Rolf Schneider – författare

This book provides the foundations for geometric applications of convex cones and presents selected examples from a wide range of topics, including polytope theory, stochastic geometry, and Brunn–Minkowski theory. Giving an introduction to convex cones, it describes their most important geometric functionals, such as conic intrinsic volumes and Grassmann angles, and develops general versions of the relevant formulas, namely the Steiner formula and kinematic formula.

In recent years questions related to convex cones have arisen in applied mathematics, involving, for example, properties of random cones and their non-trivial intersections. The prerequisites for this work, such as integral geometric formulas and results on conic intrinsic volumes, were previously scattered throughout the literature, but no coherent presentation was available. The present book closes this gap. It includes several pearls from the theory of convex cones, which should be better known.

Die Kenntnis der griechischen und römischen Antike, wie aller vergangenen Gesellschaften, ist in entscheidendem Maß von den Medien geprägt, in denen sich die jeweiligen Gesellschaften artikulieren. Die Gesetze, Konventionen und Konzepte der verschiedenen schriftlichen, bildlichen und materiellen Medien führen zu unterschiedlichen Konstruktionen geschichtlicher Wirklichkeiten. Die Beiträge dieses Bandes gehen den spezifischen Formen nach, in denen die griechische und römische Antike sich in Literatur und Inschriften, Bildwerken, Monumenten und Artefakten, Lebensräumen und Ritualen präsentiert. Für den Historiker stellt sich damit die Frage, wie die verschiedenen Konzepte der medialen Konstruktion von Wirklichkeiten zu einem Konzept von ‚Geschichte‛ zusammengeführt werden können. Darüber hinaus ergeben sich Reflexionen über die Möglichkeiten und Grenzen der Medien und Formen, in denen historische Forschung ihre Dokumentationen und Untersuchungen betreibt und vorlegt.

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.