Inversor of digits $Q^∗_2$-representative of numbers

M. V. Pratsiovytyi; Ya. V. Goncharenko; N. V. Dyvliash; S. P.  Ratushniak

doi:10.30970/ms.55.1.37-43

M. V. Pratsiovytyi National Pedagogical Dragomanov University, Kyiv, Ukraine
Ya. V. Goncharenko National Pedagogical Dragomanov University, Kyiv, Ukraine
N. V. Dyvliash National Pedagogical Dragomanov University, Kyiv, Ukraine
S. P. Ratushniak National Pedagogical Dragomanov University, Kyiv, Ukraine

DOI: https://doi.org/10.30970/ms.55.1.37-43

Анотація

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.

Посилання

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