8,436 research outputs found
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
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