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

Ethical issues of business communication in modern Russia

Modern society experiences an information explosion that results in the formation of powerful communication flows and it changes society, business and people. The Russian reality is especially risky because of mental and cultural factors shaping its national uniqueness. Large amount of Internet information and communication using manipulative technologies create problems of ethics, social responsibility of data and businesses. There remains an insufficient degree of implementation of ethical principles in corporate and professional communication of Russia. The authors using methodological approaches: systemic, deontological and ethic-axiological held a theoretical and empirical studies of massive informational flows related to social responsibility of Russian business, commercial advertising, corporate and professional ethics in Russia, taking into account public interests. Unethical technologies of astroturfing, trolling, bots, manipulation, lies and deception have been studied. The authors concluded that the process of ethical regulation in the sphere of business communication needs urgent optimization in modern Russia

Reader and Writer: Poor Liza (1792) by Nikolay Karamzin and Notes from Underground (1864) by Fyodor Dostoevsky

The article analyses the image of homo legens in Poor Liza by Nikolay Karamzin and Notes from Underground by Fyodor Dostoevsky. The novelist considers Karamzin’s short story as a part of the process of the knowledge of the human being in the 19th century. In contrast to positivist philosophical knowledge, which, according to Dostoevsky, simplifies the phenomenon of the person, the writer, with the help of Karamzin’s artistic discoveries in the short story Poor Liza, creates the image of the Underground Man as a person who both reads and writes. Typologically, the encounter of the dreamer with a girl in Notes from Underground repeats the situation in Poor Liza. Erast dreams of an idyll and “invents” his future life with Liza according to the laws of the genre, while the peasant woman, unlike the reading hero, understands that dreams cannot be realized. In Dostoevsky’s novella the situation is more complicated. Following literary models, the Underground Man creates two stories in an idyllic and anti-idyllic key, in order to manipulate the soul of another person and to affirm himself. At first, Liza does not believe the words of the visitor or the possibility of leaving the brothel. The Underground Man prefaces his stories with two biblical quotations: “the image and likeness of God” and “lay down your life for the sake of friends.” He introduces the sacred as a means of manipulation of the heroine’s feelings. Having identified these quotations, Liza sincerely believes in the possibility of leaving the brothel and offers her love to the dreamer, which the author sees as an opportunity for him to come out of “the underground.” The hero cannot accept this chance. By creating the image of homo legens in Notes from Underground Dostoevsky shows that a chaotic and blind adherence to literary genres, situations, and gestures together with the manipulation of both literary and sacred texts places man in a position of insoluble conflict with “living life.

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

Genetic association between the CYBA 640A>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

Non-canonical propagation of high-order elliptic vortex-beams in a uniaxial crystal

We have derived the corresponding equations and found their solutions both for nonparaxial and paraxial beams. The paraxial solutions we have presented in the form of the generalized Hermite-Gaussian beams propagating perpendicular to the optical axis of a uniaxial crystal. We have also constructed the generalized Laguerre-Gaussian beams at the z=0 plane and analyzed their evolution in a homogeneous isotropic medium. Comparing it with the evolution of the standard Laguerre-Gaussian beams with and in the crystal we have revealed that the additional elliptic deformation of the extraordinary beam results in topological reactions that essentially distorts field structure for the account of different rotation rates of the vortex row originated from the centered degenerate optical vortex and the conoscopic pattern. We have predicted conversion of the vortex topological charge at the beam axis similar to that in astigmatic lenses and analyzed the radical differences with this process. We have revealed the synchronic oscillations of the spin angular momentum and the sign of the vortex topological charge at the beam axis.Comment: 19 pages, 9 figure