Introduction. The global trend of urban concentration and the agglomeration effects of production, consumption, capital movements, asset accumulation, and innovation generate the issue of how environmentalism and urbanization correlate. The gradient increase of the technogenic press on the environment from small settlements to large cities causes the shift of research focus from the analysis of the ecological component of the welfare of the state to the environmental component of the welfare of cities.
Purpose. The basic hypothesis of the article is the presence of a connection (not always direct linear) between the level of welfare of cities and indicators of the environmental situation in them. It is assumed that the level of well-being (including environmental comfort) has a significant influence on both policy factor and certain non-economic factors of higher demand for environmental standards of life. Also, the purpose of the study is to identify the links between indicators that can be used in modeling the environmental indicator of the welfare state both at the national and local levels.
Method Data from the Institute for Strategic Development of the Mori Foundation (Japan) for ranking the largest cities in the world according to the Global Power City Index (GPCI) is used as the information content of the research. The study has used a set of methods for statistical analysis, namely correlation, regression and dispersion ones.
Results. The comparison of the ranks of the studied cities by the criterion of the state of the environment and for the GPCI generally indicates a moderate correlation between them (Spirman correlation coefficient rS = 0.440, with rst = 0.396 for p <0.01). This underlines the very important role of the environment of cities in the manifestation of their global "magnetism". The environmental factor, which plays the role of attractiveness of the city, is particularly important from the position of increasing global competition for attracting talent, as well as global aging of the population and reducing the proportion of the productive age population. The assumption that life attractiveness can be significantly conditioned by the environmental factor has been confirmed by the correlation results (Pearson correlation coefficient between the state of the environment and the attractiveness for life in world metropolises r = 0.463, p <0.01) and regression of linear single- and multivariate analysis.
It is established that there is no significant linear dependence that between indicators of the environment of cities and their level of economic development. At the same time, a nonlinear regression analysis made it possible to construct several adequate nonlinear models in which the variable, which characterizes the development of the city's economic sector in a complex manner, serves as an independent variable, and a generalized indicator of the state of the environment as a dependent one.
The constructed metropolitan matrix of the "economic development-ecology" ratio illustrates that, despite the importance of the urban economic development factor, it is possible to break the "enchanted circle" of poverty and bad ecology, or in other words the inability to generate demand and supply for environmental benefits, on one hand, and realize the environmental preferences of households, on other hand. The shift towards agglomerative concentration of the population and employment is a confirmation of the demand for the expansion of the taxonomy of the welfare state at the expense of an indicator of its ecological state.
Preparation of States in Open Quantum Mechanics
