Reflective Elastic Scattering at LHC

We discuss effects of reflective scattering for hadron and heavy nuclei collisions at the LHC and asymptotical energies. It is shown that the reflective scattering might lead to decreasing matter density with energy beyond the LHC energies. Limiting form of energy dependence of hadron density is obtained. Unitarity upper bound for the absolute value of the real part of elastic scattering amplitude and two-particle inelastic binary reactions amplitudes in impact parameter representation is two times less than the corresponding bound for the imaginary part of the elastic scattering amplitude. The former limit restricts a possible odderon contribution.Comment: 7 pages, 1 figure, talk given at the EDS'09 Conferenc

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