A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation

A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L² and L^∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin–Bona–Mahony) and BBMB (Benjamin–Bona–Mahony–Burgers) equations and the well-known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695–716, 1998     

On the structure of 3‐acetylamino‐5‐methyl‐1,2,4‐oxadiazole and on the fully degenerate rearrangements (FDR) of its anion: a stimulating comparison between the results of ‘in‐silicon chemistry’ and ‘laboratory chemistry’

An accurate crystal structure determination has provided evidence for a planar conformation for 3‐acetylamino‐5‐methyl‐1,2,4‐oxadiazole ( 5 ), in agreement with quantum‐mechanical calculations in the gas phase. In the crystal, a series of strong intermolecular N7H7^….O9 hydrogen bonds link the amido groups of different molecules, causing the formation of infinite parallel ordered chains. The effect of the DMSO solvent on the energy and charge distribution of compound 5 and on its relevant 5 ^? anion, involved in a fully degenerate rearrangement (FDR), has been deepened by quantum‐mechanical DFT calculations. The calculated energy barrier for the FDR increases in going from in vacuo to DMSO, in agreement with previsions based on the Hughes and Ingold rules concerning the nucleophilic substitution of an anionic reagent (the deprotonated amido group in the side chain) on a neutral substrate (the 1,2,4‐oxadiazole ring). Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis of optical re-modulation by multistage modeling of RSOA

The time-resolved multistage reservoir model well-known for semiconductor optical amplifier (SOA) is extended to analyze the behavior of a bulk homogeneous InP-InGaAsP buried heterostructure reflective semiconductor optical amplifier (RSOA). Parameters for simulation have been extracted from the experimental RSOA characteristics. We have employed the model to explain the steady-state and re-modulation dynamics in the RSOA. Electrical modulation bandwidth and intermodulation distortion in the RSOA have been derived from the model and close agreement is obtained with the reported data. It is found out that the ripples in the upstream output from the RSOA for incomplete modulation erase of downstream modulated data follow Gaussian distribution, which simplifies the calculation of upstream SNR and bit error rate. It is explained in detail that amplitude ripples in the upstream data can be reduced by judicious choice of optical and electrical parameters of the RSOA. In particular, for an average low downstream power level (<−20 dBm) a good downstream modulation erase factor about 89% and 23 dB extinction ratio in the upstream modulated signal can be achieved.     

7‐Chloro‐3,6‐di­methyl‐1H‐indene‐2‐carb­aldehyde

In the crystal structure of C₁₂H₁₁ClO, the (planar) mol­ecules give rise to a parallel packing. A model crystal obtained by semi‐empirical and packing‐energy calculations is consistent with the observed structure.     

Protein-enhanced photoreactivity--dye promoted polymerization of acrylates

The photoinduced polymerization of acrylic monomers using dyes in a protein-restricted medium is reported. We studied dyes of different families as potential polymerization catalysts, exploiting the observation that the photophysical properties of some dyes are altered when bound to biopolymers. The light induced polymerization of acrylic monomers in the presence of bovine serum albumin or gelatin using triphenylmethane and azo dyes proceeded smoothly. Using GE Miser 120 W spotlights as a convenient illumination source, we found polymerization could be achieved in some cases within 60 min of irradiation. The polymerization rates were found to be dependent on the concentrations of the dye and the protein. In the absence of protein or dye polymerization was virtually non-existent. When the reaction mixture was blanketed with nitrogen, polymerization was observed to be faster than that that in air equilibrated samples. We believe these photopolymerizations may proceed via a free-radical pathway. Our results suggest the possible role of some of these dyes as polymerization catalysts, though they had previously seemed inert in fluid solutions.     

Non-thermal effects of microwaves on protease-catalyzed esterification and transesterification

The non-thermal effects of microwave irradiation on enzyme-catalyzed reactions have been evaluated by keeping the reaction temperature constant during irradiation. Subtilisin-catalyzed transesterification and α-chymotrypsin-catalyzed esterification have been carried out in six solvents of differing polarities and at three different temperatures. In all cases, microwave irradiation was found to increase the initial reaction rates by 2.1-4.7 times at all hydration levels. It is also shown that microwave irradiation can be used in conjunction with other strategies (like pH tuning and salt activation) for enhancing initial reaction rates.