Convergence of mixed finite element approximations for the shallow arch problem

Summary The stability and convergence of mixed finite element methods are investigated, for an equilibrium problem for thin shallow elastic arches. The problem in its standard form contains two terms, corresponding to the contributions from the shear and axial strains, with a small parameter. Lagrange multipliers are introduced, to formulate the problem in an alternative mixed form. Questions of existence and uniqueness of solutions to the standard and mixed problems are addressed. It is shown that finite element approximations of the mixed problem are stable and convergent. Reduced integration formulations are equivalent to a mixed formulation which in general is distinct from the formulation shown to be stable and convergent, except when the order of polynomial interpolationt of the arch shape satisfies 1tmin (2,r) wherer is the order of polynomial approximation of the unknown variables.     

Synthesis and spectral studies on nickel(II) complexes of amide group-containing ligands

Summary Complexes of nickel(II) with N-(2-carboxyphenyl)benzamide (CPBH), 2-amino-N-(2-carboxyphenyl)benzamide (ACPBH), N-isoxazolyl benzamide (IB), N-anilinobenzamide (AB), N-(2-pyridyl)-3-carboxypropanamide (PCPA) and N-(2-pyridyl)-2-carboxybenzamide (PCBA) have been isolated and characterized by elemental analyses, magnetic susceptibility measurements, thermal studies, i.r. and electronic spectral studies. The electrochemical behaviour of some complexes has also been investigated.     

The first example of the C-3 alkylation of indoles with cyclopropyl ketones promoted by CeCl3·7H2O/LiI

Indoles undergo smooth alkylation with cyclopropyl ketones in the presence of the CeCl₃·7H₂O/LiI reagent system in refluxing acetonitrile under neutral conditions to produce the corresponding C-3 substituted indole derivatives in good to high yields and with high selectivity. The use of CeCl₃·7H₂O/LiI makes this method simple, convenient, and cost-effective.     

Potential energy curves: A simple and rapid method

The true potential energy curves for different electronic states of diatomic molecules have been constructed by a simplified and modified form of the Jarmain method. To check the validity of this new procedure potential energy curves are constructed for NO⁺, VO, Si₂, AsO, AsO⁺, PF⁺, CO and Bi₂. The results are in good agreement with the Jarmain, RKRV and Lakshman and Rao methods.     

Structural and electrochemical studies of annealed LiNiVO4 thin films

We prepared stoichiometric lithium nickel vanadate amorphous thin films by using r.f. magnetron sputtering under controlled oxygen partial pressure. The amorphous films were heated at various temperatures, 300–600 °C, for 8 h. The as‐deposited and annealed thin films were characterized by Rutherford backscattering spectroscopy, nuclear reaction analysis, Auger electron spectroscopy, X‐ray diffraction, scanning electron microscopy and atomic force microscopy. The electrochemical behavior of the various films was studied by the galvanostatic method. The cells were tested in a liquid electrolyte at room temperature, with lithium metal used as the counter and reference electrode. The best electrochemical storage value was obtained with the thin film annealed at 300 °C, which showed superior capacity and small capacity loss during cycling. Copyright © 2007 John Wiley & Sons, Ltd.     

Preparation and thermal stability of trioxalatocobaltates of bivalent metals KM2+ [Co(C2O4)3]·xH2O

Trioxalatocobaltates of bivalent metals KM²⁺[Co(C₂O₄)₃]·x H₂O, with M²⁺ = Ba, Sr, Ca and Pb, have been prepared, characterized and their thermal behaviour studied. The compounds decompose to yield potassium carbonate, bivalent metal carbonate or oxide and cobalt oxide as final products. The formation of the final products of decomposition is influenced by the surrounding atmosphere. Bivalent metal cobaltites of the types KM²⁺CoO₃ and M²⁺CoO_3—x are not identified among the final products of decomposition. The study brings out the importance of the decomposition mode of the precursor in producing the desired end products.     

An electrochemical investigation on (MoO<Subscript>3</Subscript>+PVP+PVA) nanobelts for lithium batteries

Molybdenum trioxide (MoO₃) xerogel films modified with poly(vinyl alcohol)+poly(vinyl pyrrolidone) (PVP+PVA) polyblends were obtained by ion-exchange method with sol-gel technique. Investigations were conducted using X-ray “diffractometry”, Fourier transform infrared spectroscopy, and cyclic voltammetry. The results show that the H atoms in polyblend are H-bonded with the O atoms in the Mo=O bonds of MoO₃ xerogel, which effectively shield the electrostatic interaction between MoO₃ interlayer and Li⁺ ions when MoO₃ xerogel is modified by the intercalation of (PVP+PVA). The reversibility of the insertion/extraction of Li⁺ ions is greatly improved by the modification with polyblend of MoO₃ nanocomposite films. MoO₃ and (PVP+PVA) _x MoO₃ (x = 0, 0.5) nanobelts were obtained by a simple hydrothermal process from MoO₃ sol. The electrochemical cells with configuration Li/(LiPF₆+EC+DMC)/MoO₃ modified by (PVP+PVA) were fabricated and their discharge profiles studied.