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## Some Applications of the Results of Solving the Problem of Tuning for the Analysis of the Phenomenon of Intervention in the Economy

The article discusses the development of a new stochastic model in the analysis of the intervention phenomenon in economics. We provide the theoretical fundamentals, as well as the importance and the applicability of the development of an intervention theory based on mathematical modelling. An overview of the literature on the implementation of mathematical modelling in the analysis of interventions is provided. We present the general structure of a new stochastic model of intervention, that is based on the idea of a controlled external influence, produced once the process reaches some specified set of boundary conditions. It is shown that the model represents a controlled Markov process with discrete time. The method of solving the task of the optimization of intervention is provided and it uses the results of solving the general stochastic problem of tuning.

The article analyzes the historical background of the emergence and development of the Customs Union of Russia, Belarus and Kazakhstan on the example of the Council for Mutual Economic Assistance, the German Customs Union and the Southern African Customs Union.

The subject matter of the article lies between public law and economics. The article contains sources of legal regulation in state corporations, ways of their forming, jurisdiction, priorities and results of its activities achieved in western democracies. The author stresses the dependence of effectiveness of this public law institute on checks and balances as well as individual responsibility, responsibility for doings and refraining from doing by authorities, reputation of officials.

There is now a very extensive and well-developed theoretical literature on the difficulties faced by durable goods monopolists in pricing their products. Surprisingly, the seminal article in this field did not come from a formal economic theorist but from Ronald Coase. Coase wanted to show that there are situations under which a pure monopolist might not be able to charge a monopoly price for durable products. The literature has since expanded to consider all manner of theoretical and formal conditions under which this hypothesis might or might not hold. And scholars have claimed that this body of work provides insights into everything from strategic leases to planned obsolescence and the problem of new model introductions. But how well has this literature really served to illuminate the problems facing actual business firms? While the safety razor industry has often been invoked as an example of durable goods pricing there has only been limited investigation into the actual behavior of the dominant firm in this industry – Gillette. We consider here the major ideas that have developed as an offshoot of the original Coase paper and the extent to which a case study of Gillette confirms or confounds this analysis.

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.

There is now a very extensive and well-developed theoretical literature on the difficulties faced by durable goods monopolists in pricing their products. Surprisingly, the seminal article in this field did not come from a formal economic theorist but from Ronald Coase. Coase wanted to show that there are situations under which a pure monopolist might not be able to charge a monopoly price for durable products. The literature has since expanded to consider all manner of theoretical and formal conditions under which this hypothesis might or might not hold. And scholars have claimed that this body of work provides insights into everything from strategic leases to planned obsolescence and the problem of new model introductions. But how well has this literature really served to illuminate the problems facing actual business firms? While the safety razor industry has often been invoked as an example of durable goods pricing there has only been limited investigation into the actual behavior of the dominant firm in this industry – Gillette. We consider here the major ideas that have developed as an offshoot of the original Coase paper and the extent to which a case study of Gillette confirms or confounds this analysis.

2011 International Conference on Economics and Business Information (ICEBI 2011) is the premier forum for the presentation of new advances and research results in the fields of theoretical, experimental, and applied Economics and Business Information. Topics of interest for submission include Business Information Systems, Business Performance Management, Management Information Systems, and others.

In the current context of the globalization of science, excellence is most often associated with internationalization and assessed through high-impact “international” (English-language) publications. Taking Russian economic science as a case study, this paper argues that the strategies of internationalization of national disciplinary fields are primarily determined by the parameters of the global economics itself. My analysis of the Russian publications in economics covered by Web of Science demonstrates that the very repertoire of international publication strategies of Russian authors is determined by the transnational system of communication in economics. Economics papers from peripheral nations are essentially assigned to regional or “area studies” periodicals, which do not belong to the core of the discipline. Publication in top economics journals requires a specific “international” competency usually obtained through doctoral training at Anglo-American or equivalent PhD programs and generally implies a delocalization of research objects and questions.

In this work the problem of learning and development of creativity with a view to the position of reflexive psychology, akmeology and pedagogics in the context of the human capital analysis in the conditions of modern society globalization is raised. The theme is urgent from the practical point of view in demand of a creative personality under conditions of the economic crisis and at the same time it is actual, because it interprets creativity in a new way according to interdisciplinary approach. The author emphasizes that a reflexively-creative potential is considered to be the backbone factor of professional and innovative activity in modern social space. On basis of philosophical foundations' analysis of psychology of creativity we theoretically build the conceptual model of reflexive creativity and we also examine the precedents of its psychology-pedagogical development in the secondary and high education (in case of reflexive-psycological support).

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.