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.     

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.     

Furocoumarins photolysis products induce differentiation of human erythroid cells

Psoralens, also known as furocoumarins, are a well-known class of photosensitizers largely used in the therapy of various skin disease. In this study we have evaluated the effects of crude pre-irradiated solutions of furocoumarins derivatives on (a) erythroid differentiation and apoptosis of human leukemic K562 cells and (b) hemoglobin synthesis in cultures of human erythroid progenitors derived from the peripheral blood. To prove the activity of a mixture of photoproducts generated by UVA irradiation of the three psoralen derivatives 5-methoxypsoralen (5-MOP) 8-methoxypsoralen (8-MOP), and angelicin (ANG), we employed the human leukemic K562 cell line and the two-phase liquid culture procedure for growing erythroid progenitors. The results obtained demonstrate that pre-irradiated solutions of psoralen derivatives significantly induce erythroid differentiation of K562 cells irrespective of the type of derivative used, suggesting that the active photoproduct(s) share a common structure. Interestingly, solutions of psoralens irradiated in anaerobic conditions do not exhibits erythroid inducing ability, indicating that the effect is mostly due to photooxidized psoralen products. In erythroid precursor cells, psoralens photolysis products stimulates at low concentrations an increase of hemoglobin A and hemoglobin F. Altogether, these data suggest that photoproducts of psoralen warrant further evaluation as potential therapeutic drugs in beta-thalassaemia and sickle cell anaemia.     

Time-dependent behaviour of mechanical shear deformations in a cholesteric liquid crystal

Summary In this paper we present the experimental results of time-resolved variations of the apparent pitch of a cholesteric mixture after a steplike shearing deformation is applied to it. We show that the relative variation of the wave-length of the maximum reflection ΔP/P _o varies from initial positive values (P>P ₀) to negative ones (P<P ₀ after a few seconds and finally it tends to a saturation value with ΔP/P ₀<0 in a long time. A qualitative explanation based on the mechanism of the unwinding of the twisted helix structure and a possible tilt of the molecular is also given.

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Riassunto In questo lavoro sono presentati i risultati sperimentali della variazione risolta nel tempo del passo apparente di un CLC sottoposto ad una deformazione di taglio a gradino. Si mostra che la variazione relativa della lunghezza d’onda del massimo di riflessione ΔP/P ₀ varia da un valore iniziale positivo (P>P ₀) ad un valore negativo (P<P ₀) dopo pochi secondi, e tende ad un valore di stturazione con ΔP/P ₀<0 all’infinito. Noi diamo una spiegazione qualitativa basata sul meccanismo dello srotolamento della struttura elicoidale e sul possibile tilt degli strati molecolari.

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Резюме В этой статье приводятся экспериментальные результаты для разрешенных во времени изменений видимого шага холестеричиой смеси после приложения ступенчатой деформации сдвига. Мы показываем, что относительное изменение длины волны максимального отражения ΔP/P ₀ изменяется от начальных ппложительных знаьений (P<P ₀) до отрицательных значениь (P<P ₀ после нескольких секунд и окончательно стремится к величине насьшения с ΔP/P ₀<0 в течение длительного времени. Предлагается качественное объяснение, основанное на механизме структуры закрученной спирали и возможного изменния наклона молекул.