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 co
mpact simply connected algebraic varieties. As a byproduct we present certain remarks on the Weinstein structures and Eliashberg conjectures.
In recent papers, summarized in survey [1], we construct a number of examples of non standard lagrangian tori on compact toric varieties and as well on certain non toric varieties which admit pseudotoric structures. Using this pseudotoric technique w
e explain how non standard lagrangian tori of Chekanov type can be constructed and what is the topological difference between standard Liouville tori and the non standard ones. However we have not discussed the natural question about the periods of the constructed twist tori; in particular the monotonicity problem for the monotonic case was not studied there. In the paper we present several remarks on these questions, in particular we show for the monotonic case how to construct non standard lagrangian tori which satisify the monotonicity condition. First of all we study non standard tori which are Bohr - Sommerfeld with respect to the anticanonical class. This notion was introduced in [2], where one defines certain universal Maslov class for the ${rm BS}_{can}$ lagrangian submanifolds in compact simply connected monotonic symplectic manifolds. Then we show how monotonic non standard lagrangian tori of Chekanov type can be constructed. Furthemore we extend the consideration to pseudotoric setup and construct examples of monotonic lagrangian tori in non toric monotonic manifolds: complex 4 - dimensional quadric and full flag variety $F^3$.
The natural uranium assembly, QUINTA, was irradiated with 2, 4, and 8 GeV deuterons. The $^{232}$Th, $^{127}$I, and $^{129}$I samples have been exposed to secondary neutrons produced in the assembly at a 20-cm radial distance from the deuteron beam a
xis. The spectra of gamma rays emitted by the activated $^{232}$Th, $^{127}$I, and $^{129}$I samples have been analyzed and several tens of product nuclei have been identified. For each of those products, neutron-induced reaction rates have been determined. The transmutation power for the $^{129}$I samples is estimated. Experimental results were compared to those calculated with well-known stochastic and deterministic codes.
In previous papers we define certain Lagrangian shadows of ample divisors in algebraic varieties. In the present brief note an existence condition is discussed for these Lagrangian shadows.
Special Bohr - Sommerfeld geometry, first formulated for simply connected symplectic manifolds (or for simple connected algebraic varieties), gives rise to some natural problems for the simplest example in non simply connected case. Namely for any al
gebraic curve one can define a correspondence between holomorphic differentials and certain finite graphs. Here we ask some natural questions appear with this correspondence. It is a partial answer to the question of A. Varchenko about possibility of applications of Special Bohr -Sommerfeld geometry in non simply connected case. The russian version has been translated.
In the framework of Special Bohr - Sommerfeld geometry it was established that an ample divisor in compact algebraic variety can define almost canonically certain real submanifold which is lagrangian with respect to the corresponding Kahler form. It
is natural to call it lagrangian shadow; below we emphasize this correspondence and present some simple examples, old and new. In particular we show that for irreducible divisors from the linear system $vert - frac{1}{2} K_{F^3} vert$ on the full flag variety $F^3$ their lagrangian shadows are Gelfand - Zeytlin type lagrangian 3 - spheres.
Mechanisms of the charge exchange reaction $dpto {pp}_{!s} Npi$, where ${pp}_{!s}$ is a two-proton system at low excitation energy, are studied at beam energies 1 -- 2 GeV and for invariant masses $M_X$ of the final $Npi $ system that correspond to t
he formation of the $Delta(1232)$ isobar. The direct mechanism, where the initial proton is excited into the $Delta(1232)$, dominates and explains the existing data on the unpolarized differential cross section and spherical tensor analyzing power $T_{22}$ for $M_X> 1.2$ GeV/$c^2$. However, this model fails to describe $T_{20}.
In view of the mass spectrum of heavy mesons in vacuum the analytical properties of the solutions of the truncated Dyson-Schwinger equatio for the quark propagator within the rainbow approximation are analysed in some detail. In Euclidean space, the
quark propagator is not an analytical function possessing, in general, an infinite number of singularities (poles) which hamper to solve the Bethe-Salpeter equation. However, for light mesons (with masses M_{qbar q} <= 1 GeV) all singularities are located outside the region within which the Bethe-Salpeter equation is defined. With an increase of the considered meson masses this region enlarges and already at masses >= 1 GeV, the poles of propagators of u,d and s quarks fall within the integration domain of the Bethe-Salpeter equation. Nevertheless, it is established that for meson masses up to M_{qbar q}~=3 GeV only the first, mutually complex conjugated, poles contribute to the solution. We argue that, by knowing the position of the poles and their residues, a reliable parametrisation of the quark propagators can be found and used in numerical procedures of solving the Bethe-Salpeter equation. Our analysis is directly related to the future physics programme at FAIR with respect to open charm degrees of freedom.
In this talk, we discuss the algorithm for the construction of analytical coefficients of higher order epsilon expansion of some Horn type hypergeometric functions of two variables around rational values of parameters.
We demonstrate that the high-quality cooling data observed for the young neutron star in the supernova remnant Cassiopeia A over the past 10 years--as well as all other reliably known temperature data of neutron stars--can be comfortably explained wi
thin the nuclear medium cooling scenario. The cooling rates of this scenario account for medium-modified one-pion exchange in dense matter and polarization effects in the pair-breaking formations of superfluid neutrons and protons. Crucial for the successful description of the observed data is a substantial reduction of the thermal conductivity, resulting from a suppression of both the electron and nucleon contributions to it by medium effects. We also find that possibly in as little as about ten years of continued observation, the data may tell whether or not fast cooling processes are active in this neutron star.
