О фундаментальной группе дополнения к комплексной конфигурации гиперплоскостей
This volume contains papers presented at the 13th International Conference on Rough Sets, Fuzzy Sets and Granular Computing (RSFDGrC) held during June 25–27, 2011, at the National Research University Higher School of Economics (NRU HSE) in Moscow, Russia. RSFDGrC is a series of scientific events spanning the last 15 years. It investigates the meeting points among the four major disciplines outlined in its title, with respect to both foundations and applications. In 2011, RSFDGrC was co-organized with the 4th International Conference on Pattern Recognition and Machine Intelligence (PReMI), providing a great opportunity for multi-faceted interaction between scientists and practitioners. There were 83 paper submissions from over 20 countries. Each submission was reviewed by at least three Chairs or PC members.We accepted 34 regular papers (41%). In order to stimulate the exchange of research ideas, we also accepted 15 short papers. All 49 papers are distributed among 10 thematic sections of this volume. The conference program featured five invited talks given by Jiawei Han, Vladik Kreinovich, Guoyin Wang, Radim Belohlavek, and C.A. Murthy, as well as two tutorials given by Marcin Szczuka and Richard Jensen. Their corresponding papers and abstracts are gathered in the first two sections of this volume.
We calculate characteristic polynomials of operators explicitly represented as polynomials of rank $1$ operators. Applications of the results obtained include a generalization of the Forman--Kenyon's formula for a determinant of the graph Laplacian and also provide its level $2$ analog involving summation over triangulated nodal surfaces with boundary.
The article considers the Views of L. N. Tolstoy not only as a representative, but also as a accomplisher of the Enlightenment. A comparison of his philosophy with the ideas of Spinoza and Diderot made it possible to clarify some aspects of the transition to the unique Tolstoy’s religious and philosophical doctrine. The comparison of General and specific features of the three philosophers was subjected to a special analysis. Special attention is paid to the way of thinking, the relation to science and the specifics of the worldview by Tolstoy and Diderot. An important aspect is researched the contradiction between the way of thinking and the way of life of the three philosophers.
Tolstoy's transition from rational perception of life to its religious and existential bases is shown. Tolstoy gradually moves away from the idea of a natural man to the idea of a man, who living the commandments of Christ. Starting from the educational worldview, Tolstoy ended by creation of religious and philosophical doctrine, which were relevant for the 20th century.
This important new book offers the first full-length interpretation of the thought of Martin Heidegger with respect to irony. In a radical reading of Heidegger's major works (from Being and Time through the ‘Rector's Address' and the ‘Letter on Humanism' to ‘The Origin of the Work of Art' and the Spiegel interview), Andrew Haas does not claim that Heidegger is simply being ironic. Rather he argues that Heidegger's writings make such an interpretation possible - perhaps even necessary.
Heidegger begins Being and Time with a quote from Plato, a thinker famous for his insistence upon Socratic irony. The Irony of Heidegger takes seriously the apparently curious decision to introduce the threat of irony even as philosophy begins in earnest to raise the question of the meaning of being. Through a detailed and thorough reading of Heidegger's major texts and the fundamental questions they raise, Haas reveals that one of the most important philosophers of the 20th century can be read with as much irony as earnestness. The Irony of Heidegger attempts to show that the essence of this irony lies in uncertainty, and that the entire project of onto-heno-chrono-phenomenology, therefore needs to be called into question.
The article is concerned with the notions of technology in essays of Ernst and Friedrich Georg Jünger. The special problem of the connection between technology and freedom is discussed in the broader context of the criticism of culture and technocracy discussion in the German intellectual history of the first half of the 20th century.
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.