An interlaboratory scientific seminar «Mathematical Modeling of Variations in Radon Volumetric Activity Taking into Account Hereditarity» was held to discuss a doctoral dissertation carried out in IKIR FEB RAS

The presentation was made by the Researcher of the Laboratory of Electromagnetic Radiation of IKIR FEB RAS, Cand. Sci. (Phys.-Math.) - Tverdiy Dmitriy Aleksandrovich, on October 27, 2026 at the Digital Technologies and Artificial Intelligence Research Institute, Tashkent, Uzbekistan.

The agenda item of the interlaboratory scientific seminar included discussion of the dissertation paper of the independent Researcher of the Digital Technologies and Artificial Intelligence Research Institute, Researcher of IKIR FEB RAS, Tverdiy Dmitriy Aleksandrovich, on the subject «Mathematical Modeling of Variations in Radon Volumetric Activity Taking into Account Hereditarity». The paper is submitted for the degree of Doctor of Technical Sciences (DSc) in the specialty 05.01.07 – Mathematical Modeling. Numerical methods and Software Packages.

The Scientific Advisor is the Chief Researcher of the Laboratory of Physical Process Modeling of IKIR FEB RAS, Dr. Sci. (Phys.-Math.), Senior Lecturer, Professor of FEB RAS - Parovik Roman Ivanovich.

In the course of the presentation, Dmitriy Aleksandrovich told about the results of his dissertation investigation carried out in the framework of the Agreement No. 1 from October 15, 2025 on the postgraduate study as an independent Researcher of the Digital Technologies and Artificial Intelligence Research Institute. The investigation is devoted to the study of the possibility to generalize current mathematical models of radon volumetric activity (RVA) dynamics in an accumulating chamber by the method of fractional derivative with the aim to improve the process modeling taking into account time non-locality of the radon transfer process. Scientific and practical novelty consists in the fact that new theoretical and practical results in the field of fractional computation were obtained. New mathematical hereditary models for RVA were obtained on the basis of Riccati equation with non-constant coefficients and fractional Gerasomov-Caputo variable-order derivative, that make it possible to model the RVA dynamics more accurately. Effective parallel hybrid algorithms, realizing numerical methods for solving model RVA equations, were developed, which made it possible to decrease significantly the time of solving direct and coefficient inverse problems. New method and numerical algorithm were developed on the basis of the iteration Levenberg-Markquardt method to solve coefficient inverse problems on identification of hereditary RVA model parameters when experimental data are known. A software package in the form of an application with graphic user interface for Linux OS was developed. It makes it possible to solve the problems of mathematical modeling of RVA variations, processing and visualization of data and results. A number of practical problems of mathematical modeling was solved based on RVA experimental data in the regimes of accumulation, decay, at RVA anomalous values and the data in the time vicinity of the strong earthquake in Kamchatka on August 17, 2024.

During the seminar, the reviewers expressed their opinions on the doctoral dissertation: Professor, Dr. Sci. (Phys.-Math.), Senior Lecturer - Eshmatov Bakhtier Khasanovich, from the «Tashkent Institute of Irrigation and Agricultural Mechanization” National Research University»; Professor, Dr. Sci. (Tech.) - Dzhaykov Gafur Muratbaevich from Nukus State Technical University. The reviewers made a number of comments and suggestions regarding the content, on which the candidate for the degree gave his answers. The reviewers noticed that their comments did not decrease the significance of the obtained results and conclusions. They made the conclusion that the dissertation paper by Tverdiy Dmitriy Aleksandrovich met the requirements of the State Commission for Academic Degrees and Titles of the Uzbekistan Republic for the thesis of the Doctor’s degree.

At the end of the seminar, after the voting with the result of 100%, it was decided to recommend the doctoral dissertation investigation on the subject «Mathematical Modeling of Variations in Radon Volumetric Activity Taking into Account Hereditarity» by Tverdiy Dmitriy Aleksandrovich for defense.