Франция и Россия: вокруг Блеза Паскаля
The article is devoted to the phenomenon of incompleteness of the book "Thoughts" by B. Pascal
The article is devoted to the trends and determinants of the transformation of Russian regions' industrial specialization during the period of economic growth. Using the methodology of statistic and econometric analysis it is tested whether the tendency of diversification dominates the tendency of regions’ industrial specialization in 1997-2004 and whether there is a convergence of Russian regions' industrial structures. The considered factors of industries' development in a particular location include the initial industrial structure, inter- and intraregional technologic links between industries, quality of investment climate, R&D potential, international competition.
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.