We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in L²(²) with an attractive singular perturbation supported by a line and a finite number of points. The discrete spectrum is shown to be nonempty, and furthermore, the resonance problem can be explicitly solved in this setting; by Birman-Schwinger method it is reformulated into a Friedrichs-type model.

Necessary conditions of optimality are derived for multiobjective optimal control problems with pathwise state constraints, in which the dynamics constrain is modeled as a differential inclusion. The obtained result extends results of [2] and [29].

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The construction of the Q-operator for twisted affine superalgebra Uq(C(2)(2)) is given. It is shown that the corresponding prefundamental representations give rise to evaluation modules some of which do not have a classical limit, which nevertheless appear to be a necessary part of fusion relations.