Search academic texts

Information × Registration Number 0221U103279, 0116U000011 , R & D reports Title Fractal analysis of singular and nowhere monotonic functions popup.stage_title Head Prattsovity Mikola Viktorovich, Доктор фізико-математичних наук Registration Date 17-02-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Object of study — functions with complicated local structure and fractal properties. Most of them are continuous functions on an interval. They belong to two classes: singular (continuous functions whose derivative is equal to zero almost everywhere with respect to Lebesgue measure) and nowhere monotonic (functions that does not have any arbitrary small monotonicity interval), particular nowhere differentiable functions. Objective of the work — studying fractal local and global properties of some finite- and infinite-parameter families of singular and nowhere monotonic functions as well as metric spaces of such functions. Methods of study — condensation of singularities; iterated function systems; definition of function by a system of functional equations; projectors of representations (encodings) of numbers; method of scale invariance (generalization of self-similarity and self-affinity); definition of functions by automata and transdusers for digits of representation; method of cylindrical definition of functions, etc. New methods for analytical definition and studying functions with complicated local structure are developed. These methods and other known methods are used for description of topological, metric, differential, integral and fractal properties of level sets, graphs, sets of peculiarities for some classes of singular and nowhere monotonic functions. Applications — fractal analysis and fractal geometry, function theory, metric and probabilistic number theory, probability theory. Product Description popup.authors Baranovskyi Oleksandr M Baranovskyi Oleksandr M Vasylenko Natalya A Vasylenko Natalya A Vaskevych Svitlana O Vaskevych Svitlana O Karvatsky Dmytro M Karvatsky Dmytro M Torbin Hryhorii M Torbin Hryhorii M popup.nrat_date 2021-02-17 Close