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101.
102.
We study general relativity in the framework of non-commutative differential geometry. As a prerequisite we develop the basic notions of non-commutative Riemannian geometry, including analogues of Riemannian metric, curvature and scalar curvature. This enables us to introduce a generalized Einstein-Hilbert action for non-commutative Riemannian spaces. As an example we study a space-time which is the product of a four dimensional manifold by a two-point space, using the tools of non-commutative Riemannian geometry, and derive its generalized Einstein-Hilbert action. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gravity. This field is geometrically interpreted as describing the distance between the two points in the internal space.Dedicated to H. ArakiSupported in part by the Swiss National Foundation (SNF) 相似文献
103.
104.
Hans Grabmüller 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(5):783-805
Rotationally symmetric deformations of a flat annular elastic membrane under a gravitational force are studied, with prescribed radial stresses or horizontal displacements at the edges. The small-finitedeflection theory of Föppl-Hencky as well as a simplified version of Reissner's static first approximation theory of thin shells of revolution are applied which lead to consider a single, second-order, ordinary differential equation for the derivation of the principal stresses in the membrane. Using analytical methods, the range of those boundary data is determined for which the solutions of the differential equation are wrinkle free in the sense that both the radial and the circumferential stress components are nonnegative everywhere. 相似文献
105.
106.
Arthur Greenberg Oleg P. Charkin Ralph H. Bartram István Hargittai Gyula Beke 《Structural chemistry》1992,3(3):221-224
Unsigned book reviews are by the Book Review Editor. 相似文献
107.
108.
Erika Vrkonyi-Schlovicsk Klmn Takcs Istvn Hermecz 《Journal of heterocyclic chemistry》1997,34(3):1065-1066
Diastereomeric timolol tartrates 4 are obtained in a one-pot synthesis from the racemic base 2 and optically active O,O-diacetyl- or O,O-dibenzoyltartaric anhydrides 3 , as only one of the diastereomers precipitates from acetone solution. Acidic hydrolysis as the corresponding 4 leads to timolol in high yield and optical purity. 相似文献
109.
110.
It is known that every conformai embedding of the disk into the extended complex plane possesses a r2-quasiconformal extension across eachr-level line (the r2-property of a domain). We show here that this is a characteristic property of the disk: any simply connected domain which
is not a disk does not admit ther
2-property.
Supported by the RiP-program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach. 相似文献