This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.
Studies into religion and violence often put religion first. René Girard started with violence in his book Violence and the Sacred and used the Durkheimian term 'sacred' as its correlate in his study of early religions. During the unfolding of his theory, he more and more distinguished the sacred from saintliness to address the break that the biblical revelation represented in comparison to early religions. This distinction between the sacred and saintliness resembles Henri Bergson's complementing Emile Durkheim's identification of the sacred and society with a dynamic religion that relies on individual mystics. Girard's distinction also relates to the insights of thinkers like Jacques Maritain, Simone Weil, and Emmanuel Levinas. This element explores some of Girard's main features of saintliness. Girard pleaded for the transformation of the sacred into holy, not their separation.
This book constitutes the refereed proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007, held in Aachen, Germany in February 2007. The 56 revised full papers presented together with 3 invited papers were carefully reviewed and selected from about 400 submissions. The papers address the whole range of theoretical computer science including algorithms and data structures, automata and formal languages, complexity theory, logic in computer science, semantics, specification, and verification of programs, rewriting and deduction, as well as current challenges like biological computing, quantum computing, and mobile and net computing.
This study has been revised to include new finds about the composition dates of several Mozart works. A new bibliography and a collation with the Neue Mozart-Ausgabe edition of letters, edited by O.E.Deutsch, W.A.Bauer and J.H.Eibl: Baerenreiter, 1962-75 is also included.
In 1814, Johann Wolfgang von Goethe read the poems of the great fourteenth-century Persian poet Hafiz in a newly published translation by Joseph von Hammer-Purgstall. For Goethe, the book was a revelation. He felt a deep connection with Hafiz and Persian poetic traditions, and was immediately inspired to create his own West-Eastern Divan as a lyrical conversation between the poetry and history of his native Germany and that of Persia. The resulting collection engages with the idea of the other and unearths lyrical connections between cultures. The West-Eastern Divan is one of the world’s great works of literature, an inspired masterpiece, and a poetic linking of European and Persian traditions. This new bilingual edition expertly presents the wit, intelligence, humor, and technical mastery of the poetry in Goethe’s Divan. In order to preserve the work’s original power, Eric Ormsby has created this translation in clear contemporary prose rather than in rhymed verse, which tends to obscure the works sharpness. This edition is also accompanied by explanatory notes of the verse in German and in English and a translation of Goethe’s own commentary, the “Notes and Essays for a Better Understanding of the West-Eastern Divan.” This edition not only bring this classic collection to English-language readers, but also, at a time of renewed Western unease about the other, to open up the rich cultural world of Islam.
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