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## Do we create mathematics or do we gradually discover theories which exist somewhere independently of us?

This is a preface to the paper A. Borel, "Mathematics: Art and Science" reprinted in EMS Newsletter, No. 103, March 2017.

This book series features volumes composed of select contributions from workshops and conferences in all areas of current research in mathematics and statistics, including OR and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today.

This article consider The project of the scientific and educational Center for integration of multimedia technologies in science, education and culture, as space-technological environment for the implementation of innovative scientific and educational projects of the 21st century, which should become the support for the master's programs, especially interdisciplinary; at the intersection of science, art and information technologies, and implementation of innovative scientific and commercial projects, which are to become a master's thesis.

The three already traditional volumes of the WDS Proceedings you are holding in the hands are composed of the contributions which have been presented during the 21st Annual Conference of Doctoral Students that was held in Prague, at Charles University, Faculty of Mathematics and Physics from May 29 to June 1, 2012. In this year, 100 student manuscripts were submitted to publishing and 88 were accepted after the review process.

Although research collaboration has been studied extensively, we still lack understanding regarding the factors stimulating researchers to collaborate with different kinds of research partners including members of the same research center or group, researchers from the same organization, researchers from other academic and non-academic organizations as well as international partners. Here, we provide an explanation of the emergence of diverse collaborative ties. The theoretical framework used for understanding research collaboration couples scientific and technical human capital embodied in the individual with the social organization and cognitive characteristics of the research field. We analyze survey data collected from Slovenian scientists in four scientific disciplines: mathematics; physics; biotechnology; and sociology. The results show that while individual characteristics and resources are among the strongest predictors of collaboration, very different mechanisms underlie collaboration with different kinds of partners. International collaboration is particularly important for the researchers in small national science systems. Collaboration with colleagues from various domestic organizations presents a vehicle for resource mobilization. Within organizations collaboration reflects the elaborated division of labor in the laboratories and high level of competition between different research groups. These results hold practical implications for policymakers interested in promoting quality research.

Reinterpretation of approaches of John Locke, Immanuel Kant and Charles Peirce helps to single out three integral organons of cognition. One is mathematics, or cognition of measure and art of all kind of measurement. Another is morphology or cognition of forms and art of arranging shapes and configurations. One more is semiotics or cognition of meanings and art of their transfer. It is demonstrated that all three organons vary and provide specific fields of knowledge and areas of research. Current versions and varieties of disciplinary manifestations of organons are reviewed. Mathematics is the most developed complex of scientific disciplines. Morphology is a constellation of a number of assorted and fully independent disciplines. Semiotics is rifted by a gap between rough outline of general or «pure» semiotics (Morris) and a nebula of unevenly elaborated semiologies of various sorts – that of languages, literatures, cinema, heraldry, race discrimination or ideological manipulations. Analysis of political discourses and speech acts can contribute to integration of common area of semiotic research.

Full papers (articles) of 2nd Stochastic Modeling Techniques and Data Analysis (SMTDA-2012) International Conference are represented in the proceedings. This conference took place from 5 June by 8 June 2012 in Chania, Crete, Greece.

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.

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.

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.