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

A new method for estimating frequency-dependent core shifts in active galactic nucleus jets

We discuss the opacity in the core regions of active galactic nuclei observed with Very Long Baseline Interferometry (VLBI), and describe a new method for deriving the frequency-dependent shifts of the VLBI core from the frequency-dependent time lags of flares observed with single-dish observations. Application of the method to the core shifts of the quasar 3C 345 shows a very good agreement between the core shifts directly measured from VLBI observations and derived from flares in the total flux density using the proposed method. The frequency-dependent time lags of flares can be used to derive physical parameters of the jets, such as distance from the VLBI core to the base of the jet and the magnetic fields in the core region. Our estimates for 3C 345 indicate core magnetic fields ~0.1 G and magnetic field at 1 pc ~0.4 G.Comment: 8 pages, 6 figures, accepted for publication in MNRA

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

Anhedonia in the shadow of chronic social defeat stress, or When the experimental context matters

One of the core symptoms of major depression in human is anhedonia. For that reason, one of the main requirements towards experimental depression models is that they be able to demonstrate anhedonia in animals, that have been exposed to stressful events, and other behavioral changes attributable to a depression-like state. However, the results presented in the literature are contradictory: sweet solution intake, which is considered as a parameter of hedonic/anhedonic behavior in animals, responds quite differently to stressful situations in that it is either unaffected or increased or decreased. Different experimental designs used for the study of anhedonia in male mice exposed to chronic social defeat stress were tried to understand the reasons for so contradictory responses. Anhedonia appears as an abrupt reduction in sweet solution consumption in stressed animals and by failure to attain recovery after deprivation. However, it was also demonstrated that sucrose solution intake and preference strongly depend on the experimental context; that the possible critical factor may be prior acquaintance with the hedonic stimulus – or the lack whereof. Analysis of literature data and ours allowed us to conclude that the lack of a significant decrease in sweet solution intake in stressed animals is no evidence of lack of depression. This decrease is evidence of anhedonia only provided other symptoms of depression are present. Hedonic consumable intake can be decreased over various motivations, conditions or diseases, in particular, a high level of anxiety or pathological aggression