Upper limits on gravitational-wave emission in association with the 27 Dec 2004 giant flare of SGR1806-20

At the time when the giant flare of SGR1806-20 occurred, the AURIGA "bar" gravitational-wave (GW) detector was on the air with a noise performance close to stationary Gaussian. This allows us to set relevant upper limits, at a number of frequencies in the vicinities of 900 Hz, on the amplitude of the damped GW wave trains, which, according to current models, could have been emitted, due to the excitation of normal modes of the star associated with the peak in x-ray luminosity.     

On the Bertrand paradox

In this papel we discuss the classical Bertrand paradox recalling the five known planar probabilistic models and introducing a new continuous family of planar probabilistic models, depending on a parameterx∈]1, +∞[. We also show that two of the classical models can be obtained as the limit, in law, from the new ones, whenx tends to 1 and +∞, respectively.     

On the Determination of Star and Convex Bodies by Section Functions

The i th section function of a star body in ⁿ gives the i -dimensional volumes of its sections by i -dimensional subspaces. It is shown that no star body is determined among all star bodies, up to reflection in the origin, by any of its i th section functions. Moreover, the set of star bodies that are determined among all star bodies, up to reflection in the origin, by their i th section functions for all i , is a nowhere dense set. The determination of convex bodies in this sense is also studied. The results complement and contrast with recent results on the determination of convex bodies by i th projection functions. The paper continues the development of the dual Brunn—Minkowski theory initiated by Lutwak. Received December 4, 1996, and in revised form April 14, 1997.     

On the Bertrand paradox

In this papel we discuss the classical Bertrand paradox recalling the five known planar probabilistic models and introducing a new continuous family of planar probabilistic models, depending on a parameterx∈]1, +∞[. We also show that two of the classical models can be obtained as the limit, in law, from the new ones, whenx tends to 1 and +∞, respectively.