We study Möbius and quasimöbius mappings in spaces with a semimetric meeting the Ptolemy inequality. We construct a bimetrization of a Ptolemeic space which makes it possible to introduce a Möbius-invariant metric (angular distance) in the complement to each nonsingleton. This metric coincides with the hyperbolic metric in the canonical cases. We introduce the notion of generalized angle in a Ptolemeic space with vertices a pair of sets, determine its magnitude in terms of the angular distance and study distortion of generalized angles under quasimöbius embeddings. As an application to noninjective mappings, we consider the behavior of the generalized angle under projections and obtain an estimate for the inverse distortion of generalized angles under quasimeromorphic mappings (mappings with bounded distortion).
We studied the role of disturbances in cell Ca(2+) homeostasis in plasma membrane blebbing and death of thymocytes. Capacitance Ca(2+) channels of the plasma membrane and intracellular Ca(2+) stores are involved in the induction and progression of changes in the membrane and cytoskeleton and apoptosis induced by acrylonitrile.
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