Дослідження властивостей множини неповних сум ряду мультиузагальнених чисел Фібоначчі / Investigation of the set of subsums for a series of multigeneralized Fibonacci numbers

Abstract: Доповідь складається з двох частин. Перша частина присвячена історії вивчення множин неповних сум рядів та відкритим питанням з цієї тематики. У другій частині вивчаються канторвали, що породжені одним зліченним класом рядів з мультиузагальнених чисел Фібоначчі.

The talk consists of two parts. The first part is devoted to the history of study of the sets of subsums for series and open problems on this topic. In the second part we study Cantorvals generated by one countable class of series of multigeneralized Fibonacci numbers.

Ukrainianclassical analysis and ODEsnumber theory

Audience: advanced learners

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Семінар з фрактального аналізу / Fractal analysis seminar

Series comments: Weekly research seminar on fractal analysis (online)

Topics:

• theory of fractals (fractal geometry and fractal analysis)
• Hausdorff–Besicovitch dimension, techniques and methods for its calculation and estimation
• functions and transformations preserving fractal (Hausdorff–Besicovitch, entropic, box-counting, packing, etc.) dimension
• sets of metric spaces that are essential for functions, sets, and dynamical systems
• self-similar, self-affine properties of mathematical objects
• systems of encoding for real numbers (numeral systems) and their applications
• metric number theory and metric theory of representations of numbers
• probabilistic number theory and probabilistic theory of representations of numbers
• measures supported on fractals, particularly singular measures and probability distributions
• nowhere monotonic and nowhere differentiable functions, functions with fractal properties
• theory of groups determined by invariants of transformations preserving tails of representation of numbers, digit frequencies, etc.

The talks are mostly in Ukrainian but English is also acceptable

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