Modeling the motion of a bright spot in jets from black holes M87* and SgrA*

General Relativity and Gravitation - In previous work, we established theoretical results concerning the effect of matter shells surrounding a gravitational wave (GW) source, and we now apply these...     

Some Aspects of the Implementation of Scaling Quantum Mechanical Molecular Force Fields

Some features of software implementation of the Pulay scaling procedure are considered. The advantages of the single value decomposition method for maintaining well-conditionality of the scale factor determination problem are demonstrated. The necessity of using a rational number of scale factors is shown. The possibility of obtaining transferable scale factors with the Pulay method and thus predict the vibrational spectra of related compounds is emphasized.     

Dark matter annihilation in the Galaxy

The awaited dark matter (DM) neutralino annihilation signal from the galactic halo crucially depends on the presence of small-scale clumps. A mass function of the DM small-scale clumps is calculated in the standard cosmological scenario. The final distribution of clumps in the Galaxy is influenced by their tidal destruction. The basic sources of clump destruction are (i) clumps of larger scales, (ii) the gravitational field of the galactic disk, (iii) the stars in the galactic bulge, and (iv) the stars in the galactic halo. The destruction of clumps due to their mutual tidal interactions is important at earl stages of hierarchical clustering and the galactic halo formation. The clumps surviving through the hierarchical clustering are continuously destroyed by interactions with the galactic disk and stars. It is shown that, among the Moon or Earth mass DM clumps surviving through the hierarchical clustering, only 20% will further survive near the Sun’s position mainly because of the tidal destruction by the galactic disk. This reduction of DM clump density significantly diminishes the expected DM annihilation signal from the galactic halo. The text was submitted by the authors in English.     

Fractional Hamiltonian Monodromy

We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems. Communicated by Eduard Zehnder Submitted: February 25, 2005; Accepted: November 17, 2005     

Tiled Orders and Frobenius Rings

Mathematical Notes -     

Local ν-Euler Derivations and Deligne's¶Characteristic Class of Fedosov Star Products¶and Star Products of Special Type

In this paper we explicitly construct local ν-Euler derivations , where the ξ_α are local, conformally symplectic vector fields and the are formal series of locally defined differential operators, for Fedosov star products on a symplectic manifold (M,ω) by means of which we are able to compute Deligne's characteristic class of these star products. We show that this class is given by , where is a formal series of closed two-forms on M the cohomology class of which coincides with the one introduced by Fedosov to classify his star products. Moreover, we consider star products that have additional algebraic structures and compute the effect of these structures on the corresponding characteristic classes of these star products. Specifying the constituents of Fedosov's construction we obtain star products with these special properties. Finally, we investigate equivalence transformations between such special star products and prove existence of equivalence transformations being compatible with the considered algebraic structures. Dedicated to the memory of Moshé Flato Received: 28 June 1999 / Accepted: 11 April 2002?Published online: 11 September 2002