A family of high order iterations for calculating the sign of a matrix

For the computation of a matrix sign function, a family of iterative methods is proposed. for some cases of the accelerator parameters, this method is proven to converge globally with higher rates of convergence. Its stability is discussed analytically as well. to illustrate the efficiency of the proposed methods from the family, several tests of various matrix sizes are considered to worked out.     

A synthetic route to 11-(1H-pyrrol-1-yl)-11H-indeno[1,2-b]quinoxaline derivatives exploiting a three-component coupling strategy under microwave irradiation

11H-Indeno[1,2-b]quinoxalin-11-ones generated in situ from ninhydrin and various 1,2-phenylenediamines, catalysed by montmorillonite K10 under microwave irradiation, condense with 4-hydroxyproline to produce 11-(1H-pyrrol-1-yl)-11H-indeno[1,2-b]quinoxaline derivatives in good yields.     

Synthesis,Characterization and Molecular Structure of a New Tetrameric Palladium(II) Complex Containing Schiff‐Bases Derived from AMTTO (AMTTO = 4‐amino‐6‐methyl‐1,2,4‐triazine‐thione‐5‐one)

The reactions of AMTTO = 4‐amino‐6‐methyl‐1,2,4‐triazine‐thione‐5‐one (AMTTO, 1 ) with 2‐hydroxybenzaldehyde (salicylaldehyde) and 4‐hydroxybenzaldehyde in methanol under reflux conditions led to the corresponding Schiff‐bases ( H₂L1 and H₂L2 ). The reaction of H₂L1 with palladium acetate in ethanol and additional recrystallization from toluene gave the tetrameric complex [Pd(L)]₄·2C₇H₈ ( 2 ). All compounds were characterized by infrared spectroscopy, elemental analyses as well as by X‐ray diffraction studies. Crystal data for H₂L1 at ?80 °C: space group P2₁/c with a = 1285.4(1), b = 707.7(1), c = 1348.2(1) pm, β = 109.32(1)°, Z = 4, R₁ = 0.0328, H₂L2 at ?80 °C: space group P4₃2₁2 with a = 762.5(1), b = 762.5(1), c = 4038.9(2) pm, Z = 8, R₁ = 0.025 and for 2 at ?103 °C: space group C2/c with a = 2862.5(6), b = 2847.6(6), c = 1727.8(4) pm, β = 105.18(3)°, Z = 8, R₁ = 0.0704.     

Competitive Potentiometric Study of a Series of 18-crown-6 with Some Alkali and Alkaline Earth Metal Ions in Methanol Using an Ag+/Ag Electrode

The complexation of some alkali and alkaline earth cations with18-crown-6(18C6), dibenzo-18-crown-6 (DB18C6), dicyclohexyl-18-crown-6 (DCY18C6), and dibenzopyridino-18-crown-6 (DBPY18C6) in a methanol solution has been studied by a competitive potentiometric titration using Ag⁺/Ag electrode as a probe. The stoichiometry and stability constants of the resulting complexes have been evaluated by the MINIQUAD program. The stoichiometry for all resulting complexes was 1:1. The order of stability of Ag⁺ complexes with desired crown ethers varied as DBPY18C6 > DCY18C6 > 18C6 > DB18C6.The stability of the resulting complexes for each of these crown ethers varies in the order ofK⁺ > Na⁺ and Ba²⁺ > Sr²⁺ > Ca²⁺ > Mg²⁺.For each of the used metal ions the major sequence of the stability constants of the resulting complexes varies as DCY18C6 > 18C6 > DB18C6 > DBPY18C6 with minor exceptions.     

Rotational Energy Barrier of the Polarized Carbon–Carbon Double Bond in Quinophthalone

Summary.  A dynamic NMR effect is observed in the ¹³C NMR spectra of anhydrous quinophthalone (quinoline yellow) and its monohydrate in the vicinity of 47°C and 0°C, respectively, and is attributed to a restricted rotation around the polarized carbon–carbon double bond. The free energy of activation for this process in anhydrous quinophthalone and the monohydrate is 65±2 and 55±2 kJ · mol⁻¹, respectively, in CDCl₃. Received September 25, 2001. Accepted (revised) November 14, 2001     

Application of artificial neural network to simultaneous potentiometric determination of silver(I), mercury(II) and copper(II) ions by an unmodified carbon paste electrode

The response characteristics and selectivity coefficients of an unmodified carbon paste electrode (CPEs) towards Ag⁺, Cu²⁺ and Hg²⁺ were evaluated. The electrode was used as an indicator electrode for the simultaneous determination of the three metal ions in their mixtures via potentiometric titration with a standard thiocyanate solution. A three-layered feed-forward artificial neural network (ANN) trained by back-propagation learning algorithm was used to model the complex non-linear relationship between the concentration of silver, copper and mercury in their different mixtures and the potential of solution at different volumes of the added titrant. The network architecture and parameters were optimized to give low prediction errors. The optimized networks were able to precisely predict the concentrations of the three cations in synthetic mixtures.     

Densities, Viscosities, and Excess Gibbs Energy of Activation for Viscous Flow, for Binary Mixtures of Dimethyl Phthalate (DMP) with 1-Pentanol, 1-Butanol, and 1-Propanol at Two Temperatures

Summary. Density (ρ) and viscosity (η) values of the binary mixtures of DMP + 1-pentanol, 1-butanol, and 1-propanol over the entire range of mole fraction at 298.15 and 303.15 K were measured in atmospheric pressure. The excess molar volume (V ^E), viscosity deviations (Δη), and excess Gibbs energy of activation for viscous flow (G^*E) were calculated from the experimental measurements. These results were fitted to Redlich–Kister polynomial equation to estimate the binary interaction parameters. The viscosity data were correlated with equations of McAllister. The calculated functions have been used to explain the intermolecular interaction between the mixing components.     

Some Results on Best Coapproximation in L 1 (S, X)

As a counterpart to best approximation in normed linear spaces, best coapproximation was introduced by Franchetti and Furi. In this paper, we shall show that if M is a separable, coproximinal subspace of X satisfying some additional conditions, then L ¹ (S, M) is coproximinal in L ¹(S, X).