A unifying approach to integration for bounded positive charges

This paper deals with n-monotone functionals, which constitute a generalisation of n-monotone set functions. Using the notion of exactness of a functional, we introduce a new notion of lower and upper integral which subsumes as particular cases most of the approaches to integration in the literature. As a consequence, we can characterise which types of integrals can be used to calculate the natural extension (the lower envelope of all linear extensions) of a positive bounded charge.     

A note on natural risk statistics

Recently Heyde, Kou and Peng [C.C. Heyde, S.G. Kou, X.H. Peng, What is a good external risk measure: Bridging the gaps between robustness, subadditivity, and insurance risk measures, 2007, preprint.] proposed the notion of a natural risk statistic associated with a finite sample that relaxes the subadditivity assumption in the classical coherent risk statistics. In this note we use convex analysis to provide alternate proofs of the representation results regarding natural risk statistics.     

Time-dependent natural convection in a square cavity: Application of a new finite volume method

A new finite volume (FV) approach with adaptive upwind convection is used to predict the two-dimensional unsteady flow in a square cavity. The fluid is air and natural convection is induced by differentially heated vertical walls. The formulation is made in terms of the vorticity and the integral velocity (induction) law. Biquadratic interpolation formulae are used to approximate the temperature and vorticity fields over the finite volumes, to which the conservation laws are applied in integral form. Image vorticity is used to enforce the zero-penetration condition at the cavity walls. Unsteady predictions are carried sufficiently forward in time to reach a steady state. Results are presented for a Prandtl number (Pr) of 0-71 and Rayleigh numbers equal to 10³, 10⁴ and 10⁵. Both 11 × 11 and 21 × 21 meshes are used. The steady state predictions are compared with published results obtained using a finite difference (FD) scheme for the same values of Pr and Ra and the same meshes, as well as a numerical bench-mark solution. For the most part the FV predictions are closer to the bench-mark solution than are the FD predictions.     

Natural and artificial weathering characteristics of stabilized acrylic–urethane paints

Depth-profiling by Fourier transform infrared (FTIR) spectroscopy, dynamic mechanical analysis (DMA), microhardness and scanning electron microscopy (SEM) observations have been used to monitor degradation chemistries in two-package acrylic–urethane coatings when exposed to different exposure conditions. Three artificial and three natural weathering protocols (QUV, ASTM D5894, ISO20340, Pipady (south of France), Bandol (south of France) and Kure Beach (USA)) were selected for this study. The same chemical events were found to occur under all conditions, particularly under natural and artificial exposures. Both loss of the amide II band at 1520 cm⁻¹ and carbonyl growth occurred but at relatively low rate owing to the presence of hindered-amine light stabilizers in the film. A less typical loss of urea biuret linkages also occurs during all exposures and results in a change in the balance between urethane and urea links across the depth of the film during weathering. The chemical degradation of the polymer matrix involves the formation of species that are readily ablated from the surface and results in loss of gloss, increase in hardness and a rougher topology. The dramatic loss of gloss observed after Pipady and Bandol exposures show that loss of gloss should not be systematically correlated to the advance in chemical degradation.     

Selective Iodination of Benzylic Alcohols with KI/H<Subscript>2</Subscript>SO<Subscript>4</Subscript> Supported on Natural Kaolinitic Clay Under Microwave Irradiation

Summary.  Benzylic alcohols are selectively converted into their corresponding iodides using KI/H₂SO₄ supported on natural kaolinitic clay and microwaves. Received August 20, 2001. Accepted (revised) September 18, 2001     

Synthesis of lodopyridone

The total synthesis of the unusual 4-pyridone marine metabolite lodopyridone has been achieved by late stage manipulation of the related 4-pyrone. Key reactions include a Suzuki–Miyaura coupling to form the tetracyclic core and a modified Corey–Ganem–Gilman reaction to install the ethanolamide side-chain.     

Study of chain branching in natural rubber using size-exclusion chromatography coupled with a multi-angle light scattering detector (SEC-MALS)

The different rheological behaviour of natural rubber (NR) compared to industrial synthetic poly(cis-1,4-isoprene) (SR) has been attributed to the gel phase and long-chain branching. Previous studies on branching in NR were carried out using the fractionation technique by precipitation to obtain narrow molar mass distribution. In this study, chain branching of poly(cis-1,4-isoprene) in NR was characterised by size-exclusion chromatography coupled with an online multi-angle light scattering detector (SEC-MALS). The nanoaggregates adsorbed on the column packing interfered with branching characterisation for short and medium chains (M_w < 1000 kg/mol). Using a master curve of linear standard poly(cis-1,4-isoprenes), SEC-MALS revealed no or very little branching in the higher chains (1000 < M_w < 10,000 kg/mol) of natural rubber contrary to previous studies. This study showed that the soluble portion of NR samples was composed of almost linear poly(cis-1,4-isoprene) and nanoaggregates with rather compact structures.     

Fast and selective determination of triterpenic compounds in olive leaves by liquid chromatography-tandem mass spectrometry with multiple reaction monitoring after microwave-assisted extraction

A method for fast and selective determination of the main triterpenic compounds present in olive leaves — oleanolic, ursolic and maslinic acids as triterpenic acids and, uvaol and erythrodiol as triterpenic dialcohols — is reported here. Quantitative isolation of the analytes has been accomplished in 5 min by microwave assistance using ethanol as extractant. Due to the medium polarity of triterpenic acids and dialcohols, different ethanol-water ratios were tested in order to select the optimum extractant composition for their solubilisation. Microwave assistance provided a significant shortening of the leaching time as compared to conventional procedures by maceration, which usually requires at least 5 h. After extraction, determination was carried out by liquid chromatography-tandem mass spectrometry (LC-MS-MS) with a triple quadrupole (qQq) mass detector without any clean-up step prior to chromatographic analysis. Highly selective identification of triterpenes was confirmed by multiple reaction monitoring (MRM) using the most representative transitions from the precursor ion to the different product ions, while the most sensitive transitions were used for MS-MS quantitation. Total analysis performed in 25 min enables the characterization of a fraction with particular interest in the pharmacological area.     

Numerical simulation of the horizontal Bridgman growth. Part II: Three-dimensional flow

We study the steady-state three-dimensional flow which occurs in a horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals. We find that three-dimensional effects can have a dramatic influence upon the flow, which, before the onset of periodic disturbances, differs appreciably from its two-dimensional counterpart. We also investigate the sensitivity of the flow to non-symmetric disturbances.