Journal "Research Bulletin of National Technical University of Ukraine "Kyiv Polytechnic Institute" (Naukovi visti) publishes original research results and practical developments from areas of technical, physical, mathematical, chemical and biological sciences.

# Direct Spectral Problems for the Block Jacobi Type Bounded Symmetric Matrices Related to the two dimensional real moment problem

The generalization of the classical moment problem and the spectral theory of self-adjoint Jacobi block matrix are well-known in one-dimensional case and it generalized on the two-dimensional case. Finite and infinite moment problem is solved using Yu.M. Berezansky generalized eigenfunction expansion method for respectively finite and infinite family of commuting self-adjoint operators. In the classical case one orthogonalize a family of polynomials , with respect to a measure on the real axis and shift operator on takes the form of ordinary Jacobi matrix.

# Operators of Stochastic Differentiation on Spaces of Regular Test and Generalized Functions in the Lévy White Noise Analysis

The operators of stochastic differentiation, which are closely related with stochastic integrals and with the Hida stochastic derivative, play an important role in the classical white noise analysis. In particular, one can use these operators in order to study properties of solutions of normally ordered stochastic equations, and properties of the extended Skorohod stochastic integral. So, it is natural to introduce and to study analogs of the mentioned operators in the Lévy white noise analysis.

# Estimates for Moments of Extreme Values of the Random Process with Superadditive Moment Function

This paper considers the stochastic process with superadditive moment function. The aim is to generalize the results of R. Serfling, which he received for a sequence of random variables with superadditive moment function. We have obtained the estimation for moments of supremum of a random process with the appropriate bounds for moments of this random process. We make no assumptions about the structure of the dependence of increments of a random process, but only the estimation for moments of random process.

# Convergence of Baum–Katz Series with OSV-Functions

In this paper conditions for the convergence of series

# Sufficient Conditions of Ergodicity of Solutions of Second Order Abstract Linear Differential Equations

This paper is devoted to second order abstract linear differential equations in a Banach space. For such equations the Cauchy problem is stated, and the behavior of its solutions as is examined. The aim of the paper is to study ergodicity and asymptotic behavior of the solutions of the strongly correct Cauchy problem. For this purpose the theory of complete second order linear differential equations in Banach spaces, developed by Fattorini, is used. As shown in the paper, for a wide class of equations the solutions are either ergodic or unbounded, depending on the initial values.

# Integral Transforms with the r-Hypergeometric Functions

In the paper the r-hypergeometric function is considered in the form

# Rank One Strong Singular Perturbation by Nonsymmetric Potential

For a rank one strong singular perturbation of a self-adjoint operator by nonsymmetric potential, we present a construction and investigated the corresponding eigenvalue problem.

# Asymptotic Unbiasedness and Consistency of Cross-Correlogram Estimators of Response Functions in Linear Continuous Systems

The estimation problem of an unknown real-valued response function of a linear continuous system is considered. We suppose that a family of zero-mean stationary Gaussian processes, which are close, in some sense, to a white noise, disturbs the system. Integral-type sample input-output cross-correlograms are taken as estimators of the response function from . The corresponding cross-correlogram estimator depends on two parameters (a parameter of a scheme of series and a length of an averaging interval) and is biased.

# Cleaning of Contaminated Waters Against U and Cr Compounds Using Pillared Al- and Al/Fe-Clays

In this paper a comprehensive study of adsorption properties of modified clay minerals with polyoxocomplexes (POM) of iron and aluminium with regard to removal of heavy metal ions from an aqueous medium was carried out. To determine changes in structure characteristics of the intercalated minerals have been used methods of X-ray diffraction, nitrogen adsorption with calculated specific surface area and pore size distribution, as well as adsorption of Chromium (VI) and Uranium (VI) ions from aqueous solutions at various pH values.