On the asymptotic integration of nonlinear differential equations

The aim of the present paper is twofold. Firstly, the paper surveys the literature concerning a specific topic in asymptotic integration theory of ordinary differential equations: the class of second order equations with Bihari-like nonlinearity. Secondly, some general existence results are established with regard to a condition that has been found recently to be of significant use in the theory of elliptic partial differential equations.     

Influence of 50 MeV Lithium Ion Irradiation on Hyperfine Interactions of Cr0.5 Li0.5 Fe2O4

Spinel oxide Cr_0.5 Li_0.5 Fe₂O₄ has been irradiated at Nuclear Science Centre, New Delhi, by 50 MeV lithium ions of fluence 5*10¹³ ions/cm² and irradiation effect on hyperfine interactions has been investigated by Mossbauer spectroscopy. The Mossbauer spectrum of irradiated sample shows no paramagnetic doublet contribution and the hyperfine fields corresponding to the Fe³⁺ in the octahedral (B) and the tetrahedral (A) sites are very well separated. That is the observed superimposed A and B sites in unirradiated sample are split into separate lines after Li irradiation. Further an increase of the intensity of the lines (2)–(5) with respect to (1)–(6) signals an orientation of the hyperfine magnetic field towards a direction perpendicular to the ion path due to the irradiation induced strain by the latent tracks. The computer simulation of Mossbauer spectra indicated that the irradiated Fe³⁺-site occupancy of the A-site hyperfine field increased from 43% to 55% whereas the B-site hyperfine field decreased from 57% to 45% compared to unirradiated sample.     

Controlled Quantum Teleportation of Superposed Coherent State Using GHZ Entangled Coherent State

Controlled quantum teleportation of superposed coherent states using GHZ entangled 3-mode coherent states is studied. Proposed scheme can be implemented experimentally using linear optical components such as a symmetric lossless beam splitter, two phase-shifters and two photon counters. Fidelity is found close to unity for appreciable mean number of photons in coherent states and is 0.99 for mean photon number equal to two.

     

Critical current measurements on extruded YBa2Cu3O y wires

The successful extrusion of short lengths of brittle wires of YBa₂Cu₃O _y that are superconducting above 77 K is reported. Detailed critical current measurements are presented on wires having undergone different physical treatments. The highest critical current obtained from V-I data is ⋍ 90 A/cm², but this particular wire shows clear evidence of flux-pinning forces corresponding to ⋍ 130 A/cm².     

Magnetic field dependence of critical current density in YBa2Cu3O7

We have measured the transport critical current densityJ _cof sintered YBa₂Cu₃O₇, in various applied fields up to 185 Oe at 77 K. We find a sharp decay ofJ _cwith magnetic field. We show that this sharp decay is consistent with the low field hysteresis results of Groveret al. We argue that the observed field dependence is not caused by intragranular weak links.     

Crystal growth, thermal and optical studies of nonlinear optical material: Glycine potassium sulphate

A new nonlinear optical material glycine potassium sulphate (GPS) has been synthesized and optical quality crystals were grown from aqueous solution. This material has positive temperature coefficient revealed from the solubility studies. The grown crystals were characterized by employing several techniques such as single crystal and powder X-ray diffraction, thermo gravimetric analysis, FTIR and UV-vis-NIR spectra. The etching studies have been done on the (1 0 0) plane of the grown crystal. Preliminary measurements to find second harmonic generation efficiency of GPS has been carried out.     

Liquid chromatographic methods for separation,determination, and bioassay of enantiomers of etodolac: A review

The control of enantiomeric purity and determination of individual enantiomeric drug molecules remains the subject of importance for clinical, analytical, and regulatory purposes and to facilitate an accurate evaluation of the risks posed by them to human health. A large number of pharmaceuticals are marketed and administered as racemates. Etodolac is among such nonsteroidal anti‐inflammatory drugs. Overall literature reports on its enantioseparation are scanty. Liquid chromatography (LC) methods of enantioseparation of (±)‐etodolac, including certain unconventional ones, are well covered and discussed in this paper. Methods of direct approach without using chiral columns or chiral thin‐layer chromatography plate and of indirect approach using certain chiral derivatizing agents such as (S)‐naproxen and (S)‐levofloxacin are described. Most interesting aspects include establishment of structure and molecular asymmetry of chemically different types of diastereomeric derivatives using liquid chromatography with mass spectrometry (LC–MS), ¹H NMR spectroscopy and by drawing conformations in three dimensional views by using certain software. The methods provide chirality recognition even in the absence of pure enantiomers. Besides, recovery of pure enantiomers by detagging or via solubility difference of chiral inducing reagent and the analyte, without racemization at any stage, has been achieved. The limits of detection and quantification are much lower than the industry benchmarks.     

A Grothendieck–Lefschetz theorem for equivariant Picard groups

We prove a Grothendieck–Lefschetz theorem for equivariant Picard groups of non-singular varieties with finite group actions.     

Induced crystallization and the physical properties of PbO–Sb2O3–As2O3: MoO3 glass system

PbO–Sb₂O₃–As₂O₃ glasses mixed with different concentrations of MoO₃ (ranging from 0 to 1.0 mol%) were crystallized. The samples were characterized by X-ray diffraction, scanning electron microscopy and differential thermal analysis techniques. The X-ray diffraction and the scanning electron microscopic studies have revealed the presence of Pb₅Sb₂O₈, PbSb₂O₆, SbAsO₄, Sb₂MoO₆, Sb₄Mo₁₀O₃₁, As₄Mo₃O₁₅, Pb₅Sb₄O₁₁ crystalline phases in these samples. The differential thermal analysis indicated that the surface crystallization prevails over the bulk crystallization as the concentration of the crystallizing agent is increased. The infrared (IR) spectral studies exhibit bands due to MoO₄ structural units in addition to the conventional bands due to various antimonate and arsenate structural groups. The studies on PbO–Sb₂O₃–As₂O₃: MoO₃ glass-ceramics with respect to various physical properties viz., dielectric properties over a range of frequency and temperature, optical absorption, electron spin resonance (ESR) and magnetic susceptibility at room temperature have also been reported. The optical absorption, ESR and magnetic susceptibility studies indicated that the molybdenum ions exist in Mo⁵⁺ state in addition to Mo⁶⁺ state in these samples. The redox ratio found to increase as the concentration of the MoO₃ is increased. The variations observed in all these properties with the concentration of the crystallizing agent have been analyzed in the light of different oxidation states and environment of molybdenum ions in the glass ceramic network.