The Index of Vector Fields and Logarithmic Differential Forms

We introduce the notion of logarithmic index of a vector field on a hypersurface and prove that the homological index can be expressed via the logarithmic index. Then both invariants are described in terms of logarithmic differential forms for Saito free divisors, which are hypersurfaces with nonisolated singularities, and all contracting homology groups of the complex of regular holomorphic forms on such a hypersurface are computed. In conclusion, we consider the case of normal hypersurfaces, including the case of an isolated singularity, and describe the contracting homology of the complex of regular meromorphic forms with the help of the residue of logarithmic forms.     

Synthesis of aza steroid analogs

Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 6, pp. 854–855, June, 1991.     

Oscillatory Convective Instability in a Ternary Electrolyte: Effect of the Electrode Reaction Rate

The effect the electrode reaction rate has on the oscillatory instability, which is induced by buoyancy forces in a solution containing univalent cations of two types and a common anion, is considered. It is shown that, at a decrease in the rate, the spectrum of acceptable fluctuations of concentrations of electroactive ions narrows down, thus raising the system's stability. Diagrams of nonequilibrium phase transitions are constructed for various ratios between diffusion coefficients for anions and cations.     

Dephosphorization of manganese-containing oxide melts

A process for dephosphorization of manganese-containing oxide melts with carbon monoxide was developed and studied for the first time. Thermodynamic analysis showed that, under equilibrium conditions, the reaction of carbon monoxide CO with phosphorus oxide P₂O₅ contained in a manganese-containing oxide melt does not occur. However, since both of the products of this reaction are gaseous, the reaction may occur if the reaction products are removed from the reaction zone. The dephosphorization of manganese concentrate while blowing carbon monoxide through the molten concentrate was experimentally investigated. The blowing significantly reduced the phosphorus content of the melt: the P: Mn ratio decreased by a factor of 5–10, and the degree of dephosphorization was 70–90%.     

Numerical Analysis of the Influence of Thermal Stresses on the Nonlinear Thermomolecular Pressure Difference Effect

On the basis of a numerical analysis of the non-Navier-Stokes gas-dynamic equations for slow non-isothermal gas flows, the nonlinear thermomolecular pressure difference effect due to a large temperature gradient along the lateral surface of a capillary is investigated. It is shown that the magnitude of the effect is substantially different from the values calculated using the Navier-Stokes equations. For two models of molecular interaction (Maxwell molecules and hard spheres), the possibility of a quasi-one-dimensional interpretation of the effect for experimental estimation purposes is demonstrated. The solutions of the relaxation kinetic equation for flow in a plane capillary at small Knudsen numbers and the gas-dynamic equations for slow non-isothermal flows are compared and the range of their applicability is estimated.     

Supercooled states in the benzene-naphthalene system

Precrystallization supercooled states in the benzene-naphthalene system were studied by thermal analysis methods. A sharp change in the character of the crystallization of benzene and naphthalene, from quasi-equilibrium without supercooling to nonequilibrium-explosive with supercooling depending on liquid phase superheating with respect to the temperature of fusion was observed. Such a transition occurred monotonically for alloys. The phase diagram of the benzene-naphthalene system including metastable regions with supercooling under normal crystallization conditions was constructed. The rules governing Gibbs energy changes and mean supercoolings in crystallization depending on the concentrations of the components were determined. The supercooling values were also used to calculate such nucleation parameters as the size of critical nuclei, work of their formation, and number of unit cells and molecules in them. The molecular structure of benzene and naphthalene crystals and the structural changes of these substances during fusion that influenced the character of their subsequent crystallization were described.     

Structure and properties of bis{[2-(4-<Emphasis Type="Italic">tert</Emphasis>-butyl)phen]ethyl}phosphine sulfide

Previously unknown bis[2-(4-tert-butyl)phen]ethylphosphine sulfide is obtained with a high yield from 4-tert-butyl styrene, red phosphorus, and elemental sulfur. Using single crystal XRD, multinuclear NMR, IR, and UV spectroscopy, it is found that the phosphorus atom is four-coordinated in the bis[2-(4-tert-butyl)phen]ethylphosphine sulfide molecule (regardless of the phase state of the compound: crystal, solution). By the example of phosphorylation of bis[2-(4-tert-butyl)phen]ethylphosphine sulfide acetylene in the KOH-DMSO system it is shown that the reaction proceeds by double addition with the participation of phosphorus-centered nucleophiles.     

Low temperature deposition of nanocrystalline titanium dioxide from titanium tetraisopropoxide

Effect of ozone and water vapor on the chemical deposition of TiO₂ from the gas phase in the system of titanium tetraisopropylate-oxygen was examined. Introduction of ozone in the reaction medium was shown to result in the precipitation of smooth TiO₂ layers at 240°C, and the addition of water vapor leads to the formation with higher rate of unconsolidated layers. Adding ozone to the reaction medium with low moisture content (up to 0.65 Pa) allows obtaining at temperatures 250–350°C with high rate of growth the TiO₂ layers with the anatase nanocrystals of high photocatalytic activity.     

A molecular mechanics model for imatinib and imatinib:kinase binding

Imatinib is an important anticancer drug, which binds specifically to the Abl kinase and blocks its signalling activity. To model imatinib:protein interactions, we have developed a molecular mechanics force field for imatinib and four close analogues, which is consistent with the CHARMM force field for proteins and nucleic acids. Atomic charges and Lennard‐Jones parameters were derived from a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule interacting with imatinib fragments at 32 different positions. We considered both a neutral and a protonated imatinib. The final RMS deviation between the ab initio and force field energies, averaged over both forms, was 0.2 kcal/mol. The model also reproduces the ab initio geometry and flexibility of imatinib. To apply the force field to imatinib:Abl simulations, it is also necessary to determine the most likely imatinib protonation state when it binds to Abl. This was done using molecular dynamics free energy simulations, where imatinib is reversibly protonated during a series of MD simulations, both in solution and in complex with Abl. The simulations indicate that imatinib binds to Abl in its protonated, positively‐charged form. To help test the force field and the protonation prediction, we did MD free energy simulations that compare the Abl binding affinities of two imatinib analogs, obtaining good agreement with experiment. Finally, two new imatinib variants were considered, one of which is predicted to have improved Abl binding. This variant could be of interest as a potential drug. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Nonregular phenomena in systems of quantum wells in the presence of tunneling processes

The effect of tunneling on inelastic processes in atomic collision physics has been studied using two examples: head-on collision between hydrogen atoms and protons and hydrogen-atom reflection from an impenetrable wall. These phenomena are analyzed using the numerical solution of the nonstationary Schr?dinger equation.