A finite difference scheme on a non commutative group

Summary. We propose and analyze a finite difference scheme for the Kohn Laplacian operator associated with the Heisenberg group, which is a degenerate elliptic operator of H?rmander type. We give a complete analysis for a periodic problem in a cube. In particular, we prove a discrete Poincaré-Wiertinger inequality which yields the stability. Numerical tests are presented. Received June 1, 1999 / Revised version received June 7, 2000 / Published online March 20, 2001     

The stochastic heat equation: Feynman-Kac formula and intermittence

We study, in one space dimension, the heat equation with a random potential that is a white noise in space and time. This equation is a linearized model for the evolution of a scalar field in a space-time-dependent random medium. It has also been related to the distribution of two-dimensional directed polymers in a random environment, to the KPZ model of growing interfaces, and to the Burgers equation with conservative noise. We show how the solution can be expressed via a generalized Feynman-Kac formula. We then investigate the statistical properties: the two-point correlation function is explicitly computed and the intermittence of the solution is proven. This analysis is carried out showing how the statistical moments can be expressed through local times of independent Brownian motions.     

Rearrangement of 2-aminofuro[3,2-b]pyridine-3-carboxylic esters

Ethyl 2-aminofuro[3,2-b]pyridine-3-carboxylate rearranges with sodium ethoxide in ethanol to 2-oxo-3-cyano-2,3-dihydro[3,2-b]furopyridine; the corresponding p-nitrophenyl ester undergoes the same rearrangement by dilute aqueous sodium hydroxide. In the first case it was possible to isolate the labile intermediate, which was shown to be the hemiacetal of the above mentioned cyanolactone.     

The Dissociation Constants of 1,1′-Bis (pyridinium-4-aldoxime)trimethylene dibromide

Summary. The dissociation constants of the two oxime groups of 1,1-bis(pyridinium-4-aldoxime)trimethylene dibromide (TMB-4) were determined using spectrophotometric data. Two numerical methods were applied to treat the overlapping equilibria. The results obtained by both agreed with each other and their mean values at 25°C corrected for the ionic strength of 0.05moldm^–3 are pK_a1=7.49±0.11 and pK_a2=8.96±0.09. These values were discussed in terms of the pK_as of 1,1-bis(pyridinium-4-aldoxime)oxydimethylene dichloride (Toxogonin), a similar dioxime, which were derived by extrapolation of literature data.     

Mathematical Modeling of Drug Release from Microemulsions: Theory in Comparison with Experiments

The topic of this paper is the study of the drug release from a drug-loaded microemulsion by reverting to a new mathematical model overcoming some drawbacks of previously proposed models. In particular, attention is focused on the mathematical expression of the drug fluxes existing between the oil and water phases during drug release. Indeed, not only the drug release kinetics, but also the drug oil-water partition coefficient strongly depend on these fluxes. Two microemulsion are considered: the first is composed by water, Tween80 as surfactant, and Triacetin as oil phase, while the second is composed by water, Tween80 as surfactant, and a Triacetin-benzylic alcohol mixture (1 : 1) as oil phase. Both of them are loaded by Nimesulide, an oil-soluble drug of considerable industrial relevance. The drug release is performed by resorting to a permeation experiment (Franz cells apparatus) as it demonstrated to be the most reliable methodology. The good agreement between the experimental permeation data and the model best-fitting ensures that the most important phenomena ruling this kind of drug release were properly accounted for by the new proposed model. Copyright 2000 Academic Press.     

Biocompatible channels for field-flow fractionation of biological samples: correlation between surface composition and operating performance

Biocompatible methods capable of rapid purification and fractionation of analytes from complex natural matrices are increasingly in demand, particularly at the forefront of biotechnological applications. Field-flow fractionation is a separation technique suitable for nano-sized and micro-sized analytes among which bioanalytes are an important family. The objective of this preliminary study is to start a more general approach to field-flow fractionation for bio-samples by investigation of the correlation between channel surface composition and biosample adhesion. For the first time we report on the use of X-ray photoelectron spectroscopy (XPS) to study the surface properties of channels of known performance. By XPS, a polar hydrophobic environment was found on PVC material commonly used as accumulation wall in gravitational field-flow fractionation (GrFFF), which explains the low recovery obtained when GrFFF was used to fractionate a biological sample such as Staphylococcus aureus. An increase in separation performance was obtained first by conditioning the accumulation wall with bovine serum albumin and then by using the ion-beam sputtering technique to cover the GrFFF channel surface with a controlled inert film. XPS analysis was also employed to determine the composition of membranes used in hollow-fiber flow field-flow fractionation (HF FlFFF). The results obtained revealed homogeneous composition along the HF FlFFF channel both before and after its use for fractionation of an intact protein such as ferritin.     

Effects of traditional processing methods of linseed oil on the composition of its triacylglycerols

Different oil processing methods were performed, which included washing with water and treatment with lead-based driers, with and without heating to different temperatures, giving a set of 7 oils to be investigated. The effects of the traditional processing methods of linseed oil on its triacylglycerol (TAG) composition were studied, using the following analytical methods: high performance size exclusion chromatography (HPSEC), Fourier transform infrared spectroscopy (FTIR), high-performance liquid chromatography-atmospheric pressure chemical ionisation-mass spectrometry (HPLC-APCI-MS), direct temperature resolved mass spectrometry (DTMS), matrix assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOF-MS), and electrospray ionisation Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICR-MS). A decrease of the initial cis-double bonds and the formation of trans-double bonds upon heating of the oils was observed. Heating a lead and oil mixture to 150 degrees C, or heating the oil alone to 300 degrees C led to the highest degree of oxidation. A difference was observed for the oxidation patterns for oils with and without the addition of lead. Furthermore, levels of oxygen incorporation were higher when lead was added to the oil. High temperature treatment of the oils resulted in an increased average molecular weight. The changes in the initial conformation of the double bond systems observed with FTIR were supported by HPLC-APCI-MS measurements that showed the formation of a number of new isomeric TAGs in the heated oil compared to freshly pressed, untreated oil. Oligomerisation up to hexamers was observed with HPSEC, and MALDI-TOF-MS. The formation of oligomers up to trimers only, however, was observed with ESI-FTICR-MS. Incorporation of oxygen was mainly observed with MALDI-TOF-MS and ESI-FTICR-MS whereas with DTMS and FTIR hardly any evidence was found for this.