Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Raman imaging and stress quantification in self‐assembled graphene oxide fiber ‘Latin Letters’

To probe the intrinsic stress distribution in terms of spatial Raman shift (ω) and change in the phonon linewidth (Γ), here we analyze self‐assembled graphene oxide fibers (GOF) ‘Latin letters’ by confocal Raman spectroscopy. The self‐assembly of GOF ‘Latin letters’ has been explained through surface tension, π–π stacking, van der Waals interaction at the air–water interface and by systematic time‐dependent investigation using field emission scanning electron microscopy analysis. Intrinsic residual stress due to structural joints and bending is playing a distinct role affecting the E_2g mode (G band) at and away from the physical interface of GOF segments with broadening of phonon linewidth, indicating prominent phonon softening. Linescan across an interface of the GOF ‘letters’ reveals Raman shift to lower wavenumber in all cases but more so in ‘Z’ fiber exhibiting a broader region. Furthermore, intrinsic stress homogeneity is observed for ‘G’ fiber distributed throughout its curvature with negligible shift corresponding to E_2g mode vibration. This article demonstrates the significance of morphology in stress distribution across the self‐assembled and ‘smart‐integrable’ GOF ‘Latin letters’. Copyright © 2016 John Wiley & Sons, Ltd.     

Spectroscopical splitting of Cu ion energy levels in magnesium lead fluoro silicate glasses

Homogeneous 40.0 MgO-(10-x) PbF₂-50.0 SiO₂: x CuO glasses were prepared using melt-quenching technique under controlled conditions. Spectroscopic studies (UV-vis absorption, ESR, FT-IR) are carried out for these glasses. One broad characteristic visible absorption band is observed around 700-850 nm in these glasses, the optical band gap decreases as the content of the CuO increases in the glass network up to 0.7 mol % then reversal trend is observed. ESR spectra of all these glasses show resonance peaks characteristic of Cu²⁺ ions and hyperfine splitting is resolved with increasing the CuO content in the glass network. From the observed ESR spectra, the spin-Hamiltonian parameters have been evaluated and indicate that Cu²⁺ ions have octahedral coordination with a strong tetragonal distortion in these glasses. By correlating ESR and optical absorption data, the molecular orbital coefficients have been evaluated. FT-IR spectra give important information about the nature of bonds in the glass matrix. The density of the glasses is also measured and is found to decrease with the increase CuO contents in the glass matrix. The physical parameters along with spectroscopic parameters are measured.     

Kinetics and mechanism of the oxidation of acetaldehyde by chromic acid in perchloric acid

Summary The oxidation of MeCHO by chromium(VI) has been studied in HClO₄ medium over a wide range of experimental conditions and has been found to obey the rate law;v=k[MeCHO][HCrO ₄ ^– ][H⁺]. The calculated H and-S values for the reaction are 30±2kJ mol^–1 and 171±7J mol^–1deg^–1, respectively. The mechanism is discussed in terms of carbon-hydrogen bond cleavage.     

Rationalisation of extractive protocol by high-performance thin-layer chromatographic–densitometric quantification of berberine in multiple hydroalcoholic extract of Tinospora cordifolia stem

JPC – Journal of Planar Chromatography – Modern TLC - Drug development from medicinal plants by using various hydroalcoholic solvents has been an emerging trend in the last few decades....     

Kinetics and mechanism of oxidation of methanol by acid bromate

The kinetics of oxidation of methanol by bromate ion in hydrochloric acid medium has been investigated. A mechanism consistent with the experimental observations is suggested.

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Effect of Cr doping on the ac electrical properties of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> nanoparticles

Magnesium aluminate nanoparticles with different chromium concentration (0–12%) have been synthesized by a citrate–nitrate sol–gel route. X-ray diffraction studies confirmed the formation of single-phase cubic spinel structure excluding the presence of any secondary phase. Crystallite size of the synthesized nanoparticles was found to increase from 8.5 to 19.8 nm with the increase in Cr concentration. Fourier transformed infrared spectroscopic studies confirmed the presence of AlO₆ group which led to the formation of MgAl₂O₄ spinel structure. Surface morphology of the sintered pellets was investigated with the help of a field emission scanning electron microscope which revealed the existence of both grain and grain boundary along with their aggregates. The dielectric constant, dielectric loss and ac conductivity were studied as a function of frequency of the applied electric field for different composition and their nature of variation with frequency has been elucidated on the basis of Maxwell–Wagner interfacial model. Impedance spectroscopy technique has been used to study the effect of grain and grain boundary on the electrical properties of this spinel oxide. All the electrical parameters showed strong dependence on the nanostructural properties and were found to vary consistently with the increase of doping concentration.     

Synthesis, structural characterization and catalytic activity of a multifunctional enzyme mimetic oxoperoxovanadium(V) complex

The synthesis and structural characterization of a novel oxoperoxovanadium(V) complex [VO(O(2))(PAH)(phen)] containing the ligands 2-phenylacetohydroxamic acid (PAHH) and 1,10-phenanthroline (phen) has been accomplished. The oxoperoxovanadium(V) complex was found to mimic both vanadate-dependent haloperoxidase (VHPO) activity as well as nuclease activity through effective interaction with DNA. The complex is the first example of a structurally characterized stable oxoperoxovanadium(V) complex with a coordinated bi-dentate hydroximate moiety (-CONHO(-)) from 2-phenylacetohydroximate (PAH). The oxoperoxovanadium(V) complex has been used as catalyst for the peroxidative bromination reaction of some unsaturated alcohols (e.g. 4-pentene-1-ol, 1-octene-3-ol and 9-decene-1-ol) in the presence of H(2)O(2) and KBr. The catalytic products have been characterized by GC-MS analysis and spectrophotometric methods. The DNA binding of this complex has been established with CT DNA whereas the DNA cleavage was demonstrated with plasmid DNA. The interactions of the complex with DNA have been monitored by electronic absorption and fluorescence emission spectroscopy. Viscometric measurements suggest that the compound is a DNA intercalator. The nuclease activity of this complex was confirmed by gel electrophoresis studies.     

Spectroscopic and structural features of small thiocarbonyl molecules in low-lying excited states: Further applications of a variant of the orthogonal gradient method

Structural parameters of a set of five thiocarbonyl molecules in the lowest nπ* states are calculated by using a generalized orbital optimization algorithm (a variant of the orthogonal gradient method) in an INDO MCSCF framework. Transition energies, singlet-triplet splittings, planar inversion barriers, and dipole moments in nπ* states of different spin multiplicities are reported. Predicted structural features agree reasonably well with available experimental or theoretical data. Some interesting trends are noted in the computed inversion barrier heights, singlet-triplet splittings, and dipole moments in nπ* states.