5 research outputs found
On the shape of spectra for non-self-adjoint periodic Schr\"odinger operators
The spectra of the Schr\"odinger operators with periodic potentials are
studied. When the potential is real and periodic, the spectrum consists of at
most countably many line segments (energy bands) on the real line, while when
the potential is complex and periodic, the spectrum consists of at most
countably many analytic arcs in the complex plane.
In some recent papers, such operators with complex -symmetric
periodic potentials are studied. In particular, the authors argued that some
energy bands would appear and disappear under perturbations. Here, we show that
appearance and disappearance of such energy bands imply existence of nonreal
spectra. This is a consequence of a more general result, describing the local
shape of the spectrum.Comment: 5 pages, 2 figure
Break the religious of village by broken bells: anti-bell component in the fight against religion at the turn of 1920–1930 (on the example of the Zapadnaya oblast’)
Removing bells — one of the measures of antireligious policy, designed to solve the problem of shortage of metal for industrialization and depersonalize the Orthodox churches. In fact, event resulted in a robbery and an insult to the religious feelings of the faithful communities.Снятие колоколов — одна из мер антирелигиозной политики, призванная решить проблемы нехватки металла для индустриализации и обезличить православные храмы. На деле проведение мероприятий вылилось в грабёж и оскорбление религиозных чувств общин верующих.Исследование выполнено при поддержке гранта Президента для молодых ученых – кандидатов наук (проект МК-7090.2015.6, договор № 14. Z 56.15.7090-МК от 16.02.2015 г.)