### Article

## Fuzzy regression model of the impact of technology on living standards

This paper proposes a model of the impact of technology on the standard of living based on fuzzy linear regression. The Human Development Index (HDI) was chosen as a dependent variable as an indicator of the health and well-being of the population. The explanatory variables are the Network Readiness Index (NRI), which measures the impact of information and communication technologies (ICT) on society and the development of the nation, and the Global Innovation Index (GII), which measures the driving forces of economic growth. The analysis is based on data for 2019 for four groups of countries with different levels of GDP per capita. For developed countries, the positive and balanced impact of innovation and ICT on living standards has been confirmed. For two groups of developing countries (upper and lower middle income), the GII coefficient was found to be negative. A more in-depth analysis showed that this is due to the state of political and social institutions. This fact means that without a simultaneous increase in the maturity of institutions, stimulation of other areas of innovative development (education, knowledge and technology, infrastructure) leads to a decrease in the quality of life.

This paper discusses the process of cognitization of society, i.e. increasing the role of knowledge and human capital in modern society and economy. However, in addition to knowledge and cognitive process, emotional intelligence and communication skills (Soft Skills), the presence of which gives an advantage in the labor market, are of essential importance. Thus, «cognitive inequality» is formed.

The paper estimates the share of Russian population that belong to the middle class and analyzes their values, standards, and ideas of the nation’s future vector of development. The analysis is based on nationwide representative polls conducted by the Institute of Sociology of the Russian Academy of Sciences in 2013–2014. The paper shows that everyday values of the Russian middle class are modernized and proactive and thus are different from those of other population groups; however, the middle class barely stands out from other groups in terms of political values and the vision of Russia’s future. As of now, the consensus view of the middle class (as well as other groups of Russians) is that Russia cannot just copy the Western “route” and needs to take its own way defined by its people’s values, standards and attitudes to some basic non-political institutions such as private property, rule of law etc.

In this article method of construction of living standards integral estimations for the region is considered. Special emphasis is laid on synthetic categories of living standards of population: standard of well-being, living standards of population, quality of social sphere. Convolution of individual indicators was carried out using Principle Components Analysis. For calculation of the integrated estimates of living standards of population in the Republic of Marii El, some generalized assessments were computed - indicators of advantages and regression, estimated as the ratio of the Republic of Marii El indicators values to the values of the corresponding indicators of Volga Federal District.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.