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## Введение в эконометрику. Часть 1. Эконометрика и математическая статистика

In spite of a growing body of literature investigating the determinants of youth unemployment, studies at sub-national level are still scarce, especially for Russian regions. This article is an innovative attempt to analyse econometrically the key factors affecting the youth unemployment rate and the ratio between youth and total unemployment rates for 75 Russian regions in 2000–09. The existing literature on regional labour market performance and dynamics suggested the use of a large set of explanatory variables (with indicators of the level of economic development, the demographic situation and migration processes, and the export–import levels) in a GMM panel data analysis, taking into account both spatial correlation and endogeneity problems. Although we were searching for structural determinants, we also investigated the effect of the 2008–09 financial crisis. The econometric results, presented and discussed using several models, have key policy implications for both national and regional levels of government.

The functionals related to the quality of the system control are obtained

in the analytic form. The statement that the optimal strategy of controlling

the system is a deterministic strategy is proved. Analytic form representation

for the function the absolute extremum of which is determined as the optimal

control strategy is obtained also.

The purpose of this paper is the presentation of the ideas and concepts that

form the basis of the concept of mathematical model control some processes

occurring in the Russian market of cereals. The estimated model must have a

stochastic nature, i.e. constitute some random process. Indeed, in a free market

there are objectively random factors that cannot be described by deterministic.

A general description is given of software products designed for econometric studies. Software packages Microsoft Excel, Stadium, SPSS, and MATLAB are considered in detail.

This paper presents a preliminary analysis of hotel room prices in several European cities based on the data from Booking.com website. The main question raised in the study is whether early booking is advantageous indeed, and if so, how early should it be? First a script was developed to download more than 600 thousand hotel offers for reservations from 25 March 2013 to 17 March 2014. Then an attempt to discover more details concerning the early booking effect was made via basic statistics, graphical data representation and hedonic pricing analysis. It was revealed that making reservations in advance can be really gainful, although more data and research are needed to measure the exact numbers, as they depend on at least seasonality and city.

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 ﬁnite-dimensional 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 quasi-solutions 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 quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions 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 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.