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Some problems of the pQCD jet calculus

Some problems of the perturbative quantum chromodynamics (pQCD) jet calculus are discussed. The first one is related to the terminology of the order of calculation. Due to cancelation of LO and NLO terms in the ratio of mean multiplicities in gluon and quark jets $r$ the nowadays obtained results about it should be called as 4NLO approximation. The second problem reveals itself in calculations where corrections to some values (in particular, to $r'$) are larger at present energies than lower order terms. Some characteristics which do not suffer from this deficiency are proposed. Next problem lies in interpretation of the negative values of cumulant moments which are considered as an indication to the replacement of attraction by repulsion in sets with definite particle contents. Finally, the problem of the generalization of QCD equations for generating functions is briefly discussed.