Compactly supported solutions to stationary degenerate diffusion equations

We consider non-negative solutions of the semilinear elliptic equation in Rn with n?3:

−Δu=a(x)uq+b(x)up,     

Transition from concerted to stepwise processes as a function of leaving group ability: density functional theory and experimental study of lyoxide‐promoted cleavages of phosphorothioate and phosphate triesters in water and methanol

The base‐promoted solvolysis of a series of O,O‐dimethyl O‐aryl and O,O‐dimethyl O‐alkyl phosphorothioates (1) as well as O,O‐dimethyl O‐aryl and O,O‐dimethyl O‐alkyl phosphates (2) was studied computationally by density functional theory methods in methanol and water continuum media to determine the transition between concerted and stepwise processes. In addition, an experimental study was undertaken on the solvolysis of these series in basic methanol and water. The computations indicate that the solvolytic mechanism for series 1 involves lyoxide attack anti to the leaving group in a concerted manner with good leaving groups having pK_a^Lg values < 12.3 in methanol and in a stepwise fashion with the formation of a 5‐coordinate thiophosphorane intermediate when the pK_a^Lg > 12.3. A similar transition from concerted to stepwise mechanism occurs with series 2 in methanol as well as with series 1 and 2 in water, although for the aqueous solvolyses with hydroxide nucleophile, the transitions between concerted and stepwise mechanisms occur with better leaving groups than in the case in methanol. The computational data allow the construction of Brønsted plots of log k₂^?OS versus pK_a^Lg in methanol and water, which are compared with the experimental Brønsted plots determined with these series previously and with new data determined in this work. Both the computational and experimental Brønsted data reveal discontinuities in the plots between substrates bearing O‐aryl and O‐alkyl leaving groups, with the gradients of the plots being far steeper than, and non‐collinear with, the O‐aryl leaving groups for solvolysis of the O‐alkyl‐containing substrates. These discontinuities signify that care should be exercised in interpreting breaks in Brønsted plots in terms of changes in rate‐limiting steps that signify the formation of an intermediate during a solvolytic process. Copyright © 2011 John Wiley & Sons, Ltd.     

Determination of Non-Ionic Surfactants of the Alcohol Polyethoxylate Type by Means of High Temperature Gas Chromatography and Atomic Emission Detection

High temperature gas chromatography (HT-GC) coupled to atomic emission detection (AED) has been applied for the determination of alkyl chain distribution, mole average degree of ethoxylation and weight percent distribution of the corresponding homologues of alcohol ethoxylates without all the actual homologues being available as pure references. Based upon its constant elemental response, the HT-GC-AED system has been evaluated for its applicability to compound independent calibration within the homologous series of the alcohols and alcohol ethoxylates. Discrimination against high molecular weight components by gas chromatography requires conversion to the acetyl or trimethylsilyl derivatives. The latter includes introduction of the hetero atom silicon and thus allows monitoring of the silicon trace. Thus selectivity will be enhanced by excluding detection of compounds which do not react with the derivatization reagent. The method has been validated with the analysis of the technical product Brij 30, consisting of a mixture of alcohol ethoxylates with a vendor-specified mole average degree of ethoxylation of four. The experimental result yields a mole average degree of 4.0 ± 0.1 in the carbon, silicon and oxygen traces.     

Optimal design of a 2 DOF parallel robot

This paper is aimed at presenting a study on the optimization of the Biglide mini parallel robot, which comprises two-degree-of-freedom (DOF) mini parallel robots with constant struts. The robot workspace is characterized and the inverse kinematics equation is obtained. In the paper, design optimization is implemented with Genetic Algorithms (GA) for optimization considering transmission quality index and workspace. Here, intended to show the advantages of using the GA, we applied it to a multicriteria optimization problem of 2 DOF mini parallel robot. Genetic algorithms (GA) are so far generally the best and most robust kind of evolutionary algorithms. A GA has a number of advantages. It can quickly scan a vast solution set. Bad proposals do not affect the end solution negatively as they are simply discarded. The obtained results have shown that the use of GA in such kind of optimization problem enhances the quality of the optimization outcome, providing a better and more realistic support for the decision maker. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)