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EN
It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order v if and only if v ≡0, 1, or 2 (mod 9). For all positive integers λand v, we find a maximum packing with loose 3-cycles of the λ-fold complete 3-uniform hypergraph of order v. We show that, if v ≥6, such a packing has a leave of two or fewer edges.
EN
We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.
3
Content available remote Extremes of multidimensional stationary Gaussian random fields
EN
Let {X(t) : t = (t1, t2,…, td) ϵ [0, ∞)d} be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and correlation function r satisfying r(t) < 1 for every t ≠ 0 and r(t) = 1 – Σdi=1 |ti|αi + o (Σdi=1 |ti|αi), as t → 0, with some α1, α2,…, αd ϵ (0, 2]. The main result of this contribution is the description of the asymptotic behaviour of P (sup{X(t) : t ϵ Jxm} ≤ u), as u → ∞, for some Jordan-measurable sets Jxm of volume proportional to P (sup{X(t) : t ϵ [0, 1]d} > u)−1 (1 + o(1)).
EN
In this paper we analyze a Lévy process reflected at a general (possibly random) barrier. For this process we prove the Central Limit Theorem for the first passage time.We also give the finite-time first passage probability asymptotics.
EN
In this paper, we establish some new criteria on the asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations on time scales.
6
Content available remote Mathematical modeling of aerobic wastewater treatment in porous medium
EN
A mathematical model of aerobic wastewater treatment in a porous medium, which taking into account the interaction of bacteria, organic and biological inoxidizable substances was built. An algorithm of the model of nonlinear singularly perturbed tasks of the type "filtration-convection-diffusion-mass-transfer" was proposed. A computer experiment based on it was done.
EN
The research included in the paper concerns a class of symmetric block Jacobi matrices. The problem of the approximation of eigenvalues for a class of a self-adjoint unbounded operators is considered. We estimate the joint error of approximation for the eigenvalues, numbered from 1 to N, for a Jacobi matrix J by the eigenvalues of the finite submatrix J(n) of order pn x pn, where N = max{k ∈ N : k ≤ rpn} and r ∈ (0, 1) is suitably chosen. We apply this result to obtain the asymptotics of the eigenvalues of J in the case p = 3.
EN
We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space l2(N) by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n → ∞) of the joint error of approximation for the first n eigenvalues and eigenvectors of the operator by the eigenvalues and eigenvectors of the finite submatrix of order n x n. The method applied in our research is based on the Rayleigh-Ritz method and Volkmer's results included in [7]. We extend the method to cover a class of infinite symmetric Jacobi matrices with three diagonals satisfying some polynomial growth estimates.
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