Non-Nudgable Subgroups of Permutations

Motivated by a problem from behavioral economics, we study subgroups of permutation groups that have a certain strong symmetry. Given a fixed permutation, consider the set of all permutations with disjoint inversion sets. The group is called non-nudgable, if the cardinality of this set always remains the same when replacing the initial permutation with its inverse. It is called nudgable otherwise. We show that all full permutation groups, standard dihedral groups, half of the alternating groups, and any abelian subgroup are non-nudgable. In the right probabilistic sense, it is thus quite likely that a randomly generated subgroup is non-nudgable. However, the other half of the alternating groups are nudgable. We also construct a smallest possible nudgable group, a 6-element subgroup of the permutation group on 4 elements.Comment: new version contains some simplifications and extension

X-ray Continuum Slope and X-ray Spectral Features in NLS1 Galaxies

The idea that some of the unusual features in the X-ray spectra of Narrow-Line Seyfert 1 galaxies (NLS1s) are due to the steep X-ray continuum is tested by comparing photoionization model calculations with various observed properties of Seyfert 1 galaxies. A meaningful comparison must involve the careful use of the right X-ray ionization parameter, designated here U(oxygen). When this is done, it is found that the strength of the continuum absorption features is insensitive to the exact slope of the 0.1-50 keV continuum. It is also shown that the complex of iron L-shell lines near 1 keV can produce strong absorption and emission features, depending on the gas distribution and line widths. While this may explain some unusual X-ray features in AGN, the predicted intensity of the features do not distinguish NLS1 from broader line sources. Finally, acceleration of highly ionized gas, by X-ray radiation pressure, is also not sensitive to the exact slope of the X-ray continuum.Comment: Invited talk presented at the Joint MPE,AIP,ESO workshop on NLS1s, Bad Honnef, Dec. 1999, to appear in New Astronomy Reviews; also available at http://wave.xray.mpe.mpg.de/conferences/nls1-worksho

Reverberation Mapping of High-z, High-luminosity Quasars

We present Reverberation Mapping results after monitoring a sample of 17 high-z, high-luminosity quasars for more than 10 years using photometric and spectroscopic capabilities. Continuum and line emission flux variability is observed in all quasars. Using cross-correlation analysis we successfully determine lags between the variations in the continuum and broad emission lines for several sources. Here we present a highlight of our results and the determined radius--luminosity relations for Ly_alpha and CIV.Comment: Contributed talk at conference "Quasars at all cosmic epochs", held in Padova 2-7 April 2017, published in Frontiers in Astronomy and Space Science

The largest black holes and the most luminous galaxies

The empirical relationship between the broad line region size and the source luminosity in active galactic nuclei (AGNs) is used to obtain black holes (BH) masses for a large number of quasars in three samples. The largests BH masses found exceed 10^{10} Msun and are correlated, almost linearly, with the source luminosity. Such BH masses, when converted to galactic bulge mass and luminosity, indicate masses in excess of 10^{13} Msun and sigma(*) in excess of 700 km/sec. Such massive galaxies have never been observed. The largest BHs reside, almost exclusively, in high redshift quasars. This, and the deduced BH masses, suggest that several scenarios of BH and galaxy formation are inconsistent with the observations. Either the observed size-L relationship in low luminosity AGNs does not extend to very high luminosity or else the M(BH)-M_B(bulge)-sigma(*) correlations observed in the local universe do not reflect the relations of those quantities at the epoch of galaxy formation.Comment: 12 pages, 2 figures, one table, submitted to ApJ

Particle sizing in rocket motor studies utilizing hologram image processing

A technique of obtaining particle size information from holograms of combustion products is described. The holograms are obtained with a pulsed ruby laser through windows in a combustion chamber. The reconstruction is done with a krypton laser with the real image being viewed through a microscope. The particle size information is measured with a Quantimet 720 image processing system which can discriminate various features and perform measurements of the portions of interest in the image. Various problems that arise in the technique are discussed, especially those that are a consequence of the speckle due to the diffuse illumination used in the recording process