Local root numbers of elliptic curves over dyadic fields

We consider an elliptic curve over a dyadic field with additive, potentially good reduction. We study the finite Galois extension of the dyadic field generated by the three-torsion points of the elliptic curve. As an application, we give a formula to calculate the local root number of the elliptic curve over the dyadic field.Comment: 11 page

Logarithmic mean oscillation on the polydisc, endpoint results for multi-parameter paraproducts, and commutators on BMO

We study boundedness properties of a class of multiparameter paraproducts on the dual space of the dyadic Hardy space H_d^1(T^N), the dyadic product BMO space BMO_d(T^N). For this, we introduce a notion of logarithmic mean oscillation on the polydisc. We also obtain a result on the boundedness of iterated commutators on BMO([0,1]^2).Comment: 24 page

(1+1)-dimensional turbulence

A class of dynamical models of turbulence living on a one-dimensional dyadic-tree structure is introduced and studied. The models are obtained as a natural generalization of the popular GOY shell model of turbulence. These models are found to be chaotic and intermittent. They represent the first example of (1+1)-dimensional dynamical systems possessing non trivial multifractal properties. The dyadic structure allows to study spatial and temporal fluctuations. Energy dissipation statistics and its scaling properties are studied. Refined Kolmogorov Hypothesis is found to hold.Comment: 18 pages, 9 figures, submitted to Phys.of Fluid

'I think you understand me' : studying the associations between actual, assumed, and perceived understanding within couples

The current study examined the associations between actual, assumed, and perceived understanding and partners' levels of dyadic adjustment. One hundred fifty-two couples provided questionnaire data (assumed and perceived understanding), participated in a videotaped conflict interaction, and in a video-review task to assess actual understanding (empathic accuracy). The data were analyzed by means of the Actor-Partner Interdependence Model. The results suggest that (a) some aspects of how well someone assumes that (s)he has understood the partner during a preceding conflict interaction were positively associated with his/her own objective level of understanding (actor effect), (b) that someone's perception of how understood (s)he feels was not associated with the partner's objective level of understanding (partner effect), and (c) perceived understanding, but not actual understanding, was positively associated with dyadic adjustment