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The so-called adjoint extremal problem of searching for the optimal direction of a transition through a local extremum point is posed and studied. To this end, the concepts of local asymmetry and local excess of the functional at the extremum point are introduced, the minimization of which is the goal of the investigation. A number of examples for variational functionals with nonsmooth integrands...
A commutative diagram that connects the basic objects of commutative algebra with the main objects of commutative analysis is constructed. Namely, with the help of five types of canonical embeddings we constructed a diagram between two sets of objects: Abelian semigroups — Abelian regular (cancellative) semigroups — Abelian groups, on the first hand, and convex cones — regular convex cones — linear...
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