Wavelets and their use

This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to corresponding literature. The multiresolution analysis and fast wavelet transform became a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for achievement of a goal. Analysis of various functions with the help of wavelets allows to reveal fractal structures, singularities etc. Wavelet transform of operator expressions helps solve some equations. In practical applications one deals often with the discretized functions, and the problem of stability of wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves by some examples only. The authors would be grateful for any comments which improve this review paper and move us closer to the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh

Dependence of vestibular reactions on frequency of action of sign-variable accelerations

It was revealed that during the tests with continuous action of sign variable Coriolis acceleration the development of kinetosis was proportionate to the time of head inclinations in the range of 1 to 4 seconds while illusions of rocking in sagittal plane was more expressed in fast inclinations. The obtained data provided the evidence of sufficient dependence of vestibulovegetative and vestibulosensory reactions on the period of repetition of sign variable Coriolis acceleration

Impurity center in a semiconductor quantum ring in the presence of a radial electric field

The problem of an impurity electron in a quantum ring (QR) in the presence of a radially directed strong external electric field is investigated in detail. Both an analytical and a numerical approach to the problem are developed. The analytical investigation focuses on the regime of a strong wire-electric field compared to the electric field due to the impurity. An adiabatic and quasiclassical approximation is employed. The explicit dependencies of the binding energy of the impurity electron on the electric field strength, parameters of the QR and position of the impurity within the QR are obtained. Numerical calculations of the binding energy based on a finite-difference method in two and three dimensions are performed for arbitrary strengths of the electric field. It is shown that the binding energy of the impurity electron exhibits a maximum as a function of the radial position of the impurity that can be shifted arbitrarily by applying a corresponding wire-electric field. The maximal binding energy monotonically increases with increasing electric field strength. The inversion effect of the electric field is found to occur. An increase of the longitudinal displacement of the impurity typically leads to a decrease of the binding energy. Results for both low- and high-quantum rings are derived and discussed. Suggestions for an experimentally accessible set-up associated with the GaAs/GaAlAs QR are provided.Comment: 16 pages, 8 figure

The effect of fluorine-containing inhibitors of corrosion of copper in atmospheric conditions

The effect of fluorine-containing inhibitors of corrosion of copper in atmospheric conditions was studied by method of removing anodic polarization curves and corrosion of full-scale tests. The introduction of the inhibiting compositions as corrosion inhibitor of copper polyfluorinated amines leads to a decrease of the peak current of active dissolution of copper, which increases the corrosion resistance of copper wire rod during transportation in various climate conditions