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 chemist from RUDN University has developed a catalyst for the production of eugenol acetate, a substance that destroys the larvae of mosquitoes transmitting dangerous diseases, being a safe chemical for human health.
RUDN soil scientists have revealed a direct correlation between the rate of soil formation of carbon dioxide, called CO2 emissions, and the content of microbial biomass in it. It is known that CO2 emission from soil is mainly conditioned by respiration of soil microorganisms and plant roots. The more CO2 soil emits, the more microbial biomass it usually contains. It was shown that CO2 emission by chernozem of different ecosystems (or different types of land use) correlates with the content of microbial biomass, and most closely with the rate of its microbial respiration. And the soil with good microbial properties has the “best quality”, is more fertile, provides the highest yield of crops and other plant biomass.
A RUDN chemist has synthesized a catalyst for the production of gamma-valerolactone — an energy-intensive “green” biofuel. The catalyst based on zirconium dioxide and zeolite has shown high efficiency in converting the waste of wood plant materials — methyl levulinate — to gamma-valerolactone.