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## Неограниченная теория вероятностей и ее приложения

The order statistics and the empirical mathematical expectation (also called the estimate of mathematical expectation in the literature) are considered in the case of infinitely increasing random variables. The Kolmogorov concept which he used in the theory of complexity and the relationship with thermodynamics which was pointed out already by Poincar\'e are considered. We compare the mathematical expectation (which is a generalization of the notion of arithmetical mean, and is generally equal to infinity for any increasing sequence of random variables) with the notion of temperature in thermodynamics similarly to nonstandard analysis. It is shown that there is a relationship with the Van-der-Waals law of corresponding states. A number of applications of this concept in economics, in internet information network, and self-teaching systems are also considered.

Negative pressure also means negative energy and, therefore, “holes”, antiparticles. Continuation across infinity to negative energies is accomplished by using a parastatistical correction to the Bose-Einstein distribution.

Some peculiarities of the phenomenon of transdisciplinarity in the modern science, its differences from interdisciplinarity and multidisciplinarity, are under consideration in the article. The methodological principles of transdisciplinary studies and new possibilities of synthesis of scientific knowledge based on these principles are studied. The theory of complexity, futures studies, cognitive science, and the eco-evo-devo-perspective connected with cognitive biology are regarded as the most significant fields of the modern transdisciplinary researches. It is shown that transdisciplinary researches will, by all appearances, define the character of science in the medium-term future.

Some topical problems of human existence in a complex changing multi-dimensional world are considered in the book from the standpoint of the modern scientific research, in particular, of synergetics, complexity theory, cognitive science, etc. Special attention is paid to the synergetic understanding of the complex world of human in terms of psychosynergetics, psychology, cognitive science, and social knowledge. The nonlinear processes in the modern post-nonclassical science are analyzed; the synergistic view of modern scientific objects, such as living beings, social networks, virtualities, etc. is developed. Cognitive components of the modern transformational learning, transversal competencies as skills of the 21st century, the essence and content of cognitive technologies in education as adaptive human strategies in the complex world are under consideration as well. The book is addressed to scientists, philosophers, teachers, graduate students, students, as well as to all who is interested in the problems of the philosophical comprehension of the modern scientific knowledge.

We observe the self-assembling of the dipolar hard sphere particles at low temperature by Monte Carlo simulation. We find different types of stable structures of dipolar particles which appear when the isotropic phase of the system becomes unstable. Specifically, we find an interesting case of parallel cylindrical domains. The value of the total dipole moment of each domain is significantly large compared to the average value of the whole system. Models with dipolar interactions may form structures comprised of layers with anti-parallel dipole orientation.

Main concepts and models of the modern theory of self-organization of complex systems, called also synergetics, are generalized and formulated in the book as principles of a synergetic world view. They are under discussion in the context of philosophical studies of holism, teleology, evolutionism as well as of gestalt-psychology; they are compared with some images from the history of human culture. The original and unfamiliar (to the Western readers) research results of the Moscow synergetic school which has its center at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences are expounded in the book. The heuristic value of the synergetic models of evolution and self-organization of complex systems in epistemology and cognitive psychology, education and teaching, futures studies, social management activities and systems of global security is shown in the book. Complicated and paradoxical concepts of synergetics (structure-attractors, bifurcations, blow-up regimes, non-stationary dissipative structures of self-organization, fractals, non-linearity) are translated into an intelligible language and vividly illustrated by materials and examples from various fields of knowledge, starting with the laser thermonuclear fusion and concluding with mysterious phenomena of human psychology and creativity. The style of writing is close to that of popular-science literature. That's why the book might be of interest and is quite comprehensible for students and specialists in the humanities.

The paper suggests an original credit-risk based model for deposit insurance fund adequacy assessment. The fund is treated as a portfolio of contingent liabilities to the insured deposit-holders. The fund adequacy assessment problem is treated as an economic capital adequacy problem. Implied credit rating is used as the target indicator of solvency. This approach is consistent with the contemporary risk management paradigm and the recommendations of the Basel II Capital Accord. The target level of the fund corresponding to the target solvency standard is estimated in a Monte Carlo simulation framework using the actual data on the Russian banking system covering 1998-2005. Author acknowledges the generous support and fruitful discussions with representatives of the Russian Deposit Insurance Agency. The author expresses his personal views and not the views of the Agency.

We single out the main features of the mathematical theory of noble gases. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of noble gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in thermodynamics. We consider semiclassical methods for tunnel quantization in thermodynamics as well as those for second and ultrasecond quantization (the creation and annihilation operators for pairs of particles). Each noble gas is associated with a new critical point of the limit negative pressure. The negative pressure is equivalent to covering the (P,Z)- diagram by the second sheet.

This volume collects the research articles, tool demonstrations, posters, tutorials, and keynote speeches presented at the 13th International Conference on Web Engineering (ICWE 2013). The discipline of Web engineering is a special branch of the broader area of software engineering that specifically focuses on the World Wide Web and the Internet.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.

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.