Two Optimal General Classes of Iterative Methods with Eighth-Order

Two new three-step classes of optimal iterative methods to approximate simple roots of nonlinear equations, satisfying the Kung-Traub’s conjecture, are designed. The development of the methods and their convergence analysis are provided joint with a generalization of both processes. In order to check the goodness of the theoretical results, some concrete methods are extracted and numerical and dynamically compared with some known methods.     

A note on solving Cauchy integral equations of the first kind by iterations

The successive approximation method was applied for the first time by N.I. Ioakimidis to solve practical cases of a Cauchy singular integral equation: the airfoil one. In this paper we study a more general case. We prove the convergence of the method in this general case. The proposed method has been tested for two kernels which are particularly important in practice. Finally, some numerical examples illustrate the accuracy of the method.     

On the higher dimension Boussinesq equation with nonclassical condition

This paper deals with the solvability and uniqueness of a higher dimension mixed nonlocal problem for a Boussinesq equation. Galerkin's method was the main used tool for proving the solvability of the given nonlocal problem. Copyright © 2010 John Wiley & Sons, Ltd.     

On the Symmetric H q -Semiclassical Polynomial Sequences of Even Class. Some Examples from the Class Two

In the present work, we deal with the quadratic decomposition of symmetric H _q -semiclassical polynomial sequences of even class. Some examples from class two are settled. We give an integral and discrete measure representations for each of considered symmetric forms.     

On the oscillation of fourth order strongly superlinear and strongly sublinear dynamic equations

We establish some new criteria for the oscillation of fourth order nonlinear dynamic equations on a time scale. We investigate the case of strongly superlinear and the case of strongly sublinear equations subject to various conditions. Some examples are given here to illustrate our main results.     

Solvability of a Mixed Nonlocal Problem for a Nonlinear Singular Viscoelastic Equation

The present paper deals with a nonlinear viscoelastic equation having a dissipation term. With the equation some classical and non classical boundary conditions are combined. Based on some a priori bounds, iteration processes and density arguments, we simultaneously solve the nonlinear and the associated linear problems.     

Synthesis and evaluation of new phosphonated δ-lactam and glutarimide derivatives as angiotensin converting enzyme inhibitors

An efficient synthesis of new γ,δ-insaturated δ-lactam and glutarimide derivatives bearing a phosphonomethyl group from a common allylphosphonate precursor is described. Our approach is based on a two-step procedure involving the preparation of phosphonated-1,5-ketoester and −1,5-diester followed by an amidation–heterocyclization sequence. The first step proceeds via Michael's addition of ethyl acetoacetate and diethyl malonate on an allylphosphonate starting material. The second step consists of a base-promoted intramolecular amidation-cyclization sequence with primary amines, which accounts for the construction of δ-lactams and glutarimide skeletons. We performed the evaluation of angiotensin I-converting enzyme (ACE) inhibition using an in vitro enzyme assay on six new compounds. Five compounds showed potent ACE inhibitory activity, with IC₅₀ values ranging from 0.02 to 0.27 mg/ml. Compared with Captopril, used as a reference drug, two new glutarimide derivatives exhibited higher efficiency ACE inhibition activity.     

High‐energy‐resolution diced spherical quartz analyzers for resonant inelastic X‐ray scattering

A novel diced spherical quartz analyzer for use in resonant inelastic X‐ray scattering (RIXS) is introduced, achieving an unprecedented energy resolution of 10.53 meV at the Ir L₃ absorption edge (11.215 keV). In this work the fabrication process and the characterization of the analyzer are presented, and an example of a RIXS spectrum of magnetic excitations in a Sr₃Ir₂O₇ sample is shown.     

Stability indicating method for famotidine in pharmaceuticals using porous graphitic carbon column

A simple, sensitive and rapid HPLC method was developed and validated for the simultaneous determination of famotidine (FMT) and related impurities in pharmaceuticals. Chromatographic separation was accomplished within 10 min on a porous graphitic carbon (PGC) column using 50:50 v/v ACN-water containing 0.5% pentane sulphonic acid (PSA) as the mobile phase. Separation was achieved with a flow rate of 1 mL/min and a detection wavelength of 265 nm. The calibration curves were linear over a concentration range of 1.5-100 microg/mL. The intra- and interday RSDs (n = 5) for the retention times and peak area were all less than 2%. The method was sensitive with an LOD (S/N = 3) of 0.1 microg/mL for FMT, imp. C and 0.05 microg/mL for imp. 2, A and D. All recoveries were greater than 98%. The method was demonstrated to be precise, accurate and specific with no interference from the tablet ingredients and separation of the drug peak from the peaks of the degradation products (oxidative degradation and acid and base degradation). The results indicated that the proposed method could be used for the determination of FMT in commercial dosage forms and as a stability-indicating assay.