Theory of scanning near-field magnetooptical microscopy

An analytical theory of scanning near-field magnetooptical microscopy is developed. The theory is based on the elastic scattering of light by small, resonantly polarizable particles, which are used to scan the plane surface of a nonuniformly magnetized medium. The effective polarizability of the particles is calculated with the effect of dynamic “image forces” taken into account in all orders of perturbation theory with respect to the interaction of the particle with a demagnetized ferromagnet, and the magnetooptical perturbation is calculated to first order in the magnetization. The major contributions to the magnetooptical light scattering for a ferromagnetic structure magnetized perpendicular to the surface are found, including a quasistatic approximation for the near-field particle-magnet interaction. The optical size resolution of a magnetic (dielectric) inhomogeneity is estimated. Zh. Tekh. Fiz. 68, 86–91 (July 1998)     

Transformations of cobalt trimethylacetate complexes with pyrazole upon oxidation by air in THF

Synthetic routes to oxidation of cobalt atoms in cobalt trimethylacetate complexes containing coordinated pyrazole molecules have been considered.     

Approximate method of calculating stresses in a rectangular plate locally loaded by a harmonic force

From double trigonometric series for bending moments the slowly converging components are picked out. When the loading facets are small compared with the width of the plate, they are approximately summed by the analytical method. This simplifies substantially the calculation of bending moments and stresses in the zone of small loading facets compared with the usual expansion with respect to the natural vibration forms.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 84–88, 1989.     

On properties of solutions of semilinear second-order parabolic equations

We consider semilinear second-order parabolic equations whose principal parts may have either divergence or nondivergence form and whose nonlinear terms satisfy conditions of Bernstein-Dini type. We study the qualitative properties of the classical solutions of nondivergence equations and generalized solutions of equations with divergent principal parts: the behavior of solutions in various unbounded domains and near the boundaries of domains, removability of singularities of solutions, vanishing of solutions in unbounded domains, in particular solutions of compact support and uniqueness and continuous dependence on the boundary conditions for solutions of the exterior initial/boundary problem.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 70–107, 1991. Original article submitted June 18, 1987.     

Asymptotics of a multiple Cauchy integral with rapidly oscillating exponential

An asymptotic expansion uniform with respect to a parameter is obtained for a multiple Cauchy integral with a rapidly oscillating exponential in the integrand under the assumption that the singularity lines are in a general position.Translated fromMatematicheskie Zametki, Vol. 58, No. 2, pp. 231–242, August, 1995.The work was financially supported by the Russian Foundation for Basic Research under grant No. 94-01-00193-a.