| Autor: |
Pratsiovytyi, Mykola, Lysenko, Iryna, Ratushniak, Sofiia |
| Předmět: |
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| Zdroj: |
Proceedings of the International Geometry Center; 2024, Vol. 17 Issue 2, p133-142, 10p |
| Abstrakt: |
We consider two-base Q2-representation of numbers of segment [0; 1]: ∆α1α2...αn... ≡ x = α1q1-α1 + ∑∞k=2 αkq1-αk Π k-1 i=1 qαi, which is defined by two bases q0 ∈ (0; 1), q1 = 1 - q0 and an alphabet A = {0,1}, (αn) ∈ A × A × . . . . It is a generalization of classic binary representation (q0 = 1/2 ). In the article we prove that the set of all continuous bijections of segment [0; 1] preserving “tails” of Q2-representation of numbers forms an uncountable non-abelian group with respect to composition such that it is a subgroup of the group of continuous transformations preserving frequencies of digits of Q2-representation of numbers. Construction of such transformations (bijections) is based on the left and right shift operators for digits of Q2-representation of numbers. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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