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.     

Synthesis of oxime phosphoranes from reaction between triphenylphosphine and acetylenic esters in the presence of oxime derivatives

A new one-pot, simple and effective procedure is presented for the preparation of O-containing phosphorus ylides by the Michael addition reaction of N-methylpyrrole-2-carbaldehydoxime, pyridin-2-carbaldehydoxime or acetophenonoxime with acetylenic esters.     

Column preconcentration and electrothermal atomic absorption spectrometric determination of rhodium in some food and standard samples

In the present work, an electrothermal atomic absorption spectrometric method has been developed for the determination of ultra‐trace amounts of rhodium after adsorption of its 2‐(5‐bromo‐2‐pyridylazo)‐5‐diethylaminophenol/tetraphenylborate ion associated complex at the surface of alumina. Several factors affecting the extraction efficiency such as the pH, type of eluent, sample and eluent flow rates, sorption capacity of alumina and sample volume were investigated and optimized. The relative standard deviation for eight measurements of 0.1 ng/mL of rhodium was ±6.3%. In this method, the detection limit was 0.003 ng/mL in the original solution. The sorption capacity of alumina and the linear range for Rh(III) were evaluated as 0.8 mg/g and 0.015–0.45 ng/mL in the original solution, respectively. The proposed method was successfully applied for the extraction and determination of rhodium content in some food and standard samples with high recovery values.     

Modified carbon nanotubes as a sorbent for solid-phase extraction of gold,and its determination by graphite furnace atomic absorption spectrometry

A simple, sensitive and accurate method was developed for solid-phase extraction and preconcentration of trace levels of gold in various samples. It is based on the adsorption of gold on modified oxidized multi-walled carbon nanotubes prior to its determination by graphite furnace atomic absorption spectrometry. The type and volume of eluent solution, sample pH value, flow rates of sample and eluent, sorption capacity and breakthrough volume were optimized. Under these conditions, the method showed linearity in the range of 0.2–6.0 ng L⁻¹ with coefficients of determination of >0.99 in the sample. The relative standard deviation for seven replicate determinations of gold (at a level of 0.6 ng L⁻¹) is ±3.8 %, the detection limit is 31 pg L⁻¹ (in the initial solution and at an S/N ratio of 3; for n = 8), and the enrichment factor is 200. The sorption capacity of the modified MWCNTs for gold(III) is 4.15 mg g⁻¹. The procedure was successfully applied to the determination of gold in (spiked) water samples, human hair, human urine and standard reference material with recoveries ranging from 97.0 to 104.2 %.

A sorbent based on modified carbon nanotubes was prepared and used to extract gold ion from various samples prior to its determination by graphite furnace atomic absorption spectrometry

     

Novel (4-oxothiazolidine-2-ylidene)benzamide derivatives: synthesis,characterization and crystal structures

Research on Chemical Intermediates - A convenient, one-pot, multicomponent synthesis of new (4-oxothiazolidine-2-ylidene)benzamide derivatives by unsymmetrical thioureas, various amines and methyl...     

Oscillation criteria for higher‐order nonlinear dynamic equations with Laplacians and a deviating argument on time scales

In this paper, we study the n th‐order nonlinear dynamic equation with Laplacians and a deviating argument on an above‐unbounded time scale, where n ?2, New oscillation criteria are established for the cases when n is even and odd and when α  > γ ,α  = γ , and α  < γ , respectively, with α  = α ₁?α _{n  ? 1}. Copyright © 2017 John Wiley & Sons, Ltd.     

Forced oscillation of second order differential equations with mixed nonlinearities

This article is concerned with the oscillation of the forced second order differential equation with mixed nonlinearities a(t) x ′ (t) γ′ + p 0 (t) x γ (g 0 (t)) + n i =1 p i (t) | x (g i (t)) | α i sgn x (g i (t)) = e(t), where γ is a quotient of odd positive integers, α i > 0, i = 1, 2, ··· , n, a, e, and p i ∈ C ([0, ∞ ) , R), a (t) > 0, gi : R → R are positive continuous functions on R with lim t →∞ g i (t) = ∞ , i = 0, 1, ··· , n. Our results generalize and improve the results in a recent article by Sun and Wong [29].     

Exact solutions for free flexural vibration of Lévy-type rectangular thick plates via third-order shear deformation plate theory

In this paper, exact closed-form solutions in explicit forms are presented for transverse vibration analysis of rectangular thick plates having two opposite edges hard simply supported (i.e., Lévy-type rectangular plates) based on the Reddy’s third-order shear deformation plate theory. Two other edges may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. Hamilton’s principle is used to derive the equations of motion and natural boundary conditions of the plate. Several comparison studies with analytical and numerical techniques reported in literature are carried out to demonstrate accuracy of the present new formulation. Comprehensive benchmark results for natural frequencies of rectangular plates with different combinations of boundary conditions are tabulated in dimensionless form for various values of aspect ratios and thickness to length ratios. A set of three-dimensional (3-D) vibration mode shapes along with their corresponding contour plots are plotted by using exact transverse displacements of Lévy-type rectangular Reddy plates. Due to the inherent features of the present exact closed-form solution, the present findings will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future.     

Projectively equivariant quantization and symbol on supercircle S1∣3

Czechoslovak Mathematical Journal - Let $${{\cal D}_{\lambda ,\mu }}$$ be the space of linear differential operators on weighted densities from $${{\cal F}_\lambda }$$ to $${{\cal F}_\mu }$$ as...