Accurate Localization and Identification of Six Hard X-ray Sources from Chandra and XMM-Newton data

We present the results of Chandra and XMM-Newton observations for six hard X-ray sources (IGR J12134-6015, IGR J18293-1213, IGR J18219-1347, IGR J17350-2045, IGR J18048-1455, XTE J1901+014) from the INTEGRAL all-sky survey. Based on these observations, we have improved significantly the localization accuracy of the objects and, therefore, have managed to identify their optical counterparts. Using data from the publicly available 2MASS and UKIDSS infrared sky surveys as well as data from the SOFI/NTT telescope (European Southern Observatory), we have determined the magnitudes of the optical counterparts, estimated their types and (in some cases) the distances to the program objects. A triplet of iron lines with energies of 6.4, 6.7, and 6.9 keV has been detected in the X-ray spectrum of IGR J18048-1455; together with the detection of pulsations with a period of ~1440 s from this source, this has allowed it to be classified as a cataclysmic variable, most likely an intermediate polar. In addition, broadband X-ray spectra of IGR J12134-6015 and IGR J17350-2045 in combination with infrared and radio observations suggest an extragalactic nature of these objects. The source IGR J18219-1347 presumably belongs to the class of high-mass X-ray binaries.Comment: 15 pages, 9 figures. Will be published in Astronomy Letters, 2012, Vol. 38, No. 10, pp. 629-63

Cotangent bundle quantization: Entangling of metric and magnetic field

For manifolds $\cal M$ of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field) we define a Hilbert algebra structure in the space $L^2(T^*\cal M)$ and construct an irreducible representation of this algebra in $L^2(\cal M)$. This algebra is automatically extended to polynomial in momenta functions and distributions. Under some natural conditions this algebra is unique. The non-commutative product over $T^*\cal M$ is given by an explicit integral formula. This product is exact (not formal) and is expressed in invariant geometrical terms. Our analysis reveals this product has a front, which is described in terms of geodesic triangles in $\cal M$. The quantization of $\delta$-functions induces a family of symplectic reflections in $T^*\cal M$ and generates a magneto-geodesic connection $\Gamma$ on $T^*\cal M$. This symplectic connection entangles, on the phase space level, the original affine structure on $\cal M$ and the magnetic field. In the classical approximation, the $\hbar^2$-part of the quantum product contains the Ricci curvature of $\Gamma$ and a magneto-geodesic coupling tensor.Comment: Latex, 38 pages, 5 figures, minor correction

Graphene as a quantum surface with curvature-strain preserving dynamics

We discuss how the curvature and the strain density of the atomic lattice generate the quantization of graphene sheets as well as the dynamics of geometric quasiparticles propagating along the constant curvature/strain levels. The internal kinetic momentum of Riemannian oriented surface (a vector field preserving the Gaussian curvature and the area) is determined.Comment: 13p, minor correction

Tverberg-type theorems for intersecting by rays

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set

Quantum Magnetic Algebra and Magnetic Curvature

The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of Weyl-symmetrized functions in coordinate and momentum operators satisfying nonlinear commutation relations. The multiplication in this algebra generates an associative product of functions on the phase space. This product is given by an integral kernel whose phase is the symplectic area of a groupoid-consistent membrane. A symplectic phase space connection with non-trivial curvature is extracted from the magnetic reflections associated with the Stratonovich quantizer. Zero and constant curvature cases are considered as examples. The quantization with both static and time dependent electromagnetic fields is obtained. The expansion of the product by the deformation parameter, written in the covariant form, is compared with the known deformation quantization formulas.Comment: 23 page

ANALIZA STANJA NAPREZANJA OBLOGE OKNA NA KONTAKTNOJ ZONI ANHIDRITA I KAMENE SOLI

The main question of this paper is the stress-strain state prediction of the vertical shaft’s combined lining located at the interface of two layers of dolomite and salt. The study predicts geomechanical processes at the contact of the dolomite layer and the salt layer in the vicinity of the vertical shaft’s expanded section, taking into account the operating life of a vertical shaft is equal to 50 years. The results combined lining’s stress-strain state, represented as a four – layer medium, where the external layer is concrete, and the three inner layers are used to account for the heterogeneity of cast-iron tubing and are compared with the results received when taking into account the pipe structure. The solution of the problem was carried out in a three-dimensional statement. The calculation of the tubing lining, considering its actual geometry, will increase the accuracy of the forecast of the stress state of the lining, which in turn will favourably affect the justification of its parameters.Glavna problematika ovoga rada očituje se u predviđanju stanja naprezanja – deformacije kombinirane obloge vertikalnoga okna smještene na kontaktu dvaju slojeva dolomita i soli. Studija predviđa geomehaničke procese na kontaktu dolomitnoga sloja i sloja soli u blizini proširenoga presjeka vertikalnoga okna, uzimajući u obzir radni vijek okna od 50 godina. Rezultati stanja naprezanja – deformacija kombinirane četveroslojne obloge, gdje je vanjski sloj beton, a tri unutarnja sloja od lijevanoga željeza, uzimajući u obzir heterogenost, uspoređeni su s rezultatima dobivenim kada je u obzir uzeta isključivo struktura cijevi. Rješenje problema provedeno je u trodimenzionalnome sustavu. Proračun obloge cijevi, uzimajući u obzir stvarnu geometriju, povećat će točnost predviđanja stanja naprezanja obloge, što upućuje na važnost parametara obloge

Weyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics

The knowledge of quantum phase flow induced under the Weyl's association rule by the evolution of Heisenberg operators of canonical coordinates and momenta allows to find the evolution of symbols of generic Heisenberg operators. The quantum phase flow curves obey the quantum Hamilton's equations and play the role of characteristics. At any fixed level of accuracy of semiclassical expansion, quantum characteristics can be constructed by solving a coupled system of first-order ordinary differential equations for quantum trajectories and generalized Jacobi fields. Classical and quantum constraint systems are discussed. The phase-space analytic geometry based on the star-product operation can hardly be visualized. The statement "quantum trajectory belongs to a constraint submanifold" can be changed e.g. to the opposite by a unitary transformation. Some of relations among quantum objects in phase space are, however, left invariant by unitary transformations and support partly geometric relations of belonging and intersection. Quantum phase flow satisfies the star-composition law and preserves hamiltonian and constraint star-functions.Comment: 27 pages REVTeX, 6 EPS Figures. New references added. Accepted for publication to JM

Measurement of qutrits

We proposed the procedure of measuring the unknown state of the three-level system - the qutrit, which was realized as the arbitrary polarization state of the single-mode biphoton field. This procedure is accomplished for the set of the pure states of qutrits; this set is defined by the properties of SU(2) transformations, that are done by the polarization transformers.Comment: 9 pages, 9 figure