TY - JOUR
AU - Pratsiovytyi, M. V.
AU - Goncharenko, Ya. V.
AU - Dyvliash, N. V.
AU - Ratushniak, S. P.
PY - 2021/03/06
Y2 - 2021/11/28
TI - Inversor of digits $Q^∗_2$-representative of numbers
JF - Matematychni Studii
JA - Mat. Stud.
VL - 55
IS - 1
SE - Articles
DO - 10.30970/ms.55.1.37-43
UR - http://matstud.org.ua/ojs/index.php/matstud/article/view/192
SP - 37-43
AB - 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.
ER -