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Abstract-In this work we concentrate on the long-term and short term cycles of Ukrainian stock market, being based on the nonlinear approach of the analysis of open systems. First, the paper gives an algorithmic model for the investigation of the nonlinear nature of stock market, which comprises five individual stages. Then, by analyzing the Hurst coefficient for the PFTS index for the Ukrainian stock market it is shown that it is persistent, i.e. contains the fractals. As the results, a parabolic function is used for the approximation of a nonlinear trend in the PFTS series. Moreover, the major tendency of the PFTS index gives the correlation trends of "blue chips". The elimination of trends and the usage of Fourier analysis allow one to determine the long-term and short-term cycles in the index and shares. Finally, by investigating the weight of the long-term harmonics in the cyclic component of the PFTS index, the stability of Ukrainian stock market is studied in a short-time period. The application of the results involves the forecasting of the crisis points of stock market and proves the effectiveness of shareholders Index Terms-stock market, spectral analysis, cycle, PFTS index, harmonics, fractality, nonlinear dynamic

In the current work we investigation depend of Ukrainian financial markets segments from influences of the external financial market. In the article we propose the methodology of the investigation which includes three main units. The main ideas of these units are recognition of the most influential external financial market by indicators set, forecasting of the tendencies and influences of the foreign financial markets segments, construction of adaptation decision for the regulation of the Ukrainian financial market. We used the VAR models and variance analysis for the determination of the influences foreign financial market. The investigation of MosPrime Index and DAX Index as most influential indicators of external market allowed to define the adaptation type of the stock and credit segments of the Ukrainian financial market.

In the conditions of Ukraine’s integration into the European educational area, it is vital to follow the trend of democratization of the society and obtaining freedoms in various spheres of the Ukraine’s development. Therefore, the concept of university autonomy is one of the key in development of the Ukrainian higher education system, whereas obtaining additional freedoms in management of the higher educational institutionsenhances its competitiveness. The concept of autonomy has a dual nature, thereby impacting the need to determine such a level of autonomy that would ensure high quality of higher education in the frame of the country’s national development. The article analyzes methodological approaches to calculation of autonomy of the higher education system in Ukraine. As a result, the methods of the European University, which include examination of autonomy by four components: organizational, staff, financial and academic, are chosen for the research. The development level method and the cluster analysis are selected as mathematical tools. Following the development level method, an integral indicator for each component of autonomy is obtained. On the basis of calculation, it is determined that Ukraine has a low level of autonomy across all the components. Through the use of the cluster analysis, 5 clusters of autonomy of the higher education system are built, whereupon they obtain their economic interpretation. Analysis of the Ukrainian higher education system’s place in the European educational area shows that the system of the Ukrainian higher education is categorized within the cluster with a low level of autonomy.