A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

Multivariate optimization of the hollow fiber-based liquid phase microextraction of lead in human blood and urine samples using graphite furnace atomic absorption spectrometry

The present study developed a liquid-phase microextraction based on hollow fiber coupled with graphite furnace atomic absorption spectrometry for the effective extraction and quantitation of lead from urine and blood samples. A multivariate design was used for the optimization of the experimental conditions to ensure high extraction efficiency. Six factors (solvent type, chelating agent, time extraction, temperature, donor phase pH, and acceptor phase pH) were obtained by screening eleven factors of the Plackett–Burman design; these were optimized using the central composite design of response surface methodology. The optimum conditions of donor phase pH, acceptor phase pH, temperature, and extraction time were 5, 9.5, 40 °C, and 120 min, respectively. In addition, oleic acid containing dicyclohexyl-18-krone-6 was used for the membrane phase. Under optimal conditions, the enrichment factor, limit of detection, and limit of quantification were obtained in the ranges of 21.3–18.7, 0.001–0.002 ng mL^?1, and 0.008–0.01 ng mL^?1, respectively, in urine and blood samples. The linearity of the calibration curve was established for the concentration of Pb in the range of 1–50 ng mL^?1 (r²?=?0.9983). Finally, the performance of the developed method was evaluated for the determination of lead in urine and blood samples, and satisfactory results were obtained (RSDs <?10% with recovery >?95).     

A NONLINEAR MICROBEAM MODEL BASED ON STRAIN GRADIENT ELASTICITY THEORY

A micro scale nonlinear beam model based on strain gradient elasticity is developed.Governing equations of motion and boundary conditions are obtained in a variational framework.As an example,the nonlinear vibration of microbeams is analyzed.In a beam having a thickness to length parameter ratio close to unity,the strain gradient effect on increasing the natural frequency is predominant.By increasing the beam thickness,this effect decreases and geometric nonlinearity plays the main role on increasing the natural frequency.For some specific ratios,both geometric nonlinearity and size effects have a significant role on increasing the natural frequency.     

Four‐Component Cyclocondensation of Aminodiazines,Glyoxal, Formaldehyde,and Methanol to Imidazolidines

Four‐component reaction of aminodiazines (2‐aminopyrimidine and 2‐aminopyrazine), glyoxal, formaldehyde, and methanol yields trans‐4,5‐dimetoxy‐1,3‐bis(2‐pyrimidinyl)imidazolidine (5a) and trans‐4,5‐dimetoxy‐1,3‐bis(2‐pyrazinyl)imidazolidine (5b), respectively. Changing methanol to acetonitrile leads to the formation of the corresponding 1,3‐bis(2‐pyrimidinyl) and‐1,3‐bis(2‐pyrazinyl)‐ derivatives of trans‐4,5‐dihydroxyimidazolidine (6). Details of the proposed mechanism are discussed.     

Lithium-ion mobility in layered oxides Li2Ca1.5Nb3O10,Li2Ca1.5TaNb2O10 and Li2Ca1.5Ta2NbO10,enhanced by supercell formation

The formation of a supercell and its impact on lithium-ion conductivity have been studied through syn-thesis of three layered oxides,Li2Ca1.5Nb3O10,Li2Ca1.5TaNb...