2012-2012

N/A

The project is dedicated to the study of the theoretical foundations of idempotent mathematics and its new applications to differential equations, asymptotic problems of mathematical physics and control theory, the theory of electricity networks and so on. These studies are closely connected with the procedures of dequantization and asymptotic transitions in quantum theory (in particular, with the quasi-classical approximation) . Tropical mathematics is derived from the traditional mathematics over number fields using the dequantization procedure. A generalization of tropical mathematics is idempotent mathematics, ie, mathematics over semirings with idempotent addition. It is planned the systematic development of the topological version of idempotent functional analysis with applications to specific problems. dequantization procedures will be applied to a variety of mathematical objects and theories. It is planned to investigate the hidden linearity (over idempotent semirings) in traditional non-linear problems and deterministic and stochastic control problems. Planned development of the theory of representations of semigroups in a linear idempotent Archimedean spaces. It is planned to systematically develop computing and tropical idempotent mathematics, including tropical computational geometry and idempotent interval analysis. The results obtained will be used for solving nonlinear algebraic and differential equations. It is planned to construct and study tropical and fast algorithms of idempotent linear algebra algorithms and universal. More... »

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