Робота присвячена подальшому розвитку теорії моделювання гауссових стаціонарних випадкових процесів за методом, який запропонував і розвивав Ю. В. Козаченко. Розглянуто застосування теорії L2(Ω)-процесів при моделюванні гауссових стаціонарних випадкових процесів. Використовуючи оцінки норм та деякі властивості і теореми L2(Ω)-процесів, для моделі одержано розбиття спектрального проміжку, при якому модель наближатиме процес з заданими точністю і надійністю в рівномірній метриці. У середовищі Python було змодельовано процес для часткового випадку.

The task of calculating the productivity of collective scientific subjects is a relevant issue in scientometrics. This study formalized the problem of assessing productivity trends of collective scientific subjects. The TWPR-CI method for calculating the performance based on the modified PageRank algorithm is described. Formulas for calculating productivity have been derived that make it possible to take into account a change in the productivity of collective scientific subjects over time. The indicators of the basic average absolute change in performance and the chain average relative change in performance were chosen as the basis. To select promising, from the point of view of scientific work, collective subjects, preference is given to those whose basic average absolute change in productivity is positive or the chain average relative change in productivity exceeds unity. Verification of the method for assessing performance trends of collective scientific entities based on the modified PageRank algorithm using the public dataset Citation Network Dataset was carried out. The dataset includes more than 5 million scientific publications and 48 million citations. The citation of scientific publications of 27,500 collective scientific subjects for the period from 2000 to 2022 was analyzed. For this period, for 15 selected collective scientific subjects, performance is calculated using the TWPR-CI method, as well as estimates of productivity trends based on their average relative change. There are three classes of collective scientific subjects according to productivity trends. The results indicate the relevance of the proposed method for quantifying the productivity trends of collective scientific entities (higher education institutions, scientific institutes, laboratories, and other institutions engaged in scientific activities)