Concomitant polymorphs of 1,3‐bis(3‐fluorophenyl)urea

Hydrogen bonding between urea functionalities is a common structural motif employed in crystal‐engineering studies. Crystallization of 1,3‐bis(3‐fluorophenyl)urea, C₁₃H₁₀F₂N₂O, from many solvents yielded concomitant mixtures of at least two polymorphs. In the monoclinic form, one‐dimensional chains of hydrogen‐bonded urea molecules align in an antiparallel orientation, as is typical of many diphenylureas. In the orthorhombic form, one‐dimensional chains of hydrogen‐bonded urea molecules have a parallel orientation rarely observed in symmetrically substituted diphenylureas.     

Distributed optimal control of the viscous Burgers equation via a Legendre pseudo‐spectral approach

This paper presents a computational technique based on the pseudo‐spectral method for the solution of distributed optimal control problem for the viscous Burgers equation. By using pseudo‐spectral method, the problem is converted to a classical optimal control problem governed by a system of ordinary differential equations, which can be solved by well‐developed direct or indirect methods. For solving the resulting optimal control problem, we present an indirect method by deriving and numerically solving the first‐order optimality conditions. Numerical tests involving both unconstrained and constrained control problems are considered. Copyright © 2015 John Wiley & Sons, Ltd.     

A semidefinite programming approach for solving fractional optimal control problems

This paper presents a numerical scheme for solving fractional optimal control. The fractional derivative in this problem is in the Riemann–Liouville sense. The proposed method, based upon the method of moments, converts the fractional optimal control problem to a semidefinite optimization problem; namely, the nonlinear optimal control problem is converted to a convex optimization problem. The Grunwald–Letnikov formula is also used as an approximation for fractional derivative. The solution of fractional optimal control problem is found by solving the semidefinite optimization problem. Finally, numerical examples are presented to show the performance of the method.     

Microwave-assisted expeditious hydrolysis of isobenzofuranone derivatives using silica supported acid under organic solvent-free conditions

Silica sulfuric acid was found to be an efficient, reusable and environment-friendly catalyst for fast hydrolysis of various isobenzofuranone to corresponding 2-ketomethylquinoline derivatives in a high yield under solvent-free using microwave irradiation. As the activator of silica sulfuric acid the wet SiO₂ was chosen. The reactions in conventional conditions were compared with the microwave assisted reactions. This approach can prove beneficial since the recovery of solvents from conventional reaction systems always results in some losses.     

New results in <Emphasis Type="Italic">G</Emphasis>-best approximation in <Emphasis Type="Italic">G</Emphasis>-metric spaces

The purpose of this paper is to introduce and discuss the concepts of G-best approximation and a ₀ -orthogonality in the theory of G-metric spaces. We consider the relationship between these concepts and the dual X and obtain some results on subsets of G-metric spaces similar to normed spaces.     

On-line preconcentration and determination of cobalt by chelating microcolumns and flow injection atomic spectrometry

A simple and sensitive flow injection analysis-atomic absorption spectrometric procedure is described for the determination of cobalt. The method is based upon on-line preconcentration of cobalt on a microcolumn of 2-nitroso-1-naphthol immobilized on surfactant coated alumina. The trapped cobalt is then eluted with ethanol (250 μl) and determined by flame atomic absorption spectrometry. The analytical figures of merit for the determination of cobalt are as follows: detection limit (3 S), 0.02 ng ml⁻¹; precision (RSD), 2.8% for 20 ng ml⁻¹ and 1.7% for 70 ng ml⁻¹ of cobalt; enrichment factor, 125 (using 25 ml of sample). The method has been applied to the determination of cobalt in water samples, vitamin B₁₂ and B-complex ampoules and accuracy was assessed through recovery experiment and independent analysis by furnace AAS.     

Numerical solution of the nonlinear Fredholm integral equations by positive definite functions

A numerical method for solving the nonlinear Fredholom integral equations is presented. The method is based on interpolation by radial basis functions (RBF) to approximate the solution of the Fredholm nonlinear integral equations. Several examples are given and numerical examples are presented to demonstrate the validity and applicability of the method.     

Composite spectral method for solution of the diffusion equation with specification of energy

Many physical subjects are modeled by nonclassical parabolic boundary value problems with nonlocal boundary conditions replacing the classic boundary conditions. In this article, we introduce a new numerical method for solving the one‐dimensional parabolic equation with nonlocal boundary conditions. The approximate proposed method is based upon the composite spectral functions. The properties of composite spectral functions consisting of terms of orthogonal functions are presented and are utilized to reduce the problem to some algebraic equations. The method is easy to implement and yields very accurate result. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

A numerical method for solving the hyperbolic telegraph equation

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this article, we propose a numerical scheme to solve the one‐dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function. The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008