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The set of incomplete sums of a numerical series with one nonlinear homogeneity property
Pratsiovytyi Mykola 1,2 , Savchenko Igor Oleksandrovych 2
1 Department of dynamic systems and fractal analysis, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, 01001, Ukraine
2 Department of Higher Mathematics, National Pedagogical Dragomanov University, Kyiv, 01001, Ukraine
Keywords: the set of incomplete sums
Abstract
The article is devoted to the investigation of metric, topological and fractal properties of the set of subsums of a numerical series $a_1 + a_2 + ... + a_n + a_{n+1} + ... = a_1 + a_2 + ... + a_n + r_n,$   which satisfy the following condition of homogeneity: $r_n = a_na_{n-1}...a_{n-k+1}, n ≥ k,$ where $k$  is a fixed integer number, $k ≥ 2.$ It is proved that the arithmetic sum $E\underbrace {⊕...⊕}_{s\text{ разів}} E $  of an arbitrary number of the sets $E$ of subsums is an anomalously fractal.
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Cite
ACS Style
Pratsiovytyi, M.; Savchenko, I.O. The set of incomplete sums of a numerical series with one nonlinear homogeneity property. Bukovinian Mathematical Journal. 2016, 2
AMA Style
Pratsiovytyi M, Savchenko IO. The set of incomplete sums of a numerical series with one nonlinear homogeneity property. Bukovinian Mathematical Journal. 2016; 2(2-3).
Chicago/Turabian Style
Mykola Pratsiovytyi, Igor Oleksandrovych Savchenko. 2016. "The set of incomplete sums of a numerical series with one nonlinear homogeneity property". Bukovinian Mathematical Journal. 2 no. 2-3.
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