On a boundary layer problem for the nonlinear Boltzmann equation

This article deals with a boundary-layer problem arising in the kinetic theory of gases when the mean free path of molecules tends to zero. The model considered here is the stationary, nonlinear Boltzmann equation in one dimension with a slightly perturbed reflection boundary condition. We restrict our attention to the case of hard spheres collisions, with Grad's cutoff assumption. Existence, uniqueness and asymptotic behavior are derived by means of energy estimates.     

Tracing sewage water by 15N in a mangrove ecosystem to test its bioremediation ability

Mangrove forests could be a simple and effective alternative to conventional sewage treatment, particularly for island communities given its low cost and low maintenance. Due to their high adaptation capacity, these plants are able to tolerate and bioremediate the high levels of nutrients and pollutants found in sewage water. This solution could be applied to small tropical islands with high population density such as Mayotte in the Indian Ocean. This paper reports on a trial by stable isotopic (15)N tracing of such a bioremediation process on pre-treated wastewater near the village of Malamani, in the middle of the large coastal mangrove in the bay near Chirongui. The first results show a boost in the mangrove growth, but a longer period of observation is needed to confirm the beneficial effects, and also to clarify the role of the local crab population, whose engineering activities play an important part in the ecosystem. The exact denitrification process is not yet understood, and the mass balance equation also reveals loss of nitrogen-containing compounds, which needs to be analyzed more closely.     

An allenic Pauson-Khand approach to 6,12-guaianolides

Cyclocarbonylation of α-methylene butyrolactone-containing allene-ynes affords 6,12-guaianolide ring systems. Incorporation of the α-methylene butyrolactone early in a synthetic sequence is rare for reactivity reasons; however, this moiety proves to be beneficial to the allenic Pauson-Khand reaction. The three double bonds and the ketone in the resulting 5-7-5 ring system bear significant differences in their reactivity and are ideally positioned for synthetic application to 6,12-guaianolides and analogs.     

Crystal growth,structure, electron paramagnetic resonance and magnetic properties of (NH4)2V3O8

A method to grow single crystals of ammonium vanadate (IV, V) (NH₄)₂V₃O₈ has been devised. The crystal structure is tetragonal P4bm; residual factor is R = 0.030. Cell parameters are $\text{a = 8.891 ± 0.004}\text{A}\text{?}$ and $\text{c = 5.582 + 0.002}\text{A}\text{?}$. The V⁵⁺ atom lies at the center of a triangular pyramide (VO₄ tetrahedron) while the V⁴⁺ atom is on A 4-fold rotation axis at the center of a square-based pyramide VO₅ whose symmetry point group is almost C_4v with the short V = O bond lying along the 4-fold axis parallel to the c edge of the tetragonal cell. Crystals are thin platlets with (001) cleavage planes. The platlets have very often a square or rectangular shape limited by {100} or {110} planes. Each single crystal was not large enough to record a good e.p.r. spectrum, but by sticking on the same quartz plate a score of them it was possible to gather enough crystals so to record correct spectra and by orienting the plate to obtain resonance lines separately for g_∥ = 1.9263 et g_τ = 1.9755. Measurements at 283 K on powder samples gave times for spin-spin relaxation T₂ = 0.4 × 10^?7s and for spin-lattice relaxation T₁ = 1.6 × 10^?7s. The magnetic structure is characterized by an exchange narrowing ω_e = 3 × 10¹⁰rad/s which corresponds to a transition temperature of about 0.5 K. Static susceptibility measurements at high magnetic field show a paramagnetic behaviour with an antiferromagnetic interaction which is interpreted in the magnetic space group P_2c4bm as the interaction between V⁴⁺ ions from consecutive planes parallel to (001).     

Study by differential scanning calorimetry of the structure of aliphatic chains and water in Cs soaps-water systems

Summary Caesium stearate- and caesium palmitate-water systems are investigated by DSC measurements. Thermodynamical data of transition between crystallized form and mesomorphic state indicate a greater disorder of the chains for these soaps than for lecithin, in the same lamellar structure. The study of the water melting in an extended range of concentration allows us to distinguish different behaviors: the simplest two phases model for the two extremes ranges of concentration (y < 20% and > 60%) is proposed to explain the stability of the freezing temperature and enthalpy; the solubilization of conter-ions in water and the bonding of some water molecules could explain the depression of freezing temperature and the decrease of enthalpy, in the intermediate range of concentration.

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Résumé Nous avons étudié par DSC les transitions de phase dans les systemes stearate et palmitate de cesium-eau. Les parametres thermodynamiques de la fusion des chaines paraffiniques révèle que dans les phases mésomorphis le désordre des chaines est plus grand que dans les systemes lecithine-eau. L'étude de la fusion de l'eau, a l'intérieur d'une phase lamellaire bien caractérisée, nous permet de distinguer plusieurs comportements: le modele le plus simple ä deux phases permet d'interpreter la stabilité de l'enthalpie et de la température de fusion dans les deux domaines extremes de concentration en eau (y < 20% et > 60%); la solubilisation des contre ions dans l'eau et la fixation de quelques molecules d'eau pourrait expliquer l'abaissement de la température de fusion et la diminution d'enthalpie, dans le domaine intermédaire de concentration.

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With 4 figures and 1 table     

Experimental study of the reaction vp → μ−pπ+: Gargamelle neutrino propane experiment

A sample of 357 events fitting the reaction ν + p → μ^? + p + π⁺ on free proton is obtained from the Gargamelle neutrino propane experiment at the CERN-PS. The average value of the cross section above 1 GeV is found to be (0.60 ± 0.07) 10^?38 cm². The reaction is dominated by the production of the Δ⁺⁺(1232) resonance. Results on the Δ⁺⁺ spin density matrix are given.     

Latex bead immobilisation in PDMS matrix for the detection of p53 gene point mutation and anti-HIV-1 capsid protein antibodies

Two diagnostic chemiluminescent biochips were developed for either the detection of p53 gene point mutation or the serological detection of anti-HIV-1 p24 capsid protein. Both biochips were composed of 24 microarrays of latex beads spots (4×4) (150 m in diameter, 800 m spacing) entrapped in a poly(dimethylsiloxane) elastomer (PDMS). The latex beads, bearing oligonucleotide sequences or capsid protein, were spotted with a conventional piezoelectric spotter and subsequently transferred at the PDMS interface. The electron microscopy observation of the biochips showed how homogeneous and well distributed the spots could be. Point mutation detection on the codon 273 of the p53 gene was performed on the basis of the melting temperature difference between the perfect match sequence and the one base pair mismatch sequence. The hybridisation of a 20-mer oligonucleotide form the codon 273 including a one base pair mutation in its sequence on a biochip arrayed with non-muted and the muted complementary sequences, enabled a clear discrimination at 56°C between muted and wild sequences. Moreover, the quantitative measurement of the amount of muted sequence in a sample was possible in the range 0.4–4 pmol. Serological measurement of anti-HIV-1 p24 capsid protein on the biochip, prepared with 1-m-diameter latex beads, enabled the detection of monoclonal antibodies in the range 1.55–775 ng mL^–1. Such a range could be lowered to 0.775 ng mL^–1 when using 50-nm-diameter beads, which generated a higher specific surface. The validation of the biochip for the detection of anti-HIV-1 capsid protein antibodies was performed in human sera from seropositive and seronegative patients. The positivity of the sera was easily discriminated at serum dilutions below 1:1,000.