On a family of integrable systems on S2S^2 with a cubic integral of motion

We discuss a family of integrable systems on the sphere $S^2$ with an additional integral of third order in momenta. This family contains the Coryachev-Chaplygin top, the Goryachev system, the system recently discovered by Dullin and Matveev and two new integrable systems. On the non-physical sphere with zero radius all these systems are isomorphic to each other.Comment: LaTeX, 8 page

Radiation transfer in dispersion medium in separating

The influence of a degree of separating dispersion medium layer on radiation balance regarding its optical dimensions, scattering phase function shape and albedo of single scattering was investigated. It was stated that the bleaching effect occurring at dispersion medium separating has certain space boundaries. The classical concept of the «infinitely extended dispersion medium» was clarifie

Influence of space limited of the dispersion medium on image quality characteristics

Influence of space limited of the dispersion medium on radiation distribution and the quality characteristic of image obtained through dispersing medium of the finite sizes is investigated. The way of calculation of boundary function and contrast function of a light strip is determined. It is shown, that space limited of the dispersion medium and illumination conditions render significant influence on image quality -characteristics

On integrable system on S2S^2 with the second integral quartic in the momenta

We consider integrable system on the sphere $S^2$ with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system.Comment: LaTeX, 6 page