02/19/1948 Letter from l\u27Alliance des Journaux Franco-Americains

Letter from Wilfrid J. Mathieu, Secretary of l\u27Alliance des Journaux Franco-Americains, to Louise-Philippe Gagné.https://digitalcommons.usm.maine.edu/fac-lpg-letters-1948-01-06/1013/thumbnail.jp

Moser Lemma in Generalized Complex Geometry

We show how the classical Moser Lemma from symplectic geometry extends to generalized complex structures (GCS) on arbitrary Courant algebroids. For this, we extend the notion of Lie derivative to sections of the tensor bundle $(\otimes^i E)\otimes(\otimes^j E^*)$ with respect to sections of the Courant algebroid $E$ using the Dorfman bracket. We then give a cohomological interpretation of the existence of one-parameter families of GCS on $E$ and of flows of automorphims of $E$ identifying all GCS of such a family. In the particular cases of symplectic, we recover the results of Moser. Finally, we give a criterion to detect the local triviality of arbitrary GCS which generalizes the Darboux-Weinstein theorem.Comment: 18 page

Exponential dynamical localization for the almost Mathieu operator

We prove that the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency

Alien Registration- Mathieu, Arthur J. (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/28937/thumbnail.jp

Alien Registration- Gaucheau, Mathieu J. (Brunswick, Cumberland County)

https://digitalmaine.com/alien_docs/31489/thumbnail.jp

GMRES for oscillatory matrix-valued differential equations

We investigate the use of Krylov subspace methods to solve linear, oscillatory ODEs. When we apply a Krylov subspace method to a properly formulated equation, we retain the asymptotic accuracy of the asymptotic expansion whilst converging to the exact solution. We will demonstrate the effectiveness of this method by computing Error and Mathieu functions