CORE 2.1 (COmpendium of RElations, Version 2.1)

The present CORE 2.1 (COmpendium of RElations, Version 2.1) contains various formulas and relations used in the practical calculations in the Standard Model. The properties of the Pauli, Dirac, Gell--Mann matrices, wave functions of free fermions and gauge bosons are considered. We present the full Lagrangian of the Standard Model and the corresponding Feynman rules. The method of the evaluation of the Feynman (loop) integrals and calculations in non-covariant gauges is considered. We discuss in brief the relativistic kinematic and present a large number of the matrix elements of the various processes in the Standard Model.Comment: 108 pages, the full text is submitted as four compressed and uuencoded PostScript file

Nonperturbative three-point functions of the O(N) sigma model in the 1/N expansion at NLO

We present a calculation of the three-point functions of the O(N)-symmetric sigma model. The calculation is done nonperturbatively by means of a higher-order 1/N expansion combined with a tachyonic regularization which we proposed in previous publications. We use the results for calculating the standard model process ff -> H -> WW nonperturbatively in the quartic coupling of the scalar sector

CORE 3.1 (COmpendium of RElations, Version 3.1)

The present CORE 3.1 (COmpendium of RElations, Version 3.1) contains various formulas and relations used in the practical calculations in the Standard Model. The properties of the Pauli, Dirac, Gell--Mann matrices, wave functions of free fermions and gauge bosons are considered. We present the full Lagrangian of the Standard Model and the corresponding Feynman rules. The method of the evaluation of the Feynman (loop) integrals and calculations in non-covariant gauges is considered. We discuss in brief the relativistic kinematic and present a large number of the matrix elements of the various processes in the Standard Model.Comment: 80 pages, 21 figures, scripts.sty. arXiv admin note: substantial text overlap with arXiv:hep-ph/950745

Sequential closure in the space of measures

We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of arbitrarily high levels of complexity in this sequential hierarchy. It follows that there is a compact space in which the sequential closure cannot be obtained in countably many steps. However, we show that this is not the case for our spaces where the sequential closure is always obtained in countably many steps.Comment: (18 pages, a gap in an argument from the previous version fixed

Design of Drum Type Apparatus for Processing of Bulk Materials

The article presents the development and research of drum continuous mixers, most attention is paid to the results of theoretical (using of cybernetic approach) and experimental studies of longitudinal mixing particulate material in rotating drums of continuous action, the influence of internal recycles of material flows, intensifying the process of smoothing the input fluctuations. The authors analyzed the influence of internal recycles material flows, intensifying the process of smoothing the input fluctuations. The results presented in this paper were obtained by the experiments on the smoothing ability determination during which they change the frequency of the drum rotation, the location of the Г-shaped mixer blades on the drum mixer. The article reported that the studies were conducted on three mixtures which components have different physical and mechanical systems with various dispersed liquid additives and without it