The objective of the article is constructing of the two-factor model on the basis of the statistical material of the Webometric Rating of Universities, which analytically describes the status of Ukrainian higher educational institutions in terms of Webometrics indicators, provides an opportunity for its quantitative and qualitative analysis and forecasting of development trends of market educational services and marketing research in this area. The statistical analysis of the data of the Webometric Rating of Universities was conducted using the professional statistical information processing program STATGRAPHICS Centurion XV.I. Analytical relations are obtained using the Pade approximation technique. Mathematical editor Maple has been used to visualize the results of research and illustrate a qualitative picture of the rating of Ukrainian universities in the Internet space using the Webometric Indicators system. A two-factor model of the state and forecast of academic representation of Ukrainian universities according to Webometric rating is constructed. Using the proposed model, an analytical expression is obtained that allows for quantitative and qualitative assessments of the world ranking of higher educational institutions of Ukraine in the Web-indicators system Webometrix in order to increase their academic presence on the Internet, to strengthen the international authority and raise the national science school as a whole for a qualitatively new degree of development. The scientific novelty of the work is in the inclusion in the model of the time factor, the availability of which makes it possible, firstly, to extend the statistical material used in time and, secondly, to predict the trends and prospects of presentation in the Internet space of Ukrainian universities as advanced research centers. The main results of the work can be useful as a methodological material during the educational process in higher educational institutions, in the training and improvement of the skills of management personnel, in developing programs for reforming the educational process in higher education in order to bring it closer to European requirements and achieve the level of the best world universities. The presented methodology and data analysis algorithm can be generalized to evaluate rating systems of other nature: when evaluating students' educational and community work, financial analysis, in particular, to assess the probability of default of non-lending organizations, to determine the reliability of commercial banks, to conduct sociological tests, and surveys, medical and biological research and other areas of public administration.

The article enlightens the activities of the main public online educational platforms in Ukraine, their role in the modernization of education and their socio-political influence on changes in the state. Interdependence is observed between the specificity, inherent in different stages of distance education progress. Problematic issues in the field of innovative educational technologies are highlighted: socialization of students, difficulties in control of their knowledge, metacognitive monitoring of mastering the material by them etc. The degree of organization in operation of electronic cabinets is examined and other measures supposed to introduce the telecommunicative teaching means in Ukrainian higher education.

In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O Δ E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system with very complicated (chaotic) behavior. In our paper we present examples of deterministic discretization and chaotic continualization. Continualization procedure is based on Padé approximants. To correctly characterize the dynamics of obtained ODE we measured such characteristic parameters of chaotic dynamical systems as the Lyapunov exponents and the Lyapunov dimensions. Discretization and continualization lead to a change in the symmetry of the mathematical model (i.e., group properties of the original ODE and O Δ E). This aspect of the problem is the aim of further research.

The purpose of the current paper is to emphasize the role of intellectual labor potential in economy development and digitalization and to explore the features of intellectual work and education as main source and component of the digital information economy. The consequencies of scientific fields representatives' outflow and low renumeration for such three neighboring contries as Slovakia, Ukraine and Russia are observed; their economic indeces are discussed and compared as for more than 10 past years and the beginning of 2020 year. Slovakian, Ukrainian and Russian digitalization achievements and main benefits of this process were outlined in the global transformation process.

The article is devoted to the statistical analysis of tools, used for the assessment of the international competitiveness of higher education institutions. The analysis has been made based on the Webometric ranking of universities. The aim of the study is to review in details of one of the most important and widely recognized global rankings -Ranking Web of World Universities, determine the place of Ukrainian institutions of higher education in it, identify perspectives for further development and appropriate adjustment of their Web policy.University rankings as a modern information tool for education management have been studied. An analysis of the role of rankings as a mechanism for assessment of universities as educational and research centers has been made. The specifics of Webometric indicators and their impact on the global ranking of the world's leading universities have been analyzed using the professional statistical data processing program STATGRAPHICS Centurion XV.I and the principal components analysis. Based on statistical assessment, the reasons for insufficiently high rating positions of Ukrainian universities in the Webometrics system have been identified. Suggestions on improvement of the presentation indicators of Ukrainian universities in the Internet space, their lifting in the international rating according to Webometric criteria and the qualitative development of domestic scientific and educational school in the context of world trends have been developed. The results of the research can be used by the governing bodies and management of Ukrainian higher education institutions during the creation and adjustment of development strategies, as well as by other specialists who develop, implement and evaluate the state policy of Ukraine in the sphere of higher education.