Strictly Positive Definite Kernels on a Product of Spheres II

We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result complements similar results previously obtained for strict positive definiteness on a product of circles [Positivity, to appear, arXiv:1505.01169] and on a product of high dimensional spheres [J. Math. Anal. Appl. 435 (2016), 286-301, arXiv:1505.03695]

Blepharismins used for chemical defense in two ciliate species of the genus Blepharisma, B. stoltei and B. undulans (Ciliophora: Heterotrichida)

It is known that the freshwater heterotrich ciliate Blepharisma japonicum uses five pigments called blepharismins, stored in its extrusive pigment granules, for both light perception and chemical defense against predators. In this work we focused our attention on the defensive strategies of two additional pigmented species of Blepharisma, B. stoltei and B. undulans. In particular: (1) we observed the predator\u2013prey interactions of B. stoltei or B. undulans against one multicellular and two unicellular predators; (2) we clarified the nature of B. stoltei and B. undulans pigments by means of High Performance Liquid Chromatography (HPLC) and Liquid Chromatography Mass Spectrometry (LC-MS); and (3) we demonstrated and compared the toxicity of the purified pigments on a panel of ciliated protists, and against one metazoan predator. The results indicate that the chemical defense mechanism present in B. stoltei and B. undulans is mediated by the same five blepharismins previously characterized for B. japonicum, although produced in different proportions

Vibrational properties of inclusion complexes: the case of indomethacin-cyclodextrin

Vibrational properties of inclusion complexes with cyclodextrins are studied by means of Raman spectroscopy and numerical simulation. In particular, Raman spectra of the non-steroidal, anti-inflammatory drug indomethacin undergo notable changes in the energy range between 1600 and 1700 cm$^{-1}$ when inclusion complexes with cyclodextrins are formed. By using both \emph{ab initio} quantum chemical calculations and molecular dynamics, we studied how to relate such changes to the geometry of the inclusion process, disentangling single-molecule effects, from changes in the solid state structure or dimerization processes.Comment: 14 file figure

Absorption et désorption du dioxyde de souffre par des gouttes d'eau de fort diamètre en chute.

Cet article concerne l’absorption et la désorption du SO2 par des gouttes d’eau de diamètre supérieur à 1mm en chute libre dans un mélange air-SO2 à faible et moyenne concentrations. Dans ce cas, le transfert résulte du couplage des résistances interne et externe à la goutte. Dans la phase liquide, un modèle local basé sur la vitesse de frottement inter faciale et le diamètre de la goutte permet le calcul du coefficient de transfert interne kl. Le coefficient de transfert externe kg dans la phase gazeuse est déterminé à l’aide d’une expression plus classiqueAfin de valider le modèle, des investigations expérimentales sont menées en absorption et en désorption sur une colonne de 2.3 m de hauteur dans laquelle le temps de séjour des gouttes est de l’ordre de la seconde. Le présent modèle simule fort bien l’ensemble de ces expériences réalisées pour différents diamètres de goutte [2.04 ; 4.31] mm et différentes concentrations [100 ; 2000] ppm. Le modèle proposé est aussi comparé avec succès à des résultats expérimentaux de la littérature à faible et moyenne concentrations pour des temps de contact beaucoup plus grands.Son domaine d’application couvre donc désormais l’absorption et la désorption du SO2 pour des concentrations comprises entre quelques ppm et quelque %.Mass transfer in dispersed media is of interest to fields such as nuclear engineering, process engineering and environmental engineering. It occurs when two phases, not under chemical equilibrium, are in contact. Knowledge of mass transfer mechanisms in the case of gas absorption from and/or into droplets is necessary to understand the scavenging of trace gases in clouds, rain and wet scrubbers. Our studies focus on absorption and desorption phenomena involving free falling water droplets in a mixture of air and gas. For example, acid rain is formed when a drop of rain falls through an atmosphere contaminated with gaseous acid precursors. A similar phenomenon occurs in specific atmospheric scrubbers, where pollution is trapped at the source. In all cases, the transfer of trace gases from the air into the falling droplets is controlled by molecular diffusion and by convection outside and inside the drops.For droplets, falling inside a soluble gas medium, the main transfer resistance is located in the gas phase. A survey of published studies shows that a number of good numerical models exist, as well as experimental correlations for predictions of the mass transfer coefficient in the gas film. For the liquid phase controlled resistance, Saboni (1991) proposed a model based on local scales, interfacial liquid friction velocity and drop diameter. The model was validated experimentally by Amokrane et al. (1994). The experimental study and model validation in the case of sulfur dioxide absorption by water droplets falling through air with a high gas concentration (few %) has been described previously in detail by Amokrane et al. (1994).The purpose of the present article was to extend our previous model to predict SO2 absorption and desorption by droplets (1-5 mm) falling in air with a low gas concentration. In the liquid phase, a model based on local scales, interfacial liquid friction velocity and droplet size diameter was used. In the continuous gas phase a more classical model was applied. To support the model, two types of experiments were carried out. The first type was adapted to measure the absorption of gas by droplets of known diameter. A second set of experiments gave the desorption rate from droplets with an initial concentration of sulfur dioxide falling through SO2 -free air. Absorption occurred during the fall through a 2.3 m long column for various gas concentrations and for various droplet diameters. A sketch of the experimental equipment is presented schematically in Figure 1. It consists of a cylindrical column 2.3 m in height and 0.104 m in diameter. Before each experiment, a gas mixture with the desired SO2 concentration in air, ranging between 100 and 2000 ppm, was introduced into the column. The SO2 concentration was set at the desired value by regulating the volumetric flow rates of sulfur dioxide and air with calibrated rotameters. The gas concentration in the column was measured continuously by a chemical cell analyzer. The air temperature and humidity were continually measured at the top, in the middle and at the bottom of the column. They ranged from 18°C to 20°C and from 40% to 50%, respectively. Droplets were generated using a specific injector consisting of a demineralized water tank at the base of which identical thin needles were placed. In the case of the smallest droplets, seven needles, 300 µm in diameter, were used. For the largest droplets, one needle of about 1 mm was used. The artificial rain was started by exerting an overpressure in the tank and it was stopped by exerting a depression. This device allowed the generation of almost identical water drops at a controlled rate. Droplets fell with zero initial velocity. Their diameters were determined by collecting a known number of droplets and weighing them on a precision balance. The droplets were collected in a special glass cup placed at the bottom of the rain shaft. This collector initially contained a known volume of kerosene. The presence of this organic compound allowed the creation of a film to prevent additional absorption of SO2 during the experiment and natural desorption of sulfur after the experiment. An experiment consisted of dropping 10 to 20 mL of rain. This amount is enough to precisely measure the sulfur concentration.For reversible desorption, experimentation was undertaken directly in a lab atmosphere. For these experiments, the 4.31 mm diameter droplets free fall occurred over 16.3 m. Three intermediate levels were also examined with falling times varying from 0.7 to 2.4 s. The ambient temperature was measured in the surrounding area of both the injector and the collector and the maximum variation was 2°C. Various initial sulfurous acid concentrations were obtained as a result of various contact times of demineralized water with air-SO2 mixtures. Initial concentrations ranged from 0.5 10-3 mol·L-1 to 1.8 10-3 mol·L-1. In this case, the collector initially contained a known volume of hydrogen peroxide to immediately convert sulfurous acid into sulfuric acid. This avoided additional desorption of sulfurous acid during and after the experiments. In this case, the presence of the organic film was not necessary.The results achieved with the theoretical model were compared to the experimental results. The present model was successful in correlating the experimental results carried out for various droplet diameters ranging between 2.04 and 4.31 mm, and gas concentrations ranging between 100 and 2000 ppm. The model also compared successfully with experimental results from the literature in the case of much longer contact times. The applicability of the model thus covers the absorption and desorption of SO2 for concentrations ranging between ppm to a few %

Chemical defence by sterols in the freshwater ciliate Stentor polymorphus

Heterotrich ciliates typically retain toxic substances in specialized ejectable organelles, called extrusomes, which are used in predator-prey interactions. In this study, we analysed the chemical defence strategy of the freshwater heterotrich ciliate Stentor polymorphus against the predatory ciliate Coleps hirtus, and the microturbellarian flatworm Stenostomum sphagnetorum. The results showed that S. polymorphus is able to defend itself against these two predators by deploying a mix of bioactive sterols contained in its extrusomes. Sterols were isolated in vivo and characterized by liquid chromatography-mass spectrometry (LC-MS), and nuclear magnetic resonance (NMR), as ergosterol, 7-dehydroporiferasterol, and their two peroxidized analogues. The assessment of the toxicity of ergosterol and ergosterol peroxide against various organisms, indicated that these sterols are essential for the effectiveness of the chemical defence in S. polymorphus