The main purpose of this paper is to analyze and address the challenges implementing green energy in Ukraine, particular, identify its advantages disadvantages. implementation solar renewable sources—stations, panels, batteries—is emphasized. results sociological surveys Ukrainian public opinion on environmental issues, are presented. existence demand for readiness population use sources identi...

in most of the literature, the presence of women in universities is associated with the issue of occupation. in clarifying and explaining this issue the theories of economists on human resources are, often, used. however this article focuses on other aspects of this phenomenon, and evaluates the social and cultural motives of girl’s entrance into universities. the main questions are that based ...

This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of “cut and then riffle shuffle”. This allows one to obtain information about the convergence rate of permutation statistics (such as the length of the longest increasing subsequence or position of a given card) under these processes. Similar results are given for affine...

Abstract. We compute the limit distribution for (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In two–colored case our method provides a different proof of a similar result by Tracy and Widom about...

We prove a formula for the number of permutations in Sn such that their first n−k entries are increasing and their longest increasing subsequence has length n − k. This formula first appeared as a consequence of character polynomial calculations in the work of Adriano Garsia, [2]. We give an elementary proof of this result and also of its q-analogue. In [2], Adriano Garsia derived as a conseque...