On the variational noncommutative Poisson geometry

We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in the associative words. We state the basic properties of the variational Schouten bracket and derive an interesting criterion for (non)commutative differential operators to be Hamiltonian (and thus determine the (non)commutative Poisson structures). We place the noncommutative jet-bundle construction at hand in the context of the quantum string theory.Comment: Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries' (July 18-23, 2011; JINR Dubna, Russia), 4 page

A modified Poisson-Boltzmann theory: Effects of co-solvent polarizability

In this paper within a field-theoretical approach taking into account explicitly a co-solvent with a nonzero dipole and a polarizability tensor, we derive a modified Poisson-Boltzmann equation. Applying the modified Poisson-Boltzmann equation, we formulate a generalized Gouy-Chapman theory for the case when an electrolyte solution is mixed with a polar co-solvent having a large polarizability. We show that an increase of the co-solvent concentration as well as the co-solvent polarizability lead to a significant increase of differential capacitance at sufficiently high surface potentials of the electrode, whereas the profile of the electrostatic potential becomes considerably more long-ranged. On the contrary, an increase in the permanent dipole of the co-solvent only weakly affects the differential capacitance

Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

We use a nonlocal maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field $u$ is obtained from the active scalar $\theta$ by a Fourier multiplier with symbol $i k^\perp |k|^{-1} m(k|)$, where $m$ is a smooth increasing function that grows slower than $\log \log |k|$ as $|k|\rightarrow \infty$.Comment: 11 pages, second version with slightly stronger resul

Physics of B_c mesons

In the framework of potential models for heavy quarkonium the mass spectrum for the system ($\bar b c$) is considered. Spin-dependent splittings, taking into account a change of a constant for effective coulomb interaction between the quarks, and widths of radiative transitions between the ($\bar b c$) levels are calculated. In the framework of QCD sum rules, masses of the lightest vector $B_c^*$ and pseudoscalar $B_c$ states are estimated, scaling relation for leptonic constants of heavy quarkonia is derived, and the leptonic constant $f_{B_c}$ is evaluated. The $B_c$ decays are considered in the framework of both the potential models and the QCD sum rules, where the significance of Coulomb-like corrections is shown. The relations, following from the approximate spin symmetry for the heavy quarks in the heavy quarkonium, are analysed for the form factors of the semileptonic weak exclusive decays of $B_c$. The $B_c$ lifetime is evaluated with the account of the corrections to the spectator mechanism of the decay, because of the quark binding into the meson. The total and differential cross sections of the $B_c$ production in different interactions are calculated. The analytic expressions for the fragmentational production cross sections of $B_c$ are derived. The possibility of the practical $B_c$ search in the current and future experiments at electron-positron and hadron colliders is analysed.Comment: 81 page, latex, ihep.sty is required and attached in the end of the file after \end{document}, figures are not availabl