Commutative Quantum Operator Algebras

A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is not commutativity in any ordinary sense, but it is clearly the correct generalization to the quantum context. The main purpose of the current paper is to begin laying the foundations for a complete mathematical theory of {\it commutative quantum operator algebras.} We give proofs of most of the relevant results announced in \cite{LZ10}, and we carry out some calculations with sufficient detail to enable the interested reader to become proficient with the algebra of commuting quantum operators.Comment: 22 pages, Late

An HI survey of the Bootes Void. II. The Analysis

We discuss the results of a VLA HI survey of the Bootes void and compare the distribution and HI properties of the void galaxies to those of galaxies found in a survey of regions of mean cosmic density. The Bootes survey covers 1100 Mpc$^{3}$, or $\sim$ 1\% of the volume of the void and consists of 24 cubes of typically 2 Mpc * 2 Mpc * 1280 km/s, centered on optically known galaxies. Sixteen targets were detected in HI; 18 previously uncataloged objects were discovered directly in HI. The control sample consists of 12 cubes centered on IRAS selected galaxies with FIR luminosities similar to those of the Bootes targets and located in regions of 1 to 2 times the cosmic mean density. In addition to the 12 targets 29 companions were detected in HI. We find that the number of galaxies within 1 Mpc of the targets is the same to within a factor of two for void and control samples, and thus that the small scale clustering of galaxies is the same in regions that differ by a factor of $\sim$ 6 in density on larger scales. A dynamical analysis of the galaxies in the void suggests that on scales of a few Mpc the galaxies are gravitationally bound, forming interacting galaxy pairs, loose pairs and loose groups. One group is compact enough to qualify as a Hickson compact group. The galaxies found in the void are mostly late-type, gas rich systems. A careful scrutiny of their HI and optical properties shows them to be very similar to field galaxies of the same morphological type. This, combined with our finding that the small scale clustering of the galaxies in the void is the same as in the field, suggests that it is the near environment that mostly affects the evolution of galaxies.Comment: Latex file of abstract. The postscript version of the complete paper (0.2 Mb in gzipped format) including all the figures can be retrieved from http://www.astro.rug.nl:80/~secr/ To appear in the February 1996 issue of the Astronomical Journa

The FIRST-2MASS Red Quasar Survey

Combining radio observations with optical and infrared color selection -- demonstrated in our pilot study to be an efficient selection algorithm for finding red quasars -- we have obtained optical and infrared spectroscopy for 120 objects in a complete sample of 156 candidates from a sky area of 2716 square degrees. Consistent with our initial results, we find our selection criteria -- J-K>1.7, R-K>4.0 -- yield a ~50% success rate for discovering quasars substantially redder than those found in optical surveys. Comparison with UVX- and optical color-selected samples shows that >~ 10% of the quasars are missed in a magnitude-limited survey. Simultaneous two-frequency radio observations for part of the sample indicate that a synchrotron continuum component is ruled out as a significant contributor to reddening the quasars' spectra. We go on to estimate extinctions for our objects assuming their red colors are caused by dust. Continuum fits and Balmer decrements suggest E(B-V) values ranging from near zero to 2.5 magnitudes. Correcting the K-band magnitudes for these extinctions, we find that for K <= 14.0, red quasars make up between 25% and 60% of the underlying quasar population; owing to the incompleteness of the 2MASS survey at fainter K-band magnitudes, we can only set a lower limit to the radio-detected red quasar population of >20-30%.Comment: 80 pages (single-column, preprint format) 20 figures, Accepted for publicated in Ap

Strain Gradients in Epitaxial Ferroelectrics

X-ray analysis of ferroelectric thin layers of Ba1/2Sr1/2TiO3 with different thickness reveals the presence of internal strain gradients across the film thickness and allows us to propose a functional form for the internal strain profile. We use this to calculate the direct influence of strain gradient, through flexoelectric coupling, on the degradation of the ferroelectric properties of thin films with decreasing thickness, in excellent agreement with the observed behaviour. This work highlights the link between strain relaxation and strain gradients in epitaxial films, and shows the pressing need to avoid strain gradients in order to obtain thin ferroelectrics with bulk-like properties.Comment: 4 pages, 3 embedded figures (1 color), revTex