Holonomy group scheme of an integral curve

Let Y be a projective variety over a field k (of arbitrary characteristic). Assume that the normalization X of Y is such that is normal, being the algebraic closure of k. We define a notion of strong semistability for vector bundles on Y. We show that a vector bundle on Y is strongly semistable if and only if its pull back to X is strongly semistable and hence it is a tensor category. In case , we show that strongly semistable vector bundles on Y form a neutral Tannakian category. We define the holonomy group scheme of Y to be the Tannakian group scheme for this category. For a strongly semistable principal G‐bundle , we construct a holonomy group scheme. We show that if Y is an integral complex nodal curve, then the holonomy group of a strongly semistable vector bundle on Y is the Zariski closure of the (topological) fundamental group of Y.     

Gauged Nonlinear Sigma Model in Light-Front Frame: Hamiltonian and BRST Formulations

A gauged nonlinear sigma model in one-space one-time dimension is considered in the light-front frame. The theory is seen to possess a local vector gauge symmetry. The light-front Hamiltonian and BRST formulations of this theory are investigated under some specific light-cone gauges.     

Rapid TLC Method for Estimation of Mevalonic Acid in the Leaves of Medicinal Plants

A simple, rapid, specific and sensitive thin layer chromatographic (TLC) method has been developed for the quantitative estimation of mevalonic acid (MVA) in leaves of medicinal plants; Artemisia annua, Psorelia corylifolia, Vinca rosea, Withania somnifera and Barleria proinites. The assay procedure involved conversion of MVA to its lactone, mevalonolactone (MVAL). Mevalonic acid was extracted from the leaf tissues of plants. Separation of MVAL was carried out on silica gel 60 F₂₅₄ TLC plates using benzene:acetone (3:2) as the mobile phase. The densitometric determination of MVAL was performed at 600 nm after derivatization with anisaldehyde reagent in absorption–reflectance mode. The method was validated over the linearity range of 100–500 ng spot^?1 and correlation coefficient for the calibration curve was >0.99. The average recovery of MVAL, used as internal standard, was higher than 98%. The lower limit of detection was found to be 50 ng spot^?1.     

Non-classicality of photon added coherent and thermal radiations

Production and analysis of non-Gaussian radiation fields has evinced a lot of attention recently. Simplest way of generating such non-Gaussians is through adding (subtracting) photons to Gaussian fields. Interestingly, when photons are added to classical Gaussian fields, the resulting states exhibit non-classicality. Two important classical Gaussian radiation fields are coherent and thermal states. Here, we study the non-classical features of such states when photons are added to them. Non-classicality of these states shows up in the negativity of the Wigner function. We also work out the entanglement potential, a recently proposed measure of non-classicality for these states. Our analysis reveals that photon added coherent states are non-classical for all seed beam intensities; their non-classicality increases with the addition of more number of photons. Thermal state exhibits non-classicality at all temperatures, when a photon is added; lower the temperature, higher is their non-classicality.     

Front-Form Hamiltonian and BRST Formulations of the Schwinger Model

The Hamiltonian and BRST formulations of theSchwinger model are investigated in the light-frontframe.     

Structural characteristics of some metallo-organic discogens

We have recently analysed the crystal and molecular structures of six metalloorganic discogens with substituted β-diketone ligands. The molecules consist of a rigid 11 atom core and a fringe made up of four phenyl rings substituted with alkyl/alkoxy chains. In complex (i), with four octyloxy chains, there are four oxygen atoms around the core. Complex (ii) is asymmetrically substituted with two heptyloxy and two heptyl chains and therefore has two oxygen atoms and complexes (iii) to (vi) have only alkyl chains and hence no oxygen atoms around the core. The metal atom used for coordination has been chosen as Cu/Pd/Ni. Determination of the crystal and molecular structures of these discogens has led to the identification of the following similarities: (1) All the six discogens crystallize in the triclinic space group P1. The recurrence of the space group may be correlated with the structural requirements for efficient packing of the molecules in the crystal lattice. (2) The coordination around the metal atom is square planar. (3) The 11 atom core is only nearly planar. (4) The phenyl rings and the chains are tilted with respect to the core. (5) The molecular conformation in the crystal confers a nearly rectangular shape to these discogens. (6) The chains are fully extended in an all trans conformation. (7) The molecular arrangement is tilted columnar except for the crystal structure of complex (ii).

In addition to the similarities, distinct differences in the crystal structural characteristics have also been observed. For example, when oxygen atoms are present in the fringe, the molecules have no crystallographic symmetry and they tend to pair. In the crystal structure of (i) where the repeat unit along the column is a molecular pair, the metal atoms are distributed in a zig-zag fashion. In the other crystals with columnar arrangement, the metal atoms are stacked one over another. Complex (ii) has a layer-like molecular arrangement in the crystalline phase.     

DSC and X-ray diffraction studies of HxBPA

A detailed DSC study has been done for the substance HxBPA in the temperature range 170 to 380 K and the scheme of transitions in this compound has been deduced. From X-ray work, values for the smectic layer thickness and inplane intermolecular distance have been found in two of the liquid crystalline phases, P₂ and S_H.     

Pressure induced structural transformation in thulium monotelluride

Thulium monotelluride undergoes a structural transformation at 15 GPa from NaCl-type structure to a hexagonal structure with unit cell dimensions: a = 4.07 A and c = 6.84 A. The high pressure diffraction pattern is explained reasonably well by anti-NiAs-type structure. The volume change associated with the transformation is 3.8 per cent.