Average Multiplicities in Gluon and Quark Jets in Higher-Order Perturbative QCD

The ratio of average multiplicities in gluon and quark jets is shown to become noticeably smaller in higher-order QCD compared to its lowest order value what improves agreement with experiment. QCD anomalous dimension has been calculated. It has been used to get energy dependence of mean multiplicities.Comment: Submitted to Mod. Phys. Lett.A Latex document, 10 pages. Preprint number FIAN TD-3 March 199

Moments of the truncated multiplicity distributions

In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess some typical features.In particular, the oscillations of cumulant moments at high ranks and their negative values at the second rank can be considered as ones most indicative on specifics of these distributions. They allow to distinguish between distributions of different type.Comment: 10 pages, LaTeX, 9 ps-figure

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

QCD partition function in the external field in the covariant gauge

The QCD partition function in the external stationary gluomagnetic field is computed in the third order in external field invariants in arbitrary dimension and arbitrary covariant gauge. The contributions proportional to third order invariants in gluon field strength are shown to be dependent on covariant quantum gauge fixing parameter \alph