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

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...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2020
Автори та афіліації:
  • M.V. Pratsevytyi — National Pedagogical Dragomanov University
  • I.M. Lysentko — National Pedagogical Dragomanov University
  • Yu.P. Maslova — National Pedagogical Dragomanov University
Ключові слова:keywords
Автори: Pratsevytyi, M.V., Lysentko, I.M., Maslova, Yu.P., Працевитый, Н.В., Лысенко, И.М., Маслова, Ю.П., Працьовитий, М.В., Лисенко, І.М.
Формат: Стаття
Мова:Українська
Англійська
Опубліковано: Інститут математики НАН України 2020
Онлайн доступ:https://trim.imath.kiev.ua/index.php/trim/article/view/437
Теги: Додати тег
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Назва журналу:Transactions of Institute of Mathematics of NAS of Ukraine
Завантажити файл: Pdf

Репозитарії

Transactions of Institute of Mathematics of NAS of Ukraine
Опис
Резюме: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 real numbers with zero redundancy is also introduced. It is topologically equivalent to representation of numbers by ????2 -continued fractions and by nega-binary representation. For this system, we describe geometry (properties of cylindrical sets) and foundations of metric theory.

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