A numerical scheme for solutions of the Chen system

In this paper, we will develop the Bessel collocation method to find approximate solutions of the Chen system, which is a three‐dimensional system of ODEs with quadratic nonlinearities. This scheme consists of reducing the problem to a nonlinear algebraic equation system by expanding the approximate solutions by means of the Bessel polynomials with unknown coefficients. By help of the collocation points and the matrix operations of derivatives, the unknown coefficients of the Bessel polynomials are calculated. The accuracy and efficiency of the proposed approach are demonstrated by two numerical examples and performed with the aid of a computer code written in MAPLE. In addition, comparisons between our method and the homotopy perturbation method numerical solutions are made with the accuracy of solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

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     

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     

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.