Growth of Sobolev norms for abstract linear Schrodinger equations

We prove an abstract theorem giving a (t)ϵ bound (for all ϵ > 0) on the growth of the Sobolev norms in linear Schrodinger equations of the form i Ψ = H0ψ + V(t)ψ as t → ∞. The abstract theorem is applied to several cases, including the cases where (i) H0 is the Laplace operator on a Zoll manifold and V (t) a pseudodifferential operator of order smaller than 2; (ii) H0 is the (resonant or nonresonant) harmonic oscillator in Rd and V (t) a pseudodifferential operator of order smaller than that of H0 depending in a quasiperiodic way on time. The proof is obtained by first conjugating the system to some normal form in which the perturbation is a smoothing operator and then applying the results of [MR17]

Multi-site study of a new approach to farm work within the framework of organic vegetable production: permanent crop beds

The mineralization rate of a commercial organic fertiliser was evaluated over the course of three years in an organic rice field in the Camargue (France). The effect of different mounts of fertiliser applied at different periods was tested. The organic fertiliser rapidly mineralised under flooded conditions. On the basis of this result, we demonstrated that an adaptation of organic fertilisation practices, similar to those employed for mineral fertilisers, would result in the optimisation of organic fertilisers, leading to improved profitability

Long-Lasting Metabolic Imbalance Related to Obesity Alters Olfactory Tissue Homeostasis and Impairs Olfactory-Driven Behaviors.

Obesity is associated with chronic food intake disorders and binge eating. Food intake relies on the interaction between homeostatic regulation and hedonic signals among which, olfaction is a major sensory determinant. However, its potential modulation at the peripheral level by a chronic energy imbalance associated to obese status remains a matter of debate. We further investigated the olfactory function in a rodent model relevant to the situation encountered in obese humans, where genetic susceptibility is juxtaposed on chronic eating disorders. Using several olfactory-driven tests, we compared the behaviors of obesity-prone Sprague-Dawley rats (OP) fed with a high-fat/high-sugar diet with those of obese-resistant ones fed with normal chow. In OP rats, we reported 1) decreased odor threshold, but 2) poor olfactory performances, associated with learning/memory deficits, 3) decreased influence of fasting, and 4) impaired insulin control on food seeking behavior. Associated with these behavioral modifications, we found a modulation of metabolism-related factors implicated in 1) electrical olfactory signal regulation (insulin receptor), 2) cellular dynamics (glucorticoids receptors, pro- and antiapoptotic factors), and 3) homeostasis of the olfactory mucosa and bulb (monocarboxylate and glucose transporters). Such impairments might participate to the perturbed daily food intake pattern that we observed in obese animals

Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. Borg-Marchenko type uniqueness theorems are derived for both discrete and continuous non-self-adjoint systems too

Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation

We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes. This behavior is quantified by the growth of higher Sobolev norms: given any δ[much less-than]1,K [much greater-than] 1, s > 1, we construct smooth initial data u 0 with ||u0||Hs , so that the corresponding time evolution u satisfies u(T)Hs[greater than]K at some time T. This growth occurs despite the Hamiltonian’s bound on ||u(t)||H1 and despite the conservation of the quantity ||u(t)||L2. The proof contains two arguments which may be of interest beyond the particular result described above. The first is a construction of the solution’s frequency support that simplifies the system of ODE’s describing each Fourier mode’s evolution. The second is a construction of solutions to these simpler systems of ODE’s which begin near one invariant manifold and ricochet from arbitrarily small neighborhoods of an arbitrarily large number of other invariant manifolds. The techniques used here are related to but are distinct from those traditionally used to prove Arnold Diffusion in perturbations of Hamiltonian systems