Positive integer solutions of the diophantine equation x 2 − L n xy + (−1) n y 2 = ±5 r

In this paper, we consider the equation x ²?L _n x y+(?1) ⁿ y ² = ±5 ^r and determine the values of n for which the equation has positive integer solutions x and y. Moreover, we give all positive integer solutions of the equation x ²?L _n x y+(?1) ⁿ y ² = ±5 ^r when the equation has positive integer solutions.     

Simultaneous determination of amlodipine besylate and rosuvastatin calcium in binary mixtures by voltammetric and chromatographic techniques

Voltammetric and liquid chromatographic (LC) methods have been developed for the simultaneous determination of amlodipine besylate (AML) and rosuvastatin calcium (ROS) for the first time. Detailed electrochemical behavior and simultaneous voltammetric determination of AML and ROS were investigated in detail using glassy carbon electrode (GCE). High-performance liquid chromatography (HPLC) and ultra-performance liquid chromatography (UPLC) were also developed for the comparison. Voltammetric method exhibited linear dynamic responses for the simultaneous assay of AML and ROS in the concentration range between 0.006 and 2.85 μg/mL and between 0.01 and 5.00 μg/mL, with detection limits of 0.001 and 0.003 μg/mL, respectively. On the other hand, LC methods presented a wider linearity range than that of the SWV method between 0.5 and 100 μg/mL with the detection limits of 0.011 and 0.027 μg/mL for AML and 0.034 and 0.042 μg/mL for ROS by UPLC and HPLC techniques, respectively.     

Synthesis,characterization, and reactivity of palladium(II) complexes containing piperidoimidazolin‐2‐ylidene

A series of Pd–N‐heterocyclic carbene (Pd‐NHC) complexes with pyrazine ( 1 ) or pyridine ( 2 ) and NHC ( 3 ) were synthesized and characterized by elemental analysis and spectroscopic methods. In addition, the molecular structure of 3 was determined by X‐ray diffraction studies. The effects of these ligands on catalyst activation and the performance of complexes 1 , 2 , 3 were studied on Suzuki–Miyaura reactions of phenylboronic acid with aryl chlorides. Finally, we demonstrated that complex 1 is very adept at re‐forming the Kumada–Tamao–Corriu cross‐coupling reaction. Copyright © 2013 John Wiley & Sons, Ltd.     

Revealing the Spin-Hamiltonian and Characteristic Parameters of Paramagnetic Centers in Cu2+-Doped Potassium Metabisulfite (K2S2O5) Single Crystal by Electron Paramagnetic Resonance Technique

The present study is mainly related to finding out spin-Hamiltonian parameters of Cu²⁺-doped potassium metabisulfite [K₂S₂O₅] single crystals using electron paramagnetic resonance (EPR) technique which has been applied in the temperature range from 297 to 113 K for single and powder crystals of the title compound. The existence of two complexes and two Cu²⁺ sites for each complex was concluded from the angular variation of the EPR spectra. Having constructed the g and the hyperfine tensors, the spin-Hamiltonian parameters have been obtained for these two complexes. Using these parameters, the covalency parameter (α ²), mixing coefficients (α and β) and Fermi contact term (K) have been calculated.