Observations of Sy2 galaxy NGC 3281 by XMM-Newton and INTEGRAL satellites

We present here the results of our analysis of X-ray properties of Seyfert 2 galaxy NGC 3281, based on the observational data obtained by XMM-Newton and INTEGRAL within the energy ranges 0.2-12 keV and 20-150 keV, respectively. The XMM-Newton spectrum of this object is presented for the first time. We show that fitting the X-ray spectrum of this galaxy with models based on the reflection from the disc with infinite column density yields non-physical results. More appropriate fit takes into account both transmitted and reflected emission, passed through a gas-dusty torus-like structure. Keeping this in mind, to model the inhomogeneous clumpy torus, we used the MYTorus model. Hence, we propose that the torus of NGC 3281 is not continuous structure, but it consists of separate clouds, which is in a good agreement with the results of near-IR observations. Using this assumption, we found that the torus inclination angle and the hydrogen column density are 66.98^{+2.63}_{-1.34} degrees and 2.08^{+0.35}_{-0.18}x10^{24} cm^{-2}, respectively. Also, the emission of the hot diffuse gas with temperature ~590 eV and warm absorption were detected.Comment: 8 pages, 5 figures, 2 tables, accepted for publication in Advances in Astronomy and Space Physic

On the classification of conditionally integrable evolution systems in (1+1) dimensions

We generalize earlier results of Fokas and Liu and find all locally analytic (1+1)-dimensional evolution equations of order $n$ that admit an $N$-shock type solution with $N\leq n+1$. To this end we develop a refinement of the technique from our earlier work (A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653--7660), where we completely characterized all (1+1)-dimensional evolution systems \bi{u}_t=\bi{F}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^n\bi{u}/\p x^n) that are conditionally invariant under a given generalized (Lie--B\"acklund) vector field \bi{Q}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^k\bi{u}/\p x^k)\p/\p\bi{u} under the assumption that the system of ODEs \bi{Q}=0 is totally nondegenerate. Every such conditionally invariant evolution system admits a reduction to a system of ODEs in $t$, thus being a nonlinear counterpart to quasi-exactly solvable models in quantum mechanics. Keywords: Exact solutions, nonlinear evolution equations, conditional integrability, generalized symmetries, reduction, generalized conditional symmetries MSC 2000: 35A30, 35G25, 81U15, 35N10, 37K35, 58J70, 58J72, 34A34Comment: 8 pages, LaTeX 2e, now uses hyperre

Hexakis(dimethylformamide)bis(hexaphenylcyclohexasiloxanehexaolato)hexacopper(II) Dimethylformamide Solvate

The sandwich-like title complex, hexakis(dimethylformamide)-1O,2O,3O,4O,5O,6O-bis[2,4,6,8,10,12-hexaphenylsiloxane-2,4,6,8,10,12-hexaolato(6-)-1:22O1,2:32O2,3:42O3,- 4:52O4,5:62O5,1:62O6]hexacopper(II) tetrakis(dimethylformamide) solvate, [Cu6(C3H7NO)6{(C6H5)6O12Si6}2].4C3H7NO, is comprised of two regular crown-shaped macrocyclic hexadentate organosiloxanolate ligands chelating a flat Cu6 hexagon, as in the ethanol-solvated analogue investigated previously. The title complex has a more distorted shape than the trigonal ethanol-solvated analogue, being slightly side-oblated, but still contains a large empty inner channel accessible by small molecules (the diameter of the free cross-section being about 2.5 Å). Each CuII ion has square-pyramidal coordination with four basal siloxanolate O atoms and an apical dimethylformamide (DMFA) molecule (coordinated through its carbonyl group). The average bond lengths are: Cu-O(Si) 1.964 (11) Å and Cu-O(DMFA) 2.215 (10) Å. The structure contains four additional DMFA molecules per complex unit, linked by weak C-HO hydrogen bonds. Unexpectedly, the C=O bond length is longer [1.248 (10) and 1.255 (9) Å] in the uncoordinated DMFA molecules than in the coordinated [1.214-1.227 (7) Å]

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.Comment: 14 page

Synthesis and Characterization of Large Stereoregular Organosiloxane Cycles

The large stereoregular phenyltrimethylsiloxysiloxane macrocycles of general formula [PhSi(OSiMe3)O]n (n=6 and 12) have been selectively obtained with high yields by trimethylsilylation of cage-like oligophenylmetallasiloxanes (OPMS) which we described earlier. The compounds 3 (n=6) and 4 (n=12) have been characterized by NMR-spectroscopy method and by single crystal X-ray analysis. This investigation showed unambiguously that the siloxane macrocycles keep their size and configuration (the same as in the initial OPMS) during the trimethylsilylation. Thus a synthetic route for obtaining large stereoregular siloxane macrocycles has been developed

On separable Schr\"odinger equations

We classify (1+3)-dimensional Schr\"odinger equations for a particle interacting with the electromagnetic field that are solvable by the method of separation of variables. As a result, we get eleven classes of the electromagnetic vector potentials of the electromagnetic field $A(t, \vec x)=(A_0(t, \vec x)$, $\vec A(t, \vec x))$ providing separability of the corresponding Schr\"odinger equations. It is established, in particular, that the necessary condition for the Schr\"odinger equation to be separable is that the magnetic field must be independent of the spatial variables. Next, we prove that any Schr\"odinger equation admitting variable separation into second-order ordinary differential equations can be reduced to one of the eleven separable Schr\"odinger equations mentioned above and carry out variable separation in the latter. Furthermore, we apply the results obtained for separating variables in the Hamilton-Jacobi equation.Comment: 30 pages, LaTe