E-semigroups Subordinate to CCR Flows

The subordinate E-semigroups of a fixed E-semigroup are in one-to-one correspondence with local projection-valued cocycles of that semigroup. For the CCR flow we characterise these cocycles in terms of their stochastic generators, that is, in terms of the coefficient driving the quantum stochastic differential equation of Hudson-Parthasarathy type that such cocycles necessarily satisfy. In addition various equivalence relations and order-type relations on E-semigroups are considered, and shown to work especially well in the case of those semigroups subordinate to the CCR flows by exploiting our characterisation.Comment: 14 pages; to appear in Communications on Stochastic Analysis. Minor modifications made from version

Introduction to Principal Components Analysis

Understanding the inverse equivalent width - luminosity relationship (Baldwin Effect), the topic of this meeting, requires extracting information on continuum and emission line parameters from samples of AGN. We wish to discover whether, and how, different subsets of measured parameters may correlate with each other. This general problem is the domain of Principal Components Analysis (PCA). We discuss the purpose, principles, and the interpretation of PCA, using some examples from QSO spectroscopy. The hope is that identification of relationships among subsets of correlated variables may lead to new physical insight.Comment: Invited review to appear in ``Quasars and Cosmology'', A.S.P. Conference Series 1999. eds. G. J. Ferland, J. A. Baldwin, (San Francisco: ASP). 10 pages, 2 figure

Quantum stochastic cocycles and completely bounded semigroups on operator spaces

An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of stochastic semigroups in the sense of Skorohod. One-to-one correspondences are established between classes of cocycle of interest and corresponding classes of one-parameter semigroups on associated matrix spaces. Each of these 'global' semigroups may be viewed as the expectation semigroup of an associated quantum stochastic cocycle on the corresponding matrix space. The classes of cocycle covered include completely positive contraction cocycles on an operator system, or C*-algebra; completely contractive cocycles on an operator space; and contraction operator cocycles on a Hilbert space. As indicated by Accardi and Kozyrev, the Schur-action matrix semigroup viewpoint circumvents technical (domain) limitations inherent in the theory of quantum stochastic differential equations. An infinitesimal analysis of quantum stochastic cocycles from the present wider perspective is given in a sister paper.Comment: 32 page

Spectral Properties From Lyman-alpha to H-alpha For An Essentially Complete Sample of Quasars I: Data

We have obtained quasi-simultaneous ultraviolet-optical spectra for 22 out of 23 quasars in the complete PG-X-ray sample with redshift, z<0.4, and M_B<-23. The spectra cover rest-frame wavelengths from at least Lyman-alpha to H-alpha. Here we provide a detailed description of the data, including careful spectrophotometry and redshift determination. We also present direct measurements of the continua, strong emission lines and features, including Lyman-alpha, SiIV+OIV], CIV, CIII], SiIII], MgII, H-beta, [OIII], He5876+NaI5890,5896, H-alpha, and blended iron emission in the UV and optical. The widths, asymmetries and velocity shifts of profiles of strong emission lines show that CIV and Lyman-alpha are very different from H-beta and H-alpha. This suggests that the motion of the broad line region is related to the ionization structure, but the data appears not agree with the radially stratified ionization structure supported by reverberation mapping studies, and therefore suggest that outflows contribute additional velocity components to the broad emission line profiles.Comment: 42 pages, 10 figures, 13 tables. Accepted by AJ. Supplemental figures not included. Full version available at http://physics.uwyo.edu/~shang/pgxpaper/ShangPaper.pd