Geometric conditions for the reconstruction of a holomorphic function by an interpolation formula

We give here some precisions and improvements about the validity of the explicit reconstruction of any holomorphic function on a ball of $\mathbb{C}^2$ from its restrictions on a family of complex lines. Such validity depends on the mutual distribution of the lines. This condition can be geometrically described and is equivalent to a stronger stability of the reconstruction formula in terms of permutations and subfamilies of these lines. The motivation of this problem comes from possible applications in mathematical economics and medical imaging

Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems

We give here some negative results in Sturm-Liouville inverse theory, meaning that we cannot approach any of the potentials with $m+1$ integrable derivatives on $\mathbb{R}^+$ by an $\omega$-parametric analytic family better than order of $(\omega\ln\omega)^{-(m+1)}$. Next, we prove an estimation of the eigenvalues and characteristic values of a Sturm-Liouville operator and some properties of the solution of a certain integral equation. This allows us to deduce from [Henkin-Novikova] some positive results about the best reconstruction formula by giving an almost optimal formula of order of $\omega^{-m}$.Comment: 40 page

Novel, technical advance: a new grapevine transpiration prototype for grape berries and whole bunch based on relative humidity sensors

Grape berry transpiration is considered an important process during maturation, but scientific evidence is scarce. In the literature, there is only one report showing reduced maturation when bunch transpiration is artificially slowed down. Traditionally, grape berry transpiration has been measured by weighing grape berries on scale for a given time, correctly assuming that the weight reduction is due to water lost. Commercially available instruments adequate to measure gas exchange in small fruits are not suitable for whole grape berry bunch. Here, we present an open differential chamber system that can be used with isolated grape berries or alternatively with a whole grape berry bunch for measuring grape berry/bunch transpiration based on the use of relative humidity sensors from Vaisala. When used with isolated grape berries, open differential chamber system validation was made by using Tempranillo grape berries collected at different phenological stages. For the whole bunch transpiration prototype, two different validations were made. Firstly, measurements were made inserting inside the chamber an increasing number of Eppendorf tubes filled with water. Secondly, transpiration was measured in whole Tempranillo bunches sampled at different phenological stages. An important output of this work is that the fact of detaching the bunch from the plant did not change the bunch gas exchange rates at least for several hours

Approximation de compacts fonctionnels par des variétés analytiques et applications en problème inverse

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocPARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF