Vol. 40 No. 3 (211) (2006)

Cauchy's problem for the nonlinear Korteweg-de Vriez equation is considered with the initial condition given by function, having certain behaviour at infinity. Construction of the solution of this problem by the method of the inverse scattering problem is described provided that the solution exists and has the same behaviour at infinity, as the initial data.

In the work one characteristic function is defined for matrix, which allows to get comfortable form to study the characteristic equation for two-parameter matrix equation.

A piezoactive half-space with a piezoactive layer on its surface is considered. Materials of the layer and the half-space are piezoelectrics of class 6 mm with different properties. Shear stresses between the two piezoelectrics are taken to be zero. Interaction between shear waves in the layer and the half-space is due to continuity of electrical field on their surface. Existence condition of the surface waves is obtained. It is established, that two waves of Gulayev-Bleustain type can exist in considered system

Generalized formulae for the determination of independent yields of radioactive nuclei forming in the targets via activation method are obtained. Various channels of isotopes formations are considered: immediately as a result of the reaction in the target and as products of the precursor decay. Certain cross sections of fission fragments, which are the result of the γ ⁺²³⁸U reaction under the bremsstrauhlung maximal energy, are determined.

The recoil properties of nuclei formed from the target ⁶⁵Cu by the photons beam with the energy E_{γ max} =4.5 GeV were compared with the theoretical calculations made by three versions of LAQGSM03 (Los-Alamos version of the Quark-Gluon String Model) model. The comparison showed that the experimental results are the best described by the LAQGSM03.S1 and LAQGSM03.G1 models.

The interaction of meso-tetra-(3N-pyridyl)porphyrins with different peripheral substituents was studied by methods of spectrophotometry and circular dichroism. It was shown that for less concentration these porphyrins bind to DNA preferably via intercalation. The binding constants (K_b) and the number of binding sites per base pairs (n) were calculated by Correia and co-authors’ method.

It is shown that besides antitumor drugs that form interstrand crosslink, DNA strand separation can be prohibited by compounds that induce a strong local stabilization of the double helix. Ruthenium and platinum complexes, examples of such compounds, are revealed in this work. A method of determination of concrete binding mechanism is proposed. The method is based upon comparison of results of computer modeling with experimental data on melting of DNA complexes with compounds under consideration.

In this paper a Cayley’s theorem is proved for De Morgan algebras. The theorem gives a representation of De Morgan algebras by some class of binary functions.

The message investigates the reasons of occurrence of known paradoxes in the intuitive set theory. We prove, that the process of formation of sets is non-finishing, i.e. after formation of arbitrary set of sets it is possible to form a new set, and the reason of occurrence of paradoxes is connected with representation of process of formation of sets as a finishing process, i.e. all sets can be formed.

The domen boundary thickness dependence of amphiphil substance concentration in lyotropic liquid crystal systems was investigated, through X-ray diffraction and polaroid optical microscope, the domen boundary is the water layer itself, but at higher concentration the domen boundary is the lipid bilayer of lamellas. A connection between the X-ray reflex and thicknesses of domen boundaries was obtained.