Chitosan‐Supported Ni particles: An Efficient Nanocatalyst for Direct Amination of Phenols

A practical method for the direct amination of phenols using 2,4,6‐trichloro‐1,3,5‐triazine (TCT) as an efficient promotor for the activation of phenols in the presence of an efficient and recyclable heterogeneous catalyst prepared by immobilization of nickel particles on triazole modified chitosan is described. This heterogeneous catalyst has demonstrated a promising activity for the conversion of phenolic compounds to their corresponding amine under mild conditions. Moreover, the obtained catalyst can be reused in five consecutive runs with consistent catalytic activity.     

A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel

The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag–Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional boundary value problem. Based on the convolution formula and generalized discrete Grönwall’s inequality, the numerical scheme for solving this problem is developed and its convergence is proved. Numerical simulations and comparative results show that the suggested technique is efficient and provides satisfactory results.     

C–N cross‐coupling reaction catalysed by efficient and reusable CuO/SiO2 nanoparticles under ligand‐free conditions

Nanometric copper oxide supported on silica has been found to be a highly efficient and reusable catalyst for the C–N cross‐coupling reaction of amines with aryl halides under ligand‐free conditions. Various arylamines with different substituted groups can be synthesized in moderate to good yields. The catalyst can be recycled at least five times without obvious loss in catalytic activity. Copyright © 2014 John Wiley & Sons, Ltd.     

Exact solutions for nonlinear partial differential equations via Exp‐function method

In this article, the Exp‐function method is applied to nonlinear Burgers equation and special fifth‐order partial differential equation. Using this method, we obtain exact solutions for these equations. The method is straightforward and concise, and its applications are promising. This method can be used as an alternative to obtain analytical and approximate solutions of different types of nonlinear differential equations. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Polymerization of 4,4′‐(hexafluoroisopropylidene)‐N,N′‐bis(phthaloyl‐L‐leucine) diacid chloride with aromatic diamines by microwave irradiation

A new facile and rapid polycondensation reaction of 4,4′‐(hexafluoroisopropylidene)‐N,N′‐bis(phthaloyl‐L‐leucine) diacid chloride (1) with several aromatic diamines, including benzidine (2a), 4,4′‐diaminodiphenyl methane (2b), 1,5‐diaminoanthraquinone (2c), 4,4′‐sulfonyldianiline (2d), 3,3′‐diaminobenzophenone (2e), P‐phenylenediamine (2f), 2,6‐diaminopyridine (2g), 4,4′‐diaminobenzophenone (2h), 2,4‐diaminotoluene (2i), and 4,4′‐diaminodiphenylether (2j), was developed with a domestic microwave oven in the presence of a small amount of a polar organic medium such as o‐cresol. The polymerization reactions proceeded rapidly compared to conventional solution polycondensation and finished within 12 min, producing a series of optically active poly(amide‐imide)s with quantitative yields and high inherent viscosities of 0.50–1.93 dL/g. All of the polymers were fully characterized by IR, elemental analyses, and specific rotation. Some structural characterization and physical properties of these optically active poly(amide‐imide)s are reported. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1154–1160, 2000     

Immobilization of copper nanoparticles on WO3 with enhanced catalytic activity for the synthesis of 1,2,3-triazoles

In this study, a heterogeneous catalyst based on copper nanoparticles immobilized on metal oxide, WO₃, was fabricated using an impregnation method as an easy and straightforward nanoparticle synthesis strategy. The successful synthesis of the nanocatalyst was confirmed using various spectroscopic techniques such as X-ray diffraction, scanning electron microscopy, energy dispersive X-ray analysis, and transmission electron microscopy. The catalytic performance of the well-characterized material was evaluated through the azide–alkyne cycloaddition reaction (click reaction) in the aqueous medium. To optimize reaction conditions, different reaction parameters such as nanocatalyst amount, reaction time, temperature, and solvents were studied. Experimental results showed that as-prepared nanocatalyst (Cu/WO₃) could act as an effective and reusable heterogeneous catalyst in water for the synthesis of 1,2,3-triazoles in good-to-excellent yields. In addition, Cu/WO₃ has some advantages such as simple preparation procedure, easy separation, and recyclability for three runs with no remarkable loss of catalytic activity, which is essential from a catalytic application point of view.     

High accurate NRK and MWENO scheme for nonlinear degenerate parabolic PDEs

In this paper, we propose a stable high accurate hybrid scheme based on nonstandard Runge–Kutta (NRK) and modified weighted essentially non-oscillatory (MWENO) techniques for nonlinear degenerate parabolic partial differential equations. The necessary stability condition for the combination of a Runge–Kutta and MWENO scheme is given. The stability condition provides a renormalization function such that mixture of explicit NRK and MWENO scheme is unconditionally stable. Novel scheme recovers the sixth order convergent at points of inflection and prevents the appearance of spurious solutions close to discontinuities. The good performance of this scheme is illustrated through five examples. Numerical results are presented.     

Optimizing multi-item multi-period inventory control system with discounted cash flow and inflation: Two calibrated meta-heuristic algorithms

A mixed binary integer mathematical programming model is developed in this paper for ordering items in multi-item multi-period inventory control systems, in which unit and incremental quantity discounts as well as interest and inflation factors are considered. Although the demand rates are assumed deterministic, they may vary in different periods. The situation considered for the problem at hand is similar to a seasonal inventory control model in which orders and sales happen in a given season. To make the model more realistic, three types of constraints including storage space, budget, and order quantity are simultaneously considered. The goal is to find optimal order quantities of the products so that the net present value of total system cost over a finite planning horizon is minimized. Since the model is NP-hard, a genetic algorithm (GA) is presented to solve the proposed mathematical problem. Further, since no benchmarks can be found in the literature to assess the performance of the proposed algorithm, a branch and bound and a simulated annealing (SA) algorithm are employed to solve the problem as well. In addition, to make the algorithms more effective, the Taguchi method is utilized to tune different parameters of GA and SA algorithms. At the end, some numerical examples are generated to analyze and to statistically and graphically compare the performances of the proposed solving algorithms.