Highly Selective and Sensitive Tin(II) Membrane Electrode Based on a New Synthesized Schiff's Base

Studies on complex formation of tris(3‐(2‐hydroxybenzophenone)propyl)amine (THPA) with a number of metal ions in acetonitrile solution revealed the occurrence of a selective 1 : 1 complexation of the proposed ligand with Sn²⁺ ion. Consequently, THPA was used as a suitable neutral ionophore for the preparation of a polymeric membrane‐selective electrode. The electrode exhibits a Nernstian behavior with a slope of 29.4±0.3 mV per decade and a detection limit of 2.0×10^?7 M. It also showed a good selectivity for Sn²⁺ ions in comparison with some of group A and B metal ions over a wide concentration range of 5.0×10^?7–1.0×10^?1 M. Improved selectivity was achieved compared to the best selectivity recently reported by other authors for tin(II). The electrode was successfully applied to the determination of Sn²⁺ ion in waste water and various canned products.     

The construction of operational matrix of fractional derivatives using B-spline functions

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper.     

Ultrasound-promoted an efficient method for one-pot synthesis of 2-amino-4,6-diphenylnicotinonitriles in water: a rapid procedure without catalyst

A green and convenient approach to the synthesis of 2-amino-4,6-diphenylnicotinonitriles via four-component reaction of malononitrile, aromatic aldehydes, acetophenone derivatives and ammonium acetate in water under ultrasound irradiation is described. The combinatorial synthesis was achieved for this methodology with applying ultrasound irradiation while making use of water as green solvent. In comparison to conventional methods, experimental simplicity, good functional group tolerance, excellent yields, short routine, and selectivity without the need for a transition metal or base catalyst are prominent features of this sonocatalyzed procedure.     

A GENERALIZED SEMICONJUGACY IN DIFFERENCE EQUATIONS＊

Difference equations arise in many fields.This article is concerned to generalization of semiconjugacy in difference equations.In fact,H.Sedaghat in [7] investigated the semiconjugacy in difference equ...     

The numerical solution of a nonlinear system of second-order boundary value problems using the sinc-collocation method

The sinc-collocation method is presented for solving a nonlinear system of second-order boundary value problems. Some properties of the sinc-collocation method required for our subsequent development are given and are utilized to reduce the computation of solution of the system of second-order boundary value problems to some algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the technique and a comparison is made with the existing results. The method is easy to implement and yields very accurate results.     

Solution of a semilinear parabolic equation with an unknown control function using the decomposition procedure of Adomian

The investigation of nonclassical parabolic initial‐boundary value problems, which involve an integral over the spatial domain of a function of the desired solution, is of considerable concern. In this article a parabolic partial differential equation subject to energy overspecification is studied. This problem is appeared in modeling of many physical phenomena. The Adomian decomposition method, which is an efficient method for solving various class of problems, is employed for solving this model. This method provides an analytical solution in terms of an infinite convergent power series. Some examples are reported to support the simplicity of the decomposition procedure of Adomian. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

Implicit Solution of a Two-Dimensional Parabolic Inverse Problem with Temperature Overspecification

Three different implicit finite difference schemes for solving the two-dimensional parabolic inverse problem with temperature overspecification are considered. These schemes are developed for indentifying the control parameter which produces, at any given time, a desired temperature distribution at a given point in the spatial domain. The numerical methods discussed, are based on the second-order (5,1) Backward Time Centered Space (BTCS) implicit formula, and the second-order (5,5) Crank-Nicolson implicit finite difference formula and the fourth-order (9,9) implicit scheme. These finite difference schemes are unconditionally stable. The (9,9) implicit formula takes a huge amount of CPU time, but its fourth-order accuracy is significant. The results of a numerical experiment are presented, and the accuracy and central processor (CPU) times needed for each of the methods are discussed and compared. The implicit finite difference schemes use more central processor times than the explicit finite difference techniques, but they are stable for every diffusion number.     

Ultrasound mediated efficient ring opening of epoxides by in situ generated dithiocarbamates in green reaction media

Ultrasound accelerated a safe, clean and environmentally benign one-pot, three-component synthesis of 2-hydroxy dithiocarbamate, from amine, carbon disulfide and epoxide in good to excellent yields and short reaction time with excellent chemo-, regio-, and stereoselectivities in green reaction media (water, deep eutectic solvent [DES] and polyethylene glycol [PEG]). The one-pot, three-component condensation of primary and secondary amine with carbon disulfide and epoxides under ultrasonic irradiation was developed as a green and fast protocol for the rapid high-yielding preparation of 2-hydroxy dithiocarbamate in green reaction media without organic solvent and tedious workup.     

Multigrid solution of high order discretisation for three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind

In this paper, we propose two compact finite difference approximations for three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind. In these methods there is no need to define special formulas near the boundaries and boundary conditions are incorporated with these techniques. The unknown solution and its second derivatives are carried as unknowns at grid points. We derive second-order and fourth-order approximations on a 27 point compact stencil. Classical iteration methods such as Gauss–Seidel and SOR for solving the linear system arising from the second-order and fourth-order discretisation suffer from slow convergence. In order to overcome this problem we use multigrid method which exhibit grid-independent convergence and solve the linear system of equations in small amount of computer time. The fourth-order finite difference approximations are used to solve several test problems and produce high accurate numerical solutions.