Kaiserslautern - Fachbereich Mathematik
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We compare different notions of differentiability of a measure along a vector field on a locally convex space. We consider in the \(L^2\)-space of a differentiable measure the analoga of the classical concepts of gradient, divergence and Laplacian (which coincides with the Ornstein-Uhlenbeck
operator in the Gaussian case). We use these operators for the extension of the basic results of Malliavin and Stroock on the smoothness of finite dimensional image measures under certain nonsmooth mappings to the case of non-Gaussian measures. The proof of this extension is quite direct and does not use any Chaos-decomposition. Finally, the role of this Laplacian in the
procedure of quantization of anharmonic oscillators is discussed.
Jede Wissenschaft entfaltet sich in einem Spannungsverhältnis zu ihren Nachbardisziplinen. In diesem Beitrag wird insbesondere das Disziplinenpaar Mathematik-Philosophie in den Blick genommen. Dies geschieht entlang der Leitfrage, ob und gegebenenfalls wie Philosophie auf die Entwicklung und Ausformung der Mathematik Einfluß genommen hat. Dazu wird nach philosophischen Spuren in der Mathematik gefragt, wobei jene historischen Konstellationen bevorzugt betrachtet werden, die eine grundlegende Änderung im Mathematikverständnis erbracht haben. Deshalb gilt das Hauptinteresse dieser Untersuchung dem Verhältnis von Philosophie und Mathematik in der klassischen Antike, bei Kant und in der Gegenwart.
Weighted k-cardinality trees
(1992)
We consider the k -CARD TREE problem, i.e., the problem of finding in a given undirected graph G a subtree with k edges, having minimum weight. Applications of this problem arise in oil-field leasing and facility layout. While the general problem is shown to be strongly NP hard, it can be solved in polynomial time if G is itself a tree. We give an integer programming formulation of k-CARD TREE, and an efficient exact separation routine for a set of generalized subtour elimination constraints. The polyhedral structure of the convex huLl of the integer solutions is studied.