Self-consistent droplet-like solutions of the equations of the electromagnetic field with induced nonlinearity

The properties of droplet-like configurations in a system of interacting scalar and electromagnetic fields are investigated, taking into account their own gravitational field, also in the Euclidean limit. Exact regular solutions of the corresponding equations are found, corresponding to zero values for energy and electric charge.Russian Friendship of Peoples University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 112–116, October, 1992.     

Fresnel diffraction of solitons in the Synge model

The problem of Fresnel diffraction of complex scalar solitons by an infinite rectilinear slot in an absorbing screen is considered. The intensity of the scattered solitons is computed in a first approximation of perturbation theory, and the ratio between the characteristic dimension of the soliton and the slot width is taken as the smallness parameter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–38, January, 1982.     

On conditional mathematical expectations for functions integrable in the Pettis sense

Constructed in this note is an example of a function integrable in the Pettis sense for which no conditional mathematical expectation exists relative to some -subalgebra. The example constructed shows that, in particular, the assertion of Theorem 6.1 in the M. M. Rao paper (Ref. Zh. Mat.,9B, 680, 1968) is false.Translated from Matematicheskie Zametki, Vol. 10, No. 5, pp. 565–570, November, 1971.