Combined compact difference method for solving the incompressible Navier–Stokes equations

This paper presents a numerical method for solving the two‐dimensional unsteady incompressible Navier–Stokes equations in a vorticity–velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two‐dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourth‐order five‐ to six‐alternating‐stage Runge–Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid‐mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three‐dimensional cases in which full boundary layer transition happens. Copyright © 2011 John Wiley & Sons, Ltd.     

Large graphs with given degree and diameter. II

The following problem arises in the study of interconnection networks: find graphs of given maximum degree and diameter having the maximum number of vertices. Constructions based on a new product of graphs, which enable us to construct graphs of given maximum degree and diameter, having a great number of vertices from smaller ones are given; therefore the best values known before are improved considerably.     

Determination of dihaloacetonitriles and halophenols in chlorinated sea water

The cooling effluents in power stations are chlorinated to avoid excessive biofouling. However, this disinfecting treatment leads to the formation of halogenated by-products, mainly trihalomethanes, haloacetonitriles and halophenols. There is therefore a need for precise and accurate methods that allow trace level determinations of these compounds. Experimental procedures combining liquid-liquid extraction and gas chromatography coupled to mass spectrometry were developed in this study to determine dihaloacetonitriles and halophenols. The extraction step was improved and the performance of both methods evaluated. Precise and accurate determinations were obtained, allowing the measurement of the investigated compounds in chlorinated sea water samples from three French nuclear power stations.     

Investigating the role of c-Jun N-terminal kinases in the proliferation of Werner syndrome fibroblasts using diaminopyridine inhibitors

To develop more potent small molecules with enhanced free radical scavenger properties, a series of N-substituted isatin derivatives was synthesized, and the cytoprotective effect on the apoptosis of PC12 cells induced by H₂O₂ was screened. All these compounds were found to be active, and N-ethyl isatin was found with the most potent activity of 69.7% protective effect on PC12 cells. Structure-activity relationship analyses showed the bioactivity of N-alkyl isatins decline as the increasing of the chain of the alkyl group, furthermore odd-even effect was found in the activity, which is interesting for further investigation.     

H-transfer rates in ion-neutral complexes versus those in intact aliphatic ions

The relative rates of H-transfer between partners in ion-neutral complexes were compared with those in intramolecular rearrangements using results of first differential photoionization mass spectrometry measurements. Complex-mediated H-transfers are inferred to have rates of the same order as those for intramolecular hydrogen rearrangements, suggesting a similar range of motion of the reactive sites in both types of reactions. It is also concluded that at their fastest H-transfers take place between the partners in ion-neutral complexes within at most the time of several rotations of the partners in the complexes. Copyright 1999 John Wiley & Sons, Ltd.