On the localization of topological invariants

The approach of formal differential geometry to the topological invariants which can be localized is developed. The universal space and universal characteristic forms are constructed. They give rise to primary and secondary characteristic forms.     

Metabelian groups with a single defining relation and the Magnus embedding

Translated from Matematicheskie Zametki, Vol. 47, No. 4, pp. 597–605, April, 1995.     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

Influence of high-order dispersion on self-focusing. II. Numerical investigation

The self-focusing described by the nonlinear Schrödinger equation with a higher-order derivative term is investigated numerically. We demonstrate that, depending on the sign before this term, it may lead in the final stage either to defocusing or to a steady homogeneous wave beam. In both cases the transition to the final state is shown to be oscillatory.     

Determination of U,Ra and Th in waters from the Danube Delta area

The methods applied for natural uranium, radium and thorium determinations in water samples are shortly presented together with some preliminary results. The measurements will be continued as part of an extended program of ecological study of the Danube Delta area.     

Solution of the Reich-Walczak problem regarding conformality in the Belinskii-Lavrent'ev sense

A positive answer is given to the Reich-Walczak problem relative to conformality in the Belinskii-Lavrent'ev sense of quasiconformal mappings at a point in the case of an arbitrary modulus of the complex characteristic and under an appropriate selection of its argument.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1406–1411, October, 1992.