The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows

For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact" 2-parameter family of flat polygons equipped with certain pairing of sides. For the integrable Hamiltonian systems given by the vector field $v=(-\partial f/\partial w, \partial f/\partial z)$ on ${\mathbb C}^2$ where $f=f(z,w)$ is a complex polynomial in 2 variables, geometric properties of Liouville fibrations are described.Comment: 6 page

The socioeconomic development of Russia : some historical aspects

The study is devoted to the analysis of the socioeconomic development of Russia in the context of changing technological paradigms. The authors determined the main theoretical characteristics of changing technological paradigms in the context of developing socioeconomic systems. They introduce characteristics of technological paradigms, identify processes that occurred during changing technological paradigms in the world's leading countries, and present the analysis of social, technological and economic development in Russia from the late 19th century until now.peer-reviewe

Connected components of spaces of Morse functions with fixed critical points

Let $M$ be a smooth closed orientable surface and $F=F_{p,q,r}$ be the space of Morse functions on $M$ having exactly $p$ critical points of local minima, $q\ge1$ saddle critical points, and $r$ critical points of local maxima, moreover all the points are fixed. Let $F_f$ be the connected component of a function $f\in F$ in $F$. By means of the winding number introduced by Reinhart (1960), a surjection $\pi_0(F)\to{\mathbb Z}^{p+r-1}$ is constructed. In particular, $|\pi_0(F)|=\infty$, and the Dehn twist about the boundary of any disk containing exactly two critical points, exactly one of which is a saddle point, does not preserve $F_f$. Let $\mathscr D$ be the group of orientation preserving diffeomorphisms of $M$ leaving fixed the critical points, ${\mathscr D}^0$ be the connected component of ${\rm id}_M$ in $\mathscr D$, and ${\mathscr D}_f\subset{\mathscr D}$ the set of diffeomorphisms preserving $F_f$. Let ${\mathscr H}_f$ be the subgroup of ${\mathscr D}_f$ generated by ${\mathscr D}^0$ and all diffeomorphisms $h\in{\mathscr D}$ which preserve some functions $f_1\in F_f$, and let ${\mathscr H}_f^{\rm abs}$ be its subgroup generated ${\mathscr D}^0$ and the Dehn twists about the components of level curves of functions $f_1\in F_f$. We prove that ${\mathscr H}_f^{\rm abs}\subsetneq{\mathscr D}_f$ if $q\ge2$, and construct an epimorphism ${\mathscr D}_f/{\mathscr H}_f^{\rm abs}\to{\mathbb Z}_2^{q-1}$, by means of the winding number. A finite polyhedral complex $K=K_{p,q,r}$ associated to the space $F$ is defined. An epimorphism $\mu:\pi_1(K)\to{\mathscr D}_f/{\mathscr H}_f$ and finite generating sets for the groups ${\mathscr D}_f/{\mathscr D}^0$ and ${\mathscr D}_f/{\mathscr H}_f$ in terms of the 2-skeleton of the complex $K$ are constructed.Comment: 12 pages with 2 figures, in Russian, to be published in Vestnik Moskov. Univ., a typo in theorem 1 is correcte

Functioning of Verbs <i>yavlyat’sya - yavit’sya</i> in Language of XXI Century

The semantic and stylistic features of the verbs yavlyat’sya - yavit’sya in modern speech on the material of the National corpus of the Russian language are considered in the article. It is shown that not all the meanings of these verbs recorded in explanatory dictionaries are relevant for modern speech and that yavlyat’sya - yavit’sya do not function in texts of different styles. It is specified that the verb yavlyatsya in a connective meaning is characterized by the breadth of lexical and grammatical connections, which indicates its further semantic devastation and approaching to ideal connectives. Particular attention is paid to the characterization of species relations yavlyat’sya - yavit’sya in the indicated value. The stylistic marking of these verbs in the meaning ‘come’ is grounded. Attention is drawn to the fact that in all meanings, except for the connective, the seme ‘perception’ is preserved, which in some cases makes it difficult to distinguish between the individual meanings of verbs (for example, ‘arise’ or ‘represent’). Lexical markers, allowing to distinguish between similar values are noted. The novelty of the study is a comprehensive review of the functioning of the verbs yavlyat’sya - yavit’sya to identify their semantic volume and stylistic capabilities in the language of the beginning of the XXI century

Efficiency of Developing Renewable Energy Market in Russia

The goal of this study is to systematize and provide a quantitative and qualitative assessment of potential positive economic and non-economic effects of the implementation of a new mechanism for supporting renewable energy in Russia. It should result in achieving the national medium-term objective to increase the share of renewable energy in the wholesale electricity and capacity market to 2.5 % by 2024. The introduction examines the mechanism for supporting the generators of renewable energy by capacity charge in the wholesale electricity and capacity market. It is assumed that the main positive effects from implementing this mechanism will be the replacement of hydrocarbon fuels burned for generating the electricity in traditional coal or gas power plants; improvement in the trade balance; multiplier effects from the development of RES in related industrial sectors, new value added and jobs in the sectors producing the generating and auxiliary equipment for generators; reduction of carbon dioxide emissions; decrease in average prices in the wholesale electricity market; reduction of expenditure on environmental activities and measures to protect the health in the territories with traditional power plants; additional scal charges. As a result, the quantification of these effects amounts to 47.77 billion rubles in 2024. The authors rely on the experience of foreign countries, expert estimates, forecasts by the Russian Ministry of Energy and the Ministry of Economic Development, research by the Russian Energy Agency, International Energy Agency, International Renewable Energy Agency, Community for Renewable Energy Policy in the 21st Century (REN21), statistics of Russian Federal State Statistics Service.The article has been supported by the Russian Foundation for Basic Research as part of the project 14–06–00075 “National Economic and Environmental Security: Threats, Effects, and Scenario for Interaction of Economy and Environment.

Special framed Morse functions on surfaces

Let $M$ be a smooth closed orientable surface. Let $F$ be the space of Morse functions on $M$, and $\mathbb{F}^1$ the space of framed Morse functions, both endowed with $C^\infty$-topology. The space $\mathbb{F}^0$ of special framed Morse functions is defined. We prove that the inclusion mapping $\mathbb{F}^0\hookrightarrow\mathbb{F}^1$ is a homotopy equivalence. In the case when at least $\chi(M)+1$ critical points of each function of $F$ are labeled, homotopy equivalences $\mathbb{\widetilde K}\sim\widetilde{\cal M}$ and $F\sim\mathbb{F}^0\sim{\mathscr D}^0\times\mathbb{\widetilde K}$ are proved, where $\mathbb{\widetilde K}$ is the complex of framed Morse functions, $\widetilde{\cal M}\approx\mathbb{F}^1/{\mathscr D}^0$ is the universal moduli space of framed Morse functions, ${\mathscr D}^0$ is the group of self-diffeomorphisms of $M$ homotopic to the identity.Comment: 8 pages, in Russia

Human development and income inequality as factors of regional economic growth

This paper examines the impact of the Human Development Index and the Gini index on the Real Gross Regional Product (GRP) per person employed in 68 regions of the Russian Federation during the 2000 – 2014 period. We test and compare the results from two groups of models. The first group of models reveals that higher GRP per person employed is associated with higher levels of human development and income inequality in the Russian Federation regions. These results stay robust within the models estimated by linear regression with panel-corrected standard errors, where Regional FE, Time FE and Federal District FE are controlled. The estimation results from the second group of models provide evidence that regions with higher levels of Real Gross Regional Product (GRP) per person, human development and income inequality were growing slower, on average, than regions with lower levels of these parameters.peer-reviewe

Genetic association between the CYBA 640A&gt;G polymorphism and the risk of uterine myoma

The aim of this study was to investigate the association between functional polymorphism 640A>G (rs1049255) of the CYBA (cytochrome b-245, alpha polypeptide of NADPH oxidase) gene and the risk of uterine myom

Topology of the spaces of Morse functions on surfaces

Let $M$ be a smooth closed orientable surface, and let $F$ be the space of Morse functions on $M$ such that at least $\chi(M)+1$ critical points of each function of $F$ are labeled by different labels (enumerated). Endow the space $F$ with $C^\infty$-topology. We prove the homotopy equivalence $F\sim R\times{\widetilde{\cal M}}$ where $R$ is one of the manifolds ${\mathbb R}P^3$, $S^1\times S^1$ and the point in dependence on the sign of $\chi(M)$, and ${\widetilde{\cal M}}$ is the universal moduli space of framed Morse functions, which is a smooth stratified manifold. Morse inequalities for the Betti numbers of the space $F$ are obtained.Comment: 15 pages, in Russia