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The paper is devoted to the study of conditional bounds for the expectation of the maximum of independent identically distributed standardized random variables for which the values of the skewness and kurtosis coefficients are known. With the aid of Holder’s inequality, an upper bound (in the form of a lower bound for a certain expression with parameters) is obtained and a criterion for the reachability of this estimate is formulated. A lower bound for the upper boundary of the expectation of the maximum is also found. A simpler and rougher upper bound is given in explicit form.

An ideal triangulation of a compact $ 3 $ -manifold with nonempty boundary is known to be minimal if and only if the triangulation contains the minimum number of edges among all ideal triangulations of the manifold. Therefore, every ideal one-edge triangulation (i.e., an ideal singular triangulation with exactly one edge) is minimal. Vesnin, Turaev, and Fominykh showed that an ideal two-edge triangulation is minimal if no $ 3 $ – $ 2 $ Pachner move can be applied. In this paper we show that each of the so-called poor ideal three-edge triangulations is minimal. We exploit this property to construct minimal ideal triangulations for an infinite family of hyperbolic $ 3 $ -manifolds with totally geodesic boundary.

The paper deals with the problem of recovering solutions of a generalized Cauchy–Riemann system in a multidimensional spatial domain from their values on a piece of the boundary of this domain, i.e., an approximate solution of this problem based on the Carleman–Yarmukhamedov matrix method is constructed.