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.
This paper is devoted to the numerical analysis of the various continuum models of a 1D discrete media. Namely, we consider intermediate, quasi‐continuum, and improved quasi‐continuum models. The analysis of various receptions of continualization in a linear case is carried out. For this purpose, we consider the solution in the form of a traveling wave caused by the initial perturbation. The solution is obtained by Fourier transformation inverted numerically. Then we compare solutions of discrete and continuum models for wave velocity. Numerical calculations show that all the above described nonlocal theories qualitatively equally well describe the propagation of waves in a discrete media. The disadvantage of intermediate continuum model is the high order of differential equation. For finite chain this leads to the need for the formulation of boundary conditions that do not follow naturally from the source of the problem. The quasi‐continuum approximation yields results practically identical with those obtained on the basis of improved quasi‐continuum approximation. The most accurate approximation of a discrete medium gives improved quasi‐continuum approximation. The advantage of improved quasi‐continuum approximation is manifested in those cases where you need to describe the high modes of oscillation of the discrete finite chain.
An analytical solution, describing the effective heat conductivity of composite materials with a periodic array of cylindrical inclusions with square cross-section, has been obtained by asymptotic methods and Padé approximants for any values of the concentration of inclusions and conductivity.
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