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Information × Registration Number 0224U001856, 0121U000209 , R & D reports Title Implementing the tasks of perspective plan of development of the scientific direction "Mathematical Sciences and Natural Sciences" in the National Pedagogical Dragomanov University popup.stage_title Head Pratsovytyi Mykola V., Доктор фізико-математичних наук Registration Date 31-01-2024 Organization Dragomanov Ukrainian State University popup.description2  As a result of studying systems of encoding of real numbers with an infinite alphabet and functions with locally complex structure and fractal properties, a system of encoding of real numbers with zero redundancy (B-representation, which identifies a point (number) with an infinitely two-sided sequence of alphabet elements) has been developed. Its geometry, including properties of cylinder and tail sets, has been thoroughly studied. A comparative analysis of topological-metric properties with other infinitely symbolic systems for number representation has been conducted. A continuous class of functions defined by a system of functional equations using B-representation of numbers has been introduced. Within this class, monotonic, non-monotonic, nowhere monotonic, Cantor-type, and quasi-Cantor-type functions have been identified. Functions of both bounded and unbounded variation have been explored. Examples of diverse applications in number theory, probability theory, and fractal theory provided. Additionally, research on the radiation resistance and radiation defects of quantum well light-emitting diodes (LEDs) has been carried out within the field of radiation physics of semiconductor devices. Experimental studies on the radiation resistance of quantum well LEDs have been conducted. This includes measuring radiation-induced spectra in the temperature range of 77-3000K after irradiation with certain electrons, quanta, and neutrons from the considered reactor. The impact of deep levels of radiation defects on the parameters of quantum well LEDs has been studied based on experiments. The results of annealing LEDs with radiation defects have been analyzed, revealing that the emission spectrum of ultraviolet LEDs grown on InxGa(1-x)N consists of three segments: the most intense ultraviolet band-primary, followed by significantly weaker yellow and red bands. Furthermore, it has been determined that the ultraviolet emission is due to inter-level transitions in the quantum Product Description popup.authors Vasylenko Nataliya M. Vernydub Roman M. Mosyuk Tatyana Mosyuk I. Pavlova Natalija Yu. Panchenko Larysa L. Pratsiovytyi Mykola V. Tartachnyk Volodymyr P. Trebenko Dmytro Ya. popup.nrat_date 2024-01-31 Close