The First INTEGRAL AGN Catalog

We present the first INTEGRAL AGN catalog, based on observations performed from launch of the mission in October 2002 until January 2004. The catalog includes 42 AGN, of which 10 are Seyfert 1, 17 are Seyfert 2, and 9 are intermediate Seyfert 1.5. The fraction of blazars is rather small with 5 detected objects, and only one galaxy cluster and no star-burst galaxies have been detected so far. A complete subset consists of 32 AGN with a significance limit of 7 sigma in the INTEGRAL/ISGRI 20-40 keV data. Although the sample is not flux limited, the distribution of sources shows a ratio of obscured to unobscured AGN of 1.5 - 2.0, consistent with luminosity dependent unified models for AGN. Only four Compton-thick AGN are found in the sample. Based on the INTEGRAL data presented here, the Seyfert 2 spectra are slightly harder (Gamma = 1.95 +- 0.01) than Seyfert 1.5 (Gamma = 2.10 +- 0.02) and Seyfert 1 (Gamma = 2.11 +- 0.05).Comment: 17 pages, 12 figures, accepted for publication in Ap

Integral group ring of the first Mathieu simple group

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Mathieu group M11. As a consequence, for this group we confirm the conjecture by Kimmerle about prime graphs

New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors

A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential equation is given. Alternatively, the mentioned first integral can be used in order to provide a first integral of the second-order complex equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in Class. Quantum Gra

Darboux integrable discrete equations possessing an autonomous first-order integral

All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is obtained from a subclass of these equation via a non-point transformation. The general proposition on the symmetry structure of the quad-graph equations is proved as an auxiliary result