Uniform measures and uniform rectifiability

In this paper it is shown that if $\mu$ is an n-dimensional Ahlfors-David regular measure in $R^d$ which satisfies the so-called weak constant density condition, then $\mu$ is uniformly rectifiable. This had already been proved by David and Semmes in the cases n=1, 2 and d-1, and it was an open problem for other values of n. The proof of this result relies on the study of the n-uniform measures in $R^d$. In particular, it is shown here that they satisfy the "big pieces of Lipschitz graphs" property.Comment: Minor correction

Uniform localization is always uniform

In this note we show that if a family of ergodic Schr\"odinger operators on $l^2({\Bbb Z}^\gamma)$ with continuous potentials have uniformly localized eigenfunctions then these eigenfunctions must be uniformly localized in a homogeneous sense

Uniform and Partially Uniform Redistribution Rules

This short paper introduces two new fusion rules for combining quantitative basic belief assignments. These rules although very simple have not been proposed in literature so far and could serve as useful alternatives because of their low computation cost with respect to the recent advanced Proportional Conflict Redistribution rules developed in the DSmT framework.Comment: 4 pages; "Advances and Applications of DSmT for Plausible and Paradoxical reasoning for Information Fusion", International Workshop organized by the Bulgarian IST Centre of Competence in 21st Century, December 14, 2006, Bulg. Acad. of Sciences, Sofia, Bulgari

Uniform

Colin Myers first slept with his neighbor four days after his eighteenth birthday, but he\u27d wanted Wanda Mitchell for two long summers. He liked wrapping his arms around her and tasting her salty neck in the fleeting minutes before she slid off the bed and sent him home. He lived across the street. They had not been caught, no close calls, but like adrenaline after a car accident, the possibility lingered