### Working paper

## Оценка распределения влияния в Европейском парламенте в 1979–2014гг.

The article contains an analysis of the Directive of the European Parliament and of the Council on services in the internal market. The study discusses the main amendments to the original Directive proposal; defines the content of the country of origin principle; determines the scope of the Directive and of the freedom to provide services. A particular attention is paid to the article 16 of the Directive. The author examines the principles, that Member States have to respect in order to impose requirements with regard to the provision of a service activity by providers, established within the territory of another Member State. Based on this research, the author makes an attempt to appraise the importance of this Directive for the liberalization process of trade in services sector.

This paper demonstrates that most existing voting schemes represent or can be rewritten as weighted games. However, axiomatics for power indices defined on simple games are not directly applied to weighted games, since related operations become ill-posed. The author shows that the majority of axiomatics can be adapted to weighted games. Finally, a series of examples are provided.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

This publication is devoted to issues related to religious policy of the European Parliament as well as the history of the European Union. The paper was requested by the EP.

We offer a general approach to describing power indices that account for preferences as suggested by F. Aleskerov. We construct two axiomatizations of these indices. Our construction generalizes the Laruelle-Valenciano axioms for Banzhaf (Penrose) and Shapley-Shubik indices. We obtain new sets of axioms for these indices, in particular, sets without the anonymity axiom.

At calculation of the power indices, both well-known (Banzhaf, Shapley-Shubik and others and new (depending on the agent preferences) indices, one generally has to enumerate almost all coalitions, that is, the subsets of the set of players, which makes calculations impossible if the number of players exceeds fifty. Yet, if all players have an integer number of votes, there are players with the same number of votes, many coalitions have equal total number of votes or the sum of votes of all players is small, then the algorithms based on calculations using the generating functions become efficient. But these algorithms works only for classical power indices and some particular types of the power indices based on agents’ preferences. In this paper we consider an important specific case when all players have the same number of votes. For classical power indices in this case all players have the same power. However, it is not the case for the indices which allow preferences of agents. We introduce effective algorithms for calculation of the latter indices for most types of these indices.

We address the external effects on public sector efficiency measures acquired using Data Envelopment Analysis. We use the health care system in Russian regions in 2011 to evaluate modern approaches to accounting for external effects. We propose a promising method of correcting DEA efficiency measures. Despite the multiple advantages DEA offers, the usage of this approach carries with it a number of methodological difficulties. Accounting for multiple factors of efficiency calls for more complex methods, among which the most promising are DMU clustering and calculating local production possibility frontiers. Using regression models for estimate correction requires further study due to possible systematic errors during estimation. A mixture of data correction and DMU clustering together with multi-stage DEA seems most promising at the moment. Analyzing several stages of transforming society’s resources into social welfare will allow for picking out the weak points in a state agency’s work.

This article is talking about state management and cultural policy, their nature and content in term of the new tendency - development of postindustrial society. It mentioned here, that at the moment cultural policy is the base of regional political activity and that regions can get strong competitive advantage if they are able to implement cultural policy successfully. All these trends can produce elements of new economic development.

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.