Finite element investigation of the ground states of the helium trimers 4He3 and 4He2–3He

A three‐dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers ⁴He₃ and ⁴He₂–³He. Three different He–He interaction potentials of hard‐core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Modeling of recombination kinetics of radical pairs in magnetic field. Comparison with experimental dependences on the frequency of encounters in biradicals

The recombination kinetics of spin-correlated radical pairs (RPs) with three nonequivalent magnetic nuclei were calculated under conditions of enforced encounters between radicals at time-independent frequency n_dif. The simplest two-position model of a RP was used, which includes two states (contact state and distance-separated state) of the RP, differing in magnitude of isotropic spin-spin exchange interaction between radicals. The calculated kinetic curves were treated in terms of a three-exponential model. The dependences of corresponding rate constants (k _rec) on n_dif, external magnetic field strength (B ₀), and intensity, A _eff, of isotropic hyperfine coupling (HFC) were obtained. The k _rec-vs.-n_dif or k _rec-vs.-viscosity (n_dif varies simultaneously with the inverse lifetime of the contact state) plots pass through maxima whose positions are shifted from the n_dif region near the A _eff value at B ₀ = 0.5 G toward high n_dif values with an increase in B ₀. At n_dif ≫ A _eff, the k _rec-vs.-B ₀ plots pass through maxima in the region B ₀ = A _eff. The calculated dependences are compared with experimental data on recombination of biradicals. The results of calculations show that the experimentally observed maxima on the k _rec-vs.-B ₀ or k _rec-vs.-n_dif plots can be due to peculiar features of the spin dynamics induced by the hyperfine coupling rather than the exchange interaction effects, as is commonly accepted. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1103–1110, May, 2005.     

Composition of the triacylglycerols of the phloem of Larix sibirica

The annual dynamics of the amount of acylglycerols in the phloem of the Siberian larch has been established. It has been shown that, depending on the phenological state of the wood their amount varies between 0.192 and 1.435%. The triacylglycerols of the phloem form the bulk of the acylglycerols of this tissue over the whole of the annual cycle. The stereovariety composition of the triacylglycerls of the phloem has been studied by the method of stereospecific analysis. It has been established that they have an asymmetric structure. The bulk of them contains acylglycerols in the molecules of which the sn-2 positions are acylated by unsaturated acids.Siberian Technological Institute, Krasnoyarsk. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 154–158, March–April, 1986.     

Fused polycyclic nitrogen-containing heterocycles

The condensation of methyl phenylchloropyruvate with 1-phenyl-3-(2-pyridyl)thiourea and its 3-and 4-picolyl homologs affords the corresponding 4-hydroxythiazolidines, which react with o-phenylenediamine to give one of two possible thiazolo[3,4-a]quinoxalines containing the pyridyl-or picolylimine substituents at position 1. 3a-Hydroxy-3-phenylimino-1-(2-pyridyl)thiazolo[3,4-a]quinoxalin-4-(3H,5H)-one, which is a covalent hydrate of the final product, was isolated as an intermediate in this reaction.     

Seasonal change in the essential oil ofLarix sibirica

Information is given on the qualitative and quantitative changes in the essential oil from the woody verdure of the Siberian larch. It has been established that during the vegetation period not only does the amount of essential oil in the woody verdure of the Siberian larch change but so also does the ratio of its individual components.     

Parallelization of matrix algorithms for Gröbner basis computation

Sequential and parallel implementations of the F4 algorithm for computing Gröbner bases of polynomial ideals are discussed.     

The Newton Bracketing Method for Convex Minimization

An iterative method for the minimization of convex functions f :ⁿ , called a Newton Bracketing (NB) method, is presented. The NB method proceeds by using Newton iterations to improve upper and lower bounds on the minimum value. The NB method is valid for n = 1, and in some cases for n > 1 (sufficient conditions given here). The NB method is applied to large scale Fermat–Weber location problems.