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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.

An advantage of the discontinuous Galerkin method is the ability to describe complex contact surfaces by using unstructured computational grids. However, the use of the discontinuous Galerkin method requires significant computational resources, including at the preprocessing stage. The grid-characteristic method on structured regular computational grids saves computational resources, but problems arise when taking into account complex inhomogeneities, including surface topography. Therefore, it is of interest to combine the grid-characteristic method on structured computational grids with the discontinuous Galerkin method, to which this paper is devoted. The work describes in detail the Galerkin method and the description of the contact boundary between the subdomains of the integration domain in which the grid-characteristic method and the discontinuous Galerkin method are used. The corresponding calculation algorithm is discussed. Examples are given on the calculation of the propagation of seismic waves from the hypocenter of an earthquake to the Earth’s surface, taking into account the surface topography.

For a non-empty compact set $E$ in a proper subdomain $\Omega$ of the complex plane, we denote the diameter of $E$ and the distance from $E$ to the boundary of $\Omega$ by $d(E)$ and $d(E,\partial\Omega),$ respectively. The quantity $d(E)/d(E,\partial\Omega)$ is invariant under similarities and plays an important role in Geometric Function Theory. In the present paper, when $\Omega$ has the hyperbolic distance $h_\Omega(z,w),$ we consider the infimum $\kappa(\Omega)$ of the quantity $h_\Omega(E)/\log(1+d(E)/d(E,\partial\Omega))$ over compact subsets $E$ of $\Omega$ with at least two points, where $h_\Omega(E)$ stands for the hyperbolic diameter of the set $E.$ We denote the upper half-plane by $\mathbb{H}$. Our main results claim that $\kappa(\Omega)$ is positive if and only if the boundary of $\Omega$ is uniformly perfect and that the inequality $\kappa(\Omega)\leq\kappa(\mathbb{H})$ holds for all $\Omega,$ where equality holds precisely when $\Omega$ is convex., Comment: 21 pages, 2 figures

The paper focuses on the problem of normal surface waves in an open metal-dielectric inhomogeneous waveguide of arbitrary cross-section with losses. The medium filling the waveguide is characterized by a isotropic inhomogeneous complex permittivity. The setting is reduced to a boundary eigenvalue problem for longitudinal components of the electromagnetic field in Sobolev spaces. Variational formulation of the problem is considered in terms of the analysis of operator-functions. A discreteness of the set of the sought-for eigenvalues is proved.

In this paper, we study the existence, uniqueness and boundary behavior of positive boundary blow-up solutions to the quasilinear system $$\Delta_{\infty}u=a(x)u^{p}v^{q}$$ , $$\Delta_{\infty}v=b(x)u^{r}v^{s}$$ in a smooth bounded domain $$\Omega\subset R^{N}$$ , with the explosive boundary condition $$u=v=+\infty$$ on $$\partial\Omega$$ , where the operator $$\Delta_{\infty}$$ is the $$\infty$$ -Laplacian, the positive weight functions $$a(x)$$ , $$b(x)$$ are Holder continuous in $$\Omega$$ , and the exponents verify $$p$$ , $$s > 3$$ , $$q$$ , $$r>0$$ , and $$(p-3)(s-3) > qr$$ .

The paper deals with the study of dynamical systems admitting compact attractors, which describe the behavior of trajectories of the system at infinity and play an important role in the qualitative theory of stability of motion. The properties of trajectories of a dynamical system in the attraction domain of the attractors and on the boundary are established by using concepts such as elliptic and weakly elliptic sets, as well as the pseudo-stability and pseudo-prolongation properties.

In previous works ([4–8]), the author studied the general approach to solving mixed boundary, spectral, and initial-boundary transmission problems. In this paper, this approach is applied to the mixed boundary transmission problem of the linear theory of elasticity. On the basis of the corresponding Green formulas the solution of the problem can be represented as the sum of the solutions of auxiliary problems containing a given function only in one place. As a result, four auxiliary problems are obtained. We find their weak solutions using Green’s formulas. And then we conclude that the solution of the original problem is the sum of the auxiliary solutions.