### Article

## Сокращение размерности данных в задачах имитационного моделирования

This article describes optimization of a multimodal passenger traffic system. The optimization method used is simulation modeling. The service level indicators, costs and financial indicators when changing configurations of the system are analyzed.

This book gathers contributions presented at the 7th International Conference on Soft Methods in Probability and Statistics SMPS 2014, held in Warsaw (Poland) on September 22-24, 2014. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics. Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.

This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.

The importance of strategic management today is unquestionable. However, when strategizing the organization is often regarded as a single whole, differences in aims and areas of operation of its parts not being considered. This approach works for many organizations, but in the case of a distributed structure its parts may function in the markets which have different requirements, competition intensity and qualification of consumers. Besides, the departments of that organization may have different levels of development. In our present work we do not consider the whole range of distributed organizations, but concentrate on universities, as they have common characteristics with commercial organizations and, at the same time, are very specific in their rules and areas of development. We focus on developing a new modeling method for decision support while designing a balanced hierarchical strategy for distributed universities. This implies beginning from the strategy for the whole organization and moving on to development of individual strategies for its departments. Thus, the proposed method contains two parts: a sub-method to develop departmental strategies and a sub-method to calculate interaction among departments.

This article describes the proposed structure and semantics of the model which can be used in the both of sub-methods.

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.

The purpose of developing a cognitive model has been defined as the construction and analysis of simulation models improve interaction between government and business. In line with this objective has been hypothesized that an increase in the efficiency of interaction between business and government increased the values of competition in politics and economics, which in turn are directly related to each other. The latter is not in doubt, since the state of competition in the economy is inextricably linked to the legislative machinery of antitrust restrictions, by which representative bodies suppress or support unfair competition.

Authors provide the substantiation of logistic profitability indicator introduction for problem-solving concern the evaluation of logistic system performance, incl. inventory management system.

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.