منابع مشابه
Generalised G 2 -manifolds
We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points generalise the notion of a manifold of holonomy G2, while the constrained ones give rise to a new geometry without a classical counterpart. We characterise these stru...
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A bounded convex set has constant width d iff any two parallel (and nonidentical) tangent planes to it have identical distance d from each other. Clearly balls have this property, but there are also other sets of constant width. This lecture was originally designed for a general audience as part of a series of lectures during the German “Year of Mathematics” 2008. It starts by presenting eviden...
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The magnetic backgrounds that physically give rise to spacetime noncommutativity are generally treated using noncommutative geometry. In this article we prove that also the theory of generalised complex manifolds contains the necessary elements to generate B–fields geometrically. As an example, the Poisson brackets of the Landau model (electric charges on a plane subject to an external, perperd...
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We regard classical phase space as a generalised complex manifold and analyse the B–transformation properties of the ⋆–product of functions. The C–algebra of smooth functions transforms in the expected way, while the C–algebra of holomorphic functions (when it exists) transforms nontrivially. The B–transformed ⋆–product encodes all the properties of phase–space quantum mechanics in the presence...
متن کاملGeneralised Mixability, Constant Regret, and Bayesian Updating
Mixability of a loss is known to characterise when constant regret bounds are achievable in games of prediction with expert advice through the use of the aggregating algorithm [Vovk, 2001]. We provide a new interpretation of mixability via convex analysis that highlights the role of the Kullback-Leibler divergence in its definition. This naturally generalises to what we call Φ-mixability where ...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1964
ISSN: 0026-2285
DOI: 10.1307/mmj/1028999082