Modification of Generalized Scientific Indicators Based on the Mathematical Theory of Limits

The objective of this research is to justify new scientometric parameters suitable for the diagnosis of the research activities productivity and sustainable artificial “improvement.” It is known that it is generally accepted scientometric indicators that reflect the productivity of research activities of scientists and organizations (team) are the Hirsch index (h-index) and g-index; both indices calculated on the basis of statistical method, scree. However, scientometric indicators, based on citation, give artificial “improvement”; no exception of g-index and h-index. The authors propose modified methods of the indicators calculation based on the application of the mathematical theory of limits; its application makes possible to limit the role of self-citations and citations by co-authors, attempts distortion (unfair boosting) scientometric indicators that reflect the productivity of the scientist's research activities and the importance of its results to the scientific community. At the same time, the author's method of assessment of the modified g-index and h-index does not deny the importance of reasonable (justified) self-citations and citations by co-authors. The practical significance of research results in the possibility of their use in monitoring systems research activities of scientific institutions (including higher educational institutions), the theoretical significance – the possibility of further scientific. To achieve the goal and solve the tasks set, the following complementary research methods were used: analysis of scientific literature and best practices in management of research activities in scientific organizations - higher education institutions (benchmarking); modeling; methods of Set Theory; automated system-cognitive analysis; methods of qualimetry (theory of latent variables); methods of mathematical statistics (including the scree plot method), methods of the theory of limits. The empirical stage of the research was carried out on the basis of higher educational institutions of the Krasnodar Territory. It is proved that the modified h-index and g-index more adequately reflect the productivity of the scientist's research activities, the significance of its results for the scientific community.