Horrocks Correspondence on a Quadric Surface

We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines, which includes the first cohomology module of the bundle, and prove that there is a one to one correspondence between these sets of invariants and isomorphism classes of vector bundles without line bundle summands.Comment: 19 page

Horrocks Correspondence on ACM Varieties

We describe a vector bundle \sE on a smooth $n$-dimensional ACM variety in terms of its cohomological invariants H^i_*(\sE), $1\leq i \leq n-1$, and certain graded modules of "socle elements" built from \sE. In this way we give a generalization of the Horrocks correspondence. We prove existence theorems where we construct vector bundles from these invariants and uniqueness theorems where we show that these data determine a bundle up to isomorphisms. The cases of the quadric hypersurface in $\mathbb P^{n+1}$ and the Veronese surface in $\mathbb P^5$ are considered in more detail.Comment: 18 pages, not figure

GMRT observations of X-shaped radio sources

We present results from a study of X-shaped sources based on observations using the Giant Metrewave Radio Telescope (GMRT). These observations were motivated by our low frequency study of 3C 223.1 (Lal & Rao 2005), an X-shaped radio source, which showed that the wings (or low-surface-brightness jets) have flatter spectral indices than the active lobes (or high-surface-brightness jets), a result not easily explained by most models. We have now obtained GMRT data at 240 and 610 MHz for almost all the known X-shaped radio sources and have studied the distribution of the spectral index across the sources. While the radio morphologies of all the sources at 240 and 610 MHz show the characteristic X-shape, the spectral characteristics of the X-shaped radio sources, seem to fall into three categories, namely, sources in which (A) the wings have flatter spectral indices than the active lobes, (B) the wings and the active lobes have comparable spectral indices, and (C) the wings have steeper spectral indices than the active lobes. We discuss the implications of the new observational results on the various formation models that have been proposed for X-shaped sources.Comment: The paper contains 12 figures and 3 tables, accepted for publication in MNRAS Main Journal, please note, some figures are of lower qualit

Absolute Rayleigh scattering cross sections of gases and freons of stratospheric interest in the visible and ultraviolet regions

The laboratory measurements of absolute Rayleigh scattering cross sections as a function wavelength are reported for gas molecules He, Ne, Ar, N2, H2, O2, CO2, CH4 and for vapors of most commonly used freons CCl2F2, CBrF3, CF4, and CHClf2. These cross sections are determined from the measurements of photon scattering at an angle of 54 deg 44 min which yield the absolute values independent of the value of normal depolarization ratios. The present results show that in the spectral range 6943-3638A deg, the values of the Rayleigh scattering cross section can be extrapolated from one wavelength to the other using 1/lambda (4) law without knowing the values of the polarizabilities. However, such an extrapolation can not be done in the region of shorter wavelengths

Role of spatial coherence in polarization tomography

We analyze an experimental setup in which a quasi-monochromatic spatially coherent beam of light is used to probe a paraxial optical scatterer. We discuss the effect of the spatial coherence of the probe beam on the Mueller matrix representing the scatterer. We show that according to the degree of spatial coherence of the beam, the \emph{same} scattering system can be represented by \emph{different} Mueller matrices. This result should serve as a warning for experimentalists.Comment: 3 pages, 1 figur

7Li NMR of Normal Human Erythrocytes

Lithium has been known to be an effective medication for people with bipolar disorder. The mechanisms of action of lithium in the brain is not very well understood. NMR spectroscopy and imaging are effective both in determining lithium levels in tissue and brain. We have monitored lithium levels in red blood cells. We have been able to separate intra- and extracellular compartments of lithium using shift reagents, thereby obtaining T^1 \u27s of both the compartments. Lithium uptake as a function of hematocrit was monitored weekly over a 3 week period. The time constant of 50 mM lithium uptake at 25°C and 85% hematocrit was found to be 16.5 hrs. The time constant of 1.8 mM lithium uptake at 37 °C and 45% hematocrit was found to be 11.6 hrs. Experiments on the visibility of the quadrupolar nuclei indicate that it is only 74-90% visible and the visibility decreased with decreasing concentrations

The star formation history of damped Lyman alpha absorbers

The local power law relationship between the surface densities of neutral hydrogen gas and star formation rate (SFR) can be used to explore the SFR properties of damped Lyman alpha (DLA) systems at higher redshift. We find that while the SFR densities for DLA systems are consistent with luminous star forming galaxies at redshifts below z~0.6, at higher redshifts their SFR density is too low for them to provide a significant contribution to the cosmic star formation history (SFH). This suggests that the majority of DLAs may be a distinct population from the Lyman break galaxies (LBGs) or submillimeter star-forming galaxies that together dominate the SFR density at high redshift. It is also possible that the DLAs do not trace the bulk of the neutral gas at high redshift. The metallicity properties of DLAs are consistent with this interpretation. The DLAs show a metal mass density lower by two orders of magnitude at all redshifts than that inferred from the SFH of the universe. These results are consistent with DLAs being dominated by low mass systems having low SFRs or a late onset of star formation, similar to the star formation histories of dwarf galaxies in the local universe.Comment: 9 pages, 5 figures, accepted for publication in Ap