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     

Regioselective ring opening of epoxides using NH4SCN/silica sulfuric acid： An efficient approach for the synthesis of β-hydroxy thiocyanate under solvent-free conditions

Silica sulfuric acid was developed as a stable and efficient heterogeneous catalyst in organic synthesis. This solid acid catalyzed the regioselective ring opening of epoxides by thiocyanate anion to give thiocyanohydrins as key intermediates in agricultural and pharmaceutical chemistry in high yields under solvent-free conditions.     

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.     

Pd-Cu catalyzed heterocyclization during Sonogashira coupling: synthesis of 3-benzylthiazolo[3,2-a]benzimidazole

The reaction of 2-mercaptopropargyl benzimidazole with various iodobenzenes catalyzed by Pd-Cu leads to the formation of 3-benzylthiazolo[3,2-a]benzimidazoles.     

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.     

Microwave-assisted simple, one-pot, four-component synthesis of 2,4,6-triarylpyrimidines under solvent-free conditions

2,4,6-Triarylpyrimidines are synthesized via a simple, one-pot, four-component reaction between aryl methyl ketones, benzaldehydes, aromatic nitriles, and hydroxylamine under microwave irradiation and solvent-free conditions in good to excellent yields.     

An arc flow-based optimization approach for the two-stage guillotine strip cutting problem

Despite its broad range of industrial applications, the two-stage guillotine restriction has received very scant attention in the strip cutting literature. An integer linear programming model that is based on a special graph structure is devised for this strongly NP-hard problem. In addition to being easy to implement, the empirical study on a large set of instances from the literature and from real industrial world cases shows the efficiency of the proposed method while solving instances with high multiplicity factor.     

Obviating some of the theoretical barriers of data envelopment analysis-discriminant analysis: an application in predicting cluster membership of customers

Data envelopment analysis-discriminant analysis (DEA-DA) has been used for predicting cluster membership of decision-making units (DMUs). One of the possible applications of DEA-DA is in the marketing research area. This paper uses cluster analysis to cluster customers into two clusters: Gold and Lead. Then, to predict cluster membership of new customers, DEA-DA is applied. In DEA-DA, an arbitrary parameter imposing a small gap between two clusters (η) is incorporated. It is shown that different η leads to different prediction accuracy levels since an unsuitable value for η leads to an incorrect classification of DMUs. We show that even the data set with no overlap between two clusters can be misclassified. This paper proposes a new DEA-DA model to tackle this issue. The aim of this paper is to illustrate some computational difficulties in previous DEA-DA approaches and then to propose a new DEA-DA model to overcome the difficulties. A case study demonstrates the efficacy of the proposed model.     

A green multicomponent synthesis of bioactive pyrimido[4, 5-b]quinoline derivatives as antibacterial agents in water catalyzed by RuCl3·xH2O

An efficient, convenient and environmentally benign one-pot multicomponent reaction for the preparation of pyrimido[4,5-b]quinoline derivatives as biologically, pharmacologically and antibacte- rially active products has been developed using RuC13.xH20 as a reusable homogenous catalyst. Use of water as a green solvent, purification of products by non-chromatographic methods, reusability of transition metal homogenous catalyst, saving energy by employing multicomponent reactions, short reaction times and high yields, are some of the advantages of this process.