Power expansions for the self-similar solutions of the modified Sawada-Kotera equation

The fourth-order ordinary differential equation that defines the self-similar solutions of the Kaup—Kupershmidt and Sawada—Kotera equations is studied. This equation belongs to the class of fourth-order analogues of the Painlevé equations. All the power and non-power asymptotic forms and expansions near points z = 0, z = ∞ and near an arbitrary point z = z ₀ are found by means of power geometry methods. The exponential additions to the solutions of the studied equation are also determined.      

Applicability of the critical chromatography concept to proteomics problems: Dependence of retention time on the sequence of amino acids

A peptide separation model based on the technique of liquid chromatography of macromolecules at the critical condition was proposed. In terms of this model, the array of experimental data on the separation of peptides is considered. The main phenomenological parameters of the model—effective adsorption energies of amino acid residues—were determined, thus allowing the influence of character of their alternation in the chain on retention times to be predicted. The model is applicable to investigation into the feasibility of separation in different chromatographic modes of not only peptides with the same amino acid composition and different sequences of units in the chain but also peptides containing amino acid isomers and mirror sequences with different terminal groups.     

Crystal structure of the growth surface of silicon carbide obtained by sublimation

Structural study of polycrystalline silicon carbide obtained by sublimation performed via X-ray luminescence and X-ray diffraction analysis. It is shown that chemical vapor deposition of silicon carbide results in the formation of grains with the (00.1), (01.1), and (12.3) crystallographic planes parallel to the growth surface. The grains with the (00.1) growth planes are characterized by perfect structure and by red luminescence. Domains with yellow luminescence have a mosaic structure with the (01.1) and (12.3) growth planes.     

Mössbauer study of nanodimensional nickel ferrite – mechanochemical synthesis and catalytic properties

Iron–nickel spinel oxide NiFe₂O₄ nanoparticles have been prepared by the combination of chemical precipitation and subsequent mechanical milling. For comparison, their analogue obtained by thermal synthesis is also studied. Phase composition and structural properties of iron–nickel oxides are investigated by X-ray diffraction and Mössbauer spectroscopy. Their catalytic behavior in methanol decomposition to CO and methane is tested. An influence of the preparation method on the reduction and catalytic properties of iron–nickel samples is established.     

Magnetic and petrochemical properties of rocks from the Red Sea rift zone

The magnetic and petrochemical properties of basalts dredged from the rift zone at the southern part of the Red Sea at approximately 18° N are studied. The conditions of their formation and evolution are elucidated. The formation of basalts is found to occur in two stages differing in their magma supply rates and redox conditions. Special features of magnetic behavior and the anomalous geomagnetic field in the region were used to determine the sites where the rocks had experienced strong thermodynamic effects (tectonic strain, deformation, heating, etc.). The conditions in which natural remanent magnetization of the basalts was formed are estimated.     

Polyfunctional additives to oils, based on sulfonated oligomers

Studies in the field of development of polymeric oligoalkenesulfonate additives derived from sulfonated oligomers and exhibiting multifunctional effect when added to petroleum oils are summarized.     

Decoupling Problem for Systems of Quasi-Linear pde’s

The necessary and sufficient conditions for the decoupling of a quasi-linear system of partial differential equations into k non-interacting subsystems are derived. Several necessary conditions for the decoupling are found and applied to the Benney system.