Bøger i Monographs in Contemporary Mathematics serien

One of the most important and interesting problems consists in the classification of integrable flows up to different equivalence relations such as (1) an isometry, (2) the Liouville equivalence, (3) the trajectory equivalence (smooth and continuous), and (4) the geodesic equivalence.

An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations.

The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list.

This monograph constructs correct extensions of extremal problems, including problems of multicriteria optimization as well as more general cone optimization problems. The author obtains common conditions of stability and asymptotic nonsensitivity of extremal problems under perturbation of a part of integral restrictions for finite and infinite systems of restrictions. Features include individual chapters on nonstandard approximation of finitely additive measures by indefinite integrals and constructions of attraction sets. Professor Chentsov illustrates abstract settings by providing examples of problems of impulse control, mathematical programming, and stochastic optimization.