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## Shannon's differential entropy asymptotic analysis in a Bayesian problem

We study the asymptotic behaviour of differential entropy in a Bayesian problem of estimationg a probability of success in a series

of conditionally independent trials.

The author represented Stalinism as a model of social constructivism, analyzed basic features of this type of dictatorship. New trends in Russian and international historiography of the problem are under consideration.

The Informational paradigm of discourse to the XXIst century is replaced by communicative; due to the spread of the Internet, new features and models of communication based on the subject-to-subject concept of hypertext are formed. Tekstogennost’ as a set of anthropogenically-technical factors of generation, transmission, exchange texts of public communication, leading to the formation and operation of new types of vehicles and generators of information in all spheres of life, which have an impact on them, becomes the essential characteristic of socio-economic discourse. The role of the professional communication support (PR, mass media) of all processes becomes more essential. Thus, the textual, philological, humanitarian dimension determines the effectiveness of social development.

Projects and reforms targeting infrastructure services can affect consumer welfare through changes in the price, coverage, or quality of the services provided. The benefits of improved service quality—while significant—are often overlooked because they are difficult to quantify. This article reviews methods of evaluating the welfare implications of changes in the quality of infrastructure services within the broader theoretical perspective of welfare measurement. The study outlines the theoretical assumptions and data requirements involved, illustrating each method with examples that highlight common methodological features and differences. The article also presents the theoretical underpinnings and potential applications of a new approach to analysing the effects of interruptions in the supply of infrastructure services on household welfare.

Proceedings of the 2013 IEEE 14th International Conference on Information Reuse and Integration (IEEE IRI 2013) , 14-16 August 2013, San Francisco, Ca, USA.

We are witnessing now a coming closer together of two pedagogical movements – that of media education (media literacy) and that of information literacy, both of them having previously existed parallel to each other, and without actually crossing each other’s path.

The matters of information presentation subject to specific problems of information innovation support of research and development (R&D ) results are discussed.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

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.