We prove the continuity of logarithmic capacity under Hausdorff convergence uniformly perfect planar sets. The holds when distance to limit set tends zero at sufficiently rapid rate, compared decay parameters involved in condition. may fail otherwise.

Nous étudions la trace de marche aléatoire branchante critique conditionnée à être infinie sur Zd×Z+, en dimension d=6. Sous des hypothèses appropriées les moments et loi reproduction, nous démontrons que résistance électrique entre racine le niveau n est d’ordre O(nlog−ξn) pour un certain ξ>0 qui ne dépend pas détails du modèle.

The public key cryptosystem MST1 has been introduced in [9]. Its security relies on the hardness of factoring with respect to wild logarithmic signatures. To identify ‘wild-like’ logarithmic signatures, the criterion of being totally-non-transversal has been proposed. We give tame totally-non-transversal logarithmic signatures for the alternating and symmetric groups of degree ≥ 5. Hence, basin...

Alberto Accardi(1), François Arleo(2), William K. Brooks(3), David D’Enterria(4), and ValeriaMuccifora(5)(∗) (1) Hampton University, Hampton, VA, 23668, USA, and Jefferson Lab, Newport News, VA 23606, USA (2) LAPTH(∗∗), Université de Savoie, CNRS, BP 110, 74941 Annecy-le-Vieux cedex, France (3) Departamento de Fı́sica y Centro de Estudios Subatómicos, Universidad Técnica Federico Santa Marı́a, Ca...

The operators Kn are generators of reparameterization symmetries of Witten’s cubic open string field theory. One pertinent question is whether they can be utilised to generate deformations of the tachyon vacuum and thereby violate its uniqueness. We use level truncation to show that these transformations on the vacuum are in fact pure gauge transformations to a very high accuracy, thus giving n...