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This thesis seeks to advance our knowledge of what lies behind the risk and volatility in financial and macroeconomic outcomes, and how the two are related. The first contribution of the thesis lies in constructing new long-run data series on asset prices, returns and other financial indicators, which allow us to establish some basic facts about the empirical properties of macro-financial risk (Chapters 1–3). These new data allow us to study a rich selection of asset classes – from the known equity and government bond markets to the less explored markets for housing and corporate bonds – in greater detail, across more countries and over a longer time period than previously possible. The second contribution lies in analysing these data empirically to study the underlying causes and real-world consequences of financial risk and volatility (Chapters 2–4). Third, this thesis seeks to advance our theoretical knowledge of these macro-financial linkages through both examining existing theories (Chapter 2), and proposing new ways of thinking about the real effects of time-varying financial frictions (Chapter 5).

In this paper, we study the properties of α-sets, which are one of the generalizations of convex sets. In the first part of the paper, the equivalence of two definitions of α-sets in the plane is proved. The second part of the work is devoted to the experimental study of the properties of simply connected intersections of α-sets. It follows from the results of numerical experiments that the value α of the measure of nonconvexity in a simply connected intersection of two α-sets can be greater than the initial value of α in intersected sets even when these values are very close to zero. Based on these results, we can hypothesize that, firstly, such an increase in the value of α is possible with an arbitrarily small initial α for intersected sets, secondly, this increase is limited by a linear function of the initial value of α. © 2020 Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. All rights reserved. ; The reported study was funded by RFBR according to the research project no. 18–01–00221 A. The work was supported by Act 211 Government of the Russian Federation, contract no. 02.A03.21.0006.

Abstract
The article discusses the research activities of Vladimir Mikhailovich Khvostov, his creative legacy on issues and problems of international relations of the early ХХ century; the life of V.M. Khvostov, characterization and evolution of his approaches and views on the history of international relations, foreign policy. A prominent organizer and theorist in the field of pedagogical Sciences, academician Vladimir Mikhailovich Khvostov played a significant role in the formation of the Academy of pedagogical Sciences of the USSR – the all-Union center of pedagogical thought. As its first President, he paid great attention to the development and improvement of the system of humanitarian education in the school, taking into account all the tasks and requirements imposed by the practice of Communist construction in our country. In his reports and speeches at various scientific sessions and conferences, he repeatedly emphasized the exceptional importance of social Sciences in the training of not only educated girls and boys, but also in the formation of politically literate youth.