An extension theorem for regular functions of two quaternionic variables

For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Tr\`eves theorem. Namely, we show that a ball contained in the boundary of a domain is a propagator of regular extendability across the boundary.Comment: v3: Final version, to appear in "Journal of Mathematical Analysis and Applications", 10 pages, 1 figur

Time resolved tracking of a sound scatterer in a turbulent flow: non-stationary signal analysis and applications

It is known that ultrasound techniques yield non-intrusive measurements of hydrodynamic flows. For example, the study of the echoes produced by a large number of particle insonified by pulsed wavetrains has led to a now standard velocimetry technique. In this paper, we propose to extend the method to the continuous tracking of one single particle embedded in a complex flow. This gives a Lagrangian measurement of the fluid motion, which is of importance in mixing and turbulence studies. The method relies on the ability to resolve in time the Doppler shift of the sound scattered by the continuously insonfied particle. For this signal processing problem two classes of approaches are used: time-frequency analysis and parametric high resolution methods. In the first class we consider the spectrogram and reassigned spectrogram, and we apply it to detect the motion of a small bead settling in a fluid at rest. In more non-stationary turbulent flows where methods in the second class are more robust, we have adapted an Approximated Maximum Likelihood technique coupled with a generalized Kalman filter.Comment: 16 pages 9 figure

On the Ekeland-Hofer symplectic capacities of the real bidisc

In $\mathbb{C}^2$ with the standard symplectic structure we consider the bidisc $D^2\times D^2$ constructed as the product of two open real discs of radius $1$. We compute explicit values for the first, second and third Ekeland-Hofer symplectic capacity of $D^2\times D^2$. We discuss some applications to questions of symplectic rigidity.Comment: v3: Final version, to appear in "Pacific J. Math.", 20 page

Supply of sulphur to S-deficient young barley seedlings restores their capability to cope with iron shortage

The effect of the S nutritional status on a plant's capability to cope with Fe shortage was studied in solution cultivation experiments in barley (Hordeum vulgare L. cv. Europa). Barley is a Strategy II plant and responds to Fe deficiency by secretion of chelating compounds, phytosiderophores (PS). All PS are derived from nicotianamine whose precursor is methionine. This suggests that a long-term supply of an inadequate amount of S could reduce a plant's capability to respond to Fe deficiency by limiting the rate of PS biosynthesis. The responses of barley (Hordeum vulgare L. cv. Europa) plants grown for 12 d on Fe-free nutrient solutions (NS) containing 0 or 1.2 mM SO42-, was examined after 24 h or 48 h from transfer to NS containing 1.2 mM SO42-. After the supply of S was restored to S-deprived plants, an increase in PS release in root exudates was evident after 24 h of growth in S-sufficient NS and the increment reached values up to 4-fold higher than the control 48 h after S resupply. When S was supplied to S-deficient plants, leaf ATPS (EC 2.7.7.4) and OASTL (EC 4.2.99.8) activities exhibited a progressive recovery. Furthermore, root HvST1 transcript abundance remained high for 48 h following S resupply and a significant increase in the level of root HvYS1 transcripts was also found after only 24 h of S resupply. Data support the idea that the extent to which the plant is able to cope with Fe starvation is strongly associated with its S nutritional status. In particular, our results are indicative that barley plants fully recover their capability to cope with Fe shortage after the supply of S is restored to S-deficient plants

LA VALORISATION DU GUARANA EN AMAZONIE BRESILIENNE : CULTURE DE RENTE ET/OU CULTURE DES FILIERES

N° ISBN - 978-2-7380-1284-5International audienceIn Brazil, the question of the requalification of local knowledge is hardly perceptible. It has become a main political stake for rural populations that are facing agribusiness expansion. The example of Guarana, a plant from Amazonia, is emblematic of the competition between different models of production, each of them based on specific history, beliefs, practices and botanical varieties. After numerous decades along which productivist model of production has been dominant, the commercial success of the Guarana based products and the local appropriation of the system of reference linked with sustainable development have favoured the diversification of the forms of management and economic development of the plant in its origin area. While the multinational company AMBEV, leader on the market of Guarana based soda, intends to keep the control on the market of the Guarana, various categories of producers (American Indians; caboclos, local communities, rural workers) are mobilizing for few years to stand up their know-how and the specificity of their production linked with their territory. Among those groups, the Satéré Mawé indians claim that they are depositary of the genetic diversity of the plant and that they still collect native seedlings in the forest to maintain the diversity in their fields. In this paper, we will watch the regional history and we will underline how environmental stakes (such as biodiversity conservation, traditional knowledge protection, green market) result within the territory in new cleavages related with the uses of natural resources