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Article Citation - WoS: 2Citation - Scopus: 4Constructing Stieltjes Classes for M-Indeterminate Absolutely Continuous Probability Distributions(Impa, 2014) Ostrovska, Sofiya; MathematicsIf P is a moment-indeterminate probability distribution, then it is desirable to present explicitly other distributions possessing the same moments as P. In this paper, a method to construct an infinite family of probability densities - called the Stieltjes class - all with the same moments is presented. The method is applicable for densities with support (0, infinity) which satisfy the lower bound: f(x) >= A exp{-ax(alpha)} for some A > 0, a > 0 and some alpha is an element of(0, 1/2):Article Citation - WoS: 4Citation - Scopus: 4Nonexistence of Embeddings With Uniformly Bounded Distortions of Laakso Graphs Into Diamond Graphs(Elsevier Science Bv, 2017) Ostrovska, Sofiya; Ostrovskii, Mikhail I.Diamond graphs and Laakso graphs are important examples in the theory of metric embeddings. Many results for these families of graphs are similar to each other. In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. The well-known fact that Laakso graphs are uniformly doubling but diamond graphs are not, immediately implies that diamond graphs do not admit uniformly bilipschitz embeddings into Laakso graphs. The main goal of this paper is to prove that Laakso graphs do not admit uniformly bilipschitz embeddings into diamond graphs. (C) 2016 Elsevier B.V. All rights reserved.Article Citation - WoS: 1On Lin's Condition for Products of Random Variables(B verkin inst Low Temperature Physics & Engineering Nas Ukraine, 2019) Il'inskii, Alexander; Ostrovska, SofiyaThe paper presents an elaboration of some results on Lin's conditions. A new proof is given to the fact that if densities of independent random variables xi(1) and xi(2) satisfy Lin's condition, then the same is true for their product. Also, it is shown that without the condition of independence, the statement is no longer valid.
