Деякі аспекти вдосконалення прискореного розмноження малопоширених екзотів та високодекоративних культиварів у південно-степовому регіоні України

The technologies of agrotechnics of accelerated generative reproduction of the not widespread therophyllous exotic Liriodendron tulipifera L., accelerated vegetative reproduction of 16 therophyllous species and 8 taxa of evergreen exotics and highly ornamental cultivars (the terms of grafts storage and planting, rootage, etc.) are worked up and approved.Разработана и апробирована технологии агротехники генеративного ускоренного размножения листопадного столь популярном экзота LiriodendrontulipiferaL., ускоренного вегетативного размножения 16 видов листопадных и 8 таксонов редких экзотов и высокодекоративных культиваров (сроки заготовки и посадки черенков, укоренение и т.д.).Розроблено та апробовано технології агротехніки генеративного прискореного розмноження листопадного малопоширеного екзота Liriodendron tulipifera L., прискореного вегетативного розмноження 16 видів листопадних і 8 таксонів малопоширених екзотів та високодекоративних культиварів (строки заготівлі та посадки живців, укорінення тощо)

Compatible Poisson-Lie structures on the loop group of SL2SL_{2}

We define a 1-parameter family of $r$-matrices on the loop algebra of $sl_{2}$, defining compatible Poisson structures on the associated loop group, which degenerate into the rational and trigonometric structures, and study the Manin triples associated to them.Comment: 5 pages, amstex, no figure

On third Poisson structure of KdV equation

The third Poisson structure of KdV equation in terms of canonical ``free fields'' and reduced WZNW model is discussed. We prove that it is ``diagonalized'' in the Lagrange variables which were used before in formulation of 2D gravity. We propose a quantum path integral for KdV equation based on this representation.Comment: 6pp, Latex. to appear in ``Proceedings of V conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, June 1994'' Teor.Mat.Fiz. 199

Cohomology of skew-holomorphic Lie algebroids

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.Comment: 16 pages. v2: Final version to be published in Theor. Math. Phys. (incorporates only very minor changes

On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model

We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the eigenvalues of the commuting Hamiltonians. A scalar product in the separated variables representation is found for which the commuting Hamiltonians are Hermitian. In the semi classical limit the Bethe roots accumulate on very specific curves in the complex plane. We give the equation of these curves. They build up a system of cuts modeling the spectral curve as a two sheeted cover of the complex plane. Finally, we extend some of these results to the XXX Heisenberg spin chain.Comment: 16 page

On the Quantum Inverse Problem for the Closed Toda Chain

We reconstruct the canonical operators $p_i,q_i$ of the quantum closed Toda chain in terms of Sklyanin's separated variables.Comment: 16 page

OPTIMIZATION OF CATALYST STRUCTURE FOR ASYMMETRIC ALLYLATION-TYPE REACTIONS OF FUNCTIONALIZED TRICHLOROSILANES WITH AROMATIC ALDEHYDES

The authors thank the Russian Science Foundation for Grant 18-73-10156-П

Efficient perturbation theory for quantum lattice models

We present a novel approach to long-range correlations beyond dynamical mean-field theory through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Neel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte-Carlo (QMC) results. An illustration of how the approach captures and allows to distinguish short- and long-range correlations is given.Comment: 5 pages, 5 figures; revised version with emphasis on the ladder approximatio

Tunka-Rex: the Cost-Effective Radio Extension of the Tunka Air-Shower Observatory

Tunka-Rex is the radio extension of the Tunka cosmic-ray observatory in Siberia close to Lake Baikal. Since October 2012 Tunka-Rex measures the radio signal of air-showers in coincidence with the non-imaging air-Cherenkov array Tunka-133. Furthermore, this year additional antennas will go into operation triggered by the new scintillator array Tunka-Grande measuring the secondary electrons and muons of air showers. Tunka-Rex is a demonstrator for how economic an antenna array can be without losing significant performance: we have decided for simple and robust SALLA antennas, and we share the existing DAQ running in slave mode with the PMT detectors and the scintillators, respectively. This means that Tunka-Rex is triggered externally, and does not need its own infrastructure and DAQ for hybrid measurements. By this, the performance and the added value of the supplementary radio measurements can be studied, in particular, the precision for the reconstructed energy and the shower maximum in the energy range of approximately $10^{17}-10^{18}\,$eV. Here we show first results on the energy reconstruction indicating that radio measurements can compete with air-Cherenkov measurements in precision. Moreover, we discuss future plans for Tunka-Rex.Comment: Proceeding of UHECR 2014, Springdale, Utah, USA, accepted by JPS Conference Proceeding