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.     

Reactivities of osmium (VIII) towards some aldoses,amino sugars,and methylated sugars in alkaline medium

The kinetics of oxidation of some aldoses, amino sugars and methylated sugars by osmium (VIII) have been studied spectrophotometrically in alkaline medium. The reactions are first‐order with respect to both [sugar]≤9.0×10⁻³ mol dm⁻³ and [OH⁻]≤10.0×10⁻² mol dm⁻³ but tends toward zero order with respect to each at higher concentration. Activation parameters of the reactions have been calculated and plausible reaction mechanisms have been suggested. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 477–483, 1999     

Structural features of some small carbonyls in the 1,3nπ states: An mcscf study

Structural features of a series of tetraatomic carbonyls in the ^1,3nπ* states are studied by using a recently proposed MCSCF algorithm at the INDO/2 level. The computed geometrical parameters and the inversion barrier heights agree quite well with the available experimental or ab initio theoretical data. The calculated transition energies turn out to be somewhat lower than the experimental counterparts. The specific MCSCF algorithm used is found to have excellent convergence properties.     

Relative reactivities of glycerophosphates towards permanganate in perchloric acid medium

Summary The reactivities of - and -glycerophosphates towards MnO ₄ ^– in HClO₄ medium have been examined. The reactions between glycerophosphates and MnO ₄ ^– are first order with respect to [glycerophosphate], [MnO ₄ ^– ] and [H⁺]. There is no evidence for cleavage of the C–O–P bond rather than the terminal –CH₂OH group being oxidized to the respective phosphoglyceraldehyde.     

Two highly unsymmetrical tetradentate (N3O) Schiff base copper(II) complexes: Template synthesis,structural characterization,magnetic and computational studies

Two new copper(II) complexes, [Cu₂(L¹)₂](ClO₄)₂ (1) and [Cu(L²)(ClO₄)] (2), of the highly unsymmetrical tetradentate (N₃O) Schiff base ligands HL¹ and HL² (where HL¹ = N-(2-hydroxyacetophenone)-bis-3-aminopropylamine and HL² = N-(salicyldehydine)-bis-3-aminopropylamine) have been synthesised using a template method. Their single crystal X-ray structures show that in complex 1 two independent copper(II) centers are doubly bridged through phenoxo-O atoms (O1A and O1B) of the two ligands and each copper atom is five-coordinated with a distorted square pyramidal geometry. The asymmetric unit of complex 2 consists of two crystallographically independent N-(salicylidene)-bis(aminopropyl)amine-copper(II) molecules, A and B, with similar square pyramidal geometries. Cryomagnetic susceptibility measurements (5–300 K) on complex 1 reveal a distinct antiferromagnetic interaction with J = ?23.6 cm^?1, which is substantiated by a DFT calculation (J = ?27.6 cm^?1) using the B3LYP functional. Complex 1, immobilized over highly ordered hexagonal mesoporous silica, shows moderate catalytic activity for the epoxidation of cyclohexene and styrene in the presence of TBHP as an oxidant.     

An expedient protocol for conversion of olefins to α-bromo/iodoketones using IBX and NBS/NIS

A variety of olefins have been shown to undergo conversion to the corresponding α-bromo/iodoketones when reacted with NBS/NIS and IBX in DMSO at room temperature. While the reaction is found to occur rapidly with e-rich arylolefins leading to the corresponding haloketones in 65-95% yields in 0.3-3.0 h, those containing e-withdrawing groups are found to yield diketones concomitantly, such that the latter are the exclusive products over extended duration of the reactions.     

Simple Chemical Route Synthesis of Fe2O3 Nanoparticles and its Application for Adsorptive Removal of Congo Red from Aqueous Media: Artificial Neural Network Modeling

Nanocrystalline Fe₂O₃ powder was synthesized by a simple chemical route involving FeCl₃ and NaOH. The Fe₂O₃ powder thus prepared was characterized using x-ray diffraction study, scanning electron microscopy, and Fourier transform infrared spectroscopy. The adsorption properties of crystalline Fe₂O₃ powder have been investigated with an aim to explore a possible low cost and efficient way to remove Congo red (CR) from waste water. Fe₂O₃ powder was found as an excellent adsorbent for CR from aqueous medium. Adsorption capacity as much as 203.66 mg g^?1 is reported at room temperature. Effect of different experimental parameters such as reaction pH, initial CR dye concentration, adsorbent dose, and reaction temperature were studied on adsorption capacity of Fe₂O₃ powder and modeled by artificial neural network (ANN). Optimal ANN structure (4–5–1) shows minimum mean squared error (MSE) of 0.00235 and determination coefficient (R²) of 0.991 with Levenberg–Marquardt algorithm. Isotherm analysis of experimental data exhibited better fit to the Langmuir isotherm. The adsorption process was found to follow second-order kinetics as depicted by the analysis of experimental results. Thermodynamic study shows that the adsorption process is endothermic, spontaneous, and thermodynamically favorable in the temperature range of 27°C to 60°C.