Bounds on the number of connected components for tropical prevarieties

For a tropical prevariety in Rn given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of connected components is less than k+7n−

Charged complexes at the surface of liquid helium

Charged clusters in liquid helium in an external electric field form a two-dimensional system below the helium surface. This 2D system undergoes a phase transition from a liquid to a Wigner crystal at rather high temperatures. Contrary to the electron Wigner crystal, the Wigner lattice of charged clusters can be detected directly.Comment: 6 pages, 1 figur

Electron mobility on a surface of dielectric media: influence of surface level atoms

We calculate the contribution to the electron scattering rate from the surface level atoms (SLA), proposed in [A.M. Dyugaev, P.D. Grigoriev, JETP Lett. 78, 466 (2003)]. The inclusion of these states into account was sufficient to explain the long-standing puzzles in the temperature dependence of the surface tension of both He isotopes and to reach a very good agreement between theory and experiment. We calculate the contribution from these SLA to the surface electron scattering rate and explain some features in the temperature dependence of the surface electron mobility. This contribution is essential at low temperature $T<0.5$ when the He vapor concentration is exponentially small. For an accurate calculation of the electron mobility one also needs to consider the influence of the clamping electric field on the surface electron wave function and the temperature dependence of the He3 chemical potential.Comment: 6 pages, 1 figur