The extragalactic background radiation produced by distant galaxies emitting in the far infrared limits the sensitivity of telescopes operating in this range due to confusion. We have constructed a model of the infrared background based on numerical simulations of the large-scale structure of the Universe and the evolution of dark matter halos. The predictions of this model agree well with the existing data on source counts. We have constructed maps of a sky field with an area of 1 deg 2 directly from our simulated observations and measured the confusion limit. At wavelengths 100 − 300 µm the confusion limit for a 10-m telescope has been shown to be at least an order of magnitude lower than that for a 3.5-m one. A spectral analysis of the simulated infrared background maps clearly reveals the large-scale structure of the Universe. The two-dimensional power spectrum of these maps has turned out to be close to that measured by space observatories in the infrared. However, the fluctuations in the number of intensity peaks observed in the simulated field show no clear correlation with superclusters of galaxies; the large-scale structure has virtually no effect on the confusion limit.

Primordial Black Holes (PBH) with masses of order 10 − 30M⊙ have been proposed as a possible explanation of the gravitational waves emission events recently discovered by the LIGO observatory. If true, then PBHs would constitute a sizeable fraction of the dark matter component in the Universe. Using a series of cosmological N-body simulations which include both dark matter and a variable fraction of PBHs ranging from fPBH = 10−4 to fPBH = 1, we analyse the processes of formation and disruption of gravitationally bound PBH pairs, as well as the merging of both bound and unbound pairs, and estimate the probabilities of such events. We show that they are in good agreement with the constrains to the PBH abundance obtained by the LIGO and other research groups. We find that pair stability, while being a main factor responsible for the merger rate, is significantly affected by the effects of dark matter halo formation and clustering. As a side result, we also evaluate the effects of numerical errors in the stability of bound pairs, which can be useful for future research using this methodology.

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The article develops theoretical and methodological approaches to ensuring economic security in the conditions of combating the shadow economy. In accordance with the set goal, the following tasks are solved in the article: the structure of threats to economic security is revealed and their types are determined; approaches to the concept of "shadow economy" were investigated and its definition was clarified; the influence of the shadow economy on the level of economic security was investigated; the policy of combating the shadow economy is substantiated. It has been proven that the shadow economy is a difficult phenomenon to study and account for. There are quite a few definitions of the shadow economy, which is due to the fact that it is quite diverse in structure. It is proposed to include here various types of activities that are not taken into account by official statistics, are not included in GDP, that is, that exist outside the legal field. This is the reason why the shadow economy cannot be accurately measured and often data on the size of the shadow economy from different sources differ significantly. The conducted research gives reasons to conclude about the dual nature of the shadow economy, which, in addition to clearly expressed shortcomings and threats to economic security, also has certain positive aspects, in particular, in the socio-economic sphere of the country. A significant amount of the shadow economy in our country, which continues to grow, seems very dangerous from the point of view of economic policy in the conditions of globalization. This causes the degradation of national tax systems. Also, economic policy based on incorrect indicators of economic statistics negatively affects the stability of economic development. And the results of the development of international institutions regarding the coordination of economic policy, which is a favorable factor in the functioning of the modern global economy, may also be ineffective. It has been proven that the shadow economy in the post-Soviet countries acts as a certain tool for maintaining economic and social balance. The authors believe that in the conditions of the transition period, with the help of the shadow sector, conditions are created for the survival of business and the population. Despite all the disadvantages, shadow activity also provides certain advantages: for small businesses - increased profits; the active population - the opportunity to work and receive income; consumers - to buy goods and services at lower prices. It is substantiated that, despite the listed positive aspects, any manifestation of the shadow economy is dangerous for the full development of the countries' economy. These phenomena will lead to the growth of corruption, a sharp increase in the stratification of the population, increase inflation, worsen working conditions and slow down economic development in general.

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