Very smooth points of spaces of operators

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an $M$-ideal in the space of bounded operators, a very smooth operator $T$ attains its norm at a unique vector $x$ (up to a constant multiple) and $T(x)$ is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon--Nikod\'{y}m property. We give an example of a smooth Banach space without any very smooth points.Comment: 12 pages, no figures, no table

Do Hydrogen-Deficient Carbon Stars Have Winds?

We present high resolution spectra of the five known hydrogen-deficient carbon (HdC) stars in the vicinity of the 10830 angstrom line of neutral helium. In R Coronae Borealis (RCB) stars the He I line is known to be strong and broad, often with a P Cygni profile, and must be formed in the powerful winds of those stars. RCB stars have similar chemical abundances as HdC stars and also share greatly enhanced O-18 abundances with them, indicating a common origin for these two classes of stars, which has been suggested to be white dwarf mergers. A narrow He I absorption line may be present in the hotter HdC stars, but no line is seen in the cooler stars, and no evidence for a wind is found in any of them. The presence of wind lines in the RCB stars is strongly correlated with dust formation episodes so the absence of wind lines in the HdC stars, which do not make dust, is as expected.NSFScience and Technology FacilitiesCouncilthe National Research CouncilCONICYTAustralian Research CouncilMinistﾴerio da Ciﾴencia e TecnologiaSECYTMcDonald Observator

Theoretical studies of tone noise from a fan rotor

An analytical study was made of some possible rotor alone noise sources of dipole, quadrapole and monopole characters which generate discrete tone noise. Particular emphasis is given to the tone noise caused by fan inlet flow distortion and turbulence. Analytical models are developed to allow prediction of absolute levels. Experimental data measured on a small scale fan is presented which indicates inlet turbulence interaction with a fan rotor can be a source of tone noise. Predicted and measured tone noise for the small scale rotor are shown to be in reasonable agreement

Anti-correlated hard X-ray time lags in Galactic black hole sources

We investigate the accretion disk geometry in Galactic black hole sources by measuring the time delay between soft and hard X-ray emissions. Similar to the recent discoveries of anti-correlated hard X-ray time lags in Cyg X-3 and GRS 1915+105, we find that the hard X-rays are anti-correlated with soft X-rays with a significant lag in another source: XTE J1550-564. We also find the existence of pivoting in the model independent X-ray spectrum during these observations. We investigate time-resolved X-ray spectral parameters and find that the variation in these parameters is consistent with the idea of a truncated accretion disk. The QPO frequency, which is a measure of the size of truncated accretion disk, too changes indicating that the geometric size of the hard X-ray emitting region changes along with the spectral pivoting and soft X-ray flux. Similar kind of delay is also noticed in 4U 1630-47.Comment: 14 pages, 7 figures, accepted for publication in Ap

Backward whirl in a simple rotor supported on hydrodynamic bearings

The asymmetric nature of the fluid film stiffness and damping properties in rotors supported on fluid film bearings causes a forward or a backward whirl depending on the bearing parameters and the speed of the rotor. A rotor was designed to exhibit backward synchronous whirl. The rotor-bearing system exhibited split criticals, and a backward whirl was observed between the split criticals. The orbital diagrams show the whirl pattern

Theoretical studies on tone noise from a ducted fan rotor

The method of computing radiated noise from a ducted rotor due to inflow distortion and turbulence are examined. Analytical investigations include an appropriate description of sources, the cut-off conditions imposed on the modal propagation of the pressure waves in the annular duct, and reflections at the upstream end of the duct. Far field sound pressure levels at blade passing frequency due to acoustic radiation from a small scale low speed fan are computed. Theoretical predictions are in reasonable agreement with experimental measurements