Open AccessInversor of digits $Q^∗_2$-representative of numbers
Author(s) -
Mykola Pratsiovytyi,
Ya. V. Goncharenko,
N. V. Dyvliash,
S. P. Ratushniak
Publication year - 2021
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.55.1.37-43
Subject(s) - mathematics , lebesgue integration , alpha (finance) , combinatorics , function (biology) , sequence (biology) , lebesgue measure , singularity , symbol (formal) , pure mathematics , discrete mathematics , mathematical analysis , construct validity , statistics , genetics , evolutionary biology , biology , psychometrics , computer science , programming language
We consider structural, integral, differential properties of function defined by equality$$I(\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=\Delta^{Q_2^*}_{[1-\alpha_1][1-\alpha_2]...[1-\alpha_n]...}, \quad \alpha_n\in A\equiv\{0,1\}$$for two-symbol polybasic non-self-similar representation of numbers of closed interval $[0;1]$ that is a generalization of classic binary representation and self-similar two-base $Q_2$-representation.For additional conditions on the sequence of bases, singularity of the function and self-affinity of the graph are proved.Namely, the derivative is equal to zero almost everywhere in the sense of Lebesgue measure.The integral of the function is calculated.