Stefan problem with a kinetic and the classical conditions at the free boundary

The Stefan problem is considered with the kinetic condition u⁺=u^–=k(y, )-v at the phase interface, where k(y, ) is the half-sum of the principal curvatures of the free boundary and v is the speed of its shifting in the direction of a normal. The solvability of a modified Stefan problem in spaces of smooth functions and the convergence of its solutions as 0 to a solution of the classical Stefan problem are proved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 155–166, February, 1992.     

Radio-frequency superradiance induced by the rheological explosion of polymer composites containing paramagnetic cobalt complexes

Superradiance induced by the rheological explosion of composites based on polystyrene, cobalt acetylacetonate, and/or 3,5-di-tert-butylcatechol has been investigated. The superradiance intensity is determined by solid-phase chemical reactions induced by the rheological explosion. EPR, X-ray diffraction, and electron microscopic characterization of stable products resulting from the rheological explosion in the polymer matrix has demonstrated that the superradiance intensity is related to the electronic properties and structure of two-spin intermediates, namely, radical pairs and organoelement biradicals.     

Some kinetic features of the hydrolysis of protopectin

Some features of the kinetics of the hydrolysis of apple protopectin have been studied on the basis of an analysis of monosaccharide residues of the pectin substances and determinations of characteristic viscosity. It has been shown that the fine regulation of the physicochemical parameters of the hydrolysis of protopectin leads to the formation of pectin substances with different properties.     

Effect of DNA and bivalent metal ions on the interaction of thermostable DNA polymerase <Emphasis Type="Italic">Tte</Emphasis> with dNTPs

The interaction of DNA polymerase Tte from Thermus thermophilus B35 with dUTP analog containing a fluorescein residue bound to C(5) of the base (Flu-dUTP) was studied by fluorescence titration. The dissociation constants of the enzyme—substrate complexes in the absence and in the presence of a DNA duplex containing an extended template and bivalent metal ions and the kinetic parameters of polymerization by DNA polymerase Tte in the presence of Flu-dUTP were determined. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1268–1272, May, 2005.     

Hydrocarbon specificity in the selective catalytic reduction of NOx over Cu-ZSM-5 and Co-ZSM-5 catalysts

Transformation of surface nitrates under CH₄ (CH₄+O₂) was found to ensure steady-state activity of Co-ZSM-5 in the selective catalytic reduction of nitrogen oxides by methane (CH₄-SCR). For Cu-ZSM-5, such species are mainly converted into NO. Relaxation of the coordination sphere due to oxygen and NO adsorption, stability of C,N-containing intermediates and activation routes of hydrocarbons (methane, propane) were analyzed as factors determining catalytic properties of Cu and Co cations.     

Oka's conjecture on irreducible plane sextics

We partially prove and partially disprove Oka's conjecture onthe fundamental group/Alexander polynomial of an irreducibleplane sextic. Among other results, we enumerate all irreduciblesextics with simple singularities admitting dihedral coveringsand find examples of Alexander equivalent Zariski pairs of irreduciblesextics.     

Mathematical modeling of mechanical properties of metals and alloys at large strains

We discuss problems in mathematical modeling of the mechanical behavior of metals and alloys at large strains. Attention is mainly paid to the analysis of the stress-strain state of specimens and structural fragments made of highly plastic materials with the effect of stability loss under tensile stresses taken into account. We discuss the methods for determining the true property diagram at strains exceeding the ultimate uniform strain. We process experimental data and determine the true property diagrams for AMg6, AMg6M, and 1201 aluminum alloys and BrKh08 alloy. To calculate the load-carrying capacity of structural members, one often uses the conventional ultimate strength σ _b accepted in regulations as a material characteristic. But it follows from the method for experimentally determining this characteristic that it depends on the properties of the specimen viewed as a structure. As a result, a formal use of fracture criteria recommended in regulations leads to a discrepancy between design and experimental values of fracture loads. Nowadays, the finite element method is widely used in practical strength analysis. This method permits one to study the elastoplastic strained state of geometrically complicated structures in detail, take into account physical nonlinearity at large strains, determine damage boundaries, and improve experimental methodology. The wide capabilities of this method allow one to use test results more completely.