On the Eigenvalues and Eigenvectors of a Lorentzian Rotation Matrix by Using Split Quaternions

In this paper, we examine eigenvalue problem of a rotation matrix in Minkowski 3 space by using split quaternions. We express the eigenvalues and the eigenvectors of a rotation matrix in term of the coefficients of the corresponding unit timelike split quaternion. We give the characterizations of eigenvalues (complex or real) of a rotation matrix in Minkowski 3 space according to only first component of the corresponding quaternion. Moreover, we find that the casual characters of rotation axis depend only on first component of the corresponding quaternion. Finally, we give the way to generate an orthogonal basis for ${\mathbb{E}^{3}_{1}}$ by using eigenvectors of a rotation matrix.     

Multiscale expansions in discrete world

In this paper, we show the attainability of KdV equation from some types of nonlinear Schrödinger equation by using multiscale expansions discretely. The power of this manageable method is confirmed by applying it to two selected nonlinear Schrödinger evolution equations. This approach can also be applied to other nonlinear discrete evolution equations. All the computations have been made with Maple computer packet program.     

FT-IR spectra, vibrational assignments, and density functional calculations of imidazo[1,2-a]pyridine molecule and its Zn(II) halide complexes

The geometry, frequency, and intensity of the vibrational bands of imidazo[1,2-a]pyridine (which is abbreviated as impy) were obtained by the density functional theory (DFT) calculations with BLYP, B3LYP, and B3PW91 functionals and 6-31G(d) basis set. The optimized geometric bond lengths and bond angles are in good agreement with the available X-ray data. The infrared spectrum of imidazo[1,2-a]pyridine was computed by the DFT method in order to reproduce the vibrational wavenumbers and intensities with an accuracy, which allows reliable vibrational assignments. Total energy distribution and isotopic shifts have been calculated in order to help for the perfect assignment of the vibrational modes. The zinc halide complexes Zn(impy)₂X₂ [X = Cl, Br, and I] have also been synthesized. The compounds were characterized using the elemental analysis, FT-IR spectra, and quantum chemical calculations. The geometry optimization of Zn(impy)₂X₂ yields distorted tetrahedral environment around Zn ion.     

Simulation and hybrid fuzzy-PID control for positioning of a hydraulic system

Accuracy and precision of position control of hydraulic systems are key parameters for engineering applications in order to set more economical and quality systems. In this context, this paper presents modeling and position control of a hydraulic actuation system consisting of an asymmetric hydraulic cylinder driven by a four way, three position proportional valve. In this system model, the bulk modulus is considered as a variable. In addition, the Hybrid Fuzzy-PID Controller with Coupled Rules (HFPIDCR) is proposed for position control of the hydraulic system and its performance is tested by simulation studies. The novel aspect of this controller is to combine fuzzy logic and PID controllers in terms of a switching condition. Simulation results of the HFPIDCR based controller are compared with the results of classical PID, Fuzzy Logic Controller (FLC), and Hybrid Fuzzy-PID controller (HFPID). As a result, it is demonstrated that Hybrid Fuzzy PID Controller with Coupled Rules is more effective than other controllers.     

Metal-Containing Phthalocyanines Substituted with One Branched Bulky Moiety and Six Alkylthio Groups

Summary.  Unsymmetrically substituted metal-phthalocyanines composed of three hexylthio groups and one 1-chloro-3,4-dicyano-6-[2-(2-pyridylmethylamino)phenylthio]benzene moiety was prepared by cyclization of the reactants in the presence of the anhydrous metal salts Zn(CH₃COO)₂, NiCl₂, and CoCl₂. The new unsymmetric phthalocyanines are very soluble in common organic solvents. The compounds were characterised by their elemental analyses, IR, ¹H NMR, MS and UV/Vis spectra. Corresponding author. E-mail: bayir@itu.edu.tr Received November 27, 2002; accepted (revised) December 2, 2002 Published online May 2, 2003     

Thermoelectrical and optical properties of double wall carbon nanotubes:polyaniline containing boron n‐type organic semiconductors

The electrical conductivity, thermoelectrical, and optical properties of the polyaniline containing boron/double wall carbon nanotubes (CNTs) composites have been investigated. The electrical conductivities of the composites prepared with 1%, 5%, and 8% CNT concentrations at 300 K were found to be 5.31 × 10^?6, 2.72 × 10^?4, and 1.12 × 10^?3 (S/cm), respectively. The thermoelectrical results indicate that all the samples exhibit n‐type electrical conductivity. The optical band gaps of the samples were found to be 3.71 eV for 0% DWNT, 3.32 eV for 1% DWNT, 3.15 eV for 5% DWNT, and 3.12 eV for 8% DWNT. The obtained results suggest that the electrical conductivity of PANI‐B polymer is improved by DWNT doping. Copyright © 2008 John Wiley & Sons, Ltd.     

Selective formation of spiro dihydrofurans from one-pot reaction of dimedone with BrCN and aldehydes in the presence of Et3N

Reaction of 5,5-dimethylcyclohexane-1,3-dione (dimedone), aldehydes and cyanogen bromide in the presence of triethylamine leads to the selective formation of spiro dihydrofurans in moderate to good yields at room temperature.     

Precision of a dual energy X-ray absorptiometry device

The standard method to diagnose and follow-up osteoporosis is the measurement of bone mineral density (BMD) using dual X-ray absorptiometry (DEXA). Manufacturers' manuals of DEXA devices state the intrascanner coefficient of variance is less than 0.01 g/cm². The aim of this study was to evaluate the in vivo coefficient of variance of a Lunar DPX scanner in male and female healthy adult subjects. Average BMD for females and males were 1.170±0.091 g/cm² and 1.272±0.115 g/cm², respectively. Monthly phantom measurements provided and controlled by the manufacturer were 1.243±0.008 g/cm² (range 1.222 to 1.257) and the coefficient of variance was 0.006. It is concluded that the in vivo coefficient of variance of DEXA devices can slightly be higher than that proposed by the manufacturer. This revised version was published online in August 2006 with corrections to the Cover Date.     

Voltammetry of Benzo[a]pyrene in Aqueous and Nonaqueous Media: Adsorptive Stripping Voltammetric Determination at Pencil Graphite Electrode

A detailed study of the electrochemical oxidation of Benzo[a]pyrene (BaP) at the glassy carbon and pencil graphite electrodes was carried out in aqueous and nonaqueous media. Using square‐wave stripping mode, the compound yielded a well‐defined voltammetric response at pencil graphite electrode in acetate buffer, pH 4.8 at +1.13 V (vs. Ag/AgCl) (a preconcentration step being carried out at a fixed potential of +0.70 V for 180 s). The process could be used to determine BaP concentrations in the range 0.25–1.25 μM, with a detection limit of 0.027 μM (6.82 μg L^?1). The applicability to assay of spiked human urine samples was also illustrated.