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 A criterion for the best uniform approximation by simple partial fractions in terms of alternanceM. A. Komarov 3 On the asymptotics of the mean sojourn time of a random walk on a semi-axisV. I. Lotov, A. S. Tarasenko 23 Eigenvibrations of thick cascade junctions with ‘very heavy’ concentrated massesT. A. Mel'nik, G. A. Chechkin 41 Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat–Tits buildingsYu. A. Neretin 87 Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zeroS. V. Pchelintsev, O. V. Shashkov 131 On the topology of stable Lagrangian maps with singularities of types $A$ and $D$V. D. Sedykh 159 On the Brauer group of an arithmetic model of a hyperkähler variety over a number fieldS. G. Tankeev 203