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 structure of automorphism groups of semigroup inflations

In this paper we prove that the automorphism group of a semigroup being an inflation of its proper subsemigroup decomposes into a semidirect product of two groups one of which is a direct sum of full symmetric groups

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

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

Extended effect of chronic social defeat stress in childhood on behaviors in adulthood

Individuals exposed to social stress in childhood are more predisposed to developing psychoemotional disorders in adulthood. Here we use an animal model to determine the influence of hostile social environment in adolescence on behavior during adult life. One-month-old adolescent male mice were placed for 2 weeks in a common cage with an adult aggressive male. Animals were separated by a transparent perforated partition, but the adolescent male was exposed daily to short attacks from the adult male. After exposure to social stress, some of the adolescent mice were placed for 3 weeks in comfortable conditions. Following this rest period, stressed young males and adult males were studied in a range of behavioral tests to evaluate the levels of anxiety, depressiveness, and communicativeness with an unfamiliar partner. In addition, adult mice exposed to social stress in adolescence were engaged in agonistic interactions. We found that 2 weeks of social stress result in a decrease of communicativeness in the home cage and diminished social interactions on the novel territory. Stressed adolescents demonstrated a high level of anxiety in the elevated plus-maze test and helplessness in the Porsolt test. Furthermore, the number of dividing (BrdU-positive) cells in the subgranular zone of the dentate gyrus was significantly lower in stressed adolescents. After 3 weeks of rest, most behavioral characteristics in different tests, as well as the number of BrdU-positive cells in the hippocampus, did not differ from those of the respective control mice. However, the level of anxiety remained high in adult males exposed to chronic social stress in childhood. Furthermore, these males were more aggressive in the agonistic interactions. Thus, hostile social environment in adolescence disturbs psychoemotional state and social behaviors of animals in adult life

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

Effect of sodium dodecyl sulfate on the reactivity of copper(II) complexes with 2-dimethylaminomethylphenol

The effects of the anionic surfactant sodium dodecyl sulfate on complex formation of 2-dimethylaminomethylphenol (1) with copper(II) in aqueous solutions and on the kinetics of the reactions of copper(II) complexes of 1 with 4-nitrophenylbis(chloromethyl)phosphinate (2) were studied. The reactivities of the complexes in these reactions are higher than that of 1 at all concentrations of SDS studied (0.010-0.200 mol L-1) with pH 7-9. © 1996 Plenum Publishing Corporation