Vol. 38 No. 3 (205) (2004)

The present review is devoted to the analysis of peculiarities of DNA complexation with reversibly and irreversibly binding ligands. Three classes of low molecular ligands with different types of binding were discussed. These types of ligands particularly are: bivalent transitional metal ions, porphyrin complexes, and zwitterionic amino acids. As irreversible binding ligands some Pt(II) and Ru(III) complexes were used. The systematization of the general patterns and revealing of specific differences in interaction of above mentioned ligands with double helix DNA is presented.

The biorthogonal expansions in Hardy’s $H^p( 1<p<\infty)$ spaces by the incomplete system of rational functions are uniformly summated on the compact subsets of complex plane on positive distance from the set of poles of system's functions.

The behavior of a rapid wave (the precursor) spreading in a liquid with gas bubbles has been studied. For its description, the nonlinear Klein-Gordon equation with dissipative components was modeled. Its exact partial solutions were constructed, describing the displacement of solitons (solitary waves), both at a subsonic speed (known earlier) and at a supersonic speed. Record of dissipation (viscosity) leads to solutions that describe the structures of shock waves in the examined mixture. The obtained analytic solutions correctly reflect the process of dissemination of waves observed in the experiment.

The stability of solution of game problems on guidance to convex and compact sets when objects follow the systems of ordinary linear nonstationary differential equations with constant and variable dynamics is considered. It is proved that solutions are stable with respect to small perturbation of system parameters and small perturbation of initial values.

In this work was describe the automated experimental assembly, which simulate the optical system of muon registration detectors for small deformations in CERN spectrometer experiment with calculation of laser beam passing through a thermal gradient in air. Comparison of experimental results with theory is carried out.

The paper presents a criterion of verifying hypothesis on the correlative function observed by stationary Gaussian process with zero average value.

The influence of high-order dispersion and nonlinear effects on the spectral compression process is studied. This influence is revealed in the ≤ 50 fs time scale.