on the empirical relevance of production frontiers and distances to them, and applying linear programming techniques to artificial data to illustrate the type of information they can generate, this book provides a unique study in applied production analysis. It will be of interest to scholars and students of economics and operations research, and analysts in business and government.
Debugging becomes more and more the bottleneck to chip design productivity, especially while developing modern complex integrated circuits and systems at the Electronic System Level (ESL). Today, debugging is still an unsystematic and lengthy process. Here, a simple reporting of a failure is not enough, anymore. Rather, it becomes more and more important not only to find many errors early during development but also to provide efficient methods for their isolation. In Debugging at the Electronic System Level the state-of-the-art of modeling and verification of ESL designs is reviewed. There, a particular focus is taken onto SystemC. Then, a reasoning hierarchy is introduced. The hierarchy combines well-known debugging techniques with whole new techniques to improve the verification efficiency at ESL. The proposed systematic debugging approach is supported amongst others by static code analysis, debug patterns, dynamic program slicing, design visualization, property generation, and automatic failure isolation. All techniques were empirically evaluated using real-world industrial designs. Summarized, the introduced approach enables a systematic search for errors in ESL designs. Here, the debugging techniques improve and accelerate error detection, observation, and isolation as well as design understanding.
Crete offers an incredibly multifaceted realm for walkers. Many areas of the island are still rugged and pristine. The island’s terrain is dominated by three mighty mountain ranges, furrowed by deep gorges. Lofty mountains and a deep-blue sea are in close proximity – an ideal combination for any holiday. The finest coastal and mountain walks on Greece’s largest and most diverse island can be found in the Rother Walking Guide »Crete«. The choice ranges from a pleasant walk across foothills through vineyards and sprawling groves of olive trees all the way up to the highest panoramic summits. There are even some demanding peaks, over 2000 metres in height, to climb. Breathtaking canyons can be traversed and isolated, dripstone caves are waiting to be explored. Everywhere you look, you’ll find little villages, secluded monasteries and remote caves. Coastal trails lead to tranquil coves for bathing; is there anything better than, after a walk, taking a dip in some refreshing waters? Even the classic Cretan walks, like the Samaria Gorge and Dead’s Gorge with its Minoan palace grounds, are included in this guide. Rolf Goetz, a seasoned writer of walking guides for the Bergverlag Rother, presents 70 walks on the island of Crete, all rich in diversity. Each individual walk includes a short preface with all the important key points, an exact description of the route, a pertinent height profile and a little walking map with the route marked in. Apart from these, there are many tips pertaining to the availability of refreshment, possible alternative routes as well as sites worth a visit. GPS tracks are available for downloading. Numerous delightful photos whet the appetite for making the island your first choice for your next holiday sojourn. An essential guide for Crete fans!
Suitable for students and researchers in commutative algebra, algebraic geometry, and neighboring disciplines, this book introduces various sheaves of differential forms for equidimensional morphisms of finite type between noetherian schemes, the most important being the sheaf of regular differential forms.
In this book, leading authorities on project organizing explore the growing deployment of projects and other types of temporary organizations, with a focus on the challenges created by projectification. The way projects are coordinated and handled influences the success of innovation and change within organizations and is critical for strategic development in our societies, yet it is often at odds with the institutions of traditional industrial society. Drawing on both theoretical perspectives and real-world cases, this book sheds light on the transformation toward a project society and explores the effects, opportunities, and conflicts it has created. As change continues, the authors make a case for renewing institutions and mind-sets and provide a foundation from which to discuss societal changes for the future. This is an invaluable book for researchers and students in project management and organizational theory programs, as well as professionals involved in the management of projects.
The Old Testament is a collection of writings which came into being over a period of more than a thousand years in the history of the people of Israel and which reflect the life of the people in this period. Therefore, there is a reciprocal relationship between the writings or "books" of the Old Testament and the life of Israel in its history. The understanding of the texts presupposes insights into the historical context and the development of the life of Israelite society, while at the same time the texts themselves are the most important, indeed for the most part the only, source for it. This "Introduction" attempts to take account of this reciprocal relationship. The first part deals with the history of Israel. However, its approach differs from most accounts of this history. It takes the Old Testament texts themselves as a starting point and first of all outlines the picture of historical developments and associations which the texts present. An attempt is then made, on this basis, to reconstruct historical developments by introducing material from outside the Bible. This method of working leads to close connections between the second and third parts, because it has to take account of the nature and original purpose of the texts and their function within the biblical books as they are now. The second part attempts to present the texts collected in the Old Testament as expressions of the life of Israel. The third part discusses the books of the Old Testament in their present form.
Cyprus is not only famous for its cultural heritage and 9000 year old past – “Aphrodite‘s Island“ is one of the most popular hiking destinations in the eastern Mediterranean. The centre of the island is dominated by the Troodos mountain measuring some 2000 m in height, which despite its considerable altitude is more reminiscent of European low mountains, due to its softly rounded and forested peak. This Rother hiking guide proposes 50 routes mostly ranging from easy to medium level. Next to mountain tours, it also includes a selection of coastal paths along bizarre cliffs and adventurous ravine tours. Forest paths and nature trails lead through aromatic cedar woods, silent valleys and to remote Byzantine churches and monasteries. Classic spring tours are those which take visitors across the peninsula of Akamas, when colourful carpets of flowers and orchids blossoming by the wayside unveil their typical Mediterranean charm.
Compounds labeled with carbon-14 and tritium are indispensable tools for research in biomedical sciences, discovery and development of pharmaceuticals and agrochemicals. Preparation of Compounds Labeled with Tritium and Carbon-14 is a comprehensive, authoritative and up-to-date discussion of the strategies, synthetic approaches, reactions techniques, and resources for the preparation of compounds labeled with either of these isotopes. A large number of examples are presented for the use of isotopic sources and building blocks in the preparation of labeled target compounds, illustrating the range of possibilities for embedding isotopic labels in selected moieties of complex structures. Topics include: Formulation of synthetic strategies for preparing labeled compounds Isotope exchange methods and synthetic alternatives for preparing tritiated compounds In-depth discussion of carbon-14 building blocks and their utility in synthesis Preparation of enantiomerically pure isotopically labeled compounds Applications of biotransformations Preparation of Compounds Labeled with Tritium and Carbon-14 is an essential guide to the specialist strategies and tactics used by chemists to prepare compounds tagged with theradioactive atoms carbon-14 and tritium.
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