A posteriori H1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes

The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H¹ seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications.     

A new cytotoxic limonoid from Odontadenia macrantha from the Suriname rainforest

Bioassay‐guided fractionation of the methanol extract of Odontadenia macrantha afforded a new limonoid, odontadenin A (1) and two known triterpenoids, lupeol (2) and α‐amyrin (3). The structure of 1 was established on the basis of 1D and 2D NMR and high‐resolution fast atom bombardment mass spectrometric data. The new compound was found to possess moderate cytotoxicity against A2780, the ovarian cancer cell line. Copyright © 2003 John Wiley & Sons, Ltd.     

Isospectral theory of Euler equations

Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is studied.     

Assignment of chemical shifts in benzohydroxamic acid and structure of its silylated derivatives by 15N enrichment

¹⁵N isotopic enrichment was necessary for the unequivocal assignment of the ¹H NMR lines to the protons in the NH–OH fragment of benzohydroxamic acid, BHXA, C₆H₅CONHOH, in dry dimethyl sulfoxide solutions. The assignment [δ(NH) = 11.21, δ(OH) = 9.01, ¹J(¹⁵N,¹H) = 102.2 Hz, ²J(¹⁵N,¹H) <1.5 Hz], which is opposite to that used by other authors, confirms the assignment extended to BHXA by Brown and co‐workers from the spectra of acetohydroxamic acid. The enrichment allowed also assignment of the ²⁹Si lines in the spectra of disilylated benzohydroxamic acid, (Z)‐tert‐butyldimethylsilyl N‐tert‐butyldimethylsilyloxybenzoimidate (2) and (Z)‐tert‐butyldiphenylsilyl N‐tert‐butyldiphenylsilyloxybenzoimidate (3), and confirmed structure of the monosilylated products, N‐tert‐butyldiphenylsilyloxybenzamide (4) and N‐tert‐butyldiphenylsilyloxy benzoimidic acid (5). Copyright © 2003 John Wiley & Sons, Ltd.     

NMR studies on a palladium(II) complex containing an incompletely coordinated facultative pentadentate Schiff base ligand

Palladium(II) dichloride reacts with 1,10‐bis(2‐pyrrolyl)‐2,5,9‐triaza‐1,9‐decadiene to give a [Pd(C₁₅H₂₀N₅)]Cl complex in which the ligand is four‐coordinated, leaving one pyrrole group dangling. By using COSY, gHSQC, gHMBC connectivities and NOE experiments it has been concluded that one linkage isomer exists in DMSO solution, in spite of the fact that different sets of N atoms of potentially pentadentate ligand might be involved in coordination, and that the three chelate rings in the complex cation are arranged in a sequence: five‐membered, six‐membered, five‐membered which is different from that (5–5–6) found by x‐ray studies on the related [Ni(C₁₅H₂₀N₅)]Cl compound. NMR studies allowed an unambiguous assignment of all ¹H and ¹³C NMR resonances for the complex. Results of x‐ray structural analysis of [Pd(C₁₅H₂₀N₅)](CH₃COO)H₂O supported the five‐membered, six‐membered, five‐membered ring sequence in the [Pd(C₁₅H₂₀N₅)]⁺ complex cation and show an E (trans) orientation of the dangling pyrrole group with respect to the metal center. Copyright © 2002 John Wiley & Sons, Ltd.     

Ca(NO3)2•4H2O-catalysed Biginelli Reaction: One-pot Synthesis of 1,2,3,4-Tetrahydropyrimidin-2-ones/pyrimidine-2-thiones under Solvent-free Conditions

The synthesis of 1,2,3,4-dihydropyrimidinone/thione derivatives was achieved in good to excellent yields using calcium(II) nitrate as catalyst to promote the Biginelli three-component condensation reaction from a diversity of aromatic aldehydes, β-keto compounds and urea or thiourea. The reaction was carried out under solvent-free conditions.     

Rheological properties of polyacrylates used as synthetic road binders

Most adhesives and binders, including bitumen for asphalt mixture production, are presently produced from petrochemicals after the refining of crude oil. The fact that crude oil reserves are a finite resource means that in the future, it may become necessary to produce these materials from alternative and probably renewable sources. Suitable resources of this kind may include polysaccharides, plant oils and proteins. This paper deals with the synthesis of polymer binders from monomers that could, in future, be derived from renewable resources. These binders consist of polyethyl acrylate (PEA) of different molecular weight, polymethyl acrylate (PMA) and polybutyl acrylate (PBA), which were synthesised from ethyl acrylate, methyl acrylate and butyl acrylate, respectively, by atom transfer radical polymerisation. The rheological properties of these binders were determined by means of oscillatory testing using a dynamic shear rheometer and combinations of stress/strain, temperature and frequency sweeps. The results indicate that PEA can be produced to have rheological properties similar to that of ‘soft’ 100/150 penetration grade bitumen, PMA with similar rheological properties to that of ‘hard’ 10/20 penetration grade bitumen, while PBA, due to its highly viscous nature and low dynamic moduli, cannot be used on its own as a binder. The synthetic polymers were found to be thermo-rheologically simple, and the shift factors, used to produce the dynamic moduli master curves, were found to fit an Arrhenius function.     

Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at