Convergence of a numerical scheme for SPDEs with correlated noise and global Lipschitz coefficients

The aim of this paper is to investigate the pathwise numerical solution of semilinear parabolic stochastic partial differential equations (SPDEs) with colored noise instead of the usual space–time white noise. We estimate the numerical solution in the L^∞ topology by a method that takes advantages of the smoothing effect of the dominant linear operator. We consider the case the covariance operator of the forcing does not necessarily commute with the linear operator of the SPDE because of the fact that the Brownian motions are not necessarily independent. We show convergence of this method, and numerical examples give insight into the reliability of the theoretical study. Copyright © 2015 John Wiley & Sons, Ltd.     

The density and tube energy dependency of cobalt Kα/Kβ in x‐ray fluorescence spectrometryfor thick target measurements

The relative intensity of K_α/K_β for cobalt in thick targets with cobalt mass densities from 0.51 to 22.49% has been measured by the wavelength dispersive x‐ray fluorescence (XRF) spectrometer. The measuring conditions are: tube current ranging from 10 to 60 mA and voltages ranging from 20 to 60 kV. We plotted the K_α/K_β ratio vs Co densities for different tube voltages and currents. Our study shows that the K_α/K_β ratio is below the theoretical value for low Co densities and it increases with increasing Co density. For higher x‐ray energies, the K_α/K_β ratio shows a sharp growth at the special density and then reaches a nearly constant value. However, K_α/K_β ratio is theoretically constant and independent of energy in thin target measurements. The changes of this ratio according to the x‐ray energy and the element density have been studied in thick target measurements. The results provide experimental evidence to suggest that exciting energy and element density can indeed affect the K_α/K_β ratio. Copyright © 2008 John Wiley & Sons, Ltd.     

Oxalic Acid: An Efficient and Cost-Effective Organic Catalyst for the Friedländer Quinoline Synthesis under Solvent-Free Conditions

Summary. Oxalic acid is used as an efficient catalyst in the condensation of 2-aminoaryl ketones with carbonyl compounds leading to the formation of quinolines in excellent yields under solvent-free conditions. This methodology offers significant improvements for the synthesis of quinolines with regard to the yield of products, simplicity in operation, inexpensive reagents, and green aspects by avoiding toxic catalysts and solvents.     

Selective synthesis of 2-aryl-1-arylmethyl-1H-1,3-benzimidazoles in water at ambient temperature

A highly selective synthesis of 2-aryl-1-arylmethyl-1H-1,3-benzimidazoles from the reaction of o-phenylenediamines and aromatic aldehydes in the presence of silica sulfuric acid is reported. The reactions were performed in ethanol or water and the catalyst could be reused for several runs.     

A facile three‐components,one‐pot synthesis of pyrimido[4,5‐d]pyrimidine‐2,5‐dione derivatives under microwave‐assisted conditions

Pyrimido[4,5‐d]pyrimidine‐2,5‐dione derivatives have been synthesized in high yields in a novel, onepot, and efficient process by condensation of 6‐amino‐3‐methyl‐2‐(methylthio)pyrimidin‐4(3H)‐one, aldehydes and urea under microwave‐assisted conditions.     

Combining a Click–Multicomponent Reaction: One-Pot Synthesis of 1,2,3-Triazol-4-ylmethyl 3-Amino-5,10-dihydro-5,10-dioxo-1H-pyrazolo[1,2-b]phthalazine-2-carboxylate Derivatives

(1,2,3-Triazol-4-yl)methyl-3-amino-5,10-dihydro-5,10-dioxo-1H-pyrazolo[1,2-b]phthalazine-2-carboxylate derivatives were synthesized by a four-component, one-pot condensation reaction of benzaldehyde derivatives, an active methylene compound (prop-2-ynyl-2-cyanoacetate), azides, and phthalhydrazide in the presence of Cu(OAc)₂/sodium ascorbate as catalysts and 1-methyl-1H-imidazolium trifluoroacetate ([Hmim]TFA) as an ionic liquid medium in good to excellent yields.     

Silica‐supported terpyridine palladium(II) complex as an efficient and reusable catalyst for Heck and Suzuki cross‐coupling reactions

Silica‐supported terpyridine palladium(II) was prepared and used as an effective and recyclable catalyst in Mizoroki–Heck and Suzuki–Miyaura coupling reactions. The catalyst was very effective for the Mizoroki–Heck reaction of aryl halides with olefins and conversion was in most cases excellent. The catalyst showed good thermal stability (up to 230 °C) and could be recovered and reused for four reaction cycles. The Suzuki coupling of aryl iodides with aryl boronic acids in the presence of the catalyst was also investigated and the reaction proceeded with a short reaction time and excellent conversion. Copyright © 2013 John Wiley & Sons, Ltd.     

Explicit analytical expressions for the critical buckling stresses in a monolayer graphene sheet based on nonlocal elasticity

Explicit expressions are given to study the biaxial buckling of monolayer graphene sheets. Based upon the continuum mechanics, a plate model is adopted in which the small length scale effect is incorporated into the governing equation through the nonlocal elasticity theory of Eringen. By employing the Galerkin method, analytical expressions are derived which allow quick and accurate calculation of the critical buckling loads of monolayer graphene sheets with various boundary conditions from the static deflection under a uniformly distributed load. The effectiveness of the present study is assessed by molecular dynamics simulations as a benchmark of good accuracy.