CuO‐CeO2 Nanocomposite: A Highly Efficient Recyclable Catalyst for the Green Synthesis of 1,8‐Dioxooctahydroxanthenes in Water

CuO‐CeO₂ nanocomposite is reported as a highly efficient and recyclable catalyst for the green synthesis of 1,8‐dioxooctahydroxanthenes in water. This catalyst can be recovered by simple filtration and recycled up to 8 consecutive runs without any losing of its efficiency.     

Spectrometric estimation of the content of chlorophyll in plants subjected to anthropogenic action

Optics and Spectroscopy - Spectral methods for determining the content of chlorophyll in vegetation subjected to anthropogenic action are considered. The regularities in the changes in the spectral...     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Analysis of a meshless method for the time fractional diffusion-wave equation

In this paper a numerical technique is proposed for solving the time fractional diffusion-wave equation. We obtain a time discrete scheme based on finite difference formula. Then, we prove that the time discrete scheme is unconditionally stable and convergent using the energy method and the convergence order of the time discrete scheme is \(\mathcal {O}(\tau ^{3-\alpha })\). Firstly, we change the main problem based on Dirichlet boundary condition to a new problem based on Robin boundary condition and then, we consider a semi-discrete scheme with Robin boundary condition and show when \(\beta \rightarrow +\infty \) solution of the main semi-discrete problem with Dirichlet boundary condition is convergent to the solution of the new semi-discrete problem with Robin boundary condition. We consider the new semi-discrete problem with Robin boundary condition and use the meshless Galerkin method to approximate the spatial derivatives. Finally, we obtain an error bound for the new problem. We prove that convergence order of the numerical scheme based on Galekin meshless is \(\mathcal {O}(h)\). In the considered method the appeared integrals are approximated using Gauss Legendre quadrature formula. The main aim of the current paper is to obtain an error estimate for the meshless Galerkin method based on the radial basis functions. Numerical examples confirm the efficiency and accuracy of the proposed scheme.     

Green synthesis of silver nanoparticles using Eucalyptus comadulensis leaves extract and its immobilization on magnetic nanocomposite (GO-Fe3O4/PAA/Ag) as a recoverable catalyst for degradation of organic dyes in water

The magnetically recyclable graphene oxide-Fe₃O₄/polyallylamine (PAA)/Ag nanocatalyst was prepared via a green route using Eucalyptus comadulensis leaves extract as both reducing and stabilizing agent. The catalytic activity of this nanocatalyst was investigated for the reduction reaction of methylene blue and methyl orange in the presence of NaBH₄ in aqueous medium at room temperature. The prepared nanocatalyst was characterized by different methods such as Fourier transformed infrared spectroscopy, X-ray diffraction, scanning electron microscopy–energy dispersive X–ray spectroscopy, thermogravimetric analysis, vibrating sample magnetometer, transmission electron microscopy, and UV–visible spectroscopy. The results show that graphene oxide/PAA/Ag nanocatalyst has good activity and recyclability, and can be reused several times without major loss of activity in the reduction process. The apparent rate constants of the methyl orange (MO) and methylene blue (MB) were calculated to be 0.077 s⁻¹ (3 mg of catalyst) and 0.15 s⁻¹ (2 mg of catalyst), respectively.     

The two-grid interpolating element free Galerkin (TG-IEFG) method for solving Rosenau-regularized long wave (RRLW) equation with error analysis

The two-grid method is a technique to solve the linear system of algebraic equations for reducing the computational cost. In this study, the two-grid procedure has been combined with the EFG method for solving nonlinear partial differential equations. The two-grid FEM has been introduced in various forms. The well-known two-grid FEM is a three-step method that has been proposed by Bajpai and Nataraj (Comput. Math. Appl. 2014;68:2277–2291) that the new proposed scheme is an ecient procedure for solving important nonlinear partial differential equations such as Navier–Stokes equation. By applying shape functions of IMLS approximation in the EFG method, a new technique that is called interpolating EFG (IEFG) can be obtained. In the current investigation, we combine the two-grid algorithm with the IEFG method for solving the nonlinear Rosenau-regularized long-wave (RRLW) equation. In other hand, we demonstrate that solutions of steps 1, 2, and 3 exist and are unique and also we achieve an error estimate for them. Moreover, three test problems in one- and two-dimensional cases are given which support accuracy and efficiency of the proposed scheme.     

High‐order difference scheme for the solution of linear time fractional klein–gordon equations

In this article, we apply a high‐order difference scheme for the solution of some time fractional partial differential equations (PDEs). The time fractional Cattaneo equation and the linear time fractional Klein–Gordon and dissipative Klein–Gordon equations will be investigated. The time fractional derivative which has been described in the Caputo's sense is approximated by a scheme of order , and the space derivative is discretized with a fourth‐order compact procedure. We will prove the solvability of the proposed method by coefficient matrix property and the unconditional stability and ‐convergence with the energy method. Numerical examples demonstrate the theoretical results and the high accuracy of the proposed scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1234–1253, 2014     

Hydrogen incorporation into BN fullerene-like nanostructures: A first-principles study

We performed density functional theory calculations to investigate the possibility of formation of endohedrally H@(BN)_n–fullerene (n: 24, 36, 60) and H@C₆₀ complexes for potential applications in solid-state quantum-computers. Spin-polarized approach within the generalized gradient approximation with the Perdew–Burke–Ernzerhof functional was used for the total energies and structural relaxation calculations. The calculated binding energies show that H atom being incorporated into B₆₀N₆₀ nanocage can form most stable complexes while the B₂₄N₂₄ and C₆₀ nanocages might form unstable complex with positive binding energy. We have also examined the penetration of an H atom into the respective nanocages and the calculated barrier energies indicate that the H atom prefers to penetrate into the B₂₄N₂₄ and B₆₀N₆₀ nanocages with barrier energy of about 0.47 eV (10.84 kcal/mol). Furthermore the binding characteristic is rationalized by analyzing the electronic structures. Our findings reveal that the B₆₀N₆₀ nanocage has fascinating potential application in future solid-state quantum-computers.