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In Part I, methods of nonstandard analysis are applied to deterministic control theory, extending earlier work of the author. Results established include compactness of relaxed controls, continuity of solution and cost as functions of the controls, and existence of optimal controls. In Part II,...
The paper deals with the notion of tolerance space (introduced by E. C. Zeeman, but discerned earlier by H. Poincaré), which formalizes the idea of resemblance. The category of tolerance spaces is described, their homology and homotopy theories developed. Applications include almost-fixed point...
First we propose a model of visual perception essentially based on the Keldysh-Chernavsky-Sossinsky ‘three-channel theorem’, from which three-dimensionality of space follows. Second, we associate with a system of subgroups H
1, ..., Hs of a given group G a geometric object, called a group...
Completely integrable KdV systems are described on coadjoint orbits, which are isospectral classes of periodic regular difference operators. The finite zone solutions for some field equations are then obtained if the equations are written on a jet bundle of maps with values in a Lie group and if...
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