Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics

Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed for the corresponding Borel functions. Its main property is to order the singularity structure of the Borel plane in a hierarchical way by an increasing complexity of this structure starting from the analytic one. This allows us to study the Borel plane singularity structure in a systematic way. Examples of such structures are considered for linear, harmonic and anharmonic potentials. Together with the best approximation provided by the semiclassical series the exponentially small contribution completing the approximation are considered. A natural method of constructing such an exponential asymptotics relied on the Borel plane singularity structures provided by the topological expansion is developed. The method is used to form the semiclassical series including exponential contributions for the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure

Study of metamemory in patients with chronic alcoholism using a feeling-of-knowing episodic memory task

International audienceChronic alcoholism affects both episodic memory and metamemory for novel information. Patients were relatively unaware of their memory deficits and believed that their memory was as good as that of the healthy controls. The monitoring measure (FOK) and the subjective measure of metamemory (MIA) showed that patients with chronic alcoholism overestimated their memory capacities. Episodic memory deficit and executive dysfunction would explain metamemory decline in this clinical population

Security Systems in Francophone Africa

This research report is a broad-based study that seeks to understand the structural and developmental processes that characterise the security sector in Francophone Africa. Although each country has a distinct political history and tradition, similarities in the security apparatus, rooted in its inheritance from the colonial and post-colonial periods, can be found between Francophone countries in Africa. In the former French colonies, there are similarities to the French security system which are very strong on the normative side, such as the legal and institutional framework or the defence and security actors. However, even if these Francophone African countries borrow a lot from an originally French security system in terms of the institutional design of their security apparatus, they deviate considerably from it in terms of daily practice. The issue at stake in this paper is to highlight the kind of institutional framework prevailing in this set of countries and the specific considerations that international assistance will have to take into account. The paper also analyses briefly the difference between Anglophone and Francophone security systems. Finally, it makes some recommendations that might assist the security sector reform policy agenda and donor and recipient responses to the security challenges faced in Francophone AfricaAfrican Security Sector Networ

SUITE DES NOTICES

Abstract. This is a translation of Carl Jacobi’s Suite des notices sur les fonctions elliptiques published in Crelle’s Journal in 1828. The full citation is given in reference [5]. The paper is a letter to August Crelle which continues Jacobi’s advertisement of elliptic function results published earlier in the same volume of Crelle’s Journal (see [4]). Some of the notation in Jacobi’s paper has been modernized in this translation. In this letter, Jacobi reformulates elliptic functions in terms of theta functions in order to obtain simplifications of elliptic function theory. He briefly discusses modular transformations in both elliptic function and theta function theory. He uses the Fourier expansions of the theta functions to derive a partial differential equation, specifically the heat equation, which the theta functions satisfy. He turns to an applications of an identity discovered by Poisson and concludes with a discussion of the application of elliptic functions to representations of integers as sums of squares. I add the development of elliptic functions of the second and third kinds to the formulas given in my last letter [4]. Following Mr. Legendre, define: ∆(φ): = ∆(φ, k): = 1 − k2 sin2 φ, � φ E(φ): = E(φ|k): = ∆(φ) dφ, (1) E: = E(k): = E (

Satire et parodie dans la « Complainte » du Roman de Fauvel remanié de Chaillou de Pestain (Paris, BnF, fr. 146) : pourquoi et comment rit-on des puissants au xive siècle ?

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