Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation

The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined.     

New effective reagent [Cp2ZrH2 · ClAlEt2]2 for alkene hydrometallation

New bimetallic complex [Cp₂ZrH₂ · ClAlEt₂]₂ (1) was synthesized, and its reactivity in hydrometallation reaction with the following alkenes was studied: hept-1-ene, okt-1-ene, α-methylstyrene, (1S)-β-pinene, (+)-camphene. Complex 1 shows the highest reactivity among the other known Al,Zr-bimetallic complexes: [Cp₂ZrH₂ · ClAlBuⁱ₂]₂ (2), [Cp₂ZrH₂ · AlEt₃]₂ (3), [Cp₂ZrH₂ · AlBuⁱ₃]₂ (4) and [Cp₂ZrH₂ · HAlBuⁱ₂] (5) as well as organoaluminium compounds (OAC): ⁱBu₂AlH, ⁱBu₃Al and ⁱBu₂AlCl in presence of Zr catalysts. Chlorine containing complexes 1 and 2 appear to be more effective in alkene hydrometallation, and relative hydrometallation rates are (1S)-β-pinene ? (+)-camphene < α-methylstyrene < oct-1-ene < hept-1-ene. Hydrometallation of (1S)-β-pinene and its subsequent oxidation with I₂ run with high diastereoselectivity and yield trans-myrtanol. However, the diastereoselectivity of (+)-camphene hydrometallation is less than that for (1S)-β-pinene, and the reaction gives predominately endo-camphanol.     

Titanium-catalyzed cyclocodimerization of cyclohepta-1,3,5-triene with spiro[cyclopropane-1,7′-norborna-2,5-diene]

Russian Chemical Bulletin - Titanium complexes-catalyzed codimerization of cyclohepta-1,3,5-triene with spiro[cyclopropane-1,7′-norborna-2,5-diene] affords...     

Zero-mass fermions in Coulomb and Aharonov-Bohm potentials in 2+1 dimensions

We consider the motion of a relativistic charged zero-mass fermion in Coulomb and Aharonov-Bohm potentials in 2+1 dimensions. With these singular external potentials, we construct one-parameter self-adjoint Dirac Hamiltonians classified by self-adjoint boundary conditions. We show that if the so-called effective charge becomes overcritical, then virtual (quasistationary) bound states occur. The wave functions corresponding to these states have large amplitudes near the Coulomb center, and their energy spectrum is quasidiscrete and consists of a number of broadened levels of a width related to the inverse lifetime of the quasistationary state. We derive equations for the quasidiscrete spectra and quasistationary state lifetimes and solve these equations in physically interesting cases. We study the so-called local densities of state, which can be assessed in physical experiments, as functions of the energy and the problem parameters, investigating these densities both analytically and graphically.     

Mechanism of catalytic cycloboration of α-olefins with boron trichloride: the synthesis of hardly obtainable boriranes and the mechanistic DFT study of transmetalation of titanacyclopropane intermediates

A theoretically justified mechanism of transmetalation of 2-alkyl substituted titanacyclopropanes with BCl₃ is proposed based on the DFT calculations of the thermodynamic and activation parameters of possible reaction pathways. Based on the data obtained, phenyl- and alkyldichloroboranes were proposed to be used as transmetalating agents along with BCl₃ in the catalytic cycloboration in the presence of Cp₂TiCl₂ and Mg metal. It was shown that the barely accessible 1-phenyl-2-hexylborirane can be synthesized using PhBCl₂.     

Charged vector bosons in a magnetic field at a finite temperature

Bose-Einstein condensation does not occur in a charged vector boson gas in the presence of a homogeneous external magnetic field, although a major portion of the bosons are in the ground state. Spontaneous magnetization occurs in a vector boson gas. The total birth probability of vector boson pairs in a vacuum under a strong magnetic field at a finite temperature can be determined. Expressions that can probably characterize the vacuum free energy and magnetic moment are found, and formulas for the density and magnetic moment of the vector boson pairs generated by a magnetic field at a finite temperature are derived. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 114, No. 3, pp. 439–453, March, 1998.     

1H and13C NMR spectra of biologically active compounds. IV. Diastereomers of pyrethroids and their insecticidal activity

The stereochemistry of the diastereomers of permethrin has been confirmed by¹³C NMR spectroscopy and the stereochemistry of the 9-CN derivative (cypermethrin) has been established. Diagnostic values of the diastereomeric effects have been determined for identifying diastereomers with respect to the cyclopropane ring and to the gem-dimethyl groups. It has been shown that the insecticidal activity of pyrethroids depends both on the stereochemistry of the cyclopropane fragment and on the orientation of a CN substituent in the side chain.Institute of Chemistry and Division of Biochemistry and Phytochemistry, Bashkir Branch, USSR Academy of Sciences, Ufa. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 287–292, March–April, 1988.