Boundary relations and generalized resolvents of symmetric operators

The Kreĭn-Naĭmark formula provides a parametrization of all selfadjoint exit space extensions of a (not necessarily densely defined) symmetric operator in terms of maximal dissipative (in ℂ₊) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct generalized resolvents from given parameter families. A general version of the coupling method is introduced and the role of the boundary relations and their Weyl families in the Kreĭn-Naĭmark formula is investigated and explained. These notions lead to several new results and new types of solutions to problems involving generalized resolvents and their applications, e.g., in boundary-value problems for (ordinary and partial) differential operators. For instance, an old problem going back to M. A. Naĭmark and concerning the analytic characterization of the so-called Naĭmark extensions is solved. The present research was supported by the Academy of Finland (project no. 116842).     

Intensification of the decomposition of copper-nickel sulfide ores using low-temperature plasma

It was found that copper-nickel sulfide ores can be decomposed by treating with low-temperature low-density plasma for the subsequent determination of platinum, palladium, and silver by atomic absorption spectrometry. This shortens the time of sample decomposition and reduces the reagent consumption and labor content.     

Application of multilayer structures at millimeter wavelengths

The paper presents results of theoretical analyses and experimental investigations of the optical characteristics of devices based on multilayer dielectric structures and intended for the millimeter wave band. As is shown, multilayer dielectric structures can prove useful in devices with variable optical characteristics representing coupling elements for quasioptical open resonators, adjustable reflection coefficient mirrors in narrow-band interference Fabry-Perot filters or adjustable multilayer polarizers.