Table of contents

The basic theory of the wavelet transform, an effective investigation tool for inhomogeneous processes involving widely different scales of interacting perturbations, is presented. In contrast to the Fourier transform, with the analysing function extending over the entire axis of time, the two-parametric analysing function of the one-dimensional wavelet transform is well localised in both time and frequency. The potential of the method is illustrated by analysing familiar model series (such as harmonic, fractal, and those with various types of singularities) and the long-term variation of some meteorological characteristics (Southern Oscillation index and global and hemispheric temperatures). The analysis of a number of El Nino events and of the temporal behaviour of the Southern Oscillation index reveals periodic components, local periodicity features and time scales on which self-similarity structures are seen. On the whole, both stochastic and regular components seem to be present. The global and hemispheric temperatures are qualitatively similar in structure, the main difference — presumably due to the greater amount of land and stronger anthropogenic factor — being that the warming trend in the Northern Hemisphere is slightly stronger and goes first in time.

Theoretical fundamentals of the phenomenon of optical self-switching of unidirectional distributively coupled waves (UDCW) with the linear coupling coefficient have been given in Ref. [1]. The present review deals with experimental examination of this striking phenomenon and pulse self-switching events along with the theory of UDCW self-switching in the case of a nonlinear coupling coefficient.

Formation mechanisms for spatially nonuniform temperature and charged particle density distributions in a low-temperature gas discharge plasma are reviewed. Conditions for the occurrence of, and parameter distributions in, the constricted state of the discharge are analyzed. Spatial temperature and electron density distributions and the pressure and power-input dependence of the plasma column radius are determined in local thermodynamic equilibrium. Special attention is given to a cluster-containing plasma. For this new type of spatially nonuniform discharge plasma, the cluster growth process is studied and the limiting cluster size is evaluated. The potential application of the cluster plasma as an illumination source is assessed and performance characteristics of such a source are calculated.

A more accurate formulation of the Abbe theory is presented using well-known open resonator results, namely, field representation in terms of the eigenfunctions of the optical system viewed as a segment of an equivalent lens waveguide; and the use of the mirror Fresnel number dependence of the diffraction losses of high-order Gaussian beams for describing the image distortions due to the objective aperture. The number of the degrees of freedom of the image within the zero mode waist area is estimated by using the Hermite-Gaussian functions within the paraxial approximation framework.

Main concepts of a new interdisciplinary research area known as 'Physics of Open Systems' are introduced with special reference to a criterion for the relative degree of order in nonequilibrium states of such systems. Based on this criterion, the notion of the 'norm of chaos' ('norm of order') is proposed and used to differentiate between degradation and self-organization processes. The possibility of applying methods of open system physics to investigations in economics, sociology and physiology is briefly discussed.

The paper presents a model describing a moving emitter as a local polarization region which is produced by a light spot from a moving two-dimensional Gaussian beam and scans across a plane dielectric surface. The spectral composition, angular spectrum and the refraction, reflection, and polarization properties of such a beam are examined. The amplitude coefficients of refraction and reflection of the moving Gaussian beam are found and its total reflection behaviour and the total polarization angle are examined.