Robust Exponential Decay of Correlations for Singular-Flows

We construct open sets of C ^k (k ≥ 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure.     

Simultaneous GC determination of turpentine, camphor, menthol and methyl salicylate in a topical analgesic formulation (Dologex®)

Summary A gas chromatographic assay has been developed for the simultaneous quantitative determination of turpentine, camphor, methol and methyl salicylate in a topical formualtion (Dologex^?). Eucalyptol was used as the internal standard. Compounds were separated on a cross-linked 5% phenyl polydimethylsiloxane capillary column and detected by FID. The method was validated on the basis of selectivity, recovery, linearity, precision and accuracy. Calibration graphs were linear for each analyte in the range studied. Intra and inter-day precision (coefficient of variation,CV) did not exceed 2%. The applicability of the method was demonstrated in a stability study of these compounds in samples of the formulation which had been maintained under different temperature conditions for six months.     

Solution of a General Linear Complementarity Problem Using Smooth Optimization and Its Application to Bilinear Programming and LCP

This paper addresses a General Linear Complementarity Problem (GLCP) that has found applications in global optimization. It is shown that a solution of the GLCP can be computed by finding a stationary point of a differentiable function over a set defined by simple bounds on the variables. The application of this result to the solution of bilinear programs and LCPs is discussed. Some computational evidence of its usefulness is included in the last part of the paper. Accepted 28 June 1999. Online publication 4 December 2000.     

On generators and relations for unions of semigroups

Finite generation and presentability of general unions of semigroups, as well as of bands of semigroups, bands of monoids, semilattices of semigroups and strong semilattices of semigroups, are investigated. For instance, it is proved that a band Y of monoids S _α (α∈ Y ) is finitely generated/presented if and only if Y is finite and all S _α are finitely generated/presented. By way of contrast, an example is exhibited of a finitely generated semigroup which is not finitely presented, but which is a disjoint union of two finitely presented subsemigroups. January 21, 2000     

Diastered and Regiochemical Control in the Functionalization of the Allylic [dbnd] of a Natural 5-(1-Alkenyl)-2-Enono-1,5-Lactone

The diastereo and regioselectivity of the bromohydrination of argentilactona [(5R)-(-)-δ-lactone of 5-hydroxydodeca-Z, Z-2,6-dienoic acid] and the regioselectivity of the aqueous acidic opening of its 65,75 and 6R,7R-epoxides were studied. Although the reactions occurred with low diasterofacial control, the regioselectivity observed in all cases was high, suggesting that the sequences could be of some synthetic value.     

Niobium oxide solid catalyst: esterification of fatty acids and modeling for biodiesel production

Biodiesel can be obtained from fatty acid raw materials through esterification. The reactivity of lauric, palmitic, stearic, oleic, and linoleic fatty acids with methanol using powdered niobic acid as a heterogeneous catalyst was investigated in this work, both experimentally (in a batch reactor) and theoretically. A 2³ experimental design was used, with methanol/fatty acid molar ratio, catalyst concentration, and temperature as main factors. An empirical model demonstrated that temperature is the most important variable. Fourteen heterogeneous and 56 homogeneous‐like kinetic models were tested. A homogeneous‐like model considering zero order for all species and inhibition by water was the most adequate for experiments without catalyst. A homogeneous‐like model considering a second‐order reaction in relation to the fatty acid and no water inhibition was the most adequate for niobic acid catalyzed reaction. Molecular modeling confirmed the experimental results showing that the reactivity is directly related to the increase of unsaturated bonds and the reduction of carbon chain length. The polarity of the fatty acid is determinant in the reactivity. At the molecular level, reaction occurs between the HOMO orbital of methanol and LUMO orbitals of fatty acids and reactivity is higher when the energy difference between these orbitals is lower. Copyright © 2010 John Wiley & Sons, Ltd.     

Graphite furnace and flame atomic-absorption technique for thermoanalytical investigations

Aerosol particles formed from the vapour of electrothermally heated substances were introduced into an acetylene-air flame for atomization and detection. Thus individual observations could be made on condensed phase processes taking place in the furnace. Curves of absorbance vs. furnace temperature for several zinc compounds were recorded and compared with the corresponding thermoanalytical DTG-curves.     

The reactivity of 2-vinylindoles with dimethyl acetylenedicarboxylate

The overall rates of reaction of 1-substltuted-1- (1-methyl-2-indolyl)ethenes with dimethyl acetylenedicarboxylate are considerably lower than those of the corresponding 2-vinyl- pyrroles. Steric interaction between the N-methyl group on the indole ring and the 1-substituent on the ethenyl group prevents the diene system adopting a coplanar $\text{cisoid}$ configuration and, thereby, inhibits the _π4 + _π2 cycloaddition reaction of the system with dimethyl acetylenedicarboxylate. Under such conditions, the indolylethene preferentially undergoes a Michael addition reaction at the 3-position. The _π4 + _π2 cycloaddition reaction is promoted at elevated temperatures. No evidence was found for a Cope rearrangement of the Michael adducts to give the dihydrocarbazole.