Enzymatic dissymmetrization of meso-2,3-dimethylbutane-1,4-diol and its diacetate. Synthesis of scalemic (–)-lasiol

Acylation of meso-2,3-dimethylbutane-1,4-diol with vinyl acetate in the presence of porcine pancreatic lipase (PPL) leads to the dextrorotatory monoacetate of the above diol with enatiomeric excess (ee) 58—64%. Absolute configuration of this scalemic specimen was determined by its sequential transformation to levorotatory lasiol, a metabolite of the Lasius ants. Partial hydrolysis of the corresponding meso-diacetate, mediated by PPL or by the Pseudomonas sp. lipase affords the monoacetate of opposite configuration with ee 72—86%, a formal intermediate in the synthesis of (3S,4R)-faranal. Other microbial lipases used are distinctive in low chemoselectivity.     

Manifestation of a semimetallic state in cyclotron resonance in low-symmetry HgTe-based quantum wells

Cyclotron-resonance measurements in 21-nm-thick HgTe/CdHgTe quantum wells of different crystallographic orientations have been performed. It has been found that, in contrast to the structures with the (001) orientation of the quantum-well plane, (013)-oriented quantum wells are semimetallic and their absorption spectra exhibit both electron and hole cyclotron-resonance lines. The simultaneous presence of the two types of charge carriers originates from an overlap between the upper heavy-hole quantum-confinement subbands hh1 and hh2. This overlap is caused by the strong interaction of these subbands with the Dyakonov-Khaetskii interface state. Calculations carried out using the eight-band kp-Hamiltonian indicate that, for known values of the band-structure parameters, the overlap between hh2 and hh1 subbands does not occur; this result is in agreement with the cyclotron-resonance data for (001)-oriented structures. The enhanced interaction between heavy-hole and interface states owing to the existence of steps at low-symmetry heterointerfaces may be the mechanism responsible for the appearance of an overlap between subbands in HgTe quantum wells with orientation different from (001).     

Behavior of the magnetic subsystems in Nd2BaNiO5

The temperature dependences of the heat capacity, the magnetic susceptibility, and the splitting of the ground Kramers doublet of the Nd³⁺ ion in the chain magnet Nd₂BaNiO₅ are studied. An antiferromagnetic phase transition manifests itself as anomalies in all these dependences. The parameters of the Nd-Ni and Nd-Nd interactions are estimated. The field dependence of the magnetization has two anomalies. A strong magnetic anisotropy prevents the magnetic moments of the Nd³⁺ ion from deviating from axis c in the crystal even in an external magnetic field. The processes of magnetization and the internal specific features of a chain of spins S = 1 are discussed.     

Estimates of complete rational trigonometric sums with a prime denominator

Upper bounds are proved for special complete rational exponential sums with a prime denominator.     

State diagrams for stationary arc discharge in air

The temperature and specific and integrated powers of energy mechanisms of a stationary equilibrium arc discharge in a cylindrical channel in air under pressures of 0.1 and 1 MPa are determined from the solution to the Elenbaas-Heller equation for various values of current I and radius R. The results of computations are given in the form of diagrams of state intended for estimating the basic energy characteristics of electric arcs for the given values of I and R.     

Numerical Solution of the Retrospective Inverse Problem of Heat Conduction with the Help of the Poisson Integral

We consider the retrospective inverse problem that consists in determining the initial solution of the one-dimensional heat conduction equation with a given condition at the final instant of time. The solution of the problem is given in the form of the Poisson integral and is numerically realized by means of a quadrature formula leading to a system of linear algebraic equations with dense matrix. The results of numerical experiments are presented and show the efficiency of the numerical method including the case of the final condition with random errors.     

New solution of the plane problem for an equilibrium crack

We consider the classical plane problem of elasticity about a crack in an isotropic elastic unbounded plane resulting in a singular solution for the stresses near the crack edge. Relations of generalized elasticity with a small parameter characterizing the medium microstructure are derived, and the higher order of these relations permits eliminating the singularity of the classical solution. An experimental method for determining the medium parameter is proposed, and the corresponding experimental results are given.