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In the following paper, we present a brief and easily accessible introduction to the theory of neural networks under special emphasis on the rôle of pure and applied mathematics in this interesting field of research. In order to allow a quick and direct approach even for nonspecialists, we only...
We study some classical integrable systems of dynamics (the Euler top in space, the asymptotic geodesic motion on an ellipsoid) which are linearized on unramified coverings of generalized Jacobian varieties. We find explicit expressions for so called root functions living on such coverings which...
Abstract differential geometry is a recent extension of classical differential geometry on smooth manifolds which, however, does no longer use any notion of Calculus. Instead of smooth functions, one starts with a sheaf of algebras, i.e., the structure sheaf, considered on an arbitrary...
In this paper we generalize the classical Jacobson–Bourbaki correspondence for field extensions to K-vector space extensions (K a field). Namely, for such extensions, we state and prove a correspondence theorem – the Jacobson–Bourbaki correspondence with parameters. Some examples are provided.
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