615 research outputs found
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
on where
is a complex polynomial in 2 variables, geometric properties of
Liouville fibrations are described.Comment: 6 page
Connected components of spaces of Morse functions with fixed critical points
Let be a smooth closed orientable surface and be the space
of Morse functions on having exactly critical points of local minima,
saddle critical points, and critical points of local maxima,
moreover all the points are fixed. Let be the connected component of a
function in . By means of the winding number introduced by Reinhart
(1960), a surjection is constructed. In
particular, , 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 . Let be the group of orientation
preserving diffeomorphisms of leaving fixed the critical points, be the connected component of in , and
the set of diffeomorphisms preserving
. Let be the subgroup of generated by
and all diffeomorphisms which preserve some
functions , and let be its subgroup
generated and the Dehn twists about the components of level
curves of functions . We prove that if , and construct an epimorphism
, by means of
the winding number. A finite polyhedral complex associated to the
space is defined. An epimorphism and finite generating sets for the groups
and in terms of the 2-skeleton of the complex
are constructed.Comment: 12 pages with 2 figures, in Russian, to be published in Vestnik
Moskov. Univ., a typo in theorem 1 is correcte
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.
Topology of the spaces of Morse functions on surfaces
Let be a smooth closed orientable surface, and let be the space of
Morse functions on such that at least critical points of each
function of are labeled by different labels (enumerated). Endow the space
with -topology. We prove the homotopy equivalence where is one of the manifolds , and the point in dependence on the sign of ,
and is the universal moduli space of framed Morse
functions, which is a smooth stratified manifold. Morse inequalities for the
Betti numbers of the space are obtained.Comment: 15 pages, in Russia
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