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Polysystem Modelling of Geographical Processes and Phenomena in Nature and Society

A. K. Cherkashin (2009)

Mathematical Modelling of Natural Phenomena

Polysystem methodology elaborated for comprehensive analysis of geographical objects considers them as interrelated systems of different types. Each systematic interpretation of a territorial object is formed as a theory describing this object with a special language used for construction of a certain type of models. This paper proposes new methods to develop geographical models and describes several types of systematic models constructed by these methods.

Pontryagin algebra of a transitive Lie algebroid

Kubarski, Jan (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] It was previously known that for every principal fibre bundle P there is some corresponding transitive Lie algebroid A(P) - a vector bundle equipped with some structure like the structure of a Lie algebra in the module of sections. The author of this article shows that the Chern-Weil homomorphism of P is a notion of the Lie algebroid of P, i.e. knowing only A(P) of P one can uniquely reproduce the ring of invariant polynomials ( V g * ) I and the Chern-Weil...

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