The workshop «Secondary and delocalized index invariants» was held in Copenhagen, Denmark
11- 15 June 2018 the workshop «Secondary and delocalized index invariants» was held in Copenhagen, Denmark. The organizer of the event was University of Copenhagen (QS 79). Savin A. Yu., Doctor of Physics and Mathematics, professor of the Nilkolskii Mathematical Institute, gave a plenary talk: «On the index of elliptic problems in plane compound domains». The following problem was considered there. Let D be a compact plane domain with piecewise smooth boundary and we are also given a ﬁnite system of cuts of this domain by smooth curves. We consider diﬀerential equations in D with boundary conditions imposed along the boundary of D and transmission conditions along the cuts. Under appropriate ellipticity conditions, such problems have Fredholm property in weighted Sobolev spaces (with weights prescribed at the singular points on the boundary and inside the domain). In this talk, we address the index problem in this setting. The focus is on the contributions of the singular points to the index formula. It turns out that these contributions can be described as η-invariants of conormal symbols at the singular points and to deﬁne these η-invariants, we extend the deﬁnition of η-invariant due to Melrose to parameter-dependent boundary value problems.
A team of medics from RUDN University conducted an experiment on rats and confirmed that surgeries in the nasal cavity can cause behavioral changes, namely, make the animals timider. This effect is associated with an ANS reaction triggered by stress.
Bacteria in biofilms are 1,000 times more resistant to antibiotics, disinfectants, mechanical treatment, and other types of stress. A chemist from RUDN University suggested a method to prevent the formation of biofilms and reduce the resistance of bacteria to antimicrobial medications. This might help increase the efficiency of antibacterial treatment in the food industry, medicine, and agriculture.
A specialist in spacecraft movement control analyzed the process of placing vehicle stages, boosters, and other space debris into the so-called disposal orbit and suggested cleaning lower orbits up with a spacecraft that has modules with engine units on board. These modules will attach to space debris objects and move them away. As for the geostationary orbit, a preferable way to clean it up would be a towing spacecraft that transports space debris objects into the disposal orbit.