Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.
Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.
Germany in the 20th century endured two world wars, a failed democracy, Hitler's dictatorship, the Holocaust, and a country divided for 40 years after World War II. But it has also boasted a strong welfare state, affluence, liberalization and globalization, a successful democracy, and the longest period of peace in European history. A History of Twentieth-Century Germany provides a survey of German history during a century of extremes. Ulrich Herbert sees German history in the 20th century as determined by two contradictory perspectives. On one hand, there are the world wars and great catastrophes that divide the country's history into two parts-before and after 1945. Germany is the birthplace of radical ideologies of the left and right and the only country in which each ideology became the foundation of government. This pattern left its stamp on both the first and second halves of the century. On the other hand, the rise of modern industrial society led to decades of conflict over the social and political order regardless of which political system was in force. Considering these contradictory developments, Herbert tackles the questions of both the collapse in the first half of the century and the development from a post-fascist, ruined society to one of the most stable liberal democracies in the world in the latter half. Herbert's analysis brings together wars and terror, utopia and politics, capitalism and the welfare state, socialism and liberal democratic society, gender and generations, culture and lifestyles, European integration and globalization. The resulting book sets a standard by which historians of the period will be measured in the future.
The Austrian Empire was not a colonial power in the sense that fellow actors like 19th-century England and France were. It nevertheless oversaw a multinational federation where the capital of Vienna was unmistakably linked with its eastern periphery in a quasi-colonial arrangement that inevitably shaped the cultural and intellectual life of the Habsburg Empire. This was particularly evident in the era’s colonial utopian writing, and Tropics of Vienna blends literary criticism, cultural theory, and historical analysis to illuminate this curious genre. By analyzing the works of Leopold von Sacher-Masoch, Theodor Herzl, Joseph Roth, and other representative Austrian writers, it reveals a shared longing for alternative social and spatial configurations beyond the concept of the “nation-state” prevalent at the time.
Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau ́s problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau ́s problem have no interior branch points.
The GATT and WTO dispute settlement systems have become the most frequently used international mechanisms for the settlement of trade disputes among governments. The 1994 Agreement Establishing the WTO introduced a historically unprecedented new dispute settlement procedure for conflicts involving trade in goods and services, trade-related investment measures, and intellectual property rights. This procedure provided for the compulsory jurisdiction of the WTO Dispute Settlement Body, WTO Panels, and the WTO Appellate Body. The first 18 months from the time the WTO Agreement came into force on 1 January 1995 witnessed more than 50 invocations of the new dispute settlement procedures by a large number of countries, including many from the developing world. This large response, and the proposals for further extending the scope of WTO law, suggest that the WTO dispute settlement system will continue to be the most frequently applied, worldwide systems for the legal settlement of trade disputes among governments. This book provides students, lawyers and diplomats a thought-provoking and practice-oriented analysis of the GATT/WTO dispute settlement rules, procedures, and problems. The Annexes include a useful collection of relevant texts and tables of past GATT and WTO case law.
This volume C 1 is the first supplement volume to "Phosphor" C which was published in 1965 and covers the compounds of phosphorus. Starting with the binary species formed between phosphorus and hydrogen, the present volume deals with the neutral mononuclear compounds PH through PH ; the ions featuring the same stoichiometric composition are s covered in separate sections. PH and PH are the major initial gaseous decomposition products of PH and, thus, also 2 J intermediates in many of its gas-phase reactions. Both molecules and their ions have been thoroughly investigated by a variety of modern, high-resolution spectroscopic methods during the last three decades. The coverage of their physical, and mostly molecular, properties re presents the largest part of the first two chapters (PH and ions pp. 2 to 47; PH and ions pp. 47 2 to 111). PH is the only compound described in this volume which is thermally stable under normal J conditions. It is the phosphorus analog of ammonia, but exhibits, however, a quite different chemical behavior towards most elements and compounds. The majority of its physical, and in particular spectroscopic, properties have been determined in great detail since the sixties, partially in regard to spectroscopic investigations of the atmospheres of the outer planets.
This advanced machine learning book highlights many algorithms from a geometric perspective and introduces tools in network science, metric geometry, and topological data analysis through practical application. Whether you’re a mathematician, seasoned data scientist, or marketing professional, you’ll find The Shape of Data to be the perfect introduction to the critical interplay between the geometry of data structures and machine learning. This book’s extensive collection of case studies (drawn from medicine, education, sociology, linguistics, and more) and gentle explanations of the math behind dozens of algorithms provide a comprehensive yet accessible look at how geometry shapes the algorithms that drive data analysis. In addition to gaining a deeper understanding of how to implement geometry-based algorithms with code, you’ll explore: Supervised and unsupervised learning algorithms and their application to network data analysis The way distance metrics and dimensionality reduction impact machine learning How to visualize, embed, and analyze survey and text data with topology-based algorithms New approaches to computational solutions, including distributed computing and quantum algorithms
This introductory text covers all the key concepts, relationships, and ideas behind spaceflight and is the perfect companion for students pursuing courses on or related to astronautics. As a crew member of the STS-55 Space Shuttle mission and a full professor of astronautics at the Technical University of Munich, Ulrich Walter is an acknowledged expert in the field. This book is based on his extensive teaching and work with students, and the text is backed up by numerous examples drawn from his own experience. With its end-of-chapter examples and problems, this work is suitable for graduate level or even undergraduate courses in spaceflight, as well as for professionals working in the space industry. This third edition includes substantial revisions of several sections to extend their coverage. These include both theoretical extensions such as the study of relative motion in near-circular orbits, and more practical matters such as additional details about jet-engine and general rocket performance. New sections address regularized equations of orbital motion and their algebraic solutions and also state vector propagation; two new chapters are devoted to orbit geometry and orbit determination and to thermal radiation physics and modelling.
Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are called GSW bosons after Goldstone, Salam and Weinberg and in the case of superconductors the relevant field particles are called SC bosons. One can imagine these bosons as magnetic density waves or charge density waves, respectively. Crossover from atomistic exchange interactions to the excitations of the infinite solid occurs because the GSW bosons have generally lower excitation energies than the atomistic magnons. According to the principle of relevance the dynamics is governed by the excitations with the lowest energy. The non relevant atomistic interactions with higher energy are practically unimportant for the dynamics.
Algorithms that have to process large data sets have to take into account that the cost of memory access depends on where the data is stored. Traditional algorithm design is based on the von Neumann model where accesses to memory have uniform cost. Actual machines increasingly deviate from this model: while waiting for memory access, nowadays, microprocessors can in principle execute 1000 additions of registers; for hard disk access this factor can reach six orders of magnitude. The 16 coherent chapters in this monograph-like tutorial book introduce and survey algorithmic techniques used to achieve high performance on memory hierarchies; emphasis is placed on methods interesting from a theoretical as well as important from a practical point of view.
The manifold problems of shock are still of great importance, diagnostic and therapeutic experience of the "severely ill" being supplied with new information almost every month. In the 5 periodicals which have found their way to my desk during the past few days there are no less than 10 interesting articles on questions concerning shock research [see Bibliography 41 b, 53 a, 60 a, 192 a, 242 a, 350 b, 810 a, 941 a, 1069 a, 1082 a]. The most urgent point still is to maintain as complete as possible the objective catalog of the various shock manifestations found in man and in animals - yet at the same time to view interpretations of these phenomena in their relative and temporal "truth". Problems of shock research are not only interesting for their scientific value but also for their clinical implication. In particular, almost every practicing physician is facing problems of blood replacement very frequent ly. The effective or circulating blood volume remains an important theoret ical and therapeutic problem in the shock field. For years, U. F. GRUBER has pursued this question clinically and experimentally. This volume deals with the world literature in an exceptionally thorough manner. This book is made more than a compilation by including a long list of original work done with F. D. MOORE in Boston, in the Surgical Department in Chur, with 1. E. GELIN and S. E.
E-conomics provides readers with a roadmap to the landscape of the new Internet economy and serves as a reference to the economics of the information age. Written by communication economists and experts in the media business from the US and Europe, this book provides an in-depth analysis of the Internet revolution showing how the rules of business have changed. It takes the European telecommunications industry as a focal point and features strategies for a successful Network Economy. E-conomics is essential reading for economists, managers, and business strategists requiring an understanding of the dynamics of electronic commerce.
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