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

Quenching of fluorescence of aromatic molecules by graphene due to electron transfer

Investigations on the fluorescence quenching of graphene have been carried out with two organic donor molecules, pyrene butanaoic acid succinimidyl ester (PyBS, I) and oligo(p-phenylenevinylene) methyl ester (OPV-ester, II). Absorption and photoluminescence spectra of I and II recorded in mixture with increasing the concentrations of graphene showed no change in the former, but remarkable quenching of fluorescence. The property of graphene to quench fluorescence of these aromatic molecules is shown to be associated with photo-induced electron transfer, on the basis of fluorescence decay and time-resolved transient absorption spectroscopic measurements.Comment: 18 pages, 6 figure

Operation of FDI caps in India and corporate control mechanisms

While India has generally been following an open door FDI policy, a few areas are still subject to caps on FDI and/or specific government approval. One of the justifications for the same is the need to retain a degree of control over the operations of the investee companies in Indian hands. Earlier this year, the government specified the methodology for calculating direct and indirect foreign equity in Indian companies in order to remove ambiguities in calculating the extent of FDI in a company. Based on empirical evidence this paper argues that percentage of shares or proportion of directors do not necessarily represent the extent of control and more direct intervention would be required if the objectives of imposing the caps are to be achieved.FDI; corporate control, veto powers, India, joint control, joint ventures, corporate governance

Anti-correlated time lags in the Z source GX 5-1: Possible evidence for a truncated accretion disk

We investigate the nature of the inner accretion disk in the neutron star source GX 5-1 by making a detailed study of time lags between X-rays of different energies. Using the cross-correlation analysis, we found anti-correlated hard and soft time lags of the order of a few tens to a few hundred seconds and the corresponding intensity states were mostly the horizontal branch (HB) and upper normal branch (NB). The model independent and dependent spectral analysis showed that during these time lags the structure of accretion disk significantly varied. Both eastern and western approaches were used to unfold the X-ray continuum and systematic changes were observed in soft and hard spectral components. These changes along with a systematic shift in the frequency of quasi-periodic oscillations (QPOs) made it substantially evident that the geometry of the accretion disk is truncated. Simultaneous energy spectral and power density spectral study shows that the production of the horizontal branch oscillations (HBOs) are closely related to the Comptonizing region rather than the disk component in the accretion disk. We found that as the HBO frequency decreases from the hard apex to upper HB, the disk temperature increases along with an increase in the coronal temperature which is in sharp contrast with the changes found in black hole binaries where the decrease in QPO frequency is accompanied by a decrease in the disk temperature and a simultaneous increase in the coronal temperature. We discuss the results in the context of re-condensation of coronal material in the inner region of the disk.Comment: 40 pages, 7 figures, accepted for publication in The Astrophysical Journal Supplement (ApJS

Observational evidence for mass ejection during soft X-ray dips in GRS1915+105

We investigate the connection between the X-ray and radio properties of the Galactic microquasar GRS1915+105, by analyzing the X-ray data observed with RXTE, during the presence of a huge radio flare (~450 mJy). The X-ray lightcurve shows two dips of ~100 second duration. Detailed time resolved spectral analysis shows the existence of three spectral components: a multicolor disk-blackbody, a Comptonized component due to hot plasma and a power-law. We find that the Comptonized component is very weak during the dip. This is further confirmed by the PHA ratio of the raw data and ratio of the lightcurves in different energy bands. These results, combined with the fact that the 0.5 -- 10 Hz QPO disappears during the dip and that the Comptonized component is responsible for the QPO lead to the conclusion that during the dips the matter emitting Comptonized spectrum is ejected away. This establishes a direct connection between the X-ray and radio properties of the source.Comment: Replaced with some minor changes, corrected typos. Added Journal Re