A Bessel collocation method for numerical solution of generalized pantograph equations

This article is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this article, we introduce a collocation method based on the Bessel polynomials for the approximate solution of the pantograph equations. The method is illustrated by studying the initial value problems. The results obtained are compared by the known results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Light-emitting iridium(III) and ruthenium(II) polypyridyl complexes containing quadruple hydrogen-bonding moieties

A novel compound containing both a 2,2'-bipyridine as well as a 2-ureido-4[1H]-ureidopyrimidinone supramolecular moiety (3) has been synthesised and fully characterized by 1H-NMR, MALDI-TOFMS, UV-vis and IR spectroscopy. Subsequent coordination to iridium and ruthenium polypyridyl precursors allowed the formation of iridium(III) and ruthenium(II) polypyridyl dimers (5 and 7) assembled via quadruple hydrogen-bonding as well as metal coordination interactions. The syntheses and complete characterization of these materials by means of two-dimensional NMR techniques (1H-1H COSY and 1H-1H DOSY) as well as IR and MALDI-TOFMS are described in detail. Comparative studies of the optical properties of the luminescent model complexes (5' and '7) and the dimer species (5 and 7) are also illustrated. In addition, good processability of the materials has been demonstrated by inkjet printing leading to thin films revealing their potential for light-emitting devices.     

Quantum-chemical,spectroscopic and X-ray diffraction studies on nickel complex of 2-hydroxyacetophenone thiosemicarbazone with triphenylphospine

Reaction of 2-hydroxyacetophenone thiosemicarbazone with [Ni(PPh₃)₂Cl₂] in optimized conditions afforded a mixed ligand complex with an isolated triphenylphosphine molecule. The structure was characterized by elemental analysis, IR, NMR and UV–Vis. spectroscopies and single crystal X-ray diffraction technique. In addition, the molecular geometry, vibrational frequencies and gauge including atomic orbital (GIAO) ¹H and ¹³C NMR chemical shift values of the title compound in the ground state have been calculated using the density functional theory (DFT/B3LYP) method with the 6-31G(d,p) basis set for the C, N, O, S, P, H atoms and LANL2DZ pseudo-potential for the Ni atom, and compared with the experimental data. Besides, atomic charge distributions, molecular electrostatic potential and frontier molecular orbitals (FMO) analysis of the title compound were investigated by theoretical calculations. The thermodynamic properties of the compound at different temperatures have been calculated and corresponding relations between the properties and temperature have also been obtained. Atomic charge distributions indicate that during forming the title compound, the free ligand of thiosemicarbazone ion transfers their negative charges to central Ni(II) ion. The effect of different solvents (chloroform, methanol and water) on the geometry, vibrational frequencies, total energies and dipole moments was studied using the density functional theory (DFT/B3LYP) method by applying the Onsager and the Polarizable Continuum Model (PCM).     

On the regularity condition in a convex feasibility problem

The regularity properties of a family of closed convex sets with nonempty intersection are investigated in the frame of a real Hilbert space. The significant role of these properties in solving convex feasibility problems with projection algorithms is pointed out.     

On normalized Ricci flow and smooth structures on four-manifolds with b + = 1

We find an obstruction to the existence of non-singular solutions to the normalized Ricci flow on four-manifolds with b⁺ = 1. By using this obstruction, we study the relationship between the existence or non-existence of non-singular solutions of the normalized Ricci flow and exotic smooth structures on the topological 4-manifolds , where . Received: 13 November 2008     

On a class of quasilinear eigenvalue problems on unbounded domains

We prove several existence and non-existence results for a quasilinear eigenvalue problem with nonlinear boundary condition on unbounded domain. Our paper extends previous results obtained in Chabrowski [1] and Pflüger [4].     

Studies on the Thermal Decompositions of Heteropolynuclear Glyoxylates of Cr(III) and Cu(II)

Complexes of Cr(III):Cu(II) with the glyoxylate dianion as ligand were synthesized in the range of cation atomic ratios (0.01–8):1.0. The results of non-isothermal analysis of the synthesized compounds correlated with the results of IR and UV-VIS spectroscopy, and gas chromatography of the volatile products of the decomposition allowed the formulation of a mechanism for the decomposition of the complex with Cr(III):Cu(II)=2:1 and the assumption that the other complexes are mixtures of this with the homopolynuclear complexes of Cr(III) and Cu(II), depending on the ratio of the cations Cr(III):Cu(II). The thermal conversion of the complexes takes place at relatively low temperatures, with partial transformation of the ligand into oxalate and of the oxide mixture into CuCrO₄. This revised version was published online in August 2006 with corrections to the Cover Date.     

Equiatomic binary phases of Copper-Rare Earth Elements. An overview of monocuprides from first-principles calculations

Equiatomic binary phases of copper with rare earth (RE) elements exhibit either primitive cubic ( ) or orthorhombic (Pnma) structures and in some cases both. By using density functional theory (DFT), we calculated the enthalpies of formation along the series of RE elements combined equimolarly with copper. For RE from Sc to Lu, the calculated enthalpies of formation fall in the range −49.8 kJ/mol for LuCu to −9.1 kJ/mol for the least thermodynamically stable CeCu. Except NdCu, all the other cubic or orthorhombic compounds exhibit lattice stability. Either forms of NdCu indicated lattice instability. Along the Sc-group, the hypothetical primitive cubic and orthorhombic forms of LuCu are found thermodynamically and mechanically stable. The overall trend of the formation enthalpies as a function of the Meyer Periodic Number is consistent with the energy trend of the 4 f-orbital filling as moving from Sc to Lu monocuprides. In addition, the calculated Gibbs free energies indicate that the thermodynamic stability is largely due to the entropic contributions. All standard DFT calculations were also repeated with DFT+U to better describe the correlation between the 5d–4f and 3d shells of RECu compounds. It has been found that DFT+U slightly affects the enthalpies of formation of RECu binaries. Moreover, DFT+U shifts up the f-band energies of RECu with light RE elements (such as La, Ce and Pr) and in contrast lowers them in the case of RECu with heavy RE elements from Nd to Lu.     

Development of a voltammetric method of analysis using praseodymium oxide-carbon nanotubes for the sensitive detection of dopamine in the presence of tramadol,paracetamol and ascorbic acid

A sensitive and selective method of analysis was constructed by the the combination of praseodymium oxide and carbon nanotubes. The charge transfer resistance (Rct) values of 109 in 1 × 10⁻³ M K₃[Fe(CN)₆] and 79 Ω in 5 × 10⁻⁶ M dopamine indicate that Pr₆O₁₁@MWCNTs/GCE enables an excellent electron pathway between electrolyte and electrode. The platform was successfully applied for the determination of dopamine in the presence of tramadol, paracetamol and ascorbic acid. The platform exhibited a remarkable decrease in ▵Ep for DA. A dynamic linear range from 1.2 × 10⁻⁹ M to 1.8 × 10⁻⁵ M was obtained with an LOD of 1.0 × 10⁻¹⁰ M. Such a sensitive and selective method of analysis makes Pr₆O₁₁@MWCNTs/GCE of high interest to observe trace level of DA with good accuracy and precision.