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.
RUDN University doctors have followed the recovery of patients after the treatment of a postoperative hernia using a polypropylene mesh-endoprosthesis.
A RUDN University mathematician with colleagues from Egypt, Saudi Arabia and China has collected the latest research in the field of deep learning for detecting pedestrians for vehicles with autopilot. The authors identified weaknesses and outlined targets for further research.
A RUDN engineer with colleagues from Iran proposed a new model for cooling and heating indoor air using soil energy. This eco-friendly approach is completely harmless and allows you to change the air temperature by 21%.