In this paper we are interested in the approximation of the integral \[I_0(f,\omega)=\int_0^\infty f(t)\,e^{-t}\,J_0(\omega t)\,dt\] for fairly large $\omega$ values. This singular integral comes from the Hankel transformation of order $0$, $f(x)$ is a function with which the integral is convergent.
In the paper, the research problem of cybersecurity in Ukraine and constituent elements of the cybersecurity global index were considered. The study object is the methods of predicting the indicator of the cybersecurity global index in Ukraine based on the trend extrapolation methods using one dynamic sequence. The purpose of the work is to apply predicting methods to build a prediction of the global cybersecurity index in Ukraine.
When analyzing time series to identify trends in the development of the phenomenon, for example, the draft of the structure, trends based on the results of observations are used.
Analysis of the debris flow formation factors which cause the long-term activity of debris flows is made. The methodology of the debris flows prediction subject to meteorological, hydrological, seismic, heliophysical factors is proposed. The regularities of long-term seasonality of these factors by using autocorrelation and spectral analysis are revealed. The integral rate of probability of debris flow intensification is calculated. The time series of this integral rate is extrapolated and the following peak of debris flows activation is predicted.