Special Bohr-Sommerfeld geometry: variations

In the paper we continue to study Special Bohr-Sommerfeld geometry of compact symplectic manifolds. Using natural deformation parameters we avoid the difficulties appeared in the definition of the moduli space of Special Bohr-Sommerfeld cycles for compact simply connected algebraic varieties. As a byproduct we present certain remarks on the Weinstein structures and Eliashberg conjectures

Symplectic reduction and lagrangian submanifolds in Gr(1,n)(1, n)

We study lagrangian submanifolds of algebraic variety Gr(1, n) equipped with the Kahler form given by the Plucker embedding. We use the correspondence between lagrangian submanifolds of Gr(1, n) and lagrangian submanifolds of variety M_{n-k}, given by symplectic reduction Gr(1, n)//T^k for some specially chosen moment maps, which generate T^k action on Gr(1, n). We establish that in this way one finds many topological types, realized by lagrangian submanifolds, and then one counts that Gr(1, n) admits more than n different topological types of smooth lagrangian submanifolds.Comment: in russian. since the author realized that the same method works for the case $k = 2, ..., n-1$ the previous version is replace

Increasing the Uniformity of Application of Mineral and Lime Fertilizers

Introduction. Modern agricultural production is based on the use of resource-saving technologies for agricultural production. An important element of these technologies is the use of mineral fertilizers and special importance is given to the uniformity of applying them. Aim of the Study. The study is aimed at improving the process of applying mineral and lime fertilizers through the development of a pneumatic centrifugal working body. Materials and Methods. For the theoretical studies, there were used the principles of mathematics and theoretical mechanics. The experimental studies were carried out at the testing ground of the Institute of Mechanics and Energy of Mordovia State University. The quality assessment of the operation of the unit equipped with experimental working bodies was carried out in accordance with GOST 28714-2007. Results. To better distribute mineral fertilizers of heterogeneous granulometric composition over the field surface, there has been proposed a working element, the operating principle of which is based on the total use of mechanical and pneumatic effects on the granules of the agricultural inputs. The use of the developed working bodies makes it possible to increase the uniformity of fertilizer application by 17.6%. Discussion and Conclusion. As a result of the conducted study, there has been proven the effectiveness of using the developed pneumocentrifugal working body, which makes it possible to increase the uniformity of distribution of mineral and lime fertilizers

Energy Resolution Performance of the CMS Electromagnetic Calorimeter

The energy resolution performance of the CMS lead tungstate crystal electromagnetic calorimeter is presented. Measurements were made with an electron beam using a fully equipped supermodule of the calorimeter barrel. Results are given both for electrons incident on the centre of crystals and for electrons distributed uniformly over the calorimeter surface. The electron energy is reconstructed in matrices of 3 times 3 or 5 times 5 crystals centred on the crystal containing the maximum energy. Corrections for variations in the shower containment are applied in the case of uniform incidence. The resolution measured is consistent with the design goals

Search for supersymmetry in proton-proton collisions at √s = 13 TeV in events with high-momentum Z bosons and missing transverse momentum

A search for new physics in events with two highly Lorentz-boosted Z bosons and large missing transverse momentum is presented. The analyzed proton-proton collision data, corresponding to an integrated luminosity of 137 fb−1, were recorded at √s = 13 TeV by the CMS experiment at the CERN LHC. The search utilizes the substructure of jets with large radius to identify quark pairs from Z boson decays. Backgrounds from standard model processes are suppressed by requirements on the jet mass and the missing transverse momentum. No significant excess in the event yield is observed beyond the number of background events expected from the standard model. For a simplified supersymmetric model in which the Z bosons arise from the decay of gluinos, an exclusion limit of 1920 GeV on the gluino mass is set at 95% confidence level. This is the first search for beyond-standard-model production of pairs of boosted Z bosons plus large missing transverse momentum