High-valent [Sn(Br8TPP)(OTf)2] as a highly efficient and reusable catalyst for selective methoxymethylation of alcohols and phenols: The effect of substituted bromines on the catalytic activity

High-valent tin(IV)octabromotetraphenylporphyrinato trifluoromethanesulfonate, [Sn^IV(Br₈TPP)(OTf)₂], was used for selective methoxymethylation of alcohols and phenols with formaldehyde dimethyl acetal (FDMA) at room temperature. Different primary, secondary and tertiary alcohols as well as phenols were converted to their corresponding methoxymethyl ethers with FMDA in the presence of an electron deficient tin(IV) porphyrin. The catalyst was reused several times without significant loss of its activity.     

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.     

A numerical approach for solving weakly singular partial integro‐differential equations via two‐dimensional‐orthonormal Bernstein polynomials with the convergence analysis

In this paper, we develop an efficient matrix method based on two‐dimensional orthonormal Bernstein polynomials (2D‐OBPs) to provide approximate solution of linear and nonlinear weakly singular partial integro‐differential equations (PIDEs). First, we approximate all functions involved in the considerable problem via 2D‐OBPs. Then, by using the operational matrices of integration, differentiation, and product, the solution of Volterra singular PIDEs is transformed to the solution of a linear or nonlinear system of algebraic equations which can be solved via some suitable numerical methods. With a small number of bases, we can find a reasonable approximate solution. Moreover, we establish some useful theorems for discussing convergence analysis and obtaining an error estimate associated with the proposed method. Finally, we solve some illustrative examples by employing the presented method to show the validity, efficiency, high accuracy, and applicability of the proposed technique.     

Fractional‐order orthogonal Bernstein polynomials for numerical solution of nonlinear fractional partial Volterra integro‐differential equations

In this paper, a new two‐dimensional fractional polynomials based on the orthonormal Bernstein polynomials has been introduced to provide an approximate solution of nonlinear fractional partial Volterra integro‐differential equations. For this aim, the fractional‐order orthogonal Bernstein polynomials (FOBPs) are constructed, and its operational matrices of integration, fractional‐order integration, and derivative in the Caputo sense and product operational matrix are derived. These operational matrices are utilized to reduce the under study problem to a nonlinear system of algebraic equations. Using the approximation of FOBPs, the convergence analysis and error estimate associated to the proposed problem have been investigated. Finally, several examples are included to clarify the validity, efficiency, and applicability of the proposed technique via FOBPs approximation.     

Some Properties On Isoclinism in n-Lie Algebras

The concept of n-Lie algebra were introduced by Filippov in 1987. One notes that not all properties of Lie algebras can be carried over to n-Lie algebras, as Williams showed in 2009. In the present article, among other results it is shown that the notions of isoclinism and isomorphism for two finite dimensional n-Lie algebras of the same dimension are equivalent. This was already done for ordinary Lie algebras by Moneyhun in 1994.     

A new model for automatic normalization of multitemporal satellite images using Artificial Neural Network and mathematical methods

Relative Radiometric Normalization is often required in remote sensing image analyses particularly in the land cover change detection process. Normalization process minimizes the radiometric differences between two images caused by inequalities in the acquisition conditions rather than changes in surface reflectance. A wide range of RRN methods have been developed to adjust linear models. This paper proposes an automated Relative Radiometric Normalization (RRN) method to adjust a non-linear model based on an Artificial Neural Network (ANN) and unchanged pixels. The proposed method includes the following stages: (1) automatic detection of unchanged pixels based on a new idea that uses CVA (Change Vector Análysis) method, PCA (Principal Component Analysis) transformation and K-means clustering technique, (2) evaluation of different architectures of perceptron neural networks to find the best architecture for this specific task and (3) use of the aforementioned network for normalizing the subject image. The method has been implemented on two images taken by the TM sensor. Experimental results confirm the effectiveness of the presented technique in the automatic detection of unchanged pixels and minimizing imaging condition effects (i.e., atmosphere and other effective parameters).     

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).