Polynomial striction algorithms in the detection and determination of the characteristics of non-stationary phenomena

The effectiveness of the algorithm of polynomial striction of the data is examined, and the selection of an algorithm is carried out, according to the results of measurements of the components of the permanent magnetic field in communication sequences from the Venera-9 space vehicle, where the shock waves were recorded. It is shown that the most effective algorithm, according to the coefficient of striction, is the algorithm of the zero order interpolator. Also examined is the increase in effectiveness with the introduction of a variable threshold of comparison. The root-mean-square deviation of the error of regeneration of the data with various thresholds is calculated, and qualitative analysis of the distortions is carried out, having shown a considerable change in the form of the small discontinuities, which may be interpreted as potential interplanetary shock waves

Symmetries of Electrostatic Interaction between DNA Molecules

We study a model for pair interaction $U$ of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups, and find noncommutative group of eighth order ${\cal S}$ of symmetries that leave $U$ invariant. We classify the minima using group ${\cal S}$ and employ numerical methods for finding them. The minima may correspond to several cholesteric phases, as well as phases formed by cross-like conformations of molecules at an angle close to $\rm{90}^{o}$, "snowflake phase". The results depend on the effective charge $Q$ of the phosphate group which can be modified by the polycations or the ions of metals. The snowflake phase could exist for $Q$ above the threshold $Q_C$. Below $Q_C$ there could be several cholesteric phases. Close to $Q_C$ the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules.Comment: 13 pages, 4 figure

Structural DNA Nanotechnology: Liquid-Crystalline Approach

The investigation of DNA-based materials attracts attention of scientists from various Laboratories because this is definitely an emerging area in physics, molecular biology, biotechnology, biosensorics, nanobiotechnology as well as in material science. This book compares two different approaches in the structural DNA nanotechnology, i.e. \u201chybridization\u201d approach and \u201cliquid-crystalline approach\u201d. The book reviews the state-of-the art in the fundamental studies of liquid-crystalline state of double-stranded DNA molecules appeared as a result of their phase exclusion from polymer-containing water-salt solutions. The results presented in this review demonstrate how the fundamental data obtained when studying the physico-chemical properties of doublestranded DNA liquid-crystalline dispersions can be used as a background for induction of a \u201cliquid\u201d- \u201crigid\u201d state transition, i.e. for the design of novel types of \u201crigid\u201d DNA nanoconstructions carrying various \u201cguest\u201d molecules which display unique properties of practical importance