Nega-$\tilde Q$-representation of real numbers

TL;DR

This paper introduces and models the nega-tilde Q-representation of real numbers, generalizing existing Cantor series representations, using analytic and geometric methods to explore its properties and advantages.

Contribution

It presents a new nega-tilde Q-representation of real numbers, extending Cantor series concepts with detailed modeling and analysis.

Findings

The nega-tilde Q-representation generalizes positive Cantor series.

Analytic and geometric approaches reveal advantages and disadvantages.

The representation's properties are systematically modeled and investigated.

Abstract

The article is devoted to modeling of the nega-$\tilde Q$-representation of real numbers. The representation is a generalization of representation by alternating Cantor series and positive $\tilde Q$-representation is a generalization of representation of real numbers by the positive Cantor series. Analytic and geometric approach are used for modeling of nega-$\tilde Q$-representation. Advantages and disadvantages of these approaches are investigated, the representation is modeled. The investigation was represented in seminar on fractal analysis of Institute of Mathematics of the National Academy of Sciences of Ukraine on, October 30, 2014 (http://www.imath.kiev.ua/events/index.php?seminarId=21&archiv=1) and International Conference "Probability, Reliability and Stochastic Optimization", Kyiv, April 7-10, 2015.