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

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

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.

Luminescence characteristics of magnesium aluminate spinel crystals of different stoichiometry

We are grateful to Drs E. Vasil’chenko and A. Maaroos for the help with experiments and useful discussions. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. In addition, the research leading to these results has received funding from the Estonian Research Council Institutional Research Funding IUT02-26.Magnesium aluminate spinel single crystals with different stoichiometry, MgAl2O4 (1:1 spinel) and MgO 2.5Al2O3 (1:2.5) were investigated using different optical methods (cathode-, photo- and thermally stimulated luminescence (TSL), optical absorption, "creation spectra" of TSL peaks and phosphorescence by VUV radiation). Low-temperature charge carrier traps and the position of intrinsic UV emission bands depend on the degree of stoichiometry. Antisite defects (ADs), Mg2+ or Al3+ located in a "wrong" cation site (Mg|A1 or Al|Mg) are the main as-grown structural defects, which serve also as efficient traps for electrons and holes as well as seeds for bound excitons. AD concentration is especially high in 1:2.5 spinel. There are several manifestations of ADs (electronic excitations near ADs) in the spectral region of 7-7.5 eV, slightly below the energy gap.Eesti Teadusagentuur IUT02-26; H2020 Euratom 633053; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

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

Genetic structure analysis of leaf rust resistant triticale accessions from the VIR collection using gliadin patterns

The gliadin banding patterns of important accessions from the collection of the N. I. Vavilov All‑Russian Institute of Plant Genetic Resources (VIR) registered in the form of “protein formulas” provide reliable information for the preparation of a “protein passport” for each accession and is convenient for storage and computer processing. It helps to control originality and integrity of accessions during regeneration and their use in breeding. The study involved 17 triticale accessions resistant to leaf rust. The analysis was carried out on single grains of the original accession (a sample of 13–26 kernels) according to the standard protocol adopted by VIR and approved by the International Seed Testing Association (ISTA). The gliadin electrophoretic banding patterns of triticale accessions were registered in the form of “protein formulas”; polymorphism of each accession and genetic diversity within the collection were estimated, and genetic structure of accessions was identified based on the marker protein components. A large variety of the revealed genotypes opens a possibility to identify accessions that combine resistance with other useful traits. Stable and polymorphic accessions including from 2 to 7 biotypes were found. The discovery of interbiotype hybrids and recombinant genotypes in the composition of some polymorphic accessions indicates the instability of their genetic structure and the ongoing formation process. This is due to the heterogeneity of the original parental forms, the tendency to cross‑pollination and insufficiently thorough selection. The data on the triticale genotypic structure can be used in introgressive breeding to control the transfer of rye genetic material to wheat varieties in order to increase their immunity and resistance to adverse factors

Experience in the application of non-invasive prenatal screening for the detection of Down syndrome in Russia: a retrospective cohort study

Assessment the effectiveness of non-invasive prenatal screening (NIPS) for identifying pregnant women at high risk of giving birth to a child with Down syndrom

Controlled drug release from electrospun PCL non-woven scaffolds via multi-layering and e-beam treatment

Currently, electrospun synthetic bioresorbable polymer scaffolds are applied in regenerative medicine and tissue engineering as targeted drug delivery devices because of their mechanical and physico-chemical properties. To control the rate of polymer degradation and drug release from polymer scaffolds, surface modification techniques are widely used. In this study, paracetamol-loaded poly (ε-caprolactone) electrospun fibrous scaffolds were treated by the pulsed electron beam irradiation. Pure control PCL scaffold, as well as scaffolds with four paracetamol concentrations (2 wt./wt. %, 8 wt./wt. %, 16 wt./wt. %, and 32 wt./wt.%) were modified. The mechanical and chemical properties and morphology of modified materials were examined. The sustained release of the model drug over a period of one hour for both non-treated and treated samples was demonstrated. It was shown that treatment leads to an increase in drug release rate and does not change surface morphology of scaffolds and fibers diameter distribution