@article{Pratsiovytyi_Goncharenko_Dyvliash_Ratushniak_2021, title={Inversor of digits $Q^∗_2$-representative of numbers}, volume={55}, url={http://matstud.org.ua/ojs/index.php/matstud/article/view/192}, DOI={10.30970/ms.55.1.37-43}, abstractNote={<p>We consider structural, integral, differential properties of function defined by equality<br>$$I(\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=\Delta^{Q_2^*}_{[1-\alpha_1][1-\alpha_2]...[1-\alpha_n]...}, \quad \alpha_n\in A\equiv\{0,1\}$$<br>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.<br>For additional conditions on the sequence of bases, singularity of the function and self-affinity of the graph are proved.<br>Namely, the derivative is equal to zero almost everywhere in the sense of Lebesgue measure.<br>The integral of the function is calculated.</p>}, number={1}, journal={Matematychni Studii}, author={Pratsiovytyi, M. V. and Goncharenko, Ya. V. and Dyvliash, N. V. and Ratushniak, S. P.}, year={2021}, month={Mar.}, pages={37-43} }