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We discuss resonances for Schrdinger operators on metric graphs which consists of a finite compact part and a finite number of halflines attached to it; the vertex coupling is assumed to be of the 6-type or certain modifications of it. Using exterior complex scaling on the graph we show that the resolvent and scattering resonances coincide in this case.

Various qualitative methods for analyzing the discrete spectrum of SchrOdinger operators have been elaborated during the last three decades-for a review see Eef. 1, Section XIII. 3. They are of a great physical interest, especially because they can provide us with an information about -)*the few-body and many-body Hamlltonians, for which the quantitative methods are usually difficult to be applied. lt is not strange, therefore, that new re3ulta of this type continue to appear.

Effect of the spin-involved interaction of electrons with impurity atoms or defects to the transport properties of a two-dimensional electron gas is described by using a simplifying two-component model. Components representing spin-up and spin-down states are supposed to be coupled at a discrete set of points within a conduction channel. The used limit of the short-range interaction allows to solve the relevant scattering problem exactly. By varying the model parameters different transport regimes of two-terminal devices with ferromagnetic contacts can be described. In a quasi-ballistic regime the resulting difference between conductances for the parallel and antiparallel orientation of the contact magnetization changes its sign as a function of the length of the conduction channel if appropriate model parameters are chosen. The effect is in agreement with recent experimental observations.