Графовые модели в задаче планирования траектории на плоскости
Students' internet usage attracts the attention of many researchers in different countries. Differences in internet penetration in diverse countries lead us to ask about the interaction of medium and culture in this process. In this paper we present an analysis based on a sample of 825 students from 18 Russian universities and discuss findings on particularities of students' ICT usage. On the background of the findings of the study, based on data collected in 2008-2009 year during a project "A сross-cultural study of the new learning culture formation in Germany and Russia", we discuss the problem of plagiarism in Russia, the availability of ICT features in Russian universities and an evaluation of the attractiveness of different categories of ICT usage and gender specifics in the use of ICT.
The results of cross-cultural research of implicit theories of innovativeness among students and teachers, representatives of three ethnocultural groups: Russians, the people of the North Caucasus (Chechens and Ingushs) and Tuvinians (N=804) are presented. Intergroup differences in implicit theories of innovativeness are revealed: the ‘individual’ theories of innovativeness prevail among Russians and among the students, the ‘social’ theories of innovativeness are more expressed among respondents from the North Caucasus, Tuva and among the teachers. Using the structural equations modeling the universal model of values impact on implicit theories of innovativeness and attitudes towards innovations is constructed. Values of the Openness to changes and individual theories of innovativeness promote the positive relation to innovations. Results of research have shown that implicit theories of innovativeness differ in different cultures, and values make different impact on the attitudes towards innovations and innovative experience in different cultures.
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.