Geometry of numerical series: a series as a model of a real number in a new two-character number coding system

• Date: 2020
• Author Affiliations: M.V. Pratsevytyi — National Pedagogical Dragomanov University; I.M. Lysentko — National Pedagogical Dragomanov University; Yu.P. Maslova — National Pedagogical Dragomanov University
• Keywords: keywords
• Main Authors: Pratsevytyi, M.V., Lysentko, I.M., Maslova, Yu.P., Працевитый, Н.В., Лысенко, И.М., Маслова, Ю.П., Працьовитий, М.В., Лисенко, І.М.
• Format: Article
• Language: Ukrainian; English
• Published: Інститут математики НАН України 2020
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/437
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

In the paper, we consider sets of incomplete sums of subharmonic normalized series. Their topological, metric, and fractal properties are studied. We give model examples and prove theorems of existence as well as mas- siveness of classes of series. A new polybase two-symbol system of encoding of rea...