Lobachevsky geometry of (super)conformal mechanics

We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane) . We also extend this picture to the N=2k superconformal mechanics described in terms of Lobachevsky superspace .     

Erratum to: Several Articles in JETP Letters Published Online First

JETP Letters - An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022330013     

A simple method for asymmetric trifluoromethylation of N-acyl oxazolidinones via Ru-catalyzed radical addition to zirconium enolates

A Ru-catalyzed direct thermal trifluoromethylation and perfluoroalkylation of N-acyloxazolidinones has been developed. The reaction is experimentally simple and requires inexpensive reagents while providing good yields of products with good levels of stereocontrol. Preliminary studies have shown notable compatibility with functional groups, aromatics, and certain heteroaromatic substituents. The described method provides a useful alternative for the synthesis of fluorinated materials in an experimentally convenient manner.     

Quantum diffusion description of the subbarrier-capture process in heavy-ion reactions

The capture of a projectile nucleus by a target nucleus at bombarding energies below the Coulomb barrier is studied on the basis of the quantum diffusion approach. The results obtained in this way for reactions involving spherical nuclei are in good agreement with available experimental data. It is shown that, beyond the range of nuclear forces, the decrease in the capture cross section as the bombarding energy decreases becomes slower.     

Electromagnetically Induced Transparency and optical pumping processes formed in Cs sub-micron thin cell

The Electromagnetically Induced Transparency (EIT) effect in a Λ-system formed by Cs atoms (6S_1/2 ? 6P_3/2 ? 6S_1/2) confined in an extremely thin cell (ETC) (atomic column thickness L varies in the range of 800 nm –3 µm is studied both experimentally and theoretically. It is demonstrated that when the coupling laser frequency is in exact resonance with the corresponding atomic transition, the EIT resonance parameters weakly depend on L, which allows us to detect the effect at L = λ = 852 nm. EIT process reveals a striking peculiarity in case of the coupling laser detuned by Δ from the atomic transition, namely the width of the EIT resonance rapidly increases upon an increase in Δ (an opposite effect is observed in centimeter-scale cells). The strong broadening of the EIT resonance for large values of detunings Δ is caused by the influence of atom-wall collisions on dephasing rate of coherence. The influence of the coupling laser on the velocity selective optical pumping/saturation resonances formed in ETC has been also studied. The theoretical model well describes the observed results.     

Polynomial hulls and proper analytic disks

We show how to construct the Perron–Bremermann function by using proper analytic disks. We apply this result to the polynomial hull of a compact set K defined on the boundary of the unit ball.     

The theory of micropolar thin elastic shells

A boundary-value problem of the three-dimensional micropolar, asymmetric, moment theory of elasticity with free rotation is investigated in the case of a thin shell. It is assumed that the general stress-strain state (SSS) is comprised of an internal SSS and boundary layers. An asymptotic method of integrating a three-dimensional boundary-value problem of the micropolar theory of elasticity with free rotation is used for their approximate determination. Three different asymptotics are constructed for this problem, depending on the values of the dimensionless physical parameters. The initial approximation for the first asymptotics leads to the theory of micropolar shells with free rotation, the approximation for the second leads to the theory of micropolar shells with constrained rotation and the approximation for the third asymptotics leads to the so-called theory of micropolar shells “with a small shear stiffness”. Micropolar boundary layers are constructed. The problem of the matching of the internal problem and the boundary-layer solutions is investigated. The two-dimensional boundary conditions for the above-mentioned theories of micropolar shells are determined.     

Erratum to: Natural Vibrations of Micropolar Elastic Flexible Plates and Shallow Shells

Acoustical Physics - An Erratum to this paper has been published: https://doi.org/10.1134/S1063771022340012     

On the product property of the pluricomplex Green function

We prove that the pluricomplex Green function has the product property for any domains and .