Homothetic Motions at E 4 with Bicomplex Numbers

In this paper, a matrix which is similar to Hamilton operators has been presented to bicomplex numbers in four dimensional Euclidean space E ⁴. We show that if the matrix is obtained from a curve on the Lie group M, then the motion is a homothetic motion. It has been found that the motion defined by a regular curve of order r and derivations curves on the hypersurface M has only one acceleration center of order (r - 1) at every t-instant.     

A novel method for the simultaneous determination of Pb (II), Cd (II) and Zn (II) in environmental water samples

A novel UV-VIS spectrophotometric method was developed in this study by using solid phase extraction procedure for the simultaneous preconcentration, separation and determination of trace levels of Pb (II), Cd (II) and Zn (II) ions in various water samples by using Amberlite N,N-bis(salicylidene)cyclohexanediamine (SCHD) resin. This study presents the results of experimental procedures carried out like the adsorption of analytes to the resin, influences of some analytical parameters that effect the recovery such as pH, sample volume, sample flow rate, eluent type and concentration, eluent volume, eluent flow rate and the effects of alkaline metals, earth alkaline metals and some other transition metals. The analytes in the samples with the adjusted pH range of 4–7 were adsorbed on XAD-4-SCHD resin and eluted by using 1.0 mol L^?1 nitric acid. The amounts of ions were determined by using UV-VIS spectrometer. The limits of detection were 0.03, 0.07 and 0.05 µg mL^?1 for Pb (II), Cd (II) and Zn (II), respectively. The accuracy of the method was assured by the analysis of the certified standard water sample NW-TMDA-70.2 and the observed recoveries were above 93%. Different environmental water samples that contain trace amounts of Pb (II), Cd (II) and Zn (II) were analysed by using the method developed in this study. Same samples were also analysed by ICP-MS for comparison and almost the similar results were observed. The method developed in this study was successfully applied to the various environmental water samples to determine the trace levels of Pb (II), Cd (II) and Zn (II) ions.     

Poly(ethylene glycol) as solvent for transition metal mediated living radical polymerisation

The use of poly(ethylene glycol)(PEG) with low molecular weights as a novel solvent for the transition metal mediated radical polymerisation of methyl methacrylate and styrene is reported. The utilisation of PEG leads to polymerisation kinetics that differ from those observed with more traditional organic solvents. Moreover, the amount of residual copper catalyst in the product is greatly reduced by precipitation of the polymer in ethanol.     

The channeled stopping powers of Boron ions and range calculations in Si

An analytical fitting expression is obtained for the channeled stopping power of B ions in crystalline silicon. Ions incident in the Si 〈100〉 direction at energies from 50 keV/amu to 900 keV/amu are considered. The mean projected ranges of ions have been determined within the framework of the transport theory formalism where the fitting relation obtained for the stopping power was used. For this purpose, a first order ordinary differential equation including second order stopping coefficients is solved numerically by usingFehlberg fourth-fifth order Runge-Kutta method. By using the results for the channeled ion ranges, a transformation relation is proposed for the conversion of channeled/random ion ranges for the ion target system under consideration. The obtained results are compared with widely used standard programs such as Crystal-TRIM, SRIM and PRAL and our program applied to crystalline targets is in good agreement with Crystal-TRIM.