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.     

Excess enthalpies for mixtures of cyclohexanone with isomeric propanols and butanols at 298.15 K

Excess enthalpies (H ^E ) for mixtures of cyclohexanone with propan-1-ol. propan-2-ol, butan-1-ol, butan-2-ol and 2-methyl propan-1-ol at 298.15 K have been measured over the entire composition range. All mixed endothermically with the maximum values ofH ^E occurring at equimole fraction. Comments about the molecular interactions contributing to the excess enthalpies of a cyclic ketone + an alcohol are made on the basis of these results.     

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.     

An indirect method for the spectrofluorimetric determination of trace amounts of germanium after extraction as an ion association complex with rhodamine B in the presence of chromotropic acid

A highly sensitive and selective spectrofluorimetric method for the determination of 0.05-2.00 mug germanium is described. Germanium is treated with chromotropic acid at pH 2.5 and the resultant anionic complex is extracted as an ion pair with rhodamine into toluene. Addition of butanol to the organic extract releases the fluorescent dye and facilitates its measurement at 570 nm after exciting at 540 nm. The method provides a detection limit of 0.003 mug ml(-1) and is virtually free from interference from extraneous ions. The relative standard deviaiton is 2.9% for ten determinations of 1.0 mug germanium. The method has been applied to the determination of germanium in various ores, minerals and rock samples.     

Indium-mediated allylation/propargylation of α-diazoketones: a facile synthesis of 1-bromo-2-alkyl- or 2-arylpent-4-en-2-ols

α-Diazoketones undergo smooth allylation with successive bromide insertion with allylindium bromide generated in situ from allyl bromide and indium metal to produce 1-bromo-2-alkyl- or 2-arylpent-4-en-2-ols in high yields. Addition of propargylindium bromide produces 1-bromo-2-alkyl-or 2-arylpent-4-yn-2-ols under similar conditions.     

Differentiation of Boc- alpha,beta- and beta,alpha-peptides and a pair of diastereomeric beta,alpha-dipeptides by positive and negative ion electrospray tandem mass spectrometry (ESI-MS/MS)

Positive and negative ion electrospray ionization (ESI) tandem mass spectral study of a new series of hybrid peptides, viz, BocN-alpha,beta-peptides and BocN-beta,alpha-peptides, synthesized from C-linked carbo-beta3-amino acids [Caa (S)] and L-Ala has been carried out. The alpha,beta-peptides have been differentiated from beta,alpha-peptides by the collision-induced dissociation (CID) of [M + H]+ and [M - H]- ions in positive and negative ion ESI-MS respectively. The fragment ion [M + H - C(CH3)3 + H]+ formed from [M + H]+ ions by the loss of 2-methyl-prop-2-ene in alpha,beta-peptides with L-Ala at the N-terminus is insignificant or totally absent for beta,alpha-peptides which have the Caa (S) at N-terminus. The fragment ion [M - H-C(CH3)3OH - HNCO]- formed from [M - H]- of beta,alpha-peptide acids is totally absent for alpha,beta-peptide acids. This has been attributed to the absence of the beta-methylene group in alpha,beta-peptides, and the participation of the beta-methylene group in the loss of HNCO in beta,alpha-peptide acids is confirmed by the deuteration experiments. The CID of [M + H-Boc + H]+ ions of these peptides also produce characteristic fragmentation. In the CID spectra of alpha,beta-peptides, the b(n)+ ions and the resulting y(n)+ ions occur at a mass difference of 243 and 71 Da corresponding to the successive losses of Caa and L-Ala, whereas a mass difference of 71 and 243 Da is observed for beta,alpha-peptides. In contrast to the CID of protonated peptides, the CID of [M - H]- ions of the alpha,beta- and beta,alpha-peptide acids do not give b(n)- ions and show abundant z(n) (-) ions. Further, a pair of diastereomeric dipeptide esters and acids have been distinguished by the CID of [M + H]+ ions. The loss of 2-methyl-prop-2-ene is more pronounced for Boc-NH-Caa(R)-D-Ala-OCH3 (21) and Boc-NH-Caa(R)-D-Ala-OH (23) with Caa (R) at the N-terminus, whereas it is totally absent for Boc-NH-Caa (S)-D-Ala-OCH3 (22) and Boc-NH-Caa(S)-D-Ala-OH (24) peptides, which have Caa (S) at the N-terminus. Thus, on the basis of our previous and present studies, we propose that the CID of [M + H]+ ions provides a simple and useful method for distinguishing the configuration of Caa (S or R) at the N-terminus of BocN-carbo beta,alpha- and beta,beta-dipeptides.