In this paper we investigate the image of the l-adic representation attached to the Tate module of an abelian variety over a number field with endomorphism algebra of type I or II in the Albert classification. We compute the image explicitly and verify the classical conjectures of Mumford-Tate, Hodge, Lang and Tate, for a large family of abelian varieties of type I and II. In addition, for this...

In this paper it is shown that any regular critical point of the Mumford-Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the L1 -topology.

Shah-Waardenburg syndrome (SWS) is a neurocristopathy and is characterized by Hirschsprung's disease (HD), deafness, and depigmentation of hairs, skin, and iris. Is a very rare congenital disorder with variable clinical expression. This report describes a 4-day-old male newborn with Waardenburg's syndrome associated with aganglionosis of the colon and terminal ileum, and review the relevant lit...