The role of energy-momentum conservation in emission of Cherenkov gluons

The famous formula for the emission angle of Cherenkov radiation should be modified when applied to hadronic reactions because of recoil effects. They impose the upper limit on the energy of the gluon emitted at a given angle. Also, it leads to essential corrections to the nuclear refractive index value as determined from the angular position of Cherenkov rings.Comment: 6

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

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

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