Abstract. This scientific paper is dedicated to the use of artificial neural networks for the ecological prediction of state of the atmospheric air of an industrial city for capability of the operative environmental decisions. In the paper, there is also the described development of two types of prediction models for determining of the air pollution index on the basis of neural networks: a temporal (short-term forecast of the pollutants content in the air for the nearest days) and a spatial (forecast of atmospheric pollution index in any point of city). The stages of development of the neural network models are briefly overviewed and description of their parameters is also given. The assessment of the adequacy of the prediction models, based on the calculation of the correlation coefficient between the output and reference data, is also provided. Moreover, due to the complexity of perception of the «neural network code» of the offered models by the ordinary users, the software implementations allowing practical usage of neural network models are also offered. It is established that the obtained neural network models provide sufficient reliable forecast, which means that they are an effective tool for analyzing and predicting the behavior of dynamics of the air pollution in an industrial city. Thus, this scientific work successfully develops the urgent matter of forecasting of the atmospheric air pollution index in industrial cities based on the use of neural network models.

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In the 4th part of "My Past and Thoughts", Herzen recalls his life in Novgorod in 1841–1842 and, inter alia, tells a story about a certain «Doukhobor leader», allegedly imprisoned by the Emperor Paul I. Even though the story looks rather far-fetched, it seems to stem from real historical events — the 1800 investigation into the religious dissenters from the Novgorod Gubernia and certain episodes from the life of Kondratiy Selivanov, the leader of the Scoptsy (Castrates) movement. The article deals with the social, historical, and religious contexts of the narrative told by Herzen.