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## Использование спутниковой системы измерения поля гравитации Земли (GRACE) для оценки водного баланса крупных речных бассейнов

Possible application of the satellite gravity survey data obtained under the Gravity Recovery and Climate Experiment (GRACE) for solving various hydrological problems is discussed. Former investigations linked the monthly changes of the terrestrial gravity field of the Earth to the movement of water masses within the continental part of the hydrological cycle. The GRACE technology allows obtaining the realistic mean data on the changes of land water resources on continental and regional scale. The technique could be useful for the monitoring of river discharge, snow cover, glacier melting and groundwater level oscillations over vast territories. The specific features of the technique itself and the data processing are described. The GRACE-based monthly gravity field data are transformed into the maps of water level equivalent and averaged for the catchments of the largest rivers of Russia. The temporal variability of the parameter is analyzed. Possible application of the GRACE data for the evaluation of particular components of water balance within the largest river basins of the European part of Russia is discussed.

The Higher Education and universities have high impact for regional development and youth migration. We suggest what the migration of people with a high level of knowledge (called “brain drain”) is detrimental for the region of emigration. High level universities attract the best students and growth the brain drain. There are close relationships between neighboring regions. Distance can be understood as a barrier of human capital growth. Geographical distance between parental home and college poses a potential barrier to higher education entry, and could be a deciding factor when choosing between institutions. Similar issues potentially arise when considering who goes to which universities, because students with different backgrounds and abilities choose different types and qualities of universities, and the spatial distribution of both university types and student characteristics is not uniform. But at the same time there are the researches which don’t find the impact of distance to accessibility of higher education. The distance a pupil lives from their nearest university has little effect on the likelihood that they go to university. There are many articles describe the social Neighborhood Effects of universities. But the question about geography and place is too often overlooked. The paper of Cullinan and Duggan presents a gravity model of student migration flows to HEIs in Ireland. Their analysis suggests that while geography plays a very important role in explaining student flows. Available studies about student migration cover the territory of England, Ireland, Romania, Poland, US, Canada etc. But we don’t have the works which explain the spatial effect of Russian universities to youth migration. In this article we observe the example of Kazan federal university and her spatial effect to educational migration. The case of Kazan federal university is very important. It’s a one of ten federal university of Russia. More of 30.000 students study in university, 80% of them is from Volga Federal district. The study allowed to find the neighbors of the first and second order, who are influenced by a strong neighbor.

Gravity Recovery And Climate Experiment (GRACE) twin-satellites have been observing the mass transports of the Earth inferred by the monthly gravity field solutions in terms of spherical harmonic coefficients since 2002. In particular, GRACE temporal gravity field observations revolutionize the study of basin-scale hydrology, because gravity data reflect mass changes related to groundwater redis- tribution, ice melting, and precipitation accumulation over large regions. However, to use the GRACE data products de-striping/filtering is required. We apply the Mul- tichannel Singular Spectrum Analysis (MSSA) technique to filter GRACE data and separate its principal components (PCs) at different periodicities. Data averaging over the 15 largest river basins of Russia was performed. Spring 2013 can be char- acterized by the extremely large snow accumulation occurred in Russia. Melting of this snow induced large floods and abrupt increase of river levels. The excep- tional maxima are evident from GRACE observations, which can be compared to the hydrological models, such as GLDAS or WGHM, and ground observations. Long-periodic climate-related changes were separated into PC 2. It has been ob- served that there were mass increases in Siberia and decreases around the Caspian sea. Overall trend over Russia demonstrates mass increase until 2009, when it has a maximum, following by the decrease.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.