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

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

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

Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies

3D numerical studies have shown that the vertical voltage above the Baikal deep-water fault is detectable and that respective transfer functions, Ez-responses, are sensitive to the electrical resistivity changes of the fault, i.e. these functions appear actually informative with respect to the resistivity «breath» of the fault. It means that if the fault resistivity changed, conventional electromagnetic instruments would be able to detect this fact by measurement of the vertical electric field, Ez, or the vertical electric voltage just above the fault as well as horizontal magnetic field on the shore. Other electromagnetic field components (Ex, Ey, Hz) do not seem to be sensitive to the resistivity changes in such a thin fault (as wide as 500 m). On the other hand, such changes are thought to be able to indicate a change of a stress state in the earthquake preparation zone. Besides, the vertical profile at the bottom of Lake Baikal is suitable for electromagnetic monitoring of the fault electrical resistivity changes. Altogether, the vertical voltage above the deep-water fault might be one of earthquake precursors

Structure of oxidative and sulphate-clorinating roasting products of nickel converter matte

The structure and phase composition of the nickel converter matte roasting products has been studied in the sulphate-chlorinating process stage. In stages of the converter matte oxidation in the "fluidized bed" and flash smelting remainder roasting together with silvinite the distribution of non-ferrous metals on the phase constituents has been estimated. In the article data from optical spectroscopy, as well as X-ray diffraction, microprobe and chemical analyze are used. As following from the composition of the phases formed during sulphate-chlorinating roasting and thermodynamic modeling data a number of reactions proceeding in the process is presented. © 2013 Allerton Press, Inc

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

The Four-Loop Konishi in N=4 SYM

We present the result of a full direct component calculation for the planar four-loop anomalous dimension of the Konishi operator in N =4 Supersymmetric Yang-Mills theory. Our result confirms the results obtained from superfield (arXiv:0712.3522, arXiv:0806.2095) and superstring (arXiv:0807.0399) computations, which take into account finite size corrections to the all-loop asymptotic Bethe ansatz for the integrable models describing the spectrum of the anomalous dimensions of the gauge-invariant operators and the spectrum of the string states in the framework of the gauge/string duality.Comment: 7 pages, some detailes of calculations adde

Harmonic analysis on spherical homogeneous spaces with solvable stabilizer

For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of the representations of G on spaces of regular sections of homogeneous line bundles over G/H.Comment: v2: 14 pages, minor correction