44,791 research outputs found
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 -dimensional ACM variety in
terms of its cohomological invariants H^i_*(\sE), , 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 and the Veronese
surface in 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
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