Explicit Formulas Associated with Some Families of Generalized Bernoulli and Euler Polynomials

In this paper, we propose and derive several new explicit formulas of the generalized Bernoulli and Euler polynomials in terms of the generalized Stirling numbers of the second kind. A study of some families of the modified generalized Euler polynomials yields an interesting algorithm for calculating the generalized Euler polynomials.     

Numerical Solution for a Variable-Order Fractional Nonlinear Cable Equation via Chebyshev Cardinal Functions

In this paper, a variable-order fractional derivative nonlinear cable equation is considered. It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of class of fractional partial differential equation with variable coefficient of fractional differential equation in various continues functions of spatial and time orders. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. Finally, illustrative examples are included to demonstrate the validity and applicability of the presented technique.     

Preparation of Nano Silica Supported Sodium Hydrogen Sulfate: As an Efficient Catalyst for the Trimethyl,Triethyl and t‐Butyldimethyl Silylations of Aliphatic and Aromatic Alcohols in Solution and under Solvent‐free Conditions

Nano silica supported sodium hydrogen sulfate has been prepared by mixing NaHSO₄ with activated Nano silicagel. We wish to report a new method for the synthesis of trimethyl (TMS), triethyl (TES) and t‐butyldimethyl silyl (TBS) ethers from benzylic, allylic, propargylic alcohols, phenols, naphtholes and some of phenolic drugs in the solution and under solvent‐free conditions.     

Three-component synthesis of new unsymmetrical oxindoles via Friedel-Crafts type reaction

The synthesis of 2-(3-(4-(dimethylamino)phenyl)-2-oxoindolin-3-yl)-1H-indene-1,3(2H)-diones as new unsymmetrical oxindoles via a Friedel-Crafts type three-component reaction of 1,3-indandion, N,N-dimethylaniline and isatins in ethanol in the presence of LiClO₄ is reported.     

MgO Nanoparticles as a Recyclable Heterogeneous Catalyst for the Synthesis of Polyhydroquinoline Derivatives under Solvent Free Conditions

Magnesium oxide nanopartticels in average size between 35–120 nm were prepared by sonochemistry method. Synthesis of polyhydroquinoline derivatives using MgO nanoparticles from the reaction of dimedone, benzaldehyde, ethyl acetoacetate and ammonium acetate under solvent‐free conditions is reported. Easy handling, reusability, thermal stability and non‐toxicity of the catalyst make the present protocol as an eco‐friendly and economically acceptable method for synthesis of these heterocycles.     

Two new acridone alkaloids from Glycosmis macrantha

Extraction and chromatographic separation of the extracts of dried stem barks of Glycosmis macrantha lead to isolation of two new acridone alkaloids, macranthanine and 7-hydroxynoracronycine, and a known acridone, atalaphyllidine. The structures of these alkaloids were determined by detailed spectral analysis and also by comparison with reported data.     

Isocyanide‐Based Multicomponent Reaction: One‐Pot Synthesis of New Derivatives of Iminofuranone

The one‐pot multicomponent reaction of alkyl isocyanide, alkylidene‐substituted Meldrum's acid, and arylcarboxylic acids affords new derivatives of iminofuranone in fair yields. The structure of the products was deduced from their spectroscopic data. Two equivalents of the respective isocyanides participate in this reaction.     

Soulamarin, a new coumarin from stem bark of Calophyllum soulattri

The extracts of the stem bark of Calophyllum soulattri gave a new pyranocoumarin, soulamarin (1), together with five other xanthones caloxanthone B (2), caloxanthone C (3), macluraxanthone (4), trapezifolixanthone (5) and brasixanthone B (6) one common triterpene, friedelin (7), and the steroidal triterpene stigmasterol (8). The structures of these compounds were established based on spectral evidence (1D and 2D NMR).     

Use of Reaction between Melamine and Bioxalate Ions for Monitoring Melamine Content of Petrochemical Wastewater

This study describes a turbidimetric technique for determination of melamine in wastewater of petrochemical companies. A single reagent (bioxalate ions) is used and an insoluble ion‐pair (melamine:bioxalate 1:3) produced. The reproducibility of the method is excellent and relative standard deviation for six repeated experiments is 1.5%. An interferences study was carried out, and it was found that the common species occurring in wastewater has no interference effect on the determination of melamine. The interference effect of Al³⁺ was eliminated by its precipitation as Al(OH)₃ at pH 7. Finally this method was successfully used in the determination of melamine content of Urmia Petrochemical Company, a local melamine producer.     

ESR and optical study of [Cl−2] centre in BaClF crystal

The magnetic and optical properties of the [Cl^?₂] centre in BaClF crystal created by X-irradiation at 78 K are described. Although a slightly deviation from the axial symmetry is observed, the main experimental results can be explained on the basis of this approximation.