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Requiem for an Army
Most Western models suggest that in the face of open threats to the military's core interests, the army would have fought to keep the status quo. Yet the military actually facilitated the introduction of a new democratic polity and in the process dug its own grave. Trained under a Russian-inspired system that minimized the role of the individual, this group was suddenly exposed to the radically different 'Innere Fuehrung' concept that lies at the heart of the Bundeswehr's ethos.
Riemannian Geometry and Geometric Analysis
The present textbook is a somewhat expanded version of the material of a three-semester course I gave in Bochum. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds. In the first chapter, we introduce the basic geometric concepts, like dif ferentiable manifolds, tangent spaces, vector bundles, vector fields and one parameter groups of diffeomorphisms, Lie algebras and groups and in par ticular Riemannian metrics. We also derive some elementary results about geodesics. The second chapter introduces de Rham cohomology groups and the es sential tools from elliptic PDE for treating these groups. In later chapters, we shall encounter nonlinear versions o...
Geometry and Physics
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Legitimation Crisis
Critical Theory originated in the perception by a group of German Marxists after the First World War that the Marxist analysis of capitalism had become deficient both empirically and with regard to its consequences for emancipation, and much of their work has attempted to deepen and extend it in new circumstances. Yet much of this revision has been in the form of piecemeal modification. In his latest work, Habermas has returned to the study of capitalism, incorporating the distinctive modifications of the Frankfurt School into the foundations of the critique of capitalism. Drawing on both systems theory and phenomenological sociology as well as Marxism, the author distinguishes four levels of capitalist crisis - economic, rationality, legitimation, and motivational crises. In his analysis, all the Frankfurt focus on cultural, personality, and authority structures finds its place, but in a systematic framework. At the same time, in his sketch of communicative ethics as the highest stage in the internal logic of the evolution of ethical systems, the author hints at the source of a new political practice that incorporates the imperatives of evolutionary rationality.
Inclusion Methods for Nonlinear Problems
The book covers recent developments in the construction and the analysis of numerical algorithms for the solution of nonlinear problems with emphasis on the automatic calculation of guaranteed errorbounds by machine interval operations. The bulk of the presented algorithms deal with problems from various fields in the applied sciences.
Staat und Religion
Die Bedeutung der Religion für Staat und Gesellschaft ist eine Frage, die die Politische Theorie seit ihren Anfängen begleitet hat. Der Band zeichnet dazu die wichtigsten ideengeschichtlichen Begriffe und Positionen von der Antike bis zur Gegenwart nach und thematisiert insbesondere die Veränderungen im Beziehungsgeflecht des Politisch-Religiösen, die durch das Christentum, die Reformation sowie die Säkularisierungsprozesse im modernen Staatswesen etabliert wurden. Vor diesem anspruchsvollen ideenhistorischen Hintergrund, der die Vielschichtigkeit der Verbindungslinien zwischen Politik und Religion erfasst, wird schließlich auch die ungebrochene Relevanz des religiösen Themas für den demokratischen Rechtsstaat transparent.
Assisting the Invisible Hand
This is an investigation into contemporary thinking on controlling the market, especially with regard to the problem of dealing with environmental issues. The book contributes to contemporary insight by arguing that the issue of market control must be addressed in terms of the relations between state, market and civil society. It stresses the normative dimensions of the market control issue. The position adopted by the book is that the market cannot be controlled by the state alone.
Mathematical Principles of Topological and Geometric Data Analysis
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information. In recent years there has been a fas...
New Directions in Hopf Algebras
Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.
