Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup

For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if and only if the weight semigroup of G/H satisfies some simple condition.Comment: v2: title and abstract changed; v3: 16 pages, minor correction

RadioAstron probes the ultra-fine spatial structure in the H2_2O maser emission in the star forming region W49N

H$_2$O maser emission associated with the massive star formation region W49N were observed with the Space-VLBI mission RadioAstron. The procedure for processing of the maser spectral line data obtained in the RadioAstron observations is described. Ultra-fine spatial structures in the maser emission were detected on space-ground baselines of up to 9.6 Earth diameters. The correlated flux densities of these features range from 0.1% to 0.6% of the total flux density. These low values of correlated flux density are probably due to turbulence either in the maser itself or in the interstellar medium.Comment: Accepted for publication in Advances in Space Researc

Towards proof of new identity for Green functions in N=1 supersymmetric electrodynamics

For the N=1 supersymmetric massless electrodynamics, regularized by higher derivatives, we describe a method, by which one can try to prove the new identity for the Green functions, which was proposed earlier. Using this method we show that some contribution to the new identity are really 0.Comment: 16 pages, 1 figure, an error corrected, significant change

ПРОБЛЕМИ СПІЛКУВАННЯ З ПАЦІЄНТАМИ, ЯКІ МАЮТЬ ВАДИ СЛУХУ

In the article the basic problems of communication with patients who have impaired hearing, the major categories of impaired hearing, ethical aspects of communication with such patients and examples of problem-solving communication.У статті наведені основні проблеми спілкування з пацієнтами, які мають вади слуху, основні категорії вад слуху, етичні аспекти спілкування з подібними пацієнтами та приклади вирішення проблем спілкування

Transcendental numbers and the topology of three-loop bubbles

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys. Rev. Let

Variational approach for electrolyte solutions: from dielectric interfaces to charged nanopores

A variational theory is developed to study electrolyte solutions, composed of interacting point-like ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and non-linear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image charge repulsion. Our variational equations thus go beyond the mean-field theory. The influence of salt concentration, ion valency, dielectric jumps, and surface charge is studied in two geometries. i) A single neutral air-water interface with an asymmetric electrolyte. A charge separation and thus an electrostatic field gets established due to the different image charge repulsions for coions and counterions. Both charge distributions and surface tension are computed and compared to previous approximate calculations. For symmetric electrolyte solutions close to a charged surface, two zones are characterized. In the first one, with size proportional to the logarithm of the coupling parameter, strong image forces impose a total ion exclusion, while in the second zone the mean-field approach applies. ii) A symmetric electrolyte confined between two dielectric interfaces as a simple model of ion rejection from nanopores. The competition between image charge repulsion and attraction of counterions by the membrane charge is studied. For small surface charge, the counterion partition coefficient decreases with increasing pore size up to a critical pore size, contrary to neutral membranes. For larger pore sizes, the whole system behaves like a neutral pore. The prediction of the variational method is also compared with MC simulations and a good agreement is observed.Comment: This version is accepted for publication in Phys. Rev. E

Special case of sunset: reduction and epsilon-expansion

We consider two loop sunset diagrams with two mass scales m and M at the threshold and pseudotreshold that cannot be treated by earlier published formula. The complete reduction to master integrals is given. The master integrals are evaluated as series in ratio m/M and in epsilon with the help of differential equation method. The rules of asymptotic expansion in the case when q^2 is at the (pseudo)threshold are given.Comment: LaTeX, 13 pages, 1 figur