Опис діяльності ювіляра і привітання

Two--dimensional Pad\'e type approximants are constructed and studied for some special power series using method of generalized momentrepresentations.

This review focuses on the problem of environmental pollution by lead and its impact on human health. Was provided a historical excursus on the use of human lead and product thereof. Lead is known as one of the most important types of mineral raw materials and at the same time is a global polluter, including and water. In the article summarizes the current understanding sources of receipt and the migration of lead in the environment. Lead is a substance of 1 Class of danger for humans and therefore its content in food, drinking water, air and food strictly normalized . It has been shown that the major source of lead for human is drinking water. In this article also discussed issues of lead toxicity and given the toxicological characteristic of effects on human health. Covers the question risk of lead poisoning to the growing body of the child. G iven recommendations to reduce the lead intake from drinking water.

Two-dimensional Pad'e type approximants are constructed and studied for some special power series using method of generalized moment representations.

Two-dimensional Pade type approximants are constructed for some analytic functions by means of method of generalized moment representations

Currently, a number of general methods for nanoparticles synthesis have been created. In terms of opportunities for industrial production of nanomaterials in Ukraine today, the most advanced is nanotechnology based on physical methods of their obtaining. Therefore today finding stable organic colloidal dispersions stabilized by surfactants and standardization of the experiments techniques in vitro and in vivo, development of safety criteria, and acceptable thresholds for toxicity of metal nanoparticles is an urgent problem. Physicochemical properties of nanoparticles of silver and copper oxides in colloidal solutions of albumin, polyvinylpyrrolidone, and dextran have been studied. Cytotoxicity of nanoparticles of silver and copper oxides in polyvinylpyrrolidone and dextran was evaluated. Toxicity of silver oxide nanoparticles was assessed during per os subacute experiment on Wistar rats. High toxicity of 46.6 mg/l concentration of silver oxide nanoparticles was detected. Biochemical study of enzyme system activity, measurement of trace elements content in whole blood and morphological study of blood cellular composition enabled to reveal minor changes in the composition of blood cells and amount of trace elements, as well as a significant reduction in ceruloplasmin activity and increased activity of ATP and zincprotoporphirine in response to per os subacute exposure of silver oxide nanoparticles with a size of 32 nm and 2.5 mg/l concentration.

Sorption properties of nanostructured powders of aluminum oxide, obtained by EB PVD at condensation temperatures 100-650° С, with respect to positively charged metal ions and negatively charged ions of non-metals with different ionic and atomic radius were studied.A comparative study of the adsorption capacity of nanostructured aluminum oxide, depending on the structural characteristics of the obtained materials revealed that it adsorbs predominantly positively charged metal ions. It appears that high sorption capacity of the nano-alumina takes place with ion or atom radiuses increased. However, the adsorption of anions does not depend on the structure of aluminum oxide.It is revealed that nanostructured alumina can adsorb and retain on its surface metal and nonmetal ions, which makes it a promising material for water purification.

We establish conditions for the existence of generalized moment representations introduced by Dzyadyk in 1981.

By using the method of generalized moment representations with an operator of bilinear transformation of an independent variable, we construct elements of the first subdiagonal of the Padé table for certain special power series.

By the method of generalized moment representations, we generalize the well-known invariance properties of Padé approximants under linear-fractional transformations of approximated functions.

By using the method of generalized moment representations and certain properties of biorthogonal polynomials, we establish new invariance properties of the Padé approximants.