Nekhoroshev theorem for perturbations of the central motion

In this paper we prove a Nekhoroshev type theorem for perturbations of Hamiltonians describing a particle subject to the force due to a central potential. Precisely, we prove that under an explicit condition on the potential, the Hamiltonian of the central motion is quasi-convex. Thus, when it is perturbed, two actions (the modulus of the total angular momentum and the action of the reduced radial system) are approximately conserved for times which are exponentially long with the inverse of the perturbation parameter

Microarray-based mutation analysis of the ABCA4 (ABCR) gene in autosomal recessive cone-rod dystrophy and retinitis pigmentosa.

Contains fulltext : 57320.pdf (publisher's version ) (Closed access)Mutations in the ABCA4 gene have been associated with autosomal recessive Stargardt disease (STGD1), cone-rod dystrophy (CRD), and retinitis pigmentosa (RP). We employed a recently developed genotyping microarray, the ABCR400-chip, to search for known ABCA4 mutations in patients with isolated or autosomal recessive CRD (54 cases) or RP (90 cases). We performed detailed ophthalmologic examinations and identified at least one ABCA4 mutation in 18 patients (33%) with CRD and in five patients (5.6%) with RP. Single-strand conformation polymorphism (SSCP) analysis and subsequent DNA sequencing revealed four novel missense mutations (R24C, E161K, P597S, G618E) and a novel 1-bp deletion (5888delG). Ophthalmoscopic abnormalities in CRD patients ranged from minor granular pigmentary changes in the posterior pole to widespread atrophy. In 12 patients with recordable electroretinogram (ERG) tracings, a cone-rod pattern was detected. Three patients demonstrated progression from a retinal dystrophy resembling STGD1 to a more widespread degeneration, and were subsequently diagnosed as CRD. In addition to a variable degree of atrophy, all RP patients displayed ophthalmologic characteristics of classic RP. When detectable, ERG recordings in these patients demonstrated rod-cone patterns of photoreceptor degeneration. In conclusion, in this study, we show that the ABCA4 mutation chip is an efficient first screening tool for arCRD