Nonlinear magneto-optical diffraction by two-dimensional magnetic superstructures

Nonlinear (at the second-harmonic frequency of the incident light) optical reflection by two-dimensional magnetic superstructures is theoretically studied. A square lattice of magnetic dots and a hexagonal lattice of magnetic bubbles (cylindrical magnetic domains) are considered. Because the periods of these structures are comparable with the wavelengths of the fundamental and the second-harmonic radiation, it would be possible to observe diffraction at the second-harmonic frequency. A polarization analysis of nonlinearly diffracted radiation is performed and the numbers of observable diffraction orders for the above structures are estimated. Received: 10 January 2002 / Published online: 11 June 2002     

Noncommutative four-dimensional subalgebras of conformal algebra integrable in the space R1,3

D'alambert's equation is used as an example to study the possibilities of a new method of exactly integrating systems of linear differential equations — the method of noncommutative integration (NI). The results confirm that use of the NI is equivalent to complete separation of the variables in the case of four-dimensional subalgebras of conformal algebra. However, the method does simplify determination of the exact solution in this instance.Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 120–124, February, 1995.     

Influence of Ionic Surfactants on Tetrabromophenylfluorone Ionic Associates

Stability constants of ionic associates of a hydroxyxanthene dye, tetrabromophenylfluorone, with a series of organic cations were determined spectrophotometrically. The possibility of quantitative determination of anionic surfactants (alkyl sulfates) in an aqueous solution in the form of a dye anion associate with tetrabutylammonium cation was considered.     

Symmetry and separation of variables in second-order differential equations. II

A definition of the complete separation of variables is given, and normal parabolic equations permitting separation of variables in any coordinate system are described; this involves the commutative algebra of differential (not higher than second order) symmetry operators of the equations. In particular, the necessary and sufficient conditions for the complete n separation of variables is formulated in covariant form with respect to arbitrary transformations of the independent variables.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 7–10, June, 1978.     

Formation mechanism of hexafluoropropylene oxide in low-temperature liquid-phase oxidation of hexafluoropropylene by molecular oxygen

A kinetic model has been developed for describing the non-catalytic solid-liquid reaction of aspartic acid with potassium hydroxide in solutions. It takes into consideration the effects of the aspartic acid particle size distribution by using the population balance approach. The parameters of the model have been estimated by fitting them to experimental data taken from literature.

---

- . , . , .

     

<Emphasis Type="Italic">In situ</Emphasis> analysis of the formation steps of gold nanoparticles by oleylamine reduction

A colloidal solution of gold nanoparticles is synthesized with the use of sodium tetrachloroaurate(III) as a precursor, oleylamine as a reducer and surfactant, and 1-octadecene as a solvent. Reaction stages are analyzed in situ by optical (UV-vis) absorption spectroscopy with a simultaneous analysis of particle sizes by dynamic light scattering and X-ray absorption near edge spectroscopy for the analysis of the gold oxidation state. After the synthesis the size of obtained nanoparticles is determined by transmission electron microscopy. The analysis of the obtained experimental data reveals the presence of three main steps in the reduction reaction mechanism, corresponding to Au³⁺, Au⁺, Au⁰, which enables the construction of the reaction model. The reaction mechanism involves the formation of gold(I) complexes with oleylamine, followed by polymerization and the formation of gold nanoclusters coated with oleylamine.