Synthesis and some reactions of 3-formylquinuclidine

3-Formylquinuclidine is synthesized and converted to 3-hydroxymethylquinuclidine, ß-(quinuclidyl-3) acrylic, and ß-(quinuclidyl-3) propionic acids.We would like to thank L. I. Zakharinka, V. V. Gavrilenko, and D. N. Masina for help and advice in the reduction of ethyl quinuclidine-3-carboxylate by sodium aluminum hydride.     

Cohomology of skew-holomorphic lie algebroids

We introduce the notion of a skew-holomorphic Lie algebroid on a complex manifold and explore some cohomology theories that can be associated with it. We present examples and applications of this notion in terms of different types of holomorphic Poisson structures.     

Compatible Structures on Lie Algebroids and Monge-Ampère Operators

We study pairs of structures, such as the Poisson-Nijenhuis structures, on the tangent bundle of a manifold or, more generally, on a Lie algebroid or a Courant algebroid. These composite structures are defined by two of the following, a closed 2-form, a Poisson bivector or a Nijenhuis tensor, with suitable compatibility assumptions. We establish the relationships between PN-, P Ω- and Ω N-structures. We then show that the non-degenerate Monge-Ampère structures on 2-dimensional manifolds satisfying an integrability condition provide numerous examples of such structures, while in the case of 3-dimensional manifolds, such Monge-Ampère operators give rise to generalized complex structures or generalized product structures on the cotangent bundle of the manifold.     

Muon content of ultrahigh-energy air showers: Yakutsk data versus simulations

A sample of 33 extensive air showers (EASs) with estimated primary energies above 2 × 10¹⁹ eV and high-quality muon data recorded by the Yakutsk EAS array is analyzed. The observed muon density is compared event-by-event to that expected from CORSIKA simulations for primary protons and iron using SIBYLL and EPOS hadronic interaction models. The study suggests the presence of two distinct hadronic components, “light” and “heavy.” Simulations with EPOS are in good agreement with the expected composition in which the light component corresponds to protons and the heavy component to iron-like nuclei. With SIBYLL, simulated muon densities for iron primaries are a factor of ∼ 1.5 less than those observed for the heavy component for the same electromagnetic signal. Assuming a two-component proton-iron composition and the EPOS model, the fraction of protons with energies E > 10¹⁹ eV is 0.52_−0.20^+0.19 at the 95% C.L. The text was submitted by the authors in English.     

Quasi-hopf algebras associated withsl 2 and complex curves

We construct quasi-Hopf algebras quantizing double extensions of the Manin pairs of Drinfeld, associated to a curve with a meromorphic differential, and the Lie algebrasl ₂. This construction makes use of an analysis of the vertex relations for the quantum groups obtained in our earlier work, PBW-type results and computation ofR-matrices for them; its key step is a factorization of the twist operator relating “conjugated” versions of these quantum groups.     

Status of the Baikal neutrino project

The status of the Baikal neutrino experiment is briefly reviewed and the results of the search for the natural flux of high-energy neutrinos are reported.     

One-dimensional model of inhomogeneous shear in sliding

The paper briefly describes a one-dimensional dynamic model of plastic shear deformation in a material surface layer in sliding friction, giving grounds to the reduction of the problem dimension from 3D to 1D. A selection of simulation results is presented to illustrate the peculiarities of plastic deformation under the action of two competitive processes — work hardening and thermal softening due to frictional heating. Presented also are experimental data on which to base the conclusion on the possibility of surface layer flow similar to flow of a viscous fluid. To assess from the Reynolds number whether turbulization of the surface layer is feasible, simulation results are used.