Article
A Metric View on Russian Mathematics and Russian Mathematical Diaspora (A Study Based on Frequent Russian Surnames)
What happens with Russian mathematics in terms of metric parameters? Where do Russian mathematicians work, where do they publish, how well are they cited?
This article consider The project of the scientific and educational Center for integration of multimedia technologies in science, education and culture, as spacetechnological 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.
Metrics usage in higher education management has clearly become an issue of great importance. A recent highprofile policy report on this topic, commissioned by the Higher Education Funding Council for England, is aptly named The Metric Tide. It reiterates a number of basic principles like “don’t evaluate individuals using journal impact factors” or “peer review can’t be substituted by metrics,” and stresses that, “those involved in research assessment and management should behave responsibly, considering and preempting negative consequences [of metrics usage] wherever possible” (Wilson 2015). One of the obvious consequences is gaming with indicators, which comes in various types and level of severity. This paper deals with one particular technique centered around socalled “predatory” journals indexed in Scopus database. It is a part of a broader research on the impact of metricsbased policy measures on various university systems. See the introductory article about “predatory” publishing by the foremost authority on this topic prof. Jeffrey Beall, p. 07.

One of important problems of state expenses planning is nontransparency of causeandeffect relations between measures (projects), which implementation was planned to achieve certain strategic goals. A traditional tool for overcoming these problems is creation of target programs. However, mechanical integration of projects into one target program will give no results from the standpoint of financial allocation decision making. The problem is that relationship between targets, tasks and specific projects are objectively complex. This complexity entails the possibility of arbitrary interpretations, nonpurpose expenditures, attempts to attract all financial resources to one side and etc.
One of efficient tools for solving such problems through defining of strict relationship between expenses incurred and expected specific social and economical results of governmental organizations' activities is a methodology named Performance budgeting. The essence is that for any project, included into a certain program, should be defined how and to what extent this project facilitates achieving of the final goal of the whole program. During the program buildup stage this impact will be nothing but hypothesis, which later should be specified based on accumulated statistical data about values of metrics, characterizing program immediate outputs and final outcomes (hereafter  output/outcome metrics). Actually evaluation of metrics' impact could be implemented for operational adjustment of target programs finance allocation for their most effective spending.
The paper discusses in detail the scale of translation of primary points scored by school graduates in the unified state exam in mathematics, used from 2013 to the present time. Based on the analysis of the dynamics of these scales, a conclusion is made about the annual increase in the "average" 100point result, as well as the presence of a significant increase in the final grade compared with the linear scale. Additionally, the authors describe the effect of reducing the value of primary points as they approach the maximum.
This article presents the results of a pilot study assessing the level of formation of a stochastic competence among teachers of mathematics. Besides, the indicators that reflect the competence of formation of stochastic students are identified and ranked in order of importance. Different instruments (questionnaires, tests, assignments) have been used to solve the problem under study.
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 ﬁnitedimensional 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 quasisolutions 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 quasisolutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasisolutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasisolutions 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 crosssection of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a crosssection 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 crosssection 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 crosssection 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 Wequivariant map T   >G/T where T is a maximal torus of G and W the Weyl group.