Topological properties of regular generalized function algebras

We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 page

Dihydroxyacetone conversion into lactic acid in an aqueous medium in the presence of metal salts: influence of the ionic thermodynamic equilibrium on the reaction performance

International audienceThe catalytic conversion of dihydroxyacetone (DHA) to lactic acid (LA) via pyruvaldehyde (PA) in aqueous media was studied using different homogeneous metal salts. A kinetic model was developed and the parameters corresponding to each reaction steps were estimated. Agreement between experiments and simulated results was excellent and the performance of the different catalysts was consistent with previous studies described in the literature. Aluminium salts, which show the best performance, were tested in a whole range of concentrations and at different pH, in order to identify the catalytically active ionic species. It was confirmed that the DHA to pyruvaldehyde (PA) dehydration step is catalyzed by both Brønsted and Lewis acids whereas the consecutive reaction of PA to LA is solely catalyzed by Lewis acids. Moreover, comparing thermodynamic analysis of the reaction media and kinetic parameters demonstrated that cationic hydroxyl-aluminium complexes [Al(OH)h] (3-h)+ formed in situ by the hydrolysis of the aluminium aqua complexes like [Al(OH2)6] 3+ are the most active Lewis acids

Upper ocean water masses and transports in the western tropical Pacific (165E

ABSTRACT As part of the international TOGA program, the ORSTOM Center in Nouméa (New Caledonia) initiated in January 1984 a series of semi-annual cruises along the 165"E meridian from 20"s to 10"N, across the equatorial current system of the western Pacific. This paper presents an analysis of the first six hydrographic (0-1000 m) and current (0-600 m) sections. A detailed description of "typical" January 1986 vertical structures of temperature, salinity and zonal measured velocity is offered. Differences are noted with structures previously obtained in the tropical Pacific. Compared to the central and eastern Pacific, the 165"E dataset evidences a much weaker equatorial upwelling and deeper surface isothermal layer and subsurface currents. Compared to the few western Pacific measurements, the two speed cores of the Equatorial Undercurrent (EUC) previously reported at 100 and 200 m are not observed here. Special attention is given to the eastward equatorial jet (2OS-2"N 0-75 m) measured in January 1985 when westerly winds were present from the north of New Guinea to 160"E. For the purpose of volume transport calculations, eastward flows at 165"E are not sufficiently separated to be easily differentiated. A definition based on an isodensity surface (sigma-t = 23.5 kg m-3) is thus adopted to discriminate the EUC and the North and South Subsurface Countercurrents (NSCC, SSCC) from the North and South Equatorial Countercurrents (NECC, SECC).' The EUC is assumed to lie within 2 degrees of the equator below sigma-t = 23.5 kg m-3. Using these current boundaries, transports of the South Equatorial Current (SEC), EUC and NECC agree within 30% with estimates previously computed in the westem, central and eastern Pacific; e.g., the mean NECC transport is 27 f 13 lo6 m3 s-l. A noticeable exception is the SECC transport which is two to four times as much as that estimated for the central Pacific. The weaker (stronger) EUC and the farthest northern (southern) NECC were observed during the three January (June-July) cruises. Large transport variability was observed and calls for a denser time-space sampling rate of observation. Hence, the credibility of dynamic height and geostrophic currents calculated from XBT (0-400 m) and mean temperature-salinity (T-S) curves are investigated. Major limitations, stressed by the semiannual transects, are caused b y 1) notable density variations in the 400-1000 m layer, and 2) the effects of variability of the T-S relation in the 0-400 m layer. These two points can each result in signals of as much as 6 dyn cm in the surface dynamic height and therefore significant errors in geostrophic velocities calculated from individual cruises. These errors are generally not accounted for when the geostrophic method is applied to XBT data. However, poleward of 2" latitude, a fair agreement is observed between mean geostrophic and measured currents (5 cm s-' rms difference), after eliminating the errors introduced by the 400 db reference level and mean T-S curves. In the 2"S-2"N band, the agreement is only qualitative (30 cm s-' rms difference) and better in the EUC than in surface flows. Deeper temperature sampling and a better knowledge of T-S variability than the present one are particularly recommended to monitor the equatorial current system from XBTs in the western tropical Pacific Ocean

Synthesis of hollow vaterite CaCO(3) microspheres in supercritical carbon dioxide medium

We here describe a rapid method for synthesizing hollow core, porous crystalline calcium carbonate microspheres composed of vaterite using supercritical carbon dioxide in aqueous media, without surfactants. We show that the reaction in alkaline media rapidly conducts to the formation of microspheres with an average diameter of 5 mu m. SEM, TEM and AFM observations reveal that the microspheres have a hollow core of around 0.7 mu m width and are composed of nanograins with an average diameter of 40 nm. These nanograins are responsible for the high specific surface area of 16 m(2) g(-1) deduced from nitrogen absorption/desorption isotherms, which moreover confers an important porosity to the microspheres. We believe this work may pave the way for the elaboration of a biomaterial with a large potential for therapeutic as well as diagnostic applications

Effects of gamma irradiation on the biomechanical properties of peroneus tendons

PURPOSE: This study was designed to investigate the biomechanical properties of nonirradiated (NI) and irradiated (IR) peroneus tendons to determine if they would be suitable allografts, in regards to biomechanical properties, for anterior cruciate ligament reconstruction after a dose of 1.5–2.5 Mrad. METHODS: Seven pairs of peroneus longus (PL) and ten pairs of peroneus brevis (PB) tendons were procured from human cadavers. The diameter of each allograft was measured. The left side of each allograft was IR at 1.5–2.5 Mrad, whereas the right side was kept aseptic and NI. The allografts were thawed, kept wet with saline, and attached in a single-strand fashion to custom freeze grips using liquid nitrogen. A preload of 10 N was then applied and, after it had reached steady state, the allografts were pulled at 4 cm/sec. The parameters recorded were the displacement and force. RESULTS: The elongation at the peak load was 10.3±2.3 mm for the PB NI side and 13.5±3.3 mm for the PB IR side. The elongation at the peak load was 17.4±5.3 mm for the PL NI side and 16.3±2.0 mm for the PL IR side. For PL, the ultimate load was 2,091.6±148.7 N for NI and 2,122.8±380.0 N for IR. The ultimate load for the PB tendons was 1,485.7±209.3 N for NI and 1,318.4±296.9 N for the IR group. The ultimate stress calculations for PL were 90.3±11.3 MPa for NI and 94.8±21.0 MPa for IR. For the PB, the ultimate stress was 82.4±19.0 MPa for NI and 72.5±16.6 MPa for the IR group. The structural stiffness was 216.1±59.0 N/mm for the NI PL and 195.7±51.4 N/mm for the IR side. None of these measures were significantly different between the NI and IR groups. The structural stiffness was 232.1±45.7 N/mm for the NI PB and 161.9±74.0 N/mm for the IR side, and this was the only statistically significant difference found in this study (P=0.034). CONCLUSION: Our statistical comparisons found no significant differences in terms of elongation, ultimate load, or ultimate stress between IR and NI PB and PL tendons. Only the PB structural stiffness was affected by irradiation. Thus, sterilizing allografts at 1.5–2.5 Mrad of gamma irradiation does not cause major alterations in the tendons’ biomechanical properties while still providing a suitable amount of sterilization for anterior cruciate ligament reconstruction

Isomorphisms of algebras of Colombeau generalized functions

We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the multiplicative linear functionals from the special algebra of Colombeau generalized functions on X to the ring of Colombeau generalized numbers. Up to multiplication with an idempotent generalized number, they are given by an evaluation map at a compactly supported generalized point on X.Comment: 10 page