A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasi-linear operators

A priori estimates for finite-difference approximations for the first and second-order derivatives are obtained for solutions of parabolic equations described in the title.

     

Participation of hydrogen bonds in the protonation of (η5-C5Me5)M(CO)2, M=Ir,Rh

The interaction of Cp^*M(CO)₂ (M=Ir or Rh) with CF₃COOH in low polar media results in partial protonation of these compounds giving molecular (M...HO) and ionic (MH⁺...O^–) hydrogen-bonded complexes. According to IR spectral data, a decrease in temperature results in a shift of the equilibrium toward the ionic forms. These compounds react with phenol to give molecular complexes only.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2002–2003, November, 1993.     

“New” Ginzburg-Pekar waves in the microwave range in ice

The recently discovered effect of microwave radiation spatial dispersion in freshwater ice is studied experimentally. This effect, first studied by Ginzburg and Pekar, shows up most vividly in the emergence of new waves that have the same polarization as the primary wave but different wavevectors. In the case of monochromatic radiation, four waves with different wavevectors may coexist in the medium. Interference of these waves may explain anomalies in the electromagnetic properties of the glacial structures observed earlier. New experimental results on the polarization properties of the signal transmitted through ice corroborate the spatial dispersion in the microwave range.     

Gas phase kinetic and theoretical studies of reactions of germylenes and dimethylstannylene

The results of time resolved gas phase studies of labile germylenes (GeH₂ and GeMe₂) and dimethylstannylene (SnMe₂) reactions reported to date are considered together with data of quantum-chemical investigations of the potential energy surfaces of these systems. Reaction mechanisms are discussed. A comparison of reactivity in the series of carbene analogs, ER₂ (E = Si, Ge, Sn, R = H, Me), is made.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 477–505, March, 2005.     

Advances in the Understanding and Application of Catalysts (Russian–American Seminar on Catalysis,Moscow, May 28–30, 2003)

Kinetics and Catalysis -     

A Quantum-Chemical Study of the Steric and Electronic Structure of the Molecules of Endogenic Peptides NP-4 and NP-5

The geometric parameters of the molecules of rabbit defensins NP-4 and NP-5 were fully optimized by the molecular-mechanics and semiempirical (MNDO, AM1) methods. It was suggested that the ligand - receptor binding of the molecules of these defensins occurring, according to the method of local fization of potential, in a 1:1 stoichiometric ratio is most probably due to hydrogen bonding involving the carboxy group of the pentant Glu¹⁴ chain.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 3, 2005, pp. 509–515.Original Russian Text Copyright © 2005 by Shchegolev, Rogachevskii, MacKee, Kokryakov, Plakhova, Krylov.     

Raman spectroscopic study of the phase transitions induced by hydrostatic pressure in a Rb2KScF6 crystal

The Raman spectra of Rb₂KScF₆ elpasolite crystals are studied in the pressure range up to 7 GPa. A phase transition is revealed at a pressure of approximately 1 GPa. Analysis of the changes in the spectral parameters shows that the phase transition is accompanied by a doubling of the volume of the primitive cell in the initial cubic phase. Judging from the character of the variations in the pressure dependences of the frequency of the observed vibrations, there can exist another transition to the phase with a lower symmetry at a pressure of approximately 2.1 GPa.     

Magnetic hyperfine fields for Sn atoms in rare-earth intermetallides: huge deviation from proportionality between Bhf and Sz

The magnetic hyperfine fields for ¹¹⁹Sn impurity atoms, localized in Ga sites of ferromagnetic intermetallic compounds RGa (R=Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm), were measured by the Mössbauer spectroscopy technique. At T=5 K, the hyperfine field value (B_hf) varies from 3.3 T in TmGa to 28.0 T in GdGa. Huge deviation from the proportionality between B_hf and the projection of the R³⁺ ion spin (S_z=(g−1)J) was found. As the atomic number of the R element increases, the B_hf/S_z ratio drastically decreases from 12.6 T for PrGa to 3.3 T for TmGa. This unexpected result can be explained by the strong dependency of B_hf value on the relationship between the Sn-R atomic separation (R_nn) and the radius of the magnetic 4f shell (R_4f). In the framework of this concept, the available experimental data for Sn atom in the rare-earth compounds with non-magnetic sp elements were considered. The data may be described by the universal dependency on the single parameter, λ=R_nn/R_4f.